Mathematical modeling of thermal interactions in a self-cooling pilot-scale photobioreactor

Abstract

Parameterizing high-complexity thermal models is a common challenge in bioreactor engineering. This paper rapports the mathematical modeling of thermal interactions in a photobioreactor. Energy balances, physical measurements, and mathematical relations from the literature were used. Two experiments (Tests 1 and 2) were done for model parameterization and to validate their mathematical estimation. The difficulty or impossibility of generating thermophysical properties data led to use the Kalman filter for parameter estimation. A mean absolute percentage error from 0.024 to 0.136% was obtained for parametrized models regarding estimates vs. measured values. A significative correlation was obtained for all paired measured vs. estimated values in Test 1 (r = 0.931, p < 0.01, light chamber's Temperature, r = 0. 378, p < 0.01, water's temperature and r = 0. 970, p < 0.01, heat exchanger's temperature); same for Test 2 (r = 0.932, p < 0.01, r = 0. 632, p < 0.01 and r = 0.684, p < 0.01, respectively). That demonstrates the feasibility of using recursive methods for parameterization of mathematical models focused on thermal systems with a high degree of difficulty for the direct measurement of parameters, providing a numerical approach adaptable to practical applications. As the development of thermally based process control strategies to optimize the production of microalgal biomass.