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Elizabeth G. Anklam

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 16–19, 2005

Paper Number: SPE-94314-MS

Abstract

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).

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 16–19, 2005

Paper Number: SPE-94316-MS

Abstract

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.