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The success of translating a conceptual site model for a karst site into a numerical groundwater model will depend on both the experience of the user and the capabilities and limitations of the selected computer program. Despite its numerous advantages, even MODFLOW – probably the most widely used, tested and verified modelling program currently available – has conceptual limitations that many karst hydrogeologists have to deal with on a routine basis while searching for an equivalent porous medium approach that may work. This includes assigning very high values of hydraulic conductivity to those model cells known, or suspected, to contain highly transmissive conduits, or assigning an unreasonable, very low effective porosity to the model cells with virtual ‘conduits’ to simulate high groundwater velocities. A new version of MODFLOW called MODFLOW-USG (UnStructured Grid) has been developed and released to the public domain. This new version retains full compatibility with previous versions of MODFLOW while taking advantage of unstructured grids and finite volume numerical solutions. It enables hydrogeologists to accurately translate even the most complex conceptual site models in karst into a numerical environment, thus eliminating the need for various surrogate modelling solutions based on an equivalent porous medium approach.

The objective of this paper is to present an overview of the fundamental equations governing transport phenomena in compressible reservoirs. A general mathematical model is presented for important thermo-mechanical processes operative in a reservoir. Such a formulation includes equations governing multiphase fluid (gas-water-hydrocarbon) flow, energy transport, and reservoir skeleton deformation. The model allows phase changes due to gas solubility. Furthermore, Terzaghi's concept of effective stress and stress-strain relations are incorporated into the general model. The functional relations among various model parameters which cause the nonlinearity of the system of equations are explained within the context of reservoir engineering principles. Simplified equations and appropriate boundary conditions have also been presented for various cases. It has been demonstrated that various well-known equations such as Jacob, Terzaghi, Buckley-Leverett, Richards, solute transport, black-oil, and Biot equations are simplifications of the compositional model.