Abstract

Horizontal well performance is typically estimated using a steady-state productivity index equation similar to Joshi's productivity index, which assumes constant wellbore pressure.The wellbore pressure in a horizontal well is not constant, and the pressure drop in the horizontal section can approach the reservoir drawdown.This paper presents a new model to estimate horizontal well productivity by incorporating wellbore hydraulics.The model is implemented in a program and calculates the well pressure throughout the length of the wellbore.The method reproduces the experimental results of two authors.

Introduction

The general definition of well performance is the analysis of the relationship between the flow rate and the pressure drawdown between the reservoir and wellbore.Historically, wellbore pressure has been defined as the pressure, either flowing or shut-in, located at the middle of the zone of interest, and constant over the entire zone, as shown in Figure 1.For a vertical well, this assumption is valid, since the perforated interval is very short compared to the length the fluid has to flow through to reach the surface.In other words, the pressure drop, due to gravity, friction, and other effects, over the interval is negligible compared to the pressure drop that occurs over the tubing length and to the drawdown between the reservoir and the wellbore.

For a horizontal well, this definition of wellbore pressure is not appropriate.The length of the horizontal section can be much greater than the thickness of the zone, and can approach the length of the vertical section of the well, as shown in Figure 2.As fluid flows in the horizontal well, several things occur including frictional losses due to flow, kinetic losses, phase changes, gravity changes, and momentum changes from influx.These all cause changes in the pressure distribution within the horizontal section over the entire length.Therefore, the pressure in the wellbore cannot be assumed to be constant over the length of the horizontal section.The methods others have used to determine wellbore pressure have been reviewed in an earlier paper.1This paper presents a new method to determine the performance, in terms of the productivity, of a horizontal well incorporating wellbore hydraulics effects.

The Productivity Index

The productivity index (J) or straight-line inflow performance curve is the simplest inflow performance equation.It is defined as the ratio of flow rate to pressure drop.

Equation 1

The productivity index is a function of fluid properties, reservoir properties, wellbore properties, and geometry of the system.The appendix presents several forms of the productivity index for a horizontal well.

Model Development

In developing this model, there are three elements to the problem that must be examined:the wellbore, the reservoir, and how to couple the two together.Figure 3 shows a sketch of the overall problem.The model consists of a horizontal wellbore of length, L, and diameter, D.It is centered within a homogeneous, anisotropic reservoir of thickness, h, vertical permeability, kv, horizontal permeability, kh, and average reservoir pressure, pR.The wellbore has the potential for influx along the entire horizontal length plus the toe of the section.

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