Estimation of Formation Damage in Horizontal Wells
Authors: Ozkan E. , Raghavan R. 
Published: December 2007

Abstract
This paper discusses the performance of horizontal wells under the combined influences of wellbore friction and wellbore damage. The role of nonuniform damage on well performance is also discussed. The conventional perspective, that wellbore damage may be viewed as an additional pressure drop, is correct only in infinite-conductivity wellbores with uniform damage. It is shown that wellbore damage may not be viewed merely as an additive pressure drop in the presence of friction. Wellbore hydraulics changes the flux distribution (inflow profile) along the wellbore, and, thus, results in additional pressure drops in the reservoir and across the skin zone. In this regard, the results presented here are new, represent an important departure and have ramifications well beyond the problem examined here. In particular, this study suggests that the role of the skin effect on wells intercepting finite-conductivity fractures need to be examined from the viewpoint discussed in this paper.

Introduction
This paper addresses issues concerning well productivity under the combined influences of mechanical damage and wellbore hydraulics. Particular attention is paid to the proper formulation of the wellbore model and it is shown that conventional perspectives of the skin concept do not apply if wellbore hydraulics plays an important role on productivity. The issues addressed here are examined correctly for the first time. In the first part of this paper, we show that the inflow profile along the well length (flux distribution) is affected by wellbore hydraulics. This, in turn, affects both the well deliverability and the evaluation of wellbore damage. The second part of this paper concerns itself with nonuniform damage along the well length. Considering that this situation is typical in many horizontal wells, the results presented here have a bearing on well performance and stimulation. The mathematical model used in this work is described in Ref. 1.

Basic Concepts
Here, we briefly note the principal issues that are examined in this paper. A well of length L and radius rw is assumed to run along the x-axis at an elevation zw with respect to the bottom of the formation. The skin region of radius, rs, that may be a function of x, is assumed to be concentric with the horizontal well. Let kr denote the effective permeability in the y-z plane of the reservoir and ks the permeability of the skin zone. Because the radius of the skin zone is small (infinitesimally thin skin), we assume that flow within the skin zone takes place normal to the well axis; that is, in the r direction. Under the standard assumption that the storage capacity of the skin zone is negligibly small, we assume that the fluxes as entering and leaving the skin zone are identical; that is, qh (rs,t) = qh (rw,t). Mindful of the fact that the flux is a function of the properties of the damaged zone, we use the symbol qh when there is no skin and qhs when there is skin.
We model the skin effect by defining a flux-dependent skin as follows:
(1)
Here, pf is the pressure upstream of the skin region and ps is the pressure downstream of the skin region. The coefficient of the gradient term of the denominator, (krL)/(kh), normalizes the skin factor for horizontal wells so that we may readily compare skin factors for horizontal and vertical wells. P. 901^