SOLVING EQUATIONS SIMULATING THE STEADY-STATE BEHAVIOR OF THE MULTISTAGE FLASH DESALINATION PROCESS

The paper presents an algorithm for solving the equations simulating t he steady-state behavior of the multi-stage flash(MSF) desalination pr ocess. The model can be used either for designing new plants or analys is and optimization of existing units. The set of equations relating t he large number of design and operating variables for any stage (i-th stage) in MSF plants is broken down into three subsets. The first subs et contains equations describing processes in the tubes of the preheat er inside the flashing chamber. The second subset deals with the proce sses inside the flashing chamber. These two subsets of equations are s ubsequently solved iteratively involving only a single variable for ea ch subset. These variables are: (1) saturation temperature T-vi of the flashed-off vapor and (2) temperature of the unevaporated brine flowi ng from the chamber. The third subset of equations considers the exist ing interactions between the first two subsets. This subset defines th e mass of vapor formed by flashing D-i in the i-th stage. All equation s in the above-mentioned subsets are solved by a reliable and efficien t one-dimensional fixed-point iteration. The main advantages of this m ethod are less sensitivity to initial guesses, fewer iterations to obt ain the required solution, and no need for calculating derivatives. Th e algorithm is implemented using the computer-aided design (CAD) inter ative 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 hea t transfer area, specific brine flow rate, and specific cooling water now rate, on the most significant two design variables, namely the tot al number of stages and the top brine temperature. The predicted data hem the model are compared with published data of a typical MSF plant in operation at Kuwait. The agreement was found to be very good.