10
Mass Transfer
The first requirement for any chemical reaction to take place is that the reactants are present at the
site of reaction. In multiphase systems, the maximum rates of the transport processes are often
lower than the maximum reaction rate, which in turn means that the overall reaction rate will be
limited by the transport processes. In bioreactions, the transport of nutrients to the cell surface and
the removal of metabolites from the cell surface to the bulk of the medium are rate processes with
time constants not much smaller than those of the cellular1
2
reactions. Therefore,
mass transfer
must
be included in an analysis of bioreactions alongside of stoichiometry and cellular kinetics.
In this book we have already referred to mass transfer in many places. Thus mass transfer from a
gas phase to a liquid phase was included at the start of Chapter 3 in order to set up mass balances
for the continuous steady state tank reactor and to calculate rates of bioreactions. In the analysis
of the ideal bioreactor in Chapter 9 mass transfer was also included in order to provide a
reasonable general design framework.
In the present chapter we shall review the physical foundation of mass transfer and discuss both
experimental techniques and general methods for calculation of the rate of mass transfer. We
shall refer to the vast body of empirical knowledge on mass transfer that is an essential part of
the curriculum for chemical engineering students, and in order to make translation from chemical
textbooks easier the standard nomenclature of these texts will be used as far as possible. The
resulting change of nomenclature e.g. concentrations
(cs instead of s and pA
instead of
nh
for
partial pressure) should not represent any great problem for the reader.
Mass transfer takes place by two basic processes; convection and diffusion. A full treatment of
mass transfer therefore in principle requires a fully known flow field. However, a simplified
treatment in which the overall mass transfer is schematically divided into different transfer steps is
normally used with good results. An overview of important mass transfer steps in a fermentation
process is given in Fig. 10.1, which shows the individual steps involved in oxygen transport from a
gas bubble to the reaction site inside the individual cells (Bailey and Ollis, 1986). The steps are:
1.
Diffusion of oxygen from the bulk gas to the gas liquid interface.
2. Transport across the gas liquid interface.
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