Use of Voronoi Grid in Reservoir Simulation

Abstract

Recently, a flexible gridding technique known as Voronoi or perpendicular bisection (PEBI) grid has received some attention in perpendicular bisection (PEBI) grid has received some attention in the petroleum literature. The main advantage of this grid is that individual grid points can be specified anywhere inside the domain regardless of the position of any other points. Several important issues related to the practical use of such flexible grids have not been addressed in previous works. This paper describes a practical way of using Voronoi grids for field scale simulation. Grid points are easily generated by using modules of known geometry which can be located, scaled or rotated in any position. Physical properties are specified at points that are independent of the computational grid. A new well points that are independent of the computational grid. A new well model for Voronoi grids is proposed and tested. The results of the well model are in close agreement with analytically calculated pressure drop for different injection patterns and grid geometries. pressure drop for different injection patterns and grid geometries. It is shown that, while the results of hybrid-Cartesian and hybrid-hexagonal grids are less sensitive to grid orientation than pure hexagonal grids or the 9-point scheme for the cases pure hexagonal grids or the 9-point scheme for the cases investigated, they are still dependent on the number of grid blocks. A 5-spot pattern in a heterogeneous reservoir was simulated using different grid geometries. The results art in close agreement with a fine grid simulation performed with a commercial simulator. This shows that, at least for the problems investigated, the proposed gridding technique is able to capture the main features proposed gridding technique is able to capture the main features of reservoir heterogeneities. Introduction Field scale simulation of petroleum reservoirs is performed by dividing the real domain into imaginary grid blocks and locally applying conservation laws for each fluid component in the system. The fluid flow between blocks is calculated by the discretized form of Darcy's law. Additionally, PVT and relative permeability relations are also honored. The outcome of any flow permeability relations are also honored. The outcome of any flow simulation depends on how the reservoir is divided and how the flow equations are formulated. Although several grid geometries have been presented in the literature, the combination of different geometries in a single grid system is restricted to very specific cases like local grid refinement and hybrid-Cartesian grids. Even in these situations, the specification of an individual grid block is dependent on the location of adjacent blocks. The Voronoi grid has the property that individual grid points can be specified anywhere inside the domain regardless of the position of any other points. Because of its flexibility, it has position of any other points. Because of its flexibility, it has been used in several different areas like physics, rock characterization, crystallography, electrical engineering, biology, mathematics, fluid mechanics and petroleum engineering. Although the grid blocks have been referred to by different names like Wigner-Seitz cells or PEBI grid, the vast majority of the literature refers to it as Voronoi polyhedra or grid, in honor of the mathematician who first defined it.

Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance

“…Grids based on voronoi diagrams remain predominant in reservoir simulation [9,31,58,60,61,64,76]. Voronoibased grids are locally orthogonal and permit two-point flux approximation if the permeability field is isotropic, or if the grid is generated to be K-orthogonal [64].…”

“…Voronoibased grids are locally orthogonal and permit two-point flux approximation if the permeability field is isotropic, or if the grid is generated to be K-orthogonal [64]. Voronoi grids are also called Dirichlet or Thiessen tessellations.…”

“…The grids generated, provide a means of spatial discretization required by flux approximation schemes. The flux approximation schemes used in reservoir simulation are control volume distributed, where a piecewise constant representation of flow variables and rock properties is assigned to control volumes, so that field variables are located at their centres, and/or circumcentres also called control points [64].…”

A critical assessment of simple recharge models: application to the UK Chalk

“…The model domain is discretised into nodes and cells using a Voronoi, or perpendicular bisection, grid (Palagi and Aziz, 1994), whereby cell faces are located midway between adjacent nodes and are perpendicular to the line that bisects the two nodes. Model states (ψ and θ) are specified at nodes, and fluxes are approximated across faces.…”

A Three Dimensional Grid Construction for the Simulation of Horizontal Wells in Geologically Complex Petroleum Reservoirs

“…Palagi and Aziz [12] investigated the PEBI grid and the combination with other grids for field scale simulation and for the modeling of vertical and borizontal wells.…”