A multi-scale approach to the physical adsorption in slit pores

doi:10.1016/j.ces.2011.04.045

Chemical Engineering Science

Volume 66, Issue 22, 15 November 2011, Pages 5447-5458

https://doi.org/10.1016/j.ces.2011.04.045 Get rights and content

Abstract

Adsorption isotherms are the foundation of gas storage and separation operations. The isotherm models are classified into three scale levels with empiricisms in macroscopic level, requirements of long computing time and idealized conditions in microscopic level, as well as gaps in knowledge between these two levels. A multi-scale modeling methodology is developed in this paper in order to reduce the identified limitations. Microscopic molecular simulations (MS) based on the grand canonical Monte Carlo (GCMC) method are carried out followed by the development of the localized adsorption isotherms defined as the intermediate level models. They are represented by the Boltzmann factor and the local Langmuir equations. The macroscopic models are then formulated through the integration of small scale models. The following three contributions are achieved in the paper. First of all, guidelines for the validity of the Boltzmann factor are established, showing its practical significance, and the local Langmuir isotherm is justified as a good approximation to the results from microscopic simulations. Secondly, it is demonstrated that the pore size distributions can be determined using GCMC simulations coupled with the measured adsorption isotherms as exemplified by a case study on a coal specimen. Finally, using the measurement data reported by Bae and Bhatia (2006) for carbon dioxide adsorption on coal, we show that the overall adsorption isotherms can be determined from the multi-scale approach through the integration of smaller scale models with pore size distributions without the empiricism, indicating the success of the methodology. Further work is needed to improve the prediction accuracy for methane adsorption on coal specimens.

Highlights

► A multi-scale modeling methodology is developed. ► Guidelines for the validity of the Boltzmann factor are established. ► It is demonstrated that the pore size distributions can be determined. ► Overall adsorption isotherms can be determined from the multi-scale approach.

Introduction

Research into gas separation and storage must focus on adsorption isotherms as they are fundamental to such processes. The research methodology for calculating adsorption isotherms can be classified into three models pitched at three different levels of scale. These include: a microscopic model involving Molecular Simulation (MS) such as the Grand Canonical Monte Carlo simulation (GCMC) and Molecular Dynamic simulation (MD); an intermediate (mesoscopic) model using the Boltzmann factor (Steele and Halsey, 1955, Barker and Everett, 1962) and local isotherm equations; and macroscopic models using curve fitting with experimental data. There are advantages and disadvantages of using these different scale models for predicting adsorption isotherms. First, although the molecular simulation in the microscopic model has a fundamental basis with the ability to obtain physical insights, it requires extensive computing time and idealized conditions significantly different from a real working system. Second, the macroscopic model can be used to make predictions of the adsorption isotherm, which agree with the measurement data very well. However, this model is empirical requiring expensive experiments and lacks physical insights. Lastly, the intermediate model is economic in time spent on calculations with outcomes consistent with the results obtained from molecular simulations which make it suitable for industrial applications (Wang et al., 2008). However, the intermediate model is restricted to certain conditions. For example, the Boltzmann factor is limited to low pressure conditions and local isotherm equations require fitting parameters with GCMC simulation. Furthermore, effective techniques for the development of large-scale models through the integration of small-scale models depend on particular systems, which require further studies.

Due to the limitations of the existing techniques, this work aims to develop a multi-scale modeling methodology for the development of adsorption isotherms at various scales, which is start from, and verified by comprehensive GCMC simulations including multi-center potential models under a broad range of conditions. The research starts with a focus on the development of the intermediate models represented by the Boltzmann factor and the local isotherm equation for calculating the local adsorption isotherm. The pressure limits for the validity of the Boltzmann factor for both CO₂ and CH₄ in nanopores with various sizes will be determined, and the parameters of the local isotherm equations will be identified. The macroscopic models are then formulated through the integration of small-scale models with the pore size distributions estimated in this work. The macroscopic models are used to predict the overall adsorption isotherms and the simulation results are compared with the measurement data of Bae and Bhatia (2006) on high-pressure adsorption of CH₄ and CO₂ on coal.

In previous work on coal seams (Wang et al., 2007a, Wang et al., 2007b), coal has been nominated as a receptacle for CO₂ storage as CO₂ has larger adsorption affinity on coal than CH₄. This fact allows the CH₄ in coal seams to be replaced by CO₂ with the CH₄ being sold to help cover the costs of the process. There has been a lot of work done using both the empirical and fundamental methods to describe the high pressure adsorption of fluids by activated carbons with limited work reported in the literature on the use of coal for such processes. Therefore, this paper also aims to use the macroscopic models formulated through the integration of small scale models to predict the excess absorbed amount of molecules in a coal sample. The incomplete pore size distribution reported by Bae and Bhatia (2006) is modified using simulations coupled with measured adsorption isotherms. The excess adsorbed amount of CO₂ and CH₄ computed in this work can be suitably represented by the Toth isotherm equation, which is consistent with the conclusion drawn by Bae and Bhatia (2006).

In summary, this work includes: molecular simulations using the GCMC method based on multi-site potential energy models accounting for the atom–atom and charge–charge interactions, which can be classified as the microscopic model; the integrated Boltzmann factor and the local isotherm equations of Langmuir, which constitutes the intermediate models; and the overall adsorption isotherm equations formulated from the integration of various small-scale models, which can be considered as the macroscopic model. Due to the modeling strategy involves three size scales; it is defined as a multi-scale approach.

Section snippets

Potential energy

In the conventional practice for computing potential energy, molecules are assumed to be regular hard spheres thus allowing application of the well-known Lennard-Jones 6–12 and Steele 10–4–3 potential models (Steele, 1974). This assumption is called a single-site model, which works well with small molecules. However, for large molecules, such as carbon tetrachloride and benzene, the conventional single-site potential energy model leads to significant errors due to the violation of the

Micro-scale model simulation set up

Grand canonical Monte Carlo (GCMC) is used for the simulation of the local adsorption isotherm (shown as the physical pore density or the number of particles in a pore). The fluid–fluid interaction potential is determined using Lennard-Jones 6–12 and the Coulomb law for the electrostatic interaction. The solid–fluid interaction is assumed to be slit-shaped pore whereby Steele 10–4–3 is employed for the simulation. The potential energy can be seen in Section 2.1. The Visual Studio FORTRAN

Microscopic simulation

Fig. 1 depicts information on molecular configurations. Various potential energies accounting for molecule–molecule, molecule–wall, and charge–charge interactions, and molecule density distribution in nanopores can be obtained through molecular simulations using the configurations depicted in Fig. 1. Both single-site and multi-site potential energy models are used in simulations for the comparison purpose. Although very rich information has been obtained through molecular simulations, only

Conclusion

A multi-scale modeling approach to the physical adsorption in slit pores is developed in this paper consisting of molecular simulations at the microscopic level, formulation of local and overall adsorption isotherms at the intermediate and macroscopic levels, respectively. Through a detailed analysis of the simulation results at various levels and the available experimental data, the following conclusions can be drawn:

1.
A multi-site model is recommended for the computation of potential energies

Acknowledgements

The authors thank Professor David Nicholson for his professional help and valuable discussions of GCMC simulations. The financial support from Australian Research Council Discovery Project is greatly appreciated.

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A multi-scale approach to the physical adsorption in slit pores

Abstract

Highlights

Introduction

Section snippets

Potential energy

Micro-scale model simulation set up

Microscopic simulation

Conclusion

Acknowledgements

Fuel

Colloids and Surfaces A: Physicochemical and Engineering Aspects

Chemical Engineering Science

High-pressure adsorption of methane and carbon dioxide on coal

Energy & Fuels

High temperature adsorption and the determination of the surface area of solids

Transactions of the Faraday Society

High-pressure adsorption capacity and structure of CO2 in carbon slit pores: theory and simulation

Langmuir

Adsorption Analysis: Equilibria and Kinetics

Pore characterization of carbonaceous materials by DFT and GCMC simulations: a review

Adsorption Science and Technology

Adsorption of carbon tetrachloride on graphitized carbon black and in slit graphitic pores: five-site versus one-site potential models

The Journal of Physical Chemistry B

Adsorption of benzene on graphitized carbon black: reduction of the quadrupole moment in the adsorbed phase

Langmuir

High pressure adsorption data of methane, nitrogen, carbon dioxide and their binary and ternary mixtures on activated carbon

Adsorption

High-pressure adsorption capacity and structure of CO₂ in carbon slit pores: theory and simulation