Fractal Methods Improve Mitsue Miscible Predictions
Authors: Mathews Jeffrey L. , Emanuel Alan S. , Edwards Kelly A. 
Published: December 2007

Summary
A reservoir modeling technique based on fractal geostatistics was used to interpret the displacement processes and to predict the response to a miscible-hydrocarbon water-alternating-gas (WAG) flood in a major portion of the Stage 1 project area of the Gilwood sand in project area of the Gilwood sand in the Mitsue field. The purpose was to compare projections based on geostatistical techniques with those based on conventional modeling and to compare the accuracy of the projections with current field projections with current field measurements. Results indicate that a hybrid finite-difference/streamtube technique based on fractal representations can provide a full project model for an efficient expenditure of effort and computer time. Calculated overall project response agrees reasonably well with field performance since the start of the Stage 1 WAG flood. Individual well response is predicted qualitatively. Analyses of tracer breakthrough and production logs agree with the solvent/water flow patterns predicted by the fractal model. patterns predicted by the fractal model.

Introduction
Frimodig et al. and Omoregie and Jackson describe previous studies of this project. Our methodology follows that project. Our methodology follows that established by other reservoir studies based on fractal geostatistics. A representative geologic cross section between an injector/producer pair is created from log and core data and fractal statistics. A miscibleflood simulator then uses this cross section to calculate the characteristic displacement between wells. A streamtube model is developed to represent areal conformance. Finally, fluid movement through the streamtubes is simulated to project overall field performance on the basis of calculated displacement characteristics.

Reservoir History
The Mitsue Gilwood A pool, 125 miles [201 km] north-northwest of Edmonton, Alta., Canada, was discovered in 1964. Total estimated original oil in place (OOIP) was 1 BSTB [1 X 10(9) stock-tank m3]; total OOIP for the Mitsue Gilwood A sand unit is 891 MMSTB [142x10(6) stock-tank m3]. Fig. 1 displays an areal map of the unit.
The reservoir consists of six defined channel sands lumped into three major sand bodies. Channels 1 and 2 form the upper sand body (Layer 1), and Channels 3 through 5 form the middle sand body (Layer 2). Channel 6, the lowest sand body, comprises less than 5% of the PV of the reservoir. Fig. 2 shows the spontaneous-potential/resistivity (SP) well logs for the interval studied for an injector and a producer well. The wells, 04-32-071-04W5 and 10-32-071-04W5, were used to generate the cross-sectional model.
Primary depletion of the reservoir occurred from 1964 to 1968, at which time a peripheral waterflood was initiated on the peripheral waterflood was initiated on the downdip west flank. Total unit oil recovery to the end of 1985 was 249.3 MMSTB [39.6x106 stock-tank m3], or 28% OOIP.
A hydrocarbon miscible flood is currently under way in a major portion of the unit. The wells in the Stage 1 project areas, defined by the dashed lines in the Mitsue unit map of Fig. 1, have been injected with solvent alternating with water at a WAG ratio of 1:1 to 2:1 since May 1985. Approximately 26 producing wells experienced solvent breakthrough by Feb. 1988.
The objective of the work described here was to develop a method for evaluating the solvent WAG performance for a major portion of the southern Stage 1 area as well as portion of the southern Stage 1 area as well as to predict future response. The waterflood was started as a peripheral flood on the west flank of the reservoir. Injectors were later added within the field for pressure maintenance. Producing wells were shut in when they began to produce at high WOR's, but no attempts were made to match in detail the waterflood portion of the field's injection history because of the limited ability to model changing pattern configurations and well rates.
The evaluation methods are based on a simulation model with a distribution of permeability that has a fractal character with permeability that has a fractal character with long-range correlations similar to those observed in natural property distributions. Emanuel et al.'s results showed that realistic predictions result without extensive history matching.
Hewett and Voss discuss the bases of the theory of fractal distributions. Emanuel et al. describe the procedure for predicting field response, and Hewett and predicting field response, and Hewett and Behrens give a theoretical basis for this procedure. procedure. Porosity/Permeability Reservoir Porosity/Permeability Reservoir Characteristics. Figs. 3 and 4 depict core permeability and porosity crossplots for the permeability and porosity crossplots for the injector/producer pair selected for the vertical cross-sectional model. A simple logarithmic curve was fit to the porosity/ permeability data, and a power curve was used permeability data, and a power curve was used to relate horizontal and vertical permeability data.
At this point, well log and core data are analyzed for their fractal dimension by testing of the well log or core data for the degree of correlation by the rescaled range procedure. An average fractal codimension procedure. An average fractal codimension equal to 0.75 was used. This value is typical for wells analyzed to date.
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