Analytical And Statistical Analyses of Pseudo Skin Factors For Horizontal Wells
Authors: Malekzadeh D. , Abdelgawad A. 
Published: March 2010

Abstract
The pressure behaviour of horizontal wells in bounded anisotropic reservoirs has been investigated in this paper. New equations for calculating the effective length of the horizontal well, mechanical skin factor, shape factor, and productivity index of horizontal wells are presented.
It is determined that the performance of a horizontal well of half-length Xf1 with mechanical skin can be replaced by the performance of an equivalent horizontal well of half-length Xf2 with no mechanical skin. The statistical analysis showed that pseudo skin factor for a horizontal well in a given drainage area can be directly correlated with formation thickness, and natural logarithms of horizontal well half-length and permeability anisotropy. These statistical correlations can easily be used to predict skin damage around horizontal wellbores, to evaluate stimulation treatment of horizontal wells, and to compare their performance with unstimulated vertical wells without the need to use complex numerical and/or analytical solutions which require extensive computer use.

Introduction
The growing interest in field development using horizontal well drilling necessitates development of new concepts for improved performance prediction of these wells. To predict the productivity index of horizontal wells requires the determination of the pressure drop due to formation damage around such wells. Long duration of formation exposure to drilling fluids may be the main reason for the unexpected failure of some horizontal wells(1, 2) drilled in favourable reservoirs.
The combined effect of the formation damage and the presence of impermeable barriers and low permeability regions in the vicinity of some sections of the horizontal wellbore will manifest itself as mechanical skin damage in well test analysis if the total drilled (or perforated) length of the horizontal section is used in the calculations. The total skin factor obtained from a well test is the summation of the mechanical skin factor and pseudo skin factor. The purpose of this paper is to present new analytical equations for calculating pseudo skin factor and mechanical skin factor for horizontal wells during the unsteady state and pseudo steady state flow periods. The ne\v equations can be used to determine:the fraction of horizontal well length contributing to unrestricted production, andhorizontal well productivity index based on the equivalent non-damaged length of the horizontal wellbore.
Furthermore, statistical correlations for pseudo skin factor, mechanical skin factor, and the fraction of horizontal well length contributing to unrestricted production are presented that can be used to evaluate the performance of horizontal wells without the need to use complex numerical and/or analytical solutions.

Determination of Horizontal Well Productivity Index
Malekzadeh and Abdelgawad(3) presented the dimensionless wellbore pressure, pseudo skin factor, and effective horizontal well length for horizontal wells in bounded anisotropic reservoirs, shown in Figure 1, as:
Equation 1 (available in full paper)
where the dimensionless parameters are defined as:
Equation 2–12 (available in full paper)
The late time approximation to the full solution, Equation (1) was derived as(3):
Equation 13 (available in full paper)