Effects of Pressure Drop in Horizontal Wells and Optimum Well Length
- V.R. Penmatcha (Stanford U.) | Sepehr Arbabi (Stanford U.) | Khalid Aziz (Stanford U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 1999
- Document Type
- Journal Paper
- 215 - 223
- 1999. Society of Petroleum Engineers
- 1.6.6 Directional Drilling, 1.6 Drilling Operations, 5.3.2 Multiphase Flow, 4.6 Natural Gas, 2.2.2 Perforating, 2 Well Completion, 5.2.1 Phase Behavior and PVT Measurements, 1.8 Formation Damage, 5.5 Reservoir Simulation, 7.5.3 Professional Registration/Cetification, 6.5.2 Water use, produced water discharge and disposal
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As the length of a horizontal well is increased, its contact with the reservoir increases. But at the same time, the resistance to flow in the well also increases, which has a direct negative effect on the productivity of the well. The overall performance of a horizontal well depends on the balance of these two opposing factors. A semi-analytical well model is developed for homogeneous reservoirs which can quantify the effects of both single-phase oil and two-phase oil/gas flow pressure loss in the well on the overall well performance. The model is quite flexible and can incorporate any friction factor correlation. A methodology is developed to show the effects of various reservoir, fluid, and well parameters on well productivity. We demonstrate that ignoring frictional effects could lead to unrealistically higher production estimates and longer breakthrough times for water or gas. As a result of pressure drops in the well, breakthroughs occur first at the heel of the well. A methodology is also developed to calculate the optimum horizontal well length.
Most of the analytical work published in the past1-16 on horizontal well productivity either assumed that the well is infinitely conductive or the flow is uniform along the entire well length. References 1-6 are based on the assumption of steady-state flow in the reservoir, Refs. 7 and 8 are for pseudo-steady-state flow conditions and Refs. 9-16 are for transient flow. The assumption of uniform flow was made purely for mathematical convenience. The infinite conductivity assumption is a good assumption only in certain cases when the pressure drop in the wellbore is very small compared to the drawdown in the reservoir, otherwise, the pressure drop in the wellbore should also be taken into account.
Previous work can be categorized into three types.
- Models for wells that are infinitely conductive and thus are not influenced by pressure drop in the well. Several analytical models with such an assumption are available in the literature.5,6,11-15
- Models where the reservoir is represented by an analytical model for single-phase flow. Works of Dikken,17 Novy, 18 Ozkan et al.,19 Landman,20 and Penmatcha and Aziz 21 fall into this category.
- General models that couple multiphase flow simulators with wells include works of Stone and Kristoff,22 Islam and Chakma, 23 Folefac et al.,24 and Brekke et al.25
None of the works available in the literature provides a comprehensive analytical explanation of why and by how much various reservoir, fluid, and well variables affect the frictional pressure drop in the wellbore and thereby the well productivity. In this work, we present a methodology that can be used to assess the affect of various parameters on well productivity. Results are presented for the effects of well length, well flow rate, wellbore roughness, reservoir drawdown, fluid viscosity, and reservoir permeability on well productivity. Our work provides guidelines on determining when friction might be important.
With pressure drop in the well, net revenues from a well do not continue to increase as the well length is increased. At some point the additional drilling and maintenance costs do not offset additional revenues. So far, the literature does not provide a method of calculating the optimum length of horizontal wells. We present a method to calculate the optimum length of horizontal wells. The results can be expressed explicitly for the case of steady-state, single-phase flow from a homogeneous reservoir.
Effect of Friction on Productivity
Many horizontal well models available in the literature allow us to quickly calculate the productivity index (JS) of a well. The only deficiency in these models is that they cannot tell us how the well productivity will be affected because of wellbore frictional effects. In this article, we develop a procedure which explicitly couples (using the productivity index concept to describe flow in the reservoir) available horizontal well models with wellbore frictional effects. Explicit coupling helps us in generating simpler models that may be useful for many routine applications. In Appendix A, by comparing the results from this model [one-dimensional (1D), explicit coupling] with the rigorous model of Penmatcha and Aziz21 [three-dimensional (3D), implicit coupling], we show that explicit coupling does a reasonable job and is useful for quick calculations.
Fig. 1 shows a horizontal well in a reservoir. Let pe be the pressure at the outer boundary of the reservoir and pw (x) be the varying pressure along the wellbore due to frictional pressure drop. The well inflow equation is given as
where qs(x) is the flow into the well per unit length of the wellbore and Js(x) is the productivity index per unit length of the wellbore. Js(x) can vary along the wellbore due to variation in perforation density, formation permeability, or flow end effects.
For simplicity, we assume that the reservoir is homogeneous and there is a steady-state, single-phase oil flow in the system. The steady-state flow assumption can, for example, be used in a reservoir where the oil production rate is equal to the water injection rate. Since the fluid is single-phase liquid, we assume that the density variations of the fluid along the wellbore is negligibly small. We also assume that the penetration ratio of the well in the drainage area is high enough so that we can neglect the end effects. This allows us to assume that Js(x) is constant along the wellbore.
While some models, like that of Babu and Odeh,9 allow the calculation of Js(x) at any point along a horizontal well, many other models5,6 used in the industry give only one constant Js for a well.
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