Improved Material-Balance Regression Analysis for Waterdrive Oil and Gas Reservoirs
- S.R. Sills (Arco E&P Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- May 1996
- Document Type
- Journal Paper
- 127 - 134
- 1996. Society of Petroleum Engineers
- 4.6 Natural Gas, 5.2.1 Phase Behavior and PVT Measurements, 5.5.8 History Matching, 5.4.2 Gas Injection Methods, 1.2.3 Rock properties, 5.7.1 Estimates of resource in place
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An improved material balance formulation is presented for determining original hydrocarbons-in-place (OHIP) in water-drive oil and gas reservoirs. The improved formulation reduces the number of unknowns in the regression analysis through the definition of a combined reservoir and aquifer expansion term (CET). CET formulations are presented for the van Everdingen and Hurst and small pot analytical aquifer models. Field examples analyzed using the CET are presented illustrating the non-unique nature of water-drive material balance solutions for OHIP. A method is developed for reality checking the best-fit aquifer parameters obtained from the regression analysis. The CET material balance formulation is shown to provide several advantages over existing regression analysis techniques.
Material balance analysis of water drive reservoir performance to determine OHIP requires a method for estimating water influx from the aquifer. If an analytical aquifer model is used, the aquifer description must be known or determined as part of the OHIP analysis. Havlena and Odeh, Tehrani, and others have proposed regression analysis techniques for simultaneously determining OHIP and the correct aquifer description. Several issues must be considered during a material balance regression analysis of a water drive reservoir. First, an appropriate analysis technique must be determined. Second, the potential for non-unique OHIP solutions must be considered. Finally, the results of the regression analysis must be reality-checked to ensure they correspond to a reasonable aquifer description.
In this paper, a combined reservoir and aquifer expansion term (CET) is developed which allows OHIP and the water influx constant to be determined from the slope of a simple origin constrained straight line plot. The CET method permits a single plotting technique to be used for both volumetric and water drive oil and gas reservoirs. Unlike current material balance regression analysis methods, the CET formulation ensures that consistent values of cf and cw can be specified for the reservoir and the aquifer. Although developed for the commonly used van Everdingen and Hurst (VEH) unsteady-state radial aquifer model, the new formulation may be easily extended to other analytical aquifer models.
Water-drive material balance regression analyses often yield multiple OHIP estimates with similar regression accuracies, but differing aquifer descriptions. In the VEH unsteady-state radial aquifer model, the aquifer description is determined by the values assumed for the aquifer's influx constant, U, dimensionless time constant, a, and dimensionless radius, rD. In theory, these values may be calculated directly from the properties of the aquifer. In practice, a and rD are often treated as history match parameters and U and OHIP are constants determined by the regression analysis. In this paper, field examples are presented showing that if the a and rD values are treated as unknowns, the OHIP solution obtained will be non-unique. One, and usually two time constant solutions may be found for any assumed dimensionless radius. Each solution represents different value& for the OHIP and aquifer influx constant.
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