Capillary trapping in sandstones and carbonates ...€¦ · [e.g., Stegemeier, 1977; Land, 1968;...

Capillary trapping in sandstones and carbonates:Dependence on pore structure

Y. Tanino1 and Martin J. Blunt1

Received 12 December 2011; revised 20 April 2012; accepted 30 June 2012; published 30 August 2012.

[1] Residual non-wetting phase saturation and wetting-phase permeability weremeasured in three limestones and four sandstones ranging in porosity from 0.13 to 0.28and in absolute permeability from 2 � 10�15 to 3 � 10�12 m2. This paper focuses on theresidual state established by waterflooding at low capillary number from minimumwater saturation achieved using the porous plate technique, which yields the maximumresidual under strongly water-wet conditions. The pore coordination number and porebody-throat aspect ratio of each rock were estimated using pore networks extracted fromX-ray microtomography images of the rocks. Residual saturation decreases with increasingporosity, with no apparent difference in magnitude between the limestones and sandstonesat a given porosity. Thus intraparticle/intra-aggregate microporosity does not significantlyalter the efficiency of capillary trapping in the rocks considered presently. Residualsaturation broadly decreases as conditions become less favorable for snap-off, i.e., withdecreasing pore aspect ratio and increasing coordination number. The measured residualsaturations imply that capillary trapping may be an effective mechanism for storing carbondioxide in both sandstones and carbonates provided that the systems are strongly water-wet.

Citation: Tanino, Y., and M. J. Blunt (2012), Capillary trapping in sandstones and carbonates: Dependence on pore structure,Water Resour. Res., 48, W08525, doi:10.1029/2011WR011712.

1. Introduction

[2] The trapping of a non-wetting phase in a porous mediumas discontinuous pore-scale clusters by capillary forces, orcapillary trapping, has been studied extensively because ofits importance to groundwater remediation and enhanced oilrecovery. In these applications, the goal is to maximizeextraction of the trapped liquid. In contrast, in the context ofgeological carbon storage, the goal is to maximize trapping.Here, carbon dioxide (CO2) is injected into a target geologi-cal formation, forming a continuous plume. As the injectedCO2 is driven upward by buoyancy, ambient groundwaterwill flow into its wake to replace it. This replacement of CO2

by groundwater behind the rising CO2 plume is an imbibitionprocess. Accordingly, a portion of the migrating CO2 will berendered immobile within the pores of the rock by capillaryforces, and will no longer be at risk of leakage to the atmo-sphere [Juanes et al., 2006].[3] Capillary trapping is controlled primarily by the pore

structure, rock-fluid interaction, and the flow. This paperfocuses on the effects of pore geometry under strongly water-wet conditions. In a homogeneous, strongly water-wetporous medium, trapping arises predominantly from snap-off, whereby capillary instability splits the non-wetting phase

occupying a narrow throat along the cross section of thethroat. The non-wetting phase then retracts into the porebodies on the respective ends of that throat. Once snap-offoccurs in all throats connected to a pore body, the non-wetting phase in that pore body is stable against furtherdisplacement. This mechanism is favored by a large aspectratio between the pore body and the throats connecting toit [Jerauld and Salter, 1990]. Trapped non-wetting phasehas been observed directly in sandstones [e.g., Prodanovićet al., 2007; Iglauer et al., 2010].[4] We consider capillary trapping that arises from pressure-

driven flow of the wetting-phase, known as waterflooding.The fractional volume of the pore space initially occupied bythe non-wetting phase, or the initial non-wetting phase satu-ration, is denoted by Snw,i. The fractional volume of the non-wetting phase after waterflooding, or the residual saturation,is denoted by Snw,r. Under strongly water-wet conditions, it iswell established that Snw,r increases monotonically with Snw,i[e.g., Stegemeier, 1977; Land, 1968; Spiteri et al., 2008]; weconfirmed this experimentally for two of the sandstonesconsidered in the present study [Pentland et al., 2010]. Here,capillary trapping is largely characterized by the maximumSnw,r, denoted by Snw,r

max, which in turn corresponds to highSnw,i. Indeed, Snw,r

max is the only input parameter in the empir-ical model proposed by Land [1968], which is widely used topredict the dependence of Snw,r on Snw,i.[5] This paper presents laboratory measurements of

Snw,rmax in a set of seven rocks, with porosity ranging from

f = 0.13 to 0.28 and absolute permeability ranging fromk = 2� 10�15 to 3� 10�12 m2, and explores their correlationwith topological and geometric properties of the rocks. Threeof the rocks are limestones, which contain intraparticle orintra-aggregate porosity, and four are sandstones. The pore

1Department of Earth Science and Engineering, Imperial CollegeLondon, London, UK.

Corresponding author: Y. Tanino, Department of Earth Science andEngineering, Imperial College London, Prince Consort Rd., London SW72BP, UK. ([email protected])

©2012. American Geophysical Union. All Rights Reserved.0043-1397/12/2011WR011712

WATER RESOURCES RESEARCH, VOL. 48, W08525, doi:10.1029/2011WR011712, 2012

W08525 1 of 13

geometry of each rock is characterized using mercury injec-tion porosimetry (section 2.1.1), nuclear magnetic resonance(NMR) transverse relaxation times (section 2.1.2), and X-raymicrotomography (section 2.1.3). Laboratory measurementsof permeability to brine at residual state are presented insection 3.1. Finally, the correlation of Snw,r

max with porosity,permeability, pore coordination number, and pore aspectratio is explored (section 3.2).

2. Materials and Methods

2.1. Rocks

[6] We consider seven rocks, of which three are lime-stones (Figure 1, top) and four are sandstones (Figure 1,bottom). The rocks were selected for their commercialavailability, structural strength, and spatial homogeneity atthe laboratory scale. The rocks are assumed to be stronglywater-wet. In addition, Estaillades limestone [Dautriat et al.,2011], Indiana limestone [Zhu et al., 2010; Churcher et al.,1991; Wardlaw et al., 1987], and Berea sandstone [Sinnokrot

et al., 1971; Churcher et al., 1991; Øren and Bakke, 2003;Chatzis et al., 1983; Jadhunandan and Morrow, 1995;Ioannidis et al., 1997; Lin and Cohen, 1982; Wardlaw et al.,1987] have been studied extensively, allowing for compari-son. The porosity and absolute permeability of each sample arepresented in Table 1. Also presented is the clay content foreach rock, defined as the fractional weight of particles thatare <2 mm. The clay content was measured at a commerciallaboratory (Weatherford Laboratories, East Grinstead) duringX-ray diffraction analysis for composition determination.2.1.1. Capillary Pressure and Pore Entry SizeDistribution[7] Samples of each rock were sent to a commercial lab-

oratory for drainage capillary pressure measurement bymercury injection (Autopore IV 9500, Weatherford Labo-ratories, Stavanger). Here, mercury was injected into anevacuated sample at a small constant capillary pressure. Themercury injection pressure was increased in discrete inter-vals, and the incremental volume of injected mercury wasrecorded at each pressure.

Figure 1. A two-dimensional cross section of three-dimensional X-ray scans of the (top) limestones and(bottom) sandstones considered in the present study. The diameter of each sample is 5 mm; the whitehorizontal bar in each image depicts 1 mm. White patches visible in the sandstone images are salientfeatures in X-ray scans of these rocks, and are attributed to minerals with high X-ray absorption. Eachimage is from the same scan as those from which pore networks were extracted (cf. section 2.1.3).

Table 1. Petrophysical Properties and Clay Content of the Rocks Considered in the Present Studya

Rock f k [m2] n Clay Content [wt.%]

Ketton limestone 0.23 (2.884 � 0.006) � 10�12 1 5.6Estaillades limestone 0.28 (1.6393 � 0.0005) � 10�13 2 5.4Indiana limestone 0.13 (2.4 � 0.3) � 10�15 7 3.2Doddington sandstone 0.22 (1.1 � 0.1) � 10�12 1 1.7Berea sandstone 0.22 (4.4 � 0.2) � 10�13 2 1.8Stainton sandstone 0.16 (3.45 � 0.5) � 10�15 1 3.3Springwell sandstone 0.15 (2.20 � 0.02) � 10�15 1 2.2

an is the number of independent measurements of permeability, k.Where n = 1, the uncertainty in k is the contribution from the uncertainty in dU/d(DP/L)(see equation (8)). Where n > 1, the mean k and the standard error of the mean are presented.

TANINO AND BLUNT: CAPILLARY TRAPPING—DEPENDENCE ON PORE STRUCTURE W08525W08525

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[8] The capillary pressure, Pc, may further be translatedinto an equivalent pore throat radii, rp, via the Young-Laplace equation:

rp ¼ 2s cos qPc

; ð1Þ

assuming a contact angle of q = 130� and interfacial tensionof s = 485 mN m�1. The fractional volume of the pore spacethat remained occupied by the wetting phase as Pc wasincreased, Sw(Pc) ≡ 1 � Snw,i(Pc), is then a cumulative dis-tribution function for pores with a capillary entry pressurecorresponding to rp and the corresponding probability dis-tribution function (pdf ),

f rp� � ¼ dSw

drp; ð2Þ

may be interpreted as the pore entry size distribution. Notethat the net intrusion volume at a given capillary pressure isthe fractional volume of the pore space accessible from thebulk sample surface by pore throats of the corresponding rpor larger. Accordingly, the volume of a pore contributes tof (rp) of the rp corresponding to the narrowest pore throat inthe pore channel that first connects it to the bulk samplesurface, rather than the rp corresponding to itself.[9] In Figure 2, the pore entry size distribution is illustrated

by the radius-weighted pdf, namely rp f (rp) ∝ f (log10rp), sothat the incremental area under the curve is proportional tothe fractional volume of the pores associated with that rp

[cf. Liaw et al., 1996; Lenormand, 2003]. The pore entrysize distribution of the sandstones is unimodal, with a single,distinct peak (Figure 2, bottom). In contrast, two of thelimestones, Ketton and Estaillades, exhibit a distinct bimodaldistribution (Figure 2, top). The peak at large rp is attrib-uted to inter-particle pores in Ketton limestone and inter-aggregate pores in Estaillades limestone. The peak at smallrp is attributed to intraparticle pores in Ketton limestoneand intra-aggregate pores in Estaillades limestone. Indianalimestone exhibits the most complex distribution, with threepeaks without any separation of throat sizes. Its large capil-lary entry pressure of Pc /(2scos q) = 0.17 mm�1 (Figure 3),which corresponds to a pore entry size rp = 6 mm that is anorder of magnitude smaller than the largest pores that can beseen in the X-ray images (Figure 1), suggests that a signifi-cant fraction of large, inter-particle pores in Indiana lime-stone is connected only through relatively small pores andthroats or microporosity. This is in contrast to Ketton lime-stone, for which it is evident from visual inspection of thesegmented images that the inter-particle pores are wellconnected.2.1.2. NMR Transverse Relaxation Times[10] The pore space of the three limestones was further

characterized using the transverse relaxation times, T2, ofNMR in brine-saturated samples, which were measured at acommercial laboratory (2 MHz Maran Ultra, WeatherfordLaboratories, East Grinstead). The use of NMR to charac-terize pore size distribution in rocks is a standard techniquethat is discussed in detail elsewhere [e.g., Jorand et al., 2011;

Figure 2. Pore entry size distribution, rp f (rp) (equations (1) and (2)), as determined from mercury injec-tion capillary pressure measurements. The data for Doddington sandstone and Estaillades limestonerepresent measurements on a single sample. For all other rocks, the plotted data represent the averageof measurements on two samples. Arrows represent the resolution of the X-ray scans from which porenetworks were extracted, i.e., half of the voxel size of the scans (Table 2). Vertical lines depict rpcorresponding to the drainage Pc in the coreflood experiments (equation (1); Table 5).


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Straley et al., 1997; Kenyon, 1992], so only a basic descrip-tion is included here.[11] First, a steady magnetic field is applied to a brine-

saturated sample to align the nuclear spins of the fluidmolecules in a specific direction. Next, this alignment isperturbed by a sequence of radio frequency pulses, each ofwhich induces nuclear spin magnetization transverse to thesteady field. The transverse magnetization of each nucleusdecays exponentially with time; the characteristic decay timeis denoted by T2. This decay (relaxation) is often assumed toarise predominantly from interaction with the pore surface[e.g., Jorand et al., 2011], and all nuclei residing in a givenpore is assumed to have the same value of T2. Then, T2 isproportional to the volume-to-surface ratio of that pore, i.e.,

T2 ¼ V=Sð Þ=r2; ð3Þ

where r2 is a scaling constant specific to the rock, and thesignal amplitude at the onset of the decay is proportional tothe volume of that pore. By modeling the pore to be isolatedand spherical, V/S may be translated into an equivalent poreradius: rp = 3V/S.[12] In the laboratory, only the sum of the transverse

magnetization of all nuclei in the sampled pore space can bemeasured. For a rock, which contains a continuous range ofpore sizes, this acquired signal M(t) is the sum of numerousexponentially decaying signals, each with its own charac-teristic decay time T2,i and an amplitude [Mi(t = 0)] that isproportional to the number of nuclei in all pores of radiuscorresponding to it:

M tð Þ ¼Xi

Mi 0ð Þ exp �t=T2;i� �

: ð4Þ

Note thatMi (0)∝ f (T2)dT2, where f (T2) is the pdf of T2 and,accordingly, is a proxy for pore size distribution. Finally,equation (4) is inverted to determine the values for Mi(0) for

a pre-selected set of 50 logarithmically uniformly spacedvalues of T2 that best fit the measured M(t).[13] Figures 4 and 5 present f (T2) (dotted line) for all

rocks. For convenience, the T2-weighted pdf, T2 f (T2) (solidline), is also presented: the area under T2 f (T2) over anincremental log10T2 is proportional to the fractional volumeof the associated pores (cf. section 2.1.1). f (T2) for the threelimestones each display two peaks, consistent with thebimodal pore entry size distribution (Figure 2). The ratio ofthe corresponding values of T2, which is interpreted as a ratioof the characteristic size of inter-particle/inter-aggregatepores to that of intraparticle/intra-aggregate pores, are 30, 10,and 90, for Ketton, Estaillades, and Indiana limestones,respectively. The T2-weighted pore size distribution, T2 f(T2),of Doddington sandstone resembles its pore entry size dis-tribution, rpf (rp), and is characterized by its unimodal pro-file with a distinct peak at T2 = 370 ms. In contrast,Springwell and Stainton sandstones display a broad distri-bution of T2, which is consistent with their broad pore entrysize distribution.[14] If we assume that the pore space of a given rockmay be

partitioned into two classes of pores—larger, inter-particle/inter-aggregate pores and smaller, intraparticle/intra-aggregatepores and clays which line the pores—at a single value of T2 =T2,c, the fractional volume of the pore space occupied by therespective types of pores may be estimated as

fmacro=f ¼Z ∞

T2;c

f T2ð ÞdT2 ð5Þ

and

fmicro=f ¼Z T2;c

0f T2ð ÞdT2: ð6Þ

By definition, fmicro + fmacro ≡ f.

Figure 3. Normalized drainage capillary pressure, Pc/(2s cos q) [mm�1], imposed to achieve a givenwetting phase saturation, Sw, where air and mercury were the wetting and nonwetting phases, respec-tively. The data for Doddington sandstone and Estaillades limestone represent measurements on a singlesample. For all other rocks, the plotted data represent the average of measurements on two samples.


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[15] For the sandstones, we adopt the conventional cutoffof T2,c = 3 ms for partitioning microporosity in sandstonesassociated with clay-bound water from inter-particle pores[Straley et al., 1997; Dunn et al., 2002; Jorand et al., 2011].In the absence of a similar, widely applicable criterion forcarbonates, we take T2,c = 72 ms, which coincides with thelocal minimum of T2 f (T2) measured in Ketton limestone.This choice is supported by the good agreement between thecorresponding rp(=1.1 mm), as estimated by equation (3)using r2 = 5.0 mm s�1 proposed by Fleury et al. [2007] forEstaillades limestone, and the separation of the two peaksin the bimodal distribution of the mercury injection data(Figure 2). Also, previous measurements suggest that thecut-off that segregates inter-particle porosity from secondaryporosity in carbonates broadly falls within the range T2,c ≈ 60to 100 ms [Westphal et al., 2005; Straley et al., 1997]; theselected T2,c is consistent with these observations.[16] With these values of T2,c, the pore space of Ketton

limestone is divided equally, by volume, between macro-pores and micropores. In contrast, fmacro/f = 85% and 72%

of the pore space of Estaillades and Indiana limestones isclassified as macroporosity. These inferred volumes of themacroporosity are significantly higher than those reportedelsewhere. Specifically, Dautriat et al. [2011] attributeonly 30% of the porosity in Estaillades limestone to inter-aggregate pores. Similarly, Zhu et al. [2010] estimatedfmacro/f = 32% in Indiana limestone. The discrepancysuggests that the true value of T2,c is higher in these twolimestones, but further interpretation is beyond the scope ofthis study. In the sandstones, the bulk of the porosity isattributed to interparticle porosity (Figure 5).2.1.3. Pore Connectivity and Pore Body-Throat AspectRatio[17] The pore space of each rock was imaged using X-ray

microtomography, then partitioned into larger pore bodiesand constrictions (throats) that connect them using the max-imum ball algorithm [Dong and Blunt, 2009]. Both the X-rayimaging and the extraction of the pore networks were per-formed by a commercial company (Xradia Versa, iRockTechnologies, Beijing). The basic properties of the images

Figure 4. f (T2) ([ms�1], dotted line) and the T2-weightedprobability distribution function, T2 f (T2)/9 (solid line). Thenumbers depict fmicro/f and fmacro/f (equations (5) and(6); T2,c = 72 ms (vertical dashed line)). f as measured byNMR: f = 0.240 (Ketton), 0.339 (Estaillades), and 0.113(Indiana).

Figure 5. f (T2) ([ms�1], dotted line) and the T2-weightedprobability distribution function, T2 f (T2)/9 (solid line). Thenumbers depict fmicro/f and fmacro/f (equations (5) and (6);T2,c = 3 ms (vertical dashed line)). f as measured by NMR:f = 0.216 (Doddington), 0.219 (Berea), 0.158 (Springwell),and 0.155 (Stainton).


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and the networks considered presently are summarized inTable 2. All pore networks are 1000 � 1000 � 1000 voxels3

in size. The networks for Ketton and Estaillades limestoneswere used by Blunt et al. [2012].[18] The topology of a pore network is described by the

pore coordination number, z, which is the number of throatsconnected to a given pore body. The mean coordinationnumber of each network is calculated as ⟨z⟩V = ∑z=1

zc zpZ (z),where

pZ zð Þ ¼P

j2s zð ÞVjPzcz¼1

Pj2s zð ÞVj

; ð7Þ

s(z) is the set of pore bodies with coordination number z, andVj is the volume of the jth pore body. In this paper, ⟨ � ⟩Vdenotes an average over the network weighted by the vol-ume of the pore (body). Note that pZ (z) is the probabilitymass function (pmf) of z in a given network: by definition,pZ (z) ≥ 0 for all z and ∑1

zc pZ (z) = 1. The threshold, zc, isdefined as the smallest z for which the number frequency isless than 0.5% of the total pore body. The lower limitexcludes isolated pore bodies (z = 0). The upper limit pre-vents anomalously high z from altering the estimate of themean dramatically.[19] For a non-wetting phase to be isolated within a pore

body, snap-off must take place in all throats connected to it.Accordingly, the likelihood for the nonwetting phase to betrapped by snap off in the jth pore body may be parameter-ized by rb, j/rt, j

max, where rb, j is the radius of the pore bodyand rt, j

max is the maximum radius of all pore throats connectedto it. Its volume-weighted mean, corresponding to a pdfof f (rb, j/rt, j) = Vj /∑Vj, is denoted by ⟨rb/rt

max⟩V.

[20] Computed values of pZ(z) and f (rb, j/rt, jmax) for each

rock are presented in Figures 6 and 7; the corresponding ⟨z⟩Vand ⟨rb/rt

max⟩V are presented in Table 3. Also included forreference is the mean pore coordination number based on thenumber frequency, ⟨z⟩n, corresponding to pZ(z) = n(z)/∑1

zc n(z),where n(z) is the number of pore bodies with coordinationnumber z.[21] We emphasize that only pore bodies and throats

larger than the voxel size of the X-ray scans can be resolved.Incomplete resolution in turn affects the present analysisthrough its impact on ⟨z⟩V and ⟨rb/rt

max⟩V. z is largelyinsensitive to unresolved pore space that constitutes thecorners and surface roughness of resolved pore bodies andpore throats. In contrast, unresolved throats contribute to theconnectivity of the pore space, and their exclusion from thenetworks results in an underestimation of ⟨z⟩V. The impactof incomplete resolution on ⟨rb/rt

max⟩V is less obvious. If, forexample, the aspect ratio is correlated with the absolute sizeof the pore body, as has been demonstrated for Indianalimestone [Wardlaw et al., 1987], poor resolution biases thedistribution of rb/rt

max toward those of larger pore bodies.Also, intraparticle microporosity is excluded from the net-works of Ketton and Indiana limestones. Accordingly, thecalculated ⟨z⟩V and ⟨rb/rt

max⟩V represent the connectivity andmorphology of the inter-particle porosity only. Voxel reso-lution would have to be enhanced by several orders ofmagnitude for smaller pores in low porosity rocks to be

Figure 6. Volume-weighted distribution for the pore coor-dination number (left, equation (7)) and the pore aspect ratio(right) in the networks of the limestones. Vertical linesdepict the mean (Table 3).

Figure 7. Volume-weighted distribution for the pore coor-dination number (left) and the pore aspect ratio (right) of thenetworks of the sandstones. Vertical lines depict the mean(Table 3).


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captured (Figure 2), which is beyond the scope of the presentstudy.[22] Here we briefly discuss the quality of the pore net-

work for each rock. For Berea and Doddington sandstones,the network porosity, fnetwork, is 80% and 90% of the true(measured) porosity, respectively. In addition, the distinctunimodal distribution of the pore entry size and T2 (Figures 2and 5) and the low (<2 wt.%) clay content (Table 1) areindicative of a relatively simple pore micro-structure. Unre-solved pore space may thus be assumed to be contained inthe corners and along the surface of resolved pores, and theextracted networks are interpreted to be representative of thetrue pore structure within the assumptions associated withthe idealization of the pore network. This is corroborated bythe good agreement between ⟨z⟩n = 2.93 � 0.01 of thepresent Berea network and values reported elsewhere, whichrange from 2.7 to 4.5 [Øren and Bakke, 2003; Lin andCohen, 1982; Ioannidis et al., 1997; Yanuka et al., 1986;Sheppard et al., 2006].[23] For Ketton limestone, the voxel size falls between the

two peaks of the bimodal pore entry size distribution(Figure 2, arrow) and fnetwork/f = 62%. Given the largeseparation of length scale between interparticle and intra-particle pores, the extracted network is interpreted to excludethe intraparticle porosity while largely capturing the inter-particle (macro) porosity. Indeed, ⟨z⟩n = 2.92 � 0.03 of thenetwork for Ketton limestone considered presently, whichcomprises loosely consolidated spherical grains O(500) mmin size [Figure 1; Bailey et al., 2000], is comparable to 3.2 ofa rhombohedral array of spheres [Yanuka et al., 1986] whichhas a similar f (=0.259). Similarly, intraparticle pores ofIndiana limestone were excluded entirely from its network,and only fnetwork/f = 50% of its pore space is accounted for.Nevertheless, there are significant number of large pores

Table 2. Basic Properties of the X-ray Scans and the Pore Networks Extracted From Thema

Rock Voxel Size [mm] fnetwork fnetwork/f ft/fnetwork knetwork [m2]

Ketton 2.654 0.14 0.62 0.14 7 � 10�12

Estaillades 2.6825 0.14 0.50 0.19 9 � 10�14

Indiana 2.7551 0.065 � 0.005 0.50 0.100 � 0.002 (3 � 1) � 10�15

Doddington 2.6929 0.196 � 0.002 0.89 0.1320 � 4 � 10�4 (1.62 � 0.06) � 10�12

Berea 2.7745 0.17 0.77 0.13 4 � 10�13

Springwell 2.7745 0.03 0.23 0.44 8 � 10�15

Stainton 2.7752 0.094 � 0.001 0.60 0.12 � 0.02 (4.15 � 0.05) � 10�15

aft/fnetwork denotes the fractional volume of the network occupied by throats. The permeability of the network, knetwork, was predicted by the two-phaseflow pore-network simulator developed by Valvatne and Blunt [2004]. For Indiana limestone, Doddington sandstone, and Stainton sandstone, two networkswere extracted from the same scans. The values presented for fnetwork, f

t/fnetwork, and knetwork for these rocks represent the average between the twonetworks; half of the difference between the two is presented as a measure of uncertainty associated with image segmentation.

Table 3. Mean Coordination Number and the Mean PoreBody-Throat Aspect Ratio of the Pore Networksa

Rock ⟨z⟩n ⟨z⟩V ⟨rb/rtmax⟩V

Ketton 2.92 � 0.03 6.65 � 0.05 1.631 � 0.008Estaillades 2.707 � 0.008 4.97 � 0.01 1.737 � 0.003Indiana 2.31 � 0.02 5.2 � 0.2 2.23 � 0.06Doddington 2.95 � 0.02 6.57 � 0.03 1.844 � 0.003Berea 2.93 � 0.01 6.02 � 0.02 1.848 � 0.004Springwell 2.22 � 0.01 2.91 � 0.02 1.73 � 0.03Stainton 2.09 � 0.04 3.8 � 0.2 2.2 � 0.1

aFor Indiana limestone, Doddington sandstone, and Stainton sandstone,the values presented are averages of two networks; half of the differencebetween the two is presented as a measure of uncertainty (cf. Table 2).For all other rocks, the uncertainty is the standard deviation of the mean.

Figure 8. Darcy velocity U [mm s�1] as a function of pres-sure drop per unit length at single-phase state (�), Snw,r

macro

(open markers), and Snw,rmax (solid markers) of Ketton lime-

stone, Indiana limestone, and Berea sandstone. Dashed linesare the least squares fit to the data presented.


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with a typical span of about 200 mm that are associated withinter-particle pores which, like the inter-particle pores ofKetton limestone, are relatively easy to identify (Figure 1).[24] In contrast, the micro-structure of the pore space of

Estaillades limestone is visibly complex [Dautriat et al.,2011], with no clear separation between the size of inter-aggregate (macro) pores and the intra-aggregate pores(Figure 2). Similarly, Stainton and Springwell sandstonescontain significant amount of fine structure, which are visi-ble in the X-ray images (Figure 1) and are depicted by theslow decay of the pore entry size distribution as rp decreasesbelow the unimodal peak (Figure 2). The uncertainty asso-ciated with the image segmentation, and hence the extractednetworks, is expected to be large for these rocks. The qualityof the network for Springwell sandstone is particularly poor.As demonstrated by the small fnetwork/f = 20%, much of thepore space is unresolved. This network is included in thispaper for completeness, and is not intended for use inquantitative analysis.

2.2. Experimental Procedure

[25] Laboratory experiments were conducted at ambienttemperature and pressure to measure the non-wetting phasesaturation and permeability to brine at steady state achievedduring waterflooding. Rock samples were 37.8 � 0.3 mm indiameter and varied in length between 74.94 to 89.15 mm.An aqueous solution of 5.0 wt.% sodium chloride and1.0 wt.% potassium chloride was used as the wetting phasefor sandstones. For limestones, this brine was further satu-rated with sacrificial rock to prevent dissolution of thesample during the experiment. The non-wetting phase wasn-octane for Doddington and Stainton, and n-decane for allother rocks. The basic properties of the hydrocarbons areprovided in Table 4, for reference. At any stage of theexperiment where two fluids are present, the capillarynumber Ca = mU/s, where m is the viscosity of the injectedfluid and U is its volumetric flow rate per unit cross-sectionalarea of the rock sample, was maintained at Ca ≤ 1.1 �10�6 to ensure capillary-dominated conditions [Chatzisand Morrow, 1984].[26] During the experiments, the rock samples were

housed in a custom-made horizontal Hassler-type pressurecells with radial confining pressure. Each experimental runconsists of a sequence of fluid displacement, as describedbelow. Liquids were injected using high-precision syringepumps (Teledyne ISCO 1000D).

2.2.1. Absolute Permeability and Porosity[27] Each sandstone core was cleaned by standard Soxhlet

extraction with a mixture of methanol and toluene, thenvacuum-dried at up to 95�C before each experiment. Incontrast, a new limestone core was used in each experiment.The dry weight of the core was measured prior to eachexperiment.[28] The core was evacuated, then flushed with gaseous

CO2 to expel any residual air. The core was then floodedwith a minimum of 17 pore-volumes (pv) of brine. In someexperiments, the absolute permeability, k, was determinedduring this step by changing the flow rate several times and,at each flow rate, measuring the pressure drop across thelength of the core once steady state was achieved. The per-meability was calculated as

k ¼ mdU

d DP=Lð Þ ; ð8Þ

where L is the core length and DP is the pressure differenceacross it. dU/d(DP/L) is taken as the gradient of the lineof regression of U on DP/L applied over the Darcy regime.The uncertainty of k is taken as that of dU/d(DP/L), whichin turn is estimated according to Taylor [1997, chapter 8].[29] The core was subsequently removed from the Hassler

cell and weighed. The pore volume, hence f, was deter-mined from the difference in the mass of the core between itsdry and brine-saturated state.2.2.2. Capillary Trapping[30] Initial non-wetting phase saturation. Initial (post-

primary drainage) non-wetting phase saturation was estab-lished using the porous plate technique, in which a hydrophilicdisk placed immediately downstream of the core retains thenon-wetting phase inside the core. With this method, equi-librium corresponds to uniform pressure distribution acrossthe core in each of the phases, with the difference in thepressures corresponding to Pc. Capillary end effects areeliminated, and phase saturations are uniform across thelength of the core. Furthermore, high Snw,i can be establishedat realistic Ca (≤6.0 � 10�8).[31] After its brine-saturated weight was measured, the

core was reinserted into the cell with a hydrophilic disk(Weatherford Laboratories, Stavanger; KeraNor AS, Oslo;ErgoTech Ltd., Conwy). An additional 4 to 61 pv of brinewas injected through the system.[32] Next, the non-wetting phase was injected into the core

at constant pressure until equilibrium was achieved. In thepresent experiments, drainage lasted between 5 to 55 days.In-line pressure transducers measured the pressure of thenon-wetting phase immediately upstream of the cell and the

Figure 9. Snw,r as a function of Snw,i in Berea sandstonemeasured in the present study (open square) and byViksund et al. [1998] (�) using the porous plate method.

Table 4. Fluid Properties Assumed in Calculating Permeability toBrine and Capillary Numbera

Wetting Phase n-Decane n-Octane

m [mPa s] 1.0903b 0.838c 0.508c

s � 0.04 [mN m�1] 52.33d 51.64d

am is the viscosity. s is the interfacial tension of the respective nonwettingphase with water.

bFor 5.8 wt.% aqueous sodium chloride solution at 100 kPa, 293.2 K[Kestin et al., 1981].

cAt 298 K [Haynes, 2012].dAt 293.2 � 0.1 K [Zeppieri et al., 2001].


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wetting phase immediately downstream of the cell; drainagePc was measured as the difference between the pressuresonce steady state is achieved. Sandstones with higher per-meability required lower Pc to achieve maximum Snw,i, con-sistent with mercury injection measurements (Figure 3).Accordingly, lower Pc were selected for convenience. Theapplied Pc ranged from 7.2 to 85 kPa for Doddington sand-stone to 1573 kPa for Estaillades limestone (Table 5).[33] For Springwell sandstone and Ketton, Estaillades,

and Indiana limestones, the core was removed from theHassler cell after primary drainage and weighed. In theseruns, Snw,i was determined from the difference in the mass ofthe core from its dry state. For all other rocks, Snw,i wascalculated from the volume of the injected non-wettingphase, the decrease in the mass of the Hassler cell containingthe core from its brine-saturated state prior to oil injection,and the mass of the effluent brine.[34] Residual non-wetting phase saturation. Subsequently,

10 to 27 pv of brine was injected into the sample at maximumflow rates corresponding to Ca = 1.7 � 10�8 to 6.1 � 10�7.The sample was removed from the Hassler cell and weighed.Snw,r was determined from the difference in the mass of thecore from its dry state.2.2.3. Permeability at Residual Saturation[35] The permeability to brine at residual state was mea-

sured at the end of one experiment for all rocks but Dod-dington and Stainton sandstones. After waterflooding, thecore was reinserted into the Hassler cell. Brine was injectedat a constant flow rate or at a constant pressure and, aftersteady state was achieved, the pressure at the upstream anddownstream face of the core were recorded. Flow rates wererestricted to Ca ≤ 1.1 � 10�6 to avoid remobilization of thetrapped phase, which has been found to yield higher relativepermeability at a given residual saturation in some water-wetsandstones [Morrow et al., 1983].

3. Results

3.1. Permeability to Brine at Residual State

[36] Under experimental conditions considered presently,namely Ca ≤ 1.1 � 10�6, flow velocity increased linearlywith pressure gradient at both single-phase and residualstates (e.g., Figure 8). All correlations were highly signifi-cant. Non-linear dependence reported by Morrow et al.[1983] in water-wet sandstones was not observed here,

suggesting that non-Darcy behavior at residual state is notsalient. Further, the linear increase of U with DP suggeststhat Snw,r remained constant during the permeability mea-surements, i.e., that remobilization of the trapped phase doesnot occur at Ca ≤ 1.1 � 10�6. This is in contrast to obser-vations by Kamath et al. [2001], in which Snw,r remainedCa-dependent even at Ca as low as 3.0 � 10�9 in all fourcarbonates they considered.[37] The permeability of each rock at residual state,

k(Snw,r), normalized by the absolute permeability is presentedin Table 5. The relatively small k(Snw,r

max)/k [= O (0.04 � 0.2)(1 � Snw,r

max)] is characteristic of strongly water-wet systems atresidual state [Oak et al., 1990; Amaefule and Handy, 1982],in which the non-wetting phase is retained in the largest poresafter imbibition and the wetting phase is forced to flowthrough the smaller pores.

3.2. Residual Nonwetting Phase Saturation

[38] Our experimental procedure is validated by the goodagreement between our measurements of Snw,r in Bereasandstone and those by Viksund et al. [1998] (f = 0.23) forwhich Snw,i was established using the porous plate technique(Figure 9).[39] Note that the measurements of Snw,r coincide within

experimental uncertainty for Snw,i > 0.9. Doddington andStainton sandstones also exhibit a range of Snw,i overwhich Snw,r remains independent of Snw,i. For these rocks,all such measurements are considered in calculating Snw,r

max.[40] Some studies report measurements that suggest that

there is a limit, termed irreducible wetting-phase saturation,below which 1 � Snw,i cannot be reduced by increasing theapplied capillary pressure. Other studies have found noevidence of such an asymptotic limit [e.g., Dullien et al.,1986]. Table 5 presents the imposed Pc, the correspondingrp (equation (1), q = 0�, s as in Table 4), and Snw,i achievedin the present study. Our experiments demonstrate thatSnw,i approaching 1 can be achieved, with sufficient timeand capillary pressure (e.g., Figure 9). We emphasize thatthe largest Pc considered in this study correspond to cap-illary entry pressures for pores as small as rp = O(0.1) mm(Table 5), which is an order of magnitude smaller than thecharacteristic size of clay particles [e.g., Rabaute et al.,2003; Cerepi et al., 2002]. Similarly, for the limestones,rp = O(0.1) mm implies that the non-wetting phase accessed a

Table 5. Summary of Laboratory Measurementsa

Rock Pc [kPa] rp [mm] Snw,i Snw,rmax Snw,r

macro n k(Snw,r)/k

Ketton 1177 0.09 0.69 0.294 � 0.009 - 1 0.106 � 0.00111.1 9.4 0.56 - 0.24 � 0.01 1 0.1010 � 9 � 10�4

Estaillades 1573 0.07 0.96 0.37 � 0.01 - 1 0.081 � 0.002Indiana 1273 0.08 0.86 0.47 � 0.01 - 1 0.11 � 0.02

18.9 5.5 0.23 - 0.12 � 0.02 1 0.37 � 0.05Doddington 7.2–85.5 1–14 0.78–1.00 0.364 � 0.004 - 5 n/aBerea 73–507 0.2–1.4 0.93–1.00 0.432 � 0.007 - 4 0.056 � 3 � 10�3

26 4.0 0.74 - 0.341 � 0.003 1 0.059 � 3 � 10�3

Staintonb 466–1371 0.08–0.2 0.84–0.87 0.51 � 0.02 - 3 n/aSpringwell 1161 0.09 0.78 0.39 � 0.02 - 1 0.021 � 0.002

an is the number of independent (Snw,i, Snw,r) measurements. Where n = 1, uncertainty in Snw,r is taken as the difference in measured Snw,r before and afterthe residual-state permeability measurements. Where multiple measurements were collected, the range of (Pc, Snw,i) was considered and the mean andstandard error of the corresponding Snw,r

max measurements are presented. The uncertainty in k(Snw,r)/k is the sum of the contributions from the uncertaintyin k (see Table 1) and in dU/d(DP/L) in calculating k(Snw,r) (see equation (8)). Pore entry size, rp, corresponding to the applied Pc is calculated asequation (1), taking q = 0� and s as presented in Table 4.

bTwo of the measurements were reported previously by Pentland et al. [2010].


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significant fraction of the microporosity, inferred fromFigure 2 to be rp < 1 mm.[41] Recall that intraparticle microporosity is not repre-

sented in the pore networks (section 2.1.3). The impact ofthis exclusion may be characterized by comparing themaximum residual, Snw,r

max, with Snw,r corresponding to a suf-ficiently low drainage Pc such that rp is larger than half thevoxel size of the X-ray images (Figure 2, dashed lines); thelatter is denoted by Snw,r

macro. Snw,rmacro was measured in Ketton

limestone, Indiana limestone, and Berea sandstone (Table 5).Also, in Doddington sandstone, Snw,r is independent of Snw,ifrom Pc much lower than that corresponding to the voxelsize and, accordingly, Snw,r

max may be interpreted as Snw,rmacro.

[42] In the rocks considered presently, Snw,rmacro/Snw,i does

not differ substantially from Snw,rmax /Snw,i, suggesting that

microporosity and macroporosity trap the non-wetting phasewith the same efficiency. For simplicity, Snw,r /Snw,i refersto both Snw,r

macro/Snw,i and Snw,rmax /Snw,i in the discussion that

follows.[43] Snw,r

max /Snw,i broadly decreases with increasing f and k(Figure 10), with no observable difference between sand-stones and limestones. The correlation with f is particularlyevident, and the dependence is captured well by the best-fitpower function to all data (dashed line):

Smaxnw;r

Snw;i¼ 0:166

f0:63 : ð9Þ

The exponent in the power law dependence has importantimplications for geological carbon storage. The volume ofresidual non-wetting phase per unit (bulk) volume of a res-ervoir is, by definition, fSnw,r

max. In the context of geologicalcarbon storage, fSnw,r

max may be interpreted as the capacity of a

potential storage site to secure CO2 by capillary trapping[Iglauer et al., 2011]. From equation (9), fSnw,r

max/Snw,i∝ f0.37,which increases monotonically with f. This is contrary toprevious suggestions that fSnw,r

max exhibits a maximum atf = 0.22 [Iglauer et al., 2011].[44] A qualitatively similar trend has been reported pre-

viously for Snw,rmax established by spontaneous imbibition of oil

into dry samples in sandstones [Yuan, 1981; Suzanne et al.,2001] and in carbonates [Yuan, 1981], although the correla-tion is weaker in the latter. Similarly, Snw,r

max established byspontaneous imbibition into 92 carbonates containing someinitial wetting phase saturation also exhibits this trend, albeitwith much scatter [Wardlaw and Cassan, 1978]. Morerecently, however, Snw,r

max from three gas reservoirs werefound to increase with increasing f at low f, reaching amaximum at f ≈ 0.15 to 0.19 [Suzanne et al., 2001, 2003].As f increases further in these rocks, Snw,r

max broadly mergeswith that of Fontainebleau sandstone, thus decreasing withincreasing f [Suzanne et al., 2001].[45] The tendency for Snw,r

max to decrease with increasing fis commonly attributed to, albeit without experimental vali-dation, a tendency for less porous rocks to have a higherpore body-throat aspect ratio, a lower pore coordinationnumber, or both [e.g., Yuan, 1981; Jerauld, 1997]. A nega-tive correlation between f and the pore aspect ratio emerges,for example, where the variation in porosity between rocks isassociated with different degrees of cementation and thecementation occurs uniformly around the grains [Holtz,2005]. Unfortunately, ⟨rb/rt

max⟩V ≈ 2 in all pore networksconsidered presently (Table 3), and its correlation with fcannot be verified. Nevertheless, Snw,r /Snw,i broadly increa-ses with ⟨rb/rt

max⟩V of the pore networks (Figure 11a).[46] Next, we consider the conjecture that the f depen-

dence of residual saturation is a manifestation of a correlation

Figure 10. Snw,rmax/Snw,i as a function of (a) f and (b) k/f for

limestones (open circle) and sandstones (open square). Ver-tical bars depict standard error of the mean where multiplemeasurements are available, and the difference in measuredSnw,r before and after the residual-state permeability mea-surements where they are not (see Table 5). Dashed line inFigure 10a is the best-fit power function in the least squaressense to all data (equation (9)). Horizontal bars in Figure 10brepresent uncertainty in k (see Table 1). Where the bars arenot visible, they are smaller than the marker size. Also repre-sented in Figure 10a are Viksund et al.’s [1998] measure-ments in Berea sandstone for Snw,i > 0.92 established usingthe porous plate method (solid square).

Figure 11. Snw,rmax (solid markers) and Snw,r

macro (open markers),normalized by Snw,i, as a function of (a) ⟨rb/rt

max⟩V and(b) ⟨z⟩V for limestones (circles) and sandstones (squares).Horizontal bars depict uncertainty; where the bars are notvisible they are smaller than the marker size. See captionof Figure 10 for the definition of the vertical bars. Thedashed line is pt (equation (10)).


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on pore coordination number. A positive correlation betweenf and the pore coordination number may be attributed toporosity reduction by compaction, which presumably tendsto collapse the narrower throats and pores first. This trend hasbeen reported in Fontainebleau sandstones [Lindquist et al.,2000; Doyen, 1988]. Similarly, within the sandstones con-sidered in the present study, ⟨z⟩V is larger in Doddington andBerea than Springwell and Stainton, which has lower f(Table 3). However, as discussed in section 2.1.3, a largerfraction of the pore space is unresolved in the latter, whichmay result in an underestimation of the true ⟨z⟩V, contributingto the apparent correlation.[47] Capillary trapping in rocks is often modeled as a

percolation process in three-dimensional regular lattices,with a uniform coordination number, for which the perco-lation threshold varies between pt = 1.56/z and pt = 1.43/zas z varies between 4 and 12 [Sykes and Essam, 1964], i.e.,

pt ≈1:5

zh iVð10Þ

[Yuan, 1981; Ziman, 1968; Shante and Kirkpatrick, 1971].Alternatively, a higher ⟨z⟩V may be correlated with lowerwaterflood Snw,r

max in a system in which trapping is dominatedby snap-off simply because a larger fraction of the porespace will be occupied by throats, from which the non-wetting phase is expelled during snap-off [Chatzis et al.,1983].[48] Measured Snw,r /Snw,i decreases with increasing ⟨z⟩V

(Figure 11b). However, a strong negative correlation withthe fractional volume of throats, ft/fnetwork, is not observed(Table 2). The deviation of the data for Springwell sandstoneand Estaillades limestone from those of the other rocks islikely to be a manifestation of the particularly poor quality ofthe networks for these rocks, which tends to underestimate⟨z⟩V.[49] Equation (10) significantly underestimates Snw,r /Snw,i

(dashed line). The discrepancy may be attributed to severaldifferences between the model and the experiment. First, themean coordination numbers of our rocks, which range from⟨z⟩V = 2.91 to 6.65 (Table 3), are significantly lower thanthose of the lattices described by equation (10). It has beenshown that percolation thresholds for ordinary percolationwith trapping and invasion percolation with trapping divergerapidly in 3-D lattices as their coordination number fallsbelow z < 5, with the former becoming increasingly largerthan the latter [Paterson et al., 2002]. Thus it is possible thatat conditions considered presently, trapping is particularlysensitive to the details of the percolation process. Second,spatial correlations in the pore architecture, which tend toenhance trapping, are not included in the model.

4. Conclusions

[50] Laboratory measurements of maximum residual sat-uration and permeability at residual state in three limestonesand four sandstones were presented. Both absolute perme-ability and permeability at residual state exhibit Darcybehavior. Residual saturation, normalized by the initial satu-ration, decreases with increasing porosity. Similarly, the nor-malized residual saturation broadly decreases with increasingabsolute permeability, but the correlation is not significant.Residual saturation broadly increases with increasing pore

body-throat aspect ratio and decreases with increasing porecoordination number, both of which are conditions favorableto snap-off.We emphasize that microporosity associated withintraparticle or intra-aggregate pores are not represented inthe pore networks and, accordingly, the calculated values forpore aspect ratio and coordination number only represent thatof larger pores and throats in each rock.[51] Differences in the complexity of pore structure

between limestones and sandstones do not yield notabledifference in the functional dependence of residual satura-tion within the conditions considered presently. In particular,the normalized residual saturation at a given porosityappears to be independent of the fractional volume com-prised by microporosity. The absence of a correlation isconsistent with previous observations by Yuan [1981], but isin sharp contrast to previous reports that maximum residualin sandstones with a given porosity decreases with increas-ing microporosity [Jerauld, 1997; Suzanne et al., 2001,2003]. A simple explanation is that the microporosity in therocks considered presently have similar pore aspect ratio andconnectivity as the macroporosity.[52] An interesting question that emerges from the present

study is the effect of microporosity under mixed-wet con-ditions, in which a fraction of the pore space is oil-wet. Here,the non-wetting phase is expected to come into contact withthe oil-wet areas of the pore surface, and hence is expectedto be more strongly affected by surface roughness andintraparticle microporosity [Wardlaw, 1996].

[53] Acknowledgments. This material is based on work supportedby Shell under the Grand Challenge on Clean Fossil Fuels and Qatar Petro-leum, Shell and the Qatar Science and Technology Park under the QatarCarbonates and Carbon Storage Research Centre. The authors gratefullyacknowledge Hu Dong at iRock Technologies for extracting pore networksof our samples and John Crawshaw for his assistance in the selection of thelimestones and for his comments and suggestions. The authors also thankAmer S. Syed and undergraduate students Josephine Herschan and MagaliChristensen for their assistance with the laboratory experiments, and thethree anonymous reviewers.

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Capillary trapping in sandstones and carbonates ...€¦ · [e.g., Stegemeier, 1977; Land, 1968;...

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