Minimum Entropy Generation in a Heat Exchanger in the Cryogenic Part of the Hydrogen Liquefaction Process: On the Validity of Equipartition and Disappearance of the Highway

Liquefaction of hydrogen is a promising technology for transporting large quantities of hydrogen across long distances. A key challenge is the high power consumption. In this work, we discuss refrigeration strategies that give minimum entropy production/exergy destruction in a plate-fin heat exchanger that cools the hydrogen from 47.8 K to 29.3 K. Two reference cases are studied; one where the feed stream enters at 20 bar, and one where it enters at 80 bar. Catalyst in the hot layers speeds up the conversion of ortho-to para-hydrogen. Optimal control theory is used to formulate a minimization problem where the objective function is the total entropy production, the control variable is the temperature of the refrigerant and the constrains are the balance equations for energy, mass and momentum in the hot layers. The optimal refrigeration strategies give a reduction of the total entropy production of 8.7% in the 20-bar case and 4.3% in the 80-bar case. The overall heat transfer coefficient and duty is higher in the 20 bar case, which compensates for the increase in entropy production due to a thermal mismatch that is avoided in the 80 bar case. This leads the second law efficiency of the 20 bar case (91%) to be similar to the 80 bar case (89%). We demonstrate that equipartition of the entropy production and equipartition of the thermal driving force are both excellent design principles for the process unit considered, with total entropy productions deviating only 0.2% and 0.5% from the state of minimum entropy production. Equipartition of the thermal driving force i.e. a constant difference between the inverse temperatures of the hot and cold layers represents a particularly simple guideline that works remarkably well. We find that both heat transfer and the spin-isomer reaction contribute significantly to the entropy production throughout the length of the process unit. Unlike previous examples in the literature, the process unit considered in this work is not characterized by a “reaction mode” at the inlet followed by a “heat transfer mode”. Therefore, it does not follow a highway in state space, i.e. a band that is particularly dense with energy efficient solutions. By artificially increasing the spin-isomer conversion rate, the highway appears when the conversion rate becomes sufficiently high.