New Productivity Formulae of Horizontal Wells
Authors: Lu J. 
Published: March 2010

Abstract
This paper presents new productivity formulae for horizontal wells. These new formulae are based on the average potential and the point convergence pressure. These formulae are derived from a three-dimensional solution of the Laplace equation, as opposed to the two-dimensional solutions used in previous formulae. Formulae are also given for the productivity of horizontal wells in reservoirs with either a gas cap or bottom water.
This paper applies the newly derived formulae to the Liu-Hua Reservoir in the South China Sea. Results are compared to other formulae for horizontal well productivity presented in the literature by various authors. Significant differences between the new formulae and existing formulae are demonstrated. The newly derived formulae can account for the advantages of horizontal wells, and they are more accurate than other formulae.

Introduction
A worldwide interest exists today in drilling horizontal wells to increase productivity. Because of its large flow area, a horizontal well may be several times more productive than a vertical one draining the same volume. Recent interest in horizontal wells has been accelerating because of improved drilling and completion technology. This has led to increased efficiency and economics in oil recovery. However, it is more expensive to drill a horizontal well than a vertical one. Therefore, to determine the economical feasibility of drilling a horizontal well, the engineers need reliable methods to estimate its expected productivity.
The advantages of horizontal wells can be classified under the following topics:increased productivity or injectivity;improved sweep efficiency;reduced coning or viscous fingering; andincreased drainage area. The reduction in gas or water coning may actually be considered an improvement in vertical sweep efficiency, or a result of increased productivity.
Productivity of a horizontal well can be greater than that of vertical wells for several reasons. First, horizontal wells can be open to a much greater portion of the reservoir than vertical wells. Horizontal wells can be drilled perpendicular to oriented natural fractures, and, therefore, intersect with more fractures. Also it may be possible to induce multiple hydraulic fractures in a horizontal well. The main benefit of improved productivity, obviously, is a higher oil production rate, which must be sufficient to justify the cost of drilling a horizontal well. If the main purpose for a horizontal well is to increase the oil production rate, and the well flow rate will not be limited by tubing or surface facilities, then a productivity formula can be used to estimate the well length needed to obtain the desired oil rate. Another benefit of increased productivity is reducing the drawdown for the same withdrawal rates, possibly resulting in reduced water and/or gas production. If surface facilities are limited by the gas or water handling capacity, this may mean that the overall field oil production rate can be increased. In condensate systems, increased productivity can result in reduced liquid dropout near the well.