One-Dimensional EKR Simple Model

Considering all the aforementioned aspects, a simple EKR model is proposed that assumes electromigration as the most significant transport process, neglecting the electroosmotic and diffusive transports and assuming there is no advection. The mass conservation equation is simplified to 

The electrical potential distribution is a function of the electrical resistance of the soil and therefore depends on the instantaneous local concentration and mobility of all ions existing in the pore water of the soil, which ultimately determine the electrical resistance evolution. Therefore, a set of conservation equation, one for each ion, has to be simultaneously integrated, with the difficulty that aU these differential equations are strongly coupled through the electrical potential distribution. Therefore, an analytical solution would be very difficult to obtain, if at all possible. So, a numerical solution must be used instead. 

As indicated in the previous section, the modeling of an electrokinetic soil remediation system requires a numerical integration of the mass conservation equation for each ion existing in the pore water. In a first approximation, a onedimensional model is presented here where an electrical circuit analogy is used (Wilson, Rodrfguez-Maroto, and Gdmez-Lahoz, 1995a). 

The numerical integration of the mass conservation equations consists basically in a time-iterative method with two sequential steps for each increment of time. In the first one, the transport of ions between each cell is calculated, yielding transient concentrations that are used in the second one, where the chemical equilibria and charge and mass balance equations are solved within each volume element. The first corresponds to the transport phenomena term in the differential conservation equation of each species, and the second corresponds to the rates of production of ions in those same equations. In this way, the model obtains new values that are used to perform the integration forward in time. 

The synergistic effects of multiple chemical species are not considered (water ionic strength, activities, etc.). 

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ONE-DIMENSIONAL EKR SIMPLE MODEL Therefore, the model is subject to the following constraints ... 

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