An Analytical Model for Composite Reservoirs Produced at Either Constant Bottomhole Pressure or Constant Rate
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SPE MembersAbstractIn this paper, we present a model of the complete characteristic transient response from a composite reservoir including the effects of skin, wellbore storage and phase redistribution at the well. We present six flow regimes and the combined effects of wellbore storage and phase redistribution on pressure behavior in composite reservoirs.Using an automatic history matching approach, we analyzed three buildup tests and a pressure falloff test. This method eliminated the serious uniqueness problem associated with type curve analysis. We demonstrate that incorrect reservoir parameter estimates and incorrect production performance predictions would result from the use of any model that lacks the capabilities of the model we present in this paper. We also demonstrate possible misinterpretations of pressure data that may result from not recognizing the presence of phase redistribution in the buildup test data or not recognizing the composite reservoir behavior.IntroductionNumerous analytical models have been presented In recent years to describe the pressure behavior of composite reservoir systems. Composite reservoirs are encountered in a wide variety of reservoir situations. In a composite reservoir there is a circular inner region with fluid and rock properties different from those in the outer region. Reservoirs damaged because of fluid invasion during drilling or completion; stimulated reservoirs; reservoirs being waterflooded or undergoing insitu combustion are examples of the reservoir types that can be described by a composite reservoir model. The inner zone represents the invaded or altered zone while the outer zone represents the uninvaded zone. The two zones are separated by a sharp radial discontinuity. This idealized interface may be a permeability, mobility, saturation or thermal discontinuity.During the 1960's there was great interest in the composite reservoir flow problem. Hurst discussed in detail the "sand in series" problem and presented formulas to describe unsteady state pressure behavior of fluid movement through two sands in series in a radial configuration. Loucks and Guerrero presented a theoretical study of the pressure distribution in an infinite composite reservoir. They found that under certain conditions the permeability in both zones as well as the size of the inner zone can be determined from pressure transient test data. Wattenbarger and Ramey presented a finite difference solution for the infinite composite reservoir. Other early investigators include Merrill et al., Clossmann and Ratliff, and Bixel and Van Poolen.Recently Satman presented an analytical study of interference in a composite reservoir which accounts for wellbore storage and skin at the active well. Brown presented a graphical approach for calculating mobility of the altered and unaltered zones and the radius of the altered zone. DaPrat et al. presented an application of a composite reservoir model to interpret falloff tests in an insitu combustion project.The major contribution of this paper is the presentation of the combined effects of skin, wellbore storage and phase segregation on pressure transient tests in composite reservoir systems. We also present the six flow regimes possible in a finite composite reservoir and show how the characteristic influence of wellbore storage and phase segregation may case a misinterpretation of pressure transient tests. The rate solution in a composite model with an inner steady state skin is also presented.P. 217^
