Energy efficient reactor design simplified by second law analysis

Gas heated reformer configurations which all produce the same amount of hydrogen have been investigated. By analysing various stationary states of operation formulated by optimal control theory, we find numerical support for the hypothesis of minimum entropy production, namely that the state of operation with constant entropy production, and also in some cases constant thermal driving force, are good approximations to this most energy efficient state of operation. This result applies, also for non-linear transport equations, and conditions for which there exist no rigorous mathematical description of the most energy efficient state. Based on the studies, we also formulate a set of guidelines to aid in an energy efficient reactor design, which can be used once the best available heat transfer coefficients have been obtained. The optimal reactor design depends on the relative size of the heat transfer coefficient for heat transfer across the tubular reactor wall and typical heat transfer coefficients in heat exchangers. Very efficient heat transfer across the reactor tube wall favours a design consisting of an adiabatic pre-reactor followed by a tubular reactor section exchanging heat. Very poor heat transfer across the reactor tube wall favours a design consisting of one or more adiabatic reactor stages with interstage heating/cooling in dedicated heat exchangers. The guidelines add to earlier proposals in the literature, and help define central optimization variables and boundary conditions in reactor design.