Introduction toCapillary PressureSome slides in this section are modified from NExT PERF Short Course Notes, 1999.However, many of the slides appears to have been obtained from other primarysources that are not cited by NExT. Some slides have a notes section.

Applications of Capillary Pressure DataDetermine fluid distribution in reservoir (initial conditions)Accumulation of HC is drainage process for water wet res. Sw= function of height above OWC (oil water contact)Determine recoverable oil for water flooding applicationsImbibition process for water wet reservoirsPore Size Distribution Index, Absolute permeability (flow capacity of entire pore size distribution)Relative permeability (distribution of fluid phases within the pore size distribution)Reservoir Flow - Capillary Pressure included as a term of flow potential for multiphase flow

Input data for reservoir simulation models

DRAINAGE AND IMBIBITION CAPILLARY PRESSURE CURVESDrainageImbibitionSiSmSwtPdPc00.51.0Modified from NExT, 1999, after DRAINAGEFluid flow process in which the saturation of the nonwetting phase increasesMobility of nonwetting fluid phase increases as nonwetting phase saturation increasesIMBIBITIONFluid flow process in which the saturation of the wetting phase increasesMobility of wetting phase increases as wetting phase saturation increases

Four Primary ParametersSi = irreducible wetting phase saturationSm = 1 - residual non-wetting phase saturationPd = displacement pressure, the pressure required to force non-wetting fluid into largest pores = pore size distribution index; determines shape

DRAINAGE PROCESS

Fluid flow process in which the saturation of the nonwetting phase increasesExamples:Hydrocarbon (oil or gas) filling the pore space and displacing the original water of deposition in water-wet rockWaterflooding an oil reservoir in which the reservoir is oil wetGas injection in an oil or water wet oil reservoirPressure maintenance or gas cycling by gas injection in a retrograde condensate reservoirEvolution of a secondary gas cap as reservoir pressure decreases

IMBIBITION PROCESS

IMBIBITIONFluid flow process in which the saturation of the wetting phase increasesMobility of wetting phase increases as wetting phase saturation increases

Examples:Accumulation of oil in an oil wet reservoirWaterflooding an oil reservoir in which the reservoir is water wetAccumulation of condensate as pressure decreases in a dew point reservoir

Pc vs. Sw FunctionReflects Reservoir QualityFlowUnitsGamma RayLogPetrophysicalDataPoreTypesLithofaciesCore12345CorePlugsCapillaryPressuref vs kHigh QualityLow QualityFunction moves up and right, and becomes less L shaped as reservoir quality decreases

Effect of Permeability on ShapeModified from NExT 1999, after xx)

Effect of Grain Size Distribution on ShapeModfied from NExT, 1999; after )Decreasing

CAPILLARY PRESSURE- DEFINITION -The pressure difference existing across the interface separating two immiscible fluids in capillaries (e.g. porous media).Calculated as: Pc = pnwt - pwtWhere:Pc = capillary pressurePnwt = pressure in nonwetting phasepwt = pressure in wetting phase One fluid wets the surfaces of the formation rock (wetting phase) in preference to the other (non-wetting phase). Gas is always the non-wetting phase in both oil-gas and water-gas systems. Oil is often the non-wetting phase in water-oil systems.

Capillary Tube - Conceptual ModelAir-Water System Considering the porous media as a collection of capillary tubes provides useful insights into how fluids behave in the reservoir pore spaces. Water rises in a capillary tube placed in a beaker of water, similar to water (the wetting phase) filling small pores leaving larger pores to non-wetting phases of reservoir rock.

CAPILLARY TUBE MODELAIR / WATER SYSTEMThe height of water in a capillary tube is a function of:Adhesion tension between the air and waterRadius of the tubeDensity difference between fluids

This relation can be derived from balancing the upward force due to adhesion tension and downward forces due to the weight of the fluid (see ABW pg 135). The wetting phase (water) rise will be larger in small capillaries.h=Height of water rise in capillary tube, cmaw=Interfacial tension between air and water, dynes/cm =Air/water contact angle, degreesr=Radius of capillary tube, cmg=Acceleration due to gravity, 980 cm/sec2Draw=Density difference between water and air, gm/cm3Contact angle, q, is measured through the more dense phase (water in this case).

Rise of Wetting Phase Varies with Capillary RadiusAyers, 2001

CAPILLARY TUBE MODELAIR/WATER SYSTEMWater rise in capillary tube depends on the density difference of fluids.

Pa2= pw2 = p2pa1= p2 - ra g Dhpw1= p2 - rw g DhPc= pa1 - pw1= rw g Dh - ra g Dh= Dr g Dh

CAPILLARY PRESSURE AIR / WATER SYSTEMCombining the two relations results in the following expression for capillary tubes:

CAPILLARY PRESSURE OIL / WATER SYSTEMFrom a similar derivation, the equation for capillary pressure for an oil/water system isPc = Capillary pressure between oil and waterow = Interfacial tension between oil and water, dyne/cm = Oil/water contact angle, degreesr = Radius of capillary tube, cm

Capillary PressureCapillary Pressure(1) We can infer the pore size distribution index, l, from capillary pressure data. This index can be used to calculate relative permeability using empirical correlations.(2) Capillary pressure curves are similar for the same rock type. The shape also give indication about the rock permeability.Capillary PressureCapillary Pressure

Capillary Pressure

Capillary PressurePetrophysical analyses of core samples are used to identify reservoir flow units and non-flow units. The results are used to calibrate well logs, after which well logs can be used to map flow units throughout a field.Capillary PressureCurves shift to the right (i.e., larger water saturations at a given value of capillary pressure) as the permeability decreases.Displacement pressure increases as permeability decreases.Minimum interstitial water saturation increases as permeability decreases.Capillary PressureWell-sorted grain sizesMajority of grain sizes are the same sizeMinimum interstitial water saturation is lowerDisplacement pressure is lowerPoorly sorted grain sizesSignificant variation in range of grain sizesMinimum interstitial water saturation is higherDisplacement pressure is higherCapillary Pressure

Capillary PressureCapillary Pressure

Capillary PressureCapillary PressureCapillary PressureThe following steps have been taken to drive the above relation :Capillary Pressure