A Simplistic Mathematical Model for Carbon Oxidation in Moving Bed Bioreactor.

Moving bed bioreactor is a promising technology for removing a wide range of contaminants from both municipal and industrial wastewater. For process optimization, it is crucial to have a detailed design of a reactor involving the development of a model that can predict the outcome of the operation. The present study attempts to develop a simplistic mathematical model for substrate removal in biofilms considering Fick’s Law of diffusion to illustrate the simultaneous substrate transport and its utilization within the biofilm and the microbial kinetics as explained by Monod’s theory. The mathematical solution is derived using second order differential equation with relevant boundary conditions. To investigate the applicability of the model for substrates with moderate biodegradability, experimental studies are conducted using synthetic oily wastewater, where oil and grease (O&G) primarily contribute to chemical oxygen demand (COD). The ease of practical implications of the model without any sophisticated software and tools would make it an economically viable option for process design in MBBR in treatment plants. The model is developed using FORTRAN language, implying that the same can be developed in other advanced languages. Furthermore, the model is experimentally validated at different hydraulic retention times, initial O&G concentration and biofilm density using the data obtained from laboratory-scale studies of an MBBR treating synthetic oily wastewater. The results indicate that a maximum relative error of 7.14% occurs with respect to the data obtained from the experimental analysis, implying the applicability of the model for treating moderately degradable pollutants in MBBR. Moreover, the performance precision of the model is carried out based on Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R²), where the respective values of 0.005, 0.004 and 0.97 suggest the accuracy of the model. Discussion regarding the limitations and subsequent areas for future research clearly highlights the potential for further development of process design model for MBBR treating wastewater with moderate biodegradability.Highlights: A simplistic mathematical model is derived for substrate utilization in MBBR The model is based on Monod’s kinetics and Fick’s second law of diffusion It predicts effluent substrate concentration, biofilm thickness and substrate flux Model can be executed in any language including FORTRAN to get relevant parameters Experimental validation shows results within 10% deviation of model predicted data [ABSTRACT FROM AUTHOR]