Steady states

The derivatives in the differential equations for mass balances in continuous culture can be set equal to zero (no changes at steady state) and solved for the concentrations of cells and of limiting nutrient. Another interesting plot is for productivity; in this case dilution rate times cell mass concentration gives the productivity. Productivity peaks as washout is approached because cell mass concentration falls to zero at washout.

Monod Exercise in Java

This plots the steady state values of X (cell concentration) and S (concentration of limiting nutrient) versus dilution rate as you select the coefficients. Things to explore and to explain are:
  1.  What is the effect of So on the plot of S versus D?
  2.  In what range of dilution rate is Em important?
  3.  In what range of dilution rate is Ks important?
  4.  Why does X show wash out prior to reaching the maximum m? (Hint: try low So and high Ks)

This adds little to this presentation, but you may wish to see some typical results from the old BASIC program as shown in this figure:

Productivity of cell mass is the product of dilution rate and cell mass concentration. When cells are the product or contain the product, high productivity is desired. Environmental engineers strive for poor productivity because there must be disposal of the cells, and this tends to be expensive.