Our article entitled 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 has just been accepted for publication in the International Journal of Hydrogen Energy.
In the paper, we use optimal control theory to minimize the total entropy production of a heat exchanger in the cryogenic part of the hydrogen liquefaction process. The heat exchanger is also a reactor, as catalyst is placed in some of the layers to speed up to conversion between the two spin-isomers of hydrogen, ortho- and para-hydrogen.
In recent literature, there has been a discussion about whether it is beneficial to invoke a higher operation pressure than 20 bar in the hydrogen liquefaction process. Inspired by this discussion, we investigate two reference cases; one where the feed stream enters at 20 bar, and one where it enters at 80 bar. 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 in the article 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. 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 (see figure below).
The work is an outcome of the thesis work of my previous Msc. student, Ragnhild Hånde from the Department of Physics (see picture below), who delivered her thesis last year. She is now working as a software developer.