TOWARDS MODELS COMPLEXITY IN WATER USAGE AND TREATMENT OPTIMISATION PROBLEMS

Abstract

The paper addresses water recycling in process industry, inter alia, the issues of mathematical models’ complexity problem in the “process integration”-based structural optimization of sustainable water usage and treatment networks. The nature of addressing structural optimization problems requires iteratively querying individual process models, which are incorporated as objective functions and constraints within the optimization model, throughout the process of finding a solution, therefore the goal was to explore the intricacy of mentioned models. Within the framework of the research, the impact of complexity of water network constituent parts models on the optimization performance was investigated by Monte Carlo method for one step of the optimization procedure, as well as for the optimization procedure as a whole. Units’ models in form of algebraic equations (for direct equation calculation case), algebraic equations (for root search), ordinary differential equations (for Cauchy initial value problem with a case of two differential equations), ordinary differential equations (for boundary value problem), and partial differential equations (for two spatial variables) were examined with an analysis of their applicability for optimization purposes. The justification for employing both deterministic "counter-current mass transfer" models and statistical polynomial "input-output" steady-state algebraic models were established for addressing the specific problems under investigation. As the case study, special polynomial model was constructed based on the experimental design / response surface methodology and the dynamics simulation results on adsorption wastewater treatment within the packed bed column filled with activated carbon. Central composite rotatable design was formulated and subsequently executed using computational experimentation methods for the parametric identification of a nonlinear polynomial model. The evaluation confirmed that the constructed model exhibits satisfactory predictive accuracy.