# Fundamental Analysis of continuous flow bioreactor models

## Rubayyi Turki Alqahtani

### M.Math (coursework) Project

### Spring 2009

### Abstract

This thesis describes the fundamental analysis of continuous flow bioreactor
models governed by Contois kinetics. We analyse the steady-state
treatment of industrial wastewaters in a continuous flow bioreactor with
recycle and without recycle. The one reactor with recycle is described by
a system of two non-linear ordinary differential equations. The steady-state
solutions for this model are found and their stability determined as a
function of the residence time. The performance of the reactor at
large residence times is obtained. The main advantage of using a flow reactor
with recycle for the treatment of industrial wastewaters is to improve
the performance at low residence times.

The two reactors without recycle is described by a system of four
non-linear ordinary differential equations. The steady state solutions for
this model are found and their stability determined. The main results,
is that the increasing of the number of reactors in the cascade lead to
improvement the performance of cascade which has effect to reduce the wastewater
leaving the cascade. Also, small increase in the total residence time lead
to a large decrease in the effluent concentration as the total residence
time slightly larger than washout point.

The two reactors with recycle also is described by a system of four
non-linear ordinary differential equations. The steady-state solutions
for this model are found and their stability determined for washout
numerically. The main result of the three models is the two reactors
with recycle is better than one reactor with recycle and two reactor
without recycle for large total residence time. Though, we were not
complete the analysis of last model, we use numerical method to find
interesting results.

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Page Created: 2nd December 2009.

Last Updated: 2nd December 2009.