Field determination of mechanical aperture, entry pressure .../file/gprgpaper... · Field determination of mechanical aperture, entry pressure and relative ... Accurate determination

Steele, A., Reynolds, D. A., Kueper, B. H. & Lerner, D. N. (2006). Geotechnique 56, No. 1, 27–38

27

Field determination of mechanical aperture, entry pressure and relativepermeability of fractures using NAPL injection

A. STEELE*, D. A. REYNOLDS†, B. H. KUEPER‡ and D. N. LERNER*

An in situ field technique has been developed and im-plemented to measure non-aqueous phase liquid (NAPL)entry pressure and subsequently estimate mechanicalaperture variability in an undisturbed, water-saturatedrock fracture. The field experiment also provided theopportunity to measure wetting phase relative permeabil-ity at residual non-wetting phase saturation, kw,r(Snw,r).The radial aperture determination by the injection of oil(RADIO) method employs a constant-rate injection of anon-toxic NAPL into a fracture isolated by a doublepacker array. Injection pressures are recorded to providea characteristic signature that is interpreted to revealaperture enlargements and constrictions several metresfrom the borehole. Fracture aperture values are calcu-lated by reverse modelling of the pressure signaturesusing the FRACAS fully compositional two-phase flowmodel. Pre-NAPL injection hydraulic testing establisheda baseline dataset of hydraulic apertures ranging from26 �m to 259 �m with a mean value of 86 �m. Post-NAPL injection hydraulic testing gave kw,r(Snw,r) valuesranging from 0.04 to 0.39 with a mean value of 0.15.Numerical modelling calculated fracture mechanicalapertures vary from 36 �m to .1000 �m in test 1, andfrom 46 �m to .1000 �m in test 2. Single-value approx-imations of volume-averaged fracture apertures are twoto three times larger than the respective hydraulic aper-tures, suggesting that volume balance calculations usingthe hydraulic aperture may overpredict NAPL penetra-tion distances.

KEYWORDS: environmental engineering; groundwater; in situtesting; numerical modelling; pollution migration/control; rocks/rock mechanics

Une technique in situ a ete developpee et mise en oeuvrepour mesurer la pression d’entree de NAPL (liquide dephase non aqueuse) et la variabilite mecanique estimeede l’ouverture dans une fracture rocheuse non perturbeeet saturee d’eau. Les experiences sur le terrain ontegalement donne la possibilite de mesurer la permeabiliterelative a la phase avec une saturation residuelle dephase non mouillante, kw,r (Snw,r). La methode RADIO(Radial Aperture Determination by the Injection of Oil)utilise une injection a debit constant d’un NAPL nontoxique dans une fracture isolee par un double agence-ment de remblai. Les pressions d’injection sont enregis-trees pour donner une signature caracteristique qui estinterpretee pour reveler des agrandissements et reduc-tions d’ouverture a plusieurs metre du trou de forage.Les valeurs d’ouverture de fracture sont calculees parune modelisation inverse des signatures de pression enutilisant le modele d’ecoulement biphase entierementcompositionnel FRACAS. Des essais hydrauliques preli-minaires d’injection de NAPL ont etabli un jeu dedonnees de base d’ouvertures hydrauliques allant de26 �m a 259 �m avec une valeur moyenne de 86 �m. Lesessais hydrauliques d’injection de NAPL ont donne desvaleurs kw,r (Snw,r) allant de 0,04 a 0,39 avec une valeurmoyenne de 0,15. Les ouvertures mecaniques de fracturecalculees par modelisation numerique varient de 36 �m a. 1000 �m dans l’essai 1 et de 46 �m a .1000 �m dansl’essai 2. Les approximations a une seule valeur desouvertures de fracture a volume moyen sont deux ou troisfois plus elevees que les ouvertures hydrauliques respec-tives, ce qui suggere que les calculs d’equilibre volumiqueutilisant l’ouverture hydraulique peuvent surevaluer lesdistances de penetration du NAPL.

INTRODUCTIONGroundwater contamination by dense, non-aqueous phaseliquids (DNAPLs) has affected many developed countries,particularly in urban areas. Contamination by DNAPLs suchas chlorinated solvents has proved difficult to characterisebecause of the physical and chemical properties of thesecompounds, and the complexity of subsurface media. Infractured rock, non-wetting DNAPLs will migrate in thelarger-aperture fractures, often to substantial depths becauseof low fracture volumes. The complex nature of three-dimensional fracture networks hinders complete characteri-sation by conventional site investigation techniques, and

consequently it is difficult to predict the detailed migrationpathways of DNAPLs in fracture networks.

Accurate determination of fracture apertures is importantin addressing contaminant transport and multiphase flowproblems (Murphy & Thomson, 1993). Previous modellingstudies have shown that migration of DNAPLs in singlefractures (Kueper & McWhorter, 1991; Slough et al., 1999)is influenced strongly by fracture aperture. Reynolds &Kueper (2002) have shown that small changes in fractureaperture are more influential in determining rates of DNAPLmigration than processes such as dissolution and matrixdiffusion.

Properties such as fracture spacing and orientation can bemeasured in the field, but there are few methods for char-acterising fracture apertures. Hydraulic measurements ofbulk permeability can be converted to equivalent hydraulicaperture (Rutqvist, 1996). This requires assumptions regard-ing the number of fractures encountered, and is not directmeasurement of physical aperture. Laboratory measurementsof fracture aperture have been performed by injectingNAPLs and back-calculating the apertures from the entrypressure required to initiate flow (Hinsby et al., 1996;Jorgensen et al., 1998). Reitsma & Kueper (1994) calculated

Manuscript received 26 April 2005; revised manuscript accepted 31October 2005.Discussion on this paper closes on 3 July 2005, for further detailssee p. ii.* Groundwater Protection and Restoration Group, University ofSheffield, UK.† Department of Civil Engineering, Queen’s University, Kingston,Ontario, Canada; now at Centre for Water Research, University ofWestern Australia, Crawley, Western Australia.‡ Department of Civil Engineering, Queen’s University, Kingston,Ontario, Canada.

an aperture distribution for a rough-walled fracture bycorrelating capillary pressure observed during NAPL injec-tion with local apertures in the fracture plane. Other labora-tory-based techniques to measure fracture aperture haveincluded computer-aided tomography (Keller, 1998), nuclearmagnetic resonance imaging (Dijk et al., 1999), light trans-mission methods (Nicholl et al., 1999), silicon injection (YeoYeo et al., 1998), and resin injection (Hakami & Larsson,1996; Konzuk and Kueper, 2004).

There are a number of definitions of fracture aperture.Early attempts to simulate flow in fractures described themas consisting of two parallel plates, but there are few naturalsituations in which this conceptualisation is accurate, asnatural fractures are known to be rough walled (Renshaw,1995; National Research Council, 1996; O’Hara et al.,2000). A single value of hydraulic aperture is commonlyused, but its applicability to multiphase flow is not clear.The term ‘mechanical aperture’ is used to describe thearithmetic mean aperture of a rough-walled fracture.Renshaw (1995) concluded that, for large apertures, hydrau-lic and mechanical apertures have similar values, but therelationship between the two is non-linear and breaks downfor smaller fracture apertures where aperture approximatesthe scale of surface roughness. Other work supports thehypothesis that mechanical aperture and hydraulic apertureare not equal (National Research Council, 1996).

Two other approximations of fracture aperture can bederived from tracer test breakthrough (Tsang, 1992). Themass balance aperture is derived from the mean residencetime of a tracer, the flow rate and fracture geometry.Similarly, frictional loss aperture is determined by expressingthe mean residence time of the tracer in terms of thetransport velocity. Tsang (1992) suggests that the massbalance aperture is greater than or equal to the hydraulicaperture, which in turn is greater than or equal to thefrictional loss aperture. The critical aperture controllingNAPL flow through a variable aperture fracture is theaperture corresponding to the entry pressure (Kueper &McWhorter, 1991). This is the smallest aperture constrictionwhere NAPL first forms a fully connected pathway across avariable aperture field (Steele & Lerner, 2001).

The primary objective of this study (Steele, 2000) is todescribe and implement a new in situ field technique tomeasure mechanical aperture variability and NAPL entrypressure in a naturally occurring water-saturated fracture.The secondary objective arises as an incidental benefit of thetechnique, and is to measure wetting phase relative per-meability at residual non-wetting phase saturation, kw,r(Snw,r).The technique is applied in a single borehole in fracturedbreccia and sandstone. In situ tests have significant advan-tages over laboratory tests in that the fracture aperture andinfills are undisturbed, and the fracture is subject to naturalcompressive stress conditions, which are known to influenceapertures (Reitsma & Kueper, 1994). The new field testtechnique uses a controlled injection of a non-toxic NAPLinto a fracture isolated by a straddle packer array. The test iscalled the radial aperture determination by the injection ofoil (RADIO) test. The resulting transient pressure signatureis reverse-modelled using a two-phase flow numerical modelto produce an aperture profile over several metres from theborehole.

CONCEPTUAL MODEL AND THEORYConceptual model

The RADIO test isolates a single fracture using a strad-dle-packer assembly, injects a non-wetting liquid at a pre-scribed flow rate, and measures pressure. The signature ofnon-wetting phase pressure against time at the injection

point is used (a) to calculate the fracture entry pressure, and(b) as a calibration target for a numerical two-phase flowmodel to back-calculate the range of fracture aperturesencountered. In addition to the RADIO test, conventionalhydraulic tests are performed in the borehole (a) prior toRADIO testing to provide measurement of the hydraulicapertures, and (b) post RADIO testing to provide measure-ment of the relative permeability to water in the presence ofresidual NAPL. The conceptual geometry adopted for theanalysis of both the hydraulic and RADIO tests is that offlow from a borehole through a single horizontal fracture, asshown in Fig. 1. It is assumed that

(a) wetting phase flow in the matrix does not significantlyinfluence the non-wetting phase pressure signature

(b) NAPL does not penetrate the matrix(c) the fluids are incompressible(d) fracture apertures vary along the radius and are radially

symmetrical about the borehole(e) the fractures and rock mass are rigid( f ) the interfacial tension and contact angle of the NAPL

remain constant

As with other measurements of the properties of rockmasses that assume radial symmetry, such as pumping andslug tests, the results must be understood in terms of theidealised model used. At this site tests were carried out in ahorizontally bedded sedimentary rock in which the porosityof the matrix varied, but was low enough to justify assump-tions (a) and (b) above. With respect to compressibility andrigidity, these are deemed to be met, given the generally lowcompressibility and high rigidity of fractured rock. Becausewe assume that fracture aperture varies with radius, it isclear that the results yield an approximation of the range ofapertures encountered within the fracture plane, not theprecise locations of any particular aperture value.

Theoretical analysis of hydraulic test dataHvorslev (1951) developed a method to calculate per-

meability from slug tests conducted in isolated test sectionsof aquifer below the water table. Where the length of thetest section is longer than eight times the borehole radius

T ¼ KL ¼r2ln

L

R

� �2t0

(1)

where T is the transmissivity of the test section, K ishydraulic conductivity, r is the radius of the borehole casingin which the falling head is measured, L is the length of thetest section, R is the radius of the test section of theborehole (R > r), and t0 is the time taken for the water levelto fall to 37% of its initial value. Assuming flow throughthe fracture can be approximated by laminar flow betweentwo parallel plates, T can be converted to an equivalenthydraulic aperture using the cubic law (Rutqvist, 1996)

eh ¼ffiffiffiffiffiffiffiffiffiffiffi12T�

rw gn

3

s(2)

where eh is the equivalent hydraulic aperture of a fracture, �is the viscosity of water, rw is the density of water, g is theacceleration due to gravity, and n is the number of indivi-dual fractures in the open section. In this study we employequations (1) and (2) to determine eh from hydraulic testsperformed prior to RADIO testing.

In multiphase flow, the permeability to each phase de-pends on its saturation relative to other fluid phases as wellas the intrinsic permeability of the medium. Relative per-

28 STEELE, REYNOLDS, KUEPER AND LERNER

meability to the wetting phase (kw,r) in the presence of twoimmiscible phases is defined as (Bear, 1972)

kw,r ¼kw

k(3)

where kw is the effective permeability of the wetting phase,and k is the intrinsic permeability of the fracture. The ratioof T post injection to T measured prior to NAPL injection isa direct indication of kw,r. In this study, hydraulic slug testsare conducted both before NAPL injection and after water-flooding to reduce NAPL saturation to residual non-wettingphase saturation, Snw,r, allowing kw,r(Snw,r) to be determined.

Model governing equationsCapillary pressure (Pc) is defined as the difference be-

tween the non-wetting (Pnw) and wetting phase pressures(Pw)

Pc ¼ Pnw � Pw (4)

The capillary pressure required for NAPL to traverse afracture is (Kueper & McWhorter, 1991)

Pe ¼2� cosŁ

e¼ 2�

eŁ(5)

where � is the interfacial tension between the fluids, Ł is thecontact angle measured through the wetting fluid, Pe is thefracture entry pressure, and e is the smallest aperture thatprovides the first continuous pathway across the fracture. Inthis study we employ equations (4) and (5) to determine thefracture entry pressure (Pe) from the NAPL injection data,and express this as an equivalent aperture, eŁ (¼ e=cosŁ).Contact angles are not frequently measured and can vary

(Harrold et al., 2001), and a common assumption is thatŁ ¼ �=2 so that e ¼ eŁ.

Under the assumption that the solid phase of a fracturedmedium is inert and immobile, the partial differential equa-tions governing multiphase flow and multi-component trans-port in a single fracture are (Reynolds & Kueper, 2001)

@

@ tct��S�xi�ð Þ þ = ct�xi�v�ð Þ � = �S�Di�= ct�xi�ð Þ

� �� qi� � I i� ¼ 0

� ¼ 1 . . . np, i ¼ 1 . . . nc (6)

where ct� is the molar density of phase �, � is the porosityof the medium, S� is the saturation of the � phase expressedas a fraction of void space, xi� is the mole fraction ofcomponent i in phase �, v� is the Darcy flux of phase �, Di�

is the dispersion tensor for component i in phase �, qi� is asource or sink of component i to or from phase �, Ii� is theinterphase mass transfer of component i to or from phase �,np is the number of phases, and nc is the number of compo-nents. In this study we employ a numerical model based onequation (6).

FIELD SITE AND TESTING METHODSChronology of field tests

The fieldwork commenced with borehole construction,borehole development, and geophysical logging. Testingcontinued with hydraulic testing to determine hydraulicapertures, followed by two RADIO tests, and oil injectioninto all other zones. The borehole was pumped to induce awaterflood in the formation to remove mobile NAPL, and

Fig. 1. Conceptual model of RADIO experiment and modelling grid geometry

FRACTURE APERTURE DETERMINED WITH NAPL INJECTION 29

repeat hydraulic tests were performed to determinekw,r(Snw,r).

Hydrogeological settingThe site used for the experiments was an industrial facility

near Dumfries in Scotland (Fig. 2). The site is on thewestern edge of the Dumfries Basin, where a series ofPermian breccias and water-lain sandstones known as theDoweel Breccia Formation are present, extending to over1000 m in depth at the centre of the basin (Lovell, 1991).The breccia that constitutes much of the test borehole is amuddy flood debris flow reported to have no significantintergranular porosity or permeability (Ball, 1997), and con-sequently the matrix is assumed to have negligible transmis-sivity unless otherwise stated. Fractures associated withfaulting along this western boundary form the focus for thisstudy. The basin is a locally important aquifer for the townof Dumfries (Robins and Buckley, 1988; Ball, 1997).

Experimental boreholeThe test borehole was drilled with a direct circulation

water flush to 12.25 m below ground level (bgl), and thencored at 145 mm diameter to a total depth of 30.40 m (Fig.3). The objectives of coring were to obtain a core to loggeologically and to have a smooth surface against which toset the packer apparatus; the drilling is unlikely to have beenaggressive enough to induce new fractures. The boreholewas cased to 12.25 m owing to instability of the upperweathered zone and drift, and consequently no testing waspossible above this depth. The borehole was open from12.25 m to 30.13 m, with a small length at the bottom filledby fallback of cuttings. Static water level was typically9.7 mbgl. The borehole was developed for 24 h until sedi-ment free by pumping with an electric submersible pump atthe maximum sustainable rate of 0.3 l/s. The core showedthe Doweel Breccia Formation consists of a predominantlypale red-brown breccia, well consolidated and cemented witha fine matrix of siltstone. Interbedded within the brecciawere layers of fine- to medium-grained sandstone. Fulllithological descriptions are given in Fig. 3. Over 97% corerecovery was achieved and a full fracture log obtained.

Geophysical dataThe fracture log was enhanced and finalised by correlating

with imagery obtained from downhole geophysics. Acousticteleviewer (ATV) logs (Lau et al., 1987; Williams &Johnson, 2004) provided a detailed, continuous image of theborehole wall, enabling accurate identification of the pre-sence of fractures together with their angle of dip andorientation. Lithological changes were also readily identifi-able. Fracture depth was determined to the nearest 1 cmusing the ATV imagery. This was an essential tool inselecting packer test zones for the hydraulic, RADIO andresidual saturation tests. The high resolution of the ATV logswas shown by the identification of fractures that later provedto have hydraulic apertures down to 26 �m.

Determination of hydraulic aperture from straddle packertesting

Following geophysical logging, hydraulic testing was per-formed to obtain hydraulic apertures and matrix permeabil-ity. Eighteen hydraulic tests were carried out in the boreholeover single and multiple fracture zones, and the brecciamatrix. The close spacing of some fractures prevented everyfracture being individually tested, and 14 tests coveredgroups of fractures.

The low yield of the borehole precluded any sustained testpumping of individual test zones, and consequently slugtests were performed for hydraulic testing. The apparatusused, which is pictured in Fig. 4(a), consists of two rubberpackers mounted on steel pipe suspended from the surfaceusing 46 mm ID high-density polyethylene (HDPE) piping.One end of each packer was fixed while the other slid upthe pipe, changing the packer length in response to inflation.The packers were inflated from a regulated nitrogen gassupply to ambient pressure plus 500 kPa. The interval be-tween inflated packers was 730 mm. The packers wereinflated and allowed to equilibrate to hydrostatic pressurebefore the tests. The slug tests were performed by rapidlypouring a slug of water into the test interval from thesurface. Although this was not an instantaneous rise in head,the low transmissivity of the test zones resulted in a slowfall in head over time and consequently a negligible error inrecording the early stages of the slug test. Changes in headwere recorded using two strain gauge pressure transducers(DruckTM PDCR 800 series) wired to a programmable datalogger. One transducer was located in the test zone tomonitor the slug test. The other was above the test zone todetect leakage around the top packers. Leakage was recordedin two of the test zones, and these results have beendiscounted.

RADIO test apparatusThe RADIO apparatus is based on a standard double

packer design (Fig. 4(b)). The central tubing is 90 mmHDPE piping, thread-jointed at 2 m intervals. All the tubingwas perforated to allow free movement of groundwateraround the packer during installation, testing and removal.The tubing is open at its base, and consequently the onlysection that is not at the hydrostatic pressure of the standingwater column is between the inflated packers. The packersare lowered and raised on this central tubing. The packermaterial itself is flexible reinforced rubber tubing suppliedby Archway Engineering. Two sections of rubber tubingwere threaded over the tubing and held in place at the topand bottom ends by rubber adhesive and steel banding. Asingle inflation port was fixed into each packer section frominside the central tubing, and an inflation line from thenitrogen supply was attached. The open section between the

��

��

� ��

��

�

��

��

��

Fig. 2. Location of study area, south-west Scotland


packers was 410 mm, smaller than the hydraulic test packerseparation of 730 mm to permit better isolation of individualfractures. A machined block connects the upper and lowerpackers, and hosts the injection ports and pressure monitor-ing ports just below the top packer. The block has largevertical holes through it to allow movement of the packerstring through the static water column. The NAPL injectionpipe from surface runs through the central tubing and isattached into the block. Eight radial injection holes connectfrom this port to the annular space between the packers.

The major dataset from the RADIO tests is NAPL injec-tion pressure over time for a specified flow rate. Pressuredata are collected with a Honeywell 26PCDFA1D piezo-resistive differential pressure transducer with automatic tem-

perature compensation. The pressure transducer has a linearcalibration, determined in the laboratory by chilling to thegroundwater temperature of 128C and applying a range ofpressures up to full scale with a high-quality nitrogen gasregulator. The ‘positive’ port of the pressure transducer isconnected to the NAPL injection ports in the machine block,and the ‘zero’ port is exposed to hydrostatic pressure in theborehole at the same elevation in the block. The pressuretransducer is connected to a digital pressure indicator (DPI)at the surface, which gave real-time pressure readings thatwere logged onto a laptop computer at 10 s intervals.

There are several advantages in using this type of pressuresensor. Its physical size—less than 35 mm at its largestdimension—means that the central tubing can be of a small

Fig. 3. Borehole construction, geology and test zones. NP denotes RADIO test zone results not presented here


diameter and reduces drilling costs. Such transducers areinexpensive when compared with conventional diaphragmwall pressure transducers, give good resolution and repeat-ability, and compensate for temperature variations. A differ-ential pressure transducer also compensates for water tablefluctuations during the test, as the zero port will react tochanges in standing water column head, as will the pressure

in the fracture isolated by the packer. This assumes thatpiezometric pressures fluctuate uniformly in a saturatedfracture network.

The field data consist of differential pressure against time,the pressure reading being the difference between the pres-sure of the NAPL and that of the standing water column atthe same elevation. This was converted in two stages to non-

Fig. 4. (a) Hydraulic packer apparatus; (b) RADIO apparatus (not to scale)


wetting phase pressure (Pnw) for matching to the numericalmodel output. First, the time at which NAPL first enteredthe fracture was identified from the field data and taken asthe origin of the test (t ¼ 0). All experimental times aretaken from this point. Second, the relative pressure valueshave been converted to absolute values by adding the hydro-static head measured within the packers at the depth of thefracture under test. Consequently, the field data are con-verted to Pnw against time from the point of first invasion ofthe fracture.

NAPL was pumped from the surface by a QG150-2constant flow rate pump manufactured by Fluid MeteringInc., capable of pumping water at over 100 ml/min. Thispositive displacement pump produced a constant flow ratedespite significant back-pressure and provided the constantinjection source for all the RADIO experiments. The NAPLused for the experiments was triglyceride as pure sunfloweroil. This oil is well suited to field experiments as it has verylow solubility in water, is inexpensive, and is a foodstuffwith low toxicity. It is also non-wetting in the presence ofwater. Its specific gravity of 0.92 classifies it as a light non-aqueous phase liquid (LNAPL) but, as gravity forces werenot dominant in the horizontal to sub-horizontal fracturestested, this was not of consequence. The degradation path-way of vegetable oil is well established, and its daughterproducts are not considered to be significant toxicological orecotoxicological hazards.

The apparatus integrity was tested in the laboratory byinflating inside a 129 mm ID transparent Perspex tube withnitrogen gas to ambient pressure plus 200 kPa, and injectingNAPL into the annular space between the packers. Thepackers sealed well against the tubing wall, and did not leakany NAPL into the standing water column. Logging of thewater levels in the laboratory system showed no leakagearound the packers. NAPL was continually injected until theNAPL/water interface was lowered to the position where thefracture would be located during field tests. An artificialfracture fabricated from two sheets of transparent plastic waspositioned here, and the oil was observed to invade thefracture evenly without the formation of any emulsion. Atall times there was a continuous NAPL pathway between theinjection port, ‘positive’ pressure monitoring port and theouter NAPL boundary.

RADIO field testingField testing was in the spring months following regula-

tory permission for the controlled injection of sunflower oil.Eighteen NAPL injection tests were performed over intervalsdetermined from examination of the ATV logs and core. Ifthe zone fitted the assumptions of the RADIO test, data werecollected as described above. If not, the NAPL injectionallowed the later measurement of kw,r(Snw,r).

The packers were lowered so that the injection ports weretypically 100 mm above the fracture to be tested, the pres-sure transducer was set to zero, the data loggers were startedand the packers were inflated. The test zone was left toequilibrate to the hydrostatic pressure; then the pump wasswitched on and the oil was injected into the annulus.During this priming stage water was displaced from thepacker annulus into the fracture as oil filled the space fromthe top downwards. The constant injection rate for both testsreported here was 6.2 � 0.5 ml/min, measured by recordingthe rate of mass loss from a supply container stood on abalance, averaged over a 5 min period. It consequently tookseveral hours for the annulus to be filled with NAPL and forthe water/NAPL interface to reach the fracture. There was asmall increase in annulus pressure during this injectionowing to the displacement of water into the fracture. The

annulus pressure rose distinctly once the NAPL entered thefracture. From the time of first invasion of the fracture byNAPL the fracture wall at the borehole became a constantflow rate source of NAPL to the fracture. This formed oneof the boundary conditions for the numerical model. RADIOtests ran for approximately 24 h and pressure data werecollected at 10 s intervals. At the end of each experimentthe pump was switched off and the pressures were allowedto equilibrate.

Relative permeability testing at residual saturationThere are few examples of relative permeability testing of

rock fractures in the field at residual non-wetting phasesaturation, and this series of experiments provided a goodopportunity to collect such data from a highly characterisedborehole. Oil was therefore pumped from the injection bore-hole after RADIO testing to reduce NAPL saturations toresidual values in preparation for relative permeability test-ing.

The borehole was pumped using an electric submersiblepump for 5 days at approximately 0.25 l/s, the rate increas-ing over time. Pure sunflower oil was removed in the earlystages. The oil content reduced over time, and no oil wasobserved in the final discharge. The remaining floatingproduct in the borehole was skimmed from the standingwater column and the pump was removed. The borehole wasthen allowed to sit open and was subsequently bailed,showing no floating product in the borehole. Six zones werehydraulically re-tested using the same apparatus, method-ology and depth intervals described previously.

RESULTSPre-RADIO hydraulic testing

The results of the slug tests were analysed by the methodof Hvorslev (1951) (equation (1)) using the AquiferWin32TM software package (Environmental Simulations In-ternational, 1999). Quality checking of the software by handcalculation and curve-fitting returned very similar values.The resulting transmissivities were converted to equivalenthydraulic apertures using the cubic law (equation (2)) andare presented in Table 1. Individual fractures were difficultto distinguish and identify in those zones that straddledseveral fractures, and a maximum of four fractures wasassumed for any zone.

In total, 15 measurements of hydraulic aperture wereobtained in addition to two duplicate values. Table 1 showsthat individual hydraulic apertures range from 26 �m to259 �m and show no significant pattern with depth. Thearithmetic mean hydraulic aperture determined by this meth-od was 86 �m. Two comparatively high-transmissivity zones(hydraulic test zones E and J) contribute the majority oftransmissivity to the borehole. One matrix zone (R) gave amatrix permeability of 2.5 3 10�9 m/s.

RADIO testingThe 18 NAPL injections produced a wide range of

pressure responses. Pressure observations included sharpfalls and rises in pressure, suggesting that aperture openingsand constrictions were being encountered by the leadingedge of the NAPL body. In zone E changes in hydrostaticpressure dominated the generated signal, indicating the pre-sence of very high permeability fractures. This is consistentwith the slug test results presented in Table 1, where zone Eis seen to have the highest average hydraulic aperture. Sixexperiments produced data that showed a rapid and highincrease in pressure at the start of purge pumping, which


was interpreted as pre-invasion of the fracture with NAPLby previous experiments. Thus cross-connection by subverti-cal fractures was suspected. These six experiments have notbeen analysed, as prior invasion of the fracture contravenedone of the test’s assumptions. Nine of the test zones incorpo-rated fractures in sandstone. Matrix permeability to eitherwetting or non-wetting phases is not incorporated in theconceptual model, and consequently these tests were notanalysed for aperture distribution; they were, however, ana-lysed to provide wetting phase relative permeability values.We therefore present the results of two tests where there isno evidence of the assumptions being broken. This isconsistent with the distribution of fractures observed in theATV logs and a separate outcrop-mapping exercise. Thecombined datasets show that there is a single set of approxi-mately horizontal fractures, and three sets of subverticalfractures (Wealthall, 2002). The latter fractures have a meanspacing of 3.3 m and a maximum spacing of 10.9 m (40values).

Post-RADIO hydraulic testingThe results of the second round of hydraulic testing are

given in Table 1. This provided a total of eight measure-ments of wetting phase relative permeability at residual non-wetting phase saturation. The mean kw,r(Snw,r) was 0.15, witha range of 0.04 to 0.39. There is no discernible trend withhydraulic aperture. Although the two largest values ofkw,r(Snw,r) are near the top of the borehole, there is not asignificant trend with depth.

NUMERICAL ANALYSIS OF RADIO TEST RESULTS BYREVERSE MODELLINGFRACAS numerical model

The FRACAS model is fully described by Reynolds &Kueper (2003) and is only summarised here. The governing

equations described in equation (6) are solved through theuse of the control volume finite element method (CVFE)(Forsyth, 1991). The constitutive relationship between capil-lary pressure and saturation of Brooks & Corey (1966) isused in FRACAS, as well as their functional relationship forrelative permeability as a function of saturation in a two-phase system. FRACAS incorporates the linearised hysteresisapproach of Gerhard et al. (1998) for the Pc –Sw constitutiverelationship for all wetting pathways. The model solves fortwo-phase flow in a three-dimensional orthogonal fracturenetwork, but is applied here to a single, horizontal fracture.

The finite element mesh generator TRIANGLE was usedto generate exact Delaunay triangulation grids for the model.Computational time was significantly reduced by adopting a108 wedge as an approximation to full radial flow, conse-quently reducing the injection rate by a factor of 36. Amaximum radial distance of 20 m was adopted for thedomain, following sensitivity testing that showed that do-mains with radial distances in excess of 20 m did not sufferfrom boundary effects caused by the outer circumferenceedge. The boundary condition at the point of the boreholewas specified as a constant non-wetting phase flux, and bothsides were specified as no-flow boundaries to either phase.The outer circumference of the wedge was specified ashaving a constant wetting phase saturation of 1 (Sw ¼ 1)with a free-exit condition to both phases. Individual aper-tures were specified for each radial distance from the bore-hole. The maximum radial distance between any twoadjacent nodes was 130 mm, although it was typically50 mm. Using this grid, good resolution of variation infracture aperture was obtained. Simulations were run withidentical radial aperture profiles in full circle and wedgegrids, which gave near-identical results, indicating that thewedge grid was a good approximation to simulating radialflow.

No measured values of the residual wetting phase satura-tion (Sw,r) were available, and a literature value of 0.1 used

Table 1. Pre- and post-NAPL injection hydraulic testing results

Test zone Upperinterval:

m

Lowerinterval:

m

K atSw ¼ 1:*

m/s

Number offractures¶

Hydraulicaperture:†

�m

Kw,r(Snw,r):‡m/s

kw,r§

A 12.25 12.98 LeakageB 12.98 13.71 6.11 3 10�8 1 41C 13.71 14.44 8.64 3 10�8 2 46 2.42 3 10�8 0.28D 14.27 15.00 5.00 3 10�8 1 38 5.17 3 10�9 0.10E 16.27 17.00 1.57 3 10�5 4 259 6.09 3 10�6 0.39E (repeat) 16.27 17.00 1.20 3 10�5 4 237F 15.00 15.73 1.68 3 10�8 1 26 2.39 3 10�9 0.14G 18.85 19.58 6.58 3 10�7 4 90 2.91 3 10�8 0.04H 18.12 18.85 1.61 3 10�7 3 56I 19.58 20.31 4.36 3 10�8 3 36J 21.04 21.77 5.43 3 10�6 4 182 4.63 3 10�7 0.09J (repeat) 21.04 21.77 5.25 3 10�6 4 180K 22.30 23.03 1.12 3 10�7 2 50L 23.03 23.76 9.96 3 10�7 4 103 8.58 3 10�8 0.09M 23.76 24.49 5.90 3 10�7 4 87 4.00 3 10�8 0.07N 24.49 25.22 5.59 3 10�7 2 85O 25.22 25.95 2.38 3 10�8 3 30P 26.75 27.48 3.77 3 10�6 4 161Q 28.04 28.77 LeakageR 17.00 17.73 2.48 3 10�9 Breccia matrixMean 1.89 3 10�6 86 8.42 3 10�7 0.15

* Wetting phase hydraulic conductivity prior to NAPL injection.† Average hydraulic aperture of each fracture in the tested zone.‡ Wetting phase hydraulic conductivity at residual non-wetting phase saturation.§ Wetting phase relative permeability at residual non-wetting phase saturation.¶ The maximum number of fractures permitted per test zone was 4.


by Reynolds & Kueper (2001) was taken. This is a possiblesource of error in the analysis. The model was sensitive toaperture, and 5% variations in aperture to both the modelledcurve matches are shown in the results to demonstrate theeffect of minor changes in aperture on the goodness of fit.Table 2 presents the parameters used in the model.

Pressure curve-matchingFor each of the two experiments presented here a series of

approximately 200 simulations was run to iteratively matcha synthetic aperture distribution to the field data. Theambient hydrostatic pressure was specified in the model tobe the same as that used in the conversion of field data. Aconstant flux rate was specified for the injection nodesimulating the borehole, with model output consisting of Pnw

at the injection node. Initial interpretations of field data wereconfirmed when the model showed that Pnw at the injectionnode varied both up and down as the leading edge of theNAPL encountered aperture constrictions and openings re-spectively. As no data on fracture aperture can be inferredbeyond the leading edge of the NAPL at the end of the test,the measured value of hydraulic aperture has been applied toall of the outer nodes in both simulations. An iterativeapproach to curve-matching was taken by specifying theradial aperture profile, running the model, comparing theresultant Pnw curve from the injection node with field data,adjusting the aperture profile, and re-running the model. Theprocess did not lend itself to automatic curve-matchingtechniques as adjustments to the aperture profile requiredconsiderable editing of the input file to the model and a

good conceptual understanding of the adjustments beingmade. The process was continued until a good visual fit wasmade to the field data.

RADIO test resultsTest 1 was in the interval 13.76 m to 14.17 m, which

consisted of breccia with no sandstone present. The intervalhosted a single subhorizontal fracture at 13.99 m. The Pnw

profile (Fig. 5) shows three distinct pressure increases duringthe test, which lasted 73 820 s (approximately 20.5 h). Thesepressure steps were replicated in simulation 1 with threeaperture constrictions in the resultant aperture profile (Fig.6). Test 1 displayed apertures from 43 �m to >1000 �m.Points A–H in Fig. 5 are also placed in Fig. 6 to illustratethe relationship between pressure changes and calculatedaperture. Point B, for example, denotes the beginning of apressure increase in Fig. 5, and corresponds to an aperturereduction in Fig. 6. Fig. 6 also lists the volume of NAPLinjected up to each point, and a total of 7.63 litres wasinjected during the test.

The smallest aperture in the profile is 43 �m, close to thehydraulic aperture of 46 �m. This aperture constrictioncauses the large increase in Pnw between F and G andconsequently controls the injection pressures for the latterhalf of test 1. Invasion of this controlling aperture isrequired to allow NAPL to migrate across the variable-aperture fracture, and we therefore denote the capillarypressure value at the leading edge of the NAPL derived fromequation (3) to be the entry pressure Pe. The RADIO testtherefore provides a measurement of Pe under natural flow,stress and infill conditions.

Test 2 was in the interval 22.20 m to 22.61 m, whichconsisted of breccia from 22.20 m to 22.42 m, and fine-grained sandstone from 22.42 m to 22.61 m and had a singlesubhorizontal bedding plane fracture at 22.42 m. Althoughfine sandstone is present in the lower part of this section,the NAPL was present only over the upper section and isnot thought to have invaded the matrix. The Pnw curve fromtest 2 (Fig. 7) shows a large rise in injection pressure atapproximately 22 000 s. This curve does not have multipleabrupt pressure increases similar to test 1, implying lessvariability of aperture. Fig. 8 shows the resultant apertureprofile across the domain, which is simpler than that for test1. However, the aperture continually changed throughout theprofile, and a sharp aperture constriction (point B) was

Table 2. Parameters used in the numerical model

Parameter Value

Aperture distribution index* 2.0Residual wetting phase saturation, Sw,r* 0.1Wetting phase viscosity: Pa s 1.0 3 10�3

Non-wetting phase viscosity:† Pa s 8.5 3 10�2

Wetting phase density: kg/m3 1000Non-wetting phase density:† kg/m3 920Aperture Radially variableMatrix permeability 0

* Reynolds & Kueper (2001).† Laboratory-measured values.

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needed to reproduce the field data. The iterative modellingprocedure achieved a good match (simulation 6 in Fig. 7),with physical apertures from 36 �m to >1000 �m. In thiscase the smallest aperture was 36 �m, distinctly differentfrom the hydraulic aperture of 50 �m, and suggesting thatthere is not a simple relationship between NAPL-controllingand hydraulic apertures.

To demonstrate the accuracy of the modelled matches,aperture profiles 5% smaller and greater than the matchedprofile were simulated for both tests, with results for simula-tions 2 and 3 for test 1 shown in Fig. 5 and simulations 7and 8 for test 2 in Fig. 7. These small variations in aperturehave a significant effect on the resultant Pnw curve. Thesesensitivity analyses show that the aperture profile can beuniquely determined with respect to a given set of values ofthe other parameters in Table 1. These parameters areconstant across the domain, so any uncertainty in them willbias the profile rather than change its internal pattern.

There is significant scale dependence in both tests. In test1 the entry pressure aperture is >125 �m for the first 2 m,and reduces to 43 �m out to �4.9 m. In test 2 the aperturereduces to approximately 75 �m over the first 2.9 m, fol-lowed by a step change to 36 �m, which is the value out to5 m. Clearly the entry pressure aperture is a function ofscale, and large-scale tests are required to find representativevalues. Until a larger test is carried out, we do not knowwhether the �5 m radius test is sufficiently large for thissite.

The consequences for predicting NAPL migration of usingsingle-valued estimates of aperture were examined. The twotests were simulated first with the hydraulic aperture apply-

ing across their entire domains, and second by using avolume-averaged aperture, ev. This was defined as

ev ¼X ei˜Ai

A(7)

where ei is the local aperture for a segment of area ˜Ai,and A is the total area of the invaded fracture. Hydraulicand volume-averaged apertures are summarised in Table 3for the two tests together with the areas of fracture invadedby NAPL and time taken for NAPL to reach the radiusinvaded in the original test for all three representations ofaperture. The predicted pressure curves are shown in Figs 5and 7.

The resultant Pnw curves for the hydraulic aperture simu-lations are significantly different from the matched apertureprofiles, showing that a single hydraulic aperture value is apoor approximation when simulating two-phase flow in realfractures. The apertures giving the best fit are larger than thehydraulic aperture, which is to be expected given that thenon-wetting phase migrates preferentially through the largestaperture regions of a fracture plane. The results in Table 3demonstrate that using the hydraulic aperture overestimatesthe extent (and volume) of NAPL invasion by factors 2–2.8,and underestimates the time for invasion to occur by similarfactors.

Using volume average apertures gives better approxima-tions to the Pnw curves (Figs 5 and 7), but clearly does notmatch the pressure steps detected by the RADIO test. Itdoes, however, provide a good approximation of the areainvaded, and consequently of migration times (Table 3). On

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this basis it would appear prudent in modelling of two-phaseflow to use a volume-averaged aperture that is considerablylarger than the hydraulic aperture, by a factor 2–3 for thesetwo examples.

It is useful to place the aperture profiles presented here inthe context of a real physical model. The RADIO testproduces a range of fracture apertures encountered by artifi-cially induced two-phase flow conditions. Consequently, therange of fracture apertures determined is limited at both thesmaller and larger aperture ends. Any finite value of irredu-cible wetting phase saturation, as well as limitations on themaximum value of capillary pressure attained, prevent fullaccess to the invading NAPL, and consequently the verysmallest apertures cannot be invaded (Steele & Lerner,2001). Accurate measurement of larger apertures is limitedby pressure transducer sensitivity at the higher end of theaperture distribution (low differential pressure), and thelocation of the borehole within the variable-aperture fracture.The location affects the detectable range, as the largestaperture that can be tested is limited by the displacementpressure of the area of fracture encountered at the intersec-tion with the borehole. We therefore propose that theRADIO test results constitute a subset of the range ofapertures occurring in the fracture.

CONCLUSIONSA new field testing technique using a constant flow rate

NAPL injection test in an isolated fracture has been devel-oped, the results of which have been analysed using theFRACAS two-phase flow model and compared with hydrau-lic apertures. The RADIO test gives a detailed approxima-tion of aperture variability in natural fractures, and has beenapplied to detect aperture constrictions and enlargements upto 5 m from the borehole invading up to 80 m2 of fracture inthe two tests presented here. The range of apertures deter-mined was from 36 �m to >1000 �m.

The RADIO test has some limiting assumptions, whichwill determine whether it can be used on particular sites.Principally, the NAPL is assumed to be injected into asingle, horizontal fracture without bifurcations or intersec-tions with other fractures, and not to enter the matrix. Radialsymmetry is assumed, and so the test measures an effectiveaperture, just as a pumping test measures an effectivehydraulic conductivity of the heterogeneous rock mass thatis being tested.

Identification of small-aperture fractures was one of theproblems in selecting test zones, and resulted in someuncertainty of the exact location of every fracture in theborehole, even using high resolution ATV logs. The primarypractical limitations with the RADIO test are the lack ofknowledge of the fracture network geometry needed to

analyse the data, and the potential effects of backgroundfluctuations in piezometric pressure during experiments.

Assuming the conceptual geometry used in this analysis,we have determined the smallest aperture constriction in thefraction of a variable aperture fracture used by non-wettingphase fluid flow. This constriction is the controlling aperture,and the macroscopic entry pressure for the fracture can becalculated, knowing the physicochemical properties of thefluids and the smallest aperture invaded.

Hydraulic aperture did not adequately approximatephysical aperture in the small-aperture fractures tested. Vo-lume-averaged apertures that are capable of approximatingpressure responses and accurate transport times are two orthree times larger than the hydraulic aperture. The conse-quences of this are that numerical models using hydraulicapertures may overpredict the penetration distances ofDNAPL releases, and underpredict the migration times.

Sunflower oil proved to be a suitable fluid for carryingout multiphase flow injection tests in the field as it isinexpensive and degrades to relatively harmless end pro-ducts. The RADIO test could be improved by using aneutral-density NAPL, removing any errors in analysis dueto buoyancy forces in non-horizontal fractures.

Pumping of oil from the fractures after the RADIO testspermitted derivation of a mean kw,r value of 0.15 at Snw,r.

ACKNOWLEDGEMENTSThe authors are grateful for funding for this work from

the UK Engineering and Physical Sciences Research Coun-cil. Du Pont (UK) are thanked for logistical support, as arethe British Geological Survey for the loan of field equip-ment. Other contributions were provided by Kerfoot PackedOils Ltd and Honeywell Control Systems Ltd. Paul Dews-bury is thanked for field assistance, Gary Wealthall for fieldassistance and use of fracture mapping data, and GavinHarrold for determining the physicochemical properties ofsunflower oils. The support of the Environment Agency ofEngland and Wales, the Scottish Environmental ProtectionAgency and ICI Chemicals and Polymers Ltd is acknowl-edged. TRIANGLE was used with permission of J. R.Shewchuk of the University of California at Berkeley.

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Table 3. Summary of apertures and travel distances and times from modelling of test 1

Test 1 2

Simulation* 1 4 5 6 9 10

Aperture: �m Variable 46 136 Variable 50 104Invaded surface area by end of test: m2 74.8 210.9 71.5 80.0 160.3 80.0Radial travel distance: m 4.88 8.19 4.77 5.04 7.14 5.04Time to limit of test:† s 73 964 25 443 61 050 29 587Smallest aperture: �m 43 46 136 36 50 104Largest aperture: �m >1000 46 136 >1000 50 104

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