spe-167753-pa - understanding shale gas flow behavior using numerical simulation

Understanding Shale Gas Flow BehaviorUsing Numerical Simulation

Hao Sun, Adwait Chawathe, Hussein Hoteit, Xundan Shi, and Lin Li, Chevron Energy Technology Company

Summary

Shale gas has changed the energy equation around the world, andits impact has been especially profound in the United States. It isnow generally agreed that the fabric of shale systems comprisesprimarily organic matter, inorganic material, and natural fractures.However, the underlying flow mechanisms through these multi-porosity and multipermeability systems are poorly understood.For instance, debate still exists about the predominant transportmechanism (diffusion, convection, and desorption), as well as theflow interactions between organic matter, inorganic matter, andfractures. Furthermore, balancing the computational burden ofprecisely modeling the gas transport through the pores vs. runningfull reservoir scale simulation is also contested. To that end, com-mercial reservoir simulators are developing new shale gasoptions, but some, for expediency, rely on simplification of exist-ing data structures and/or flow mechanisms.

We present here the development of a comprehensive multi-mechanistic (desorption, diffusion, and convection), multiporosity(organic materials, inorganic materials, and fractures), and multi-permeability model that uses experimentally determined shale or-ganic and inorganic material properties to predict shale gasreservoir performance. Our multimechanistic model takes intoaccount gas transport caused by both pressure driven convectionand concentration driven diffusion. The model accounts for allthe important processes occurring in shale systems, includingdesorption of multicomponent gas from the organics’ surface,multimechanistic organic/inorganic material mass transfer, multi-mechanistic inorganic material/fracture network mass transfer,and production from a hydraulically fractured wellbore.

Our results show that a dual porosity, dual permeability(DPDP) model with Knudsen diffusion is generally adequate tomodel shale gas reservoir production. Adsorption can make sig-nificant contributions to original gas in place, but is not importantto gas production because of adsorption equilibrium. By compar-ing triple porosity, dual permeability; DPDP; and single porosity,single permeability formulations under similar conditions, weshow that Knudsen diffusion is a key mechanism and should notbe ignored under low matrix pressure (Pematrix) cases, whereasmolecular diffusion is negligible in shale dry gas production. Wealso guide the design of fractures by analyzing flow rate limitingsteps. This work provides a basis for long term shale gas produc-tion analysis and also helps define value adding laboratorymeasurements.

Introduction

Shale gas refers to natural gas that is trapped within fine grainedsedimentary rocks called shale or mudstone that can be richsource rocks for oil and natural gas. Over the past decades, tech-nological advances such as horizontal drilling and hydraulic frac-turing have allowed access to large volumes of shale gas thatwere previously uneconomic. The “shale gas revolution” hasrejuvenated the natural gas industry in the US and the globalenergy markets. In 2013, the Energy Information Administration

(EIA) estimated approximately 7,300 Tcf of shale gas resourcesand 345 billion bbl of shale oil resources in 137 shale formationsin 41 countries that are technically recoverable (EIA 2013). Glob-ally, 32% of the total estimated natural gas resources are in shaleformations, whereas 10% of estimated oil resources are in shaleor tight formations (EIA 2013). The US alone has 665 Tcf of tech-nically recoverable shale gas resources (EIA 2013), which cansupply more than 30 years of US gas demand.

Shale reservoirs have distinctive features compared with tradi-tional reservoirs. Shale gas reservoirs form within the organic richsource rock but with much smaller pore sizes—and thus lower per-meability—and without fluid migration. Furthermore, the low per-meability and adsorption on the shale retard the migration of gasto a more permeable reservoir. The shale reservoir is both thesource rock and the seal. Dominant pore diameters of most shalereservoirs are smaller than 2 nm instead of 1 to 100 mm pores ofconventional sandstone and carbonate reservoirs (Swami et al.2012). The permeability of conventional reservoirs is in the 10 to10,000 md range; shale is much tighter. For the same shale sam-ple, different test methods may give very different permeabilityvalues, or data from different laboratories can be very different.Diffusion can enhance the gas transport through the nanopores ofa shale gas reservoir. On the basis of laboratory observations, thegas transport speed in a 10 nm capillary is comparable with that ina 100 nm capillary because of the increased gas diffusion throughthe smaller sized capillary space (Roy et al. 2003). The mean freepath of the methane molecule is even smaller than the nanometer-scale pore radius. Gas molecules bump along the nanopores duringtransport (Albo et al. 2006). This gas transport enhancement isdefined as Knudsen diffusion and cannot be modeled by the con-ventional constant permeability convection model. Despite this,shale yields a low ultimate recovery (less than 20%) even aftermultistage fracturing (Dahaghi and Mohaghegh 2011).

Because of the limited understanding of the nanopores and theintrinsic production mechanisms in shale, multiphase flowthrough shale reservoirs—through the complex and multiscalepathways ranging from nanopores and micrometer scale pores tomillimeter scale apertures of fractures (Olson et al. 2009; Anderset al. 2014)—cannot be modeled comprehensively in existingcommercial simulators. The current reservoir simulators, whichare primarily modeled after conventional reservoir transportmechanisms, are limited in their ability to generate robust shalegas production forecasts. The current commercial simulators thatwe are aware of lack explicit modeling of the shale pore structure(organics, inorganics, and fractures) and the underlying multime-chanistic flow mechanisms. Some may have many shale gas spe-cific options—such as explicit logarithmically spaced local gridrefinement dual permeability modeling of hydraulic fracturesalong the horizontal well, microseismic data input, geomechanicalcoupling, or gas/gas molecular/Knudsen diffusion for matrix andmatrix subdivision (Rubin 2010)—but may lack a triple porosity,dual permeability modeling option (CMG 2010). A model usingdesorption and gas/gas molecular diffusion in the dual porositymodel was commercially implemented in EMpower software in2011 (Leahy-Dios et al. 2011). However, this model lacks matrixKnudsen diffusion. Still another model has gas/liquid and gas/gasmolecular diffusion, fracture/matrix/vug triple porosity option,and a fracture matrix diffusion, but lacks a matrix gas Knudsendiffusion term (Schlumberger 2010).

Laboratories also need guidance on value adding shale propertiesthat need to be measured (diffusivity or permeability; separating

Copyright VC 2014 Society of Petroleum Engineers

This paper (SPE 167753) was accepted for presentation at the SPE/EAGE EuropeanUnconventional Resources Conference and Exhibition, Vienna, Austria, 25–27 February2014, and revised for publication. Original manuscript received for review 7 October 2013.Revised manuscript received for review 9 August 2014. Paper peer approved 21 August2014.

J167753 DOI: 10.2118/167753-PA Date: 20-December-14 Stage: Page: 1 Total Pages: 13

ID: jaganm Time: 11:50 I Path: S:/3B2/J###/Vol00000/140070/APPFile/SA-J###140070

2014 SPE Journal 1

properties of organics from those of inorganics, such as organicporosity or inorganic porosity, organic diffusivity, inorganic per-meability or inorganic diffusivity). Reservoir engineers also needto understand the use of laboratory measured properties correctlyfor reservoir simulation to generate better predictions. Currently,most research is focused on pore scale shale gas molecular simu-lation by use of the lattice Boltzmann method (Akkutlu and Fathi2011, 2012), core scale permeability/diffusivity measurement(Cui et al. 2009), apparent permeability function derivation, andthe implementation of apparent permeability function to the reser-voir simulator (Javadpour et al. 2007; Javadpour 2009). A system-atic work flow from laboratory measurement to reservoir scalesimulation has not been established to truly understand shale gasproduction mechanisms (Mirzaei and Cipolla 2012).

We have performed a systematic study on shale gas transportmechanisms by use of laboratory derived measurements as wellas reservoir simulation. Gas transport kinetics were measuredexperimentally in our laboratory by use of both gravimetric andvolumetric methods. The gravimetric method consists of meas-uring the weight gain or loss by a sample under an equilibriumpressure and temperature. The intelligent gravimetric analyzerequipment involves continuously monitoring and analyzing theweight data after a controlled change in gas pressure. The temper-ature range is 70–300�F, and pressure can be up to 6,000 psi. Thisreal time analysis both determines the kinetic parameters and pre-dicts the exact point of equilibrium uptake. The equilibrium pointsare collected and plotted as an isotherm, whereas the kinetics datacan be extracted from the weight vs. time data between pressuresteps. The volumetric apparatus was built in-house and consists oftwo volume chambers, pressure sensors, valves, and a vacuumsystem. The volumes of both cells need to be carefully measuredbefore operating the unit. Each measurement of the total quantityof gas admitted into the system and of the amount of gas remain-ing in the gas phase at the adsorption equilibrium are determinedby recording pressure and temperature of both cells. The kineticanalysis for both gravimetric and volumetric methods is the same.On the basis of the mass transfer characteristics of shale samples,a dual porosity model was developed to analyze the gas uptake orrelease of dynamic data and to obtain mass transfer parameters ineach step.

According to our internal laboratory results, effective diffusiv-ity, which lumps both convection and diffusion, depends on shaleparticle sample size. If the shale particle sample size is smallenough, the characteristic dimension of inorganic material is com-parable with that of organic material. Therefore, the effective dif-fusivity measured in the laboratory mostly represents organicmaterial properties. On the other hand, the effective diffusivity ofa larger particle depends on mass transfer properties of both or-ganic and inorganic materials of the shale sample. Analyzing thedata collected in our internal laboratories, we concluded that theeffect of particle size on the effective diffusivity measured in thelaboratory could not be matched by a single porosity (matrix

only) model but required a dual porosity (organic and inorganicmaterials) model. This important observation was also supportedby previous coal literature, in which a bidisperse (two pore) modelwas required to match the experimental data of some coal types(Clarkson and Bustin 1999). Therefore, we concluded that it isnecessary to separately model slow gas transport in the organicsand relatively quick gas transport in inorganic material. However,is this conclusion from the laboratory study still valid at the reser-voir scale? Do we still need to model gas transport in organic ma-terial separately from that in inorganic material (Hudson et al.2012)? Is the gas transport in organic material still the limitinggas production at the reservoir scale? How important is the diffu-sion mechanism compared with the convection inside both or-ganic and inorganic material? Which diffusion—molecular,Knudsen, or both—should be implemented in a shale gas reser-voir simulator?

To answer all these key questions, we have built a new simula-tor that explicitly captures all our current understanding of theshale pore structure and the gas/water flow mechanisms throughorganic material, inorganic material, and the fracture networks ofshale reservoirs. Relying on this tool with guidance from labora-tory observations, we improved our understanding of multiphasegas and water transport through shale reservoirs. This simulatorprovides a basis for long term shale gas production analysis andhelps define value adding laboratory measurements.

Shale Gas Reservoir Structure andFlow Mechanism Model Development

Fig. 1a shows the scanning electron microscope photomicrographof a fine grained mudrock; Fig. 1b shows the comparison of scaleof porosity observed in the organic matter in a Silurian gas shale(eastern Europe) rock. The scale bar for the mudrock is 10 mmand 500 nm for the organic matter (inset image), representing adifference in scale of two orders of magnitude. Tiny organic mate-rial (including kerogen and bitumen) is scattered through predom-inantly inorganic material in shale. This is the opposite oftraditional coal structures, in which tiny inorganic material is em-bedded through organic material (Kang et al. 2010). The darkgray region is organic material (Fig. 1b). Organic pores are nar-rowly distributed in the nanometer scale and appear black becauseof the light reflection. Gas, such as methane (CH4) or ethane, isadsorbed inside these pores within the organic material. Lightgray regions are inorganic material (Fig. 1b). Inorganic poreshave a wide pore size distribution from nanometer (nm) to micro-meter (mm). According to external, and our internal, laboratorymeasurements, shale samples have a narrow pore size distributionof approximately 2 nm, indicating that nanopores in both organicand inorganic regions dominate the shale gas reservoir pore struc-ture. Therefore, understanding shale gas mass transfer throughthese nanopores is essential for understanding the overall shalegas production mechanisms.

Inorganic material

10 μm

detTLD

HV10.0 kv

spot3.0

mag150 000 x

HFW1.99 μm

500 nm Bureau of Economic Geology

WD5.4 mm

detETD

HV15.0 kv

spot5.0

mag12 000 x

HFW24.9 μm

10 μm Bureau of Economic Geology

WD10.0 mm

500 nm

2 1 Organic material

Fig. 1—(a) Scanning electron microscope photomicrograph of a fine grained mudrock; (b) comparison of scale of porosityobserved in the organic matter of Silurian gas shale (eastern Europe) rock. The scale bar for the mudrock is 10 lm and 500 nm forthe organic matter (inset image), representing a difference in scale of two orders of magnitude. Numbers in blue circles help relateFigs. 1, 2, and 3 (photograph courtesy of Douglas McCarty, Chevron Energy Technology Company).



2 2014 SPE Journal

At the same time, the gas transport mechanism within shale isa function of pore size. In the nanopores, CH4 molecules form adense, liquid like adsorption layer that covers internal surfaces ofthe nanopore walls. The thickness of the adsorption layer is equalto the CH4 molecule diameter (0.37 nm). If there is still porespace besides the adsorption layer, there can be a phase transitionlayer. The molecules in the phase transition layer are relativelyless dense and more mobile, but are still under the influence of thewall. The thickness of the transition layer is approximately twicethe CH4 molecule diameter. Therefore, mass transport inside thenanopores is approximately three CH4 molecule diameters thick(1.11 nm) and can be under the influence of the wall. Knudsendiffusion adequately describes this mass transport under wallinfluence. The traditional no slip boundary condition in the con-tinuum flow regime is therefore considered invalid (Clarksonet al. 2011).

For mass transport of molecules in the larger pores (mm in di-ameter and larger), the influence of pore surface can be ignored.The flow mechanisms are convection and molecular diffusionbecause of pressure gradient and mole fraction gradient, respec-tively. For the molecular diffusion model, mass migration isassumed to take place only between the fluid molecules in thesame phase. Molecular diffusion has been used to model gas/soliddiffusionally controlled reaction (Sun et al. 2012; Zygourakiset al. 2013), and is an important mechanism for gas injectionenhanced oil recovery in naturally fractured reservoirs (Hoteit andFiroozabadi 2009).

On the basis of our understanding of shale pore structures, theconceptual triple porosity, dual permeability (TPDP) multime-chanistic (desorption, diffusion, and convection) and multicompo-nent gas/water flow model for a shale gas reservoir is built (Fig.2). This modeling concept is an extension of the methodologydeveloped at Pennsylvania State University for modeling coalbedmethane reservoirs (Chawathe 1995; Thararoop et al. 2012). Tosummarize, we propose three interacting domains to describeshale gas mass transport: organic nanopores, inorganic nanoporesto micropores, and the natural and hydraulic fracture systemshown in Fig. 2. On the basis of the discussion in the precedingparagraph, we assume that Knudsen diffusion dominates the nano-pores, which feed the inorganic pore system. Furthermore, it doesnot make sense to model molecular diffusion for single compo-nent gas systems. As mentioned previously, the inorganic matrixhas a wide pore size distribution, from nanometers to millimeters.Therefore, we anticipate Knudsen diffusion and convection trans-port to be dominant in this domain. The inorganic pores will thenact as a source for the fracture system, in which pure convectivetransport will come into play. This results in a TP (organic nano-pores, inorganic nanopores to micropores, and millimeter scale

aperture fractures) and DP (organic-to-inorganic material andinorganic material-to-fracture) system.

The TPDP system is modeled as three explicit grids to describegas transport in organic material, inorganic material, and the frac-ture system (Fig. 3). The induced hydraulic fractures are modeledexplicitly as high permeability fine grids, and dual permeabilityincludes the pressure dominated flow within the inorganic materi-als and flow within fracture grids. The organic material is embed-ded in the vast inorganic material. The organic material isgenerally considered disconnected in the entire reservoir. There-fore, we do not consider flow within the organic material grids(Grid No. 1). Inside the organic material, the shale gas concentra-tion in the nanopores is in instantaneous equilibrium with thatadsorbed on the solid surface, which is described by the multicom-ponent gas Langmuir isotherm. The gas desorption rate at the solidsurface is much faster compared with the gas mass transfer ratethrough the shale porous media. During gas production, theadsorbed gas is desorbed to the organic nanopores driven by thepressure drop caused by the production at the well. The mean freepath of a free gas molecule is comparable with or larger than thenanopore diameter. The free gas molecules bump along the nano-pore surface and flow outside into vast inorganic material becauseof the gas density gradient during gas production. This transportmechanism is well described by Knudsen diffusion, which is dif-ferent from the pressure gradient driven convection. The lattermechanism is not suitable to describe the slip flow in the nanoporestructures and hence is ignored in Grid No. 1. In the vast inorganicmaterial, both Knudsen diffusion and conventional convectionmechanisms are modeled in Grid No. 2 during gas productionbecause of the wide pore size distribution from nanometer to micro-meter scales. In natural and hydraulic fractures (Grid No. 3), pureconvection is assumed to be the predominant flow mechanism.

In summary, there are two key assumptions used in our model.The first assumption is that during gas production, gas is first

produced from a natural and hydraulic fracture network driven byconvection. Then, gas is released from inorganic material to thefracture network because of density gradient triggered diffusionand pressure gradient triggered convection. At last, gas is fedfrom organic material into inorganic material because of density

Organic material(desorption + diffusion)

Inorganic material(diffusion + convection)

1

2

3Natural/hydraulic-fracture network

(convection)

Fig. 2—Conceptual multimechanistic model for shale gas sys-tems. This conceptual model can be easily extended for allunconventional reservoirs, including shale oil systems, byswitching specific mechanisms on or off.

Hydraulic fractures

Interporositytransferterm

1

2

3

Interporositytransferterm

Disconnected micropore organic(diffusion + desorption)

Mesopore-to-micropore inorganic(diffusion + convection)

Millimeter fractures(convection)

Fig. 3—Grid representation of the conceptual TPDP modelshown in Fig. 2, for reservoir simulation. In Grid No.1, becausethe organic material is considered dispersed in the inorganic do-main, no intrablock flux terms are assumed, whereas intrablockflux terms exist in Grid Nos. 2 and 3, resulting in a TPDP model.



2014 SPE Journal 3

gradient triggered diffusion. The whole transport process appearsto occur in a serial mode, and the gas production rate depends onthe total resistance for mass transfer, which is the sum of resist-ance of each component involved. The step with largest resistancemay become the rate limiting step (in shale gas, this is the travelthrough inorganic matter, as will be shown later). Because organicmaterial amount is relatively small, sparse organic material ismore likely to directly connect with vast inorganic materialinstead of fracture networks. Given this, other conceptual mod-els—such as gas transport in parallel in both organic and inor-ganic material, ending in the fracture network (Kang et al.2010)—are not considered in our study.

The second assumption is that there is no water transport in or-ganic material. Because of the nanopore size of the organic mate-rial, gas, not liquids, is assumed to be the only flowing fluid.Water transport in inorganic material and fracture networks ismodeled as convective flow under pressure gradient only. Gas dif-fusion through water is neglected in this study. The reason is thatCH4 has small solubility in water (0.007 g/kg of water) at standardconditions. The diffusivity of CH4 in water is four orders of mag-nitude lower than that in gas. Water diffusivity in organic materialis also slower than CH4 diffusivity in organic material.

Shale Gas Reservoir Simulation

A common approach in the literature is to lump Knudsen diffu-sion with convection in the form of the Klinkenberg correctionfactor for permeability for modeling gas transport in the tight ma-trix (Ertekin et al. 1986; Clarkson et al. 2012). That is,

ka ¼ k1 1þ ba

pg

� �; ð1Þ

where ba ¼pgcglgDg

ak1(for single phase flow), ba ¼

SgpgcglgDg

akrgk1(for multiphase flow), ka is the apparent gas permeability, ba is thegas slippage factor, k1 is the liquid equivalent permeability, pg isthe mean gas pressure, Dg is the diffusivity, cg is the gas compres-sibility, lg is the gas viscosity, a is the unit conversion factor, Sg is

the gas saturation, and krg is the gas relative permeability.It is apparent that the Klinkenberg correction factor still needs

the value of diffusivity and is a lumped function of diffusivity,pressure, gas composition, pore structure, and temperature. Theimplementation of this approach in the reservoir simulator createshuge efforts. In our model, we implement convection and diffu-sion terms separately. The permeability and diffusivity terms aremeasured directly from laboratory and scaled up for reservoirscale simulation. We also implemented the extended Langmuirisotherm for multicomponent gas adsorption in the organic mate-rial gas mass transport equation (Hall et al. 1994).

The multimechanistic, multicomponent equations for gas andwater transport in the organic material, inorganic material, andfracture are as follows.

Inorganic material water mass transport:

@/IbwSwI

@t¼ r � kI

kr;wIbw

lw

rUwI

� �þ rIkI

kr;wIbw

lw

DUwI�F:

� � � � � � � � � � � � � � � � � � � ð2Þ

Fracture water mass transport:

@/FbwSwF

@t¼ r � kF

kr;wFbw

lw

rUwF

� �

þ qww þ rIkIkr;wIbw

lw

DUwF�I: � � � � � � � � � � � � � � � � ð3Þ

Organic material gas mass transport (gas component i):

@qrockxi

@tþ @/ObgSgOyO;i

@t¼ rOSgDgODCgO�I;i: ð4Þ

Inorganic material gas transport (gas component i):

@/IbgSgIyI;i

@t¼ r � ðkI

yI;ikr;gIbg

lg

rUgI þ SgDgIrCgI;iÞ

þ rOSgDgODCgI�O;i

þ rIðkIyI;ikr;gIbg

lg

DUgI�F

þ SgDgIDCgI�F;iÞ: ð5Þ

Fracture gas transport (gas component i):

@/FbgSgFyF;i

@t¼ r � kF

yF;ikr;gFbg

lg

rUgF

!þ yF;iqgw

þ rIðkIyI;ikr;gIbg

lg

DUgF�I

þ SgDgIDCgF�I;iÞ: ð6Þ

In Eqs. 2 through 6, /O,/I , and /F denote the porosity of or-ganic material, inorganic material, and fractures, respectively;SgO,SgI , and SgF refer to the gas phase saturation of organic material,inorganic material, and fractures, respectively; yO;iyI;i, andyF;i arethe mole fraction of component i in the gas phase of organic mate-rial, inorganic material, and fractures, respectively; SwI and SwF referto the water phase saturation of inorganic material and fractures,respectively; kr;wI and kr;wF refer to the water phase relative perme-ability of inorganic material and fractures, respectively; kr;gI andkr;gF refer to the gas phase relative permeability of inorganic mate-rial and fractures, respectively; UwI and UwF are water phase poten-tial of inorganic material and fractures, respectively; UgI and UgF

are gas phase potential of inorganic material and fractures, respec-tively; kI and kF are inorganic material and fracture permeability(md), respectively; lw and lg are water and gas phase viscosity(cp), respectively; rO andrI are shape factors (ft�2) of organic andinorganic material, respectively; and qww and qgw are water and gaswell production rate (lbm-mol/ft3/D), respectively. DgO and DgI aregas diffusivity in organic and inorganic material (ft2/D), respec-tively; bw and bg are water and gas molar density (lbm-mol/ft3),respectively; CgO;i, CgI;i, and CgF;i are gas phase component i con-centration (lbm-mol/ft3) in organic and inorganic material and frac-tures, respectively; qrock is rock density (lbm/ft3); and xi is gasphase component i adsorption amount (lb-mol/lb rock).

These equations are solved simultaneously to describe themultiphase (multicomponent gas and water), multimechanisticflow in shale systems. Fig. 4 shows a simplified flow chart of ourfully implicit, 3D, multicomponent gas, multiphase (gas andwater), multimechanistic (desorption, convection, and diffusion)code.

The algorithm is composed of six parts:• The Model Definition part defines phases and components in

phases and initializes all variables.• The Property Computation part computes properties such as

phase mobility, transmissibility, well index, and mass ofeach component present at each timestep.

• The Accumulation, Flux, and Well part linearizes accumula-tion, flux, and well terms in mass balance equations of everycomponent.

• The Matrix Assembler part assembles and copies the reser-voir and well equation derivatives of primary variables intocorresponding parts in linear solver data structure.

• The Linear Solver part solves the linear system to update theprimary variables.

• The Nonlinear Updater part updates all the variables afterlinear solver solution. Then, if the equation residuals andprimary variables converge, it moves to the Property Com-putation part for the new timestep, according to the dynamictimestep calculator. Otherwise, it cycles back to the PropertyComputation part until it converges at the current timestep.

. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .



4 2014 SPE Journal

Results and Discussions

Model Setup. We consider a hypothetical shale reservoir in thispaper. The depth of the reservoir is nominally assumed at 2,000ft. The dimension of the reservoir is 1,000�1,000�100 ft. Thegrid size is 30�10�5 in the x-, y-, and z-direction, respectively.Water is assumed to be at the irreducible saturation (Swir) in theorganic/inorganic material and natural fractures. Slickwater is dis-tributed with the constant nonequilibrium water saturation(Sw > Swir) in the hydraulic fracture grids to mimic fracture fluidsinjection. The conceptual model setup includes a horizontal wellwith five hydraulic fractures. We applied a logarithmically spacedglobal grid refinement (tartan grid) along the hydraulic fracturesto capture the rapid gas release (Fig. 5). By comparing three, five,and seven level grid refinement along the fractures, we learnedthat five level grid refinement is sufficient to capture the rapid gasrelease along the fractures, which is also reported elsewhere(Rubin 2010). The width of the hydraulic fracture grid is 2 ft tospeed up the convergence rate. The fracture conductivity of the 2ft wide gridblock is conserved with an effective permeability(keff ¼ kHFWHF

wgrid) (Rubin 2010). For instance, a 2 ft wide fracture

grid with 2 md permeability has the same fracture conductivity asa 0.002 ft wide fracture with 2,000 md permeability. The kv=kh ra-tio is 0.1 in the organic and the inorganic grids.

Benchmarking. We first benchmarked our basic model devel-oped here with our internal CHEARSTM simulator, under constantgas flow rate and bottomhole pressure control conditions.Throughout this work, the model is referred to as the researchmodel. The methane (CH4), nitrogen (N2), and water daily pro-duction rates from our research simulator matched exactly withthose from the internal simulator (CHEARS simulator) in bothsingle porosity, single permeability (SPSP) and dual porosity,dual permeability (DPDP) cases (Fig. 6). We also benchmarkedour research simulator with the CMG simulator (CMG 2010) forthe gas adsorption SPSP case (Fig. 6). In all cases, the resultsfrom these three simulators match within 0.2% for cumulativegas/water production after 100 years.

Model Comparisons (SPSP vs. DPDP vs. TPDP) and

Sensitivity Analysis. To systematically study the effects of reser-voir parameters and compare the predictions from the TPDP

model with the existing DPDP and SPSP models, we used the po-rosity, desorption, diffusivity, and permeability data of a realshale measured in our internal laboratory and scaled up for reser-voir simulation inputs (Table 1). Laboratory measured organicdiffusivity is scaled up for reservoir simulation usage. Because or-ganic material cluster size ðLOÞlaboratory is on mm scale, the labora-tory measured organic diffusivity ðDgOÞlaboratory does not dependon the organic matter size (mm). The stretching of the feet scalereservoir simulator organic matter grid size ðLOÞreservoir forced usto adjust the organic diffusivity value ðDgOÞreservoir to maintain thesame characteristic flow time measured in the laboratory (Eq. 7).

torganics ¼L2

O

DgO

� �laboratory

¼ L2O

DgO

� �reservoir

: ð7Þ

Fig. 7 shows the impact of diffusion in organics in the TPDPmodel. In addition to an experimental design, we also studied thebehavior of these systems at extreme conditions. We comparedthe cumulative CH4 production at the low end case (all the param-eters are set at their lowest values), at the middle value case (allthe parameters are set at their middle values), and at the high endcase (all the parameters are set at their highest values).

During 30 years of gas production, the cumulative CH4 pro-duction with organic diffusion and without organic diffusion forthe low end case does not show a major difference. The reason isthat gas resides in organic material either as free or as adsorbedgas and occupies only 6 wt% of original gas in place (OGIP) inthe reservoir. Therefore, the contribution of the gas productionfrom the organic material is negligible compared with other partsin the reservoir, such as inorganic material. In contrast, the cumu-lative CH4 production with organic diffusion far exceeds thatwithout organic diffusion at both middle value and high end cases,which is because gas in organic material occupies 25 and 58 wt%of OGIP, respectively, at middle value and high end cases. There-fore, the amount of gas released from organic material can besignificant.

Because the amount of gas released from organic material canbe significant, how quickly the gas is released from organic mate-rial is a key question. The gas in the organic material is producedslower than that in the inorganic material, as demonstrated in thelaboratory scale measurements. Therefore, we had concluded thatwe need to model the mass transport inside organic material sepa-rately. The TPDP approach is one such approach. Fig. 8 showsthe comparisons among SPSP, DPDP, and TPDP models. Interest-ingly, the DPDP model yields results comparable with those ofthe TPDP model for all low end, middle value, and high endcases. However, the SPSP model cannot predict the shale reser-voir production in all cases. This indicates that the speed of gasrelease from organic material is rapid enough to be represented bythe DPDP model. Why is this? Why do the reservoir scale resultsdiffer from intuition and laboratory scale measurements? Thecombination of the OGIP distribution for real shale (Fig. 9) andthe TPDP model’s characteristic flow time for real shale (Table2) can answer the question. The characteristic flow time is esti-mated as 1 mol of gas transferring through the different pore sys-tems. As seen from Fig. 9, in the middle case, we assume 1 wt%of OGIP is free CH4 in organic material, 5 wt% of OGIP isadsorbed CH4 in organic material, 83 wt% of OGIP is free CH4 ininorganic material, and the rest (or 11 wt% of OGIP) is free CH4

in fractures. In general, the majority of gas is stored in organic orinorganic material depending on the reservoir maturity. In termsof the characteristic time, for 1 mol of gas traveling through theorganic material, inorganic material, natural fracture, and hydrau-lic fracture regions, tinorganics is significantly the longest. Thisresult is consistent for all other cases, such as the high end andlow end cases. Although by intuition and core scale measurement,the much slower diffusion through the organic materials hindersthe whole gas flow process, the simulation shows that the distancefor 1 mol of gas to travel in the organic material region (weassume organic material form 1 mm clusters and are embeddedthrough the reservoir) is far shorter compared with the distance

. . . . . . . . .

Model Definition

Next Timestep

Property Computation

Accum, Flux, Well

Matrix Assembler

Linear Solver

Nonlinear Updater

Converged ?

N

Y

k = k + 1 n = n + 1

Fig. 4—Fully implicit, 3D, multicomponent gas, multiphase (gasand water), multimechanistic (desorption, convection, and dif-fusion), multidomain simulator flow chart.



2014 SPE Journal 5

that the gas molecules travel in the inorganic material. Becausegas flow through the previously mentioned four regions appears tobe in serial, the slowest step (tinorganics) determines the whole pro-duction process and can become the rate limiting step. In otherwords, it is not the rate of gas release but the actual transport of agas molecule through the organic material to the wellbore in a se-rial mode that determines the gas production. The DPDP modelwith diffusion should therefore be sufficient to model shale gasproduction instead of a more complicated TPDP model, when theorganic material size is similar to that assumed for real shale (1 mmclusters). This important conclusion is also supported by a previ-ous publication in which the travel time in organic matter is smallcompared with inorganic matter because of mm cluster size,although we used different approaches (Clarkson et al. 2012).

Once we had established that a DPDP model with diffusion isadequate, we also performed an experimental design study tounderstand the effects of different parameters on the recovery pro-file by use of the DPDP model. Fig. 10 shows the Pareto chart ofstandardized effects for cumulative CH4 production. As expected,the natural fracture permeability leads the list as the most impor-

tant parameter. Matrix diffusion/convection ratio and matrix per-meability follow in the list because these two parametersdetermine the diffusivity and permeability in the inorganic mate-rial. By itself, the matrix diffusion/convection ratio result is coun-terintuitive. The positive absolute value of the effect estimateimplies that as this parameter increases, so does gas production.Matrix diffusion/convection ratio can increase with reduction ininorganic permeability, but that interpretation would be incorrect.Thus, the matrix diffusion/convection ratio should always be con-sidered with matrix permeability, which is also significant and hasa positive effect estimate. These three parameters appear as statis-tically significant (p¼ 0.05) and determine the whole gas produc-tion process. Matrix porosity, CH4 adsorption amount, and naturalfracture porosity are relatively unimportant within the parameterranges that we studied.

Figs. 11a and 11b show the desorption effects for real shaleunder both high (1,000 psi) and low (250 psi) bottomhole pres-sure. The Langmuir pressure of CH4-shale is 341 psi, whichmeans half of the amount of adsorbed CH4 is desorbed when thereservoir pressure is dropped to less than 341 psi. When the

Water Saturation

Water Saturation

(a) (b)

(c)

0.0 0.2 0.4 0.6 0.8 1.0

Water Saturation0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

2,000

0

200

400

600

800

1,000–200 200 400 600

X

Y

800 1,000 1,2000

2,020

2,040

2,060 Z (

dept

h)

2,080

2,100

1,000

2,000

2,020

2,040

2,060

Z (

dept

h)

2,080

2,1000 200 400 600

Y800 1,000

1,000

800

800

600600Y X400

400

200

200

0

0

X

Y

Z

Fig. 5—(a) Logarithmically spaced global grid refinement (LS-GR) grids for a horizontal well with multiple hydraulic fractures; (b)x–y layer; and (c) y–z layer. Note that the horizontal well grid is too fine to display properly at this scale, so the well has been super-imposed for convenience.



6 2014 SPE Journal

adsorbed gas increases from 5 to 33 wt% of the total gas, OGIPincreases by 45% but gas production increases by 9–13% only,which is similar to previous results (Cipolla et al. 2010). Itappears that when combined with diffusion and convection,adsorption may contribute significant OGIP, but has a relativelysmall contribution to production, and is consistent with the previ-ous rate limiting characteristic time analysis.

Pe ¼ U � L

Dg: ð8Þ

In Eq. 8, the Peclet number Pe can be used to gauge whetherdiffusion or convection dominates, and U is bulk velocity, L is the

characteristic length, and Dg is diffusivity. Fig. 12a shows theeffects of molecular diffusion and Knudsen diffusion for realshale in the high matrix permeability case (0.1 md) (Pematrix¼2,000, convection dominates) by use of the SPSP model; Fig. 12bshows a low matrix permeability case (5�10�5 md) (Pematrix¼ 1,diffusion dominates) by use of the DPDP model. As expected, thediffusion effect from molecular diffusion and Knudsen diffusionis negligible compared with convection in the high permeabilitycase. Knudsen diffusion yields 23% more gas production in thelow permeability case after 10 years of production compared withthe convection only case. The density gradient, which is the driv-ing mechanism for Knudsen diffusion, is adequate to describeflow of gas in low permeability shale gas reservoirs. However,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

egnaR seulaV retemaraPMaximum N2 desorption amount (lb-mol/lb rock) 0.8665×10–5 0.8665×10–4

Maximum CH4 desorption amount (lb-mol/lb rock) Langmuir isotherm relation for N2 and CH4 (1/psi)

Organic material porosity (φO)*Upscaled organic material diffusivity (DgO) (m2/s)

Inorganic material permeability (kI) (md) Inorganic material diffusivity (DgI) (m2/s)

Natural fracture porosity (φNF)Natural fracture permeability (kNF) (md)

* Organic material diffusivity is scaled up from laboratory measurement for reservoir simulation input.

1.097×10–5 1.097×10–4

1.03×10–3 2.932×10–3

1×10–3 1×10–1

1×10–4

5×10–7

5×10–10

1×10–3

5×10–5

1×10–2

5×10–5

5×10–8

1×10–2

5×10–2

Table 1—Reservoir simulation parameters.

(a) (b)

(c)

Gas

Pro

duct

ion

Rat

e (M

scf/D

)

Time (years)

120

100

100

80

80

60

60

40

40

20

200 0

1

2

3

4

5

6

7

8

9

10CH4 (CHEARSTM simulator)

N2 (CHEARSTM simulator)

H2O (CHEARSTM simulator)

CH4 (research simulator)

N2 (research simulator)

H2O (research simulator)

0

Wat

er P

rodu

ctio

n R

ate

(sto

ck ta

nk m

3 /d)

Gas

Pro

duct

ion

Rat

e (M

scf/D

)

Time (years)

120

100

100

80

80

60

60

40

40

20

200 0

1

2

3

4

5

6

7

8

9

10

0

Wat

er P

rodu

ctio

n R

ate

(sto

ck ta

nk m

3 /d)CH4 (CHEARSTM simulator)

N2 (CHEARSTM simulator)

H2O (CHEARSTM simulator)




CH4 (CMG simulator)

N2 (CMG simulator)

H2O (CMG simulator)




Gas

Pro

duct

ion

Rat

e (M

scf/D

)

120

100

80

60

40

20

0

Time (years)100806040200

0

1

2

3

4

5

6

7

8

9

10

Wat

er P

rodu

ctio

n R

ate

(sto

ck ta

nk m

3 /d)

Fig. 6—(a) Benchmarking with internal simulator at constant gas flow rate and bottomhole pressure control condition for singleporosity, single permeability (SPSP) case; (b) dual porosity, dual permeability (DPDP) case; and (c) benchmarking with CMG simu-lator (CMG 2010) for gas adsorption SPSP case. In all cases, the results from these three simulators match within 0.2% for cumula-tive gas/water production after 100 years.



2014 SPE Journal 7

molecular diffusion is negligible in this case because the mecha-nism is driven by mole fraction gradient. Therefore, the commonbelief that diffusion is unimportant in shale reservoir productionmay not be valid. This result also supports the observations inFig. 10. High pressure, low diffusivity, and high permeability res-ervoir conditions can lead to convection domination results simi-lar to those in Fig. 12a, and opposite reservoir conditions can leadto diffusion domination results similar to those in Fig. 12b.

Fracture Design. Transient pressure analysis is useful to guidehydraulic fracture design (Cinco-Ley et al. 1978; Cinco-Ley andSamaniego-V. 1981; Chaudhary 2011). Table 3 shows the dimen-sionless fracture conductivity (FCD) analysis. FCD analysis is use-ful to guide the fracture design instead of the use of fractureconductivity (kHFWHF) alone because FCD combines the matrixproperties with the fracture properties and is independent of theporosity and the total compressibility of the matrix and the frac-ture. After determining that multiphase flow and diffusion canbe important for gas transport, we modified FCD from the tradi-tional form (Cinco-Ley et al. 1978; Cinco-Ley and Samaniego-V.1981),

FCD ¼kHFWHF

kMxHF; ð9Þ

to

FCD ¼kHFkr;gHFWHF

kMkr;gM þPematrixDgMlg

P � PBHP

� �xHF

; ð10Þ

to capture multiphase flow and contribution of diffusion, whereDgM is gas diffusivity in matrix (ft2/D), P is average reservoirpressure (psi), and PBHP is well bottomhole flowing pressure (psi).

For high FCD, pressure drop is negligible in high conductivityfractures. As FCD decreases, it is important to overcome the flowrestrictions created by the pressure drop in fractures. Low FCD

means low fracture permeability, long fracture length, high matrixpermeability, or all of these. As the fracture permeabilityapproaches the matrix permeability, the pressure drop distributioncorresponds to that for radial flow (Cinco-Ley et al. 1978; Cinco-Ley and Samaniego-V. 1981).

Table 3 shows that for the base case, for a typical fracture halflength (xHF¼ 250 ft), FCD is 1.78. Under this condition, increas-ing the length of the fracture farther may not be as helpful, andthe use of more/better proppant is required. If the situation is mis-judged and the effort is spent in an even longer fracture (fracturehalf length of 1.8 * xHF¼ 450 ft), the FCD will actually drop to0.98, thus hampering production. If the fracture length is

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . .

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

5

4

3

2

1

00 5 10 15

Time (years)

(a)

TPDP with Organics Diffusion

TPDP without Organics Diffusion

20 25 30

4.5

3.5

2.5

1.5

0.5

× 104

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

6

5

4

3

2

1

00 5 10 15

Time (years)

(b)



20 25 30

× 105

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

12

10

8

6

4

2

00 5 10 15

Time (years)

(c)



20 25 30

× 105

Fig. 7—Effects of organics diffusion in TPDP model (a) at low end case, (b) at middle value case, and (c) at high end case. Notethat after Fig. 6, N2 is no longer shown in the figures.



8 2014 SPE Journal

comparable with the stimulated reservoir volume (SRV) dimen-sion, physically the flow spends an equal amount of time travelingthrough the fractures and the matrix. It is apparent that fractureslose their acceleration advantage. Therefore, the right approach in

this case is to create wider fractures (100 kHFWHF ¼ 4 md � ft) byuse of more proppant. For such a fracture, FCD increases signifi-cantly to 178. If the fracture length is comparable with the SRVdimension, the physical meaning is that flow moves 178 timesfaster through fractures than as in the matrix. In this case, it isapparent that fractures accelerate the gas production significantlybecause the radius of influence for an infinite fracture conductiv-ity (FCD > 200) is approximately 4 xHF (Cinco-Ley et al. 1978)and covers the whole reservoir. However, for infinite fracture con-ductivity (FCD > 200) (200 kHFWHF ¼ 8 md � ft), more/betterproppants are of limited value (Table 3). Fig. 13 shows CH4 cu-mulative gas production under different fracture design cases,which is consistent with our analysis. Extending fracture lengthdoes not help if FCD is low. Therefore, the gas production in thebase case overlaps with that in 1.8 * xHF. Increasing fracture con-ductivity requires additional proppant, but the cost of additional

5

4

3

2

1

00 5 10 15

Time (years)

(a)

20 25 30

4.5

3.5

2.5

1.5

0.5

× 104

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

TPDP with Inorganics DiffusionDPDP with Matrix Diffusion

SPSP with Diffusion


SPSP with Diffusion


SPSP with Diffusion

6

5

4

3

2

1

00 5 10 15

Time (years)

(b)

20 25 30

× 105

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

12

10

8

6

4

2

00 5 10 15

Time (years)

(c)

20 25 30

× 105

Fig. 8—The comparisons among SPSP model, DPDP model, and TPDP model (a) at low end case, (b) at middle value case, and (c)at high end case. The TPDP model with inorganics diffusion data is coincident with the DPDP model with matrix diffusion data.

11 wt%

83 wt%

1 wt% 5 wt%Free CH4 in organics

Free CH4 in inorganics

Free CH4 in fracture

Adsorbed CH4 in organics

Fig. 9—OGIP distribution for real shale.

Table 2—TPDP model characteristic flow time for real shale.



2014 SPE Journal 9

proppant may not be justified because of diminishing returns in pro-duction with time. Therefore, the gas production in 200 kHFWHF justmarginally exceeds that in 100 kHFWHF. In terms of the recom-mended fracture design, for FCD < 2, longer but thinner fracturedesign is not efficient, and shorter but wider fractures are recom-mended. For infinite fracture conductivity (FCD > 200), more andbetter proppants are of limited value.

Conclusions

We introduced a 3D triple porosity, dual permeability (TPDP)multimechanistic (desorption, diffusion, and convection) and mul-ticomponent gas/water flow research simulator. This new modelsimultaneously and systematically models all known shale gasflow mechanisms and domains (organic, inorganic, and fracture)by use of real shale data from internal laboratory measurements toguide reservoir simulation. In agreement with earlier literaturestudies, our main conclusions are as follows.1. Dual porosity, dual permeability (DPDP) with Knudsen diffu-

sion is adequate to model shale gas reservoir production by com-paring TPDP, DPDP, and single porosity, single permeability

formulations for real shale data. Triple porosity or more com-plex quad porosity models may not be needed for data similar tothe real shale (where the organic shale is interspersed withinvast inorganic shale) considered in the paper.

2. The most appropriate way to model diffusion in shale reservoirs isKnudsen diffusion. Molecular diffusion, which is modeled afterthe mole fraction gradient, has negligible contribution and is notappropriate for dry gas production. We showed that Knudsen diffu-sion is a key mechanism and yields 23% more gas production inlow permeability cases studied at 10 years (Pematrix¼ 1, diffusiondominates). As expected, both molecular diffusion and Knudsendiffusion are negligible compared with convection in the high per-meability cases studied (Pematrix¼ 2,000, convection dominates).High pressure, low diffusivity, and high permeability reservoirconditions can lead to convection domination results, and the op-posite reservoir conditions can lead to diffusion dominationresults.

3. When the adsorbed gas increases from 5 to 33 wt% of the totalgas, the original gas in place (OGIP) increases by 45% but gasproduction increases by only 9–13%. Adsorption can make a

Natural Fracture Permeability

Matrix Diffusion/Convection Ratio

CH4-Adsorption Amount 0.477

2.130

2.889

3.099

3.964

0.160

0 1 2 3 4 5

Matrix Permeability

Matrix Porosity

Natural Fracture Porosity

Effect Estimate (absolute value)

p-value = 0.05 significance limit

Fig. 10—Pareto chart of standardized effects for cumulative CH4 production in the DPDP model.

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

12

10

8

6

4

2

00 5 10 15

CH4: adsorbed gas/total = 5 wt%CH4: adsorbed gas/total = 20 wt%CH4: adsorbed gas/total = 33 wt%

Time (years)

(b)

20 25 30

× 105

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

7

6

5

3

4

2

0

1

0 5 10 15

CH4: adsorbed gas/total = 5 wt%CH4: adsorbed gas/total = 20 wt%CH4: adsorbed gas/total = 33 wt%

Time (years)

(a)

20 25 30

× 105

Fig. 11—Desorption impacts for real shale when (a) bottomhole pressure (1,000 psi) is greater than the CH4-shale Langmuir pres-sure (341 psi) and when (b) bottomhole pressure (250 psi) is less than the CH4-shale Langmuir pressure (341 psi).



10 2014 SPE Journal

significant contribution to the OGIP, but might not be impor-tant to gas production until later field life because of adsorptionequilibrium. This is consistent with previous findings.

4. Extending fracture length does not help if fracture conductivityis low. Increasing fracture conductivity requires additional prop-pant, but the cost of additional proppant may not be justifiedbecause of diminishing returns in production with time.

5. This work provides a basis for long term shale gas productionanalysis and helps define value adding laboratory measure-ments; for example, differentiating organic porosity from inor-ganic porosity is not necessary, but differentiating matrixpermeability from diffusivity is very important.

Nomenclature

ba ¼ gas slippage factor, psiabg ¼ gas molar density, lbm-mol/ft3

bw ¼ water molar density, lbm-mol/ft3

cg ¼ coefficient of gas isothermal compressibility, 1/psiCgF,i ¼ gas phase component i concentration in fractures, lbm-

mol/ft3

CgI,i ¼ gas phase component i concentration in inorganic mate-rial, lbm-mol/ft3

CgO,i ¼ gas phase component i concentration in organic material,lbm-mol/ft3

Dg ¼ gas diffusivity, ft2/DDgM ¼ gas diffusivity in matrix, ft2/DDgO ¼ gas diffusivity in organic material, ft2/DDgI ¼ gas diffusivity in inorganic material, ft2/D

FCD ¼ fracture conductivity, dimensionlesska ¼ apparent gas permeability, mdkF ¼ fracture permeability, mdkI ¼ inorganic material permeability, md

krg ¼ gas relative permeabilitykr,gF ¼ gas phase relative permeability of fractures

kr,gI ¼ gas phase relative permeability of inorganic materialkr,wF ¼ water phase relative permeability of fractureskr,wI ¼ water phase relative permeability of inorganic materialk1 ¼ liquid equivalent permeability, mdpg�¼ average reservoir pressure, psi

PBHP ¼ well bottomhole flowing pressure, psiqgw ¼ gas well production rate, lbm-mol/ft3/Dqww ¼ water well production rate, lbm-mol/ft3/D

Sg ¼ gas saturationSgF ¼ gas phase saturation of fracturesSgI ¼ gas phase saturation of inorganic material

SgO ¼ gas phase saturation of organic materialSw ¼ water saturation

SwF ¼ water phase saturation of fracturesSwir ¼ irreducible water saturationSwI ¼ water phase saturation of inorganic materialyF,i ¼ mole fraction of component i in the gas phase of

fractures

FCD kHFWHF

Base case (xHF = 250 ft) 1.78 0.04 md·ft 1.8 * xHF 0.98 0.04 md·ft 100 * kHFWHF 178 4 md·ft 200 * kHFWHF 356 8 md·ft

Table 3—Dimensionless fracture conductivity (FCD) analysis.

CH

4 C

umul

ativ

e P

rodu

ctio

n (M

scf)

7

6

5

3

4

2

0

1

0 5 10 15Time (years)

20

base case1.8 * xHF

100 * kHF WHF

200 * kHF WHF

25 30

× 105

Fig. 13—CH4 cumulative gas production under different frac-ture design cases. The line for 1.8 * xHF is coincident with theline for the base case.

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

7

6

5

3

4

2

0

1

0 5 10 15

CH4: without diffusionCH4: with molecular diffusionCH4: with knudsen diffusion

Time (years)

(a)

20 25 30

× 105

Cum

ulat

ive

CH

4 P

rodu

ctio

n (M

scf)

6

5

3

4

2

0

1

0 5 10 15

CH4: without diffusionCH4: with molecular diffusionCH4: with knudsen diffusion

Time (years)

(a)

20 25 30

× 105

Fig. 12—The effects of molecular diffusion and Knudsen diffusion for real shale (a) at high permeability case (kM 5 0.1 md)(Pematrix 5 2,000, convection dominates) by use of SPSP model and (b) at low permeability case (kM 5 531025 md) (Pematrix 5 1, dif-fusion dominates) by use of the DPDP model. (a) The line for methane (CH4) with molecular diffusion is coincident with the linesfor CH4 without diffusion and for CH4 with Knudsen diffusion; (b) the line for CH4 with molecular diffusion is coincident with theline for CH4 without diffusion.



2014 SPE Journal 11

yI,i ¼ mole fraction of component i in the gas phase of inor-ganic material

yO,i ¼ mole fraction of component i in the gas phase of organicmaterial

xHF ¼ fracture half length, fta ¼ unit conversion factor

lg ¼ gas phase viscosity, cplw ¼ water phase viscosity, cprF ¼ shape factor of fractures, ft-2

rI ¼ shape factor of inorganic material, ft-2

rO ¼ shape factor of organic material, ft-2

qrock ¼ rock density, lbm/ft3

/F ¼ porosity of fractures/I ¼ porosity of inorganic material/O ¼ porosity of organic material

UgF ¼ gas phase potential of fractures, psiUgI ¼ gas phase potential of inorganic materials, psixi ¼ gas phase component i adsorption amount, lb-mol/lb

rock

Acknowledgments*

The authors gratefully acknowledge the Shale Gas Unit within theChevron Energy Technology Company for funding this work. Wealso acknowledge the Chevron Energy Technology Company man-agement for permission to publish this work. We also acknowledgeDouglas K. McCarty for generously providing the scanning elec-tron microscope images. We also appreciate helpful discussionswith Baosheng Liang, Shengkai Duan, and Yih-Bor Chang duringthe course of the project. We appreciate three anonymousreviewers’ comments to improve the quality of the article.

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* Disclaimer: All information in this paper is provided as is for informational purposes only,as related to our experience to understand shale gas production mechanisms through res-ervoir simulation. It is not intended, or should not be construed, to grant any license underany patent or other intellectual property right of Chevron. It is not intended to be and shallnot be interpreted to be suggestions, advice or recommendations for the use of any productor application of any process in a manner that infringes any patent or other intellectual prop-erty of a third party.



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Hao Sun is a lead reservoir engineer at Chevron Energy Tech-nology Company and has been with the company since2012. His current focus is to provide unconventional resources/enhanced oil recovery related technical services for Chevronbusiness units and provide guidance on developing Chevron’sshale gas reservoir simulation capabilities. Sun received the2012 SPE Outstanding Technical Editor Award. He holds a PhDdegree in chemical engineering from Rice University.

Adwait Chawathe leads the Unconventional Resources andEnhanced Oil Recovery Simulation and Workflow Develop-ment group with Chevron Energy Technology Company. He

has been with Chevron for 17 years. Chawathe has authoredor coauthored more than 25 technical papers. He is an activemember of SPE and has served on various SPE Workshop andForum committees. Chawathe has been the review chair forSPE Reservoir Evaluation & Engineering and is the recipient ofnumerous SPE Outstanding Technical Editor awards. He holdsa PhD degree in petroleum and natural gas engineering fromPennsylvania State University.

Hussein Hoteit is a senior reservoir engineer with ChevronEnergy Technology Company in the Integrated Oil Recovery-Enhanced Oil Recovery unit. His current focus is to improveChevron’s chemical enhanced oil recovery simulation capa-bilities and to provide chemical enhanced oil recoveryrelated technical support for business units. Before joiningChevron, Hoteit worked for ConocoPhillips for 5 years. He hasapproximately 12 years of experience in reservoir engineeringand has published more than 25 peer-reviewed papersrelated to flow modeling in fractured reservoirs, miscible flood-ing, steam-assisted gravity drainage, and hydrocarbon phasebehavior. Hoteit was selected as an SPE Distinguished Lecturerin 2008 and has served as an associate editor for SPE Journalsince 2006. He holds a PhD degree in applied mathematicsfrom the University of Rennes, France.

Xundan Shi is a senior staff research scientist at Chevron EnergyTechnology Company. He has been working on reservoir simula-tion development for more than 11 years. Shi has authored orcoauthored 22 technical papers. He holds a bachelor’s degreein mechanical engineering and a master’s degree in engineer-ing mechanics from Zhejiang University, China, as well as a mas-ter’s degree in computer science and software engineering anda PhD degree in mechanical engineering from Auburn University.

Lin Li is a senior staff research engineer at Chevron EnergyTechnology Company, with responsibilities of managing andconducting strategic research and technology developmentprojects for both downstream and upstream applications. Hehas more than 25 years of academic and industrial experi-ence in the field of chemical engineering. Li holds bachelor’s,master’s, and PhD degrees, all in chemical engineering, fromTianjin University, China.



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