Predicting Displacement Efficiency From Water-Cut or Gas-Cut Field Data

Welge, H.J., SPE-AIME, Petroleum Research Consultants, Inc. A procedure for predicting oil-displacement efficiency using field data is presented. The method is somewhat simpler than previous methods and is particularly applicable when well are previous methods and is particularly applicable when well are not developed in a regular pattern. Introduction A method for predicting the efficiency of oil displacement using field data is presented. The method is particularly applicable when the wells are not developed in a regular pattern, such as alternating rows of injection and producing pattern, such as alternating rows of injection and producing wells, or five-or nine-spot patterns.We assume, nevertheless, that the displacement occurs in a more or less linear manner, as in the portion of an oil field shown in Fig. 1. Here there is a single north-to-south trending row of water injection wells drilled near the center line of the field. The injected water flows mainly toward the east or the west, displacing the oil toward the other (producing) wells. The method presented is somewhat simpler and more straightforward than previous methods. Procedure Procedure We need, first, an average plot showing fw (the fraction of water in the flowing stream delivered at a well under reservoir conditions) as a function of pore volumes of injection, Wi. To arrive at Wi, we draw a rectangle on the areal map of the oil field (Fig. 1). Two of the opposite sides of this rectangle lie along the direction of average flow of fluids; and these two sides if extended, each pass midway between two injection wells. The other two sides of the rectangle pass through the injection well and nearest producing well, respectively. Thus, this producing well can be considered as withdrawing a "sample" of the fluids flowing past it. The pore volume of the porous body lying under the rectangle, divided into the cumulative volume of water injected into (or through) the rectangle, gives Wi. For Wells I-2 and P-1 in Fig. 1, the fw vs Wi plot shown in Fig. 2 is a reasonable average of the plots for other neighboring wells for which adequate data are available.The scatter of points shown in Fig. 2 is caused partly by the fact that the fw values are obtained from field data by an incremental or derivative process, which tends to magnify any inaccuracies in measurement and any errors caused by shifting streamlines when neighboring wells come on or off stream.To proceed with the displacement prediction, the first step is to arrive at the average water saturation, Sw, in the rectangle that includes Wells I-2 and P-1 (Fig. 1). This average saturation at any throughput will be given by the area above and to the left of the fw vs Wi curve (the smooth curve in Fig. 2) as follows: Volume of water displaced = .........(1) where Qi is the total fluid produced at reservoir conditions. Volume of water injected = .............(2) Volume of water left inside porous body= .........................(3) Dividing by the pore volume gives..................(4) JPT p. 944