Journal of Petroleum Science and Engineering 71 (2010) 169–178
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Journal of Petroleum Science and Engineering
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Research paper
Pore-scale modeling: Effects of wettability on waterflood oil recovery
Xiucai Zhao a,b,⁎, Martin J. Blunt a, Jun Yao b
a Department of Earth Science and Engineering, Imperial College, London SW7 2AZ, United Kingdomb College of Petroleum Engineering, China University of Petroleum (East China) 257061, China
⁎ Corresponding author. Department of Earth ScienCollege, London SW7 2AZ, United Kingdom.
We study the effects of wettability on waterflood oil recovery using a capillary-controlled pore-scalenetwork model. We validate the model against experimental data in the literature on mixed-wet Bereasandstone and then apply it to study multiphase flow through four networks extracted from different typesof rock: a sand pack, a poorly consolidated sandstone from the Middle East, a granular carbonate and Bereasandstone. We study the effects of initial water saturation, contact angle distribution and oil-wet fraction onrecovery. For a uniformly-wet system, where the contact angle everywhere falls within a relatively narrowrange, recovery increases as the system becomes less water-wet and reaches a maximum for oil-wetconditions where recovery is approximately constant for average intrinsic contact angles above 100°. As theinitial water saturation increases, recovery decreases in water-wet systems whereas in oil-wet systems itinitially increases and then decreases. For mixed-wet systems that contain water-wet and oil-wet regions ofthe pore space, the oil-wet fraction plays a more important role in determining recovery than the contactangle in the oil-wet regions. Optimal recovery occurs when a small fraction of the system is water-wet. Porestructure plays a relatively minor role in the generic behavior, although it does influence the initial saturationfor maximum recovery and the magnitude of the recovery. These results are explained in terms of pore-scaledisplacement mechanisms and fluid configurations.
The wetting condition of a reservoir rock plays a significant role indetermining transport properties such as capillary pressure, relativepermeability and oil recovery. Many experimental investigations onthe impact of wettability have been conducted and several excellentreview papers are available (Anderson, 1987a,b; Morrow, 1990;Jadhunandan, 1990). The wettability of a crude oil/brine/rock systemcan only be determined by indirect measurements of macroscopicbehavior, such as the imbibition of water and oil in an Amott test; thefluid distribution andwetting state at the pore scale is not knownwithcertainty. Network modeling, where displacement is simulatedthrough a lattice of pores connected by throats, doesmake predictionsof the microscopic fluid distribution and relates this to macroscopicparameters, such as wettability index and oil recovery (Blunt andKing, 1991; Blunt, 1998; Øren et al., 1998; Dixit et al., 1999, 2000;Al-Futaisi and Patzek, 2003; Øren and Bakke, 2003) and hence is auseful tool for understanding the impact of rock structure andwettability on multiphase flow.
Kovscek et al. (1993) proposed a theoretical model for wettabilityalteration after primary drainage where areas of the pore space in
direct contact with oil changed their oil/water contact angle forwaterflooding, while water-filled regions remained water-wet. Thismodel has been applied in network modeling to explore the effects ofwettability on relative permeability and waterflood oil recovery(Blunt, 1998; Øren et al., 1998; Dixit et al., 1999, 2000). There are twodistinct types of wettability. The first is what we describe asuniformly-wet, where all the pores and throats have approximatelythe same contact angle, within some relatively narrow range: thewettability varies from water-wet (contact angle less than 90°) toneutrally-wet (contact angles close to 90°) to oil-wet (contact anglesgreater than 90°). The second type is mixed-wettability (Salathiel,1973) where some pores and throats are water-wet while others areoil-wet. Here thewettability is controlled principally by the fraction ofthe pores that are oil-wet.
McDougall and Sorbie (1995, 1997) investigated trends in relativepermeability and recovery efficiency with a regular cubic network.Recovery was shown to be maximum in a network where half thepore space was oil-wet. McDougall et al. (1996) and Dixit et al. (1999)used the same network structure and introduced the regime theory ofwettability classification and analysis, with which they explainedexperimental trends in waterfood oil recovery in terms of wettabilitycharacterized by the oil-wet fraction of pores and contact angledistributions. Al-Futaisi and Patzek (2003) studied the impact ofwettability alteration on two-phase flow characteristics with anetwork extracted from a sample of Bentheimer sandstone. Theyshowed that as the system became less water-wet, the residual oil
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saturation initially decreased but increased dramatically at thetransition from water- to oil-wet conditions and then decreased to aminimum in oil-wet systems.
Jadhunandan and Morrow (1995) investigated the relationshipbetween wettability and waterflood oil recovery in a series of Bereacores. They used crude oil as a wettability-altering agent. By varyingthe initial water saturation Swi and aging conditions, they reproduceddifferent mixed-wet systems representing a range of reservoirconditions. Their study showed that oil recovery by waterfloodinginitially increased and then decreased as thewettability changed fromstrongly water-wet to oil-wet, with maximum recovery observed atweakly water-wet conditions. Tomodel this behavior, Bakke and Øren(1997) and Øren et al. (1998) constructed a geologically realisticnetwork of Berea sandstone. Using this network, Jackson et al. (2003)predicted the recovery trend as a function of wettability. Theyassumed that all oil-invaded pores after primary oil flooding becomeoil-wet and then matched the experimental wettability indices byvarying the contact angle distribution. Øren and Bakke (2003)proposed a method for estimating the oil-wet fraction and contactangle distributions from experimentally measured Amott water andoil indices. With their model, they obtained a quantitative match withthe experimental recoveries. Valvatne and Blunt (2004) studied theeffects of initial water saturation and could reproduce the trend inrecovery with Swi. The water index was matched by varying the oil-wet fraction during secondary waterflooding while the oil index wasmatched by adjusting the contact angle distributions for oil-wet pores.The recovery trend was well predicted, although the maximumrecovery was obtained from weakly oil-wet systems.
The combination of representative networks with an improvedunderstanding of pore-scale physics allows the successful reproduc-tion of experimental results. However, most studies have beenperformed on either cubic networks or on a relatively homogeneousnetwork representing just one sandstone— Berea. Micro-CT scanning(Arns et al., 2003, 2004) has enabled the pore structure of a widerange of rock samples to be determined. In this paper we will extendprevious studies to investigate the effects of wettability usingnetworks derived from micro-CT images of different rock types.
The paper is organized as follows. In Section 2, we will reproducethe experimental results from Jadhunandan and Morrow. The pore-scale model used to simulate flooding cycles will be briefly introducedand validated.We then select four networks, each of which representsa different rock system. The effects of wettability, initial watersaturation, and oil-wet fraction on waterflood oil recovery in differentrock systems are systematically studied. The results from uniformly-and mixed-wet systems will be presented in Section 3 and Section 4respectively. In the last section, we conclude our work.
2. Comparison with experiment
As mentioned above, Jadhunandan and Morrow (1995) conducteda systematic experimental study of waterflood recovery in Bereasandstone. The flow rate was sufficiently low to reproduce capillary-dominated conditions (capillary numbers were 10−6 and lower). Aseries of rock sampleswere initially filled withwater and then floodedwith crude oil to some initial water saturation Swi between 0.079 and0.32. All the cores were aged to alter their wettability states, and thenwaterflooded until 20 pore volumes had been injected. The wettingstates of the cores are determined by the Amott test (Amott, 1959)which combines both spontaneous imbibition and forced displace-ment. The Amott index for each phase p is given by
Ip =ΔSps
ΔSps + ΔSpfð1Þ
where ΔSps and ΔSpf are the saturation changes contributed byspontaneous imbibition and forced displacement respectively. The
Amott water index Iw and Amott oil index Io are combined to give theAmott–Harvey index Iw–o= Iw− Io, which varies between +1(strongly water-wet) and −1 (strongly oil-wet).
We now use pore-scale network modeling to reproduce theexperiments and see whether the same trend and results could bepredicted. We use a similar methodology to that presented byValvatne and Blunt (2004). We use Øren et al's geologically realisticBerea network as the input to a two-phase simulation code (Valvatneand Blunt, 2004). Contact angle hysteresis is included by adoptingMorrow's experimental results (Morrow, 1975), which relate thereceding and advancing contact angles to the intrinsic contact angle.The network properties are listed in Table 1 and presented in Fig. 1.We assume capillary-controlled displacement meaning that there isno effect of flow rate on the results.
All systems are assumed to have the same connate watersaturation 0.079, the minimum value achieved in experiments. Fluidproperties are consistent with their experimental values. Water andoil viscosities are 0.99 and 5.23 mPa s respectively and the interfacialtension is 12 mN/m. The network is initially water saturated and thenoil flooded to the experimentally measured Swi. During this primaryoil flooding, the receding contact angles are assumed to be 0°.Water isthen injected to displace oil and in this flooding cycle, the intrinsiccontact angles for water-wet pores are between 50° and 60°. Weadjust the oil-wet fraction of the network to match Iw; to match Io wekeep the lower bound of intrinsic contact angle in the oil-wet fractionat 80° and adjust the upper bound. During secondary water flooding,water and oil relative permeabilities are calculated and used to predictoil recoveries using Buckley–Leverett analysis.
Our predictions are illustrated in Fig. 2. Both the experimental andpredicted maximum recoveries occur at nearly neutrally-wet condi-tions although our prediction is shifted to more oil-wet conditions.
3. Effects of wettability on waterflood oil recovery
3.1. Network preparation
We have built up a library of images of sand packs, sandstonesand carbonates obtained using micro-CT scanning (Dong and Blunt,2009). A maximal ball algorithm (Silin et al., 2003; Patzek and Silin,2006; Al-Kharusi and Blunt, 2007; Dong and Blunt, 2009) is used toextract topologically equivalent networks of pores and throats fromthe selected target area of the images. We select networks S, F and Cfrom three different rock systems. S is a poorly consolidated sand-stone from an Arabian oilfield. It mainly consists of quartz grains,which show a bimodal grain-size distribution, and some poikilotopiccements. Sand pack F is made from quartz sand, which is ungroundsilica provided by US Silica Company. The grains are well sorted andthe average size is 0.29 mm. Carbonate C is a typical calcrete orlithified paleosol, enclosing carbonate clastic detritus and rhizoliths(calcified root tubules). Further analysis of its thin-section imagessuggests it probably developed as a weathering rind of limestonesduring exposure (uplift or sea-level drop). Fig. 3 shows 2-D sectionsof the micro-CT images from samples S, F, C and their extractednetworks.
The average properties of the three networks are listed in Table 1while pore size, throat size, aspect ratio and coordination numberdistributions are presented in Fig. 1. Three important features aboutthe pore structures of different rock systems should be noted. First, Chas much wider pore and throat size distributions than Berea and Swhile most parts of its pore space are smaller. Diagenesis andstructural changes play key roles in determining the carbonate'spore space after sedimentation, while compaction and cementationdominate the pore space development for the sandstones studied. Inthis example, which is typical of carbonates, complex diageneticprocesses lead to a wide distribution of pore sizes with many verysmall elements. Second, while a small fraction of pores in C have
Table 1Network properties for different rock systems. ϕ, K, rp, rt refer to porosity, permeability, pore and throat radius respectively. The coordination number is number of throats connectedto each pore. The aspect ratio is the average ratio of the pore radius to the average radius of its connected throats.
Network Rock type Network size/mm Pores Throats ϕ K/mD Ave. rp/μm Ave. rt/μm Ave. coord. no. Aspect ratio
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quite large coordination number, it is more remarkable that thereare many of dead-end pores, which can act as fluid storage space butwhich are not effective fluid transport paths. Third, the sand pack F,as expected, has large pores and throats since the medium iscomposed of relatively large grains that remain unconsolidated. Thesandstone S tends to have higher aspect ratios (ratio of pore to throatsize) than Berea, which is surprising, since it is poorly consolidated;however this is related to the wide range of grain size, apparent inFig. 3.
We perform water–oil flow simulations on these four networks tostudy the effects of wettability. The results are presented in thefollowing two subsections. Water and oil physical properties are thesame as those used when we reproduced the experimental results inthe previous section and three pore volumes of water are injected topredict waterflood oil recovery using Buckley–Leveratt theory basedon the computed relative permeabilities.
3.2. Effects of wettability in uniformly-wet systems
For each network model, we displace the initially water-filledsystemby oil to a pre-determinedwater saturation Swi. In themodel weassume thatwater can remain connected down to zero saturation—wedo not allow for a genuinely irreducible saturation due to clays ordisconnected water. During this primary oil flooding, the recedingcontact angle is set to 0 everywhere. During secondary water flooding,we adjust the intrinsic contact angles to obtain different wettabilities
Fig. 1. Network static pro
indicated by the Amott–Harvey Index Iw–o. The intrinsic contact anglesare randomly distributed to pores and throats in the network. For eachsystem, they follow a uniform distribution with a range of 20°. Byadjusting the average of the intrinsic contact angle interval, we canobtain different wetting systems from strongly water-wet to oil-wet.Fig. 4 illustrates the correlation between Iw–o and the average intrinsiccontact angle θ. As θ increases, the wetting state changes from water-wet (Iw–oN0, θb80°) to oil-wet (Iw–ob0, θN100°), with a neutrally-wetplateau where θ ranges from 80° to 100°. It is also clear that the systembecomes slightly more water-wet as Swi increases.
The predicted recoveries as a function of Iw–o for the differentnetworks are presented in Fig. 5.
3.2.1. Effects of wettabilityThese results indicate that oil recovery increases as the system
becomes less water-wet. When the system is weakly water-wet, oilrecovery improves dramatically as Iw–o decreases towards neutralwettability (80°bθb100°). The maximum recovery occurs for oil-wetconditions (θN100°), where recovery becomes a constant function ofIw–o. In Fig. 6 we present the relative permeabilities, fractional flowsand recovery curves as a function of wettability for one example case:network F with an Swi of 0.05.
Water relative permeability and residual oil saturation increasewith Iw–o. The trend in residual saturation has been discussed byseveral authors previously (McDougall and Sorbie, 1995; Blunt, 1997,1998). After primary oil flooding, oil occupies the centers of large
perty distributions.
Fig. 2. Comparison of predicted and experimental oil recovery, in the units of fraction ofoil in place (FOIP), after three pore volumes of water injection as a function of Amott–Harvey index Iw–o.
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pores and throats while their corners and smaller elements are stillfilled with water. In strongly water-wet media, water can flow readilythrough the wetting layers in the corners of the pore space, pref-erentially filling the narrowest elements by snap-off. Oil is stranded inthe larger pores. As the contact angle increases, snap-off is less favoredin comparison with piston-like advance of water into oil, which leadsto a connected front and less trapping. When the medium becomesoil-wet, oil remains connected in layers sandwiched betweenwater inthe corners and water — as the non-wetting phase — in the centers ofthe pores. These layersmaintain continuity of the oil down to very lowsaturations.
The trend in water relative permeability is counter-intuitive,however. As the system becomes more oil-wet, water preferentiallyinvades the larger pore spaces which have the greatest conductance to
Fig. 3. 2-D sections of the micro-CT images of samples S, F and C and their extracted netwrespectively. The network properties are listed in Table 1.
flow. Hence, at a given water saturation one would expect the waterrelative permeability to increase as the system becomesmore oil-wet;instead we see the opposite — although larger values of the waterrelative permeability are reached in oil-wet media, this is only at highwater saturations. The reason for this behavior is that the waterremains poorly connected through the pore space at low andintermediate water saturation. In a water-wet medium, a connectedpathway of smaller elements across the system is established at lowerwater saturations than when the larger elements (that have morevolume) are filled. It is only when there is a connected path of water-filled pores and throats in the larger elements — at high watersaturations — that the water relative permeability is large andincreasing steeply with saturation in oil-wet media.
Similarly the oil relative permeability increases as the systembecomes more oil-wet; again this is at first sight the opposite of whatwould be expected. The explanation rests on the connectivity of theoil phase. In a water-wet system, the filling of small elements by snap-off effectively disconnects conductive pathways of oil between thelarger pores and the oil relative permeability drops rapidly withincreasing water saturation. In neutrally-wet media, there is a moreconnected advance of water and the oil remains better connected. Inoil-wet media, oil layers maintain the connectivity of the oil phaseeven in elements whose centers are water-filled; these layers retainflow paths across pores and throats between oil-filled regions andallow the oil relative permeability to stay relatively high.
The combination of low water relative permeability and residualoil saturation gives the best waterflood recovery for oil-wet media.While this can be explained, it is contrary to the analysis of theexperimental data we performed in the previous section, where itappeared that neutrally-wet media gave the best recoveries. Again wehave an apparent contradiction whose explanation hinges on thelikely typical nature of the distribution of wettability in apparently oil-wet media, which we discuss in the subsequent sections.
orks. The image resolutions for sample S, F and C are 9.1 μm, 9.996 μm and 5.345 μm
Fig. 4. Amott–Harvey index Iw–o as a function of average intrinsic contact angle θ on different rock systems.
Fig. 5. Recovery as a function of Amott–Harvey index Iw–o on different rock systems (the recovery is computed after three pore volumes of water are injected).
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Fig. 6. Influence of wettability on relative permeability, fractional flow and waterflood oil recovery for a sand-pack network, F with Swi=0.05.
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3.2.2. Effects of initial water saturation (Swi)As shown in Fig. 5, the oil recovery decreases with Swi for water-wet
systems regardless of rock type. For oil-wet systems, the oil recoveryinitially increases and then decreases as Swi increases. We plot recoveryas a function of Swi in Fig. 7 for different rock types for oil-wet systems(θN100°). It is clear that there exists a range of Swi that gives optimal oilrecovery and that this range depends on the rock type.
We again choose network F as an example to interpret thepredicted results. For both water- and oil-wet conditions, threesystems with different initial water saturations are selected. Theintrinsic contact angles are [60°, 80°] for water-wet and [105°, 125°]for oil-wet conditions. The effects of Swi on relative permeability areshown in Fig. 8.
As Swi increases, the number of elements initially filled with wateras well as the thickness of corner water will increase; therefore, the
Fig. 7. Recovery after three pore volumes of water injected as a function of initial watersaturation under oil-wet conditions (θN100°) for different rock types.
water conductivity increases, while the oil conductivity, restricted bywater blocking flow channels, will decrease. Hence the initial oilrelative permeability decreases and the initial water relative perme-ability increases with Swi.
Under water-wet conditions, an increase in Swi leads to more flowin wetting layers and more snap-off and oil trapping, resulting inincreasing residual oil saturations and lower recoveries. Note that thewater relative permeability is not independent of Swi, but increaseswith increasing Swi, since the water is better connected throughoutthe system. With a low Swi there is less snap-off and piston-likeadvance needs to fill a large number of elements to establish aconnected pathway of water-filled elements, whereas for a larger Swi,the water is initially relatively well connected and further fillingrapidly adds to the water conductivity (Valvatne and Blunt, 2004).
For oil-wet conditions, the behavior has been described for Bereanetworks (Valvatne and Blunt, 2004). Piston-like advance is favoredand water prefers to fill the large pores and throats by displacementfrom initially water-filled elements. When Swi is low, there arerelatively few of these elements. Therefore, to connect across thesystem through the centers of the pore space, water has to find apathway of larger elements. As Swi increases, the number of initiallywater-filled elements will increase. However, most of these areisolated and only connected to each other through wetting layers. Aswater preferentially displaces oil in large pores and throats, the watersaturation increases while its conductivity changes only very slowly,which results in low krw and high kro over a large Sw range. When Swi
becomes high, some initially water-filled clusters are more closelyconnected. Therefore, they can be easilymerged by injectedwater andform high-conductivity flow paths, resulting in a rapid increase in krw.A low water relative permeability gives a macroscopically highadvancing shock front and good recovery. Oil recovery is highest forintermediate values of Swi: when Swi is very low, the pathway of largeelements, once connected, allows krw to increase rapidly with
Fig. 8. Effects of initial water saturation Swi on relative permeability for a sand pack F: left for water-wet and right for oil-wet conditions.
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saturation, while higher Swi leads to poorer connectivity until Swi issufficiently large to allow water to be well connected. This trend inrecovery has been discussed in the context of waterflooding transitionzone reservoirs, where the decrease of Swi with height above the oil/water contact leads to variation in wettability (Jackson et al., 2003).
3.3. Effects of wettability in mixed-wet systems
To simulate mixed-wet conditions, we assign a target volumefraction of oil-filled pores and throats and alter their wettability afterprimary oil flooding. The intrinsic contact angle for water-wetelements is between 30° and 50°. We keep the lower bound of theintrinsic contact angle distribution for oil-wet elements at 90°, andthen adjust both its upper bound and the oil-wet fraction to obtaindifferent wetting conditions. We calculate water and oil relativepermeabilities and use Buckley–Leverett analysis to predict oilrecoveries. Again, three pore volumes of water are injected to displaceoil in the recovery prediction.
The results obtained from our four networks show the samegeneric features and thus we present the results from Berea here as anexample. The effects of oil-wet fraction andwettability on oil recovery
Fig. 9. Recovery as a function of Amott–Harvey index Iw–o at different Swi for Berea sands
are shown in Fig. 9, where each figure represents a mixed-wet systemwith a different initial water saturation. Oil recovery is approximatelya constant function of Iw–o for a given oil-wet fraction, since theresidual oil saturation remains approximately constant, at a low value,for the oil-wet regions as the contact angle is altered.
However, both Swi and the oil-wet fraction have a significantimpact on oil recovery. Initial water saturation gives the same trend inrecovery for both uniformly-wet and mixed-wet systems. The effectsof oil-wet fraction on relative permeability and water fractional floware illustrated in Fig. 10 for Berea with an initial water saturation of0.1. The behavior is similar to that observed with initial watersaturation: lowering the oil-wet fraction is equivalent to increasingSwi with the same non-monotonic trend in recovery, with the optimaldisplacement achieved at some intermediate oil-wet fraction. How-ever, there are two differences between the relative permeabilitybehavior, evident from a comparison of Figs. 8 and 10. First, the oil andwater relative permeabilities at the beginning of waterflooding arethe same regardless of oil-wet fraction, since the initial distribution ofwater is the same. Second, the residual oil saturation increases as theoil-wet fraction decreases. This is because oil can be trapped by snap-off in the water-wet portions of the pore space.
tone. Fraction represents the fraction of initially oil-filled elements that are oil-wet.
Fig. 10. Effects of oil-wet fraction on relative permeability and water fractional flow (Berea, Swi=0.1).
176 X. Zhao et al. / Journal of Petroleum Science and Engineering 71 (2010) 169–178
Wenow combine these results to show oil recovery as a function ofoil-wet fraction for all four networks and for different values of Swi,see Fig. 11. As we have already discussed, the contact angles in the oil-wet regions have little effect on recovery: in Fig. 11, the oil-wetregions have a contact angle distribution in the range [90°, 120°].There is, however, a non-monotonic trend in recovery withwettability, similar to that observed for uniformly-wet systems,Fig. 7: in Fig. 11, oil recovery initially increases and then decreaseswith oil-wet fraction. When the oil-wet fraction is high, displacementproceeds by piston-like advance through the wider elements: oncethese connect, the water relative permeability increases rapidly,leading to modest overall oil recovery. The water-wet regions of thepore space are filled first during waterflooding. When the fraction ofwater-wet elements is small, these regions are filled first, but do notsignificantly increase the connectivity of thewater. Once filled, furtherdisplacement of larger elements occurs, seeded from these water-wetpatches. Only at relatively high water saturation is the waterconnected across the system through the centers of the pore space.This leads to a very low water relative permeability over a widesaturation range, giving a favorable oil recovery. As more of the pore
Fig. 11. Oil recovery as a fun
space becomes water-wet, these regions connect and the waterrelative permeability is higher. Furthermore, oil can be trapped in thewater-wet portions of the pore space. These two effects lead to alower recovery when the water-wet fraction is larger. There is anoptimal water-wet fraction (around 15%–30% for Berea, 5%–20% for S,10%–30% for F). The key to our successful reproduction of theexperimentally-observed variation in recovery — Section 2 — is thedifference in oil-wet fraction.
Network C, in contrast, displays a rather different behavior. Foreach value of Swi, the recovery is initially very high but decreasesdramatically with a minor increase in water-wet fraction. The lowcoordination number of this network allows oil and water to becomeeasily disconnected.When the network is entirely oil-wet, oil remainsconnected through layers and the residual saturation is very low,leading to high recoveries. However, a small number of water-wetpores — which are filled first during waterflooding — is sufficient togive a high residual oil saturation, as filling a few elements strandssignificant quantities of oil. This is confirmed by the relativepermeabilities and fractional flows shown in Fig. 12: a smallproportion of water-wet elements is sufficient to give a very large
ction of oil-wet fraction.
Fig. 12. Effects of oil-wet fraction on relative permeability and water fractional flow (network C with Swi=0.15).
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residual oil saturation. The poor connectivity of the network meansthat there is only a narrow range of saturation where both oil andwater relative permeabilities are greater than around 0.01.
4. Conclusions
We have studied the effects of wettability on waterflood oilrecovery using a pore-scale network model. We validated the modelagainst experimental data in the literature on mixed-wet Bereasandstone and then applied it to study multiphase flow through fournetworks extracted from different types of rock: a sand pack, a poorlyconsolidated sandstone from the Middle East, a granular carbonateand Berea sandstone. We studied the effects of initial watersaturation, contact angle distribution and oil-wet fraction on recovery.Our key conclusions are outlined below.
For a uniformly-wet system recovery increases as the systembecomes less water-wet and reaches a maximum for oil-wetconditions where recovery is approximately constant for averageintrinsic contact angles above 100°. As the initial water saturationincreases, recovery decreases in water-wet systems whereas in oil-wet systems it initially increases and then decreases.
For mixed-wet media the oil-wet fraction plays a more importantrole in determining recovery than the contact angle in the oil-wetregions. Optimal recovery occurs when a small fraction of the systemis water-wet. Pore structure plays a relatively minor role in thegeneric behavior, although it does influence the initial saturation foroptimal recovery and the magnitude of the recovery.
NomenclatureFOIP fraction of oil in placeIw Amott water indexIo Amott oil indexIw–o Amott–Harvey indexK water absolute permeability, mDkrw water relative permeabilitykro oil relative permeabilityPV pore volumeSwi initial water saturationrp pore radius, μmrt throat radius, μmϕ porosityθ average intrinsic contact angle
Acknowledgments
The authors wish to thank the members of the Imperial CollegeConsortium on Pore-Scale Modeling (BG, BHP, BP, JOGMEC, Schlum-berger, Shell, Statoil and Total) for their financial support. We also
thank China Scholarship Council for funding Xiucai Zhao's time atImperial College. Nasiru Idowu, Olumide Talabi, Hu Dong and StefanIglauer are also thanked for their support of this work. The networkmodeling code used in this study can be downloaded from http://www3.imperial.ac.uk/earthscienceandengineering/research/perm/porescalemodelling.
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