The Second Law Optimal Path of Operation

The question of constrained optimisation is answered in a standard manner by Euler-Lagrange optimisations. By formulating the problem with optimal control theory, Johannessen and Kjelstrup explained that the Hamiltonian of the problem was constant in a study of chemical reactors. The total entropy production for a plug flow reactor was written as a function of a position-dependent state variable vector x(z) and the control variable u(z)  

The solution to the problem is given by 2(m- -2) differential equations for the temperature, pressure, degrees of conversion, and for Lagrange multipliers (T, P, k, Xp, kp, and A. ), with partial derivatives of //, where m is the number of reactions between the components. The constant Hamiltonian of this problem was reduced to a solution with constant entropy production. O , in the case of a heat exchange process. Using NET, it was also found that this solution was approximated by a solution with constant driving force, How to realise this in practice, remains to be solved. 

The results for the corresponding adiabatic column are also shown for comparison. The most important trays for distributed heating were the trays closest to the reboiler and condenser. 

A new design that takes the varying vapour flows into account was proposed. The effect of the changing hydrodynamic conditions has not yet been explored. It is still too early to conclude on the precise outcome of these optimisation studies, since the assumption of equilibrium on each tray was also used in the model. Progress in the methods of Section 4 may lead to improvements in the future. It is documented that the lost work can be reduced, but the increased investment costs are not yet clarified. Nevertheless, it is important to understand the thermodynamic conditions for optimal performance, independent of technical-economic considerations. 

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