Development of a statistical and mathematical hybrid model to predict membrane fouling and performance

In this study, we explored the potential of a hybrid model combining mathematical and statistical models. Mathematical models are capable of simulating microscopic phenomena but fail to explain the complicated situations in practical cases. On the other hand, statistical models are suitable to predict complex and non-linear behaviors. Thus, a hybrid model can have advantages in both mathematical and statistical models. This paper focusses on the techniques to combine mathematical models with statistical models. As a mathematical model, we have applied the Hagen–Poiseuille equation and filtration models modified with the critical flux concept to predict the performance of hollow fiber membranes. Statistical model such as ANN (artificial neural networks) was used to correlate operating conditions with membrane fouling. Experimental data were collected from a pilot plant using hollow fiber microfiltration membranes for surface water treatment. Different methods to hybridize mathematical and statistical models were compared to develop a feedforward guidance simulator. Comparison of model calculations with experimental results revealed that the hybrid model was useful to evaluate membrane fouling characteristics. An algorithm for process controller based on the hybrid model was also suggested as an initial step toward an “intelligent” membrane system.