8/9/2019 SPE-170940-MS

1/15

SPE-170940-MS

Production Performance Evaluation of Wells Completed in UnconventionalReservoirs Using Capillary Pressure Data and Relative Permeability Effects

B.D. Poe Jr., Schlumberger

Copyright 2014, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Amsterdam, The Netherlands, 2729 October 2014.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Techniques that have been developed and used for evaluation of the production performance of horizontalwells completed in low-permeability reservoirs that are intersected by multiple transverse fractures are presented in this paper. Specifically, the effects of capillary pressure and relative permeabilities areincluded in the production analyses in a practical way using appropriately defined multiphase pseudo- pressure and pseudotime integral transformations and laboratory-determined capillary pressure measure-ments of low-permeability formation cores. The principal type of low-permeability, unconventionalresources that have been of greatest interest for exploration and development in North America recentlyare liquids-rich unconventional resources, due primarily to economic considerations. The principal focusof the analysis techniques reported in this paper therefore pertain primarily to liquids-rich unconventionalresources, but the same general multiphase analysis approach may also be utilized in unconventional gasreservoir analyses as well.

Multiphase expressions have been developed and used in this study for the pseudopressure and pseudotime integral transformations in order to effectively linearize the multiphase diffusivity equationsgoverning the flow of multiple fluids in the reservoir. The multiphase analysis examples reported in this paper utilize Mercury Injection Capillary Pressure (MICP) data for computation of multiphase flowrelative permeability relationships. This type of capillary pressure measurement is likely only directlyapplicable for low (microDarcy) or higher permeability formations, as MICP measurements may tend to

destroy the pore structure of extremely low-permeability (nanoDarcy) cores due to very high injection pressures. In extremely low-permeability formations, other capillary pressure measurement methods may be employed with the multiphase reservoir analysis techniques reported in this paper, without any loss of overall generality.

Capillary pressure measurements can be used to evaluate relative permeabilities for multiphase flowanalyses. The Burdine relative permeability relationships have been used in this study. However, themultiphase analyses developed in this work are readily amenable for the use of other relative permeabilitycorrelations as well. The production analyses and examples presented in this paper demonstrate thatcapillary pressure and relative permeability effects may not be assumed as negligible in low-permeability,unconventional reservoir analyses in general. Omission of these important effects in unconventional

8/9/2019 SPE-170940-MS

2/15

reservoir analyses may lead to significant errors in the estimates of the reservoir intrinsic properties and well completion effectiveness.

The multiphase production performance analysis techniques introduced in this study are demonstrated with an application to a representative example of the production performance of a liquids-rich uncon-ventional resource. The example demonstrates the importance that capillary pressure and relative perme-ability effects can have on the production performance of unconventional reservoirs.

IntroductionA number of investigations have been reported in the literature concerning the evaluation of the production performance of low-permeability unconventional gas reservoirs using numerical reservoir simulation. Among the more directly applicable of these have been the investigations reported by Cipollaet al. [2009] , Freeman et al. [2009] , Moridis et al. [2010] , Miller et al. [2010] , Freeman et al. [2010] , and Jayakumar et al. [2011] . These studies were conducted mainly for the identification of the dominantreservoir properties and production mechanisms affecting the production performance of unconventionalgas reservoirs.

Investigations using an analytic or semi-analytic reservoir-well model approach rather than a numericalsimulation approach for evaluating the production performance of unconventional gas reservoirs haveincluded contributions by Bello and Wattenbarger [2008] , Mattar et al. [2008] , and Anderson et al. [2010] .The transient behavior of horizontal wells intersected by multiple transverse vertical fractures were alsoearlier extensively characterized in investigations reported by van Kruijsdijk and Dullaert [1989] , Robertset al. [1991] , Raghavan et al. [1994] , Larsen and Hegre [1994], Chen and Raghavan [1996] , Wan and Aziz[1999] , and Brown et al. [2009] .

In the investigations previously cited, the effects of capillary pressure and relative permeability on the production performance of unconventional gas reservoirs have only been considered in the studies usingnumerical simulation. For the investigations conducted with analytic or semi-analytic production perfor-mance models or analyses, the traditional use of pseudopressure and pseudotime integral transformationsto account for the pressure-dependent reservoir and fluid properties generally do not include the practicalmultiphase flow effects of capillary pressure and relative permeability. In more moderate to high permeability formations, the assumption of negligible capillary pressure effects may not present asignificant problem. Additionally, in reservoirs that have limited changes in reservoir fluid saturationswith production, small changes in reservoir relative permeability in moderate to high permeabilityformations may have only a small effect on the production performance of the well. However, theseassumptions cannot in general be considered to be applicable in very low-permeability unconventionalreservoirs.

In low-permeability formations, capillary pressures are often obtained with Mercury Injection CapillaryPressure (MICP) measurements ( Purcell [1949] ). Recent examples of the use of MICP measurements for determining capillary pressures in low-permeability formations are readily available in the literature. Acouple of these examples are the investigations reported by Jensenius [2003] and Chu et al. [2012] .Mercury Injection Capillary Pressure measurements are commonly used in low-permeability formations because (1) the measurements are relatively inexpensive to obtain, (2) are well suited to low-permeabilitycores due to high injection pressures, (3) the method provides numerous measurement values, (4)technique is relatively unaffected by formation layering, and (5) the technique requires relatively limited core handling. The negative aspects of using MICP measurements are (1) the fact that mercury is not anenvironmentally friendly substance to work with (toxic), (2) air is the wetting phase in MICP measure-ments and is more highly compressible that other fluids (liquids), and (3) damage and destruction of the pore structures in the core and potential clay particle transport due to very high mercury injection pressures in low-permeability cores.

2 SPE-170940-MS

8/9/2019 SPE-170940-MS

3/15

Capillary pressures for a mercury-air system can be obtained in low-permeability formations usingMICP measurements, and then those results can be readily converted to other two-phase systems (such asoil-water, gas-oil, or gas-water) using the industry standard Leveritt and Lewis [1941] J functionrelationship.

(1)

The contact angle ( ) of a mercury-air system is generally considered to have a value of about 130 and the interfacial tension ( ) of a mercury-air system is about 487 dyne/cm. The contact angles for gas-water and gas-oil systems are typically assumed to be equal to about 0 (due mainly to a lack of accurateexperimental measurements), while an oil-water system tends to have a contact angle value of about 30.Therefore, with the appropriate values of interfacial tension for gas-water and gas-oil systems, thecapillary pressures for gas-water, gas-oil, and oil-water systems can be readily obtained from the MICPmeasurements. For extremely low-permeability formations where MICP measurements are not wellsuited, other techniques may be used to derive values for two-phase system capillary pressures to be used in the multiphase analysis techniques reported in this paper.

In multiphase systems, the fundamental relationship between the pressures of each of the fluid phases,expressed in terms of the two-phase capillary pressures, is given by Eq. 2. In practice, we may find thatan exact balance (as defined in Eq. 2) does not result from the two-phase system capillary pressuremeasurements and system conversions. In such cases, a corrected balance for the multiphase system isevaluated using the residual (R) of the two-phase capillary pressure balance (defined in Eq. 3) with thesystem definitions given in Eqs. 4-7.

(2)

(3)

(4)

(5)

(6)

(7)

With the appropriate sets of two-phase capillary pressure values available, the corresponding sets of two-phase relative permeability relationships can be constructed directly from the capillary pressure data.The Burdine [1953] relationships have been used to compute the wetting and non-wetting phase relative permeability values using the corresponding two-phase capillary pressure data ( Honarpour, Koederitz, and Harvey [1986] ). It is possible to derive the relative permeability relationships from capillary pressuremeasurements because the capillary pressures and relative permeabilities are fundamentally related ( Liand Horne [2003] ). Many other capillary pressure-relative permeability relationships are also available inthe literature to perform this conversion, such as Purcell [1949] , Corey [1954] , and Land [1968] . However,the Burdine [1953] relationships were found to be fully adequate for the multiphase analyses conducted in this reservoir study and are given in Eqs. 8 and 9.

(8)

SPE-170940-MS 3

8/9/2019 SPE-170940-MS

4/15

(9)

For low-permeability unconventional reservoir analyses, the use of empirical relative permeabilityrelationships that are decoupled from the observed (measured) capillary pressures is not recommended.With the large capillary pressures and high residual wetting phase saturations often encountered in

low-permeability unconventional reservoirs, it may be quite difficult to properly calibrate the empiricalrelative permeability relationships that are independent of capillary pressures to match the observations.

An investigation of capillary pressure and relative permeability effects on the analysis of multiphase production performance of wells completed in low-permeability unconventional reservoirs has beenconducted in this research effort. Low-permeability unconventional reservoirs are currently commonlycompleted with horizontal wellbores intersected by multiple transverse fractures. This study was under-taken in order to attempt to quantify the magnitude of the capillary pressure and relative permeabilityeffects on well performance analyses, as well as to determine the significance of neglecting those effectsin the production performance analyses of unconventional reservoirs have on the parameter estimates of the reservoir intrinsic properties and well completion effectiveness determined with these analyses. Thesefindings can then be used to improve the production performance analyses of wells completed in

unconventional reservoirs.

Mathematical ModelThe flow of multiple fluids in a uniform height, homogeneous reservoir in which gravitational effects areconsidered negligible is classically described by the diffusivity relationships given in Eqs. 10 , 11 , and 12for the oil, water, and gas phases, respectively. The system saturation balance is given in Eq. 13 .

(10)

(11)

(12)

(13)

The spatial and temporal gradients of the pressure-dependent reservoir and fluid properties ( , Bo , Bw , B g , R so , R sw , o , w and g ) can be evaluated for a specified spatial coordinate system. An evaluationtechnique that may also be used to evaluate the diffusivity relationships governing multiphase flow in thereservoir is the introduction of an integral transformation to account for the non-linear reservoir and fluid properties with respect to the dependent variable (pressure). The spatial and temporal gradients of thesaturation-dependent reservoir properties that appear in these relationships [capillary pressure and relative permeabilities: P cgo , P cgw , P cow , k ro , k w , and k rg )] may also be recast as functions of the dependent variable(pressure). The reservoir fluid saturations needed for the capillary pressure and relative permeabilityevaluations in that approach are explicitly determined from the changes in the pore pressure level.

It is beyond the scope of this study to attempt to address or evaluate the numerous possible combinationrules that have been developed and reported in the literature for estimating three-phase flow oil relative permeabilities. In three-phase flow, it has been found that the oil relative permeability is stronglyinfluenced by the wettability of the formation and that a single combination rule for three-phase flow oilrelative permeabilities has not been identified to provide satisfactory results in all cases ( Pejic and Maini[2003] ). Other reasonably recent references that are related to three-phase flow oil relative permeabilityestimation may be found in Honarpour, Koederitz, and Harvey [1986] , Baker [1988], and Blunt [1999].

4 SPE-170940-MS

8/9/2019 SPE-170940-MS

5/15

8/9/2019 SPE-170940-MS

6/15

case, a multiphase correlation function to account for the variation of the reservoir and fluid propertiesvariation with respect to time may be evaluated using Eq. 21 . If sufficient production from the reservoir

has occurred such that the average reservoir pressure and fluid saturations and spatial distributions havechanged measurably (i.e. finite systems or significant saturation changes at wellbore), a more rigorousmultiphase pseudotime correlation function must be utilized. One method for effectively evaluating finitereservoir average saturation changes is to compute the average reservoir fluid saturations using theSchilthuis [1936] material balance, similar to the technique reported in Dake [1978] .

(21)

where:(22)

(23)

The multiphase pseudotime correlation function can also be expressed in a dimensionless form that isapplicable for use in analyses using classical slightly-compressible liquid flow solutions in dimensionlessform.

(24)

A total reservoir flow rate for use in correlating the multiphase flow solutions can be evaluated as given by Eq. 25 .

(25)

A total reservoir cumulative production may also be defined for use in correlating the multiphasereservoir response as shown in Eq. 26 .

(26)

ApplicationAn example application of the multiphase analysis approach developed in this study to a liquids-rich,low-permeability, unconventional reservoir can be used to demonstrate the importance of includingcapillary pressure and relative permeability effects in a production performance analysis. In addition, thesignificance of neglecting these effects in the production performance analyses of unconventional

Figure 1Example MICP mercury-air system capillary pressures.

6 SPE-170940-MS

8/9/2019 SPE-170940-MS

7/15

reservoirs are illustrated by the deviations in reservoir property and well completion effectiveness parameter estimates obtained. This data available for this example analysis includes the MICP data, petrophysical properties, PVT, and production performance data.

Mercury Injection Capillary Pressure (MICP) data were obtained for several cores from this well. TheMICP measurements were reasonably similar for all of the samples tested, likely because the formationwas relatively uniform and low-permeability. A representative sample of the MICP data was chosen for use in the multiphase analysis (illustrated in Fig. 1), of which an abbreviated listing of the correspondingcomputed two-phase equivalent capillary pressures for gas-water, gas-oil, and oil-water systems are givenin Table 1 . Note that the two-phase system equivalent capillary pressures are referenced to the MICPmeasurement mercury saturations and J function values in this table.

The normalized relative permeabilities computed using the Burdine [1953] correlations that are derived from the MICP data are presented in Fig. 2. Note the high residual wetting phase saturation that isassociated with this example relative permeability data. This characteristic is quite common for therelative permeability response of low-permeability unconventional reservoirs.

The pertinent petrophysical, reservoir and fluid properties reservoir necessary for the evaluation of the production performance analysis are given in Table 2 . Note that the well is a horizontal well with a 4,000

ft lateral, perforated and fractured with 58 perforation clusters geometrically-spaced at about 68 ft apart.The production rates for the well are shown in Fig. 3 and the corresponding cumulative production

values are presented in Fig. 4. The recorded wellhead and computed bottomhole flowing pressures of the production history are given in Fig. 5.

A non-linear regression production history match of the well performance using the fractured hori-zontal well transient model of Brown et al. [2009] and the multiphase flow analysis correlations of thisstudy are illustrated in Fig. 6. The match was obtained in 10 iterations with a Chi-squared residual of 0.727. Comparable agreement was also observed for the match of the total reservoir flow rate correlationfunction (qrt ).

The production history match in which the capillary pressures and associated relative permeabilityeffects are included in the analysis results in estimates for the formation total mobility ( t ) of 9.35 10

3

mD/cp, an average fracture half-length (X f ) of 81 ft, an average fracture conductivity (k f w) of 1.4 mD-ft,and an estimated Stimulated Reservoir Volume (SRV) of about 15 acres. The equivalent average effective permeability to oil (k o ) from the analysis is 1.1x10

3 md and the average effective permeability to water (k w ) that corresponds to the match is 1.68 10

4 mD. The corresponding computed average reservoir evaluated with the production performance match is illustrated in Fig. 7, along with the computed producing gas-oil ratio (solution gas) and water cut.

A similar match of the production data assuming negligible capillary pressure effects results in parameters estimates for the effective permeability to oil of 3 10 4 mD, an average effective fracturehalf-length of 126 ft and an effective area of the Stimulated Reservoir Volume of 23 acres. A look at thecapillary pressure table ( Table 1 ) for an oil-water system indicates that the capillary pressure is initially

a little over 600 psia and the relative permeability to the non-wetting (oil) phase (from Fig. 2) is indicated to initially be about 0.45. The relative permeability to the wetting phase (water in this case) is essentiallyzero up to approximately 90 % wetting phase saturation. The high residual wetting phase saturation resultsin retention of large amounts of the fracture fluid (water) remaining in the formation, reducing theeffective permeability to the non-wetting phase as well, which can exist even after a long production time.

SPE-170940-MS 7

8/9/2019 SPE-170940-MS

8/15

Table 1Two-Phase System Capillary Pressures from MICP Data

8 SPE-170940-MS

8/9/2019 SPE-170940-MS

9/15

Figure 2Computed relative permeabilities from MICP data.

Table 2Example petrophysical, reservoir and fluid properties.

h 200 ft r w 0.33 ft 7 % S o 70 % S w 30 % P i 6000 psia T 255F n f 58 d f 68 ft

0 55API g 0.6 c f 3 106 1/psia ct 1.32 10

5 1/psia Bo 2.1 rb/STB R so 2168 scf/STB 0 0.13 cp co 1.32 10

5 1/psia Bw 1.054 rb/STB R sw 28.2 scf/STB 0.25 cp cw 3.13 10

6 1/psia B g 0.66 rb/Mscf g 0.025 cp c g 1.1 10

4 1/psia

Figure 3Production rates of example well.

SPE-170940-MS 9

8/9/2019 SPE-170940-MS

10/15

Figure 4 Cumulative production values for example well.

Figure 5Wellhead and computed bottomhole flowing pressure history.

Figure 6 Multiphase correlation function match of production performance.

10 SPE-170940-MS

8/9/2019 SPE-170940-MS

11/15

ConclusionsThis study has investigated the influence of capillary pressure and relative permeability effects on themultiphase production performance of a low-permeability unconventional reservoir. The results of thisinvestigation suggest a few significant observations and conclusions.

1. Capillary pressure and relative permeability effects can be quite significant in low-permeabilityunconventional reservoir analyses. These effects are not negligible in general.

2. Low-permeability formations commonly encountered in unconventional reservoirs can have veryhigh residual wetting phase saturations, leading to the retention of large amounts of stimulationfluids in the formation.

3. Neglecting capillary pressure (and associated relative permeability) effects in low-permeabilityunconventional reservoir production performance analyses can result in significant errors inestimating values of the reservoir intrinsic properties and well completion effectiveness.

AcknowledgementsThe author wishes to acknowledge Schlumberger for providing the resources and opportunity to conductthis investigation, and for the permission to present the results of the research effort.

Nomenclature B g Gas formation volume factor, rcf/scf Bo Oil formation volume factor, rb/STB Bw Water formation volume factor, rb/STBc f Formation pore compressibility, 1/psiac

g

Gas compressibility, 1/psiaco Oil compressibility, 1/psiacw Water compressibility, 1/psiact System total compressibility, 1/psiad f Average distance between adjacent fractures, ftG P Cumulative gas production, MMscf h Reservoir net pay thickness, ft J Leveritt capillary pressure correlation functionk Formation absolute permeability, mDk o Original formation absolute permeability, mD

Figure 7Computed average reservoir pressure, producing gas-oil ratio, and water cut.

SPE-170940-MS 11

8/9/2019 SPE-170940-MS

12/15

8/9/2019 SPE-170940-MS

13/15

t Time, hrsT Average reservoir temperature, deg Ft a Multiphase pseudotime correlation function, md-psia-hrs/cpt D Dimensionless timeW p Cumulative water production, STB

t System total mobility, mD/cp

g Gas specific gravity (air 1) o Stock tank liquid gravity, deg API g

Gas viscosity, cpo

Oil viscosity, cpw

Water viscosity, cp w Formation effective porosity, frac BV o Original formation effective porosity, frac BV Interfacial tension, dyne/cm Contact angle, deg

ReferencesAnderson, D.M., Nobakht, M., Moghadam, S. et alet al. 2010. Analysis of Production Data from

Fractured Shale Gas Wells. Paper SPE 131787 presented at the SPE Unconventional Gas Conference,Pittsburgh, Pennsylvania, USA. doi: 10.2118/131787-MS.

Aziz, K. and Settari, A. 1979. Petroleum Reservoir Simulation . Applied Science Publishers, London,England.

Bello, R.O. and Wattenbarger, R.A. 2008. Rate Transient Analysis in Naturally Fractured Shale GasReservoirs. Paper SPE 114591 presented at the CIPC/SPE Gas Technology Symposium 2008 JointConference, Calgary, Alberta, Canada. doi: 10.2118/114591-MS.

Brown, M., Ozkan, E., Raghavan, R., and Kazemi, H. 2009. Practical Solutions for Pressure TransientResponses of Fractured Horizontal Wells in Unconventional Reservoirs. Paper SPE 125043 presented atthe SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, Oct. 4-7.

Burdine, N.T. 1953. Relative Permeability Calculations from Pore Size Distribution Data. Trans., AIME, 198, 7178.

Chen, C.C. and Raghavan, R. 1996. A Multiply-Fractured Horizontal Well in a Rectangular DrainageRegion. Paper SPE 37072 presented at the SPE International Conference on Horizontal Well Technology,Calgary, Alberta, Canada, Nov. 18-20.

Chu, L., Ye, P., Harmawan, I., Di, L., and Shepherd, L. 2012. Characterizing and Simulating the Non-Stationariness and Non-Linearity in Unconventional Oil Reservoirs : Bakken Application. Paper SPE161137 presented at the SPE Canadian Unconventional Resources Conference, Calgary, Alberta, Canada,Oct. 30-Nov. 1.

Cipolla, C.L., Lolon, E., Erdle, J. et alet al. 2009. Modeling Well Performance in Shale-GasReservoirs, Paper SPE 125532 presented at the SPE/EAGE Reservoir Characterization and SimulationConference, Abu Dhabi, UAE. doi: 10.2118/125532-MS.

Corey, A.T. 1954. The Interrelation Between Gas and Oil Relative Permeabilities. Prod. Mon., 19, 38.Dake, L.P. 1978. Fundamentals of Reservoir Engineering . Elsevier Scientific Publishing Co., New

York City, New York, USA. 8586.Freeman, C.M., Ilk, D., Moridis, G.J., and Blasingame, T.A. 2009. A Numerical Study of Performance

for Tight Gas and Shale Gas Reservoir Systems. Paper SPE 124961 presented at the SPE AnnualTechnical Conference and Exhibition, New Orleans, Louisiana, USA. doi: 10.2118/124961-MS.

SPE-170940-MS 13

8/9/2019 SPE-170940-MS

14/15

Freeman, C.M., Moridis, G.J., Ilk, D. and Blasingame, T.A. 2010. A Numerical Study of Transportand Storage Effects for Tight Gas and Shale Gas Reservoirs Systems. Paper SPE 131583 presented at theSPE International Oil & Gas Conference and Exhibition, Beijing, China, June 8-10.

Honarpour, M., Koederitz, L., and Harvey, A.H. 1986. Relative Permeability of Petroleum Reservoirs .CRC Press, Inc. Boca Raton, Florida, USA.

Jayakumar, R., Sahai, V., and Boulis, A. 2011. A Better Understanding of Finite Element Simulationfor Shale Gas Reservoirs through a Series of Different Case Histories. Paper SPE 142464 presented at theSPE Middle East Unconventional Gas Conference and Exhibition, Muscat, Oman. doi: 10.2118/142464-MS.

Jensenius, J. 2003. A New Capillary Curve Modelling Method for North Sea Chalk and Other LowPermeability Reservoirs. Paper presented at the SPWLA 44th Annual Logging Symposium, June 22-25.

Land, C.S. 1968. Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flowfrom Rock Properties. SPEJ, June, 149.

Larsen, L. and Hegre, T.M. 1991. Pressure-Transient Behavior of Horizontal Wells with Finite-Conductivity vertical Fractures. Paper SPE 22076 presented at the SPE International Arctic TechnologyConference, Anchorage, Alaska, USA, May 29-31.

Leveritt, M.C. and Lewis, W.B. 1941. Steady Flow of Gas-Oil-Water Mixtures Through Unconsol-idated Sands. Trans. AIME, 142, 107116.

Li, K. and Horne, R. 2003. Numerical Simulation with Input Consistency Between Capillary Pressureand Relative Permeability. Paper 79716 presented at the SPE Reservoir Simulation Symposium, Houston,Texas, USA, Feb. 3-5.

Mattar, L., Gault, B., Morad, K., Clarkson, C.R., Freeman, C.M., Ilk, D., and Blasingame, T.A. 2008.Production Analysis and Forecasting of Shale Gas Reservoirs: Case History-Based Approach. Paper SPE119897 presented at the SPE Shale Gas Production Conference, Fort Worth, Texas, USA. doi: 10.2118/119897-MS.

McKee, C.R., Bumb, A.C., Koenig, R.A. 1988. Stress-Dependent Permeability and Porosity of Coaland Other Geologic Formations. SPEFE, March 1988, 8191.

Medeiros, F., Ozkan, E., and Kazemi, H. 2006. A Semianalytical, Pressure-Transient Model for Horizontal and Multilateral Wells in Composite, Layered, and Compartmentalized Reservoirs. Paper SPE102834 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA.doi: 10.2118/102834-MS.

Miller, M.A., Jenkins, C.D., and Rai, R.R. 2010. Applying Innovative Production Modeling Tech-niques to Quantify Fracture Characteristics, Reservoir Properties, and Well Performance in Shale GasReservoirs. Paper SPE 139097 presented at the SPE Eastern Regional Meeting, Morgantown, WestVirginia, USA. doi: 10.2118/139097-MS.

Moridis, G.J., Blasingame, T.A., and Freeman, C.M. 2010. Analysis of Mechanisms of Flow inFractured Tight-Gas and Shale-Gas Reservoirs. Paper SPE 139250 presented at the SPE Latin Americanand Caribbean Petroleum Engineering Conference, Lima, Peru. doi: 10.2118/139250-MS.

Pejic, D. and Maini, B.B. 2003. Three-Phase Relative Permeability of Petroleum Reservoirs. Paper 81021 presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Port-of-Spain, Trinidad, West Indies, April 27-30.

Purcell, W.R. 1949. Capillary Pressures-Their Measurement Using Mercury and the Calculation of Permeability. Trans., AIME, 186, 39.

Raghavan, R.S., Chen, C.C., and Agarwal, B. 1994. An Analysis of Horizontal Wells Intercepted byMultiple Fractures. Paper SPE 27652 presented at SPE Permian Basin Oil and Gas Recovery Conference,Midland, Texas, USA, Mar. 16-18; SPEJ, Vol. 2, Sep. 1997, 235245.

14 SPE-170940-MS

8/9/2019 SPE-170940-MS

15/15

Roberts, B.E., van Engen, H., and van Kruijsdijk, C.P.J.W. 1991. Productivity of Multiply Fractured Horizontal Wells in Tight Gas Reservoirs. Paper SPE 23113 presented at SPE Offshore Europe Confer-ence, Aberdeen, UK, Sep. 3-6.

Schilthuis, R.J. 1936. Active Oil and Reservoir Energy. Trans., AIME . 118, 3352.van Kruijsdijk, C.P.J.W. and Dullaert, G.M. 1989. A Boundary Element Solution of the Transient

Pressure Response of Multiply Fractured Horizontal Wells. 2nd European Conference on the Mathematicsof Oil Recovery, Cambridge, England.

Wan, J. and Aziz, K. 1999. Semi-Analytical Well Model of Horizontal Wells With Multiple HydraulicFractures. Paper SPE 81190 presented at the SPE West Regional Meeting and Exhibition, Anchorage,Alaska, USA. May 26-27; SPEJ, Dec. 2002, 437445.

SPE-170940-MS 15