Abstract

The objective of this paper is to review the current methods of determining how the effects of wellbore hydraulics are incorporated into the evaluation of the productivity of a horizontal well.Wellbore hydraulics includes the effects of friction, acceleration, gravity, and fluid influx.Knowledge of the pressure distribution within the horizontal wellbore is important to more accurately determine the performance of the horizontal well and aides in the design of the well profile, completion, and stimulation.

Introduction

Horizontal wells increase the efficiency of hydrocarbon recovery by enhancing the contact between the reservoir and the wellbore, which results in lower fluid velocities around the wellbore without sacrificing economical flow rates.Over the past two decades, interest in horizontal wells has increased significantly due primarily to improvements in the drilling and completion technologies necessary to successfully develop a horizontal well.However, the development of reservoir engineering concepts for the horizontal well has only recently begun to keep pace with the drilling and completion sides.Research into reservoir engineering aspects of horizontal wells has generally been in the development of site specific simulations, primarily due to the complexity of the problem of flow to, around, and through the horizontal well. This paper will review several papers that model fluid flow in the horizontal wellbore and present the reasons behind the necessity of incorporating a wellbore pressure model into any horizontal well performance equation.

Horizontal Inflow Performance Equations

In general, well performance is the analysis of the pressure-rate relationship.This relationship can be steady-state, pseudo-steady state, depletion, or pressure transient, and for either single phase or multiphase fluids.For this paper, the most common well performance equation, the productivity index, for single phase liquid (i.e. pwf > pb), steady and pseudo-steady state relationships will be summarized.

Several authors[1–7] have developed equations to determine the productivity of a horizontal well.They all have the same basic format.Each equation consists of breaking the three dimensional horizontal well problem into two coupled two-dimensional problems, a vertical portion and a horizontal portion. Table 1 presents the various equations.

Basically, the primary difference in the productivity equations presented in Table 1 is the geometry of the drainage area for the horizontal well.The drainage areas are radial, elliptical, rectangular, or a combination of different geometries.Except for Babu and Odeh, the primary similarity of the equations is the assumption of infinite conductivity of the horizontal wellbore, i.e. constant wellbore pressure.Babu and Odeh[4, 5] assume uniform flux in the development of their productivity equation, which allow the wellbore pressure to vary from toe to heel.However, they eliminate that consideration by assuming the pressure at the midpoint of the wellbore (L/2) provides the best representation of the well's performance.

Fluid Mechanics

In order to have flow, whether in a reservoir, a pipe, or a wellbore, there must be a driving force.[3]For reservoir fluid flow, that force is the pressure differential, or drawdown between the reservoir and the wellbore.In the development of reservoir fluid flow models, the wellbore is assumed to be either under a uniform flux (constant flow rate, varying pressure) or infinite conductivity (constant pressure, varying flow rate) condition.The generally accepted definition of wellbore flowing pressure, pwf, is the pressure at the midpoint of the zone open to flow and is essentially constant over the entire zone.

For a vertical well, the assumption of constant wellbore pressure is valid because the pressure drop between the bottom of the reservoir and the top of the reservoir is small compared to the pressure drop between the reservoir boundary and the wellbore, as shown in Figures 1 and 2.As such, the wellbore flowing pressure can be measured at the center of the formation and assumed constant in the inflow performance equations.The effects of friction, acceleration, and gravity on the wellbore pressure are taken into account in the tubing intake curves.These effects, along with the effects of influx, are considered negligible within the area and length open to flow for the vertical well.This is because the length open to flow (h) is generally much smaller than the length of the tubing (D).

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