A fixed point iterative algorithm for solving equations modeling the multi-stage flash desalination process

Abstract

The paper presents an algorithm for solving the equations simulating the steady state behavior of the Multi Stage Flash (MSF) desalination process. The model can be used either for design of new plants or analysis and optimization of existing units. The set of equations relating the large number of design and operating variables for any stage ( ith stage) in MSF plant are decomposed into three subsets. The first subset contains equations describing processes in the tubes of the preheater inside the flashing chamber. The second subset deals with the processes inside the flashing chamber. These two subsets of equations are subsequently solved iteratively involving only a single variable for each subset. These variables are: (i) Saturation temperature T vi of the flashed-off vapor and (ii) Temperature of the unevaporated brine flowing from the chamber. The third subset of equations considered the existing interactions between the first two subsets. This subset defines the mass of vapor formed by flashing D i in the ith stage. All equations in the above-mentioned three subsets are solved by a reliable and efficient one-dimensional fixed-point iteration. The main advantages of this method are less sensitivity to initial guesses, requires a small number of iterations to obtain the required solution, and there is no need for calculating derivatives. The algorithm is implemented using the Computer-Aided Design (CAD) interactive package L-A-S (Linear Algebra and Systems). Detailed results are presented to show the dependence of the important factors controlling the fresh water cost, which are plant performance ratio, specific heat transfer area, specific brine flow rate, and specific cooling water flow rate, on the most significant two design variables, namely the total number of stages and the top brine temperature. The predicted data from the model are compared with published data of a typical MSF plant in operation at Kuwait. The agreement is found to be very good.