The Effects of Size, Shape, and Orientation of an Impermeable Region on Transient Pressure Testing

Abstract

Summary. A practical consideration of the effects of the shape, size, and orientation of an impermeable reservoir region on transient pressure testing is presented. The constant-rate production well is external to the impermeable region. Impermeable regions may be in the form of sealing fractures of finite length that have little volume associated with them and that are only a local restriction to fluid flow. These regions may also be shale lenses or reduced-permeability regions that, in addition to being a restriction to flow, occupy a significant reservoir volume. This paper considers a single impermeable region with various sizes, shapes, and orientations with respect to the active source well. The transient pressure response of the constant-rate well is generated by replacing the impermeable boundaries by a set of line sources and then applying the method of superposition. This method can be extended to include pressure responses of interference wells. The method is validated by matching the pressure responses of simple cases like a linear no-flow boundary and an internal circular no-flow boundary. The key issue of this paper is the detectability of large-scale impermeable reservoir regions by transient pressure analysis. The presence of an impermeable region causes the pressure response to deviate from the homogeneous line-source response. This pressure deviation is the indication that the reservoir is heterogeneous. Four major parameters affect the pressure response of the active source well in the presence of an impermeable region:the shortest distance between the well and the impermeable region,the size of the region,the shape of the region, andthe orientation of the region. This paper presents combinations of these four parameters that significantly affect the transient pressure response, as well as some criteria for deciding what impermeable regions may be uniquely detected. Introduction Many transient pressure analysis methods are aimed at attainment of such homogeneous reservoir properties as transmissivity and storativity or such wellbore properties as storage and skin. While early and intermediate-time data provide estimations of the local flow characteristics around the well, late-time data are usually used to obtain information about reservoir boundaries or large-scale het-erogeneities. Flow systems composed of two or more regions with different flow properties are known as composite reservoirs. Essentially constant-pressure subregions may occur in reservoirs as original gas caps, or they can be generated by steamflooding, in-situ combustion, immiscible gas drive, aquifer gas storage, or as secondary gas caps when the reservoir pressure declines below the bubblepoint pressure. Large-scale impermeable reservoir regions may occur as shale lenses or during the injection of low-mobility and -compressibility fluids into a reservoir whose fluids are more mobile and compressible, as occurs in some EOR methods like polymer flooding. Can large-scale reservoir heterogeneities be detected by transient pressure analysis? The key parameters in detecting the presence of impermeable subregions are the shortest distance between the observation well and the boundary, the relative size of this boundary, and its shape and orientation with respect to the active well. In some cases, the combined effects of these four parameters make it impossible to detect the presence of heterogeneous subregions, and the pressure response at the active well is similar to the line-source response. Most of the transient pressure problems posed in petroleum engineering have their counterpart in the heat transfer field. The differential equations, or system of equations, and the boundary conditions are of the same kind; therefore, the techniques used to solve problems in one field are used to solve the corresponding problems in the other. Carslaw and Jaeger presented the solution for the heat-conduction problem corresponding to the constant-flow-rate, line-source well in a homogeneous, infinite slab porous medium. van Everdingen and Hurst extended the solution for a finite wellbore radius. Their results demonstrated that at intermediate times, after the effects of wellbore storage and skin have ended, finite-size reservoirs show an "infinite-acting" flow behavior, described by Theis. By using line-source imaging, Stallman generated the response of a well producing at constant flow rate near an infinite linear boundary. He presented log-log curves for both constant-pressure and impermeable linear boundaries. The pressure responses of other semi-infinite reservoirs bounded by linear boundaries have been described in the literature. Tiab and Kumar studied the transient pressure behavior of a constant-rate well arbitrarily located between two parallel sealing faults. Tiab and Crichlow presented type curves for the case of multiple sealings faults and bounded reservoirs. Prasad considered the case of a well located near two intersecting boundaries in an otherwise infinite system. He developed an analytical solution that is valid for all angles of inter-section and well locations using the concept of fluid flow in edge. Yaxley described the effects of a partially communicating fault on transient pressure behavior. In his approach, he treated the well as a constant-rate line source and the partially communicating fault as an infinitely long vertical semipermeable barrier. van Everdingen and Hurst studied circular reservoirs with different internal and external boundary conditions. Earlougher and Ramey described interference testing in closed rectangular reservoirs. The effects of internal reservoir discontinuities have not been considered extensively in the literature. Carslaw and Jaeger derived the Green's function for a point source external to a nonconductive circular boundary in an infinite slab medium. However. this solution is not readily integrated in space and time to yield the continuous line source. Cinco-Ley et al. studied the transient flow behavior of a well near an infinite-conductivity natural fracture of finite length. Sageev and Horne considered single-well transient pressure analysis near a circular constant-pressure or impermeable subregion. Their method allows the detection of the minimum distance between the active well and the circular boundary. SPEFE P. 595^