Modeling the Competitive Adsorption of CO2 and Water at High

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Modeling the Competitive Adsorption of CO2 and Water at High Pressures on Wet Coals Sayeed A. Mohammad and Khaled A. M. Gasem* School of Chemical Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, United States ABSTRACT: Traditional modeling of gas adsorption on wet coals does not include water as a separate adsorbed component and treats water as a “pacifier” of the coal matrix. Thus, the conventional modeling approach does not consider the competitive adsorption between the adsorbing gas and water in coals. In this work, we modeled the competitive adsorption of CO2 and water on wet coals by considering water as an active component in a binary mixture. A new data reduction method was implemented that accounts for the presence and effect of water in as many as three equilibrium phases (gas, liquid, adsorbed). Using the new data reduction method, we employed the simplified local-density (SLD) model to investigate the effects of water present in coals on gas adsorption under the conditions encountered in coalbed methane and CO2 sequestration applications. For this purpose, the SLD model was modified to account for the unique molecular interactions of water in the adsorbed phase and a new modeling approach was formulated for gas/water mixture adsorption on coals. The modified SLD model was then utilized to investigate CO2/water mixture adsorption on four well-characterized coals. Finally, a phase-check analysis was performed to investigate the possible formation of a third (aqueous) phase in these systems. Results indicate that the SLD model is capable of representing the adsorption of this highly asymmetric mixture within the experimental uncertainties, on average. The model parametrization used and the molecular interactions considered for describing water adsorption on coals illustrate a viable method to obtain precise representations of the adsorbed CO2/water mixtures. The phase-check analysis of the same mixtures indicated potential formation of a water-rich liquid phase in these systems for coals that contained large amounts of moisture.

’ INTRODUCTION The presence of water in a high-pressure, near-critical gas adsorption system requires special attention. Water can significantly affect the adsorption capacity for other gases (e.g., methane, CO2) by blocking the porous adsorbent structure and limiting the accessibility of the adsorbing gas.1 Measured adsorption isotherms on wet coals have also revealed marked effects of water on gas adsorption capacity. Joubert et al.2 reported data which showed that moisture can reduce methane adsorption by as much as 40% on Pittsburgh coal and 15% on Pocahontas coal. Clarkson and Bustin3 showed that 2% moisture can cause 20% reduction of both methane and CO2 adsorption capacity on a wet coal when compared to the adsorption on the dry coal. Similarly, Levy et al.4 observed that 4% moisture can reduce the methane adsorption by as much as 60% from that of the dry coal. Our measurements on wet Illinois coal have shown that 9% moisture can cause 50% reduction of CO2 adsorption at 3 MPa. These results demonstrate the significant effect of moisture on gas adsorption behavior. Thus, proper accounting for moisture effects is critical in experimental data reduction and interpretation. Current experimental data reduction techniques for highpressure adsorption systems do not account for the presence and effect of moisture in all three equilibrium phases (gas, aqueous, and adsorbed). This inadequacy in data reduction methods can result in significant errors in the estimated gas adsorption capacity, adsorbed phase density, and the partitioning of constituents in a gas mixture. Simulations of enhanced coalbed methane (ECBM) recovery processes require an adsorption model that is capable of predicting the adsorption equilibria of coalbed gases (methane, nitrogen, CO2) r 2011 American Chemical Society

and water. The current approach for modeling gas adsorption on wet coals has been to assume water as a “pacifier” of the coal surface. In other words, water in coals is assumed to reduce gas adsorption capacity by occupying a portion of the pore space, and this effect is considered to be independent of bulk gas pressure. However, there is competitive adsorption between water and coalbed gases because the adsorbing gas competes with adsorbed water for the available pore space in coals. Thus, a more rigorous approach for investigating the effects of water on gas adsorption behavior involves considering water as an active component in equilibrium with the coalgas system and modeling the competitive adsorption of coalbed gases and water as a function of bulk pressure. In the present work, we investigate this approach by considering water in coals as a separate adsorbed component in thermodynamic equilibrium with a gas such as CO2. Specifically, we model the adsorption of CO2 on moisture-equilibrated coals as a particular case of binary mixture adsorption of CO2/water on coals. The remainder of this paper is organized in the following manner: section 2 discusses the simplified local-density (SLD) adsorption model framework, section 3 discusses the modifications introduced in the SLD model to account more accurately for the molecular interactions of adsorbed water, section 4 presents the SLD model for mixtures, and section 5 presents the new modeling strategy formulated to investigate the effects of water on gas adsorption behavior. Section 5 also discusses the newly devised data reduction method for gas adsorption isotherms on Received: September 18, 2011 Revised: November 16, 2011 Published: December 06, 2011 557

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where fbulk is the bulk fugacity and f0 is the fugacity at an arbitrary reference state. In a similar manner, the chemical potential of the adsorbed fluid due to fluidfluid interactions can be written as ! f ff ðzÞ ð4Þ μff ðzÞ ¼ μ0 ðTÞ þ RT ln f0

wet coals. Further, the section includes the adsorption modeling results and the phase-check analysis for gas/water mixture adsorption on four coals that were utilized in this work.

2. SLD ADSORPTION MODEL In our earlier works on gas adsorption, we have utilized the simplified local-density (SLD) theory to model high-pressure gas adsorption of pure and mixed-gases on a variety of coals and activated carbons.57 In the present work, the SLD model is extended to the case of gas/water mixture adsorption on coals. The SLD model was developed first by Rangarajan et al.8 by applying the mean-field approximation to the more general density functional theory. The model superimposes the fluid solid potential on a fluid equation of state to predict the adsorption on flat walls8 and in slit-shaped pores.9 The fluid equation of state in SLD is further simplified with a local-density approximation in calculating the configurational energy of the inhomogeneous adsorbing fluid, thus giving the model its name. The essential details of the SLD model used in the present work are discussed below. The main assumptions used in developing the SLD model are as follows:8 (1) The chemical potential at any point near the adsorbent surface is equal to the bulk phase chemical potential. (2) The chemical potential at any point above the solid surface is the sum of the fluidfluid and fluidsolid interactions.Further, the fluidsolid attractive potential, at any point z, is assumed to be independent of the temperature and the number of molecules at or around that point. Thus, at equilibrium, the molar chemical potential can be given by the sum of the fluidfluid and fluidsolid interactions as μðzÞ ¼ μbulk ¼ μff ðzÞ þ μfs ðzÞ

where fff(z) is the fluid fugacity at a position z and f0 is the fugacity at the same arbitrary reference state as in eq 3. For a parallel slit, the fluidsolid chemical potential can be given as follows: μfs ðzÞ ¼ N A ½Ψfs ðzÞ þ Ψfs ðL zÞ

where NA is Avogadro’s number, Ψ(z) and Ψ(L z) are the fluidsolid interactions from the two surfaces of a slit of length L. Substituting eqs 35 into eq 1 yields the equilibrium criterion for adsorption within a slit: ! Ψfs ðzÞ þ Ψfs ðL zÞ ð6Þ fff ðzÞ ¼ f bulk exp kT where k is the Boltzmann’s constant and T is the absolute temperature. The fluidsolid potential energy function, Ψfs(z), is given by Lee’s partially integrated 10-4 potential model.12 Following the work of Chen et al.,9 Ψ ðzÞ ¼ fs

4πFatoms εfs σ2fs

σ10 1 4 σ4fs fs 10 0 0 2 i ¼ 1 ðz þ ði 1Þσss Þ4 5ðz Þ

∑

!

ð7Þ

ð1Þ

where subscripts bulk, ff, and fs refer to the bulk, fluid fluid, and fluidsolid chemical potentials, respectively, and z refers to the distance from the adsorbent surface. Different geometries such as rectangular slits, cylindrical pores, flat surfaces, etc. can be used to model the porous adsorbent structure. The SLD model utilized in this work envisions the adsorbent (coal) as composed of slit-shaped pores. The slit-pore model has been used successfully in earlier works to describe gas adsorption.6,7,9 Further, as discussed in a later section, the molecular model developed in this work evolved from studies in the literature10,11 that utilized the slit geometry for the adsorbent, thus making it a useful choice. Using the rectangular-slit model, the adsorbate is envisioned to reside within the two-surface slit and thus has interactions with both the walls of the adsorbent. Using the slit geometry, eq 1 can be written as μðzÞ ¼ μbulk ¼ μff ðzÞ þ μfs1 ðzÞ þ μfs2 ðL zÞ

ð5Þ

εfs ¼

pffiffiffiffiffiffiffiffiffiffi εff εss

ð8Þ

where εfs is the fluidsolid interaction energy parameter, εss is the solidsolid interaction energy, Fatoms = 0.382 atoms/Å2 is the carbon atom density, σff and σss are the molecular diameters of the adsorbate and the carbon interplanar distance, respectively. The carbon interplanar distance was taken to be that of graphite, 0.335 nm,13 and the values of σff and εff were taken from Reid et al.14 The fluidsolid molecular diameter, σfs, and the distance coordinate, z0 , which is the perpendicular distance between the centers of the fluid molecule and the first plane of carbon atoms, are defined as follows: σ fs ¼

ð2Þ

σ ff þ σss 2

ð9Þ

σss 2

ð10Þ

z0 ¼ z þ

where L is the slit-length and z or L z refers to the position of the adsorbate molecule from either of the surfaces of the slit. Further, the position of the adsorbate, z, is measured normal to the plane of the outermost carbon atoms. The chemical potential for the bulk fluid can be written in terms of the fugacity as ! f bulk ð3Þ μbulk ¼ μ0 ðTÞ þ RT ln f0

Further, the fluidsolid interactions given by eq 7 were truncated at the fourth plane of carbon atoms from the solid surface.9 The SLD model requires a fluid equation of state (EOS) to evaluate the densities and fugacities of the bulk and adsorbed phases, as seen in eq 6. Several authors have used different EOSs with the SLD theory. These include the van der Waals, Peng Robinson, ElliotSureshDonohue, and Bender EOSs.8,9,1519 Following our previous works,6,7 the PengRobinson (PR) EOS is utilized in the current study. The PR EOS20 can be 558

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significant effect on the local density of the adsorbed fluid near the surface. An empirical correction, Λb, was applied to the covolume to account more accurately for the repulsive interactions of adsorbed fluid at high pressures, given as

Table 1. Physical Properties of CO2 and Water CO2

water

TC (K)

304.13

647.09

PC (MPa)

7.377

22.065

σff (nm)

0.3941

0.2641

εff/k (K)

195.2

809.1

bads ¼ bð1 þ Λb Þ

Typical values of Λb range from 0.4 to 0.0 for coalbed gases. The value is expected to be dependent to some extent on the amount of moisture on the coal. This is reasonable because the adsorbed-phase density of wet adsorbents can be expected to be higher than that of dry coals. With this modification, eq 16 can be written as

expressed as the following: P 1 aðTÞF pffiffiffi pffiffiffi ¼ FRT ð1 FbÞ RT½1 þ ð1 2ÞFb½1 þ ð1 þ 2ÞFb

ð11Þ

ln

where aðTÞ ¼ b¼

0:457535αðTÞR 2 T 2C PC

1 bads FðzÞ ln RTFðzÞ " # pffiffiffi aads ðzÞ 1 þ ð1 þ 2ÞFðzÞbads pffiffiffi ln pffiffiffi 1 þ ð1 2ÞFðzÞbads 2 2bads RT

ð13Þ

In eq 12, the term α(T) was calculated with the following expression developed at Oklahoma State University:21 αðTÞ ¼ expððA þ BTr Þð1 TrC þ Dω þ Eω ÞÞ 2

ð14Þ

nEx ¼

AZ 2

right side of slit left side of slit

ðFðzÞ Fbulk Þ dz

ð19Þ

where nEx is the excess adsorption in number of moles per unit mass of adsorbent and A is the surface area of the adsorbate on a particular adsorbent. The equation contains A/2 because both walls contribute to the total surface area. The lower limit in the integration of eq 19 is 3/8σff or 3/8 the diameter of an adsorbed molecule touching the left plane surface. The upper limit is L 3/8σff, which is the location of an adsorbed molecule touching the right plane surface. Further, the local density is assumed to be zero for distances less than 3/8σff from the wall. The value of 3/8σff is chosen to account for most of the adsorbed gas; details are given elsewhere.15 In solving for the local density using the SLD equilibrium criterion, the slit is divided into two halves and each half is subdivided into 50 intervals. The local density is then determined for each interval. Once the local density is determined across the slit, the excess adsorption is calculated by the numerical integration of eq 19. Thus, the SLD model for pure components typically has three regressed parameters: A, εss, and L.

f bulk bF aðTÞF ¼ P 1 bF RTð1 þ 2bF b2 F2 Þ " pffiffiffi # P Pb aðTÞ 1 þ ð1 þ 2ÞFb pffiffiffi pffiffiffi ln ln RTF RT 2 2bRT 1 þ ð1 2ÞFb

ð15Þ where P is the bulk fluid pressure, F is the density, and a and b are the EOS constants given by eqs 12 and 13. By analogy, the fugacity for fluidfluid interactions of the adsorbed fluid can be written as ln

ð18Þ

Thus, eqs 15 and 18 are used to calculate the fugacities of the bulk and adsorbed phases, which are necessary to solve the adsorption equilibrium criterion given by eq 6. The density profiles that result from the application of eqs 6, 15, and 18 have been illustrated in an earlier work.5 The excess adsorption, nEx, in the SLD model is given as

where A, B, C, D, and E are correlation parameters and their respective values are 2.0, 0.8145, 0.134, 0.508, and 0.0467. These values were based on an accurate description of saturation properties for coalbed gases under conditions encountered in CBM operations. The physical properties for CO2 and water used in the SLD model are listed in Table 1. The fugacity of a bulk fluid using the PR EOS is given as ln

f ff ðzÞ bads FðzÞ aads ðzÞFðzÞ ¼ P 1 bads FðzÞ RT½1 þ 2bads FðzÞ b2ads FðzÞ2

ð12Þ

0:077796RT C PC

ð17Þ

f ff ðzÞ bFðzÞ aads ðzÞFðzÞ ¼ P 1 bFðzÞ RTð1 þ 2bFðzÞ b2 F2 ðzÞÞ " # pffiffiffi P Pb aads ðzÞ 1 þ ð1 þ 2ÞFðzÞb pffiffiffi pffiffiffi ln ln RTFðzÞ RT 2 2bRT 1 þ ð1 2ÞFðzÞb

3. MODIFICATIONS TO SLD MODEL FOR WATER ADSORPTION We have reviewed several aspects of pure water adsorption behavior on coals and carbons. The detailed findings of that review are summarized elsewhere.22 In this paper, we highlight only the findings from that review that are essential to this study. In particular, the review had shown that the molecular interactions of water with the carbon surface are quite distinct from those that appear in the adsorption of nonpolar adsorbates. Further, the adsorption of pure water on carbons is bimodal and occurs by two different mechanisms. In the following paragraphs, we discuss these aspects briefly.

ð16Þ In eq 16, the attractive term in the EOS, aads(z), is a function of position in the slit, and therefore, it accounts for the fluidfluid interactions in the slit. Chen et al.9 developed the equations for aads(z), which depend on the ratio of slit length L to the molecular diameter σff. The covolume bads in the PR EOS was adjusted in an earlier work15 to improve the predictive capability for adsorption of pure gases on activated carbon and coals. The covolume has a 559


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3.1. Molecular Interactions of Adsorbed Water. Two types of molecular interactions are important when considering water adsorption on activated carbons and coals. These two interactions are the following: (1) the hydrogen bonds between the adsorbed water molecules and the oxygenated groups on the adsorbent surface and (2) the electrostatic interactions between adsorbed water molecules (waterwater interactions) due to the large dipole moment of water.The fluidsolid potential function, Ψ(z), in the SLD model is estimated typically from the partially integrated 10-4 Lee’s potential,12 as shown in eq 7. This potential accounts for dispersive interactions alone, which are the significant interactions for nonpolar adsorbates. Because the contributions of the electrostatic and polar interactions are significant in water adsorption, Lee’s potential was augmented with terms for (a) the hydrogen-bond energy10 and (b) the dipole interactions11 within water molecules as follows: ΨðzÞ ¼ 4πFatoms εfs σ 2fs

σ 4fs σ 10 1 4 fs 10 2 i ¼ 1 ðz0 þ ði 1Þσ ss Þ4 5ðz0 Þ

þ εHB þ Φ

∑

the adsorbed phase: " # 2 μ4 2μ2 α0 3 0 2 þ þ ðα Þ I ξ¼ 3 ð4πε0 Þ2 kT 4 4πε0

where the three terms correspond to dipoledipole, dipole induced dipole, and induced dipoleinduced dipole attractive potentials, respectively. The physical constants used in eq 22 are defined as23 μ= α0 = I= ε0 = k=

¼ εHB ¼0

if

r AB < σHB otherwise

dipole moment of water, C 3 m (α/4πε0) = polarizability volume of water, m3 ionization potential of water, J permittivity of free space, C2/J 3 m Boltzmann’s constant, J/K

The values of these physical constants were adopted from Tester et al.23 and Prausnitz et al.24 Based on eq 22, the value of ξ at 0 °C is estimated to be about 250 1079 J 3 m6 and was used in this work at the appropriate temperature because one of the terms is a function of temperature. In particular, the dipole dipole energy or the first term in eq 22 is inversely proportional to the absolute temperature. Kotdawala et al.11 have developed the following expression for the polar interactions of water with the carbon surface:

!

ð20Þ

where εHB is the hydrogen-bond potential between the functional groups on the carbon surface and water molecules and Φ refers to the sum of three types of electrostatic contributions resulting from the dipole moment of water. Hydrogen Bond Potential. The hydrogen bond potential for water was adopted from the Grand Canonical Monte Carlo (GCMC) simulation work of Muller et al.1 This potential models water as a Lennard-Jones sphere with four sites arranged in a tetrahedral geometry. In their simulations, Muller et al.1 used two sites for representing hydrogen atoms and the other two sites represented a lone pair of electrons capable of forming hydrogen bonds with the surface, and the oxygen atom was represented by the sphere. An off-center square-well potential was used to represent the interaction potential of the hydrogen bond. Thus, the hydrogen bond potential of water with the adsorbent surface can be written as ϕHB ϕHB

ð22Þ

" # 8πξ 3σ ff σ 3ff Fp N ϕ¼ 3 þ 2ðL 2σ fs Þ þ 3σ ff ðL 2σ fs Þ 2 4ðL 2σ fs Þ2

ð23Þ where Fpis the pore density of water calculated in this work from the SLD model and N is the Avogadro’s number. Other quantities have been defined earlier in section 2. eq 23 was used in the present work to account for the electrostatic interactions of water molecules in the adsorbed phase. 3.2. Excess Adsorption Equation for Water Adsorption. In addition to the modifications discussed above, the excess adsorption isotherm equation in SLD given by eq 19 was also modified to account for the bimodal nature of water adsorption. Several authors10,2527 have observed that the adsorption of water on activated carbons is bimodal. The adsorption of water is thought to first occur at oxygenated surface sites on the carbon (or coal), and then, the secondary adsorption of water molecules occurs on the three-dimensional clusters formed by water molecules.1,10 To account for this dual mechanism of water adsorption, the excess isotherm equation for water in the SLD model was modified as

ð21Þ

On the basis of our analysis of the SLD model parametrization, a value of 90 K was used for εHB/k in this work. Dipole Interactions of Water. Kotdawala et al.11 applied the mean-field perturbation theory to model the adsorption of polar molecules in nanopores. The authors considered the electrostatic interactions of water molecules, which included the permanent dipoledipole, dipoleinduced dipole and induced dipoleinduced dipole interactions. The relative contributions of these terms are about 80, 15, and 5%, respectively, at 0 °C.23,24 These electrostatic interactions are also dependent on the pore density of water molecules.11 Following this approach, three dipole interaction terms23 were added to the fluidsolid potential function in SLD to account for the polar nature of water molecules in

nGibbs water ¼

Ap As þ 2 2

Z

right side of slit left side of slit

ðFðzÞ Fbulk Þ dz

ð24Þ

where Ap represents the surface area for primary adsorption of water molecules at the surface sites and As represents the surface area for secondary adsorption in water clusters. Additional details on these modifications are given in section 5, which includes a discussion of the modeling approach formulated in this work for modeling the competitive adsorption of CO2/water mixtures on wet coals. 560


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4. SLD MODEL FOR MIXTURE ADSORPTION In this section, the SLD model for mixture adsorption is described. The one-fluid mixing rules are used to extend the SLD model for pure gas adsorption described in section 2 to mixtures. When dealing with mixtures, the bulk fugacity of a component i using the PR EOS is given as ! ^f bulk bi pb i ¼ ðZ 1Þ ln Z ln RT yi P b 0 1 2 ∑ yj aij pffiffiffi ! a Bb i ð1 þ Fbð1 þ 2ÞÞ j C pffiffiffi þ pffiffiffi @ A ln a 2 2RTb b ð1 þ Fbð1 2ÞÞ

The cross-coefficient (bads)ij is obtained from a linear combining rule with the empirical correction discussed in the previous section: ! bi ð1 þ Λb, i Þ þ bj ð1 þ Λb, j Þ ðbads Þij ¼ ð32Þ 2 where the Λb values for each component are from pure component adsorption. The equilibrium criterion in SLD for mixed gas adsorption, subject to the mass balance constraints, is given as ! ! ^f ads ½ x ðzÞ, Fads ðzÞ Ψfsi ðzÞ þ Ψfsi ðL zÞ i B ¼ ln ^f bulk kT i i ¼ 1, NC

ð25Þ

ð33Þ

The familiar one-fluid mixing rules are used for the EOS constants a and b in the bulk phase and are given as a¼

∑i ∑j yi yjðabulk Þij

ð26Þ

b¼

∑i yi bi

ð27Þ

where the fugacity of the adsorbed phase is a function of pressure, temperature, local density, and local composition, at a given point z in the slit. The fluidsolid potential function of each component for mixed gas adsorption is also calculated with the Lee’s partially integrated 10-4 potential.12 The potential function for mixture adsorption is given as follows:15,19

Similarly, the fugacity of a component i in the adsorbed phase using the PR EOS is given as ^f ads ðzÞ i xi ðzÞP

!

2

∑j xj ðzÞbij b

Ψfsi ðzÞ ¼ 4πFatoms ðεfs Þi ðσ2fs Þi

!

P 1 Fads ðzÞRT b 0 ! 2 xj ðzÞbij b P Pb aðzÞ B j ln þ pffiffiffi @ Fads ðzÞRT RT b 2 2RTb

ln

¼

σ4fs, i ðσ 10 1 4 fs Þi 5ðz0 Þ10 2 i ¼ 1 ðz0 þ ði 1Þσss Þ4

∑

∑

2

∑j xj ðzÞ aijðzÞ aðzÞ

ðεfs Þi ¼

1

pffiffiffi ! ð1 þ Fads ðzÞ bð1 þ 2ÞÞ C pffiffiffi A ln ð1 þ Fads ðzÞ bð1 2ÞÞ

nEx i ¼

The mixing rules for the EOS constants in the adsorbed phase are given as

∑i ∑j xi xj ðaads Þij

ð29Þ

b¼

∑i ∑j xi xj ðbads Þij

ð30Þ

ð34Þ

ð35Þ

where (εfs)i is the fluidsolid interaction energy parameter of component i. The other physical quantities in these equations are similar to the case of pure gas adsorption. The excess adsorption of a component i in a mixture is given as

ð28Þ

a¼

pffiffiffiffiffiffiffiffiffiffiffiffi εff , i εss

!

A Z L ð3=8Þσff , i ðFads ðzÞxi ðzÞ Fbulk yi Þdz 2 ð3=8Þσff , i

ð36Þ

As shown in eq 36, the excess amount adsorbed of each component is dependent on the composition in the bulk and adsorbed phases, as well as the densities in the bulk and adsorbed phases. For mixture adsorption calculations, the pressure, temperature, feed mole fractions, and void volume are necessary input information to calculate the experimental component excess adsorption for each component. Specifically, a mass balance equation is formulated and is given as

The cross-coefficient (aads)ij in eq 29 is calculated with the geometric mean combining rule. For asymmetric/polar mixtures such as CO2/water, a binary interaction parameter (BIP), Cij, is also used in the adsorbed phase as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðaads Þij ¼ ðaads Þi ðaads Þj ð1 Cij Þ ð31Þ

zi ¼

Further, the attractive constant aads of each component i is calculated using the same method outlined for pure components. The constant aads is a function of position in the slit and fluidfluid molecular distance, and the equations relating these were given by Chen et al.9

nEx i þ Fbulk V void yi nEx tot þ Fbulk V void

i ¼ 1, NC

ð37Þ

where zi is the feed molar fraction of component i. eq 37 is written for each component in the mixture, and the set of equations are solved simultaneously, as described elsewhere.7 561


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5. MODELING OF CO2/WATER MIXTURE ADSORPTION ON WET COALS In this section, CO2 adsorption data for four wet coals are used to investigate the effects of water on gas adsorption behavior. The experimental data for these systems were acquired in an earlier work.28 A new data reduction method was developed that attempts to account for the presence of water in up to three phases (gas, adsorbed, and liquid). The newly reduced data is then used to perform CO2/water mixture adsorption calculations, wherein water is treated as an active component. Finally, a phase-check analysis is conducted to analyze the possible formation of a third phase in these systems.

CO2 and adjusted this density by 1% to account for the presence of water in the gas phase. The reference equation of state36 for pure CO2 provides densities with an uncertainty of less than 0.1%, and therefore, it can be used to incorporate corrections to the gas-phase density, in the absence of a highly accurate equation of state for wet gas mixtures. As mentioned above, the correction was based on our analysis of limited density measurements available for CO2/water mixtures in bulkfluid systems.34,35 The reasoning behind modification c has been discussed in a review.22 Briefly, the review had shown that the thermodynamic behavior of adsorbed water is markedly different from liquid water.3743 In particular, a significant portion of adsorbed water was nonfreezable37,39 and also had an ice-like structure.41,42 On the basis of the congelation characteristics and other (indirect) physical evidence, it appears reasonable that the gas solubility in adsorbed water would be quite small (if not zero). To our knowledge, it is not possible currently to measure experimentally the solubility of gas in adsorbed water. Thus, in the absence of more information, we have assumed zero solubility for the gas in adsorbed water, as this appears more accurate than assuming liquid water-like solubility for the gas in adsorbed water. Further, the amount of adsorbed water in each coal was estimated to be equal to the equilibrium moisture content of coal. Any moisture in excess of equilibrium moisture content was assigned the same gas solubility as bulk liquid water, since the excess moisture exhibits thermodynamic properties identical to liquid water.22 The nominal values used in modifications a and b are assumptions that were necessary as a result of the unavailability of vapor phase composition and density data for CO2/water mixtures on wet adsorbents. Nonetheless, the method is expected to provide a reasonable approximation to test the hypothesis in this work; these estimates may be revised when additional data are available for these systems. In particular, measuring the gas-phase densities with an accurate density meter would be greatly helpful in delineating some of these effects. Further, note that in the present work, the new data reduction method is applied only for CO2/water mixtures. A similar (and simpler) approach may be used for mixtures of water with other coalbed gases (e.g., methane and nitrogen). Adsorption Isotherms for CO2/Water Mixtures on Wet Coals. The excess adsorption for each component (CO2 and water) on coals was calculated as a function of bulk pressure using the new data reduction method. For this purpose, we reprocessed the isotherm data for CO2 adsorption on wet coals presented in an earlier work.28 The four coals utilized in the present work are Beulah Zap, Wyodak, Upper Freeport, and Pocahontas coals. These coals are from the premium coal sample program at the Argonne National Laboratory.44 Table 2 presents the ultimate and proximate analyses of these coals. The Beulah Zap and Wyodak coals contain about 32% and 28% moisture, respectively, and they can be regarded as high-moisture containing coals. In contrast, Pocahontas and Upper Freeport coals contain about 0.65% and 1.1% moisture, respectively, and they can be considered as low-moisture containing coals. Such a large variation in inherent moisture levels of these coals is helpful in investigating the effects of inherent coal moisture on gas adsorption. The CO2 adsorption isotherm measurements were conducted using a volumetric method. In the following, we highlight only the modifications introduced to the traditional data reduction based on the volumetric method of isotherm measurement.

5.1. New Data Reduction Method for CO2/Water Mixture Adsorption. The traditional data reduction method for gas

adsorption on wet adsorbents assumes that all of the water present in coals is adsorbed and the bulk gas phase is considered to be free from water (i.e., the bulk gas is treated as being dry). Further, the traditional method typically includes the gas solubility in adsorbed water, wherein adsorbed water is assumed to possess the same gas solubility as liquid water. In contrast, the new data reduction method developed in this work attempts to account for the presence of water in as many as three equilibrium phases. The method accounts for (a) the presence of water vapor in the gas phase (b) the ensuing change in the wet gas density over the dry gas density and (c) the lack of gas solubility in adsorbed water. The following three modifications (a, b, and c) were introduced to the traditional data reduction method: (a) The molar fraction of water vapor in the bulk gas-phase was assumed to be 1% (i.e., ywater = 0.01). (b) The wet gas density was estimated by increasing the dry gas density by 1%. The wet gas density refers to the density of gas/water mixture and the dry gas density refers to pure gas (CO2) density. (c) The adsorbed water was excluded from gas solubility calculations. In other words, the adsorbing gas (CO2) was assumed to be soluble only in the excess (liquid-phase) water present on coals. The excess water was estimated to be the water present on coals that was in addition to the equilibrium moisture content of coals. To our knowledge, experimental measurements for the phase composition and density of wet gas in a high-pressure adsorption system are unavailable in the literature at the time of this writing. As a result, we utilized the limited available experimental data2935 for the phase equilibrium of CO2/water mixtures to obtain estimates for modifications a and b. Our analysis of these data showed that the composition of water vapor in the gas can be considered to be about 1%, to a reasonable approximation. Further, the wet gas density appeared to be about 1% higher than the dry gas (pure CO2) density, especially at the higher pressures. Our analysis showed that the gas density correction is significant in calculating the adsorbed amounts at the higher pressures. Therefore, we designed these modifications to provide more reliable estimates, especially at the higher pressures. At the lower pressures, these corrections have a relatively smaller effect. At the time of this writing, there appears to be no equation of state (to our knowledge) that is sufficiently accurate for high-pressure adsorption isotherm data reduction of CO2/water mixtures. As a result, we utilized the highly accurate equation of state for pure 562


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Table 2. Compositional Analyses of Coals analysisa

Beulah Zap

Wyodak

Upper Freeport

Pocahontas

91.1

Ultimate carbon %

72.9

75.0

85.5

hydrogen %

4.8

5.4

4.7

4.4

oxygen %

20.3

18

7.5

2.5

sulfur %

0.8

0.6

2.3

0.7

vol. matter %

30.5

32.2

27.1

18.5

fixed carbon %

30.7

33.0

58.7

76.1

moisture %

32.2

28.1

1.1

0.7

ash %

6.6

6.3

13.0

4.7

Proximate

a

Figure 1. Excess adsorption of CO2 on Beulah Zap coal at 328.2 K: comparison of data reduction methods.

Argonne National Laboratory.

Thus, familiarity of the reader with the volumetric measurement method for adsorption isotherms is implicitly assumed. A more detailed discussion of the experimental technique and traditional data reduction method can also be found in our earlier works on gas adsorption measurements.28,45,46 In the volumetric method of measuring adsorption, a known amount of pure gas is injected into a sample cell containing a wet adsorbent. The amount of water in the adsorbent is also known based on prior gravimetric measurement of the sample. Thus, the total amount of water in the system is known, and the amount of pure, dry gas injected into the sample cell can be calculated based on measurements of pressure, temperature, and the volume injected from the reference cell at a fixed pressure. The amount of gas (CO2) injected into the cell is given as 2 nCO inj ¼

PΔV ZRT

Figure 2. Excess adsorption of CO2 on Wyodak coal at 328.2 K: comparison of data reduction methods.

ð38Þ

where P is the bulk pressure, ΔV is the injected volume from the reference cell, Z is the compressibility factor of CO2, and T is the absolute temperature, where these variables refer to conditions of the pump. Similarly, at adsorption equilibrium, the amount of unadsorbed, gas-phase CO2 remaining in the sample cell is given as 2 nCO unads ¼

PV void yCO2 Zmix RT

ð39Þ

where Vvoid is the void volume, yCO2 is the bulk gas mole fraction of CO2, and Zmix is the compressibility factor for CO2/water gas temperature, where these variables refer to conditions of the pump. The modification a is used to estimate the molar fraction of CO2 in the gas phase (i.e., yCO2 = 0.99), and Zmix is estimated using modification b. Thus, the excess adsorption of CO2 is given as CO2 CO2 nEx CO2 ¼ ninj nunads nsol

Figure 3. Excess adsorption of CO2 on Upper Freeport coal at 328.2 K: comparison of data reduction methods.

ð40Þ Thus, the excess adsorption of water can be calculated by invoking the void volume definition and using the total amount of water present in the sample cell. The excess adsorption of water is given as

where nsol is the amount of gas dissolved in the excess water present (if any). The amount of water in the gas phase can be calculated with an equation analogous to eq 39 as nwater unads ¼

PV void ywater Zmix RT

liquid

total water nEx water ¼ nwater nunads nwater

ð41Þ

ð42Þ

where ntotal wateris the total amount of water present in the system and nliquid water is the amount of free, liquid water present (if any).

where ywater is the bulk gas mole fraction of water estimated from modification a (i.e., ywater = 0.01). 563


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Figure 4. Excess adsorption of CO2 on Pocahontas coal at 328.2 K: comparison of data reduction methods.

Figure 6. SLD model representations for CO2/water mixture adsorption on wet Wyodak coal at 328.2 K.

Figure 5. SLD model representations for CO2/water mixture adsorption on wet Beulah Zap coal at 328.2 K.

Figure 7. SLD model representations for CO2/water mixture adsorption on wet Upper Freeport coal at 328.2 K.

In this manner, the excess adsorption of both CO2 and water can be calculated as a function of bulk pressure to yield complete isotherms for the binary mixture of CO2 and water. Using the new data reduction method, the raw data for CO2 adsorption on four wet coals mentioned above were reprocessed. Figures 14 present the CO2 adsorption isotherms on Beulah Zap, Wyodak, Upper Freeport, and Pocahontas coals, respectively, using the newly devised data reduction method. For comparison, the CO2 adsorption isotherms on both dry and wet coals using the traditional data reduction method are also shown in these figures. The error bars in these figures represent the expected experimental uncertainties in the amounts adsorbed. As evident from these figures, the new approach results in increasing the calculated excess adsorption values on coals with large amounts of adsorbed moisture. Figures 1 and 2 illustrate that the calculated excess adsorption of CO2 on these coals is significantly higher than that calculated from the traditional method. The calculated excess adsorption values using the new approach for two of the coals that contained less than 1% moisture— Pocahontas and Upper Freeport—are almost identical to the values calculated using the traditional method. This is shown in Figures 3 and 4 for the two coals. Because these coals contain extremely low-levels of moisture, the correction applied to these isotherms to account explicitly for moisture is also small. We also investigated the separate effect of modifications ac on CO2 adsorption isotherms and compared these to the isotherms calculated based on the traditional data reduction approach.

Figure 8. SLD model representations for CO2/water mixture adsorption on wet Pocahontas coal at 328.2 K.

Our analysis showed that accounting for the presence of water in the gas phase (modification a) increases the calculated values of excess adsorption. Similarly, the exclusion of solubility of gas in adsorbed water (modification c) also increases the calculated values of excess adsorption. In contrast, accounting for the density of wet gas (modification b) lowers the calculated values of adsorption. Further, the analysis showed that modification c was a significant correction for coals that contained larger amounts of moisture and modification b was significant at the higher-pressures. For brevity, these findings are not shown here graphically. 564


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The first term in eq 47 represents the fluidfluid interactions of water in the adsorbed phase obtained in the usual manner in the SLD model. The second term in eq 47 represents the fluid solid dispersive interactions of water with the solid adsorbent. The first two terms are included for any adsorbing fluid, because these terms represent the nonpolar, dispersive interactions, which are considered significant in the adsorption of most nonpolar adsorbates. The third term in eq 47 accounts for the hydrogen-bond type interactions of water with the oxygenated surface sites on the adsorbent. Thus, this term represents the polar fluidsolid interactions of water in the slit. The fourth term in eq 47 is the sum of three types of electrostatic interactions that are considered significant in a water molecule.23,24 Figure 9 illustrates an idealized depiction of these molecular interactions within a twosurface slit. The figure depicts water and CO2 molecules in the slit and shows the partitioning of molecular interactions discussed above. For the modeling of this mixture, the component excess adsorption of CO2 and water are calculated from eqs 19 and 24, respectively. Note that eq 24 accounts for the bimodal nature of water adsorption. Further, the component material balances for CO2 and water are given as

Figure 9. Idealized depiction of molecular interactions of adsorbed water in the slit (slit geometry adapted from Fitzgerald15).

Figures 58 present the excess adsorption isotherms for the CO2/water binary mixture based on the new data reduction approach. The solid symbols in these figures represent the reprocessed experimental data using the new data reduction method. The open symbols in these figures are SLD model predictions as discussed in section 5.3. The excess adsorption of water would appear to be nearly constant, as the bulk pressures shown are well beyond the saturation pressure of water at the given temperature. However, accounting for water as a separate component alters the calculated values of component CO2 adsorption, which, in fact, is the main focus of this work. 5.2. Competitive Adsorption of CO2/Water Mixtures: Modeling Approach. In this section, the modeling approach formulated for competitive adsorption of CO2/water mixtures on wet coals is described. The partitioning of the molecular interactions of water and CO2 within a slit in the SLD model is discussed with a special emphasis on calculations involving this mixture. The SLD model partitions the molecular interactions of an adsorbing species in the slit into two contributions: fluidfluid and fluidsolid. For each component in a gas mixture, the molecular interactions in the bulk and adsorbed phases are accounted for in the following way: ¼ μffi þ μfsi μbulk i

ZCO2 ¼

Zwater ¼

where the superscripts bulk, ff, and fs refer to the bulk, fluid fluid, and fluidsolid interactions, respectively. For example, in a CO2/CH4 mixture, eq 43 yields ð44Þ

ff fs μbulk CH4 ¼ μCH4 þ μCH4

ð45Þ

These equations are solved simultaneously to model the competitive adsorption of a binary mixture comprised of these components. When water is one of the components in a mixture, additional terms are needed to more effectively account for the unique molecular interactions of water in the adsorbed phase. The necessary modifications were discussed in section 3. When the polar and electrostatic interactions of water are included in the SLD model, the chemical potential for CO2 and water can be written as ff fs μbulk CO2 ¼ μCO2 þ μCO2

ð46Þ

ff fs fs ff μbulk water ¼ μwater þ μwater þ μHB þ μdipole

ð47Þ

nEx total þ V void Fgas nEx water þ V void Fgas ywater nEx total þ V void F gas

ð48Þ

ð49Þ

EX where nEx CO2 and nwater are given by eqs 19 and 24, respectively, Ex and ntotal is the total excess adsorption. Thus, eqs 48 and 49 are solved simultaneously to model the competitive adsorption of this mixture, wherein the molecular interactions in the binary mixture are accounted for through eqs 46 and 47. The CO2/water mixture on coals with large amounts of adsorbed moisture represents a highly asymmetric mixture. In particular, the amount of water adsorbed on some of these coals can be 12 orders of magnitude larger than the amount of CO2 adsorbed at a given pressure. This asymmetry coupled with the subcritical/supercritical nature of the two adsorbates and the bimodal nature of water adsorption introduces computational challenges in modeling the adsorption behavior of this system. Several modifications highlighted above were necessary to successfully model this mixture. The regressed model parameters included the accessible surface areas for water and CO2, slit length, and a binary interaction parameter in the adsorbed phase. Further, the slit length parameter was assumed to vary as a linear function of pressure. A binary interaction parameter (Cij) was used in the adsorbed phase (eq 31) to account for the asymmetric mixing of CO2/water mixture in the adsorbed phase. Overall, five or six parameters were regressed for representing the CO2/water binary mixture adsorption on each coal. This is similar to the number of parameters typically regressed for conventional binary mixtures (e.g., CO2/CH4). Ideally, the two surface areas for water (Ap and As) would be determined from the low-pressure isotherm for pure water adsorption. However, for the four coals studied in this work, this information was unavailable at the time of this writing. Therefore, the two surface areas for water were determined along with other parameters through simultaneous regression of CO2/water binary mixture adsorption data on these coals.

ð43Þ

ff fs μbulk CO2 ¼ μCO2 þ μCO2

nEx CO2 þ V void Fgas yCO2

eq 47 gives the chemical potential of water in the adsorbed phase and contains four interaction terms that are explained as follows: 565


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Table 3. SLD Modeling Results for CO2/Water Mixture Adsorption on Wet Coals regressed parameters water surface areas coal

CO2 surface area (m2/g)

Ap (m2/g)

WAAD slit length function

As (m2/g)a

Cij

slope (nm/psia) 4

intercept (nm)

CO2

water

95.0

194.8

950

0.122

2.64 10

0.92

0.23

0.62

115.0

166.8

650

0.266

3.11 104

1.00

0.28

0.74

Upper Freeport

92.6

94.5

0.180

1.65 104

0.81

0.53

1.10

Pocahontas

91.9

69.5

0.160

9.01 105

0.92

0.57

1.36

0.40

0.95

Beulah Zap Wyodak

Overall a

As (secondary surface area for water) was regressed only for high-moisture coals and was set to zero for low-moisture coals.

Figure 10. Component fugacities of water in gas and liquid phases for adsorption on wet Wyodak coal at 328.2 K.

Figure 11. Component fugacities of water in gas and liquid phases for adsorption on wet Upper Freeport coal at 328.2 K.

As mentioned above, the effective slit length was considered to be a linear function of pressure. This was done to account for the “pore-blocking effect” of adsorbed water in coals. In particular, preadsorbed water in coals blocks the entrance to the smaller (and more energetically favorable) pores in coals. As a result, CO2 adsorbing gas would be able to access proportionally larger pores only, and this effect is expected to be more significant with increases in bulk gas pressure. Thus, the slit length was assumed to vary linearly with pressure. The regression results discussed in the next section confirmed this view. Specifically, the effective slit length or pore-width of each coal was found to increase with bulk gas pressure. We also note that no correction has been made in this work for possible swelling of the coal matrix in the presence of CO2. Such effects, which are considered significant by some investigators for describing CO2 adsorption on coals,4749 will be considered in a future study. 5.3. SLD Modeling Results for CO2/Water Mixture Adsorption on Wet Coals. Table 3 presents the SLD modeling results for the competitive adsorption of CO2/water mixtures on four wet coals. The table lists the regressed model parameters and the weighted average absolute deviation (WAAD) for CO2 and water adsorption on these coals. The weights used in regressions were the expected experimental uncertainties in the amounts adsorbed. The secondary surface area was set to zero (not regressed) for the two low-moisture containing coals (Upper Freeport and Pocahontas), because the two coals are almost dry and are not expected to exhibit significant levels of clustering (secondary adsorption of water molecules). As shown in Table 3, the new parametrization of the SLD model coupled with the modeling strategy described

in the previous section was capable of precise representations for the adsorption of this mixture on these coals. The overall WAAD for CO2 and water component adsorptions on these coals was 0.40 and 0.95, respectively. Figures 58 illustrate the quality of model representations for the adsorption on wet Beulah Zap, Wyodak, Upper Freeport, and Pocahontas coals, respectively. 5.4. Phase-Check Analysis for CO2/Water Mixture Adsorption on Wet Coals. For adsorption on dry adsorbents, at equilibrium, two distinct phases are formed: gas and adsorbed. However, when the adsorbent is wet, water may form a third, water-rich phase, especially when the adsorbent surface is exposed to a supercritical gas such as CO2. In this section, we determine the possibility of the existence of a water-rich phase in coals when the coal surface is exposed to a high-pressure supercritical gas such as CO2. A rapid method of conducting a phasecheck analysis is to evaluate the component fugacities in each possible phase. The SLD model parameters obtained for the four wet coals were used to evaluate the component fugacities of water in the gas (and adsorbed) phase. The component fugacities of water in a liquid-like phase at the given temperature, pressure, and composition were also calculated. A direct comparison of the component fugacities of water in the gas and liquid phases was made for each coal. If the component fugacity of water in liquid state is lower than in the gas phase, this would indicate the possible formation of a water-rich liquid phase. While this approach does not involve the simultaneous application of the material balance and the equilibrium relations for three coexisting phases (i.e., a complete Gibbs energy minimization to establish the equilibrium condition), it provides some insight on the potential formation of 566


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an aqueous phase. A more rigorous algorithm consisting of a Gibbs energy minimization routine is under development at Oklahoma State University. The phase-check analysis indicated the formation of a waterrich liquid phase for coals that contained high-levels of moisture (e.g., Wyodak coal). The Wyodak coal contains about 28% inherent moisture. In contrast, the results for low-moisture coals (wet Upper Freeport and Pocahontas) did not indicate the formation of a liquid phase. For illustrative purposes, Figures 10 and 11 present the component fugacities of water in liquid and gas phases as a function of bulk pressure for Wyodak and Upper Freeport coals, respectively. As shown in the figures, the third phase formation is predicted for Wyodak coal.

(3) Clarkson, C. R.; Bustin, R. M. Binary Gas Adsorption/Desorption Isotherms: Effect of Moisture and Coal Composition upon Carbon Dioxide Selectivity over Methane. Int. J. Coal Geol. 2000, 42 (4), 241–271. (4) Levy, J. H.; Day, S. J.; Killingley, J. S. Methane Capacities of Bowen Basin Coals Related to Coal Properties. Fuel 1997, 9 (76), 813–819. (5) Fitzgerald, J. E.; Sudibandriyo, M.; Pan, Z.; Robinson, R. L.; Gasem, K. A. M. Modeling the Adsorption of Pure Gases on Coals with the SLD Model. Carbon 2003, 41 (12), 2203–2216. (6) Fitzgerald, J. E.; Robinson, R. L.; Gasem, K. A. M. Modeling High-Pressure Adsorption of Gas Mixtures on Activated Carbon and Coal Using a Simplified Local-Density Model. Langmuir 2006, 22 (23), 9610–9618. (7) Mohammad, S. A.; Chen, J. S.; Robinson, R. L.; Gasem, K. A. M. Generalized Simplified Local-Density/PengRobinson Model for Adsorption of Pure and Mixed Gases on Coals. Energy Fuels 2009, 23 (12), 6259–6271. (8) Rangarajan, B.; Lira, C. T.; Subramanian, R. Simplified Local Density Model for Adsorption over Large Pressure Ranges. AIChE J. 1995, 41 (4), 838–845. (9) Chen, J. H.; Wong, D. S. H.; Tan, C. S.; Subramanian, R.; Lira, C. T.; Orth, M. Adsorption and Desorption of Carbon Dioxide onto and from Activated Carbon at High Pressures. Ind. Eng. Chem. Res. 1997, 36 (7), 2808–2815. (10) McCallum, C. L.; Bandosz, T. J.; McGrother, S. C.; Muller, E. A.; Gubbins, K. E. A Molecular Model for Adsorption of Water on Activated Carbon: Comparison of Simulation and Experiment. Langmuir 1999, 15 (2), 533–544. (11) Kotdawala, R.; Kazantzis, N.; Thompson, R. An Application of Mean-Field Perturbation Theory for the Adsorption of Polar Molecules in Nanoslit-Pores. J. Math. Chem. 2005, 38 (3), 325–344. (12) Lee, L. L. Molecular Thermodynamics of Non-Ideal Fluids; Butterworths: Stoneham, MA, 1988. (13) Subramanian, R.; Pyada, H.; Lira, C. T. Engineering Model for Adsorption of Gases onto Flat Surfaces and Clustering in Supercritical Fluids. Ind. Eng. Chem. Res. 1995, 34 (11), 3830. (14) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. (15) Fitzgerald, J. E. Adsorption of Pure and Multi-Component Gases of Importance to Enhanced Coalbed Methane Recovery: Measurements and Simplified Local-Density Modeling. Ph.D. Dissertation, Oklahoma State University, Stillwater, OK 2005. (16) Chen, J. S. Simplified Local-Density Modeling of Pure and Multi-Component Gas Adsorption. M.S. Thesis, Oklahoma State University, Stillwater, OK, 2007. (17) Puziy, A. M.; Herbst, A.; Poddubnaya, O. I.; Germanus, J.; Harting, P. Modeling of High-Pressure Adsorption Using the Bender Equation of State. Langmuir 2003, 19 (2), 314–320. (18) Yang, X.; Lira, C. T. Theoretical Study of Adsorption on Activated Carbon from a Supercritical Fluid by the SLD-ESD Approach. J. Supercrit. Fluids 2006, 37 (2), 191–200. (19) Soule, A. D.; Smith, C. A.; Yang, X.; Lira, C. T. Adsorption Modeling with the ESD Equation of State. Langmuir 2001, 17 (10), 2950–2957. (20) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fund 1976, 15 (1), 59–64. (21) Gasem, K. A. M.; Gao, W.; Pan, Z.; Robinson, R. L., Jr. A Modified Temperature Dependence for the PengRobinson Equation of State. Fluid Phase Equilib. 2001, 181 (12), 113–125. (22) Gasem, K. A. M.; Robinson, R. L., Jr.; Mohammad, S. A.; Chen, J. S.; Fitzgerald, J. E., Improved Adsorption Models for Coalbed Methane Production and CO2 Sequestration, Final Technical Report, 2008. (23) Tester, J. W.; Modell, M. Thermodynamics and Its Applications. 3rd ed.; Prentice-Hall: NJ, 1997; p 936. (24) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G., Molecular Thermodynamics of Fluid-Phase Equilibria., 3rd ed.; Prentice-Hall: NJ, 1999; p 860.

6. CONCLUSIONS A new modeling approach that considers the competitive adsorption between CO2 and water on coals was presented. A new data reduction method that accounts for the presence of water in up to three equilibrium phases was also developed. The SLD model was modified to accommodate the unique molecular interactions of adsorbed water and the bimodal nature of water adsorption on carbons. Further, a phase-check analysis was conducted to ascertain the existence of a waterrich liquid phase in the binary mixture adsorption of CO2 and water on four coals. Results indicate that the newly devised data reduction method can result in significant differences in the estimated CO2 adsorption capacities relative to the traditional data reduction method, especially for coals that contain large amounts of moisture. These differences arise mainly as a result of the assumptions regarding the solubility of gas in adsorbed water and the corrections to the wet gas density relative to the dry gas density. The approach developed here included assumptions about the gas densities and solubilities for CO2/water mixtures on coals. The measurement of gas-phase densities in situ with an accurate density meter may yield valuable information to delineate some of the factors considered in this work. The SLD modeling for CO2/water binary mixture adsorption on wet coals indicate a viable method to investigate the multiphase behavior of this highly asymmetric adsorptive mixture. The phase-check analyses performed on these coals indicate the possible existence of a water-rich liquid phase for coals with high levels of moisture. ’ AUTHOR INFORMATION Corresponding Author

*Phone: (405) 744-5280. Fax: (405) 744-6338. E-mail: gasem@ okstate.edu.

’ ACKNOWLEDGMENT The financial support of the U.S. Department of Energy and Advanced Resources International, Inc. is gratefully acknowledged. ’ REFERENCES (1) Muller, E. A.; Hung, F. R.; Gubbins, K. E. Adsorption of Water VaporMethane Mixtures on Activated Carbons. Langmuir 2000, 16 (12), 5418–5424. (2) Joubert, J. I.; Grein, C. T.; Bienstock, D. Sorption of Methane in Moist Coal. Fuel 1973, 52 (3), 181–185. 567


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Modeling the Competitive Adsorption of CO2 and Water at High

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