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Modeling of CO2 sorption on coal

P. Dutta 1, S. Harpalani *, B. Prusty 2

Southern Illinois University, Carbondale, IL 62901, USA

Received 5 June 2007; received in revised form 13 November 2007; accepted 14 December 2007Available online 24 January 2008

Abstract

This paper discusses moderate pressure CO2 sorption behavior of Illinois coals. The results fit the Langmuir and Dubinin–Astakhov(D–A) sorption models satisfactorily although the fit is better for D–A equation. Since factors like swelling of coal with CO2 sorption andCO2 dissolution in coal matrix contribute to uncertainties in estimating the void volume in and around the sample, an attempt was madeto account for these by modifying the conventional adsorption equation. Re-fitting the experimental data using the modified equationresults in improved fit for both models. The adsorption capacities of coals tested, as predicted by the equations, also reduce by 7% to32%. The effect of volumetric uncertainty is more in lower rank coals than the higher rank ones. Furthermore, it explains the excess sorp-tion behavior observed by others when extrapolated beyond the experimental pressure range. 2008 Elsevier Ltd. All rights reserved.

Keywords: Sorption isotherm; Langmuir; Dubinin–Astakhov; Sequestration; Swelling

1. Introduction

Global warming, resulting from increasing amounts of greenhouse gases, is regarded as one of the most importantenvironmental issues facing mankind. Of all the greenhousegases, anthropogenic emission of carbon dioxide (CO2) isconsidered the main contributor to global warming. Theprimary source of atmospheric CO2 emission is the burningof fossil fuels, which continues to grow. Estimates of eco-nomic growth and associated emissions from the usage of fossil fuels as provider of primary energy suggest that theconcentration of CO2 in the atmosphere will continue toincrease during this century, unless significant steps are

taken to reduce the release of CO2 to atmosphere. There-fore, in addition to other avenues of emission reductionthrough fuel switching, conservation, and efficiencyimprovements in the existing processes, stabilization of atmospheric CO2 would require large-scale and low-costcarbon sequestration. Of the various options for CO2

sequestration currently being considered, geological

sequestration in deep and unmineable coal seams is a par-ticularly promising one since it has the potential of leadingto enhancement in the production of coalbed methane(CBM), partially offsetting the cost of sequestration.

Primarily, CO2 is stored in coal in an adsorbed staterather than compressed or liquefied state, as in the caseof other conventional gas reservoirs. When injected intocoal, CO2 molecules get competitively adsorbed on the coalmicropores and replace the adsorbed methane molecules,releasing additional methane in the process. Coals areknown to exhibit much higher sorption affinity to CO2 thanmethane due to the higher adsorption energy and smaller

molecular diameter of CO2 [1], with a preferential sorptionratio of CO2 to methane of 2:1. However, results of a fewrecent studies indicate widely varying ratios, all the wayfrom 10:1 for low rank coals to less than 2:1 for low tomedium volatile bituminous coals [2–5]. It is, therefore,critical to determine the adsorption capacity of coal andits ability to retain CO2, both of which are affected by thenature of coal and other environmental factors.

The adsorption capacity is determined by establishingadsorption isotherms in the laboratory, either by gravimet-ric or by volumetric methods. The laboratory adsorption

0016-2361/$ - see front matter 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.fuel.2007.12.015

* Corresponding author. Tel.: +1 6184537918; fax: +1 6184537455.E-mail address: [email protected] (S. Harpalani).

1 Currently at Bengal Engineering and Science University, India.2 Currently at Central Institute of Mining and Fuel Research, India.

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Fuel 87 (2008) 2023–2036

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data is conventionally modeled by the Langmuir mono-layer adsorption equation. However, recent studies haveindicated that Dubinin–Astakhov (D–A) equation, basedon the theory of pore filling, fits the CO2 adsorption databetter than the Langmuir equation [5–8]. In fact, Langmuirmodel often fails to do so accurately, particularly when the

sorbing gas is CO2. Another problem that may arise whileevaluating the experimental CO2 adsorption data is the vol-umetric swelling of the coal sample with CO2 adsorption,resulting in inaccuracies in measurement [7,9,10]. There-fore, the method of calculation may have to consider theeffect of swelling in order to correctly evaluate the adsorp-tion capacity of coals.

This paper presents, following a brief review of theLangmuir and D–A model equations, the results of a lab-oratory adsorption study carried out on a set of mois-ture-equilibrated Illinois coals up to moderate pressurerange (5000 kPa). The results of the adsorption studywere utilized for conventional isotherm modeling using

the Langmuir and D–A equations. Finally, an effort wasmade to account for the inaccuracies in isotherm measure-ment caused by volumetric swelling of the coal samples bymodifying the conventional adsorption modeling equation.

2. Sorption isotherm models

Several sorption isotherm models have been proposed torepresent the adsorption of gases on solids. Some of these,like the Langmuir monolayer model, BET multi-layermodel, or Dubinin’s pore filling model are based on theo-retical foundation. The others, like the Langmuir–Freund-

lich, Toth, UNILAN, modified BET, etc., are empirical innature and were derived to provide the best fit to experi-mental data. Of these, the Langmuir monolayer and theDubinin–Astakhov pore-filling models are explained inmore detail below.

2.1. Langmuir model

The classical theory used to describe the Type I isothermfor microporous materials is based on the Langmuir equa-tion [11]. Type I isotherm displays a steep increase in thevolume adsorbed at low pressures due to enhanced adsorp-tion caused by the overlapping adsorption potentialsbetween the walls of pores with diameters commensuratein size with the adsorbate molecules. The isotherm thenflattens out into a plateau region at higher pressures, whichis believed to be caused by the completion of the formationof a monolayer of adsorbed gas. The Langmuir modelassumes that a state of dynamic equilibrium is establishedbetween the adsorbate vapor and the adsorbent surfaceand that adsorption is restricted to a single monolayer.The adsorbent surface is thought to be composed of a reg-ular array of energetically homogeneous adsorption sites,upon which an adsorbed monolayer is assumed to form.The rate of condensation is assumed to be equal to the rate

of evaporation from the adsorbed monolayer at a given rel-

ative pressure and constant temperature. The equation forthe Langmuir isotherm is given as:

g ¼ ðV LbP Þ=ð1 þ bP Þ ð1Þ

where g is the adsorbed volume at equilibrium pressure P , b

is a constant known as the pressure constant, V L is the

maximum monolayer capacity, also known as the Lang-muir volume. At high pressures, all the sites available onthe adsorbent are occupied by the adsorbate. Hence, be-yond a certain pressure, the adsorbent can adsorb no moreadsorbate. This pressure is known as the saturation pres-sure, and the sorbed volume corresponding to the satura-tion pressure is the Langmuir volume. At half coverage,that is, when the sorbed volume is half of the Langmuirvolume, the pressure value is referred to as the Langmuirpressure, P L. The above equation can be re-written in termsof V L and P L, the commonly used form of the Langmuirisotherm, as:

g ¼ ðV L P Þ=ð P þ P LÞ ð2Þwhere, P L is the inverse of b.

The Langmuir equation correctly expresses the adsorp-tion behavior for a wide range of pressures. The pressureconstant is a measure of the isotherm curvature. Largerthe value of b, greater is the initial slope of the isotherm.

2.2. Dubinin–Astakhov (D–A) model

For multi-layer adsorption, Polyanyi assumed the exis-tence of a potential field around the surface of the solidinto which each adsorbed gas molecule falls [12]. The sur-

face force field can be represented by equipotential surfacesand the space between each set of equipotential surfacescorresponds to a definite adsorbed volume. The adsorptionpotential is defined as the work done per mole of adsorbatein transferring molecules from the gaseous state to theadsorbed state. It represents the work done by the temper-ature-independent dispersion forces. Hence, the potentialcurve is not dependent on temperature and is a functionof only the volume enclosed by an equipotential surfacesurrounding the adsorbent surface. The sorbed volumebecomes a function of the adsorption potential, A, repre-sented as:

g ¼ f ð AÞ ð3ÞThe above relationship is characteristic of a gas–solid

system, and is known as the characteristic curve [13].Assuming ideal gas behavior for the adsorbate gas, theadsorption potential is given as:

A ¼ RT ln P 0

P

ð4Þ

where R is the Universal Gas Constant, T is the adsorptiontemperature in absolute units, P is the adsorption pressure,and P 0 is the saturation vapor pressure of the adsorbate attemperature T . Dubinin [14] used this theory to describe

adsorption on microporous adsorbents and postulated

2024 P. Dutta et al./ Fuel 87 (2008) 2023–2036



that, in micropores, the adsorbate occupies the pore vol-ume by the mechanism of volume filling, and hence, doesnot form a discrete monolayer in the pores. Based on this,Dubinin and Astakhov proposed an equation representingthe isotherms expressed as [15]

g ¼ ðV 0 exp½f K lnð P 0= P Þgn ð5Þ

where, g is the amount adsorbed, V o is the volume of micropores, n is the structural heterogeneity parameter, K

is a constant for a particular adsorbent–adsorbate system,and is equal to (RT/bE )n, where, E is the characteristic heatof the adsorption system, and b is the adsorbate affinitycoefficient. P 0 is the saturation vapor pressure of the adsor-bate at temperature T , and P is the equilibrium vapor, orfree gas, pressure.

3. Volumetric method of adsorption measurement

3.1. Establishment of adsorption isotherm

Establishing adsorption isotherm by the volumetricmethod involves injecting a known amount of gas into asample cell, containing pulverized coal, in steps of increas-ing pressure, and maintaining a constant temperaturethroughout the experimental duration. The void volume,which is the volume of the cell not occupied by the solidcoal, is determined by injecting a known amount of heliuminto the cell and employing real gas laws before start of theexperiment, since helium is assumed to be non-adsorbingon coal. The amount of gas adsorbed at every pressurestep, after pressure equilibrium is reached in the cell, fol-

lowing gas injection, is determined by the following equa-tion [16]:

ge ¼ gt qV 0 ð6Þ

where ge is the adsorbed volume in moles, gt is the totalnumber of moles of gas transferred to the cell, q is the mo-lar density of gas in free phase, and V o is the void volumedetermined by helium expansion. However, calculation of the adsorbed volume using Eq. (6) ignores the volume of the gas in the adsorbed phase, and therefore, does not rep-resent the actual adsorbed amount, and is termed the ex-cess adsorbed amount. The actual adsorbed amount,considering the volume of gas in the adsorbed phase is gi-

ven by the absolute adsorbed amount. The relationshipbetween the excess and absolute adsorbed amount is givenas:

ge ¼ ga=ð1 q=qaÞ ð7Þ

where ga is the absolute adsorbed amount in moles, and qa

is the molar density of gas in the adsorbed phase. At a gi-ven pressure, the isotherm model equations, like the Lang-muir or D–A, provide an estimate of the absolute adsorbedamount. The parameters of the two equations can be ob-tained by statistically fitting these equations to the absoluteadsorption data calculated from the experimental excess

adsorption using Eq. (7).

3.2. Effect of coal swelling on CO 2 adsorption

Eq. (7) is valid for a rigid solid structure of the adsor-bent, that is, when there is no change in the volume of the adsorbent with adsorption [7]. For several adsorbents,this is perhaps the case. However, adsorption, and some

dissolution, of CO2 in the coal matrix induce significantswelling of the solid coal, thus increasing the volume of the coal matrix considerably [17–20]. In some cases, 2–3%swelling has been observed at CO2 pressure as low as1 MPa [9,10]. This is even more evident at higher pressures.During a high pressure (10 MPa) sorption experiment withCO2, 45% swelling was estimated with a residual swelling of 20% after completion of the experiment [10]. Also, themolar volume of CO2 dissolved in the coal is not known.Therefore, at each equilibrium pressure step in an adsorp-tion experiment, the volume of the coal sample is largerthan that measured originally, with unknown pore volumeand surface area. Furthermore, at pressures above 1–

1.5 MPa, there may be more CO2 dissolved in the coalmatrix than adsorbed on the surface [9]. Hence, the voidvolume, V o, in Eq. (6) derived from expansion of a non-swelling gas like Helium, does not remain constant duringthe duration of the experiment. Actually, it reduces withevery pressure step as the coal matrix swells continuouslywith CO2 adsorption. On the contrary, coals contain cer-tain pores that may be inaccessible to helium but accessibleto CO2 [21]. The volume of the sample accessible to CO2

but inaccessible to Helium, known as the envelope volume,will induce error in determination of V o and result in anoverestimation of the adsorbed volume. In summary, con-

siderable volumetric uncertainties may creep in during thecalculation of adsorbed volume due to coal swelling andthe various associated phenomena. Evaluation of theexperimental sorption data using Eq. (7) ignores theseaspects, and may be one of the reasons for the poor fit tothe isotherm equations commonly reported, and providinginaccurate estimates of the sorbed quantities.

3.3. Adsorption calculation accounting for volumetric

uncertainties

As evident from the discussion in the last section, exper-imental data from the volumetric sorption experimentsneed to be re-adjusted to take into account the uncertain-ties associated with the void volume determination in thesample cell. Combining Eqs. (6) and (7), the followingequation can be derived:

gt ¼ qV 0 þ gað1 q=qaÞ ð8Þ

However, accounting for volumetric uncertainties asso-ciated with the void volume determination, Eq. (7) can bere-written as:

gt ¼ qðV 0 þ dV Þ þ gað1 q=qaÞ ð9Þ

where dV accounts for the volumetric change resulting from

swelling of the coal sample with adsorption. Laboratory

P. Dutta et al. / Fuel 87 (2008) 2023–2036 2025



results have shown that volumetric swelling of coals in-creases with increasing pressure, closely following the pat-tern of typical adsorption isotherms [17–20]. Hence, thevalue of dV should also vary with pressure. Replacing(gt qV o) with ge, Eq. (9) can then be re-written as:

ge ¼ ga ð1 q=qaÞ þ qdV ð10Þ

As can be seen from Eq. (10), the experimentally deter-mined excess adsorbed volume ge has two components. Theterm qdV accounts for volumetric correction at any givenpressure and ga (1 q/qa) represents the volume correctedexcess adsorption amount. Instead of the conventionalapproach to model the excess adsorption data using Eq.(7), the modified approach would involve using Eq. (10),and replacing ga with Langmuir or D–A equations. Thestatistical best fitting exercise would then give the estimateof dV , along with the new values of the model equationparameters.

Ozdemir et al. [7] also discussed the uncertainties in vol-

ume estimation due to the reason explained above, and afew other factors, like compressibility of the adsorbent withpressure, widening of previously constricted pore entranceswith swelling, change in the volume of adsorbent due todissolution of the adsorbate, etc. Most of these factorsare immeasurable during a sorption experiment. Combin-ing all these parameters, the authors propose a modifica-tion of Eq. (7) for evaluation of the experimentalsorption data, very similar to that of Eq. (10). The erroranalysis, further corroborated by Romanov et al. [9] statedthat ‘‘CO2 swelling and the rate of swelling are possiblecontributing factors” when measuring CO2 adsorption in

the laboratory. Therefore, for modeling of experimentaladsorption data, it is suggested that swelling of coal inthe sample cell should be taken into consideration.

The primary objective of the current investigation wasto improve the accuracy of the sorption data obtained fromlaboratory experiments, and application of various sorp-tion models. Hence, as a first step, Langmuir and D–Aabsolute adsorption model equations were fit with Eq. (7)to moderate pressure CO2 sorption experimental dataobtained for a set of Illinois coals. Based on the qualityof fit, the hypothesis that accounting for volumetric swell-ing of the coal samples within the sample cell results inimproved fit of the experimental data was pursued andthe data analyzed using Eq. (10).

4. Experimental work

Coal samples procured from Seelyville, Herrin, andDanville seams in the Illinois Basin were used for the study.The samples were preserved by wrapping with water-tightpaper and keeping immersed under water to minimize oxi-dation due to contact with air. Ash and moisture content of the samples were determined as per standard ASTM proce-dures [22,23]. Some indicative compositions of the samplesare given in Table 1. For sorption measurement, the sam-

ples were pulverized to a size of 40–100 mesh (0.149 mm–

0.420 mm) and moisture-equilibrated by storing in an envi-ronmental chamber for 48 h at the experimental tempera-ture and relative humidity of 96%. Between 70 and 100 gof pulverized coal samples were taken and the volumetricmethod was employed to establish the adsorption isothermof the samples up to a pressure of 5000 kPa, the antici-pated maximum pressure for CO2 injection in the basin.Throughout the experiment, the temperature was main-tained at 28.6 C, the approximate reservoir temperature,by immersing the entire experimental setup in a constanttemperature water bath (accuracy ± 0.1 C). A schematicof the experimental setup is shown in Fig. 1. The experi-mental setup consisted of a reference cell (150 cm3) anda sample cell (170 cm3), separated by a valve. The emptyvolumes of the cells, including the dead spaces within thevalves and other fittings, were accurately determined byhelium expansion and employing the Real Gas Law andAngus equation of state for helium [24]. The pressure read-ings of the cells were independently monitored throughpressure transducers (accuracy ± 0.05% of FS) connectedto a data acquisition system. Pulverized coal samples were

then placed in the sample cell and the void volume, thatis, the volume not occupied by the coal, was deter-mined following the same procedure as that followed for

Table 1Details of coal samples

Seam Proximate analysis (wt%) ondry basis

Calorific valuedaf, eq. moistBtu/lb for rankdetermination

Rank

Moisture Ash Volatilematter

Fixedcarbon

Seelyville 6.21 14.17 38.19 47.64 14374 HV Bit. AHerrin 8.51 12.21 36.33 51.46 13923 HV Bit. BDanville 8.13 15.23 35.64 49.13 13898 HV Bit. B

GSRC

SC

WB

DAS

PT

PT

Fig. 1. Schematic of the gas adsorption experimental setup. (GS: gassupply, RC: reference cell, SC: sample cell, WB: constant temperature

water bath, PT: pressure transducer, DAS: data acquisition system.)

2026 P. Dutta et al./ Fuel 87 (2008) 2023–2036



determination of the empty volume. Each adsorption stepconsisted of injecting a known volume of gas, calculatedfrom the pressure and temperature of the reference cellbefore and after injection, into the sample cell and record-ing the final equilibrium pressure. The number of molesadsorbed at each step was calculated employing mass

balance in the two cells and the gas compressibility factorsusing a package prepared by National Institute of Standards and Techniques (NIST), based on the Peng– Robinson equation of state for CO2 [25]..

5. Results and discussion

5.1. Fitting Langmuir and D–A model equations to the

experimental data

Experimental work described above yielded the excessadsorbed volume (dry, ash-free basis) at the end of each pres-

sure step. Error estimate was carried out by simple errorpropagation equations considering the uncertainty in eachof the measured experimental quantities. The average uncer-tainty was found out to be 3%. The experimental excessadsorption data was then evaluated by Eq. (7). Two separatemodels were evaluated by considering ga to be representedfirst by the Langmuir equation, and then the D–A equation.The D–A equation requires the value of saturation vaporpressure, Po, which was calculated to be 6967 kPa(1011.2 psia) at 28.6 C for sub-critical CO2 using informa-tion from published literature [26]. The density, q, of freeCO2 was calculated at different pressures using the NISTpackage. The density of the adsorbed phase, qa, is not an

experimental variable. A number of methods are availableto estimate this parameter and, depending on the estimate,the absolute adsorbed amount may vary up to 15% at higherpressures [27]. However, within the pressure range used forthis study, all the estimates yielded comparable results.Hence, it was assumed to be 26.81 mmol/cm3 (1.18 g/cm3),the liquid density of CO2.

The experimental excess adsorption data, ge, was statisti-cally fitted separately to Langmuir and D–A equations,using the SPSS statistical package, employing Levenberg– Marquardt algorithm [28]. The algorithm is an iterative pro-cedure and starts with a user-provided initial estimate of the

parameters. The iteration process continues and the solutionconverges when the sum of the squares of the deviations fallsbelow a prescribed minimum. The results of the non-linearregression analysis using the Langmuir and D–A equations,along with the calculated values of the constants are shownin Tables 2 and 3, respectively. The percentage average

relative error (ARE), indicating the overall quality of fitfor the model equations, was calculated as:

% ARE ¼ ð100= N ÞX

ðgecalc ge

exptÞ=geexpt

h i ð11Þ

where N is the total number of data points, and gecalc andgeexpt are the values of ge, calculated from the models and

the experimental results, respectively.All coals tested, as indicated in Table 1, are of high vol-

atile bituminous grade with progressively lower rank fromSeelyville to Danville. The monolayer adsorption capacity

or the micropore volume filling capacity, as indicated inTables 2 and 3, respectively, is the maximum for the Dan-ville coal. This is followed by the Herrin and Seelyvillecoals, respectively. This observation is generally consistentwith the results of other studies on sorption of CO2 oncoals – the sorption capacity increases with decrease inrank [4,7]. Fig. 2 depicts the isotherms using Langmuirand D–A equations, along with the experimental excessadsorption data. The results of the model fitting exercisesuggest that, for moderate pressures adsorption in the sam-ples, both equations fit the experimental data satisfactorily.The quality of fit, as indicated by the R2 and ARE values, isbetter for Seelyville and Herrin samples. Previous work byresearchers on fitting these models to CO2 adsorption datahas indicated similar results [5]. Fitzgerald et al. [26] alsoreported ARE of 2% for Langmuir model fitting. How-ever, apparently, the quality of fit with the D–A equationis better than that with the Langmuir equation. This is indi-cated by the higher R2 values for all samples, and higherARE values for two out of the three samples. This is fur-ther evident from the deviation plots shown in Fig. 3.The deviation plots were obtained by calculating the differ-ence between the measured absolute adsorption and thatobtained from the models. As can be seen in Fig. 3, devia-tions for most of the points are less for D–A equation than

the Langmuir equation. Based on the work completed todate, it is difficult to comment with certainty that theD–A equation is significantly better than the Langmuirequation for evaluation of experimental CO2 adsorptiondata. However, it certainly does corroborate the findingsof other studies [5,6].

5.2. Fitting of Langmuir and D–A model equations after

accounting for volumetric uncertainties

The primary objective of this study was to provide aninsight into understanding the complex CO2 –coal interac-

tion behavior. Hence, effort was made to work on the

Table 2Results of Langmuir model fitting

Coal V L (mmol/g) P L (kPa) R2 ARE (%)

Seelyville 1.209 2030 0.998 2.7Herrin 1.346 2394 0.998 2.4

Danville 1.396 1332 0.989 4.3

Table 3Results of D–A model fitting

Coal V o (mmol/g) K n R2 ARE (%)

Seelyville 0.929 0.458 1.420 0.999 1.8Herrin 0.998 0.484 1.356 0.999 2.6Danville 1.198 0.408 1.418 0.993 4.0

P. Dutta et al. / Fuel 87 (2008) 2023–2036 2027



hypothesis that swelling of coal with adsorption, and pos-sibly, the other factors mentioned earlier, lead to uncer-tainty in the void volume determination in the samplecell, and the significance of taking this effect into accountwhen evaluating the model equations with experimental

adsorption data. Hence, the same models were refitted to

the experimental data using Eq. (10), and the results areshown in Tables 4 and 5. Fig. 4 shows the isothermsobtained using the modified Langmuir and D–A equations,along with the experimental excess adsorption data. It isapparent that there is very little improvement as revealed

by Figs. 2 and 4. However, the improvements in the quality

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 1000 2000 3000 4000 5000 6000

Pressure, KPa

E x c e s s A d s o p r t i o n , m m o l / g

Experimental

Langmuir

D-A

Seelyville

0.00

0.10

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0.30

0.40

0.50

0.60

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Pressure, KPa

E x c e s s A d s o p r t i o n , m m o l / g

Experimental

Langmuir

D-A

Herrin

0.00

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1.00

1.20

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure, KPa

E x c e s s A d s o r p t i o n , m m o l / g

Experimental

Langmuir

D-A

Danville

Fig. 2. Langmuir and D–A equations best fit for experimental excess adsorption.

2028 P. Dutta et al./ Fuel 87 (2008) 2023–2036



-0.015

-0.010

-0.005

0.000

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0.010

0.015

0.020

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0 1000 2000 3000 4000 5000 6000

Pressure, KPa

D e v i a t i o

n , m m o l / g

Langmuir

D-A

Seelyville

-0.020

-0.015

-0.010

-0.005

0.000

0.005

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Pressure, KPa

D e v i a t i o n , m m o l / g

Langmuir

D-A

Herrin

-0.060

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0.000

0.020

0.040

0.060

0.080

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure, KPa


Langmuir

D-A

Danville

Fig. 3. Deviation plots comparing Langmuir and D–A equations.

Table 4Results of Modified Langmuir model fitting

Coal V L (mmol/g) P L (kPa) dV (cm3/g) R2 ARE (%)

Seelyville 1.026 1618 0.030 0.999 1.3Herrin 1.029 1663 0.048 1.000 1.3

Danville 1.009 826 0.102 0.995 2.6

Table 5Results of Modified D–A model fitting

Coal V o (mmol/g) K n dV (cm3/g) R2 ARE (%)

Seelyville 0.865 0.440 1.506 0.016 0.999 1.6Herrin 0.765 0.416 1.707 0.058 1.000 1.2

Danville 0.816 0.336 2.119 0.121 0.995 2.6

P. Dutta et al. / Fuel 87 (2008) 2023–2036 2029



of fit between the two rounds of fitting exercise can beassessed from a comparison of the R2 and ARE values.Comparison of Tables 2 and 4 shows the change in thequality of fit obtained from this modified fitting exercisewith Langmuir model. Tables 3 and 5 show the same forthe D–A model. It can be seen that, irrespective of the

model used, both R2 and ARE values improve with themodified model fitting exercise for all the samples. Forexample, in case of Herrin sample, with Langmuir equa-tion, the R2 value improves from 0.998 to 1.000. For thesame sample and equation combination, ARE comes downfrom 2.4 to 1.3. Similar improvements in the parameters

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E

x c e s s A d s o p r t i o n , m m o l / g

Experimental

Modified Langmuir

Modified D-A

Seelyville

0.00

0.10

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0 1000 2000 3000 4000 5000 6000

Pressure, KPa

E x c e s s A d s

o p r t i o n , m m o l / g

Experimental

Modified Langmuir

Modified D-A

Herrin

0.00

0.20

0.40

0.60

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1.00

1.20

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure, KPa

E x c e s s A d s o r p t i o n , m

m o l / g

Experimental

Modified Langmuir

Modified D-A

Danville

Fig. 4. Modified Langmuir and D–A models best fit isotherms.

2030 P. Dutta et al./ Fuel 87 (2008) 2023–2036



indicating the quality of fit are observed for the other sam-ples as well. To further augment this observation, deviationplots were obtained between the conventional and modifiedmodel equations. Fig. 5 shows the deviation plots betweenLangmuir and modified Langmuir equations, and Fig. 6

shows the same for the D–A model. The deviations, asobserved for most of the data with both model equations,are less for the modified equations than the conventionalequations. Therefore, it can be said with reasonable cer-tainty that the introduction of the additional parameter

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Langmuir

Modified Langmuir

Seelyville

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-0.005

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0 1000 2000 3000 4000 5000 6000

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D e v i a

t i o n , m m o l / g

Langmuir

Modified langmuir

Herrin

-0.060

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-0.020

0.000

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0.060

0.080

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure, KPa

D e v i a t i o n , m m o

l / g

Langmuir

Modified Langmuir

Danville

Fig. 5. Deviation plots comparing Langmuir and modified Langmuir models.

P. Dutta et al. / Fuel 87 (2008) 2023–2036 2031



dV in the model equation results in improved fitting of theexperimental adsorption data. It certainly confirms thefindings of Ozdemir et al. [7]. However, they did not quan-tify the improvement in the quality of fit. Hence, the results

of this study could not be compared with that of Ozdemiret al. [7]. The values of Langmuir parameters and D–Aequations also change with introduction of the additionalparameter, dV , as shown in Tables 4 and 5. It further indi-

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0 1000 2000 3000 4000 5000 6000

Pressure, KPa


D-A

Modified D-A

Seelyville

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0 1000 2000 3000 4000 5000 6000

Pressure, KPa

D e v i a

t i o n , m m o l / g

DA

Modified D-A

Herrin

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure, KPa


D-A

Modified D-A

Danville

Fig. 6. Deviation plots comparing D–A and modified D–A models.

2032 P. Dutta et al./ Fuel 87 (2008) 2023–2036



cates that, with modified fitting, the adsorption capacitiesof the coals reduce significantly. While the reduction inLangmuir monolayer adsorption capacity ranges from15% to 28%, corresponding reduction in volume fillingcapacity varies between 7% to 32%. It indicates that had

conventional equations been used, the adsorption capaci-ties would have been overestimated. Also, this reductionis the minimum in Seelyville coal and the maximum inDanville coal signifying that the lower rank coals areaffected more by volumetric uncertainties.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0 1000 2000 3000 4000 5000 6000

Pressure, KPa

A

d s o r b e d V o l u m e , m m o l / g

Excess Best Fit

Excess Volume Corrected

Volumetric Correction

Seelyville

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0 1000 2000 3000 4000 5000 6000

Pressure, KPa

A d s o r b e d V o

l u m e , m m o l / g

Excess Best Fit



Herrin

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Pressure, KPa

A d s o r b e d V o l u m e , m m o l / g

Excess Best Fit



Danville

Fig. 7. Effect of volumetric correction on the adsorbed volume.

P. Dutta et al. / Fuel 87 (2008) 2023–2036 2033



5.3. Effect of volumetric uncertainties on the adsorption

capacity

The value of dV for the Langmuir and D–A equationsvaries between 0.016 and 0.121 mmol/g. Also, consistent

with the observation above, the value of dV increases pro-gressively with lowering of rank. The positive values of dV

indicate the presence of more volume in non-adsorbed statewithin the sample cell than that originally estimated byHelium expansion. This can be attributed to a combination

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure, KPa

A d s o r b e d V

o l u m e , m m o l / g

Excess Best Fit


Absolute

Herrin

Extrapolated

Region

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure, KPa

A d s o r b e d V o l u m e , m m o l / g

Excess Best Fit


Absolute

Extrapolated

RegionSeelyville

Fig. 8. Extrapolated adsorbed volume beyond the experimental pressure range using Eq. (10).

2034 P. Dutta et al./ Fuel 87 (2008) 2023–2036



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