University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2016 On Hydraulic Fracturing of Tight Gas Reservoir Rock Maulianda, Belladonna Maulianda, B. (2016). On Hydraulic Fracturing of Tight Gas Reservoir Rock (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/27177 http://hdl.handle.net/11023/2906 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca
Transcript
University of Calgary
PRISM: University of Calgary's Digital Repository
Graduate Studies The Vault: Electronic Theses and Dissertations
2016
On Hydraulic Fracturing of Tight Gas Reservoir Rock
Maulianda, Belladonna
Maulianda, B. (2016). On Hydraulic Fracturing of Tight Gas Reservoir Rock (Unpublished doctoral
thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/27177
http://hdl.handle.net/11023/2906
doctoral thesis
University of Calgary graduate students retain copyright ownership and moral rights for their
thesis. You may use this material in any way that is permitted by the Copyright Act or through
licensing that has been assigned to the document. For uses that are not allowable under
copyright legislation or licensing, you are required to seek permission.
Downloaded from PRISM: https://prism.ucalgary.ca
UNIVERSITY OF CALGARY
On Hydraulic Fracturing of Tight Gas Reservoir Rock
by
Belladonna Maulianda
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR PHILOSOPHY IN PETROLEUM ENGINEERING
GRADUATE PROGRAM CHEMICAL AND PETROLEUM ENGINEERING
2.5.3 Pressure Drop and Fracture Aperture Estimation ................................................... 51
2.5.4 Effect of Geomechanical Properties on the SRV .................................................... 52
2.6 Behavior of Naturally Fractured Reservoir .................................................................... 52
2.6.1 Flow Regimes for Multi-fractured Horizontal Well in a Naturally Fractured Reservoir ................................................................................................................................ 55
2.6.2 Flow Regions for Multi-fractured Horizontal Well in a Naturally Fractured Reservoir ................................................................................................................................ 58
2.6.3 Rate Transient Analysis (RTA) in a Naturally Fractured Reservoir ....................... 60
2.7 What is Missing in the Literature? ................................................................................. 61
CHAPTER 4: GEOMECHANICAL CONSIDERATION IN STIMULATED ROCK VOLUME DIMENSION MODELS PREDICTION DURING MULTI-STAGE HYDRAULIC FRACTURES IN HORIZONTAL WELLBORE – GLAUCONITIC TIGHT FORMATION IN HOADLEY FIELD ..................................................................................................................... 103
4.2.2 Stimulated Rock Volume (SRV) Models for Tight Rock Unconventional Reservoirs ............................................................................................................................ 107
4.2.3 Microseismic Monitoring during Hydraulic Fracturing ....................................... 111
4.3 Hoadley Field Project ................................................................................................... 113
4.4 Research Workflow ...................................................................................................... 118
4.4.1 Derivation of Equations for the SRV Dimensions ................................................ 118
4.4.2 Analysis of Microseismic Events.......................................................................... 120
CHAPTER 5: DETERMINATION OF FRACTURE CHARACTERISTICS WITHIN STIMULATED ROCK VOLUME USING DIFFUSIVITY EQUATION AND PRODUCTION ANALYSIS ................................................................................................................................. 159
5.1.1 Objective of Study ................................................................................................ 160
5.2 Literature Review ......................................................................................................... 160
5.2.1 Behavior of Naturally Fractured Reservoir ........................................................... 160
5.2.2 Dual Porosity Model (Pseudo Steady State and Transient) .................................. 163
5.2.3 Flow Regimes of Multi-Fractured Horizontal Well in Naturally Fractured Reservoir .............................................................................................................................. 163
5.2.4 Flow Regions of Multi-Fractured Horizontal Well in Naturally Fractured Reservoir 164
5.5.2.2 Identifying Flow Regimes Using Type Curves .................................................... 186
5.5.2.3 Unconventional Reservoir Analysis (Unconventional Gas Module) .................... 190
5.5.2.4 History Match Using Horizontal Multifractured Enhanced Fracture Region Analytical Model ................................................................................................................. 192
5.5.2.4.1 Case 1 With Constant FCD, SRV Half-Length, and Matrix Permeability ....... 192
5.5.2.4.2 Case 2 With Constant SRV Half-Length .......................................................... 197
Table 4.3: Results of all stages first time step event distance, SRV growth, number of events fitted within the estimated SRV, and Figures showing results............................................................. 127
Table 4.4: The estimated SRV dimensions results and the located microseismic events. .......... 147
Table 4.5: Comparison of SRV width and hydraulic fracture port spacing................................ 147
Table 4.6: Diffusivity coefficient ratios for maximum and minimum horizontal stresses direction...................................................................................................................................................... 149
Table 4.7: Stage 7 Mohr-Coulomb failure envelope properties for Case 2. ............................... 151
Table 4.8: Stage 7 SRV dimensions and Mohr-Coulomb failure envelope properties comparison Cases 1 and 2. ............................................................................................................................. 152
Table 5.6: Case 1 simulation results for constant FCD, SRV half-length and matrix permeability...................................................................................................................................................... 194
Table 5.7: Case 2 simulation results for constant SRV half-length. ........................................... 198
x
List of Figures
Fig. 1.1: Resource pyramid for natural gas [2]. .............................................................................. 2
Fig. 1.2: Tight gas production in the United States showing natural gas response as a function of DOE and GRI investment in research and State and Federal production incentives [6]. ............... 2
Fig. 1.3: Natural gas sources production by region with unconventional gas becoming the largest source of North America gas supply [7]. ........................................................................................ 3
Fig. 1.4: Tight gas resources distribution in Canada [9]. ................................................................ 4
Fig. 1.5: Geology of tight gas reservoir as a continuous gas accumulation [12]. ........................... 5
Fig. 1.6: Pressure – depth plot, Elmsworth area, Cadotte formation as an example of sub-normally pressured formation [14]. ................................................................................................................ 6
Fig. 1.7: Schematic of relative permeability curves, capillary pressures, cross section and structural map for conventional reservoir [13]. .............................................................................................. 9
Fig. 1.8: Schematic of relative permeability curves, capillary pressures, cross section and structural map for unconventional reservoir [13]. ........................................................................................ 10
Fig. 1.9: Example of orthogonal regional fractures in Devonian Antrim shale, Michigan Basin [28]........................................................................................................................................................ 11
Fig. 1.10: Chart for estimating pore-throat aperture as a function of porosities and permeability and possible ranges of oil (bpd), and gas flow rates (scfd) for different pore-throat aperture [34]........................................................................................................................................................ 12
Fig. 1.11: Porosity distribution in naturally fractured reservoir Type A, B, and C [27]. ............. 13
Fig. 1.12: Hydraulic fracture equipments are water truck (top left), fracturing sand transport truck (top right), water storage tank (bottom left) and HF process layout (bottom right) [40, 41]. ...... 17
Fig. 1.13: Fracture orientation as a function of wellbore orientation relative to in-situ stresses orientation [42].............................................................................................................................. 18
Fig. 1.14: Estimating SRA from microseismic mapping data [45]............................................... 19
Fig. 2.2: (a) Triaxial strength test with β is the angle between failure plane with σ3, (b) a series of triaxial tests at different effective confining pressure (usually flattens as confining pressure increase), and linear simplification of the Mohr-Coulomb failure envelope [4, 6]. ..................... 27
Fig. 2.3: (a) Stress relationships for shear failure Mohr circle on Mohr-Coulomb failure envelope and (b) typical failure characteristics of intact rock plotted in terms of Mohr circle and Mohr-Coulomb failure envelope [5]. ...................................................................................................... 29
Fig. 2.4: Reservoir contact comparison between vertical well, unstimulated horizontal well, and multi-fractured horizontal well [17].............................................................................................. 32
Fig. 2.5: Completion types for stimulation: (a) openhole completion, (b) perforated or slotted liner, (c) blank liner with very limited clustered perforations, (d) casing packer, and (e) fully cemented liner [21]........................................................................................................................................ 36
xi
Fig. 2.6: (a) The PKN and (b) KGD fracture models [25]. ........................................................... 37
Fig. 2.8: (a) Mechanical testing apparatus and hydraulic testing apparatus, and (b) hydraulic fracture intersecting a natural fracture [44]. ................................................................................. 45
Fig. 2.9: (a) Hydraulic fracture propagates from the tip of natural fractures and (b) hydraulic fracture propagates from weak point along natural fracture [45]. ................................................ 46
Fig. 2.10: Microseismic downhole monitoring using downhole receiver array during hydraulic fracture [47]. ................................................................................................................................. 48
Fig. 2.11: Surface microseismic monitoring during hydraulic fracture (red lines represented travel time and blue lines represented surface arrays) [52]. ................................................................... 49
Fig. 2.12: Realization of heterogeneous porous medium [68]. ..................................................... 53
Fig. 2.13: Fracture compressibility as a function of net stress on fracture [72]. .......................... 55
Fig. 2.14: Early bilinear flow within the fracture and formation [75]. ......................................... 55
Fig. 2.15: Early linear flow from the formation to the fracture [75]. ........................................... 56
Fig. 2.16: Early radial flow from the formation to the fracture [75]. ........................................... 56
Fig. 2.17: Compound linear flow from the unstimulated reservoir region to the stimulated reservoir volume [75]. .................................................................................................................................. 57
Fig. 2.18: Late radial flow around the multifractured horizontal well [75]. ................................. 57
Fig. 2.19: Trilinear model schematic in multi-fractured horizontal [78, 79]. ............................... 58
Fig. 2.20: Horizontal well multifractured enhanced fracture model schematic [80]. ................... 59
Fig. 2.21: Enhanced fracture region model for quarter of a fracture [80]. ................................... 59
Fig. 3.1: Finite element model mesh for hydraulic fracturing (SRV) simulation………………………………………………………………………………………...78
Fig. 3.2: Bottom-hole injection pressure (field) data and predicted results from FEA. ............... 81
Fig. 3.3: Pore pressure (Pa) in different steps: (a) initial condition, (b) after in-situ stresses and boundary conditions are loaded on the domain step, (c) pump step-1 second, (d) pump step-551 s, (e) pump step-1,101 s, and (f) end of injection-2,250 s for Case 1 with k=23.4 D (deformation scale factor of 3,505.7 with final displacement of 6.853e-3 m). .................................................. 82
Fig. 3.4: Pore pressure (Pa) in different steps: (a) initial condition, (b) after in-situ stresses and boundary conditions are loaded on the domain step, (c) pump step-1 second, (d) pump step-551 s, (e) pump step-1,101 s, and (f) end of injection-2,250 s for Case 2 with k=45.85 D (deformation scale factor of 3,016.07 with final displacement of 7,957e-3 m). ................................................ 83
Fig. 3.5: Effect of Young’s modulus on bottom-hole pressure for (a) Case 1 and (b) Case 2. .... 84
Fig. 3.6: (a) Pore pressure and (b) total maximum horizontal stress as a function of distance along SRV length at various injection times for Case 1 with k=23.4D (assuming Biot’s constant=1). . 86
xii
Fig. 3.7: (a) Pore pressure and (b) total minimum horizontal stress as a function of distance along SRV width at various injection times for Case 1 with k=23.4D (assuming Biot’s constant=1). 88
Fig. 3.8: (a) Pore pressure and (b) total vertical stress as a function of distance along SRV height above injection ports at various injection times for Case 1 with k=23.4D (assuming Biot’s constant=1). ................................................................................................................................... 89
Fig. 3.9: (a) Pore pressure and (b) total maximum horizontal stress as a function of distance along SRV length at various injection times for Case 2 with k=45.85D (assuming Biot’s constant=1).90
Fig. 3.10: (a) Pore pressure and (b) total minimum horizontal stress as a function of distance along SRV width at various injection times for Case 2 with k=45.85D (assuming Biot’s constant=1). 91
Fig. 3.11: (a) Pore pressure and (b) total minimum horizontal stress as a function of distance along SRV height above injection ports at various injection times for Case 2 with k=45.85D (assuming Biot’s constant=1). ........................................................................................................................ 92
Fig. 3.12: Pore pressure as a function of distance using the cubic law equation for (a) Case 1 and (b) Case 2. ..................................................................................................................................... 94
Fig. 3.13: Top view of the minor fractures (natural fractures) are assumed to be inclined 30o with the major fractures (hydraulic fractures) (not to scale). ................................................................ 95
Fig. 3.14: Procedures to calculate the fracture aperture, numbers and spacing. ........................... 96
Fig. 3.15: Relationship any number of fractures, fracture aperture and fracture pressure gradient for (a) Case 1 and (b) Case 2. ....................................................................................................... 98
Fig. 4.1: (a) The site location and the maximum stress direction (45o NE) and (b) hydraulic fracture treatment location near Red Deer [39]…………………………………………………………..114
Fig. 4.3: Depth distribution of microseismic events from two horizontal wellbores hydraulic fracture [39]. ............................................................................................................................... 115
Fig. 4.4: Executive summary of the two treatment wellbores, observation wellbore, producing wellbore and observed microseismic events during 12 stages of hydraulic fracture [39]. ......... 116
Fig. 4.5: Bottomhole injection pressure for horizontal wellbore A during 12 stages of hydraulic fracture [39]. ............................................................................................................................... 117
Fig. 4.6: (a) Pressure drop derived from finite element analysis in Chapter 3 and (b) Stage 7 Mohr-Coulomb failure envelope for Case 1. ........................................................................................ 126
Fig. 4.7: Stage 7 SRV length versus width for Case 1. ............................................................... 128
Fig. 4.8: Stage 7 SRV length versus height for Case 1. .............................................................. 128
Fig. 4.9: Stage 7 SRV width versus height for Case 1. ............................................................... 129
Fig. 4.10: Stage 7 SRV length versus best fit width (using microseismic data) for Case 1. ...... 129
Fig. 4.11: Stage 1 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height........................................................................................................................................... 130
xiii
Fig. 4.12: Stage 5 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height........................................................................................................................................... 131
Fig. 4.13: Stage 8 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height........................................................................................................................................... 132
Fig. 4.14: Stage 9 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height........................................................................................................................................... 133
Fig. 4.15: Stage 11 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height. .............................................................................................................................. 134
Fig. 4.16: Stage 2 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height........................................................................................................................................... 135
Fig. 4.17: Stage 3 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height........................................................................................................................................... 136
Fig. 4.18: Stage 4 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height........................................................................................................................................... 137
Fig. 4.19: Stage 6 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height........................................................................................................................................... 138
Fig. 4.20: Stage 10 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height. .............................................................................................................................. 139
Fig. 4.21: Stage 12 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height. .............................................................................................................................. 140
Fig. 4.22: (a) SRV dimensions differences with microseismic events for six interpreted stages and (b) SRV best fit using microseismic event data for all stages. ................................................... 141
Fig. 4.23: (a) Pressure drop from finite element analysis in Chapter 3, (b) pressure drop derived from transient analysis equation for intact natural fractures, and (c) pressure drop derived from transient analysis equation for open natural fractures. ................................................................ 142
Fig. 4.24: Mohr-Coulomb stress failure envelope of stage 7 for Case 2. ................................... 150
Fig. 4.25: Plot of Case 1 and Case 2 effective maximum horizontal stress versus effective minimum horizontal stress for intact rock and naturally fractured reservoirs............................................. 152
xiv
Fig. 4.26: SRV dimensions of Stage 7 for Case 2 SRV dimensions: (a) SRV length versus width, (b) SRV length versus width best fit with microseismic events, (c) SRV length versus height, and (d) SRV width versus height. ...................................................................................................... 153
Fig. 5.1: Production data history………………………………………………………………...167
Fig. 5.2: Geometry with edge labels displayed. .......................................................................... 172
Fig. 5.3: SRV with triangular element mesh............................................................................... 173
Fig. 5.4: Pressure contour plot in SRV during (a) 157.5 hours, (b) 2,992.5 hours, and (c) 6,300 hours production. ........................................................................................................................ 176
Fig. 5.5: Permeability contour plot in SRV during (a) 157.5 hours, (b) 2,992.5 hours, and (c) 6,300 hours production. ........................................................................................................................ 177
Fig. 5.6: Porosity contour plot in SRV during (a) 157.5 hours, (b) 2,992.5 hours, and (c) 6,300 hours production. ........................................................................................................................ 178
Fig. 5.7: Pressure profile as a function of (a) time and (b) distance from SRV boundary to wellbore...................................................................................................................................................... 180
Fig. 5.8: Permeability profile as a function of (a) time and (b) distance from SRV boundary to wellbore....................................................................................................................................... 181
Fig. 5.9: Porosity profile as a function of (a) time and (b) distance from SRV boundary to wellbore...................................................................................................................................................... 182
Fig. 5.10: Comparison of (a) field gas flow rate and (b) bottomhole pressure with new diffusion model with porosity of 0.16 and 0.17 (no changes). ................................................................... 184
Fig. 5.11: Blasingame finite conductivity fracture with median filter. ....................................... 187
Fig. 5.12: Blasingame elliptical with median filter. .................................................................... 188
Fig. 5.13: Blasingame horizontal with median filter. ................................................................. 189
Fig. 5.14: Wattenbarger with median filter. ................................................................................ 190
Fig. 5.15: Unconventional gas module square root time plot to identify the pessimistic boundary dominated flow (green vertical line), .......................................................................................... 191
Fig. 5.16: Unconventional gas module typecurve plot to identify the pessimistic boundary dominated flow (green vertical line). .......................................................................................... 192
Fig. 5.17: History match with horizontal multifrac enhanced fracture region using unconventional reservoir analysis for constant FCD, SRV half-length and matrix permeability with PSS dual porosity model. ........................................................................................................................... 194
Fig. 5.18: History match with horizontal multifrac enhanced fracture region using unconventional reservoir analysis for constant FCD, SRV half-length and matrix permeability with slabs model...................................................................................................................................................... 195
Fig. 5.19: History match with horizontal multifrac enhanced fracture region using unconventional reservoir analysis for constant FCD, SRV half-length and matrix permeability with cubes model...................................................................................................................................................... 196
xv
Fig. 5.20: History match with horizontal multifrac enhanced fracture region using unconventional reservoir analysis for constant FCD, SRV half-length and matrix permeability with sticks model...................................................................................................................................................... 197
Fig. 5.21: History match with horizontal multifrac enhanced fracture region for constant SRV half-length with PSS model. ............................................................................................................... 199
Fig. 5.22: History match with horizontal multifrac enhanced fracture region for constant SRV half-length with slabs model. ............................................................................................................. 200
Fig. 5.23: History match with horizontal multifrac enhanced fracture region for constant SRV half-length with cubes model. ............................................................................................................ 201
Fig. 5.24: History match with horizontal multifrac enhanced fracture region for constant SRV half-length with sticks model. ............................................................................................................ 202
xvi
CHAPTER 1: INTRODUCTION
1.1 Tight Gas Sands
There are several types of unconventional gas reservoirs including tight gas sand, coal bed
methane, shale gas, and natural gas hydrates. Tight gas sand definitions are defined in different
ways by different organizations. Tight gas sand reservoirs were originally defined by the U.S.
government in 1978 as formations with permeability equal or less than 0.1 mD [1]. This definition
is the most commonly accepted one by the oil and gas industry today. A second definition is the
U.S. legal definition that described tight gas sands that have an averaged un-stimulated initial gas
rate less than a maximum specified value for a given depth [2]. Tight gas sand reservoir properties
are also defined as a function of the reservoir properties including pressure, fluid properties,
reservoir and surface temperature, permeability, net pay, drainage and wellbore radius, skin and
non-Darcy constant [3]. The research documented in this thesis focuses on a study of a tight gas
sand reservoir. Given the low permeability of the reservoir and the requirement to raise its
permeability, hydraulic fracturing from horizontal wells is most used to stimulate these reservoirs.
Unconventional reservoir characteristics such as hydrocarbon amount and qualification can be
explained simply by using a resource pyramid [4]. The resource pyramid was improved by
suggesting that high-grade natural resources occupied the peak and as the grade decreased the
hydrocarbon amount increased [5]. Unconventional gas reservoir qualification also followed the
resource pyramid which meant that poorer reservoir characteristics would decrease the reservoir
permeability as shown in Figure 1.1 [2]. Low-permeability reservoirs had larger size than high-
quality reservoirs.
1
Fig. 1.1: Resource pyramid for natural gas [2].
Tight gas production in the U.S. has been impacted greatly by natural gas research and
successful technology application in the form of hydraulic fracturing [6]. The tight gas production
curve from the Greater Green River and the Piceance Basins, displayed in Figure 1.2, showed a
large positive increase in 1985 following about $165 million combined investment in research by
the Department of Energy (DOE) and Gas Research Institute (GRI) [6].
Fig. 1.2: Tight gas production in the United States showing natural gas response as a function of DOE and GRI investment in research and State and Federal production incentives [6].
2
The research investment produced 11 trillion cubic feet (tcf) of natural gas up to year of 2000
[6]. In addition to tight gas, other unconventional gas sources were also contributing significantly
to North America gas production as of 2014; at this time, as shown in Figure 1.3, unconventional
gas production was the largest source of gas [7].
The Harvard Business School and the Boston Consulting Group wrote a report on America’s
unconventional energy opportunity in 2014 which stated that the U.S. government needed to
encourage ongoing private and public sector research investment in cost-effective and low-carbon
energy technologies including potentially broader use of unconventional natural gas [8].
Fig. 1.3: Natural gas sources production by region with unconventional gas becoming the largest source of North America gas supply [7].
Canada was anticipated to have the same success level as that achieved in the U.S. for tight
gas reservoirs. It was supported by the vast volumes of gas in place for the tight gas reservoirs
estimated by different Canadian organizations [2]. Canada’s gas in place resources from both
conventional and unconventional reservoirs was estimated to be almost 4,000 tcf including a large
contribution from unconventional resources; the largest deposits are shown in Figure 1.4 [9]. The
4,000 tcf value was the sum of gas in place for tight gas (1,311 tcf), coal bed methane (801 tcf),
shale gas (1,111 tcf), and conventional gas (692 tcf). This data was also supported by the data from
National Energy Board of Canada that placed tight rock gas in place between 89 and 1,500 tcf
3
[10]. Figure 1.4 showed the tight gas projected in place mainly were located at the Western Canada
Sedimentary Basin [9].
Fig. 1.4: Tight gas resources distribution in Canada [9].
permeability barriers, net inter-bedded coals, and shales are some of the factors that must be
considered to estimate tight gas sand properties and gas in place [2]. The present definition of the
tight gas sand, on a geological basis, was defined as a basin-center or continuous gas accumulation
[11] with large dimensions, low permeability and no apparent boundaries that are in close
proximity to source rocks with very low recovery factors as shown in Figure 1.5 [12]. The
continuous gas accumulation was visualized as a collection of gas charged cells where these cells
could be productive with productivity changing from cell to cell depending on the extent of natural
fractures [2].
4
Fig. 1.5: Geology of tight gas reservoir as a continuous gas accumulation [12].
There were contrary points of view where tight gas sands occurred in low-permeability
reservoirs in conventional structural, stratigraphic or combination traps [13]. It was explained that
if the conventional theory was correct, then it would produce less amounts of gas than that
anticipated from the estimated volumes of gas in place [2]. The continuous gas accumulation was
first described as having characteristic pressures as either sub-normal or super-normal [14].
Pressure-depth data used to determine sub-normal and super-normal pressure profiles of the
continuous gas accumulations in North America revealed that the sub-normally pressured profile
occurred in Upper and Lower Cretaceous rocks of Alberta, Canada and Lower Silurian rocks of
Eastern Ohio, U.S. whereas super-normally pressured reservoirs occurred in Tertiary and Upper
Cretaceous rocks of Wyoming, U.S. Davis (1984) showed an example of sub-normally pressured
gas sand in Cadotte Formation, Elmsworth area, Alberta displayed in Figure 1.6. The examples
consistently showed no associated down-dip water which were opposed to the conventional
interpretation of gas and oil systems with gas and oil trapped above water.
5
Fig. 1.6: Pressure – depth plot, Elmsworth area, Cadotte formation as an example of sub-normally pressured formation [14].
The basin-centered gas accumulation characteristics are maybe sub-normally pressured, low
permeability (less than 0.1 mD), continuous gas saturation, and no down-dip water leg [2]. If any
of these properties were missing, the reservoir could not be defined as a continuous gas
accumulation but it was possible to have conventional structural traps within it [15]. The
continuous gas accumulation concept had been evaluated by many other researchers [16, 27, 18,
29, 20, 21, 22].
6
1.2.2 Conventional Gas Accumulations
The contrary points of view from the continuous gas accumulation stated that low permeability
reservoirs from Greater Green River basin of Southwest Wyoming were not part of the continuous
gas accumulation and its productivity was dependent on the development of sweet spots [13]. The
gas fields in this basin occurred in low-permeability rocks that were trapped in conventional traps.
The data were examined from gas fields producing from Tertiary and Cretaceous reservoirs in the
Greater Green River Basin and it was concluded that these gas fields occurred in conventional
structural, stratigraphic [13]. They used 54 fields to support their conclusion that 100% of these
fields occurred in conventional traps
An improvement permeability jail model (unconventional reservoir model) was used to
describe their theory [13]. Byrnes (of the Kansas Geological Survey) was the first to propose the
permeability jail model [13]. The permeability jail model was used to describe the saturation region
with negligible water and gas effective permeability. The permeability jail model is illustrated in
Figure 1.7 and Figure 1.8 which compare two reservoirs with the same structural configuration:
Figure 1.7 shows a conventional reservoir whereas Figure 1.8 shows an unconventional reservoir.
Figure 1.7 and Figure 1.8 show relationships between capillary pressure, relative permeability, and
position within a trap. Figure 1.7 and Figure 1.8 represent a thin reservoir pinched out in a
structurally up-dip direction. Figure 1.7 shows that for a conventional reservoir, water production
extends down-dip to a free-water level (FWL), where in the middle part of reservoir both gas and
water are produced with water decreasing up-dip. In the up-dip portion of the reservoir is
characterized by water-free production of gas. Figure 1.8 shows that for an unconventional
reservoir, significant water production is limited to low structural positions near the FWL. Figure
1.8 shows that, in most cases, the effective permeability to water is sufficiently low so that there
is little to no fluid flow at or below the FWL (permeability jail). At up-dip portion of the reservoir,
water-free gas production is found. For the conventional reservoir in Figure 1.7, between 50 and
90% water saturations, there are non-zero values of relative permeability with respect to both gas
and water. The unconventional reservoir in Figure 1.8 has zero relative permeability with respect
to gas and water for 50% to 90% water saturations. This shows that there is a saturation region
within which neither gas nor water are able to flow. Figure 1.7 shows irreducible and critical water
can be of the same order of magnitude in the conventional reservoir. But in the unconventional
reservoir, the irreducible and critical water can be significantly different. It was concluded that the
7
unconventional reservoirs such as those found in the Greater Green River Basin were not examples
of basin-center or continuous gas accumulations [13].
8
Fig. 1.7: Schematic of relative permeability curves, capillary pressures, cross section and structural map for conventional reservoir [13].
9
Fig. 1.8: Schematic of relative permeability curves, capillary pressures, cross section and structural map for unconventional reservoir [13].
10
1.3 Naturally Fractured Reservoirs
Natural fractures are discontinuities within the rock that result from stresses that exceed the
rupture strength of the rock [25]. Naturally fractured reservoirs contain fractures – they can have
a positive or negative impact on fluid flow [26]. It was important to understand the magnitude and
direction of in-situ stresses, fractures azimuth, dip, spacing, and permeability, and matrix and
fracture water saturation in naturally fractured reservoir [27]. These data help in calculations of
gas in-place distribution between matrix and fractures. The sources of naturally fractured reservoir
information come from direct (core analysis, cutting analysis, and downhole cameras) and indirect
(drilling mud log, log analysis, well testing, and production history) sources of information [26].
1.3.1 Geological Classification
Naturally fractured reservoir classification based on the geological point of view could be
classified as tectonic (fold or fault related), regional, contractional (diagenetic), and surface related
[25, 28, 29]. Figure 1.9 shows an example of regional fractures [28].
Fig. 1.9: Example of orthogonal regional fractures in Devonian Antrim shale, Michigan Basin [28].
11
1.3.1.1 Pore System Classification
Naturally fractured reservoir classification based on the pore system determines the
preliminary estimate of productive reservoir porosity classes [30]. Porosity classes are defined by
pores geometry and pore size. The geometry include intergranular, intercrystalline, vuggy, and
fracture. The pore size is classified using different techniques such as Winland [31] and Aguilera
[32] techniques. The pore size classification are megaporosity (r35>10 microns), macroporosity
(r35 between 2-10 microns), mesoporosity (r35 between 0.5-2 microns), and microporosity (r35<0.5
microns). The pore size flow capacity were: megaports were able of flowing of 10,000 bpd,
macroports of 1,000 bpd, mesoports of 100 bpd, and microports of 10 bpd [33]. Naturally fractured
reservoir pore-throat aperture estimation and its relationship with oil and gas flow rates,
permeability, and porosity are shown in Figure 1.10 [34]. Figure 1.9 follows the same format
presented by [33] using Winland’s equation.
Fig. 1.10: Chart for estimating pore-throat aperture as a function of porosities and permeability and possible ranges of oil (bpd), and gas flow rates (scfd) for different pore-throat aperture [34].
12
1.3.1.2 Storage Classification
Naturally fractured reservoirs were classified based on the storativity as being Type A, B or C
as shown in Figure 1.11. Based on this classification, many reservoirs became producible because
of the presence of the natural fractures. The reservoir Type A had a large amount of hydrocarbon
stored in the matrix porosity (low permeability) and small amount of hydrocarbon stored in the
fractures (high permeability) [27]. Type B had half of the hydrocarbon stored in the matrix (low
permeability) and half stored in the fractures (high permeability) [27]. Type C had all the
hydrocarbon stored in the fractures with no contribution from the matrix [27].
Fig. 1.11: Porosity distribution in naturally fractured reservoir Type A, B, and C [27].
1.3.1.3 Matrix-Fracture Interaction
Core provided excellent source for direct information for determining the interaction between
matrix and fracture [35]. The interaction is divided into (1) no mineralization within the fractures
and hydrocarbon flows freely from the matrix to the fractures, (2) some mineralization within the
fractures with limited hydrocarbon flow, (3) complete mineralization so hydrocarbon flow is very
low, and (4) vuggy fractures where parts of the reservoir had large porosities (up to 100%) in some
intervals where hydrocarbon flow is high if the vugs are connected.
13
1.4 Hydraulic Fracturing
1.4.1 Hydraulic Fracturing Basic Concepts
Hydraulic fracturing enhances the permeability and drainage area of unconventional reservoirs
enabling wells to be economically viable. Hydraulic fracturing produces fractures in the rock
formation that stimulates the flow of hydrocarbons which increases volumes that can be recovered
[34]. The fractures are created by pumping large quantities of fluids at high but controlled pressure
down the wellbore into the target rock formation [35]. The process is designed to create small
cracks within the formation and propagate the fractures to a desired distance from the wellbore by
controlling the rate, pressure, and fluid injection duration. Hydraulic fracturing fluids include water
based fluids, oil based fluids, energized fluids (inert gas of N2 or CO2), multi-phase emulsions, and
acid fluids [36]. The additives are gelling agents, cross-linkers, breakers, fluid loss additives,
bactericides, surfactants, and clay control additives [36]. Hydraulic fractures can extend up to
several hundred ft away from the wellbore. Proppant is carried into the newly formed fractures to
keep them open after the pressure drops. This allows the trapped hydrocarbon to flow through the
fractures more efficiently. Some of the hydraulic fracture fluids and proppant remain in the
reservoir rock whereas some of the hydraulic fracture fluids return to the surface with the
hydrocarbon and formation water (flow-back process).
1.4.2 Hydraulic Fracturing – Industrial Practice
Floyd Farris of Stanolind Oil and Gas Corporation (Amoco) performed a study in 1947 to
establish relationships between observed well performance and treatment pressure [37]. This study
produced a better understanding of fracture breakdown pressures during water injection. From this
work, Farris formulated the idea of hydraulically fracturing a formation to enhance production
from oil and gas wells. This study was performed in 1947 in the Hugoton gas field in Grant County
(Kansas). A total of 1,000 gallon of naphthenic acid and palm oil (napalm) thickened gasoline was
injected followed by a gel breaker to stimulate a gas producing limestone formation at a depth of
2,400 ft. The well deliverability did not change appreciably but it was the start of hydraulic
fracturing.
14
In 1948, the hydraulic fracture operation patent was issued by J. B. Clark of Stanolind Oil [37].
This patent gave exclusive license to the Halliburton Oil Well Cementing Company (Howco) to
carry out the new hydraulic fracturing process. Howco performed the first two commercial
hydraulic fracturing treatments on March 17, 1949 with the hydraulic fracture treatment cost of
$1,000 in Archer County, Texas. Howco used a blend of crude and gasoline and 150 lb of sand. In
the first year, 332 wells were hydraulically fractured with average production increased of about
75%. The application of hydraulic fracturing increased greatly and it reached more than 3,000
wells a month during the mid-1950s. In 2008, more than 50,000 hydraulic fractures stages were
completed worldwide at a cost between $10,000 and $6 million per well [37]. It was a common
industry practice to have from 8 to 40 hydraulic fracture stages in a single well [37]. Hydraulic
fracturing was estimated to have increased U.S. recoverable reserves of oil by at least 30% and gas
by 90% [37].
The setting of hydraulic fracturing has changed throughout the years. The common practice
for industry nowadays is to use complex wellbores such as horizontal wells to intersect a larger
interval of hydrocarbon bearing rock. The hydraulic fracture process steps are:
1. Pad stage: injection of hydraulic fracture fluid (slickwater, fracture liquid and gas if any)
to initiate hydraulic fracture creation and propagate the created fracture.
2. Slurry stage: injection of hydraulic fracture fluid and proppant to place the proppant in the
created fracture.
3. Spacer stage: injection of hydraulic fracture fluid to make sure the proppants in place.
4. Flush stage: injection of slickwater to clean the wellbore from any hydraulic fracture fluids
and proppants.
5. Stop pumping and flow-back to the well to recover any hydraulic fracture fluids from the
wellbore while leaving the proppant in place in the reservoir.
The type of hydraulic fracturing used is dependent on a number of variables [38]:
1. In-situ stresses direction.
2. Drilled well type.
3. Target formation reservoir properties.
4. Reservoir depth, thickness, temperature, and pressure.
5. Well completion type.
15
6. Hydraulic fractures stages to be completed in the wellbore.
7. Choice of fracturing fluids and materials.
8. Cost of fracturing and materials.
The hydraulic fracturing best industry practices were summarized as: (1) hydraulic fracture
fluid of 60,000 gal and proppants of 100,000 lb with the largest treatments exceeding 1 million gal
fluid and 5 million lb proppant, (2) water as a fracturing fluid with gelling agent (e.g. borate gel
breaker), (3) surfactant as emulsions minimizer, (4) formation fluid and potassium chloride as clay
impact minimizer, (5) foams and alcohol as water usage enhancement, and (6) aqueous fluids as
the base fluid in approximately 96% of all fracturing treatments [37]. Metal-based crosslinked
fluid have been used since 1970s to enhance the viscosity of gelled water based fracturing fluids
for high temperature wells. Gel and chemical stabilizers have also been used in high temperature
reservoirs.
The first proppant that had been used by the industry was river sand and construction sand that
were filtered through a window screen. There are different trends in the proppant sizes from the
beginning, but 20/40 U.S. standard mesh sand (diameter of 0.42-0.84 mm) are used in
approximately 85% of the total world hydraulic fracturing jobs. Different proppants have been
evaluated throughout the years, including plastic pellets, steel shot, Indian glass beads, aluminum
fused zirconium [37]. From the total proppant market usage, 80% of the market used sand, 10%
used resin-coated sand, and 10% used ceramics [39]. The concentration of proppant (lb/gal)
remained low until 1960s, when viscous fluids such as cross-linked water-based gels were
introduced [37]. Hydraulic fracture equipment commonly includes pumps, trucks, and tanks. An
example of a hydraulic fracturing operation is shown in Figure 1.12 [40, 41].
16
Fig. 1.12: Hydraulic fracture equipment are water truck (top left), fracturing sand transport truck (top right), water storage tank (bottom left) and HF process layout (bottom right) [40, 41].
Horizontal well stimulation creates different types of hydraulic fractures [42]. Hydraulic
fractures can be transverse, longitudinal, and oriented fractures. The type of hydraulic fracture
depends on the horizontal wellbore direction with respect to the minimum in-situ stress as shown
in Figure 1.13 [42].
17
Fig. 1.133: Fracture orientation as a function of wellbore orientation relative to in-situ stresses orientation [42].
1.5 Stimulated Rock Volume Concept and Application
The stimulated reservoir volume or stimulated rock volume (SRV) is the approximated 3-D
volume of the created fracture network during hydraulic fracturing in low permeability reservoir
that can be estimated from the microseismic event cloud [45]. The SRV properties depend on the
hydraulic fracture properties such as injection fluids, proppant, pressure, rate, and injection
duration. Reservoir properties such as natural fracture network, initial pressure, in-situ stresses
magnitude and direction, thickness, elastic properties (Young’s modulus and Poisson’s ratio), and
initial permeability also affect SRV properties. The reservoir properties dictate the complexity of
the SRV. In unconventional reservoirs, a large SRV dimension is required to create maximum
fracture-surface contact area with the unconventional formations through both size and density.
In 2002, there was a first discussion of a large fracture network creation during hydraulic
fracturing in the Barnett shale and it showed the relationship between treatment properties and
18
SRV size [46, 47]. Figure 1.14 shows the example of estimating the stimulated reservoir area
(SRA) from the microseismic mapping data [45].
Fig. 1.144: Estimating SRA from microseismic mapping data [45].
It was found that the effective fracture network dimensions could be smaller than the SRV
dimensions [45]. The concept of SRV dimensions, hydraulic fracture injection port spacing, and
SRV permeability as well performance driver could be used to optimize the hydraulic fracture
design. The most of the reservoir engineering models that used the SRV concept did not consider
fracture mechanics [48].
1.6 Research Questions
Production of tight gas sands is important to Canada. Shale and tight gas resource production
is increasing which is helping to counterbalance the conventional resource production decline. In
2014, shale gas was 4% of total Canadian natural gas production whereas tight gas was 47% [49].
19
National Energy Board forecasts by 2035, shale and tight gas productions together will represent
90% of Canada’s natural gas production [49]. In Canada, shale and tight gas production activities
are located mainly in Western Canada Sedimentary Basin. Tight gas production requires hydraulic
fractures and horizontal well completion for optimum production. The research questions that arise
from the literature review, presented in Chapter 2, are as follows:
1. How can SRV effective permeability and in-situ stresses change during hydraulic
fracturing?
2. What is the impact of Young’s modulus on SRV effective permeability?
3. What are the characteristics of the fracture network inside SRV?
4. What are the impacts of rock mechanical properties, effective stresses, and fracture fluid
injection volume on SRV dimensions?
5. How does the SRV evolve as a function of distance and time during production?
6. Can characteristics of SRV be deduced from the gas flow rate production?
1.7 Thesis Outline
This thesis consists of three research chapters in addition to the literature review and
introduction. The first research chapter describes a new method to estimate fracture characteristic
within stimulated reservoir volume using both finite element and semi-analytical approaches. The
second research chapter uses geomechanical theory to analyze a multi-stage hydraulic fracturing
operation in a tight gas sand formation. The third research chapter uses a novel application of the
pressure diffusion equation to examine the permeability of the fracture network. The final chapter
lists conclusions and recommendations that arise from the research documented in this thesis. The
units are used in this thesis are field units and other units.
20
1.8 References
[1] Kazemi, H. 1982. Low-Permeability Gas Sands. J Pet Technol 34 (10): 2229-2232. SPE 11330 PA. http://dx.doi.org/10.2118/11330-PA
[2] Aguilera, R., and Harding, T. 2007. State-of-the-Art of Tight Gas Sands Characterization and Production Technology. Presented at the Petroleum Society’s 8th Canadian International Petroleum Conference (58th Annual Technical Meeting), Calgary, Alberta, Canada, 12-14 June. http://dx.doi.org/10.2118/2007-208
[3] Holditch, S. A. 2006. Tight Gas Sands. J Pet Technol 58 (06): 86-93. SPE 103356. http://dx.doi.org/10.2118/103356-JPT
[4] Gray, J. K. 1977. Future gas reserve potential Western Canadian Sedimentary Basin: 3d Natl. Tech. Conf. Canadian Gas Assoc.
[5] Masters, J. A. 1979. Deep Basin Gas Trap, Western Canada. AAPG Bulletin 63(2):152. [6] Bureau of Economic Geology: The University of Texas. 2000. Natural Gas. In-house
presentations. http://www.beg.utexas.edu/techrvw/presentations/talks/tinker/tinker01/page05.htm (Downloaded 16 December 2015).
[7] BP World Energy Outlook Booklet 2035. 2015. http://www.bp.com/content/dam/bp/pdf/energy-economics/energy-outlook-2015/bp-world-energy-outlook_booklet_2035.pdf. (Downloaded 16 December 2015)
[8] Harvard Business School and Boston Consulting Group. 2014. http://www.hbs.edu/competitiveness/Documents/america-unconventional-energy-
opportunity.pdf. (Downloaded 16 December 2015).
[9] Heffernan, K., and Dawson, F. M. 2010. An Overview of Canada’s Natural Gas Resources. CSUG report 2010. http://www.csug.ca/images/news/2011/Natural_Gas_in_Canada_final.pdf (Downloaded 16 December 2015).
[10] National Energy Board Of Canada, Canada’s Energy Future 2013: Energy Supply and Demand Projections to 2035; copyright Her majesty the Queen in Right of Canada (49). https://www.neb-one.gc.ca/nrg/ntgrtd/ftr/2013/2013nrgftr-eng.pdf (Downloaded 16 December 2015).
[11] Schmoker, J. W. 1995. U.S. Method for assessing continuous-type (unconventional) hydrocarbon accumulations, in Gautier, D.L., Dolton, G.L., Takahashi, K.I., and Varnes, K.L., eds., 1995, 1995 National assessment of United States oil and gas resources—Results, methodology, and supporting data: U.S. Geological Survey Digital Data Series DDS–30, 1 CD–ROM.
[12] Schenk, C. J., and Pollastro, R. M. 2002. Natural Gas Production in the United States; U.S. Geological Survey Fact Sheet FS-113-01, January. http://pubs.usgs.gov/fs/fs-0113-01/ (Downloaded 16 December 2015).
[13] Shanley, K., Cluff, R. M., and Robinson, J. W. 2004. Factors Controlling Prolific Gas Production From Low-Permeability Sandstone Reservoirs: Implications for Resource Assessment, Prospect Development and Risk Analysis. AAPG Bulletin (1083-1121), August.
[14] Davis, T. B. 1984. Subsurface Pressure Profiles in Gas Saturated Basins. AAPG Memoir (38): 189-203.
[15] Shirley, K. 2004. How did the Tight Gas Get Here? Debate Taps Petroleum Systems, AAPG Explorer, April.
[16] McPeek, L. A. 1981. Eastern Green River Basin: A Developing Giant Gas Supply from Deep, Overpressured Upper Cretaceous Sandstones. AAPG Bulletin (65): 1078–1098.
[17] Law, B. E., and Dickenson, W. W. 1985. Conceptual model for origin of abnormally pressured gas accumulations in low-permeability reservoirs. AAPG Bulletin (69): 1295–1304.
[18] Spencer, C. W. 1987. Hydrocarbon Generation as a Mechanism for Overpressuring in the Rocky Mountain region. AAPG Bulletin (71): 368-388.
[19] Spencer, C. W. 1989. Review of characteristics of low permeability gas reservoirs in western United States. AAPG Bulletin (73).
[20] Law, B. E., and Spencer C. W. 1989. Geology of tight gas reservoirs in the Pinedale anticline area, Wyoming, and at the multiwell experiment site, Colorado. U.S. Geological Survey Bulletin (1886).
[21] Surdam, R. C. 1997. A New Paradigm for gas Exploration in Anomalously Pressured ‘‘Tight-Gas Sands’’ in the Rocky Mountain Laramide Basins, in R. C. Surdam, ed., Seals, traps, and the petroleum system. AAPG Memoir (67): 283–298.
[22] Selley, R. C. 1998. Elements of Petroleum Geology, second edition. Waltham: Academic Press.
[23] Law, B. E., and Curtis J. B. 2002. Introduction to unconventional petroleum systems. AAPG Bull., 86 (11):1851–1852.
[24] Zou, C. N. 2012. Unconventional Petroleum Geology. Beijing: Elsevier (373). [25] Stearns, D. W. 1994. AAPG Fractured Reservoirs School Notes 1982-1994, Great Falls,
Montana. [26] Aguilera, R. 2010. Naturally Fractured Reservoir Courses Notes, University of Calgary,
Calgary, Alberta, Canada. [27] Aguilera, R. 2003. Geologic and Engineering Aspects of Naturally Fractured Reservoirs.
CSEG Recorder, February. [28] Nelson, R. 1985. Geologic Analysis of Naturally Fractured Reservoirs, Contributions in
Petroleum Geology and Engineering, Vol. 1, Texas: Gulf Publishing Co. [29] Aguilera, R. 1998. Geologic Aspects of Naturally Fractured Reservoirs. The Leading Edge,
December: 1667-1670. [30] Coalson, E. B., Hartmann, D. J., and Thomas, J. B. 1985. Productive Characteristics of
Common Reservoir Porosity Types. Bulletin of the South Texas Geological Society 15 (6): 35-51.
[31] Kolodzie, S., Jr. 1980. Analysis of Pore Throat Size and Use of the Waxman-Smits Equation to Determine OOIP in Spindle Field. Paper SPE 9382 was presented at the Colorado Society of Petroleum Engineers 55th Annual Fall Technical Conference.
[32] Aguilera, R. 2002. Incorporating Capillary Pressure, Pore Throat Aperture Radii, Height Above Free Water Table, and Winland r35 Values on Pickett Plots. AAPG Bulletin 86 (4): 605-624.
22
[33] Martin, A. J., Solomon, S. T., and Hartmann, D. J. 1997. Characterization of Petrophysical Flow Units in Carbonate Reservoirs. AAPG Bulletin 83 (7): 734-759.
[35] Geological Society of America. 2015. GSA Critical Issue: Hydraulic Fracturing. http://www.geosociety.org/criticalissues/hydraulicFracturing/glossary.asp#Hydraulicfracturing
[36] Montgomery, C. 2013. Fracturing Fluids, Effective and Sustainable Hydraulic Fracturing. Dr. Rob Jeffrey (Ed.), ISBN: 978-953-51-1137-5, InTech, DOI: 10.5772/56192.
[37] Montgomery, C. T., and Smith, M. B. 2010. Hydraulic Fracturing-History of an Enduring Technology. Society of Petroleum Engineers, JPT Online.
[38] CSUG (Canadian Society for Unconventional Gas). 2015. http://www.csug.ca/images/CSUG_publications/CSUG_HydraulicFrac_Brochure.pdf. (Downloaded 17 December 2015).
[39] Cadre Proppant. 2012. http://www.cadreproppants.com/files/120724%20Denver%20Conference%20Cadre%20Proppants.pdf. (Downloaded 17 December 2015).
[40] Conoco Phillips Canada. 2015. http://www.conocophillips.ca/technology-and-innovation/unconventional/Pages/default.aspx. (Downloaded 17 December 2015).
[41] Driscoll, M. 2013. Proppant Prospects for Bauxite. 19th Bauxite & Alumina Seminar, Miami, USA, 13-15 March. http://www.indmin.com/Stub.aspx?StubID=4061 (Downloaded 17 December 2015).
[42] Abass, H. H., Soliman, M. Y., Tahini, A. M., Suriaatmadja, J., Meadows, D. L., and Sierra, L. 2009. Oriented Fracturing: A New Technique to Hydraulically Fracture Openhole Horizontal Well. Paper SPE 124483 was presented at the 2009 SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, 4-7 October.
[43] Hubbert, M. K., and Willis, D. G. 1957. Mechanics of hydraulic fracturing, Trans. Am. Inst. Min. Metall. Pet. Eng., 210: 153–168.
[44] Jaeger, J. C., Neville G. W. Cook, and Robert Wayne Zimmerman. 2007. Fundamentals of rock mechanics. Malden, MA: Blackwell Pub.
[45] Mayerhofer, M. J., Lolon, E. P., Warpinski, N .R., Cipolla, C. L., Walser, D., and Rightmire C. M. 2010. What is stimulated reservoir volume? SPE Prod & Oper 25(01): 89-98. SPE-119890. http://dx.doi.org /10.2118/119890-PA
[46] Fisher, M. K., Wright, C. A., Davidson, B. M., Goodwin, A. K., Fielder, E. O., Buckler, W. S., and Steinsberger, N. P. 2002. Integrating Fracture Mapping Technologies to Optimize Stimulations in the Barnett Shale. Paper SPE 77441 was presented at the SPE Annual Conference and Exhibition, San Antonio, Texas, 29 September–2 October.
[47] Maxwell, S. C., Urbancic, T. I., Steinsberfer, N., and Zinno, R. 2002. Microseismic Imaging of Hydraulic Fracture Complexity in the Barnett Shale. Paper SPE 77440 was presented at the SPE Annual Conference and Exhibition, San Antonio, Texas, 29 September–2 October. http://dx.doi.org/10.2118/77440-MS
[48] Cipolla, C., and Wallace, J. 2014. Stimulated Reservoir Volume: A Misapplied Concept? Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA, 4-6 February.
[49] Natural Resources Canada. 2015. Exploration and Production of Shale and Tight Resources. http://www.nrcan.gc.ca/energy/sources/shale-tight-resources/17677
A rock fails when large stress is applied to the rock and produces permanent change of rock
shape and its integrity. The failure state is usually accompanied with much lower capability to
carry loads [1]. The stress level when the rock fails is called the rock strength and it is usually
determined in the laboratory using uniaxial or triaxial tests or Brazilian test [2].
2.1.1 Tensile Failure
Tensile failure happens when the effective stress across a plane within the rock exceeds a
critical limit referred to as the tensile strength. The tensile strength for most rocks is low (typically
of order of a few MPa) and when there are natural fractures in the rock, the tensile strength, T0, is
expected to be close to zero [3]. The minimum effective stress, σ3’, is given by [1]:
𝜎𝜎3′ = −𝑇𝑇0 (1)
A hydraulic fracture is a form of tensile failure that occurs when the fluid pressure exceeds the
sum of the minimum total stress and the tensile strength of the rock [1]. Tensile failure extension
occurs when the injection pressure is higher than the minimum stress [4]. Continuous pumping of
fluid into the rock at high pressure causes the fracture to grow in the direction of the least resistance
which is the direction normal to the minimum stress. An example is illustrated in Figure 2.1a [1].
25
Fig. 2.1: (a) Tensile failure and (b) shear failure [1].
2.1.2 Shear Failure
Shear failure happens if the shear stress along some planes in the rock is high enough and it
develops a failed zone along the failure plane where the two sides of the plane move relative to
each other as shown in Figure 2.1b [1].
Shear failure can be determined by using a Mohr-Coulomb failure envelope. T The failure
envelope is built from the cohesion as the intercept and the internal friction angle as the slope [5].
High cohesion and internal friction angle are typical of strong rocks which are hard to fail. A
naturally fractured reservoir is a relatively weak rock with lower cohesion which is easier to fail
than strong rocks. The Mohr circle consists of maximum and minimum effective stresses [5].
The Mohr-Coulomb failure envelope was produced by using test results from triaxial tests
(Figure 2.2a and Figure 2.2b) [4, 6]. Triaxial tests involve applying a load on the sample (σ1) while
the confining pressure (σ3) is held constant until the sample fails. The Mohr-Coulomb failure
envelope slope usually decreases for most rocks as the confining pressure increases (Figure 2.2b).
But for most rocks, it is allowable to consider a linearized Mohr-Coulomb failure envelope as
shown in Figure 2.2b [4]. The linearized Mohr-Coulomb failure envelope criterion is given by [4]:
26
𝜏𝜏 = 𝐶𝐶 + 𝜎𝜎𝑛𝑛𝜇𝜇𝑖𝑖 (2) 𝜏𝜏 = 𝐶𝐶 + 𝜎𝜎𝑛𝑛𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 (3)
(a)
(b)
Fig. 2.2: (a) Triaxial strength test with β is the angle between failure plane with σ3, (b) a series of triaxial tests at different effective confining pressure (usually flattens as confining pressure increase), and linear simplification of the Mohr-Coulomb failure envelope [4, 6].
27
where τ is the shear stress, C is the rock cohesion, σn is the normal stress, µi is the slope of the
failure envelope, and ϕ is the internal friction angle. The normal stress on a failure plane is inclined
at an angle β to the least stress 𝜎𝜎3, where the minor principal stress is 𝜎𝜎3 as shown in Figure 2.2a,
is [1, 4]:
𝜎𝜎𝑛𝑛 = 𝜎𝜎1+𝜎𝜎32
+ 𝜎𝜎1−𝜎𝜎32
𝑐𝑐𝑐𝑐𝑐𝑐2𝛽𝛽 (4)
𝜏𝜏 = 𝜎𝜎1−𝜎𝜎32
𝑐𝑐𝑠𝑠𝑡𝑡2𝛽𝛽 (5)
2𝛽𝛽 = 90𝑜𝑜 + 𝑡𝑡 (6)
𝛽𝛽 = 45𝑜𝑜 + 𝜙𝜙2 (7)
The shear failure criterion is met when the Mohr circle touches the Mohr-Coulomb failure line.
This criterion shows a linear relationship between the effective stresses with the rock cohesion and
the internal friction angle as shown in Figure 2.3a. The triangle OAB in Figure 2.3a produces:
𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡 =12
(𝜎𝜎1−𝜎𝜎3)
�𝐶𝐶+12(𝜎𝜎1+𝜎𝜎3)𝑡𝑡𝑡𝑡𝑛𝑛𝜙𝜙� (8)
28
(a)
(b)
Fig. 2.3: (a) Stress relationships for shear failure Mohr circle on Mohr-Coulomb failure envelope and (b) typical failure characteristics of intact rock plotted in terms of Mohr circle and Mohr-Coulomb failure envelope [5].
29
Rearranging Equation (8) yields:
12
(𝜎𝜎1 − 𝜎𝜎3)𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡 = 𝐶𝐶𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡 + 12
(𝜎𝜎1 + 𝜎𝜎3)𝑐𝑐𝑠𝑠𝑡𝑡𝑡𝑡 (9)
𝜎𝜎1 = 2𝐶𝐶𝐶𝐶𝑜𝑜𝐶𝐶𝜙𝜙(1−𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙) + 𝜎𝜎3(1+𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙)
(1−𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙) (10)
Shear failure of rocks during hydraulic fracturing is induced by the increase of pore pressure. There
is an alternative method to produce a shear failure envelope by plotting the effective maximum
horizontal stress and the effective minimum horizontal stress to support the results of shear failure
from the Mohr-Coulomb failure envelope [5].
Warpinski and Teufel (1987) found that shear failure occurred during hydraulic fracturing at
some distance from the center of the main hydraulic fracture [7]. Geomechanical analysis was used
to predict the shear failure and revealed that the extent of the shear failure zone was affected by
the fracture pressure. The results were verified by using microseismic monitoring data.
Jupe et al. (1993) explained that the microseismic data of a geothermal site in Urach, Germany
showed that the dominant mechanism that enhanced SRV permeability was shear failure along
pre-existing natural fractures [8].
Duchane (1998), by using microseismic observations and geological information of several
geothermal sites (such as in Los Alamos, New Mexico and Falkenberg, Sweden), showed that the
hydraulic vertical fractures were created from reopened sealed natural fractures (shear failures)
instead of induced new hydraulic vertical fractures (tensile fracture) [9].
Rahman et al. (2002) developed a model to integrate tensile-induced hydraulic fractures and
shear failure of natural fractures [10]. Their results revealed that the enhanced permeability of the
SRV was 30 times that of the initial formation permeability [10].
Warpinski et al. (2004) found that in a water saturated reservoir that a shear failure zone
extended further away from the main hydraulic fracture to create a wider SRV [11].
Palmer et al. (2007) discovered that the shear failures occurred at natural fractures far from the
central hydraulic fracture during hydraulic fracturing in the Barnett shale due to remote slippage
of natural fractures. They also determined that the enhanced permeability induced from hydraulic
30
fracturing during production might not be equal because the shear or tensile fractures that were
induced during the operation might partially close during production [12].
2.2 Hydraulic Fracturing
2.2.1 Hydraulic Fracturing from Vertical and Horizontal Wells
Wellbore completion technology for hydraulic fracturing has been developed greatly since the
1980s. The wellbore completion type consists of vertical, horizontal, and multilateral wellbore. Elf
Aquitaine, in the early 1980s, had reported major success through horizontal wellbore on a low
permeability and naturally fractured reservoir at Prudhoe Bay and Rospo Mare field, offshore Italy
[13]. The Rospo Mare field was a good candidate for horizontal well completion because of the
oil was contained in fractures and vugs with a very low permeability formation. A horizontal well
was more appropriate to intersect many natural fractures systems in such formations.
Giger et al. [13] defined the criteria for drilling horizontal wells in preference to vertical wells
were defined as follows: (1) tight reservoirs especially if vertical natural fractures were present,
(2) thin formation, and (3) soft formations such as chalk which were liable to collapse [13].
Borisov [14] conducted field case studies to compare the productivity index between horizontal
and vertical wellbores. The results showed that the productivity improvement would rarely be
more than a factor of 5 except in the case of naturally fractured reservoirs. This study was
supported by other studies from Mukherjee and Economides [15].
Soliman et al. [16] explained that even though an unstimulated horizontal well might have been
successful in naturally fractured reservoirs and in reservoirs with water or gas coning problems,
there were conditions where fracturing a horizontal well might be a good option.
Bobrosky [17] compared reservoir contact between vertical, unstimulated horizontal, and
multi-fractured horizontal wellbores with a maximum reservoir contact was achieved by multi-
fractured horizontal wellbore. Figure 2.4 displays a comparison of the contact area achieved by
using a vertical well, an unstimulated horizontal well, and a hydraulically fractured horizontal well
[17]. The analysis reveals that the hydraulically fractured horizontal well has a contact area
roughly 1,000 times that of the vertical well.
31
Fig. 2.4: Reservoir contact comparison between vertical well, unstimulated horizontal well, and multi-fractured horizontal well [17].
Soliman et al. [16] mentioned that fracturing a horizontal well might dictate how the wellbore
might be completed and oriented. They summarized the situations for fracturing a horizontal well
might be a good option for these conditions: (1) restricted vertical flow caused by low vertical
permeability, (2) low formation productivity due to low formation permeability, (3) natural
fracture occurrence in a direction different from induced hydraulic fractures, and (4) low stress
contrast between pay zone and surrounding layers. The important parameters to be considered
during fracturing a horizontal and vertical wellbores were rock mechanics, reservoir engineering,
and operational aspects [16].
The stress distribution around a horizontal wellbore follows the same equations used in vertical
wells. The equations for radial, tangential, and vertical stresses for a horizontal wellbore parallel
to the minimum horizontal stress with assumption of no pore pressure penetration occurs are given
by [18]:
32
For σH> σV
𝜎𝜎𝑟𝑟 = 𝑝𝑝𝑖𝑖 (11)
𝜎𝜎𝜃𝜃 = 3𝜎𝜎𝑉𝑉 − 𝜎𝜎𝐻𝐻 − 𝑝𝑝𝑖𝑖 (12)
𝜎𝜎𝑧𝑧 = 𝜎𝜎ℎ − 2𝑣𝑣(𝜎𝜎𝐻𝐻 − 𝜎𝜎𝑉𝑉) (13)
For σH<σV
𝜎𝜎𝑟𝑟 = 𝑝𝑝𝑖𝑖 (14)
𝜎𝜎𝜃𝜃 = 3𝜎𝜎𝐻𝐻 − 𝜎𝜎𝑉𝑉 − 𝑝𝑝𝑖𝑖 (15)
𝜎𝜎𝑧𝑧 = 𝜎𝜎ℎ − 2𝑣𝑣(𝜎𝜎𝑉𝑉 − 𝜎𝜎𝐻𝐻) (16)
where σr, σθ, σz are the effective normal stresses, pi is the wellbore pressure, σH, σh, σV are the in-
situ stresses, and v is the Poisson’s ratio
El Rabaa [19] explained that if a wellbore is drilled at an angle with respect to the maximum
stress, then multiple transverse fractures might be created. If the horizontal wellbore was drilled
parallel with the maximum stress, the created longitudinal fracture would propagate along the
wellbore [19]. Longitudinal fractures have not been as popular as the transverse fracture because
of the less reservoir contact that they yield.
2.2.2 Stress Interference due to Hydraulic Fracture Presence
Hydraulic fracture creation could change the stress field in its surroundings and potentially
affect subsequent new hydraulic fractures.
2.2.2.1 Stress Interference due to Semi-Infinite Fracture
Sneddon and Elliot [20] conducted research on stress interference caused by hydraulic
fracturing specifically studying the stress distribution in the neighborhood of the crack in an elastic
medium. They simplified the problem by assuming the crack was rectangular with limited height
while the crack length was infinite and the crack width was extremely small compared to its height
and length. In their analysis, the crack was open due to internal pressure. They developed equations
to predict the changes in three principal stresses. Their results suggested that if the stress contrast
between the in-situ stresses was very large, then the effect of stress interference might not affect
33
the fracture initiation and direction. If the stress contrast was not large, then it was possible that
the preferred fracture direction might be different. The stress direction change was a function of
stress contrast, fracture height, and distance between created fractures. The study would be more
realistic if it was for a finite fracture.
2.2.2.2 Stress Interference due to Penny-Shaped Fracture
Soliman et al. [16] presented the simplified finite fracture by a penny-shaped fracture (circular
fracture). This case would be closely similar to the case of small multi-fractures intersecting a
horizontal wellbore (multiple transverse fractures) where the fracture height and length were
approximately equal. Sneddon [20] presented a mathematical solution for the stress distribution in
the neighborhood of a penny fracture for three dimensional case.
2.2.2.3 Stress Interference due to Multiple Fractures in Horizontal Well
In general, hydraulic fractures are created transverse to the wellbore to achieve maximum
reservoir contact. Therefore, it is important to understand stress changes during hydraulic
fracturing along a horizontal wellbore. Soliman et al. [16] stated that due to the creation of multiple
transverse propped open fractures, it was expected that the effect of stress interference grew as the
number of fractures increased. They used the penny-shaped fracture model to calculate the effect
of multiple fractures on the stress distribution [16]. The conducted study used the calculated stress
for 5 hydraulic fractures and for distance to fracture diameter ratios from 0.5 to 1 [16]. The results
showed that if the distances between the fractures were equal to the fracture diameter, then while
creating a fourth fracture, it would be expected that net pressure increased by about 21% above the
net pressure encountered during creation of the first fracture [16]. The analysis showed that the
same net pressure was expected to occur during creation of the fifth fracture [16]. If the distance
between fractures was half that of the fracture diameter, then the expected net pressure during
creation of the third fracture was about twice that encountered during creation of the first fracture
[16]. It was also found that the interference between fractures caused changes in all in-situ stresses
[16]. The minimum horizontal stress (perpendicular to the fracture) grew by a larger degree than
the other two stresses [16].
34
2.2.3 Hydraulic Fracturing on Horizontal Well Completion
The horizontal well completion design affects well performance. Hydraulically fractured
horizontal well completions are typical based on McDaniel and Willet’s (2002) guidelines, as
shown in Figure 2.5, given as follows [21]:
1. Open-hole completion is the cheapest and simplest technique. It is used when wellbore
instability is not a problem. The open-hole completion does not have control over fracture
placement in most cases.
2. Perforated or slotted liner is used when the wellbore instability is a concern or if the
operator requires limited control of fluid placement during completion or workover. Pre-
perforated or slotted liners offer significant improvement over open-hole completions but
may have poor distribution of fractures and they allow placement of larger stimulation fluid
volume than that of open-hole completions.
3. Blank liner with limited clustered perforations (un-cemented) is used mostly to improve
hydraulic fracturing in a horizontal well by allowing fracture fluid to reach all desired
intervals. By placing a number of perforations in the liner and plugging the toe, an operator
can choose where fluids exit the liner for better control of fracture placement. The lowest
cost application of blank liner is to use it as a retrievable treating string instead of a
permanent liner. During proppant fracturing treatments, some wellbore conditions can
increase the risk of getting the liner stuck and not being able to be retrieved.
4. Casing packers are more costly than other techniques. A casing packer completion features
inflatable packers that clamp onto the liner.
5. Partially cemented liners are used with an inflatable casing packer near the middle of the
horizontal where the un-cemented section of the liner is pre-perforated with a limited
number of clustered perforations to place well-distributed fractures.
6. Cemented casings are done by cementing the entire length of horizontal wellbore. It
provides the most control over fracture placement.
35
Fig. 2.5: Completion types for stimulation: (a) openhole completion, (b) perforated or slotted liner, (c) blank liner with very limited clustered perforations, (d) casing packer, and (e) fully cemented liner [21].
2.2.4 Simple Theories for Hydraulic Fracturing
To optimize the design of a hydraulic fracturing job, it is necessary to predict the growth of the
SRV versus the hydraulic fracturing injection parameters. SRV growth in heterogeneous
formations with low ratios of the stresses remains difficult to predict with a high level of certainty.
36
Throughout the years, various models have been developed to approximate fracture geometry.
Fracture models can be separated into a two-dimensional (2D) and a three-dimensional (3D)
categories. The KGD (Khristianovitch and Zheltov 1955, Geertsma and de Klerk 1969) [22, 23]
and PKN (Perkins and Kern 1961) [24] models are the most popular 2D models; both are depicted
in Figure 2.6 [25].
Fig. 2.6: (a) The PKN and (b) KGD fracture models [25].
Barree (2009) stated that in all 2D models only the fracture width and length were derived
from the models whereas the fracture height remains constant. The PKN and KGD models both
used the Sneddon (1946) [20] equation. Sneddon (1946) proposed an equation for the width of a
crack as follows [20]:
𝑤𝑤 = 2𝑢𝑢 = 4�1−𝑣𝑣2�𝑃𝑃0𝜋𝜋𝜋𝜋
𝑐𝑐 (17)
where w is the crack width, u is the crack half width, v is the Poisson’s ratio, P0 is the applied
pressure, E is the Young’s modulus, and c is the crack half length. Nordgren (1970), Barree (2009),
and Rahman and Rahman (2010) summarized the different assumptions for the PKN and KGD
models [25, 26, 27]. The PKN model assumptions are:
1. The crack length is larger than the crack height.
2. The crack height is restricted to a given section due to the existence of upper and lower
barriers.
37
3. There is no vertical extension in each vertical section; therefore the fracture shape is
elliptical.
4. A 2D plane strain deformation in the vertical plane is assumed.
The PKN equation provides an estimate of the crack width [24]:
𝑤𝑤 = 𝑢𝑢 = 2�1−𝑣𝑣2��𝑃𝑃𝑓𝑓−𝜎𝜎3�𝜋𝜋
𝐻𝐻 (18)
where H is the crack height.
The KGD model assumptions are:
1. The crack height is larger than the crack length.
2. The crack height is constant and uniform along the entire crack length; therefore, the cross
section is rectangular.
3. The crack width is constant in the vertical direction.
4. A 2D plane strain deformation in the horizontal plane is assumed.
The KGD equation produces the crack width is following [28]:
𝑤𝑤 = 𝑢𝑢 = 2�1−𝑣𝑣2��𝑃𝑃𝑓𝑓−𝜎𝜎3�𝜋𝜋
𝑥𝑥𝑓𝑓 (19)
where xf is the crack half-length.
2.2.5 Numerical Studies of Hydraulic Fracturing
Economides and Nolte [29] summarized the available models such as planar 3D, pseudo 3D,
and general 3D models for hydraulic fracturing. The planar 3D model assumes that the fracture is
planar and perpendicular to the minimum stress. This model is applicable when the surrounding
zones have stresses lower or similar to the stresses of the formation. The pseudo 3D model is
divided into lumped and cell based models. The lumped based model has two half-ellipses joined
at the center in the vertical profile. The fracture half-length and height are calculated at each time
step with the assumed shape is elliptical. The cell based model considers the fractures as a series
of connected cells. These models do not have fixed shapes but they do not consider fully coupled
fluid flow in vertical direction to fracture geometry calculation. The general 3D model does not
38
have any assumption on the fracture orientation. The fracture orientation is affected by wellbore
perforations and orientations and stress orientations.
There are several analytical pseudo 3D and general 3D models proposed recently. Fisher et al.
(2002) did hydraulic fracture diagnostic projects in the Barnett naturally fractured shale reservoir
[30]. They showed that the fracture half-length was a function of injected fluid volume where the
fracture half-length stopped growing after a significant amount of injected fluid volume was
injected [30]. The SRV half-length and width were observed by using microseismic monitoring
[30].
Maxwell et al. (2002) observed the monitored microseismic events during hydraulic fracturing
in a Barnett naturally fractured shale reservoir [31]. They discovered from the microseismic
observations that the hydraulic fracture occasionally grew at an angle to the assumed fracture
direction (the maximum stress direction) and into the neighboring wells [31]. The results also
showed that the hydraulic fractures grew at an angle because they intersected the natural fracture
network [30]. It was also discovered that the hydraulic fracture grew toward neighboring wells
because of the depleted zones around the neighboring wells [31].
Xu et al. (2009) used a semi-analytical pseudo 3D geomechanical model to study the
interaction between fractures and injected fluid volume [32]. They found that the fracture network
complexity and its dimensions were affected by the ratio of stresses within the reservoir [32].
Maxwell et al. (2010) showed that there were cases with critically stressed fractures located
close to the point of hydraulic fracture deformation [33]. These critically stressed fractures could
trigger small stress changes which resulted in remote triggering of microseismic events [33]. This
explained one of the causes of microseismic measurement uncertainties [33].
Mayerhofer et al. (2010) predicted the SRV after hydraulic fracturing using microseismic
mapping beyond a horizontal well [34]. They illustrated the SRV as a summation of several
rectangles with constant width containing microseismic events [34]. These rectangles were parallel
with maximum stress [34]. They were located between the wellbore and the farthest event in both
sides of horizontal well [34]. In order to complete the 3D modeling of SRV, the SRV height was
estimated for the individual rectangle [34]. The limitation of this method was the requirement of
adequate microseismic events and it was only applied to a particular field [34].
39
Weng et al. (2011) developed an analytical 3D fracture network model in a naturally fractured
reservoir to determine SRV dimensions; the model was solved by using numerical simulation [35].
Their simulation results showed that stress anisotropy, natural fractures, and internal friction angle
affected complexity of fractures network [35]. Lowering the stress anisotropy changed the fracture
dimensions from a bi-wing fracture configuration to a complex fracture network [35].
Yu and Aguilera (2012) presented an analytical 3D model to determine the SRV dimensions
after hydraulic fracture operation in an unconventional gas reservoir by using microseismic events
and pressure diffusivity equation [36]. The SRV dimensions were obtained as a function of
injection pressure, minimum pressure that triggered microseismic events, microseismic event
occurrence time, and hydraulic diffusivity coefficient [36]. They determined the hydraulic
diffusivity coefficient to calibrate the model to predict SRV dimensions [36]. The hydraulic
diffusivity coefficient could be determined from a slope of a straight line plot between distances
of microseismic event distance from the wellbore versus the square root of occurrence time of the
microseismic event [36].
Nassir et al. (2012) developed a geomechanical 3D finite element model of SRV propagating
into tight formations [37]. Their results were in agreement with the shapes of SRVs obtained from
microseismic monitoring [37]. The dimensions of the SRV were found to be affected by low rock
cohesion and high initial contrast between the minimal and maximal stresses [37]. Their simulation
results suggested that a rock with a low rock cohesion (less than 1 MPa) produced a wider SRV
[36]. Therefore, the conclusions were that large and wide SRVs would only be found in formations
where the rock was weakened by natural fractures (low rock cohesion) [37].
McClure and Horne (2013) developed a computational model that coupled fluid flow, stresses
and deformation induced by fracture opening/sliding, and fracture propagation in a 2D discrete
fracture network [38]. The model was able to couple fluid flow and earthquake models [38]. The
model was used to investigate the interaction between fluid flow, permeability evolution, and
induced seismicity during hydraulic fracture injection into a single fault [38]. Using this model,
they explained the critical importance of including the change of state of stress induced by the
deformation caused by hydraulic fracturing [38]. These stresses directly impacted the mechanism
of the hydraulic fracture propagation and the resulting fracture network properties [38]. The
40
limitations of the model was a 2D model and it required the paths of newly forming fractures to
be specified in advance [38].
2.3 Laboratory Studies of Hydraulic Fracturing
The design of a hydraulic fracturing job requires rock mechanical property data. Rock
mechanical properties include in-situ stress magnitude and direction, pore pressure, elastic
modulus, and strength parameters. The main data sources to provide the rock mechanical
properties are core testing and field measurements (measurement while drilling, wireline logs,
seismic data, and well tests).
Fjaer et al. (2008) explained that logs provided continuous data versus depth with limited depth
of investigations around the wellbore [1]. Logs themselves did not directly provide the required
rock mechanical properties [1]. For example, the rock strength could not be measured from
wireline logs, but rock strength might be estimated if appropriate correlations are used [1].
Cores provide direct measurement of rock strength and static elastic properties. The tested
cores in the laboratory may not be fully representative of the study formation because they may
have been disturbed during coring and any subsequent handling. The disturbance can be overcome
with proper sample preparation procedures, test procedures, and correction procedures. Some
considerations need to be applied for different types of rocks. For example, shales need both
special preparation procedures and special test procedures. The following are the details in the
laboratory testing to provide the properties of stimulated rock volume (complex fracture network).
The fracture network is created from the interaction of the induced hydraulic fractures and the
natural fractures.
2.3.1. Laboratory Studies on Fractured Tight Sand and Shale Permeability
Cui and Glover (2014) explained that the matrix permeability in unconventional reservoirs
could be measured using several techniques such as Gas Research Institute (GRI) or pressure-
decay technique, pressure-pulse decay (PPD), and steady-state techniques as shown in Figure 2.7
[39]. This technique is required to fill gas up pore space from all directions and measured an
41
average permeability value in all directions for different pore-throat sizes and it did not consider
effective stresses [39]. This technique limitations were applicable on homogeneous rock and not
considering effective stresses. Cui and Glover (2014) also state that the pressure-pulse decay
technique could measure horizontal and vertical permeability separately on core plugs [39]. It was
affected by diffusion and confining stress [39].
Singhai and Gupta (2013) stated that the steady-state technique used constant injection rate
and pressure and Darcy’s law to determine the matrix permeability in fractured unconventional
reservoir [40]. But this technique was only applicable in high conductivity rocks [40].
2.3.2. Laboratory Studies on Hydraulic Fracture and Natural Fracture
Interaction
There were several laboratory experimental studies done in the past to evaluate the effect of
natural fractures on the propagation of the hydraulic fractures. Lamont and Jessen (1963)
conducted a series of laboratory experiments on six different types of rocks [44]. The tests were
under triaxial compression up to 1,142 psi and with angles of approach, θ, between the hydraulic
fracture and natural fracture varying from 30o to 60o as shown in Figure 2.8 [44]. The results
showed that some of the hydraulic fracture crossed the natural fracture [44]. Other results showed
that the hydraulic fracture propagated along the natural fracture and the hydraulic fracture would
exit from the natural fracture from the weakest point of the natural fracture [44]. The weakest point
was defined as the point with a high pressure within the natural fracture to overcome the local
fracture toughness [44]. This would cause the fracture break out of the natural fracture and initiate
a hydraulic fracture [44].
44
(a)
(b)
Fig. 2.8: (a) Mechanical testing apparatus and hydraulic testing apparatus, and (b) hydraulic fracture intersecting a natural fracture [44].
Potluri et al. (2005) performed detailed laboratory experiments on the natural fractures and the
hydraulic fractures interaction using Warpinski and Teufel’s interaction criterion (Figure 2.9) [45].
The results showed that: (1) the hydraulic fractures crossed the natural fractures when normal
stress on the natural fractures was high relative to the rock fracture toughness, (2) the hydraulic
fractures propagated within the natural fractures then broke out from the natural fractures tip (the
pressure at natural fracture tip exceeded the net pressure required to break out), and (3) the
hydraulic fracture propagated within the natural fracture then broke out from along the natural
45
fractures (the pressure in the natural fracture was high enough to overcome the local fracture
toughness) [45].
(a)
(b)
Fig. 2.9: (a) Hydraulic fracture propagates from the tip of natural fractures and (b) hydraulic fracture propagates from weak point along natural fracture [45].
Zhang et al. (2013) conducted a series of experiments to measure propped induced hydraulic
fractures and propped natural fractures conductivity in Barnett shale using a modified API
conductivity cell at room temperature were performed [46]. If the proppant permeability was
known then the propped fracture aperture could be determined [46]. The results showed that the
fracture conductivity increased with proppant size and concentration [46].
46
2.4 Microseismic Monitoring during Hydraulic Fracturing
A microseismic event is a micro-earthquake that happens during hydraulic fracturing. The
precise location of the microseismic event is defined as the location of a new fracture or an existing
fracture when it is reopened. The time at which to the microseismic event is detected at the receiver
is the time which it takes for the P and S waves to travel the distance from the event location to
the receiver’s location. The wave velocity models for different formations are built by using a
dipole sonic log and a perforation shot arrival time. The microseismic event location is determined
by using the distance between the sensor and the microseismic event based on the P and S wave
and also using the orientation (azimuth and dip) determined from wave propagation direction [47].
Microseismic monitoring during hydraulic fracturing is a passive measurement of
microseismic events and it provides microseismic event arrival time, location, and magnitude. The
growth of the dimensions of the SRV during hydraulic fracturing is important for hydraulic
fracturing effectiveness. There are two methods of microseismic monitoring which are downhole
and surface monitoring. Historically, Bailey in his patent, explained about these two monitoring
methods procedures [48]. The general microseismic monitoring during the hydraulic fracture are:
1. Injecting high pressurized fluid down to wellbore.
2. Increasing fluid pressure with time to cause rock to fail and creating fractures.
3. Injecting fluid continuously into the fracture to cause the fracture to propagate and
eventually the injection fluid pressure decreasing.
4. Microseismic sensors are located around the hydraulic fracture treatment wellbore to
receive the seismic wave produced by the induced fracture.
5. Seismic arrival times are measured.
6. Predetermined wave velocity and seismic arrival time are used to determine the
microseismic events locations.
7. Using a polarization analysis to determine the microseismic event orientation (azimuth and
dip).
Raleigh et al. (1976) conducted the first microseismic monitoring application of hydraulic
fracturing during what was called the Rangely experiments [49]. They conducted experiments on
controlled fluid injection to detect the induced microseismicity. They used downhole and surface
47
microseismic monitoring. The downhole monitoring used arrays of geophones in a nearby
observation wellbore and the surface monitoring used surface array sensors.
Downhole microseismic monitoring is the main direct observation method to monitor
hydraulic fracture dimensions at depth as shown in Figure 2.10.
Fig. 2.100: Microseismic downhole monitoring using downhole receiver array during hydraulic fracture [47].
Wright (1998) explained that tiltmeters identify changes in the sensor’s angular position [50].
Warpinski et al. (2006) stated that the sensor was very sensitive with a sensitivity equivalent to 0.2
inch movement over a 3,000 mile range [11]. The angular position provided a measure of the earth
deformation process [11]. The sensor only measured the tilt along one axis [11]. It was required to
have two orthogonal sensors to provide a full tilt measurements (magnitude and angle) [11].
Hydraulic fracturing produced tilt signatures that were inverted to define the dimensions of the
hydraulic fractures [11].
Surface microseismic monitoring is done by placing a large number of arrays on the surface.
For example, Hall and Kilpatrick (2009) used a surface arrays consist of 1,078 stations of 12
geophones spread out in a radial pattern around the hydraulic fracture well [51]. These geophones
48
were buried to a depth of one foot to get maximum signals to noise ratio by reducing rainfall
interference (Figure 2.11) [52].
Fig. 2.111: Surface microseismic monitoring during hydraulic fracture (red lines represented travel time and blue lines represented surface arrays) [52].
2.5 Stimulated Rock Volume
2.5.1 Stimulated Rock Volume Permeability Prediction
Oda (1986) predicted the effective permeability tensor of a naturally fractured reservoir by
using the geometry of the fracture network [53]. Here, they used the cubic law by modeling the
reservoir as a cubic block of a rock containing the natural fractures that were arranged into smaller
cubes. The effective permeability could be determined by using the total number of cubes and
fracture intersections, the fracture intersection length and aperture, the fluid viscosity, and the
distance between the two adjacent cubes.
Rahman et al. (2002) found that the SRV permeability was a function of the stimulation
pressure, the in-situ stresses, and the fracture density [10]. They developed a model to consider
both the fracture propagation and the shear slippage of natural fractures. They found that the
average permeability of the SRV increased sharply with the increase of the stimulation pressure
beyond a threshold value. The threshold pressure was a function of the in-situ stresses and the
natural fractures properties in the reservoir. They also found that the permeability enhancement
was nearly linearly dependent on the natural fracture density. And they emphasized the need to
49
characterize the fracture density as accurately as possible to obtain realistic permeability
enhancement prediction.
Ge and Ghassemi (2011) developed a procedure to determine the SRV permeability by
matching the calculated SRV dimensions with the volumes interpreted from the microseismic [54].
They developed a relationship between the net fracture pressure with the SRV permeability and
the SRV dimensions. They initially guessed a permeability value and then for the selected net
fracture pressure, they found the pore pressure and the in-situ stress distributions. They used this
pore pressure distribution with the Mohr-Coulomb failure envelope to determine the amount of
shear failure in the formation around the hydraulically induced fracture. From the failure envelope,
they constructed the extent of the shear failure around the hydraulic fracture thus defining the SRV.
They repeated the trial and error procedure to predict the SRV permeability until the SRV
dimensions matched the microseismic SRV.
Bahrami et al. (2012) derived a semi-analytical equation to model the fracture permeability as
a function of the well test permeability, the fracture aperture, and the fracture spacing [55]. A fitted
correlation was derived based on the sensitivity analysis of the well test permeability with the
fracture parameters such as the fracture permeability, aperture, spacing and compressibility.
Johri and Zoback (2013) presented a study that showed that the fracture permeability was
enhanced during the hydraulic fracturing caused by the slip of natural fractures [56].
Nassir (2013) developed a coupled reservoir-geomechanics model to determine the SRV
permeability [57]. He observed that the maximum permeability enhancement resulted at high
Interactions between hydraulic fractures and natural fractures have been studied both
experimentally and numerically since the 1960s [44]. The hydraulic fracturing experiments,
conducted by Blanton (1982), in a pre-fractured material in the laboratory under tri-axial loads
revealed that the hydraulic fractures preferred to cross the pre-existing fracture only under high
differential stresses and high angles of approach [58].
50
Warpinski and Teufel (1987) showed that the interaction of hydraulic fractures and natural
fractures was affected by the in-situ stresses contrast, the natural fracture spacing and permeability,
and the hydraulic fracture treatment pressure [7].
Shimizu et al. (2014) investigated the influence of natural fracture permeability and approach
angle on hydraulic fracturing simulation [59]. They found that when the angle was high and the
permeability was low, the hydraulic fracture ignored the existence of the natural fractures and the
hydraulic fracture propagated straight to the direction of the maximum in-situ stress.
Pirayehgar and Dusseault (2014) used a Universal Distinct Element Code (UDEC) to analyze
fluid injection through fractures in an impermeable reservoir [60]. It was observed that branching
occurred at a short distance from the injection point and the branching was usually suppressed
under a high in-situ stress ratio. It was also found that the natural fractures were reopened mostly
parallel with the maximum in-situ stress.
2.5.3 Pressure Drop and Fracture Aperture Estimation
Barenblatt et al. (1960) modeled the pressure drop in the naturally fractured reservoir
combining a high diffusivity continuum (fracture network) and a low diffusivity continuum
(porous rock matrix) [61]. A relationship between the liquid pressure in the matrix and the natural
fractures was proposed. The fluid transfer was evaluated between the natural fractures and the
matrix in the naturally fractured reservoir.
Kim and Schechter (2009) used a discrete fracture network model, image logs and core analysis
to estimate fracture aperture [62]. The results showed that the model could estimate fracture
aperture by incorporating the outcrop maps, the image logs, the computer tomographic imaging,
and the core fracture data.
Yu and Aguilera (2012) developed an analytical model to solve a 3D pressure diffusion
equation and predict SRV dimensions [36]. The hydraulic diffusivity coefficient was determined
to calibrate the model and then the SRV dimensions were predicted. The hydraulic diffusivity
coefficient could be determined from the slope of a straight line plot between the distances of the
microseismic event distance with the wellbore versus the square root of the occurrence time of the
microseismic event. Izadi and Elsworth (2014) used a combination of cubic law and Darcy’s law
51
to determine the pressure drop along the SRV [63]. This combined relationship was a function of
the fracture initial aperture, permeability, and spacing.
Estimation of fracture network characteristics such as the fracture aperture and spacing have
not been modeled adequately in the recent studies.
2.5.4 Effect of Geomechanical Properties on the SRV
Key geomechanical properties used in the analytical models (KGD and PKN) for the hydraulic
fracture are Young's modulus and the Poisson’s ratio [64]. Bratton (2011) has shown that in-situ
stresses anisotropy dictated the complexity of the fracture network where a smaller in-situ stresses
anisotropy would not exhibit a pronounced directional preference of the hydraulic fracture network
[65]. Nassir (2013) showed cohesion to be important; the effective stresses were proportional to
the cohesion of the rock [57]:
𝜎𝜎1′ = 2𝑆𝑆0𝐶𝐶𝑜𝑜𝐶𝐶𝜙𝜙1−𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙
+ 𝜎𝜎3′1+𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙1−𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙
(27)
where 𝜎𝜎1′ is the maximum effective stress, 𝜎𝜎3′ is the minimum effective stress, S0 is the cohesion
and 𝑡𝑡 is the friction angle.
Fang et al. (2015) found a relationship between important parameters such as the bulk modulus,
critical stress intensity factor, fracture aperture, spacing, and permeability [66].
2.6 Behavior of Naturally Fractured Reservoir
Bulnes and Fitting (1945) and Imbt and Ellison (1946) had differentiated the types of porosities
in rocks [67, 68]. Void systems of sandstones were typical of primary porosity. Secondary porosity
was small in openings and it was controlled by fracturing or jointing where it was not highly
interconnected. These types of porosity could be channels or vugular voids that had been
developed during weathering or burial such as limestones or dolomites. Joints or fissures were
another types of secondary porosities in shale, siltstone, limestone or dolomite and they were
usually vertical. In most cases, the two types of porosities were found together in the rock.
52
The realization of this porous medium was as a complex of discrete volumetric elements with
anisotropic primary porosities coupled with secondary porosities as shown in Figure 2.12 [69].
Fig. 2.122: Realization of heterogeneous porous medium [68].
Warren and Root (1963) were the first to propose the reservoir contained the primary
(intergranular) and the secondary (fissure or vugular) porosities. They assumed the primary
porosity region contributed significantly to the pore volume but contributes insignificantly to the
flow capacity [69]. They developed an idealized model to study the behavior of dual porosity
systems (naturally fractured reservoir) with pseudo steady fluid transfer from matrix to fracture.
This study proposed two parameters to describe the deviation of the behavior of dual porosity
medium from a homogeneous porous medium. The first parameter was ω. It was a secondary fluid
capacity measurement (storativity ratio). The second parameter was λ. It was a ratio of matrix
permeability to the fracture permeability (interporosity flow coefficient). The two parameters are
as shown below:
𝜔𝜔 = 𝜙𝜙𝑓𝑓𝐶𝐶𝑓𝑓𝜙𝜙𝑓𝑓𝐶𝐶𝑓𝑓+𝜙𝜙𝑚𝑚𝐶𝐶𝑚𝑚
(28)
𝜆𝜆 = 𝛼𝛼𝑟𝑟𝑤𝑤2𝑘𝑘𝑚𝑚𝑘𝑘𝑓𝑓
(29)
where 𝑡𝑡𝑓𝑓 and 𝑡𝑡𝑚𝑚are the fracture and matrix porosity, 𝑐𝑐𝑓𝑓 and 𝑐𝑐𝑚𝑚 are the fracture and matrix
compressibility, α is the shape factor, rw is the wellbore radius, kf and km are the fracture and matrix
permeability.
53
Stearns (1982) defined the natural fracture as a macroscopic planar discontinuity that results
from stresses that exceeded the rupture strength of the rock [70]. Nelson (1985) defined the natural
fracture as a naturally occurring macroscopic planar discontinuity in rock due to deformation and
it could have positive or negative effects on the fluid flow [71]. Aguilera (1998) explained all
reservoirs contained at least some natural fractures but if the natural fractures effect were negligible
then the reservoir could be classified as a conventional reservoir [72]. The natural fractures were
the main production factor in a wide range of unconventional reservoirs including tight gas
reservoir.
Aguilera (2003) also mentioned that it was important to know the magnitude and orientation
of in-situ stresses; spacing, aperture, permeability and porosity of the fractures; also permeability
and porosity of the matrix [73]. This information would lead to estimates of hydrocarbon in place
and distribution between the fracture and the matrix based on the flow capacity of the fracture and
the matrix. Stearns (1982), Nelson (1985), and Aguilera (1998) classified the natural fractures from
the geological point of view as tectonic (fold or fault related), regional, contractional (diagenetic)
and surface related [70, 71, 72].
An important property of naturally fractured reservoirs was the fracture compressibility.
Aguilera (2003) stated that the fracture compressibility for zero mineralization within the fracture,
should be higher than the matrix compressibility because of the unrestricted fluid flow [73]. The
differences between these values depended on the amount of the secondary mineralization within
the fractures, the fracture orientation, the in-situ stresses and the reservoir pressure condition [73].
Aguilera’s (1998) correlation for the fracture compressibility is shown in Figure 2.13 [72].
54
Fig. 2.133: Fracture compressibility as a function of net stress on fracture [72].
2.6.1 Flow Regimes for Multi-fractured Horizontal Well in a Naturally
Fractured Reservoir
Chen and Raghavan (1997) proposed the flow regimes for a multifractured horizontal well in
a rectangular drainage region for two fractures [74]. They neglected wellbore storage effects. The
first flow regime was bilinear or linear flow. Bilinear flow occurred when the fracture conductivity
was finite and the fracture length was greater than the fracture height. Linear flow within the
fracture toward the horizontal well and within the formation is shown in Figure 2.14 [75].
Fig. 2.14: Early bilinear flow within the fracture and formation [75].
Nobakht et al. (2011) proposed the second flow regime to be early linear flow. It occurred
when there was linear flow from the formation toward the fractures and the flow within the
55
fractures was negligible [76]. In multifractured horizontal well in unconventional reservoir, the
early linear flow was expected to be dominant and could last for years depended on the formation
permeability as shown in Figure 2.15.
Fig. 2.15: Early linear flow from the formation to the fracture [75].
The third flow regime was early radial flow is shown in Figure 2.16. This flow regime was
fluid flow from the fracture tip toward the horizontal wellbore. This flow regime depended on the
fracture length and spacing. It happened after the early linear flow and before the fracture
interference. It was only observed when the fracture was very short or far apart [74]. Early time
flow such as early radial flow within the fractures could occur when the horizontal wellbore length
was larger than the formation thickness within a range of LD ≤ 20. The fluid flowed radially from
all directions that were perpendicular to the horizontal wellbore [77].
𝐿𝐿𝐷𝐷=𝐿𝐿𝑤𝑤ℎ �
𝑘𝑘𝑧𝑧𝑘𝑘𝑥𝑥
(41)
where Lw is the horizontal wellbore length, h is the formation thickness, kz and kx are the
permeability in the z and x axis.
Fig. 2.16: Early radial flow from the formation to the fracture [75].
56
The fourth flow regime was the compound linear flow as shown in Figure 2.17. It occurred
once the fractures had interfered each other. The fluid flowed from the unstimulated reservoir
volume toward the stimulated reservoir volume.
Fig. 2.17: Compound linear flow from the unstimulated reservoir region to the stimulated reservoir volume [75].
The fifth flow regime was late radial flow as shown in Figure 2.18. The flow occurred around
the multifractured horizontal well boundaries. The flow pattern was similar to the late time
production of the vertically fractured well. It only occurred if the well existed all alone in an
undeveloped field and usually it required very long production time to be developed in tight
unconventional reservoirs [74, 75]. Lastly was the boundary dominated flow, it could be a pseudo
steady state flow (no flow boundaries) or steady state flow (constant pressure boundaries).
Fig. 2.18: Late radial flow around the multifractured horizontal well [75].
57
2.6.2 Flow Regions for Multi-fractured Horizontal Well in a Naturally
Fractured Reservoir
This section presents literature that discusses the flow regions that occurring in multifractured
horizontal wells. Ozkan et al. (2009) and Brown et al (2009) proposed a trilinear flow model where
the drainage volume of multifractured horizontal well was limited to the inner reservoirs between
the fractures (Figure 2.19) [78, 79]. The basis of the trilinear flow model was the production life
of the multifractured horizontal well that was dominated by the linear flow regimes. The trilinear
flow model coupled the linear flow in three adjacent flow regions. The flow regions were the outer
reservoir, the inner reservoir between fractures and the hydraulic fractures. They assumed uniform
distribution of identical hydraulic fractures along the length of the horizontal well.
Fig. 2.19: Trilinear model schematic in multi-fractured horizontal [78, 79].
To allow production from the inner reservoir region between the hydraulic fractures, the region
was assumed to have natural fractures (dual porosity model). The flow regime in the inner reservoir
region was assumed to be transient flow and the model used the transient interporosity coefficient.
The latest model was a horizontal well multi-fractured enhanced fracture region model from
Stalgorova and Mattar (2012) as shown in Figure 2.20 and Figure 2.21 [80]. The model used the
same concept from [78] but it assumed the unstimulated reservoir region beyond the fracture tip
(the shaded area) contribution was negligible and the unstimulated reservoir region (darker color
area) between the fractures contribution was taken into account. Stalgorova and Mattar (2012)
adapted the branch fracture concept from Daneshy (2003) [80] (Figure 2.22) [80]. It was explained
that the branched fracturing could be caused by wellbore orientation respect to in-situ stresses,
58
perforation pattern and natural fractures [81]. It could also be caused by low anisotropy of in-situ
stresses.
Fig. 2.20: Horizontal well multifractured enhanced fracture model schematic [80].
Fig. 2.21: Enhanced fracture region model for quarter of a fracture [80].
Fig. 2.22: (a) Biwing fracture and (b) branched fracture [81].
59
2.6.3 Rate Transient Analysis (RTA) in a Naturally Fractured Reservoir There are different methods available to analyze production data. The two distinct methods are
typecurve and non-typecurve methods. Arps (1945) was the first to develop production data
analysis methods [82]. He developed decline curves for oil and gas production during transient
flow. The traditional decline analysis had limitations: it was not able to disassociate the production
forecast from operating conditions [82]. He assumed the historical operating condition stayed
constant for future production.
Fetkovich (1980) then extended the decline curve into the typecurve concept for production
data analysis, where before the typecurve concept was only used for pressure transient analysis
[83]. It was found that late time (boundary dominated flow) data could be matched to typecurves.
Both of these traditional decline curves relied on matching the model with the production data.
The limitations was the assumption that the productions parameters would remain constant with
time.
Recent methods considered variable production parameters. These included Wattenbarger
(1998), Blasingame et al. (1991), and Agarwal et al. (1998) [84, 85, 86]. The improvement on
traditional analysis was the use of a normalized rate and a pseudotime. The normalized rate used
the pressure drop (q/Δp) that allowed the effect of pressure changes to be taken into account in the
analysis. The pseudotime was the time function for gas reservoirs that took into account
compressibility changes of gas with pressure that would allow the gas material balance to be dealt
carefully as the reservoir pressure decreased with time.
Blasingame et al. (1991) provided the typecurves for radial flow, elliptical well, fractured
vertical well, horizontal well with no fractures, finite conductivity fractures and infinite
conductivity fractures [84]. The same procedure from Wattenbarger et al. (1998) was used by
plotting the logarithm of the logarithm (log log) of the normalized rate with material balance
pseudotime with options of having rate integral and rate derivative on the y axis [84, 85]. Their
limitations were the rate integral was very sensitive with early time errors and did not distinguish
the different flow regimes.
Wattenbarger et al. (1998) typecurves were used to analyze linear flow specifically in tight
reservoirs where the linear flow could be dominant and last for years [85]. It assumed a vertical
well with fractures in the center of a rectangular reservoir where the fractures were assumed to
60
reach the reservoir boundaries. The log log plot of the normalized rate with material balance
pseudo time was used with another option of having pressure derivative on the y axis. Their
limitation was the fact that the typecurve was only applicable for the linear flow and not for the
boundary dominated flow. Agarwal et al. (1998) provided the typecurves for radial flow and a
fractured vertical well [86]. It used the same procedure from Wattenbarger et al. (1998) and
Blasingame et al. (1991) but with different transient characterization using dimensionless reservoir
boundaries parameters [86]. It was found that this typecurve was more unique than Blasingame et
al. (1991). But all these available typecurves are only applicable for vertical wells, both fractured
and un-fractured.
2.7 What is Missing in the Literature?
In the previous studies summarized in the literature review, investigations of some important
SRV parameter were missing. The missing SRV parameter studies are: (a) the SRV effective
permeability, in-situ stresses, and pressure drop during hydraulic fracturing and production at
reservoir conditions as a function of distance and time, (b) the impact of modulus properties on
SRV effective permeability, (c) the effect of fracturing operation parameters on the induced
hydraulic fractures and re-opening natural fractures aperture, numbers, and spacing, (d) the impact
of rock mechanical properties, effective stresses, and fracture fluid injection volume on SRV
dimensions during hydraulic fracturing, and (e) the application of nonlinear diffusivity equation
solution to solve flow rate, permeability, pore pressure, and porosity within SRV as a function of
distance and time during production.
61
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Pressure Drop/Variable Flow rate Systems. Paper SPE 21513 presented at the SPE Gas Technology Symposium, 23-24 January.
[85] Wattenbarger, R. A., El-Banbi, A. H., Villegas, M. E., and Maggard, J. B. 1998. Production Analysis of Linear Flow into Fractured Tight Gas Wells. Paper SPE 39931 presented at the 1998 Rocky Mountain Regional/Low Permeability Reservoirs Symposium and Exhibition, Denver, USA, 5-8 April.
[86] Agarwal, R. G., Gardner, D. C., Kleinsteiber, S. W. and Fussell, D. D. 1998. Analyzing Well Production Data Using Combined Type Curve and Decline Curve Concepts. Paper SPE 57916 presented at the 1998 SPE Annual Technical Conference and Exhibition, New Orleans, 27-30 September.
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CHAPTER 3: ESTIMATION OF FRACTURE
CHARACTERISTIC WITHIN STIMULATED ROCK
VOLUME USING FINITE ELEMENT AND SEMI-
ANALYTICAL APPROACHES
Summary Hydraulic fracturing has been proven to effectively increase the drainage area and the permeability
of unconventional oil and gas reservoirs by creating a fracture network or stimulated rock volume
(SRV) within the reservoir rock. The dimensions of the SRV and its permeability are the key
parameters that enhance the unconventional reservoirs’ performance after the hydraulic fracture
operation. Simulation of the SRV to obtain its dimensions and permeability is required to
determine the optimum hydraulic fracture treatment parameters and production. In this study, finite
element analysis is used to determine the SRV characteristics based on field data from a hydraulic
fracturing job in a horizontal well penetrating the Glauconitic formation in the Hoadley Field,
Alberta, Canada. The dimensions of the SRV are calibrated from microseismic data. The fracture
propagation pressure of the finite element model is matched to the field value by altering the
permeability of the SRV. The matched model is used to obtain the in-situ stress changes and the
pressure drop within the SRV. The SRV permeability and the pressure drop are used to calculate
the aperture, the number and the spacing of the fractures within the SRV using a semi-analytical
approach. The final outputs can be used to optimize the future hydraulic fracture design at the
Hoadley field or at other fields that have similar geomechanical properties. It could also be used
to provide estimates of changes in the in-situ stresses around a stimulated horizontal wellbore.
3.1 Introduction
With declining conventional fossil fuel production, there has been greater production from
unconventional resources such as tight gas reservoirs. With immense petroleum volume in place
and long-term production potential, tight gas has become a crucial component of the fossil fuel
energy future. These unconventional reservoirs require stimulation technologies, such as hydraulic
69
fracturing, to be commercially productive. Multistage hydraulically fractured horizontal wells are
becoming the standard method to produce unconventional gas reservoirs. Multi-fractured
horizontal well completion in a naturally fractured reservoir results in a fracture network or
stimulated rock volume (SRV) with large drainage area and high permeability created by the
interaction of the hydraulic fractures and the natural fractures. The dimensions and the
permeability of the SRV are the main factors that control the performance of the recovery process
from unconventional reservoirs. Despite its importance, the interaction between hydraulic
fractures and natural fractures have not been fully understood due to difficulties and expensive
cost of interpreting core (laboratory) and microseismic (field) data.
3.1.1 Objective of Study
Previous studies have shown that SRV permeability is affected by important parameters
including hydraulic fracture injection operating conditions, in-situ stresses, stimulated rock
volume dimensions and natural fracture characteristics.
In this study, a three-dimensional (3D) finite element analysis (FEA) is used to model the fluid
injection and pressure into the SRV in a tight gas formation. The SRV is assumed to be isotropic
linear elastic with an enhanced permeability. The simulated effective permeability from the FEA
is used as an input into a semi-analytical approach to determine the fracture network characteristics
such as fracture aperture and spacing. The semi-analytical approach makes uses of equivalent flow
characteristics and the mass conservation principle.
The objectives of this study are: (i) determination of SRV permeability during hydraulic
fracturing using 3D FEA and (ii) development of a semi-analytical approach to evaluate the
fracture characteristics within the SRV.
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3.2 Literature Review
3.2.1 Prediction of Stimulated Rock Volume Permeability
Oda (1986) predicted the effective permeability tensor of a naturally fractured reservoir using
the geometry of the fracture network [1]. Oda (1986) used cubic law to model the reservoir as a
cubic block of a rock containing the natural fractures that were arranged into smaller cubes [1].
Oda (1986) found that the effective permeability could be determined using the total number of
cubes and fracture intersections, the fracture intersection length and aperture, the fluid viscosity,
and the distance between the two adjacent cubes [1].
Rahman et al. (2002) proposed the SRV permeability as a function of the stimulation pressure,
the in-situ stresses, and the fracture density [2]. A model that considered both the fracture
propagation and the shear slippage of natural fractures was developed [2]. Rahman et al.’s (2002)
study results showed that the average permeability of the SRV increased sharply with a increase
stimulation pressure beyond a threshold value [2]. The threshold pressure was a function of the in-
situ stresses and the natural fractures properties in the reservoir [2]. Rahman et al. (2002) also
found that the permeability enhancement was nearly linearly dependent on the natural fracture
density [2].
Ge and Ghassemi (2011) developed a procedure to determine the SRV permeability by
matching the calculated SRV dimensions with the volume from microseismic monitoring [3]. Ge
and Ghassemi (2011) proposed a relationship between the net fracture pressure with the SRV
permeability and the SRV dimensions. A permeability was initially guessed, and then for the
selected net fracture pressure, the pore pressure and in-situ stress distributions were found [3]. This
pore pressure distribution was used with a Mohr-Coulomb failure envelope to determine the
amount of the shear failure in the formation around the hydraulically induced fracture [3]. From
the failure envelope, the extent of the zone of shear failure around the hydraulic fracture (thus
defining the SRV) was constructed [3]. The trial and error procedure were repeated to predict the
SRV permeability until the SRV dimensions matched the microseismic SRV [3].
Bahrami et al. (2012) proposed a semi-analytical equation to model the fracture permeability
as a function of the well test permeability, the fracture aperture, and the fracture spacing [4]. A
71
fitted correlation was derived based on the sensitivity analysis of the well test permeability with
the fracture permeability, aperture, spacing and compressibility [4].
Johri and Zoback (2013) conducted a study that showed the fracture permeability was
enhanced during the hydraulic fracturing caused by the slip of natural fractures [5].
Nassir (2013) developed a coupled reservoir-geomechanics model to determine the SRV
permeability [6]. The maximum permeability enhancement was observed to result from high
Interactions between hydraulic fractures and natural fractures have been studied both
experimentally and numerically since the 1980s. Hydraulic fracturing experiments were conducted
by Blanton (1982) using a pre-fractured material in the laboratory under tri-axial loads [7]. His
experiments results revealed that the hydraulic fractures preferred to cross the pre-existing fracture
only under high differential stresses and high angles of approach [7].
Warpinski and Teufel (1987) showed that the interaction of hydraulic fractures and natural
fractures was affected by the in-situ stress contrast, the natural fracture spacing and permeability,
and the hydraulic fractures treatment pressure [8].
Shimizu et al. (2014) investigated the influence of natural fracture permeability and approach
angle on the hydraulic fracturing simulation [9]. It was found that a high approach angle and a low
natural fracture permeability caused the hydraulic fracture to ignore the existence of the natural
fractures [9]. And the hydraulic fracture propagated straight to the direction of the maximum in-
situ stress [9].
Pirayehgar and Dusseault (2014) used the Universal Distinct Element Code (UDEC) to analyze
the fluid injection through the fractures in an impermeable reservoir [10]. Pirayehgar and
Dusseault’s (2014) results showed branching was occurring when the stress ratio was small [10].
Branching was a condition in which no explicitly favored path existed for fractures to propagate
[10]. Their simulation showed that branching occurred at a short distance from the injection point
and the branching was usually suppressed under a high in-situ stress ratio [10].
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3.2.3 Estimation of Pressure Drop and Fracture Aperture
Barenblatt et al. (1960) modeled the pressure drop in the naturally fractured reservoir by using
a high permeability fracture and a low permeability porous rock [11]. From their study, a
relationship was found between liquid pressure in the matrix and the natural fractures [11].
Another study was performed by Kim and Schecter (2009), who used a discrete fracture
network model, image logs and core analysis to estimate fracture aperture [12]. Their model results
showed that the fracture aperture could be estimated by incorporating outcrop maps, image logs,
computed tomography imaging, and core fracture data. Yu and Aguilera (2012) developed an
analytical model to solve a 3D pressure diffusion equation to predict the pressure drop within the
SRV [13]. They determined the hydraulic diffusivity coefficient to calibrate the model and then
the pressure drop within the SRV was predicted [13].
Izadi and Elsworth (2014) performed a study combining the cubic law and the Darcy’s law to
determine the pressure drop within the SRV [14]. This combined relationship was a function of
the initial fracture aperture, permeability, and spacing [14].
Estimation of fracture network characteristics such as the fracture aperture and spacing have
not been modeled adequately in recent studies.
3.2.4 Rock Geomechanical Properties Effect on Stimulated Rock Volume
Valko and Economides (2001) stated that the key geomechanical properties used in the
analytical models (KGD and PKN) for the hydraulic fracture are Young's modulus and Poisson’s
ratio [15].
Bratton (2011) showed that in-situ stress anisotropy dictated the complexity of the fracture
network where smaller in-situ stress anisotropy would not produce a pronounced directional
preference of the hydraulic fracture network [16].
Nassir (2013) showed that the cohesion was an important parameter in determining the Mohr-
Coulomb shear failure envelope; where the effective stresses were proportional to the cohesion of
the rock in the Mohr-Coulomb shear failure criterion [6]:
73
𝜎𝜎1′ = 2𝐶𝐶 𝐶𝐶𝑜𝑜𝐶𝐶𝜙𝜙1−𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙
+ 𝜎𝜎3′1+𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙1−𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙
(1)
where 𝜎𝜎1′ is the maximum effective stress, 𝜎𝜎3′ is the minimum effective stress, C is the cohesion
and 𝑡𝑡 is the friction angle.
Fang et al. (2015) found a relationship between the important parameters such as the bulk
modulus, the fracture aperture, spacing, and permeability [17].
3.3 Hoadley Field Properties
The part of the Hoadley Field in Rimbey, Alberta, Canada focused on in this study has a target
formation of tight gas hosted in a Glauconitic Formation interval located at 1892 m TVD with a
thickness of about 43 m. The stress regime in this field is a strike slip fault regime where the
maximum in-situ stress is the maximum horizontal stress with direction of 48o NE, the intermediate
in-situ stress is the vertical stress, and the minimum in-situ stress is the minimum horizontal stress.
The overlying formations are the Medicine River coal formation with a thickness of about 5 m and
the Mannville sandstone formation with a thickness of about 80 m. The underlying formation is
the Ostracod limestone formation with a thickness of about 87 m. At the initial in-situ condition,
the Glauconitic Formation average permeability is 0.07 mD (it was determined from build-up test
in the study well and nearby well core test [18]). Natural fractures were observed from the
microseismic data and inferred from the Mohr-Coulomb failure envelope with a predicted inclined
angle of 30o respect to the maximum horizontal stress. The initial formation properties are listed
in Table 3.1. The dynamic modulus properties are calculated from logs. It is assumed that the logs
represent intact rock nearby wellbore with the dynamic and the static modulus properties are
assumed to be equal. And they are expected to be higher compared to static modulus as proposed
by Jizba et al. (1990) [19]. The results of the estimated SRV dimensions from the microseismic
monitoring are listed in Table 3.2.
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Table 3.1: Initial formation properties.
Initial formation properties Values
Pore pressure gradient (kPa/m) 4.86
Pore pressure at injection depth (MPa) 9.19
Total minimum horizontal stress gradient (kPa/m) 11.66
Total minimum horizontal stress at injection depth (MPa) 22.06
Total maximum horizontal stress gradient (kPa/m) 25.79
Total maximum horizontal stress at injection depth (MPa) 48.78
Total vertical stress gradient (kPa/m) 24.09
Total vertical stress at injection depth (MPa) 45.57
Initial permeability (mD) 0.07
Dynamic Poisson ratio of Mannville Formation 0.24
Dynamic Poisson ratio of Medicine River Coal Formation 0.28
Dynamic Poisson ratio of Glauconitic Formation 0.23
Dynamic Poisson ratio of Ostracod Formation 0.20
Dynamic Young's modulus of Mannville Formation (GPa) 35.38
Dynamic Young's modulus of Medicine River Coal Formation (GPa) 5.48
Dynamic Young's modulus of Glauconitic Formation (GPa) 45.04
Dynamic Young's modulus of Ostracod Formation (GPa) 45.03
Table 3.2: SRV dimensions.
SRV Dimension Values
SRV length (m) 174
SRV width (m) 60
SRV height (m) 60
90% SRV length (m) 157
90% SRV width (m) 54
90% SRV height (m) 54
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3.4 Finite Element Analysis Model
3.4.1 Constitutive Model for Tight Sand in Finite Element Analysis
Tight sandstone is dominated by clean sandstone deposited in high-energy depositional settings
whose intergranular pores have been largely occluded by authigenic cements (mainly quartz and
calcite). Post-depositional diagenetic events reduce the effective porosity and permeability of the
rock. Masters (1979) defined low permeability gas saturated Cretaceous sandstone reservoirs of
western Alberta characteristics as: 1. low porosity (value in range 7-15%), 2. low permeability
(value in range 0.1-1 mD), and 3. moderate water saturation (value in range 34-45%) [20].
This research treats the tight sandstone as a linear elastic material and porous medium. The
constitutive equation for the material is given by:
𝜎𝜎 = 𝐷𝐷𝑒𝑒𝑒𝑒𝜀𝜀𝑒𝑒𝑒𝑒 (2)
where σ is the total stress, Del is the fourth order elasticity tensor, and εel is the total elastic strain.
The simplest form of the linear elasticity is the isotropic case, where the stress-strain relationship
is given by (Abaqus 2013) [21]:
⎩⎪⎨
⎪⎧𝜀𝜀11𝜀𝜀22𝜀𝜀33𝛾𝛾12𝛾𝛾13𝛾𝛾23⎭
⎪⎬
⎪⎫
=
⎣⎢⎢⎢⎢⎢⎢⎢⎢⎡1𝜋𝜋
−𝑣𝑣𝜋𝜋
−𝑣𝑣𝜋𝜋
0 0 0−𝑣𝑣𝜋𝜋
1𝜋𝜋
−𝑣𝑣𝜋𝜋
0 0 0
−𝑣𝑣𝜋𝜋000
−𝑣𝑣𝜋𝜋000
1𝜋𝜋
0 0 0
0 1𝐺𝐺 0 0
0 0 1𝐺𝐺
0
0 0 0 1𝐺𝐺 ⎦⎥⎥⎥⎥⎥⎥⎥⎥⎤
⎩⎪⎨
⎪⎧𝜎𝜎11𝜎𝜎22𝜎𝜎33𝜎𝜎12𝜎𝜎13𝜎𝜎23⎭
⎪⎬
⎪⎫
(3)
where E is Young’s modulus, ν is Poisson’s ratio, G is shear modulus, ε is normal strain, and γ is
shear strain. The porous medium model used here considers the reservoir rock filled with a single
fluid phase (linear linked gel fracturing fluid of WF130 with viscosity of 30 cP and specific gravity
of 1.028). It assumes that the constitutive response of the porous medium follows the linear
elasticity for the liquid and the solid together with a constitutive theory for the solid skeleton as
76
explained by (Nuth and Laloui 2008) [22]. Temperature effects are considered as small and thus
the system is considered as isothermal. Biot’s coefficient is assumed to be unity.
3.4.2 Pore Fluid Flow in Finite Element Analysis
For fluid flow in a porous medium, the governing equation is the Forchheimer’s modification
of the Darcy’s law that relates the fluid flow velocity to the pressure as follows [21]:
𝑐𝑐𝑡𝑡𝑣𝑣𝑤𝑤 + 𝛽𝛽𝑐𝑐𝑡𝑡(𝑣𝑣𝑤𝑤)2 = −𝑘𝑘� 1𝑔𝑔𝜌𝜌𝑤𝑤
�𝜕𝜕𝑢𝑢𝑤𝑤𝜕𝜕𝜕𝜕
− 𝑔𝑔𝜌𝜌𝑤𝑤𝜕𝜕𝑧𝑧𝜕𝜕𝜕𝜕� (4)
𝛽𝛽 = 2.33 1010
𝑘𝑘1.201 (5)
𝐾𝐾� = 𝜐𝜐𝑔𝑔𝑘𝑘� (6)
where sn is the fluid volume fraction, β is the Forchheimer’s coefficient, vw is the fluid velocity,
uw is the wetting liquid pore pressure, x is the position, ρw is the fluid density, g is the gravitational
acceleration, 𝑘𝑘� is the hydraulic conductivity in m/s (permeability used in the FEA), 𝐾𝐾� is the
permeability in m2, and 𝜐𝜐 is the wetting liquid kinematic viscosity.
3.4.3 Finite Element Analysis Model
The commercial finite element software package, Abaqus [9], is used to model the interaction
of fluid and solid during the fracture fluid injection. The code uses the Petrov-Galerkin finite
element method to solve the governing equations for both solid (stress equilibrium) and fluid
phases (continuity). The liquid is injected into the domain through a boundary condition at the
location of the well injection port.
Within the porous medium, the flow of liquid obeys the Forchheimer's modification of the
Darcy’s law. For the fluid flow in the porous medium, a linear tetrahedral finite element (equal
order for velocity and pressure) is used [9]. For the solid mechanics (displacement and pore
pressure), a C3D4P four-node linear tetrahedral finite element is used [9]. The governing equations
are integrated through time using backward Euler time stepping. At each time step, the set of
coupled non-linear equilibrium and continuity equations are solved using Newton's method.
77
3.4.4 Model Geometry
The model, displayed in Figure 3.1, consists of a four-layer block computational domain with
the following overall dimensions: length in x-axis 240 m and width in y-axis 240 m. The total
block thickness is 215 m which includes the lower Ostracod formation with a thickness of 87 m,
the target sandstone formation (Glauconitic) interval with a thickness of 43 m, the thin layer of
coal (Medicine River) with a thickness of 5 m, and the top sandstone formation (Mannville
formation) with a thickness of 80 m. The bottom surface of the domain is located at a depth of
2,000 m. At a depth of 1,892 m, the hydraulic injection port is modeled as an open flow boundary
condition (the wellbore is not modeled). From the microseismic observations, the SRV half-length
in x-axis direction is 87 m, the SRV half-width in y-axis direction is 30 m, and the SRV total height
in z-axis direction is 60 m [23]. The model dimensions were chosen to be three times of the SRV
length to be representative of the stress field. The mesh sizes were chosen to be bigger size for
non-SRV (16 m) and smaller size for SRV (5 m). The mesh was generated by assigning elements
numbers for each edge.
Fig. 3.1: Finite element model mesh for hydraulic fracturing (SRV) simulation.
78
The model is partitioned into seven intervals: the Glauconitic-non SRV, the Glauconitic-SRV,
the Medicine River-non SRV, the Medicine River-SRV, the Mannville-non SRV, the Mannville-
SRV and the Ostracod-non SRV. The intervals are derived from the examination of the
microseismic SRV dimensions. The model assumes that the SRV is a relatively high permeability
volume during the fluid injection. Each layer of the model has its own density, Young's modulus,
Poisson's ratio, permeability, void ratio and specific weight of the host fluid. The Young’s modulus
and Poisson’s ratio were derived from logs.
Because of the inherent symmetry of the geometrical model about the x=0 and y=0 planes,
only one quarter of the geometrical model is meshed and analyzed. The meshed model is
discretized into 9,676 tetrahedral finite elements and the meshed model consists of two distinct
sections: (i) the bulk section representing the four formations (with mesh size equal to 16 m in
length, height and width) and (ii) the finer section covering the expected SRV including the
hydraulic fracture injection port (with mesh size 5 m in length, height and width).
3.4.5 Initial and Boundary Conditions
To specify the initial condition (in equilibrium state), the parameters that need to be defined
are: (a) the effective stresses with the maximum in-situ stress being the maximum horizontal stress
which is parallel to the direction of hydraulic fracture, (b) the pore pressure, and (c) the void ratio.
The initial properties of the formation are listed in Table 3.1.
To achieve the initial static equilibrium, the loads on the domain are: (a) the gravity load is
applied on the whole model with applied acceleration 9.8 m/s2 in the negative z-direction and (b)
the overburden stress applied to the top surface is equal to 43 MPa (assumed uniform across the
top of the model domain).
In the second step, a single hydraulic fracture stage is simulated. The hydraulic fracture
operation is divided into three steps with total duration of 37.5 minutes (2,250 s). The durations of
the three steps are 1, 10, and 2,239 s. The first two steps are divided into 10 equal sub-steps and
the last step has time steps equal to 5 s. The reason for choosing smaller time increments in the
early stages is to capture the consolidation that occurs following the load application. In the second
step there is an additional load applied which is the injection velocity based on 5 m3/min injection
79
flow rate. There is also a pore pressure boundary condition on the four outer surfaces that is equal
to the initial pore pressure.
In total, an average of 90 minutes of (wall-clock) time is required to simulate the model on a
4-core, 2.2 GHz machine with 16 GB of memory.
3.5 Results and Discussion
3.5.1 Determination of Effective Permeability
To determine the effective permeability of the SRV, a search was conducted by varying the
values of the permeability until the average simulated fracture propagation pressure matched the
field data.
The value of the pressure to be matched, from the field average fracture propagation pressure
data, is equal to 27.62 MPa as shown in Figure 3.2. This analysis does not model the deformation
and the fracture breakdown pressure. Therefore the model is only matching the average fracture
propagation pressure at the final injection time. From the search, the effective permeability that
yields the best match to the field data is found to be equal to 23.4 D (permeability is assumed to
be isotropic) for 100% SRV dimensions (Case 1).
80
Fig. 3.2: Bottom-hole injection pressure (field) data and predicted results from FEA.
To find the effect of the SRV dimensions change on the effective permeability and to deal with
the microseismic uncertainties, simulations are done for Case 2 (90% of base SRV dimensions).
For Case 2, each SRV dimension is reduced by 10% resulting in a reduction of the SRV volume
by 33%. The matched effective permeability for Case 2 is equal to 45.8 D.
Figure 3.2 also shows that Case 2 has a higher bottom-hole injection pressure gradient (6.6
kPa/s) between early and late time (from 0 second to 2,002 s) compared to Case 1 (4.9 kPa/s).
However, Case 1 and Case 2 have similar bottom-hole injection pressure gradients at late time
(from 2,002 s until the final injection time). Case 3 is simulated by reducing the grid dimensions
to 63% of Case 1. It yields 0.17 % change in the results of the final pore pressure as shown in
Figure 3.2 (0.7% change in the deformation and 0.1% change in the stresses, they are not shown
in Figure 3.2). Figure 3.3 shows the pore pressure distribution within and around the SRV versus
time for Case 1. Figure 3.3a is the pre-calculation pore pressure distribution (initial condition) and
Figure 3.3b is the initial pore pressure distribution after the in-situ stresses are applied on the
domain. Figures 3.3c, 3.3d, and 3.3e display the pore pressure distributions after 1, 551, and 1,101
s of the fluid injection. After 1,101 s of fluid injection, the pore pressure has almost reached the
target pressure. Finally, Figure 3.3f shows the maximum pore pressure after 2,250 s at the injection
7
14
21
28
35
42
0 500 1000 1500 2000 2500
BHP
(MPa
)
Time (s)
Bottom Hole Pressure
BHP Field Data BHP FEA for Case 1BHP FEA for Case 2 BHP FEA for Case 3
81
port and nearby the injection port is 27.62 MPa and the pore pressure on the SRV boundary is
equal to about 20.1 MPa (the pressure drop along the SRV is 7.52 MPa).
Fig. 3.3: Pore pressure (Pa) in different steps: (a) initial condition, (b) after in-situ stresses and boundary conditions are loaded on the domain step, (c) pump step-1 second, (d) pump step-551 s, (e) pump step-1,101 s, and (f) end of injection-2,250 s for Case 1 with k=23.4 D (deformation scale factor of 3,505.7 with final displacement of 6.853e-3 m).
Figure 3.4 shows that a uniform target bottom-hole pressure distribution within the SRV is
achieved faster in Case 2 compared to Case 1 as shown in the Figure 3.3f and Figure 3.4f.
82
Fig. 3.4: Pore pressure (Pa) in different steps: (a) initial condition, (b) after in-situ stresses and boundary conditions are loaded on the domain step, (c) pump step-1 second, (d) pump step-551 s, (e) pump step-1,101 s, and (f) end of injection-2,250 s for Case 2 with k=45.85 D (deformation scale factor of 3,016.07 with final displacement of 7,957e-3 m).
3.5.2 Parametric Studies of Young’s Modulus
Parametric studies were conducted with the reduction of the base Young’s modulus of the
Glauconitic, the Medicine River and the Mannville formations that form the SRV in the finite
element model and are in contact with the hydraulic fracture fluid. The Young's modulus of the
SRV in the finite element model was reduced from the base values to 90, 80, and 70% of the base
values. The results of the sensitivity runs for Case 1 show that the final injection pressures are
27.01, 26.39, and 25.76 MPa when the Young's modulus of the SRV are reduced to 90, 80, and
70%, respectively (Figure 3.5a). For Case 2 (Figure 3.5b), show that the final injection pressures
are 26.78, 25.97, and 25.14 MPa when the Young’s modulus of the SRV are reduced to 90, 80,
and 70%, respectively.
83
(a)
(b)
Fig. 3.5: Effect of Young’s modulus on bottom-hole pressure for (a) Case 1 and (b) Case 2.
Additional parametric study was also done to find the matched effective permeability with the
reduced values of the Young's modulus that led to an injection pressure of 27.62 MPa. The results
for Case 1 are as follows:
1. 70% of initial Young's modulus gives a matched effective permeability of 18.4 D,
2. 80% of initial Young's modulus gives a matched effective permeability of 20 D, and
3. 90% of initial Young's modulus gives a matched effective permeability of 21.5 D.
51015202530
0 500 1000 1500 2000 2500
Pore
Pre
ssur
e (M
Pa)
Time (s)
Young's modulus Effect on Pore Pressure - Case 1 (k=23.4 D)
Base E 90%E 80%E 70%E
51015202530
0 500 1000 1500 2000 2500
Pore
Pre
ssur
e (M
Pa)
Time (s)
Young's modulus Effect on Pore Pressure - Case 2 (k=45.85 D)
Base E 90%E 80%E 70%E
84
The parametric studies done on Case 2 yield the following results:
4. 70% of initial Young's modulus gives a matched effective permeability of 27 D,
5. 80% of initial Young's modulus gives a matched effective permeability of 35.8 D, and
6. 90% of initial Young's modulus gives a matched effective permeability of 39.78 D.
From the parametric studies, the results show that the reduction of the Young's modulus lowers
the effective permeability of the SRV. Also, reduction in the Young’s modulus is not linearly
related with the reduction of the effective permeability. This permeability dependence with
Young’s modulus occurs due to the inverse relationship between Young’s modulus and fracture
aperture. Reduction in the SRV dimensions leads to a higher increase of the effective permeability
in a lower Young’s modulus.
3.5.3 Pore Pressure and In-Situ Stresses from Finite Element Analysis
The pore pressure and the total maximum horizontal stresses are plotted versus distance (in the
SRV length direction) for Case 1 at the base Young's modulus in Figure 3.6. The results reveal
that the maximum pressure decrease happens at a distance of about 10 m from the injection port
and the pressure drop from the 10 m distance to the SRV boundary is small.
85
(a)
(b)
Fig. 3.6: (a) Pore pressure and (b) total maximum horizontal stress as a function of distance along SRV length at various injection times for Case 1 with k=23.4D (assuming Biot’s constant=1).
The maximum horizontal stress increase is within a distance of 10 m from the injection port.
This stress increases due to the poro-elastic effect and the fluid injection. The causes of increase
in the total in-situ stresses are explained by Vermylen (2011) [24]. Vermylen (2011) stated that
there were three general causes of the stress changes in the reservoir due to the hydraulic fracture:
(a) creation of tensile fractures of induced hydraulic fracture, (b) poroelastic effects when the fluid
0
10
20
30
0 10 20 30 40 50 60 70 80 90Pore
Pre
ssur
e (M
Pa)
Distance from injection (m)
Pore Pressure along SRV Length for Case 1 (k=23.4D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
-65
-60
-55
-50
-450 10 20 30 40 50 60 70 80 90
Tota
l SH
(MPa
)
Distance from injection (m)
Total SH along SRV Length for Case 1 (k=23.4D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
86
leaked off from the hydraulic fracture and increased the pore pressure in the reservoir, and (c)
propagation of hydraulic fractures [24]. Afterward the stress would relieve and cause stress
relaxation [24]. This combination of actions would change the in-situ stresses [24]. The total
minimum horizontal stress and the total vertical stress also produce responses similar to the
maximum horizontal stress as shown in Figure 3.7 and Figure 3.8, respectively.
The total maximum stresses drop is small from a distance of about 10 m to the SRV boundary
as shown in Figure 3.6. The total maximum horizontal stress after the hydraulic fracture increases
to between 49 MPa and 61 MPa (in-situ total maximum horizontal stress is 49 MPa) near the
injection port. Then, there are no changes between the distances of 10 m from the injection port to
the SRV boundary over the time period of 1 second. However, at late injection (551, 1,101 and
2,250 s), there are smaller total maximum horizontal stress increases to between 50 MPa and 56.5
MPa between distance of 10 m to the SRV boundary. The changes in the total in-situ stresses
calculated by Abaqus might be overestimated because in this study, the Biot’s constant is assumed
to be unity. This assumption yields that a change in the pore pressure generates an equal and
opposite change in the total in-situ stresses, according to the principle of effective stress. For Biot’s
constant of less than unity which is valid for the Glauconitic formation, the changes in the total in-
situ stresses induced by the pore pressure would be reduced.
87
(a)
(b)
Fig. 3.7: (a) Pore pressure and (b) total minimum horizontal stress as a function of distance along SRV width at various injection times for Case 1 with k=23.4D (assuming Biot’s constant=1).
05
1015202530
0 5 10 15 20 25 30 35Pore
Pre
ssur
e (M
Pa)
Distance from injection (m)
Pore Pressure along SRV Width for Case 1 (k=23.4D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
-35
-30
-25
-200 5 10 15 20 25 30 35
Tota
l Sh
(MPa
)
Distance from injection (m)
Total Sh along SRV Width for Case 1 (k=23.4D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
88
(a)
(b)
Fig. 3.8: (a) Pore pressure and (b) total vertical stress as a function of distance along SRV height above injection ports at various injection times for Case 1 with k=23.4D (assuming Biot’s constant=1).
The pore pressure and the total in-situ stresses for Case 2 as shown in Figure 3.9, Figure 3.10
and Figure 3.11) produce responses similar to those in Case 1. The only differences between Case
1 and Case 2 results are Case 1 produces the pore pressure of 20.1 MPa at the SRV boundary with
the pressure drop along the SRV length of 7.52 MPa where Case 2 produces higher pore pressure
on the SRV boundary of 23.84 MPa and lower pressure drop along the SRV length of 3.84 MPa.
05
1015202530
0 5 10 15 20 25 30 35 40Pore
Pre
ssur
e (M
Pa)
Distance from injection (m)
Pore Pressure along SRV Top Height for Case 1 (k=23.4D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
-60
-55
-50
-45
-400 5 10 15 20 25 30 35 40
Tota
l SV
(MPa
)
Distance from injection (m)
Total SV along SRV Top Height for Case 1 (k=23.4D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
89
The other differences are Case 2 results at the final injection time (2,250 s) showing similar stresses
gradient with Case 1 at shorter distance and higher gradient at longer distance from the injection
port. The final horizontal stresses at the SRV boundaries during final injection time for Case 2 are
higher compared to Case 1.
(a)
(b)
Fig. 3.9: (a) Pore pressure and (b) total maximum horizontal stress as a function of distance along SRV length at various injection times for Case 2 with k=45.85D (assuming Biot’s constant=1).
05
1015202530
0 10 20 30 40 50 60 70 80 90Pore
Pre
ssur
e (M
Pa)
Distance from injection (m)
Pore Pressure along SRV Length for Case 2 (k=45.85D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
-65
-60
-55
-50
-450 10 20 30 40 50 60 70 80 90
Tota
l SH
(MPa
)
Distance from injection (m)
Total SH along SRV Length for Case 2 (k=45.85D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
90
(a)
(b)
Fig. 3.10: (a) Pore pressure and (b) total minimum horizontal stress as a function of distance along SRV width at various injection times for Case 2 with k=45.85D (assuming Biot’s constant=1).
05
1015202530
0 5 10 15 20 25 30Pore
Pre
ssur
e (M
Pa)
Distance from injection (m)
Pore Pressure along SRV Width for Case 2 (k=45.85D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
-30
-25
-200 5 10 15 20 25 30
Tota
l Sh
(MPa
)
Distance from injection (m)
Total Sh along SRV Width for Case 2 (k=45.85D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
91
(a)
(b)
Fig. 3.11: (a) Pore pressure and (b) total minimum horizontal stress as a function of distance along SRV height above injection ports at various injection times for Case 2 with k=45.85D (assuming Biot’s constant=1).
05
1015202530
0 5 10 15 20 25 30 35Pore
Pre
ssur
e (M
Pa)
Distance from injection (m)
Pore Pressure along SRV Height for Case 2 (k=45.85D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
-60-55-50-45-40
0 5 10 15 20 25 30 35
Tota
l SV
(MPa
)
Distance from injection (m)
Total SV along SRV Height for Case 2 (k=45.85D)
(t=1s) (t=551s) (t=1101s) (t=2250s)
92
3.5.4 Determination of Fracture Aperture Using Cubic Law
The pore pressure gradient along a fracture is calculated analytically using the cubic equation
as a function of fracture aperture and half-length [25].
𝑄𝑄 = −𝐿𝐿 𝑑𝑑3
12𝜇𝜇𝑑𝑑𝑃𝑃𝑑𝑑𝜕𝜕
(7)
where Q is flow rate, L is fracture width in direction normal to fluid flow, d is fracture aperture, µ
is fluid viscosity, P is fluid pressure, and x is distance.
The SRV half-length and the fracture aperture are varied as shown in Figure 3.12a for Case 1
and Figure 3.12b for Case 2. For Case 1 (Figure 3.12a), the fracture aperture is varied from 1.43
mm to 7 mm with the maximum SRV half-length of 87 m. The fracture aperture of 1.43 mm
matches the finite element pore pressure of 20.1 MPa at the SRV boundary. Figure 3.12b also
shows that fracture aperture is varied from 1.78 mm to 7 mm with the maximum SRV half-length
of 78 m for Case 2. The fracture aperture of 1.78 mm matches the finite element pore pressure of
23.84 MPa at the SRV boundary.
93
(a)
(b)
Fig. 3.12: Pore pressure as a function of distance using the cubic law equation for (a) Case 1 and (b) Case 2.
The differences between the pore pressure modeling of cubic law model and finite element are
that the cubic law model assumes a steady state flow whereas the finite element modeling assumes
transient flow and the cubic equation does not take geomechanics effect into account.
2022242628
0 10 20 30 40 50 60 70 80 90Pore
Pre
ssur
e (M
Pa)
Distance from injection (m)
Pore Pressure along SRV Length -Cubic Law for Case 1
3.5.5 Determination of Fracture Characteristics Using Semi-Analytical
Approach
In this section, a semi-analytical approach is developed to calculate the fracture characteristics.
The semi-analytical approach neglects leak-off. The fracture network within the SRV is assumed
to consist of the major and the minor fractures (the minor fractures are assumed to be the natural
fractures). The hydraulic fractures (major fractures) grow in the SRV length direction (x-axis) and
the natural fractures (minor fractures) are assumed to have an inclined angle of 30o respect to the
maximum horizontal stress (Figure 3.13). The major fractures contribute to the SRV enhanced
permeability (since major fractures connect SRV boundaries) and the injected volume where the
minor fractures are assumed only to contribute to the injected volume because the minor fractures
are assumed to be dead-end (do not connect SRV boundaries). The approach assumes that the
major fractures created by the hydraulic fractures intercept the natural fractures and they propagate
along the natural fractures and create another major fractures inside the SRV. Therefore the
hydraulic fractures and the natural fractures are assumed to be connected and contribute to injected
fracture fluid volume.
Fig. 3.13: Top view of the minor fractures (natural fractures) are assumed to be inclined 30o with the major fractures (hydraulic fractures) (not to scale).
95
The numbers of the major and minor fractures, aperture and spacing are calculated based on
two criteria (i) equivalent flow characteristics and (ii) mass conservation:
5. Calculate total minor fracture length = 𝑇𝑇𝑐𝑐𝑡𝑡𝑡𝑡𝑣𝑣 𝑓𝑓𝑟𝑟𝑡𝑡𝑐𝑐𝑡𝑡𝑢𝑢𝑟𝑟𝐼𝐼 𝑣𝑣𝐼𝐼𝑡𝑡𝑔𝑔𝑡𝑡ℎ 𝑆𝑆𝑆𝑆𝑆𝑆 � 𝑉𝑉𝑖𝑖𝑤𝑤𝐻𝐻� −
𝑚𝑚𝑡𝑡𝐼𝐼𝑐𝑐𝑟𝑟 𝑓𝑓𝑟𝑟𝑡𝑡𝑐𝑐𝑡𝑡𝑢𝑢𝑟𝑟𝐼𝐼 𝑣𝑣𝐼𝐼𝑡𝑡𝑔𝑔𝑡𝑡ℎ, where Vi is injected volume, w is fracture aperture, H is fracture height
96
Case 1 produces a fracture aperture of 1.43 mm, a major fracture number of 5 with a spacing
of 13.1 m, and a minor fracture number of 12 with a spacing of 14.9 m. Case 2 produces a fracture
aperture of 1.78 mm, a major fracture number of 4 with a spacing of 13.1 m, and a minor fracture
number of 12 with a spacing of 12.9 m.
Figure 3.15a shows that for Case 1 with increasing a fracture aperture from 1 to 2.1 mm, the
number of major fractures and the pressure drop along the SRV length decrease where the number
of minor fracture increases until the fracture aperture is 1.43 mm and then the minor fracture
number decreases. This phenomenon is related to the major and minor fracture volumes because
the total injected volume is needed to match the total fracture volume from the major and the minor
fractures.
Figure 3.15b also shows that for Case 2 with increasing the fracture aperture from 1.1 to 2.25
mm, the number of major fractures and the pressure drop along the SRV length decrease where
the number of minor fractures increases until the fracture aperture is 2.1 mm and then the minor
fracture number decreases. The differences between Case 1 and Case 2 are for a fracture aperture
of 1.1 mm Case 1 yields 10 major fractures and Case 2 yields 18 major fractures.
97
(a)
(b)
Fig. 3.15: Relationship any number of fractures, fracture aperture and fracture pressure gradient for (a) Case 1 and (b) Case 2.
From Table 3.3, it can be seen that for constant fracture aperture and reducing the effective
permeability decreases the number of the major fractures and increases the number of minor
fractures. Case 2 produces responses similar to those in Case 1 with the constant fracture aperture.
050100150200250300
0
5
10
15
1 1.25 1.5 1.75 2 2.25
dP/d
x (k
Pa/m
)
Num
ber o
f Fra
ctur
es
Fracture Aperture (mm)
Number of Fractures for Case 1 (k=23.4D)
Number of Major Fracture Number of Minor Fracture
dP/dx
050100150200250
05
101520
1 1.25 1.5 1.75 2 2.25 2.5dP
/dx
(kPa
/m)
Num
ber o
f Fra
ctur
es
Fracture Aperture (mm)
Number of Fractures for Case 2 (k=45.85D)
Number of Major Fracture Number of Minor FracturedP/dx
98
Table 3.3: Parametric study results – effect of Young’s modulus and SRV on numbers of major and minor fractures.
Fracture aperture (mm)
Young’s modulus SRV
Permeability (D)
Number of Major Fracture
Number of Minor Fracture
1.43 100% Case 1 23.4 5 12
1.43 90% Case 1 21.5 4 12
1.43 80% Case 1 20 4 13
1.43 70% Case 1 18.4 4 13
Fracture width (mm)
Young's modulus SRV
Permeability (D)
Number of Major Fracture
Number of Minor Fracture
1.78 100% Case 2 45.85 4 12
1.78 90% Case 2 39.78 4 13
1.78 80% Case 2 35.8 3 13
1.78 70% Case 2 27 2 15
3.6 Conclusions
This study provides insights on fracture characteristics within a SRV created the hydraulic
fractures using finite element analysis and a semi analytical approach. The fracture characteristics
are the enhanced permeability, the pressure drop, and the in-situ stresses change created by the
hydraulic fractures within the SRV. The major and minor fracture aperture, numbers and spacing
are calculated using the semi-analytical approach with the inputs of the injected fracture fluid
volume and the simulated enhanced permeability. Case 1 produces the matched effective
permeability of 23.4 D, the fracture aperture of 1.43 mm, the major fracture number of 5 with the
spacing of 13.1 m, and the minor fracture number of 12 with the spacing of 14.9 m. Case 2 produces
the matched effective permeability of 45.89 D, the fracture aperture of 1.78 mm, the major fracture
number of 4 with the spacing of 13.1 m, and the minor fracture number of 12 with the spacing of
12.9 m. These parameters can be used to optimize the hydraulic fracture design (placement and
amount of injection) in the Glauconitic Formation at Hoadley field or at other fields that have
similar geomechanical properties. The results can be used to predict the reservoir production after
99
the hydraulic fracture and provides how the in-situ stresses change around the stimulated
horizontal wellbore.
The developed workflow in this study using the finite element analysis and the semi-analytical
approach to characterize the fracture network within the SRV is novel. The conclusions of the
study are as follows:
1. Reduction of the Young’s modulus decreases the effective permeability.
2. Reduction of the SRV dimensions by 10% increases the effective permeability within the
SRV and decrease the pressure drop along the SRV length.
3. The hydraulic fracture induces an increase in the total in-situ stress values. The changes in
the total in-situ stresses calculated by Abaqus are likely overestimated.
4. Reduction of the SRV dimensions increases fractures aperture and number of major
fractures and decreases the number of minor fractures to produce the same pressure drop
along the SRV length.
5. Reduction of the Young’s modulus decreases the number of major fractures and increases
the number of minor fractures for constant fracture aperture.
100
3.7 References
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[2] Rahman, M. K., Hossain, M. M., and Rahman, S. S. 2002. A Shear-Dilation Based Model for Evaluation of Hydraulically Stimulated Naturally Fractured Reservoirs. Int J Numer and Anal Meth Geomech 26 (5):469-497. http://dx.doi.org/10.1002/nag.208
[3] Ge, J. and Ghassemi, A. 2011. Permeability Enhancement in Shale Gas Reservoirs after Stimulation by Hydraulic Fracturing. Presented at the 45th US Rock Mechanics/Geomechanics Symposium, San Francisco, CA, 26-29 June. ARMA 11-514.
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[6] Nassir, M. 2013. Geomechanical Coupled Modeling of Shear Fracturing in Non-Conventional Reservoirs. Ph. D. Thesis, University of Calgary, Calgary, Alberta (January 2013).
[7] Blanton, T. L. 1982. An Experimental Study of Interaction between Hydraulically Induced and Pre-existing Fractures. Presented at the SPE/DOE Unconventional Gas Recovery Symposium of the Society of Petroleum Engineers, Pittsburgh, PA, 16-18 May. SPE/DOE-10847.
[8] Warpinski, N. R. and Teufel, L. W. 1987. Influence of Geologic Discontinuities on Hydraulic Fracture Propagation. J Pet Technol 39 (02).
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Fracturing in Pre-Fractured Rock. Presented at the 48th US Rock Mechanics/Geomechanics Symposium, Minneapolis, 1-4 June. ARMA 14-7365.
[10] Pirayehgar, A. and Dusseault, M. B. 2014. The Stress Ratio Effect on Hydraulic Fracturing in The Presence of Natural Fractures. Presented at the 48th US Rock Mechanics/Geomechanics Symposium, Minneapolis, 1-4 June. ARMA 14-7138.
[11] Barenblatt, G. I., Zheltov, I. P., and Kochina, I. N. 1960. Basic Concepts in the Theory of Seepage of Homogeneous Liquids in Fissured Rocks (Strata). J Appl Math Mech 24 (5): 1286-1303.
http://dx.doi.org/10.1016/0021-8928(60)90107-6 [12] Kim, T. H. and Schechter, D. S. 2009. Estimation of Fracture Porosity of Naturally fractured
Reservoirs with No Matrix Porosity Using Fractal Discrete Fracture Networks. Presented at the 2007 SPE Annual Technical Conference and Exhibition, Anaheim, California, 11-14 November. SPE-110720.
[13] Yu, G. and Aguilera, R. 2012. 3D Analytical Modeling of Hydraulic Fracturing Stimulated rock volume. Presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Mexico City, Mexico, 16-18 April. SPE-153486.
[14] Izadi, G. and Elsworth, D. 2014. Reservoir stimulation and induced seismicity: Roles of fluid pressure and thermal transients on reactivated fractured networks. Geothermic 51: 368-379.
http://dx.doi.org/10.1016/j.geothermics.2014.01.014 [15] Valko, P. and Economides, M. J. 2001. Hydraulic Fracture Mechanics. West Sussex: John
Wiley and Sons. [16] Bratton, T. 2011. Hydraulic Fracture Complexity and Containment in Unconventional
Reservoirs. Oral presentation given at the ARMA Workshop on Rock Mechanics/Geomechanics, San Francisco, 23 June.
[17] Fang, Y., Elsworth, D., and Cladouhos, T. T. 2015, Estimating In-Situ Permeability of Stimulated EGS Reservoirs using MEQ Moment Magnitude: an Analysis of Newberry MEQ Data. Presented at the Fortieth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, 26-28 January.
[18] Core Laboratoies – Canada Ltd. 1985. Core Analysis of Amoco Canada Petroleum Company Ltd – Amoco et al WROSES 11-20-43-2W5 Glauconitic Formation in Westerose South Alberta. 16 October
[19] Jizba, D., Mavko, G., and Nur, M. 1990. Static and Dynamic Moduli of Tight Gas Sandstones. Paper was presented at SEG Conference, San Francisco, California, 23-27 September.
[20] Masters, J.A. 1970. Deep Basin gas trap, Western Canada. AAPG Bulletin 63 (2): 152-181. [21] Abaqus Release Notes 6.13, 2013, Dassault Systemes. [22] Nuth, M. and Laloui, L. 2007. Effective Stress Concept in Unsaturated Soils: Clarification
and Validation of a Unified Framework. Int J Numer Anal Meth Geomech 32 (7):771-801. http://dx.doi.org/10.1002/nag.645
[23] Maulianda, B.T., Hareland, G., and Chen, S. 2014. Geomechanical Consideration in Stimulated rock volume Dimension Models Prediction during Multi-Stage Hydraulic Fractures in Horizontal Wells – Glauconite Tight Formation in Hoadley Field. Presented at the 48th US Rock Mechanics/Geomechanics Symposium, Minneapolis, Minnesota, 1-4 June. ARMA 14-7449.
[24] Vermylen, J.P. 2011. Geomechanical Studies of the Barnett Shale, Texas, USA. Ph. D. Thesis. Stanford University, Stanford, California (May 2011).
[25] Brown, S.R. 1987. Fluid Flow through Rock Joints: The Effect of Surface Roughness. J of Geophys Res 92 (82):1337-1347. http://dx.doi.org/10.1029/JB092iB02p01337
Fig. 4.3: Depth distribution of microseismic events from two horizontal wellbores hydraulic fracture [39].
115
Fig. 4.4: Executive summary of the two treatment wellbores, observation wellbore, producing wellbore and observed microseismic events during 12 stages of hydraulic fracture [39].
The determination of the Hoadley field stress regime is based on the world stress map. Most
of the North Western part of the North America are under compression which causes high
horizontal stress. Therefore, the greatest stress in Figure 4.1 is generally perpendicular to the front
ranges in a SW-NE direction and it is often the maximum horizontal stress. In Alberta the least
principal stress is often horizontal [40, 41]. Therefore, the Hoadley field is assumed to be in a
strike slip fault regime with the greatest stress being the maximum horizontal stress and the least
stress being the minimum horizontal stress.
The regional stress map shows that the maximum stress direction is 45°NE (± 3°) (Figure 4.1a).
This direction is parallel to the direction of the observed hydraulic fracture (48°NE with ± 3°)
based on the microseismic events. This indicates that the direction of fracture growth is mainly
controlled by the maximum horizontal stress direction.
116
The data used in this study are as follows: formation properties, open hole logs, hydraulic
fracture injection report, interpreted microseismic events locations, horizontal well trajectory, and
interpreted fracture dimensions via microseismic from 6 hydraulic fracture stages. Figure 4.5
shows the bottomhole pressures (BHP) from the hydraulic fracture injection report [39].
Fig. 4.5: Bottomhole injection pressure for horizontal wellbore A during 12 stages of hydraulic fracture [39].
Each hydraulic fracture injection stage comprised pad, slurry, spacer and flush injection stages.
The pad stage consisted of linked gel (WF130) and gas (N2), the slurry stage consisted of linked
gel (WF130) and gas (N2) with proppants (Jordan unimen of 20/40 mesh with median particle
diameter of 0.662 mm and Jordan unimen of 100 mesh with median particle diameter of 0.19 mm),
the spacer stage consisted of linked gel (WF130) and gas (N2), and the flush stage consisted of
slick water. These fluid properties are listed on Table 4.1. The total average slurry injection volume
effective stresses. The Poisson’s ratio and the Young’s modulus are calculated by using the
compressional and the shear wave velocities from logs. The Young’s modulus and the Poisson’s
ratio are required to calculate the plane strain modulus. The plane strain modulus is an input for
the tensile failure SRV dimensions model.
𝐸𝐸′ = 𝜋𝜋1−𝑣𝑣2
(20)
Where E’ is plane strain modulus, E is Young’s modulus, and v is Poisson’s ratio. The naturally
fractured reservoir cohesion and internal friction angle are needed to calculate the shear failure
SRV dimensions. The naturally fractured reservoir cohesion is determined from the intercept of
Mohr-Coulomb failure envelope when the Mohr circle touches the envelope.
The pore pressure at shear failure is predicted from Chapter 3 because there is no field data
available. In this chapter, the field BHP data is used to determine:
1. Tensile failure pressure (fracture breakdown pressure) and duration.
2. Shear failure duration is from 5.5 minutes after hydraulic fracture starts (starts of hydraulic
fracture propagation) until the end of injection.
The shear failure pressure of 12.12 MPa is estimated at 5.5 minutes after hydraulic fracture
starts and distance of 6.55 m (estimated half natural fracture distance) from Chapter 3 as shown in
Figure 4.6a. The horizontal wellbore is assumed to be in the middle of two natural fractures.
The internal friction angle is calculated using the natural fracture angle equation (it is explained
in the next section). The Mohr circle is built using the maximum and minimum effective stresses
and the Mohr circle radius.
The minimum horizontal stress gradient was determined for Glauconitic Formation with a
value of 11.66 kPa/m (0.52 psi/ft) from the instantaneous shut-in pressure [39]. This value was
similar to values from nearby wells [42]. The overburden stress gradient of 24.09 kPa/m (1.07
psi/ft) was estimated using the density log from the formation depth of 1,900 m until 1m923.5 m.
The maximum horizontal stress gradient of 25.79 kPa/m (1.14 psi/ft) was determined by using a
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commercial geomechanics software analysis package (STABView). The inputs were the
minimum and maximum horizontal and the overburden stress gradients, the initial formation pore
pressure gradient, and the horizontal wellbore radius. The simulation output was the wellbore
breakout (from caliper logs) at the nearby vertical wellbore. The maximum horizontal stress was
determined by simulating the inputs that produced the wellbore breakout matched the nearby
vertical wellbore breakout. The initial pore pressure gradient of 4.86 kPa/m (0.21 psi/ft) was
determined from the pressure build up test in horizontal Well 1 [39].
The microseismic events showed that the natural fracture plane was at 30° inclined (θ) with
respect to the maximum horizontal stress. This observation led to the calculation of normal stress
at natural fracture plane inclination with respect to maximum horizontal stress of 60° (β):
𝛽𝛽 = 90𝑜𝑜 − 𝜃𝜃 (20)
The internal friction angle of the naturally fractured reservoir rock was assumed to be equal
with the intact rock internal friction angle (ϕ). The internal friction angle of 30° was calculated by
using Equation (7). This study assumed the natural fracture was reopened by the shear failure
induced by the hydraulic fracture.
The sonic travel time of 263.12 μs/m (80.2 μs/ft) was used to determine the intact rock
unconfined compressive strength (UCS) of 40 MPa using empirical relationship from Hareland
and Nygaard (2007) [44]. The internal friction angle and the UCS were used to calculate the intact
rock cohesion (C) of 11.54 MPa using the equation from (Goodarzi and Settari 2009) [45]:
𝐶𝐶 = 𝑈𝑈𝐶𝐶𝑆𝑆(1−𝐶𝐶𝑖𝑖𝑛𝑛𝜙𝜙)2𝐶𝐶𝑜𝑜𝐶𝐶𝜙𝜙
(21)
The calculated intact rock cohesion was too high for the Mohr circle to touch the Mohr-Coulomb
failure envelope and create shear failures. The natural fractures caused a lower rock cohesion.
Hoek (1983) explained that the natural fracture lowered the formation shear strength and the
formation strength was defined by the naturally fractured reservoir internal friction angle and
cohesion [46]. The lowest strength occurred when the natural fracture was at a certain inclination
with respect to the maximum stress. To support this, Hoek (1983) provided a set of triaxial tests
results for fractured sandstone with the lowest strength occurred when the natural fracture plane
was at 30° inclined with respect to the maximum horizontal stress [46].
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The cohesion of the naturally fractured reservoir of 0.69 MPa (100 psi) was estimated from the
intercept of Mohr-Coulomb failure envelope when the Mohr circle touched the failure envelope.
The Mohr circle is determined using the shear failure pore pressure from Chapter 3, maximum
horizontal stress, and minimum horizontal stress. The complete inputs for the models simulation
are shown in Table 4.2.
Table 4.2: Glauconitic Formation properties.
Parameters Values Units Minimum horizontal stress gradient 11.66 kPa/m Maximum horizontal stress gradient 25.79 kPa/m Overburden stress gradient 24.09 kPa/m Biot’s coefficient 1 Average depth 1900 m Poisson’s ratio 0.23 Porosity 15 % Intact rock and naturally fractured rock friction angle 30 degree Intact rock cohesion 11.55 MPa
4.4.4 Calibration of Stimulated Rock Volume using Microseismic Data
The calibration constants are determined by finding the constants that match the estimated
Stage 7 SRV dimensions with the Stage 7 SRV dimensions interpreted from microseismic events.
The failure type needs to be determined prior to calibrating the model. The first time step BHP is
required to initiate the fracture and associated SRV via tensile failure. The first time step BHP and
hydraulic fracture injection duration are different for all stages that lead to different first time step
SRV dimensions. Stages 1, 11, and 12 have the highest tensile failure BHP compared to the other
stages; this might be caused by less intersection with the natural fractures compared to the other
stages.
The pore pressure at which tensile failure occurs in the first time step of Stage 7 is equal to
41.5 MPa. The pore pressure at which shear failure occurs in the second time step of Stage 7 is
12.12 MPa as shown in Figure 4.6a (330 s and 6.55 m). The Mohr circle for original reservoir
pressure assumes a Biot’s constant of unity and no shear failure. In this study, a linear
simplification of the Mohr-Coulomb failure envelope is used as shown in Figure 4.6b [4]. The
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calibration constants are k1, k2 and k3. The calibration constants determined for the first time step
under tensile failure are k1 = 200, k2 = 100 and k3 = 150. The calibration constants found for the
second time step under shear failure are k1 = 0.6485, k2 = 0.3336, and k3 = 0.1474. These constants
are applicable for the Glauconitic Formation at Hoadley field or other formations that have similar
reservoir and geomechanical properties.
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(a)
(b)
Fig. 4.6: (a) Pressure drop derived from finite element analysis in Chapter 3 and (b) Stage 7 Mohr-Coulomb failure envelope for Case 1.
126
4.5 Results
4.5.1 Constant Total Stress
The first results are produced using constant total stresses (Case 1). The SRV length, width
and height for Stage 7 are calibrated to match the closest first time step event. The second time
step SRV length, width and height for Stage 7 are calibrated to match SRV dimensions interpreted
via microseismic events. The Stage 7 calibration constants for the tensile and shear time steps (k1,
k2, and k3) are applied to the other stages.
Here, the distances obtained from the first time step events are compared to the cutoff, SRV
growth (yes or no), number of events in the estimated SRV, and number of events in the region
double the size of the estimated SRV. The comparison is presented in Table 4.3. The SRV
dimensions for the six stages with dimensions interpreted from microseismic observations are
shown in Figures 4.7 to 4.15. The SRV dimensions estimated with no interpretations from
microseismic observations are shown in Figures 4.16 to 4.21.
Table 4.3: Results of all stages first time step event distance, SRV growth, number of events fitted within the estimated SRV, and Figures showing results.
Stages First time step event distance from wellbore
Fig. 4.7: Stage 7 SRV length versus width for Case 1.
Fig. 4.8: Stage 7 SRV length versus height for Case 1.
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Fig. 4.9: Stage 7 SRV width versus height for Case 1.
Fig. 4.10: Stage 7 SRV length versus best fit width (using microseismic data) for Case 1.
129
Fig. 4.11: Stage 1 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
130
Fig. 4.12: Stage 5 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
131
Fig. 4.13: Stage 8 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
132
Fig. 4.14: Stage 9 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
133
Fig. 4.15: Stage 11 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
134
Fig. 4.16: Stage 2 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
135
Fig. 4.17: Stage 3 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
136
Fig. 4.18: Stage 4 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
137
Fig. 4.19: Stage 6 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
138
Fig. 4.20: Stage 10 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
139
Fig. 4.21: Stage 12 SRV dimensions for Case 1: (a) SRV length versus width, (b) SRV length versus best fit width (using microseismic events), (c) SRV length versus height, and (d) SRV width versus height.
The following are some investigation on some stages of first time events that are not reliable
and located away from the horizontal wellbore from Table 4.3:
1. The first time step microseismic events data for Stage 1 are not reliable since there is only
one event that occurred and it is located relatively far away from the horizontal wellbore.
Caffagni and Eaton (2015), in a study of the same well, explained that some events are not
detected because the first time step tensile failure have signal-to-noise ratio (SNR) <<1 and
signal levels <5% of the reference waveform [47].
2. The closest first time step event for Stage 5 and Stage 8 are located outside the cutoff and
towards the East side because it is affected by the depleted zone around an old production
wellbore (microseismic observation wellbore not in operation) on the West side of the
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horizontal wellbore. The fracture fluid may increase the pressure within the depleted zone
without creating shear failure and consequent microseismic events.
The differences between the interpreted SRV dimensions from microseismic events with the
estimated SRV dimensions are shown in Figure 4.22a. The average differences for the SRV length,
width, and height are 31%, 24%, and 10%, respectively. On average, 36% of the total microseismic
events are within the estimated SRV as shown in Figure 4.22b.
Fig. 4.22: (a) SRV dimensions differences with microseismic events for six interpreted stages and (b) SRV best fit using microseismic event data for all stages.
The pressure drop along the SRV width is calculated by using the transient pressure drop
equation presented by Ahmed and McKinney (2005) [48]. Shear failure pressure from Ahmed and
McKinney (2005) [48] is compared with the shear failure pressure estimated from finite element
analysis conducted in Chapter 3. The results is shown in Figure 4.23 and the Ahmed and McKinney
(2005) pressure drop equation is given as follows [48]:
Δ𝑃𝑃 = 162.6𝑞𝑞𝑞𝑞𝜇𝜇𝑘𝑘ℎ
�log 𝑡𝑡 + 𝑣𝑣𝑐𝑐𝑔𝑔 � 𝑘𝑘𝜑𝜑𝜇𝜇𝐶𝐶𝑡𝑡𝑟𝑟2
� − 3.23 + 0.87𝑐𝑐� (22)
where ΔP is the pressure drop along the extent of the SRV (psi), q is the injection flow rate (bpd),
B is the formation volume factor for the hydraulic fracture fluid (bbl/stb) (it is assumed to be equal
1), µ is the hydraulic fracture fluid viscosity (cP), k is the reservoir equivalent permeability (mD),
h is the formation thickness (ft.), t is the injection time (hours), φ is the formation porosity fraction),
ct is the total formation compressibility (1/psi), r is the distance (ft.), and s is the formation skin.
141
(a)
(b)
(c)
Fig. 4.23: (a) Pressure drop from finite element analysis in Chapter 3, (b) pressure drop derived from transient analysis equation for intact natural fractures, and (c) pressure drop derived from transient analysis equation for open natural fractures.
5
10
15
20
25
30
0 5 10 15 20 25 30
P (M
Pa)
x (m)
Pore Pressure Along SRV Width
t=1s t=330s t=1101s t=2250s
5
10
15
20
25
30
0 5 10 15 20 25 30
P (M
Pa)
x (m)
Pore Pressure Along SRV Width
t=1s t=330s t=1101s t=2250s
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A skin of negative seven is assumed based on typically expected hydraulically fractured
reservoir skin values [49]. The equivalent SRV permeability and natural fractures spacing are
calculated from Chapter 3. The transient pressure drop is calculated using Equation (22) only for
Stage 7 with the following assumptions:
1. A low pressure drop is created when the fracture is open. This open fracture is assumed to
be a tensile fracture created by hydraulic fracture or shear fracture along an open natural
fracture. These fractures are assumed to have a high permeability (k=23.4 D) as found in
Chapter 3.
2. A high pressure drop is created by shear fracture created by reopening an intact natural
fracture. This shear fracture is assumed to have a lower permeability (k<23.4 D) that
produces pore pressure equal to the initial reservoir pore pressure (9 MPa). It is assumed
that by the end of reopening the natural fracture, the pore pressure is equal to the initial
reservoir pore pressure.
3. Four time periods are defined to represent different conditions – each time period
represents different failures at different distances and injection times. The first time period
(1 s) represents tensile failure at a distance of 1 m. The second time period (330 s)
represents shear failure at a distance of 6.55 m (first natural fracture). The third time period
(1,101 s) represents shear failure at a distance of 19.65 m (second natural fracture). The
fourth time period (2,250 s) represents shear failure at a distance of 30 m (assumed to be
the boundary of the SRV).
4. Each time period has initial injection BHP. The initial injection BHPs are from Chapter 3.
The first time period has an initial injection BHP of 15.9 MPa. The second time period has
an initial injection BHP of 18.2 MPa. The third time period has an initial injection BHP of
22 MPa. The fourth time period has an initial injection BHP of 27.62 MPa.
5. Equation (22) is used to calculate two cases: (a) intact natural fractures and (b) open natural
fractures.
6. For intact natural fractures case, the natural fractures have lower permeability (less than
23.4 D) and higher pressure drop (shear failure pressure is equal to initial reservoir pressure
of 9 MPa).
143
7. For open natural fractures case, the natural fractures have higher permeability (equal to
23.4 D) and lower pressure drop (shear failure pressure is higher than initial reservoir
pressure but lower than the initial injection BHP).
8. The permeability along the SRV width for the intact natural fractures case calculated using
Equation (22) are: (a) the first time period assumes k=23.4 D for locations less than 1 m
and k=6.11 D for distance between 1 m and 30 m, (b) the second time period assumes
k=23.4 D for locations less than 6.55 m and k=3.93 D for locations between 6.55 m and 30
m, (c) the third time period assumes k=23.4 D for positions less than 19.65 m and k=3.09
D for distances from 19.65 m to 30 m, and (d) the fourth time period assumes that k=23.4
D for the interval from 0 to 30 m. The permeability is assumed constant from the natural
fracture location to the SRV width boundary. This constant permeability is used to produce
constant pressure from the natural fracture to the SRV width boundary equal to initial
reservoir pressure.
9. The permeability along the SRV width for the open natural fractures case calculated using
Equation (22) are: (a) the first time period assumes k=23.4 D for locations between 0 m
and 1 m and k=6.76 D for distance between 2 m and 30 m, (b) the second time period
assumes k=23.4 D for locations between 0 m and 6.55 m and k=4.22 D for locations
between 10 m and 30 m, (c) the third time period assumes k=23.4 D for positions between
0 m and 19.65 m and k=3.16 D for distances from 23 m to 30 m, and (d) the fourth time
period assumes that k=23.4 D for the interval from 0 to 30 m. The permeability is assumed
constant from the natural fracture location to the SRV width boundary. This constant
permeability is used to produce constant pressure from the natural fracture to the SRV
width boundary equal to initial reservoir pressure.
For intact natural fractures case, the shear failure pressure at 6.55 m and 5.5 minutes (330 s),
equal to initial reservoir pressure, is determined by using Equation (22) as presented in Figure
4.17b. This intact natural fracture case shear failure pressure is lower than the shear failure pressure
of 12.12 MPa obtained from Chapter 3. The smaller shear failure pressure is caused by a higher
pressure drop from the transient pressure drop at intact natural fracture location (lower
permeability) compared to the pressure drop from the analysis in Chapter 3. Moreover, the intact
natural fracture case using the transient pressure drop equation considers a sudden permeability
drop between the open hydraulic fractures and intact natural fractures. The sudden permeability
144
drop is used to produces the pressure at intact natural fractures equal to the initial reservoir
pressure.
The open natural fracture case, the shear failure pressure at 6.55 m and 5.5 minutes (330 s),
equal to 16.95 MPa, is determined by using Equation (22) as presented in Figure 4.17c. This open
natural fracture case shear failure pressure of 16.95 MPa is higher than the shear failure pressure
of 12.12 MPa obtained from the analysis in Chapter 3. The higher shear failure pressure is caused
by a lower pressure drop from the transient pressure drop at open natural fracture location (high
permeability) compared to the pressure drop from the analysis in Chapter 3. The smaller pressure
drop from open natural fractures case using transient analysis can be caused by Equation (22) does
not consider the pressure drop induced by the rock consolidation.
The intact natural fracture case from Equation (22) results in shear failure at initial reservoir
pressure, which does not occur as shown Mohr-Coulomb failure in Figure 4.6 at the lowest
cohesion (C=0). And the open natural fracture case from Equation (22) produces the shear failure
between initial injection BHP and initial reservoir pressure and it does not consider the pressure
drop induced by the rock consolidation. Therefore, this study uses the shear failure pressure
obtained from Chapter 3 to generate the Mohr circle on the Mohr-Coulomb failure envelope
(Chapter 3 considers pressure drop induced by the rock consolidation).
The estimated SRV dimensions of some stages have differences with the interpreted SRV
dimensions via microseismic. For example, the estimated SRV length of Stage 9 is 36% longer
than the microseismic interpretation. From the microseismic observation, the estimated SRV
length fits better with the results estimated from the microseismic events. The estimated SRV
covers 49% of total microseismic events. The estimated SRV widths of Stages 8 and 9 are 56%
and 47% shorter than the interpreted SRV width estimated from the microseismic data. This
phenomenon might be caused by the effect of an old depleted zone around the Stages 8 and 9.
There is an old wellbore on the North East side of the Stages 8 and 9 which has been producing
since 1982. Hydraulic fracturing of new wells in the vicinity of the old well might create shear
failures along natural fractures triggering additional non-productive microseismic events. Maxwell
et al. (2002) discovered that the hydraulic fractures grew toward old neighboring wells because of
the depleted zones around the older wells [21]. Maxwell et al. (2010) showed that these cases
occurred when critically stressed fractures existed in the neighborhood of the hydraulic fracture
145
failures [21]. These critically stressed fractures could trigger small stresses changes and result in
remote triggering of microseismic events [21]. Therefore the wider SRV by these trigger events
might not have any connection to the SRV dimensions of Stages 8 and 9. Furthermore, these
reopening natural fractures might not contribute to the horizontal wellbore production in the future.
The SRV length of Stage 5 is 47% shorter than the interpreted microseismic events. The
microseismic observations shows that there are two clouds of second time step events around Stage
5. The dimensions of the SRV are estimated by using the first cloud of second time step events.
The closest second cloud event from the first time step event center is located at 270 m. Therefore
it is assumed that the first time step and the second time step cloud are not connected and that the
estimated SRV length of Stage 5 fits better with the microseismic events.
The average estimated SRV length, width and height are 166.30 m, 56.83 m, and 62.0 m for
all the 12 stages as listed in Table 4.4. The SRV dimensions are a complex fracture network (they
are not bi-wing fracture) because of the low ratio between the maximum horizontal stress with the
overburden stress. Weng et al. (2011), from their simulations, showed that the stress ratio, natural
fractures, and internal friction angle affected the complexity of the fracture network [25].
Specifically, their results showed that lowering the stress ratio changed the system from a bi-wing
fracture to a complex fracture network.
This study suggests an optimum fracture spacing that will drain all the area (SRV) between the
injection ports. An optimum fracture spacing is assumed to be uniform and equal to the average
estimated SRV width (56.83 m), the interpreted SRV dimensions from microseismic were only
done for six stages. It is shorter than the hydraulic fracture injection port spacing (116.82 m) listed
in Table 4.5. Therefore, it is suggested that the hydraulic fracture injection port spacing should be
shorter and equal to that of the SRV width to improve drainage from the reservoir.
146
Table 4.4: The estimated SRV dimensions results and the located microseismic events.
Stages SRV length (m) SRV width (m) SRV height (m) Number of events
The first results in the previous section are produced assuming constant total stresses (Case 1).
The results in this section are produced using total stress changes (Case 2). The total stress change
and the pore pressure for Case 2 are estimated from Chapter 3. The changes in the total stress affect
the Mohr circle in the Mohr-Coulomb failure envelope (Figure 4.24). From Chapter 3, the total
stresses (both the maximum and the minimum horizontal stress) increase with the injection time.
In Case 2, it is assumed only the minimum horizontal stress change with the maximum horizontal
stress and the overburden stress are constant. Therefore only the width of the SRV changes (SRV
length and height constant).
149
Fig. 4.24: Mohr-Coulomb stress failure envelope of stage 7 for Case 2.
The first time step of Case 2 uses the minimum horizontal stress increases of 4.54 MPa
(minimum horizontal stress value at 1 s and located at the wellbore from Chapter 3), BHP of 41.5
MPa (fracture breakdown pressure) and fracture breakdown pressure duration of 5.5 minutes. The
second time step of Case 2 uses the minimum horizontal stress increase of 0.9 MPa (minimum
horizontal stress value at 330 s and located at 6.55 m from Chapter 3), and pressure of 12.12 MPa,
and fracture propagation duration (from 5.5 minutes after hydraulic fracture starts which is the
start of hydraulic fracture propagation until the end of injection).
Case 1 and Case 2 have naturally fractured rock cohesion equal to 0.69 MPa. Case 2 SRV
width is shorter by 4.11% compared to the Case 1 SRV width. This suggests that the SRV
dimensions are overestimated when total stresses changes are not considered. Mcclure and Horne
(2013) studied the effect of stress changes during hydraulic fracturing and explained the
importance of including the stresses induced by the deformation in hydraulic fracture modeling
[28]. These stresses directly impact hydraulic fracture propagation and resulting fracture network
properties [28]. The Mohr-Coulomb failure envelope properties and plot for the Case 2 are
presented in Table 4.7.
150
Table 4.7: Stage 7 Mohr-Coulomb failure envelope properties for Case 2.
Mohr-Coulomb failure envelope properties
Tensile failure (not shown in Mohr-Coulomb
failure envelope
Shear failure (red Mohr circle)
Effective Sh (psi) -2140.31 1593 Effective Sh (MPa) -14.76 10.88 Effective SH (psi) 1088 5349 Effective SH (MPa) 7.5 36.88 Additional Sh (MPa) 4.54 0.9 Additional Sh (psi) 658 131 Additional SH (MPa) 0 0 Additional SH (psi) 0 0 Pore pressure cause failure (MPa)
41.5 12.12
Pore pressure cause failure (psi) 6019 1758
Table 4.8 compares the Mohr-Coulomb failure envelope properties for Case 1 and Case 2. To
support the shear failure determined by using the Mohr-Coulomb failure envelope, the effective
stresses are plotted for the intact rock and the naturally fractured reservoir based on the study done
by Hoek and Martin (2014) (Figure 4.25) [51]. For intact rock, tensile strength is calculated by
using the Stage 7 fracture breakdown BHP and tensile strength is assumed to be zero for naturally
fractured reservoir. The UCS is calculated in Section 4.4 with no shear failure data. Therefore for
intact rock, the shear failure envelope is assumed to be a straight line extension from the tensile
strength and UCS.
151
Table 4.8: Stage 7 SRV dimensions and Mohr-Coulomb failure envelope properties comparison Cases 1 and 2.
Stage 7 Case 1 Case 2 Differences %
SRV width (m) 60 58 4 Increase Sh at tensile failure (MPa) 4.5 Increase Sh at tensile failure (psi) 658.9 Tensile failure Sh (MPa) -19.3 -14.8 Tensile failure Sh (psi) -2799.2 -2140.3 Increase Sh at shear failure (MPa) 0.9 Increase Sh at shear failure (psi) 130.9 Shear failure Sh (MPa) 10.1 11 Shear failure Sh (psi) 1462 1593 BHP shear failure (MPa) 12.12 12.12 BHP shear failure (psi) 1758 1758 Cohesion (MPa) 0.69 0.69 Cohesion (psi) 100 100
Fig. 4.25: Plot of Case 1 and Case 2 effective maximum horizontal stress versus effective minimum horizontal stress for intact rock and naturally fractured reservoirs.
152
The UCS of 2.38 MPa is calculated by using the estimated cohesion for the naturally fractured
reservoir. The naturally fractured reservoir for Case 1 and Case 2 only has one failure point that
touches the failure envelope. The failure point for the cases have pore pressure of 12.12 MPa. The
failure point for Case 1 and Case 2 have the same effective maximum horizontal stress and
different effective minimum horizontal stress. Case 2 has a higher effective minimum horizontal
stress of 11 MPa compared to the Case 1 effective minimum horizontal stress of 10.1 MPa. The
failure line between the UCS and failure point for the Cases 1 and 2 have small differences in
inclination (0.45o) which is negligible. This plot supports that the initial reservoir pressure does
not experience the shear failure yet (not touching the failure line for Case 1 or Case 2). The SRV
dimensions results for the minimum horizontal stress case are shown in Figure 4.26.
Fig. 4.26: SRV dimensions of Stage 7 for Case 2 SRV dimensions: (a) SRV length versus width, (b) SRV length versus width best fit with microseismic events, (c) SRV length versus height, and (d) SRV width versus height.
153
4.6 Conclusions
New models to estimate the dimensions of SRV are derived and they can be used to optimize
the design of future hydraulic fracture jobs. It is found that the SRV dimensions can be related to
the effective stresses, injected fluid volume, and plane strain modulus as well as the naturally
fractured reservoir cohesion strength and internal friction angle. The models are calibrated with
SRV dimensions interpreted via microseismic events from 6 hydraulic fracture stages. The models
have the ability to estimate the evolution of SRV dimensions during hydraulic fracturing by using
microseismic events center of two consecutive time periods. The SRV dimensions represent the
extent of the fracture network created by the multi-stage hydraulic fracture in a horizontal well in
a naturally fractured reservoir.
The conclusions of this chapter are as follows:
1. Two different time periods with each pressure and injection time are required to represent
tensile and shear failure. The first time step that experiences tensile failure has BHP that is
measured from field fracture breakdown pressure and it is assumed there is no pressure
drop from the horizontal wellbore to the tensile failure location. The second time step that
experiences shear failure has no pore pressure measured at the field. It is assumed that shear
failure occurs at natural fracture location and start of fracture propagation until the end of
injection.
2. Growth of the SRV is not apparent for some of the hydraulic fracture stages. In some stages,
the first time step events are not triggered in the proximity of the horizontal wellbore. This
phenomenon could be caused by the first time step events were not detected by the receiver.
And also, it could be caused due to low signal to noise ratio and signal levels compare to
reference waveform signal. Another reason to this phenomenon as because the events were
affected by depleted zone at old production wellbore on the West side of the horizontal
wellbore. The fracture fluid may be increasing the pressure within the depleted zone.
3. The impact of the total stress changes on the dimensions of the SRV reveals that total
stresses must be included to avoid overestimation of the dimensions of the SRV. The total
stress changes affect the Mohr circle in the Mohr-Coulomb failure envelope.
154
4.7 References
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Stimulation Coupling Flow and Geomechanics, first edition. Heidelberg, Germany: Springer International Publishing.
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Equation (32) used unit conversion 1010 to convert 105 ft3/hours (field flow rate is in magnitude
of 105 ft3/days) to ft3/hours.
𝐼𝐼 = 𝜑𝜑𝜇𝜇𝐶𝐶𝑡𝑡0.000264
= 𝜑𝜑𝑖𝑖�1−𝐶𝐶𝑡𝑡(𝑃𝑃0−𝑃𝑃)� 𝜇𝜇𝐶𝐶𝑡𝑡0.000264
(33)
𝑡𝑡 = 0 (34)
𝑓𝑓 = 0 (35)
The parabolic nonlinear PDE is solved using the wellbore production time (8 months or 6,300
hours) as shown in Table 5.4. Then the parabolic nonlinear PDE is solved using the Matlab code
editor lines as a function of u0, production time, boundary condition, and PDE nonlinear
coefficients. The detailed Matlab nonlinear parabolic PDE code is listed in Appendix A.
174
Table 5.4: Matlab PDE nonlinear simulation time.
Time (hours) 6300
Time simulation spacing (hours) 157.5
Gas flow rate is calculated using Darcy’s law and Matlab simulation outputs (permeability and
pressure drop gradient). The simulated gas flow rate is then compared with the field gas flow rate.
5.5.1.3 Matlab Nonlinear PDE Code Editor Results
The Matlab nonlinear PDE solver uses the Galerkin finite element method to solve the PDE
together with forward Euler time integrator and Newton’s method to deal with the nonlinearity of
the PDE. The default relative tolerance of 1x10-3 and absolute tolerance of 1x10-4 are used in the
Matlab nonlinear PDE solver. The triangular mesh is created for the 2D geometry using Delaunay
triangulation. The mesh size is determined from the geometry shape and the defined maximum
mesh size of 5 m.
After u is found, then the pressure, porosity, and permeability are calculated by using Equations
(22), (26), and (29). The results from Matlab is presented in contour plots at three different
production times: early production time (t=157.5 hours), mid production time (t=2,992.5 hours),
and final production time (t=6,300 hours). The pressure plots are presented in Figures 5.4a to 5.4c,
permeability in Figures 5.5a to 5.5c, and porosity in Figures 5.6a to 5.6c. The pressure and porosity
contour plots show small changes during early, mid, and late production time. But the permeability
contour plots show great changes during early, mid, and late production time.
175
(a)
(b)
(c)
Fig. 5.4: Pressure contour plot in SRV during (a) 157.5 hours, (b) 2,992.5 hours, and (c) 6,300 hours production.
176
(a)
(b)
(c)
Fig. 5.5: Permeability contour plot in SRV during (a) 157.5 hours, (b) 2,992.5 hours, and (c) 6,300 hours production.
177
(a)
(b)
(c)
Fig. 5.6: Porosity contour plot in SRV during (a) 157.5 hours, (b) 2,992.5 hours, and (c) 6,300 hours production.
178
The pressure plots are presented in Figures 5.7a and 5.7b, permeability in Figures 5.8a and
5.8b, and porosities in Figure 5.9a and 5.9b. From Figure 5.7b, the pressure of 11.8 MPa results at
two meters distance from wellbore during the end of production (262.5 days). This pressure is
higher than the initial reservoir pressure (9 MPa). The pressure of 11.8 MPa produces permeability
of 2,763 mD. These responses show that the SRV pressure and permeability are still high and
allow the SRV to be drained for later production.
179
(a)
(b)
Fig. 5.7: Pressure profile as a function of (a) time and (b) distance from SRV boundary to wellbore.
0
5
10
15
20
25
0 50 100 150 200 250 300
Pres
sure
, MPa
Time, days
Pressure During 8 Months Production within SRV
y=18.5 m y=32 m y=45.6 m y=48.2 m y=55.4 my=59.5 m y=60.8 m y=64 m y=67 m y=70.5 my=70.7 m y=74.6 m y=78.6 m y=80.1 m y=81 my=85 m y=87 m
0
5
10
15
20
25
0 20 40 60 80 100
Pres
sure
, MPa
Distance, m
Pressure from SRV Boundary to Wellbore
t=0 days t=0.4 days t=0.8 days t=1.3 dayst=1.7 days t=2.1 days t=6.6 days t=13.1 dayst=19.7 days t=26.3 days t=32.8 days t=39.4 dayst=46 days t=52.5 days t=59.1 days t=65.6 dayst=72.2 days t=78.8 days t=85.3 days t=92 dayst=98.4 days t=105 days t=111.6 days t=118 dayst=124.7 days t=131.3 days t=137.8 days t=144.4 dayst=151 days t=157.5 days t=164 days t=170.6 dayst=177.2 days t=183.8 days t=190.3 days t=197 dayst=203.4 days t=210 days t=217 days t=223 dayst=230 days t=236.3 days t=243 days t=249.4 dayst=256 days t=262.5 days
180
(a)
(b)
Fig. 5.8: Permeability profile as a function of (a) time and (b) distance from SRV boundary to wellbore.
0
5,000
10,000
15,000
20,000
25,000
30,000
0 50 100 150 200 250 300
Perm
eabi
lity,
mD
Time, days
Permeability During 8 Months Production within SRV
y=32 m y=45.6 m y=48.2 m y=55.4 my=59.5 m y=60.8 m y=64 m y=67 my=70.5 m y=70.7 m y=74.6 m y=78.6 my=80.1 m y=81 m y=85 m y=87 m
0
5,000
10,000
15,000
20,000
25,000
0 20 40 60 80 100
Perm
eabi
lity,
mD
Distance, m
Permeability from SRV Boundary to Wellbore
t=0 days t=0.4 days t=0.8 days t=1.3 dayst=1.7 days t=2.1 days t=6.6 days t=13.1 dayst=19.7 days t=26.3 days t=32.8 days t=39.4 dayst=46 days t=52.5 days t=59.1 days t=65.6 dayst=72.2 days t=78.8 days t=85.3 days t=92 dayst=98.4 days t=105 days t=111.6 days t=118 dayst=124.7 days t=131.3 days t=137.8 days t=144.4 dayst=151 days t=157.5 days t=164 days t=170.6 dayst=177.2 days t=183.8 days t=190.3 days t=197 dayst=203.4 days t=210 days t=217 days t=223 dayst=230 days t=236.3 days t=243 days t=249.4 dayst=256 days t=262.5 days
181
(a)
(b)
Fig. 5.9: Porosity profile as a function of (a) time and (b) distance from SRV boundary to wellbore.
0.000.020.040.060.080.100.120.140.160.18
0 50 100 150 200 250 300
Poro
sity,
frac
tion
Time, days
Porosity During 8 Months Production within SRV
y=18.5 m y=32 m y=45.6 m y=48.2 m y=55.4 my=59.5 m y=60.8 m y=64 m y=67 m y=70.5 my=70.7 m y=74.6 m y=78.6 m y=80.1 m y=81 my=85 m y=87 m
0.000.020.040.060.080.100.120.140.160.18
0 20 40 60 80 100
Poro
sity,
frac
tion
Distance, m
Porosity from SRV Boundary to Wellbore
t=0 days t=0.4 days t=0.8 days t=1.3 dayst=1.7 days t=2.1 days t=6.6 days t=13.1 dayst=19.7 days t=26.3 days t=32.8 days t=39.4 dayst=46 days t=52.5 days t=59.1 days t=65.6 dayst=72.2 days t=78.8 days t=85.3 days t=92 dayst=98.4 days t=105 days t=111.6 days t=118 dayst=124.7 days t=131.3 days t=137.8 days t=144.4 dayst=151 days t=157.5 days t=164 days t=170.6 dayst=177.2 days t=183.8 days t=190.3 days t=197 dayst=203.4 days t=210 days t=217 days t=223 dayst=230 days t=236.3 days t=243 days t=249.4 days
182
The gas flow rate is calculated by using Darcy’s law and the permeability and pressure gradient
at the wellbore. This calculated gas flow rate is compared with the field gas flow rate. The initial
gas flow rate is matched by finding the total compressibility (field measured formation
compressibility of 3x10-6 1/psi and total compressibility of 5.81x10-4 1/psi). The matched total
compressibility of 4.0559x10-4 1/psi is similar to the total compressibility of 5.81x10-4 1/psi. This
total compressibility is assumed to be driven by the fracture compressibility (fluid and formation
compressibility are assumed to be small and neglected). The matched fracture compressibility is
compared to fracture compressibility from empirical correlations [6]. Aguilera (1999) presented
for net stress on fracture of 3,742 psi (net stress is reduction of total overburden stress of 6,642 psi
with pressure within SRV at the end of hydraulic fracture of 2,900 psi), the fracture compressibility
is between 3x10-5 1/psi (for 50% mineralization within fracture) and 1.25x10-4 1/psi (for zero
mineralization within fracture) [6]. The matched fracture compressibility is within the magnitude
of Aguilera’s (1999) fracture compressibility with zero mineralization within the fracture.
The cross section area on the production port considers the z-direction. A permeability of 0.3
mD at the wellbore tip is determined from the Matlab simulation and it is constant during
production. The simulated gas flow rate has overall good match with the field gas flow rate
especially from Day 25 to the end of the time period as shown in Figure 5.10. There are some
differences in early production time (smaller than 25 days) that may be caused by different pressure
drop gradient in the simulation and the field. A higher initial porosity of 0.17 is simulated, but the
simulated gas flow rate is similar (1 e3m3/day of differences) with the initial porosity of 0.16. This
concludes that the initial porosity does not affect the flow rate. The matched gas flow rate profile
shows that the model is applicable for the other fields with similar reservoir properties to the
Hoadley field.
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(a)
(b)
Fig. 5.10: Comparison of (a) field gas flow rate and (b) bottomhole pressure with new diffusion model with porosity of 0.16 and 0.17 (no changes).
0
10
20
30
40
50
0 50 100 150 200 250 300
Gas P
rodu
ctio
n, e
3m3/
d
Production time, days
Gas Production
q por=0.16 q por=0.17 q field
0
1
2
3
4
5
0 50 100 150 200 250 300
BHP,
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Production time, days
Bottomhole Pressure
BHP Matlab BHP Field
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5.5.2 Application of Rate Transient Analysis Simulator (IHS Harmony
(Figure 5.13), and Wattenbarger (Figure 5.14). Doublet et al. (1994) found the Blasingame type
curve to be useful in the modeling of elliptical flow that transitioned into boundary dominated flow
[29]. The Blasingame finite conductivity fracture represented a square or cylindrical reservoir with
finite conductivity fracture in the center, the Blasingame elliptical represented an elliptical
reservoir with a finite conductivity fracture in the center, and the Blasingame horizontal
represented a square reservoir with a horizontal well in the center. The Wattenbarger type curve
was also used to fit the field data. The type curve analysis was useful to analyze unconventional
gas reservoir with long term linear flow. Several points at Wattenbarger normalized rate plot and
derivative (half slope of derivative blue points) plot fitted nicely with the field data. The plots
showed the flow regime was linear flow regime. The Blasingame finite conductivity fracture type
curve fitted better with the field data and the type curve outputs were used for the unconventional
reservoir analysis inputs. The Blasingame finite conductivity fracture type curve fitted better with
the field data because fracture permeability of 23,400 mD and fracture aperture of 0.0047 ft (1.43
mm) from Chapter 3 analysis produced the fracture flow capacity of 109.98 mD.ft. Fracture flow
capacity of less than 10,000 mD.ft represented a finite conductivity fracture and the fracture flow
capacity was the product of fracture permeability and fracture aperture.
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Fig. 5.11: Blasingame finite conductivity fracture with median filter.
187
Fig. 5.12: Blasingame elliptical with median filter.
188
Fig. 5.13: Blasingame horizontal with median filter.
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Fig. 5.14: Wattenbarger with median filter.
5.5.2.3 Unconventional Reservoir Analysis (Unconventional Gas Module)
The input for the unconventional gas module were the reservoir properties, Blasingame finite
conductivity fracture type curves, number of hydraulic fracture stages (12), and effective
horizontal well length (hydraulic fracture stages port 1 to 12 distance of 1268.1 m), then the
simulator calculated the reservoir permeability.
The first plot was the square root of time plot showing a straight line which was confirming
the linear flow regime from the type curve with no departure from the straight line (boundary
dominated flow) (Figure 5.15a). The dotted green line (boundary dominated flow starting point)
was chosen at the end of the linear flow to get the optimistic assessment of the SRV that was
indicating the minimum SRV. The dotted green line was tied to the extrapolation red line on the
flowing material balance at Figure 5.15. The next plot is the log-log type curve between flow rate
and time representing the model from the square root of time plot as shown in Figure 5.16. The
red type curve showed a bounded drainage volume and the brown type curve assumed the linear
flow occurred for infinite time and it was not bounded by any drainage volume. The red type curve
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was an optimistic forecast for the well. Changing the slope at the log-log type curve would change
the skin values. The skin value that matched the type curve slope was zero (it was a hydraulically
fractured well). The input for this unconventional gas module was the horizontal wellbore length
and number of hydraulic fracture stage, then the software calculated the reservoir permeability
using the square root of time plot slope relationship with reservoir permeability.
Fig. 5.15: Unconventional gas module square root time plot to identify the pessimistic boundary dominated flow (green vertical line),
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Fig. 5.16: Unconventional gas module typecurve plot to identify the pessimistic boundary dominated flow (green vertical line).
5.5.2.4 History Match Using Horizontal Multifractured Enhanced Fracture
Region Analytical Model
5.5.2.4.1 Case 1 With Constant FCD, SRV Half-Length, and Matrix
Permeability
To determine the SRV permeability and reservoir permeability, the reservoir properties and
the unconventional gas module output were applied into the horizontal multifractured enhanced
fracture region analytical model [19]. This model was chosen due to the assumption that there was
unstimulated reservoir volume between SRV from created hydraulic fractures. The input for this
analytical model were the reservoir properties and unconventional gas module simulation results.
These inputs were used as the simulation starting point. The horizontal multifractured enhanced
fracture region analytical model was used to simulate SRV permeability and reservoir
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permeability. The analytical model produced a history match between the gas flow rate and
flowing field data with the simulated data. To improve the history match, two cases were
simulated. Case 1 used constant dimensionless fracture conductivity (FCD) of 105, SRV half-
length of 6.7 m, and reservoir permeability (k2) of 0.00648 mD. Case 1 produced SRV
permeability (k1) of 827 mD (PSS model), 9,736 mD (slabs model), 1,136 mD (cubes model), and
15,516 mD (sticks model). The PSS model assumes the flow between matrix and fractures is in
pseudo steady state [16]. The transient model assumes the flow between matrix and fractures is
transient and it has three types of matrix geometry (slabs, cubes and sticks geometries) [16].The
results showed the transient models have a higher permeability compared to the PSS model which
might be caused by the transient models assuming the flow has only reached the closest SRV but
it has not reached the furthest SRV yet. Also the PSS model assumes the flow has already reached
all the no flow SRV boundaries. The results are listed on Table 5.6 with each model history match
shown in Figure 5.17 to 5.20. Case 1 produced a good match on the gas flow rate but only average
good match on the flowing pressure.
Case 1 produced a higher FCD compared to the expected FCD of 5.5. It also produced smaller
reservoir permeability (k2) compared to field reservoir permeability of 0.07 mD, smaller SRV half-
length compared to field SRV half-length of 87 m, a much smaller SRV permeability (k1)
compared to the Matlab results, and much smaller reservoir boundaries of around 23 m compared
to the field SRV half-length.
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Table 5.6: Case 1 simulation results for constant FCD, SRV half-length and matrix permeability.
Simulation results Hz Multifrac Enhanced fracture region model
Dual porosity model
PSS slabs cubes sticks
FCD 105 105 105 105 k1 (mD) SRV 827 9736 1136 15516 k2 (mD) reservoir 0.0065 0.0065 0.0065 0.0065 xf (m) 6.7 6.7 6.7 6.7 ye (m) 23.8 23.7 23.8 23.7 omega 0.10 0.01 0.15 0.01 lamda 0.00 0.00 0.00 0.00 S 0.00 0.03 1.73 1.56 P Match Average good Average good Average good Average good Q Match Good Good Good Good
Fig. 5.17: History match with horizontal multifrac enhanced fracture region using unconventional reservoir analysis for constant FCD, SRV half-length and matrix permeability with PSS dual porosity model.
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Fig. 5.18: History match with horizontal multifrac enhanced fracture region using unconventional reservoir analysis for constant FCD, SRV half-length and matrix permeability with slabs model.
195
Fig. 5.19: History match with horizontal multifrac enhanced fracture region using unconventional reservoir analysis for constant FCD, SRV half-length and matrix permeability with cubes model.
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Fig. 5.20: History match with horizontal multifrac enhanced fracture region using unconventional reservoir analysis for constant FCD, SRV half-length and matrix permeability with sticks model.
5.5.2.4.2 Case 2 With Constant SRV Half-Length
Case 2 used a constant SRV half-length of 87 m (the SRV half-length is from Chapter 3) and
matrix permeability of 6.5 x10-5 mD. This case produced different values of FCD of 5 (PSS model),
2 (slabs model), 2 (cubes model), and 0.23 (sticks model). The simulated SRV permeability (k1)
were 13,528 mD (PSS model), 21,037 mD (slabs model), 22,288 mD (cubes model), and 22,345
mD (sticks model). The simulated matrix permeability (k2) were 6.5 x10-5 mD (PSS model),
6.5x10-5 mD (slabs model), 6.5x10-5 mD (cubes model), and 6.7x10-5 mD (sticks model). This case
produced smaller matrix permeability compared to the field data of 0.07 mD but it used the SRV
half-length of 87 m from the field data (microseismic). This case produced a similar FCD
compared to expected FCD of 5.5, much smaller matrix permeability (k2), a good range of SRV
permeability (k1) compared to the Matlab results (higher range compared to Case 1), and good
reservoir boundaries of around 200 m (longer than the field SRV half-length). In conclusion, Case
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2 is better compared to Case 1 due to a better match to the Matlab results and the field reservoir
properties except the matrix permeability. The smaller matrix permeability in the order of 6x10-5
mD could be expected in tight gas reservoir. The results are listed in Table 5.7 and Figure 5.21 to
5.24.
Table 5.7: Case 2 simulation results for constant SRV half-length.
Simulation results Hz Multifrac Enhanced fracture region model
Dual porosity model PSS slabs cubes sticks FCD 5 2 2 0.23 k1 (mD) SRV 13528 21037 22288 22345 k2 (mD) Matrix 6.5E-05 6.5E-05 6.5E-05 6.7E-05 xf (m) 87 87 87 87 ye (m) 249 218 205 198 omega 2.8E-02 3.4E-03 3E-03 2E-01 lamda 1.4E-08 3.8E-08 1.3E-07 2E-08 S 0.00 0.01 0.01 0.00 P Match Average good Average good Average good Average good Q Match Good Good Good Good
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Fig. 5.21: History match with horizontal multifrac enhanced fracture region for constant SRV half-length with PSS model.
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Fig. 5.22: History match with horizontal multifrac enhanced fracture region for constant SRV half-length with slabs model.
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Fig. 5.23: History match with horizontal multifrac enhanced fracture region for constant SRV half-length with cubes model.
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Fig. 5.244: History match with horizontal multifrac enhanced fracture region for constant SRV half-length with sticks model.
5.6 Conclusions
A nonlinear diffusivity PDE is derived for the flow and pressure in the SRV and solved by
using Matlab PDE nonlinear code editor to determine the pressure, permeability, and porosity
profile as a function of distance and time within the SRV during the production. The porosity and
permeability are simulated as a function of the PDE solution (pressure). The simulated
permeability and pressure drop are used to simulate the gas flow rate. The conclusions of this
chapter are:
1. The production data could be reasonably well matched by using the new nonlinear diffusivity
theory. This match is done by finding appropriate total compressibility.
2. There are some gas flow rate differences with the field data at early time (simulated gas flow
rate is smaller than field gas flow rate). This may be caused by higher field pressure drop at
early time compared to simulated pressure drop (flow rate is affected by pressure drop). The
higher field pressure drop could be caused by proppant crushing due to fractures close and in-
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situ stress changes during early time production; factors which are not considered within PDE
diffusivity solution.
3. The matched gas flow rate profile shows that the model is applicable for other fields with
similar reservoir properties to the Hoadley field.
4. IHS Harmony Case 2 produces similar SRV permeability to the nonlinear PDE and reservoir
boundary to field for all models (PSS, slabs, cubes, and sticks) using field SRV half-length.
5. The nonlinear PDE SRV permeability is a function of distance and time during production
whereas the IHS Harmony SRV permeability is a single value.
6. The nonlinear PDE solution provides a better and more detailed view of the SRV permeability
distribution compared to that of IHS Harmony.
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5.7 References
[1] Bulnes, A. C., and Fitting, R. U. 1945. An Introductory Discussion of the Reservoir Performance of Limestone Formations. Trans., AIME. Vol. 160, 179.
[2] Imbt, W. C., and Ellison, S. P. 1946. API Drill and Prod. Prac. 364. [3] Warren, J. E., and Root, P. J. 1963. The Behavior of Naturally Fractured Reservoirs. SPEJ
426. [4] Stearns, D. W. 1982-1994. AAPG Fractured Reservoirs School Notes. Great Falls, Montana. [5] Nelson, R. 1985. Geologic Analysis of Naturally Fractured Reservoirs. Contributions in
Petroleum Geology and Engineering, Vol. 1, Gulf Publishing Co., Houston, Texas. [6] Aguilera, R. 1998. Geologic Aspects of Naturally Fractured reservoirs. The Leading Edge,
pp. 1667-1670, December. [7] Aguilera, R. 2003. Geologic and Engineering Aspects of Naturally Fractured Reservoirs.
CSEG Recorder, February. [8] McNaughton, D. A. and Garb, F. A. 1975. Finding and Evaluating Petroleum Accumulations
in Fractured Reservoir Rock. Exploration and Economics of the Petroleum Industry, v.13, Matthew Bender & Company Inc.
[9] Aguilera, R. 1995. Naturally Fractured Reservoirs, Tulsa: PennWell Books. p.521. [10] Brown, M., Ozkan, E., Raghavan, R., and Kazemi, H. 2009. Practical Solutions for Pressure
Transient Responses of Fractured Horizontal Wells in Unconventional Reservoirs. Paper SPE 125043 presented at the 2009 SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, 4-7 October.
[11] Kazemi, H. 1969. Pressure Transient Analysis of Naturally Fractured Reservoirs with Uniform Fracture Distributions. Soc. Pet. Eng. Jour. (Dec.) 451-461: Trans., AIME, Vol. 261.
[12] de Swan-O, A. 1976. Analytical Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing. Soc. Pet. Eng. Jour. (June) 117-122, Trans., AIME, Vol. 261.
[13] Serra, K., Reynolds, A. C., and Raghavan, R. 1983. New Pressure Transient Analysis Methods for Naturally Fractured Reservoirs. Jour. Pet. Tech.:2271-2283.
[14] Wattenbarger, R. A., El-Banbi, A. H., Villegas, M. E., and Maggard, J. B. 1998. Production Analysis of Linear Flow into Fractured Tight Gas Wells. Paper SPE 39931 presented at the 1998 Rocky Mountain Regional/Low Permeability Reservoirs Symposium and Exhibition, Denver, USA, 5-8 April.
[15] Chen, C. C., and Raghavan, R. 1997. A Multiply-Fractured Horizontal Well in a Rectangular Drainage Region. SPE J. (2): 455-465. SPE 37072 PA.
[16] Fekete reference material, 2015, Dual Porosity. http://www.fekete.com/SAN/WebHelp/FeketeHarmony/Harmony_WebHelp/Content/HTML_Files/Reference_Material/General_Concepts/Dual_Porosity.htm, sited: May 1st 2015.
[17] Nobakht, M., Clarkson, C., and Kaviani, D., 2011, New Type Curves for Analyzing Horizontal Well with Multiple Fractures in Shale Gas Reservoirs. Paper CSUG/SPE 149397 presented at the Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, 15-17 November.
[18] Ozkan, E., Brown, M., Raghavan, R., and Kazemi, H. 2009. Comparison of Fractured Horizontal –Well Performance in Conventional and Unconventional Reservoirs. Paper SPE 121290 presented at the 2009 SPE Western Regional Meeting, San Jose, California, USA, 24-26 March.
[19] Stalgorova, E., and Mattar, L. 2012. Practical Analytical Model to Simulate Production of Horizontal Wells with Branch Fractures. Paper SPE 162515 presented at the SPE Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, 30 October – 1 November.
[20] Daneshy, A. A. 2003. Off Balance Growth: A New Concept in Hydraulic Fracturing. Journal of Petroleum Technology 55(4): 78-85. SPE 80992-MS. http:dx.doi.org/10.2118/80992-MS.
[21] Arps, J. J. 1945. Analysis of Decline Curves. Trans. AIME, 160, 228. [22] Fetkovich, M. J. 1980. Decline Curve Analysis using Type Curves. JPT (June), 1065. [23] Blasingame, T. A., McGray, T. I., Lee, W. J. 1991. Decline Curve Analysis for Variable
Pressure Drop/Variable Flow Rate Systems. Paper SPE 21513 presented at the SPE Gas Technology Symposium, 23-24 January.
[24] Agarwal, R. G., Gardner, D. C., Kleinsteiber, S. W. and Fussell, D. D. 1998. Analyzing Well Production Data Using Combined Type Curve and Decline Curve Concepts. Paper SPE 57916 presented at the 1998 SPE Annual Technical Conference and Exhibition, New Orleans, 27-30 September.
[25] Batchelor, G. K. 1967. An Introduction to Fluid Dynamics. Cambridge: Cambridge Mathematical Library.
[26] Darcy, H. 1856. Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris. [27] Bear, J., Tsang, C-F., and De Marsily, G. 2012. Flow and Contaminant Transport in
Fractured Rock. San Diego: Academic Press Inc. [28] Carman, P. C. 1956. Flow of Gases Through Porous Media. New York City: Academic Press
Inc. [29] Timur, A. 1968. An Investigation of Permeability, Porosity, and Residual Water Saturation
Relationships for Sandstone Reservoirs. The Log Analyst 9 (4). [30] Gates, I. D. 2011. Basic Reservoir Engineering. Dubuque: Kendall Hunt Publishing
Company. [31] Doublet, L. E., Pande, P. K., McCollum, T. J., Blasingame, T. A. 1994. Decline Curve
Analysis Using Type Curves-Analysis of Oil Well Production Data Using Material Balance Time Application to Field Cases. Paper SPE 28688 was presented at the 1994 Petroleum Conference and Exhibition of Mexico, Veracruz, Mexico, 10-13 October. http://dx.doi.org.ezproxy.lib.ucalgary.ca/10.2118/28688-MS
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CHAPTER 6: CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
The main objective of this study was to optimize the hydraulic fracture design during multi-
stages hydraulic fracture in horizontal well of tight gas formations with pre-exiting natural
fractures by determining the stimulated rock volume (SRV) characteristics such as enhanced
permeability, fracture spacing, pressure and in-situ stress changes profile during hydraulic
fracturing and production. To meet the objective, the study was divided into three different parts.
In the first part, the impact of SRV dimensions and Young’s modulus on the SRV effective
permeability during hydraulic fracturing using a 3D finite element analysis (Abaqus FEA) was
evaluated. The first part also included an investigation of fracture aperture, spacing, and number
within SRV using a new semi-analytical approach.
The second part investigated the impact of rock mechanical properties and injected volume
during hydraulic fracturing on SRV dimensions using a new analytical model. The model was
calibrated using microseismic data.
The third part explored a nonlinear diffusivity PDE solution using Matlab PDE nonlinear and
IHS Harmony to analyze field gas flow rate and pressure. The third part solved SRV permeability,
pressure, and porosity as a function of distance and time, and gas flow rate with field data.
The novel aspects of the thesis are as follows. First, for the first time, the developed workflow
using the 3D finite element analysis and the semi-analytical approach to characterize the fracture
network characteristics within the SRV during hydraulic fracturing was applied for the Glauconitic
Formation (Hoadley, AB). Second, this study establishes a new analytical SRV dimensions model
that combines rock mechanical properties and injected volume during hydraulic fracturing and
uses microseismic monitoring data for calibration. Third, for the first time the nonlinear diffusivity
PDE solution was solved to determine the SRV permeability, pressure, and porosity as a function
of distance and time and then the solutions are compared with the RTA simulator (IHS Harmony)
results.
206
From this research, several conclusions have been made:
1. Finite element analysis shows that a reduction of Young’s modulus decreases the effective
permeability. A reduction of SRV dimensions by 10% increases the effective permeability
within SRV and decreases the pressure drop along SRV length.
2. A hydraulic fracture induces an increase in the total in-situ stress values. Changes in the total
in-situ stresses calculated by the finite element analysis are overestimated. The overestimated
in-situ stresses result from the unavailability of core testing on Biot’s constant and the Biot’s
constant is assumed equal to unity. This implies that the finite element analysis calculates the
maximum impact of hydraulic fracturing on the increase of in-situ stresses. It also implies that
the total in-situ stresses increase in the field induced by hydraulic fracturing is lower than the
in-situ stress increase calculated by the finite element analysis.
3. The new semi-analytical approach results reveal that a reduction of Young’s modulus
decreases the number of major fractures for constant fracture aperture. This implies that the
harder the rock, it is easier to be hydraulically fractured.
4. SRV growth is not apparent for some of hydraulic fracture stages. In some stages, microseismic
events are not triggered in the proximity of horizontal wellbore due to effect of depleted zones
surrounding old wellbores near the horizontal wellbore. This implies that the hydraulic fracture
fluid may grow toward neighboring wells and increase the pressure within the depleted zone
without creating shear failure and consequent microseismic events.
5. Some SRV dimensions are shorter than interpreted SRV dimensions via microseismic due to
the presence of depleted zones around old wellbores. During hydraulic fracturing, the injection
fluid reopens natural fractures in proximity of the depleted zone which triggers microseismic
events. The results suggest that these reopened natural fractures do not contribute to the gas
production.
6. The changes of the total stress and their impact on SRV dimensions reveal that total stresses
must be included to avoid overestimation of the dimensions of the SRV.
7. The nonlinear PDE model derived for the SRV yields results that are consistent with the field
gas production profiles. The only history match parameter adjusted to match the field data was
the total compressibility. The theory provides a starting point for multidimensional methods to
generate type curves for tight gas systems.
207
8. IHS Harmony results with constant field SRV half-length of 87 m and matrix permeability of
6.5 x10-5 mD produce similar SRV permeability during production to the SRV permeability
from finite element analysis during hydraulic fracturing.
9. The effective permeability of the SRV during hydraulic fracturing from the FEA is estimated
to be of order of several tens of Darcies (23.4 D).
10. The SRV effective permeability during production from the new nonlinear PDE theory is of
the order of several tens of Darcies and it varies both spatially and temporally from 23.4 D (at
early production time and SRV boundary) to 0.0007 D (at late production time). This reveals
that the closure of the hydraulic fracture network occurs and the effect on permeability is
significant.
11. IHS Harmony analysis only produces one value of SRV effective permeability for all
production time and SRV distance. The SRV effective permeability from the best case of IHS
Harmony with constant field SRV half-length of 87 m and matrix permeability of 6.5 x10-5
mD is 13.5 D for PSS model and 22.3 D for sticks, slabs, and cubes models.
6.2 Recommendations
The recommendations for future research are:
1. Conduct core testing from a nearby well of Glauconitic Formation in Hoadley, AB to determine
the rock mechanical and the natural fractures properties for better and more accurate study.
2. Apply the finite element analysis on different reservoirs that have different values of Young’s
modulus and SRV dimensions to determine their impact on the SRV effective permeability.
3. Build our own elements in Abaqus to code cohesive elements to model hydraulic fractures to
implicitly model coupled pressure/deformation to model progressive damage of mechanical
strength, hydraulic conductivity, flow of fracturing fluid during opening fracture, and
permeability as a function of distance and time during hydraulic fracturing
4. Model hydraulic fracture propagation when intersecting a natural fracture as a function of
codes % Problem Parameters using average viscosity and average Z. All units in % oilfield. % SRV and gas properties miu=0.0198319; % gas viscosity in cP, using Lee, Gonzales and Eakin equation http://checalc.com/solved/gasVisc.html at gas gravity 0.8, P=2900 psi (20MPa), T=158 F(70C), N2=0.05 mole %, CO2=0.0218 mole %, ,H2S=0 mole %. por=0.16; % porosity after hydraulic fracturing ct=4.024E-04; % ct in 1/psi that matches initial flow rates for por=0.16 S=7043.812016; % Carman-Kozeny specific surface, m2/m3 % Geometry and Mesh % For SRV rectangle, the geometry and mesh are defined as shown below: length= 570.866; % SRV length, ft (174 m) width= 196.85; % SRV width, ft (60 m) % For wellbore production rectangle, the geometry and mesh are defined as shown below: Wlength= 3.28084; % wellbore producing port length, ft (1 m) Wwidth= 3.28084; % wellbore producing port width, ft (1 m) % Define the rectangle by giving the 4 x-locations followed by the 4 % y-locations of the corners. % Rectangle is code 3, 4 sides, followed by x-coordinates and then y-coordinates % Rectangle SRV geometry R1 = [3 4 0 width width 0 0 0 length length]'; % Rectangle wellbore production edges geometry R2=[3 4 96.78458 100.06542 100.06542 96.78458 283.79458 283.79458 287.08 287.08]'; % Pad R2 with zeros to enable concatenation with R1 and R2 geom = [R1,R2]; % Names for the two geometric objects ns = (char('R1','R2'))'; % Set formula sf='R1-R2'; % Use this example: Deflection of a Piezoelectric Actuator % Create geometry g = decsg(geom,sf,ns); % View geometry % Plot the geometry and display the edge labels for use in the boundary % condition definition. figure;
210
pdegplot(g, 'edgeLabels', 'on'); axis([0 600 0 600]); % in ft title 'Geometry With Edge Labels Displayed'; % Create the triangular mesh on the rectangular with approximately % ten elements in each direction. hmax = 16.4; % element sizehmax = 5 m (16.4 ft) within SRV, no need to use refinemesh [p, e, t] = initmesh(g, 'Hmax', hmax); figure; pdeplot(p,e,t); axis([0 600 0 600]); % in ft title 'SRV With Triangular Element Mesh' xlabel 'X-coordinate, feet' ylabel 'Y-coordinate, feet' % Boundary Conditions % Use PDE problem setup-BC-Examples-Applying constant BC % Create a pde entity for a PDE with a single dependent variable numberOfPDE = 1; pb = pde(numberOfPDE); % Scalar problem % Create a geometry entity pg = pdeGeometryFromEdges(g); % Create geometry object % BC: PDE problem setup-BC-examples-applying constant BC % Boundary conditions for P wellbore assumed to be equal average production % during 8 months after stabilize % welllbore P 500.23516 psi (3.449 MPa) need to convert P to u at wellbore bc3 = pdeBoundaryConditions(pg.Edges(3),'u',16224497.3); bc4 = pdeBoundaryConditions(pg.Edges(4),'u',16224497.3); bc5 = pdeBoundaryConditions(pg.Edges(5),'u',16224497.3); bc8 = pdeBoundaryConditions(pg.Edges(8),'u',16224497.3); % Put all the boundary conditions into a problem container. pb.BoundaryConditions =[bc3,bc4,bc5,bc8]; % All boundary conditions. % Solve the parabolic PDE with these boundary conditions with the PDE % nonlinear coefficients d and c, the nonlinear solver pdenonlin must be used to obtain the solution. % Definition of PDE Coefficients % The expressions for the coefficients required by the PDE toolbox can % easily be identified by comparing the equation with the scalar parabolic % equation in the PDE toolbox documentation % Permeability as a function of pressure % c=k, PDE nonlinear c coefficient, assumes kx=ky=kz, cx=cy=cz % c-coefficient using pseudo p c=sprintf('((%g.*(1-%g.*(2900.75-0.124190785.*(u.^0.5)))).^3)./(5.*(%g.^2).*(1-(%g.*(1-%g.*(2900.75-0.124190785.*(u.^0.5)))).^2)).*(10.^10)',por,ct,S,por,ct); % it works, c is in m2 originally needs to convert to mD by multiply 10^15. U0=2900.75 psi (20 MPa)
211
%c equation above is following the example of "Nonlinear Heat Transfer In a %Thin Plate" when a-coefficient is a function of u a= 0; % if a is not 0 the solution plot profile is more realistic f= 0; % if f is not 0 the solution plot profile is more realistic % d-coefficient using pseudo p d= sprintf('(%g.*(1-%g.*(2900.75-0.124190785.*(u.^0.5))).*%g.*%g)./0.00005', por, ct, miu, ct); % we use 0.00005 to convert to field units, d=porf*miu*ct units are second. % Transient solution endTime = 6300; % Production in 828 days, hours tlist = 0:157.5:endTime; % Set the initial pressure of all nodes to initial reservoir pressure, 9 % MPa % Initial condition for pore pressure definition u0 =5.45562928746E+08; % initial pressure of all nodes average pressure along SRV after HF (start of production) in psi (20 MPa) rtol = 1.0e-3; atol = 1.0e-4; % The transient solver parabolic automatically handles both linear % and nonlinear problems, such as this one. u = parabolic(u0, tlist, pb,p,e,t,c,a,f,d); figure; % Post processing Pressure Pressure=0.124190785.*(u.^0.5); plot(tlist, Pressure(:,:)); grid on title 'Pressure as a Function of Time' xlabel 'Time, hours' ylabel 'Pressure, psi' figure; % Plot Pressure pdeplot(p, e, t, 'xydata', Pressure(:,end), 'contour', 'on', 'colormap', 'jet', 'mesh', 'on'); title(sprintf('Pressure In SRV (psi) (%d hours)\n', ... tlist(1,end))); % tlist(1,end), means end means final time or 19872 hours it is the same with tlist(end,end), if tlist(1,1) means time 1 or 0 hours it is the same with tlist(end,1) xlabel 'X-coordinate, feet' ylabel 'Y-coordinate, feet' axis ([0 600 0 600]); figure;
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% Porosity porf=sprintf('%g.*(1-%g.*(2900.75-0.124190785.*(u.^0.5)))', por, ct); % porosity final=por*(1-ct*(u0-u)) in fraction porf=por*(1-ct*(2900.75-0.124190785.*(u.^0.5))); % Plot porosity pdeplot(p, e, t, 'xydata', porf(:,end), 'contour', 'on', 'colormap', 'jet', 'mesh', 'on'); title(sprintf('Porosity In SRV (fraction) (%d hours)\n', ... tlist(1,end))); % tlist(1,end), means end means final time or 19872 hours it is the same with tlist(end,end), if tlist(1,1) means time 1 or 0 hours it is the same with tlist(end,1) xlabel 'X-coordinate, feet' ylabel 'Y-coordinate, feet' axis ([0 600 0 600]); figure; % Plot porosity vs time plot(tlist, porf(:,:)); title 'Porosity As a Function of time' xlabel 'Time, hours' ylabel 'Porosity, fraction' figure; % Plot permeability vs time k=((porf.^3)./(5.*S.*S.*((1-porf).^2))).*(10.^15); plot(tlist,k(:,:)); title 'Permeability As a Function of time' xlabel 'Time, hours' ylabel 'Permeability, mD' figure; % Plot Permeability vs distance at particular time pdeplot(p, e, t, 'xydata', k(:,end), 'contour', 'on', 'colormap', 'jet', 'mesh', 'on'); title(sprintf('Permeability In SRV (mD) (%d hours)\n', ... tlist(1,end))); % tlist(1,end), means end means final time or 19872 hours it is the same with tlist(end,end), if tlist(1,1) means time 1 or 0 hours it is the same with tlist(end,1) xlabel 'X-coordinate, feet' ylabel 'Y-coordinate, feet' axis ([0 600 0 600]); % Calculate dp/dx and dp/dy at each time separately [ux1,uy1] = pdegrad(p,t,u(:,1)); unx1 = pdeprtni(p,t,ux1); dpdx1=0.06209.*(u(:,1).^(-0.5)).*unx1; uny1 = pdeprtni(p,t,uy1); dpdy1=0.06209.*(u(:,1).^(-0.5)).*uny1; [ux2,uy2] = pdegrad(p,t,u(:,2)); unx2 = pdeprtni(p,t,ux2);
