PROCEEDINGS, TOUGH Symposium 2003Lawrence Berkeley National Laboratory, Berkeley, California, May 12–14, 2003

- 1 -

LINKING REACTION, TRANSPORT, AND HYDROLOGICAL PARAMETERS INUNSATURATED FRACTURED ROCK:

TOUGHREACT IMPLEMENTATION AND APPLICATION

Eric Sonnenthal, Nicolas Spycher, and Tianfu Xu

Lawrence Berkeley National LaboratoryEarth Sciences Division

Berkeley, CA, 94720, USAe-mail: elsonnenthal@lbl.gov

INTRODUCTION

Modeling coupled water-gas-rock interactions inunsaturated fractured rock requires conceptual andnumerical model considerations beyond those devel-oped for saturated porous media. This paper focuseson the integration of the geological and hydrologicalparameters into the calculation of reactive-transportparameters and the feedback of mineral precipita-tion/dissolution to flow and transport. These basicrelations have been implemented in the reactivetransport code TOUGHREACT (Xu et al., 2003) thatcouples equilibrium and kinetic water-gas-rock inter-actions with multiphase flow and aqueous andgaseous species transport. Simulation results arepresented illustrating the effects of water-rock inter-action accompanying the heating of unsaturatedheterogeneous fractured tuff.

Unknowns associated with modeling water-rockinteraction in fractured unsaturated systems are thearea of the fracture surface that is wetted and whichfractures are active components of the overall flowsystem. The wetted fracture area is important notonly to water-rock interaction but to flow andtransport between fluids flowing in fractures and theadjacent matrix. The other unknown relations arethose describing permeability and capillary pressuremodification during mineral precipitation and disso-lution. Here we discuss solely the relations developedfor fractures and the fracture-matrix interface.

REACTIVE SURFACE AREAS

The fundamental parameter coupling kinetically-controlled mineral-water reactions to fluid flow is thereactive surface area. Rates of mineral dissolutionand precipitation close to equilibrium can bedescribed via a relationship of the rate to the satura-tion index (Q/K), as follows (based on Steefel andLasaga, 1994):

†

R = sgn log QK( )È

Î Í ˘ ˚ ˙ kA Q

K( )m

-1È

Î Í

˘

˚ ˙

n

(Eq. 1)

where R is the rate (mol s-1 kg-1w), w refers to water,

m and n are empirically determined exponents, k isthe rate constant, “sgn” refers to the sign of thereaction (dissolution is positive and precipitation isnegative) and A is the reactive surface area expressedin units of

†

mm2 /kgw .

Fracture Mineral Reactive Surface Areas

Reactive surface areas of minerals on fracture wallscan be calculated from the fracture-matrix interfacearea/volume ratio, the fracture porosity, and volumefractions of minerals. The total fracture-matrix inter-face areas can be based on measured fracture densi-ties and an assumption of the fracture geometry, e.g.,as planar disks. The wall of the fracture is treated asa surface covered by mineral grains and having someroughness. This geometric surface area of the fracturewall per unit volume of fracture can be approximatedby:

†

Ar = pAf-mx

2f fv

(Eq. 2)

where Ar is the reactive surface area (

†

m2 /m f3), Af-m is

the fracture-matrix interface area/volume ratio(

†

m f2 /m f +m

3 ), ff-m is the fracture porosity of the rock,and p/2 is the roughness factor. Af-m is the surfacearea used as input to the model simulations as anapproximation of the reactive surface area. Thismodel for the fracture surface area considers that theareal coverage is approximately equivalent to themineral volume fraction. A further modification,relates the 3-D cross-sectional area to the 2-D surfacearea in the fracture, yields a factor of 3/2, i.e., anincrease of 50% in the reactive surface area.

The reactive surface area of each mineral (Ai given inunits of

†

mm2 /kgw ) used in Equation 1 is then given

by:

†

Ai (m2/ kgwater ) =

Ar fi

rwf f

(Eq. 3)

where fi is the volume fraction of the mineral in the

- 2 -

mineral assemblage, rw is the density of water (takenas a constant 1,000 kg/m3), and ff is the porosity ofthe fracture medium, as opposed to the fractureporosity of the rock. This is the surface area/watermass ratio for a mineral in a liquid-saturated system.

To provide the correct rock/water ratio in an unsatu-rated system, the form of this surface area can bewritten as:

wfw

iri S

fAA

fr= )kg/ (m water

2 (Eq. 4)

where Sw is the water saturation. However, as Sw goesto zero, the reactive surface area would tend toinfinity. In this case, the question is whether thewater takes the form of a thin film across much of thefracture surface, as narrow rivulets of water, coveringonly a portion of the surface, or as some combination.Under a condition of very small water flux and lowliquid saturation, the surface area of the rockcontacted by water is likely much smaller than thetotal area.

Two methods have been implemented to address thisphenomenon. The first method considers that thesurface area contacted by water is directly propor-tional to the liquid saturation. This yields thesaturated surface area given by Equation 3. Thesecond method employs the active-fracture-modelconcept (Liu et al., 1998) that has been modified toconsider water-rock reactions taking place below theresidual saturation. The form of the active fractureparameter for reaction is then given by the followingset of equations:

†

Sar = (Sw - Sm )/(1- Sm ) (Eq. 5)

†

afmr = Sar(1+g ) (Eq. 6)

where Sm is the minimum liquid saturation for whichwater-rock reactions are considered and Sar is theeffective saturation available for reaction. The activefracture parameter, g , is determined throughiTOUGH2 inversions to matrix saturation, assuminga known infiltration rate (Liu et al., 2003). The factorthat reduces the surface area contacted by the waterphase is given by afmr. Sm is usually set to a very smallvalue around 10-4, to ensure that reactions take placeuntil virtually no water is left (e.g., during dry out viaventilation or heating). Finally, the reactive surfacearea, using this modified form of the active fracturemodel, is given by:

†

Ai(m2/kgwater ) =

Arafmr

rwf f Sw

(Eq. 7)

The surface area calculated in this way is applicableonly to reactions taking place in the fracture medium.

In the dual permeability method, the porosity of thefracture medium can be taken as 1.0; however, formodeling of mineral dissolution and precipitation,there would then be no rock to dissolve. Therefore,an adequate volume of rock adjoining the open spaceof the fracture needs to be considered as the startingrock fraction.

HYDROLOGICAL PROPERTY CHANGES

Porosity

In this analysis, porosity changes in matrix andfractures are directly tied to the volume changes as aresult of mineral precipitation and dissolution. Themolar volumes of hydrous minerals, such as zeolitesor clays, created by hydrolysis reactions withanhydrous phases, such as feldspars, are commonlylarger than those of the primary reactant minerals.Therefore, constant molar dissolution-precipitationreactions can lead to porosity reductions. Thesechanges are taken into account in TOUGHREACT.The porosity of the medium (fracture or matrix) isgiven by:

†

f =1- frmm=1

nm

 - fru(Eq. 8)

where nm is the number of minerals, f rm is thevolume fraction of mineral m in the rock(Vmineral/Vmedium, including porosity), and fru is thevolume fraction of nonreactive rock. As the frm ofeach mineral changes, the porosity is recalculated ateach time step. The porosity is not allowed to gobelow zero.

Fracture Permeability Changes

Fracture permeability changes can be approximatedusing the porosity change and an assumption of planeparallel fractures of uniform aperture (cubiclaw—Steefel and Lasaga, 1994). Assuming nochange in fracture spacing or density, the updatedpermeability, k, is given by:

†

k = k0ff0

Ê

Ë Á

ˆ

¯ ˜

3

(Eq. 9)

where k0 and f 0 are the initial permeability andporosity, respectively. This law yields zero perme-ability only under the condition of zero fractureporosity.

In most experimental and natural systems, perme-ability reductions to values near zero occur at poros-ities significantly greater than zero. This generally isthe result of mineral precipitation preferentiallyclosing the narrower interconnecting apertures. Thehydraulic aperture, as calculated from the fracturespacing and permeability (as determined through air-permeability measurements) assuming a cubic law

- 3 -

relation, is a closer measure of the smaller aperturesin the flow system. Using the hydraulic aperture, amuch stronger relationship between permeability andporosity can be developed. This relationship can beapproximated as follows:

The initial hydraulic aperture b0,h (m) is calculatedusing the following cubic law relation (Steefel andLasaga, 1994):

†

b0,h = 12k0s[ ]1

3 (Eq. 10)

where k0 is the initial fracture permeability (m2) and sis the fracture spacing (m). The permeability (k’)resulting from a change in the hydraulic aperture isgiven by:

†

¢ k =b0,h + Db( )3

12s(Eq. 11)

where Db is the aperture change resulting frommineral precipitation or dissolution. The aperturechange resulting from a calculated volume changecan be approximated by assuming precipitation of auniform layer over the entire geometric surface areaof the fracture, assuming also that this area (as wellas the fracture spacing) remains constant. In geologicsystems, the actual distribution of mineral alterationis much more heterogeneous and depends on manyfactors that are active at scales much smaller than theresolution of the model. The combined effect of theinitial heterogeneities and localized precipitationprocesses can only be treated through model sensi-tivity studies and experiments. The initial apertureavailable for precipitation (bg, the geometric, ratherthan the hydraulic, aperture) can be approximatedfrom the ratio of the initial fracture porosity (ff,0) tothe fracture surface area (Af), as follows:

†

bg =f f ,0

Af(Eq. 12)

For a dual-permeability model, changes in thefracture porosity are calculated based on the porosityof the fracture medium, so that Db can be approxi-mated by

†

Db =¢ f fm - f fm,0( )

f fm,0

bg(Eq. 13)

Equations 10, 11, and 13 were implemented inTOUGHREACT with input parameters of bg and s.

Changes to Capillary Pressures

Changing permeability and porosity also results inchanges in the unsaturated flow properties of therock. This effect is captured by modification of thecalculated capillary pressure (Pc) using the Leverett

scaling relation to obtain a scaled Pc´ as follows:

†

P ¢ c = Pc k0fkf0

(Eq. 14)

Simulations performed with TOUGHREACT havethe maximum capillary pressure limited by the cutoffprescribed in the input file.

SIMULATION OF REACTIVE TRANSPORT INHETEROGENEOUS FRACTURED TUFF

Here we present an example of the coupling betweenmineral-water reactions and unsaturated flow inheterogeneous fractured tuff. The model was devel-oped to investigate processes accompanying theproposed emplacement of nuclear waste in emplace-ment drifts in the unsaturated welded tuffs at YuccaMountain, Nevada. Detailed discussions of themodel development and parameters are discussed inSonnenthal and Spycher (2001) and Spycher et al.(2003).

The model represents at 2-D vertical cross-sectionperpendicular to a 5.5m emplacement drift that isheated according to a defined heat loading curve andconsidering an initial 50-year period of ventilation-induced heat removal. By symmetry the model isreduced to a half-drift and extends horizontally to themidpoint between two adjacent drifts (40.5m). Themodel extends upward to the ground surface anddownward to the water table. An initial randomheterogeneous fracture permeability distribution wascreated at a scale of 0.2 m, which was then averagedover the area of ach numerical grid block. The initialrange in fracture permeability was 4 orders ofmagnitude. A prescribed step-wise infiltration-ratewas applied (6 mm/yr to 600y, 16 mm/yr to 2000y,and 25 mm/yr to 20,000y) to approximate a possibleclimate change scenario.

The geochemical model used for the simulation is asimplified system consisting of several primaryaqueous, gaseous and mineral species, capturing thedominant effects of mineral precipitation on unsatu-rated flow. The primary aqueous species consideredare Ca2+, Na+, SiO2, HCO3

-, Cl-, F-, and SO42-. Gases

include water vapor, air, and CO2. Minerals includesilica polymorphs (quartz, tridymite, cristobalite, andamorphous silica), calcite, gypsum, and fluorite. Thesilica polymorphs and fluorite are treated as kineticphases, whereas calcite and gypsum, being relativelyfast-reacting, are set to react under equilibriumconditions. Aqueous and gaseous species aretransported by diffusion and advection. The dualpermeability model considered differentmineralogical and geochemical properties for thefracture and matrix continua as well as unsaturated

- 4 -

flow properties.

In addition to the reactive surface area, fluid fluxesalso control the rate and extent of mineral-waterreactions. Liquid saturations and fluxes are stronglytied to the permeability and capillary properties, asshown in Figure 1, which exhibits the dry-out and aheterogeneous condensation zone around an above-boiling repository drift after 600y. Percolation fluxesabove the drift are higher than below (capillarydiversion effect) and therefore the condensation zoneis developed more strongly above the drift. At theedge of the boiling front, mineral precipitation isdriven by a combination of mineral-water-reactionsand evaporative concentration.

Figure 1.Fracture saturation and liquid fluxvectors at 600y for a proposed above-boiling nuclear waste emplacement drift.

The net effect of these processes over 20,000y is achange in permeability that is strongest in areas ofinitially low permeability but high liquid fluxes andsaturation (Figure 2). The distribution of permeabilitychanges is, however, a combined effect of differentminerals precipitating in varying patterns. Forexample, amorphous silica has an increased solubilityat higher temperatures and only precipitates at theboiling front by evaporative concentration (Figure 3).Calcite also precipitates by evaporativeconcentration, but also by degassing of CO2 andheating of percolating fracture water from thesurface, thus leading to abundant precipitation wellabove the boiling zone (Figure 4).

Figure 2. Ratio of fracture permeability at 20 ky tothe initial value.

Figure 3. Amorphous silica precipitated in fractures(volume %) after 20 ky.

- 5 -

Figure 4. Calcite precipitated in fractures (volume%) after 20 ky for a proposed above-boiling nuclear waste emplacement drift.

CONCLUSIONS

Modeling water-rock interaction in unsaturated rockrequires additional considerations for the calculationof reactive surface areas and the coupling of mineralprecipitation and dissolution to flow. In this paperwe have described some possible relationshipsbetween reactive surface areas in unsaturatedfractures and the conceptual model of fracturegeometry and the fracture-matrix interaction factor.The reactive surface area in unsaturated fractures hasbeen related directly to the fracture-matrix interactionfactor as given by the “active fracture model” (Liu etal., 1998). These relationships have beenimplemented into the reactive-transport codeTOUGHREACT. Modeling of water-rock interactionin boiling unsaturated heterogeneous fractured rockexemplifies the strong feedbacks between water-rockinteraction and unsaturated flow. In particular,increased liquid saturation as a result of highercapillary pressures in smaller aperture fractures leadsto increased rates of reaction and further reductionsin permeability.

ACKNOWLEDGMENTS

The authors wish to acknowledge input to variousaspects of the model development by John Apps andCharles Haukwa and improvements through earlierreviews of related work by Pat Dobson and PeterPersoff. This work was supported by the Director,Office of Civilian Radioactive Waste Management,U.S. Department of Energy, through MemorandumPurchase Order EA9013MC5X between BechtelSAIC Company, LLC and the Ernest OrlandoLawrence Berkeley National Laboratory (BerkeleyLab). The support is provided to Berkeley Labthrough the U.S. Department of Energy Contract No.DE-AC03-76SF00098.

REFERENCES

Liu, H.H., C.B. Haukwa, C.F. Ahlers, G.S.Bodvarsson, A.L. Flint, and W.B. Guertal. Modelingflow and transport in unsaturated fractured rock: anevaluation of the continuum approach Journ .Contam. Hydrol., 62-63, 173-188, 2003.

Liu, H.H., C. Doughty, and G.S. Bodvarsson. Anactive fracture model for unsaturated flow and trans-port in fractured rocks, Water Resour. Res., 34(10),2633–2646, 1998.

Sonnenthal, E., and N. Spycher, N., 2001. Drift-Scalecoupled processes (DST and THC seepage) models.AMR N0120/U0110 Rev.01, Yucca Mountain Project,Lawrence Berkeley National Laboratory, Berkeley,California.

Spycher, N., E. Sonnenthal, and J. A. Apps. Predic-tion of fluid flow and reactive transport aroundpotential nuclear waste emplacement tunnels atYucca Mountain, Nevada, Journ. Contam. Hydrol.,62-63, 653-673, 2003.

Steefel, C.I. and A.C. Lasaga. A coupled model fortransport of multiple aqueous species and kineticprecipitation/dissolution with application to reactiveflow in single-phase hydrothermal systems. Am. Jour.Sci., 294, 529-592, 1994.

Xu, T., E. Sonnenthal, N. Spycher, and K. Pruess,TOUGHREACT User’s Guide: A SimulationProgram for Nonisothermal Multiphase ReactiveGeochemical Transport in Variably SaturatedGeologic Media, Lawrence Berkeley NationalLaboratory, Berkeley, Calif., in prep.