Derivation of integral energy balance for the manotea facility

A path integral based on mass and energy, rather than fluid mechanical, considerations is derived in order to characterize the physical mechanisms governing MANOTEA transients. This equation is further simplified to obtain an expression that frames transients in term of liquid inventory alone. Using data obtained from an actual transient, the path integral is implemented using three variables (change in liquid inventory, liquid inventory as a function of time, and change in metal temperature) to predict the outcome of a fourth independently measured variable (condenser pressure as a function of time). The implementation yields a very good approximation of the actual data. The inventory equation is also implemented and shows reasonable agreement. These equations, and the physical intuition that they yield, are key to properly characterizing MANOTEA transients and any subsequent modeling efforts.