Solution of SNLAE model of backward feed multiple effect evaporator system using genetic algorithm approach

Abstract

This paper presents the genetic algorithm approach to solve the highly complex set of fourteen simultaneous nonlinear algebraic benchmark problem for the backward feed seven effect evaporator. Generally, Newton’s method may be considered a better numerical technique to solve such nonlinear problems. However, a higher number of effects (seven in this case) complicates the evaluation of a 14 × 14 Jacobian matrix that involves determining the analytical derivative of all system variables. Also, such a simultaneous nonlinear algebraic equations model exhibits the problem of divergence and instability when initial values have not been chosen appropriately. In this work, genetic algorithm approach has been demonstrated to be very efficient to solve such complex nonlinear models for a large number of effects in evaporative system without any complications. To make the model more realistic and representative of physico-thermal properties of liquor, boiling point elevation of the liquor during evaporation has been incorporated. Finally, the developed models are solved using genetic algorithm to determine the process variables, namely liquor and steam flow rates, which yield process performance parameters of energy efficiency (steam economy and consumption). The results indicate that a maximum steam efficiency may be achieved for a 50 % steam split in the first two effects. © 2016, The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.