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Lab-Scale Investigation of Sorption Kinetics of Methane/Ethane Mixtures in Shale Devang Dasani, Yu Wang, Theodore T. Tsotsis, and Kristian Jessen Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02431 • Publication Date (Web): 18 Aug 2017 Downloaded from http://pubs.acs.org on August 22, 2017

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Industrial & Engineering Chemistry Research

Lab-Scale Investigation of Sorption Kinetics of Methane/Ethane Mixtures in Shale Devang Dasani, Yu Wang, Theodore T. Tsotsis, Kristian Jessen*

Mork Family Department of Chemical Engineering and Materials Science, Univerity of Southern California, 925 Bloom Walk, HED 311, Los Angeles, CA-90089, USA *

Corresponding author: [email protected]

Keywords: Sorption isotherms and dynamics; Thermogravimetric analysis; Binary mixtures; Competitive sorption; Shale gas.

Abstract Natural gas produced from shales is composed primarily of methane (CH4), accounting for up to 87-96 mol%. In addition to CH4, shale gas contains a host of secondary components are, including nitrogen (N2), helium (He), and hydrocarbons such as ethane (C2H6) and propane (C3H8). CH4 and the other hydrocarbons are thought to be stored in the adsorbed state in the micropores and mesopores of the shale, and as free gas in the (natural) fracture networks. Although convective and diffusive transport account for the short-term behavior during shale gas production, desorption is thought to dominate the long-term dynamics of shale-gas production. The key objective of this study, therefore, is to investigate the sorption kinetics of methane/ethane mixtures in gas shales. Specifically, we study here the adsorption/desorption behavior of pure CH4 and C2H6, and their mixtures in a whole shale sample (cube) using Thermogravimetric Analysis (TGA). The choice of ethane is because it is, typically, the second largest component of shale gas and is

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thought to compete for the same adsorption sites as methane. To this end, we first determine the steady-state isotherms of the pure component gases and their binary mixtures, which are essential to predicting the gas storage capacity of the shale. We then study the dynamics towards equilibrium during the sorption process in order to better understand the role of desorption during the later times of shale gas production. We apply the well-established Langmuir approach to analyze and interpret the experimental dynamic sorption observations. Our experimental data predict a lag in ethane production relative to that of methane due to the preferential sorption of ethane on the shale. This provides for added insight to interpret field-scale production data in terms of the produced gas compositions. The experimental observations and their analysis pave, therefore, a path towards improving the interpretation of production data from shale-gas operations via an enhanced understanding of desorption dynamics (and subsequent mass transfer) of gas mixtures in shale.

1.1 Introduction Gas shales have been considered as a key source of natural gas in the United States for over a decade now, and are expected to contribute significantly to the natural gas production in the future, estimated to account for approximately 70% of the total US natural gas production by the year 20401. In light of the extensive work done towards multiscale characterization of gas shales in the past 5-7 years2-6, it is now widely accepted that such shales consist of both organic and inorganic components, and have complex porous structures with pores spanning the entire range from micropores to macropores. Natural gas exists in shales both as free gas and as adsorbed gas. During shale gas production, it is first produced from fracture networks (induced and natural) and macropores 2 ACS Paragon Plus Environment

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where it exists as free gas, over a relatively short period of time. This is followed by the evolution, over a longer period of time, of free gas residing in mesopores, and of the sorbed gas in the mesopores and micropores. In order for the sorbed gas to be produced, gas must first desorb from the micropores and mesopores and then transport to the macropores and the fracture networks, and to finally transfer via viscous flow to the well-bore. Methane is the single largest component of shale gas. However, ethane is typically the second largest component accounting for more than 15 vol. % in certain cases7. Over the last decade, a number of studies have been performed, both experimentally and theoretically, with emphasis on generating sorption isotherms for pure methane and its binary mixtures with heavier gas components8-13: Gas adsorption/desorption data obtained from laboratory experiments facilitate accurate gas-in-place estimates. Zhang et al.12 performed CH4 adsorption experiments on organic-rich shales and isolated kerogens at temperatures up to 65 °C and pressures up to 15 MPa to study the effect of organic matter type and thermal maturity on CH4 sorption on shales. They used the Langmuir isotherm to describe CH4 sorption on their samples. Mosher et al.13 used grand canonical Monte Carlo (GCMC) simulations to predict CH4 excess adsorption isotherms in carbon-based slit pores of varying widths in the microporous and mesoporous regions for pressures up to 20 MPa. Their simulation results under-predicted the experimental data from the literature at lower pressures, and over-predicted them at higher pressures. Yuan et al.10 performed experimental studies and applied a bi-disperse diffusion model to study adsorption and diffusion of methane in shale samples (which were assumed to be spherical particles) from the Sinchuan Basin, China. They used the Langmuir isotherm to describe methane storage in their samples and calculated the diffusivities for both the macropores and micropores, assuming Fickian diffusion in the macropores and Knudsen

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diffusion in the micropores. It should be noted, that in their work they use the macropore and micropore terminologies purely to distinguish two different pore sizes (their definitions not aligned with the IUPAC classification). Akkutlu and Faithi16 performed and analyzed pressure pulse-decay experiments, using methane, to investigate gas transport in shales by means of a dual-porosity model that accounts for diffusive transport and sorption (described by the Langmuir isotherm) in kerogen pores, and pure transport in the inorganic pores. Chareonsuppanimit et al.14 measured adsorption isotherms of CO2, CH4, and N2 on New Albany shale samples at 328.2 K and for pressures up to 12.5 MPa. They found the simplfied localdensity (SLD) model to represent their experimental data with reasonable accuracy. They observed, as expected, that CO2 adsorbs to a greater extent on to their shale samples than CH4 and N2. Chen et al.15 investigated the adsorption of pure CH4 and pure C2H6 on an Illitic clay at temperatures up to 120 °C and pressures up to 30 MPa using GCMC simulations, and compared their results to experimental data available in literature. They concluded that the excess adsorption of CH4 is half that of C2H6, however, the maximum loading for both the gases is the same. Alnoaimi and Kovscek17 performed pulse-decay experiments using CO2, He, and CH4 at the core-scale, and developed a numerical model to study the interplay between flow and sorption in pore sizes ranging from micropores to microcracks. The gas flow in their model is described by Darcy’s law, while the Langmuir and BET models describe CH4 and CO2 sorption, respectively. While a good body of work has been established over the past decade to describe multiscale transport in gas shales, primarily focusing on methane, there is noticeable lack of studies that investigate the kinetics of sorption of methane-ethane binary mixtures during shalegas production. In previous work11, our Group reported adsorption/desorption isotherm data for


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pure methane and ethane, as well as for their binary mixtures at different concentrations and temperatures using a powdered shale sample from the Marcellus formation. The data were generated in a Thermogravimetric Analysis (TGA) set-up (Rubotherm, Germany). In that investigation of the competitive sorption behavior of methane and ethane, it was demonstrated that ethane sorbs preferentially over methane. This type of preferential sorption behavior can have a significant impact on the interpretation of shale gas production data, particularly during later times when ethane starts to desorb (at lower pressures), resulting in a lower methane concentration in the production stream. In this work, as part of the effort to improve the understanding of the processes involved during long-term shale gas recovery, we seek to advance the understanding of the impact of competitive sorption of methane and ethane on production dynamics. We do so, by studying the adsorption dynamics of pure components methane and ethane, as well as methane-ethane gas mixtures in the shale. In contrast to our previous study11, which focused on generating equilibrium isotherm data from powdered samples, our present study focuses on scorpion kinetics and employs a whole shale cube obtained from the Marcellus formation. The reason for employing a whole shale sample rather than using a powdered sample, is that prior studies have indicated that gas diffusion and sorption kinetics in shales and coal are controlled by the grain sizes, with gas diffusing much faster to reach sorption sites in smaller particles18. Cloke et al.19 reported, in addition, that grinding of the coal and size fractionation (sieving) of the resulting powders can result in compositional differences among the various sub-samples with differing particle sizes. In their study, for example, maceral composition differed from the smallest particle size fraction (inertinite-enriched) to the larger particle size fraction (vitrinite-enriched). Spears and Booth20 observed that mineral matter tends to be enriched in the smaller size



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fractions. Busch et al.21 reported that these compositional changes can also result in different sorption capacities. To avoid these added complexities and to be able to generate sorption data that are more representative of the phenomena at the matrix-level of shales, we utilize in this study a whole shale (cube) sample. Unlike the powdered shale samples used in our previous studies11,22, the use of shale cube samples alleviates concerns that the sorption properties measured may not be representative of those of the shale matrix. In the study of equilibrium sorption with powdered shale samples11 the Multicomponent Potential Theory of Adsorption (MPTA) was used to analyze the isotherm data. The choice of the MPTA was because it is the only continuum approach available to directly model excess adsorption data. MPTA is, however, currently not convenient to use in modelling of dynamic sorption experiments. We use here, instead, the classical multicomponent Langmuir sorption model to interpret the adsorption dynamics of the shale cube. To correlate the modeling results directly with the experimental excess adsorption data, one must be able to estimate the adsorbate phase densities accurately. To this end, we use the so-called lattice density functional theory (LDFT) method23. The ability of this approach to describe the densities of the adsorbate phase is validated based on isotherm data. The LDFT method is then employed to analyze the shale adsorption dynamics. A discussion of the experimental observations and the derived sorption kinetics parameters concludes the manuscript.

1.2 Experimental approach The shale sample used in this study was extracted from the depth of 7,860 ft of the Marcellus shale formation in the Appalachian basin. The formation temperature is ~60 oC at the sample depth of 7860ft (reported by operating company) corresponding to a geothermal gradient of ~25 6 ACS Paragon Plus Environment

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o

C/km. The formation pressure at 7860 ft is ~ 230 bar (reported by operating company)

corresponding to a pressure gradient of ~0.45 psi/ft. The shale samples were collected from the subsurface following standard procedures (wire-line coring) and delivered to Core-Laboratories. The core samples were then labeled, wrapped in plastic film, boxed in 3ft (~1 m) sections and placed in chilled storage to reduce water vaporization and oxidation. The sample used in this work (~1 cm3), shown in Figure 1, was extracted from a larger diameter core using a mechanical saw. and stored in a zip-locked bag to minimize further exposure to the laboratory air environment.

Figure 1 - Shale cube sample of approximately 1 cm3 in volume prepared for this study.

In on our previous work with Marcellus shales (Wang et al.11), we demonstrated that evacuation of shale samples at 120 oC for 24 hrs is sufficient to reproduce CH4 sorption isotherms, and we utilize the same sample preparation approach in this work. Accodringly, prior to the initiation of the sorption experiments, the sample was evacuated in situ at 120 oC for 24 hrs in the TGA system. The TGA apparatus is equipped with an online mass spectrometer. Typically, during degassing water is first detected but soon afterwards its concentration falls below the detection limit of the instrument. However, with a TGA balance accuracy of 1 µg, the lack of a weight change over the 24 hr evacuation period provides a more sensitive indicator of water removal



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than the online mass spectrometer can provide. At the end of each sorption experiment, the sample was regenerated under vacuum at 120 oC for 24 hr. This procedure assures that all gases that may potentially remain adsorbed at the end of an experiment are desorbed prior to the initiation of the next experiment11. The TGA technique was used to measure the sorption isotherms and dynamics for CH4, C2H6, and the CH4/C2H6 mixtures. The core component of the TGA set-up (Rubotherm, Germany) is a magnetic suspension balance (MSB), which is capable of measuring changes in weight of the sample due to sorption with an accuracy of 1 µg. During a sorption experiment, the weight change of the sample in the sorption chamber in the analytical balance is measured/recorded in 6 sec intervals in a contactless manner via the magnetic suspension mechanism. Prior to the sorption experiments, the weight and the volume of the sample container, along with the weight and the skeletal volume of the sample itself, were measured via helium (He) sorption/buoyancy experiments. Details of the measurement technique and the operational theory of the TGA are discussed in more detail elsewhere11. The sorption experiments were performed by varying the gas phase pressure in the sorption chamber in a stepwise manner, for example, from 10 to 20, 20 to 30 bar, etc., and for each step, data were recorded until steady state was reached. During the course of the experiments, the TGA balance measures any potential drift from its original zero-point (ZP) position every 10 min, and if a drift is detected, the balance resets the ZP to its original position. The weight measurements during the 10 min period are corrected for any ZP drift by assuming that any drift present is linear in time. We have found this approach to be quite accurate for the measurement of adsorption isotherm (equilibrium) data. After the initial 10 min period, and following the first ZP correction, the drift, if present at all, is very minimal


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and linear in time. However, it was found that immediately after the step-change in the chamber pressure (e.g., from 20 bar to 30 bar) a temporary fluctuation in the ZP would occur in the form of an overshoot/undershoot, potentially, as a result of a short-lived flow perturbation in the chamber generated by the change in the pressure. After this initial change, the ZP was observed to drift slowly, if at all, towards its position prior to the first ZP correction. As noted above, this temporary ZP variation has no impact on the measured isotherms but it does impact the short-term sorption dynamics. The conventional approach, employed by the TGA balance itself, which assumes that the ZP change occurs in a linear manner, is not capable of accommodating the initial fluctuation in the ZP. To account for the effect of the ZP fluctuation on the sample weight measurements, a “blank” run with an inert substance (solid quartz) of the same volume as the shale sample, was carried out. Following the exact same experimental protocol for the “blank” run with quartz as for the sorption experiments (i.e., stepwise changes in pressure) on the shale sample, the weight data were recorded. Based on the assumption that CH4/C2H6 do not adsorb onto the quartz (verified experimentally), the weight measurements for the quartz can be utilized to infer the ZP fluctuation behavior. By assuming that the balance will experience the same disturbances in the flow field in the presence of equal volumes of shale and quartz loaded onto the balance bucket, one can then utilize the ZP behavior for quartz to correct the initial dynamic sorption data generated with the shale sample. Further details on the weight correction procedure and theory can be found in the supplementary materials in this manuscript.



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1.3 Modeling approach 1.3.1

Equilibrium data

To model the dynamic sorption phenomena in the shale cube for CH4, C2H6 and their mixtures we use a Langmuir-type dynamic model (see further discussion in Sec. 1.3.2 below). Prior analysis of the equilibrium sorption on shale materials11 via the MPTA approach, indicates that in addition to occupying the micropore space, CH4 and C2H6 occupy the mesopore space to an extent that does not exceed the volume of a full monolayer. The use of the computationally inexpensive, Langmuir model, that assumes that the adsorption/desorption rates are directly proportional to the unoccupied and occupied sorption sites, respectively, is consistent with observation of monolayer coverage18, 21, 24. The Langmuir isotherm for single gases is given as =

,

(1)

where nabs (mmol.g-1) is the absolute sorption capacity in equilibrium with gas at pressure p (Pa), (mmol.g-1) is the maximum gas sorption capacity of the sample, and KA is the adsorption

equilibrium constant (Pa-1). A well-known downside of the Langmuir sorption model11 is that it calculates the absolute adsorption rather than the excess adsorption (nexc) that is measured by the TGA and other (e.g., volumetric, chromatographic) techniques. To use the Langmuir model in the analysis of excess sorption data, one requires an appropriate adsorbate density model to convert the experimental excess adsorption data into absolute sorption according to the following equation: =

1 −

.

(2)

In eq 2, ρgas (mol.m-3) is the molar bulk-phase gas density, calculated here using the Peng-


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Robinson equation of state (PR-EOS)25 including volume translation (shift), and ρα (mol.m-3) is the molar adsorbate phase density. Wang et al.26 compared different adsorbate phase density models to interpret CH4/C2H6 adsorption phenomena on powdered shale samples and concluded that two of these density models, namely the LDFT and the law of rectilinear diameters (LRD) model are the most appropriate ones to use. The LDFT model was selected for use in this investigation in order to reduce the number of model parameters, and due to its predictive capability with respect to binary mixtures (further discussed later in this manuscript). The LDFT method, first proposed by Ottiger et al.23, expresses the adsorbate phase density via a mapping function, g(θ) , that depends on the lattice occupancies, θ, or the surface coverage = =

where =

! " #

! $#$ " $%#

,

(3)

. ρc (mol.m-3) is the critical molar density of the gas and ρmax (mol.m-3) is the

maximum molar adsorbate density that is evaluated from an assumption of “close packing of spheres”. The critical and maximum molar adsorbate density values used in our work are tabulated in the appendix section (See Table A1). The LDFT method, calculates an increase in the adsorbate phase density with an increase in the bulk phase pressure. Accordingly, it is consistent with recent molecular simulation studies, for example, by Mosher et al.13 using GCMC simulations, who reported the adsorbate layer density of CH4 in gas shale and coal systems to increase with increasing bulk phase pressure. Malheiro et al.27 also found a similarly increasing trend of the adsorbate phase density in their model for argon and nitrogen sorption in slit carbon micropores. In summary, when using the LDFT method in calculating the adsorbate phase density of 11 ACS Paragon Plus Environment


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pure gases, we only need to estimate the Langmuir parameters (KA and ). For binary

mixtures, we apply the extended Langmuir model (ELM), to calculate the absolute adsorption on the shale:

,

(4)

,

(5)

where, subscripts 1 and 2 represent CH4 and C2H6, respectively, KA,1 and KA,2, are their (singlegas) sorption equilibrium constants (Pa-1), and p1 and p2, their partial pressures (Pa), denotes the maximum moles of CH4 adsorbed per unit weight of the sample (mmol/g), and

is effectively the ratio of shale surface occupied by a single C2H6 molecule to that occupied by a single CH4 molecule, assuming that the internal surfaces of the shale sample are equally accessible to CH4 and C2H6. To utilize eqs 4 and 5 to calculate the excess adsorption data, as measured by the TGA, the adsorbate density is needed. For the LDFT model, we follow the approach of Ottiger et al.23 and predict the adsorbate phase density of the mixture using eq 3 above. To apply eq 3 to a mixture, we calculate the critical (& and maximum (& ) molar densities of the mixture from & =

# and #( ∑) *+, " (

& =

# , # ( ∑) *+, ! (

with the fractional occupancies (surface

coverage) for CH4 and C2H6 obtained from ELM. We note, that for the binary mixtures, the LDFT approach is completely predictive.


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1.3.2

Sorption dynamics

Figure 2 below provides a schematic of the shale cube sample which includes arrows indicating the directions of mass transfer in (during adsorption – in the opposite direction out during desorption).

Figure 2 - Illustration of the shale cube and assumed directions for mass transfer used for modeling. As Figure 2 indicates, we assume here that there is no mass transfer in the vertical (z) direction of the shale, and that the gas transports only in the x and y directions. This assumption is consistent with the measurements reported by our group28 for these shales, whereby the vertical permeability (permeance) perpendicular to bedding plane, was found to be very low, and at least two orders of magnitude lower than that in the horizontal direction (x-y plane). Within the sample cube, we assume that the gas exists in two states: as free and as adsorbed gas. For the free gas, we assume that two different modes of transport prevail in the form of Knudsen diffusion and convection, while sorption is described by non-linear Langmuirtype kinetics. A general material balance for the shale cube can then be written as



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1 ∂ (ε p Z ) ∂n abs ∂J ∂J + (1− ε ) ρs =− x − y , RgT ∂t ∂t ∂x ∂y

(6)

where, Rg (J.K-1.mol-1) is the universal gas constant, T (K) is the temperature, Z is the compressibility factor of the bulk gas, ρs (kg.m-3) is the skeletal (true solid) density of the sample, nabs (mol/kg of solid) is the adsorbed phase concentration, Jx and Jy are the fluxes (mol.m-2.s-1) in the x and y directions, respectively. We further assume here that the transport properties in the x and y directions are equivalent, and thus eq 6 takes the following form

1 ∂ (ε p Z ) ∂n abs + (1− ε ) ρs = RgT ∂t ∂t p B0 ∂p  ∂  DM ∂ ( p Z ) p B0 ∂p  1  ∂  DM ∂ ( p Z ) +ε +ε  ε  + ε  RgT  ∂x  τ ∂x Z µτ ∂x  ∂y  τ ∂y Z µτ ∂y 

,

(7)

where DM is the Knudsen diffusivity (m2.s-1), τ is the tortuosity (we assume here that τ = 1/ε29), Bo (m2) is the viscous term, and µ (Pa.s-1) is the gas viscosity. The rate of change in the adsorbed concentration is described by

,

(8)

where, b is the internal surface area per unit volume of adsorbent (m2.m-3), and R (mol.m-2.s-1) is the net sorption rate described by the Langmuir sorption model abs R = ka (ZCRgT ( nmax − n abs ) −

n abs ) . KA

(9)

where ka (kg.bar-1.m-2.s-1) is the adsorption rate constant, KA (KA = ka/ kd ) is the sorption equilibrium constant (Pa-1), where kd (kg.m-2.s-1)is the rate constant for desorption, and

(mol/kg of solid) is the maximum sorption capacity. The change in porosity, ε, due to sorption


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can be can be described as

,

(10)

where εo is the initial porosity of the sample, and ρα (mol.m3) is the adsorbate phase density. The initial and boundary conditions to complete the cube model for pure gases are given as follows (for the first pressure step – conditions are adjusted accordingly for the remaining steps): 6

- = 0, 0 = 0, 12 = 0, 3 = 4 = 35 , 0 = 05 , 3 = 4 = 0,

6

6

= 67 = 0

.

(11)

For a binary mixture, the mass balance in the shale cube can be written as

(

)

1 ∂ εp Z ∂n abs + (1− ε ) ρs = ∂t ∂t RgT , (12)      ∂ p Z ∂ p Z  p B0 ∂p  ∂  D1M p B0 ∂p  1 ∂  D1M + ε B] +ε ε B] +ε   [ [ RgT  ∂x  τ ∂x Z µτ ∂x  ∂y  τ ∂y Z µτ ∂y   

(

)

(

)

where

,

(13)

,

(14)

,

(15)

.

(16)

n1abs and n2abs are the adsorbed phase concentrations (mol/kg of solid), C1 and C2 are the free gas 15 ACS Paragon Plus Environment


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phase concentrations (mol.m-3) corresponding to p1 and p2, D1M (m2.s-1) is the Knudsen diffusivity of CH4, and µ (Pa.s-1) is the gas viscosity (Pa.s-1). The matrix B is given by

[ B] =

 λ+x x1 1   M1 λ + x2 M 2  x2 M 2 M1 

1

λ + x1 + x2

    

,

(17)

where

,

,

.

(18)

D12 (m2.s-1) is the binary diffusivity coefficient of the CH4-C2H6 mixture in the shale, D2M (m2.s1

) is the Knudsen diffusivity of C2H6, and M1 and M2 are the molecular weights of CH4 and C2H6,

respectively. The binary gas sorption on the shale is described as

   abs   k  p n max − n abs − an abs −  n1  ( ) a,1 1 abs 1 2 K  abs    A,1   ∂n ρs = b   ∂t  n abs  max  ka,2  p2 ( nabs − n1abs − an2abs ) a −  2     K A,2  

       

,

(19)

where, 8 = ⁄% is the ratio of shale surface occupied by a single C2H6 molecule to that occupied by a single CH4 molecule, and is the maximum concentration of adsorbed species that the shale sample can accommodate (equal to , the maximum sorption capacity of CH4).

The binary diffusion coefficient, D12 is evaluated at a given pressure using the Chapman-Enskog theory30


Page 17 of 40

:% =

A .

Ethane

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