Multiphase Analysis for High-Pressure Adsorption ... - ACS Publications

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Multiphase Analysis for High-Pressure Adsorption of CO2/Water Mixtures 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 consider water as a separate adsorbed component and treats the adsorbed water as a “pacifier” of the coal matrix. In a recent work, we presented a new modeling approach for investigating the competitive adsorption of gas/water mixtures in high-pressure systems. We used the simplified local-density (SLD) model to investigate the effect of including the competitive adsorption of water present in coals on gas adsorption under the conditions encountered in coalbed methane (CBM) and CO2 sequestration applications. In continuation of that work, we present here a new multiphase algorithm to investigate the three-phase adsorption equilibrium of CO2/water mixtures on wet coals. When water is treated as one of the adsorbed components in a high-pressure gas adsorption system, as many as three fluid phases may coexist at equilibrium (gas, adsorbed, and liquid phases). A new algorithm is presented in this work to facilitate a Gibbs energy-driven multiphase analysis of the system. The algorithm employs a phase-insertion technique, which involves formally inserting a water-rich, bulk liquid phase and solving a three-phase flash problem, wherein the three phases are the adsorbed, bulk gas, and liquid phases. At equilibrium, the Gibbs energy of the system is calculated based on the phase distribution obtained at each step. This calculation is repeated sequentially with incrementally increased amounts of the inserted third phase. A minimum in the Gibbs energy at the given temperature and pressure, subject to material balance constraints, provides the equilibrium phase distribution in these systems. Multiphase analysis was performed for high-pressure CO2/water mixture adsorption on four wet coals utilizing this algorithm. Analysis indicates that a water-rich liquid phase is present in coals that contain large amounts of inherent moisture. For these coals, the water-rich phase appeared at the higher pressures in the isotherm and the fraction of this phase increased with bulk pressure, reaching a maximum near the CO2 critical pressure. In contrast, the low-moisture coals did not appear to contain a third-phase at equilibrium.

1. INTRODUCTION Simulations of enhanced coalbed gas recovery and CO2 sequestration in coalbeds require accurate and realistic models capable of predicting gas adsorption behavior. Since most coalbeds contain significant amounts of water, a reliable adsorption model must describe the significant effect of water on coalbed gas adsorption, the competitive adsorption in mixtures, and the densities of the gas and adsorbed phases. Traditional modeling of gas adsorption on wet coals does not include water as a separate adsorbed component and treats water only as a “pacifier” of the coal matrix. That is, water is envisioned to have the constant (pressure independent) effect of reducing the surface area available to the adsorbing gas. A more realistic approach would be to treat water as an independently adsorbed component in a gas mixture. This approach can be expected to yield a more realistic description of coalbed gas adsorption phenomena and accurate estimates of the amount of adsorbed gas in a coalbed reservoir. Water significantly affects gas adsorption behavior on coals and can dramatically reduce the gas adsorption capacity of coals.1−5 Although this significant effect of water on gas adsorption on coals is well documented qualitatively, there has been very limited effort to account quantitatively for its competitive adsorption effect in coalbed gas adsorption models. This, we believe, is largely due to the current gaps in the interpretation and understanding of water adsorption phenomena on coals, which has led to water being treated in simplified fashion as having a constant, pacifying effect on the coal surface. © 2012 American Chemical Society

Modeling the simultaneous adsorption of water and coalbed gases is an equilibrium problem that requires accurate description of the different molecular interactions involved in the process. The molecular interactions that are significant in water adsorption on carbon matrices include the formation of hydrogen bonds and three-dimensional clusters of water molecules.6 Adsorbed water is also believed to cause significant pore-blocking on the carbon surface,7 thus leading to competitive adsorption between adsorbates such as CO2 and water. Further, a high-pressure adsorption system comprised of a supercritical gas such as CO2 and subcritical water can exhibit up to three fluid phases at equilibrium. A rigorous approach to obtain the correct number of phases in a multiphase system is to minimize the Gibbs energy of the system. A minimum in the Gibbs energy at a specified temperature and pressure, subject to mass balance constraints, yields the phases stable at equilibrium. In a recent work,8 we presented a new modeling approach wherein the competitive adsorption of CO2/water mixtures was modeled by considering the water present in coals as a separate adsorbed component in thermodynamic equilibrium with a gas such as CO2. Specifically, the adsorption of CO2 on moistureequilibrated coals was treated as a particular case of binary mixture adsorption of CO2/water on coals. In the current work, Received: January 21, 2012 Revised: May 4, 2012 Published: May 15, 2012 3470

dx.doi.org/10.1021/ef300126x | Energy Fuels 2012, 26, 3470−3480

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current work, we present an algorithm that minimizes the Gibbs free energy for the given specifications of temperature, pressure, and total number of moles of each species. Since the application of our method is geared toward coalbed reservoir work, the specifications of temperature and pressure are more appropriate for these systems. Further, the current work utilizes an inhomogeneous, three-dimensional model to describe the adsorbed phase, and the calculations involve actual components and experimental data for high-pressure adsorption systems acquired in our laboratory. The remainder of this paper is organized as follows: section 2 presents the details of the simplified local-density (SLD) model, section 3 highlights the recent modifications introduced into the SLD framework to extend it to water adsorption on carbons and coals, section 4 discusses briefly the SLD model for mixtures, and section 5 presents the new multiphase algorithm and the results obtained on four wet coals.

we extend that approach by developing a new multiphase algorithm for investigating the multiphase (three-phase) behavior of CO2/water mixture adsorption on wet coals. A phase-insertion scheme was developed to investigate the possible formation of a water-rich, bulk liquid phase in wet coals. Figure 1 shows an idealized schematic of the phase-

Figure 1. Idealized schematic of an adsorption equilibrium cell: illustration of different fluid phase volumes and phase-insertion scheme.

2. SLD ADSORPTION MODEL In some of our previous works, 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.21−23 In the current work, the SLD model was extended to the case of gas/water mixture adsorption on coals and a new multiphase algorithm was developed, as detailed in a later section. The SLD model has been discussed in some of our previous works.8,22 For brevity, only a summary is provided in this section, and additional details are available in our previous publications on this subject.8,24 Nonetheless, several aspects dealing with competitive adsorption of CO2/water mixtures have been developed recently8 and these will be discussed in section 3. Rangarajan et al.25 developed the SLD model by superimposing the fluid−solid potential on a fluid equation of state to predict the adsorption on flat walls25 and in slit-shaped pores.26 A mean-field approximation is used in the SLD model, and the equation of state includes a local-density approximation in calculating the configurational energy of fluid in the adsorbed phase. Different geometries such as rectangular slits, cylindrical pores, flat surfaces, etc. may be used to model the porous adsorbent structure. The SLD model envisions the adsorbent (coal) as composed of slit-shaped pores. The slit-pore model has been used in earlier works to describe gas adsorption.22,23,26 As discussed later in section 3, the modifications introduced into the SLD model in this work evolved from studies in the literature6,27 that utilized the slit geometry for the adsorbent, thus making it a suitable choice. Using the criterion of equality of chemical potentials of the bulk and adsorbed fluids and expressing the chemical potentials in terms of fugacities, it has been shown that the SLD model provides the following equilibrium relation for describing adsorption in a slit:26

insertion scheme developed in this work. The figure is a simplified schematic of the different fluid phases that can exist in an adsorption equilibrium cell containing a wet adsorbent. As depicted in Figure 1, a trial fluid phase was inserted in an adsorption system comprised initially of two fluid phases. A Gibbs energy-driven algorithm was used to obtain the number and the distribution of equilibrium phases on wet coals, wherein up to three fluid phases may coexist (adsorbed, bulk gas, and bulk liquid). The phase-insertion scheme and the details of the multiphase algorithm developed in this work are explained in a later section of this paper. For multiphase problems such as vapor−liquid−liquid equilibrium, several algorithms and methods have been presented in the literature. These include the isofugacity methods, extended phase-check procedures, Gibbs (or Helmholtz) free energy minimization methods, and tangent plane distance/phase-stability analysis, utilizing local or global optimization methods.9−19 In principle, any of these methods may be extended to multiphase adsorption equilibria problems. However, the computational complexity of the local-density adsorption model utilized in this work made some of these direct and/or global minimization methods unattractive (computationally) when applied to gas/water mixture adsorption considered in this work. Thus, we elected to utilize a phase-insertion method coupled with an indirect minimization method for Gibbs energy. In other words, the complexity (and the theoretical rigor) of our adsorption model was retained and the choice of the Gibbs energy minimization method was determined by considering a combination of computational speed, accuracy and reliability of the overall algorithm. Very few studies are available in the literature (to our knowledge) on multiphase problems involving an adsorbed phase as one of the equilibrium phases. Cabral et al.20 presented an algorithm to investigate multiple bulk and adsorbed phases. The authors formulated the problem as a minimization of Helmholtz free energy for given specifications of temperature, volume, adsorbent area, and total number of moles of each species. They used a two-dimensional lattice-gas model to describe the adsorbed phase and presented a parametric study utilizing hypothetical components to illustrate the different phase distributions that are provided by the method. In the

⎛ Ψ fs(z) + Ψ fs(L − z) ⎞ ⎟ fff (z) = fbulk exp⎜ − kT ⎝ ⎠

(1)

where f ff(z) is the fugacity of the adsorbate due to fluid−fluid interactions in the slit, f bulk is the fugacity of bulk fluid, and Ψfs is the fluid−solid potential function. In eq 1, f ff(z) denotes that the fluid fugacity is dependent on the position of the adsorbate molecule in the slit. Further, Ψfs(z) and Ψfs(L − z) denote the 3471


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fluid−solid interactions from the two walls of the slit, since the adsorbing fluid has interactions with both walls of the adsorbent slit, where L is the slit length. The fluid−solid potential, Ψfs(z), in eq 1 is given by Lee’s partially integrated 10-4 potential model,28 which is a truncated form of the Steele’s 10-4-3 potential,29 fs

Ψ (z ) =

fs Ψ disp (z )

=

⎛ σ 10 1 × ⎜⎜ fs 10 − 2 ⎝ 5(z′) εfs =

Using the PR EOS, the fugacity of bulk gas or liquid was calculated as follows: ln

4πρatoms εfsσfs2 4

∑ i=1

⎞ ⎟⎟ (z′ + (i − 1) ·σss)4 ⎠

(3)

ln

CO2

water

304.13 7.377 0.3941 195.2

647.09 22.065 0.2641 809.1

(5)

(6)

The temperature-dependence function, α(T), in eq 5 was calculated as follows: α(T ) = exp((A + BTr)(1 −

⎡ 1 + (1 + aads(z) ln⎢ 2 2 bRT ⎣ 1 + (1 −

2 )ρ (z )b ⎤ ⎥ 2 )ρ (z )b ⎦

(9)

(10)

where Λb is a regressible parameter. Thus, the modified covolume term, bads, was used where “b” appears in eq 9. The values of Λb range typically from −0.4 to 0.0 for adsorption on wet coals, as observed in our previous work.22,34 The value is expected to be dependent to some extent on the amount of moisture on the coal and the adsorbate. This is reasonable because the adsorbed-phase density of wet adsorbents can be expected to be higher than that of dry coals and different fluids may exist at different densities in the adsorbed phase. Using the slit geometry and the density profile obtained by solving eq 1, the excess adsorption of a gas can be obtained by integrating the following equation:

where

2 TrC + Dω + Eω ))

aads(z)ρ(z) bρ(z) − P 1 − bρ(z) RT (1 + 2bρ(z) − b2ρ2 (z)) ⎡ P Pb ⎤ − ln⎢ − ⎥ ⎣ RTρ(z) RT ⎦ =

bads = b(1 + Λb)

(4)

0.077796RTC PC

2 )ρ b ⎤ ⎥ 2 )ρ b ⎦

The assumptions used in developing eq 9 have been discussed elsewhere.25,26 Further, the density profile obtained by using eq 9 in eq 1 have also been presented in an earlier work.21 Equation 9 includes two key modifications in comparison to eq 8. First, the attractive parameter, aads(z), is dependent on the position of the slit. The detailed expressions were developed by Chen et al.,26 which show that aads(z) depends on the ratio of slit length L to the molecular diameter σff. Second, the covolume term, b, has been modified empirically to improve the description of repulsive interactions at higher pressures. The covolume term has been modified as21

An equation of state is necessary in the SLD model to calculate properties of the different fluid phases. In this work, the Peng−Robinson equation of state (PR EOS) was used to calculate phase densities and fugacities for all three phases (bulk gas, bulk liquid, and adsorbed fluid). The PR EOS32 is given as P 1 = ρRT (1 − ρb) a(T )ρ − RT[1 + (1 − 2 )ρb][1 + (1 + 2 )ρb]

b=

fff (z)

−

Table 1. Physical Properties of CO2 and Water31,45

0.457535α(T )R2TC2 PC

=

where ρ is the phase density and a(T) and b are given by eqs 5 and 6, respectively. The fugacity of the adsorbed fluid is calculated with an expression analogous to eq 8 as

(2)

where εff, εss, and εfs are the fluid−fluid, solid−solid, and fluid− solid interaction energy parameters, respectively. Further, 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,30 and the values of σff and εff were taken from Reid et al.31 Table 1 lists the values of these parameters.

a(T ) =

a(T )ρ bρ − 1 − bρ RT (1 + 2bρ − b2ρ2 ) ⎡ 1 + (1 + ⎡ P a(T ) Pb ⎤ − ln⎢ − ln⎢ ⎥− ⎣ RTρ RT ⎦ 2 2 bRT ⎣ 1 + (1 − P

(8)

σfs4

εff × εss

TC (K) PC (MPa) σff (nm) εff/k (K)

fbulk

n Ex =

(7)

A 2

Right Side of Slit

∫Left Side of Slit

(ρ(z) − ρbulk )dz

(11)

where A is the accessible surface area of the gas on the adsorbent. The lower and upper limits in eq 11 were 3/8σff and L − 3/8σff, respectively. Detailed explanation has been provided elsewhere.35 For performing the numerical integration in eq 11, half of the slit is divided into 50 segments and eq 1 is used to obtain the “local” density at each of these 50 segments in the slit. Note that eq 11 was applied for component CO2 adsorption in CO2/water mixtures. For component water adsorption, the surface area “A” in eq 11 was partitioned into two contributions

where A, B, C, D, and E have values of 2.0, 0.8145, 0.134, 0.508, and −0.0467, respectively. Equation 7 was developed in an earlier work, where it was found capable of precise representations of saturated vapor pressures of several classes of compounds.33 Further, the values for A−E listed above are based on accurate description of saturation properties of coalbed gases under phase conditions relevant to CBM reservoirs. The physical properties for CO2 and water used in this work are listed in Table 1. 3472


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(Ap and As) to account for the bimodal nature of water adsorption, as explained in the next section.

In the SLD model, the hydrogen bond potential was modeled as a mean-field potential term in the slit and functional sites were not modeled explicitly, as was the case in the original GCMC simulations of Muller et al.7 This simplification allows for simpler and faster integration of the total potential across the slit (i.e., over the lateral solid structure as indicated by eq 12) in our analytical model compared to the GCMC calculations. Further, to limit the number of regressed parameters, a fixed value of 90 K was used for εHB/k of water adsorption based on our earlier work.8 Dipole Interactions of Water. Kotdawala et al.27 used the mean-field perturbation theory to investigate the adsorption of polar molecules in nanopores. The authors considered the electrostatic interactions of water molecules, which included the permanent dipole−dipole, dipole−induced dipole, and induced dipole−induced dipole interactions. These electrostatic interactions are also dependent on the pore density of water molecules.27 Following their approach, three dipole interaction terms were added to the fluid−solid potential function in the SLD model to account for the polar nature of water molecules in the adsorbed phase. The dipole interaction terms can be written as

3. MODIFICATIONS TO SLD MODEL FOR WATER ADSORPTION In a recent work, we presented modifications to the SLD model to extend it to the case of water adsorption on carbons and coals.8 For completeness, we discuss in this section the essential details of these modifications to accommodate the special nature of water adsorption on coals. 3.1. Molecular Interactions of Adsorbed Water. The molecular interactions of adsorbed water in carbonaceous adsorbents are believed to be quite distinct from those of nonpolar adsorbates such as nitrogen and methane.6,7 The two types of molecular interactions that play a significant role in water adsorption on activated carbons and coals are (1) the hydrogen bonds formed between the adsorbed water molecules and the oxygenated groups on the adsorbent surface and (2) the electrostatic interactions between adsorbed water molecules (water−water interactions) due to the large dipole moment of water. For nonpolar adsorbates, the fluid−solid potential function, Ψfsdisp(z), in the SLD model is estimated usually from the 10-4 Lee’s potential,28 as evident from eq 2. However, this potential accounts solely for the dispersive interactions, which are the significant interactions for nonpolar adsorbates. Since the contributions of the electrostatic and polar interactions are significant in water adsorption, Lee’s potential was augmented in a recent work8 with terms for (a) the hydrogen-bond energy6 and (b) the dipole interactions27 within water molecules as follows:

⎤ ⎡2 2μ2 α′ μ4 3 2 ⎥ ( ) I + + α ′ ξ = −⎢ 4πε0 4 ⎦ ⎣ 3 (4πε0)2 kT

where the three terms correspond to dipole−dipole, dipole− induced dipole, and induced dipole−induced dipole attractive potentials, respectively. The physical constants used in eq 14 are defined as36 μ= dipole moment of water, C·m α′ = α/4πε0 = polarizability volume of water, m3 I = ionization potential of water, J ε0 = permittivity of free space, C2/J·m k = Boltzmann’s constant, J/K The values of these physical constants were adopted from Tester et al.36 and Prausnitz et al.37 Using these dipole interaction terms, Kotdawala et al.27 developed the following expression for the polar interactions of water with the carbon surface:

fs Ψ fsWater(z) = Ψ disp (z) + ΦHB + ΦDipole(z)

⎛ σ 10 = 4πρatoms εfsσfs2⎜⎜ fs 10 ⎝ 5(z′) 4 ⎞ σfs4 1 ⎟ + ΦHB − ∑ 2 i = 1 (z′ + (i − 1)σss)4 ⎟⎠ + ΦDipole(z)

ΦDipole(z) =

(12)

where ΦHB is the hydrogen-bond potential between the functional groups on the carbon surface and water molecules and ΦDipole refers to the sum of three types of electrostatic contributions resulting from the dipole moment of water. Thus, eq 12 has two additional terms for water adsorption, which are explained below. Hydrogen Bond Potential. The hydrogen bond potential for water was adopted from the Grand Canonical Monte Carlo (GCMC) simulation work of Muller et al.7 The authors modeled the water molecule as a Lennard-Jones sphere with four sites arranged in a tetrahedral geometry. Further, they modeled the oxygenated functional sites on the carbon surface as hydroxyl groups. An off-center square-well potential was used by Muller et al.7 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 = −εHB ΦHB = 0

+

⎡ −3σ 8πNξ ff ×⎢ + 2(L − 2σfs) − 2σfs) ⎣ 2

3σff3(L

⎤ ⎥ ρ (z ) 4(L − 2σfs)2 ⎦ σff3

(15)

where ρ(z) is the pore density (calculated from the SLD model in this work), N is Avogadro’s number, and ξ is given by eq 14. In this manner, eq 15 was used in this 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 augmented potential function for water adsorption that has been discussed above, the excess adsorption in the SLD model given by eq 11 was modified to account for the bimodal nature of water adsorption. Several authors6,38−40 have observed that water adsorption on carbonaceous adsorbents is bimodal. Specifically, the primary adsorption of water first occurs at oxygenated/polar surface sites on the carbon (or coal), and then, secondary adsorption of water occurs on the three-dimensional clusters formed by water molecules.6,7 To account for this dual mechanism of water

if rAB < σHB

otherwise

(14)

(13) 3473


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where εfs,i and εff,i are respectively the fluid−solid and fluid− fluid interaction energy parameters of component i. Note that eq 18 is used for gas adsorbates (such as CO2) whereas eq 12 is used for water adsorption as the fluid−solid potential function. The excess adsorption of each component in a mixture is given as

adsorption, the excess isotherm equation for water in the SLD model was modified as ⎛ Ap A ⎞ Gibbs nWater =⎜ + s⎟ 2⎠ ⎝ 2

Right Side of Slit

∫Left Side of Slit

(ρ(z) − ρbulk ) dz (16)

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. Thus, the total surface area “A” (in eq 11) was partitioned into two contributions for describing water adsorption (Ap and As). Note that the same density profile ρ(z) was used for both Ap and As, as indicated by eq 16. This simplification was necessary for the coals studied in this work, as explained below. The two surface areas for water adsorption (Ap and As) are estimated ideally from pure-water adsorption isotherm data. Reasonable (but approximate) techniques for estimating the primary and secondary adsorption of water from pure-water isotherm data have been presented in the literature.41,42 However, for the coals studied in this work, the pure-water adsorption isotherm data at low-pressures were unavailable at the time of this writing. As a result, the two surface areas for water were calculated based on the CO2/water mixture adsorption isotherms on each coal. Further, reasonable initial values for Ap and As were obtained based on the inherent moisture levels and the model-derived pore volumes of the coals used in this study. This calculation method may be improved when appropriate data on these coals become available. The above modifications formed the essential elements of modeling water adsorption through the SLD theoretical framework. Additional details on these modifications are also available in one of our earlier works,8 which also includes a discussion of the new approach formulated for modeling the competitive adsorption of CO2/water mixtures on wet coals. These aspects are not repeated here for brevity.

zi =

a=

b=

i=1

⎞ ⎟ (z′ + (i − 1)σss) ⎠ 4⎟

εff, iεss

i = 1, NC (21)

∑ ∑ xixj(aads)ij (22)

j

∑ ∑ xixj(bads)ij (23)

j

In eq 22, (aads)ij was given as (aads)ij =

(aads)i (aads)j (1 − Cij)

(24)

where Cij is a binary interaction parameter (BIP). Similar expressions were used for the bulk-phase, where the BIPs were optimized in a recent work based on the vapor−liquid equilibrium of gas/water mixtures.43

5. SLD MODELING AND MULTIPHASE ANALYSIS FOR CO2/WATER MIXTURE ADSORPTION ON WET COALS 5.1. Model Parameterization. The SLD model discussed above typically includes the following parameters: surface area of each adsorbate (Ai), slit length (L) and interaction energy parameters (such as εss/k and εHB/k). Using the approach presented recently for describing the competitive adsorption of CO2/water mixtures on coals,8 the SLD parameters regressed in this work were surface area for CO2 (ACO2), primary and secondary surface areas for water (Ap and As), slit length (L),

i = 1, NC (18)

εfs, i =

Ex ntot + ρbulk Vvoid

i

fs, i Ψ disp (z) = 4πρatoms (εfs)i (σfs2)i

σfs,4 i

(20)

niEx + ρbulk Vvoidyi

i

where NC is the number of components. In this manner, eq 17 is written for each component in the mixture. The fluid−solid potential function for an adsorbate in a gas mixture can be written as

4

(ρads ⃗ (z)xi(z) − ρbulk yi ) dz

where zi and yi are the feed and gas-phase molar fractions of Ex component i, respectively. Further, nEx and ntot are the i component and total excess adsorptions, and Vvoid is the specific void volume. Note that a constraint on the summation of yi is also included, and the resulting equations given by eq 21 are solved simultaneously. PR EOS was used for performing mixture adsorption calculations. For brevity, the detailed expressions for the mixture equation of state are not repeated here, since they have been summarized elsewhere.8,23 We only note here that the one-fluid mixing rules were used in the EOS for both the bulk and adsorbed phases. For example, the mixing rules for the EOS constants in the adsorbed phase are given as

(17)

∑

ff, i

where Ai = ACO2 for CO2 and Ai = (Ap + As)/2 for water component adsorptions, respectively. The input information required for mixture adsorption calculations includes the pressure, temperature, feed molar fractions, and specific molar volume. An adsorption flash calculation is performed using this information. The flash calculation is an analog of vapor−liquid flash calculations and includes the material balance as follows:

⎛ ̂ads ⎞ ⎛ Ψ fs(z) + Ψ fs(L − z) ⎞ f [x (⃗ z), ρads (z)] ⎟ i ⎟⎟ = −⎜⎜ i ln⎜ i bulk ⎜ ⎟ kT ̂ ⎝ ⎠ f ⎝ ⎠ i

⎛ (σ 10) 1 × ⎜⎜ fs 10i − 2 ′ 5( z ) ⎝

L − 3/8σff, i

∫3/8σ

i = 1, NC

4. SLD MODEL FOR MIXTURE ADSORPTION The SLD model for mixture adsorption is an extension of the pure-gas adsorption model outlined above. Modeling of mixture adsorption requires simultaneous description of equilibrium between each gas adsorbate and the adsorbent. The equilibrium relation for mixture adsorption is the multicomponent analog of eq 1 and is given as

i = 1, NC

Ai 2

niEx =

(19) 3474


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for the presence of water in as many as three phases has also been presented.8 It is this new data reduction method that has been used in the current work to conduct model regressions for the four coals. Table 3 presents the SLD model parameters and statistics for the four coals used in the analysis. The model parameters in Table 3 are slightly different than those reported previously,8 since the equation of state used in the current work was optimized to predict accurately the vapor−liquid equilibrium of gas/water mixtures.43 Nonetheless, the model parameters and statistics reported in Table 3 are quite comparable to those reported earlier.8 Overall, the adsorption data on the four coals were represented with a weighted average absolute deviation (WAAD) of 0.5 and 1.0 for CO2 and water, respectively, where the weights are the expected experimental uncertainty. Thus, the model represented the data within the experimental uncertainties, since a WAAD of 1.0 corresponds to one standard deviation in the measurements. 5.3. Multiphase Adsorption Equilibrium Algorithm. Conventional adsorption calculations for gas mixtures consider the equilibrium between a single bulk (gas) phase and an adsorbed phase, and the existence of additional phases is generally not considered. However, for the systems considered in this work, more than one bulk phase may coexist with an adsorbed phase at equilibrium. As mentioned earlier, when a high-pressure gas such as CO2 is injected in a coal system, the water present on coals may form a third, water-rich liquid phase. This is possible due to the possible displacement of preadsorbed water by the supercritical CO2. To investigate this possibility, a new multiphase algorithm was devised and implemented within the SLD framework and tested with the CO2/water mixture adsorption isotherms on the four coals listed in Table 3. The required specifications for the multiphase algorithm are the temperature, pressure, total volume of the system, and the number of moles of each component in the feed. Using these specifications, a two-phase calculation (gas and adsorbed phases) is first conducted that corresponds to either a local or a constrained minimum, since the number of phases is fixed at two. Then, a third, water-rich, bulk liquid phase (Vliq) is inserted formally in the system, and a three-phase flash calculation is conducted that satisfies the overall material and volume constraints. The Gibbs energy of the system is calculated at each step of the algorithm based on the distribution of phases obtained at that step. The phaseinsertion continues until a minimum in the Gibbs energy is located, which yields the stable distribution of the phases (and of each component) at equilibrium. Thus, the overall scheme corresponds to a phase-stability analysis for these systems. In the following paragraphs, we present the essential details of the algorithm that were used in combination with the simplified local-density/Peng−Robinson adsorption model described in sections 2−4. For a given temperature, pressure, and number of moles of each component in the feed, the number of stable phases that coexist at equilibrium can be obtained by minimizing the Gibbs energy of the system. The Gibbs energy, G, is given as

and a binary interaction parameter (Cij) in the adsorbed phase (eq 24). Further, the slit length (L) was considered as a linear function of bulk pressure (L = A + BP), where A and B are the intercept and slope, respectively. To reduce the number of regressed parameters, εss/k and εHB/k were fixed at 30 and 90 K, respectively, since these were found to be reasonable values for the coals studied in this work. In summary, five to six parameters were regressed for CO2/water binary mixture adsorption on each coal. Thus, the number of parameters regressed in this work was comparable to that utilized for conventional binary mixture adsorption such as methane/ nitrogen, etc.22 The modeling results for the CO2/water mixture adsorption are analyzed in terms of the weighted average absolute deviation (WAAD) in excess adsorption, where the weights σexp were the expected experimental uncertainties in adsorption measurements. The WAAD is given as

WAAD =

⎛ n exp − n cal ⎞ NPTS ∑i = 1 abs⎜ i σ i ⎟ ⎝ exp ⎠

(25) NPTS where and are the experimental and calculated excess adsorption for each component and NPTS is the number of data points. 5.2. SLD Modeling Results. The first stage in conducting the multiphase analysis was to obtain model parameters from a mixture adsorption calculation, wherein the competitive adsorption of CO2 and water is considered. For this purpose, the data for CO2 adsorption on four wet coal samples originating from the Argonne premium coal sample program44 were used in the analysis. Table 2 presents the ultimate and

nexp i

ncal i

Table 2. Compositional Analyses of Coals analysis

a

Beulah Zap lignite

Wyodak subbituminous

vitrinite 0.25 reflectance (%) Ultimate (Dry, Ash-Free Basis) carbon % 72.9 hydrogen % 4.8 oxygen % 20.3 sulfur % 0.8 Proximate (As-Received Basis) vol. matter % 30.5 fixed carbon % 30.7 moisture % 32.2 ash % 6.6 a

0.32

Upper Freeport medium-volatile bituminous

Pocahontas low-volatile bituminous

1.16

1.68

75.0 5.4 18 0.6

85.5 4.7 7.5 2.3

91.1 4.4 2.5 0.7

32.2 33.0 28.1 6.3

27.1 58.7 1.1 13.0

18.5 76.1 0.7 4.7

Argonne National Laboratory.

proximate analyses of these coals. The four coals were wet Beulah Zap, Wyodak, Upper Freeport, and Pocahontas coals. The coals vary widely in rank and cover the range of interest for coalbed methane work. Further, the equilibrium moisture content of these coals varies from about 1% to 32% providing a wide range of moisture contents over which the multiphase algorithm can be tested. The adsorption isotherms for these coals were measured at their reported inherent moisture levels,44 at a temperature of 328 K and pressures to 13 MPa. The experimental data for these coals were presented in an earlier work,34 and a new data reduction method for gas adsorption on wet coals that accounts

n

G=

m

n

∑ (Fzj)Gj0+RT ∑ ∑ Nij ln fiĵ j

i

j

(26)

where Nij and fiĵ are the number of moles and fugacity of the jth component in ith phase, respectively, zj is the feed molar 3475


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

WAADb

slit length

coal

CO2 surface area (m2/g)

Ap (m2/g)

As (m2/g)a

Cij

Wyodak Beulah Zap Upper Freeport Pocahontas Overall

131.4 77.6 86.7 91.0

219.5 197.0 88.7 50.3

560 890

−0.308 −0.375 −0.111 −0.160

slope (nm/psia) 2.7 2.5 1.4 9.9

× × × ×

10−4 10−4 10−4 10−5

intercept (nm)

CO2

water

1.03 0.96 0.89 0.90

0.40 0.27 0.57 0.88 0.5

0.77 0.68 1.02 1.66 1.0

a

As (secondary surface area for water) was regressed only for high-moisture coals and was set to zero for low-moisture coals. bWAAD is the weighted average absolute deviation.

adsorption equilibrium comprised of three fluid phases can be written as

fraction of component j, and G0j is the standard state Gibbs energy. Equation 26 is subject to the following mass balance constraints:

fluid Vtotal = Vads + Vgas + Vliq

where Vads, Vgas, Vliq, and are the adsorbed, gas, liquid, and total-fluid volumes, respectively. Figure 1 presents an idealized schematic of a multiphase adsorption system (or the coexisting fluid phases) and depicts the volume terms in eq 32. The figure also illustrates graphically the phase-insertion scheme implemented in this work. The algorithm can briefly be summarized as follows: 1. Initialize the calculations with a two-phase calculation as highlighted in section 5.2. Calculate the Gibbs energy of the system (ΔG) for this initial phase distribution. 2. Formally insert a third, water-rich bulk phase into the system (by displacing a portion of the water from the adsorbed phase). Update the material and volume balances so that the total amounts of components in the overall system are unchanged. Conduct a three-phase flash calculation for the adsorbed, bulk gas, and liquid phases. When the component fugacities are equal in all three phases, calculate ΔG. 3. If the ΔG in step 2 is less than that in step 1 (or the ΔG from the previous phase-insertion step), insert an additional amount of material into the third-phase and conduct a three-phase flash calculation. Calculate ΔG for this phase distribution. 4. The calculations in step 3 are repeated until ΔG begins to increase. The lowest Gibbs energy found for each pressure and temperature yields the equilibrium phase distribution for that datum of the adsorption isotherm. 5. Repeat steps 1−4 for each datum of a given adsorption isotherm. Our analysis showed that the initial two-phase calculation was a reasonable starting guess for the multiphase analysis, since these initial estimates also included the competitive adsorption behavior of CO2/water adsorbed mixtures.8 In fact, depending on the actual number of phases that exist at equilibrium, the initial guess represented either a local or a constrained minimum for each system. Thus, the multiphase algorithm was provided with an appropriate initial guess in nearly all cases considered in the current work. Further, once a minimum in Gibbs energy was located, stability of that solution was checked to ensure that the minimum found was not a local (or a false) minimum. The phase-insertion scheme can be explained in the following way: As mentioned previously, the calculations are initialized with a two-phase, constrained solution that considers the competitive adsorption of CO2/water mixtures. Thus, all

m

∑ Nxi ij − Fzij = 0 for j = 1, n

(27)

i n

n

∑ xj = ∑ zj = 1.0 j

(28)

j

where F is the total number of moles in the feed, and i and j represent the number of phases and the number of components, respectively. For an adsorption calculation involving gas/water mixtures, expanding and rearranging eq 26 yields gas ads ΔG = RT ∑ Vadsρads xjads ln f ĵ + Vgasρgas yjgas ln f ĵ j liq + Vliqρliq xjliq ln f ĵ

(29)

where V and ρ represent the volume and density of the phases gas liq denoted by the respective subscripts and xads j , yj , and xj are th the phase compositions of j component in the adsorbed, gas phase, and liquid phase, respectively. The Gibbs energy, ΔG, is evaluated from eq 29 at each step of the algorithm. A step of the algorithm denotes a given phaseinsertion/three-phase flash calculation, wherein the component fugacities in each of the coexisting phases are equal (within a specified tolerance) as fi ̂

ads

gas liq = fi ̂ = fi ̂

i = 1, NC

(30)

The bulk phase fugacities in eq 30 are calculated with the Peng−Robinson EOS and the adsorbed phase fugacities are obtained through the SLD adsorption model, as discussed in section 4. To conduct three-phase calculations, an extended material balance equation was formulated based on eq 21 as zi =

niEx + ρgas Vvoidyi + ρliq Vliqxi Ex ntot + ρgas Vvoid + ρliq Vliq

(32)

Vfluid total

i = 1, NC (31)

where zi, yi, and xi are the feed, gas phase and liquid phase molar fractions of component i, respectively. In addition to the material balance constraints, a volume balance is also required for the overall system such that the total volume of the system remains constant. A volume balance for 3476


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occurred (roughly) near the corresponding maxima in excess adsorption of CO2 on both coals. At these near-critical pressures, the water content in the bulk liquid phase ranged from 6 to 12% of the amount of water in the adsorbed phase for the two coals. Further, the water content of the liquid phase was much lower at pressures below 4 MPa, as shown in Figure 2. The wet Wyodak and Beulah Zap coals have about 28% and 32% inherent moisture, respectively, and can be regarded as high-moisture containing coals. In contrast, for wet Upper Freeport and Pocahontas coals, the algorithm did not predict the presence of a water-rich, third phase, and only two phases (gas and adsorbed) existed at equilibrium for these two coals. The wet Upper Freeport and Pocahontas coals contain only about 1.1% and 0.65% inherent moisture and can be regarded as low-moisture containing coals. Since these two coals contain very little moisture on the coal surface, the predictions of the multiphase analysis showing the absence of a water-rich, liquid phase appear to be reasonable. Accounting for the existence of a third-phase for the two high-moisture coals resulted in lowering the predicted excess adsorption of water and increasing the excess adsorption of CO2 for these coals. Figures 3 and 4 illustrate the predictions

the water present in the system is initially either in the adsorbed or the gas phase. Then, a portion of water (typically 0.1−1% of the amount of water present in coal) is moved from the adsorbed phase to a trial, water-rich liquid phase. This is followed by a three-phase flash calculation, and the total Gibbs energy of the system is calculated at equilibrium. The above steps are repeated by inserting incremental amounts of water from the adsorbed to the water-rich phase until a minimum in the total Gibbs energy is located, which provides the stable distribution of these phases. During the entire process of phaseinsertion, the total material and volume balances for the system are constrained to be constant. In summary, the phase-insertion scheme corresponds to redistributing water among three possible phases without altering the total amount of water in the system. Thus, the overall molar feed at a given temperature and pressure remains constant during the calculations, but the material is redistributed among three possible phases until a minimum in total Gibbs energy is found. In fact, this is also the standard method/scheme for performing phase-insertion for traditional multiphase problems, and it has been utilized in this work. 5.4. Multiphase Analysis of Coals: Results and Discussion. A Gibbs energy-driven multiphase analysis was conducted for four coals with the parameters listed in Table 3. A fixed step size was used to insert a third phase and the calculations were repeated sequentially. In each case, the total Gibbs energy was evaluated and the phase distribution at the lowest Gibbs energy was retained. Thus, the multiphase algorithm predicted the CO2 and water excess adsorption isotherms for the four coals and also provided estimates of the amount of third-phase present (if any) as a function of pressure for the four coals. Results indicate that wet Wyodak and Beulah Zap coals contain a third (water-rich) phase that becomes progressively larger with increase in bulk pressure, attaining a maximum between 8 to 12 MPa and then decreased slightly. Figure 2

Figure 3. Multiphase predictions for CO2/water mixture adsorption on wet Wyodak coal at 328.2 K.

obtained with the multiphase analysis algorithm for the wet Wyodak and Beulah Zap coals, respectively. The predictions are

Figure 2. Comparison of water content of the adsorbed and bulk liquid phases in CO2/water mixture adsorption on wet Wyodak and Beulah Zap coals at 328.2 K.

compares the amount of water in the bulk liquid and adsorbed phases predicted by the algorithm for the two coals. As shown in the figure, the algorithm predicted a standing-water phase at each pressure for these coals. The maximum amount of the standing-water phase for wet Wyodak and Beulah Zap coals was predicted at pressures beyond the critical pressure of CO2 and

Figure 4. Multiphase predictions for CO2/water mixture adsorption on wet Beulah Zap coal at 328.2 K. 3477


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compared with experimental data obtained utilizing the data reduction method for competitive adsorption calculations that has been presented earlier.8 As shown in Figure 3, the amount of CO2 adsorbed on Wyodak coal was greater at the higher pressures and less water was in the adsorbed phase than obtained originally by using only a two-phase assumption. Evidently, the existence of a third phase becomes crucial only at the higher pressures of the isotherm, where the predicted amounts of adsorbed gas and water are outside the expected experimental uncertainties. Figure 4 illustrates the multiphase predictions for wet Beulah Zap coal. The amount of water in the adsorbed phase was again less for this coal than obtained originally by assuming a two-phase solution to the problem. Although the adsorption isotherms on these coals were measured at their reported equilibrium (or inherent) moisture levels, the existence of a third phase in a CO2/water adsorbed mixture could be due to the partial “stripping” of adsorbed water by the supercritical CO2 gas. It appears plausible that the CO2 adsorbing gas would compete with preadsorbed water on the coal and alter the thermodynamic equilibrium between coal and water. Thus, the injection of high-pressure CO2 may cause partial displacement of water from the adsorbed phase and the development of a water-rich, liquid phase. In other words, the third phase formed is the result of displacement of some of the adsorbed water from the coal surface by CO2. For highmoisture coals such as Beulah Zap and Wyodak coals, the adsorbed water displaced is greater than the solubility limit of the gas phase for water vapor, thus resulting in the formation of a water-rich, liquid phase. In this manner, a physical description of third-phase formation may be provided. Further, in all calculations, it is the minimum in total Gibbs energy that provides the stable phase distribution and the amounts of any “standing-water” phase, if any. This is true because the equality of fugacities of each component in each phase (from the multiphase flash calculations) is only a necessary, but not a sufficient, condition for thermodynamic equilibrium. The multiphase calculations with wet Upper Freeport and Pocahontas coal showed that the formation of third phase was not favorable energetically. Figures 5 and 6 present the adsorption isotherm predictions for wet Upper Freeport and Pocahontas coals, respectively. The predictions were essentially identical to the two-phase assumption since the multiphase analysis showed the absence of a significant amount of third-

Figure 6. Multiphase predictions for CO2/water mixture adsorption on wet Pocahontas coal at 328.2 K.

phase. Thus, the two-phase solution (gas and adsorbed) was the stable solution predicted for these two coals. To highlight the effect that the number of stable phases present at equilibrium could have on adsorption isotherm predictions, Figure 7 presents model predictions for the excess

Figure 7. Comparison of predictions from the two- and three-phase models for CO2/water mixture adsorption on wet Wyodak coal at 328.2 K.

adsorption of CO2 and water on wet Wyodak coal. The figure shows model predictions based on a two-phase assumption as well as the predictions obtained by conducting a multiphase analysis and minimizing the total Gibbs energy. As shown in the figure, there would be a significant difference between the isotherms if one were to ignore the presence of a third phase, especially at the higher pressures of this isotherm. In summary, the multiphase analysis presented in this work has shown the presence of a third phase for coals that contain large amounts of moisture on the surface. This was especially true at higher pressures of the isotherm for these coals, where the algorithm predicted adsorption amounts quite different from those obtained with using only a two-phase assumption. Unlike the predictions for high-moisture coals, the algorithm did not predict the formation of a water-rich phase for lowmoisture coals and only two phases (as is usually assumed) existed for the low-moisture coals. At present, most commercial CBM simulators use simpler models such as the well-known Langmuir model for predicting

Figure 5. Multiphase predictions for CO2/water mixture adsorption on wet Upper Freeport coal at 328.2 K. 3478


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(4) Goodman, A. L.; Busch, A.; Bustin, R. M.; Chikatamarla, L.; Day, S.; Duffy, G. J.; Fitzgerald, J. E.; Gasem, K. A. M.; Gensterblum, Y.; Hartman, C.; Jing, C.; Krooss, B. M.; Mohammed, S.; Pratt, T.; Robinson, R. L., Jr.; Romanov, V.; Sakurovs, R.; Schroeder, K.; White, C. M. Interlaboratory comparison II: CO2 isotherms measured on moisture-equilibrated Argonne premium coals at 55 °C and up to 15 MPa. Int. J. Coal Geol. 2007, 72 (3−4), 153−164. (5) 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, 2005−2007; Prepared for Advanced Resources International: 2008. (6) 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. (7) Muller, E. A.; Hung, F. R.; Gubbins, K. E. Adsorption of water vapor−methane mixtures on activated carbons. Langmuir 2000, 16 (12), 5418−5424. (8) Mohammad, S. A.; Gasem, K. A. M. Modeling the competitive adsorption of CO2 and water at high pressures on wet coals. Energy Fuels 2012, 26 (1), 557−568. (9) Soares, M. E.; Medina, A. G.; McDermott, C.; Ashton, N. Three phase flash calculations using free energy minimization. Chem. Eng. Sci. 1982, 37 (4), 521−528. (10) Wu, J. S.; Bishnoi, P. R. An algorithm for three-phase equilibrium calculations. Comput. Chem. Eng. 1986, 10 (3), 269−276. (11) Nghiem, L. X.; Li, Y.-K. Computation of multiphase equilibrium phenomena with an equation of state. Fluid Phase Equilib. 1984, 17 (1), 77−95. (12) Nelson, P. A. Rapid phase determination in multiple-phase flash calculations. Comput. Chem. Eng. 1987, 11 (6), 581−591. (13) Bünz, A. P.; Dohrn, R.; Prausnitz, J. M. Three-phase flash calculations for multicomponent systems. Comput. Chem. Eng. 1991, 15 (1), 47−51. (14) Baker, L. E.; Pierce, A. C.; Luks, K. D. Gibbs energy analysis of phase equilibria. SPE J. 1982, 42 (5), 731−742. (15) Michelsen, M. L. The isothermal flash problem. Part I. Stability. Fluid Phase Equilib. 1982, 9 (1), 1−19. (16) Cairns, B. P.; Furzer, I. A. Multicomponent three-phase azeotropic distillation. 2. Phase-stability and phase-splitting algorithms. Ind. Eng. Chem. Res. 1990, 29 (7), 1364−1382. (17) Sofyan, Y.; Ghajar, A. J.; Gasem, K. A. M. Multiphase equilibrium calculations using gibbs minimization techniques. Ind. Eng. Chem. Res. 2003, 42 (16), 3786−3801. (18) McDonald, C. M.; Floudas, C. A. GLOPEQ: A new computational tool for the phase and chemical equilibrium problem. Comput. Chem. Eng. 1996, 21 (1), 1−23. (19) Nichita, D. V.; Gomez, S.; Luna, E. Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method. Comput. Chem. Eng. 2002, 26 (12), 1703−1724. (20) Cabral, V. F.; Castier, M.; Tavares, F. W. Thermodynamic equilibrium in systems with multiple adsorbed and bulk phases. Chem. Eng. Sci. 2005, 60 (6), 1773−1782. (21) 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. (22) 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. (23) Mohammad, S. A.; Chen, J. S.; Robinson, R. L.; Gasem, K. A. M. Generalized simplified local-density/peng-robinson model for adsorption of pure and mixed gases on coals. Energy Fuels 2009, 23 (12), 6259−6271. (24) Mohammad, S. A.; Arumugam, A.; Robinson, R. L.; Gasem, K. A. M. High-pressure adsorption of pure gases on coals and activated carbon: measurements and modeling. Energy Fuels 2012, 26 (1), 536− 548.

adsorption behavior of coalbed gases. However, the simpler models may not be reliable for adsorption predictions for wet systems and the investigation of the effects of water on gas adsorption behavior is beyond the scope of simpler models such as the Langmuir model and its variants. This work focused on developing a more rigorous approach to understand and investigate gas adsorption behavior on moist/wet coals. The complexity of the multiphase algorithm may hinder its direct application in a CBM simulator. However, this does not diminish the usefulness of the analysis presented in this work. Our aim is to utilize the reliable predictions from the multiphase analysis to “recalibrate” existing CBM adsorption models. In this manner, the multiphase analysis can provide improved estimates of gas adsorption capacity on wet coals and would be helpful in improving the parameters of the conventional CBM models, thus enhancing their accuracy, which has been deficient for wet coals. Notwithstanding the results presented here, additional work will be required to further delineate the effects of water present in coals on the high-pressure gas adsorption behavior. In the current work, the focus was on CO2 adsorption on wet coals. A similar scheme may be implemented for other coalbed gases such as methane, nitrogen, etc. Additional development and refinement of the multiphase algorithm reported in this work is underway currently at Oklahoma State University.

6. CONCLUSIONS A multiphase adsorption equilibrium algorithm was developed to conduct Gibbs energy-driven phase-stability analysis for mixture adsorption of CO2 and water on wet coals. The algorithm utilized a phase-insertion technique to test for the stability of the phases existing in high-pressure gas adsorption systems containing water. Results indicated the presence of a third (water-rich) phase for coals that contained large amounts of moisture on the surface. The presence of a third phase could have a significant effect on gas adsorption capacity at higher pressures for large moisture-containing coals. For the lowmoisture coals, third-phase formation was not predicted and the usual two-phase assumption appeared to be appropriate for those coals.

■

AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We gratefully acknowledge the financial support received from the U.S. Department of Energy and the Coal-Seq Consortium.

■

REFERENCES

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