Modelling the Impact of Stacking Patterns and Fractures on ...

Maranu Ricardo

Master of Science Thesis, August 16, 2016

Modelling the Impact of Stacking Patterns and Fractures on the Connectivity of Deltaic Reservoirs

Modelling the Impact of Stacking Patterns and Fractures on the Connectivity of Deltaic Reservoirs

By

Maranu Ricardo

in partial fulfilment of the requirements for the degree of

Master of Science

in Petroleum Engineering and Geosciences

at the Delft University of Technology,

to be defended publicly on Tuesday, August 16, 2016 at 14:00 PM.

Supervisor: Dr. J. E. A. Storms, Applied Geology, TU Delft

Thesis committee: Dr. A. Barnhoorn, Applied Geophysics & Petrophysics, TU Delft

Dr. N. J. Hardebol, Applied Geology, TU Delft

H. van der Vegt, Msc., Applied Geology, TU Delft

An electronic version of this thesis is available at http://repository.tudelft.nl/.

Track Reservoir Geology Department of Petroleum Engineering and Geosciences Faculty Civil Engineering and Geosciences, Delft University of Technology Delft, the Netherlands

http://repository.tudelft.nl/

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Abstract Deltaic reservoirs are important reservoirs for the oil and gas production. Most of the hydrocarbons

produced from deltaic reservoirs are obtained from the matrix or primary porosity. Besides primary

porosity, secondary porosity, formed after deposition takes place, can have a positive contribution on

hydrocarbon production. One of the processes that form secondary porosity is fracturing in addition

with the addition of dissolved grains and cements. However, the role of fracturing is surprisingly

unknown for one of the leading reservoir types in the world.

Stacking of sediment packages is cyclic base level change causes the stacking of sediment

packages. It commonly occurs in the deltaic system and gives rise to a high degree of interaction

between sand and shale. This interior interaction between sand and shale will affect the connectivity

of the reservoir, especially vertical connectivity (it could lead to permeability baffles or barriers).

Sand to sand contacts are the favourable spots for connectivity to exist, hence, it is impractical to

just rely on the sand to sand contacts to maximize the hydrocarbon production.

Fractures might be one of the factors that influence the reservoir connectivity besides the sandstone

to sandstone contacts, especially if fractures are open and not filled by cements or minerals. The

presence of fractures only gives small additions in pore volume, but the biggest impact is that the

effective permeability can be increased significantly, affecting the hydrocarbon production.

The permeability of fractures is very dependent on the fracture connectivity. Fracture connectivity is

a function of fracture intensity, geometry, and orientation. The combination of these parameters

mentioned before play a significant role for the development of self-connected clusters, which are

networks of connected fractures. The more self-connected clusters within the field, the more

hydrocarbons will be recovered (with the assumption of open fractures).

The role of fracture connectivity is really dependent on the sandstone architecture in the deltaic

reservoirs. It is significant when the reservoir distribution is scattered and no major connected

sandstone bodies are formed. The occurrence of fractures, indeed, will increase the interconnectivity

of the sand bodies and the effectiveness in terms of reservoir productivity. However, the role of

fractures is less crucial on an evenly distributed sandstone together with the existence of major

connected sandstone bodies, since the interconnectivity within the sandstone is already preserved

as a factor of sedimentological domain. Fractures may only improve the effectiveness of reservoir

productivity when connecting the major bodies to the non-connected minor sandstone bodies.

Acknowledgements I would like to thank my supervisors Dr. Joep Storms for his expertise in Sedimentology and all his

guidance, suggestions, feedbacks and the time he gives during the work of this study. Dr. Nico

Hardebol for his expertise in structural geology that help me a lot in understanding the conceptual of

all relevant knowledge related to this study, thank you for your persistent suggestions and reviews to

my work. I would like to thank Helena van der Vegt for her guidance and help during the beginning of

my working period and also for being my Assessments Committee. I would also like to thank Dr.

Auke Barnhoorn for being in my Assessments Committee.

Special thanks to Neal Josephson and Golder Associates for the use of FracMan.

Special thanks to Doan, Alex, Andro, Thio, Theo, Abi, Dimas, Barnaby, Paul, Rahul, and Fida, for

the chats, the coffee breaks, the dinner, the football, the trip, and the laughs we share together

during the last two years. I also would like to thank all my classmates in Reservoir Geology and

Petroleum Engineering, and the Indonesian Student Society (PPI Delft) for their friendship and the

joyful moments while living in the Netherlands. Prof. Dr. Giovanni Bertotti for the one time discussion

that give me deeper understanding about rock mechanics. Furthermore I would also like to thank all

of my friends and family, especially my brothers. Last, but not least, I would like to express my

sincere gratitude to my parents, for their constant pray and support in my whole life. I could not have

finished my study without your love and support.

God, for His bless and guidance throughout my entire life, I’m grateful for all the opportunities You

have given to me.

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Contents Abstract ......................................................................................................................................................... 5

Acknowledgements ....................................................................................................................................... 6

Contents ........................................................................................................................................................ 7

Figures ........................................................................................................................................................... 9

Tables .......................................................................................................................................................... 11

Acronyms/Abbreviations .............................................................................................................................. 12

1. Introduction ......................................................................................................................................... 13

1.1. Background/Motivation .................................................................................................................. 13

1.2. Research Objectives ..................................................................................................................... 14

2. Theoretical Background ...................................................................................................................... 16

2.1. Fracture Stratigraphy ..................................................................................................................... 16

2.2. Stratabound and Non-Stratabound Fracture ................................................................................. 16

2.3. Fracture Networks ......................................................................................................................... 17

2.3. Fracture Connectivity .................................................................................................................... 21

3. Methodology ....................................................................................................................................... 22

3.1. Overall Workflow Outline ............................................................................................................... 22

3.2. Sediment Architecture Model ........................................................................................................ 23

3.3. DFN Distribution ............................................................................................................................ 29

3.4. Connectivity Analysis .................................................................................................................... 33

4. Results ................................................................................................................................................ 35

4.1. Properties Definition ...................................................................................................................... 35

4.2. Fracture Probability ....................................................................................................................... 39

4.3. Base Case Discrete Fracture Network Model ............................................................................... 41

4.4. Facies Architecture ........................................................................................................................ 43

4.5. Self-Connected Clusters Analysis ................................................................................................. 45

4.6. Sensitivity Analysis of Self-Connected Clusters ............................................................................ 47

5. Discussion ........................................................................................................................................... 49

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5.1. Connectivity Analysis of the Deltaic reservoirs ............................................................................. 49

5.2. Reservoir Evaluation ..................................................................................................................... 53

6. Conclusions ........................................................................................................................................ 59

7. Recommendations .............................................................................................................................. 61

Bibliography ................................................................................................................................................. 62

Appendix ..................................................................................................................................................... 67

A. Discrete Fracture Network Distribution ............................................................................................ 67

B. Connectivity Analysis ....................................................................................................................... 69

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Figures Figure 1. Schematic diagram of stratabound (a) and non-stratabound fractures (b) and their major

features (Odling et al., 1999). ...................................................................................................................... 17

Figure 2. Joint shapes in Poisson plane model (Veneziano, 1978). ............................................................ 19

Figure 3. Schematic workflow of this study ................................................................................................. 23

Figure 4. Stacking of parasequence sub-domain to generate progradational sequence model (Lipus,

2015) ........................................................................................................................................................... 25

Figure 5. Cross section of schematic drawing of eroding process in stacking the individual

parasequence in Delft3D. Yellow and orange colored grid cells represent arbitrary cell attributes of

individual parasequence (Lipus, 2015). ....................................................................................................... 26

Figure 6. Example of a cross section after stacking and incision (D50 = 100 μm) (Lipus, 2015). ............... 26

Figure 7. Relationship between standard deviation particle size distribution and the porosity from

field observations (Lipus, 2015) after (Takebayashi and Kamito, 2014). ..................................................... 28

Figure 8. Function used in defining Fracture Potential ................................................................................ 30

Figure 9. Relationship between the dimensionality of the intensity measurement and sampling

structure or measurement region (modified after Dershowitz (1984)). ........................................................ 32

Figure 10. S-N cross section of Brittleness Index of retrogradational stacking pattern ............................... 36

Figure 11. S-N cross section of porosity ...................................................................................................... 36

Figure 12. S-N cross section of lithology. Red represents sandstone, yellow represents shaly sand,

green represents shale ................................................................................................................................ 37

Figure 13. S-N cross section of initial and vertical upscaled model comparison of lithology ....................... 38

Figure 14. S-N cross section of vertical upscale of Brittleness Index .......................................................... 39

Figure 15. S-N cross section of vertical upscaled porosity .......................................................................... 39

Figure 16. Relationship between Fracture Potential with cell height and BI ................................................ 40

Figure 17. Relationship between Fracture Proneness with porosity and lithology ...................................... 41

Figure 18. Histogram of cell height which represents cell thickness ........................................................... 42

Figure 19. Realization of base case scenario of DFN (P32 = 0.1 m2/m3 global fracture intensity) ............ 43

Figure 20. Cross section of lithology that shows facies distribution of deltaic environment ........................ 44

Figure 21. 3D Visualization of connected sand bodies. Variation in color indicates non-connected

sand bodies. ................................................................................................................................................ 45

Figure 22. Cross section that shows natural fracture may connect isolated sandstone bodies .................. 46

Figure 23. Results of sensitivity analysis on self-connected clusters using 0.3 m2/m3 P32 global

fracture intensity .......................................................................................................................................... 48

Figure 24. The top picture is the scattered distribution of sand bodies with shaly sand and shale are

excluded (for the visualization purpose). The bottom picture is 3D view of one of fracture cluster

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(created from DFN using 0.3 m2/m3 P32 global fracture intensity) connecting the sand bodies, where

shaly sand and shale are excluded. ............................................................................................................ 50

Figure 25. 3D view of sand bodies distribution with the exclusion of other lithologies (top picture). 3D

view of self-connected clusters (created from DFN using 0.4 m2/m3 P32 global fracture intensity)

connecting the sand bodies (bottom picture). ............................................................................................. 51

Figure 26. The distribution of sand bodies of Volume 1 that indicates a permeability baffle. ...................... 52

Figure 27. Comparison of sandstone architecture for 60% cut-off and 50% cut-off model. ........................ 54

Figure 28. Comparison of sandstone architecture for 40% cut-off and 50% cut-off model. ........................ 55

Figure 29. 3D view of sand bodies distribution with the exclusion of other lithologies (top picture) for

the 60% cut-off model. 3D view of one of self-connected clusters (created from DFN using 0.3 m2/m3

P32 global fracture intensity) connecting the sand bodies (bottom picture). ............................................... 57

Figure 30. 3D view of sand bodies distribution with the exclusion of other lithologies (top picture) for

the 40% cut-off model. 3D view of one of self-connected clusters (created from DFN using 0.3 m2/m3

P32 global fracture intensity) connecting the sand bodies (bottom picture). ............................................... 58

Figure 31. Detail dimensions for the sensitivity analysis of self-connected clusters for Two Fracture

Sets scenario ............................................................................................................................................... 67

Figure 32. Detail dimensions for the sensitivity analysis of self-connected clusters for the Minimum

Number of Fractures in a Cluster scenario .................................................................................................. 67

Figure 33. Detail dimensions for the sensitivity analysis of self-connected clusters for Aspect Ratio

scenario ....................................................................................................................................................... 68

Figure 34. Detail dimensions for the sensitivity analysis of self-connected clusters for Fracture Size

scenario ....................................................................................................................................................... 68

Figure 35. Detail dimensions for the sensitivity analysis of self-connected clusters for Fracture

Proneness scenario ..................................................................................................................................... 68

Figure 36. Sandstone distribution of the connected sandstone bodies for the 35% sand model (with

cut-off of minimum 100 cells to form sand body). It shows evenly distributed sandstone throughout

the entire area that leads to excellent sandstone interconnectivity caused by sedimentological

domain. ........................................................................................................................................................ 69

Figure 37. Sandstone distribution of the connected sandstone bodies for the 35% sand model with

the self-connected clusters (created from DFN using 0.3 m2/m3 P32 global fracture intensity). The

occurrence of fractures will not give significant impact to the interconnectivity of sand bodies. ................. 69

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Tables Table 1. Two Delft3D model input used in this study. The D50 grain size mean diameter is being

used to describe the sediment composition for all the classes. ................................................................... 24

Table 2. Base case input for DFN distribution ............................................................................................. 43

Table 3. Statistics for connected volumes of sandstone for the base case model. ..................................... 45

Table 4. Detail dimensions of self-connected fractures for the base case scenario .................................... 47

Table 5. DFN input parameters in the base case scenario (model input) and variations of some

parameters for sensitivity analysis. Subparameters with italic letters are subjected to sensitivity

analysis. Red colors letters show the assigned values of subparameters for sensitivity analysis. .............. 47

Table 6. Detailed dimensions of self-connected fractures using 35% sand delta as an input. .................... 53

Table 7. Key statistics of sandstone distribution from models generated by using three different cut-

offs in defining the sandstone. ..................................................................................................................... 56

Table 8. Statistics for connected volume of sandstone from 35% sand delta model................................... 70

Table 9. Statistics for connected volumes of sandstone from 60% cut-off of sandstone definition

model ........................................................................................................................................................... 70

Table 10. Statistics for connected volumes of sandstone from 40% cut-off of sandstone definition

model ........................................................................................................................................................... 70

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Acronyms/Abbreviations BI Brittleness Index

CDF Cumulative Distribution Function

DFN Discrete Fracture Network

P32 Volumetric Fracture Intensity (m2/m3)

2D Two Dimensional

3D Three Dimensional

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1.

Introduction Around 30% of the global oil and gas reserves are from siliciclastic deltaic sediments (Tyler, 1992);

e.g. Mahakam delta, Niger delta, Mississippi delta, and Nile delta. In these reservoirs, the majority of

the hydrocarbons are present in the sandstone pores (primary porosity), which are connected

(primary permeability). Such sandstones are either connected or not connected. The latter implies

that shales are present between the sandstones bodies (either laterally or vertically). In case they

are connected, the connected volume of hydrocarbons is much larger, and the field will be easier to

produce with fewer production wells. Sandstone connectivity can be caused by sand-to-sand

contact, or by fractures, thereby increasing the potential connectivity of sandstone bodies. Nelson

(2001) stated that fractures can give positive influence to the reservoir attributes by providing

essential reservoir porosity and permeability plus assisting permeability in the existing producible

reservoir. Thus, fractures may cut through the shale beds to provide essential porosity and

permeability to the non-connected sandstone bodies in deltaic reservoirs. Natural permeability can

boosted up significantly if the fractures that cut through the reservoir are open (Laubach, 2003). In

this condition, when fractures provide essential permeability, the pattern of fluid flow is dependent on

the connectivity of the fracture network. This fracture network connectivity then becomes crucial for

field development as it significantly affects well productivity and recovery factor.

1.1. Background/Motivation

Adler and Thovert (1999) stated that fracture networks are usually formed as arrangements of the

individual properties of fractures and intersecting properties that normally intersect at random.

Moreover, fracture networks are really important for the development of naturally fractures

reservoirs. Unfortunately, with the current knowledge, it is really difficult to predict the fracture

network distributions; especially in the deltaic reservoirs, which are complex and heterogeneous.

Deltaic reservoirs typically show large sedimentological heterogeneities, which can be both vertical

and lateral (Choi et al., 2007). As a delta progrades, channels extent seawards and form

bifurcations. Simultaneously, avulsion upstream may cause channel abandonment and the initiation

on new channels. These processes are driven by a complex interaction of hydrodynamics,

morphodynamics, and external parameters such as base level change and sediment supply change.

Predicting local connectivity of channelized sand bodies is therefore very difficult in deltaic

environments (Willis and Fitris, 2012). With the recent developments in process-based modeling, it is P a g e | 13

possible to simulate geologically realistic delta deposits by simulating the above mentioned

interaction between hydrodynamics, morphodynamics, and allogenic forcing conditions. This study

uses a simulated prograding delta output that is created using the numerical model, Delft3D®

(Deltares, 2014). The grain size variabilities in the resulted model are explained into 5 different grain

sizes, it varies from clay, silt, very fine, fine, and medium sand.

Basically, in terms of reservoir connectivity, facies configuration in the deltaic reservoirs is the key in

order to determine the connectivity of high and low permeable areas. If one coarse grain

sedimentary bodies are bounded by another coarse grain bodies, the higher the degree of

interconnectivity between those bodies. However, if the coarse grain bodies are bounded by the very

fine-clay grain bodies, the higher the chances for those bodies are not connected. This condition is

not favorable in terms of hydrocarbon production and it will lead to higher production cost and lower

recovery factor. Nevertheless, natural fractures, formed after lithification of the rocks, may connect

sand bodies that are bounded by smaller grain and pore throat sizes facies in between them. If the

width of the fracture is not closed, so there is a path for fluid to flow and connect the two sand

bodies.

Given the process-based forward simulations of Delft3D model (grain size concentration); this study

aims to analyze connectivity of deltaic reservoirs based on connected fractures that are generated

during the Discrete Fracture Network (DFN) distribution in the deltaic reservoirs synthetic model.

1.2. Research Objectives

To deal with the aim of this study, two principal research objectives are introduced in this study. The

first objective of this study is to analyze the connectivity of high and low permeability sedimentary

bodies and the role of local fractures on the interconnectivity of sand bodies across fine grains flow

baffles or barriers. Grain size distributions may indicate high and low sedimentary bodies by defining

lithology of clastic rocks such as sandstone or shale. As commonly known, shale has a big role in

influencing fluid pathway or flow. Shale has the characteristic to block fluid pathway due to its small

grains that lead to small pore-throat sizes and create barriers for hydrocarbons to move. Another

flow pattern that occurs when dealing with low permeability sedimentary bodies is flow baffles. This

occurs due to fluid pathways of hydrocarbons are being partially or locally blocked by smaller grains

and pore-throat sizes.

In order to achieve the first research objective; three research approaches are being introduced. The

first one is to combine the output of process-based forward simulations, performed in Delft3D, to

construct reliable reservoir models in Petrel® (SCHLUMBERGER, 2015). The model built in Delft3D

and used as an input in Petrel is deltaic reservoirs model with grid cell dimensions of 50 m x 50 m x

30 cm with number of cells of 51 x 51 x 100. Since the vertical resolution from Delft3D is really high,

this model needs to be upscaled vertically to generate more reliable and handy model to be used in P a g e | 14

further processing where the DFN would be generated. The aim of this upscaling step is to equate

the resolution of fracture with vertical grid input, because 30 cm is relatively too small for fracture

size for the scope of this study.

The second research approach is to quantify the 3D stratigraphy of stacked sandy channel and

shaly intervals using data from process-based model. Resolution is the key in order to fulfill this

objective, instead of 30 cm vertical resolution, layer or bedding surfaces are built for each

sedimentary facies type that is derived from Delft3D model. As mentioned earlier, the input from the

Delft3D is only grain size distribution and this distribution, combined with geological knowledge, will

give a clear image or pattern of sedimentary facies in deltaic settings. Separating each facies into

one body or layer is the step needed to be performed in order to quantify the 3D stratigraphy of

stacked sandy channel and shaly intervals.

The last research approach is to generate the fracture network (DFN) and to analyze its connectivity

by conducting the fracture cluster analysis process. FracMan® (7.5 Version), a software developed

by Golder Associates Inc., is utilized to generate the fracture network and analyze the network

connectivity. The output from Delft3D (grain size distribution) is then derived into specific

sedimentary properties, which are related to mechanical properties of the rocks. This will be

translated directly into some fracture-controlled property. This property will be used as the key input

in the generation of a DFN. The resulting DFN will then be the main source of information for

FracMan to analyze the connectivity in the fracture network during fracture cluster analysis.

The second research objective of this study is to analyze the reservoir behavior based on the effects

of sedimentology and fractures on connectivity. It is really essential to understand the reservoir

behavior in this type of deltaic setting. Which one of sedimentology and fractures controlled the

development of fluid pathway is. Either rock matrix or fractures permeability might be great for the

hydrocarbon production, but both of them will give different development planning to maximize the

recovery. Especially in the complex depositional environment like deltaic setting, it requires

comprehensive analysis on reservoir behavior to reduce the risk in terms of exploration and

production.

To achieve this objective, volume of connected sand bodies will be generated and calculated in

Petrel. Based on this method, qualitative and quantitative analysis of reservoir distribution can be

conducted to give deeper insight on factors that are controlled interconnectivity in the sand bodies.

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2.

Theoretical Background 2.1. Fracture Stratigraphy

Literatures exist on methodical confinement of fractures to a single or a group of several

sedimentary beds in well-stratified sequences (Narr and Suppe, 1991; Becker and Gross, 1996;

Laubach et al., 1998; Odling et al., 1999; Bai and Pollard, 2000b; Underwood et al., 2003; Bertotti et

al., 2007). This was followed by the evolution of the concept of a single fracture unit. A fracture unit

is considered as a set of one or more sedimentary layers that have similar fracture attribute

distribution. Fracture growth and fracture pattern development can be estimated or predicted by

using fracture unit thickness as the main component (Laubach et al., 2009). “Mechanical stratigraphy

subdivides stratified rocks into discrete intervals (mechanical units) according to their material

properties; e.g. tensile strength, elastic stiffness, brittleness, and fracture mechanics properties”,

(Laubach et al., 2009). Mechanical stratigraphy is a result of depositional composition and structure,

where chemical and mechanical changes occurred in the rock composition, texture, and interfaces

after deposition of the rock (Laubach et al., 2009).

On the other hand, “fracture stratigraphy subdivides rocks into intervals according to the vertical

extent, intensity, or some other observed fracture attribute and reflects a specific loading history and

mechanical stratigraphy during failure”, (Laubach et al., 2009). These two terms are sometimes

mixed up, but both are different. Mechanical stratigraphy reflects diagenesis and fracture

stratigraphy development related with loading history, and thus differs from fracture stratigraphy

(Laubach et al., 2009).

2.2. Stratabound and Non-Stratabound Fracture

There are two hypothetical end-member scheme classification depending on lithological layering;

stratabound and non-stratabound fractures systems (Odling et al., 1999). Stratabound systems

(Figure 1a) are established when there is little mechanical coupling between one lithological layer to

an adjacent layer that result in fracture growth confined to a single layer, which is terminated by

bedding surfaces. Stacked layers are the main component for 3D fracture systems with each layer

having its own fracture system. The fracture spacing is independent from adjacent layers. Such a

system occurs in rocks with dominant layered influence that are decoupled mechanically by weak

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bound crossway bedding planes or interbedded weak and strong beds. Examples are interbedded

sandstones, limestones and shales, and well bedded sandstones or limestones.

Figure 1. Schematic diagram of stratabound (a) and non-stratabound fractures (b) and their major features (Odling et al., 1999).

Non-strata bound systems (Figure 1b) occur in more massive lithologies with fracture dimensions

covering a wider range. Typical characteristics for these systems are that fractures are not confined

to a layer and exhibit growth across layers clustered in spacing (Odling et al., 1999).

Both stratabound and non-stratabound fracture systems of all stages can occur in nature. “Besides,

a fracture system may have a hierarchical structure, with stratabound and non-stratabound systems

dominating within different scale ranges, controlled by layer thickness on different scales from

individual beds to basin or crustal thicknesses”, (Odling et al., 1999).

2.3. Fracture Networks

“A group of individual fractures that may or may not cut across to each other is defined as a fracture

network” (Adler and Thovert, 1999). A fracture network can be recognized by detecting its

intersection with earth exterior features, such as outcrops, cliffs and ground surfaces. These

intersections leave marks in exterior features and are called as traces or chords while the

intersection of a fracture network with an observation surface is defined as a trace map (Adler and

Thovert, 1999). Two basic concepts of topology may then be introduced to give better understanding

in describing fracture networks, specifically percolation and solid blocks (Adler and Thovert, 1999).

Percolation is described as those fractures in the fracture network that connect from one side to the

opposite site of the observation area. Percolation is clearly essential in determining the pathway of

the fluid as fluid can flow as long as the network is percolating. Furthermore, the concept of

percolation is widely used as one of the methods to analyze fracture connectivity (Stauffer, 1985;

Berkowitz, 1995; Belayneh et al., 2006). A solid block is basically a part of the solid where a series of

fractures lies and is separated from the rest of the solid matrix. With respect to an oil fields, this is

the block where accumulated oil flows through the fracture network to the well.

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Adler and Thovert (1999) stated that to geometrically characterize the fracture networks, the

properties are divided into two classes. The first class is individual fracture properties and the

second one refers to fracture network properties. Statistical distributions of size, shape or orientation

are typical parameters that fall into the first category. The second category includes the degree of

fracturing and spatial organization (for instance cluster), the presence of groups of fractures that

share parallel orientation or the hierarchical organization of such groups. This first category is similar

to the distributional parameter, proposed for characterization of rock joints as described by

Dershowitz (1984). (Dershowitz, 1984) stated that the joint characterization is classified into three

groups: geometric characteristics, such as shape, size, location, orientation, and planarity of joints;

distributional parameters, such as distributions of joint shape, size, orientation, location, and

planarity; joint properties that include joint stiffness, strength, effective hydraulic aperture, and

aperture.

The description on rock joints (Dershowitz, 1984) emphasizes more on individual properties,

whereas the explanation on fracture networks (Adler and Thovert, 1999) emphasizes on about the

properties of fracture networks. In the following section, individual fracture properties will be

explained in detail based on the Dershowitz’s rock joints description and the later explanation will be

Adler and Thovert’s study.

2.3.1. Individual Fracture Properties

2.3.1.1. Geometric Characteristics

Fracture Shape

Due to large variations in the geological conditions, it is commonly assumed that fractures are

represented as basic shapes since to have more tractable analysis and simulation of the fracture

systems (Dershowitz, 1984). It seems difficult to observe the 3D shape of a fracture in the rock

mass. To overcome that, assumptions of simplifying the shape of fractures need to be implemented.

Shapes are used to give a close illustration of the fractures; hence, the common shapes that used in

the fracture modeling are polygons, circles, or ellipses.

Fracture Size

Fractures relate to a wide range of scales from centimeters to hundreds of meters. Based on that,

fracture size can be categorized into two classed; unbounded and bounded (Dershowitz, 1984).

Unbounded fracture size refers to fractures that range beyond the scale or go across the entire rock

mass. As for the bounded fracture size, it can be characterized by the fracture area, or, for regular

joint shapes, by joint radius or join edge dimensions. Fracture size for the bounded type is mostly

assumed to be either constant or stochastic. The assumption of stochastic fracture size is mostly

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used for the 3D fracture size predictions, defined by a joint radius or edge dimension distribution

(Einstein et al., 1979; Warburton, 1980a, b).

Fracture Orientation

Fractures orientation is usually described with two parameters; dip direction (the angle of azimuth of

fracture surface line with respect to the north) and dip (the angle of fracture surface line with respect

to the horizontal plane). Fracture orientation can be expressed by the correlation among the

orientations of all joints within a rock mass. The orientation of fractures can be specified with two

processes; deterministic and stochastic processes (Dershowitz, 1984). The deterministic process is

usually characterized by parallel fracturing, where the orientation of fractures are relatively identical.

Groups of fractures with this kind of behavior are referred to as “fracture sets”. A fracture network,

may have numerous fracture sets, however a maximum of three fracture sets is the most common

assumption. Probability distributions are used to specify the stochastic fracture orientation. Another

used of fracture set is applied for this case; it refers to collection of fractures that used a single

distribution about a mean value to specify it (Dershowitz, 1979).

2.3.1.2. Distributional Parameters

Fracture Shape

Constant fracture shape is the most used assumption in modeling the fracture network. The forming

of polygons by a system of Poisson lines in a plane (Veneziano, 1978) can be used as an example

to describe the stochastic distribution of fracture shapes (Figure 2).

Figure 2. Joint shapes in Poisson plane model (Veneziano, 1978).

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Fracture Size

Fracture sizes measured only in 2D show large variations of size. Some of the commonly used

distributions for expressing fracture sizes are log normal, exponential or power-law distribution

(Berkowitz, 1995; Bour and Davy, 1997; Masihi et al., 2008). Fracture sizes can be specified in two

ways; by using trace-length distribution parameters for polygons with a vertical elongation axis or in

trace-height distribution parameters for a horizontal elongation axis (length > height) (Strijker, 2013).


The Fisher distribution is the most commonly accepted distribution for specifying the fracture

orientation. Fisher distribution is regarded to be perfect comparison to a normal distribution in

orienting the data, which are distributed on a hemispherical rather than a planar surface (Mardia,

1972). Another additional advantage in using the Fisher distribution is the ease of applying it since

the parameters can be derived from in-situ data and the availability of a closed form Cumulative

Distribution Function (Dershowitz, 1979).

2.3.2. Fracture Network Properties

The basic parameter is the quantity of fractures generated in the network. Generally, there are a

wide range of factors that may influence the number of fractures created (fracture intensity). Here,

the number of fractures created is closely related with the fracture spacing. The more fractures

created (high intensity fractures) the closer the spacing of each fractures is. The behavior of fracture

spacing is controlled by several geological parameters; composition, grain size, porosity, lithological

layering, and structural position (Nelson, 2001). Quantitatively, it is really difficult to single out each

parameters role individually related to the fracture spacing. However, Nelson (2001) observed the

general behavior of fracture spacing that related to the geological parameters mention above. The

first one is smaller fracture spacing is commonly found in the lithologies that has a high percentage

of brittle constituent. For the second one, in a low porosities and small grain sizes, fractures tend to

develop with a smaller spacing. Lastly, closer-spaced fractures are commonly observed near high

localized-strain fractures such as faults and folds.

Another observation is that fractures in thinner beds are tend to have smaller spacing than thicker

beds with the assumptions that all other rock parameters and loading conditions are equal and in the

absence of structural features (Ladeira and Price, 1981; Narr and Suppe, 1991; Bai and Pollard,

2000a; Nelson, 2001). Ladeira and Price (1981) also stated that beds with more than 1 – 1.5 m of

thickness, spacing is roughly constant. The term mechanical unit is commonly used to give a better

understanding of the behavior of fractures in relation to lithological layering. A Mechanical unit can

be described as bed or several beds possessing homogeneous fracture patterns (Bertotti et al.,

2007). Bertotti et al. (2007) also discovered some patterns of mechanical unit and sedimentology

relation, which are given in three statements: P a g e | 20

a. Intense fracturing was commonly found at the lower and uppermost boundaries of the bed

in the thick sandstone, as an evidence of a significant internal variability.

b. There was evidence in the thickest beds that package of thick amalgamated layers tend to

form as a single mechanical unit.

c. Thinner beds were commonly fractured in a close contact with thick beds of the adjacent

layer and they do not act as joint-free interlayers.

Rives et al. (1992) stated that distribution of spacing may change with the following evolution of the

fracture set. Initially, new fractures are formed in random nucleation (resulting in negative

exponential distribution), followed by a greater number of fracture shadows development (resulting in

a log normal distribution), to a saturated system (resulting in a normal distribution). The term fracture

shadows is well explained by the concept of “stress shadow”, it is basically explained that the growth

of new fracture is inhibited within an area where the stress decreased adjacent to the development

of open fracture that is proportional to the height of the fracture. This relationship can be described

more by the process of “sequential infilling”, which means that fracture spacing decreases by new

fractures nucleating between earlier formed fractures while the remote strain decreases (Gross,

1993). While in a saturated system, all fractures are really close to each other such that no more

fractures can infill, even under progressive strain. Further deformation for this condition will result in

additional opening of the existing fractures. The typical condition for fracture saturation is reached

when the ratio between spacing to layer thickness is 0.8-1.2 (Bai and Pollard, 2000a).

2.3. Fracture Connectivity

All parameters described above are important in order to analyze the connectivity of the fracture

within the fracture network. Fracture connectivity can be quantified by measuring the number of

intersections per fracture with other ones (Adler and Thovert, 1999). Thus, fracture connectivity is

sensitive to the geometry and characteristics of individual fractures. Connectivity also depends on

the spatial distribution of different fracture sets (Balberg and Binenbaum, 1983; Balberg et al., 1991;

Odling et al., 1999). Increasing fracture propagation leads to the formation of clusters or connected

fractures. Field studies (Rouleau and Gale, 1985; Odling, 1992; Gillespie et al., 1993; Odling, 1993;

Bloomfield, 1996; Castaing et al., 1996; Odling, 1997) suggest that connectivity and cluster are

dependent on fracture lengths, densities, dispersion, and spacing. In general, connectivity increases

as (1) an increasing number of fractures of the same set are added to the system, (2) the length of

the fractures increases (3) the orientation of fractures in a set exhibits a higher degree of dispersion,

or (4) fractures of multiple sets are added to the system.

P a g e | 21

3.

Methodology This study use a model of deltaic siliciclastic succession derived from process-based simulation

superimposed by a stochastic fracture network. To model and analyze the connectivity in the deltaic

reservoirs; stacking pattern process, as a function of system tracts, is the most crucial step that will

influence the initial connectivity of the deltaic reservoirs from the sedimentary modeling point of view.

As for the structural aspects, connectivity is investigated by using the stochastic process of DFN.

Here, fractures are considered as discrete disc shaped geometries that occur in a rock volume

following certain statistical descriptions for building the fracture network. Within the generation of

DFN, the translation of sedimentary properties to fracture-controlled properties is introduced to

comprehend how sedimentary properties may affect the fracturing process. The sensitivity of DFN

connectivity is tested for variations in some parameters to address model uncertainties.

Subsequently, the impact on the flow will be determined based on the resulting connectivity in the

fracture network. Generation of volume of sand bodies will be conducted prior to give qualitative and

qualitative analysis in examining the role of structural and sedimentological domain for

interconnectivity of reservoir bodies.

3.1. Overall Workflow Outline

The parameters required for the generation of a fracture network can be derived from the properties

of lithostratigraphic succession as provided by Delft3D. These parameters are fracture distribution,

intensity, and shape. As illustrated in Figure 3, the approach is started by converting the output from

Delft3D as the input for the model into some properties of lithostratigraphic succession. In this case,

they are grain size distribution and lithostratigraphic architecture. Subsequently, the definitions of the

properties that translate stratigraphy parameters into fracture-controlled parameter are essential to

bridge the relation between sedimentary processes to the fracture network development. Thus, the

generation of DFN can be performed followed by the connectivity analysis. In modeling the DFN, all

properties, which are generated in Petrel, are being exported to FracMan as the main input for

building the DFN. As the input model is already in the 3D grid, geocellular set definition of FracMan

module is used to model fracture sets of DFN. It is a module to generate fractures in a 3D grid on the

basis properties of the grid. In defining parameters in the geocellular set definition module, some of

them are specified as a function of property distribution. Thus, using a correlation with some

properties to quantify those parameters is possible in FracMan. Those parameters are relative

P a g e | 22

fracture intensity, fracture size and shape. Multiple realizations by varying some parameters used in

building the DFN are then performed in addressing the uncertainty in the model. After the generation

of fracture network, fracture cluster analysis is conducted to assess the existence of self-connected

clusters in the fracture network. The result of the fracture cluster analysis will be used as source of

information for further analysis of fracture network connectivity.

Figure 3. Schematic workflow of this study

3.2. Sediment Architecture Model

The input for this study is the output model resulted from a Delft3D simulation of a prograding delta

with grid dimension of 50 m x 50 m x 30 cm. The output of Delft3D is grain size volume distribution

per grid cell for five different sediment classes. Two synthetic deltaic reservoirs models, produced in

Delft3D, are used for the generation of DFN. They are 25% sand delta and 35% sand delta. Table 1

shows the composition of sediment classes in the synthetic models. Each sediment class represents

the percentage of sediment out of 100 g total sediment transported into the basin in 1 m3 of the

discharge. Thus the 25% sand delta model is representing the deltaic reservoirs where percentage

of sand is a quarter out of 100 g total sediment, while the 35% sand delta model has a 35 g out of

100 g of sand percentage in the synthetic deltaic reservoirs. With respect to the geological

explanation, the 25% sand delta synthetic model represents a delta deposit with less material of

fluvial input compare to the 35% sand delta model. The 25% sand delta input will be utilized as a

base model for the base case scenario in the fracture network distribution. As for the 35% sand delta

P a g e | 23

model, it will be used as a sensitivity case model in order to see the effect of different

lithostratographic architecture in fracture network connectivity.

Table 1. Two Delft3D model input used in this study. The D50 grain size mean diameter is being used to describe the sediment composition for all the classes.

3.2.1. Stacking Process

Delft3D is a computationally expensive model that is restricted to modeling progradational deltas

with a static base level. Such progradational delta can be considered as a parasequence (Van

Wagoner, 1985, 1988). In order to study a systems tract (set of tracked parasequences), we

superimposed parts of the Delft3D model using MATLAB® (MATLAB, 2014) (Figure 4). The main

reason for this is that we can study the vertical connectivity of stacked parasequences. The stacking

pattern can be formed as retrogradational, aggradational, or progradational. For example, if the

progradational stacking pattern is built, the lowermost parasequence is then taken at a more distal

location of the Delft3D model. The next parasequence, which is stacked on top of it, is coming from

an intermediate location of the model. While the uppermost parasequence is selected from Delft3D

model that located close to the shoreline. On the other hand, the retrogradational stacking pattern

model is stacked in a same way to the progradational pattern but in reciprocal sequence. For the

aggradational stacking pattern, all the three parasequences are selected approximately in the same

distance from the delta apex.

Furthermore, since an individual parasequence has a thickness less than 10 m, a thicker reservoir

interval by stacking three parasequences is created. A thicker reservoir interval will lead to a more

realistic fracture pattern.

Type of Sediment Medium -fine sand Fine - very fine sand Very fine sand Silt ClayD50: mean grain size 250 μm 150 μm 100 μm 17 μm 4 μm

[g/m3] [g/m3] [g/m3] [g/m3] [g/m3]Delta 1: ‘25% sand delta’ 4 8 13 50 25Delta 2: ‘35% sand delta’ 6 12 17 48 17

P a g e | 24

Figure 4. Stacking of parasequence sub-domain to generate progradational sequence model (Lipus, 2015)

In stacking the parasequences, care should be taken to ensure that channels may cut into the

underlying substrate (created from underlying parasequence), which commonly occurs in the deltaic

environment. Two steps are performed during the generation of deltas (Lipus, 2015):

1. One grid block of shale (30 cm) is assigned to cover the parasequences. This shale represents

the transgressive deposits.

2. Active cells at the base of sequential parasequence incises 5 grid blocks (1.5 m) into the older

underlying strata, eroding and replacing the grid cell properties of the lower deposits (Figure 5).

These approaches have been applied for the uppermost parasequence sub-domain eroding into

middle sub-domain as well as the middle sub-domain into the lower sub-domain. The resultant

parasequences can be seen in Figure 6.

In this study, the model that will be utilized as the main dataset for further DFN distribution is the

retrogradational stacking pattern of 25% sand delta for the base case scenario. While for the

sensitivity scenario, the dataset used is the retrogadational stacking pattern of 35% sand delta.

P a g e | 25

Figure 5. Cross section of schematic drawing of eroding process in stacking the individual parasequence in Delft3D. Yellow and orange colored grid cells represent arbitrary cell attributes of individual parasequence (Lipus,

2015).

Figure 6. Example of a cross section after stacking and incision (D50 = 100 μm) (Lipus, 2015).

3.2.2. Lithostratigraphic Succession Properties

After the deltaic model layers are stacked and built, all the grain size classes are exported to Petrel

in order to build a model that will be used in the distribution of DFN. In Petrel, the inputs from Delft3D

are used to define three properties; two continuous properties (Brittleness Index and porosity) and

one discrete property (lithology). Continuous properties represent properties that occupy any value

over a continuous range. The range for the continuous properties is from 0 to 1. Both Brittleness

Index and porosity are classified as continuous properties because they are going to be used as

input for the properties defined for translating sedimentary to fracture-controlled properties. In

contrast, the discrete property is presented as categorical data to give better definition. The discrete

P a g e | 26

property (lithology), as lithology will be used to analyze lithostratigraphic architecture in the later

process. Subsequently, the grid cells will be upscaled vertically in order to define the lithological

layer. This process will adjust the grid size in vertical direction from homogeneous 30 cm thick into

some kind of varied layer thickness of lithology. Then, the upscaled properties will be exported from

Petrel to FracMan, as these properties will be used as the main input in the DFN distribution. This

step is essential for the further fracture network distribution process, as thickness of the lithological

layer plays an important role in defining the fracture distribution, intensity, and shape.

Brittleness Index

In this study, Brittleness Index (BI) is defined to describe how favorable fracturing is as a function

mineralogical composition. It is often used in hydraulic fracturing studies as a key parameter for

hydraulic fracturing initiation and propagation in a low permeability rock, like shale (Holt et al., 2011).

The definition of BI is performed by assigning a formula that relates BI to the mineralogy composition

(Jarvie et al., 2007), which is given as:

𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝐼𝐼𝐵𝐵𝐼𝐼𝐵𝐵𝐼𝐼 =𝑄𝑄

𝑄𝑄 + 𝐶𝐶 + 𝐶𝐶𝐵𝐵 (1)

where Q, C, and Cl are the representation of quartz, carbonate, and clay weight percentage in the

rock, respectively. According to grain size input from the Delft3D models, the grain size class of 1-3

of sand grain can be classified as Q or quartz because the main mineral for the sandstone is Quartz.

On the other hand, for the grain size class of 4-5, they are classified as Cl or clay since the grain

size represents the clay mineral that mostly formed in the siliciclastic rock. Since quartz is the main

grain composing the sandstone, it can be roughly stated that BI is a ratio between the amounts of

sand grain to the total grain in the rock mass. In this study, no C or calcite mineral is assigned

because the assumption of siliciclastic reservoir models (no influx from carbonate materials).

Porosity

Porosity determination in this study is based on the study performed by (Lipus, 2015). Derivation of

porosity from grain size inputs is done by extracting the parameters from grain size distribution to

estimate porosity or even permeability (Panda and Lake, 1994). Since porosity is the only parameter

that is going to be used in this study, the derivation of permeability will not be discussed further.

Because of the dispersion of data distribution when grain diameter is plotted with fraction on a linear

scale, the modification of Krumbein-Phi-Scale (Krumbein and Sloss, 1964) is used. It is basically

using a logarithmic scale to see the relationship between grain diameters with porosity. The purpose

is to introduce the possibility of fitting a normal distribution of grain size (logarithmic scale). Based on

the distribution, parameters like mean, standard deviation, and skewness can be derived. Then, the

empirical relations between standard deviation of the grain size distribution of bed material and

porosity (Takebayashi and Kamito, 2014) is used. The result of the empirical relations from

P a g e | 27

Takebayashi and Kamito (2014) is shown in Figure 7. Figure 7 shows the increasing uncertainty of

the porosity from estimation with the increase in standard deviation. The limit of around 10% porosity

differences is tolerable (Lipus, 2015). The formula used for the empirical fit between porosity and

standard deviation is given as:

𝛷𝛷 = 𝐶𝐶1 ∗

𝐶𝐶2 𝜎𝜎𝐶𝐶31 + 𝐶𝐶2 𝜎𝜎𝐶𝐶3

(2)

where 𝛷𝛷 = porosity, C1 = 0.38, C2 = 3.7632 and C3 = -0.7552 and σ = standard deviation.

Figure 7. Relationship between standard deviation particle size distribution and the porosity from field observations (Lipus, 2015) after (Takebayashi and Kamito, 2014).

Lithology

Facies types based on grain size distribution will be used to define the lithological layer. This

property is important, since it will be used as the main input for defining model layer. The merging of

grid cells into a grid of lithological layers is based on a classification of lithology following discrete

categories of the grain size distributions. Cells are classified as sandstone if the sum of the volume

fractions of grain size classes of 250 μm (medium-fine sand), 150 μm (fine-very fine sand), and 100

μm (very fine sand) is bigger or equal than 50% of the total cell volume. If summation of the sand

grain classes is bigger or equal than 20% and less than 50%, they are classified as shaly sand and

the rest of the cells are classified as shale (if the summation of the sand grain classes are less or

equal than 50%).

Lithological Layers Definition

After lithology is defined, it will be used for vertical upscaling the model. Since the model is

generated by stacking three parasequences domain into one model, top and bottom surfaces of

sandstone, shaly sand, and shale then generated in Petrel per each parasequence or stacking P a g e | 28

pattern interval. In total, there are twelve surfaces used as an input for the vertical upscaling process

with the top and bottom surfaces of the whole model are flat surfaces. The output of the vertical

upscaling process consists of 11 lithological layers from 100 layers of the initial model. This

lithological layer thickness definition would give more variation compared to homogeneous cell

thickness (30 cm) of the initial 3D grid model.

Upscaled BI and porosity

The new lithological layers definition is then used to upscale the porosity and BI vertically, so that

each cell will have thickness values variation of BI and porosity compared to the original one which

has a homogeneous cell thickness (30 cm) of BI and porosity. These properties will be used as the

key properties for distributing some of the parameters for the DFN distribution.

3.3. DFN Distribution

As previously mentioned, geocellular set definition module is used to model the DFN. Several

parameters should be defined in order to run the module. They are grid properties, global and

relative fracture intensity, fracture orientation, shape, and size. One of those parameters requires

having correlation with a grid property in their distribution process, that parameter is relative fracture

intensity. Thus, Fracture Probability is introduced as the correlation property. More importantly,

fracture probability is property that defined as the translation of sedimentary properties to fracture-

controlled properties.

In the following description, explanation of Fracture Probability will be given first, then followed by

explanation of parameters needed to build the DFN.

Fracture Probability

Fracture Probability is key property to measure how each cell has a tendency to be fractured. It is

categorized into two; Fracture Potential and Fracture Proneness. The former will be assigned to the

base case scenario and the latter will be used in as one of the sensitivity parameters in defining

some parameters for the DFN distribution. Fracture Potential is a quantitative parameter to measure

the potential of cells to be fractured and is defined as a function of the upscaled BI. The higher the

Fracture Potential means that the higher the chance of the cells to be fractured. In calculating

Fracture Potential, four functions are proposed in this study (Figure 8), This functions are tentatively

postulated in acknowledgement of some geological concepts based on extensive literature in terms

of fracture intensity, layer thickness, and lithology (Ladeira and Price, 1981; Bertotti et al., 2007;

Jarvie et al., 2007). It is widely known that thinner the layer thickness is, higher the fracture intensity

of a rock is, as there is inversely proportion relationship between fracture intensity and layer

thickness. Fracture intensity can be related to lithology of the rocks; in general, more brittle the rock

is, higher the fracture intensity is. Only three lithologies are assumed (sand, shale, and shaly sand)

P a g e | 29

in this study, this means that sand should have the highest fracture intensity followed by shaly sand

and later is shale. Each function is applied for several conditions; the first function (top of the

formula) is applied for cells that have model thickness less than 2 meter, the second function is used

for cells with model thickness more than 2 meter and Brittleness Index bigger than 0.5, the third

function is only for cells with model thickness bigger than 2 meter and Brittleness Index bigger than

0.25 and less or equal than 0.5, while the last function is for cells with model thickness more than 2

meter and Brittleness Index less or equal than 0.25.

Figure 8. Function used in defining Fracture Potential

Subsequently after defining Fracture Potential, Fracture Proneness is the next parameter to be

derived. Fracture Proneness is a parameter to estimate the tendency of cells to be fractured based

on the relationship between fracture spacing and porosity. Cooper et al. (2001) provides a

relationship between fracture spacing and porosity based on data measurements in siliciclastic rocks

in Teapot Dome, Wyoming. The original relationship is given in relation between fracture spacing

and amount of cements in the rock. Since they also mention that porosity is inversely proportioned

with cementation, so they relationship between fracture spacing and porosity can be inferred. The

formula for the fracture spacing and porosity relationship is given as:

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑆𝑆 = 0.04241𝐵𝐵10.71𝛷𝛷 (3)

As it is commonly known that the bigger the spacing the lower the intensity of the fractures is. So

arbitrarily, the Fracture Proneness can be written as:

𝐹𝐹𝐵𝐵𝑆𝑆𝑆𝑆𝐵𝐵𝐹𝐹𝐵𝐵𝐵𝐵 𝑃𝑃𝐵𝐵𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 =2

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑆𝑆 (4)

Grid properties

The upscaled properties (BI and porosity) exported from Petrel are used directly as the main input

for defining the grid properties module. Besides cells dimensions, this base grid also contains

information about the property’s value assigned to the cell. To conclude, the information contained in

each grid cell is the source information to define other fracture parameters such as fracture intensity, P a g e | 30

size, and shape. As in defining those parameters, correlation with grid properties is performed to

determine them.

Fracture Intensity

In FracMan, fracture intensity can be represented by two other parameters; global fracture intensity

and relative fracture intensity. The former is defined as a parameter to define the amount of fractures

in the whole 3D model; while the latter is defined as a property distribution so that it can be

correlated to match a grid property. The assigned distribution of relative fracture intensity will be

normalized over the grid to keep the sum of the local fracture intensities will equal to global fracture

intensities. This scheme is beneficial to define the spatial variation of fracture intensity.

1. Global Fracture Intensity

FracMan use the terms of P10, P32, P33, or fracture count as measuring methods. The used of P10,

P32, P33 terms are based on the Pxy terminology introduced by Dershowitz (1984) (Figure 9). Since

no single data related to fracture intensity are available, the assumption of several P32 values is

performed; ranging between 0.2-0.5 m2/m3. Right intensity value will be specified based on further

evaluation in connectivity analysis, depending on how cluster are developed in each global fracture

intensity values (for each DFN distribution).

P a g e | 31

Figure 9. Relationship between the dimensionality of the intensity measurement and sampling structure or measurement region (modified after Dershowitz (1984)).

2. Relative Fracture Intensity

As mentioned earlier, relative fracture intensity is defined to specify how the fracture intensity should

vary spatially in the model by correlating it with a grid property. To determine the distribution of

relative fracture intensity, a positive correlation with Fracture Probability, a grid property, is assigned.

Two types of Fracture Probability are generated to give variations in determining the relative fracture

intensity for the sensitivity analysis. Fracture Potential will be assigned to distribute the DFN in the

base case scenario while Fracture Proneness will be given in sensitivity case of fracture network

connectivity.


Fracture orientation is given as vector distribution in FracMan. Mean pole values of trend and plunge

and distribution parameter are two parameters that need to be addressed in the module. Fisher

0 1 2 3

Line (Borehole)

Area (Traceplane)

Volume

Point Measures

Linear Measures

Areal Measures

Volumetric Measures

0

1

2

3

P22 [-] Fractures area per unit area of sampling plane (areal porosity)

P32 [1/m] Fractures area per unit volume of rock (volumetric intensity)

P33 [-] Fractures volume per unit volume of rock (volumetric porosity)

P10 [1/m] Number of fractures per unit length of scanline (frequency)

P20 [1/m2] Number of trace centers per area of sampling surface (areal density)

P30 [1/m3] Number of fracture centers per unit volume of rock (volumetric density)

P11 [-] Total fracture aperture per unit length of scanline (l ineal porosity)

P21 [1/m] Length of fracture traces per unit area of sampling surface (areal intensity)

Dimensions of FeatureNumber of Fractures

Fracture Trace Length

Fracture Area Fracture Volume

P00 [-] Number of fracture samples per point sample of rock

Density

P a g e | 32

distribution is chosen as distribution parameter with constant distribution of 100 and treated as fixed

variables when running for each scenario in modeling the DFN. Conversely, variations in mean pole

values of trend and plunge are assigned to see how sensitive fracture orientation is in terms of

connectivity of fracture network.

Fracture Shape

In terms of fracture shape, there are three parameters that need to be specified in FracMan. They

are number of sides of fracture shape, elongation axis, and the aspect ratio, which is defined as ratio

between the fractures length with fractures height. The number of shape will be assigned as a

constant value, in this case is 4, in order to avoid longer modeling time due to complexity of the

shape of fracture. For the elongation axis, it is assigned that the value of elongation is in the same

direction with the strike of fractures. On the other hand, aspect ratio will be varied to see how

sensitive aspect ratio is to give diversity in fracture network connectivity.

Fracture Size

Fracture size is specified with respect to the equivalent radius of fractures or in terms of length/ratio,

which both are user defined. In this study, equivalent radius is used to determine the size of the

fracture. The variations of radius are then assigned for the fracture network connectivity sensitivity.

For defining the DFN distribution using geocellular set definition module, this parameter is the key for

modelling the fracture in relation with definition of theoretical stratabound or non-stratabound fracture

system (Odling et al., 1999). The minimum fracture size is set at 0.5 m since FracMan has limitation

in modeling very small size of fracture.

3.4. Connectivity Analysis

The connectivity of fracture network is analyzed based on the process called fracture cluster

analysis, which is performed in FracMan. After each DFN distribution is simulated, the resulted DFN

will be used as the main input for the fracture cluster analysis process.

In fracture network, a set of fractures that connected to each other are classified as cluster, concepts

from percolation theory (Stauffer, 1985; Chelidze, 1986; Bebbington et al., 1990; Berkowitz and

Balberg, 1993; Berkowitz, 1995; Guéguen et al., 1997). Fracture cluster analysis is performed based

on the cluster analysis module in FracMan. Fracture cluster is built when FracMan examines all the

preferred fracture sets defined by user and discriminates secluded groups of self-connected

fractures. This isolated groups self-connected fractures display compartmentalization in the fractures

network.

Once the fracture cluster analysis is simulated, connectivity analysis is performed subsequently. This

process will give quantitative analysis in assessing the connectivity of fracture network in the

resulted multilayer DFN. All the fractures that connected will form a cluster, which is then being P a g e | 33

analyzed to assess the degree of fracture network compartmentalization. The assessment is

basically based on the identification of self-connected fracture clusters that exist inside a DFN

model. The establishment of self-connected clusters is really depending on the minimum number of

fractures required to make a cluster, which is defined by the user. Hence, variations in number of

fractures values will be used to assess the sensitivity of fracture network connectivity.

Evaluation of some statistical data, provided by FracMan, of every self-connected clusters built is

implemented to analyze the connectivity of fracture network. Some of the data, which are used for

the evaluation, are the total number of fractures constructing the cluster and dimension of the

cluster.

Another intriguing approach is also conducted in terms of how the self-connected clusters distributed

in the model. The approach is to overlay the facies distribution with the cluster distribution. This will

give clear view of how fractures connect different sand bodies or just randomly distributed in the

rock. Finally, the role of fractures can be examined regarding to interconnectivity, especially vertical

connectivity, within reservoir bodies.

Qualitative and quantitative analysis of connected sand bodies within the model are conducted to get

deeper understanding of what domain is controlling the interconnectivity of sand bodies. Initial

volume of connected sand bodies is then compared with the volume of connected sand bodies after

the presence of fractures to underline the role of both sedimentological and structural domain.

P a g e | 34

4.

Results The results are presented and described in this section. The description will be based on the

workflow (Figure 3) explained in the methodology chapter. Results are classified into two groups; the

first one is called properties definition and the other one is defined as DFN distribution.

4.1. Properties Definition

The results in this group are mainly related to direct used or derivation of the grain size input data,

which is processed in Petrel. There are three properties that can be categorized into this group:

Brittleness Index, porosity (both are continuous) and lithology (discrete). These properties are

important before defining other parameters that will be used in advanced to distribute the DFN.

4.1.1. Brittleness Index (BI)

The result of BI calculation is displayed in Figure 10; with red color represents highest BI value and

purple represents lowermost BI value. The section shows that the top parasequence is overall the

least brittle; then it followed by the bottom parasequence and the middle parasequence with

increasing brittleness.

It can be also seen from the section that the evolution of brittle rocks distribution area changes for

every parasequence. In the lowermost parasequence, the brittle rocks are mostly deposited in the

northern-central part of the study area; however, it starts to concentrate more to the south during the

middle parasequence deposition and it continues until the youngest parasequence deposition. The

brittle rocks distribution is related with the channel evolution as most of the brittle rocks are

deposited in the vicinity of the channels. Incision can be also found in the section. It is located in the

middle parasequence, where the brittle rocks of southern channel erode the mechanically soft rocks

of the underlying parasequence. The difference in ductile rocks distribution in each parasequence is

observed in the section. In the lowermost parasequence, the ductile rocks are deposited in the top

part and covering the brittle rocks that deposited in the channel. As for the middle parasequence, the

ductile rocks are lying both under and above the brittle rocks. The ductile rocks in the uppermost

parasequence are distributed in the upper part except for some part in the middle-south area where

the brittle rocks overlie, or even incise them.

P a g e | 35

Figure 10. S-N cross section of Brittleness Index of retrogradational stacking pattern

4.1.2. Porosity

The porosity in the model is portrayed in Figure 11, with red color indicates high porosity and purple

color depicts low porosity value. The distribution of high porosity region is concentrated in the middle

parasequence, then bottom parasequence followed by the top parasequence. All the high porosity

rocks are accumulated in the vicinity of the channels and their distribution is also shifting from north

to south upward. Some subtle trends of low-medium porosity values can be found too in the section.

In the lowermost parasequence, they are accumulated in the upper part of the middle-south part of

the study area. In the uppermost parasequence, the subtle trends are deposited in the central part of

the study area and show features of parallel bedding of low and medium porosity layers.

Figure 11. S-N cross section of porosity

4.1.3. Lithology

Lithology is crucial for the vertical upscaling process because it will be used for the redefinition of cell

thickness, which plays an important role in the DFN distribution.

P a g e | 36

Before upscaling the cells vertically, lithology is classified based on the criteria discussed in the

methodology section (Figure 12). Figure 12 depicts that coarser materials (sand and shaly sand) are

predominantly deposited in the two lower parasequences, while finer material of shale are the

dominant lithology in the upper parasequence.

Figure 12. S-N cross section of lithology. Red represents sandstone, yellow represents shaly sand, green represents shale

Figure 12 also gives clear indication of the shape of each lithology bodies. Based on this, top and

bottom surface of each lithology can be mapped and generated. These surfaces will be used as

input to generate horizons that bound uniform lithologies in order to proceed the vertical upscaling.

Petrel allows the user to map the top and bottom of specified discrete facies (in this case lithology) to

generate surfaces. Before running this function, the selection of desired lithology to be mapped is

executed to get specific top and bottom surface for each lithology. This process will be applied for

every parasequence to honoring their relative ages. Figure 12 also shows how the sand channel

deposits (middle parasequence at 500 m from the south) cuts unto the underlying parasequence. As

this is a 3D data grid, channels will cut through the parasequence boundaries at several locations.

4.1.4. Upscaled Properties

The lithological classification needs to be upscaled vertically in order to extracting the true thickness

of lithological units. The thickness depends on the shape of facies bodies. This thickness will be

used to define the parameters needed for the DFN distribution.

Upscaled Lithology

After all lithology bodies in each parasequence have been defined, then the new layer definition can

be generated by upscaling the initial model vertically using the surfaces resulted from the lithology

top and bottom mapping. As a result, 11 new layers or beds model are created from the 100 layers

of initial model, which are called lithological layers. Overall, the result from the upscaling process is

good since the resulted lithological layers shows relatively similar shape of facies bodies compared

P a g e | 37

to the initial model (Figure 13). However, some inaccuracy may occur in the upscaling process, as

shown in the upper part of middle parasequence where some of the shale are being converted into

sand or shaly sand.

Figure 13. S-N cross section of initial and vertical upscaled model comparison of lithology

Upscale Brittleness Index

It can clearly be seen that the accumulation of brittle rocks, represented by green-red color, is

concentrated in the second layer from the lowermost parasequence, upper part in the middle-

southern area of the middle parasequence, and small area in the upper part in the north region of

uppermost parasequence (Figure 14). Brittle rocks in the lowermost parasequence are deposited in

the vicinity of the channels and then covered by the overlying relatively ductile rocks. Furthermore in

the middle parasequence, high BI values, represented by green-red color, are defined as brittle

rocks and occur in layers that exhibit the vicinity of channels (Figure 14). The distribution of the

brittle rocks is varied in each parasequence. In the lowermost parasequence, brittle rocks are

accumulated in the bottom-middle layers and then covered by overlying relatively less brittle rocks.

The first two layers in the middle parasequence are where the brittle rocks deposited, but they are

limited to the middle-southern part region of study area where they are overlying the underlain less

brittle rocks. For the uppermost parasequence, brittle rocks distribution is limited only in the upper-

northern part while the ductile rocks are accumulated in the middle-upper layers.

P a g e | 38

Figure 14. S-N cross section of vertical upscale of Brittleness Index

Upscaled Porosity

The distribution of high porosity values (yellow-red) is similar to the distribution of brittle rocks. High

porosity rocks are distributed in the vicinity of the channels, in the lowermost parasequence, upper

layers in the middle-southern region of the middle parasequence, and limited in the upper layers in

the northern part of uppermost parasequence (Figure 15). A noticeable low porosity rocks

distribution, represented by blue layer, are concentrated largely in the bottom layer of the uppermost

parasequence and the rest is randomly distributed in the bottom part of the lowermost

parasequence. In the correlation with both BI and lithology, low porosity rocks in this section are

referred to shaly sand and relatively slightly ductile rocks (low-medium values of BI). Moreover, the

ductile rocks (low BI values) are represented by shale with fair porosity values. Finally, the high

porosity rocks exhibit brittle rocks and sandstone.

Figure 15. S-N cross section of vertical upscaled porosity

4.2. Fracture Probability

As explained earlier in the Methodology section, it is necessary to define a new property called

fracture probability that will be proxy for relative fracture intensity definition. In fact, this property is P a g e | 39

defined as the property that translates sedimentary properties into fracture-controlled properties.

Specifically, there are two competing factors that control the intensity of fracturing: Fracture Potential

versus Fracture Proneness. Fracture Potential considers layer thickness and BI, while Fracture

Proneness excludes the mineralogical control on fraccability as expressed by the BI by considering

porosity and grain size.

Fracture Potential

As described in Methodology section, Fracture Potential is postulated in consideration of geological

concepts related to fracture intensity, layer thickness, and lithology. To validate that the resultant

Fracture Potential honors the geological sense, relationship between Fracture Potential, upscaled

cells height, and BI is given in Figure 16

The section gives a clear description how Fracture Potential relates to layer thickness and

mineralogy composition at each point in the 3D grid. Group 1 has the highest Fracture Potential

value, as this group indicates the upscaled cells with less than 2 meter thickness, without

considering BI value. It shows that smaller the thickness is greater the Fracture Potential is. Fracture

Potential is also defined as a function of brittleness for layers thicker than 2 meters, represented by

Group 2-4. Therefore, a lithological layer with a height of 4 meter may either have a Fracture

Potential of 14 for Group 2, 8 for Group 3, and 4 for Group 4, in effect of different Brittleness Index.

This model result thus produces a geological sensible outcome that Fracture Potential is a function

of layer thickness, but that not all layers of 4 meter have the same potential. A Shaly sand with BI of

0.4 will have a potential of 12 whereas a sandstone of BI of 0.7 also has a potential of 12 because it

is thicker than shaly sand.

Figure 16. Relationship between Fracture Potential with cell height and BI

P a g e | 40

Fracture Proneness

The decrease in porosity is correlated with the increase in Fracture Proneness for 3 different

lithologies (Figure 17). It can be seen from the section that sandstone has low Fracture Proneness

due to its high porosity and shaly sand with low porosity gives the highest Fracture Proneness.

Figure 17. Relationship between Fracture Proneness with porosity and lithology

4.3. Base Case Discrete Fracture Network Model

After the definition of Fracture Probability, the DFN can be modelled stochastically. Several

parameters are assigned prior to simulating the DFN in FracMan (Table 2). In defining those

parameters, some specific descriptions (subparameters), which are user-defined, are required by

FracMan. To define global fracture intensity, measurement type is user-defined input required in

FracMan. As previously explained in the Methodology section, P32 method is preferred as the

measurement method in global fracture intensity definition. Here, the intensity is tested with values

varying from 0.2-0.5 m2/m3. Fracture Potential is a grid property that defines to have equal values

with the relative fracture intensity for this case. Fracture orientation is modelled with Fisher

distribution. Trend and plunge distribution are set as constant distribution of 400 for trend and 900

degree for plunge. Fracture distribution is expected to be more concentric, for that reason the

concentration input is assigned with 100, as the higher the value the more concentric the distribution.

The aspect ratio and number of sides are user-defined input parameters to characterize the fracture

shape. Fracture size is specified by applying normal distribution (mean and standard deviation) to

define the equivalent radius. Subsequently, the fracture height from the histogram of the cell height

(Figure 18), which represents the thickness, will be used to define the mean and standard deviation

P a g e | 41

value in normal distribution. By applying this, it is expected that the fracture size is set to be within

the thickness range.

Figure 18. Histogram of cell height which represents cell thickness

As the variations of some parameters will be performed to see how sensitive is each parameter

related to the DFN, base case scenario is designed first as a reference input. In determining each

parameter used in the realization, no specific data from field measurement or well log is used. The

assumption is based on some plausible arbitrary justification. Moreover, variations in global density

values will be given for every case, not only base case, in order to analyze the development of

fracture network cluster after the realization of DFN. An example of the result of DFN realization is

given in Figure 19.

P a g e | 42

Table 2. Base case input for DFN distribution

Figure 19. Realization of base case scenario of DFN (P32 = 0.1 m2/m3 global fracture intensity)

4.4. Facies Architecture

Before analyzing the vertical connectivity of the deltaic reservoirs, the understanding of facies

architecture that constructs the deltaic reservoirs is necessary. “Are the sand bodies in the deltaic

reservoirs already connected?” “What are things that cause non-connected sand bodies?” Those

questions are type of questions that come up regarding the natural connectivity of sand bodies in

deltaic reservoirs. Figure 20 illustrates the distribution of sand bodies in one of the section of deltaic

depositional environment.

Parameter Subparameter Model InputGlobal Fracture Intensity P32 (m2/m3) 0.2

P32 (m2/m3) 0.3P32 (m2/m3) 0.4P32 (m2/m3) 0.5

Relative Fracture Intensity Correlation Fracture PotentialDistribution Fisher

Trend 40°Plunge 90°

Concentration 100No. of sides 4

Aspect Ratio 2Distribution Normal

Equivalent radius (mean, std dev) 5,3Fracture Size


Model Size (2550m x 2550m x 30m)

Fracture Shape

P a g e | 43

Figure 20. Cross section of lithology that shows facies distribution of deltaic environment

The section portrays isolated sand bodies distribution of deltaic reservoirs, slight connection might

occur in the top right sand bodies. This Compartment of reservoir is favorable since the sand bodies

are surrounded by finer grain deposits (shaly sand and shale). The occurrence of finer grain deposits

will block or restrain the fluid to flow to other sand bodies. Shaly sand might favor the restraining of

fluid flow due to its role as permeability baffle, especially if the fluid is oil. Likewise, would function as

permeability barrier.

A more quantitative result is given in Table 3. It is statistical data extracted from Petrel under

connected volumes for discrete module. This module calculates how many connected volumes (grid

cells) of the discrete data, are there in the 3D grid model. Petrel allows the user to select either all

lithology or only specific lithology to be processed. The selection of sandstone, as the only data to

work with, is then made and resulted in the exclusion of the other lithologies (shaly sand and shale)

from the model. To simplify, connected volumes refer to connected sand bodies. Petrel assigns the

largest volume into code 0, the second one gets code 1, and so on. The selection of 10 largest

volumes (more than 100 cells) are presented in the Table 3, each volume contain information of the

percentage of connected volumes (%), number of connected cells (N), and interval thickness for the

connected volumes (minimum, mean, maximum thickness, and standard deviation). The distribution

of largest connected sand bodies is mostly concentrated in the lower part of the model, while the

distribution of the rest of the connected sand bodies is scattered and located in the middle-upper

part of the model (Figure 21). Connected sand bodies of Volume 1 (pink color) have the largest

portion of total connected sand bodies in the study area. They constitute around 85% of the total

connected sand bodies that are deposited in the study area (Table 3). For the rest of connected

sand bodies, each of them constitute no more than 5% of the total connected sand bodies. Vertical

connectivity of the connected sand bodies can be represented by the thickness data. Again, sand

body of volume 1 has the largest vertical connectivity and its maximum vertical connectivity can

reach up to 16.8 m and is concentrated in the southwestern part of the study area (Figure 21).

P a g e | 44

Table 3. Statistics for connected volumes of sandstone for the base case model.

Figure 21. 3D Visualization of connected sand bodies. Variation in color indicates non-connected sand bodies.

4.5. Self-Connected Clusters Analysis

Natural fractures can connect all the isolated reservoir bodies especially in vertical direction. Figure

22 displays the possibility of the resulted DFN to connect the isolated sand bodies in the study area.

It indicates that the isolated sand bodies in the southern part of the study area (lowermost and

uppermost parasequence) might be connected with the occurrence of fractures.

Min Mean Max Std0 Volume 1 84.51 27700 0.3 2.1 16.8 2.1831 Volume 2 4.97 1630 0.3 1.3 7.2 1.2852 Volume 3 2.79 916 0.3 1.2 6.6 1.0963 Volume 4 2.08 681 0.3 1.2 5.7 1.2194 Volume 5 1.93 633 0.3 1.6 4.2 1.1195 Volume 6 1.88 615 0.3 2 11.4 2.7086 Volume 7 0.62 204 0.3 3.1 10.5 3.147 Volume 8 0.5 164 0.3 0.8 3 0.58468 Volume 9 0.37 120 0.3 1 2.1 0.56129 Volume 10 0.34 113 0.3 1.1 3 0.7564

Statistics for connected volumes of sandstone

CodeSand

volume% N

Thickness (m)

P a g e | 45

Figure 22. Cross section that shows natural fracture may connect isolated sandstone bodies

In order to analyze the connectivity within reservoir bodies, investigation of fracture networks are

performed after the DFN models were completed. In FracMan, there is a module called cluster

analysis to provide the user with detailed information related to the presence of self-connected

clusters. The representation of the DFN as clusters gives better insight in the role of fractures in

connecting reservoir bodies. One of the key options that are provided in the module is the definition

of the minimum number of fractures in a cluster. Any self-connected fractures with fewer fractures

than the specified minimum number will be neglected. This option allows the user to specify the

number of fractures needed to set up a self-connected cluster. For the base case, 2000 fractures is

set as the minimum number of fractures needed for a self-connected cluster to be formed. Later this

parameter will be varied to be included in the sensitivity analysis. There is no specific literature

discussing the minimum number of fractures to form a self-connected cluster. The number is justified

based on the exercise given in the FracMan module.

Variations of P32 global fracture intensity between 0.2-0.5 m2/m3 were applied to each realization

scenario. Analysis is started when self-connected clusters formed and ended when no further self-

connected clusters could be formed. Therefore, cluster analyses are not given for all DFN realization

at lower and higher limits of the input range in P32 global intensity. Table 4 shows example of cluster

analysis result for the base case scenario. According to Table 4, no self-connected clusters is

developed below the 0.3 m2/m3 P32 global fracture intensity. Furthermore no additional self-

connected clusters could be generated at 0.4 m2/m3 P32 global fracture intensity or more, the

increase in global fracture intensity will only increase the number of fractures, the size of self-

connected clusters, and the P32 of self-connected clusters (Table 4). P32 of self-connected clusters

parameter is introduced to give additional illustration in estimating the extent of self-connected

clusters. It is a result of total area of fracture surfaces that formed self-connected clusters divided by

total volume encompassed by self-connected clusters. Larger the P32 of self-connected clusters,

higher the intensity of self-connected cluster formed in the model.

P a g e | 46

Table 4. Detail dimensions of self-connected fractures for the base case scenario

4.6. Sensitivity Analysis of Self-Connected Clusters

Since the uncertainty in determining some parameters of DFN distribution in this study is really high,

sensitivity analyses, for the parameters defined in FracMan, are then performed to provide better

insight on model predictions in terms of their variability. There are five parameters are included in the

sensitivity analysis for the connectivity (Table 5).

Table 5. DFN input parameters in the base case scenario (model input) and variations of some parameters for sensitivity analysis. Subparameters with italic letters are subjected to sensitivity analysis. Red colors letters show

the assigned values of subparameters for sensitivity analysis.

Relative fracture intensity, fracture orientation, shape and size are the parameters that are being

varied for the sensitivity analysis in the process of DFN realizations. The variations in this process

are based plausible common geological knowledges and concepts to see the robustness of fracture

network connectivity in the presence of uncertainty.

Length Width Height(m) (m) (m)

0.1 0 0 - - - -0.2 0 0 - - - -

2584.13 2169.8 44.3839.28 643.98 39469.18 586.45 37.7606.86 605.18 37.06530.16 374.62 38.14

0.4 1 413182 2588.94 2587.79 46.87 0.1070.5 1 586499 2627.41 2631.08 43.47 0.153

0.3 5 132583 0.016

Base Case

P32 (Global Fracture Intensity - m2/m3)

Total number of clusters

Total number of fractures

Self-connected cluster size P32 of self-connected cluster (m2/m3)

Parameter Subparameter Model Input VariationsRelative Fracture Intensity Correlation Fracture Potential Fracture Proneness

Distribution Fisher FisherTrend 40° 125° & 205°

Plunge 90° 90°Concentration 100 100

No. of sides 4 4Aspect Ratio 2 6Distribution Normal Normal

Equivalent radius (mean, std dev) 5,3 Function of cell heightMinimum fractures in a cluster Number 2000 1500


Fracture Shape

Fracture Size

Model Size (2550m x 2550m x 30m)

P a g e | 47

For the fracture orientation, the variation is given by simulating two set of fracture sets instead of one

set, which is the case for the base case. In the two fracture sets scenario, each set is assigned with

two different trend directions: N125°E & N205°E. The values assigned are arbitrary, but they are set

to be orthogonal to each other. In terms of sensitivity on fracture shape, a variation is applied only on

the aspect ratio. The number of fracture side is kept to be constant. This is mainly because aspect

ratio is proven to have more impacts in terms of connected fracture network. Another supporting

reason is the change in number of sides will cost substantially more time in simulating the DFN. The

variation in fracture height is given as a function of thickness (cell height) and lithology. Theoretically,

lithological layering can influence the development of fractures. There are two fractures systems that

are related to the type of lithology where the fractures growth: stratabound and non stratabound

systems (Odling et al., 1999). In this study, fractures growth in sandstone and shale are assumed to

be classified as non stratabound systems, while fractures growth in shaly sand are classified as

stratabound systems. The assumption is based on the behavior of shaly sand that may have more

interbedded weak and strong bed than relatively massive shale and sandstone (Odling et al., 1999).

In addition with variation of some parameters in DFN distribution, variation for fracture cluster

analysis also conducted by varying minimum number of fractures in a cluster for the establishment of

self-connected cluster. All of these parameters will be realized and sensitivity analysis will be

examined along with varying the P32 global fracture intensity for each value of a series of P32 global

fracture intensity between 0.2-0.5 m2/m3. One of the results is summarized in Figure 23.

Figure 23. Results of sensitivity analysis on self-connected clusters using 0.3 m2/m3 P32 global fracture intensity

P a g e | 48

5.

Discussion 5.1. Connectivity Analysis of the Deltaic reservoirs

Natural fractures are essential for the connectivity of the sand bodies of deltaic reservoirs because

the isolation of sand bodies is prominent throughout the study area. The distribution of self-

connected cluster that resulted from the realizations is the key to evaluate the behavior of the

reservoir. “Are the self-connected clusters connecting the isolated sand bodies by penetrating across

the fine grained flow baffles and flow barriers?” That is the type of question for addressing the role of

self-connected clusters in order to gain maximum recovery from the isolated reservoir.

Figure 24 indicates that the vertical connectivity of the isolated sand bodies is created with the

establishment of one self-connected clusters. The existence of self-connected clusters connects

several non-connected sand bodies, in this case sand bodies from Volume 2, 4, 5, 6, 7, 10 are

connected to sand bodies Volume 1. Thus, self-connected clusters play a role in increasing the

maximum recovery of hydrocarbon produced. The cluster given in the Figure 24 is coming from one

of the self-connected clusters resulted from the base case scenario by assuming a constant 0.3

m2/m3 of P32 global fracture intensity.

Based on the analysis in the realization of self-connected clusters, it needs relatively high global

fracture intensity to form a self-connected cluster (0.3 m2/m3 P32 global fracture intensity). This

means that for P32 global fracture intensity lower than 0.3 m2/m3, there is no connectivity that is

caused by fractures between each reservoir sand bodies. Moreover, for any P32 global fracture

intensity higher than 0.3 m2/m3, there is no further connected cluster formed. The increase in fracture

intensity will only increase the number of fractures formed and size of the connected fracture.

Moreover, this will lead to an increase in the number of connected sand bodies due to the self-

connected clusters covering a wider area that enhances the reservoir connectivity, both lateral and

vertical (Figure 25).

The sensitivity analysis over various DFN parameters also provides insights into the role of fracture

characteristics on connectivity. Figure 23 depicts that variation in aspect ratio gives the highest

intensity of self-connected clusters formed and the lowermost one is given by the variation of

fracture orientation for the realization using similar P32 global fracture intensity is 0.3 m2/m3.

According to Figure 23, Fracture Potential creates more connected fractures than Fracture

P a g e | 49

Proneness. However, the difference is not that intense, around 1 connected fractures surface per

every 100 m3 (very low fracture frequencies). This is acceptable since the ranges of these two

parameters are similar (Figure 16 and Figure 17).

Figure 24. The top picture is the scattered distribution of sand bodies with shaly sand and shale are excluded (for the visualization purpose). The bottom picture is 3D view of one of fracture cluster (created from DFN using 0.3

m2/m3 P32 global fracture intensity) connecting the sand bodies, where shaly sand and shale are excluded.

P a g e | 50

Figure 25. 3D view of sand bodies distribution with the exclusion of other lithologies (top picture). 3D view of self-connected clusters (created from DFN using 0.4 m2/m3 P32 global fracture intensity) connecting the sand bodies

(bottom picture).

The role of sedimentology for the reservoir connectivity can be explained by examining the

distribution of sand bodies of Volume 1 (Figure 26), which comprises around 85% of the sand bodies

in the model (Table 3). Most of the connected sand is found in the lower-middle stacking pattern of

the study area where lateral connectivity is dominant (Figure 26). This indicates that the role of

P a g e | 51

fractures is not really significant for the lower stacking pattern reservoir, as almost all the sand in this

interval are connected.

On the other hand, in terms of vertical connectivity, sand to sand contacts that connect lower sand

bodies to the upper sand bodies are not well distributed throughout the entire study area. There are

only three spots or areas that connect sand bodies in the upper to the lower stacking pattern (Figure

26). This condition affects the fluid path pattern. Vertical permeability baffle is prominent as it may

lead to ineffectiveness in terms of reservoir productivity in the study area. For this evidence,

fractures are essential to enhance the permeability that leads to the increase of reservoir

productivity.

Figure 26. The distribution of sand bodies of Volume 1 that indicates a permeability baffle.

The DFN distribution is also conducted using different sets of grain size distribution as an input. The

data is grain size distribution that consists of 35% of sand delta. In realizing the case, the same

parameters and processes from the base case are applied and the result is shown in the Table 6.

P a g e | 52

Table 6. Detailed dimensions of self-connected fractures using 35% sand delta as an input.

The 35% sand delta model requires 0.2 m2/m3 P32 global fracture intensity to form a connected

fracture cluster, while the 25% sand delta model needs P32 0.3 m2/m3 of global fracture intensity.

Such a result indicates that more sand fraction portion in the model results in lower global fracture

intensity to form connected fracture cluster.

5.2. Reservoir Evaluation

As explained earlier in the Methodology section, in defining the lithology, 50% is used as the cut-off

for the summation of the volume fractions for three biggest grain classes to define sandstone.

Sensitivity of this cut-off is also conducted to analyze how the architecture of the sandstone changes

and how the change affects the interconnectivity within the reservoir bodies. Prior to that reason, the

cut-off was changed to 40% and 60%. The used percentage of 40% as the cut-off will contribute to

large volume of sandstone compares to the base case model (50% cut-off) and the cut-off of 60%

will result in less sandstone.

The sandstone architecture in the 60% cut-off model shows less connected sandstone distribution

compared to the base case model of 50% cut-off (Figure 27). The figure portrays the development

of the sand bodies of Volume 1 in both model. In 60% cut-off model, the distribution of sand bodies

of Volume 1 is only in the lower stacking pattern while in the base case model, it goes to the middle

and upper stacking pattern. This indicates that in 60% cut-off model, permeability barrier is the main

cause to the vertical connectivity of the reservoir in the deltaic reservoirs. On the other hand,

permeability barriers are not an issue for the vertical connectivity in base case model, only


0.1 0 0 - - - -0.2 1 3024 523.26 776.13 20.31 0.0087

532.95 446.04 22.261148.16 602.38 23.5668.02 5224 13.74598.5 427.44 21.371556 1203.57 29.23898.8 553.14 17.64

2597.83 2597.62 40.59529.6 343.2 19.83483.9 689.02 20.91

918.15 588.62 20.751003.98 568.63 17.64398.59 929.15 16.26

0.5 1 500645 2612.33 2605.55 41.64 0.1335

60.4 283153 0.0335

60.3 38896 0.0043

35% sand delta





P a g e | 53

permeability baffles. The role of fractures is more significant in the 60% cut-off model than the base

case model in terms of the vertical connectivity.

Figure 27. Comparison of sandstone architecture for 60% cut-off and 50% cut-off model.

Another comparison for 40% cut-off to base case model is displayed in Figure 28. It shows that the

connected sand bodies of Volume 1 is larger in the 40% cut-off model, especially in the middle

stacking pattern compare to the base case model. Some non-connected sand bodies in the base

case model merge into connected sand bodies of Volume 1, which are sand bodies of Volume 2, 3,

and 9. Thus, interconnectivity caused by sedimentology is significant in the 60% cut-off model. Most

of the sandstone in this model is connected, with both lateral and vertical connectivity, especially in

the southern-central part of the study area in the lower and middle stacking pattern. The role of

fractures in 60% model is less important compare to the base model; however fractures may still

connect the sandstone vertically in the northern area of the model to increase the efficiency of

hydrocarbon production.

P a g e | 54

Figure 28. Comparison of sandstone architecture for 40% cut-off and 50% cut-off model.

Quantitative analysis for all three lithology models in terms of connectivity of the sandstone is

presented in Table 7. It gives detailed information about the distribution of sandstone, connected

sandstone, and sand bodies in three model variations of lithology definition. In the red column, it

gives information about sandstone distribution. Inside this sandstone, there are connected

sandstone and non-connected sandstone. Connected sandstone is where cells classified as

sandstone are laterally or vertically in contact with another sandstone cells. The connected cells will

continue connecting until there are no sandstone cells surrounding them. These connected cells will

form sand bodies that in Petrel are classified as connected volumes. The detail information about the

connected sandstone is given in blue column and red column for detail information about sand

bodies.

Based on the Table 7, the percentage of total sandstone present in the model for 40%, 50%, and

60% cut-off model are 17.78%, 13.83%, and 10.53%, respectively. Within the sandstone, the

percentages of the connected sandstone are 91.15%, 93.56%, and 87.46% for the 40%, 50%, and

60% cut-off model. Again, for the 40%, 50%, and 60% cut off model, the percentages of the P a g e | 55

connected sandstone within the whole model are 12.6%, 16.63%, and 9.21%, respectively. The last

column in is given for brief description about the contribution of the two largest sand bodies to the

connected sandstone for each model.

Table 7. Key statistics of sandstone distribution from models generated by using three different cut-offs in defining the sandstone.

The role of fractures is really significant for reservoir connectivity in the 60% cut-off model. Fractures

are connecting most of non-connected sand bodies (Figure 29). All the sand bodies in the northern-

central part of the study area are being connected by the fractures where total connected sand

bodies volume increase from 47.27% to 97.3% (Table 9), only sand bodies (sand bodies from

Volume 7, 9, and 12) from the upper stacking pattern and located in the northern part of the study

area are not being connected by the fractures. This connectivity will increase the productivity of the

conceptual deltaic reservoirs in this model.

On the other hand, from the illustration given in the Figure 30, the impact of fractures occurrence is

less significant in terms of reservoir connectivity in the 40% cut-off model. Still, fractures connect

several sand bodies in the model, but the volume of the largest sand bodies (sand bodies of Volume

1) covers the majority of the connected sand bodies in the model, around 90.65% (sand bodies-1 in

connected sandstone, Table 7). These connected sand bodies are evenly distributed in the lower

and middle stacking pattern of the model that leads to good sandstone interconnectivity caused by

sedimentological domain. To simplify, the occurrence of fractures will increase the effectiveness of

reservoir productivity but it is less significant for the reservoir connectivity throughout the entire study

ParametersCut-off variation in determining sandstone Quartz > 0.5 Quartz > 0.4 Quartz > 0.6Total Sandstone cells 35960 46238 27383Sandstone in the model (%) 13,83% 17,78% 10,53%Connected sandstone cells 32776 43260 23948Connected sandstone in sandstone (%) 91,15% 93,56% 87,46%Connected sandstone in the model (%) 12,60% 16,63% 9,21%Sand bodies-1 cells 27700 39217 11320Sand bodies-1 in connected sandstone (%) 84,51% 90,65% 47,27%Sand bodies-1 in sandstone (%) 77,03% 84,82% 41,34%Sand bodies-1 in the model (%) 10,65% 15,08% 4,35%Sand bodies-2 cells 1630 985 9060Sand bodies-2 in connected sandstone (%) 4,97% 2,28% 37,83%Sand bodies-2 in sandstone (%) 4,53% 2,13% 33,09%Sand bodies-2 in the model (%) 0,63% 0,38% 3,48%

Sandstone

Connected sandstone

Two largest sand bodies in each sandstone cut-off definition

Key statistic of sandstone distribution in the model

ModelTotal number of cells in model = 260100

P a g e | 56

area for this model. The increase in connected sandstone volume is only around 9% from 90.65% to

99.2% (Table 10).

Figure 29. 3D view of sand bodies distribution with the exclusion of other lithologies (top picture) for the 60% cut-off model. 3D view of one of self-connected clusters (created from DFN using 0.3 m2/m3 P32 global fracture

intensity) connecting the sand bodies (bottom picture).

P a g e | 57

Figure 30. 3D view of sand bodies distribution with the exclusion of other lithologies (top picture) for the 40% cut-off model. 3D view of one of self-connected clusters (created from DFN using 0.3 m2/m3 P32 global fracture

intensity) connecting the sand bodies (bottom picture).

P a g e | 58

6.

Conclusions The proposed workflow given in this study has been successfully applied to analyze the role of local

fractures and reservoir architecture on the interconnectivity of sand bodies across fine grained flow

baffles or barriers.

The role of fractures is significant when the distribution of the reservoir in the model is scattered and

no major connected sand body that covers more than 50% in the study area exists. This type of

reservoir distribution will produce ineffectiveness on the interconnectivity of the sand bodies due to

no significant sand-to-sand contacts created as these contacts are crucial for the interconnectivity

from the sedimentological domain. Fractures will increase the reservoir connectivity, which is crucial

for the fluid flow pattern, as the increase in reservoir connectivity will improve the reservoir

productivity.

The impact of fractures is less important for the reservoirs that are evenly distributed and have one

major connected sand body that covers more than 50% in the study area. The interconnectivity of

sand bodies in this distribution is controlled by the sedimentological domain which was already

created during the deposition of the sediments. The evenly distributed sandstone will limit the role of

finer sediments (shaly sand and shale) to block or to detour the fluid pathway (permeability barrier or

permeability baffle) in the reservoir. In this case, the role of fractures is limited to increasing the

effectiveness of the reservoir productivity as fractures may connect the rest of minor sand bodies

that might not be connected to the major connected sand body.

This study demonstrates that fracture connectivity is really dependent on the DFN distribution, which

is controlled by fracture intensity, geometry, and distribution. It requires relatively high intensity of

global fracture intensity (0.3 m2/m3 P32 global fracture intensity) to create fracture clusters, for the

intensities above 0.5 m2/m3 P32 global fracture intensity, no more fracture clusters are created. It

only affects the size of the fracture cluster formed and the number of fractures in the fracture cluster.

From the sensitivity analysis, for other DFN parameters (fracture geometry and distribution), fracture

shape has the most influence in modeling the fracture connectivity where variation in fracture aspect

ratio contributes to the highest intensity of self-connected clusters formed, which is 0.07 m2/m3 P32

of self-connected clusters with respect to change in aspect ratio of three times bigger from the base

case. This result implies that the growth of fractures within the sediments bodies influence the

fracture connectivity. Such a big aspect ratio may lead fractures to cut through to the other adjacent

P a g e | 59

layers and to intersect other fractures that already reside in the adjacent layers. Thus, this will result

in the possibility of cross-connectivity that will have big influence on the increase of fracture

connectivity.

P a g e | 60

7.

Recommendations To improve this study, it is significant to use field measurement or well log data in determining

parameters needed in building the DFN stochastically as a validation of the workflow proposed in

this study.

One more thing that can be added into this study is to apply more iteration on running the realization

of constructing the DFN. Montecarlo simulation is one of the methods that can be used for running

more iteration since this method is already in the FracMan module.

Last but not least is to bring the output of this study, which is the DFN and self-connected clusters

into dynamic reservoir simulation. This method will give more insight quantitatively on how big the

role of fracture networks is on connecting the isolated sand-bodies and estimating the additional

recovery for the hydrocarbon produced besides from the matrix properties in the deltaic reservoirs.

P a g e | 61

Bibliography

Adler, P. M., and Thovert, J.-F., 1999, Fractures and fracture networks, Springer Science &

Business Media.

Associates, G., 2014, FracMan Version 7.5: Redmond, WA, USA, Golder Associates Inc.

Bai, T., and Pollard, D. D., 2000a, Closely spaced fractures in layered rocks: initiation mechanism

and propagation kinematics: Journal of Structural Geology, v. 22, no. 10, p. 1409-1425.

-, 2000b, Fracture spacing in layered rocks: a new explanation based on the stress transition:

Journal of Structural Geology, v. 22, no. 1, p. 43-57.

Balberg, I., Berkowitz, B., and Drachsler, G., 1991, Application of a percolation model to flow in

fractured hard rocks: Journal of Geophysical Research: Solid Earth, v. 96, no. B6, p. 10015-

10021.

Balberg, I., and Binenbaum, N., 1983, Computer study of the percolation threshold in a two-

dimensional anisotropic system of conducting sticks: Physical Review B, v. 28, no. 7, p.

3799.

Bebbington, M., Vere-Jones, D., and Zheng, X., 1990, Percolation theory: a model for rock fracture?:

Geophysical Journal International, v. 100, no. 2, p. 215-220.

Becker, A., and Gross, M. R., 1996, Mechanism for joint saturation in mechanically layered rocks: an

example from southern Israel: Tectonophysics, v. 257, no. 2, p. 223-237.

Belayneh, M., Masihi, M., Matthäi, S., and King, P., 2006, Prediction of vein connectivity using the

percolation approach: model test with field data: Journal of Geophysics and Engineering, v.

3, no. 3, p. 219.

Berkowitz, B., 1995, Analysis of fracture network connectivity using percolation theory: Mathematical

Geology, v. 27, no. 4, p. 467-483.

Berkowitz, B., and Balberg, I., 1993, Percolation theory and its application to groundwater hydrology:

Water Resources Research, v. 29, no. 4, p. 775-794.

P a g e | 62

Bertotti, G., Hardebol, N., Taal-van Koppen, J., and Luthi, S., 2007, Toward a quantitative definition

of mechanical units: New techniques and results from an outcropping deep-water turbidite

succession (Tanqua-Karoo Basin, South Africa): AAPG bulletin, v. 91, no. 8, p. 1085-1098.

Bloomfield, J., 1996, Characterisation of hydrogeologically significant fracture distributions in the

Chalk: an example from the Upper Chalk of southern England: Journal of hydrology, v. 184,

no. 3, p. 355-379.

Bour, O., and Davy, P., 1997, Connectivity of random fault networks following a power law fault

length distribution: Water Resources Research, v. 33, no. 7, p. 1567-1583.

Castaing, C., Halawani, M., Gervais, F., Chilès, J., Genter, A., Bourgine, B., Ouillon, G., Brosse, J.,

Martin, P., and Genna, A., 1996, Scaling relationships in intraplate fracture systems related

to Red Sea rifting: Tectonophysics, v. 261, no. 4, p. 291-314.

Chelidze, T., 1986, Percolation theory as a tool for imitation of fracture process in rocks: pure and

applied geophysics, v. 124, no. 4-5, p. 731-748.

Choi, K., Jackson, M. D., Hampson, G., Jones, A. D. W., and Reynolds, A. D., Impact of

heterogeneity on flow in fluvial-deltaic reservoirs: Implications for the giant ACG Field, South

Caspian Basin, in Proceedings EUROPEC/EAGE Conference and Exhibition2007, Society of

Petroleum Engineers.

Cooper, S. P., Lorenz, J., and Goodwin, L. B., 2001, Lithologic and structural controls on natural

fracture characteristics: Teapot Dome, Wyoming, Sandia National Laboratories.

Deltares, 2014, Delft3D-FLOW, User Manual: Delft, The Netherlands, Deltares.

Dershowitz, W., 1979, A probabilistic model for the deformability of jointed rock masses: MS Thesis,

Massachusetts Institute of Technology, Cambridge, Massachusetts.

Dershowitz, W. S., 1984, Rock joint systems: Massachusetts Institute of Technology.

Einstein, H., Baecher, G., Veneziano, D., Chan, H., Dershowitz, W., Glynn, E., Galzi, J., Lanney, N.,

O'Reilly, K., and Scull, W., 1979, Risk analysis for rock slopes in open pit mines: Part I and

Final Technical Report to US Bureau of Mines.

Gillespie, P., Howard, C., Walsh, J., and Watterson, J., 1993, Measurement and characterisation of

spatial distributions of fractures: Tectonophysics, v. 226, no. 1-4, p. 113-141.

P a g e | 63

Gross, M. R., 1993, The origin and spacing of cross joints: examples from the Monterey Formation,

Santa Barbara Coastline, California: Journal of Structural Geology, v. 15, no. 6, p. 737-751.

Guéguen, Y., Chelidze, T., and Le Ravalec, M., 1997, Microstructures, percolation thresholds, and

rock physical properties: Tectonophysics, v. 279, no. 1, p. 23-35.

Holt, R., Fjær, E., Nes, O., and Alassi, H., A shaly look at brittleness, in Proceedings 45th US Rock

Mechanics/Geomechanics Symposium2011, American Rock Mechanics Association.

Jarvie, D. M., Hill, R. J., Ruble, T. E., and Pollastro, R. M., 2007, Unconventional shale-gas systems:

The Mississippian Barnett Shale of north-central Texas as one model for thermogenic shale-

gas assessment: AAPG bulletin, v. 91, no. 4, p. 475-499.

Krumbein, W., and Sloss, L., 1964, Stratigraphy and sedimentation, JSTOR.

Ladeira, F., and Price, N., 1981, Relationship between fracture spacing and bed thickness: Journal

of Structural Geology, v. 3, no. 2, p. 179-183.

Laubach, S., Marrett, R., Olson, J., and Scott, A., 1998, Characteristics and origins of coal cleat: a

review: International Journal of Coal Geology, v. 35, no. 1, p. 175-207.

Laubach, S. E., 2003, Practical approaches to identifying sealed and open fractures: AAPG bulletin,

v. 87, no. 4, p. 561-579.

Laubach, S. E., Olson, J. E., and Gross, M. R., 2009, Mechanical and fracture stratigraphy: AAPG

bulletin, v. 93, no. 11, p. 1413-1426.

Lipus, M. P., 2015, Analysis of the impact of sedimentological heterogeneity and fractures on fluid

flow properties in a deltaic reservoir setting using numerical models: TU Delft, Delft University

of Technology.

Mardia, K., 1972, Probability and mathematical statistics: statistics of directional data: London:

Academic.

Masihi, M., King, P. R., and Nurafza, P. R., 2008, Connectivity prediction in fractured reservoirs with

variable fracture size: analysis and validation: SPE Journal, v. 13, no. 01, p. 88-98.

MATLAB, 2014, MATLAB Version R2014b: Natick, Massachusetts, United States, The MathWorks

Inc.

Narr, W., and Suppe, J., 1991, Joint spacing in sedimentary rocks: Journal of Structural Geology, v.

13, no. 9, p. 1037-1048. P a g e | 64

Nelson, R., 2001, Geologic analysis of naturally fractured reservoirs, Gulf Professional Publishing.

Odling, N., Gillespie, P., Bourgine, B., Castaing, C., Chiles, J., Christensen, N., Fillion, E., Genter,

A., Olsen, C., and Thrane, L., 1999, Variations in fracture system geometry and their

implications for fluid flow in fractured hydrocarbon reservoirs: Petroleum Geoscience, v. 5,

no. 4, p. 373-384.

Odling, N. E., 1992, Network properties of a two-dimensional natural fracture pattern: Pure and

Applied Geophysics, v. 138, no. 1, p. 95-114.

-, 1993, An investigation into the permeability of a 2D natural fracture pattern: Pure and Applied

Geophysics, v. 138, p. 97-114.

-, 1997, Scaling and connectivity of joint systems in sandstones from western Norway: Journal of

Structural Geology, v. 19, no. 10, p. 1257-1271.

Panda, M. N., and Lake, L. W., 1994, Estimation of single-phase permeability from parameters of

particle-size distribution: AAPG bulletin, v. 78, no. 7, p. 1028-1039.

Rives, T., Razack, M., Petit, J.-P., and Rawnsley, K., 1992, Joint spacing: analogue and numerical

simulations: Journal of Structural Geology, v. 14, no. 8, p. 925-937.

Rouleau, A., and Gale, J., Statistical characterization of the fracture system in the Stripa granite,

Sweden, in Proceedings International Journal of Rock Mechanics and Mining Sciences &

Geomechanics Abstracts1985, Volume 22, Elsevier, p. 353-367.

SCHLUMBERGER, 2015, Petrel E&P Software Platform Version 2013.8.

Stauffer, D., 1985, Introduction to Percolation Theory, 1st Edition: London, Taylor and Francis Ltd.

Strijker, G., 2013, Multi-scale Fracture Analysis from an Outcrop Analogue: A Case Study from the

Cambro-Ordovician Sequence in Petra, Jordan, TU Delft, Delft University of Technology.

Takebayashi, H., and Kamito, R., 2014, River Flow 2014.

Tyler, N., 1992, Architectural controls on the recovery of hydrocarbons from sandstone reservoirs.

Underwood, C. A., Cooke, M. L., Simo, J. A., and Muldoon, M. A., 2003, Stratigraphic controls on

vertical fracture patterns in Silurian dolomite, northeastern Wisconsin: AAPG bulletin, v. 87,

no. 1, p. 121-142.

P a g e | 65

Van Wagoner, J., Reservoir facies distribution as controlled by sea-level change, in Proceedings

Society of Economic Paleontologists and Mineralogists Mid-Year Meeting, Golden, Colorado,

Abstract, August1985, p. 11-14.

-, 1988, An overview of the fundamentals of sequence stratigraphy and key definitions.

Veneziano, D., 1978, Probabilistic model of joints in rock: Unpublished Manuscript, MIT, Cambridge,

MA.

Warburton, P., A stereological interpretation of joint trace data, in Proceedings International Journal

of Rock Mechanics and Mining Sciences & Geomechanics Abstracts1980a, Volume 17,

Elsevier, p. 181-190.

-, Stereological interpretation of joint trace data: influence of joint shape and implications for

geological surveys, in Proceedings International Journal of Rock Mechanics and Mining

Sciences & Geomechanics Abstracts1980b, Volume 17, Elsevier, p. 305-316.

Willis, B. J., and Fitris, F., 2012, Sequence Stratigraphy of Miocene Tide-Influenced Sandstones In

the Minas Field, Sumatra, Indonesia: Journal of Sedimentary Research, v. 82, no. 6, p. 400-

421.

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Appendix

A. Discrete Fracture Network Distribution

Figure 31. Detail dimensions for the sensitivity analysis of self-connected clusters for Two Fracture Sets scenario

Figure 32. Detail dimensions for the sensitivity analysis of self-connected clusters for the Minimum Number of Fractures in a Cluster scenario


0.1 0 0 - - - -0.2 0 0 - - - -

788.79 606.57 13.911188.28 816.61 16.28528.27 784.14 16.75476.25 456.12 19.45409.39 800.98 15.16

2597.15 2593.06 40.260.5 1 527570 2607.36 2607.59 40.78 0.141

Two Fracture Sets





0.3 3 11982 0.002

308994 0.0760.4 3


0.1 0 0 - - - -0.2 1 496.55 658.03 21.43 0.002

502.71 351.03 21.72447.26 459.25 23.7940.79 859.71 27.32

2595.68 2200.53 38.711032.96 403.62 14.87641.71 456.7 20.56

2602.93 2593.76 39.620.5 1 586680 2605.49 2612.89 40.41 0.154

Minimum Number of Fractures in a Cluster





0.4 3 313665 0.052

0.3 4 122718 0.022

P a g e | 67

Figure 33. Detail dimensions for the sensitivity analysis of self-connected clusters for Aspect Ratio scenario

Figure 34. Detail dimensions for the sensitivity analysis of self-connected clusters for Fracture Size scenario

Figure 35. Detail dimensions for the sensitivity analysis of self-connected clusters for Fracture Proneness scenario


0.1 0 0 - - - -905.33 637.3 17.94

2604.35 1951.95 23.350.3 1 259060 2617.28 2611.82 37.37 0.070.4 1 451793 2625.8 2615.85 37.46 0.120.5 1 640762 2625.97 2629.19 38.63 0.163

Aspect Ratio





0.2 2 46843 0.0127


0.1 0 0 - - - -693.03 832.56 40.56

1006.63 1066.34 37.581406.23 953.65 34.811895.6 864.82 47.04

0.3 1 88769 2649.61 2658.97 46.81 0.0580.4 1 224789 2642.48 2667.05 55.23 0.1020.5 1 329103 2666.85 2660.43 53.3 0.149

Fracture Size





22628 0.0130.2 4


0.1 0 0 - - - -0.2 0 0 - - - -

519.62 493.06 16.73535.98 647.27 18

1569.23 683.46 24.841469.08 1176.51 35.151117.62 2211.29 36.12

538.1 258.77 16.42602.09 2603.92 40.78

0.5 1 402008 2616.46 2600.8 41.04 0.131

Fracture Proneness





0.3 5 80880 0.01

0.4 2 241476 0.076

P a g e | 68

B. Connectivity Analysis

Figure 36. Sandstone distribution of the connected sandstone bodies for the 35% sand model (with cut-off of minimum 100 cells to form sand body). It shows evenly distributed sandstone throughout the entire area that

leads to excellent sandstone interconnectivity caused by sedimentological domain.

Figure 37. Sandstone distribution of the connected sandstone bodies for the 35% sand model with the self-connected clusters (created from DFN using 0.3 m2/m3 P32 global fracture intensity). The occurrence of fractures

will not give significant impact to the interconnectivity of sand bodies.

P a g e | 69

Table 8. Statistics for connected volume of sandstone from 35% sand delta model

Table 9. Statistics for connected volumes of sandstone from 60% cut-off of sandstone definition model

Table 10. Statistics for connected volumes of sandstone from 40% cut-off of sandstone definition model

Min Mean Max Std0 Volume 1 99.18 73475 0.3 2.4 22.8 2.9261 Volume 2 0.21 153 0.3 1.5 4.2 1.0712 Code 2 0.11 84 0.3 0.8 2.1 0.43753 Code 3 0.08 60 0.3 1.1 2.7 0.73874 Code 4 0.08 58 0.3 1.7 5.4 1.5055 Code 5 0.08 56 0.6 1.7 2.7 0.73736 Code 6 0.07 54 0.3 0.6 2.4 0.43867 Code 7 0.07 54 0.3 0.4 0.9 0.1658 Code 8 0.06 46 0.9 2.8 4.8 1.459 Code 9 0.06 41 0.3 0.5 1.2 0.2666


Code Sand volume

% NThickness (m)

Min Mean Max Std0 Volume 1 47.27 11320 0.3 2.2 9.6 2.2491 Volume 2 37.83 9060 0.3 1.7 10.8 1.7832 Volume 3 3.27 783 0.3 1.4 6 1.3463 Volume 4 2.07 496 0.3 1.4 4.2 0.94214 Volume 5 1.98 473 0.3 2.9 9.6 2.9885 Volume 6 1.55 371 0.3 1.1 5.1 1.0016 Volume 7 1.42 339 0.3 1.6 6.6 1.4827 Volume 8 1.2 287 0.3 1.3 5.7 1.2938 Volume 9 1.1 263 0.3 0.8 3 0.53119 Volume 10 0.86 205 0.3 0.8 2.1 0.4874

10 Volume 11 0.8 191 0.3 3.4 10.5 3.24211 Volume 12 0.67 160 0.3 1.3 5.4 1.11


Code Sand volume

% NThickness (m)

Min Mean Max Std0 Volume 1 90.65 39217 0.3 2 17.1 2.1391 Volume 2 2.28 985 0.3 1.4 6 1.3772 Volume 3 1.7 737 0.3 1.8 11.4 2.523 Volume 4 1.66 718 0.3 1.8 4.5 1.2754 Volume 5 0.6 260 0.3 1.9 10.5 2.7365 Volume 6 0.58 250 0.3 0.9 3 0.57636 Volume 7 0.54 234 0.3 0.8 2.4 0.47897 Volume 8 0.46 197 0.3 0.8 2.4 0.44998 Volume 9 0.38 164 0.3 1 3 0.68729 Volume 10 0.35 152 0.3 1.1 3.3 0.7471

10 Volume 11 0.31 134 0.3 0.8 3.9 0.449911 Volume 12 0.25 110 0.3 1 2.1 0.687212 Volume 13 0.24 102 0.3 0.6 1.5 0.7471


Code Sand volume

% NThickness (m)

P a g e | 70

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