American Institute of Mining, Metallurgical and Petroleum Engineers Inc.
Conventional reservoir simulation models use four-directional flux calculating procedures and accordingly compute fluid injection procedures and accordingly compute fluid injection performance with an inherent inaccuracy that performance with an inherent inaccuracy that often is of substantial magnitude. Tests show that the velocity of frontal movements computed are too slow diagonal to the grid axes and too fast parallel to the grid axes. The magnitude of the inaccuracy was found to range from +42% to -32% when referenced to a more accurate eight-flux procedure herein described. The four-flux inaccuracy can lead to especially serious error when matching limited fluid injection performance.
The eight-flux concept presented requires that the model's grids be viewed as symmetrical octagons for the purpose of computing the resistance to fluid flow from one grid to another.
The conclusion is reached that a model using the eight-flux computational procedure calculates saturation fronts more accurately; results in better reservoir performance matching and flood performance predictions; and is computationally more stable. The alternating direction explicit-type computational procedures are well suited to handle the procedures are well suited to handle the eight flux calculations.
Normally, in grid-type reservoir simulation models, flux calculations are made in only four directions with respect to each cell. These flux streams run between each cell and the four abutting cells along lines perpendicular to the four faces. For fluids to move perpendicular to the four faces. For fluids to move diagonally with respect to the axes of the cells, it proceeds in a stair-step fashion, making a 90 degree turn at the center of each cell. As a result of this procedure the flood fronts resulting from model simulation are distorted.
One technique for improving flood front tracking in a numeric model is to compute flux into and out of each cell in eight directions rather than four. Thus, as far as flux calculations are concerned, the cells are treated as symmetrical-octagons.