Modeling Gas Adsorption in Marcellus Shale With Langmuir...

Modeling Gas Adsorption in MarcellusShale With Langmuir and BET Isotherms

Wei Yu Texas AampM University and Kamy Sepehrnoori and Tadeusz W Patzek University of Texas at Austin

Summary

Production from shale-gas reservoirs plays an important role innatural-gas supply in the United States Horizontal drilling andmultistage hydraulic fracturing are the two key enabling technolo-gies for the economic development of these shale-gas reservoirsIt is believed that gas in shale reservoirs is mainly composed offree gas within fractures and pores and adsorbed gas in organicmatter (kerogen) It is generally assumed in the literature that themonolayer Langmuir isotherm describes gas-adsorption behaviorin shale-gas reservoirs However in this work we analyzed fourexperimental measurements of methane adsorption from the Mar-cellus Shale core samples that deviate from the Langmuir iso-therm but obey the Brunauer-Emmett-Teller (BET) isotherm Tothe best of our knowledge it is the first time to find that methaneadsorption in a shale-gas reservoir behaves similar to multilayeradsorption Consequently investigation of this specific gas-desorption effect is important for accurate evaluation of well per-formance and completion effectiveness in shale-gas reservoirs onthe basis of the BET isotherm The difference in calculating origi-nal gas in place (OGIP) on the basis of both isotherms is dis-cussed We also performed history matching with one productionwell from the Marcellus Shale and evaluated the contribution ofgas desorption to the wellrsquos performance History matching showsthat gas adsorption obeying the BET isotherm contributes more tooverall gas recovery than gas adsorption obeying the Langmuirisotherm especially at early time in production This work pro-vides better understanding of gas desorption in shale-gas reser-voirs and updates our current analytical and numerical models forsimulation of shale-gas production

Introduction

In recent years the growth of shale-gas production was fueled bythe improvements in horizontal drilling and multistage hydraulic-fracturing technologies As a result shale gas has become anincreasingly important source of natural-gas supply in NorthAmerica and around the world In nature gas shales are character-ized by extremely small grain size extremely low permeability onthe order of nanodarcies (106 md) small porosity and high totalorganic carbon (TOC) For instance the TOC in Marcellus Shaleranges from 2 to 20 wt and clay content is 10 to 45 wt (Boyceet al 2010) Shale can serve as both source and reservoir rockThe amount of gas in place in shale is strongly affected by theTOC clays and the adsorption ability of methane on the internalsurface of the solid (Martin et al 2010) In general complex frac-ture networks that are generated connect the shale formation andthe horizontal well Shale matrix has strong gas-storage capacitybut cannot transport the gas for long distance because it is verytight a fracture network can transport the gas efficiently becauseof large hydraulic conductivity but has limited storage capacity(Lane et al 1989 Carlson and Mercer 1991) Because a part ofgas in shale reservoirs is adsorbed investigation of gas adsorptioncan provide critical insights into evaluation of well performanceshale characterization and optimization of fracture design inshale-gas reservoirs

Generally natural gas in shale reservoirs is stored as free gasin both organic matter (kerogen) and larger mineral pores and nat-ural fractures as well as adsorbed gas within organic matter(Leahy-Dios et al 2011) The adsorbed gas has a higher densitythan the surrounding free gas Clarkson and Haghshenas (2013)presented five mechanisms for methane existence in shale-gas res-ervoirs (1) adsorption on internal surface area (2) conventional(compressed gas) storage in natural and hydraulic (induced) frac-tures (3) conventional storage in matrix porosity (organic andinorganic) (4) solution in formation water and (5) absorption (so-lution) in organic matter The organic matter is nanoporous mate-rial primarily consisting of micropores (pore length less than2 nm) and mesopores (pore length between 2 and 50 nm) (Kanget al 2011) The pore-size heterogeneity such as varying poresize shape and surface roughness greatly influences the gas-transport and -adsorption properties in shale-gas reservoirs (Fir-ouzi et al 2014a b) The organic matter occupies only a part ofthe bulk rock as connected clusters embedded in the rock or dis-persion among mineral grains (Silin and Kneafsey 2012) In theAppalachian Basin the well performance from darker zoneswithin Devonian shale with higher organic content is better thanthat from organic-poor gray zones (Schmoker 1980) Lu et al(1995) showed that the relationship between gas-adsorptioncapacity and TOC is approximately linear when the TOC is highwhereas for a very low TOC illite plays an important role in gasstorage in Devonian shales The adsorption process in shale-gasreservoirs is mainly physical adsorption which means that theadsorption is fully reversible allowing gas molecules to com-pletely adsorb and desorb and the interaction force between thesolid surface and the adsorbed gas molecules is controlled by theweak van der Waals force The specific surface area defined assurface area per gram of solid plays an important role in control-ling the adsorption capacity The rougher solid surface and thesmaller pore sizes can contribute a larger specific surface area(Solar et al 2010) One can calculate the specific surface areawith the BET method (Brunauer et al 1938) A rough solid sur-face with many nanometer-scale cavities can adsorb gas morestrongly than an ideally polished surface (Rouquerol et al 1999Solar et al 2010)

A recent study conducted by the Energy Information Adminis-tration (US EIA 2014) concludes that the Marcellus Shale is oneof six key tight-oil and shale-gas regions which account for 95of US oil-production growth and all US natural-gas productiongrowth during 2011 to 2013 The Marcellus Shale is in the Appa-lachian Basin across six states Pennsylvania New York WestVirginia Ohio Virginia and Maryland The Marcellus Shale cov-ers a total area of more than 100000 sq miles and the depth is inthe range of 4000 to 8500 ft with an average thickness of 50 to200 ft (US DOE 2013) The average estimated ultimate recoveryis approximately 2325 Bcf per well the average porosity is 8and TOC is 12 wt (US EIA 2011) The Marcellus Shale has1500 Tcf of OGIP with 141 Tcf of technically recoverable gas(US DOE 2013) Reservoir temperature in the Marcellus Shale isobserved to be approximately 140 F and bottomhole pressure(BHP) is up to 6000 psi (Williams et al 2011) The kerogen typeof Marcellus Shale is primarily Type II with a mixture of Type III(Weary et al 2000)

Most publications to date have used the Langmuir isotherm todescribe gas desorption in shale-gas reservoirs In this paper weobserved that the gas desorption in some areas of the MarcellusShale follows the BET isotherm on the basis of laboratory

Copyright VC 2015 Society of Petroleum Engineers

This paper (SPE 170801) was accepted for presentation at the SPE Annual TechnicalConference and Exhibition Amsterdam 27ndash29 October 2014 and revised for publicationOriginal manuscript received for review 3 December 2014 Revised manuscript received forreview 29 October 2015 Paper peer approved 3 November 2015

J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 1 Total Pages 12

ID balamuralil Time 0859 I Path SJVol00000150132CompAPPFileSA-J150132

2015 SPE Journal 1

measurements The Langmuir and BET isotherms were comparedwith experimental data In addition through history matchingwith one production well in the Marcellus Shale we evaluated theeffect of gas adsorption on well performance at short and longproduction times

Adsorption Model for Shale-Gas Reservoirs

Adsorption at the gassolid interface is referred to as the enrich-ment of one or more components in an interfacial layer (Singet al 1985) The organic matter in shale has a strong adsorptionpotential because of the large surface area and affinity to methaneTo simulate gas production in shale-gas reservoirs an accuratemodel of gas adsorption is very important According to the Inter-national Union of Pure and Applied Chemistry (IUPAC) standardclassification system (Sing et al 1985) there are six differenttypes of adsorption The shape of the adsorption isotherm isclosely related to the properties of adsorbate and solid adsorbentand the pore-space geometry (Silin and Kneafsey 2012) One canfind the detailed description of the six isotherm classifications inSing et al (1985)

The most commonly applied adsorption model for shale gas-reservoirs is the classic Langmuir isotherm (Type I) (Langmuir1918) which is based on the assumption that there is a dynamicequilibrium at constant temperature and pressure betweenadsorbed and nonadsorbed gas Also it is assumed that there isonly a single layer of molecules covering the solid surface TheLangmuir isotherm has two fitting parameters

veth pTHORN frac14 vLp

pthorn pL eth1THORN

where v( p) is the gas volume of adsorption at pressure p vL isLangmuir volume referred to as the maximum gas volume ofadsorption at the infinite pressure and pL is Langmuir pressurewhich is the pressure corresponding to one-half Langmuir vol-ume Instantaneous equilibrium of the sorbing surface and thestorage in the pore space is assumed to be established for theLangmuir isotherm (Freeman et al 2012) Gao et al (1994) dem-onstrated that the instantaneous equilibrium is a reasonableassumption because the ultralow permeability in shale leads tovery low gas-flow rate through the kerogen component of shale

At high reservoir pressures one can expect that natural gassorbed on the organic carbon surfaces forms multimolecularlayers In other words the Langmuir isotherm may not be a goodapproximation of the amount of gas sorbed on organic carbon-rich mudrocks Instead multilayer sorption of natural gas shouldbe expected on organic carbon surfaces and the gas-adsorptionisotherm of Type II should be a better choice Type II isothermoften occurs in a nonporous or a macroporous material (Kuilaand Prasad 2013) In 1938 Stephen Brunauer Paul HughEmmett and Edward Teller (BET) published their theory in theJournal of the American Chemical Society (ACS) (Brunaueret al 1938) The BET isotherm model is a generalization of theLangmuir model to multiple adsorbed layers The expression isshown as follows

veth pTHORN frac14 vmCp

ethpo pTHORNfrac121thorn C 1eth THORNp=po eth2THORN

where po is the saturation pressure of the gas vm is the maximumadsorption gas volume when the entire adsorbent surface is beingcovered with a complete monomolecular layer and C is a con-stant related to the net heat of adsorption which is defined as

C frac14 expE1 EL

RT

eth3THORN

where E1 is the heat of adsorption for the first layer and EL is thatfor the second and higher layers and is equal to the heat of lique-faction The assumptions in the BET theory include homogeneoussurface no lateral interaction between molecules and the upper-most layer being in equilibrium with gas phase

The standard BET isotherm assumes that the number ofadsorption layers is infinite But in the case of n adsorption layersin some finite number then a general form of the BET isothermis given

veth pTHORN frac14vmC

p

po

1 p

po

1 ethnthorn 1THORN p

po

n

thorn np

po

nthorn1

1thorn ethC 1THORN p

po C

p

po

nthorn1

26664

37775 eth4THORN

When nfrac14 1 Eq 4 reduces to the Langmuir isotherm Eq 1When nfrac141 Eq 4 reduces to Eq 2

Here v(p) is the specific volume of gas adsorbed at the reser-voir pressure and temperature per unit mass of bulk rock refer-enced to a standard pressure and temperature [stock-tank (ST)condition in the oil industry] The customary cubic fields are ei-ther the standard cubic feet of sorbed gas per ton of bulk rock(scfton) or the standard cubic centimeters of gas per gram ofrock The conversion factor is

1scf

ton of bulk rock

frac14 1

32

standard cm3

g of bulk rock

eth5THORN

One should note that it is very challenging to apply the BETmodel to physically explain the supercritical-methane adsorptionbecause there is no concept of a liquid if the reservoir temperatureis above the critical-methane temperature Consequently the satu-ration pressure ( po) also loses its physical meaning (Ozdemir2004) To avoid this issue the saturation pressure ( po) is treatedas pseudosaturation pressure ( ps) for the high-pressuretempera-ture methane adsorption (Clarkson et al 1997) Clarkson et al(1997) summarized various methods to estimate the pseudosatura-tion pressure at any temperature above critical temperature Inthis study the method of extrapolation of the Antoine equation isused to calculate the pseudosaturation pressure for supercritical-methane adsorption as follows (NIST 2011 Hao et al 2014)

lnps frac14 77437 13065485

194362thorn T eth6THORN

where T is temperature (K) and ps is pseudosaturation pressure(MPa)

In this study we mainly focus on fitting the experimentalmeasurements of supercritical-methane adsorption by fixing thepseudosaturation pressure and tuning three fitting parameters ofvm C and n For practical application the BET-isotherm modeleasily can be used in a reservoir simulator to model the contribu-tion of gas desorption on well performance in some shale-gas res-ervoirs Although there are some physical-adsorption models suchas the simplified local-density model the 2D equation-of-state(EOS) model (Chareonsuppanimit et al 2012 Clarkson andHaghshenas 2013) and molecular simulation (Firouzi and Wilcox2012 Firouzi et al 2014b) we did not use the mentioned modelsin this study

Fig 1 compares shapes of the Langmuir and BET isothermsGas desorption along the BET isotherm contributes more signifi-cantly at early time of production than that with the Langmuir-iso-therm curve This is because the slope of the BET-isotherm curveat high pressure is larger than that of the Langmuir-isothermcurve resulting in more adsorbed gas releasing at early produc-tion times In addition under the same pressure drop from the ini-tial reservoir pressure to the BHP the amount of releasedadsorbed gas with the BET-isotherm curve is larger than that withthe Langmuir-isotherm curve

Gas-Flow Model in Shale

An equation to describe mass balance of gas flow in shale-gas res-ervoirs by considering the gas-desorption effect is given next (Pat-zek et al 2013 Yu et al 2014a)



2 2015 SPE Journal

frac12qgSgthorn 1 eth THORNqat

frac14

qgug

x

thorn qgug

y

thorn qgug

z

24

35 eth7THORN

where ug is Darcy velocity of gas Sg is initial gas saturation qg isthe free-gas density and qa is the adsorbed-gas mass per unit shalevolume (kilograms of adsorbed gas per cubic meter of solid)

The final governing nonlinear equation-of-transient gas flow inshale-gas reservoirs considering the gas-desorption effect isshown next and one may find more details about the derivation inour previous work (Yu et al 2014a)

x

qgk

lg

p

x

thorn

y

qgk

lg

p

y

thorn

z

qgk

lg

p

z

frac14 frac12Sg thorn 1 eth THORNKacgqg

p

t eth8THORN

where k is reservoir permeability cg is the isothermal gas-com-pressibility factor and Ka is the differential equilibrium partition-ing coefficient of gas at a given temperature (Patzek et al 2013)defined as follows

Ka frac14qa

qg

T

eth9THORN

The mass balance of adsorbed gas in one-unit bulk volume isdescribed as

qaVb 1 eth THORN frac14 qg pST TSTeth THORNqbVbv eth10THORN

where qb is bulk density of shale Vb is unit volume of bulk rockv is the specific volume of gas adsorbed per unit mass of bulkrock (scfton) which is measured at the reservoir pressure andtemperature and then transferred to standard condition and qg( pstTst) is the ST gas density

One can calculate the adsorbed-gas mass per unit shale volumeat the standard condition as

qa frac14qg pST TSTeth THORNqbv

1 eth11THORN

One can express the differential equilibrium partitioning coef-ficient of gas by

Ka frac14qa

qg

T

frac14qg pST TSTeth THORNqb

1 v

p

p

qg

eth12THORN

One can determine the isothermal gas-compressibility factor as

cg frac141

qg

qg

p

T

eth13THORN

The EOS for real gas is given by

qg frac14pM

Zeth pTHORNRT eth14THORN

where p is pressure in kPa M is the molecular weight of the gas(Mfrac14 cgMair where Mairfrac14 29 kgkmol is the molecular weight ofair) R is the ideal-gas constant with 83145 kPa m3(kmol K) T isabsolute temperature (K) and Z( p) is the gas-compressibility factor

Mahmoud (2014) developed a new correlation for calculatingthe real-gas compressibility as follows

cg frac14cpr

pc eth15THORN

cpr frac141

ppr 1

Zeth pTHORN

1404e25Tpr

ppr 5524e25Tpr

eth16THORN

ppr frac14p

pc eth17THORN

and

Tpr frac14T

Tc eth18THORN

where pc is the gas critical pressure cpr is the reduced gas compressi-bility ppr is the reduced pressure and Tpr is the reduced temperature

Substituting Eq 13 into Eq 12 yields

Ka frac14qa

qg

T


1 eth THORNqgcg

v

p eth19THORN

Consequently for the Langmuir-isotherm equation the differen-tial equilibrium partitioning coefficient of gas can be expressed as

Ka frac14qa

qg

T


1 eth THORNcgqg

vLpL

pL thorn peth THORN2


1 eth THORNcgqg

v2pL

vLp2 eth20THORN

For the general form of the BET isotherm the differentialequilibrium partitioning coefficient of gas can be expressed as

300

250

200

150

100

50

00 1000 2000 3000 4000

Pressure (psi)

(a) Langmuir isotherm (b) BET isotherm

BHP

Releasedadsorbed gas


Langmuir isotherm curve BET isotherm curve

Sto

rage

Cap

acity

(sc

fton

)

300

250

200

150

100

50

0

Sto

rage

Cap

acity

(sc

fton

)

Pi BHP Pi

5000 6000 0 1000 2000 3000 4000

Pressure (psi)

5000 6000

Fig 1mdashComparison of the Langmuir and BET isotherms (a) Langmuir isotherm (b) BET isotherm



2015 SPE Journal 3

Ka frac14qa

qg

T


1 eth THORNcgqg

A Bthorn vps

p ps peth THORN

eth21THORN

A frac14 vmCp

ps ps peth THORN n nthorn 1eth THORN p

ps

n

n nthorn 1eth THORN p

ps

n1

1thorn C 1eth THORN p

ps C

p

ps

nthorn1

eth22THORN

and

B frac14 v

ps

C 1 C nthorn 1eth THORN p

ps

n


ps C

p

ps

nthorn1 eth23THORN

Methane-Adsorption Measurements inMarcellus Shale

In this study measurements for methane adsorption were con-ducted by Weatherford Laboratories isotherm equipment featur-ing two independent covered oil baths metal-to-metal seals onpressure cells in place of O-ring seals pressure capabilities to10000 psi and temperatures up to 350 F The volumetric methodis used with a reference cell connecting to a sample cell Inde-pendent pressure transducers and a thermocouple or resistancetemperature detectors are used to monitor the pressure and tem-perature change within each cell Pressure and temperature dataare monitored by a computer data-acquisition system that can col-lect data at 05-second intervals Two cells are immersed in an oilbath maintained at constant temperature to minimize errorscaused by transient temperature fluctuations Free gas is containedwithin the void volume of the cells whereas the sorbed gas is con-tained in the micropores of the shale material within the samplecell There are two primary steps in measuring isotherm dataincluding a calibration step and an isotherm-measurement stepDuring calibration the empty reference- and sample-cell volumesand the void volume within the sample cell after it is filled with asorbing material are determined with helium because it does notadsorb into the sample The isotherm-measurement step involvesrepeated pressure steps with methane to determine the stabilizedequilibrium pressure and temperature conditions for each step Afull computerized interpretation is implemented to account forslight temperature and pressure variations and to improve the ac-

curacy of the measured stabilized pressure and temperature condi-tions at the end of each isotherm step which greatly increases therepeatability and consistency of the isotherm measurements Inaddition the shale samples were immediately preserved at thewellsite so that in-situ fluids are not altered by means of desicca-tion or imbibition

The Gibbs-isotherm data determined from the experimentswere corrected to the total isotherm on the basis of the followingequation (Sircar 1999 Ambrose et al 2012)

Gs frac14 Gs0

1 qf =qs

eth24THORN

where Gs0 is Gibbs-isotherm storage capacity scfton Gs is total-isotherm storage capacity scfton qf is free-gas density lbmft3and qs is sorbed-gas density lbmft3 The free-gas density dependson the Z-factors which are calculated with the NIST REFPROPprogram (NIST 2013)

For Marcellus Shale isotherm measurements of this study amass of approximately 250 g of shale samples was used and allexperiments were conducted at 130 F TOC is measured by aLECO carbon analyzer We analyzed gas-adsorption laboratorymeasurements on four samples from the lower Marcellus Shaleas shown in Fig 2 One can see that the adsorption measurementsdo not obey the Langmuir isotherm but obey the BET isothermWe used both the Langmuir and BET isotherms to fit the experi-mental measurements as shown in Fig 3 The fitting parametersof Langmuir and BET isotherms are listed in Tables 1 and 2respectively The coefficient of determination also known as R2is used to evaluate goodness of fit The measurements are betterapproximated by the BET isotherm than by the Langmuir iso-therm There are very few published high-pressure methane-adsorption data for shale Chareonsuppanimit et al (2012) pro-vided a summary of literature sources for high-pressure gas-adsorption data on shales (Nuttall et al 2005 Beaton et al 2010Weniger et al 2010) in which the highest pressure used to mea-sure gas adsorption was approximately 4000 psi However thehighest pressure used for measuring methane adsorption in thisstudy was more than 7000 psi Vermylen (2011) measured N2CH4 and CO2 adsorptions for four Barnett Shale samples with themaximum pressure of 1500 psi and found that CH4 and N2 obeythe Langmuir isotherm whereas CO2 obeys the BET isothermThis study to the best of our knowledge for the first time showsthat CH4 adsorption at high pressure in some areas of MarcellusShale behaves similar to multilayer adsorption and the BET iso-therm fits the data well

The relationship between the TOC and gas-storage capacity atthe reference pressure of 5000 psi is shown in Fig 4 illustratinga good linear relationship

Comparison of Free Gas and Adsorbed Gas

One can see from Eq 8 that (1ndash)Ka and Sg represent the contri-butions of adsorbed gas and free gas in shale The actual reservoirproperties of Marcellus Shale are used Porosity of 0142 and ini-tial gas saturation of 90 are used for calculation We calculatedthe (1ndash)Ka of four samples with Eq 20 for the Langmuir iso-therm and Eqs 21 through 23 for the BET isotherm respectivelyas shown in Fig 5 For the Langmuir isotherm Fig 5a shows thatgas desorption is comparable to free gas at low reservoir pressurewhereas gas desorption is less important at high reservoir pres-sure However for the BET isotherm Fig 5b illustrates that gasdesorption is significant at both high and low reservoir pressure

Calculation of OGIP

The traditional method for calculating the OGIP for free gas isexpressed next (Ambrose et al 2012)

vf frac14 320368 Sgi

qbBg eth25THORN

250Sample 1Sample 2Sample 3Sample 4

200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0 1000 2000 3000 4000 5000 6000Pressure (psi)

7000 80000

Fig 2mdashExperimental measurements of gas adsorption from thelower Marcellus Shale



4 2015 SPE Journal

where vf is the free-gas volume in scfton is reservoir porositySgi is the initial gas saturation qb is the bulk-rock density in gcm3 and Bg is the gas-formation volume factor (FVF) in reservoirvolumesurface volume

Ambrose et al (2012) proposed a new method to calculate thefree-gas volume by considering the volume occupied by theadsorbed gas on the surface on the basis of the Langmuir-isothermequation The porosity occupied by adsorbed gas on the basis ofthe Langmuir isotherm is

a Langmuir frac14 1318 106Mqb

qs

vLp

pthorn pL

eth26THORN

The final governing expression is shown as

vf Langmuir frac14320368

Bg

1 Sweth THORN

qb

1318 106M

qs

vLp

pthorn pL

eth27THORN

where Sw is the initial water saturation M is molecular weight ofnatural gas lbmlbm mol and qs is the adsorbed-gas density gcm3 Note that the direct measurement of the adsorbed-gas densityis difficult and it is typically assumed that the adsorbed-gas

250 160

140

120

100

Sto

rage

Cap

acity

(sc

fton

)

80

60

40

20

0

200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

0 1000 2000 3000

Sample 1-Lab data

Langmuir modelBET model

Sample 3-Lab data

Langmuir model

BET model

Sample 2-Lab data


Sample 4-Lab data


Pressure (psi)

(a) Sample 1 (b) Sample 2

(c) Sample 3 (d) Sample 4

4000

0 1000 2000 3000 4000

Pressure (psi)

5000 6000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000 8000

Fig 3mdashComparison of fitting results with the Langmuir and BET isotherms (a) Sample 1 (b) Sample 2 (c) Sample 3 and (d) Sam-ple 4

Langmuir Parameters Sample 1 Sample 2 Sample 3 Sample 4 pL (psi) 535 1240 1144 7764vL (scfton) 1964 1603 1006 507R2 0908 0961 0840 0195

Table 1mdashLangmuir-isotherm parameters used for fitting the measurements

BET Parameters Sample 1 Sample 3 Sample 2 Sample 4 vm (scfton) 12453 8347 4901 2411C 3663 2184 2456 7382N 403 276 446 764R2 0998 0999 0998 0995

Table 2mdashBET-isotherm parameters used for fitting the measurements



2015 SPE Journal 5

density is equal to the liquid-phase density however in manycases in which the pore volume is dominated by micropores theadsorbed-gas density is larger than that of the liquid-phase density(Mosher et al 2013) In addition Mosher et al (2013) pointed outthat the molecular simulation can provide the unique opportunityto predict the adsorbed-gas density In this study the adsorbed-gas density of methane is calculated by the following equationwhich was proposed by Riewchotisakul and Akkutlu (2015) onthe basis of the nonequilibrium molecular dynamic simulation toaccount for the change of adsorbed phase density with pressure inorganic nanopores

qs frac14 01057ln peth THORN 04629 eth28THORN

where the adsorbed-gas density (qs) is in gcm3 and pressure (p) isin psi

One can obtain the total OGIP by summation of free-gas vol-ume and adsorbed-gas volume

vt Langmuir frac14 vf Langmuir thorn va Langmuir eth29THORN

where vf_Langmuir is the free-gas volume that is based on the Lang-muir isotherm scfton va_Langmuir is the adsorbed-gas volume thatis based on the Langmuir isotherm scfton and vt_Langmuir is thetotal-gas volume that is based on the Langmuir isotherm scfton

In this work we modified the model for calculating OGIP pro-posed by Ambrose et al (2012) by considering the BET isotherm

The porosity occupied by adsorbed gas is modified as followsfor the BET isotherm

a BET frac14 1318 106Mqb

qs

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

37775 eth30THORN

The governing equation is obtained here

vf BET frac14320368

Bg

1 Sweth THORNqb

1318 106M

qs

8gtgtgtltgtgtgt

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

377759gtgtgt=gtgtgt

eth31THORNOne can obtain the total OGIP by summation of free-gas vol-

ume and adsorbed-gas volume

vt BET frac14 vf BET thorn va BET eth32THORN

where vf_BET is the free-gas volume on the basis of the BET iso-therm in scfton va_BET is the adsorbed-gas volume on the basisof the BET isotherm in scfton and vt_BET is the total-gas volumeon the basis of the BET isotherm in scfton

The actual reservoir properties of Marcellus Shale are used forthe calculation of OGIP as shown in Table 3 With Eqs 26through 32 the porosities of gas adsorption free gas in placeadsorbed gas in place and the total OGIP are calculated as sum-marized in Tables 4 and 5 As shown the average total OGIP inplace is 521 scfton calculated with the BET isotherm which islarger than the 510 scfton calculated with the Langmuir isothermHence characterizing the gas-adsorption isotherm is importantfor quantifying the total OGIP and evaluating the economicpotential of gas shales

Numerical-Simulation Methods

In this work a compositional simulator is used to model multiplehydraulic fractures and gas flow in Marcellus Shale reservoirs

300

y = 25904xR 2 = 097240

Gas

-Sto

rage

Cap

acity

(sc

fton

)

180

120

60

00 002 004 006 008 01

TOC (wt fraction)

Fig 4mdashRelationship between gas-storage capacity and theTOC

1Sample 1Sample 3

Sample 2Sample 4

φSg φSg

Sample 1Sample 3

Sample 2Sample 4

01

001

0001

1

01

001

00010 1000 2000 3000 4000 5000

Pressure (psi)

(a) Langmuir isotherm used for calculation (b) BET isotherm used for calculation

(1ndashφ

) K

a

(1ndashφ

) K

a

6000 0 1000 2000 3000 4000 5000

Pressure (psi)

6000

Fig 5mdashComparison of free gas and adsorbed gas with different isotherms (a) Langmuir isotherm used for calculation (b) BET iso-therm used for calculation



6 2015 SPE Journal

(CMG 2012) In our simulation model local grid refinement withlogarithmic cell spacing is used to accurately model gas flowfrom shale matrix to hydraulic fractures Non-Darcy flow is con-sidered for which the non-Darcy Beta-factor used in the For-chheimer number is determined with a correlation proposed byEvans and Civan (1994) This approach was extensively used tomodel transient gas flow in hydraulically fractured shale-gas res-ervoirs (Rubin 2010 Yu and Sepehrnoori 2014a 2014b Yu et al2014b) In the simulation model the Langmuir isotherm is used tomodel gas desorption Also the adsorption data can be entered ina table form Increase in gas recovery is used to assess the contri-bution of gas desorption in this work and it is defined by

Increase in gas recovery frac14 QGas Desorption Qi

QGas Desorption

eth33THORN

where QGas Desorption is cumulative gas production with gas-desorption effect whereas Qi is cumulative gas production with-out gas-desorption effect

Basic Reservoir Model

A Marcellus Shale area of approximately 207 acres was simulatedby setting up a basic 3D reservoir model with dimensions of6000 1500 130 ft which corresponds to length width andthickness respectively as shown in Fig 6 The reservoir has twoshale layers Porosity of bottom and upper layers is approximately142 and 71 respectively The horizontal well is stimulated inthe bottom layer with 16 fracturing stages and four perforationclusters per stage with cluster spacing of 50 ft The total welllength is 3921 ft There are almost 190 days of production dataavailable for performing history matching and evaluating theeffect of gas desorption on well performance

Table 6 summarizes the detailed reservoir and fracture proper-ties of this well The reservoir is assumed to be homogeneousand the fractures are evenly spaced with stress-independent po-rosity and permeability The flowing BHP in Fig 7 is used to con-strain the simulation and cumulative gas production is thehistory-matching variable Table 7 lists reservoir permeabilityand fracture properties with a good history match without consid-ering the gas-desorption effect as shown in Fig 8

In the subsequent simulation studies we performed historymatching by considering gas desorption from the four shale sam-

Parameter Value Unit Initial reservoir pressure 5000 psiReservoir temperature 130 oFReservoir porosity 14 ndashInitial water saturation 10 ndashBg 00033 ndashM 20 lbmlbm mol ρb 263 gcm3

Table 3mdashParameters used for calculation in the Marcellus Shale

Sample φa_BET va_BET (scfton) vf_BET (scfton) vt_BET (scfton) 1 0038 24236 32330 565662 0021 13230 38769 519993 0016 9914 40710 506244 0010 6042 42975 49017

Table 4mdashOGIP calculation based on the BET isotherm

Sample φa_Langmuir va_ Langmuir (scfton) vf_ Langmuir (scfton) vt_ Langmuir (scfton) 1 0028 17744 36128 538722 0020 12842 38997 518383 0013 8187 41720 499074 0007 4385 43944 48330

Table 5mdashOGIP calculation based on the Langmuir isotherm

6000 ft15

00 ft

Well-1

Fig 6mdashA basic 3D reservoir model for the Marcellus Shale

Parameter Value Unit Initial reservoir pressure 5100 psiReservoir temperature 130 oFReservoir permeability 800 ndReservoir porosity (upper layer) 71 ndashReservoir porosity (bottom layer) 142 ndashInitial water saturation 10 ndashTotal compressibility 3times10ndash6 psindash1

Horizontal well length 3921 ftNumber of stages 16 ndashCluster spacing 50 ftFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ftTotal number of fractures 64 ndashGas specific gravity 058 ndash

Table 6mdashReservoir and fracture parameters for the Marcellus shale

well



2015 SPE Journal 7

ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas

5000

4000

3000

2000

Bot

tom

ehol

e P

ress

ure

(psi

)

1000

00 50 100 150

Time (days)

200

Fig 7mdashFlowing BHP of the Marcellus Shale well

Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft

Table 7mdashReservoir and fracture parameters used for a good history

match

3000

2500

2000

1500

1000

500

00 50 100 150

Field data

Without desorption

Time (days)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

200

Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well

3500 21000

18000

15000

12000

9000

6000

3000

0

3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

50 100 150

Field data

Without desorptionLangmuir

BET

Field dataWithout desorptionLangmuirBET

200

Time (days)

(a) History matching (b) Production forecasting

0 5 10 15 20 25 30

Time (years)

00

Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting

3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days)


Time (years)

0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0




8 2015 SPE Journal

recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81

whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively

Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production

Conclusions

We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower

Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm

bull A good linear relationship between gas-storage capacity andTOC is obtained

3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days) Time (years)


0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200

Field dataSample 1Sample 2Sample 3Sample 4

Time (days)

0

Fig 13mdashHistory matching by considering the BET isotherm offour samples



2015 SPE Journal 9

bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure

bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm

bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151

Nomenclature

Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor

cpr frac14 reduced gas compressibility

C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer

EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2

Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature

n frac14 maximum number of adsorption layersp frac14 pressure psi

pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa

ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa

QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf

Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf

Sg frac14 initial gas saturationT frac14 temperature K

Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms

va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton

va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton

Vb frac14 unit volume of bulk rock m3

vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton

vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton

vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete

unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton

vt_BET frac14 total gas volume that is based on the BET iso-therm scfton

vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton

Z( p) frac14 gas-compressibility factor frac14 reservoir porosity

a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm

a_BET frac14 porosity of adsorbed gas that is based on BETisotherm

qa frac14 adsorbed-gas mass per unit shale volume gm3

qb frac14 bulk density of shale gcm3

qg frac14 free-gas density gm3

qs frac14 adsorbed-gas density gcm3

Acknowledgments

We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study

References

Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-

in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17

(1) 219ndash229 SPE-131772-PA httpdxdoiorg102118131772-PA

Beaton A P Pawlowicz J G Anderson S D A et al 2010 Rock

EvalTM Total Organic Carbon and Adsorption Isotherms of the Duver-

nay and Muskwa Formations in Alberta Shale Gas Data Release

Energy Resources Conservation Board ERCBAGS Open File Report

2010-04 Edmonton Alberta

Boyce M L Yanni A E and Carr T R 2010 Depositional Control of

Organic Content in the Middle Devonian Marcellus Interval of West

Virginia and Western Pennsylvania Presented at the AAPG Hedberg

Research Conference Austin Texas USA 5ndash10 December

Brunauer S Emmett P H and Teller E 1938 Adsorption of Gases in

Multimolecular Layers J Am Chem Soc 60 309ndash319 http

dxdoiorg101021ja01269a023

Carlson E S and Mercer J C 1991 Devonian Shale Gas Production

Mechanisms and Simple Models J Pet Technol 43 (4) 476ndash482

SPE-19311-PA httpdxdoiorg10211819311-PA

Chareonsuppanimit P Mohammad S A Robinson Jr R L et al 2012

High-Pressure Adsorption of Gases on Shales Measurements and

Modeling Int J Coal Geol 95 34ndash46 httpdxdoiorg101016

jcoal201202005

Clarkson C R Bustin R M and Levy J H 1997 Application of the

MonolayerMultilayer and Adsorption Potential Theories to Coal Meth-

ane Adsorption Isotherms at Elevated Temperature and Pressure Carbon35 (12) 1689ndash1705 httpdxdoiorg101016S0008-6223(97)00124-3

Clarkson C R and Haghshenas B 2013 Modeling of Supercritical Fluid

Adsorption on Organic-Rich Shales and Coal Presented at the SPE

Unconventional Resources Conference The Woodlands Texas USA

10ndash12 April SPE-164532-MS httpdxdoiorg102118164532-MS

CMG 2012 GEM Userrsquos Guide Computer Modeling Group Ltd

Evans R D and Civan F 1994 Characterization of Non-Darcy Multi-

phase Flow in Petroleum Bearing Formations Report US DOE Con-

tract No DE-AC22-90BC14659 School of Petroleum and Geological

Engineering University of Oklahoma

Firouzi M and Wilcox J 2012 Molecular Modeling of Carbon Dioxide

Transport and Storage in Porous Carbon-based Materials Microporous

Mesoporous Materials 158 195ndash203 httpdxdoiorg101016

jmicromeso201202045

Firouzi M Alnoaimi K Kovscek A et al 2014a Klinkenberg Effect on

Predicting and Measuring Helium Permeability in Gas Shales Int JCoal Geol 123 62ndash68 httpdxdoiorg101016jcoal201309006

Firouzi M Rupp E C Liu C W et al 2014b Molecular Simulation

and Experimental Characterization of the Nanoporous Structures of

Coal and Gas Shale Int J Coal Geol 121 123ndash128 httpdxdoiorg

101016jcoal201311003

Freeman C M Moridis G J Michael G E et al 2012 Measurement

Modeling and Diagnostics of Flowing Gas Composition Changes in

Shale Gas Wells Presented at the SPE Latin American and Caribbean

ParameterWithout

DesorptionDesorption(Sample 1)

Desorption(Sample 2)



400 300 330 320 35095 85 95 95 95

Fracture half-length (ft)Fracture height (ft)

Table 8mdashmdashFracture half-length and fracture height used for a good history match



10 2015 SPE Journal

Petroleum Engineering Conference Mexico City Mexico USA


Gao C Lee J W Spivey J P et al 1994 Modeling Multilayer Gas Res-

ervoirs Including Sorption Effects Presented at the SPE Eastern Re-

gional Conference and Exhibition Charleston West Virginia USA

8ndash10 November SPE-29173-MS httpdxdoiorg10211829173-MS

Hao S Chu W Jiang Q et al 2014 Methane Adsorption Characteris-

tics on Coal Surface Above Critical Temperature Through Dubinin-

Astakhov Model and Langmuir Model Colloids and Surfaces A Phys-icochemical Eng Aspects 444 104ndash113 httpdxdoiorg101016

jcolsurfa201312047

Kang S M Fathi E Ambrose R J et al 2011 Carbon Dioxide Storage

Capacity of Organic-rich Shales SPE J 16 842ndash855 SPE-134583-

PA httpdxdoiorg102118134583-PA

Kuila U and Prasad M 2013 Specific Surface Area and Pore-size Distri-

bution in Clays and Shales Geophysical Prospecting 61 341ndash362

httpdxdoiorg1011111365-2478

Lane H S Watson A T and Lancaster D E 1989 Identifying and

Estimating Desorption From Devonian Shale Gas Production Data

Presented at the SPE Annual Technical Conference and Exhibition

San Antonio Texas USA 8ndash11 October SPE-19794-MS http

dxdoiorg10211819794-MS

Langmuir I 1918 The Adsorption of Gases on Plane Surfaces of Glass

Mica and Platinum J Am Chem Soc 40 1361ndash1403 http


Leahy-Dios A Das M Agarwal A et al 2011 Modeling of Transport

Phenomena and Multicomponent Sorption for Shale Gas and Coalbed

Methane in an Unstructured Grid Simulator Presented at the SPE An-

nual Technical Conference and Exhibition Denver USA 30 Octoberndash2

November SPE-147352-MS httpdxdoiorg102118147352-MS

Lu X Li F and Watson A T 1995 Adsorption Measurements in De-

vonian Shales Fuel 74 (4) 599ndash603 httpdxdoiorg1010160016-

2361(95)98364-K

Mahmoud M 2014 Development of a New Correlation of Gas Compres-

sibility Factor (Z-Factor) for High-Pressure Gas Reservoirs Journal of

Energy Resources Technology 136 1ndash11 httpdxdoiorg101115

14025019

Martin J P Hill D G Lombardi T E et al 2010 A Primer on NewYorkrsquos Gas Shales httpofficescolgateedubselleckAppBasin

GasshaleMartinpdf

Mosher K He J Liu Y et al 2013 Molecular Simulation of Methane

Adsorption in Micro- and Mesoporous Carbons With Applications to

Coal and Gas Shale Systems Int J Coal Geol 109ndash110 36ndash44

httpdxdoiorg101016jcoal201301001

NIST 2011 Thermophysical Properties of Fluid Systems httpwebbook

nistgovchemistryfluid

NIST 2013 NIST Reference Fluid Thermodynamic and Transport Prop-

erties (REFPROP) Version 91

Nuttall B C Drahovzal J A Eble C F et al 2005 Analysis of the De-

vonian Black Shale in Kentucky for Potential Carbon Dioxide Seques-

tration and Enhanced Natural Gas Production Kentucky Geological

Survey University of Kentucky Lexington Kentucky

Ozdemir E 2004 Chemistry of the Adsorption of Carbon Dioxide by

Argonne Permium Coals and a Model To Simulate CO2 Sequestration inCoal Seams PhD dissertation University of Pittsburgh (September 2004)

Patzek T W Male F and Marder M 2013 Gas Production in the Bar-

nett Shale Obeys a Simple Scaling Theory PNAS 110 (49)

19731ndash19736 httpdxdoiorg101073pnas1313380110

Riewchotisakul S and Akkutlu I Y 2015 Adsorption Enhanced Trans-

port of Hydrocarbons in Organic Nanopores Presented at the SPE An-

nual Technical Conference and Exhibition Houston USA 28ndash30

September SPE-175107-MS httpdxdoiorg102118175107-MS

Rouquerol J Rouquerol F and Sing K S W 1999 Adsorption by

Powers and Porous Solids Principles Methodology and Applications

London Academic Press

Rubin B 2010 Accurate Simulation of Non-Darcy Flow in Stimulated

Fractured Shale Reservoirs Presented at the SPE Western Regional

Meeting Anaheim California USA 27ndash29 May SPE-132093-MS

httpdxdoiorg102118132093-MS

Schmoker J W 1980 Organic Content of Devonian Shale in Western

Appalachian Basin AAPG Bull 64 (12) 2156ndash2165 httpdxdoiorg

1013062F919756-16CE-11D7-8645000102C1865D

Silin D and Kneafsey T 2012 Shale Gas Nanometer-Scale Observa-

tions and Well Modeling J Can Pet Technol 51 (6) 464ndash475 SPE-

149489-PA httpdxdoiorg102118149489-PA

Sing K S W Everett D H Haul R A W et al 1985 Reporting Phys-

isorption Data for GasSolid Systems With Special Reference to the

Determination of Surface Area and Porosity (Recommendations

1984) Pure Appl Chem 57 (4) 603ndash619 httpdxdoiorg101351

pac198557040603

Sircar S 1999 Gibbsian Surface Excess for Gas AdsorptionmdashRevisited IndEng Chem Res 38 3670ndash3682 httpdxdoiorg101021ie9900871

Solar C Blanco A G Vallone A et al 2010 Adsorption of Methane

in Porous Materials as the Basis for the Storage of Natural Gas In Nat-ural Gas ed P Potocnik Rijeka Crootia Sciyo httpwwwinte-

chopen combooksnatural-gas

US Department of Energy (DOE) 2013 Modern Shale Gas Development

in the United States An Update httpwwwnetldoegovFile20Li-

braryResearchOil-Gasshale-gas-primer-update-2013pdf

US Energy Information Administration (EIA) 2011 Review of Emerging

Resources US Shale Gas and Shale Oil Plays httpwwweiagov

analysisstudiesusshalegaspdfusshaleplayspdf

US Energy Information Administration (EIA) 2014 Drilling Productivity

Report httpwwweiagovpetroleumdrillingtabs-summary-1

Vermylen J P 2011 Geomechanical Studies of the Barnett Shale Texas

USA PhD dissertation Stanford University (May 2011)

Weary D J Ryder R T and Nyahay R 2000 Thermal Maturity Pat-

terns (CAI and Ro) in the Ordovician and Devonian Rocks of the

Appalachian Basin in New York State US Geological Survey Open

File Report 00-496 httppubsusgsgovof2000of00-496NY_TEXT

PDF

Weniger P Kalkreuth W Busch A et al 2010 High-Pressure Methane

and Carbon Dioxide Sorption on Coal and Shale Samples From the

Parana Basin Brazil Int J Coal Geol 84 190ndash205 httpdxdoiorg

101016jcoal201008003

Williams H Khatri D Keese R et al 2011 Flexible Expanding

Cement System (FECS) Successfully Provides Zonal Isolation Across

Marcellus Shale Gas Trends Presented at the Canadian Unconven-

tional Resources Conference Calgary 15ndash17 November SPE-

149440-MS httpdxdoiorg102118149440-MS

Yu W and Sepehrnoori K 2014a Simulation of Gas Desorption and

Geomechanics Effects for Unconventional Gas Reservoirs Fuel 116

455ndash464 httpdxdoiorg101016jfuel201308032

Yu W and Sepehrnoori K 2014b An Efficient Reservoir Simulation

Approach to Design and Optimize Unconventional Gas Production J

Can Pet Technol 53 (2) 109ndash121 SPE-165343-PA httpdxdoiorg

102118165343-PA

Yu W Huang S Wu K et al 2014a Development of a Semi-analytical

Model for Simulation of Gas Production in Shale Gas Reservoirs Pre-

sented at the Unconventional Resources Technology Conference Den-

ver USA 25ndash27 August URTeC-1922945

Yu W Luo Z Javadpour F et al 2014b Sensitivity Analysis of Hy-

draulic Fracture Geometry in Shale Gas Reservoirs J Petro Sci Eng113 1ndash7 httpdxdoiorg101016jpetrol201312005

SI Metric-Conversion Factors

ft 3048 Endash01 frac14 m

ft3 2832 Endash02 frac14 m3

(Fndash32)18 frac14 C

cp 10 Endash03 frac14 Paspsi 6895 Ethorn00 frac14 kPa

ton 9072 Ethorn02 frac14 kg

acre 4047 Ethorn03 frac14 m2

scfton 3121 Endash02 frac14 m3ton

Conversion factor is exact



2015 SPE Journal 11

Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE

Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the

director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin

Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland



12 2015 SPE Journal

measurements The Langmuir and BET isotherms were comparedwith experimental data In addition through history matchingwith one production well in the Marcellus Shale we evaluated theeffect of gas adsorption on well performance at short and longproduction times

Adsorption Model for Shale-Gas Reservoirs

Adsorption at the gassolid interface is referred to as the enrich-ment of one or more components in an interfacial layer (Singet al 1985) The organic matter in shale has a strong adsorptionpotential because of the large surface area and affinity to methaneTo simulate gas production in shale-gas reservoirs an accuratemodel of gas adsorption is very important According to the Inter-national Union of Pure and Applied Chemistry (IUPAC) standardclassification system (Sing et al 1985) there are six differenttypes of adsorption The shape of the adsorption isotherm isclosely related to the properties of adsorbate and solid adsorbentand the pore-space geometry (Silin and Kneafsey 2012) One canfind the detailed description of the six isotherm classifications inSing et al (1985)

The most commonly applied adsorption model for shale gas-reservoirs is the classic Langmuir isotherm (Type I) (Langmuir1918) which is based on the assumption that there is a dynamicequilibrium at constant temperature and pressure betweenadsorbed and nonadsorbed gas Also it is assumed that there isonly a single layer of molecules covering the solid surface TheLangmuir isotherm has two fitting parameters

veth pTHORN frac14 vLp

pthorn pL eth1THORN

where v( p) is the gas volume of adsorption at pressure p vL isLangmuir volume referred to as the maximum gas volume ofadsorption at the infinite pressure and pL is Langmuir pressurewhich is the pressure corresponding to one-half Langmuir vol-ume Instantaneous equilibrium of the sorbing surface and thestorage in the pore space is assumed to be established for theLangmuir isotherm (Freeman et al 2012) Gao et al (1994) dem-onstrated that the instantaneous equilibrium is a reasonableassumption because the ultralow permeability in shale leads tovery low gas-flow rate through the kerogen component of shale

At high reservoir pressures one can expect that natural gassorbed on the organic carbon surfaces forms multimolecularlayers In other words the Langmuir isotherm may not be a goodapproximation of the amount of gas sorbed on organic carbon-rich mudrocks Instead multilayer sorption of natural gas shouldbe expected on organic carbon surfaces and the gas-adsorptionisotherm of Type II should be a better choice Type II isothermoften occurs in a nonporous or a macroporous material (Kuilaand Prasad 2013) In 1938 Stephen Brunauer Paul HughEmmett and Edward Teller (BET) published their theory in theJournal of the American Chemical Society (ACS) (Brunaueret al 1938) The BET isotherm model is a generalization of theLangmuir model to multiple adsorbed layers The expression isshown as follows

veth pTHORN frac14 vmCp

ethpo pTHORNfrac121thorn C 1eth THORNp=po eth2THORN

where po is the saturation pressure of the gas vm is the maximumadsorption gas volume when the entire adsorbent surface is beingcovered with a complete monomolecular layer and C is a con-stant related to the net heat of adsorption which is defined as

C frac14 expE1 EL

RT

eth3THORN

where E1 is the heat of adsorption for the first layer and EL is thatfor the second and higher layers and is equal to the heat of lique-faction The assumptions in the BET theory include homogeneoussurface no lateral interaction between molecules and the upper-most layer being in equilibrium with gas phase

The standard BET isotherm assumes that the number ofadsorption layers is infinite But in the case of n adsorption layersin some finite number then a general form of the BET isothermis given

veth pTHORN frac14vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

37775 eth4THORN

When nfrac14 1 Eq 4 reduces to the Langmuir isotherm Eq 1When nfrac141 Eq 4 reduces to Eq 2

Here v(p) is the specific volume of gas adsorbed at the reser-voir pressure and temperature per unit mass of bulk rock refer-enced to a standard pressure and temperature [stock-tank (ST)condition in the oil industry] The customary cubic fields are ei-ther the standard cubic feet of sorbed gas per ton of bulk rock(scfton) or the standard cubic centimeters of gas per gram ofrock The conversion factor is

1scf

ton of bulk rock

frac14 1

32

standard cm3

g of bulk rock

eth5THORN

One should note that it is very challenging to apply the BETmodel to physically explain the supercritical-methane adsorptionbecause there is no concept of a liquid if the reservoir temperatureis above the critical-methane temperature Consequently the satu-ration pressure ( po) also loses its physical meaning (Ozdemir2004) To avoid this issue the saturation pressure ( po) is treatedas pseudosaturation pressure ( ps) for the high-pressuretempera-ture methane adsorption (Clarkson et al 1997) Clarkson et al(1997) summarized various methods to estimate the pseudosatura-tion pressure at any temperature above critical temperature Inthis study the method of extrapolation of the Antoine equation isused to calculate the pseudosaturation pressure for supercritical-methane adsorption as follows (NIST 2011 Hao et al 2014)

lnps frac14 77437 13065485

194362thorn T eth6THORN

where T is temperature (K) and ps is pseudosaturation pressure(MPa)

In this study we mainly focus on fitting the experimentalmeasurements of supercritical-methane adsorption by fixing thepseudosaturation pressure and tuning three fitting parameters ofvm C and n For practical application the BET-isotherm modeleasily can be used in a reservoir simulator to model the contribu-tion of gas desorption on well performance in some shale-gas res-ervoirs Although there are some physical-adsorption models suchas the simplified local-density model the 2D equation-of-state(EOS) model (Chareonsuppanimit et al 2012 Clarkson andHaghshenas 2013) and molecular simulation (Firouzi and Wilcox2012 Firouzi et al 2014b) we did not use the mentioned modelsin this study

Fig 1 compares shapes of the Langmuir and BET isothermsGas desorption along the BET isotherm contributes more signifi-cantly at early time of production than that with the Langmuir-iso-therm curve This is because the slope of the BET-isotherm curveat high pressure is larger than that of the Langmuir-isothermcurve resulting in more adsorbed gas releasing at early produc-tion times In addition under the same pressure drop from the ini-tial reservoir pressure to the BHP the amount of releasedadsorbed gas with the BET-isotherm curve is larger than that withthe Langmuir-isotherm curve

Gas-Flow Model in Shale

An equation to describe mass balance of gas flow in shale-gas res-ervoirs by considering the gas-desorption effect is given next (Pat-zek et al 2013 Yu et al 2014a)



2 2015 SPE Journal


frac14

qgug

x

thorn qgug

y

thorn qgug

z

24

35 eth7THORN



x

qgk

lg

p

x

thorn

y

qgk

lg

p

y

thorn

z

qgk

lg

p

z


p

t eth8THORN


Ka frac14qa

qg

T

eth9THORN






1 eth11THORN


Ka frac14qa

qg

T


1 v

p

p

qg

eth12THORN


cg frac141

qg

qg

p

T

eth13THORN


qg frac14pM




cg frac14cpr

pc eth15THORN

cpr frac141

ppr 1

Zeth pTHORN

1404e25Tpr

ppr 5524e25Tpr

eth16THORN

ppr frac14p

pc eth17THORN

and

Tpr frac14T

Tc eth18THORN



Ka frac14qa

qg

T


1 eth THORNqgcg

v

p eth19THORN


Ka frac14qa

qg

T


1 eth THORNcgqg

vLpL



1 eth THORNcgqg

v2pL

vLp2 eth20THORN


300

250

200

150

100

50

00 1000 2000 3000 4000

Pressure (psi)


BHP




Sto

rage

Cap

acity

(sc

fton

)

300

250

200

150

100

50

0

Sto

rage

Cap

acity

(sc

fton

)

Pi BHP Pi

5000 6000 0 1000 2000 3000 4000

Pressure (psi)

5000 6000




2015 SPE Journal 3

Ka frac14qa

qg

T


1 eth THORNcgqg

A Bthorn vps

p ps peth THORN

eth21THORN

A frac14 vmCp


ps

n


ps

n1


ps C

p

ps

nthorn1

eth22THORN

and

B frac14 v

ps


ps

n


ps C

p

ps

nthorn1 eth23THORN





Gs frac14 Gs0

1 qf =qs

eth24THORN






Calculation of OGIP



qbBg eth25THORN


200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0 1000 2000 3000 4000 5000 6000Pressure (psi)

7000 80000




4 2015 SPE Journal




qs

vLp

pthorn pL

eth26THORN



Bg

1 Sweth THORN

qb

1318 106M

qs

vLp

pthorn pL

eth27THORN


250 160

140

120

100

Sto

rage

Cap

acity

(sc

fton

)

80

60

40

20

0

200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

0 1000 2000 3000

Sample 1-Lab data


Sample 3-Lab data

Langmuir model

BET model

Sample 2-Lab data


Sample 4-Lab data


Pressure (psi)



4000

0 1000 2000 3000 4000

Pressure (psi)

5000 6000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000 8000








2015 SPE Journal 5










qs

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

37775 eth30THORN


vf BET frac14320368

Bg

1 Sweth THORNqb

1318 106M

qs

8gtgtgtltgtgtgt

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

377759gtgtgt=gtgtgt








300

y = 25904xR 2 = 097240

Gas

-Sto

rage

Cap

acity

(sc

fton

)

180

120

60

00 002 004 006 008 01

TOC (wt fraction)


1Sample 1Sample 3

Sample 2Sample 4

φSg φSg

Sample 1Sample 3

Sample 2Sample 4

01

001

0001

1

01

001

00010 1000 2000 3000 4000 5000

Pressure (psi)


(1ndashφ

) K

a

(1ndashφ

) K

a

6000 0 1000 2000 3000 4000 5000

Pressure (psi)

6000




6 2015 SPE Journal



QGas Desorption

eth33THORN












6000 ft15

00 ft

Well-1





well



2015 SPE Journal 7


5000

4000

3000

2000

Bot

tom

ehol

e P

ress

ure

(psi

)

1000

00 50 100 150

Time (days)

200




match

3000

2500

2000

1500

1000

500

00 50 100 150

Field data

Without desorption

Time (days)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

200


3500 21000

18000

15000

12000

9000

6000

3000

0

3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

50 100 150

Field data


BET


200

Time (days)


0 5 10 15 20 25 30

Time (years)

00


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days)


Time (years)

0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0




8 2015 SPE Journal




Conclusions




3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200


Time (days)

0




2015 SPE Journal 9




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal


frac14

qgug

x

thorn qgug

y

thorn qgug

z

24

35 eth7THORN



x

qgk

lg

p

x

thorn

y

qgk

lg

p

y

thorn

z

qgk

lg

p

z


p

t eth8THORN


Ka frac14qa

qg

T

eth9THORN






1 eth11THORN


Ka frac14qa

qg

T


1 v

p

p

qg

eth12THORN


cg frac141

qg

qg

p

T

eth13THORN


qg frac14pM




cg frac14cpr

pc eth15THORN

cpr frac141

ppr 1

Zeth pTHORN

1404e25Tpr

ppr 5524e25Tpr

eth16THORN

ppr frac14p

pc eth17THORN

and

Tpr frac14T

Tc eth18THORN



Ka frac14qa

qg

T


1 eth THORNqgcg

v

p eth19THORN


Ka frac14qa

qg

T


1 eth THORNcgqg

vLpL



1 eth THORNcgqg

v2pL

vLp2 eth20THORN


300

250

200

150

100

50

00 1000 2000 3000 4000

Pressure (psi)


BHP




Sto

rage

Cap

acity

(sc

fton

)

300

250

200

150

100

50

0

Sto

rage

Cap

acity

(sc

fton

)

Pi BHP Pi

5000 6000 0 1000 2000 3000 4000

Pressure (psi)

5000 6000




2015 SPE Journal 3

Ka frac14qa

qg

T


1 eth THORNcgqg

A Bthorn vps

p ps peth THORN

eth21THORN

A frac14 vmCp


ps

n


ps

n1


ps C

p

ps

nthorn1

eth22THORN

and

B frac14 v

ps


ps

n


ps C

p

ps

nthorn1 eth23THORN





Gs frac14 Gs0

1 qf =qs

eth24THORN






Calculation of OGIP



qbBg eth25THORN


200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0 1000 2000 3000 4000 5000 6000Pressure (psi)

7000 80000




4 2015 SPE Journal




qs

vLp

pthorn pL

eth26THORN



Bg

1 Sweth THORN

qb

1318 106M

qs

vLp

pthorn pL

eth27THORN


250 160

140

120

100

Sto

rage

Cap

acity

(sc

fton

)

80

60

40

20

0

200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

0 1000 2000 3000

Sample 1-Lab data


Sample 3-Lab data

Langmuir model

BET model

Sample 2-Lab data


Sample 4-Lab data


Pressure (psi)



4000

0 1000 2000 3000 4000

Pressure (psi)

5000 6000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000 8000








2015 SPE Journal 5










qs

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

37775 eth30THORN


vf BET frac14320368

Bg

1 Sweth THORNqb

1318 106M

qs

8gtgtgtltgtgtgt

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

377759gtgtgt=gtgtgt








300

y = 25904xR 2 = 097240

Gas

-Sto

rage

Cap

acity

(sc

fton

)

180

120

60

00 002 004 006 008 01

TOC (wt fraction)


1Sample 1Sample 3

Sample 2Sample 4

φSg φSg

Sample 1Sample 3

Sample 2Sample 4

01

001

0001

1

01

001

00010 1000 2000 3000 4000 5000

Pressure (psi)


(1ndashφ

) K

a

(1ndashφ

) K

a

6000 0 1000 2000 3000 4000 5000

Pressure (psi)

6000




6 2015 SPE Journal



QGas Desorption

eth33THORN












6000 ft15

00 ft

Well-1





well



2015 SPE Journal 7


5000

4000

3000

2000

Bot

tom

ehol

e P

ress

ure

(psi

)

1000

00 50 100 150

Time (days)

200




match

3000

2500

2000

1500

1000

500

00 50 100 150

Field data

Without desorption

Time (days)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

200


3500 21000

18000

15000

12000

9000

6000

3000

0

3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

50 100 150

Field data


BET


200

Time (days)


0 5 10 15 20 25 30

Time (years)

00


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days)


Time (years)

0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0




8 2015 SPE Journal




Conclusions




3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200


Time (days)

0




2015 SPE Journal 9




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal

Ka frac14qa

qg

T


1 eth THORNcgqg

A Bthorn vps

p ps peth THORN

eth21THORN

A frac14 vmCp


ps

n


ps

n1


ps C

p

ps

nthorn1

eth22THORN

and

B frac14 v

ps


ps

n


ps C

p

ps

nthorn1 eth23THORN





Gs frac14 Gs0

1 qf =qs

eth24THORN






Calculation of OGIP



qbBg eth25THORN


200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0 1000 2000 3000 4000 5000 6000Pressure (psi)

7000 80000




4 2015 SPE Journal




qs

vLp

pthorn pL

eth26THORN



Bg

1 Sweth THORN

qb

1318 106M

qs

vLp

pthorn pL

eth27THORN


250 160

140

120

100

Sto

rage

Cap

acity

(sc

fton

)

80

60

40

20

0

200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

0 1000 2000 3000

Sample 1-Lab data


Sample 3-Lab data

Langmuir model

BET model

Sample 2-Lab data


Sample 4-Lab data


Pressure (psi)



4000

0 1000 2000 3000 4000

Pressure (psi)

5000 6000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000 8000








2015 SPE Journal 5










qs

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

37775 eth30THORN


vf BET frac14320368

Bg

1 Sweth THORNqb

1318 106M

qs

8gtgtgtltgtgtgt

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

377759gtgtgt=gtgtgt








300

y = 25904xR 2 = 097240

Gas

-Sto

rage

Cap

acity

(sc

fton

)

180

120

60

00 002 004 006 008 01

TOC (wt fraction)


1Sample 1Sample 3

Sample 2Sample 4

φSg φSg

Sample 1Sample 3

Sample 2Sample 4

01

001

0001

1

01

001

00010 1000 2000 3000 4000 5000

Pressure (psi)


(1ndashφ

) K

a

(1ndashφ

) K

a

6000 0 1000 2000 3000 4000 5000

Pressure (psi)

6000




6 2015 SPE Journal



QGas Desorption

eth33THORN












6000 ft15

00 ft

Well-1





well



2015 SPE Journal 7


5000

4000

3000

2000

Bot

tom

ehol

e P

ress

ure

(psi

)

1000

00 50 100 150

Time (days)

200




match

3000

2500

2000

1500

1000

500

00 50 100 150

Field data

Without desorption

Time (days)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

200


3500 21000

18000

15000

12000

9000

6000

3000

0

3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

50 100 150

Field data


BET


200

Time (days)


0 5 10 15 20 25 30

Time (years)

00


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days)


Time (years)

0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0




8 2015 SPE Journal




Conclusions




3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200


Time (days)

0




2015 SPE Journal 9




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal




qs

vLp

pthorn pL

eth26THORN



Bg

1 Sweth THORN

qb

1318 106M

qs

vLp

pthorn pL

eth27THORN


250 160

140

120

100

Sto

rage

Cap

acity

(sc

fton

)

80

60

40

20

0

200

150

100

Sto

rage

Cap

acity

(sc

fton

)

50

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

120

100

80

60

Sto

rage

Cap

acity

(sc

fton

)

40

20

0

0 1000 2000 3000

Sample 1-Lab data


Sample 3-Lab data

Langmuir model

BET model

Sample 2-Lab data


Sample 4-Lab data


Pressure (psi)



4000

0 1000 2000 3000 4000

Pressure (psi)

5000 6000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000

0 1000 2000 3000

Pressure (psi)

4000 5000 6000 7000 8000








2015 SPE Journal 5










qs

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

37775 eth30THORN


vf BET frac14320368

Bg

1 Sweth THORNqb

1318 106M

qs

8gtgtgtltgtgtgt

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

377759gtgtgt=gtgtgt








300

y = 25904xR 2 = 097240

Gas

-Sto

rage

Cap

acity

(sc

fton

)

180

120

60

00 002 004 006 008 01

TOC (wt fraction)


1Sample 1Sample 3

Sample 2Sample 4

φSg φSg

Sample 1Sample 3

Sample 2Sample 4

01

001

0001

1

01

001

00010 1000 2000 3000 4000 5000

Pressure (psi)


(1ndashφ

) K

a

(1ndashφ

) K

a

6000 0 1000 2000 3000 4000 5000

Pressure (psi)

6000




6 2015 SPE Journal



QGas Desorption

eth33THORN












6000 ft15

00 ft

Well-1





well



2015 SPE Journal 7


5000

4000

3000

2000

Bot

tom

ehol

e P

ress

ure

(psi

)

1000

00 50 100 150

Time (days)

200




match

3000

2500

2000

1500

1000

500

00 50 100 150

Field data

Without desorption

Time (days)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

200


3500 21000

18000

15000

12000

9000

6000

3000

0

3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

50 100 150

Field data


BET


200

Time (days)


0 5 10 15 20 25 30

Time (years)

00


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days)


Time (years)

0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0




8 2015 SPE Journal




Conclusions




3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200


Time (days)

0




2015 SPE Journal 9




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal










qs

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

37775 eth30THORN


vf BET frac14320368

Bg

1 Sweth THORNqb

1318 106M

qs

8gtgtgtltgtgtgt

vmC

p

po

1 p

po


po

n

thorn np

po

nthorn1


po C

p

po

nthorn1

26664

377759gtgtgt=gtgtgt








300

y = 25904xR 2 = 097240

Gas

-Sto

rage

Cap

acity

(sc

fton

)

180

120

60

00 002 004 006 008 01

TOC (wt fraction)


1Sample 1Sample 3

Sample 2Sample 4

φSg φSg

Sample 1Sample 3

Sample 2Sample 4

01

001

0001

1

01

001

00010 1000 2000 3000 4000 5000

Pressure (psi)


(1ndashφ

) K

a

(1ndashφ

) K

a

6000 0 1000 2000 3000 4000 5000

Pressure (psi)

6000




6 2015 SPE Journal



QGas Desorption

eth33THORN












6000 ft15

00 ft

Well-1





well



2015 SPE Journal 7


5000

4000

3000

2000

Bot

tom

ehol

e P

ress

ure

(psi

)

1000

00 50 100 150

Time (days)

200




match

3000

2500

2000

1500

1000

500

00 50 100 150

Field data

Without desorption

Time (days)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

200


3500 21000

18000

15000

12000

9000

6000

3000

0

3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

50 100 150

Field data


BET


200

Time (days)


0 5 10 15 20 25 30

Time (years)

00


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days)


Time (years)

0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0




8 2015 SPE Journal




Conclusions




3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200


Time (days)

0




2015 SPE Journal 9




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal



QGas Desorption

eth33THORN












6000 ft15

00 ft

Well-1





well



2015 SPE Journal 7


5000

4000

3000

2000

Bot

tom

ehol

e P

ress

ure

(psi

)

1000

00 50 100 150

Time (days)

200




match

3000

2500

2000

1500

1000

500

00 50 100 150

Field data

Without desorption

Time (days)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

200


3500 21000

18000

15000

12000

9000

6000

3000

0

3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

50 100 150

Field data


BET


200

Time (days)


0 5 10 15 20 25 30

Time (years)

00


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days)


Time (years)

0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0




8 2015 SPE Journal




Conclusions




3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200


Time (days)

0




2015 SPE Journal 9




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal


5000

4000

3000

2000

Bot

tom

ehol

e P

ress

ure

(psi

)

1000

00 50 100 150

Time (days)

200




match

3000

2500

2000

1500

1000

500

00 50 100 150

Field data

Without desorption

Time (days)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

200


3500 21000

18000

15000

12000

9000

6000

3000

0

3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

50 100 150

Field data


BET


200

Time (days)


0 5 10 15 20 25 30

Time (years)

00


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30

Time (days)


Time (years)

0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0




8 2015 SPE Journal




Conclusions




3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200


Time (days)

0




2015 SPE Journal 9




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal




Conclusions




3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000C

umul

ativ

e G

as P

rodu

ctio

n(M

MS

CF

)6000

3000

0


3000

2500

2000

1500

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1000

500

0 50 100 150

Field data

Without desorption

Langmuir

BET

Field data

Without desorption

LangmuirBET

200 0 5 10 15 20 25 30



0

18000

15000

12000

9000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

6000

3000

0


3000

2500

2000

Cum

ulat

ive

Gas

Pro

duct

ion

(MM

SC

F)

1500

1000

500

0 50 100 150 200


Time (days)

0




2015 SPE Journal 9




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal




Nomenclature





























Acknowledgments


References






















jcoal201202005
















jmicromeso201202045






101016jcoal201311003




ParameterWithout





400 300 330 320 35095 85 95 95 95





10 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal










jcolsurfa201312047






















2361(95)98364-K




14025019


GasshaleMartinpdf































1013062F919756-16CE-11D7-8645000102C1865D








pac198557040603



















PDF




101016jcoal201008003












102118165343-PA


















2015 SPE Journal 11







12 2015 SPE Journal







12 2015 SPE Journal

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Modeling Gas Adsorption in Marcellus Shale With Langmuir...

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