In this paper, we present a new analytical model for formation damage skin factor and the resulting reservoir inflow, including the effect of reservoir anisotropy and damage heterogeneity. The shape of the damaged region perpendicular to the well is based on the pressure equation for an anisotropic medium and, thus, is circular near the well and elliptical far from the well. The new model can be used for various distributions of damage along the well, depending on the time of exposure during drilling and completion. The inflow equation for a damaged, parallel-piped-shape reservoir illustrates the importance of the ratio of the reservoir thickness to the drainage length perpendicular to the well on the influence of formation damage for horizontal well productivity. Our model gives a simple, analytical expression for determining this effect.
Horizontal well completion technology has become an important part of oil and gas recovery. Horizontal wells have proven to be excellent producers for thin reservoirs or for thicker reservoirs with good vertical permeability. A horizontal well creates a drainage pattern that is quite different from that for a vertical well. The flow geometry in a horizontal well is more likely to be radial near the well and linear far from the well while, in general, the vertical well has radial flow geometry. Another major difference between horizontal and vertical wells is the strong influence of horizontal to vertical permeability anisotropy on horizontal well productivity. Because of these factors, near-wellbore formation damage has a different effect on a horizontal well than on a vertical one and must be described with a different skin-factor model.
Another critical difference between vertical and horizontal wells is that the damage distribution around a horizontal well is likely to be highly nonuniform. Reservoir anisotropy may lead to an elliptically shaped damage zone perpendicular to the well, depending on the ratio of the vertical to horizontal permeability. Because of the large formation length contacted by a horizontal well, formation damage is not likely to be uniformly distributed. Therefore, the damage zone around a horizontal wellbore cannot be assumed to be simply a cylindrical region of reduced permeability, as is the usual assumption for vertical wells.
The objective of this paper is to provide a basis for estimating the overall damage-skin effect for horizontal wells and for determining the horizontal well productivity, including the productivity loss caused by formation damage near the wellbore in an anisotropic reservoir. Our model accounts for the effects of permeability anisotropy and can be used for various damage distributions along the well.
There are two key parts to our new model of the formation damage skin factor. The first is a model of the local skin factor, s(x), describing the effect of damage in the y-z plane perpendicular to the wellbore (Fig. 1). The second element of the new model is the manner of accounting for any arbitrary distribution of damage along the horizontal well, as illustrated in Fig. 2.
To derive an analytical model of the local skin factor at Position x along a horizontal well, we must make some assumptions about the distribution of damage in the y-z plane. We assume that the cross section of damage perpendicular to the well (Fig. 1) mimics the isobars given by Peaceman's solution1 for flow through an anisotropic permeability field to a cylindrical wellbore. This solution shows that isobars are a series of concentric ellipses with aspect ratios (ratio of the major to minor axis lengths) being 1 at the wellbore and increasing as the distance from the wellbore increases. Because formation damage is often directly related to flux or velocity, we assume that the damage is distributed similar to the pressure field (i.e., the outer boundary of the damaged zone will lie on an isobar).
With this assumption about the distribution of the damage in the y-z plane, Hawkins' formula2 can be transformed for anisotropic space, and an analytical expression for local skin can be derived, as shown in Appendix A.