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

Capillary End Effect During immiscible displacement –In the bulk of the core plug P c = f (S wet ) –At the outflow face P c = 0  S wet =1 –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”

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

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

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

Rel. Perm. - Unsteady State Unsteady State Method for relative permeability provides –Relative permeability ratio (k r,nonwet /k r,wet ) as a function of wetting phase saturation (S wet ) –Irreducible wetting phase saturation (drainage) –Residual nonwetting phase saturation (imbibition)

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

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

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

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

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 f wet = q wet /q total ; where q total = q wet + q nonwet production rate measured at outflow face

Rel. Perm. - Unsteady State Relative Permeability Ratio usually plotted semi-log –hysteresis due to saturation process (drainage, imbibition)