Fundamental optimal relation of a generalized irreversible four-reservoir chemical pump

A new cyclic model of a four-reservoir chemical pump with irreversible mass transfer, mass leakage, and internal dissipation is proposed in this paper. The optimal relation between the coefficient of performance (COP) and the rate of energy pumping of the generalized irreversible four-reservoir chemical pump is derived by using finite-time thermodynamics or thermodynamic optimization. The maximum COP and the corresponding rate of energy pumping, as well as the optimal time parameters of the four mass transfer processes and the optimal chemical potentials of the working fluid are also obtained. Moreover, the influences of these irreversibilities on the optimal performance of the chemical pump are revealed. It is found that the mass leakage affects the optimal performance qualitatively, and the characteristic curve changes from a monotonic decreasing function without mass leakage to a parabolic-like one with mass leakage; while the internal dissipation affects the optimal performance quantitatively, it does not change the shape of the characteristic curve but only decreases the peak value. The results obtained herein can provide some new theoretical guidelines for the optimal design and development of a class of chemical pumps.