Optimal steady-state design of bioreactors in series with Monod growth kinetics

Sammanfattning: Bioreactors are used to carry out bioprocesses and are commonly used in e.g. biogas production and wastewater treatment. Two common hydraulic models of bioreactors are the continuous stirred tank reactor (CSTR) and the plug-flow reactor (PFR). In this paper, a differential equation system that describes the substrate, biomass and inert biomass in the bioreactors is presented. It is used in a steady-state analysis and design of CSTRs in series. Monod kinetics were used to describe the specific growth rate and the decay of biomass was included. Using the derived systems of differential equations, two optimization problems were formulated and solved for both CSTRs in series and for a CSTR+PFR. The first optimization problem was to minimize the effluent substrate level given a total volume, and the second was to minimize the total volume needed to obtain a certain substrate conversion. Results show that the system of differential equations presented can be used to find optimal volume distributions that solves the optimization problems. The optimal volume for N CSTRs in series decreases as N increases, converging towards a configuration of a CSTR followed by a PFR. Analyzing how the decay rate affects the results showed that when the total volume was kept constant, increasing the decay rate caused less difference between the configurations. When the total volume was minimized, increasing the decay rate caused the configurations to diverge from each other. The presented model can be used to optimally divide reactors into smaller zones and thereby increasing the substrate conversion, something that could be of interest in e.g. existing wastewater treatment plants with restricted space. A fairly accurate approximation to the optimal design of N CSTRs in series is to use the optimal volume for the CSTR in the configuration with a CSTR+PFR and equally distribute the remaining volumes.