Modelling of displacement washing of packed bed of fibers

Abstract

-The mechanism of displacement washing of packed bed of porous, compressible and cylindrical particles, e.g., fibers, is presented with the help of an axial dispersion model involving Peclet number (Pe) and Biot number (Bi). Bulk fluid concentration, intra-pore solute concentration and concentration of solute adsorbed on the fiber surface are taken to be the function of washing time and position in the bed. Concentration of solute adsorbed on the fiber surface and intra-pore solute concentration are related by a Langmuir adsorption isotherm. Experiments have been performed on pulp beds formed from unbeaten, unbleached kraft fibers. Displacement washing has been simulated using a laboratory washing cell. Model equations are solved by using orthogonal collocation on finite elements (OCFE). Model predicted values are compared with the experimental values and key industrial parameters such as displacement ratio and efficiency are expressed in terms of exit and average solute concentrations.

An efficient scheme for numerical solution of Burgers’ equation using quintic Hermite interpolating polynomials

“…Problem 3.1 has been solved numerically using different techniques such as QHCM, OCFE [4,7], pdepe solver, OCM [15,18] for different values of ε and τ . In Tables 3, 4, 5, 6 and 7, the comparison between exact and the numerical solution with different techniques has been shown.…”

“…It reduces the system of partial differential equations into a system of ODEs instead of the system of differential algebraic equations as in orthogonal collocation on finite elements (OCFE) [4,7]. After implementation of QHCM, the system of equations defined in Eqs.…”

A robust technique of cubic hermite collocation for solution of two phase non linear model

“…Therefore, DR also depends upon these factors. To calculate displacement ratio, model equations are simulated using the experimental data given in Arora and Potu˚cˇek (2009). It is obvious from Fig.…”

Application of Mathematica Software to Solve Pulp Washing Model

“…Extensive study of axial dispersion model has been carried out by [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The model has been solved using analytic and numerical techniques like Laplace transform technique [2-4, 10, 15, 23, 26], finite difference technique [25], orthogonal collocation method [5,7,12], orthogonal collocation on finite elements [6,20,21], Galerkin/Petrov Galerkin method [8,19], Hermite collocation method by [11,17,24] and Spline collocation method [13].…”