Methane and Carbon Dioxide Adsorption on Illite - ACS Publications

Nov 8, 2016 - *E-mail: [email protected]. Cite this:Energy ... Yi Pan , Dong Hui , Pingya Luo , Yan Zhang , Lei Sun , and Ke Wang. Energy & Fuels...
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Methane and Carbon Dioxide Adsorption on Illite Junfang Zhang,*,† Michael B. Clennell,† Keyu Liu,†,‡ Marina Pervukhina,† Guohui Chen,†,‡ and David N. Dewhurst† †

CSIRO Energy, 26 Dick Perry Avenue, Kensington, Western Australia 6151, Australia School of Geosciences, China University of Petroleum, Qingdao, Shandong 266580, China

‡

S Supporting Information *

ABSTRACT: The adsorption of CH4 and CO2 onto illitic clay was investigated at the temperatures 298, 313, 328, 358, and 423 K (25, 40, 55, 85, and 150 °C) over a range of pressures up to 50 MPa using grand canonical Monte Carlo (GCMC) simulations. Our simulation results showed spontaneous and exothermic adsorption behavior of illite for CH4 and CO2 with enthalpy changes of −3.50 kJ/mol and −25.09 kJ/mol, respectively. Our results indicated that the interlayer counter cations (K+) play an important role in CO2 adsorption. Methane adsorption is mainly affected by the clay surface layers rather than the interlayer counter cations. The density and volume of CH4 and CO2 in their adsorbed phase at saturation were extrapolated from the linear portion of the excess adsorption isotherm. The resulting values were compared with available experimental data, and possible factors causing inconsistency were described. We discussed some issues associated with the Langmuir fit to experimental excess adsorption data in the case of low pressures. Our findings may provide some insights into gas adsorption behavior in illite-bearing shales.

1. INTRODUCTION Shale gas refers to gas that is trapped within organic shale formations either by adsorption or as free gas. It has recently been identified as an important alternative gas supply to conventional natural gas in the U.S. Some analysts expect that shale gas will take an increasing role in the fossil fuel mix in the near future.1 Despite the increasing interest and the need for the shale gas,2 there remain some challenging scientific problems to be solved, such as the effect of shale compositions and pore structures upon gas storage,3 the effect of mineralogy, organic richness, and thermal maturity on adsorption4,5 and the phase behavior and local species adsorption and distribution in shale formation. Major challenges for gas adsorption in shale lie in the fact that the density of the adsorbed phase within varying pores is unknown and fundamental understanding of the sorption mechanism is insufficient. Shale gas occurs as free gas in macro−nanopores or adsorbed gas on organic matter and inorganic clay minerals. Therefore, for understanding shale gas accumulations, gas interaction with minerals via adsorption is of importance to improve exploration success as well as production design and efficiency. The mechanism of gas adsorption on montmorillonite clay, including the adsorption sites6 and the effects of surface area7 and particle size8 on gas adsorption, has been previously investigated. There are some molecular simulations regarding clay minerals adsorption.9−17 Some authors have investigated gas intercalation mechanisms and structures, and the transport properties of the gas in the interlayer of montmorillonite clays using the NVT ensemble (constant number of particles, constant volume, and constant temperature) and NPT ensemble (constant number of particles, constant pressure, and constant temperature) molecular dynamics.18−20 The disadvantage of molecular simulations in the NVT and NPT ensembles is that they are not as flexible as the μVT emsemble © XXXX American Chemical Society

(constant chemical potential, constant volume, and constant temperature) to allow the exchange of gas molecules between the system studied and the gas reservoir. Recently, some authors21,22 have performed GCMC simulations to investigate the effect of clay pore structures, chemical heterogeneities, and water on methane and CO2 adsorption in slit-like clay pores. It is generally believed that the behavior of gas adsorption in shale reservoirs is complex and is dependent on various rock properties, organic fraction, moisture content, and thermodynamic conditions. The carbon dioxide storage potential of shale is typically assessed by measuring and comparing its excess adsorption uptakes. In practice, however, one must take into account the total storage capacity, which is the sum of the absolute amount adsorbed, described by most models,23−25 and the amount of free gas compressed in large pore space available to it. The volume occupied by the adsorbed gas must be subtracted from the measured pore volume when calculating the volume available for free gas storage. However, the adsorbed phase volume and adsorbed phase density cannot be experimentally determined. In this work, we use GCMC simulations to investigate the effect of temperature, pressure, clay surface, and interlayer counter cations (K+) on CH4 and CO2 adsorption in a 2 nm illite slit-shaped nanopore, as illite plays an important role in shale gas adsorption behavior. We chose 2 nm pore size, since it has been concluded by Aringhieri26 that the micropore system formed by 2 nm pores contributes significantly to defining some of the most notable physicochemical properties of clays and that pores smaller than 2 nm contribute the vast majority of Received: July 20, 2016 Revised: September 26, 2016 Published: November 8, 2016 A

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Energy & Fuels surface area in clays and coal.27−29 In our simulations, temperature varies over a wide range up to 423 K (150 °C) and pressure is up to 50 MPa, representing the pressures and temperatures characteristic of the depths of shale in the subsurface. We aim at quantifying these effects and offer detailed information on the adsorbed phase density, volume, and adsorption mechanisms for the two species from a molecular-level perspective.

parts: gas in the adsorbed phase (na) and gas in the bulk phase (nb). The total amounts of CH4 and CO2 on illite at 298, 313, 328, 358, and 423 K are simulated up to a pressure of 50 MPa. Our simulation results of the total uptake of CH4 and CO2 are presented as the total amount of gas per pore volume in the unit of mmol/cm3 in Figure 2a. The pore volume calculation is

2. ILLITE STRUCTURE Illite is a 2:1 clay mineral and is a typical constituent of sedimentary rocks, especially shales. In 2:1 clay minerals, an octhehedral sheet is sandwiched between two tetrahedral sheets.30 In this study, we use the composition of Kx[Si(8−x)Alx](Al4)O20(OH)4 and chose x = 1 to have an overall clay charge equal to −1.0e per unit cell. In the simulation cell, isomorphic substitutions are made by replacing one Si by one Al in every replicated unit cell. Interlayer counter cations (potassium cations, K+) are distributed randomly in the clay interlayer space to counterbalance the electrostatic charges induced by the isomorphic substitutions in the clay layers. The K+ cations are able to move in the interlayer space. The unit cell has the parameters of a = 0.516 nm, b = 0.896 nm, c = 0.935 nm, α = 91.03°, β = 100.37°, and γ = 89.75°.31,32 The simulation cell contains 15 clay unit cells (5 × 3 × 1 supercell), resulting in a clay patch of 2.580 nm × 2.689 nm with a slit pore width of 2 nm. The pore width is defined as the distance between the planes of the centers of oxygen atoms in the inner surface layers, as shown in Figure 1. The simulation box contains one Figure 2. (a) Total uptake of CH4 and CO2 normalized by the pore volume in a clay slit-shaped pore of 2 nm at temperatures of 298, 313, 328, 358, and 423 K (25, 40, 55, 85, and 150 °C) and a range of pressures up to 50 MPa. (b) Total uptake ratio of CO2 to CH4 under the same conditions.

detailed in the Supporting Information. The total uptake of CH4 and CO2 increases with increasing pressure and decreases with increasing temperature. The total uptake of CO2 can be divided into two stages: “build-up” and “approaching levelingoff”. The pressure dividing the two stages is around 7, 10, and 15 MPa for the temperatures 298, 313, and 328 K, respectively. For the temperatures 358 and 423 K, the slope of the curves at the “build-up” stage drops significantly. For a given temperature, the initial slope and total uptake of CO2 are higher than those of CH4, exhibiting higher affinity and adsorption capacity of the illite for CO2 than for CH4. Illitic clays are built up of a certain number of unit layers. By changing the number of unit layers, the mass can be changed and therefore the specific pore volume (generally expressed in the units of m3/kg or cm3/g) is altered. Specific volume is a property of solids defined as the total pore volume of a material per unit of mass. Our simulations indicate that, for a given pore volume, changing the specific pore volume has negligible effect on the illite adsorption for the gases specified. In other words, for a given pore volume, altering the thickness of the solid (mass) hardly affects the adsorption amount in the nanopore. We do not show the result here. Therefore, it does not make sense to compare our loading amount of gas in the clay slit pore in the units of mol/kg or kg/kg with experimental data for gas adsorption on shale powder or particles. Instead, we could compare them in the units of mmol/cm3 or kg/m3 (average pore density of gas) with available experimental or simulation data.

Figure 1. Snapshot of illite and CO2 with the color scheme: O, red; H, white; Si, yellow; Al, pink; K, blue; C, gray. Illite layers are represented by bond structures; CO2 molecules are represented by spheres. Channel width is defined as the distance between the planes of the centers of oxygen atoms in the inner surface layers.

illite layer. The channel width is formed by the periodic image of the illite layer. Molecular models for CH4, CO2, and illite, and implementation of simulations are detailed in the Supporting Information.

3. RESULTS AND DISCUSSION 3.1. Total Uptake of CO2 and CH4 in Illite. Total Uptake of Gas. The total amount of gas (nt) refers to the actual amount of adsorbate present in the illite slit pore. It consists of two B

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Energy & Fuels Jin and Firoozabadi7 have investigated the adsorption behavior of CH4 and CO2 in montmorillonite clay nanopores with different pore sizes at 298 K. Their results showed that, at the maximum pressure of 5 MPa studied, the average densities of CH4 and CO2 in a montmorillonite slit pore are 12 and 18 mmol/cm3 for the pore size of 1 nm and 5 and 12 mmol/cm3 for the pore size of 4 nm. Our simulation results show the total uptake of CH4 and CO2 as 4.2 and 19.1 mmol/cm3 for an illite slit pore with the pore size of 2 nm at the same pressure and temperature. Our value of 4.2 mmol/cm3 for the CH4 total uptake is smaller than their results of 12 and 5 mmol/cm3 for the total uptake of CH4 in a montmorillonite clay nanopore with the pore sizes of 1 and 4 nm. The experimental results of Ji et al.33 have also shown that montmorillonite has a higher adsorption capacity for CH4 compared with illite. Here we need to emphasize the total uptake present in the clay slit-shaped nanopores is normalized by the pore volume. In ref 33, Ji et al. used the channel volume as the pore volume. In our simulations, we used a helium void volume which is around 85% of the channel volume of Ji et al.33 That means our calculated CH4 and CO2 total uptake of 4.2 and 19.1 mmol/ cm3 is equivalent to their value of 3.6 and 16.2 mmol/cm3. For CH4, it is even smaller than their values, but for CO2, our value of 16.2 mmol/cm3 for the pore size of 2 nm is between their values of 18 and 12 mmol/cm3 for the pore sizes of 1 and 4 nm. Our lower CH4 value for illitte compared with their experimental data for montmorillonite supports their conclusion that montmorillonite has a higher adsorption capacity for CH4 compared with illite. The ratio of the total uptake of CO2 to CH4 is shown in Figure 2b. It decreases significantly with increasing pressure. However, the pressure dependence is negligible if the pressure is above 10 MPa. The temperature dependence of the ratio is pronouced at the lowest pressures. This is due to the more significant effect of the temperature on CO2 adsorption than CH4 at low pressure points. For example, at 0.1 MP, the total loading of CH4 is around 2 times that at 423 K, but for CO2 at 298 K, it is around 12 times of that at 423 K. Therefore, the ratio of the total uptake of CO2 to CH4 drops significantly when temperature is raised. 3.2. Bulk Gas Density and Excess Adsorption. Bulk Gas Density. In Figure 3, we present the bulk gas density of CH4 and CO2 obtained using the Peng−Robinson equation of state.34 The bulk gas density of CH4 and CO2 increases with pressure but decreases with temperature. The decrease in the bulk phase density with increasing temperature is simply reflected by the decrease in the total uptake when temperature is raised, as shown in Figure 2a. For CO2, the linearity exists up

to a pressure of around 5 MPa. Its nonlinear behavior is more pronounced than that of CH4. In the case of 298 K, which is below the critical temperature of CO2 (304 K), there is a sharp increase from 5.6 to 14.2 mmol/cm3 in the bulk gas density of CO2 when pressure is raised from 6.44 to 6.45 MPa. As shown in Figure 3, we observe an inflection point for CO2 at 8.85, 10.70, 13.68, and 18.00 MPa for the temperatures 313, 328, 358, and 423 K, respectively. Bae and Bhatia24 have reported an inflection point in the CO2 bulk phase density at a pressure of 8.93 MPa at 313 K. The pressure corresponding to the inflection point shifts to higher values with increasing temperature. As temperature increases, the bulk phase densities for both CH4 and CO2 approach linearity. Excess Adsorption. The excess adsorption rather than the amount adsorbed is the quantity accessible to experimental measurement, but at lower pressures the difference between the two quantities becomes negligible. The excess adsorption (ne), is the difference between the total uptake of adsorbate (nt) present in the pore space and that which would be present in the same pore volume, but in the bulk phase:

ne = nt − Vpρb

(1)

where Vp and ρb are pore volume and bulk gas density, respectively. From molecular simulations, the total uptake nt can be directly obtained, as shown in Figure 2a. Bulk gas density ρb (shown in Figure 3) is obtained using the Peng− Robinson equation of state.34 The excess adsorption based on the helium void (eq 1) can be negative. The adsorbed phase density and adsorbed phase volume are extracted from the excess adsorption as follows. In eq 1, the total uptake, nt, can be expressed as nt = na + nb = Vaρa + (Vp − Va)ρb

(2)

where Va and ρa are adsorbed phase volume and adsorbed phase density, respectively. The total amount nt includes two parts: gas in the adsorbed phase (na) and gas in the bulk phase (nb). The total amount nt reduces to the absolute adsorption na, when only the adsorbed phase is formed in the pore space or the free gas contribution compared with that from the adsorbed phase is negligible.35−37 From eqs 1 and 2, we obtain ne = (ρa − ρb )Va = (ρa − ρb )Vpϕa

(3)

where ϕa is the volume fraction of the adsorbed phase V (ϕa = Va ). From eq 3 excess adsorption normalized by the pore p

volume can be expressed as ne = (ρa − ρb )ϕa Vp

(4)

Equation 4 would tend to zero when pressure reaches the value where the bulk gas density reaches the adsorbed phase density. In other words, the adsorbed phase density at saturation can be determined by the bulk phase density where the adsorbed gas and free gas become indistinguishable and the excess adsorption becomes zero. The intercept of the excess adsorption with the bulk density axis provides an estimate of the adsorbed phase density at saturation. In the case that the adsorbed phase is saturated, the first term on the right-hand side of eq 4 can be treated as a constant, and the excess adsorption would show linear behavior with respect to the bulk gas density with a slope of −ϕa in the high bulk gas density region.

Figure 3. Bulk phase density of CH4 and CO2 obtained using the Peng−Robinson equation of state.34 C

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120 bar at 318 and 328 K by the gravimetric method38 also showed a maximum near the critical pressure. For CH4, the maximum of 2.4 mmol/cm3 appears at 10 MPa for 298 K. As temperature increases to 423 K, the maximum drops to 0.87 mmol/cm3 at ∼15 MPa. The crossover is at ∼19−27 MPa for all the temperatures specified. The CH4 maximum is far lower than that of CO2. The CO2 maximum is around 6.0−6.7 times of the CH4 maximum. CH4 excess adsorption for all temperatures specified shows negative values at pressures higher than 32 MPa. The lower the temperature, the sooner the excess adsorption becomes negative. The degree of the negativity largely depends on the accuracy of the estimated pore volume. Do et al.39 have shown that there is a significant change in the way the excess amount behaves if the accessible pore volume is overestimated by a mere 2%, and they have pointed out an urgent need for techniques that determine the accessible volume as accurately as possible. Adsorbed Phase Density at Saturation. In Figure 5, we plot the excess adsorption of CH4 and CO2, normalized by the pore

Figure 4 shows the excess adsorption of CH4 and CO2 versus pressure.We observe that both CH4 and CO2 pass through a

Figure 4. Excess adsorption isotherms of CH4 and CO2, normalized by the pore volume, at the temperatures 298, 313, 328, 358, and 423 K (25, 40, 55, 85, and 150 °C) in a clay slit-shaped pore of 2 nm expressed as a function of pressure: (a) CH4; (b) CO2..

maximum and then drop. The maximum occurs at the pressure where the rate of change of the adsorbed phase density with pressure is equal to that of the bulk gas density (eq 4). For CO2, the maximum excess adsorption appears at 5, 6, 7, 10, and 12 MPa for the corresponding temperatures of 298, 313, 328, 358, and 423 K. At temperatures not far above the critical point (304 K), there is a large change in bulk gas density for a small variation in pressure (shown in Figure 3). However, for temperatures far above the critical temperature, this change in the bulk gas density is no longer significant and the maximum in the excess adsorption becomes less pronounced and even disappears at high enough temperatures. After passing the maximum, the excess adsorption isotherms for the lower temperature decline more rapidly than the higher temperature isotherms. This results in an intersection of the isotherms at the pressure range 6−19 MPa for CO 2. The intersection corresponds to a reversal point of the temperature dependence of the excess adsorption isotherms. At pressures below 6 MPa, excess adsorption decreases with increasing temperature. In contrast to the low pressure range, the excess adsorption increases with temperature when pressure is above 19 MPa. This effect is clearly related to the change in the bulk phase density of the CO2 as shown in Figure 3. It is evident that, for high pressures, the bulk phase density is much higher at lower temperatures, and the excess amount reduces more quickly. When the bulk phase density approaches the adsorbed phase density, the excess adsorption would become zero. A negative excess adsorption can be expected if the density of the adsorbed phase is less than that of the free gas phase (see eq 4). The excess adsorption isotherms of illite for CO2 measured up to

Figure 5. Excess adsorption isotherm of CH4 and CO2, normalized by the pore volume, at the temperatures 298, 313, 328, 358, and 423 K (25, 40, 55, 85, and 150 °C) in a clay slit-shaped pore of 2 nm expressed as a function of the gas density: (a) CH4; (b) CO2. The saturation regime can be associated with the linear region of this isotherm.

volume, expressed as a function of their gas density at the corresponding pressure and temperature conditions. The onset of the linear regime is around 10 mmol/cm3 (160 kg/m3) for CH4 and 7 mmol/cm3 (308 kg/m3) for CO2. Beyond the onset value, the excess adsorption decreases linearly. The adsorbed phase density and volume can be calculated from the intercept and slope of the linear part shown in Figure 5. The intercept of the linear trend with the bulk density axis provides an estimate of the density of the adsorbed phase at saturation (see eq 4 and Figure 5). At this point the adsorbed phase density and the density of the free phase are identical. The adsorbed densities at saturation at varying temperatures obtained by this procedure D

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Energy & Fuels range from 9.10 to 12.55 mmol/cm3 (146−201 kg/m3) for CH4 and from 18.25 to 22.65 mmol/cm3 (803−997 kg/m3) for CO2. The CO2 adsorbed phase density at saturation is around twice that of CH4. We have obtained an adsorbed phase density of 148 kg/m3 for CH4 adsorption on dry bituminous coal at 308 K and 10 MPa37 from molecular simulations. Khosrokhavar et al.40 have reported a value of 255 kg/m3 for adsorbed CO2 density on shale at 318 K and at pressures up to 10.5 MPa using the manometric method. Jeon et al.38 have obtained a low adsorbed density of CO2 on illite (352 kg/m3 at 318 K and 228 kg/m3 at 328 K) by fitting their excess adsorbed isotherm up to around 13 MPa with a modified Dubinin−Radushkevich (DR) equation. There might be uncertainty involved in fitting the three free parameter model to the excess adsorption isotherm, and the data experimentally obtained at pressures lower than 13 MPa might not be sufficient enough for the fitting. De Silva and Ranjith41 have shown that, for less dense phase conditions, isotherm models gave comparable results to the experimental adsorption isotherms, while for highly dense phase conditions there were varying results. Compared with the results of Khosrokhavar et al.40 and Jeon et al.,38 a relatively high adsorbed phase density of CO2 on illite from our simulations might contribute to the interlayer counter cations (K+), as discussed in section 3.4, and the dry illite used in our simulations. In nature, water would be present in clay minerals and on their surfaces and would hydrate the potassium ions, potentially reducing the adsorption of CO2. In the literature there is a large variety of adsorbed densities of CO2 on coal:42 1178 kg/m3 by Span and Wagner,43 1400 kg/m3 by Fitzgerald et al.,44 1035 kg/m3 by Humayun and Tomasko.45 Sakurovs et al.23 have obtained the adsorbed phase density of ∼1500 for CO2, and 600 for CH4 by fitting modified DR isotherms to their experimental data of CO2 and CH4 adsorption on coal at 53 °C. They have discussed the errors in the adsorbed phase density caused by the modified DR model. In the experiments of Battistutta et al.,46 the Langmuir model fitted density of the adsorbed CO2 on coal at 318 and 338 K is varying between 961 and 1936 kg/m3. Liu and Wilcox28 have investigated the effect of surface chemistry on the CO2 density (the total amount of CO2 per unit volume) up to the pressure of 25 MPa using the GCMC method and reported an average CO2 density of 883− 1056 kg/m3 and 854−1019 kg/m3 for the temperatures 298 and 313 K. The Langmuir model fitted density of the adsorbed CH4 on black shale with high illite content at 333 K and pressures up to 25 MPa is 295−323 kg/m3 by Gasparik et al.5 The adsorption capacity nmax and adsorbed phase density ρa are generally determined by fitting the Langmuir equation (eq 5)5,24,47 to experimental excess adsorption data ne =

ρ ⎞ nmax bP ⎛ ⎜⎜1 − b ⎟⎟ ρa ⎠ 1 + bP ⎝

ρa =

ρs bP 1 + bP

(6)

where the Langmuir constant b can be estimated by the initial slope of the excess adsorption curve. We calculated the adsorbed density based on eq 6 and present the results in Figure 6. The adsorbed phase density increases with increasing

Figure 6. Adsorbed phase density of CH4 and CO2 versus pressure. The adsorbed phase density increases with increasing pressure and decreasing temperature. The adsorbed density changes significantly with pressure when pressure is below 15 MPa for CH4 and 5 MPa for CO2.

pressure and decreasing temperature. Our results indicate that the adsorbed density changes significantly with pressure when pressure is below 15 MPa for CH4 and 5 MPa for CO2. Therefore, treating adsorbed density as a constant in eq 5 is not appropriate, especially in the low pressure range. As discussed in the effect of pore volume in the excess adsorption, the former also significantly affects the adsorbed phase density ρa through ρs (eq 6). Overestimation of the pore volume causes the excess adsorption curves to shift to lower values, and consequently, the intercept of the excess adsorption curves with the axis would also shift to lower values (Figure 5). As a result, the adsorbed phase density at saturation will be underestimated. Adsorbed Phase Volume at Saturation. Equation 4 indicates that in the case when the adsorbed phase is saturated, the first term on the right-hand side of eq 4 can be treated as a constant and the excess adsorption shows linear behavior with respect to the bulk density with a slope of −ϕa in the high density region. This is confirmed by the linearity shown in Figure 5. To determine the volume fraction of the adsorbed phase ϕa, in Figure 7, we plot the derivative of the excess adsorption with respect to the corresponding bulk gas density. As expected, beyond a bulk density of 10 mmol/cm3 (160 kg/ m3 for CH4 and 440 kg/m3 for CO2), the derivative of the excess adsorption with respect to the corresponding bulk

(5)

In eq 5, the adsorbed phase density ρa is treated as a constant. nmax, ρa, and b are treated as independent parameters. We have shown that the adsorbed phase density is pressure dependent,37 not a constant. In addition, nmax depends on ρa. Hence, they cannot be treated as free parameters. As the adsorbed phase density at saturation ρs is determined from the linear intercept of the excess adsorption with the bulk gas density axis (eq 4 and Figure 5), the adsorbed density ρa could be expressed as E

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(8)

ΔG = ΔH − T ΔS

where K is the thermodynamic equilibrium constant. From eqs 7 and (8), the temperature dependent K is expressed as

ln K =

ΔS ΔH − R RT

(9) −1

−1

where R is the universal gas constant (8.314 J mol K ) and T is the absolute temperature. The thermodynamic equilibrium constant K was obtained by calculating the apparent equilibrium constant Ke at different initial bulk gas densities and extrapolating the apparent equilibrium constant to zero pressure. In our simulations, the apparent constant, Ke, is defined as the ratio of the equivalent density of the adsorbate (which is the amount adsorbed divided by the pore volume) to the bulk gas density. We calculate Ke at very low pressure or bulk densities of the adsorbate and then extrapolate it to zero bulk density to obtain K. The Gibb’s free energy changes, calculated from eq 7 and the logarithm of K, are shown in Table 1 and plotted in Figure 8 and Figure 9, respectively. The extrapolation procedure can be referred to our previously published paper.48

Figure 7. Derivative of excess adsorption of CH4 and CO2 with respect to bulk phase density: (a) CH4; (b) CO2. Beyond a bulk density of 10 mmol/cm3 (160 kg/m3 for CH4 and 440 kg/m3 for CO2), the derivative of the excess adsorption with respect to the corresponding bulk density becomes a constant. The opposite of this constant provides an estimate of the volume fraction of the adsorbed phase.

density becomes a constant. The derivative is taken by averaging the slopes of two adjacent data points. The constant value is an average of the data at high pressure points where the derivative fluctuates around a horizontal line. The opposite (slope multiplied by −1) of this constant provides an estimate of the volume fraction of the adsorbed phase (see eq 4 and Figure 7). The volume fraction values for CH4 and CO2 obtained by this procedure are around 0.40 and 0.56, respectively. The CO2 adsorbed phase volume fraction is higher than that of CH4. 3.3. Adsorption Thermodynamics. For an adsorption process to be spontaneous, there must be a decrease in free energy of the system; that is, the Gibb’s free energy change, ΔG, must have a negative value. The thermodynamic parameters of the Gibb’s free energy change, ΔG, enthalpy change, ΔH, and entropy change, ΔS, for the adsorption processes are calculated using the following equations:

Figure 8. Gibb’s free energy change, ΔG, versus temperature, T. The Gibb’s free energy is found to be linear. The negative values of ΔG suggest that the adsorption process is favorable and spontaneous for both CH4 and CO2 adsorption on illite at the temperature ranges studied.

The Gibb’s free energy change, ΔG, versus temperature, T, is found to be linear (Figure 8). Our results are consistent with the well established adsorption thermodynamics. The negative values of ΔG suggest that the adsorption process is favorable and spontaneous for both CH4 and CO2 adsorption on illite at the temperature ranges studied. More negative values of ΔG with decreasing temperature, especially for CO2, indicate that the adsorption process becomes more favorable at lower temperatures. Comparison between CH4 and CO2 indicates that illite is more favorable to adsorb CO2 than CH4, as ΔG for CO2 is more negative than that of CH4.

(7)

ΔG = −RT ln K

Table 1. Logarithm of the Equilibrium Constants, ln K, and Gibbs Free Energy Change, ΔG, for the Adsorption of CH4 and CO2 in an Illite Slit Pore of 2 nm at Different Temperatures Specified 298 K ΔG (kJ/mol) ln K

313 K

328 K

358 K

423 K

CO2

CH4

CO2

CH4

CO2

CH4

CO2

CH4

CO2

CH4

−12.61 5.09

−2.21 0.89

−12.04 4.63

−2.14 0.82

−11.30 4.15

−2.09 0.76

−10.06 3.38

−1.93 0.65

−7.41 2.11

−1.67 0.48

F

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consistent. It is shown that it is more favorable for CO2 than for CH4 to be adsorbed in slit shaped pores in illite. 3.4. Interaction Energy and Radial Distribution Functions. Interaction energy can indicate the affinity of the gases to illite. The interaction energy of illite−CO2 includes van der Waals (VDW) interactions and electrostatic interactions. In regard to CH4, as it is treated as a not charged united atom, only van der Waals (VDW) potential energy contributes to the total interaction energy. The adsorbent (illite) is a multisite structure, each of which interacts with the adsorbate and contributes to the energy. We calculated all the interaction energy between each site of adsorbent and each site of adsorbate, summed them up, and determined the averaged ensemble value for the illite−adsorbate interaction energy. Similarly, we calculated the interaction energy between adsorbate−adsorbate and presented the results in Figure 10.

Figure 9. Natural logarithm of the adsorption equilibrium constants for CH4 and CO2 versus the reciprocal of temperature. A good linear relationship between the natural logarithm of the adsorption equilibrium constant and the reciprocal of temperature exists.

Figure 9 shows the linear relationship between ln K and the inverse of temperature, 1/T. The constant K provides information about the relative adsorption affinity of the clay toward the adsorbate. The value of K appears to decrease with increasing temperature, especially for CO2. The values of K for CO2 are larger than those of CH4, again indicating that the illite has a higher adsorption affinity toward CO2 than CH4. Temperature variations seem to affect the CH4 adsorption to a lesser extent compared with CO2. The enthalpy change, ΔH, and entropy change, ΔS, for the adsorption processes can be estimated from the slope and intercept of the linear relationship between ln K and 1/T (eq 9). The estimated results are presented in Table 2. As listed in

Figure 10. Interaction energy of adsorbate−adsorbate and illite− adsorbate in the units kJ/mol of adsorbed gas, showing dominating energies of illite−adsorbate over that of adsorbate−adsorbate. For the purpose of clarity, the results only at 298 K are shown.

Table 2. Enthalpy Change, ΔH (kJ/mol), and Entropy Change, ΔS (J/mol/K), for the Adsorption of CH4 and CO2 in an Illite Slit Pore of 2 nm CH4 CO2

ΔH (kJ/mol)

ΔS (J/mol/K)

−3.50 −25.09

−4.35 −41.89

For the purpose of clarity, only the results at 298 K are shown. The interaction energy between the illite and CO2 is much higher (more negative) than that between the illite and CH4. The interaction energy between CO2−CO2 and CH4−CH4 becomes more negative with increasing pressure. The increasingly negative energies signify greater interactions between the adsorbate molecules with increasing pressure. In contrast, the interaction energy (expressed as kJ per mole of gas adsorbed) between the illite and adsorbates decreases with increasing pressure. This is due to the fact that with increasing pressure the number of adsorbed gas molecules increases. As discussed, the interaction energy between adsorbate−adsorbate becomes stronger. As a result, the rate of increase in the interaction energy between illite and the adsorbate is slower than the rate of increase in the total number of adsorbate molecules present in the pore space. Therefore, the ratio of these two (interaction energy per mole of adsorbed gas) becomes smaller (less negative) as pressure increases. The interaction energy of CO2−CO2 and illite−CO2 is sensitive to pressure at pressures below 7 MPa at 298 K, which correlates to the “build-up” stage on the total uptake curves shown in Figure 2a. Based on the observation that the illite−adsorbate interaction is around 60%−97% of the total interaction energy (illite−adsorbate plus adsorbate−adsorbate) at the “build-up” stage, we infer that the unsaturated “build-up” adsorption stage for CO2 is mainly controlled by the intermolecular interactions between illite and adsorbate.

the table, a more negative enthalpy change is observed for CO2 than for CH4, further indicating that adsorption on illite is more favorable for CO2 than for CH4. The isosteric heat of adsorption is given as q = −ΔH, at the zero coverage limit. The isosteric heat of CO2 adsorption in illite (25.09 kJ/mol) is 6 times higher than that of CH4 (3.50 kJ/mol) from our GCMC simulation results. The isosteric heat of adsorption at zero loading is directly proportional to the adsorption affinity quantified as the slope of the linear region of the isotherms, hence the higher value of the adsorption heat for CO2 and the stronger adsorption affinity of illite for CO2 and for CH4. The higher value of adsorption entropy ΔS for CH4 compared with that of CO2 indicates an increased randomness for CH4 adsorption. The more negative entropy of CO2 compared with CH4 indicates that CO2 molecules have a more orderly arrangement than CH4 and thus show better performance in adsorption. This observation is consistent with the point, discussed in section 3.1, that the total uptake of CO2 in illite is higher than that of CH4. These GCMC results of Gibb’s free energy, enthalpy, and entropy change, as well as the isosteric heat of adsorption, are G

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adsorbate−adsorbate in the clay slit-like pore at 298 K and 30 MPa in Figure 12a and 12b, respectively. The position of the

To further investigate the contribution of the interlayer counter cations (K+) to the interaction between illite and adsorbate, we separate the illite−adsorbate interactions into two parts: interactions between the illite surface layer (without K+) and adsorbate and between K+−adsorbate. We compare the two parts in Figure 11. For CH4, its interaction with K+

Figure 11. Interaction energy of interlayer counter cations−adsorbate and illite surface layer−adsorbate in the units kJ/mol of the adsorbed gas at 298 K, showing dominating energies of K+−adsorbate over that of the illite surface layer−adsorbate. For CH4, its interaction with K+ contributes only around 8% to the total illite−CH4 interaction, while its interaction with the illite surface layer covers 82%. In contrast to CH4, the K+−CO2 interaction covers as high as 76% of the total interaction between illite and CO2.

Figure 12. RDFs of K+−adsorbate and adsorbate−adsorbate in the clay slit pore at 298 K and 30 MPa. (a) K+−adsorbate; (b) adsorbate− adsorbate. Closer packing of CO2 molecules around K+ compared with the packing of CH4 around the cations is observed as a result of a preferential attractive accumulation of CO2 molecules near the K+ cations. The RDFs of adsorbate−adsorbate indicate that CO2 molecules are more closely packed compared with CH4 molecules.

contributes only around 8% to the total illite−CH4 interaction, while its interaction with the illite layer covers 82%. In contrast to CH4, the interaction of K+−CO2 covers as high as 76% of the total interaction between illite−CO2. As illustrated in Table 1, the illite−CH4 and K+−CH4 interactions are from the nonelectrostatic LJ interactions, while the illite−CO2 and K+−CO2 interactions include not only the LJ interactions, but also the electrostatic interactions as well. We identify that the interaction of K+−CO2 dominates the interaction of illite−CO2, especially at low pressure. As pressure increases, the dominance becomes less pronounced. The interlayer countercation is the main contribution to the adsorption of CO2 in illite. In contrast to CO2, the adsorption of CH4 in illite is mainly determined by the illite surface layer. Comparison between the contributions of the illite layer and the interlayer counter cations to the total interaction between the illite−adsorbate demonstrates the different controlling factors for the adsorption of the two species. Similar phenomena have also been reported on gas adsorption in montmorillonite clays by Jin and Firoozabadi7 using MC simmulations. They have investigated the effect of cation exchange on CH4 and CO2 adsorption and concluded that the cation exchange increases CO2 adsorption, especially at low pressure, but has a negligible effect on the overall CH4 adsorption. Melnitchenko et al.49 have discussed the effect of the exchange cations on CO2 retention in kaolinite derivatives. They concluded that surface exchange cations affect CO2 adsorption based on their experimental measurements. Radial distribution functions (RDFs) are defined as the ratio between the local density of a specified atom or molecule at a distance r from a given atom and the average density of the specified atom or molecule within the unit cell of the system. To further investigate the effect of packing of the adsorbate on adsorption, we compare the RDFs of K+−adsorbate and

first peak in the K+−O (CO2) RDF is at ∼0.3 nm. The peak of K+−CH4 is relatively low and broad, and occurs at a larger distance of ∼0.38 nm. The nonzero value of the K+−O (CO2) and K+−CH4 RDF starts at ∼0.26 and 0.30 nm, respectively. The shorter separation of K+−O(CO2) compared with that of K+−CH4 indicates a closer packing of CO2 molecules around K+ than for CH4, as a result of a preferential attractive accumulation of CO2 molecules near the K+ cations. In addition, the first peaks of K+−O(CO2) and K+−C(CO2) are more distinct and sharp than the K+−CH4 peak, and a second sharp peak is also observed for K+−O(CO2), indicating stronger interaction between the CO2 molecules and K+. The CO2 molecules have no net charge, but they have partial charges on their atoms and a linear quadrupole moment, and thus a stronger interaction exists between the CO2 molecules and the positively charged K+. The RDFs of CH4−CH4 and CO2−CO2 at 298 K and 30 MPa are shown in Figure 12b. The distance of the closest contact in the O−O and C−C RDFs of CO2 is ∼0.26 nm, but for the CH4−CH4 the closest contact appears at 0.33 nm. This indicates that the distances between CO2 molecules are shorter and CO2 molecules are more closely packed compared with CH4 molecules. The CH4−CH4 RDF is above the CO2−CO2 RDF due to the lower average density of CH4 in the slit pore and the fact that the RDF is normalized relative to the average adsorbate density in the slit pore. H

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4. CONCLUSIONS GCMC simulations were used to investigate the adsorption of pure CH4 and CO2 in dry slit shaped pores in K+−illite with a pore width of 2 nm at different temperatures of 298, 313, 328, 358, and 423 K (25, 40, 55, 85, and 150 °C) over a range of pressures up to 50 MPa. The effects of pressure, temperature, and interlayer counter cations on the preferential adsorption behavior of CO2 as compared to CH4 were quantified. Our results indicate that, at the pore size of 2 nm, the volume fraction of the adsorbed phase in the pore volume is ∼0.40 and 0.56 for CH4 and CO2, respectively. The CO2 adsorbed phase density at saturation is ∼1.8−2.0 times that of CH4. The adsorbed phase density varies with pressure significantly when pressures are lower than 15 MPa for CH4 and 5 MPa for CO2. Therefore, fitting the Langmuir model (eq 5) in which the adsorbed phase density is treated as a constant to experimental data obtained at pressures not high enough to estimate a constant adsorbed density and adsorption capacity is not appropriate. We observed a linear relationship between the natural logarithm of the adsorption equilibrium constant and the reciprocal of temperature for K+−illite, which provides a way to quantify the adsorption capacity of the illite for different gases. This linear relationship allows the determination of the thermodynamic parameters such as enthalpy and entropy changes involved in the adsorption process. Both CH4 and CO2 show exothermic behavior with enthalpy changes of −3.50 and −25.09 kJ/mol for the adsorption of CH4 and CO2, respectively. The negative values of Gibb’s free energy change indicate that both CH4 and CO2 adsorption are spontaneous. For CH4, its interaction with interlayer counter cations contributes only around 8% to the total illite−CH4 interaction, while its interaction with the illite surface layer covers 82%. The adsorption of CH4 in illite is mainly determined by the illite surface layer. In contrast to CH4, the K+−CO2 interaction covers as high as 76% of the total interaction between illite− CO2. We identify that the interaction of K+−CO2 dominates the interaction of the illite−CO2 and plays an important role in CO2 adsorption on illite. As pressure increases, the dominance becomes less pronounced. Further analyses on the structural properties of RDFs confirm our adsorption and interaction energy results. Stronger interaction between the CO2 molecules and K+ exist. We observe a closer packing of CO2 molecules around K+ compared with the packing of CH4 around the cations as a result of a preferential attractive accumulation of CO 2 molecules near the K+ cations. The RDFs of CH4−CH4 and CO2−CO2 show that CO2 molecules are more closely packed around themselves compared with CH4 molecules. That is why the total adsorption amount of CO2 is higher than that of CH4. Our simulation results of adsorption, interaction energies, RDFs, and thermodynamic parameters are self-consistent. The findings may provide some new insights into gas adsorption behavior in clay slit pores. The natural illite structure is not as ideal as that used in the simulation. The isomorphic replacement should be much more random in both numbers and positions, the counter cations present in the channel space could be more diverse than just the K+ cation used in our model, and some lattice imperfections and other surface irregularities also exist in natural illites. In future work, we will investigate the water effect on the adsorption of gases on clay minerals. In nature, water would be

present in clay minerals and hydrate the counterions, and the adsorption of CO2 could be affected. There are other factors to consider, such as the effect of different types of substitutions in the octahedral sheets of illite, and the presence of NH4+ rather than K+ within the pores, plus pore sizes and whether supercritical CO2 needs its own force field parameters.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.6b01776. Molecular models for CH4, CO2, and illite; implementation of simulation; determination of pore volume; and tables of nonbonded species potential parameters and charges, and bond parameters for CO2 molecules (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the National Computing Infrastructure (NCI) national facility for a generous allocation of computing time during the course of this work. We thank the reviewers for their very insightful comments toward improving this paper.

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REFERENCES

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