An engineering approach to the treatment of constant pressure boundary condition in block-centered grid in reservoir simulation

Block-centered grid and point-distributed grid are the most widely used grids to describe a petroleum reservoir as units in reservoir simulation. In the point-distributed grid, the boundary grid point falls on the boundary, whereas the point that represents the boundary grid block is half a block away from the boundary. As a result, the point-distributed grid gives accurate representation of constant pressure boundary condition. In the block-centered grid, the approximation of a constant pressure boundary is implemented by assuming the boundary pressure being displaced half a block coincides with the point that represents the boundary grid block and by assigning boundary pressure to boundary grid block pressure. This is a first-order approximation. A second-order approximation was suggested, but it has not been used because it requires the addition of an extra equation for each reservoir boundary of a boundary grid block. Furthermore, the extra equations do not have the form of a flow equation. This article presents an engineering approach for the representation of a constant pressure boundary condition in a block-centered grid. The new approach involves adding a fictitious well term per boundary to the flow equation of a boundary grid block. This treatment is valid in both rectangular and radial-cylindrical grids. The flow toward a fictitious well is linear in rectangular coordinates and radial in radial-cylindrical coordinates. The flow rate equations for fictitious wells were derived from the inter-block flow rate term between a boundary grid block and the grid block that falls immediately outside reservoir boundary. These flow rate equations are presented and tested. With the new treatment, both block-centered grid and point-distributed grid produce pressure profiles with comparable accuracy. In other words, the use of the point-distributed grid does not offer any advantage over the block-centered grid in rectangular and radial-cylindrical coordinates for the case of constant pressure boundaries.