Pressure Drop in Horizontal Wells and Its Effect on Production Performance

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Summary: Fluid flow in horizontal pipes becomes turbulent at Reynolds pipes becomesturbulent at Reynolds numbers larger than 2,000. In practical situations, turbulent flow in practical situations, turbulent flow in horizontal wells mayoccur at rates of thousands of cubic feet per day (for a 24.4-cm [9-in.] casedwell). Wells flowing in a turbulent regime experience a flow resistance manyorders of magnitude higher than that for laminar flow. Therefore, along-holewell-pressure gradients generally cannot be neglected, and a proper descriptionof horizontal well flow needs to be included in the design of these wells (andin reservoir simulators). This is particularly imperative in situations of verylow drawdowns (to avoid gas or water cresting). This paper presents a simpleanalytical paper presents a simple analytical method that links single-phaseturbulent well flow to stabilized reservoir flow. The resulting second-orderdifferential equation is solved numerically for the appropriate boundaryconditions, Results are presented in dimensionless form for generalapplicability. A practical example is presented for a horizontal well in ahighly presented for a horizontal well in a highly permeable oil rim underlainby water. permeable oil rim underlain by water. Drawdown is limited to about100 kPa [1 bar] to produce at subcritical rates for water cresting. In theexample, it is observed that for an 11.4-cm [4-in.] well of 300 m [985 ft], little additional production results from extending the horizontal section. Introduction: Horizontal wells are of great interest throughout the petroleum industry forquite obvious reasons. From a reservoir-engineering viewpoint, (long)horizontal producers are of interest when production by means of vertical wellsis unattractive because of a low PI (e.g., in tight or pancake reservoirs). Insituations with a high risk of gas or water coning, horizontal holes may alsoprovide an attractive alternative to vertical wells, In the case of coning, thedifferent orientation of the horizontal well with respect to gravity is alsobeneficial: at the moment of gas or water breakthrough, the cone (subsequentlyreferred to as the crest) displaces a much larger volume of oil than a conenear a vertical well at breakthrough. Because of the great directional controlthat can currently be achieved in drilling, horizontal wells may also be ofgreat use in attempts to link up a well with productive parts of a reservoir(e.g.. fractured or parts of a reservoir (e.g.. fractured or fissured zones) orwith several reservoir compartments. Detailed discussions on the pros and consof horizontal wells are presented in Refs. 1 and 2. This paper analyzes in detail one aspect often ignored in discussions onhorizontal wells: the along-hole well-pressure gradient (related to the finiteconductivity of a horizontal well). I present a simple isothermal model thatincorporates turbulent well flow. Note that the effects of nonlaminar well floware most significant in high-PI wells that are operated at a low initialdrawdown (e.g., to avoid gas or water production from highly permeable oilrims). production from highly permeable oil rims). It has been argued that theflow in horizontal wells is predominantly laminar. However, a simplecalculation shows differently. Single-phase turbulent flow occurs at Reynoldsnumbers, NRe, larger than 2,000. For a fluid with a viscosity of 1 mPas [1 cp]and a density of 500 kg/m [31.2 lbm/ft ], we find that a transition fromlaminar to turbulent flow occurs at a maximum rate of 60 m /d [377 B/D] for a24.4-cm [9-in.] cased well. (Inner radius = 11 cm [4.3 in.]) - This case issomewhat hypothetical because these large inner radii are commonly forhigh-rate wells- i.e., >3200 m/d [>20,000 B/D].) This threshold ratedrops linearly for smaller diameters and higher fluid densities. Therefore, inmost practical situations, a horizontal well will exhibit nonlaminar(transition or turbulent) well flow. Consequently, the well conductivity can nolonger be considered to be infinite in all cases (particularly when the initialdrawdown is low). This paper presents equations that model this phenomenon, with boundaryconditions and underlying assumptions. The solution technique is discussed, andexample calculations for cresting are presented. Details can be found inAppendices A through D. Model Description: Assumptions. Well Flow. Flow inside the well is assumed to be single phaseand turbulent. The single-phase assumption can be regarded as a crude firstapproximation for multiphase flow, provided that complete mixing of theproduced phases occurs in the horizontal section and results in a homogeneousfluid phase with average properties. Also, it is assumed that the wholeproperties. Also, it is assumed that the whole horizontal section is open toproduction (openhole production or slotted liner). For simplicity, we do notincorporate the transition from turbulent to laminar flow at positions fartheralong hole where the positions farther along hole where the Reynolds numberbecomes subcritical. (It was demonstrated in the introduction that the laminarregion of the well contributes a small portion of the total well rate in mostcases.) Reservoir Flow. Along-hole pressure gradients in the reservoir are assumedto the negligible compared to the pressure gradients perpendicular to thehorizontal producer. Consequently, the reservoir can producer. Consequently, the reservoir can be divided into thin vertical cross sections perpendicular tothe well for which the flow perpendicular to the well for which the flow istreated independently from other cross sections. Radial flow near the tip ofthe well is ignored (i.e., large penetration is assumed), but can beincorporated if desired. The reservoir has constant properties along hole(homogeneous reservoir). JPT, November 1990 P. 1426

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