On the Efficiency of the Direct Substitution Approach for Reactive Transport Problems in Porous Media

Abstract

Nonlinear reactive transport problems can be solved using the Operator Splitting (OS) approach, where transport and reaction processes are separated or the Direct Substitution Approach (DSA) where chemical and transport equations are solved simultaneously. The OS techniques can be very attractive, but are known to introduce splitting errors with SNIA (Non Iterative OS) and have low convergence rate with SIA (Iterative OS). These problems are avoided with DSA which is more robust than OS schemes. On the other hand, DSA is more complicated and very demanding in terms of computing time and memory requirements. This can make DSA less efficient than OS schemes especially for fine discretizations and chemically simple problems. In this work, DSA, SIA and SNIA are combined with a new sparse direct (unifrontal/multifrontal) solver. The efficiency of this solver is not dependent on the matrix conditioning. The performance of the three approaches is studied for two transport problems with simple and difficult chemical reactions and for different number of unknowns. Results show that when combined with an efficient sparse direct solver, DSA is more efficient than SIA and SNIA even for chemically simple problems and large number of unknowns.