Computer Simulation of the Ternary Problem – Technical Aspects and Possibilities

Abstract

Interaction between groundwater contaminants (e.g. radioactive elements), soil and humic matter plays a crucial role in transport prognoses. This type of interaction, denoted as the ternary problem, may speed up propagation of a contaminant in comparison with the case in the absence of humic compounds. It is very difficult (almost impossible) to find a simple description of the ternary problem in the form of chemical equations. This difficulty is caused by the complex nature of humic substances. Rather than with particular chemical equations, the ternary problem is commonly described by schematic expressions which consider groups of species. The usual approach for the problem formulation is grouping of species resulting in a system of differential and algebraic equations (DAE). This article introduces a different approach allowing a semi-automatic formulation of a system of ordinary differential equations (ODE) for the same problem. The proposed method enables to avoid an operator-splitting already during the model formulation process. The approach for the model formulation and its solution has been implemented using two different open-source software packages. The results have been compared with reference results of a traditional solution approach using DAE systems. The implementation in Python verified the possibility of automation of the formulation and solution. A sensitivity analysis has been performed to evaluate the behaviour of the system with respect to parameter variation.