Efficiency and utility of collocation methods in solving the performance equations of flow chemical reactors with axial dispersion

Fan, L.T.; Chen, G.K.C.; Erickson, Larry E.

doi:10.1016/0009-2509(71)83013-0

Cited by 41 publications

(3 citation statements)

References 11 publications

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“…Collocation Points. In the present study, zeros of shifted Chebyshev polynomials have been used as collocation points, which tend to minimize the error as proposed by Fan et al [38] and yield satisfactory results for the unsymmetrical boundary value problems. The equidistant spacing in the collocation points is usually not preferred due to Runge divergence phenomenon (Villadsen and Stewart [15]).…”

Section: Numerical Proceduresmentioning

confidence: 98%

Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method

Ganaie

Arora

Kukreja

2013

International Journal of Differential Equations

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A convenient computational approach for solving mathematical model related to diffusion dispersion during flow through packed bed is presented. The algorithm is based on the mixed collocation method. The method is particularly useful for solving stiff system arising in chemical and process engineering. The convergence of the method is found to be of order 2 using the roots of shifted Chebyshev polynomial. Model is verified using the literature data. This method has provided a convenient check on the accuracy of the results for wide range of parameters, namely, Peclet numbers. Breakthrough curves are plotted to check the effect of Peclet number on average and exit solute concentrations.

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Section: Numerical Proceduresmentioning

confidence: 98%

Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method

Ganaie

Arora

Kukreja

2013

International Journal of Differential Equations

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“…In the radial domain, the zeros of shifted Chebyshev polynomial have been used due to its tendency to keep the error down to a minimum at the corners of a single spherical particle (Fan et al 1971) since results are required at the corners in radial domain.…”

Section: Application Of Orthogonal Collocation On Finite Elements Met...mentioning

confidence: 99%

Dynamic studies of binary adsorption system in fixed beds

Olafadehan

Amoo

Oyedeko

et al. 2023

Preprint

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In this study, a generalized, comprehensive and feasible mathematical model was developed for the description of the adsorption of multicomponent system in a fixed bed containing solid adsorbent. It took into cognizance of all the factors considered negligible in the literature, which included intraparticle, interparticle and interphase diffusional resistances, conditions of non-equilibrium and non-linear binary adsorption of butan-2-ol and 2-methylbutan-2-ol onto activated carbon. The resulting 4N hyperbolic and parabolic differential equations were numerically solved using orthogonal collocation on finite element method. Excellent agreements were achieved between the experimental data and the simulated results of breakthrough times and concentrations of the solutes in fixed beds of 0.41, 0.82 and 1.23 m. Equally, the observed chromatographic tops of the less strongly adsorbed component (butan-2-ol) and the effects of adsorber length on times of breakthrough of the components and height of peaks were precisely simulated. The results of this study are of beneficial use in the design and analysis of fixed beds employed for the treatment of multicomponent aqueous wastewater effluents from industry.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

Application of Mathematica Software to Solve Pulp Washing Model

Kumar¹,

Ganaie

Kukreja

2013

ISRN Chemical Engineering

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The removal of the bulk liquor surrounding the pulp fibers using less concentrated liquor is known as pulp washing. In the present study, a pulp washing model involving diffusion-dispersion through packed beds of finite length is presented. Separation of variables is applied to solve system of governing partial differential equations and the resulting equations are solved using Mathematica. Results from the present case are compared with those of previous investigators. The present case is giving better results than the previous investigators.

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Efficiency and utility of collocation methods in solving the performance equations of flow chemical reactors with axial dispersion

Cited by 41 publications

References 11 publications

Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method

Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method

Dynamic studies of binary adsorption system in fixed beds

Application of Mathematica Software to Solve Pulp Washing Model

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