Correcting for Wettability and Capillary Pressure Effects...

Copyright 2000, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 2000 SPE Annual Technical Conference andExhibition held in Dallas, Texas, 1–4 October 2000.

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AbstractConventional formation tester interpretation techniques havelong assumed that the measured tester pressure is identical tothe pressure of the continuos phase in the virgin zone of theformation. As such, a series of pressure measurements atdifferent depths would be expected to consistently yield apressure gradient corresponding to the density of the formationfluid. Recent work by the authors of this papers as well as byothers has shown that the formation testers will actuallymeasure the pressure of the continuos phase present in theinvaded region, typically the drilling fluid filtrate. Themeasured tester pressure is, thus, different from formationpressure by the amount of capillary pressure. This capillarypressure has been shown to be a strong a function of thewetting phase saturation. The effects of the rock wettabilityand capillary pressure on wireline formation testermeasurements are manifested as pressure gradient changesand/or fluid contact level changes on many logs, particularlythose recorded with oil-based mud in the borehole.

This paper summarizes the effects of wettability and capillaryon wireline formation measurements and investigates in detailthe possible techniques for recognition and estimation of andcorrection for those effects. The older techniques rely on theuse of core capillary pressure data log-computed flushed zonesaturations, but they can often yield inconsistent results.Amongst the more innovative techniques suggested in this

paper is the use of NMR measurements to estimate themagnitude of capillary pressure effects and hence correct themeasured tester pressure. Also discussed in the use of thepump-out capability of the Modular Dynamics Tester(MDTTM) to estimate the capillary pressure effect by makingmeasurements before and after the removal of drilling mudfiltrate. This allows accurate correction for capillary pressureeffects, or better still, the elimination of the need for thecorrection altogether.

IntroductionIn an oil reservoir, water will normally compete with oil andgas for pore space. This is because water was present in thepores before oil migrated into the reservoir. Thus, at the samedepth in a formation, pressures will be different depending onwhether oil or water is filling the pores. The amount ofpressure difference between the two fluids is largely controlledby pore geometry, rock wettability and the interplay ofcapillary pressures between rocks and fluids. Capillarypressure (Pc), represents the pressure differential that must beapplied to the nonwetting fluid in order to displace a wettingfluid. The value of capillary pressure is dependent on thesaturation of each phase, on which phase is the wetting phase,and on the shape and size of the pores and pore throats.Wettability is the property of a liquid to stick to and spreadonto a solid surface. It is normally quantified by the value ofthe contact angle, such that a value less than 90 degreesindicates a water-wet system, and a value greater than 90degrees indicates an oil-wet system. The following paragraphstake a closer look at the wettability and capillary pressureconcepts.

WettabilityWettability is an important petrophysical parameter, whichdetermines the fluid distribution in a porous medium and thusaffects saturation and recovery. In order to minimize thesystem’s specific surface free energy, the wetting phase coatsthe surface of the solid grains, occupies the small pores, whichhave high specific surface area, and occupies the corners of

SPE 63075

Correcting for Wettability and Capillary Pressure Effects on Formation TesterMeasurements

H. Elshahawi, SPE, M. Samir, SPE, and K. Fathy, SPE, Schlumberger Oilfield Services

2 H. ELSHAHAWI, M. SAMIR, K. FATHY SPE 63075

grain contacts. The non-wetting phase, on the other hand, staysin the center of the pores and is concentrated in the largerpores. Fig.1 shows the situation that would occur if the rockhad a preference for being water-wet, wherein an isolateddroplet of oil is being squeezed from all directions by water.As a result, the pressure of the oil becomes higher than that ofthe surrounding water by an excess amount termed capillarypressure. On the other hand, if a rock is preferentially oil-wet,the reverse occurs, with the oil being the continuous phase andthe pressure being higher in the water. Fig.2 shows how thesurrounding oil in an oil-wet rock squeezes the water dropletsfrom all directions.

In their natural state, rocks may be either water-wet or oil-wetaccording to the atoms exposed in the grain or pore surface. Inthe case of water-wet rocks, they become thus when theoxygen atoms exposed at their surfaces attract hydrophilichydrogen from the water molecules. If polar impurities such asresins or asphaltenes can reach the surface, they will substitutelipophilic radicals for the H or OH, rendering the surfaces oil-wet (Chiligarian and Chen, 1983). Note that while only basicimpurities will attach to quartz, both basic and acidicimpurities can attach to calcite. This might explain the largepercentage of carbonate reservoirs found by severalresearchers to be oil-wet. Few formations are neutrally wet,but some researchers have reported fractional wettabilityconditions, in which some portions of the rock are stronglyoil-wet and others strongly water-wet (Chiligarian and Chen,1983). Salathiel (1972) identified mixed wettability reservoirsin which the polar impurities reach the larger but not thesmaller pores, resulting in a case wherein the larger pores(higher porosity) become oil-wet, the smaller pores (lowerporosity) remain water-wet, and both remain continuouslyconnected. He hypothesized that configurations of oil in poresinvolve either direct contact between oil and rock in the largergrains and pores (Fig.3); or separation of the oil phase fromthe solid by aqueous films in the smaller grains and pores(Fig.4). In the larger grains and pores, the oil saturation ishighest. When a critical capillary pressure is exceeded, waterfilms destabilize and rupture to an adsorbed molecular film ofup to several water mono-layers. Crude oil now contacts rockdirectly, allowing the polar oil species to adsorb and/or depositonto the rock. It is this process that locally reverses thewettability of certain sections of the rock from water-wet tooil-wet (Hirasaki et al., 1996). (Elshahawi et al., 1999) detailthe case of a mixed wettability reservoir which displays eitherwater-wet or oil-wet features depending on the petrophysicalproperties of the rock.

Capillary PressureCapillary pressure is defined by the following equation:Pc = Pnonwetting phase- Pwetting phase (1)where Pc is the capillary pressure and Pnonwetting phase, Pwetting phase

are the pressure of the nonwetting phase and wetting phase,respectively. The combined effects of wettability andinterfacial tension cause a wetting fluid to be simultaneously

imbibed into a capillary tube, an often used, yet admittedlysimplistic, representation of a pore throat. For the capillarytube, capillary pressure can be expressed as:

Pc = Pnw – Pw = 2σ cosθ/r = (ρw-ρnw) gh (2)

Where σ is the interfacial tension between the two fluids, θrepresents the wettability of the capillary tube, r is the radiusof the capillary tube, Pw, Pnw are the pressures of the wettingand non-wetting phases, respectively, and ρw and ρnw are thewetting and non-wetting phase densities, respectively. For apendular ring at the contacts of two spherical sand grains in anidealized porous medium consisting of a cubic pack ofuniform spheres (Fig. 5), the capillary pressure can beexpressed by the following Laplace equation (Eq.3).

Pc= σ (1/r1 + 1/r2) (3)

Where r1 and r2 are the two principal radii of curvatures of theinterface in two perpendicular planes as shown on Fig 5. Asthe wetting fluid saturation in the pendular ring is increased,the radii of curvature will be increased, and capillary pressurewill decrease. Vice versa, as the wetting fluid saturation in thependular ring is reduced, the radii of curvature will be reducedand capillary pressure will increase. This can be expressed inthe general form below:

Pc = fn(Sw) ∝ σ/rm (4)

Where rm represents mean radius of curvature. Of course, foran actual porous medium, the complexity of the pore structureand the fluid interface arrangements therein precludes the useof the above equation directly to calculate the capillarypressure. Instead, the capillary pressure is measuredexperimentally as a function of the wetting fluid saturation.

The Capillary Pressure CurveThe capillary pressure curve for a porous medium is a functionof pore size, pore size distribution, pore geometry, fluidsaturation, fluid saturation history or hysterisis, wettability,and interfacial tension. Fig.6 shows drainage and imbibitioncapillary pressure curves. The drainage capillary pressurecurve describes the displacement of the wetting phase from theporous medium by a non-wetting phase, as is relevant for theinitial fluid distribution in a water-wet reservoir as well as forthe water front advance in an oil-wet reservoir. The imbibitioncapillary pressure curve, on the other hand, describes thedisplacement of a non-wetting phase by the wetting phase, asis relevant for water front advance in a water-wet reservoir. Inboth cases, the capillary pressure is equal to the non-wettingphase pressure minus the wetting phase pressure as given byEq.2. The capillary pressure curve has several characteristicfeatures. Focusing on the drainage curve and describing it inmore detail, one finds that the minimum threshold pressure isthe displacement pressure that must be applied to the wettingphase in order to displace the non-wetting phase from thelargest pore connected to the surface of the medium such that:

Pc(Displace)=(Pnw–Pw)displace=2σcosθ/rLargest pore…………………..…...(5)

SPE 63075 CORRECTING FOR WETTABILITY AND CAPILLARY PRESSURE EFFECTS ON FORMATION TESTER MEASUREMENTS 3

A lower displacement pressure indicates larger poresconnected to the surface, which generally implies higherpermeability. As the pressure of the non-wetting phase isincreased, increasingly smaller pores are invadedcorresponding to the flat section of the curve. A lowercapillary flat section indicates larger pores, and consequentlyhigher permeability. A capillary pressure curve that remainsessentially flat over its middle section indicates that manypores are being invaded by the non-wetting fluid at the sametime, implying that the grains are well sorted and the rock isfairly homogeneous. Inversely, the higher the slope of themiddle section of the capillary pressure curve, the worse thesorting and the wider the grain and pore size distributions.Such a rock has lower porosity and generally lowerpermeability as well. A very steep capillary pressure curve thatis nearly vertical over its middle section implies poor reservoirrock with extremely fine grains, very poor sorting, lowporosity, and low permeability. Eventually, when theirreducible wetting fluid saturation is reached, the capillarypressure curve becomes nearly vertical. At this stage, thewetting phase becomes discontinuous and can no longer bedisplaced from the porous medium simply by increasing thenon-wetting phase pressure. A lower wetting phase irreduciblesaturation is generally indicative of relatively larger grains andpores. Generally speaking, therefore, a higher capillarypressure curve describes poorer reservoir quality compared toa lower curve.

The Static Pressure Gradient of a ReservoirAll petroleum reservoirs were initially saturated with waterbefore oil migrated into the reservoir, displacing the water.The resulting fluid distribution is governed by the equilibriumbetween gravitational and capillary forces. In the case of awater-wet reservoir, this distribution is simulated by adrainage capillary pressure curve. The Free water level (FWL)in a reservoir is the level at which the oil-water capillarypressure vanishes. It is the oil-water interface that would existat equilibrium in an observation borehole, free of capillaryeffects, if it were to be drilled in the porous medium and filledwith oil and water. The Oil-water contact (OWC), on the otherhand, is the level at which oil saturation starts to increase fromsome minimum saturation. In a water-wet rock, that minimumsaturation is essentially zero. Using the FWL as the referencedatum, The water and oil phase pressure at a distance z abovethe FWL datum are given by the following two expressions:

Pw(z) = PFWL - ρwgz (6)

Po(z) = PFWL - ρogz (7)

Subtracting the two equation yields an expression for thecapillary pressure, Pc:

Pc(z) = (ρwgz - ρogz)/144 = ∆ρgz/144 (8)

where Pc is in psi, ∆ρ is in lbm/cu.ft, and z is in ft. The FWL isgenerally not coincident with the OWC but, instead, differs byan amount related to the displacement pressure. In a water-wet

reservoir, the FWL occurs at a depth do below the oil-watercontact given by:

do = (PD/∆ρg) x 144 (9)

where PD is the displacement pressure (oil displacing water) inpsi, ∆ρ is in lbm/cu.ft, and z is in ft. It is determined by largestpore of the pore size distribution. The capillary transition zone(Fig. 10) is the region above the OWC where the watersaturation decreases from its maximum to the irreduciblewater saturation. The height of the transition zone is a functionof wettability, the fluid density contrast, and the oil-waterinterfacial tension. The shape of this transition zone is alsodependent on the same factors that affect the capillary pressurecurve. The elevation (h) above the OWC of any particularsaturation within the transition zone is given by:

h(Sw) = (Pc(Sw) - PD) /∆ρg x 144 (10)

In an oil-wet reservoir (Fig.11), the situation described aboveis slightly different. In this case, it is the water that is the non-wetting phase, and hence, its pressure is higher than it wouldbe in a water-wet medium. Even though the reservoir wasinitially saturated with water before oil migrated into thereservoir and displaced the oil, an imbibition capillarypressure curve, rather than a drainage curve better describesthe situation once the reservoir has become preferentially oil-wet reservoir. As an imbibition curve would predict, theminimum oil saturation encountered below the zero capillarypressure line is not zero, but rather a residual value, Sor. Sinceit is easier to displace water than oil in this case, the portion ofthe capillary pressure curve below the zero line (correspondingto the FWL) is larger than the part above. Consequently, heOWC in this case is the lowest level that the oil will reach (atwhich the oil saturation will start to increase from itsminimum value). The FWL is located above the OWC by adistance do given by: do = (PD/∆ρg) x 144 (11)

Which is generally larger than the equivalent distance in awater-wet rock. Also unlike for a water-wet reservoir, thisdistance is determined by the smallest-rather than the largest-pore of the pore size distribution.

Recognizing Wettability and Capillary PressureEffects on Tester Gradient MeasurementsConventional formation tester interpretation methods assumethat the tool measures the true formation pressure of thecontinuous mobile formation fluid in the virgin zone. Thefallacy of this assumption is made clear by examining Fig.7 (ato h), which details the saturation profile for various wettingfluid-drilling mud-formation fluid combinations. Fig.8 (a to h),on the other hand, details the capillary pressure distributioncorresponding to each combination while Fig.9 (a and b)details the effect of these combinations on the wirelinepressure tester gradient measurements. For a well drilled withwater-based mud in a water-wet formation, the oil in theflushed zone of an oil-bearing interval (Fig.7-c) is close toresidual saturation so that the capillary pressure in the invaded


zone becomes small (Fig.8-c). The result is that the water-phase pressure actually measured is only marginally lowerthan the oil phase pressure that we desire to measure, shiftingthe oil gradient slightly to the left (top of left plot of (Fig.9-a)).In the water-bearing interval (Fig.8-a), there will be nocapillary pressure difference between the mud filtrate and theformation water, and the tool measures the true formationpressure (Fig. 8-a) and (bottom of left plot of (Fig.9-a)).

For a well drilled with oil-based mud in a water-wetformation, there is no capillary pressure difference betweenthe mud filtrate and the formation oil in an oil-bearinginterval. Thus, the tool measures the actual formation gradient(Fig.7-d), (Fig.8-d) and by The formation tester over-estimatesthe value of the true formation gradient by In the water-bearing zone (Fig.7-b), the water saturation in the invadedzone is close to connate or irreducible, and the capillarypressure is large (Fig.8-b). The value of the oil pressureactually measured is thus higher than the water pressure that isdesired by Pc(Swc). The measured water gradient is thusshifted to the right (bottom of right plot of (Fig.9-a)). In a gasreservoir drilled with oil-based mud, the pressure measured inthe water zone is similarly boosted by an amount equal to thecapillary pressure. The situation is further complicated by theexistence of three phases but can be simplified by treating thewater and oil as a single wetting phase and the gas as the non-wetting phase which controls the capillary pressure. In theinvaded zone, however, gas saturations are normally close toresidual levels, and the capillary pressure is nearly nil, so thecapillary effect on the pressure measurement can be safelyneglected.

For a well drilled with water-based mud in an oil-wetformation, the oil in the flushed zone of an oil-bearing intervalis close to residual saturation (Fig.7-g), and the capillarypressure is maximum (Fig.8-g). The measured water phasepressure is higher than the oil phase pressure by the amount ofPc(Sor). The formation tester thus over-estimates the value ofthe true formation pressure, shifting the oil gradient line to theright (top of left plot of (Fig.9-b)). In the water-bearinginterval, there will be no capillary pressure difference betweenthe mud filtrate and the water, and the tool measures the trueformation gradient (Fig.7-e, Fig.8-e and bottom of left plot of(Fig.9-b)).

For a well drilled with oil-based mud in an oil-wet formation,there is no capillary pressure difference between the mudfiltrate and the formation oil in an oil-bearing interval, so thetool measures the actual formation gradient (Fig.7-h, Fig. 8-hand top of right plot of (Fig.9-b)). In the water-bearing zone,the water saturation in the invaded zone is close to irreducible,and the capillary pressure is a small value (Fig.7-f and Fig.8-f). The result is that the measured oil pressure is slightlylower than the desired water pressure. Thus, the measuredwater gradient is slightly shifted to the left (bottom of left plotof (Fig.9-b)).

When one of the two phases becomes discontinuous at lowsaturation, its pressure follows the gradient of the other(continuous) phase. The pressure of a discontinuous phase isunobservable except under lab conditions and is of nopractical importance. In silty sandstone reservoirs, theirreducible water saturation corresponding to the top of thecapillary transition zone may be quite high yet the oil phase iscontinuous and the well produces oil. A magnetic resonancelog would be able to differentiate moveable from bound fluid,but if only conventional logs are available, potentialrecoverable oil will probably be missed. In such a case,formation tester gradients can be used to distinguish betweenmoveable oil, which appears as a continuous oil gradient onthe pressure measurements despite the high water saturation,and residual oil, which appears as a continuous water gradient.The importance of this for reserve estimation is obvious.

Recognizing Wettability and Capillary PressureEffects on Tester Fluid Level MeasurementsThe effects of wettability and capillary pressure on thewireline formation tester’s fluid level measurement are closelylinked to their effects on gradient measurements. Ordinarily,the intersection of the continuous phase pressure lines on adepth-pressure diagram occurs at the FWL as shown in Fig.10and Fig.11 for water-wet and oil-wet reservoirs, respectively.The intersection of the water and hydrocarbon continuousphase pressure lines as measured by the wireline formationtester is an indication of the FWL. In general, however, thisintersection will differ from the FWL in a direction thatreflects the rock wettability and by an amount that isdependent on the degree of wettability, the magnitude ofcapillary pressure, and the type of drilling mud used (Fig.9aand b).

In a water-wet medium, the capillary pressures in the oil-filledpores are higher than in the water-filled ones, and the FWL islocated below the OWC by a distance determined by thecapillary threshold or displacement pressure (Fig.10). Asshown in Fig.9-a, the actual intersection of the oil and watergradients from the wireline formation will be generally higherthan the true FWL. This is true for wells drilled with eitherwater and oil-based muds. As explained in the previoussection, with water-based mud (WBM) in the oil zone, themeasured pressure will be the water phase pressure, which willbe lower than the oil phase pressure we are aiming to measure.Therefore, the measured oil line will be shifted to the left ofthe true formation oil pressure line, making the intersectionhigher than the actual FWL (left plot of Fig.9a). On the otherhand, with an oil-based mud (OBM) in the water zone, themeasured pressure is the oil filtrate pressure, which will begreater than the water phase pressure. Thus, the measuredwater line will be shifted to the right of the true formationwater pressure line, making the intersection again higher thanthe actual FWL (right plot of Fig.9a).


In an oil-wet medium, the capillary pressures in the water-filled pores are higher than in the oil-filled pores, and the FWLis located above the OWC by a distance again determined bythe capillary threshold or displacement pressure (Fig.11). Theactual intersection of the oil and water gradients from thewireline formation tester will be generally lower than the trueFWL as shown by Fig.9b. This is true for wells drilled witheither water and oil-based muds. As discussed in the previoussection, with a WBM in the oil zone, the measured pressurewill be the water phase pressure, which will be higher than theoil phase pressure we are aiming to measure. Therefore, themeasured oil line will be shifted to the right of the trueformation oil pressure line, making the intersection lower thanthe actual FWL (left plot of Fig. 9b). On the other hand, withOBM in the water zone, the measured pressure is the oilfiltrate pressure, which will be lower than the water phasepressure. Thus, the measured water line will be shifted to theleft of the true formation water pressure line, making theintersection again lower than the actual FWL (right plot ofFig. 9a).

Fig. 12 and Fig.13 show how rock wettability was detected in-situ in a mixed-wettability sandstone by its effect on thewireline formation pressure measurements (Hiekal at al.,1998). Fig.12 shows the OWC at a depth of 4835 ft-TVDss,20 ft-TVD below the FWL at 4815 ft-TVDss in a highporosity system of the reservoir with strong preference to beoil wet. On the other hand, Fig.13 shows the OWC at a depthof 4835 ft-TVDss, 35 ft-TVD above the FWL at 4870 ft-TVDss in a low porosity system reservoir which has a strongaffinity to be water-wet.

Recognizing and Correcting for SuperchargingEffects on Formation Tester MeasurementsAs a consequence of mud filtrate invasion in the immediatevicinity of the wellbore, the formation may exhibit pressureshigher than the actual formation pressure. This over-pressuretends to dissipate when a mud cake is established and furtherinvasion becomes negligible. Even if a mud cake is built,however, this overpressure may still exist at the time of thepressure measurement. This effect is called supercharging andshould not be confused with capillary or intrinsic formationover-pressures. Such confusion is common sincesupercharging is similar to capillary over-pressure effects inthe sense that both are inversely related to effectivepermeability. As a consequence of supercharging, allpermeable zones are locally, and often temporarily, over-pressured by the invading filtrate. Levels affected bysupercharging in either the oil or the water zones will appearto the right of the expected formation pressure line, withgradients tending to be more scattered as the mobility of themeasured phase decreases. In capillary transition zones, whereoften both oil and water phases are mobile, the total mobilityis reduced, leading to an increase in the possibility ofsupercharging. As the pressure difference between the mudcolumn and the formation increases with depth, and with

everything else being equal, supercharging could possibly leadto an apparent increase in gradient.

The primary factors affecting supercharging are the degree ofpressure differential across the sand-face, the extent of mudcake build-up and its effectiveness in preventing filtrate-fluidloss into the formation, and the total mobility of the formation.Fergusson and Koltz (1954) defined three stages of mudfiltrate invasion. These are the initial spurt loss leading to arapid buildup of mud cake; the dynamic filtration, whichoccurs when the mud cake attains an equilibrium thicknessand while mud is still circulated; and the static filtration whichtakes place after circulation of the mud has ceased. Halford(1983) reviewed the processes of mud filtrate invasion andmade some conclusions, which can be summarized as follows.Firstly, if filtration is governed by the mud cake, which is thecase except in very low permeability formations, then afterseveral hours, the dynamic rate converges to a constant rateequilibrium rate. Secondly, after about fifteen hours of staticfiltration, which is typical of the condition wherein formationtester surveys are run, that static loss rate may be consideredconstant. Thirdly, oil-based muds show lower dynamic andstatic loss rates compared to water-based muds. Despite thislatter conclusion, oil-based muds do not always form mudcakes, and dynamic filtrate invasion continues even during thewireline formation tester survey. In extreme cases, evenmoderately high permeability zones may appear superchargedat the time of the survey.

To reduce the effects of supercharging, the formation testersurvey should be run as late as possible after a circulation ofthe well in order to maximize the time-dependent decay of therelatively large dynamic filtrate loss-rate. In fact, theusefulness of the widely used practice of routinely runningwiper trips prior to wireline formation tester surveys is ratherdubious, since these trips often only serve to stir up the mudcolumn and scrape off the mud cake, leading to increasedfiltration rates, increased supercharging effects, and greaterchances of getting differentially stuck. The true formationpressure can be obtained by applying a correction technique tocorrect the effects of supercharging in low permeabilityformation. This method can be applied by measuring Pbh“wireline borehole pressure” and Pwf “wireline formationpressure” more than two times at the same point. By plottingPwf versus Pbh, the true formation pressure is obtained at thepoint where a line drawn through the data crosses a 45o linewith Pbh =Pwf as shown in Fig.14. This technique was appliedto correct the effect of supercharging in a low-permeabilityformation. Fig.15 shows the pressure profile obtained with theformation tester tool. Two pretest points were identified assupercharged. The pretests were repeated after applying 300 atthe mud column. The measured pressures changed at bothdepths, and the correction was computed according to thetechnique described above.


Using NMR to Correct for Wettability and CapillaryPressure EffectsOne possible method of correcting for wettability and capillarypressure effects on wireline formation tester pressures is toconstruct the Leverett J-function (Leverett, 1941) for thereservoir from core samples and transform it to reservoir fluidconditions. The Leverett J-function is, defined as:

J(Sw) = (6.848 Pc √(k/φ)lab)/(σ cosθ)lab

= (6.848 Pc √(k/φ)res)/(σ cosθ)res (12)

Lab (core) capillary pressure data can thus be translated toreservoir conditions as follows:

Pc)res = Pc)lab√((φres klab)/(φlab kresevoir))x((σcosθ)res/(σ cosθ)lab) (13)

It is possible to correct the measured formation pressure ateach point by adding (or subtracting) the capillary pressurecorresponding to the value of invaded zone saturation (Sxo)measured at that point (Awad, 1982) such that

Pcorrected = Pmeasured + Pc(Sxo) (14)

If a nuclear magnetic resonance (NMR) log is available, thenthe downhole capillary pressure correction can be computeddirectly.

The NMR signal originates from the hydrogen nuclei presentin the pore fluids. The initial signal amplitude provides totalporosity while the signal relaxation or decay rate providesindication of pore size. Under some plausible assumptions, thetransverse relaxation time of the NMR signals from fluids inan individual pore is proportional to its surface-to-volumeratio. This transverse relaxation time is termed T2-deacy. Thetotal NMR signal, being the superposition of signals from adistribution of individual pores, is simply a summation of theindividual exponential decays. A T2-distribution is displayedby plotting the amplitudes versus their associated relaxationtimes on a logarithmic scale. The computed T2-distribution isused to compute logs of NMR porosities, free fluid porosities,capillary bound fluid porosities and logarithmic meanrelaxation times. In a rock where the saturating phase is thesame as the wetting phase, T2-relaxation will relate directly topore size. Providing T2-relaxation takes place within the fast-diffusion limit, and the transverse surface relaxivity (ρ2) isknown, T2 can be converted to pore size and capillarypressure using the following process (Marschall et al, 1995):

1) Convert T2 to pore size (Fig. 16) using data obtained fromcore analysis (e.g. laboratory NMR vs Mercury InjectionCapillary Pressure, MICP) or from published scaling factorssuch as those found in the NMR Sandstone and CarbonateRock Catalogs, if core data is not available (Kleinberg, 1996).

2) Convert pore size to a cumulative plot by summing NMRnon-shale porosity (φEffective) such that φ at max porediameter=0, and φ at min pore diameter=(φEffective). Wheneversmall pores (short T2's) can be shown to relate to clay-bound

water, they should be removed from the total NMR porositybefore summing up, otherwise clay-bound water will betreated as capillary bound water in the conversion to Pc.

3) Convert pore size to capillary pressure using equation 15(Fig. 17) Capillary pressure can be computed for dualcombinations of gas/air/water/oil/mercury using appropriateinterfacial tension and contact angle constants.

The number of pressure steps in the T2-derived Pc curvedepends on the number of points or bins used in the inversionof the time-domain data (echo train), which in turn is limitedby the signal to noise ratio. Core NMR experiments typicallyachieve S/N levels > 100/1, which allows 50 to 100 points tobe used in the inversion. Log NMR experiments typicallyachieve S/N levels <10/1, which allows between 10-30 pointsto be used in the inversion. Stacking the log data will increaseS/N and hence the number of points used in the inversion, butstacking will also reduce the vertical resolution of themeasurement.

In wells drilled with oil-based mud (OBM), or where there is anative oil remaining in the flushed zone, the T2 distributionwill contain a combination of pore size and bulk fluidinformation. In water-wet rocks, the lower mode at short T2snormally represents bound water (unless gas or heavy oil ispresent) and contains pore size information because water is incontact with the pore walls. On the other hand, the mode atlong T2s represents oil from the OBM filtrate, formation oil,or a combination of these and contains bulk fluid informationbecause the oil is not in contact with the pore walls. Underthese conditions, only the early part of the T2 distribution canbe converted to pore size, and hence Pc. Generating thecomplete Pc curve (i.e. Sw=0-1) requires extrapolation of theT2 distribution out to long T2s.

Volikitin et al. (1999) presented a method for completing theT2 distribution in rocks with partial water saturation. Theirmethod uses a predicted mean T2 value obtained from anempirical relationship between geometric mean T2 and Swirr.A moveable water spectrum is then added to the T2distribution such that the sum of amplitudes equals porosity,and the resultant mean T2 value matches the predicted meanT2 value.

Thomeer (1960) and Swanson (1981) showed the maximumturning point on a hyperbola fitted through an air/mercurycapillary pressure curve (log Pc vs log Sw expressed as %bulk volume) could be used to predict permeability. Based onthis work, Lowden (2000) developed a method predicting theT2 values at long times by fitting a hyperbola through theearly times. The method involves converting T2 and

cumulative NMR porosity to log scales with 1/T2 (∝Pc) on

the Y-axis and NMR porosity (∝ Sw) on the X-axis Fig. 18a.The data is normalized such that they both sum up to unity sothat it is in a form suitable for fitting a rectangular hyperbola.


A curve is then fitted through the data ensuring the best matchoccurs at short T2s equation 16. The shape of the curve isadjusted by changing the point where the asymptotes to thecurve intercept the X and Y axes, and by adjusting theexponent a for values of Y ranging from 0 to 1. The values ofX and Y for the predicted curve are then converted toconventional units, Sw (%), and Pc (psi), to generate thecomplete Pc curve (Fig. 18b). A drawback of this curve fittingmethod compared to the method of Volikitin is that it does nottake into account fluid lining the walls of large pores. Pore-lining fluid increases amplitude (porosity) at short T2s, and inorder to generate a correct Pc curve, this additional porosityshould be redistributed to long T2s (=large pores). If pore-lining fluid is expected, the fitted curve should be shifted justbelow the actual curve, thus redistributing the pore lining fluidto longer T2s since the sum of porosities is always maintainedat the same value.

Using the MDT to Overcome Wettability andCapillary Pressure EffectsThe state of the art Modular Dynamics Tester MDT offersconvenient solutions to overcome the wettability and capillarypressure effects described earlier. The MDT can beequipped with a probe module (similar to RFT probe) and withan inflatable dual packer module simultaneously (Fig. 19).More information about MDT can be found in Zimmerman etal. (1998). The measurement of the formation pressure withMDT single probe follows the same principle as the RFT,however, it has more advanced features. The MDT probereading will be affected by capillary pressure in a similar wayas the RFT when carrying out a standard pretest. The abilityto “pump out” mud filtrate enables the measurement offormation pressure before and after capillary pressure effectremoval, and hence allows the estimation of the amount ofcapillary pressure. The same facility also minimizessupercharging and reduces its disturbing effect on themeasured gradients. On the other hand, the flow identificationabilities of the MDT such as the flow line resistivity and theoptical fluid density can indicate the type and quantity of mudfiltrate as well as the moveable reservoir fluid, which wouldhelp establish and confirm and correct the measured pressuregradient.

The dual packer module is made of two inflatable rubberelements. Each element is about one meter and the distancebetween them is about one meter. The two elements areinflated in with a downhole pump out module isolating one-meter or longer of the formation between the two elements.The same downhole pump is activated to remove the mudfiltrate and to pump it to the borehole, until formation fluid issensed via an optical fluid analyzer. Once the pump outs isstopped, a build-up is initiated to measure the "true" formationfluid phase directly. This pressure will be little affected bycapillary pressure effects since mud filtrate is removed beforeprior to making the measurement. The dual packerarrangement provides the ability to test formations too tight or

too unconsolidated to respond to the standard probe. Anexample is shown in Fig. 20. Without pumping out, the singleprobe measures the mud filtrate pressure. Assuming a water-wet system, the water base mud filtrate pressure (wettingphase) can be expected to be lower than the gas pressure (non-wetting phase) by the amount of capillary pressure. Asexpected, the single probe data reads less than the trueformation pressure in the gas zone due to capillary pressureeffects. The dual packer, on the other hand, yields what can beconsidered as true pressure because its measurements weremade after the mud filtrate had been pumped out for nearly 20mins at each depth. Note also that the FWL measured by thesingle probe is displaced upward when compared to the dual-packer-indicated contact. This situation is very similar to thehypothetical one depicted in Fig. 9(a).

Correcting for Wettability and Capillary PressureEffects in the Absence of NMR and MDTMasurements

There are many cases in which neither core data nor NMRdata is available, and in which MDT could not be run forwhatever reason. In these cases, it is possible to derive apseudo-drainage capillary curve similar to fig. 10 and 11 byplotting the height above the OWC in the transition zone vs.the water saturation as computed from the openhole logs. Thistype of correction generally results in adjustment of thegradient towards the correct direction but may result in largescatter. This is due to the simplicity of this type of correctionthat fails to take into account the vertical flow occurringwithin the invaded zone as detailed earlier. It is important torealize that without correction, the intersection of thehydrostatic gradients in a well drilled with OBM in a water-wet reservoir will indicate the top of the transition zone ratherthan the actual FWL. This is a potentially very usefulmeasurement in its own right as it indicates the highestproducible water level.

Conclusions1. Wireline formation testers measure the pressure of the

continuous phase present in the invaded region.2. Conventional interpretation techniques assume that this

pressure is identical to the pressure of the formation fluid,implying that the wireline tester measurement isunaffected by the invasion process. This in not true asproven by many field examples, particularly in OBM.

3. The concepts of free fluid level, fluid contacts, rockwettability, and pore fluid pressures are intimately related.

4. The effect of wettability and capillary pressure will makethe measured formation pressure either too high or toolow depending on the specific wetting fluid-drilling mud-formation fluid combination. This will result in shiftedgradient lines, altered gradient slopes, or greater scatter.

5. In a water-wet medium, the FWL is expected to occurbelow the OWC, while in an-oil wet medium, the FWL isexpected to occur above the FWL.


6. In a water-wet medium, the measured contact willgenerally appear too high compared to the FWL, while inan oil-wet medium, it will generally appear too lowcompared to the FWL. In the latter case, the measuredcontact will indicate the highest producible water level.

7. Capillary pressure effects can be corrected for, providedcore and intermediate zone saturation data are available.NMR data may supplement or replace these sources.

8. The MDT offers several features that reduceuncertainties arising from capillary and superchargingeffects. These include the ability to pump out mud filtrateand formation fluid. Overcoming capillary pressureaffects is possible by removing mud filtrate before takingthe measurement.

ReferencesAwad, M.: “Phase Pressure Measurement by the RFT in theHydrocarbon Zone,” prepared for the 2nd WirelineInterpretation Symposium, Ridgefield, 12-15 July, 1982.

Chilingarian, G.V. and Chen, T.F.: “Some Notes onWettability and Relative Permeabilities of Carbonate Rocks,Energy Sources,” Vol.7, No.1 (1983), pp. 67-75.

Elshahawi, H., Samir, M. and Fathy, K.: “Wettability andCapillary Pressure Effects on Wireline Formation TesterMeasurements, ” SPE Annual Technical Conference andExhibition held in Houston, Texas, Paper No. 56712, 3–6October 1999.

Hiekal, S., Kamal, M., Hussein, A and Elshahawi, H.: “TimeDependence of Swept Zone Remaining Oil Saturation In aMixed-Wet Reservoir,” Paper presented at SPWLA Japan, 24-25 September, 1998.

Hirasaki, G.J.: “Dependence of Waterflood Remaining OilSaturation on Relative Permeability, Capillary Pressure, andReservoir Parameters in Mixed-Wet Turbidite Sands,” SPEReservoir Engineering, May 1996.

Kaminsky, R. and Radk, C.J.: “water Films, Asphaltenes, andWettability Alteration,” SPE/DOE IOR Symposium, Tulsa,Oklahoma, Paper No. 39087, 19-22 April 1998.

Kleinberg, R.L., 1996. Utility of NMR T2 Distributions,Connection with Capillary Pressure, Clay Effect, andDetermination of the Surface Relaxivity Parameter rho2.Magnetic Resonance Imaging 14, 761-767.

Leverett, M.C.: “Capillary Behaviour in Porous Solids,” TransAIME (1941), Vol. 142.

Lowden, B.: “Some Simple Methods for RefiningPermeability Estimates from NMR and Generating CapillaryPressure Curves,” Published in DiaLog (The On-lineNewsletter of the London Petrophysical Society), Vol. 8, IssueI, March 2000.

Marschall, D., Gardner, J.S., Mardon. D., and Coates, G.R.,1995. Method for correlating NMR relaxometrry and Mercury

Injection Data. Trans. International Symposium of the SCA,San Fransisco, California. Sept. 12-15, 1995.

Purcell, W.R., 1949. Capillary Pressures - Their MeasurementUsing Mercury and the Calculation of PermeabilityTherefrom. Pet. Trans. AIME. 186, 39-48.

Phelps, G.D., Stewart, G., and Peden, J.M.: “The Analysis ofthe Invaded Zone Characteristics and Their Influence onWireline Log and Well Test Interpretation,” SPE 13287(1984).

Salathiel, R.A.: “Oil Recovery by Surface Film Drainage InMixed-Wettability Rocks,” Journal Schlumberger: MiddleEast Well Evaluation Review, November 7, 1989, pp. 36-39.

Swanson, B.F., 1981. A Simple Correlation BetweenPermeabilities and Mercury Capillary Pressures. Jour. Pet.Tech. Pp 2498-2504.

The NMR Sandstone Rock Catalogue. 1997. AppliedReservoir Technology Ltd.

The NMR Carbonate Rock Catalogue. 1999. AppliedReservoir Technology Ltd.

Volokitin, Y., Looyestijn, W., Slijkerman, W., and Hofman, J.,1999. Constructing Capillary Pressure Curves From NMR LogData in the Presence of Hydrocarbons. Trans 40th AnnualLogging Symposium, SPWLA, Oslo, Norway, paper KKK.

Zimmerman,T., Maclnnis, J, Hoppe, J. and Pop, J., 1998:“Application of Emerging Wireline Formation TestingTechnologies”

_______________________________________

Trademark of Schlumberger


Water

Oil

Fig.1-Schematic of Pore Cross-section in a water-wet porousmedia, (grains rock are surrounded by thin film of brine andare not contacted by oil).

W ater

O il

Fig.2-Schematic of Pore Cross-section in an oil-wet porousmedia, (grains are surrounded by thin film of oil and are notcontacted by water).

Fig.3-In larger grains/pores, the water film ruptures, and oiland rock in direct contact, locally altering wettability topreferentially oil-wet.

Fig.4:-In smaller grains/pores, the water film covers the grainsurfaces completely, thus maintaining those grains water-wet.

Solid

r2

r1

Solid

Fig.5-Radii of curvatures for pendular rings around a sphericalsand grain junction.

Fig.6-Drainage and imbibition capillary pressure curves for awater-wet system.

10
H. ELSHAHAWI, M. SAMIR, K. FATHY SPE 63075
1-Sor

Sor

1-Swc

Swc

So

Sw

1-Sor

Sor

1-Swc

Swc

1-Swc

1-Swc

Swc

Swc

1-Sor

1-Sor

Sor

Sor

OBMInvaded zone Virgin zoneIntermediate zone

WBMInvaded zone Virgin zoneIntermediate zone







Figure 7-d: Saturation Profile, Oil Zone & Water WetFigure 7-c: Saturation Profile, Oil Zone & Water Wet

Figure 7-f: Saturation Profile, Water Zone & Oil Wet.Figure 7-e: Saturation Profile, Water Zone & Oil Wet.

Figure 7-h: Saturation Profile, Oil Zone & Oil WetFigure 7-g: Saturation Profile, Oil Zone & Oil Wet.

Figure 7-b: Saturation Profile, Water Zone & Water WetFigure 7-a: Saturation Profile, Water Zone & Water Wet

Sw

Sw

Sw

Sw

Sw

Sw

Sw

So

So

So

So

So

So

So


Pw

Po

Pw

Pw

Po

Pw

Po

Po

Pw

Pw

Po

Po



no oil phase

no water phase







Figure 8-g: Capllary Pressure Profile, Oil Zone & Oil Wet

Figure 8-h: Capllary Pressure Profile, Oil Zone & Oil Wet

Figure 8-e: Capllary Pressure Profile, Water Zone & Oil Wet

Figure 8-f: Capllary Pressure Profile, Water Zone & Oil Wet

Figure 8-c: Capllary Pressure Profile, Oil Zone & Water Wet

Figure 8-d: Capllary Pressure Profile, Oil Zone & Water Wet

Figure 8-b: Capllary Pressure Profile, Water Zone & Water Wet

Pw

Figure 8-a: Capllary Pressure Profile, Water Zone & Water Wet

12 H. ELSHAHAWI, M. SAMIR, K. FATHY SPE 63075D

epth

Dep

th

True PressureMeasure Pressure

Wireline tester interpretation

Free water level

P

Water Base Mud Oil Base Mud

True PressureMeasure Pressure

Free water level

Water Base Mud Oil Base Mud

Dep

th

Dep

th

ressure Pressure Pressur

OWC

Pc

00

Reservoir

FWL

Oil

Dep

th

Water

OWC

0

Reservoir

FWL

OilDep

th

Water

Fig.9-a: Capillary pressure effects on pressuremeasurement in a water wet system

Fig.10-Fluid pressure, capillary pressure, and saturation d

Fig.11-Fluid pressure, capillary press

irreducible watersaturation, water maybecome disconnected

irreducible watersaturation, water maybecome disconnected

Wireline tester interpretation

e Pressure

Capillarythreshold

Sw (%)

Capillary curve

Transition zone

100

Sw (%)

Pc

Capillary curve

Transitionzone

100

Fig.9-b: Capillary pressure effects onpressure measurement in an oil wet system

istribution a water-wet reservoir

ure, and saturation distribution an oil-wet reservoir


-5000

-4950

-4900

-4850

-4800

2200

2250

2300

2350

2400

2450

Pressure (PSIA)

Dep

th, T

VD

ss, f

t

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Saturations and Porosity, (Fraction)

Oil Water Sw-A1 fOH Linear (Water) Linear (Oil)

OOWC

FWL

φφφφ oh

Fig.12-Example of pressure behavior in oil-wet NubianSandstone rocks from well L7.

-5000

-4950

-4900

-4850

-4800

-4750

220

0

225

0

230

0

235

0

240

0

245

0

250

0

Pressure (PSIA)

Dep

th, T

VD

ss, f

t

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Saturations and Porosity, (Fraction)

Oil Water Sw-A1 fOH Linear (Water) Linear (Oil)

OOWC

Swoh

FWL

φφφφ oh

Fig.13-Example of pressure behavior in water-wet NubianSandstone rocks from well A1.

Wireline borehole pressure

Wir

elin

e fo

rmat

ion

pres

sure Pfw = Pbh

Pfw

Pbh

Data

Fig.14: Wireline formation pressure plotted against wellborepressure.

X200

X220

X240

X260

X280

X300

X320

Dep

th, f

t

Pressure, psiX670 X680 X690 X700 X710 X720

corrected points

Supercharged

Fig.15: Pressure profile showing how two supercharged pointsfall into the formation gradient line after correction.


Fig. 16 : T2 distribution for brine-saturated core plugconverted to pore size using a scaling factor (~rho2)obtained from MICP analysis conducted on an end trimfrom the same plug

Fig. 17: A T2 derive air/mercury capillary pressure curveobtained for a brine-saturated core plug. The predicted Pccurve is plotted against MICP data for the same sample. Thered circle shows the threshold pore size controlling flow.

Fig. 18 a-b: Illustration of the method used to generate a capillary pressure curve from NMR data when part of the signalis dominated by bulk fluid response. Panel A shows an hyperbolic curve fitted through the short T2s. Panel B shows thecomplete Pc curve obtained from the equation for the fitted curve.

SPE 56613 CAPILLARY PRESSURE AND ROCK WETTABILITY EFFECTS ON WIRELINE FORMATION TESTER MEASUREMENTS 15

Fig. 20: MDT Pressure profiles as measured by the probe and by the packer.

1840.00

1890.00

1940.00

1990.00

2040.00

2090.00

2140.00

2190.00

2240.00

2290.00

2340.00

2000.00 2200.00 2400.00 2600.00 2800.00 3000.00 3200.00 3400.00 3600.00

For m atio n Pr e s s u re p s ia

De

pth

m

0.10 1.00 10.00 100.00 1000.00 10000.00

M o b ility m d /cp

Formation Pressure from ProbeFormation Pressure from PackerMobility from ProbeMobility from Packer

Probe Test Points

Packer Test Points

Hydraulic power module

Probe module

Electrical power Module

Pumpout module

Dual-packer module

Sample module

Fig. 19: MDT Dual Packer

Correcting for Wettability and Capillary Pressure Effects...

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