Introduction

In this chapter, mathematical models for analysis, design and optimisation of a variety of continuous, batch and fed-batch UF systems are developed. In all cases the system is assumed to be operating under limiting flux conditions, i.e., Eq. 4.22 applies. It should be recalled that this equation implies complete rejection of the solute. It is seen that, despite the relative simplicity of the models, the presence of the logarithmic term in the flux expression requires one to routinely use numerical techniques to solve the model equations. In addition, it is shown how a graphical method can be useful for certain types of calculations and also it is demonstrated that by employing special functions, numerical solution can be avoided in solving certain batch and continuous problems.

In the next section, continuous feed-and-bleed systems are examined, where the basic computational problem is to solve systems of non-linear algebraic equations (NLAEs). First, process analysis calculations are examined where the goal is to calculate the exit concentration for a given system. In process design calculations, the required area for a given process specification is computed. In process optimisation calculations, the problem of how to minimise the required area in multi-stage systems is examined. Subsequent sections examine batch, fed-batch and single pass continuous systems.