SPE Production & Operations
Volume 23, Number 2, May 2008, 232-240

Summary

Numerous studies have examined the roles of wellbore pressure drop and near-wellbore formation damage on the production performance of horizontal wells. These studies identified particular conditions for which these effects are important, but no quantitative general guidelines have been developed. In this paper, we present simple, analytical expressions that can be used to determine the relative effects of wellbore pressure drop and formation damage on horizontal well inflow. The equations developed are used to show how horizontal wells or laterals can be designed so that neither of these effects causes significant flow restrictions.

The relative importance of the pressure drop in a horizontal wellbore is shown to be a simple function of two dimensionless numbers: the Reynold’s Number for the flow in the wellbore and a new dimensionless number called the Horizontal Well Number. With this relationship, we illustrate how the wellbore diameter and length can be designed to ensure that the wellbore pressure drop is not restricting production.

In this paper, we also illustrate a technique for identifying the most critical part of the well flow system (far-field reservoir flow, near-well convergent flow, or flow through the completion) from the relative sizes of different terms in the inflow equations. This analysis method shows that the importance of formation damage and the efficiency of well stimulation depend on formation thickness, well length, and reservoir extent in the horizontal plane. Guidelines are presented to show how much damage can be tolerated while still maintaining productivity within a prescribed fraction of the undamaged productivity.

Introduction

The productivity of a horizontal well can be described by an inflow equation that relates the flow rate from the reservoir to the combined pressure drops in the reservoir, through the completion, and in the near-well vicinity. For mathematical simplicity, the near-well and completion pressure drops can be accounted for by including a skin factor in the inflow equation. The skin factor accounts for the altered flow path and the possibly altered permeability field (i.e., when the well is damaged or stimulated) as the produced fluid approaches the completion (Furui et al. 2005). Most inflow equations are based on the assumption that the wellbore flowing pressure, p_wf , is constant over the length of the horizontal well, implying that the wellbore pressure drop is negligible compared with other pressure drops in the system. If this is not the case, the predictions of well performance and of the reservoir drainage pattern may be erroneous.

To examine the effects of wellbore pressure drop in different parts of the horizontal well flow system, we can use a steady-state inflow equation and steady-state pipe flow equations to describe wellbore flow. The results are general to other reservoir flow conditions, such as pseudo-steady-state flow, because the relative sizes of the pressure drops should be similar, even though the reservoir far-field boundary condition is different.

For steady-state flow to a fully penetrating horizontal well (i.e., the well length is equal to the reservoir extent in the direction along the wellbore) in a parallelapiped-shaped reservoir, the inflow equation of Furui et al. (2003) or Butler (1994) is shown in Eq. 1:

[Equation 1]  .....(1)

If the well is not fully penetrating, the partial-penetration skin factor developed by Babu and Odeh (1989) for pseudosteady-state flow can be used to account for the convergence of flow to the wellbore, assuming the streamlines in steady-state flow are the same as the streamlines in pseudosteady-state flow. In this case, the wellbore length is replaced by the reservoir length in the direction of the wellbore, 2x_b , as illustrated in Fig. 1, and the partial-penetration skin factor, s_R , is added to the denominator:

[Equation 2]  .....(2)

where k is reservoir permeability (√k_H k_V ), x_b is one-half the reservoir extent in the direction of the well, p_e is the pressure at the drainage boundary (y = y_b ), µ and B_o are the oil viscosity and formation volume factor, h is reservoir thickness, r_w is wellbore radius, y_b is the distance from the well to the drainage boundary in the horizontal direction perpendicular to the well, I_ani is the index of anisotropy (√k_H / k_V ), s is the skin factor accounting for completion and damage or stimulation effects, and s_R is the partial-penetration skin factor. The partial-penetration skin factor can be calculated with the method of Babu and Odeh (1989, 1988). The constant 141.2 in these equations reconciles the inconsistent oilfield units; in consistent units, 2π appears in the numerator instead of 141.2 in the denominator.

Several investigators (Asheim et al., 1992; Su and Gudmundsson, 1994; Yuan et al. 1996; Ouyang et al., 1998, Yuan et al. 1998; Yalniz and Ozkan 1998) developed methods to calculate the pressure drop in a horizontal wellbore. The fact that inflow to the wellbore is occurring all along the well adds two complications to a standard pipe flow analysis. First, the continuous addition of more flow along the well means that the flow rate is constantly changing, resulting in a continuously changing frictional pressure drop along the well. Second, the fact that flow is entering the wellbore perpendicular to the axial flow in the pipe may alter the frictional drag behavior along the pipe wall, requiring an alteration of the standard friction factor used for pipe flow, and adds a kinetic energy contribution to the pressure drop. In this paper, we adopt a simple procedure to estimate wellbore pressure drop that is accurate enough to show the comparative effect of wellbore pressure drop relative to other parts of the system.

To show the relative contributions of each part of the system to the overall pressure drop, it is convenient to re-arrange Eq. 2 to

[Equation 3]  .....(3)

Bringing the constant –1.224 into the logarithmic term yields

[Equation 4]  .....(4)

Eq. 4 shows that the overall pressure drop between the reservoir boundary and inside the wellbore is related to four factors corresponding to the four terms in the parentheses on the right side of the equation. These factors are the radial (or elliptical in an anisotropic permeability field) flow occurring in the reservoir relatively close to the horizontal well, the linear flow occurring from the reservoir boundary to the radial flow region, the near-well and completion effects accounted for by the skin factor, and the partial penetration effect. We explore the relative magnitudes of each of these factors, as well as the effect of wellbore pressure drop.

© 2008. Society of Petroleum Engineers

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History

• Original manuscript received: 25 February 2006
• Meeting paper published: 12 June 2006
• Revised manuscript received: 24 May 2007
• Manuscript approved: 9 October 2007
• Version of record: 20 May 2008