A kinetic model for ideal plug-flow reactors

ArticleinWater Research 23(5):647-654 · May 1989with30 Reads
Impact Factor: 5.53 · DOI: 10.1016/0043-1354(89)90031-6
Abstract

Simultaneous differential equations of plug-flow reactors resulting from mass balances on substrate and biomass around an infinitesimal volume element are solved analytically taking the longitudinal biomass gradient into account under steady-state conditions. A relationship between substrate and biomass concentrations and an analytical solution for substrate and/or biomass concentration as a function of hydraulic residence time are developed. Design examples are given and these have shown that results of analytical solution are in good agreement with those of differential equations obtained by the finite difference method. Results of this work may help engineers to acquire a new understanding about the plug-flow reactors.

    • "Note that Eq. (17) means that h is given as an explicit function of S. A similar implicit expression was derived by Ali San [19] for the case of a PFR with biomass recycle. "
    [Show abstract] [Hide abstract] ABSTRACT: This paper deals with steady-state analysis and design of bioreactors consisting of a number of completely stirred tank reactors (CSTRs) in series. The study is confined to one consumed (substrate) and one consuming constituent (biomass). The specific microbial growth rate is assumed to be described by Monod kinetics. The death of biomass is assumed to be negligible. Two optimal design problems for a large number of CSTRs in series are studied: to minimize the effluent substrate concentration for a given total volume, and to minimize the total volume for a given effluent substrate concentration. As an appealing alternative to solve these problems numerically, it is proposed to consider the asymptotic case where the number of CSTRs tends to infinity. This is shown to correspond to one CSTR in series with a plug flow reactor (PFR). A CSTR with a sufficient large volume is needed to avoid wash-out of the biomass. The main result is that both design problems for the CSTR + PFR configuration have the same solution with respect to the optimal volume of the CSTR, which is given as an explicit function of the incoming substrate concentration, the volumetric flow rate and the coefficients of the Monod growth rate function. Numerical results indicate that the plug flow approach may be used as a feasible design procedure even for a reasonably low number of CSTRs in series.
    Full-text · Article · Aug 2015 · Biochemical Engineering Journal
    0Comments 2Citations
    • "Apply the simple model of CSTR in series in FBR reactor Do not model the gas phase in the reactor For initial simulation to understand the general reactor behavior Iliuta and Larachi (2005) Model the reactor with CFD simulation in 3d Assume plug flow conditions in gaseous phase To study the process in detail and focalize on local phenomena in the reactor and the oxygen dispersion Biofilter reactor/trickling filters Baquerizo et al. (2005). Model all the phases of the reactor: liquid, solid and gaseous Without calibration and validation For initial simulation to understand the general reactor behavior Among the models cited previously only San (1989 San ( , 1992) solved the proposed equations using finite difference technique, the other authors (Lawrence and McCarty, 1990; Milbury et al., 1965 ) proposed algebraic solutions of the equations introducing some simplifications. Many authors performed tracer experiments that estimate the hydraulic parameters and characterize the hydraulic reactor model. "
    [Show abstract] [Hide abstract] ABSTRACT: Existing mathematical models of wastewater treatment plants focus primarily on the bioconversion processes and often do not cope with the reactor hydrodynamics. However, in the literature several aerobic plug flow bioreactors with both kinetics modeling and hydrodynamics description are reported. The present article reviews mathematical models of aerobic plug flow reactors, such as Activated Sludge Reactors, Fluidized Bed Reactors, Biofilters and Trickling Filters focusing on their hydrodynamic approach and on the role of the reactor configuration on the process performance. For each reactor type the following modeling approach is compared: i) ideal model, such as plug flow or complete mixed; ii) tank in series model; iii) dispersion model and computational fluid dynamic model.
    Full-text · Article · Oct 2014 · Critical Reviews in Environmental Science and Technology
    0Comments 5Citations
    • "Apply the simple model of CSTR in series in FBR reactor Do not model the gas phase in the reactor For initial simulation to understand the general reactor behavior Iliuta and Larachi (2005) Model the reactor with CFD simulation in 3d Assume plug flow conditions in gaseous phase To study the process in detail and focalize on local phenomena in the reactor and the oxygen dispersion Biofilter reactor/trickling filters Baquerizo et al. (2005). Model all the phases of the reactor: liquid, solid and gaseous Without calibration and validation For initial simulation to understand the general reactor behavior Among the models cited previously only San (1989 San ( , 1992) solved the proposed equations using finite difference technique, the other authors (Lawrence and McCarty, 1990; Milbury et al., 1965 ) proposed algebraic solutions of the equations introducing some simplifications. Many authors performed tracer experiments that estimate the hydraulic parameters and characterize the hydraulic reactor model. "
    [Show abstract] [Hide abstract] ABSTRACT: Existing mathematical models of wastewater treatment plants focus primarily on the bioconversion processes and often do not cope with the reactor hydrodynamics. However, in the literature several aerobic plug flow bioreactors with both kinetics modelling and hydrodynamics description are reported. The authors review mathematical models of aerobic plug flow reactors, such as activated sludge reactors, fluidized bed reactors, biofilters, and trickling filters focusing on their hydrodynamic approach and on the role of the reactor configuration on the process performance. For each reactor type the following modelling approach is compared: (a) ideal model, such as plug flow or complete mixed, (b) tank in series model, (c) dispersion model and (d) computational fluid dynamic model.
    Full-text · Dataset · Sep 2014
    0Comments 1Citation
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