Laboratory%20Measurement%20of%20Relative%20Permeability%20-%20Capillary%20End%20Effect%20-Unsteady%20State%20Method

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Laboratory MeasurementofRelative
Permeability- Capillary End Effect-Unsteady
State Method
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Capillary End Effect

• During immiscible displacement
• In the bulk of the core plug
• Pc f (Swet)
• At the outflow face
• Pc 0 ? Swet1
• There must be a gradient of saturation from the
  the bulk of the core to the outflow face
• This saturation gradient is the Capillary End
  Effect

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Capillary End Effect

• Comparison for low flow rate
• Theoretical gradient (dashed line)
• Experimental data (circles)
• Saturation gradient extends over half of the
  length of the core plug

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Capillary End Effect

• Comparison for higher flow rate
• Theoretical gradient (dashed line)
• Experimental data (circles)
• At higher flow rate, saturation gradient extends
  over only 1/5 of the length of the core plug

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Capillary End Effect

• Eliminating errors due to end effect in
  measurement of relative permeability functions
• Measure saturation far enough away from outflow
  face (e.g. Penn State Method)
• Use high flow rates to make error in measured
  saturation negligible

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Rel. Perm. - Unsteady State

• Unsteady State Method for relative permeability
  provides
• Relative permeability ratio (kr,nonwet/kr,wet) as
  a function of wetting phase saturation (Swet)
• Irreducible wetting phase saturation (drainage)
• Residual nonwetting phase saturation (imbibition)

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Rel. Perm. - Unsteady State
Saturation in Core Plug
Production Rates

• Imbibition Relative Permeability Ratio Function
• Stage 1 Preparation for drainage
• core saturated with wetting phase
• Stage 2 Irreducible wetting phase (drainage)
• inject non-wetting phase until steady state,
  measure saturation
• no wetting phase will be produced after steady
  state

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Rel. Perm. - Unsteady State
Saturation in Core Plug
Production Rates

• Imbibition Relative Permeability Ratio Function
• Stages 3-6 Inject wetting phase
• Stage 3 (A) Wetting phase has not yet reached
  outflow face
• only nonwetting phase produced at outflow face
• Stage 4 (B) Wetting phase just reaches outflow
  face, called breakthrough
• wetting phase will be produced at outflow face

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Rel. Perm. - Unsteady State
Saturation in Core Plug
Production Rates

• Imbibition Relative Permeability Ratio Function
• Stages 3-6 Inject wetting phase
• Stage 5 (C) As injection of wetting phase
  continues, production of nonwetting phase
  decreases (unsteady state)
• Important to take many data points during this
  decrease
• cummulative nonwetting phase produced
• production rate for both phases

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Rel. Perm. - Unsteady State
Saturation in Core Plug
Production Rates

• Imbibition Relative Permeability Ratio Function
• Stages 3-6 Inject wetting phase
• Stage 6 (D) Eventually, no more nonwetting phase
  is produced, allowing residual nonwetting phase
  saturation to be determined

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Rel. Perm. - Unsteady State

• Analysis Procedure
• Assumptions
• immiscible displacement
• incompressible fluids
• linear, 1-D flow
• capillary pressure neglected
• Determination of average saturation
• cumulative nonwetting phase production
• Determination of relative permeability ratio from
  fractional flow
• fwet qwet/qtotal where qtotal qwet
  qnonwet
• production rate measured at outflow face

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Rel. Perm. - Unsteady State

• Relative Permeability Ratio usually plotted
  semi-log
• hysteresis due to saturation process (drainage,
  imbibition)