Approximation of a PSA process based on an equivalent continuous countercurrent flow process: Blow-up and blow-down representation

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Abstract

To design cyclic separation processes by adsorption, such as pressure swing adsorption (PSA) processes, one has to simulate the start-up time in order to determine the cyclic steady state (CSS), which can be very time-consuming. A fast way to estimate the CSS reached by a PSA process is proposed by Suzuki (1985)—assuming equivalency between the PSA system and a continuous countercurrent flow system (CCF). The CCF model is improved in the present paper, taking into account the gaseous phase located in a column when the system switches from a constant pressure step to another step. By performing a parametric study, the limits of the CCF model are tested. It is shown that this model can quantitatively predict the purities and recoveries obtained at CSS for kinetically controlled separation by comparison with a detailed model of PSA. It is also shown that the CCF model can also give a good approximation of the dynamic behavior of the PSA process. Finally, the simulation of dry air separation is proposed.

Introduction

Since the early 1960s, separation processes by adsorption, such as pressure swing adsorption (PSA) processes, have become important industrial operations.

Due to bed saturation phenomenon, the adsorption bed has to be regenerated in all adsorption-based processes. This is why these processes differ from other separation processes such as absorption, extraction, and distillation, in one essential feature: they operate under transient conditions. In addition, an adsorption column is a distributed system. This is why the mathematical modeling of an adsorption bed leads to a system of partial differential equations involving time and spatial coordinates.

After a start-up time, the PSA system reaches a cyclic steady state (CSS), at which the process state variables at some instant within a cycle have the same values as at the corresponding instant within each subsequent cycle.

The efficiency of a PSA process is determined at the CSS, but many cycles are needed to reach it. Thus, using the traditional way of simulating such a process—which is to carry out simulations of each step from a given initial condition, over a large number of cycles—the design and the optimization of a PSA process are very difficult and require very time-consuming computations, even when a simplified mass transfer model is used.

A fast and accurate estimation of the CSS profiles and performances of a PSA process could be of great help to design a process and to study the influence of all relevant process parameters. To this end, some authors have investigated the use of numerical methods in order to speed up the convergence rate (Kvamsdal and Hertzberg, 1997, Smith and Westerberg, 1992, Ding and LeVan, 2001, Choong et al., 2002).

Todd et al. (2003) switch from a simplified mass transfer model based simulator to a complex mass transfer model based simulator: the CSS state profiles obtained with the simplified model are used as initials conditions to the more realistic one.

In 1985, Suzuki has proposed another strategy in order to estimate the CSS, assuming equivalency of the PSA system operated on a Skarstrom cycle and the continuous countercurrent flow (CCF) system. The model is then largely simplified, and computation times are strongly decreased. The model, however, preserves a physical meaning and gives a good comprehension of the process and parameters which determine its performances.

Suzuki developed the CCF model for a trace component system. Sundaram (1993) solved analytically the CCF model for a single adsorbing component, under isothermal conditions. Farooq and Ruthven (1990) extended the CCF model for a bulk separation process, and Farooq et al. (1994) applied the CCF model to a bulk PSA process operated on a Skarstrom cycle in which the durations of the individual steps are different.

The simulations results obtained by Farooq and Ruthven (1990) and Carta (2003) give only qualitative trends: the purities of the products are over-estimated by the CCF model. This deviation can be related to the accumulated products present in the interstitial volume at the end of each constant pressure step.

The aim of this paper is to extend Suzuki's model by introducing a correction based on the quantities involved when the process switches from one step to another. After a presentation of the Suzuki's model, we describe how we improved it. Then, the influence of those improvements was checked by comparing simulations obtained using the Suzuki's model, our improved CCF model and a detailed PSA model.

Section snippets

Skarstrom cycle

The PSA process is a cyclic separation process based on adsorption in fixed beds. The smallest PSA system is composed of two packed adsorbent beds (Ruthven et al., 1994).

During a PSA cycle, the pressure varies, adsorption being favored at high pressure, and desorption at low pressure. A PSA cycle is then a succession of high pressure adsorption steps, and of low pressure desorption (purge) steps. Between an adsorption step and a purge step, an intermediate blow-down step is intercalated. And

Equivalent CCF approximation

In this part, the principle of the approximation of a cyclic process by a continuous one as proposed by Suzuki (1985) for kinetic controlled PSA processes is firstly presented. A model of the CCF system is subsequently described.

Representation of the switching effect

The model described above only predicts qualitative trends in the case of bulk separation (Farooq and Ruthven, 1990). The variation from the experimental data can be related to one of the major consequence of the switching phenomena of the PSA system: all the molecules present in the gas phase at the end of an adsorption step will be present at the beginning of the next blow-down step, leading to a direct mass transfer from the high pressure step to the low pressure step without diffusing

Complete PSA model

In order to study the CCF model accuracy and efficiency, a complete PSA model has been developed, using assumptions that have already been successfully applied to simulate a PSA process (Takamura et al., 2001), and is used as reference. The present model differs from the Takamura et al. (2001) one by doing the state variable change: in their model, the LDFG model is used, but q¯i and not c¯i is used as the adsorbed phase state variable.

By using the same assumptions as for the CCF model, one

Dimensional analysis

The above equations are written in dimensionless form, using the column length and the adsorption step duration as references. The time and spatial coordinates areθtΔtads,χzL.Any adsorption isotherm can be used in the previous models, provided that their derivatives are defined for every value of ci*. In order to illustrate non-linear systems, the thermodynamic equilibriums are represented by multi-component Langmuir isotherms:qiqiS=bici*1+j=1ncbjcj*.These isotherms give the following

Conclusion

The necessity to reach the cyclic steady state (CSS) in order to estimate the efficiency of a pressure swing adsorption (PSA) process makes the design and the optimization of such a system difficult. In the literature, the model based on the equivalency of the PSA system and a continuous countercurrent flow (CCF) system only gives qualitative trends.

An improved CCF model is developed in this paper, taking into account the gaseous phase located in a column when the PSA system switches from a

Notation

asspecific particle area, m-1
biLangmuir equilibrium constant, m3mol-1
cii component gas phase concentration, molm-3
c0ii component concentration at the inlet, molm-3
c¯i*i component average concentration of a gaseous phase in equilibrium with the adsorbed phase at q¯i, molm-3
cisuri component concentration of the fluid phase at the adsorbent surface, molm-3
cTtotal concentration in gas phase, molm-3
DLaxial dispersion coefficient, m2s-1
Fii component molar flux, molm-2s-1
FiFHi component molar flux of

Acknowledgements

This work was partially supported by the EU-project GeoPleX EU-IST-2001-34166, see http://www.geoplex.cc. The authors would also like to thank the Institut Français du Pétrole for its financial support.

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