Simulation of 1/8 Five-/Nine-Spot Patterns

Abstract

Abstract Simulation of complex recovery processes often is performed using a single pattern, which may be a five-, seven-, or nine-spot. This approximation of a total-field multiple-pattern development by a representative pattern significantly reduces computing time and cost. This Forum is limited to a single pattern in a network of repeated five- or nine-spot patterns in an areally homogeneous formation. The formation may have arbitrary vertical heterogeneity and any number of layers. The single pattern contains two wells in the five-spot case and four wells in the nine-spot case. The four sides of the square pattern are no-flow or insulated boundaries. The single-pattern simulation should be performed for the smallest symmetrical element of the pattern to minimize computing cost. This well-known element is one-eighth of a pattern. Nevertheless, simulations of one-half and one-fourth pattern elements with areal homogeneity and square (uniform) grid blocks continue in practice and occasionally appear in the literature. Owing to symmetry within the pattern, the pressure (and saturation, composition, etc.) distribution within the one-eighth element defines the distribution throughout the pattern. Transmissibility and block PV alterations necessary for exact reproduction of five- or nine-spot results by a one-eighth pattern calculation are well-known for the five-point difference scheme and are omitted here. This Forum describes a simple alteration necessary for identity of one-half or one-fourth pattern and one-eighth pattern results using the nine-point difference scheme1 with either parallel or diagonal grids.2