A fixed point iterative algorithm for solving equations modeling the multi-stage flash desalination process (Q1371755)

We present an algorithm for solving the equations simulating the steady state behavior of the multi-stage flash 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 (\(i\)th stage) is 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. The third subset of equations considers the existing interactions between the first two subsets. This subset defines the mass of vapor formed by flashing \(D_i\) in the \(i\)th stage. All equations in the above-mentioned three subsets are solved by a one-dimensional fixed-point iteration. The main advantages of this method are less sensitivity to initial guesses, 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 interactive package L-A-S (Linear Algebra and Systems).