Maximum power from membrane mixing processes.

It is well known that the free mixing of fluids having different compositions results in exergy losses. It has also been reported in the literature that the use of semi-permeable membranes allows to convert the exergy of mixing to mechanical/electrical power. This paper presents a method to define the conditions for obtaining maximum power from such a conversion process. An endoreversible model of a mixing process based on Finite Time Thermodynamics is proposed. It allows the combination of an ideal mixing process with the basic transport equations for mass transfer. Application of the model for power maximization confirms an interesting and general result reported previously in the scientific literature but for processes other than mixing. It is shown that the maximum power from a process can be achieved when half of the exergy rate expended within the mixing process is lost due to transport irreversibility and the other half is transformed into useful power. This theoretical result is only valid in the linear model approximation. However it allows new and relevant guidelines to be established for the design of membrane processes for gas stream mixing. It is illustrated here for methane-hydrogen mixing. Maximum power is achieved at a thermodynamic efficiency of 50%, independently of the initial conditions of the gases and of the value of the transfer coefficients characterizing the transport of these gases through membranes.