Bringing a new reservoir simulator to the market, we inevitably have to verify the model results by comparison with the market leaders. We also get a lot of questions about the technical description of our software and equations that the simulator solves. In this section, we present a brief review of the simulator parts and the methods applied in the main blocks.
Equations of fluid flow in porous media. Molar densities and pressure are set to the state variables that allow a general compositional model formulation, where the black oil model is a special case. The model takes into account the following aspects:
- Darcy’s law for fluid flow
- PVT tables with multiple PVT relative permeability regions
- Absolute permeability as a function of pressure
- Different options for aquifers
- Networks and gas gathering systems
- Tracer models
Time approximations. tNavigator utilizes a fully implicit time scheme that allows large time steps based on approximation criteria. This approach is implemented in most of the reservoir simulators.
Space approximations. Finite-volume method with finite-difference approximation of the differential operators is utilized. It assumes upstream approximation. Non-neighbor connections, faults, and pinchouts are fully supported.
Non-linear system of equations. We use the Newton method with full Jacobian with analytic derivatives for solving the non-linear system of equations.
Linear systems with Jacobian and matrix operations. We use BCGS (BiConjugate Gradient Stabilized) algorithm to solve the system of linear equations. This is a novel method that gets automatically adjusted to the problem at hand. We employ ILU(0) as a preconditioner for the linear system solver. This method is a variation of LU-dcomposition that is designed specially for the tNavigator package.
When solving a linear system with Jacobian one has to store both the sparse matrix and the preconditioner. tNavigator contains a block-oriented modification of the widely used MSR (Modified Sparse Row) method yielding improvement both in memory volume and speed.
Interactive operations and data handling in tNavigator. In order to optimize hard disk operations during the simulation runs, tNavigator treats only state variables of the model. Since the simulation core and the visualizer are in fact one application, the rest of the information can be immediately recovered by the user request. This approach allows operations with the model during the run and quick visualization with no time spent on writing and reading data from the disk.