The relationship between nutrient feed rate and specific growth rate in fed batch cultures

Summary Equations are described which relate nutrient feed rate to specific microbial growth rate in fed batch culture. Fed batch cultures are classified into three types: 1) those allowing constant specific microbial growth rate, 2) those in which the rate of change of flow rate is constant and 3) those in which the nutrient flow rate is constant. The basic properties of these three types are described.Symbols F medium flow rate, L³ T^–1 - F_o medium flow rate at zero time, L³ T^–1 - g rate of change of flow rate with time, L³ T^–2 - K_v volume constant, being the total cell weight at zero time divided by the product of the yield coefficient and growth-limiting substrate concentration in the feed, L³ - s_r growth limiting substrate concentration in the feed, ML^–3 - V volume of liquid in the growth vessel, L³ - V_f volume of medium fed to the growth vessel, L³ - V_o volume of liquid in the growth vessel at zero time, L³ - X total weight of cells, M - x concentration of cells, ML^–3 - X_g total weight of cells grown, M - X_o total weight of cells at zero time, M - Y yield coefficient, weight of cells grown per unit weight of growth-limiting substrate - specific microbial growth rate, T^–1