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Relative-Permeability Measurements:
An Overview
M. Honarpour, SPE, Natl. Inst. for Petroleum & Energy Research
S.M. Mahmood, SPE, Natl. Inst. for Petroleum & Energy Research

introduction
Fluid transport through reservoir recks is complex and cannot the calculation scheme is based on Darcy’s law. Unsteady-state
be described by theory alone. Darcy’s law, an empirical twhniques present many uncertainties in calculation schemes.
equaiion describing the Iami”ar flow of incompressible fluids, Operational constraints connected with use of viscous oils and
is largely used for calculation of fluid flow through porous high injection rates diminish the role of capillarity such that
media. It relates the macroscopic veloci~ (flux) of a fluid of the influence of nettability cannot always be manifested.
known viscosity to the pressure gradient by a pmpotiionalky Folfowing is a description of both methods.
factor called absolute permeability, expressed in darcies.
Permeability is a measure of the abtily of porous materials to Stesdy-State Techniques. The most reliable relative-
conduct flow and is, dictated by the geometry of the pore permeability data me obtained by steady-state methods in
network. Generally, the fluid flow in hydrocarbon reservoirs which two or three fluids are injected simultaneously at
involves more than one fluid, in which case the ablity of each constant rates or pressore for extended durations to reach
fluid to flow is reduced by the presence of other fluids. equilibrium. The saturations, flow rates, and pressure gradients
Darcy’s equation has been extended to such situations using the are measured and used in Darcy’s law to obtain the effective
concept of effective permeabtky, which is the apparent permeability for each phase. Conventionally, cumes of relative
permeability of a fluid at a given saturation. The sum of the p.mmabifity vs. saturation are obtained, in a stepwise fashion,
effective permeabllities for all phases is less than the absolute by changing the ratio of injection rates and repeating the
permeability because of the interference between fluids tlat measurements as equilibrium is attained. Saturation changes are
share the same channels. The effective permeability to a fluid controlled to be unidirectional (i.e.,’ imbibition or drainage) to
becomes zero while its saturation is finite because the fluids avoid hysteresis.
bikome discontinuous at low satmaticms. The steady-state methods are inherently time-consuming
Another meti. concept in describing the flow of nlultiphase because e.quilibrimn attainment may require se.eraf hours or
systems is relative permeability, which is defined as the ratio days at each saturation level. lu addition, fhese methods
of the effective permeability of a fluid to the absolute re@re independent measurement of fluid saturations in the
permeability of the rock. Relative permeability has a first-order core. Their advantages are greater reliability and the ability to
dependency on saturation level. However, many interstitial determine relative permeability for a wider range of saturation
fluid distributions are possible for each level of satwation, levels. The steady-state methods include the Hassler metiod,
dependins on the direction of saturation changes, Thus, values singl~sample dynamic, stationary phase, Penn State, and
of relative permeabili~ vs. saturation obtained for drainage modified Penn State. 1.2 Tiiey vary in the method of
(reduction of wetting-phase saturation) maybe different from establishing capillary equilibrium between fluids and reducing
those for imbibition (increase in wetting-phase saturation). This or eliminating end effects. Frutler details of these methods are
phenomenon is called hysteresis. provided in subsequent sections.
Fig. 1 shows a typical plot of two-phase relative
permeability vs. saturation. It is ASOhelpful to present such Unsteady-Stste Te.ehniques. The quickest laboratory methods
plots on a semilog scale to expand the relative-permeability of obtaining relative-permeability data me unsteady-state
characteristics nea the endpoint saturation. techniques. fn these techniques, saturation equilibrium is not
Relative-permeability data are essential for almost all attaine& thus, an entire set of relative-permeability vs.
calculations of fluid flow in hydrocarbon reservoirs. The data saturation curves can be obtained in a few hours. A typicaf mn
are used in making mgimming esdrnatm of pmdwdivity, involves displacing in-situ fluids by constant-rate (or con.stant-
i~ectivity, and ultimate recove~ from reservoirs for pressure) injection of 2 driving fluid wiile monitoring the
evaluation and planning of production operations and also cfffnent volumes continuously. The production data ze
can be used to diagnose formation damage expected under analyzed, and a set of relative-permeability curves is obtained
vxious operational conditions. These data are unquestionably using various matbwnatical methods. 3,4
one of the most important data sets required in reservoir The Buckley-Le.verett equation for lines displacement of
simulation studies. immiscible and incompressible fluids is the basis for all
analyses. This equation relates the saturation levels, at each
point and time, to capilky pressure, the ratio of fluid
Laboratory Determination of Effective viscosities, the flow rates, and the relative permeabilities. The
Permeability and Relative Permeability Welge, Johnson-Bossier-Namnarm, and Jones-Roszefle methods
Steady-state methods for determining permeabilities have the are most commonly used for analysis. 1
widest application and greatest reliability because the capilfary Many difticukies are tierent in unsteady-state methods.
equilibrium prevails, the saturation is measured directly, and Operational problems such as capiffary end effects, viscous
fingering, and channeling” in heterogeneous cores are dfikult
to monitor and to account for properly. Unless the mobility
copyright1988Societyof Prnmleurn
Engineers (the ratio of effective to of the
 Nolen for three-phase relative-pemneabili~ calculations. These
models require two-phase relative.permeablliiy values as
90
parameters.

Calculation From Field Data

80
Relative pemneabtiity may be determined from the production
70 history of a reservoir and its fluid properties. 1 However, the
1 agreement between laboratory-determined relative
permeabilities and those calculated from production data is
generally poor. Relative-penneabif ity ccdculatiom from this
method require complete production-history data and provide
average values influenced by pressure and saturation gradients,
differences in stages of depletion, amd saturation variations in
stratified reservoirs.
Pressure-transient testirig is another potential method for
determining ir-situ effective permeability, provided that it is
used in conjunction witi accurate downhole flow-measurement
instnune”ts.

Laboratory Measurement Techniques for

Saturation Determination
WATm SATURATION, percent
Relative-permeability measurements require accurate saturation
detennimtion. Accuracies of *2% are often desirable. There
are two approaches to saturation determination external and
in-situ techniques.

External Techniques. In these techniques, the saturation in $e

displacing fluid is much higher than that of the in-sire fluids, mm is inferred indirectly by measuring fluid production. They
the time between the front breakthrough and complete floodout provide an average vahie and do not reveal the Wuration
is usually small, introducing computational difficulties, The protile. The most common external technique is material
interpretation techniques involve many uncemdnties because of balance, in’which cumulative injection and production volumes
gross simplifying assumptions. The values obtained from these are measured and the difference is assumed to be retained in
methods, therefore, should .k considered only as qualitative, the core. Significant errors may be introduced, especially when
The main advantages of these methods include fewer the PV of tbe core is small, because of the presence of dead
instrumentation requirements and substantially reduced test volume in the system, fluid separation problems, and
times compared with steady-state tests. evaporation losses. Closed-loop systems are sometimes used to
The centrifuge technique is an unsteady-state technique in reduce the errors associated with these volumetic methods of
which relatively small and presaturated cores are rotated at an saturation determination. Other cotioa techniques are
elevated anguk speed, exposing them to a known centrifugal gravimetric and extraction methods. fn the gravimetic method,
force, and the rate of production of liquid effluents is the core is weighed before and during the test and the
measured with time. Relative permeabilities are then saturation is inferred from weight changes, whereas the
determined from the test data by mathematical methods. 5 quantity of water is determined by distillatiorJexMaction in the
The centrifuge method is faster than the steady-state extraction method. Both methods require removal of the core
methods, and it is cla@?d that viscous-fingering problems, from the core holder, subjecting it to saturation changes.
commonly associated with the dynamic displacement methods
do not affect the results. Nevertheless, the interpretation of fi-Situ Techniques. The quantity of fluids inside the core is
iesults requires many simplifying assumptions, and as such, measured directly, without disturbing the in-sire fluid
the values should be comidered to be only qualitative. The distribution. These techniques offer greater accuracy and
centrifuge method does not provide’ relative-permeability data reliability than external techniques.. Attainment of accuracies of
for the displacing phase md also suffers from capilfmy end
*1% is not unusual. These methods are also capable of
effwts, just as other methods do. It has been show”, however, measuring point saturations., which can be used in constructing
that the centrifuge method-simulates the gravity drainage twq- and three-dimensional samration profiles.
process better than any other method. 6 In principle, some kind of known stimulus is applied to the
fluid in the core, and the resultant response is measured. A
Empirical Techniques calibration curve is generally established before the test by
Because of tbe difficulties involved in measurement, empirical scanning the core twice—at completely dry conditions and after
models are sometimes used to estimate relative permeability. it is fully saturated with the test fluid to be monitored.
This alternative is not a good substitute for laboratory One of the most popular in-situ techniques is X-ray
measuremems, but these models ‘we often used for absorption, but nuclear magnetic resonance, gamma ray
extrapolation of limited laboratory data. attenuation, neutron bombardment, and sonic (radiowave)
Several predctive models have been proposed, 1 idealizing mctbods have also been used successfully. The microwave
the porous medium as a bundle of capillaries. The flow attenuation technique, unlike most other methods, measures
through a single capillary is described mathematically, then the water saturation without requiring any fag m dye and, as such,
total flow through the entire set of capillaries is obtained using is ari emerging technique. F]ndirig a safe and suitable tagging
the concept of capillmy pressure. Some published models agent that mixes with the test fluids completely and does not
based on this strategy include Corey’s model for drainage, interact with roc!dfluid interfaces is sometimes difficult.
Naw-Wygai’s and Naar-Henderson’s models for imbibition, Recently, nydtidimensional scanning techniques, such as
and Land’s model for both drainage and imbibhion computerized tomography (CT) scan and nuclear magnetic
proce~~e~, 1,2
resonance imaging, have become popular for relative-
Statistical methods i have also been used to describe the permeability measurements determined to obtain additional
randomness ,of pore-size distribution in porous media. Some diagnostic information about rock heterogeneity and saturation
notable probabilistic mcdels include Stone’s Mcdel 1, Stone’s distribution, With image-reconstruction software, frontal
Model II and modifications Dktrich and Bondor and
 Electrical resistivity is another method by which brine Inaccuraciescausedby hysteresis may seem easy to eliminate,
saturation Cm be determined. It is based on interpolation of but they are operationally diflicuh to control and require
electrical responses between two cahbration points by use of careti-desigr-of the ex~rimentd procedure.
Archie’s equation. The stimulus here is a known electrical For laboratory data to be useful in scaling up to the field
current, and the response is the potential drop across a known level, measurements should be taken at conditions
length of core. Even though electrical resistivity is an in-situ representative of those found in the reservoir. This involves
technique, practicdy it provides only average saturations along performing the tests with the appropriate combinations of
@e core. other limitations include its dependence on direction viscous, capillary, and gravity forces such that a stable
of saturation changes (hysteresis), imccuracies at lower brine displa.cemeht through the core is ensured, while at the same
satur~tions caused by the dkcontirmity of flow channels, and time the similarity in the microscopic flow behavior between
operational problems with electrodes, which could imroduge the reservoir and the core is still maintained.9 Linear scaling
noises on the same order of magniti& as the response itself. criteria should be used as guidelines to achieve this objective.
Relative-pnneability tests mnducted at room temperature
Important ~xperlmental Considerations using dead crude or even refined ol can sometimes be useful,
provided that sui%cient tests under simulated reservoir
Accurate relative-permeability measurements in tie labO~OW
condkions are performed to evaluate the reliability of such
require careful design of the apparams and operating
idea!ized tests.
conditions. Due consideration should be given to address
problems such as capillary end effects, hysteresis, and scaling
effects. 7 Important Considerations for Corhw, Handling,
me most common source of error is the capillary end effect, and Sample Selsction
a phenomenon causing the saturation of the wetting phase to be Representative cores should be obtained from each stfatum to
higher close to the inlet and outlet ends of ~e mck samples. be used in laboratory measurements. Native-stake cores are
These higher saturations at the ends are the result of greater preferred to provide a close representation of reservoir
affinity of the wetting phase to remain in pore capillaries nettability, which is cmcial for obtaining realistic relative-
rather tin to exit to a noncapillaiy space. permeability data. Fresh-state samples may also have wetting
Several techniques have been proposed to reduce or to characteristics similar to those in the reservoir, provid@ hat a
eliminate end effects. Perhaps the most important one is bland mud is used as the coring fluid. However, flushing by
Hassler’s technique, and some of its mvdiiications, in which mud filtrate generally changes the initial water saturation.
porous plates (of nettability sin+w to that of the rock) are Coring operations should be designed to minimiie mud
placed in contact witi both ends, The wetting phase bas to ftitration so that undesirable flushing before laboratory testing
pass tbmugh these tidly saturated plates, whereas the is avoided. Retrieving Iargedmeter cores also reduces the
nonwetting phase is introduced dmctly into the core face. The influence of flushing by drilling muds and miniinizes the core
pressures are maintained lower than the tbfe.shold pressure, so contamination. Weathering may result in wettab~l~ cbmgw
that the nonwetting phase does not enter the plates. Even thus, recovered cores should be presemed without unnecessary
though it is operationally cumbersome, this technique delays. Core cleaning and handling in the laboratory shouId
eliminates end effects. The Hassler technique is also capable of aiso be minimal, because they can affmt the we~b$tty of the
measuring the pressure of each phase separately, thus taking core drastically and may damage pore structure. Anempts to
into account the pressure dtierence between immiscible restore reservoir wettabtity are often unsuccesstil and could
phases, which is caused by the capillary forces involved in a lsad to erroneous determination of relative permeabilities.
complex rocldfluid system. If this pressure difference in phases Enough core samples should be selected to cover tie entire
is not properly accounted for, significant error may %e range of rock propeties evident in the formation. Cores should
introduced whose magnitude will depend on the saturation level preferably be screened by CT scan to identify any
and wettabili~ of the system. heterogeneities. Nonconforming samples (for example, cores
A similar approach to reduce the end effects is used in the having layers of large permeability conmasts) shopld be
Penn State method, in which porous material is placed in excluded. ff longer samples are not available, a composite core
contact with the inlet and outlet faces of tie test cOre. lt can be made by placing several closely matched plugs in
differs from the Hassler technique in that all fluids are passed series, using appropriate capillary bridges between the cores,
through the porous ends, so that the pressure drop cannot be and ‘applying tiaxial compression.
measured separately for each phase. Levine, 8 however,
measured pressures in both phases using pressure taps
Recent Studies
connected to the periphery of an Alundumw core. The
pressure in the water phase was measured through a pressure Recent advances in muftipbase relative-penneabili~
tap containing a hydrophilic porous porcelain plate in capillary measurements have been maidy in the improvement of
contact with the core. The pressure in the oil phase was continuous in-situ saturation determination techniques. These
measured through another pressure tap, placed on the opposite improvements have provided the opportunity tb screen the
side, containing another pornus porcelain plate wbicb was cores and to monitor flow bebaviors and saturation
made oleophilic by treatment with Dri-Filmm (G.E.). distributions. The use of a high-speed centrifuge for relative-
Other techniques for reducing the influence of end effects permeability measurements is also a relatively new
include displacement at high flow rates @afford and dispersed- development. This meffiod is faster than the steady-state
feed) so that the influence of viscous forces becomes much >technique and is apparently not subject to viscous-
greater than capilb.rity, and use of longer cores while fmgering problems.
restricting the pressure and saturation measurements to the Advances have afso been made in the design and fabrication
imer sections of the cores. Pressure drops for each phase of relative-permeability apparatus capable of performing tests
cannot be measured separately in these methods. under simulated reservoir conditions 10 and for various EOR
A less common technique for eliminating end effects is to processes. Quality control in measurements and application of
keep one of tie phases stationary. This is accomplished by scaling criteria are currently being emphasized.
placing a porous plate at the producing end and allowing a Severaf mathematical techniques for deteru@ng relative
single fluid to flow at such a low pressure gradient that tie permeability from unsteady-state tests have been proposed.
second fluid remains immobile. This te+nique, called the Empirical correlations for calculation of two- and three-phase
statiomuy-phase method, is useful for generating data close to relative permeabilities have also been published. Curve-fitting
the endpoint saturation of the nonstationary fluid. algorithms have been suggested for interpoladon (and
Another important consideration ti relative-permeability extrapolation) of laboratory data, with schemes ranging in
i i d d fit
Conclusions 4, Jones, S.D. and Roszdle, W, O.: “Graphical Techniques f~r
Determining RelativePenneabiliy From Displacement Experiments,, S
Significmt advances have been made in methods for accurate
JPT (May 1978) 807-17; THIS.; AIME, 265.
measurements of saturations and fluid dktributions. Further 5. Van Summon. E.: “Three-PhaseRelative Penneabilitv Measurements
research is needed to reduce (or properly account for) capillary Using”theCenfise. Mefhod,’, paper SPE 10688pres~med at the ‘1982
end effects, to control hysteresis, and to minimize wettabiiily SPEIDOE Enhanced Oil Recovery Symposium, Tulsa, April 4-7.
changes involwd in flow experiments. Studies are needed on 6. ~;~oo~ J.: “Oil Recovery by Gravity Draiwrge,’- SPEJ (June 1980)
modeling complex displacements in reservoirs with flow tes~
performed at idealized laboratory conditions. Similarly, 7. Hemysi&, J., Black, C,J.J,, and Berry, J.F.: “Fundamema3sof Relative
improvements in interpretation of laboratory data and in Permeability Expaimentd and Theoretical Comiderations,,, paper SPE
scaling up for field use are still required, Until add~tionrd 12173 presemed at. the 1983 SPE Ammal Technical Conference and
Exhibidcm, San Francisco, Oct. 5-8.
advances in technology are made, the best course of action is
8. Levine, J.S.: “DispImermnt Experimentsin a Consolidatedporous 5ys-
to generate both steady- and unsteady-state laboratory data, tmn, s, JPT (Mzcb 1954) 21-3% TrmLs., AIME,
under simulated reservoir conditions, on carefully selected and 9. Bafycky, J.P. t=rcd.: ‘Ynterpretirg Relative Permeability and Netta-
preserved cores. bility Fmm Unsteady-State Displacement Measurements,,, SPEJ (June
1981) 296-308,
References 10. Bra.., E.M. and Blackwdl, R,],: ‘LASteadyWate Tdmiqw for Ma-
uring Od-Waler RelativePermeabilityC.rves at Re$avoir Cmdiiom,,,
1. Honarpour, M., Kcm&riu, L,F,, and Ham.q, A, H.: Rekui.e
Penmabiliy of Pcwokwn Reservoirs, CRC Press Inc., B.xa Ratcm, PaPer SpE 10155 Piesenfed at the 1981 SPE Annuat TechnicaJ Con-
ference md Exhibitim, San Antonio, Oct. G7.
FL (1986).”
2. Ro;, W, ; “Rd/lfive Penneabilhj,,, Pemkwn Production Hmdbook, J3’T
SPE, Richmdsm, TX (1987), Chap. 28, 28-l-28-16.
3. Johnson, E. F., Bowler, D. P., and Nauman., V. O.: “Catudation of ml. paperis SPE i 8565, Technology Today S.68s wM., provide useful s.mmwy in.
format
ion.. bo!h classic and enwming .oncepls In petroleum engineering. Purpose To
Relativepemneab~ Fmm DisplacememEx@ments,,, Trans., AIME Pr.vfde the 9e.e~l reader with a bsic ..dmtmm.+ a significant cmcepl, technlq..,
(1959) 216,370-72, or devd’opmmt WM. a specific ,,,8 of technology.