# introduction effective permeability & relative permeability

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Introduction Effective Permeability & Relative Permeability

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• 1. Introduction toEffective PermeabilityandRelative Permeability

2. Review: Absolute Permeability Permeability, k, previously discussed applies onlyto flow when pores are 100% saturated with onefluid sometimes called absolute permeability Absolute permeability can be calculated from thesteady-state flow equation (1D, Linear Flow; DarcyUnits):q = k A DpLm 3. Multiphase Flow in ReservoirsCommonly, reservoirs contain 2 or 3 fluids Water-oil systems Oil-gas systems Water-gas systems Three phase systems (water, oil, and gas) Multi-phase flow is common in most petroleum reservoirs. Insuch multi-phase systems, we need to quantify the flow of eachphase in the presence of other phases. This is done through effective and relative permeability data. 4. Multi-phase flow is common in most petroleumreservoirs. In such multi-phase systems, weneed to quantify the flow of each phase in thepresence of other phases. This is done througheffective and relative permeability data. We use sets of relative permeability data thatcorrespond to the fluids moving in the reservoir. Example : We need to use a water-gas relativepermeability set to perform reservoir engineeringcalculations when we study dry gas reservoirsunder water influx from an aquifer 5. Effective PermeabilityEffective permeability is a measure of the conductancecapacity of a porous medium for one fluid phase when themedium is saturated with more than one fluid. The porous medium can have a distinct and measurableconductance to each phase present in the medium Effective permeabilities: (ko, kg, kw) When pore space contains more than one fluid, Darcysequation becomes. Effective permeability is a function of:(a) geometry of the pores of the rock (b) rock wettingcharacteristics (c) fluid saturation 6. Multiphase Flow in Porous Rock Oil Water Gas= DFo oLq k Ao mo= DFw wLq k Aw mwg gLk Aqg mgDF=Steady state, 1D, linear flowequation (Darcy units):qn = volumetric flow rate for aspecific phase, nA = flow areaDFn = flow potential drop forphase, n (including pressure,gravity and capillary pressureterms)mn = fluid viscosity for phase nL = flow length 7. Darcys equation for multiple fluids in linear flow, in oilfieldunits; 8. Relative PermeabilityRelative Permeability is defined as the ratio of the effectivepermeability of a fluid at a given 100%saturated(absolute permeability), i.e.It is normally assumed that the effective permeability at100% saturation is the same for all fluid in a rock. (except inshaly sand) 9. OilRelative Permeability Water Gaskkk oro(0.5,0.3)(0.5,0.3) =kkk wrw(0.5,0.3)(0.5,0.3) =kkk grg(0.5,0.3)(0.5,0.3) =So =0.5Sw =0.3Sg = 0.2 10. Typical relative permeability curve Use subscript wp to represent the wetting phase & subscriptnwp to represent the non-wetting phase 11. Effect of Saturation history There are types of relative permeability curves;(a) drainage curve wetting phase is displaced by non wettingphase, i.e., wetting phase saturation is decreasing.(b) imbibition curve non-wetting phase is displaced bywetting phase, i.e., wetting phase saturation is increasing. 12. Relative Permeability Functionsfraction)0.80(Permeability Two-Phase Flow0.40Relative 0.200Water Saturation (fraction) 0 0.20 0.40 0.60 0.80 1.001.000.60Waterkrw @ SorOilRegionIrreducibleWaterSaturationkro @ SwiResidual OilSaturation Wettability and direction ofsaturation change must beconsidereddrainageimbibition Base used to normalize thisrelative permeability curve iskro @ Swi As Sw increases, kro decreasesand krw increases untilreaching residual oilsaturationModified from NExT, 1999Imbibition Relative Permeability(Water Wet Case) 13. The figure represents typical oil-water relativepermeability data. Usually the experiment is done inthe direction of increasing water saturation tosimulate water injection in the reservoir. The baseused to normalize the relative permeability data is theeffective oil permeability at the irreducible watersaturation.As water saturation increases, the relativepermeability to oil decreases and the water relativepermeability increases until it reaches a maximum atthe residual oil saturation. 14. Effect of Wettability for Increasing Sw0.80.40.20Oil0 20 40 60 80 100Water Saturation (% PV)Relative Permeability, Fraction1.00.6WaterStrongly Water-Wet Rock0.80.40.200 20 40 60 80 100Water Saturation (% PV)Relative Permeability, Fraction1.00.6Oil WaterStrongly Oil-Wet Rock Water flows more freely Higher residual oil saturationModified from NExT, 1999 15. In a strongly oil-wet system, water is expected to floweasier than in a strongly water-wet system. In addition, wegenerally would expect that the residual oil saturation willbe higher. 16. Factors Affecting Relative Permeability Fluid saturations Geometry of the pore spaces and pore sizedistribution Wettability Fluid saturation history (i.e., imbibition ordrainage)After Standing, 1975 17. The effect of fluid saturations was shown onprevious slides. In general, relative permeabilityto a particular fluid increases as the saturation ofthat fluid increases. The geometry of the rock pore spaces and grainsize distribution also affect both the shape of therelative permeability curves and their end points.Different rock characteristics are expected toproduce different relative permeability curves. The effect of wettability and saturation history isshown in the following few slides. 18. Characteristics of Relative PermeabilityFunctions Relative permeability is unique for differentrocks and fluids Relative permeability affects the flowcharacteristics of reservoir fluids. Relative permeability affects the recoveryefficiency of oil and/or gas.Modified from NExT, 1999 19. Relative permeability data influence theflow of fluids in the reservoir. Relativepermeability curves determine howmuch oil, gas, and water are flowingrelative to each other. 20. Applications ofRelative Permeability Functions Reservoir simulation Flow calculations that involvemulti-phase flow in reservoirs Estimation of residual oil (and/orgas) saturation 21. Effective and relative permeability data are used in almostall reservoir engineering calculations that involvemovements of several fluids together. Relative permeability data is an important input to reservoirsimulation models. Reservoir simulation is used to studythe reservoir behavior under a variety of conditions.Among the many uses of reservoir simulation models are: - Prediction of reservoir performance - Development planning - Alternative production plans evaluation (water injection,gas injection, EOR etc) - Alternative well configurations (fractured wells,horizontal wells etc) Relative permeability is also an input to simple models thatcalculate flow of more than one fluid (e.g. water floodingmodels). Relative permeability can also be used to estimate residualhydrocarbon saturation.

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