Numerical Method

The problem of solving the major dependent variables is given a Lagrangian formulation using a relaxed volume balance with Newton-Raphson iterations. The time-scheme for solving both the temperature, the pressure, the fluid and solid multi-component concentrations is implicit, but can optionally each be solved with an explicit time marching, should the user choose so.

The deformation of minerals used to calculate the compaction is solved with a Runge-Kutta method using VS2010 concurrent algorithms.

The multi-phase equilibrium and the equation of state for all active phases are solved with a Levenberg-Marquardt method also using VS2010 concurrent algorithms.

The user defined input wells are transformed into a none-rectangular grid using the techniques of Voronoi gridding (Watson, 1981) and isoparametic jacobians (Tortorelli, 1994).

The solver used can optionally be an iterative solver or a direct solver. The iterartive solver is a conjugate gradient method with a modified Jacobi preconditioner. The direct solver is a SuperLU sparse matrix solver developed by Demmel et al. (1999-2010).