A Control-Volume Finite Element Method for Multiphase Fluid Flow in Basin Modeling

Ulisses T. Mello¹, José Roberto P. Rodrigues², and André Rossa^3
1IBM T. J. Watson Research Center, USA
²CENPES, Petrobras R&D Center, Brazil
³ESSS, Brazil

Three-dimensional basin modeling software is now routinely used in commercial petroleum exploration. However, there is an increasing need to model structurally complex models which includes processes such as fault and salt motion with time. In this paper, we describe a novel basin model to simulate the evolution of compacting sedimentary basins using unstructured tetrahedral meshes to describe adequately complex, evolving geological objects, without requiring an excessive number of mesh elements. The main focus of this paper is on the mathematical and numerical methods used to solve the coupled partial differential equations governing geological processes. We present a Control-Volume Finite-Element (CVFE) discretization with an adaptive implicit approach to achieve a stable, efficient, and reliable solution. This approach is locally conservative and allows the solution of multiphase fluid flow for slightly variable density, and compressible fluids. In addition, we describe how this approach was expanded to allow the inclusion solution of salt flow and flow along thin faults. We used an Arbitrary Lagrangian-Eulerian scheme to model salt motion and reduce associated remeshing required when large deformations occurs. For applications in basin modeling, the control volumes had to be modified to accommodate the motion of the top boundary due to deposition and erosion. The Newton method was used to solve the sparse Jacobian systems resulted from the linearization of the non-linear partial differential equations governing compaction, fluid transfer and heat transfer. These systems are solved with the GMRES method with an ILU preconditioner for faster inner iteration convergence rates. We also discuss some challenges and details related to the design and C++ implementation of a basin simulator, such as data-structures which facilitate the parallelization of the code. We applied this model to various synthetic and real cases and we briefly describe its results.

AAPG Search and Discover Article #90066©2007 AAPG Hedberg Conference, The Hague, The Netherlands