A new formulation for the non-equilibrium allowance in MSF processes

This paper presents an alternative method for the quantification of the irreversible phenomena that characterize the flashing process in a stage of a MSF desalination plant, and that lead to an increase in the brine temperature of the flashing tank with respect to the ideal equilibrium conditions. The current calculation of the irreversibilities is based on the determination of a factor, the non-equilibrium allowance (NEA), representing the difference between the real temperature of the brine exiting the stage and the temperature corresponding to thermodynamic equilibrium with the prevailing pressure in the flashing vacuum. We propose instead to use a stage efficiency, in some aspects similar to the polytropic efficiency, commonly adopted in gas in a turbine and compressor. The results show that the use of this efficiency leads to a more physically complete problem formulation. The numerical values for design specifications can be chosen from a range of assigned values, in a similar fashion to the use of the polytropic efficiency. The results of a numerical application show that the interval of allowable values is rather limited and that the set of operational parameters influencing the choice is small.

The new and original formulation proposed here is aimed at the calculation of the effects of irreversible losses on the evaporation (flashing) balance of the stage. It has been shown that it simplifies the process calculation procedure, and it has been proven that the results of the adoption of the classical theory about NEA and the results of the newly introduced stage efficiency lead to the some outcome (in terms of flow diagram). In particular, use of stage efficiency is very convenient for the solution of inverse design problems when the hardware data of each single stage are not yet known, and therefore is not possible to determine an exact value for the NEA. In such cases, since it is entirely possible to attribute a reasonable value to the stage efficiency, the iterative procedure required to drive the NEA calculation to convergence can be dispensed with. The value of α assigned by design must be then, of course, validated by a proper choice of the relevant design parameters characterizing both the stage and its operating conditions. The stage efficiency value is by force connected to the NEA by a deterministic relation and depends on the stage geometry and thermophysical conditions, but its value varies within a very small numerical range and can be conveniently assigned in advance, with relatively high confidence. The proposed theory makes the design of a MSF stage similar to that of a thermal engine, where the designer first assumes a tentative value for the polytropic efficiency of each component and checks this original assumption only after a detailed design has been generated.