An Improved Unsteady-State Procedure for Determining the Relative-Permeability Characteristics of Heterogeneous Porous Media (includes associated papers 8028 and 8777 )
Authors: Sigmund P.M. , McCaffery F.G. 
Published: December 2007

Abstract
With typical heterogeneous carbonate coresamples, large uncertainties of unknown magnitudecan occur in the relative permeabilities derived using different methods. This situation can beimproved by analyzing the recovery and pressureresponse to two-phase laboratory displacement tests by a nonlinear least-squares procedure. Thesuggested technique fits the finite-differencesolution of the Buckley-Leverett two-phase flowequations(which include capillary pressure) to theobserved recovery and pressure data. The procedureis used to determine relative-permeability curves characterized by two parameters and their standarderrors for heterogeneous cores from two Albertacarbonate reservoirs.

Introduction
Several recent investigations have recognizedpossible problems when obtaining reliable two-phasedisplacement data from heterogeneous carbonate core samples. Huppler stated that waterfloodresults on cores with significant heterogeneitiescan be sensitive to flooding rate, core length, andwettability, and that these effects should beconsidered before applying the laboratory results atfield flooding rates. Brandner and Slotboomsuggested that realistic displacement results maynot be obtainable when vertically flooding aheterogeneous core with a nonwetting phase becauseof the fluid's inability to maintain a properdistribution when the sample length is less than the height of capillary rise. Ehrlich noted thatstandard relative-permeability measurement methodsusing core plugs cannot be applied when the media are heterogeneous.
Archer and Wong reported that application of theconventional Johnson- Bossler - Neumann (JBN)methods for determining relative permeabilities froma waterflood test could give erroneous results forheterogeneous carbonate as well as for relativelyhomogeneous porous media having a mixed wettability (see Refs. 1, 6, and 7). The observedstepwise or humped shape of water relativepermeability curves mainly were attributed to theeffect of water breakthrough ahead of the main floodfront entering into the JBN calculation. Archer andWong suggested that such abnormally shapedrelative-permeability curves do not represent theproperties of the bulk of the core sample, and proposed the use of a reservoir simulator forinterpreting laboratory waterflood data.
The work referred to above provides the majorbackground for this study involving the developmentof an improved unsteady-state test method tocharacterize the relative-permeability properties ofheterogeneous carbonate core samples. The methodcan be applied to all porous media, regardless ofthe size and distribution of the heterogeneities.However, the presence of large-scaleheterogeneities, especially in the form of vugs, fractures, and stratification, could cause the derivedrelative-permeability relations to be affected by viscosityratio and displacement rate. Remember also that extrapolation of any core test data to a field scaleis associated with many uncertainties, particularlyfor heterogeneous formations. The inclusion ofcapillary pressure effects permits the interpretationof displacement tests at reservoir rates.
The proposed calculation procedure extends theapproach suggested by Archer and Wong in thatthe degree of fit between observed laboratory dataand simulator results is quantified. We suggest thatrelative-permeability curves for a variety of rocktypes can be expressed in terms of two adjustable parameters and their standard error estimates.To illustrate the method, the results of displacementtests performed on cores from Swan Hills Beaverhill Lake limestone oil reservoir and Rainbow F KegRiver dolomite oil reservoir are interpreted.
SPEJ
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