Determining Relative Permeability

Determining Relative Permeability - SPE 6045 Graphical...

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SPE 6045 “@ Graphical Techniques for Determining Relative Permeability From Displacement Experiments A S. C. Jones, SPE-AIME, MarathonOil Co, W. 0, Roszelle, SpE-AIME, Marathonoil Co, Introduction To find oil and water relative permeabilities by the dis- placement or unsteady-state method, a small linear core usually issaturatedwith water, thenoilflooded to irreduc- ible water saturation. Subsequently, the core is water- flooded, and during the process, prcasure dmp (either constant or variable) across the entire core and water injection rate (constant or variable) are determined. Ef- fluent fractions arecollected and the amount of water and oil in each is measured. Augmented by the absolute permeability and pore volume of the core and by oil and water viscosities, these data are sufficient to develop relative permeability curves. The average saturation in the core at any time in the flood can be found from an over-all material balance, However, to calculate relative permeability, the satura- tion history at somepohu in the core must be determined, not the average saturation history. The Welge’ equation yields saturations at the effluent end of the core when the average saturation history is known. Simihuly, to compute relative permeability, the poiw pressure gradient per unit injection rate is needed, not the average. The equation developed by Johnson et al.= converts average relative injectivity to a pint vahu, accomplishing the rquired task. While the equations of Welge and Johnson et al, have been used successfully for years, they require tedious computation and aresubject to emorbecauseof the evalu- ation of derivatives. The graphical techniques presented [email protected]\$O0.2S c 1978 Scwdy of [email protected] of AlME in this sNdy are equivalent to these equations, but are easier to usc and can give a mom accurate evaluation of relative permeability. Lefebvre du Reps has presented graphical construc- tions based on curves of vohime of oil produced vs time and pressure drop vs time to develop the requiti point functions. These constructions am limited to constant rate displacements. The constructions presented here are general and apply to constant rate, constant presswe, or variable rate-pressure displacements, Constant-rate and constant-pressure examples are given to help clarify the methods, The graphical techniques make it easy to see that double or triple saturation values, so extensively dis- cussed in the pas~” simply do not result fmm the frac- tional flow curve generated by a single displacement, such as a waterflood or an oiiflood. Theory Ignoring gravity effects and capilhry pressure, water and oil relative permeabilities (expressed as functions of saturation) are &~,,.= /L,J,,.2/A2-’, . . . . . . . . . . . . . . . . . . . . . , .(1) and k m = gJo2/A2-1, . . . . . . . . . , .,,. .0. .. . . . . (2) To use these equations, the fractional flow of water or oil and effective viscosity, A-*, must be determined as func- tions of saturation. These must be point values, not aver- This paper presents graphical constructions that simplifi the calculation of relative permeabilityfiom displacetnent data. These constructions convert raw data to relative

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This note was uploaded on 02/02/2011 for the course PETE 100 taught by Professor Eric during the Spring '11 term at University of Louisiana at Lafayette.

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Determining Relative Permeability - SPE 6045 Graphical...

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