Multicomponent Potential Theory Of Adsorption Research Articles

Advanced modeling of diffusion and convection in multiphase compositional simulation for tight porous media

Small pore sizes influence the mass transport in gas enhanced oil recovery (EOR) in tight formations through complex phenomena such as diffusion and sorption. However, conventional simulators use relatively simple models for diffusion and sorption that do not properly represent non-ideal fluid interactions at high pressures. This paper presents a novel implementation of coupled diffusion and convection for multicomponent transport via the sorbed and bulk regions in tight porous media. Case studies highlight the important implication of convection in diffusion-dominant compositional transport in tight porous media.The simulator uses multicomponent diffusion based on the dusty-gas model (DGM), which uses the fugacity gradient as the driving force. The adsorption model used is an approximate solution based on the Multicomponent Potential Theory of Adsorption (MPTA) using the sorbed and central regions. The capillary pressure is included both in the flow equations and the flash calculations by minimizing the Helmholtz free energy using the Peng-Robinson equation of state at a fixed temperature, pore volume, and overall composition.A case study presents CO2 injection into a 1-D tight porous medium with a ternary mixture of methane, n-butane, and n-decane as the initial oil. Before CO2 injection, n-decane is most attracted to the pore wall and contained at a high concentration in the sorbed region. During CO2 injection, CO2 displaces n-decane from the pore wall, causing the counter-current transport of CO2 and n-decane.Simulation results show that the mixing of reservoir oil with CO2 in small pores results in local pressure changes, which tend to drive both diffusion and convection. In all cases, convection enhances multicomponent transport by dissipating these pressure changes. When CO2 is strongly attracted to the pore walls, a large pressure change on mixing accelerates the CO2 diffusion into the reservoir through the sorbed region and also the counter-current transport of oil components through the central region.

Capillary condensation: Limitations of the multicomponent potential theory of adsorption (MPTA)

Capillary condensation: Limitations of the multicomponent potential theory of adsorption (MPTA)

Application of multicomponent sorption for diffusive transport in numerical simulation of tight reservoirs

One of the main challenges in modeling compositional transport in tight formations is to include the complex interaction of chemical species with rock surfaces. Such interactions result in compositional variations near the surfaces, which can significantly affect the compositional diffusive transport through tight pores.This paper presents the application of the Multicomponent Potential Theory of Adsorption (MPTA) for the fluid compositions in the central and near-wall sorbed layers subject to a wall chemical potential. The two-layer approximation of MPTA is implemented in the diffusive transport simulation that computes the mass transfer driven by fugacity gradient based on the dusty gas model for the central and sorbed layers of pores. This simulator uses a partially implicit formulation to solve the multiphase multicomponent mass transfer equations including the sorbed layer.The main novelty of this paper lies in the detailed analysis of the interplay between fluid components and rock surfaces, which became possible with the two-layer MPTA coupled with multicomponent diffusion. The diffusion simulation for a ternary case of methane, n-butane, and n-decane with the approximate MPTA shows that the sorption and capillary pressure can cause the compositional segregation between the central and sorbed layers. The segregation enhances the rates of methane injection and n-decane production in their counter-current diffusion. Methane (the lightest) is transported deep into the reservoir by diffusing through the central layer while n-decane (the heaviest) is diffused primarily through the sorbed layer. n-Butane (the intermediate) does not show preferential partitioning into either layer, resulting in relatively inefficient transport. In the absence of sorption and capillary pressure, the countercurrent diffusion occurs between methane (the lightest) and n-butane (the intermediate) while n-decane (the heaviest) remains nearly immobile. That is, whether the simulation considers the surface-fluid interactions can substantially affect the compositional transport (e.g., produced fluid composition) through tight porous media.The multicomponent Langmuir model is often used for computing the sorbed excess in micropores. However, results show that the Langmuir model becomes physically inconsistent at high pressures because it predicts a monotonically increasing function of pressure. The new approach developed in this research is sufficiently flexible and reasonably accurate for modeling multicomponent sorption at high pressures.

Simulation of high-pressure sour natural gas adsorption equilibrium on NaX and NaY zeolites using the multicomponent potential theory of adsorption

Simulation of high-pressure sour natural gas adsorption equilibrium on NaX and NaY zeolites using the multicomponent potential theory of adsorption

Adsorption behavior modeling of confined hydrocarbons in shale heterogeneous nanopores by the potential theory

AbstractIn this article, a new method is proposed to quantificationally evaluate the effect of pore heterogeneity on the adsorption behavior of fluids in nanopores. First, the assumptions of furrowed, sinusoidal, and ravine pore surfaces are proposed to represent the heterogeneous nanopores in shale. Under the assumptions, a multicomponent potential theory of adsorption (MPTA) is coupled with Peng–Robinson equation of state (PR EOS) to model the adsorption behavior of hydrocarbons in nanopores. And, the geometrical and chemical heterogeneities in shale nanopores are, respectively, simulated by a spatial alteration and an amplitude deformation on potential energy. The fluid–fluid interaction is modeled by PR EOS, and the fluid‐pore wall surface interaction is simulated by a Steel 10‐4‐3 model for slit‐like nanopores and by a modified Lennard–Jones (LJ) 12‐6 model for cylindrical ones. Thereafter, the results of our theory are compared against the experimental data of shale rocks to validate its accuracy.

Modeling confined fluids with the multicomponent potential theory of adsorption and the SAFT-VR Mie equation of state

In this work, the SAFT-VR Mie equation of state is used in conjunction with the Dubinin-Radushkevich-Astakhov (DRA) and Steele potentials, according to the Multicomponent Potential Theory of Adsorption (MPTA), to model the thermodynamic behavior of fluids confined in porous media. The problem specifications are the temperature, volume, and number of moles of each component, yielding a Helmholtz energy-minimization problem. Calculation results show very good agreement with experimental adsorption data for systems of methane, nitrogen, carbon dioxide, ethane, ethylene, and isobutane adsorbed on activated carbon and molecular sieve.

Decoupled multicomponent potential theory of adsorption of gas mixtures

In this paper, we present a new implementation of the Multicomponent Potential Theory of Adsorption model. The proposed interpretation establishes a clear cut between parameters that depends on the adsorbent from those depending on the adsorbate, which leads to a better understanding of the parameters signification. The interdependence between pure isotherms is eliminated, which mean that each component can be individually finely adjusted. This new approach was tested against 14 datasets for a total of 510 experimental mixture adsorption data of CH4, CO2, N2, H2, O2, H2S, C2H6, C3H6 and C3H8 on activated carbons, MOF and zeolites. A slight improvement of 4.67% on excess adsorption predictions was found, leading to an overall average error of 6.97% for total excess adsorption and 15.30% for combined mixtures and components excess adsorption predictions.

Ammonia/Ethanol Mixture for Adsorption Refrigeration

Adsorption refrigeration has become an attractive technology due to the capability to exploit low-grade thermal energy for cooling power generation and the use of environmentally friendly refrigerants. Traditionally, these systems work with pure fluids such as water, ethanol, methanol, and ammonia. Nevertheless, the operating conditions make their commercialization still unfeasible, especially owing to safety and cost issues as a consequence of the working pressures, which are higher or lower than 1 atm. The present work represents the first thermodynamic insight in the use of mixtures for adsorption refrigeration and aims to assess the performance of a binary system of ammonia and ethanol. According to the Gibbs’ phase rule, the addition of a component introduces an additional degree of freedom, which allows to adjust the pressure of the system varying the composition of the mixture. The refrigeration process was simulated with isothermal- isochoric flash calculations to solve the phase equilibria, described by the Peng-Robinson-Stryjek-Vera (PRSV) equation of state for the vapor and liquid phases and by the ideal adsorbed solution theory (IAST) and the multicomponent potential theory of adsorption (MPTA) for the adsorbed phase. In operating condenser and evaporator, pressure levels around atmospheric pressure can be achieved using an ammonia/ethanol mixture with a mole fraction of ethanol in the range of 0.70−0.75. A good agreement in the predictions of the adsorbed phase composition was also reported using the IAST and the MPTA methods.

Gas Adsorption and Interfacial Tension with Classical Density Functional Theory

A classical density functional theory (DFT) that reduces to the perturbed chain statistical associating fluid theory equation of state has been implemented. This DFT implementation allows the use of molecular and binary interaction parameters fitted to the vapor–liquid equilibria of pure compounds and binary mixtures, respectively. Different functionals of dispersion forces are investigated and applied to the calculation of interfacial tension and adsorption of pure gases and their mixtures. The predictions of interfacial tension have been compared with both molecular simulations and experimental data, and good agreements have been seen. The DFT approaches also show good performance in correlating and predicting gas adsorption, and they are further compared with the multicomponent potential theory of adsorption and other DFT approaches available in the literature.

Influence of Adsorption and Capillary Pressure on Phase Equilibria inside Shale Reservoirs

As a result of the small pore sizes and organic content of shale, capillary pressure and adsorption are two effects that should be taken into account in the study of phase equilibrium inside shale. The inclusion of both effects in the phase equilibrium modeling can shed light on how bulk phase composition inside the porous media changes with the temperature and pressure and how the phase equilibrium changes accordingly. In the long run, such a model can be used in reservoir simulation for more complicated analysis. In this study, we present a calculation method that can effectively include adsorption and capillarity. We propose to introduce an excess adsorbed phase and treat the remaining substance inside the pores as a bulk phase (gas, liquid, or both) to make the mass balance formulation simpler. The adsorbed phase is modeled by the multicomponent Langmuir (ML) equation for its simplicity and computational efficiency. A more theoretical adsorption model, the multicomponent potential theory of adsorption...

Numerical Implementation of the Multicomponent Potential Theory of Adsorption in Python Using the NIST Refprop Database

In this paper, we present a detailed numerical implementation of the multicomponent potential theory of adsorption which is among the most accurate gas mixtures adsorption models. The implementation uses the NIST Refprop database to describe fluid properties and applies to pure gases and mixtures in both subcritical and supercritical regimes. The limitations of the model and the issues encountered with its implementation are discussed. The adsorption isotherms of CH4 / CO2 mixture are modeled and parameterized as implementation examples.

Modeling of mixed-gas adsorption on shale using hPC-SAFT-MPTA

Knowledge of mixed-gas adsorption behavior on shale is important for reserve estimation, production forecast, and carbon dioxide sequestration. In this work, we combined the multicomponent potential theory of adsorption (MPTA) with the hybrid perturbed-chain statistical associating fluid theory equation of state (hPC-SAFT EOS) to describe mixed-gas adsorption on shale. In the hPC-SAFT-MPTA model, the fluid-solid interaction is modeled using the Dubinin-Radushkevich-Astakhov (DRA) potential and the fluid-fluid interaction is described by the hPC-SAFT EOS. Extending the hPC-SAFT-MPTA model to excess adsorption is straightforward and has no need to estimate the adsorbed phase density. Experimental data on the pure-component and mixture adsorption of CH4, C2H6, CO2, and N2 on activated carbon and shale were used to test the hPC-SAFT-MPTA model. Activated carbon was employed asa reference adsorbent because its pore structure is simpler than that of shale. The hPC-SAFT-MPTA model can predict the mixture adsorption with average relative errors of 10.34%–17.12% on the basis of the pure gas adsorption data. The hPC-SAFT-MPTA model provides an alternative approach to modeling mixed-gas adsorption on shale and complements sophisticated methods such as density functional theory and the grand canonical Monte Carlo simulation method. The hPC-SAFT-MPTA model is anticipated to be useful in simulations of shale gas production and CO2 sequestration in shale.

Study of the confined behavior of hydrocarbons in organic nanopores by the potential theory

To accurately describe the confined behavior of hydrocarbons in nanopores has become a top priority for the effective development of unconventional resources. In this paper, the multicomponent potential theory of adsorption (MPTA) is coupled with the cubic Peng-Robinson (PR) equation of state (EOS) to investigate and represent the confined behavior of pure hydrocarbons and their mixtures in organic nanopores. In this theory, the fluid–fluid interactions are modeled by the PR EOS. For the fluid-solid interactions, the 10-4-3 Steele potential is used for slit-like nanopores, and a modified Lennard-Jones (LJ) 10-6 potential is used for cylindrical nanopores. Then a prediction process for the behavior of methane, ethane, propane and their mixtures (binary and ternary mixtures) is performed. The results are compared against experimental data on the adsorbents of activated carbons (slit-like nanopores) and MCM-41 silica (cylindrical nanopores) to validate the accuracy of the theory and process. Results indicate that for the sets of experimental data considered in this work, the theory is capable of predicting the confined behavior of pure components in wide ranges of pressure and temperature. For pure components, because of the different interaction energy between fluids and solid walls, the density of confined fluids in the slit-like nanopores (activated carbon type) is much higher than that in the cylindrical nanopores (MCM-41 silica type). As a position (z) approaches the pore surface, the effect of fluid-solid interactions is enhanced, and the density of confined fluids is increased. For binary mixtures, the mole fraction of the heavier component (C2H6/C3H8) around the pore surface is extremely higher than that of the lighter component (CH4). The higher the difference between the two components, the higher the difference of the mole fractions and fluid densities of the two components in nanopores. For a ternary mixture, the confined behavior of the three components within nanopores is significantly different. As a position approaches the pore center, the mole fraction of the lightest component is increased gradually, and the mole fraction of the heaviest component is reduced gradually. The medium component shows a tendency of increasing first and reducing then. This investigation makes it possible to get some new insights on the confined behavior of hydrocarbons in nanopores with different geometries.

Potential theory for prediction of high-pressure gas mixture adsorption on activated carbon and MOFs

While selective adsorption of carbon dioxide has recently attracted special interest due to concerns over greenhouse emissions, separation of methane from its mixtures with carbon dioxide and nitrogen is a key operation for biogas and natural gas enrichment. Herein we present a detailed study of the multicomponent potential theory of adsorption’s (MPTA) capabilities to predict published experimental adsorption data of binary and ternary mixtures of carbon dioxide, methane and nitrogen from each gas’ pure component adsorption data on activated carbons Norit R1 and Calgon F-400 and on the metal–organic frameworks (MOFs) MOF-508b and MOF-5. It is observed that at temperatures below its critical temperature (304K), and pressures in the vicinity of its critical pressure (7.37MPa), carbon dioxide content in the binary mixtures adsorbed on Norit R1 has significant influence on the accuracy of MPTA’s predictions, as sharp mixture density increases due to possible carbon dioxide phase changes cause convergence difficulties in the model’s numerical iterations. This phenomenon is not observed in the studied ternary mixtures’ case. Here, discrepancies are rather attributed to the inherent limitations of using four adjustable parameters to describe multicomponent adsorption at high pressure, and to the additive errors associated with the volumetric experimental measurement technique. Carbon dioxide’s high selectivity due to its strong quadrupole moment is well predicted by the MPTA, on activated carbon as well as on MOFs.

Performance comparison of adsorption isotherm models for supercritical hydrogen sorption on MOFs

Modeling of adsorption on porous material plays a crucial role in providing a better understanding of adsorption phenomena, isotherms, and isosteric heats, and predicting the thermodynamics of adsorption-based storage systems. In this work, the multicomponent potential theory of adsorption (MPTA) coupled with the modified Dubinin potential (MDP), the modified Dubinin–Astakhov (DA) model, and the Unilan model are compared for their effectiveness in nonlinear least square fitting of experimental hydrogen adsorption data on three prototypical metal–organic frameworks (MOFs) in two temperature ranges: 30K—room temperature (RT) for MOF-5, and 77K—RT for MOF-5, Cu-BTC, and MIL-101. The ability of each model to accurately describe excess adsorption is found to depend on the pore size and the energetic pore heterogeneity of MOFs, and the latter's relation to the assumptions used within each model. The simpler Langmuir-like Unilan model complies best with the monolayer type adsorption mechanism in MOFs with large pores and homogenous pore distribution, such as in MOF-5, while the pore filling models like modified DA and MPTA–MDP better represent the adsorption phenomena in MOFs with smaller pores and heterogeneous pore distributions, such as Cu-BTC and MIL-101. In the vicinity of hydrogen's critical temperature, adsorbed hydrogen inside the pores of MOF-5 undergoes a phase-transition to solid-like phase with densities higher than that of bulk solid hydrogen, which is attributed to the increased force field in the confined pores of MOF-5.

Potential Theory of Adsorption for Associating Mixtures: Possibilities and Limitations

The applicability of the multicomponent potential theory of adsorption (MPTA) for the prediction of the adsorption equilibria of several associating binary mixtures on different industrial adsorbents was investigated. In the MPTA, the adsorbates are considered to be distributed fluids subject to an external potential field emitted by the adsorbent. In this work, the theory was extended to include the cubic-plus-association (CPA) equation of state (EoS) for the description of the fluid–fluid interactions of associating mixtures. The Dubinin–Radushkevich–Astakhov (DRA) potential function was utilized to describe the solid–fluid interactions. The potential was extended to include adsorbate–absorbent-specific capacities rather than an adsorbent-specific capacity. Correlations of pure-component isotherms were generally found to be excellent with individual capacities, although adsorption on silicas at different temperatures still poses a challenge. The quality of the correlations was usually found to be independent of the applied EoS. Predictions for binary mixtures indicate that MPTA + SRK is superior when adsorption occurs on nonpolar or slightly polar adsorbents, whereas MPTA + CPA performs better for polar adsorbents or when the binary mixtures contain only associating compounds. Predictions were typically improved by about 3% when individual capacities were employed, but improvements in some cases were as large as 45%. When individual capacities and the best-performing EoS were used, average absolute deviations of the selectivity were as low as 7–12%. Predictions of the selectivity were generally found to be superior to predictions of the adsorbed amounts. The sensitivity of the model was also tested, and it was concluded that the predictions are very sensitive to the adsorption energies.

Modified potential theory for modeling supercritical gas adsorption

Theoretical modeling of adsorption plays a crucial role in providing better understanding of the adsorption phenomena, isotherms and isosteric heats. However, when modeling the adsorption of gas mixtures containing hydrogen, it is necessary to accommodate a wide temperature range because of hydrogen's low critical temperature. In this work, we extend the multicomponent potential theory of adsorption's (MPTA) capability of predicting adsorption isotherms to a wide temperature range by introducing a temperature dependent Dubinin potential parameter and use it to model adsorption isotherms of supercritical hydrogen, nitrogen and methane on various activated carbons. This extended MPTA can accurately predict the adsorption isotherms when used with NIST equation of state (EOS). The resulting isosteric heats of adsorption of hydrogen agree well with the experimental data for similar volume filling scenarios. Hydrogen's low temperature adsorbed-phase pressure inside the activated carbon's micropore volume reaches the melting pressure of solid hydrogen. This causes the transition of adsorbed hydrogen from supercritical gas to solid-like phase which is clearly observed in our model. Our study, thus, provides a better understanding of physisorption of hydrogen inside the micropores.

Study of high-pressure adsorption from supercritical fluids by the potential theory

The multicomponent potential theory of adsorption (MPTA), which has been previously used to study low-pressure adsorption of subcritical fluids, is extended to adsorption equilibria from supercritical fluids up to high pressures. The MPTA describes an adsorbed phase as an inhomogeneous fluid with thermodynamic properties that depend on the distance from the solid surface (or position in the porous space). The description involves the two kinds of interactions present in the adsorbed fluid, i.e. the fluid–fluid and fluid–solid interactions, accounted for by means of an equation of state (EoS) and interaction potential functions, respectively. This makes it possible to generate the different MPTA models by combination of the relevant EoS/potentials. In the present work, the simplified perturbed-chain statistical associating fluid theory (sPC-SAFT) EoS is used for the thermodynamic description of both the adsorbed and the gas phases. We have also evaluated the performance of the classical Soave–Redlich–Kwong (SRK) EoS. The fluid–solid interactions are described by simple Dubinin–Radushkevich–Astakhov (DRA) potentials. In addition, we test the performance of the 10-4-3 Steele potential. It is shown that application of sPC-SAFT slightly improves the performance of the MPTA and that in spite of its simplicity, the DRA model can be considered as an accurate potential, especially, for mixture adsorption. We show that, for the sets of experimental data considered in this work, the MPTA is capable of predicting adsorption of pure components and binary mixtures in wide ranges of pressure and temperature. A good agreement with the theoretical predictions is achieved in most of the cases. The MPTA is capable to correctly describe complex physical behavior observed at supercritical/high-pressure conditions. Some limitations of the model are also discussed.

Modeling adsorption of liquid mixtures on porous materials

The multicomponent potential theory of adsorption (MPTA), which was previously applied to adsorption from gases, is extended onto adsorption of liquid mixtures on porous materials. In the MPTA, the adsorbed fluid is considered as an inhomogeneous liquid with thermodynamic properties that depend on the distance from the solid surface (or position in the porous space). The theory describes the two kinds of interactions present in the adsorbed fluid, i.e. the fluid–fluid and fluid–solid interactions, by means of an equation of state and interaction potentials, respectively. The proposed extension of the MPTA onto liquids has been tested on experimental binary and ternary adsorption data. We show that, for the set of experimental data considered in this work, the MPTA model is capable of correlating binary adsorption equilibria. Based on binary adsorption data, the theory can then predict ternary adsorption equilibria. Good agreement with the theoretical predictions is achieved in most of the cases. Some limitations of the model are also discussed.

Prediction of adsorption from liquid mixtures in microporous media by the potential theory

Despite its industrial importance, adsorption from the liquid phase has been studied much less extensively than adsorption from the gas phase. In this paper, we study the adsorption of liquid mixtures on the basis of the multicomponent potential theory of adsorption (MPTA). The MPTA is based on the potential concept originally developed by Polanyi. In this theory, the driving force for physical adsorption is measured by the adsorption potential that is a function of the distance from the solid surface. In this way, the adsorbate is considered as a heterogeneous substance segregated in the external field emitted by the adsorbent, with thermodynamic parameters that are function of the distance from the solid. The MPTA then uses a thermodynamic model to describe the equilibrium between bulk and adsorbed phases (or the fluid–fluid interactions), and potential models for the fluid–solid interactions. With this approach, few parameters are needed to predict adsorption equilibria. The MPTA has been so far used to successfully predict adsorption equilibria of multicomponent gas mixtures. The aim of this work is to extent the MPTA onto adsorption from liquid solutions. We show that such extension is straightforward, obtaining relatively simple models useful for engineering applications. Comparison with experimental data shows good agreement and high degree of predictability.