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Title: Operator-splitting errors in coupled reactive transport codes for flow and transport under atmospheric boundary conditions or layered soil profiles

Author
item JACQUES, D - SCK, CEN, BELGIUM
item SIMUNEK, JIRKA - UC RIVERSIDE, CA
item MALLANTS, D - SCK, CEN, BELGIUM
item Van Genuchten, Martinus

Submitted to: Journal of Contaminant Hydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/30/2006
Publication Date: 8/17/2006
Citation: Jacques, D., Simunek, J., Mallants, D., Van Genuchten, M.T. 2006. Operator-splitting errors in coupled reactive transport codes for flow and transport under atmospheric boundary conditions or layered soil profiles. Journal of Contaminant Hydrology. Vol 88:197-218

Interpretive Summary: The fate and transport of many organic and inorganic contaminants (including nutrients, heavy metals, and organic chemicals) in the subsurface is most often affected by a multitude of interactive physical, chemical, mineralogical, geological, and biological processes. Simulation of these processes requires a coupled reactive transport code that integrates the physical processes of water flow and solute transport with a range of biogeochemical processes. One approach for solving the coupled equations for transient flow, transport and geochemistry is to use an operator-splitting approach in which the transport and chemistry equations are solved separately, but sequentially. This method is relatively easy to implement by combining existing codes for water flow, solute transport and the geochemistry. However, a disadvantage is the occurrence of errors resulting from both the operator-splitting approach itself and from the time and spatial discretizations in the required numerical solution. The objective of this study was to analyze numerical errors associated with the operator-splitting approach in coupled reactive codes for typical soil-related flow and transport problems, especially for applications involving transient flow and transport in heterogeneous soil profiles. Two benchmark problems were considered for this purpose: (i) a first-order decay chain of linearly or nonlinearly sorbing contaminants during precipitation and evapotranspiration, and (ii) a multicomponent transport problem involving cation exchange reactions in a multi-layered soil profile. Simulations were carried out with the recently developed HP1 code for unsaturated water flow and multicomponent solute transport problems in soils. Results compared favorably with simulations obtained using HYDRUS-1D for simplified geochemical transport situations, and with a more general code (CRUNCH) for more complicated. HP1 is a public domain software package that can be downloaded freely from http://www.sckcen.be/hp1/.

Technical Abstract: One possible way of integrating subsurface flow and transport processes with (bio)geochemical reactions is to couple by means of an operator-splitting approach two completely separate codes, one for variably-saturated flow and solute transport and one for equilibrium and kinetic biogeochemical reactions. This paper evaluates the accuracy of the operator-splitting approach for multicomponent systems for typical soil environmental problems involving transient atmospheric boundary conditions (precipitation, evapotranspiration) and layered soil profiles. The recently developed HP1 code was used to solve the coupled transport and chemical equations. For steady-state flow conditions, the accuracy was found to be mainly a function of the adopted spatial discretization and to a lesser extent of the temporal discretization. For transient flow situations, the accuracy depended in a complex manner on grid discretization, time stepping and the main flow conditions (infiltration versus evaporation). Whereas a finer grid size reduced the numerical errors during steady-state flow or the main infiltration periods, the errors sometimes slightly increased (generally less than 50%) when a finer grid size was used during periods with a high evapotranspiration demand (leading to high pressure head gradients near the soil surface). This indicates that operator-splitting errors are most significant during periods with high evaporative boundary conditions. The operator-splitting errors could be decreased by constraining the time step using the performance index (the product of the grid Peclet and Courant numbers) during infiltration, or the maximum time step during evapotranspiration. Several test problems were used to provide guidance for optimal spatial and temporal discretization.