A control-volume finite-element method for three-dimensional multiphase basin modeling

In this paper we describe a 3D control-volume finite-element method to solve numerically the coupled partial differential equations (PDEs) governing geological processes involved in the evolution of sedimentary basins. These processes include sediment deposition and deformation, hydrocarbon generation, multiphase fluid flow, and heat transfer in deforming porous media. These integrated processes possess a wide range of time-scales, indicating the need for implicit methods. In addition, sedimentary basins are geometrically complex environments, requiring unstructured tetrahedral meshes to adequately represent the problem realistically without the need for an excessive number of mesh elements. Here, we also present a general formulation for problems involving back-oil, thermal, or compositional models using overall component mass concentrations, and an arbitrary Lagrangian–Eulerian (ALE) formulation to deal with salt motion conservatively. The Newton method is used to solve the sparse Jacobian systems resulting from the linearization of the coupled non-linear PDEs for multiphase flow and energy transfer. These systems are solved with the generalized minimal residual method (GMRES) method with an incomplete lower–upper (ILU) preconditioner for faster inner iteration convergence rates. We applied this model to a sedimentary basin and we describe the results for this basin.