Chapter 5Production from Horizontal WellsPETE 662Production EngineeringVertical Well Flow PatternpepwfreTop ViewCross-Sectional ViewRadial drainage patternHorizontal Well Flow PatternsHeelToeCombination of radial, linear, and elliptical drainage patternsHorizontal WellsAdvantages Over Vertical Wells: Larger and more efficient drainage pattern leading to increased overall hydrocarbon recovery efficiency Increased production rate due to greater wellbore length exposed to the pay zone Reduced water and gas coning resulting from reduced drawdown in the reservoir for a given production rate Reduced pressure drop around the wellbore Lower fluid velocities around the wellbore A general reduction in sand production from reduced pressure drop around the wellbore and the resulting low fluid velocities around the wellboreHorizontal WellsImportant Factors Affecting Well Productivity: Vertical permeability – low vertical permeability or discontinuities detrimental to productivity Permeability anisotropy in horizontal plane – higher well productivity from horizontal wells drilled normal to the large horizontal permeability direction Direction of maximum horizontal stress – direction of maximum horizontal permeability the same as that of maximum horizontal stressHorizontal WellsSteady-State Inflow Performance Joshi Modely-z planex-y planexzyqvqhHorizontal WellsSteady-State Inflow Performance Joshi ModelIntegrating flow long the x-y plane over the thickness h yields, )15(2/2/ln222LLaaBpkqohAssumptions made in deriving Eq. 5-1:- elliptical drainage area with length of major axis = 2a- constant pressure at the drainage boundaryHorizontal WellsSteady-State Inflow Performance Joshi ModelIntegrating flow long the y-z plane over the well length L yields, )25(2ln2wovrhBpkqAssumptions made in deriving Eq. 5-2:- Radial flow from the vertical boundary located 2/h from the well- Pressure at the boundary = pressure at the elliptical horizontal boundaryHorizontal WellsSteady-State Inflow Performance Joshi Modelvqp /hqp /qp /=+From Eq. 5-1 and Eq. 5-2, for an isotropic formation, we obtain )35(2ln2/2/ln222woHrhLhLLaaBphkqHorizontal WellsSteady-State Inflow Performance For an anisotropic formation, Eq. 5-3 becomes (Economides, et al.) )45(1ln2/2/ln2.14122aniwanianiowfeHIrhILhILLaaBpphkqwhere)55( VHanikkINote: Eq. 5-4 was derived assuming the horizontal well is centered in the drainage volumeHorizontal WellsSteady-State Inflow Performance Rearranging Eq. 5-4, we obtain the following IPR equation based on Joshi’s Model )75(1ln2/2/ln2.14122aniwanianiHoewfIrhILhILLaahkqBppTo account for that the ends of the horizontal well are the foci of the ellipse in the horizontal plane, by equating the areas of the ellipse to that of a cylinder of radius, re, Joshi developed the following equation to relate ɑ with re.)65(2/25.05.025.05.04LrLaeHExample 5-1 Well Performance with Joshi ModelA 2000-ft horizontal lateral is producing from a 100-ft thick reservoir where kH= 10 md, kV= 1 md. The lateral has an rw= 3 in draining from a region 4000 ft in the direction of the well where pe= 4000 psi, µo= 5 cp, Bo= 1.1. Determine q when pwf= 2000 psi.Solution: )75(1ln2/2/ln2.14122aniwanianiHoewfIrhILhILLaahkqBpp)55(3.162 110VHanikkIft 200024000aSubstituting in Eq. 5-7 and consolidate yields,)95(74.14000 qpwfFrom Eq.5-9, q = 1149 STB/d when pwf= 2000 psi.)95(74.14000 qpwfExample 5-1 Well Performance with Joshi ModelSolution (cont’d):Horizontal WellsSteady-State Inflow Performance Furui et al. Model In the cross-sectional area perpendicular to the wellbore, Furui Model assumes radial flow in the near wellbore region and linear flow beyond thatlprpSteady-State Inflow Performance Furui et al. ModelHorizontal Wells)105( lrppp )115(12ln2anianiwtrIIrrkLqp)135()()2/(hLkIyyqpanilbl)125( VHkkkwhere)145(222 hIyranittlprpFurui et al. ModelHorizontal WellsSteady-State Inflow Performance )105( lrpppCombining/consolidating Eqs. 5-11, 5-12, 5-13, 5-14 and substituting into Eq. 5-10 yields, )175()2//(12ln2anibanianiwaniIhyIIrhIkLqpFurui et al. ModelHorizontal WellsSteady-State Inflow Performance Defining skin factor as)185(2 skLqpskin )195()2//(12ln2 sIhyIIrhIkLqpanibanianiwaniWith skin included, Eq. 5-17 becomesSolving for q using field units, we obtainIncluding partial penetrating skin, sR, Eq. 5-20 becomes )215(224.11ln2.141)(RanibaniwaniowfesshIyIrhIBppkbq )205(224.11ln2.141)(shIyIrhIBppkLqaniLaniwaniowfewhere, b is the total length of the reservoir.Example 5-2 Well Performance with Furui et al. ModelA 2000-ft horizontal lateral is producing from a 100-ft thick (h = 100 ft) reservoir where kH= 10 md, kV= 1 md. The lateral has an rw= 3 in draining from a region 4000 ft in the direction of the well where pe= 4000 psi, µo= 5 cp, Bo= 1.1. Determine q when pwf= 2000 psi.Solution: )215(224.11ln2.141)(RanibaniwaniowfesshIyIrhIBppkbqmd 162.3110 VHkkk3.162 110VHanikkIft 17322ft 20002ft 400022b2222LybSTB/d 912 qBabu and Odeh ModelHorizontal WellsPseudosteady-State Inflow Performance The
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