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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.
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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
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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
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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
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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
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Pc vs. Sw FunctionReflects Reservoir QualityFlowUnitsGamma
RayLogPetrophysicalDataPoreTypesLithofaciesCore12345CorePlugsCapillaryPressuref
vs kHigh QualityLow QualityFunction moves up and right, and becomes
less L shaped as reservoir quality decreases
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Effect of Permeability on ShapeModified from NExT 1999, after
xx)
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Effect of Grain Size Distribution on ShapeModfied from NExT,
1999; after )Decreasing
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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.
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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.
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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).
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Rise of Wetting Phase Varies with Capillary RadiusAyers,
2001
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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
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CAPILLARY PRESSURE AIR / WATER SYSTEMCombining the two relations
results in the following expression for capillary tubes:
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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