Study of Two-Phase Nonlinear Advection Dispersion Model for Displacement Washing of Porous Particles Using OCFE with Lagrangian Basis

  • Shelly AroraEmail author
  • Dereje Alemu Alemar
  • František Potůček
Research Article - Chemical Engineering


A comprehensive diffusion dispersion model has been presented for displacement washing of porous particles. Model equations have been divided into two phases, namely bulk fluid phase and particle phase. Both the phases have been characterized by particle geometry and pore radius of particles. Inter-pore and intra-pore solute concentrations have been related to Langmuir adsorption isotherm. Nonlinear set of model equations has been solved by using the technique of orthogonal collocation on finite elements with Lagrangian basis. Effect of different parameters such as Péclet number, bed porosity and distribution ratio has been shown graphically via breakthrough curves and surface plots. Stability of the numerical technique has been checked by L2 and L norms for different values of parameters. Validity of the model on the laboratory-scale washer has been verified by comparing experimental and model-predicted values. Applicability of the model has also been discussed through industrial parameters.


Orthogonal collocation Axial dispersion coefficient Péclet number Bed porosity Pore radius of particles Particle geometry 

List of Symbols


Cross-sectional area of drum (m2)


Particle geometry


Biot number \( \left( {\frac{{k_{\text{f}} \beta R}}{{KD_{\text{F}} }}} \right) \)


Concentration of bulk fluid (kg/m3)


Average solute concentration (kg/m3)


Initial solute concentration (kg/m3)


Dimensionless solute concentration (c/C0)


Inter-particle solute concentration (kg/m3)


Dimensionless inter-particle solute concentration (q/C0)


Intra-particle solute concentration (kg/m3)


Initial intra-particle solute concentration (kg/m3)


Dimensionless intra-particle solute concentration (n/N0)


Film resistance mass transfer coefficient (m/s)


Forward rate constant (1/s)


Backward rate constant (1/s)


Cake thickness (m)


Peclet number (uL/DL)


Variable pore radius of particles (m)


Pore radius of particles (m)


Time of washing (s)


Interstitial velocity (m/s)


Variable cake thickness (m)

Greek Symbols


Porosity of particles


Porosity of packed bed


Variable element size


Dimensionless pore radius of particles (r/R)


Dimensionless variable


Dimensionless parameter \( \left( {\frac{a(1 - \varepsilon )}{\varepsilon }} \right) \)


Dimensionless time (tDF/R2)


Dimensionless thickness (z/L)


Dimensionless parameter (R2u/LDF)


Dimensionless variable


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Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  • Shelly Arora
    • 1
    Email author
  • Dereje Alemu Alemar
    • 2
  • František Potůček
    • 3
  1. 1.Department of MathematicsPunjabi UniversityPatialaIndia
  2. 2.Department of Mathematics, College of Natural and Computational ScienceJigjiga UniversityJigjigaEthiopia
  3. 3.Department of Wood, Pulp and Paper TechnologyUniversity of PardubicePardubiceCzech Republic

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