Model Studies of the Inverted Nine-Spot Injection Pattern
Authors: Watson R.E. , Silberberg I.H. , Caudle B.H. 
Published: December 2007

Abstract
The production history of an inverted nine-spot injection pattern was studied with a porous plate model similar to Habermann's. Colored fluids were used so the boundary movements could be photographed. By varying the production rates of the side and corner producing wells, the optimum pattern sweep efficiency can be obtained. Results of the laboratory tests indicate that interpolation of the pattern sweep and conductivity ratio data will permit application of the data to predicting fluid injection operations with mobility ratios between 0.1 and 10 and production rate ratios between 1 and the optimum values.

Introduction
The inverted nine-spot injection pattern in Fig. 1 has some unique advantages over other regular injection patterns (five spot, line drive, etc.) used in secondary recovery operations. It has three producing wells for each injection well, while the five-spot and line-drive patterns require an equal number of injectors and producers. Furthermore, of the eight producing wells surrounding each injection well, four are of the "side well" type which lie nearer the injection well than the remaining four "corner wells". This allows the production rates of these two types of wells to be adjusted independently of each other to obtain better pattern sweep efficiency. This latter advantage may well be the reason why the nine-spot patterns have not been studied as extensively as the patterns containing only one type of injection or producing well. The pattern sweep efficiency of the inverted nine spot is affected almost as much by operating with different producing rates of the corner and side wells as by differing mobility ratios. Possibly because of this added operating parameter, published studies of nine-spot systems have been limited in their coverage of the pertinent variables. The model studies reported here covered the mobility-ratio range normally found in waterflood operations, as well as the variation in well production rates necessary to achieve optimum pattern sweep efficiency. Conductivity ratios-a measure of the change in total flow at constant pressure difference-were obtained during each model run.

EXPERIMENTAL TECHNIQUE
A porous-plate model with miscible fluids representing the in-place and injected fluids was used in this study. This model technique is the same as that used in both X-ray shadowgraph and visual techniques described in the literature. Using miscible fluids eliminates residual oil in the model, and the permeability to the injected fluid is the same as to the in-place fluid. Thus the mobility ratio in the model is given by the ratio of the viscosity of the displaced fluid to the viscosity of the injected fluid. Because of the non-linear nature of the viscosity vs composition curve for two miscible liquids, the mobility change across the boundary between the two fluids is reasonably sharp. This technique thus represents the displacement of a region of one fluid mobility by a region of possibly different mobility in an isotropic system under steady-state flow conditions.
JPT
P. 801ˆ