Comprehensive -Simulation of Horizontal-Well Performance

Abstract

Summary. The simulation of the performance of a horizontal well has generated certain new and important challenges. These include the partial penetration of the well in the horizontal direction within the allocated drainage area, the positioning of the well between the vertical boundaries, the distance from the parallel horizontal boundaries, and the permeability anisotropy. In addition, there are special problems in the simulation of the response of fractures (natural and induced) in regard to their contact with the well (longitudinal or transverse), their conductivity, and the conductivity distribution along the fracture. We developed new numerical techniques to facilitate the simulation of these diverse problems. We use a locally refined perpendicular bisection grid to describe the horizontal (or deviated) perpendicular bisection grid to describe the horizontal (or deviated) wellbore. The grid is strictly orthogonal for the anisotropic case, and wellbore blocks are almost regular octagonal prisms. The transition to the coarse Cartesian grid is also orthogonal. The fully implicit formulation ensures the stability of the numerical solution. Our results are found to be in excellent agreement with published analytical or semianalytical approximations. In addition, the results offer flexibility that is not possible with analytical solutions. The grid system used is particularly amenable to handle practical problems with real reservoir geometries and configurations. This paper presents a comprehensive numerical simulation of problems associated with horizontal wells, including the arbitrary problems associated with horizontal wells, including the arbitrary positioning of the well within a fully anisotropic medium. Hydraulic positioning of the well within a fully anisotropic medium. Hydraulic or natural fractures that intersect the well in the longitudinal or transverse direction are simulated for both infinite and finite conductivities. Introduction As the technology for drilling highly deviated and horizontal wells matured, several successful production cases that used this type of wet completion were reported. 1–9 The improved technology resulted in the need to screen appropriate reservoir candidates for their viability to these alternative wells. Various works have shown that the PI ratio between a horizontal well and a vertical well (of a given length) is higher if the horizontal/vertical permeability anisotropy and the reservoir thickness are both small. The permeability anisotropy and the reservoir thickness are both small. The latter, of course, implies that a plausible thickness for the vertical-well completion be used for comparison. In addition, the position of the well in relation to vertical and horizontal boundaries was studied, and Babu and Odeh and Mutalik et al. quantified production from horizontal wells subjected to boundary interference. Horizontal-well stimulation, both to remove near-wellbore damage (matrix stimulation) and to identify hydraulic fracturing, is an obvious new concern. Needless to say, it is inappropriate to compare the production of unstimulated horizontal wells with that of fully stimulated vertical wells. Economides et al. proposed a method for the matrix stimulation of horizontal wells, and Renard and Dupuy studied the influence of formation damage on the flow of horizontal wells. Fracturing of horizontal wells, the resulting production behavior, and the comparison of fractured vertical and horizontal wells have received considerable attention. In fracturing horizontal wells, two production scenarios are interesting: either the well is drilled in the expected fracture direction so that it will accept a longitudinal fracture or it is drilled in the orthogonal direction. In the orthogonal case, multiple fractures can be executed with proper orthogonal case, multiple fractures can be executed with proper zonal isolation. The two scenarios are mutually exclusive, with the longitudinal fracture favoring horizontal wells that can accept low-conductivity fractures and the orthogonal configuration favoring reservoirs that can accept high-conductivity fractures. These are the cases for high-and low-permeability reservoirs, respectively. While the above two configurations can be construed as ideal, if the entry point from the well into the formation is long (1.5 d), the fracture first will initiate longitudinally, regardless of the well direction in relation to the far-field stresses. The fracture will turn normal to the minimum stress. Horizontal-Well Simulation We used a numerical reservoir simulator to examine the performance of a horizontal well. Important features of the simulator include a flexible grid scheme that uses a finite-volume technique to simulate difficult geometries and features (faults, horizontal wells, and irregular boundaries) that do not follow the standard Cartesian orthgonality of other simulators. In addition, because the grid is based on perpendicular bisectors, it is particularly suited for use within windows of interest, with standard particularly suited for use within windows of interest, with standard Cartesian grids used outside these windows. Appendix A describes the salient points of the simulator and the grid system. Our first task was to compare the numerical results with wellknown analytical solutions to assess the reliability of the simulation model in general and to determine how it would apply to horizontal-well cases. An infinite-acting reservoir, saturated with a single fluid and having a fully penetrating vertical well, was simulated for constant production rate. The numerical results agreed with the line-source solution to four digits. For the specific simulation of horizontal wells, a constant-pressure outer-boundary ellipse was used with the half-axis of the ellipse, a, related to the well length, L, as given by Refs. 9. and 11. The permeability anisotropy between the horizontal and vertical planes was handled by use of multiplication factors to account for the planes was handled by use of multiplication factors to account for the transmissibility of each gridblock. Fig. 1 shows the grid system used. A constant-pressure outer boundary was modeled (with gridpoints exactly on the boundary) to represent the drainage ellipse of the horizontal well. Simulations were done until steady state was established, and constant pressure was maintained at the well. (For easier comparison with the analytical solutions, no pressure drops were calculated.) Table 1 gives the well and reservoir variables used for an example application. Fig. @ shows that, after 1 year, the pressure profile had taken the elliptic shape of the drainage pressure profile had taken the elliptic shape of the drainage area formed by the well. We also compared horizontal-well performance predictions made with this numerical simulator and Joshi's analytical expression. Table 2 presents a sample of the results for the PI ratio (between a presents a sample of the results for the PI ratio (between a horizontal and a vertical well) obtained with various values of the permeability anisotropy index, As can be seen, a deviation exists permeability anisotropy index, As can be seen, a deviation exists between the solutions for I values that do not represent a perfectly isotropic formation. Efforts to improve the accuracy of the numerical solution (e.g., adding more vertical layers and diminishing the horizontal block size) showed that the numerical solution could not converge to Joshi's formula. The considerable differences, especially in highly anisotropic cases, made it necessary to investigate the reason for these discrepancies. SPEFE P. 418