Parametric Sensitivity of CSTBRs for Lactobacillus casei: Normalized Sensitivity Analysis

Abstract

In this paper, a sensitivity analysis of a continuous stirred tank bioreactor (CSTBR) was conducted to determine a parametrically sensitive regime. The growth of a lactic acid bacterium, namely, <i>Lactobacillus casei</i>, in a pH-controlled CSTBR was considered as a process model. Normalized objective sensitivities of the minimum pH were determined with respect to input parameters. A generalized criterion for sensitivity was defined for determining the parametric range of three input variables, i.e., dilution rate base stream (θ), base concentration (R), and initial pH (pH₀) for maintaining optimal pH range in the reactor. The system exhibits sensitive behavior for θ, R, and pH₀, from 0.095 to 0.295, 0 to 0.865, and 4.42 to 4.77, respectively. The critical values of θ, R, and pH₀ are 0.0195, 0.48, and 4.6, respectively. The mathematical model can also be used to determine a parametrically sensitive regime for other important parameters, namely, temperature, the concentration of metabolites, and other byproducts. The mathematical tool can also be used in bioreactor design and the improvement of control strategies.