A Rigorous Formation Damage Skin Factor and Reservoir Inflow Model for a Horizontal Well

Abstract

Summary 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. Introduction 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. Formation-Damage-Skin Model for a Horizontal 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. Local Skin-Factor Model, s(x). 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.

A New Method To Predict Performance of Horizontal and Multilateral Wells

“…In this work, the Furui et al (2003) inflow model with some modifications has been used in order to calculate the specific productivity index. Typically, J s (x) varies along the wellbore because of variations in formation permeability, nearwellbore formation-damage distribution, perforation density, or reservoir-flow characteristics (e.g., spherical vs. radial flow).…”

“…The production rate calculated by this model is also compared with production rates given by the models of Economides et al (1991), Furui et al (2003), and Guo et al (2007). The first two models are based on the infinite-conductivity-drainhole assumption, while Guo et al (2007) considered pressure drop along the wellbore in their model.…”

“…These models (Borisov 1964;Giger et al 1984;Joshi 1988;Babu and Odeh 1989;Butler 1994;Helmy and Wattenbarger 1998;Furui et al 2003) are widely adopted because they are easy to use. Simple analytical solutions derived on the basis of the assumption of infinite drainhole conductivity.…”

Modeling Well Performance for Fractured Horizontal Gas Wells

“…The analytical models are developed under assumptions about boundary conditions. Steady-state models assumed a constant pressure at the drainage boundary (Butler, 1994;Furui et al, 2003), pseudosteady-state models assumed no flow crossing the boundary with either constant pressure gradient or constant flow rate 1989), and transient flow models uses an infinite acting drainage domain (Goode and Thambynayagam, 1987;Ozkan, 1988 and1989;Frick and Economides, 1994). For low permeability formation, transient flow period for a horizontal well may be significantly longer than for conventional formations.…”

Flow Control Devices in SAGD Completion Design: Enhanced Heavy Oil/Bitumen Recovery Through Improved Thermal Efficiencies

“…horizontal and/or vertical permeability distribution (Al-Khelaiwi et al 2010;Baker et al 2008;Nasr et al 2000;Yang and Butler 1992), variations in porosity (Llaguno et al 2002), water saturation heterogeneity/characteristics (Baker et al 2008), variations in the distance between the wellbore(s) and fluid contacts (Al-Khelaiwi et al 2010;Baker et al 2008;Edmunds and Chhina 2001), variations in localized reservoir pressure (Al-Khelaiwi et al 2010;Tabatabaei and Ghalambor 2011), changes in capillary pressure and relative permeability along the wellbore (Wang and Leung 2015), localized skin damage or fractures (Furui et al 2003;Tam et al 2013), changes in mineralogy or wettability (Ipek et al 2008;Le Ravalec et al 2009;Pooladi-Darvish and Mattar 2002), changes in temperature (Bois and Mainguy 2011;Irani and Cokar 2016), changes in fluid density, viscosity, or both Larter et al 2008), or the presence or absence of insitu emulsifiers that blend reservoir and/or introduced fluids into something novel (Ezeuko et al 2013).…”