PARTIAL MOLAR EXCESS PROPERTIES, NULL SPACES, AND A NEW UPDATE FOR THE HYBRID METHOD OF CHEMICAL PROCESS DESIGN

A new thermodynamically consistent quasi-Newton formula is proposed for building iterative representations of the approximated part of the Jacobian matrix in the hybrid method of chemical process design. This update exploits the fact that the excess enthalpy and activity coefficient functions are homogeneous functions of degree zero in mole numbers which, in turn, gives rise to a natural null space for the approximated part of the Jacobian matrix that is defined by the component molal flow rates. The new formula builds iterative approximated parts that satisfy this null space constraint in addition to the usual overall secant condition and the desired sparsity constraints. The new quasi-Newton formula is derived using the variational calculus approach first for the nonsparse case. This solution is then extended to the sparse case.