Prediction of Tracer Performance in a Five-Spot Pattern

Abstract

Abstract A method has been developed for predicting the produced concentration profile for a miscible slug in a five-spot pattern. The technique consists of dividing the five-spot into radial elements and applying an approximate radial solution of the dispersion equation to each element. To test the method, laboratory experiments were conducted in five-spot models. The models were 2-ft X 2-ft X 2-in. Berea sandstone slabs simulating one quarter of a five-spot. An aqueous system was used with tritated water as the tracer fluid. Effluent concentration profiles were obtained for slug sizes ranging from 0.7 to 10.2 per cent of the pore volume. Agreement between predicted and experimental profiles was excellent. A prediction was also made for a field tracer test. For this case the predictive technique was modified to account for strafication by use of a layer cake model. Introduction Dispersion in porous media is of growing interest to the petroleum industry because of the increasing importance of secondary recovery operations. One of the controlling factors in the recovery of oil by miscible displacement or by the use of waterflood additives is the degree of mixing between the fluids of interest. Consequently, one of the prerequisites of any recovery prediction is an adequate method of predicting dispersion. Also, any quantitative interpretation of waterflood tracer tests is dependent upon the ability to determine the dispersion of the tracer as it flows through the reservoir. During the past few years there have been reported in the literature the results of a large number of investigations, both theoretical and experimental, concerning dispersion in porous media. (An excellent review of these results has been presented by Perkins and Johnston.) Only a few of these investigations, however, deal with non-linear flow systems. Raimondi et al. have presented an approximate solution of the dispersion equation for radial. diverging flow. Lau et al. and Bentsen have presented laboratory data for radial systems and have shown that the dispersion can be adequately predicted by Raimondi's solution. Bentsen has also presented a small amount of data for a radial, converging system. Brigham and Smith have applied Raimondi's solution, with approximating assumptions, to a five-spot pattern to predict the behavior of a field tracer test. The afore-mentioned investigations have been concerned almost entirely with radial diverging flow and have neglected the effect of converging flow. For this reason the present investigation was undertaken to develop a method of predicting dispersion in a five-spot pattern including the effects of both diverging and converging flow. The method which was developed consisted of dividing the five-spot into diverging-converging radial elements and applying an approximate solution of the dispersion equation to each element. DEVELOPMENT OF PREDICTION METHOD The development of the prediction method consisted of two phases: construction of a radial model of a five-spot pattern and derivation of equations to describe the dispersion in the radial model. FIVE-SPOT MODEL A radial model which simulated the flow characteristics of a five-spot pattern was constructed by dividing the fivespot into diverging-converging radial elements (Fig. 1). Because of symmetry the model represented only an octant of a complete five-spot. Each element had an included angle of 1 degrees (making a total of 45 elements) and a radius re such that the sum of the individual element areas was equal to the area of the five-spot octant. The normal five-spot fractional flow behavior was determined by averaging the experimental five-spot data of Caudle and Witte, Dyes, Caudle and Erickson and Fay and Prats. JPT P. 513ˆ