Efficient numerical techniques for modeling multicomponent ground-water transport based upon simultaneous solution of strongly coupled subsets of chemical components

• Published in: Advances in water resources 2000-01, Vol.23 (4), p.307-324
• Main Authors: Robinson, Bruce A., Viswanathan, Hari S., Valocchi, Albert J.
• Format: Article
• Language: English
• Subjects: chemical reactions; chemical speciation; computer simulation; Earth sciences; Earth, ocean, space; elements; equations; Exact sciences and technology; Freshwater; Geochemistry; groundwater; groundwater contamination; groundwater flow; Hydrogeology; Hydrology. Hydrogeology; mathematical models; Mineralogy; neptunium; pollutants; reactive transport equations; Silicates; simulation models; solutes; transport processes; Water geochemistry
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/S0309-1708(99)00034-2

An iterative solution technique for reactive transport problems is developed, which we call the selective coupling method, that represents a versatile alternative to traditional uncoupled iterative techniques and the fully coupled global implicit method. The chemical formulation studied allows a combination of equilibrium and kinetic reactions, and therefore is a more versatile model formulation than a purely equilibrium-based system. However, this is a very challenging system for obtaining an efficient numerical solution. Techniques that sequentially compute the concentrations of aqueous components possibly ignore important derivatives in the Jacobian matrix of the full system of equations. The selective coupling method developed here allows only the strongly coupled components to be solved together, and the transport iteration consists of solving groups of components simultaneously. We also develop a method denoted as coupled normalization to reduce the computational work and memory requirements for particular types of reactive transport problems. These approaches can result in computational savings relative to the global implicit method by achieving a similar iteration count while reducing the cpu time per iteration. More importantly, the memory requirements of the selective coupling technique are controlled by the maximum number of coupled components, rather than by the total number of components. For complex aqueous chemical systems and grids with a large number of nodes, memory efficiency is the characteristic that makes the selective coupling method particularly attractive relative to the global implicit method. A series of example cases illustrate the efficiency of the new approach. These test problems are also used to address the implementation issues surrounding the most efficient strategy for coupling the aqueous components when carrying out the chemical transport iteration. In-depth knowledge of the behavior of the chemical system is required to select an appropriate solution strategy.