Efficient and accurate numerical simulation of nonlinear chromatographic processes

Javeed, Shumaila; Qamar, Shamsul; Seidel‐Morgenstern, A.; Warnecke, Gerald

doi:10.1016/j.compchemeng.2010.10.002

Cited by 103 publications

(183 citation statements)

References 17 publications

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“…For this purpose a high resolution finite volume scheme (HR-FVS) of Koren [34] is used . This scheme guarantees the positivity of the solution.…”

Section: Resultsmentioning

confidence: 99%

“…Since the influence of the boundary conditions is often not discussed in sufficient detail, we have further compared the moment expressions for Danckwerts and Dirichlet BCs. To validate the analytical solutions and the moment expressions, a high resolution finite volume scheme (HR-FVS) of Koren [33,34] is employed. Moreover, different parametric case studies are considered.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of One-Dimensional Advection–Diffusion Model with Variable Coefficients Describing Solute Transport in a Porous medium

2017

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This work presents the analytical solution and temporal moments of one-dimensional advection-diffusion model with variable coefficients. Two case studies along with the two different sets of boundary conditions are considered at the inlet and outlet of the domain. In the first case, a time dependent solute dispersion in the homogeneous domain along uniform flow is taken into account, whereas in the second case, due to inhomogeneity of domain, velocity is taken spatially dependent and the dispersion is assumed proportional to the square of the velocity. The Laplace transform is used to obtain the analytical solutions. The analytical temporal moments are derived from the Laplace domain solutions. To verify the correctness of the analytical solutions, a high resolution second order finite volume scheme is applied. Different case studies are considered and discussed. Both analytical and numerical results are in good agreement with each other.Keywords Advection-diffusion equation · rectangular pulse injections · analytical solutions · moment analysis · finite volume method · dynamic simulations. Mathematics Subject Classification (2000) 80A23 · 26A33 · 42A16

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“…For this purpose a high resolution finite volume scheme (HR-FVS) of Koren [34] is used . This scheme guarantees the positivity of the solution.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of One-Dimensional Advection–Diffusion Model with Variable Coefficients Describing Solute Transport in a Porous medium

2017

Self Cite

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“…At the last step of the simulations, the observation data z δ is used as input, and the retrieved parameters are compared with the exact ones. Note that in order to achieve high accuracy we use a semi-discrete flux-limiting finite volume scheme [19] to discretize the chromatography problem.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Estimate the constant M in (15) by numerical experiments. Estimate the error level of observed data δ and bounds of regularization parameters β min and β max such that χ(β min ) < < χ(β max ), where the discrepancy function χ is defined by (19). Set λ = .…”

Section: Algorithmmentioning

confidence: 99%

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A modified coupled complex boundary method for an inverse chromatography problem

Cheng

Lin

Zhang

et al. 2017

Journal of Inverse and Ill-Posed Problems

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Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method.

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Simulation of Process Chromatography

Nilsson

Andersson

2017

Preparative Chromatography for Separation of Proteins

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Efficient and accurate numerical simulation of nonlinear chromatographic processes

Cited by 103 publications

References 17 publications

Analysis of One-Dimensional Advection–Diffusion Model with Variable Coefficients Describing Solute Transport in a Porous medium

Analysis of One-Dimensional Advection–Diffusion Model with Variable Coefficients Describing Solute Transport in a Porous medium

A modified coupled complex boundary method for an inverse chromatography problem

Simulation of Process Chromatography

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