MODELING DIFFUSION AND REACTION IN SOILS .1. A DIFFUSION AND REACTIONCORRECTED FINITE-DIFFERENCE CALCULATION SCHEME

Numerically accurate calculation of stimultaneous diffusion and reacti on in soil systems is a prerequisite for realistic model simulations o f diffusion-controlled chemical fate processes and analysis of experim ental data, Recent studies have shown that the inclusion of a first-or der reaction term in numerical transport models results in complex num erical calculation errors in both convection and dispersion and even i n the reaction rate itself. This suggests the need for very small time increments to ensure sufficient accuracy. However, in the case of dif fusion-reaction, and using a comprehensive Taylor expansion analysis, we show that the first-order errors (errors in reaction) and second-or der errors (errors in diffusion) in an explicit finite difference calc ulation scheme reduce to simple functions of only two parameters, the time increment and the first-order reaction rate coefficient. Based on this, we present a Diffusion And Reaction Corrected (DARC) calculatio n scheme that allows for rapid and accurate solution of simultaneous o ne-dimensional diffusion and first-order reaction in the soil gaseous or liquid phases. A general criterion for ensuring numerical stability when using the DARC scheme is derived, Tests against analytical solut ions and data for methane consumption in intact soil columns show that the DARC scheme allows for the use of much larger time increments com pared with the traditionally used non-corrected scheme without signifi cant loss of accuracy. The combined procedure for deriving terms for c orrection of numerical errors and criteria for avoiding numerical inst ability seems useful for better controlling numerical errors in simula tion models for transport and transformations.