Formation Damage Effects on Horizontal-Well Flow Efficiency (includes associated papers 23526 and 23833 and 23839 )
Authors: Renard Gerard , Dupuy J.M. 
Published: December 2007

Summary
Wellbore damage commonly is accounted for by an apparent skin factor. A better relative index for determining the efficiency with which a well has been drilled and completed is the "flow efficiency," the ratio of a well's actual PI to ideal PI. The flow effieicny of horizontal wells is derived assuming steady-state flow of an incompressible fluid in a homogeneous, anisotropic medium. A comparison between the flow efficiencies of vertical and horizontal wells indicates that permeability reduction around the wellbore is less detrimental to horizontal wells. This paper shows that the effect of damage around a horizontal wellbore is reduced slightly by increasing the well length. Conversely, if the vertical permeability is less than the horizontal permeability, the anisotropy ratio, kH/kV, magnifies the influence of formation damage near the horizontal wellbore. Examples of flow efficiency calculations assuming a formation damage or a formation collapse around a liner in poorly consolidated formations are provided for horizontal and vertical wells.

Introduction
Many technical aspects of horizontal wells have been compared with more-conventional wells (vertical or deviated) to determine their effectiveness as a new alterative to reach and produce oil and gas reservoirs. The most obvious comparison, well-documented in the literature,1,2 is the productivity performance of horizontal wells vs. unstimulated or fully stimulated(acidized/fractured) vertical wells. Two of the newest application areas to compare horizontal and vertical wells and to adapt methods applied to conventional wells to horizontal wells are hydraulic fracturing and matrix acidizing.
Recent papers have expressed different viewpoints on the role of formation damage in the performance of horizontal wells. Some3,4 suggest that, as horizontal-well length, L, increases, the influence of formation damage on total pressure drop can become negligible, resulting in an additional advantage over vertical wells. Others5 indicate that the damaged zone may affect productivity more in horizontal wells than in vertical wells, and that skin damage sometimes can prevent horizontal-well projects from succeeding. These two opposing interpretations of the influence of formation damage on horizontal-well productivity come from a lack of well-defined criteria (reservoir and well characteristics) to quantify the effect of formation damage on the flow efficiency of horizontal wells.
The objective of this paper is to provide a basis for comparing the flow efficiencies of vertical and horizontal wells. Analytical expressions are derived assuming steady-state flow of an incompressible fluid in a homogeneous anisotropic medium. Both the top and bottom horizontal boundaries of the reservoir have no-flow conditions. The comparison considers an altered zone of the same radius and reduced permeability around the vertical and horizontal wellbores.

Flow Efficiency of Vertical Wells
van Everdingen6 and Hurst7 quantified the pressure drop caused by a permeability reduction near and at the wellbore in terms of the skin factor, sV: Equation 1
Hawkins8 showed that this skin factor could be related to the altered zone of permeability ks, which extends to the distance rs into the formation, by Equation 2
and that the flow efficiency, EV, the ratio of actual well PI to ideal PI (the PI if the permeability were unaltered all the way to the well's sandface), could be expressed in terms of ?ps and the total drawdown, ?pw, as Equations 3 and 4

Flow Efficiency of Horizontal Wells
Merkulov9 originally reported the expression for the ideal PI of a horizontal well in an isotropic reservoir. Giger1 and Joshi2 presented the pressure profile created by 3D steady-state flow to a horizontal well located inside an ellipsoidal drainage area (Fig. 1a). Their solution, which is suitable for horizontal wells that have small lengths compared with the drainage radius, was extended by Giger1 to the case of a rectangular drainage area fed laterally (Fig. 1b) to account for wells that have large lengths compared with the distance to the feeding boundary. As indicated in Appendix A, the ideal PI of a horizontal well for both geometries in a reservoir of permeability anisotropy ratio ß can be written as Equation 5
with rw=[(1+ß)/2ß]rw and X depending on the shape and dimensions of the area drained by the well.