Calculation of fluid-mineral equilibria using the simplex algorithm

A new method for computing fluid-rock equilibria and associated geochemical mass transfer has been developed which utilizes the SIMPLEX algorithm to solve the set of coupled mass balance and mass action equations. The technique does not require differentiation of the governing equations, nor does it require the use of matrices. It is essentially a batch-type calculation which speciates the fluid and computes the masses of minerals that must precipitate or dissolve in order to maintain chemical equilibrium. The classic problem of titrating K-feldspar into water and computing the mineral paragenesis and fluid composition has been used as a test of the algorithm. The algorithm, coded in Microsoft QuickBASIC, can generate a complete paragenesis from unsaturated solution to saturation with K-feldspar in less than 5 min on a 80386 desktop running at 25 MHz with a math coprocessor