A comprehensive application of a composite reservoir model to pressure transient analysis
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Copyright 1987, Society of Petroleum Engineers. This paper presents analytical solutions for interpreting pressure transient tests for wells producing from a finite composite reservoir system. We also present rate solutions and methods for analyzing long term production data and forecasting production of oil or gas in a finite composite reservoir. Composite reservoirs are reservoirs made up of two concentric zones of different hydraulic diffusivities. This type of reservoir consists of an inner and outer zone of uniform reservoir and fluid properties separated by a discontinuity. Composite systems include reservoirs with a fluid bank, reservoirs with a burning front, reservoirs with reduced permeability around the wellbore due to drilling fluid invasion and reservoirs with increased permeability around the wellbore due to acidizing or, as a good approximation, even fracturing. This paper demonstrates that a composite reservoir model can be used to analyze wells with a high negative skin or wells intercepting a finite or an infinite conductivity hydraulic fracture. The differential equations for continuity of mass flow in the two regions are solved using Laplace transformation techniques for both the constant rate and constant pressure inner boundary conditions. The pressure solution is presented for a well in a finite or infinite-acting reservoir with wellbore storage effects. Both finite and infinite-acting reservoir solutions are presented for the constant pressure case. The paper demonstrates the behavior of pressure at the well located in the inner zone of the composite system with different permeability ratios of the inner and outer zone and different radii of the inner zone. Pressure and rate solutions are presented for different values of effective fracture permeability and effective fracture lengths. These type curves are equivalent to finite conductivity fracture type curves with wellbore storage effects included. The pressure and rate solutions for reservoirs with a fluid bank are also presented. Dimensionless pressure and pressure derivative curves are presented with suitable parameters for type curve analysis. A step-by-step procedure for analyzing pressure transient data is presented. Permeability of the inner zone or the effective fracture permeability can be estimated. The radius of the inner zone which corresponds to an effective fracture length associated with the estimated effective fracture permeability, the radial distance of acid stimulation or the average radial distance of a waterflood front can be estimated. Forecases of production increase associated with varying effective fracture permeability and length can be made. This paper presents three field examples to demonstrate the application of the type curve analysis method to buildup and falloff test data.
