Finite element modelling of Gassmann fluid substitution of heterogeneous rocks

Abstract

The traditional method of fluid substitution requires the rock to be microhomogeneous with a fully connected porespace that ensures hydraulic equilibrium of the pore fluid. These assumptions may be violated for multimineral rocks, such as shaley sediments, due to a large contrast in elastic properties of the host mineral and shale, and due to the ability of clay to inhibit the movement of fluids. In this paper, we investigate the sensitivity of Gassmann’s equation to microheterogeneity for different quartz/clay mixtures using a numerical approach. In order to test the accuracy of Gassmann’s predictions, we utilize a scheme, which combines Gassmann’s equation in its traditional and generalized form with numerical experiments. For a simple double shell model, we show that the accuracy of Gassmann’s equation depends significantly on contrast in elastic properties of the solid constituents. With larger contrast, the common mineral-mixing rules introduce larger errors into the predictions. However, verification of Gassmann’s theory for periodic spheres models with different shape and location of clay show that the theory remains adequate for these more realistic high porous structures with a large contrast between the elastic properties of mineral phases.