tters 244 (2006) 186–200www.elsevier.com/locate/epsl

Earth and Planetary Science Le

Evolution of fracture permeability through fluid–rockreaction under hydrothermal conditions

Hideaki Yasuhara a,⁎, Amir Polak b, Yasuhiro Mitani c, Abraham S. Grader d,Phillip M. Halleck d, Derek Elsworth d

a Department of Civil and Environmental Engineering, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime, 890-8577, Japanb Civil and Environmental Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel

c Institute of Environmental Systems, Dept. of Civil Engineering, Faculty of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku,Fukuoka, 812-8581, Japan

d Energy Institute and Department of Energy and Geo-Environmental Engineering, Pennsylvania State University,403 Academic Activities Building, University Park, PA 16802, USA

Received 20 July 2005; received in revised form 18 January 2006; accepted 22 January 2006Available online 15 March 2006

Editor: R.D. van der Hilst

Abstract

We report flow-through experiments on a natural fracture in novaculite under moderate effective stresses (∼1.4 MPa) andtemperatures (20–120 °C) to examine the effect on flow and transport characteristics. The efflux of fluid and dissolved mineralswere measured throughout the 3150-h experiment. After the experiment the fracture was imaged by X-ray CT, impregnated withWood's metal, and a cast recovered of the Wood's metal-filled fracture. These measurements constrain the evolution of fracturestructure, and the change in permeability that resulted from stress- and temperature-dependent dissolution at both proppingasperities and fracture void surfaces. During the first 1500 h, the aperture of one fracture decreased from 18.5 to 7.5 μm, when itwas loaded with constant effective stress of 1.4 MPa, at room temperature, and a flow rate decreasing with time from 1 to 0.0625mL/min. This reduction is attributed to the removal of mineral mass from bridging asperities. After 1500 h the fracture apertureincreased, ultimately reaching 13 μm. Apparently the dominant dissolution process switched from prop removal to etching of thevoid surfaces. We used X-ray CT images, digital radiographs, and fracture casts as independent methods to constrain the resultingarchitecture of the evolved fracture porosity, and developed a simple process-based model to examine the relative roles of asperityremoval and free-face dissolution. The comparison of the model with the measurements identifies the relative importance of massremoval at fracture faces and at propping asperities. The experiments underscore the importance of dissolution in determining thesense, the rates and the magnitude of permeability-enhancement within rock fractures stimulated by chemical permeants ingeothermal and petroleum reservoirs, and to a lesser degree under natural conditions pushed far-from-equilibrium.© 2006 Elsevier B.V. All rights reserved.

Keywords: fracture permeability; pressure solution; free-face dissolution; geochemistry

⁎ Corresponding author. Tel./fax: +81 89 927 9853.E-mail address: hide@dpc.ehime-u.ac.jp (H. Yasuhara).

0012-821X/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.epsl.2006.01.046

1. Introduction

In fractured rock masses with low matrix perme-ability, fluid flow predominates within fractures. An

Fig. 1. Schematic illustration of experimental setup for flow-throughexperiment.

187H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

understanding is crucial of how the flow and transportcharacteristics within rock fractures evolve in spaceand time, and is significant to many engineering orscientific applications. These include the effectiverecovery of targeted fluids in geothermal andpetroleum reservoirs and the long-term and safeisolation of long-lived wastes in underground repos-itories. The influence of mechanical and chemicaleffects on the permeability of fractured reservoirs iswell recognized, however the interaction betweenmechanical and chemical influences remains ill-constrained. To date, no conclusive view exists ofthe evolution in fracture permeability when arbitrarystresses, temperatures, and chemical potentials areapplied—specifically whether permeability will in-crease or reduce under net dissolution. Reduction isdriven as bridging asperities are removed and/orsecondary minerals are reprecipitated (i.e., pressuredissolution). Increase is driven as the fracture void isetched by net dissolution (i.e., free-face dissolution).Sealing, likely driven by pressure solution, resultingfrom either removal of bridging asperities or mineralprecipitation, is reported in some instances at elevatedtemperature (>300 °C) [1–5], at modest temperature(50–150 °C) [6–8], and under low effective stress (0.2MPa) with an acidic solution [9]. Conversely, gapingdriven by free-face dissolution is suggested incarbonate reservoirs, e.g., [10], and in the develop-ment of karst, e.g., [11]. Importantly, these opposingbehaviors operate concurrently, but to varying degrees.Subtle changes in local conditions of applied stress,temperature or chemical potential may trigger switch-ing between dominant mechanisms. Thus, besidesmonotonic sealing or gaping of a fracture, thebehavior may switch, either in response to changingstress, temperature or chemical conditions, or sponta-neously, with no apparent trigger [12].

This study examines changes in permeability withnet dissolution that proceed within a natural fracturein Arkansas novaculite. Specifically, our focus isplaced on defining the critical factors controlling theoverall behavior; fracture gaping or closing. Experi-mental measurements of evolving fluid pressuredifferential between sample inlet and outlet, pre-scribed flow rates and confining pressure, and non-destructive CT images of the fracture, are used toconstrain the evolution of fracture porosity. Finalfracture void morphology is anchored by a Wood'smetal cast of the fracture. These ensemble observa-tions are used to constrain the competing processesthat contribute to permeability augmentation andreduction.

2. Experimental method

The flow-through experiment was conducted on acylindrical sample of Arkansas novaculite (50.0 mmdiameter×89.5 mm length) containing a single diam-etral fracture along its cylindrical axis. The fracturewas split open by prying it open with a chisel,following coring. Arkansas novaculite is >99.5%quartz [13], and distilled water was used as a permeant.Thus, the chemical system was relatively simple (i.e.,SiO2+H2O). During the end-to-end flow test, themeasured axial pressure differential yielded a contin-uous record of the averaged fracture transmissivity, thatmay be converted to permeability, and then to averageaperture. Pre-experiment, the fracture surfaces wereeach profiled, and post-experiment the aperture distri-bution within a fracture was measured first by X-rayCT, and then by destructive casting with Wood's metal.

2.1. Experimental system

The fluid flow system configuration is shown in Fig.1. The upper and lower rock samples were carefullymated to avoid introducing small debris within thefracture, and the mated core was confined within aViton® sleeve and placed inside an 80-cm long tri-axialpressure cell of 9.5-cm outside diameter. Stainless-steelend plugs pierced by fluid supply tubes cap the ends ofthe carbon fiber-reinforced aluminum pressure cell

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(Temco Inc.). Heating was by thin cylindrical electricalresistance heaters regulated to within ±2 °C bythermocouples located inside the top and the bottomparts of the coreholder. The injected fluid was preheatedby cable heaters before injection through the coreinterior. A combination of preheating and efficientinsulation maintained injected fluid temperatures con-gruent with those of the core specimen. The confiningpressure and prescribed flow rates were established byindependently controlled pressure generators. Backpressure was prescribed at 345 kPa (50 psi) by apressure regulator located close to the outlet of thecoreholder—this maintained a prescribed pore pressureat the outlet and prevented vaporization of fluid at hightemperatures (>100 °C). The differential pressurebetween the sample inlet and outlet was recordedthroughout the duration of the flow-through experimentby a pressure transducer (accurate to within ±40 Pa)exposed directly to the pore fluid.

2.2. Procedure for flow-through experiment

Constrained within the coreholder, the confiningfluid was pressurized to 1.72 MPa (250 psi) resulting ina net effective stress of 1.38 MPa (200 psi) applied to thesample; the maximum differential pressure between thesample inlet and outlet is less than 0.1 MPa and themean effective stress was maintained quasi-steadythroughout the experiment. The flow-through experi-ment was initiated at a controlled flow rates andtemperature of 1.0 mL/min, and 20 °C, and alteredwith progress of the test, in the range Q=1.0–0.0625mL/min and T=20–120 °C, respectively. Experimentalconditions during the entire length of the experiment(3150 h) are given in Table 1. With the fluid flowrate prescribed, differential pressure between thesample inlet and outlet was logged throughout the

Table 1Experimental conditions

Time(h)

Temperature(°C)

Flow rate(mL/min)

Flow direction

0–121 20 1.0 Original121–380 20 0.5 Original380–858 20 0.25 Original858–930 20 0.0 –930–1266 20 0.25 Original1266–1292 20 0.125 Original1292–1494 20 0.125 Reversed1494–1869 20 0.0625 Original1869–2255 40 0.0625 Original2255–2875 80 0.0625 Original2875–3150 120 0.125 Original

3150-h duration experiment. Measured fracture trans-missivity, translated to an equivalent hydraulicaperture, was evaluated from the known differentialpressure, flow rate, temperature-dependent viscosityof the fluid, and the length and width of the sample,via the parallel plate approximation, e.g., [14,15].

2.3. Chemical analysis

Deionized water was circulated throughout the expe-riment. A total of 120 fluid samples were taken from theflow outlet at regular intervals (one sample per day) todetermine effluent Si concentrations. Samples wereassayed by inductively coupled plasma-atomic emissionspectrophotometer (analytical precision within ±5%). Inaddition, pH was measured by a ROSS combination pHelectrode (Thermo Orion) on 14 samples of the effluent,and 7 samples of the influent flux.

2.4. Roughness profilometry

Prior to the flow-through experiment the fracture wasopened and both surfaces profiled for roughness [16].These data were used to digitally reconstruct the aperturedistribution for the mated fracture. The 3-D automatedroughness profiling systemcomprises anX–Ypositioningtable (stroke length of 250×150 mm2, positioningaccuracy of ±15 μm, and repositioning accuracy of±3 μm) and a 3-D laser scanner (spot dimensions of45×20 μm2, measurement range of ±8 mm, andmaximum resolution of 0.5 μm for elevation). Themaximum resolution of the 3-D laser displacementsensor is 0.5 μm in the vertical direction, but is limited bytemperature variations during measurements (approxi-mately ±5 μm error per ±2 °C). Correspondingly,vertical resolution is limited to 10 μm. Profiles (z) of thetwo 50.0×89.5mm fracture surfaces were measured on a50 μm grid in the x, y plane (horizontal), with positive-xaligned with the flow direction. Aperture distributionwithin the mated fracture was determined from point-by-point subtraction of the two digitized surfaces (Fig. 2),after first de-skewing the data by maintaining the meanplanes of the fractures parallel.

2.5. X-ray CT imaging

Volumetric imaging of the sample was completed byX-ray CT (Universal systems Inc.) as a sequence ofstacked sections orthogonal to the long-axis of core.Each slice comprises an array of 1000×1000 voxels,each defined by a single CT number. CT number is ameasure of the X-ray attenuation of the voxel, and in

Fig. 2. Oblique view of the parallel rough surfaces digitized by the 3-Dlaser profilometer system.

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turn depends on a combination of the density and meanatomic number of the target, and on the properties of theX-ray beam. A more detailed description on thecapability and limitations of X-ray CT in core analysismay be found in Stock [34], Ketcham and Carlson [35],and Wildenschild et al. [36].

In this experiment one scanning sequence wasperformed after the termination of the experiment; thescanner recorded 1477 two-dimensional slices thatspanned the sample, each with a thickness of 60.6 μmand an in-plane pixel resolution of 50 μm (energy levelof 180 kV at 600 μA).

2.6. Wood's metal fracture casting

Fracture casting has been used to characterize thepore structure of cements and concrete [17,18], thedistribution of natural fractures in coal [19], and themorphology of pore space in mudstones [20]. A fracturecast was taken at the conclusion of the experiment usingWood's metal. This alloy (50% Bi, 25% Pb, 12.5% Cd,and 12.5% Sn) has a density of 9.67 g cm−3, and meltsat 65.5 °C with the characteristics of a non-wettingliquid. At the conclusion of the flow-through experi-ment the Viton® sleeved sample was removed, end-capped, heated in an oven to 90 °C, and pressureinjected with Wood's metal at 345 kPa (50 psi).

3. Experimental results and analyses

The evolution of permeability within a fracture maybe attributed to the redistribution of mineral mass fromcontacting asperities and/or fracture void surfaces.Dissolution at the contacting asperities may result in anet-decrease in fracture aperture, provided this effectoutstrips gaping induced by dissolution from thefracture surface. These dynamic processes are con-strained from concurrent measurements of evolving

permeability, mineral efflux, and post-experiment im-aging by X-ray CT, anchored to final destructive castingof the fracture using Wood's metal.

3.1. Evolution in fracture aperture

The overall experiment is divided into two stages; thefirst over 1494 h at constant temperature (20 °C) but atvarying flow rate (1.0–0.125 mL/min and a reversedflow of 0.125 mL/min), and the second over 1656 h atfixed flow-rate (in two sequential stages 0.0625 and0.125 mL/min) but with stepped temperatures (20, 40,80, 120 °C) (see Table 1). The first stage evaluates therole of flow rate, and the second the role of temperaturein driving permeability changes, all as invariantconfining stress (1.72 MPa).

Fig. 3a shows the evolving changes in normalizeddifferential pressure and hydraulic aperture with time.Hydraulic aperture is evaluated from the recordeddifferential pressures and flow rates via the cubic law.Logged differential pressure implies the effects ofprescribed flow rates and temperatures, and may benormalized to remove the influence of temperature onviscosity. Normalized differential pressure is calculatedfrom the ratios of both flow rates and fluid viscositiesbetween the initial and followed conditions, given by,

Dpn ¼ DprQi

Qlil; ð1Þ

where Δpn and Δpr are the normalized and recordeddifferential pressures, respectively.Q and μ are flow rateand dynamic viscosity of fluid, and the subscript idenotes the initial conditions (Qi =1.0 mL/min andμi =1.0×10

−3 Pa·s at 20 °C).

3.1.1. Invariant temperature test under various flowrates (0–1494 h)

The hydraulic aperture decreased monotonicallyfrom 18.5 to 10.3 μm during the first 858 h of thetest, with a reduction in the flow rates from 1.0 to0.25 mL/min. After 72 h shutdown, flow was resumed ata rate of 0.25 mL/min and the aperture slightly increasedto 10.6 μm, followed by a consistent reduction inaperture. After the flow direction was reversed at 1292 h,the aperture reduced to 7.5 μm during 1292–1494 h.Abrupt decreases in fracture aperture were apparentwhen the flow was reversed at both 1292 and 1494 h; themeasured Δp's (instead of normalized Δp) before theswitching of the flow direction were 50 and 93 kPa, andrapidly increased to 65 and 108 kPa after each switching,respectively. This instantaneous closure in aperture is

Fig. 3. Experimental measurements: (a) changes in hydraulic aperture and normalized differential pressure with time and (b) change in Siconcentration with time. Measured differential pressure is normalized by the flow rates and fluid viscosities (Eq. (1)).

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interpreted as a switch of the stress distribution. Effectivestress at the sample inlet is smaller than that at theoutlet because of the higher pore pressure applied at theinlet; this may correspondingly accommodate a largeraperture at the inlet. Switching of flow directions iscorrelated with the switching of stress distributions, andaccordingly this may reduce aperture around theprevious inlet (i.e., outlet after reverse of the flow),resulting in net-closure within the fracture.

Monotonic reduction in aperture throughout the1494 h stage of the experiment may be attributed tothe relative dominance of either mass dissolution atcontacting asperities or mechanical creep of thefracture including mechanical crushing of the proppingasperities due to high stress concentration, relative tothat at free fracture surfaces. Both viable processesmay result in an increase in average contact areawithin the fracture, with a consequent decrease in the

rate of aperture reduction, as apparent in Fig. 3a.Although the duration of the mechanical creep is long(throughout the 1494 h stage) the contribution ofcrushing at the asperities and removal by dissolutioncannot be ruled.

3.1.2. Fixed flow-rate test at elevated temperatures(1494–3150 h)

The hydraulic aperture continued to decrease through-out the initial 1494-h of the experiment, but monotoni-cally increases as temperatures were elevated for theremainder of the experiment. The switch from aperture-reduction to -increase has been previously reported incarbonates [12], and the phenomenon of switchingbetween permeability-reduction to permeability-increaseis interpreted as a switch in the dominant process ofmineral redistribution—from beneath the bridgingasperities to the faces of the fracture. Dissolution at

Table 2pH measured from inlet and outlet samples

Time (h) Inlet pH Outlet pH

19 6.25 6.4168 – 6.11259 – 6.32427 6.69 6.34595 – 6.34616 7.26 –764 – 6.391076 – 7.981123 7.18 –1221 – 7.831366 – 7.361680 – 7.001819 8.21 –2326 – 7.722585 6.97 –2627 – 6.622825 6.85 –2831 – 7.352974 – 7.15Ave. 7.06±0.42 6.92±0.52

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contacting asperities is stress-dependent, e.g., [21,22].The stress at the asperities decreases with an increase incontact area as the fracture closes, reducing the mass rateof removal from beneath the asperities relative to thatetched by free-face dissolution. This correspondinglyresults in a change from net closure to net gaping, with aconcomitant change in permeability.

After re-initiating flow in the original direction at1494 h, fracture aperture slightly increased to 7.7 μmduring 1494–1869 h at 20 °C. This is followed by aconsistent augmentation in aperture as temperatureswere elevated to 120 °C. The rates of aperture gapingincreased as temperatures were raised, although this isrelatively small between 20 °C (1.62×10−13 m/s) and40 °C (2.31×10−13 m/s). This is attributed to an increasein the apparent dissolution rate with temperatures.Dissolution rates exhibit an Arrhenius-type dependenceon temperature, e.g., [23,24], given by,

kþ ¼ k0þexpð−Ekþ=RTÞ ð2Þ

where k+ is dissolution rate constant. k+0 and Ek+ are

pre-exponential factor and activation energy, respec-tively (k+

0 =1.59 mol m2 s−1 and Ek+=71.3 kJ mol−1

for quartz [23]). R is the gas constant and T istemperature. The dissolution rate constant at 120 °C isthree orders of magnitude larger than that at 20 °C,explaining the observed growth in aperture evolutionrate.

3.2. Surface dissolution

The change in measured effluent Si concentration isshown in Fig. 3b. Corresponding pH magnitudes areshown in Table 2, and vary slightly from inlet to outlet,with average values of 7.06 and 6.92, respectively. Thedistilled water was supplied from the same distillerthroughout the experiment, although the slight variationin pH measured at the inlet is due variability in theoutput of the unit. Concentrations measured at 20 °Cwere in the range 0.13 to 1.20 ppm with a mean of 0.76ppm, and showed slight fluctuation through this stage.The mean values at elevated temperatures increasedwith the increase of temperature; their values at 40, 80,and 120 °C were 1.30, 2.96, 8.10 ppm, respectively.Measured Si concentrations are clearly temperaturedependent, and show the Arrhenius-type dependence(Fig. 4). The activation energy of Si solubility isreported by Iler [25] at 21.7 kJ mol−1, and this value isclose to that determined from measurements in thisstudy (22.2 kJ mol−1). In contrast, the measuredconcentrations are much lower than Si solubilities

(∼9, 17, 44, 94 ppm at 20, 40, 80, 120 °C,respectively [25]) due to the short residence time ofthe fluid within the fracture (ca. a few tens of seconds).This implies that precipitation remained inactive withinthe fracture throughout the 3150 h duration of theexperiment, and suggests that net dissolution prevailedthroughout.

The role of dissolution at contacting asperities hasbeen examined in terms of the rate of aperture reduction,db / dt, [7,26] recorded from flow-through tests whereindependent estimates of the hydraulic fracture apertureare derived from the effusing fluid and mineral flux.Hydraulically measured aperture reduction rates, db / dt,in the first 858-h duration are in the range 2.0×10−11 to5.0×10−13 m/s as shown in Fig. 5. The hydraulicallymeasured rates may be augmented by estimates frommineral mass efflux, where an assumption is maderegarding the contact-area ratio, Rc, as,

dbdt

¼ Qd CSiO2

Rcd Afqgð3Þ

where Af is the total fracture area (Af=8.95×10−3 m2)

and ρg is grain density (2650 kg m−3 for quartz).Varying the unmeasured fractional contact area in therange 1% to 30%, the rates of aperture reduction, db / dt,may be determined from the mean Si concentrations,CSi, of 0.18, 0.77, and 0.87 ppm, equivalent to SiO2

concentration, CSiO2, of 0.39, 1.63, and 1.86 ppm, at

prescribed flow rates, Q, of 1.0, 0.5, and 0.25 mL/min,

Fig. 4. Relation between Si concentration and temperature. Solid dots represent mean measured concentrations and error bars show the maximum andminimum concentrations at the temperatures. Measured Si concentration is strongly correlated to temperature by an Arrhenius-type relation. Solidline represents the solubility curve by Iler [25]. with activation energy of 21.7 kJ mol−1, and dotted line is the regression curve for the measured withapparent activation energy of 22.2 kJ mol−1.

192 H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

respectively. These estimates, in the range 1.1×10−10 to2.0×10−12 m/s, are close to, but slightly higher thanthose recovered from the hydraulic measurements. Thismismatch may result either from an unaccountedcontribution of dissolution at the fracture void walls,or from an underestimate of assumed fracture contactarea. If crushing beneath asperities and subsequentremoval by dissolution does contribute to the observedresponse, this response would be of similar form to thatobserved—i.e., a rapid initial closure, followed by a

Fig. 5. Comparison of change in rate of aperture reduction, db / dt. Solid line reSolid circles, open triangles, and open circles represent predictions by Eq. (3

slowing in closure as the contact area builds and thedriving stress drops.

3.3. X-ray CT analysis

Non-invasive imaging was used to evaluate the 3Dstructure of the fracture surfaces. The left side of Fig. 6shows two CT images taken at the termination of theflow experiment from the upper (a) and lower (b) partsof the rock sample. The fracture is clearly visible in the

presents the change in direct observation of db / dtwith time (0–858 h).) at different flow rates in the range of 1.0 to 0.25 mL/min.

Fig. 7. A digital radiograph (DR) of the fracture cast of Wood's metal:(a) plane view and (b) side view. The white areas represent the filledpores.

Fig. 6. Images of the CT scan obtained at the end of the flowexperiment. The left images show two CT images of the rock sampletaken at the top (a) and bottom (b) parts of the sample. The fracture isclearly visible at the center of the image where the large black pores areareas where pieces of the fracture surface was missing. The right image(c) shows a 3D reconstruction of 1477 CT images representing acomplete view of the fracture surface. The white areas are fracturevoids demarked with a threshold CT number of 2650.

193H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

center of the image (marked in black). Some of the largeblack areas are places where pieces of rock are missinglikely due to mechanical brakeage prior to the start of theexperiment. The black spots in the rocks matrix are areaswhere the density of the rock is lower relative to the restof the matrix. These regions are not interconnected andexert no influence on the in-fracture flow. The right sideof Fig. 6 shows a 3D reconstruction of 1477 imagesrepresenting a complete view of the rock fracture. Thetwo yellow lines demark the scans where two imagesshown on the left were captured. The white regions inthe 3D reconstruction are fracture voids demarked witha threshold CT number of 2650 that was chosen by trialand error to characterize the fracture plane in an optimalway. The 3D reconstruction suggests that there are nocontinuous paths within the fracture, however thisaberration results from the finite resolution of theimaging (50×50×60.6 μm). By counting the number ofpixels that have a CT number lower than the chosenthreshold of 2650 and multiplying them by the size ofeach pixel (50×50×60.6 μm), we may calculate thetotal volume of the fracture (white area) and estimate theaverage fracture aperture of the whole rock sample. Thetotal fracture volume was calculated to be 390 mm3

(2,563,798 pixels), which for the scanned area of4200 mm2 gives an average fracture aperture of 95 μm.

The average fracture aperture estimated from the CTimages is larger than the hydraulic aperture at the end ofexperiment (i.e., 13 μm), which may be attributed to thechosen threshold CT number; the larger the prescribedthreshold, the larger the resulting void volume andaperture. However, the estimated aperture hereinaboveis still plausible and indexes to the actual valueevaluated from the flow-through experiment althoughthe CT resolution is insufficiently high.

3.4. Extraction of Wood's metal fracture

Following the injection of Wood's metal, theimpregnated rock sample was re-imaged by X-ray CT.The clarity of imaging is limited by the very highdensity of the Wood's metal alloy (9.67 g cm−3) and bybeam guiding in the dense fracture plane. Alternatively,Fig. 7 shows two digital radiographs (DR) of the rocksample. The white regions are voids filled with Wood'smetal. The left image shows a plan view of the fracturethat depicts no continuous flow paths along the fractureplane, similar to the 3D reconstruction by the X-ray CT(Fig. 6). The side view on the right image indicates thatthe fracture has a measurable but unquantified thickness,and is continuous through the sample, implying thatWood's metal penetrated through most of the fracture.

The Wood's metal cast was removed from thenovaculite by first trimming the sample to close to thefracture, and then immersing the remaining ingot inside

Fig. 8. Wood's metal fracture extracted through chemical dissolutionusing hydrofluoric acid: (a) whole fracture—white region is residualrock sample, and (b) black-and-white representation of the boxed areain (a). Black area represents regions in contact and calculated contactarea is 14.5%.

194 H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

a bath filled with hydrofluoric acid (∼25 wt.%).Immersion for 166 h removed the surrounding rockmatrix, although a small portion of the fracture top wasbowed (Fig. 8a). It is apparent that Wood's metalpropagated throughout the fracture except not into theregions in contact. No preferential flow paths areapparent within the cast, which is congruent with theCT and DR observations. Importantly, the alloy fracturecast enables the contact area to be quantitativelyevaluated from the digitized black-and-white image(∼65% of the whole fracture) as shown in Fig. 8b. Thecalculated contact-area ratio is 14.5% and may beconsistent with the plausible amount in rock fractures,e.g., [15,27].

4. Process-based model

A process-based model is presented to describe theevolution of fracture aperture mediated by the compet-ing processes of dissolution at contacting asperities (themost viable process that reduces a fracture aperture)and at fracture walls. The model is applied to examinethe experimental observations—a net-reduction inaperture switched to a net-increase with the applicationof heating. The model is a diagnostic representation

because the observed mineral efflux is used as inputdata, but is capable of deconvolving the relativedominance of the dissolution processes, which is notapparent from the raw experimental measurements ofchanges in the hydraulic aperture and the mineralconcentration. Also, this enables the rates and magni-tudes of aperture changes to be followed with timefrom a mechanistic standpoint.

4.1. Relation between fracture aperture and contactarea

The dissolution processes irreversibly alters thegeometry of the contacting fracture surfaces, requiringthat the initial fracture geometry be identified. For this, asimple relation between the mean fracture aperture andcontact-area ratio is determined using images of tworough surfaces digitized by the 3-D roughness profilingsystem. Fig. 9 shows the relation between the meanmechanical aperture, <b>, and the contact-area ratio, Rc.The mean aperture is defined as the arithmetic averageaperture obtained by the point-by-point subtractionbetween the two digitized surfaces (negative valuesresulting from subtraction are set to be zero in the localaperture). The contact-area ratio is merely defined by theratio of the number of equally spaced profile pointsrepresenting interpenetrated surfaces, to the totalnumber of measurement points. The relation showsexponential decay of fracture aperture as the contact areaincreases. Note that this aperture configuration is anumerical product, not equivalent to the physicallyrealistic aperture constrained under the experimentalconditions, although they may be comparable to eachother. Actually, it is impossible for the digitallyreconstructed fracture to replicate the physical oneunder experimental conditions because the mating ofthe real surfaces may result in block rotations and aresulting skewing in the aperture data. Correspond-ingly, the digitized surface data were de-skewed bymaintaining the mean planes of the fractures parallel.Point-by-point subtraction was then used to determinethe equivalent physical fracture, to a first-orderapproximation.

4.2. Constitutive relations

The digitized fracture, obtained from profilometry,constrains the relation between the fracture aperture andthe contact-area ratio as shown in Fig. 9. This relation isapproximated by the regression curve, given by [26],

hbi ¼ br þ ðb0−brÞexpð−ðRc−Rc0Þ=aÞ; ð4Þ

Fig. 9. Relation between mean aperture and contact-area ratio. Circles are evaluated from point-by-point subtraction using the profiling data, and thedotted line is the regression curve of <b>=2.5+16.0 exp(− (Rc−Rc0) /20) with the correlation coefficient, R2=0.92.

195H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

where <b>, br, and b0 are the mean mechanical, residualand initial apertures, respectively. Rc is the contact-arearatio, and a is a constant. The initial aperture is set to be18.5 μm because the hydraulic aperture evaluated fromthe flow-through experimental measurements startedinitially with this value. Although these mechanical andhydraulic apertures may not be equivalent [28–30],reckoning them as equivalent is reasonable to a first-order approximation. The regression analysis obtainedin Fig. 9 shows the residual and initial apertures to be2.5 and 18.5 μm, respectively.

The evolution of fracture aperture incorporates thecombined effects of asperity interpenetration (decreasein aperture) and of free-face etching (increase inaperture). Precipitation may also influence hydraulicbehavior, but the short residence times reflected in theobserved undersaturation of the circulating fluid to Sisuggests that precipitation will exert a minor influence.Consequently the effects of precipitation are notconsidered.

In defining effusing mass, it is convenient to considerthe dissolved mass flux, dM / dt, evaluated fromprescribed flow rates and measured quartz concentra-tions, given as,

dMdt

¼ QCSiO2 : ð5Þ

The relative contributions of dissolution at contactingasperities and fracture void walls to the evolution infracture aperture may be deconvolved and quantified byapplying an arbitrary ratio of mass sourced from either

contact area or free surface over total dissolved mass,defined by,

VCtþDt ¼ VC

t þ dMdt

Dtqg

!rC; ð6Þ

V FtþDt ¼ V F

t þ dMdt

Dtqg

!rF; ð7Þ

where VτC and Vτ

F represent the volume dissolved fromcontacting asperities and free fracture wall at t=τ, res-pectively. rC and rF are ratios of mass fluxes sourcedfrom contact area and free surface area over total massefflux, respectively, which results in rC+ rF=1. The vo-lume dissolved from the contact area during the infi-nitesimal time interval, dt, is given by,

dVCt ¼ WLRcjtdu; ð8Þ

where W and L are the width (50.0 mm) and the length(89.5 mm) of novaculite sample, respectively. durepresents change in displacement driven by dissolutionat contact area during dt. The relation between themechanical aperture, <b>, and displacement, u, can bedefined by,

du ¼ −dhbi1−Rcjt

; ð9Þ

because <b> is the arithmetic average of the localapertures with contacting asperities (the negative sign isdue to the fact that the aperture reduces by dissolution).

196 H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

Substituting this into Eq. (8), the cumulative volumedissolved from contact area can be evaluated byintegrating Eq. (8) using Eq. (4) with respect to thecontact-area ratio, as,

VCtþDt ¼ −WL

Z RcjtþDt

Rc0

Rcjt1−Rcjt

dhbidRc

dRc

¼ b0−brð ÞWLexp − 1þ RcjtþDt

� �=a

� �� ½exp 1þ Rc0ð Þ=að Þ−exp 1þ RcjtþDt

� �=a

� �þ exp Rc0 þ RcjtþDt

� �=a

� �=aðEi 1−Rc0ð Þ=að Þ

−Ei 1−RcjtþDt

� �=a

� ��� ð10Þ

where Ei(x) is the exponential integral function and forthe positive value of x the function is expressed usingthe Puiseux series [31], as,

Ei xð Þ ¼ gþ lnxþXln¼1

xn

n!n; ð11Þ

where γ(=0.5772…) is the Euler–Mascheroni constant.Consequently, Eq. (10) is rearranged as,

VCtþDt ¼ b0−brð ÞWLexp − 1þ RcjtþDt

� �=a

� �"exp 1þ Rc0ð Þ=að Þ−exp 1þ RcjtþDt

� �=a

� �þ exp Rc0 þ RcjtþDt

� �=a

� �=a

� ln1−Rc0

1−RcjtþDtþXln¼1

ð1−Rc0Þn−ð1−RcjtþDtÞnann!n

!#

ð12ÞSubstituting this into Eq. (6), the contact-area ratio isupdated, and the average fracture aperture mediated bydissolution at contacting asperities is also evaluatedusing Eq. (4), given as,

hbicjtþDt ¼ 2:5þ 16:0expð−ðRcjtþDt−Rc0Þ=20Þ; ð13Þ

where ⟨b⟩c|t+Δt denotes the updated fracture aperturemediated by dissolution at contacting asperities, whichdoes not include the contribution of free-face dissolu-tion. The effect is evaluated from Eq. (7). The volumedissolved from the fracture void walls is given by,

V FtþDt ¼ hbiFjtþDtWL; ð14Þ

where ⟨bF⟩|t+Δt represents the change in aperture due tofree-face dissolution at t= t+Δt. Substituting thisequation into Eq. (7), yields ⟨bF⟩|t+Δt. Note that theprocess of dissolution at the free surfaces assumes nocontribution to changes in contact-area ratio anddisplacement, and merely augments the volume of

fracture void. Finally, the average fracture aperture att= t+Δt is defined as,

hbijtþDt ¼ hbicjtþDt þ hbiFjtþDt; ð15Þwhere ⟨b⟩|t+Δt denotes the average fracture aperture att= t+Δt. The iterative procedure is employed to marchthrough time.

4.3. Replicating experimental measurements

The evolution in the fracture aperture is followed intime using the model presented in Section 4.2.Dissolution mass fluxes, dM / dt, are evaluated fromEq. (5) at six different stages as shown in Fig. 10; stagesI, II, and III represent the early isothermal experiment at20 °C with the experimental period divided to pre-reverse (stage I), reversed (stage II), and post-reverse(stage III) flow stages. And stages IV, V, and VI are the40, 80, and 120 °C experiments, respectively. To followthe experimental measurements of aperture change, theunmeasured, but necessary parameters of rC and rF inEqs. (6) and (7) are prescribed arbitrarily at each stage.During the experiments, two sharp reductions inaperture resulted from the reversing of the flow directionat 1292 and 1494 h. This is followed by resetting theaperture according to that measured in the experimentand the contact-area ratio is updated using Eq. (4).

Predicted changes in fracture aperture and normal-ized differential pressure evaluated from the cubic laware shown in Fig. 11, together with the experimentalmeasurements. Predictions show good agreement withthe measurements when the unknown magnitudes of rCand rF are suitably prescribed; rC=0.59 and rF=0.41 instage I, rC=1.0 and rF=0.0 in stage II, and rC=0.0 andrF=1.0 in stages III–VI. In stage I the fracture aperturemonotonically decreases with time. As shown in Fig.12, the prediction shows that the contact-area ratioincreases up to ∼28% in stage I. The relatively smallercontact area amplifies the rate of aperture reduction overthe increase produced by etching of the open fracture(∼72%). This results in an observable net-decrease inaperture. In stage II rC=1.0 and rF=0.0 are prescribed tomaximize the rate of aperture decrease. However, therates measured in the experiment are still higher thanthose predicted (apparent in Fig. 11b). Also, it isdifficult to understand why no dissolution at the fracturevoid surfaces proceeds despite the severe undersatura-tion in Si; the average Si concentration measured instage II is 0.77 ppm, whereas the Si solubility at 20 °C is∼9 ppm [25]. This discrepancy between the experimentand the prediction may be interpreted as non-accom-modated mechanisms such as mechanical creep and

Fig. 10. Input data for prediction; (a) the average dissolution mass fluxes at six different stages evaluated from the measured Si concentrations andprescribed flow rates and (b) comparison of Si concentrations with time between the experiment and the inversely calculated using the input ofdissolution mass fluxes.

197H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

crushing of propping asperities and crushed debrisclogging flow-path, resulting in the sharp increase ofimpedance. In stages III to VI the fracture apertureconsistently increases as dissolution proceeds. Signifi-cantly, the model simulations show that dissolution atcontacting asperities may not occur throughout thesestages, rather than that the etching process dominatesover the minor effect of aperture reduction due todissolution at contacting asperities. Rates of dissolutionat contacting asperities decrease as the contact areagrows, and will effectively halt when stress acting oncontact area reaches a critical stress [32,33,26]. Abruptdecreases of aperture were measured immediately afterthe switching of the flow direction in stage II. Thismechanical effect of the destruction of contactingbridges enlarges overall contact-area ratio, and thusthe contact stresses may fall below some critical stress,

leading to inactive dissolution at contacting asperitiesduring stages III to VI.

The ultimate contact area that has evolved by the endof the 3150-h test is predicted to be ∼34% as shown inFig. 12, and overestimates that measured by Wood'smetal impregnation (14.5%). This is attributed to theoverly simple representation of the relation betweenfracture aperture and contact area (i.e., Eq. (4) and Fig.9), which is incapable of representing the spatiallydistributed change in aperture resulting from spatialconditions of flow, stress, and chemistry. The occur-rence of clogging (aperture reduction) without anincrease in contact area may be triggered by localprecipitation, which is not accommodated in the currentmodel. This implicates that further topographicalconstraints of two rough surfaces in contact are neededto accommodate a spatial complexity of flow, stress, and

Fig. 11. Comparisons of changes in (a) aperture and (b) normalized differential pressure with time between experimental results and predictions. Solidline represents the experiments, and open circles are predictions with appropriately applied ratios of rC and rF.

198 H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

chemistry and to achieve a more realistic understandingof the evolution in fracture aperture.

5. Conclusions

Experimental measurements of fluid and mineralmass effluxes, constrained by non-destructive imagingby X-ray CT and digital radiography, and by destructiveimaging of a fracture cast, allow the evolution offracture aperture to be followed. For isothermal flow atlow temperature (20 °C), the fracture closed monoton-ically as the bridging asperities are progressivelyremoved. This amounts to a 60% reduction in fractureaperture over the initial 1500 h duration of theexperiment. Subsequently, free-face dissolution dom-inates over the effects of dissolution at contactingasperities, and results in an augmentation in fracture

aperture. The rate of gaping increases with an increase intemperature, corresponding to the exponential (orArrhenius-type) dependence on the mineral effluxesmeasured. The activation energy constrained in thiswork is 22.2 kJ mol−1, congruent with that obtainedfrom Iler [25] (i.e., 21.7 kJ mol−1).

The post-experiment observations by the X-ray CT,digital radiograph, and Wood's metal cast revealed thedetailed distribution of local apertures and regions incontact within the fracture. The three independentmeasurements imply no presence of a preferential flowpath generated during the experiments. The averageaperture evaluated from the CT images is sevenfoldlarger than the hydraulic aperture at the end of theexperiment. This mismatch is likely due to limitations inthe resolution of the CT imaging, and in the choice ofthreshold CT number.

Fig. 12. Predicted progress in fracture aperture with contact-area ratio. In stages I and II the contact-area ratio monotonically increases with decreaseof aperture due to dominant process of dissolution at contacting asperities, whereas in stages III to VI dissolution at free fracture wall controls net-dissolution and enlarges void space without increase of contact area.

199H. Yasuhara et al. / Earth and Planetary Science Letters 244 (2006) 186–200

A process-based model is applied to examine theexperimental observations—that aperture closureswitches to aperture growth, but all the time due to netmineral dissolution. Employing a simple relationbetween fracture aperture and contact-area ratio, andassigning the sources of mineral dissolution evaluatedfrom measured Si concentrations to contact area and freevoid walls with certain ratios, the model is capable offollowing the rates and magnitudes of aperture changesmeasured in the experiment. However, the ultimatecontact area predicted significantly overestimates thatconstrained by the profile of a Wood's metal cast of thefracture.

The measured Si concentrations are significantlybelow equilibrium solubilities at all temperatures, due tothe high prescribed flow rates, and the resulting shortresidence time in the fracture. Examining this far-from-equilibrium behavior is important in considering therates and magnitudes of permeability-enhancementwithin rock fractures stimulated by chemical permeantsin geothermal and petroleum reservoirs. The currentexperimental measurements showed permeability deg-radation first and then enhancement with the increasedrates with an increase in temperature, but the importantfactors (i.e., temperature, stress, and chemistry in thepore fluid) triggering this switching remain insufficient-ly constrained (moreover, it is uncertain whether suchswitching will occur under in situ conditions thatapplied temperatures, stresses, and fluid chemistrieswithin fractured rock masses of interest may be in quasi-steady state before hydraulic and chemical stimulation).

Thus, further detailed investigations are required toachieve more realistic understanding on the evolution infracture permeability mediated by coupled thermal,hydraulic, mechanical, and chemical processes.

Acknowledgements

This work has been supported by grants DOE-BES-DE-FG02-00ER15111, DOE-DE-PS26-01NT41048,DOE-DE-FG36-04GO14289, and ARC DP0209425.This support is gratefully acknowledged. The commentsof two anonymous reviewers significantly contributedto the quality of the final manuscript.

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