×

Modeling of bioactive carbon adsorbers: A hybrid weighted residual-finite difference numerical technique. (English) Zbl 0847.92022

Summary: Phenomenological mathematical models incorporating adsorption, mass transfer, and biofilm degradation were developed for performance prediction/simulation of bioactive carbon fixed-bed and fluidized-bed adsobers in wastewater treatment. The model equations were solved by a numerical technique combining a weighted residual technique such as orthogonal collocation with a finite difference method. This hybrid technique was numerically consistent and stable and provided accurate solutions at computing times lower than those corresponding to pure orthogonal collocation. The bioadsorber model parameters were independently determined from carefully designed laboratory-scale experiments and correlations. The model predictions of bioadsorber effluent concentration profiles were in strong agreement with the experimental data, illustrating the good predictive capability of the model. Sensitivity studies were performed to identify the influence of model parameters on the bioactive adsorber dynamics.

MSC:

92D40 Ecology
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
92E99 Chemistry
92F05 Other natural sciences (mathematical treatment)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Software:

DIFSUB
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Andrews, G. F.; Tien, C., Bacterial film growth in adsorbent surfaces, AIChE Journal, 27, 3, 396-403 (1981)
[2] Arfken, G., Sturm-Liouville theory of orthogonal functions, (Mathematical Methods for Physicists (1970), Academic Press: Academic Press New York), 424-449
[3] Bouwer, E. J.; McCarty, P. L., Removal of trace chlorinated organic compounds by activated carbon and fixed-film bacteria, Environmental Science and Technology, 16, 12, 836-843 (1982)
[4] Chakrabarti, A., Elements of Ordinary Differential Equations and Special Functions (1990), John Wiley: John Wiley New York · Zbl 0897.34001
[5] Chang, H. T.; Rittmann, B. E., Mathematical modeling of biofilm on activated carbon, Environmental Science and Technology, 21, 3, 273-280 (1987)
[6] Chung, S. F.; Wen, C. F., Longitudinal dispersion of liquid flow through fixed and fluidized beds, AIChE Journal, 14, 6, 857-866 (1968)
[7] Finlayson, B. A., The Method of Weighted Residuals and Variational Principles (1972), Academic Press: Academic Press New York · Zbl 0319.49020
[8] Finlayson, B. A., Nonlinear Analysis in Chemical Engineering (1980), McGraw-Hill: McGraw-Hill New York
[9] Gear, C. W., The automatic integration of ordinary differential equations, Communications of the Association of Computing Machinery, 14, 176-179 (1971) · Zbl 0217.21701
[10] Gear, C. W., DIFSUB for solution of ordinary differential equations, Communications of the Association of Computing Machinery, 14, 185-190 (1971)
[11] Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations (1976), Prentice-Hall: Prentice-Hall Engelwood Cliffs, New Jersey · Zbl 0173.44403
[12] Goyal, S. K.; Esmail, M. N.; Bakshi, N. N., Application of orthogonal collocation to some transport phenomena problems in co-axial cylinders and spheres, Canadian Journal of Chemical Engineering, 65, 833-844 (1987)
[13] Jain, M. K., Numerical Solution of Differential Equations (1979), John Wiley: John Wiley New York · Zbl 0409.65002
[14] Kim, S. H., Mathematical Modeling of Integrated Biological and Physico-chemical Processes for Industrial Wastewater Treatment, Ph.D. Dissertation (1987), submitted to the Department of Civil Engineering, University of Southern California, Los Angeles, CA
[15] Kim, S. H.; Pirbazari, M., Bioactive adsorber model for industrial wastewater treatment, Journal of Environmental Engineering, 115, 6, 1235-1256 (1989)
[16] Pirbazari, M. J.; Weber, W. J., Adsorption of benzene from water by activated carbon, (Cooper, W. J., Chemistry in Water Reuse, Vol. 2 (1981), Ann Arbor Science: Ann Arbor Science Ann Arbor, MI), 285-307
[17] Rittmann, B. E.; McCarty, P. L., Substrate flux into biofilm of any thickness, (Journal of the Environmental Engineering Division, 107 (1981), ASCE), 831-849, (4)
[18] Segal, N. L.; MacGregor, J. F.; Wright, J. D., Collocation methods for solving packed bed reactor models with radial gradients, Canadian Journal of Chemical Engineering, 62, 808-817 (1984)
[19] Smith, E. H.; Weber, W. J., Evaluation of mass transfer parameters for adsorption of organic compounds from complex organic matrices, Environmental Science and Technology, 23, 9, 713-722 (1989)
[20] Speitel, G. E.; Dovantzis, K.; DiGiano, F. A., Mathematical modeling of biofilm regeneration in GAC columns, Journal of Environmental Engineering, 113, 1, 32-48 (1987)
[21] Villadsen, J. V.; Stewart, W. E., Solution of boundary value problems by orthogonal collocation, Chemical Engineering Science, 22, 1483-1501 (1967)
[22] Ying, W.; Weber, W. J., Bio-physicochemical adsorption model systems for wastewater treatment, Journal of Water Pollution Control Federation, 1, 9-24 (1979)
[23] Williamson, K.; McCarty, P. L., A model of substrate utilization by bacterial film, Journal of the Water Pollution Control Federation, 48, 1, 9-24 (1976)
[24] Williamson, J. E.; Bazaire, K. E.; Geankoplis, C. J., Liquid-phase mass transfer at low Reynolds numbers, Industrial and Engineering Chemistry Fundamentals, 2, 2, 126-129 (1963)
[25] Winneberger, J. H.; Austin, J. H.; Klett, C. A., Membrane filter weight determination, Journal of Water Pollution Control Federation, 35, 5, 807-820 (1963)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.