Abstract

We formulate a mathematical model for temperature-swing adsorption systems. A finite-volume method is derived for the numerical solution of the model equations. We specifically investigate the influence of the choice of spatial discretization scheme for the convective terms on the accuracy, convergence rate and general computational performance of the proposed method. The analysis is performed with the nonlinear Dubinin-Radushkevich isotherm representing benzene adsorption onto activated carbon, relevant for gas cleaning in biomass gasification.The large differences in accuracy and convergence between lower- and higher-order schemes for pure scalar advection are significantly reduced when using a non-linear isotherm. However, some of these differences re-emerge when simulating adsorption/desorption cycling. We show that the proposed model can be applied to industrial-scale systems at moderate spatial resolution and at an acceptable computational cost, provided that higher-order discretization is employed for the convective terms.

Highlights

  • Separation processes account for roughly 10–15% of the world’s energy consumption (Sholl and Lively, 2016)

  • The present results suggest that numerical modeling of non-linear adsorption systems is less sensitive to numerical dispersion from lower-order spatial discretization than previously believed

  • We present a finite-volume method for numerical simulations of industrial temperature-swing adsorption processes

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Summary

Introduction

Separation processes account for roughly 10–15% of the world’s energy consumption (Sholl and Lively, 2016). This regeneration can be performed by increasing the temperature of the gas passing through the bed, which causes desorption of the adsorbent This process scheme is referred to as temperature-swing adsorption. The physicochemical nature of the adsorption process tends to produce sharp concentration and temperature fronts that propagate through the system The sharpness of these fronts, in conjunction with the large size of the equipment in many industrial applications where adsorption columns can be many meters wide and tall, poses great challenges for many traditional numerical modeling techniques. The model is general in its formulation, but in our own work primarily intended for application in gas cleaning of producer gas from biomass gasification, where benzene is the main adsorbate species, the bed consists of activated carbon and the process is carried out at ambient pressure (Thunman et al, 2018). Our objective is in particular to assess the effect of spatial resolution on the ability of different discretization schemes to accurately resolve this approach towards cyclic steady state in temperature-swing adsorption with a non-linear isotherm

Governing equations
Main model - partial differential equations
Ancillary expressions - heat and mass transfer correlations
Ancillary expressions - adsorption isotherm
Initial and boundary conditions
Finite volume method
TVD Schemes
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Discretization of each equation
Solution process
Simulations of transport and adsorption
Numerical dispersion
Conclusions
Declaration of Competing Interest
Full Text
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