Abstract

Modeling the flow of fluids (water, oil, steam) and transport of mass and energy in geologic media is often difficult, since the transport parameters (permeability, porosity, and velocity) commonly vary over several orders of magnitude. Furthermore, hydraulic conditions often force fluids flowing through a large volume of rock (e.g., oil reservoir) into a much smaller volume (e.g., fractures) such that the scale of interest can vary from kilometer to centimeter size.

We are using triangular unstructured finite element grids in combination with higher order finite element and finite volume methods and Strang operator splitting to accurately simulate fluid flow and mass and energy transport in geologic media. Unstructured finite element grids provide a detailed representation of the geologic media and allow the study of flow phenomena from the centimeter to kilometer scale. The use of triangular finite elements with quadratic interpolation functions yields a very good solution of Darcy's law and linear velocity fields for each triangle can be computed. By employing barycentric finite volumes, we can use these velocities on an element-by-element basis to calculate the flux of fluid, mass, or energy, which is governed by the advection-diffusion equation, across the control volume. The advection-diffusion equation is separated into its two components and solved by Strang operator splitting. The hyperbolic advective component is solved by a second order finite volume method with slope limiting to minimize numerical diffusion, while the parabolic diffusive component can be easily solved by a higher-order finite element methods.

Numerical experiments were carried out for mass transport in geologic media with varying velocities, for mass transport in a fracture network with a strongly heterogeneous velocity field, and for flow of two incompressible fluid phases. The proposed method shows very good results for all experiments.

Full Paper (Size: 218 KB)