A NEW IMPLEMENTATION FOR ANALYTICAL DERIVATIVES OF THERMODYNAMIC PROPERTIES AND ITS BENEFICIAL APPLICATION ON DYNAMIC SIMULATION

A formulation to obtain analytical partial thermodynamic derivatives (PTHDs) of thermodynamic functions with respect to selected state variables for liquid, vapour or liquid-vapour systems, is presented. The objective of this paper is first to illustrate the advantages using analytical PTHD information and secondly to present a systematic procedure, based on an implicit system of nonlinear equations, which allows the user to choose his own state variables and to obtain analytical derivaties of any property (also chosen by the user) with respect to these state variables. The procedure is based on few PTHDs with respect to a basic set of state variables, coded explicitly and an algorithm that allows to compute all the other PTHDs needed, with respect to any set of state variables. The algorithm presented is completely independent of the mathematical solution procedure and independent of the thermodynamic model used. It therefore does not modify the structure of the system describing the plant units. It is now implemented in BELSIM-EPIC thermodynamic package. Its flexibility and contribution to solution accuracy are illustrated. Computer time savings using the algorithm, are presented and analyzed in the case of liquid-vapour equilibria calculations using different thermodynamic models and also in dynamic simulation of multicomponent distillation units in refinery plants.