Modeling, simulation, and optimization of a microalgae biomass drying process

Abstract

Summary The aim of the present work was to develop a transient mathematical model focused on microalgae biomass drying, considering two phases: solid (wet biomass) and gas (drying air). Mass and thermal energy balances were written for each phase producing a system of ordinary differential equations (ODE). The solution of the ODE set delivers the temperature and air humidity ratio and biomass profiles with respect to time. The numerical results were directly compared with temperature experimental measurements—for both phases—and with the biomass humidity content. Data from experiment 1 were used to carry out the mathematical model adjustment, whereas data from experiment 2 were used for the experimental validation of the model. The model was adjusted by proposing a new correlation for the mass transfer coefficient and by calibrating the heat transfer coefficient. The transient numerical results were in good quantitative and qualitative agreement with the experimental results, ie, within the experimental error bars. Then the experimentally validated mathematical model was utilized to optimize the following parameters: (i) the electric heater power ( Q̇res) and the dry air mass flow rate ( ṁda) and (ii) the convection oven length to width ratio (L/W). The goal was to minimize system energy consumption (objective function). The optimization procedure was subject to the following physical constraints: (i) fixed convection oven total volume and (ii) fixed biomass and drying air contact surface area. For the oven original geometry, Q̇italicres,italicopt = 3.0 kW and ṁitalicda,italicopt = 9 g s−1 were numerically found for minimum energy consumption, so that 36.9% and 43.5% energy consumption decreases were obtained, respectively, in comparison with the measurements of experiment 1. Next, the numerical geometric optimization found (L/W)opt = 9, with Q̇italicres,italicopt and ṁitalicda,italicopt, which was capable to reach a 51.6% energy consumption reduction in comparison with the original system tested in experiment 1. The novelty of this work consists of the development and experimental validation of a physically based microalgae biomass drying mathematical model, ie, instead of using empirical correlations to predict the drying time and temperature profiles and then minimize system energy consumption. Therefore, the results show that it is reasonable to state that the model could be used to design, control, and optimize drying systems with configurations similar to the one analyzed in this study.

The control‐oriented model of coordinated control system based on stochastic differential equations

“…The models based on ODEs or PDEs indicate that the coordinated control system was treated as a deterministic system 28 . The same inputs would lead to unique and same outputs.…”

“…The correlation tests of residuals would assist in evaluating the model accuracy. These types of model evaluations are common in other research areas; however, they are inadequate for the establishment of a model with coordinated control system 21,22,24‐30 . This gap in literature may mislead a more accurate model 30,31 and it should be employed for improvements.…”