Development of particle tracking algorithms for various types of finite elements in multi-dimensions

Modeling concentrated solutions demands the use of ion-interaction models such as Pitzer equations, which involve a large number of operations. Implementation of these models in large reactive transport simulations significantly increases the computation time with respect to traditional activity coefficient models. CPU time depends on the efficiency of (1) the Pitzer algorithm itself, and (2) the speciation algorithm. We present an implementation of the Pitzer model that improves traditional implementations by using a compact matrix approach. This facilitates programming and computation of derivatives. The use of analytic derivatives allows the use of Newton–Raphson algorithms, which converge quickly. The approach is implemented in an object-oriented programming (OOP) scheme by creating an entity that represents the thermodynamic behavior of both dilute and concentrated solutions. This entity is readily linked to any geochemical or reactive transport codes. We show that the code is robust, in that its implementation improves the convergence in a broad range of geochemical calculations, and efficient, in that its CPU time compares favorably with other codes.