Laboratory Measurement of Relative Permeability Effective and Relative Permeabilities 1 Laboratory Measurement of Relative Permeability

Hysteresis Effect on Rel. Perm. Effective and Relative Permeabilities 2 Hysteresis Effect on Rel. Perm. Non-wetting phase Wetting phase Imbibition krnw krnw krw Drainage Relative Permeability, % Process begins with rock completely saturated with wetting phase, i.e., Swp = 100% The wetting phase is displaced with the non-wetting phase (i.e., drainage process) until wetting phase ceases to flow. At this point, the wetting phase saturation equals the minimum interstitial wetting phase saturation. Then, the non-wetting phase is displaced with the wetting phase, (i.e., imbibition process) until the non-wetting phase ceases to flow. At this point, the non-wetting phase saturation equals the equilibrium or residual non-wetting phase saturation. The term “hysteresis” describes the process in which the relative permeabilities are different when measurements are made in different directions. Irreducible wetting phase saturation Residual non-wetting phase saturation Wetting Phase Saturation, %PV

Hysteresis Effect on Rel. Perm. During drainage, the wetting phase ceases to flow at the irreducible wetting phase saturation This determines the maximum possible non-wetting phase saturation Common Examples: Petroleum accumulation (secondary migration) Formation of secondary gas cap During imbibition, the non-wetting phase becomes discontinuous and ceases to flow when the non-wetting phase saturation reaches the residual non-wetting phase saturation This determines the minimum possible non-wetting phase saturation displacement by the wetting phase Common Example: waterflooding water wet reservoir

Effective and Relative Permeabilities 4 Review: Effective Permeability Effective and Relative Permeabilities 4 Steady state, 1D, linear flow equation (Darcy units): qn = volumetric flow rate for a specific phase, n A = flow area Fn = flow potential drop for phase, n (including pressure, gravity and capillary pressure terms) n = fluid viscosity for phase n L = flow length Oil Water Gas Modified from NExT, 1999; Amyx, Bass, and Whiting, 1960; PETE 311 NOTES

Rel. Perm. - Steady State Purpose: determination of two phase relative permeability functions irreducible wetting phase saturation (drainage) residual non-wetting phase saturation (imbibition)

Rel. Perm. - Steady State Process (oil/water, water wet case): simultaneously inject constant rates of oil and water until steady state behavior is observed production will be constant at same oil and water rates as injection pressure drop for each phase will be constant determine saturation of core sample usually by resistivity or weighing this is typically not the same as the injection ratio change injection ratio and repeat

Rel. Perm. - Steady State Imbibition Relative Permeability Functions Stage 1: Preparation for drainage core saturated with wetting phase steady state injection of wetting phase used to determine absolute permeability Stage 2: Irreducible wetting phase inject non-wetting phase until steady state, measure saturation no wetting phase will be produced at steady state

Rel. Perm. - Steady State Imbibition Relative Permeability Functions (continued) Stage 3 (A-C): determination of points on imbibition relative permeability function steady state injection at constant rates of wetting and non-wetting phase Initially ratio qw/qnw is small measure saturation and phase pressure drops at steady state saturation ratio will in general, not be the same as injection ratio repeat with increasing rate ratio, qw/qnw

Rel. Perm. - Steady State Imbibition Relative Permeability Functions (continued) Stage 4: determination of residual non-wetting phase saturation inject wetting phase until steady state behavior observed measure saturation and pressure drop

Capillary End Effect During immiscible displacement In the bulk of the core plug Pc= f (Swet) At the outflow face Pc= 0  Swet=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

STEADY-STATE RELATIVE PERMEABILITY TEST EQUIPMENT (HASSLER METHOD) Effective and Relative Permeabilities 14 STEADY-STATE RELATIVE PERMEABILITY TEST EQUIPMENT (HASSLER METHOD) Oil inlet Oil burette To atmosphere Po Gas outlet inlet Pg Pc Core Porcelain plate

PENN STATE METHOD FOR MEASURING STEADY-STATE RELATIVE PERMEABILITY Effective and Relative Permeabilities 15 PENN STATE METHOD FOR MEASURING STEADY-STATE RELATIVE PERMEABILITY x x x x Differential pressure taps Packing nut Thermometer section End Bronze screen Test Mixing Inlet Outlet Highly permeable disk Copper orifice plate Electrodes

HAFFORD’S METHOD FOR MEASURING STEADY-STATE RELATIVE PERMEABILITY Effective and Relative Permeabilities 16 HAFFORD’S METHOD FOR MEASURING STEADY-STATE RELATIVE PERMEABILITY Oil pressure pad Oil Gas pressure gauge Gas meter Oil burette Porous end plate

DISPERSED FEED METHOD FOR MEASURING STEADY-STATE RELATIVE PERMEABILITY Effective and Relative Permeabilities 17 Lucite-mounted core Gas-pressure gauge Gas Core material Gas meter Lucite Oil Oil burette Dispersing section section face

Saturation by Weighing (Review) Determine mass of fluid Solve from Mass Balance mfluid = moil + mwater = Vp(1 - Sw)ro + VpSwrw