Volume:13, Issue: 10, 2019 Page No: 184 - 188

ISSN: 2517-9934

8 Downloads

model is analyzed using finite difference method based on

Crank-Nicolson scheme. A practical problem of filter cake washing

of chemical engineering is analyzed. The model is converted into

dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the

Crank-Nicolson spatial derivative scheme is used in space domain

and forward difference scheme is used in time domain. The scheme is

found to be unconditionally convergent, stable, first order accurate in

time and second order accurate in space domain. For a test problem,

numerical results are compared with the analytical ones for different

values of parameter.

Addison-Wesley, 1999.

[2] H. Brenner, The diffusion model of longitudinal mixing in beds of finite

length. Numerical values, Chem. Eng. Sci. 17(4) (1962) 229-243.

[3] J. Crank, P. Nicolson, A practical method for numerical evaluation of

solutions of partial differential equations of the heat conduction type,

Proc. Cambridge Philosophy Soc. 43(1) (1947) 50-67.

[4] M.J. Cocero, J. Garcia, Mathematical model of supercritical extraction

applied to oil seed extraction by CO2+ saturated alcohol I.Desorption

model, J. Supercritical Fluids 20(3) (2001) 229-243.

[5] P.V. Danckwerts, Continuous flow systems distribution of residence

times, Chem. Eng. Sci. 2(1) (1953) 1-44.

[6] S. Farooq, I.A. Karimi, Dispersed plug flow model for steady-state

laminar flow in a tube with a first order sink at the wall, Chem. Eng.

Sci. 58(1) (2003) 7180.

[7] M. Feiz, A 1-D multigroup diffusion equation nodal model using the

orthogonal collocation method, Annals of Nuclear Energy 24(3) (1997)

187-196.

[8] L. Gardini, A. Servida, M. Morbidelli, S. Carra, Use of orthogonal

collocation on finite elements with moving boundaries for fixed bed

catalytic reactor simulation, Comp. Chem. Eng. 9(1) (1985) 1-17.

[9] B. Giojelli, C. Verdier, J.Y. Hihn, J.F. Beteau, A. Rozzi, Identification of

axial dispersion coefficients by model method in gas/liquid/solid fluidised

beds, Chem. Eng. P. 40(2) (2001) 159-166.

[10] C. Grossman, H.G. Roos, M. Stynes, Numerical Treatment of Partial

Differential Equations, Springer-Verlag, Heidelberg 2007.

[11] S. Karacan, Y. Cabbar, M. Alpbaz, H. Hapoglu, The steady-state

and dynamic analysis of packed distillation column based on partial

differential approach, Chem Eng. P. 37(5) (1998) 379-388.

[12] I.A. Khan, K.F. Loughlin, Kinetics of sorption in deactivated zeolite

crystal adsorbents, Comp. Chem. Eng. 27(5) (2003) 689-696.

[13] J.H. Koh, P.C. Wankat, N.H.L. Wang, Pore and surface diffusion and

bulk-phase mass transfer in packed and fluidized beds, Ind. Eng. Chem.

Res. 37(1) (1998) 228-239.

[14] V.K. Kukreja, A.K. Ray, V.P. Singh, N.J. Rao, A mathematical model

for pulp washing on different zones of a rotary vacuum filter, Indian

Chem. Eng., Sec- A 37(3) (1995) 113-124.

[15] V.K. Kukreja, A.K. Ray, Mathematical modeling of a rotary vacuum

washer used for pulp washing: A case study of a lab scale washer,

Cell. Chem. Tech. 43(1-3) (2009) 25-36.

[16] L. Lefevre, D. Dochain, S.F. Azevedo, A. Magnus, Optimal selection of

orthogonal polynomials applied to the integration of chemical reactor

equations by collocation methods, Comp. Chem. Eng. 24(12) (2000)

2571-2588.

[17] J.R. LeVeque, R. Bali, Finite Difference Methods for Ordinary

and Partial Differential Equations Steady-State and Time-Dependent

Problems, SIAM, Philadelphia, 2007.

[18] W.S. Long, S. Bhatia, A. Kamaruddin, Modeling and simulation of

enzymatic membrane reactor forkinetic resolution of ibuprofen ester,

J. Membrane Sci. 219(1-2) (2003) 69-88.

[19] C.G. Mingham, D.M. Causon, Introductory Finite Difference Methods

for PDEs, Ventus Publishing, 2010.

[20] F. Potucek, Washing of pulp fibre beds, Collect. Czech. Chem. Commun.

62(4) (1997) 626-644.

[21] A.K. Ray, V.K. Kukreja, Solving pulp washing problems through

mathematical models, AIChE Symposium Series, 96(324) (2000) 42-47.

[22] R.D. Richtmyer, K.W. Morton, Difference Methods for Initial Value

Problems, Interscience Publishers, John Wiley & Sons, New York, 1967.

[23] L. Sajc, G.V. Novakovic, Extractive bioconversion in a four-phase

external-loop airlift bioreactor, AIChE J. 46(7) (2000) 1368-1375.

[24] N.V. Saritha, G. Madras, Modeling the chromatographic response of

inverse size-exclusion chromatography, Chem. Eng. Sci. 56(23) (2001)

6511-6524.

[25] G.D. Smith, Numerical Solutions of Partial Differential Equations:

Finite Difference Methods, Clarendon press-Oxford, New York, 1985.

[26] P. Sridhar, Implementation of the one point orthogonal collocation

method to an affinity packed bed model, Ind. Chem. Eng., Sec. A 41(1)

(1999) 39-46.

[27] J.C. Strikwerda, Finite Difference Schemes and Partial Differential

Equations, SIAM, Philadelphia 2004.

[28] L.M. Sun, F. Meunier, An improved finite difference method for fixed

bed multicomponent sorption, AIChE J. 37(2) (1991) 244-254.

[29] M.K. Szukiewicz, New approximate model for diffusion and reaction in

a porous catalyst, AIChE J. 46(3) (2000) 661-665.