Multi-temperature method for high-pressure sorption measurements on moist shales

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  • Multi-temperature method for high-pressure sorption measurements onmoist shalesMatus Gasparik, Amin Ghanizadeh, Yves Gensterblum, and Bernhard M. Krooss

    Citation: Rev. Sci. Instrum. 84, 085116 (2013); doi: 10.1063/1.4817643 View online: View Table of Contents: Published by the AIP Publishing LLC.

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    Multi-temperature method for high-pressure sorption measurementson moist shales

    Matus Gasparik, Amin Ghanizadeh, Yves Gensterblum, and Bernhard M. Kroossa)Energy and Mineral Resources Group (EMR), Institute of Geology and Geochemistry of Petroleum and Coal,Lochnerstr. 4-20, RWTH Aachen University, 52056 Aachen, Germany

    (Received 21 April 2013; accepted 22 July 2013; published online 22 August 2013)A simple and effective experimental approach has been developed and tested to study the temperaturedependence of high-pressure methane sorption in moist organic-rich shales. This method, denotedas multi-temperature (short multi-T) method, enables measuring multiple isotherms at varyingtemperatures in a single run. The measurement of individual sorption isotherms at different tem-peratures takes place in a closed system ensuring that the moisture content remains constant. Themulti-T method was successfully tested for methane sorption on an organic-rich shale sample. Ex-cess sorption isotherms for methane were measured at pressures of up to 25 MPa and at temperaturesof 318.1 K, 338.1 K, and 348.1 K on dry and moisture-equilibrated samples. The measured isothermswere parameterized with a 3-parameter Langmuir-based excess sorption function, from which ther-modynamic sorption parameters (enthalpy and entropy of adsorption) were obtained. Using these, weshow that by taking explicitly into account water vapor as molecular species in the gas phase withtemperature-dependent water vapor pressure during the experiment, more meaningful results are ob-tained with respect to thermodynamical considerations. The proposed method can be applied to anyadsorbent system (coals, shales, industrial adsorbents) and any supercritical gas (e.g., CH4, CO2) andis particularly suitable for sorption measurements using the manometric (volumetric) method. 2013AIP Publishing LLC. []


    There is a considerable research interest in sorption prop-erties of coals, and more recently shales, stimulated by theireconomic potential (coal bed methane, shale gas) and devel-opment of concepts to mitigate the climate change throughcapture and storage of CO2 in geologic formations. The cru-cial role of moisture in sorption process is widely recog-nized in the literature. The sorption capacities to methaneand carbon dioxide were shown to decrease significantly inthe presence of moisture in coals (Joubert et al., 1973, 1974;Krooss et al., 2002; Hildenbrand et al., 2006; Busch et al.,2006; Siemons and Busch, 2007; Crosdale et al., 2008; Dayet al., 2008; Ozdemir and Schroeder, 2009; Battistutta et al.,2012; vbov et al., 2012), shales (Busch et al., 2008;Ross and Bustin, 2009), and activated carbons (e.g.,Gensterblum et al., 2009; Billemont et al., 2011). The detri-mental effect of moisture on the sorption capacity of gas(CH4, CO2) is attributed to water and gas molecules compet-ing for sorption sites or by simple volumetric displacement.On the other hand, some studies on methane sorption in ac-tivated carbons suggested that the moisture can enhance thesorption capacity through the formation of methane hydrateunder specific experimental conditions (Zhou et al., 2002;Miyawaki et al., 1998).

    Published high-pressure sorption data for moist coals arecommonly reported as sorption isotherms at given moisturecontents on coal samples that were moisture-equilibrated atsome specified relative humidity conditions. There is, how-

    a)Electronic mail:

    ever, limited data available up to date on the temperature de-pendence of sorption capacity for coals and none for shales.The major experimental difficulty lies in the fact that smallchanges in the moisture content between the individual mea-surements at respective temperatures can greatly affect themethane sorption capacity. Hence, the resulting changes insorption capacity do not depend on temperature alone. Thechanges may arise during evacuation cycles if isothermsare measured on a single sample in a consecutive manner,or when split samples moisturized at the same relative hu-midity conditions are used to measure each isotherm. Inter-laboratory studies on CO2 sorption on moist coals (Goodmanet al., 2004, 2007) suggested that much of the variation insorption capacity between individual laboratories results fromdifferences in moisture contents. Modifications of the exper-imental sorption setup can enable some control on the mois-ture content of the adsorbent sample in the sample cell. Forexample, Billemont et al. (2011) modified their gravimetricRubotherm setup to allow in situ moisture-equilibration ofthe sample directly in the sample cell. The gravimetric setupsare particularly suitable for this approach as they are basedon direct measurement of weight change and, this way, thein situ moisture content can be directly measured prior to thestart of the sorption experiment. This approach is, however,not applicable for manometric (volumetric) sorption devices.

    Here, we present a simple experimental approach formanometric apparatus to measure sorption isotherms atdifferent temperatures under closed system conditions. Thus,it enables to keep the moisture constant at all temperatures.In addition, the measuring times can be significantly reducedas the sample need not be de-gassed between individual

    0034-6748/2013/84(8)/085116/9/$30.00 2013 AIP Publishing LLC84, 085116-1

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  • 085116-2 Gasparik et al. Rev. Sci. Instrum. 84, 085116 (2013)

    FIG. 1. Schematic representation of the high-pressure manometric sorptionapparatus.

    measurements at different temperatures. This multi-temperature technique was successfully tested on dry andmoisture-equilibrated samples. Excess sorption isothermsfor methane were measured at pressures of up to 25 MPaand temperatures of 318 K, 338.1 K, and 348.1 K on adry and moisture-equilibrated organic-rich shale sample.The measured isotherms can be accurately represented bya 3-parameter function, which is based on the Langmuirfunction for absolute sorption and a density term relatingexcess and absolute sorption. The results are discussed withrespect to the thermodynamic parameters derived from thetemperature dependency of the Langmuir pressure constant.


    A. Manometric high-pressure sorption setupA schematic representation of the manometric sorption

    setup (also referred to as Sievert-type apparatus) is shown inFigure 1. It consists of two stainless steel chamberssamplecell (SC) and reference cell (RC), shut-off valves and apressure gauge connected via 1/16 in. tubing. The appara-tus is connected to methane and helium gas supplies with agas purity of 99.995% and 99.999%, respectively. Two high-pressure VICI R valves (v1 and v2) are used as shut-off valvesin front of the RC cell and between RC and SC. Due to theirconstruction and operation mode, the dead volume of thesevalves is the same irrespective of the position. A three-portvalve (v3) is used to switch between the gas supply and avacuum pump. Valves v1 and v2 are operated by computer-controlled electric actuators. A high-precision piezoresistivepressure transmitter (Tecsis P3382; all metal, no polymerseals) with a 25 MPa range attached to the reference cell is

    used to monitor the pressure. The accuracy given by the ven-dor is 0.05% of full scale value (= 0.0125 MPa). The samplecell is sealed by metal face seal fittings (VCR R, Swagelok)as described in Checchetto et al. (2004) using nickel gas-kets with an integrated 0.5 m filter. Both cells including thevalves v1 and v2 and the pressure transmitter are kept at con-stant temperature using a gas chromatograph (GC) oven. Thetemperature stability is within 0.1 K. Temperature readingsare taken from a Pt-100 (class 1/10 B) resistance temperaturedetector (RTD) with an estimated accuracy of 0.1 K.

    The volumes of the reference and the sample cell weredetermined by helium expansion. Multiple gas expansionsinto the empty sample cell and into the sample cell containinga stainless steel cylinder of accurately known volume (refer-ence volume) were performed up to 10 MPa. For the experi-mental setup used in this study the volumes of the reference(Vrc) and the sample cell (Vsc) were 1.350 0.007 cm3 and11.35 0.05 cm3, respectively.

    B. Samples and sample preparation

    High-pressure sorption isotherms were measured on adry and moisture-equilibrated shale sample that was crushedand sieved to 0.51.0 mm particle size. The basic geo-chemical properties of the studied sample are listed inTable I. The drying procedure consisted of pre-drying thesample overnight in a vacuum oven and additional dryingwas performed in situ at 383 K under vacuum after the sam-ple was transferred into the sample cell. This in situ dryingis necessary to remove any moisture taken up by the sam-ple in contact with air humidity during its placement into thesample cell since even small amounts of moisture can have asignificant effect on the sorption capacity. The moist samplewas prepared by moisture-equilibration at room temperaturein an evacuated desiccator over a saturated salt solution ofK2SO4 under constant relative pressure of water vapor (p/p0= 0.97). The moisture content (m.c.) was calculated fromEq. (1):

    m.c. = (mme mdry)mme

    100%. (1)

    Here, mme and mdry are the weight of moisture-equilibratedand dry samples, respectively.

    C. Measuring procedureThe manometric technique of high-pressure sorption

    measurements has been described in detail elsewhere(Mavor et al., 1990; Krooss et al., 2002; Busch et al., 2003;Gensterblum et al., 2009; Van Hemert et al., 2009). The

    TABLE I. Basic geochemical properties of the studied shale sample. The equilibrium moisture content is calculated by Eq. (1). Helium densities for dry andmoist sample were obtained from the void volume measurements with He at 318.1 K on dry and moisture-equilibrated samples, respectively.

    XRD (wt. %)

    Total organic Vitrinite Quartz and Total Eq. moisture He-density, He-density,carbon, TOC (wt. %) reflectance(VRr%) feldspars clays Carbonates (wt. %) dry (g/cm3) moist (g/cm3)

    5.7 2.4 38.7 59.0 0.6 2.69 2.556 0.002 2.476 0.001

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  • 085116-3 Gasparik et al. Rev. Sci. Instrum. 84, 085116 (2013)

    FIG. 2. Measuring program used in the multi-T method showing thechange in pressure (a) and the variation in temperature (b) during the firstfour gas injection steps. From the equilibrium data at respective temperaturesthe individual isotherms are calculated.

    multi-T technique described here differs from the conven-tional measurement in that the temperature is varied in a con-trolled manner during the sorption experiment. This is illus-trated in Figure 2 which shows the change in pressure andtemperature during the first four measurement steps in thesorption experiment. Initially, the reference cell is loaded withgas (methane) at T = 318.1 K. After reaching thermal equi-librium the gas is then expanded into the sample cell and al-lowed to equilibrate with the sample. When no more gas up-take is observed the temperature is increased from 318.1 K to338.1 K. During this period, a new equilibrium is establishedcorresponding to the change in pressure in a constant vol-ume and simultaneous change in the sorption capacity upontemperature increase. The temperature is then increased to348.1 K and decreased finally to 318.1 K for time intervalsnecessary to reach the equilibrium. This way, during a singlegas injection, data points corresponding to three isotherms at318.1 K, 338.1 K, and 348.1 K can be determined simultane-ously. This procedure is repeated for consecutive steps untilthe equilibrium pressure in the sample cell reaches 25 MPa.The restoration of the initial temperature of 318.1 K at the endof each temperature program cycle is not a necessity and theloading of the reference cell can be performed at 318.1 K and348.1 K in an alternating manner. Here, the isotherms for theinitial and the final 318.1 K are compared for consistency.

    The benefit of the multi-T experimental procedure is thatthe water content within the system remains constant at alltemperatures. This ensures that (1) the change in the moisturecontent of the sample with temperature is negligible, providedthe void volume is sufficiently small, or that, at least, (2) itcan be accounted for by simple mass-balance considerations.Moreover, the measuring time can be significantly reducedcompared to consecutive isotherm measurements. This comesmainly from the fact that in the latter approach the measuringspeed is limited by the need to degas the sample after each in-dividual sorption test. This can be a very lengthy process formoist coal and shale samplesespecially, if care is given not

    to lose moisture during the degassing process (e.g., by cool-ing the sample cell and short evacuation intervals followed bymonitoring of the degassing).

    D. Calculation of the excess sorption

    The excess sorption (Gibbs surface excess) for the ithstep is calculated as a difference between the total mass ofgas transferred into the sample cell and the mass of gas occu-pying the void volume (V 0void ) at density CH4eq correspondingto (p,T) in the sample cell:

    mCH4excess,i = mCH4transf erred,i V 0voidCH4eq,i . (2)

    The mass of methane transferred from the reference cell intothe sample cell for N successive injection steps is calculatedfrom:

    mCH4transf erred,i = Vrc



    CH4rc,i CH4eq,i

    ), (3)

    where Vrc is the volume of the reference cell; CH4rc and CH4eqare, respectively, the density of methane in the reference cellduring the loading step and the equilibration step. In the multi-T experiment the temperature during the loading of the refer-ence cell (T0) was always equal to 318.1 K. Normalized todry sample weight (mdry), the excess sorbed mass (mCH4excess),respectively, the excess sorbed amount (nCH4excess) for each tem-perature (Tj) is calculated from Eqs. (4a) and (4b):

    mCH4excess,i(Tj ) =





    CH4rc,i (T0) CH4eq,i (Tj )


    V 0voidCH4eq,i (Tj ), (4a)

    nCH4excess,i(Tj ) =





    CH4rc,i (T0) CH4eq,i (Tj )


    V 0voidCH4eq,i (Tj ), (4b)where MCH4 is the molar mass of methane. The void volumeV 0voidwas measured by helium expansion (V 0void = V Hevoid ) at318.1 K. The same value of V 0void is assumed for the tem-peratures of 338.1 K and 348.1 K (i.e., in this temperaturerange the net volumetric effect of the thermal expansion ofthe sample cell and the sample is assumed to be negligible).The void volume was measured over a range of pressures andno significant change with pressure was observed (Figure 3).

    E. Consideration of the water vapor pressurein the excess sorption calculation

    After the installation of the moist sample into the samplecell and initial evacuation (performed at room temperature fora few minutes), the system is equilibrated at the starting ex-perimental temperature (T0 = 318.1 K). The minimum pres-sure in the sample cell will correspond to the pressure of thewater vapor (pv) that is in equilibrium with the moisture ofthe shale sample at T0. The value of the vapor pressure willvary with the experimental temperature (Tj). We consider this

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  • 085116-4 Gasparik et al. Rev. Sci. Instrum. 84, 085116 (2013)

    FIG. 3. Void volume measured by helium expansion at 318.1 K versus pres-sure in the sample cell.

    temperature-dependent water vapor pressure in the mass bal-ance approach described here and demonstrate that it has anon-negligible effect on the resulting methane excess sorp-tion for the studied shale sample. Moreover, as we will showlater, the results of this procedure are consistent from a ther-modynamic point of view.

    At vacuum and at temperature Tj, the water vapor pres-sure will be equal to saturation pressure, pv0(Tj ), multipliedby water activity of the shale sample (aw). The water activityis assumed to be equal to the water activity (relative pressure,p/p0) during the moisture equilibration in the desiccator (i.e.,no water is lost or gained during the sample installation intothe sample cell and the void volume is sufficiently small com-pared to the overall water content of the sample to cause anysignificant change in moisture content when a new equilib-rium between the moisture of the sample and the vapor phaseoccupying the void volume is established). Then, for the va-por pressure:

    pv(Tj ) = awpv0(Tj ), (5)where aw = p/p0 = 0.97. The saturated vapor pressure at Tjcan be conveniently estimated using, e.g., the Antoine equa-tion (Poling et al., 2001, p. 7.4):

    log10 pv0(Tj ) = A B

    Tj + C 273.15 , (6)

    where Tj is in Kelvin. Parameters for water are: A = 5.11564,B = 1687.537, and C = 230.17 and pv0 in Eq. (6) is in bar(Poling et al., 2001).

    The values for pv(Tj ) were calculated from Eqs. (5) and(6). These were then compared with the measured pressuredata obtained by running the experimental temperature pro-gram in the evacuated sample cell. The measured and calcu-lated pressure values are in a very good agreement as shownin Figure 4.

    Since the measurement of the sorption isotherms at dif-ferent temperatures in the multi-T experiment is performedunder closed-system conditions, the total amount of water re-mains constant during the experiment. The total amount of

    FIG. 4. Variation of the temperature (a) and the corresponding change in thevacuum pressure (b) in the sample cell containing the moist sample. Thedots in (b) represent the measured pressure data and the green line corre-sponds to the calculated vapor pressure (Eqs. (5) and (6)).

    water in the system (mH2Ototal) is a sum of the sorbed water (i.e.,the moisture content of the shale sample) (mH2Osorbed ) and thefree water (i.e., water vapor) (mH2Of ree) in the void volume ofthe sample cell:

    mH2Ototal = mH2Osorbed (Tj ) + mH2Of ree(Tj ) = const. (7)

    As the temperature is increased, the increase in the vaporpressure, and hence increase in the amount of free water in thegas phase, must be accompanied by corresponding decreasein the sorbed water. However, given the range of experimen-tal temperatures in this study and the fact that (1) the amountof sorbed water is sufficiently large, while (2) the void vol-ume is sufficiently small, the change in moisture content upontemperature increase is negligibly small. This can be easilyshown by calculating the change in moisture content at eachtemperature Tj based on the water vapor pressure pv(Tj ) andthe volume corresponding to the sum of void volume (V 0void= 6.130 106 m3) and reference cell volume (Vrc = 1.350 106 m3). The calculated change in moisture content for thehighest experimental temperature (348.1 K) is only 0.010wt. % (Table II) and is assumed to have negligible effect onthe sorption capacity to methane at m.c. = 2.69 wt.%.

    TABLE II. Calculated water vapor pressure (pv) and change in moisturecontent (m.c.) for the three experimental temperatures (Tj). The initialmoisture content is 2.69 wt. %.

    Tj (K) pv (MPa) m.c. (wt. %)

    318.1 0.010 . . .338.1 0.025 0.006%348.1 0.039 0.010%

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  • 085116-5 Gasparik et al. Rev. Sci. Instrum. 84, 085116 (2013)

    FIG. 5. Calculated molar fractions of methane (yCH4i ) in the sample cell ver-sus pressure (p) for each experimental temperature (Tj). yCH4i were calculatedfrom Eq. (8) to Eq. (10). The values deviate increasingly from unity at highertemperatures and lower pressures.

    Next, during the sorption experiment a gas mixture ofmethane and water (from now on we will refer to the watervapor phase as simply water) will be present in the sam-ple cell. For the calculation of the excess sorption, however,only the methane component should be considered. Althoughno direct measurement of the gas composition is possible ina conventional manometric setup designed for pure gas mea-surement, the composition of the gas phase can be estimated.A quantitative approach to estimate the gas composition, andhence the actual methane density, is outlined here under theassumption that (1) the absolute water pressure is indepen-dent of total pressure in the sample cell and only depends onthe experimental temperature Tj and (2) the gas phase in thereference cell (the gas injected into the sample cell) can beconsidered as pure methane. The molar fraction of methanein the ith step (yCH4i ) is expressed as the amount of substanceof methane (nCH4i ) divided by the sum of the amounts of sub-stance of methane and water (nwi ) in the sample cell:

    yCH4i =


    nwi + nCH4i. (8)

    From the assumption (1), nwi = nw0 which is calculated fromthe gas equation assuming ideal behavior (low pressure):

    nw0 (Tj ) =pv(Tj )V 0void

    RTj. (9)

    FIG. 6. Resulting excess sorption isotherms for methane on dry (full sym-bols) and moisture-equilibrated (open symbols) shale sample at temperaturesof 318.1 K, 338.1 K, and 348.1 K.

    The amount of substance of methane is calculated from theamount of gas transferred through the reference cell into thesample cell under the assumption (2):

    nCH4i (Tj ) =





    CH4rc,i (T0) CH4eq,i (Tj )

    ]. (10)

    From Eqs. (8)(10), the change in molar fraction of methaneduring the sorption experiment was calculated for each tem-perature and is shown in Figure 5. Note that the molar fractionof methane deviates increasingly from unity at lower pres-sures and with increasing temperature.

    From the (p,T) data and the calculated composition(yCH4i ) of the gas mixture in the sample cell, the density of themethane-water gas mixture (CH4H2Oeq,i ) was calculated usingthe GERG2004 equation of state (EOS) (Kunz et al., 2007).The actual methane density in the sample cell at each Tj isthen obtained from:

    CH4eq,i (Tj ) = yCH4i (Tj )




    )CH4H2Oeq,i , (11)where MCH4H2O(yCH4i ) is the molar mass of the methane-water gas mixture calculated from the GERG2004 EOS.

    F. Parameterization of the excess sorption isotherms

    The measured excess sorption data were fitted bya 3-parameter (nL, pL, a) excess sorption functionbased on the Langmuir function for absolute sorption

    TABLE III. Fitting parameters of the excess sorption function (Eq. (12)) for the dry sample.

    Fitting parameters (Eq. (12)) Quality of fit No. of data pointsT (K) 1/T (K1) 103 nL (mmol/g) pL (MPa) a (kg/m3) n 104 N

    318.1 3.144 0.219 2.38 545 5.86 18338.1 2.958 0.219 3.66 545 6.93 18348.1 2.873 0.219 4.43 545 7.79 18

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  • 085116-6 Gasparik et al. Rev. Sci. Instrum. 84, 085116 (2013)

    TABLE IV. Fitting parameters of the excess sorption function (Eq. (12)) for the moisture-equilibrated sample with consideration of the water vapor pressure.

    Fitting parameters (Eq. (12)) Quality of fit No. of data pointsT (K) 1/T (K1) 103 nL (mmol/g) pL (MPa) a (kg/m3) n 104 N

    318.1 3.144 0.103 5.69 545 4.70 16338.1 2.958 0.103 7.90 545 4.49 16348.1 2.873 0.103 9.07 545 5.03 16

    (Gensterblum et al., 2009, 2010; Gasparik et al., 2012):

    nf itexcess(Tj ) = nLp

    p + pL(Tj )

    (1 g

    (p, Tj


    ), (12)

    where nf itexcess (mmol/g) denotes the excess sorbed amount ofsubstance at the pressure p obtained by the fit to the experi-mental data. pL (MPa) is the Langmuir pressure, correspond-ing to the pressure at which half of the sorption sites areoccupied, and nL (mmol/g) is the maximum Langmuir ca-pacity (corresponding to the Langmuir volume), denotingthe amount sorbed at full occupancy of the Langmuir mono-layer. The second term on the right-hand side of Eq. (12)containing the ratio of free (g) and sorbed phase density (a)results from the mass balance considerations between excessand absolute sorption. At low pressures (g a) the densityratio approaches zero and Eq. (12) transforms into the well-known Langmuir function.

    For the fitting procedure, in order to minimize the num-ber of degrees of freedom, the parameters nL and a wereheld constant and only the Langmuir pressure pL was allowedto vary with temperature. The values of nL, pL, and a can-not be determined separately from isotherm measurements.They can either be fitted simultaneously or for parameter re-duction a meaningful value for the density of the adsorbedphase (a) may be selected. In this work, a value from thebest fit of the lowest-temperature isotherm (318.1 K) was usedwhich has the highest sensitivity to a (higher g(p, T) at thistemperature).

    With the Langmuir adsorption model, thermodynamicparameters describing the sorption process can be obtainedfrom the temperature dependence of the Langmuir pressureconstant, pL (Myers and Monson, 2002):

    ln pL = HRT


    + ln p0, (13)where H is the enthalpy of sorption, which is equal in mag-nitude to the isosteric heat of adsorption qst but with a negative

    sign, (H = qst); S is the molar entropy of sorption andp0 = 0.1 MPa is the pressure at the perfect-gas reference state(Myers and Monson, 2002). The H and S parameters areobtained from the slope and the y-axis intercept, respectively,of the plot of ln pL versus 1/T.

    The fitting performance was characterized by the param-eter n according to the equation:

    n = 1N


    (nexp nf it )2, (14)

    where N is the number of data points, nexp and nfit are the mea-sured and calculated values for excess sorption for individualpoint, respectively.


    A. Temperature dependence of methane sorption fordry and moisture-equilibrated sample

    The results of the sorption measurements on dry andmoisture-equilibrated sample at temperatures of 318.1 K,338.1 K, and 348.1 K using the multi-T method are shownin Figure 6. The isotherms for the moisture-equilibrated sam-ple were calculated with explicit consideration of the watervapor pressure as described above. The excess sorption ca-pacity of the moisture-equilibrated sample is reduced by upto 60% as compared to the dry sample. The excess sorptionisotherms for the dry sample exhibit maxima which are typi-cally observed on dry coals and shales. The solid and dottedlines in Figure 6 represent the fitted 3-parameter excess sorp-tion functions (Eq. (12)). Representative fits to the measuredexcess sorption isotherms were obtained for the entire rangeof pressures and temperatures. The resulting fitting parame-ters for the dry and moisture-equilibrated samples are listedin Tables III and IV.

    TABLE V. Fitting parameters of the excess sorption functions (Eq. (12)) for the moisture-equilibrated sample without consideration of the water vapor pressure.

    Fitting parameters (Eq. (12)) Quality of fit No. of data pointsT (K) 1/T (K1) 103 nL (mmol/g) pL (MPa) a (kg/m3) n 104 N

    318.1 3.144 0.105 6.06 545 4.93 16338.1 2.958 0.105 10.09 545 3.37 16348.1 2.873 0.105 13.35 545 3.76 16

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  • 085116-7 Gasparik et al. Rev. Sci. Instrum. 84, 085116 (2013)

    FIG. 7. Resulting excess sorption isotherms for methane for the moisture-equilibrated sample without (a) and with (b) consideration of the water vaporpressure.

    In order to examine if the explicit consideration of thewater vapor in the mass balance calculation of methane excesssorption has a significant effect, the excess sorption isothermswere calculated additionally without considering the watervapor (i.e., assuming a molar fraction of 1 for CH4 in thegas phase). The fitting parameters for this case are listedin Table V. A comparison of the calculated excess sorptionisotherms for methane without and with consideration of thewater vapor is shown in Figures 7(a) and 7(b), respectively.It shows that the overall temperature effect on the calculatedexcess sorption is different. When the correction for watervapor is applied, the magnitude of the temperature effect onthe excess sorption is smaller. From the temperature depen-dency of the Langmuir pressure (Eq. (13)) the sorption en-thalpies (H) and sorption entropies (S) were calculatedand are listed in Table VI. The calculated sorption enthalpyfor the measurement on the dry sample is 19.1 kJ/mol andis comparable to reported data for coals (e.g., Zhang et al.,2012). For the moisture-equilibrated sample, the calculatedsorption enthalpy is 24.0 and 17.8 kJ/mol for the case with-out and with explicit consideration of the water vapor phase,respectively. It shows that the latter approach is more consis-tent from the thermodynamic point of view because the pres-ence of moisture is expected to reduce rather than increasethe sorption enthalpy. This is due to the preferential sorp-tion of water molecules on the higher-energy sites (Busch andGensterblum, 2011). When water vapor pressure is explic-

    TABLE VI. Sorption enthalpy H and sorption entropy S obtained fromthe temperature dependency of the Langmuir pressure pL (Eq. (13)) for thedry sample and for the two cases for moisture-equilibrated sample withoutand with correction for the water vapor.

    Dry Moist Moist (corr.)

    H (kJ mol1) 19.1 0.2 24 1 17.8 0.2S (J mol1 K1) 86.4 0.5 110 3 89.0 0.5

    itly considered, the calculated sorption enthalpy is slightlysmaller than that for the dry sample. This is consistent fromthe thermodynamic point of view and shows that for sorp-tion measurements on moist low-sorbing materials (such asshales) the effects of water vapor must be considered in themass balance approach.


    We present a simple and efficient experimental approachto determine the effect of temperature on high-pressuremethane sorption in moist organic-rich shales. In this multi-temperature (multi-T) method the temperature of the mea-suring cell is varied systematically in each pressure step,thus allowing to measure multiple isotherms in a single mea-surement. The moisture content of the system remains con-stant because no de-gassing and evacuation of the samplebetween individual measurements is required and eventualmoisture loss is avoided. The method was successfully testedon one carbonaceous shale sample in the dry and moisture-equilibrated states, respectively. The mass balance approachused here takes explicitly into account the water vapor presentin the sample cell and its temperature-dependence duringthe sorption experiment. These considerations are necessarywhen studying temperature dependence of sorption in thepresence of moisture on materials with low sorption capac-ity. The thermodynamic consistency of this approach wasdemonstrated.


    The GASH consortium is acknowledged for providingfunds and sample material for this study. Pieter Bertier isthanked for carrying out and providing the interpretation ofthe XRD analysis. The suggestions and comments of ananonymous reviewer are gratefully acknowledged.

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  • 085116-8 Gasparik et al. Rev. Sci. Instrum. 84, 085116 (2013)


    Symbol Unit Physical quantityaw [] Water activity of the moisture-equilibrated

    shale sampleMCH4 [kg/ mol] Molar mass of methaneMCH4H2O [kg/ mol] Molar mass of the methane-water mixturem.c. [wt. %] Moisture content in weight percentmdry [g] Weight of dry shale samplemme [g] Weight of moisture-equilibrated shale samplem

    H2Ototal [kg] Total mass of water in the sample cell

    mH2Osorbed [kg] Mass of sorbed water (sample moisture) in the

    sample cellm

    H2Of ree [kg] Mass of free water (water vapor) in the sample


    mCH4transf erred [kg] Mass of gas methane transferred from the

    reference cell into the sample cellm

    CH4excess [kg], [kg/g] Excess sorbed mass of methane

    nCH4excess [mmol/g] Excess sorbed amount of methane normalized

    to dry sample weightnexp [mmol/g] Experimentally determined excess sorbed

    amountnfit [mmol/g] Calculated excess sorbed amountn

    CH4i [mol] Amount of substance methane in the

    methane-water gas mixturenw0 [mol] Initial amount of substance water in the

    methane-water gas mixturep [MPa] Pressurepv [MPa] Water vapor pressurepv0 [MPa] Saturation pressure of the water vaporp0 [MPa] Pressure at the perfect-gas reference stateR [J/mol/K] Universal gas constant (8.3145 J/mol/K)Tj [K] Experimental temperature of sorption

    measurementT0 [K] Starting temperatureVrc [m3] Volume of the reference cellV 0void [m3] Void volumeV Hevoid [m3] Void volume determined by the helium


    yCH4i [] Molar fraction of methane in the

    methane-water gas mixtureH [J/mol] Sorption enthalpyn [mmol/g] Quality of fit parameterS [J/mol/K] Sorption entropya [kg/m3] Density of the adsorbed phaseg [kg/m3] Density of the free gas phase

    CH4eq [kg/m3] Density of (pure) methane in the sample cell

    during the equilibration step

    CH4rc [kg/m3] Density of (pure) methane in the reference cell

    during the loading step

    CH4H2Oeq,i [kg/m3] Density of the methane-water gas mixture in

    the sample cell during the equilibration step

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