Background

As a first approximation in the analysis of the digestive system, the system shall be assumed to operate at steady state conditions. However, in the actual case digestive reaction rates may be affected by changes in temperature, in pH, and in the composition of the microbial community. Also, to apply the design equations for ideal reactors, variations in volume due to the absorption of digestive products are assumed to be negligible ².

The rate of digestion in the complex stomach can be modeled as either an enzyme catalyzed digestion or an autocatalytic microbial fermentation. In autocatalytic digestion, microbes break down the feed, and in the process produces more microbes along with a digestion product P.

or more precisely

The rate law for the rate of disappearance of feed in the stomach is of the following form. [See Chapter 9 and Summary Notes]¹

Here C_A is the concentration of hippo feed in (kg/m³) , C_B is the concentration of microbes (kg microbes/ m³ of stomach), and K_M is the Monod constant (kg/m³). We note that -r_AM1 is in a basis of mass per unit time per unit volume rather than moles per unit time per unit volume, which is the basis for -r_A. Letting X be the conversion of feed in the stomach, in kg converted per kg feed we can arrive at X.

Derive

and the corresponding levenspiel plot is:

In Chapter 3¹ we will learn how to specify a rate law in terms of concentration and then to convert concentration to conversion so that we will then have the rate law as solely a function of conversion