Determination of the Drainage Area of Horizontal Wells in the Presence of Vertical Wells: Effect of Reservoir and Well Parameters
Authors: Abdelgawad A. , Malekzadeh D. 
Published: March 2010

Abstract
The accurate calculation of horizontal and vertical wells' productivity indices is not possible if their respective drainage areas are not estimated accurately. The determination of their respective drainage areas is of great importance in field development when utilizing both horizontal and vertical wells, or when planning to convert some of the vertical wells into horizontal drainholes. This paper suggests the use of a mathematical model describing the interference testing of an active horizontal well in the presence of another active vertical well located in a bounded, homogeneous, and anisotropic oil reservoir in order to estimate the drainage areas of both wells for various combinations of well and reservoir properties. This is the first time this new concept has been introduced to the reservoir engineering discipline. In order to accurately compare horizontal well and vertical well performances, one needs to establish some criteria taking into account the wells' operating conditions. This study has introduced two criteria for the comparative study. These criteria are based on production rate and bottomhole flowing pressure for these wells. This is also the first time in the reservoir engineering discipline that such criteria are used to determine drainage area ratio, production rate ratio, and productivity index ratio ofthese two different types of wells utilizing an analytical model. The values of drainage area ratio, production rate ratio, and productivity index ratio obtained from this new method can be used to determine well spacing and optimum horizontal well length when these two types of wells are to be drilled in the same reservoir.
The highest Ahw/Avw and qh /qv ratios correspond to long horizontal wells drilled in thin and isotropic reservoirs developed in a manner that yields a high value of drainage area length compared to drainage area width (i.e., high value of Xe/Ye ratio). It was observed that the advantage of horizontal wells over vertical wells increases when well spacing in a reservoir developed by both horizontal and vertical wells is chosen to be small, such as the one chosen in depleted reservoirs and reservoirs undergoing enhanced oil recovery operations. The results presented in this paper show that the new concept yields drastically different results than the one assumed by Joshi. It is important to note that Joshi's results are based solely on his assumptions regarding the geometry, while the concept introduced in this paper is based on the fundamentals of fluid flow through porous media.

Introduction
Due to the significant breakthroughs in drilling technology in the early 1980s, horizontal well drilling became an attractive alternative. Horizontal wells have higher productivity than vertical wells in certain reservoirs such as naturally fractured reservoirs, thin reservoirs, low permeability reservoirs, and compartmentalized reservoirs. Efficient implementation of horizontal well technology requires further understanding of the fluid flow behaviour of these wells.
The accurate determination of drainage area of horizontal wells in comparison to that of vertical wells for a given set of reservoir parameters is of great importance in field development when utilizing both horizontal and vertical wells.