A Numerical Model for Trickle Bed Reactors

Abstract

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 use high-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 recast evolution 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 problems relevant to trickle bed reactor modeling.

A cell-centered adaptive projection method for the incompressible Navier–Stokes equations in three dimensions

“…Another possible direction would be the implementation of higher-order finite-volume schemes, such as those found in [6]. In general, we foresee application of these ideas to other coupled ellipticparabolic-hyperbolic systems, such as those found in porous media flows [24] and non-ideal MHD [27].…”

Hydrodynamics and Kinetics of Phenols Removal from Industrial Wastewater in a Trickle Bed Reactor (Part I: Hydrodynamic Study)

“…The liquid phase flows over the catalyst as a thin film, while the gas phase flows continuously between the catalysts. [8][9][10] Various flow regimes exist in TBRs depending on the superficial mass velocity, fluid properties and bed characteristics are (trickle flow, pulsing An experimental investigation of the hydrodynamic parameters in a trickle bed reactor is presented. The operating conditions are selected for the operating system to be at trickle flow regime.…”

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media

“…Our approach is similar to the approach introduced by Hornung & Trangenstein (1997) and to the approach discussed by Propp (1998). In these approaches, the solution is represented on a hierarchical sequence of nested grids with successively finer spacing in both time and space.…”

“…An alternative approach to local refinement is based on structured-grid adaptive mesh refinement (AMR). This type of approach, based on the strategy introduced for gas dynamics by Berger & Colella (1989), was first applied to porous media flow by Hornung & Trangenstein (1997) and by Propp (1998). Additional developments are discussed in the work by Trangenstein (2002), Trangenstein & Bi (2002) and Hoang & Kleppe (2006).…”

“…The methodology is implemented in parallel using the BOXLIB framework discussed in Rendleman et al (2000) and Crutchfield (1991). A similar approach was used by Propp (1998); however, his algorithm used a different approach to synchronization and was limited to two dimensions.…”