Mass transfer from cylinders and plane surfaces buried in packed beds in alignment with the flow direction

The present work describes the mass transfer process between a moving fluid and a slightly soluble cylinder buried in a packed bed, in alignment with the direction of flow. The bed of inert particles is taken to have uniform voidage. Numerical solution of the partial differential equation (PDE) describing mass conservation of the solute gave the concentration field near the soluble surface and the mass transfer flux was integrated to give values of the Sherwood number as a function of the relevant parameters. A mathematical expression is proposed (given as Eq. (32) in the paper) that describes accurately the dependence found numerically between the value of the Sherwood number and the values of Peclet number and aspect ratio, L/d1, of the cylinder. For large enough diameter of the cylinder, the problem degenerates into mass transfer from a plane surface and the same equation applies, with L/d1 = 0. The equation was tested through the measurement of diffusivity for different solutes released by slightly soluble solids, and the experimental values obtained were in excellent agreement with the values found in literature. An important feature of the paper is the detailed discussion of the finite difference method adopted, with emphasis on the high-resolution schemes used in the discretisation of the convection term of the PDE. 2005 Elsevier Ltd. All rights reserved.

[1]  P. Gaskell,et al.  Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm , 1988 .

[2]  M. A. Latifi,et al.  Boundary element method in modelling of momentum transport and liquid-to-wall mass transfer in a packed-bed reactor , 2000 .

[3]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[4]  Anthony G. Dixon,et al.  Wall-to-liquid mass transfer in fixed beds at low flow rates , 2003 .

[5]  C. Chrysikopoulos,et al.  Mass transfer coefficient and concentration boundary layer thickness for a dissolving NAPL pool in porous media. , 2003, Journal of hazardous materials.

[6]  Eckhard Worch,et al.  Eine neue Gleichung zur Berechnung von Diffusionskoeffizienten gelöster Stoffe , 1993 .

[7]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[8]  D. Spalding.  A novel finite difference formulation for differential expressions involving both first and second derivatives , 1972 .

[9]  J. Delgado,et al.  Overall map and correlation of dispersion data for flow through granular packed beds , 2005 .

[10]  Wei Shyy,et al.  A study of finite difference approximations to steady-state, convection-dominated flow problems , 1985 .

[11]  C. Chrysikopoulos,et al.  Mass transfer correlations for nonaqueous phase liquid pool dissolution in saturated porous media , 1999 .

[12]  P. Sweby.  High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , 1984 .

[13]  C. Wilke,et al.  Correlation of diffusion coefficients in dilute solutions , 1955 .

[14]  M. Darwish,et al.  NORMALIZED VARIABLE AND SPACE FORMULATION METHODOLOGY FOR HIGH-RESOLUTION SCHEMES , 1994 .

[15]  Peter Grathwohl,et al.  Time scales of organic contaminant dissolution from complex source zones: coal tar pools vs. blobs. , 2002, Journal of contaminant hydrology.

[16]  C. Laguérie,et al.  Diffusivité de l'acide benzoi'que dans l'eau: Influence de la température , 1975 .

[17]  J. Carvalho,et al.  Transverse dispersion in granular beds. I: Mass transfer from a wall and the dispersion coefficient in packed beds , 1988 .

[18]  M. A. Alves,et al.  Mass transfer and dispersion around active sphere buried in a packed bed , 1999 .

[19]  F. Pinho,et al.  A convergent and universally bounded interpolation scheme for the treatment of advection , 2003 .

[20]  J. Schuster,et al.  Evaluation of steady flow profiles in rectangular and circular packed beds by a variational method , 1983 .

[21]  H. Hofmann,et al.  Implementation of radial porosity and velocity distribution in a reactor model for heterogeneous catalytic gasphase reactions (TORUS-Model) , 1990 .

[22]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[23]  R. Wilhelm,et al.  Mass and Momentum Transfer in a Solid-Liquid System , 1949 .

[24]  M. Tyner,et al.  Solubility and Diffusivity of 2-Naphthol in Water , 1953 .

[25]  R. Courant,et al.  On the solution of nonlinear hyperbolic differential equations by finite differences , 1952 .

[26]  B. P. Leonard,et al.  Simple high-accuracy resolution program for convective modelling of discontinuities , 1988 .

[27]  A. B. Metzner,et al.  Wall effects in laminar flow of fluids through packed beds , 1981 .

[28]  J. Carvalho,et al.  Transverse dispersion in granular beds. II: Mass transfer from large spheres immersed in fixed or fluidised beds of small inert particles , 1988 .