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

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