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Fuel 86 (2007) 2696–2706

Impact of mass balance calculations on adsorption capacitiesin microporous shale gas reservoirs

Daniel J.K. Ross *, R. Marc Bustin

Department of Geological Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC, Canada V6T 1Z4

Received 10 November 2006; received in revised form 28 February 2007; accepted 28 February 2007Available online 2 April 2007

Abstract

Determination of the adsorbed reservoir capacity of gas shales by adsorption analyses as done routinely by mass balance maybe insignificant error if the effects of pore-size dependent void volume (porosity) is not considered. It is shown here that with increasing pres-sure, helium, which is invariably used to measure void volume, can access pores that are not available for adsorption to gases with largerkinetic diameters as highlighted by experiments with zeolites of known pore-size distribution. Helium can diffuse and/or adsorb inrestricted pores of the microporous samples, as indicated by a larger void volume with pressure. The error in adsorption calculationsdue to helium void volume calibrations for high pressure methane isotherms is most significant with low organic-carbon content, mois-ture-equilibrated shales and mudrocks in which the overall adsorptive capacity is low. In such samples negative adsorption can be cal-culated due to the void volume of helium used in the mass balance calculations exceeding the void volume to methane – a reflection ofgreater pore-space accessibility of the smaller helium molecule than methane. The amount of the error introduced by using helium voidvolume in mass balance calculations is pore-size and pore-size distribution dependent. Organic-rich shales and mudrocks or coals whichdo not show negative methane adsorption also maybe in error but the error is masked by their larger adsorbed gas capacities. Such find-ings underline the importance of analysis gas-type as kinetic diameter size will influence the penetrability/diffusion of the gas through thesample and hence the calculated adsorbed gas capacities.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Shale gas; Methane; Helium; Negative adsorption; Porosity

1. Introduction

Gas shales and coal beds are important unconventionalgas reservoirs in which much of the gas is stored in theadsorbed state [1]. For shale gas and coalbed methane res-ervoir evaluation, adsorption isotherms (mainly methane)are used to determine the adsorbed gas capacity. Adsorbedgas capacities are then extrapolated to regional reservoirscales and hence even small errors in adsorption capacitycan result in significant over or underestimation of pre-dicted gas in place and severely impact the perceived eco-nomics of development. Adsorbed gas capacities are alsocompared with actual gas contents from the well-site to

0016-2361/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.fuel.2007.02.036

* Corresponding author. Tel.: +1 604 8223706; fax: +1 604 8226088.E-mail address: [email protected] (D.J.K. Ross).

determine the degree of gas saturation. Saturated rocks willdesorb gas upon initial pressure drawdown which generallyis accomplished by water production. In under-saturatedreservoirs the saturation level is important to the econom-ics of the reservoirs since the degree of under-saturationdictates to what pressure the reservoir must be depletedto allow desorption to occur which is referred to as the crit-ical desorption pressure [2].

For both coals and shales, gases adsorb onto the inter-nal surfaces of the matrix. Typically a Type I isotherm(Langmuir) fits and is used for microporous1 materialswhereby gas adsorption increases rapidly at relatively low

1 Using the International Union of Applied and Pure Chemistry(IUAPC) pore classification, micropores are pores <2 nm in diameter,mesopores 2–50 nm and macropores >50 nm.

D.J.K. Ross, R. Marc Bustin / Fuel 86 (2007) 2696–2706 2697

pressures while adsorption sites are being filled [3]. There-after, the isotherm plateaus as the system reaches gas satu-ration. However our recent research has shown negativecalculated methane adsorption isotherms for many shales[4] (Fig. 1) and negative ethane isotherms for some coals.The calculation of negative adsorption reveals fundamentalproblems with the mass balance calculations that areinvariably used for calculating adsorption. Calculated neg-ative adsorption is particular evident in high pressureadsorption experiments of organic poor gas shales in whichadsorption is low (relative to organic-rich shales and coals)and errors are easier to recognize. Due to the significantlateral and vertical extent of shale/mudrock strata, anymis-calculations will have significant implications on gas-in-place (GIP) estimations.

Porous materials such as coals have been described as anetwork of slit-like pores which are interconnected by nar-row capillary constrictions [5]. Therefore pore accessibilityis affected by both the geometry of pore-throats and thepore-diameter. The diffusion of gases through pore-throatsto adsorption sites is also dependant on the kinetic diame-ter of the gas. For example Cui et al. [6] reported a highermicropore diffusivity of carbon dioxide than those of meth-ane and nitrogen due to the smaller kinetic diameter of car-bon dioxide.

The pore-structure of coals (related to the organic frac-tion) controls, to a large extent, the adsorption of gases

Fig. 1. Examples of calculated negative adsorption of

whether it be multilayer adsorption in meso-macro pores[7] or the pore-volume filling of micropores due toenhanced adsorption energies [8]. For shales, it has beenalso shown that the organic matter mainly controls gasadsorption [4,9–11] despite lower organic matter contents.Shales and mudrocks also have microporosity associatedwith clay minerals. Clays such as illite, kaolinite and mont-morillonite have a predominance of pores with an effectiveradius between 1 and 2 nm. Microporosity of kaolinite andillite is attributed solely to the size of the clay crystalswhereas montmorillonite has different pore-size distribu-tions depending on the exchangeable cation saturation aswell as crystal size [12,13].

Negative adsorption results for methane have beenreported on zeolites [14] but the data were not includedin their results as they have ‘no physical meaning’. Froma suite of Pennsylvanian coals, Krooss et al. [15] reportednegative excess adsorption of carbon dioxide (between 8and 10 MPa) which was partly attributed to the inadequacyof the Gibbs approach (as described later) for a stronglynon-ideal gas at high pressures and low temperatures.

To investigate the occurrence and the importance ofnegative adsorption of shale/mudrock units and coal, boththe void volume calculation and adsorption experimentneed to be examined. It is not the purpose of this paperto provide further insight into the theories of adsorptionphenomenon which is widely addressed in the literature

Jurassic (a and b) and Devonian (c and d) shales.

2698 D.J.K. Ross, R. Marc Bustin / Fuel 86 (2007) 2696–2706

[16–28] but to rather investigate the failure of mass balancecalculations to the determination of adsorption capacity ofmicroporous unconventional reservoir rocks and shale gasreservoirs in particular.

2. Methods

2.1. Samples

Shale samples were selected from Jurassic and Devonianstrata in northeastern British Columbia, Canada. Addi-tionally, pure clay mineral standards of illite, smectiteand kaolinite used in this study were purchased from theUniversity of Missouri-Columbia Source Clay MineralsRepository. The inorganics (including quartz) were chosenon the basis that they are the primary constituents of shalesand mudrocks. The weight of the samples was approxi-mately 200 g and crushed to a particle size of 250 lm andanalyzed in both the dry and moisture equilibrated state.Synthetic zeolites (named ZeoSorb�) 33, 43 and 61 werealso analyzed as they have known pore-size diameters of0.31, 0.41 and 0.74 nm respectively. The suites of zeolitesare in extrudate and powder form and were manufacturedby TRICAT� Inc.

2.2. High pressure adsorption analysis – experimental setup

and calculations

Prior to the adsorption experiment, a series of heliumexpansions corrected for non-ideality from a known refer-ence volume to a sample cell are performed to calculate thevoid volume. In our experiments the expansions are carriedout over 10 pressure steps ranging from 0.25 MPa to5 MPa. The void volume is calculated from

P2� P3

P3� P1ð1Þ

where with appropriate correction for non ideality, P1 isthe initial sample cell pressure, P2 is the pressure in the ref-erence cell after charging with helium and P3 is the pressurein the sample cell and reference cell after expansion.

A volumetric Boyles Law gas adsorption apparatus wasused to measure high pressure methane isotherms at30.0 �C. The following mass balance calculation was usedin conjunction with the real-gas law to calculate pure gasadsorbed volume isotherms of samples with mass, ms, (atSTP conditions; T = 273.15 K, P = 0.101325 MPa) at eachisotherm step:

V ads ¼T STD

TP STDms

� �

� V ref

P I�1ref

z� P I

ref

z

� �� ðV void � V sÞ

P Isc

z� P I�1

sc

z

� ��

ð2Þ

The sample void volume (Vvoid), which is the volume in thesample cell not occupied by solid sample (includes free

space in the sample chamber and accessible porosity inthe sample), corrected for the volume occupied by theadsorbate (Vs) by assuming a molar density of the adsor-bate which is taken here as that at normal boiling whichfor methane, a value of 0.423 g/cm3 was used. If the adsor-bate volume is neglected, the Gibbs isotherm is obtained.The effect of the assumed density of adsorbate is not con-sidered in this paper but accepting any reasonable valuesdo not detract from the conclusions of this study. Gas com-pressibility factors for pure gas isotherms were determinedusing the Peng-Robinson equation of state (EOS) [29].From our analyses, changing the EOS does not changethe outcome of negative shales and mudrocks we haveexamined.

The adsorption data are fitted to the Langmuir equation[30]:

V E ¼V LP g

P L þ P g

ð3Þ

where VE is the volume of absorbed gas per unit volume ofthe reservoir in equilibrium at pressure Pg, VL is the Lang-muir volume (based on monolayer adsorption), the maxi-mum adsorption capacity of the absorbent, Pg is the gaspressure, PL is the Langmuir pressure, the pressure atwhich total volume absorbed and VE, is equal to one halfof the Langmuir volume, VL. Pressure points were collectedup to 9 MPa using high-precision pressure transducers(precision of 0.05% of the full scale value). For both heliumcalibrations and methane adsorption analysis, the system iskept at a constant bath temperature at ±0.01 �C as minorfluctuations in temperature effect the pressure. Before he-lium and methane analyses, the system manifold and cellsare leak tested with helium to check for isolated cell leaksand through-valve leaks. Typically the system is evacuatedand pressured up to 9 MPa. Several minutes are allowedfor thermal equilibration, and pressure readings are takenevery 15 min for a 1-2-hour period. In addition, the highpressure fittings are leak tested with SNOOP�.

Moisture capacities were determined by water satura-tion at 30 �C [31] which is recommended for moisture con-tent under reservoir conditions. The method consisted ofequilibrating samples over a saturated solution of potas-sium sulfate for more than 72 h in a vacuum dessicator.For dry basis analysis, all samples were oven dried for24 h at a temperature of 110 �C.

2.3. Considerations of volumetric calculation for gas

adsorption

Using the Gibbs excess approach [32] the amount of gasadsorbed is determined experimentally by [21]

nsorbed ¼ ntotal � cgasV void ð4Þ

where ntotal is the total amount of gas in the system andcgasVvoid is the gas occupying the void volume calcu-lated from the molar concentration in the gas phase, cgas

utilizing an EOS of the gas at various pressure/temperature

Fig. 2. Helium void volume calibration of ZeoSorb 61 (pore-diameter of0.74 nm). Note that above 2 MPa, the pressure ratios between referencecell and sample cell are relatively consistent.

Fig. 3. Calibration examples of organic-rich mudrock samples showingrelative increase in measured void volume at higher pressure expansions.Note scales are not uniform.


conditions. The void volume in these calculations includesfree space within the sample bomb and porosity within thesample not occupied by sorbate. During the adsorptionexperiments the void volume progressively decreases asthe sorbate occupies space which is considered in the massbalance calculations. The volume also decreases due toswelling of the organic matter during adsorption [33], theamount of which is organic matter and gas dependent.Although swelling is important as it results in a decreasein the void volume, the error introduced by not consideringthe swelling effects due to methane adsorption cannot ac-count for negative adsorption. The impact of swelling isconsidered in a future paper.

To calculate the adsorbed gas component (or excessadsorption), precise measurement of the void volume(Vvoid) is required. Helium expansions are used for voidvolume calculations as it is considered to give precise mea-surement of the void space, hence sample volume by differ-ence [34]. Helium is used as a choice of volumetric fluid fortwo reasons: (1) it has a small kinetic diameter whichenables penetration to the finest microporosity [35]; and(2) it is commonly assumed that helium has a low adsorp-tion coefficient at room temperature and moderate pressure(up to 9 MPa). Such an assumption however has beenquestioned since solid atoms can attract He [25,36] withhelium even adsorbing in inert solids such as silicates [26].

3. Results

The results of the paper are divided into two sections.Section 1 focuses on the use of helium as an analyticalgas for void volume calibrations in adsorption experimentsof heterogeneous materials, and in doing so examines theeffects of pressure, helium adsorption and time. Section 2discusses the adsorption implications of Section 1 to massbalance calculations in heterogeneous microporous materi-als. In order to demonstrate the importance of the hetero-geneous and microporous pore structure of organic matterand minerals in coals and shales we have also carried par-allel experiments using synthetic zeolites of known pore-size distribution and these results are included in the followsections.

3.1. Section I: helium effect

If the pore-sizes are comparatively large, adsorption andsample compressibility negligible, void volumes (free spacebetween particles and accessible sample porosity) measuredat various pressures with helium should be constant assum-ing appropriate corrections are made for non-ideality ofthe gas. These assumptions appear to be valid, for the Zeo-Sorb 61 sample which has a uniform pore-size of 0.74 nmand for which the void volume (ratio of (P2 � P3)/(P3 � P1)) calculated by helium expansion is constant withincreasing experimental pressures (Fig. 2). However for dryshale samples and the pure minerals kaolinite, smectite andillite (Figs. 3 and 4a–c), the calculated void volume overall

increases with increasing pressure. No continuous increasein void volume with higher pressure expansions is evidentfor quartz (>3.5 MPa; Fig. 4d). For moisture equilibratedsamples (Fig. 5) the trend to increasing void volume withpressure is less pronounced than their dry counter parts,or is non-existent (e.g. smectite).

Fig. 4. Helium void volume calibrations for major constituents of shale/mudrock samples (all on dry-basis): (a) kaolinite; (b) smectite; (c) illite; (d) quartz.Note the increasing void volume trend at higher cell expansions is not apparent for quartz.


The apparent increase in void volume for the naturalmaterials (Figs. 3–5) may be a manifestation of heliumadsorption at high pressure or helium being able to accessfiner pores at higher pressures. Helium adsorption has beenreported in previous literature for zeolites [14], activatedcarbons [23] and inert silicates [26]. Although some adsorp-tion of helium cannot be ruled out in our study, the absenceof an increase in calculated void volume with increase pres-sure for ZeoSorb 61 suggests that adsorption is not signif-icant. Additionally if adsorption of helium was responsiblefor the trend in void volume with pressure, we would antic-ipate that the calculated void volume would plateau athigher pressures, mimicking a Langmuir adsorption iso-therm. The general slopes of the helium isotherm curvesare rather continuous and relatively constant (Fig. 6) sug-gesting that helium is not significantly being adsorbed asno saturation point is reached (hence labelled as excesshelium capacity rather than helium adsorption [27,37]).The time-dependant diffusive nature [38] of helium is alsosuggested from calculated excess helium capacities for dif-ferent calibration times (i.e. the time given between theshut-in of the cell and recording cell pressure). For exam-ple, there is a systematic decrease in the excess void volume(or using the Gibbs methods amount of He adsorbed) froma calibration time of 1000, 300 and 30 s (Fig. 7). The results

suggest that for shorter calibration times there is less timeavailable for helium to diffuse and/or adsorb into the sam-ple which produces a smaller void volume.

Although we cannot entirely separate the helium capil-lary effect from the helium adsorption effect for void spacecalculations, our experiments indicate that pore access athigher pressures is important. Hence the increasing trendin void volume with pressure is thus considered mainly aconsequence of greater accessibility of helium to restrictedpores at higher pressures (i.e. a capillary effect). Essentiallya ‘‘squeezing’’ of molecules through pore openings and intomicropores occurs [39,40]. Diffusion of helium is confirmedby the slow and continuous decrease of equilibrium pres-sure as the He penetrated the interconnected network ofpores.

Many of the helium isotherms have a ‘step-like’ profile(e.g. Fig. 6c) which may reflect the gradual infilling ofpores. The filling of microporosity (associated with theorganic component?) can explain changes of the heliumisotherm for the shale sample in Fig. 6c which contains11 wt% organic matter. The diffusion of helium into themicroporosity is not controlled by the diffusion ratethrough the bulk sample (i.e. chemically assimilated inthe matrix) as helium is not soluble over the time-scale ofthese experiments (unlike, for example, carbon dioxide

Fig. 5. Void volume calibration examples of moisture equilibrated mudrock and clay samples with moisture contents shown in graphs: (a–c) mudrocksamples; (d) smectite. Note for low EQ moisture samples, void volume calibration shows similar trend to dry samples indicating greater void space is stillavailable at higher pressures. Samples with high EQ moisture contents (5378-1 and smectite) show no clear trend.


[41]). As noted by Larsen et al. [41], the diffusion of heliumdoes raise an interesting point: is the ability of heliumaccessing pore-space due to the small movement requiredof the samples molecular segments (and/or moisture) toallow its passage or is the micropore network continuouson the small-scale size of the helium atom? From theresearch here, no definitive conclusion can be made.

Diffusion and adsorption of helium is also effected bythe presence of moisture in shale and mudrock samples.The occupation of adsorption sites and pore-throats bywater creates less space for the helium molecule to occupyand may restrict helium diffusion, as suggested by the lesssignificant increase in void volume in moist samples. Theabsence of a trend in void volume for quartz is because itis not a microporous material. For the microporous Zeo-Sorb 61, the absence of a trend in void volume with pres-sure is because pore-size is comparatively large anddistribution is even and the sample dry such that heliumsaturation occurs at lower pressures than for shale sampleswhich do not have the consistent internal structure of thezeolites.

If as our results suggest, there is a gas capillary effect athigher pressures with the natural microporous materials,then this change in void volume must be taken into consid-eration and accounted for in the mass balance calculation.

With greater pore-space (and hence void space) accessibleto helium and thus presumably analyses gases at higherpressures, a unique void volume exists for each pressurestep. To determine the excess adsorption for a particularpressure the corresponding pressure dependent void vol-ume is required. If an average void volume is used forthe entire isotherm, adsorption at low pressures will beoverestimated and at high pressures underestimated.

3.2. Section II: helium calibrations and methane adsorption

experiments – pore-size effect

Isolating the effects of pore-size and pore-size distribu-tion on the void volume calculations of gas shales or coalsis difficult due to their heterogeneous character, variablemoisture content and organic matter type and abundance.Hence in this section we first demonstrate the importanceof helium vs. methane porosity on the adsorption calcula-tions using synthetic zeolites of know pore-sizedistribution.

Methane adsorption isotherms were measured on zeo-lites 33, 43 and 61 at pressures up to 9 MPa utilizing heliumto measure the void volume as routinely done in adsorptionexperiments of gas shales and coals. For both the 43 and61 zeolites, methane isotherm data fit well to the Type I

Fig. 6. Helium isotherms with monotonous trends: (a) smectite; (b) and (c) mudrock samples. Occasionally isotherms have humps, perhaps a reflection ofthe slow diffusion into the microporosity.

Fig. 7. Calculated helium isotherms of a shale sample with different voidvolume calibration time. With longer calibration time, the moleculeaccessibility/adsorption is similar to the actual adsorption experimenthence lower excess helium capacity is calculated for the longer calibrationtime (i.e. 1000 s). The curves follow identical trends as only the voidvolume calibrations, and not the adsorption experiment, are varied withtime.


Langmuir model (Figs. 8a and b). Conversely ZeoSorb 33(0.31 nm pore-size) yields a calculated negative adsorptionat every pressure step (Fig. 8c). During the initial low pres-sure adsorption steps, sample cell pressure does notdecrease indicating that adsorption is not taking place

(Fig. 9, example 1). At higher pressure steps, however sam-ple-cell pressures gradually decrease (Fig. 9, examples 2and 3), implying gas is either adsorbing and/or diffusingeven though negative adsorption is calculated by massbalance.

Two aspects of the high-pressure adsorption experi-ments need to be taken into consideration to explain thecalculated negative adsorption for ZeoSorb 33: (1) the dif-ference of kinetic diameters of the analytical gases – heliumhas a kinetic diameter of 0.26 nm whilst methane has akinetic diameter of 0.38 nm [14]; and (2) the equation usedto calculate adsorbed gas capacities. If equal pore-spacewas available to both helium and methane and no adsorp-tion occurred (i.e. ntotal = Vvoid from Eq. (4)), then zeroadsorption would be calculated. For ZeoSorb 43 and 61,positive adsorption is recorded as both helium and meth-ane can penetrate all pores (pore-size 0.41 and 0.74 nm)and methane can adsorb onto the high internal surfaceareas (i.e. ntotal > Vvoid). However negative adsorption ofZeoSorb 33 indicates Vvoid is larger than ntotal. This is aresult of steric hindrance where helium can access pore-space methane cannot, as the permeance of these gases iscontrolled by their kinetic diameters, molecular geometry,the pore dimensions and pore geometry of the samples.Methane with its larger kinetic diameter cannot penetratethe 0.31 nm pores, thus a larger void volume to helium

Fig. 8. Methane adsorption isotherms of zeolites with known pore-size distribution: (a) ZeoSorb 61: 0.74 nm pore-size; (b) ZeoSorb 43: 0.41 nm pore-size;(c) ZeoSorb 33: 0.31 nm pore-size).


exists than for methane. The larger void volume combinedwith extremely low levels of methane adsorption (as thereare minimal amounts of adsorption sites available to meth-ane due to the pore-size) produces a calculated negativeadsorption. The minute pressure drops in sample cell pres-sure for ZeoSorb 33 is a reflection of methane adsorbingonto the external surface area as all internal surface areas(i.e. 0.31 nm pores) are inaccessible. Since the amount ofadsorbed gas is minimal and the void volume is errone-ously large, negative adsorption is calculated by massbalance.

The sieving effect of gas molecules shown by ZeoSorb 33helps explain why negative adsorption isotherms are calcu-lated for low organic carbon content (TOC) shales (e.g.Fig. 1). For TOC-lean shales, adsorbed gas capacities arelow as there are minimal adsorption sites available to meth-ane (minimal microporous organics). Similar to ZeoSorb33, shales with negative adsorption show reductions insample cell pressures (Fig. 10) indicating gas is adsorbingduring the experiment. However the magnitude of pres-sure-change due to adsorption is too small to compensatefor the negative effects that are an artifact of the void vol-ume to helium exceeding the void volume available tomethane (Vvoid > ntotal). Helium can penetrate more ofthe sample whether it is ultra-fine microporosity [5] orrestricted pore-throats which cannot be accessed bymethane.

In Fig. 11 we consider the adsorption isotherm on anorganic lean, low methane adsorbing shale with a totalhelium porosity of 2.64% and organic carbon content of1.65%. Utilizing the void volume to helium averaged overa series of helium expansions yields negative adsorptionvalues at high pressures in spite of adsorption occurringas evident from pressure changes in the sample cell. If theporosity available to methane is not 2.64% (helium poros-ity) but 1.99% (for example), positive adsorption is calcu-lated (ntotal > Vvoid). Assuming (in this example) that0.65% porosity (2.64% minus 1.99%) is available to heliumbut not methane has a marked effect on the isotherm shapeand the calculated adsorptive capacity. The actual amountof porosity available to helium but not methane will varyfrom sample to sample due to heterogeneous pore-throatdiameters, pore-size distributions and surface roughnessand hence must be measured for each sample. ZeoSorb33 with a 0.31 nm pore-size is the most dramatic exampleof pore sieving since the pore-size are uniformly larger thanhelium and smaller than methane whereas in naturallymaterials the pore-size and pore-size distribution will varymarkedly.

The example selected here (Fig. 11) is a low adsorbingshale and hence the errors resulting from inappropriatevoid volume are striking. Errors will also exist in morestrongly adsorbing organic-rich shales (and coals) howeverthe errors are masked unless the experiments are run to

Fig. 9. Selected pressure steps of ZeoSorb 33 showing negative adsorption at all pressure steps. Example 1 shows no adsorption/diffusion of methane (nopressure decrease). However at further pressure intervals (e.g. examples 2 and 3), negative adsorption occurs despite cell pressure reductions.


pressures high enough that adsorption is negligible. Theamount of the error will be proportional to the pore-sizeand pore-size distribution of the sorbate (mainly theorganic fraction) and the analysis gas. For example someof our laboratory experiments have shown that ethaneadsorption experiments on some coals do produce calcu-lated negative isotherms at moderate to higher pressureseven though there is adsorption taking place as evidentfrom the pressure changes in the sample cells.

4. Conclusions

The data presented here documents the effect and errorsthat may result if helium is used as a void volume calibra-tion gas for high pressure adsorption experiments in heter-ogeneous microporous materials. Experimental analysisreveals that both pressure and time affect the amount ofhelium which penetrates, and possibly adsorbs, into a sam-ple: potentially more pore-space is available to helium at

greater pressures and increased calibration time. If poreaccessibility to various gases change with increasing pres-sure as suggested by our data, using an average void vol-ume will results in calculated adsorbed gas volumes thatare too high at low pressures and too low at high pressures,even if the volume is corrected for sorbate volume.

Experiments with zeolites of known pore-size highlightshow the porous structure of the adsorbent contributes toadsorption which depends on the accessibility of the mole-cule to the adsorption sites and underlining the deficienciesof mass balance calculations. The accessibility to internalsurface area is controlled by the diameter size of the pores,pore-throats and kinetic diameter of the gas molecule andneeds to be taken into consideration where helium is usedto measure the void volume. Experiments with the syn-thetic zeolite, ZeoSorb 33, which a pore-diameter of0.31 nm underlines the importance of pore-size: negativeadsorption is calculated by mass balance at all pressuresbecause the helium can access the internal pore structure

Fig. 10. Mudrock sample with negative methane adsorption yet raw pressure data reveals gas diffusion and/or adsorption.

Fig. 11. Hypothetical example showing the reduction of porosity (orexcess void space which is only accessible to helium) required to calculatepositive adsorption using mass balance calculations on low-adsorbingshales.


and methane cannot and thus the void volume to heliummarkedly exceeds that available to methane.

Calculated negative adsorption of shale samples lean intotal organic carbon content is a result of the void volume(free space plus sample pore-space) available to heliumexceeding that available to methane and hence the massbalance calculation is in error – negative adsorption is cal-culated even though adsorption occurs as evident from dis-tinctive pressure drop in the sample cells. In organic-richshales and coals, their larger adsorbed gas capacities maskerrors due to inappropriate void volumes. However evenwith organic-rich samples and positive adsorption, theadsorbed gas capacity is underestimated.

Mass balance techniques when used with out due con-sideration for the pore-size distribution are inappropriatefor heterogeneous microporous materials such as shales,mudrocks and coals. For gas shales and coalbed methanedeposits even relatively small errors is adsorption calcula-tions may result in substantial errors when extrapolatedto the reservoir scale.

Future work on this topic will include expansion of thecurrent dataset by incorporating a broader suite of compo-


sitionally diverse, low-sorbing shales and mudrocks. Toassess the effect of kinetic diameter hindrance in shalesand mudrocks, gases of variable size will be utilized for vol-umetric adsorption calculations (e.g. ethane, krypton, andargon). Further investigation of negative adsorption forcoals is also required as from our limited dataset, ethaneadsorption experiments can produce negative isotherms.

Acknowledgements

Funding for this study was provided by NSERCawarded to R.M. Bustin. The authors would like to thanktwo anonymous reviewers for their careful review of thismanuscript.

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