Numerical simulation module

blogswt

Jun 30, 2021

2 min

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.

Grid

Generation of a 2D Voronoi grid
Placement of template elements on the grid: well, boundary
Types of template wells: vertical, vertical with fracture, deviated, limited entry, with multiple perforations, horizontal, horizontal with fracture
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 the system of linear equations. Linearization is performed using the Newton-Raphson method for solving the system of nonlinear equations.

Tests

An analytical calculation was performed to verify the numerical simulation. The pressure at the well bottomhole 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 against the analytical calculation, a comparison was made with another numerical simulator, accepted as a reference. The time interval from 1e-5 to 1e+5 h was divided into 354 time values. The grid of the reference simulator contained 813 cells. 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.