Numerical simulation module

The numerical simulation module for single-phase filtration has been developed. This module will be included in the second generation of SiamWellTest. The control volume method is used with the generation of an unstructured irregular grid (Voronoi grid) to solve the differential diffusivity equation.

Currently, the following functionality has been developed:

Grid:

• Generation of 2D Voronoi grid
• Placement of template elements on the grid: well, bound
• Types of template wells: vertical, vertical fractured, slanted, limit entry, with multiple perforations, horizontal, horizontal fractured
• Refinement of the grid around the calculated elements
• Setting the heterogeneity of reservoir properties by cells

Calculations:

• Single-phase filtration of oil, gas, water
• Wellbore storage model: constant, changing
• Reservoir model: homogeneous, dual porosity PSS
• Fracture model: infinite conductivity fracture, finite conductivity fracture
• Boundary model: constant pressure boundary, no flow boundary, constant rate boundary

A Biconjugate gradient stabilized method (BiCGStab) with ILU preconditioning is used to solve a system of linear equations. Linearization is performed using the Newton-Raphson method in the case of solving a system of nonlinear equations.

Tests:

A similar analytical calculation was performed to verify the numerical simulation. The pressure at the well bottom-hole was checked. Single-phase linear filtration was checked in the time interval from 1e-5 to 1e+5 h divided into 101 time values. The grid consisting of 804 cells was generated for numerical modeling. The average error relative to the analytical calculation is 0.48%.

In addition to checking with the analytical calculation, a compare was made with another numerical simulator, which was accepted as a reference. The time interval from 1e-5 to 1e+5 h was divided into 354 time values. The grids of the developed module and the reference simulator are shown below. The number of cells in the reference simulator was 813. The average error relative to the reference simulator is 0.23%. The calculation time of the developed numerical solution turned out to be comparable with the reference simulator.

Path forward plan

• Generation of a Voronoi grid for a layered reservoir
• Adding of multiphase nonlinear filtration, including the Black oil model
• Include of gravity and capillary forces to the calculations
• Include of heat exchange processes to the calculations