Trickle Bed Reactor1

Journal of Computational Physics 165, 311–333 (2000) doi:10.1006/jcph.2000.6604, available online at http://www.idealibrary.com on

A Numerical Model for Trickle Bed Reactors1
Richard M. Propp, Phillip Colella, William Y. Crutchfield, and Marcus S. Day
Lawrence Berkeley National Laboratory, Berkeley, California 94720 E-mail: RMPropp@lbl.gov, PColella@lbl.gov, WYCrutchfield@lbl.gov,MSDay@lbl.gov Received March 18, 1999; revised January 25, 2000

Trickle bed reactors are governed by equations of flow in porous media such as Darcy’s law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We usehigh-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recastevolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problemsrelevant to trickle bed reactor modeling. c 2000 Academic Press Key Words: trickle bed reactor; conservation laws; porous media flows; Godunov methods.

1. INTRODUCTION

A trickle bed reactor is a fixed bed of catalyst particles through which gas and liquid are allowed to flow. Typically the gas and liquid flow concurrently downward through the reactor; the liquid phase flows over the catalyst as a thinfilm, while the gas phase flows continuously between the catalysts [22]. These reactors have been used mainly in the
Research supported at UC Berkeley by the US Department of Energy Mathematical, Information and Computational Sciences Division, Grants DE-FG03-94ER25205 and DE-FG03-92ER25140; and at the Lawrence Berkeley National Laboratory by the US Department of Energy Mathematical, Information andComputational Sciences Division, Grant DE-AC03-76SF00098. The first author was also supported by the Computational Sciences Graduate Fellowship Program of the Office of Scientific Computing in the Department of Energy. 311
0021-9991/00 $35.00 Copyright c 2000 by Academic Press All rights of reproduction in any form reserved.
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petroleum industry for hydrotreatingprocesses, such as hydrodesulfurization and hydrocracking. However, there are applications in other fields, such as chemical processing, waste treatment, and biochemical processing [13]. There have been a few numerical simulations of flow distribution in a trickle bed reactor. For example, Stanek et al. [24] used a radial diffusion model, while Zimmerman and Ng [30] used a computer-generated model ofrandomly packed spheres. Anderson and Sapre [2] modeled a reactor using the same general porous media equations that are typically used in petroleum reservoir simulations (for a description of petroleum reservoir simulations, see the book by Aziz and Settari [3] or the paper by Stevenson et al. [25]). Although there has been relatively little effort in modeling trickle bed reactors, similar porous mediaproblems have been modeled extensively, mainly in the context of subsurface flows (typically petroleum reservoirs). While the same general governing equations model flow in a reactor and flow in a reservoir, there are a few key differences. First of all, there are geometry and size differences. Reactors are typically cylindrical and 10–30 meters tall [13]; on the other hand, petroleum reservoirs...