Models for coupled fluid flow, mineral reaction, and isotopic ...Models for coupled fluid flow,...

American Mineralogist, Volume 77, pages 577-591, 1992

Models for coupled fluid flow, mineral reaction, and isotopic alteration during contactmetamorphism: The Notch Peak aureole, Utah

JonN M. Fnnnv, GnBconv M. Drppr,nDepartment of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218, U.S.A.

AssrRAcr

Three different models were developed to simulate the effect of contact metamorphismand fluid-rock interaction on the prograde mineralogical and O isotopic evolution ofcal-careous aryillites from the Notch Peak aureole, Utah. All models assume local mineral-fluid equilibrium, a steady-state temperature profile corresponding to peak metamorphicvalues, and the thermodynamic data for minerals and fluid of Berman (1988). The pre-ferred model, metamorphism with flow of a time-integrated fluid flux of 2 + 0.5' 104 mol/cm2 in the direction of increasing temperature, successfully reproduces the principal pet-rologic and isotopic features of the aureole: (l) occurrence and positions (in map view) ofdiopside-in, tremolite-out, g,rossular-in, wollastonite-in, and quartz-out isograds; (2) stablecoexistence of tremolite + calcite + qtJartz + diopside over an = I km distance betweenthe diopside-in and tremolite-out isograds; (3) variable whole-rock t8O depletions of =6-

9Vmadjacent to the contact; and (4) a gradual and irregular increase in D'EO with increasingdistance from the pluton. One unsuccessful model considered interaction of rock with atiny, stagnant, fluid-filled porosity with fluid pressure equal to either lithostatic or hydro-static pressure. Regardless offluid pressure, the model fails to predict the position ofthetremolite-out isograd; the occurrence ofgrossular, wollastonite, and quartz-out isograds atany position; and '8O depletions >0.3V-. The other unsuccessful model, flow of magmaticfluid in the direction of decreasing temperature through the aureole, fails to predict theobserved range of whole-rock isotopic compositions within 0.5 km of the contact, theobserved position of the diopside isograd, and the observed spatial distribution of trem-olite + calcite + qvarlz + diopside. Results demonstrate how isotopic and petrologic datafor contact aureoles can be integrated to provide quantitative constraints on the magnitudeand geometry of metamorphic fluid flow.

IlmnonucrroN 1990b; Baumgartner and Ferry, l99l; Dipple and Ferry,

The emplacement of plutons at shallow levels of the l99l;ferry, l99l; Ferry and Dipple, l99l), it is now

crust in rocks of no.-ui permeability almost i"""ituUf' possible to interpret quantitatively the isotopic and min-

leads to the development of hydrothermat conlr"cii* eralogical .record

of fluid-rock interaction in contact

systems (e.g., Norton and Knight, 1977). conseo""itrt metamorphic terranes in terms of time-integrated fluid

contact metamorphism commonly involves not onty ei- flux and flow direction relative to temperature gradients.

evation of tempeiature in the aureole but also fluid-rock The purpose of this report is to demonstrate how appli-

interaction. Fluid-rock interaction during contact meta- cation of these models can lead to a comprehensive un-

morphism leaves a distinctive record in Uotft ti" tiuUi" derstanding of the mineralogical and stable isotopic

isotopic and mineralogical composition of metamor- structureofindividualcontactmetamorphicterranes.The

pfrosiO rocks (cf. reviews by Rice and Ferry, f SSZ; Vul- study focuses specifically on calcareous argillites of the

ley, 1986; Ferry, 1986, l99l). Especially good records are fie lorry Limestone Member of the orr Formation in

left in impure carbonate rocks both because their pre- the Notch Peak contact aureole' utah' The Notch Peak

metamorphic O isotopic composition is usually ,r..yiif- aureole was chosen because there is exceptionally thor-

ferent from that of normal metamorphic n"ias a"i Le- ough published documentation of its geology, mineralo-

cause interaction of siliceous carbonate rocks with;;;t gy' and whole-rock and stable isotope geochemistry'

fluids at elevated temperature readily drives mineral de-carbonation reactions. With the recent development of GnolocY, PETRoT-roGYr lxn O rsoroPE

models grounded in continuum mechanics that rigorous GEocHEMrsrRY oF THE

ly coupli fluid flow to mineral and isotopic reactlons in NorcH Pnnr coNucr AUREoLE

rocks(e.g., BickleandMcKenzie, 1987; Baumgartnerand The composite Notch Peak stock consists of graniteRumble, 1988; Lasaga, 1989; Bickle and Baker, 1990a, andquartzmonzonite(Nabeleketal., 1986)andintruded

0003404x/92l0506-o577$02.00 s77

578

Fig. l. Simplified geologic and metamorphic map of the east-ern and northeastern portion of the Notch Peak contact meta-morphic aureole, Utah (modified after Fig. 5 of Hover-Granathet al., 1983). Models described in text attempt to reproduce theobserved sequence offour isograds, the spacing between isogradsand the pluton-metasediment contact, and the occurrence oftremolite (Tr) + calcite (Cal) + quartz (Qz) + diopside (Di) inrocks between the diopside-in and tremolite-out isograds over adis tanceof =1km.

the Cambrian Big Horse Limestone Member of the OrrFormation in Jurassic time (Hover-Granath et al., 1983).The Big Horse Limestone Member is composed of gentlydipping interbedded siliceous limestones and calcareousargillites and their contact-metamorphosed equivalents.

The mineralogical and petrologic effects of contactmetamorphism are described by Hover-Granath et al.(1983) and Labotka et al. (1988a). The first-order petro-logic features of metamorphosed calcareous argillites inthe contact aureole are summarized in Figure I and Tablel: (l) the appearance, with increasing proximity to the

FERRY AND DIPPLE: MODELS FOR CONTACT METAMORPHISM

pluton-metasediment contact, of diopside at the diopsideisograd; (2) coexistence of reactants and products of thediopside-forming reaction (tremolite + calcite + quartz+ diopside) over a distance of =l km in the diopsidezone; (3) the disappearance of tremolite at the tremolite-out isograd; (4) the appearance ofgrossular or vesuvianiteor both at the grossular * vesuvianite isograd; (5) theappearance of wollastonite at the wollastonite isograd;and (6) the absence of reactants of the wollastonite-form-ing reaction (quartz is consumed) in the innermost partof the aureole. The distances of the isograds from thepluton-metasediment contact (Table l) were measured inthe eastern part of the contact aureole from Figure 5 ofHover-Granath et al. (1983), which is reproduced in sim-plified form as Figure I of this report. Isograds in thesouthern portion ofthe aureole are bunched and difficultto interpret. Inferred pressure of contact metamorphismwas 2 kbar, and the maximum temperature at the pluton-metasediment contact was =600 "C (Labotka et al.,I 988a).

The stable isotopic effects of contact metamorphism onthe Big Horse Limestone Member were reported by Na-belek et al. (1984). The first-order isotopic features ofargillites in the contact aureole are summarized in TableI and Figure 2: (l) whole-rock D'8O decreases conlinu-ously from xl9%m (SMOW) in unmetamorphosed sam-ples 2-5 km from the pluton to 8-l5V- within =400 mof the contact and (2) the 6180 of argillites close to thepluton is not uniform but varies over a significant rangeof =7Vn. In contrast to the argillites, the O isotope com-position of interbedded limestones is uniform throughoutthe aureole and was unaffected by contact metamorphism(Nabelek et al., 1984). The difference in isotopic com-position between argillites and limestones led Nabelek etal. (198a) to conclude that fluid flow was highly channel-ized during metamorphism, with enhanced flow along ar-gillite layers and little or no flow along the limestone lay-ers.

The whole-rock major- and minor-element geochem-

Tmu 1, First-order isotopic and petrologic features of the Notch Peak contact aureole

Observation' P,: P,

No flow models*'

Up-tempera-ture flow model%: ( 1 -3 ) . 104

mol/cm,

Down-temperatureflow modelst

Model ofq- :2 '106 Labotka etmol/cm, al. (1988a)P' : P^

Appearance of diopsideTremolite + calcite + quartz + diopside stableDisappearance of tremoliteAppearance of grossular or vesuvianiteAppearance of wollastoniteWollastonite-forming reaction completedlqod at or near @ntactd'aO* * 1 km from contact

*1.4-2.2 kmr1-2 km

E0.7-1.2 kmE0.6-1.1 km-0.4-0.8 km

<ry0.4-0.8 km*U1scfta

x12 -1%

1.80 km0.21-1.80 km

0.21 kmnot predictednot predictednot predicted

[email protected]*

1.80 km0.46-1.80 km

0.46 kmnot predictednot predictednot predicted

18.79-19.@-

1.80 km0.98-1.80 km0.98-1-18 km0.86-1.16 km0.47-0.66 km0.34-{.52 km9.O-15.49*

11.8-15.4E6'

0.49 km 0.59 km0.49 km 0.59 km0.49 km 0.59 km0.20 km 0.43 km0.19 km 0.42km0.19 km 0.42 km9.3E* 9.39-

19.7V- 19.3E-'lsograds from east and northeast side of contact aureole (Hover-Granath et al., 1983; Fig. 1); isotopic compositions from Nabelek et al. (1984).

Distances measured away from the pluton with 0 at the pluton-metasediment contact.** Results for fluid pressure (A) equal lithostatic pressure (4) and fluid pressure equal hydrostatic pressure (Pn).t Results in first column for time-integrated H"O fiux of 2.1F mol/cm, outward trom the contact (z: 0); model of Labotka et al. (1988a) refers to

perfect chemical eguilibration of argillite with magmatic HrO in the innermost 400 m of the contact aureole and a time-integrated flux of 900 moycm,HrO outward from a position at z: 400 m.

FERRY AND DIPPLE: MODELS FOR CONTACT METAMORPHISM 579

istry of the contact metamorphosed Big Horse LimestoneMember was investigated by Labotka et al. (1988b). Ex-cept within a few meters of the pluton, contact meta-morphism of all carbonate rocks was isochemical or near-ly so.

Ixrncurnn MTNERALocTcAL AND rsoroprcMODELS OF CONTACT METAMORPHISM

Summary of approach

Fluid-rock interaction during metamorphism in theNotch Peak aureole was investigated by considering amodel rock with bulk chemical composition that is aslightly simplified analogue to that of average argillite.The metamorphism is simulated in a one-dimensionalcontact aureole where the distribution of temperature withdistance throughout the duration of fluid flow and meta-morphism is similar to the distribution of peak temper-atures in the Notch Peak aureole. Fluid is considered abinary COr-HrO solution. Equations grounded in trans-port theory are used to predict mineralogical and isotopicalteration that result from various types offluid-rock in-teraction (e.g., no fluid flow; flow in the direction of in-creasing temperature; flow in the direction ofdecreasingtemperature). Predicted mineralogical and isotopic alter-ation are then compared with observed petrologic andisotopic features of the Notch Peak aureole (Figs. 1,2;Table l) to determine which type of fluid-rock interactionbest accounts for the observed features. The goal of thestudy was to identify the simplest possible model thatreproduces the first-order petrologic and isotopic featuresofthe aureole.

Input parameters to simulations

Composition and mineralogy of model rock. The bulkcomposition of an analogue argillite in the system CaO-MgO-AlrOr-SiOr-COr-HrO was calculated from the av-erage mode of samples from the wollastonite zone (Table4 of Labotka et al., 1988a) and simplified compositionsof the constituent minerals (their Table 3). A relativelysmall amount of KrO (1.3 oxide molo/o on an HrO-COr-free basis) was simply omitted for two reasons. First, theK-free analogue composition is capable of reproducingthe first-order petrologic features of the contact aureole(i.e., diopside, tremolite-out, grossular, and wollastoniteisograds). Second, regardless ofthe type offluid-rock in-teraction, all models of metamorphism involving aK-bearing analogue composition fail to reproduce the ob-served subassemblage phlogopite * calcite + quartz +tremolite * potassium feldspar + diopside in the diop-side zone. The subassemblage never develops becausecurrent thermodynamic data bases (e.g., Berman, 1988)predict that it is unstable at all temperatures at 2 kbarin the system CaO-K'O-MgO-AlrOr-SiOr-CO,-HrO(CKMASCH), a prediction unequivocally confirmed bythe experimental results of Wones (1970). The assem-blage biotite + calcite + quartz + calcium amphibole *potassium feldspar * calcium pyroxene is stabilized inmetamorphic rocks by non-CKMASCH components (e.9.,

r fc)600' 378" 270" 202' 175' t 75'

0 1000 2000 3000 4000 5000

distance trom contact, z (m)

{ flow direction

Frg.2. Measured and calculated whole-rock O isotope com-positions of calcareous aryillites as a function of distance fromthe pluton-metasediment contact (Z : O). Measured distance-6180 data from Nabelek et al. (1984), Table l, and Labotka etal. (1988a), Table l. Curves calculated from Equation 1 in textfor four different values of time-integrated mole fluid flux andflow in the direction of increasing temperature (curve for 4* :

10000 mol/cm'?highlighted by shading). Curves for the four dif-ferent fluxes superimpose along their inclined portions and atdistances >4000 m. Most observed '8O depletions within 500m ofthe pluton in the Notch Peak aureole can be explained byflow of (1.5-2.5)' lOa mol/cm'z fluid through the contact aureoleand up-temperature flow (shaded area). Only six of20 analyzedsamples (black circles) deviate by more than xl%oo from valuespredicted by this preferred model. Temperatures calculated fromequation for temperature profile in Table 2'

Hewitt, 1973). The inclusion of K in an analogue rockcomposition therefore appeared to introduce unnecessarycomplications.

The mineral content of the analogue protolith was con-sidered tremolite + anorthite * calcite + quartz; relativeamounts of the minerals (Table 2) were computed fromthe bulk composition of the analogue argillite and themineral formulas in Table 3 of Labotka et al. (1988a).This low-grade metamorphic assemblage was chosen be-cause it is the simplest assemblage that reproduces thefour mapped isograds (Fig. l) with the fewest number ofprograde reactions, and it is consistent with the nascentdiopside zone assemblage ofLabotka et al. (1988a, theirTable 5). Models of metamorphism considered the de-velopment of diopside, grossular, and wollastonite fromthe protolith mineral assemblage. Vesuvianite was ne-glected because there exists no data for its thermodynam-ic properties consistent with those of Berman (1988).

Mineral reections and mineral-fluid equilibria. Figure3 illustrates all possible stable reactions involving trem-olite, calcite, anorthite, quarlz, diopside, g,rossular, wol-lastonite, and CO,-HrO fluid at 0.75 and 2 kbar and Z :

350-650 "C. The reactions constitute isograd reactions in

20

= 1 8E

E ''uo€',o

14Looi 1 26.C! r o

a o measured data

time-integrated flux inmol fluid/cm2 rock

580 FERRY AND DIPPLE: MODELS FOR CONTACT METAMORPHISM

TABLE 2. Parameterization of integrated isotopic and mineralogical models of contact metamorphism

Parameter

Temperature profile: f (K) : 873-0.33362(m) + 1.530 'lO oZ2 - 4.909.10 aZ + 8.426.10 1224 - 5.391.16 roTs 10-4 km)Ambient temperature: 448 K (Z > 4 km)Initial whole-rock 61oO: +197o6'"0,-* - 613OH"o: 2.78.1061T2 - 2896'"0,** - 518Oco.: 1.8034.10Yf, - 10.611 .1O3lT + 2.7798Calcite + quartz : wollastonite + CO, equilibrium: Xco" : 3.0808.10 56f10.61e7 (f : 698-873 K)Anorthite + quartz + 2calcite : grossular + 2CO, equilibriufi: Xco, : 1.4318.10 a6T15e21 (T:623-853 K)Tremolite + 3calcite + 2quartz:sdiopside + 3CO, + H.Oequilibiium: X"o":9.3705 10 7rf4e7s8(f :623-768 K)

)Go.: 1.4776 10 87T2sBo23 (r : 768-808 K)Anorthite + wollastonite + calcite: grossular + CO, equilibrium: Xco.: 1.7360.10 22111oss (f :843-873 K)Initial rock (mol/kg): 0.5146 anorthite + 0.1962 tremotite + 3.3088 quartz + 4.9818 calcite

Note.'1 : Similar to curve in Labotka et al. (1988a), their Figure 6, extrapolated smoothly to E175 .C at 4000 m. 2 : Average of 200 qC and valuelisted in Labotka et al. (1988a), their Table 6. 3 : Nabelek et al. (1984), greatest value reported for "unmetamorphosed" samples. 4 : Friedman andO'Neif (1977) for calcite. 5 : Calculated lot P: p@" * pr"o : 2000 bars from data in Berman (1988) with COr-HrO mixing after Kerrick and Jacobs(1981). 6 : Calculated on a K-free basis using average wollastonite zone mineral abundances in Table 4 and idealized mineral compositions in Table3 of Labotka et al. (1988a).

1234455c

o

the analogue argillite. Simple analytical expressions forf-Xcoz conditions of four reactions are listed in Table 2(X"", is the mole fraction CO, in fluid). Except for thehigh-temperature expression for the diopside-forming re-action, expressions reproduce X.o, values calculated fromthe data of Berman (1988) over the stated range of tem-perature to within +0.005. For a given X.o, the high-temperature expression for the diopside-forming reactionreproduces equilibrium conditions calculated from Ber-man's (1988) data to + I oC or better in the stated tem-perature range. The 623-K limit on two equalions rep-resents the low-temperature limit of the applicability ofBerman's data base and Kerrick and Jacobs' ( I 98 I ) equa-tion of state for COr-HrO fluids to calculation of mixedvolatile mineral-fluid equilibria.

Isotopic composition of model rock and fluid-rock iso-tope exchange equilibria. The initial O isotope compo-sition of the analogue argillite (D'sO : l9%n) was taken asthe maximum value of all "unmetamorphosed" argillitesreported by Nabelek et al. (1984). Fluid-rock O isoropeexchange reaction was approximated by the system cal-cite-HrO-CO, because the fractionation of '8O betweencalcite and HrO-CO, fluid is intermediate between thatof quafiz on one hand and diopside, anorthite, and am-phibole on the other (Friedman and O'Neil, 1977.,Chibaet al., 1989). From a more fundamental standpoint, cal-cite was chosen as a model for argillite in computationsof isotopic alteration because there is no analytical modelthat rigorously couples fluid flow along temperature gra-dients with simultaneous mineral decarbonation reac-tions and mineral-fluid isotopic exchange. The isotopiceffects of prograde reactions in aryillite, however, are small(-2V*, Nabelek et al., 1984). Because the goal of modelsdeveloped in this study is to explain '8O depletions ofuplo 6-8Vu in argillite, the neglect of decarbonation reac-tions in computation of isotopic alteration is consideredacceptable. The temperature dependencies of O isotopefractionation between calcite and HrO and between cal-cite and CO, (Table 2) were taken from Friedman andO'Neil (r977).

Flow path and temperature profile. Isotopic data un-ambiguously demonstrate that metamorphic fluid flow inthe Notch Peak aureole was largely confined to the cal-careous argillites (Nabelek et al., 1984). Bedding is sub-horizontal in the contact aureole (Hover-Granath et a1.,1983). Numerical models of pluton-driven hydrothermalcirculation indicate that fluid flow in the country rockshould be radial to the pluton (e.9., Norton and Knight,1977). The one-dimensional models of contact meta-morphic fluid flow in this study therefore consider thatflow was subhorizontal and radial to the pluton. The spe-cific goals ofthe models are to (l) reproduce the sequenceand spacing of isograds and mineral assemblages along aground-surface transect perpendicular to isograds in Fig-ure I and (2) to reproduce the profile of whole-rock Oisotope compositions plotted as a function of radial dis-tance from the pluton-metasediment contact (Fig. 2).Distance along the one-dimensional flow path is repre-sented by Z measured from 0 at the pluton-metasedimentcontact.

Variation in temperature along the flow path must bespecified in the models. For a geothermal gradient of 25"C/km, the ambient temperature at a depth that corre-sponds to a pressure of 2 kbar would be x200 "C. La-botka et al. (1988a), however, suggest that the ambienttemperature prior to metamorphism was 150 .C (theirTable 6). As a compromise, a value of 175 'C was adopt-ed. Prograde contact metamorphism therefore involvedpeak temperatures in the range 175-600 .C. The equationfor the temperature profile during metamorphism in Ta-ble 2 is a smooth curve between Z: 600 "C al. Z : 0(the contact) and 175 "C at Z: 4 km (T : 175 "C for Z> 4 km). The curve is similar both to the locus of radialdistance-peak temperature points from a thermal modelof the aureole and to the ground-surface locus of temper-ature-radial distance points recorded by calcite-dolomitegeothermometry (Labotka et al., 1988a, their Fig. 6). Be-cause fluid flow during metamorphism was subhoizontalparallel to lithologic layering and radial to the pluton, theground-surface temperature profile represented by the


equation in Table 2 was taken as the temperature profilealong the metamorphic fluid flow path. The justificationfor and consequences ofbasing calculations on a steady-state temperature profile are discussed in a later section.

Metamorphism with no fluid flow

For completeness the first models considered corre-spond to progressive metamorphism without fluid flow.One model considers fluid pressure (P) equal to lithostat-ic pressure (P,); the other considers Prequal to hydrostaticpressure (P).

P, : Pr: 2 kbar. The conventional model of meta-morphism involves increasing temperature at Pr: P, inthe absence of infiltration of rock by fluids. If the ana-logue argillite, initially containing a tiny porosity filledwith Hro-rich COr-HrO fluid (left, for example, fromsedimentation and diagenesis), is heated to peak temper-atures and local mineral-fluid equilibrium is attained, therock's mineralogical evolution can be predicted from Fig-ure 2 and equations in Table 2. The temperature at whichreaction begins is constrained by the observed positionof the diopside isograd in the field (Z:1.8 + 0.4 km)and the model temperature profile: T : 287 (+ 4l)"C.The assemblage tremolite + anorthite + quaftz * calciteis stable at T < 287 "C (Z > 1.8 km), and the assemblagetremolite + anorthite + qvarlz * calcite + diopside isstable between 287 T. and the maximum temperature onthe curve for the diopside-forming reaction, 537 "C (Z :

0.21 km). If porosity is very small, the progress of thediopside-forming reaction in the interval T : 287-537"C is correspondingly small. Virtually all tremolite reactswith calcite and quartz to form diopside at 537 "C. At T> 531 "C argillite is composed of diopside + calcite +quartz + anorthite and no further reactions occur below600 "C (Z < 0.21 km). Specifically, neither grossular norwollastonite develop. The final relationship between tem-perature and X.o, of the pore fluid at the peak of meta-morphism is illustrated by the thick shaded curve in Fig-ure 3a for ?" : 350-600 "C.

If porosity is very small, the O isotope composition ofaryillite remains +l9Vm at T < 537 "C (Z > 0.21 km).There is a small shift in isotopic composition (-0.3V*D'8O) caused by the diopside-forming reaction at 537 "C,computed from the expression for Rayleigh distillation(Eq. 5 of Rumble, 1982), the composition of fluid at 537"C (X"or: 0.75, Fig. 3a), and expressions for O isotopefractionation in Table 2. At T: 537-600 "C (Z:0-0.21km) model argillite has 6'80 : +18.7Vm.

Pr: Po:0.75 kbar. Alternatively, progressive contactmetamorphism could occur with increasing temperaturein the absence of infiltration but with & : Ph (: 0.75kbar for a depth in crustal rocks of normal density cor-responding to P, : 2 kbar). Such a circumstance coulddevelop, for example, if rocks were in chemical com-munication with vertical fluid-filled fractures that extend-ed to the Earth's surface. An approximate thermodynam-ic treatment of mineral-fluid equilibria when P. + P' isto consider that P, is the determining pressure (Bruton

856

121 0

856

1 2100.0 0.2 0.4 0.6 0.8 1.0

*"o,

Fig. 3. Isobaric T-X"ordiagrams illustrating phase equilibriaamong tremolite (Tr), calcite (Cal), quartz (Qz), diopside (Di),grossular (Gr), wollastonite (Wo), and H,O-CO' fluid at 350-650 qC calculated from data in Berman (1988) and the equationof state for H,O-CO' fluid of Kerrick and Jacobs ( 1981): (a) 2000bars pressure; (b) 750 bars pressure. Thick shaded curves in aand b delineate rhe T-X.o, path of fluid for the case of modelprograde metamorphism in the absence of fluid flow (4- : 0).Dashed and dotted paths in a delineate the T-X"orconditions ofthe system after passage of 14 and 75 mol fluid/cm2 rock, re-spectively, flowing in the direction ofincreasing temperature (seetext for details). Distance from contact computed from equationfor temperature profile in Table 2.

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and Helgeson, 1983). The mineralogical evolution of ar-gillite under these conditions therefore can be predictedfrom the reaction curves for 0.75 kbar in Figure 3b, andthe evolution is similar to that under conditions Pr: P,.Tremolite, however, is consumed at a lower temperature,475 "C (Z : 0.46 km). At T > 475'C model argillite iscomposed of diopside * calcite + quartz * anorthite andno further reactions occur below 600 'C (Z < 0.46 km).Neither grossular nor wollastonite develop. The final re-lationship between temperature and Xco2of the pore fluidat the peak of metamorphism is illustrated by the thickshaded curve in Figure 3b for Z: 350-600 'C.

There is a small shift in O isotopic composition, -0.3Vm6'80, caused by the diopside-forming reaction, computedby the same procedure used in the model for metamor-phism at P,: P, At T : 475-600 "C (Z :0-0.46 km)model argillite has d'8O : +18.7Vm.

Metamorphism with fluid flow in the direction ofincreasing ternperature

A second set of models considers flow of fluid inwardtoward the Notch Peak pluton during contact metamor-phism in the direction of increasing temperature. Boththe degree of O isotopic alteration and the identity andprogress ofprograde devolatilization reactions in the con-tact aureole were computed for a range of time-integratedfluid fluxes.

Coupled fluid flow and isotopic reaction. A number ofstudies have rigorously coupled fluid flow and chemicalreaction in porous media, and they fundamentally followthe same analytical approach (Lichtner, 1985; Bickle andMcKenzie, 1987; Baumgartner and Rumble, 1988; Las-sey and Blattner, 1988; Norton, 1988; Bickle and Baker,1990a, 1990b). Solution of the equations is greatly sim-plified by making several assumptions appropriate for theelevated temperatures and relatively large spatial scalesof fluid-rock interaction during metamorphism: (l) localmineral-fluid equilibrium; (2) negligible mass transfer bydifusion and dispersion; and (3) one-dimensional flow.To further simplify analysis, a steady-state temperatureprofile along the flow path was assumed. Discussion andjustification of these simplifications appear in a later sec-tron.

Under these circumstances, the relationship betweenthe whole-rock O isotope alteration at any point, z, in theflow system and the time-integrated mole fluid flux is

d'8Or,*(z) - D'sO,.,*(z) : D'8O,.0(z - B) - d'8O,0(z) (l)

where the first subscript to d refers to initial (i) conditionsprior to fluid flow or final (0 conditions after flow is com-plete; the second subscript refers to rock (rk) or fluid (fl);B : (q^Nrtv); 4* is the mole fluid flux (mol fluid/cm'zrock), integrated over the entire duration of flow; N, isthe number of moles O per mole fluid; and Z. is thenumber of moles O per unit volume of rock (see Bickleand Baker, 1990a, 1990b, or Dipple and Ferry, 1991, forfurther detail). Equation I neglects shifts in isotope com-position caused by devolatilization reactions. As argued

earlier, this simplification is an acceptable first approxi-mation for contact metamorphism in the Notch Peak au-reole.

Metamorphic fluids during contact metamorphism inthe Notch Peak aureole were nearly pure H'O (Labotkaet al., 1988a). Prior to fluid flow, model argillite is con-sidered to contain initially a small porosity filled withH,O fluid in isotopic exchange equilibrium with calciterock of D'8O : -ll9Vm. For HrO fluid and calcite rock, N,: I mol O/mol fluid and Z. : 0.081 mol O/cm3 rock(Berman, 1988). For fluid flow in the direction of increas-ing temperature, the spatial coordinate z in Equation I isantiparallel to distance variable Z measured from thepluton-metasediment contact. After fluid flow commenc-es, the O isotopic alteration ofrock as a function of z (orZ) and I can be computed from Equation I for specifiedvalues of time-integrated mole flux, 4-. Results are illus-trated in Figure 2. Little O isotopic alteration occurs ifq^ < =2.103 mol /cm2 (< l7m D'8O). For 4* : (1.5-2.5) 'l}a moUcm2, fluid flow results in '8O depletions near thepluton-metasediment contact of 6-9V* D'80, spanning therange of most observed values. Fourteen of the 20 mea-surements in Figure 2 are within t l7o of values predict-ed by the model for flow of (1.5-2.5)'lOa mol/cm'z fluidthrough the contact aureole in the direction ofincreasingtemperature (open circles). The six discordant data points(filled circles, Fig. 2) can be explained if time-integratedfluid fluxes were spatially variable during metamorphismin the outer portion ofthe aureole. Specifically, taken atface value, the filled circles in Figure 2 imply that time-integrated fluid fluxes were as low as (0.2-l)'lOa mol/cm2 in some parts of the contact aureole more than 500m from the contact.

The maximum predicted reduction in d'8O, -l}Vm, oc-curs when q^: 3.25 ' lOa mol /cm2. For q^: 3.25 ' l0omol/cm2, the model contact aureole is fully equilibratedisotopically with the input fluid (HrO fluid in isotopicexchange equilibrium with initial unaltered calcite at 175'C), and no further reduction in whole-rock dtsO occurseven if 4- > 3.25' l0a mol/cm'?.

Coupled fluid flow and mineralogical reaction. Themineral content of the system prior to flow is consideredto be that produced by heating model argillite, with asmall fluid-filled porosity, to peak metamorphic temper-atures in the absence of fluid flow. The pore fluid couldbe left, for example, from sedimentation and diagenesis.The initial pore fluid composition is specified so that di-opside develops at the position observed in the field (Z: 1.8 km), given the model temperature profile in Table2 (T : 287 "C at Z : 1.8 km) and the T-Xco,conditionsof the tremolite + calcite + qvartz + diopside + fluidequilibrium. Using the relevant equation for mineral-flu-id equilibrium from Table 2, calculated fluid compositionis X.o, : 7 '10 5. Although the value is uncertain becausecalculations applied the T-X"o, expression outside itstemperature limits, the exact value is unimportant in sub-sequent calculations provided that the T-Xco, curve forthe anorthite + calcite + quartz + grossular equilibrium

FERRY AND DIPPLE:MODELS FOR CONTACT METAMORPHISM 583

continues to asymptotically approach Xcoz: 0 at I <350 "C. After heating, pore fluid composition is repre-sented as a function of distance and temperature by thethick shaded curve in Figure 3a. Fluid flow in the direc-tion of increasing temperature toward the pluton there-fore involves infiltration of HrO-rich fluid distal from thepluton into the contact aureole. Mineral-fluid reactionresults from continuous adjustment of fluid compositionto increasing values ofX.o, specified both by equilibriumbetween reactants and products and the increasing tem-perature along the flow path (cf. Fig. 3a). Under thesecircumstances, assuming local mineral-fluid equilibriumat each point at all times, negligible mass transfer by dif-fusion and dispersion, and one-dimensional flow, the re-lationship between progress, {, ofa decarbonation-dehy-dration reaction at any point in the flow system andq- ls

4[r.o, - X.o,(r.o, * rr,o)]L ln -

(d Xco,/ AT) p(dT / dz) + (0 X.",/ iP),(dP / d.z)

where z.o, ?Dd zrro are stoichiometric coefficients of CO,and HrO in the reaction, z is the spatial coordinate ori-ented parallel to the direction of flow, and { is measuredwith reference to I cm3 rock (see Baumgartner and Ferry,i991, or Ferry and Dipple, 1991, for further detail). Forfluid flow in the direction of increasing temperature, thespatial coordinate z in Equation 2 is antiparallel to dis-tance variable Z measured from the pluton-metasedi-ment contact. In order for fluid to have flowed in thecontact aureole there must have been a decrease in fluidpressure (hydraulic head) along the flow path duringmetamorphism. Because metamorphic fluid flow wasnearly horizontal and because normally (dxco2/dP)r <<(dxcor/ AT) p for geologically relevant decarbonation-de-hydration reactions (e.g., Ferry and Dipple, l99l), theterrn (0X.or/0P)r(dP/dz) in Equation 2 was ignored.

Mineralogical effects of fluid flow as a function of time-integrated flux were computed for model argillite usingEquation 2 and equations in Table 2 over the tempera-ture range 350-600 "C. For all values of 4- considered,argillite is composed of tremolite + calcite + anorthite+ quartz + diopside at 350'C and a range of 7" > 350"C (cf. Fig. 3a). For model rock with protolith mineralcontent listed in Table 2, tremolite is exhausted by thediopside-forming reaction when fo, : 5.39' l0 a mol/cm3.The model tremolite-out isograd therefore always occursat the position where (q-) (0X""r/67)"(dT/dz)/(3 - 4X.o,): {or : 5.39'10-o mol/cm3. If q^: 14 mol/cmz, for ex-ample, the tremolite-out isograd is located at Z : 0.25km (?" : 525 "C; X.or: 0.46; cf. dashed curve, Fig. 3a).As a corollary, taking the position of the diopside isogradfrom field observation, the assemblage tremolite * cal-cite * anorthite + quartz + diopside would be stable inthe interval Z : 0.25-1.80 km when S^: 14 mol/cm2.

With increasing time-integrated flux, the tremolite-outisograd migrates away from the pluton and the X"o, offluid along the flow path evolves to more HrO-rich com-positions. When 4- : 75 mol/cm2, for example, the trem-

r fc)466' 427"

1 100

dlstance from contact, z (m)

< flowdirection

Fig. 4. Positions ofisograds calculated from Equation 2 as afunction oftime-integrated fluid flux flowing in the direction ofincreasing temperature (see text for details). The + sign indicatesappearance of mineral with increasing grade of metamorphism(decreasing Z); the - sign indicates disappearance of mineral.Observed positions of the isograds in the Notch Peak aureolecan be explained by up-temperature flow of (1.5-2.5)' 100 moVcm'? fluid through the contact aureole (shaded area). Tem-peratures calculated from equation for temperature profile inTable 2.

olite-out isograd occurs at 0.35 km (?" : 500 "C', X.or:0. I 8) and wollastonite first appears at the contact (cf. dot-ted curve, Fig. 3a). For model rock with protolith mineralcontent listed in Table 2, the wollastonite-forming reac-tion progresses at the point Z : 0 until (q*")(|X.or/0T),(dT/dz)/(l - X.",) : {wo: 8.01'10-3 moVcm3, where

4*" is the time-integrated flux through the metamorphicsystem after wollastonite first forms. Accordingly, reac-tion is first complete at the contact (quartz is exhausted)when 4r" : 527 mol/cm2. A model quartz-out isogradtherefore first appears at the contact afler a time-inte-grated flux q^: 75 + 527 : 602 mol/cm2 has flowedthrough the system.

Progress of each of the prograde mineral reactions inTable 2, and the corresponding positions of isograds inthe model system were evaluated as a function of increas-ing time-integrated flux in a similar way. Results are pre-sented for Z > 100 m in Figure 4. Results for Z < 100m are more complicated, are irrelevant to the discussion,and were omitted for clarity. Because of the temperaturelimitations of equations in Table 2, computations wereterminated when the tremolite-out isograd reached a po-sition corresponding to 350 "C (Z : l.2l km). For a valueof q^: 1.5'104 mol/cm2, the quartz-out isogtad occursat 0.40 km, the minimum distance consistent with ob-servation (Table l), whereas for 4- : 2.5'104 moUcm2,the tremolite-out isograd occurs at l.2km, the maximum

J

t sooooN

Eopf

p zooooxf

ItIEF 10000c'ioE

(2)

584 FERRY AND DIPPLE:MODELS FOR CONTACT METAMORPHISM

500 1000 1500

distance trom contact,Z (m)

{ tlow direction

T ('C)488' 409"

- - - - - - - ' t

93n = 20000

mot fluid/cm2 rock

grossular

wollastoniteIIIII

b

0 400 800 1200

distance from contact,Z (m)

{ flow direction

Fig. 5. Modes for diopside and tremolite (a) and grossularand wollastonite (b) as a function of distance from the pluton-metasediment contact calculated from Equation 2 in rext for thecase of flow of 2. l9o moVcm2 fluid in the direction of increasingtemperature through the contact aureole. The increase in diop-side at distances <l.l km and the increase in grossular at dis-tances <0.6 km results from decrease in volume of the rockrather than from participation ofthe two minerals in reactions.Calculated distribution of minerals agrees with observed distri-bution in the contact aureole. Temperatures computed fromequation for temperature profile in Table 2.

distance consistent with observation. Up-temperaturefluid flow results in positions of isograds spanning therange of observed values (Table l) when 4-: (1.5-2.5).lOa mol/cm2 (shaded region of Fig. 4), consistent with theanalysis ofO isotopic alteration (shaded area ofFig. 2).

The best fit to the observed positions of the isogradsoccurs for q^ = 2' lOa mol/cm2. The total calculated in-ternal production ofvolatiles at distances greater than theposition where quartz is exhausted is <3 molo/o of thistime-integrated flux; internal production of volatilestherefore was ignored in calculating the positions of theisograds.

Equation 2 canbe used to predict not only the progradereactions and positions of isograds in the model flow sys-tem but also reaction progress and hence the mode ofmodel argillite at each point Z. The changes in modes asa function of Z for the case of q^:2.104 mol/cm2, forexample, are illustrated in Figure 5. There is a gradualincrease in the amount ofdiopside and a gradual decreasein the amount of tremolite with Z in the diopside zone.In contrast, the amount of grossular and wollastonite inmodel argillite increases rapidly at values of Z less thanthose at which the two minerals first appear. The modesfor T < 350'C are only approximate, however, becausethey were computed from the equation for T-X.o, con-ditions of the diopside-forming reaction in Table 2 ex-trapolated beyond its limit.

Metamorphism with fluid flow in the direction ofdecreasing temperature

A third set of models considers flow of fluid away fromthe Notch Peak pluton during contact metamorphism inthe direction of decreasing temperature. One case con-siders flow of magmatic fluid outward from the plu-ton-metasediment contact and a range of likely time-integrated fluxes. A second case attempts to predict themineralogical and isotopic consequences of the physicalmodel for fluid flow in the aureole proposed by Labotkaet al. (1988a). In both cases considered, the spatial co-ordinate z in Equation I is parallel to and numericallyidentical to distance Z measured from the pluton-meta-sediment contact.

Coupled fluid flow and isotopic reaction. Prior to fluidflow argillite is considered to contain initially a small po-rosity filled with HrO fluid in isotopic exchange equilib-rium with calcite rock of 6'80 : +l9V-. Temperature isdefined along the direction of flow by the equation inTable 2. The chemical and isotopic composition of fluidemanating from the pluton is pure HrO and 6'80 : t8.5%m(Nabelek et al., 1984). In the first case considered, fluidsimply flows out of the pluton into the argillite. Giventhe radius of the Notch Peak pluton (8 km) and the prob-able HrO content of the parent magma (30lo), both fromLabotka et al. (1988a), the maximum time-integratedmagmatic fluid flux that could have flowed horizontallyinto the aureole from the pluton may be computed. As-suming densities of magma and fluid equal to 2.5 and Ig/cm3, respectively, the time-integated mole flux, 4- :

r cc)466' 378. 3170

30600'

600"

270"

2000

351"

E20oC'

oCL(E

It

E 1 0

40

30

trEg. zo(EItoE

1 0

\_ -11__ l

diopside \tremolite

Q6 = 20000

molfluid/cm2 rock

It\\

\ a

a

@

@u@

@

@@

@

6

@

@ measured data

time-integrated flux =2O0O mol fluid/cm2 rock

=E 1 8oIL: 1 6o

: 1 4(,oi r z6E; 1 0

r fc)600' 378" 270" 202" 175" 175"

1000 2000 3000 4000 5000

distance from contact, z (m)flow direction >

r fc)270" 175"

2000 4000 6000distance from contact, z (m)

flow direction >


1667 mol/crn2. IJnless there was significant focusing offluid flow, the range in likely 4- values is =0-2000 mol/cm2.

After fluid flow commences, the O isotope alterationof rock as a function of z (= Z) and Z can be computedfrom Equation I for specified values of 4-. Results areillustrated in Figure 6a for the likely maximum 4n : 2000mol/cm2. Down-temperature flow and q^: 2000 mol/cm2 produce a discontinuity in whole-rock 6'tO of 9.7V*at Z : 246 m, which represents the original discontinuityin isotopic composition of fluid at the contact sweptdownstream by flow. On the side of the discontinuityclose to the pluton, rocks have A'8O : 9.3-10.07m result-ing from complete equilibration between argillite andmagmatic fluid with d'EO : +8.5Va. On the other side ofthe discontinuity, rocks have d'8O greater than the initialvalue (l9.7%n). For values of q^ < 2000 mol/cm'z, thediscontinuity retreats to distances <246 m from the con-tact. The model therefore predicts that down-temperatureflow of magmatic fluid produces '8O depletion in argillitesonly within x246 m of the contact and (formally) nowhole-rock isotopic compositions in the range l0-l9%*.In nature, the computed discontinuity in Figure 6a wouldbe smoothed slightly by diffusion and dispersion, and acontinuous range of isotopic compositions would devel-op. The transition from low-d'8O values to high-dl8O val-ues, however, would occur over a relatively small dis-tance, and it would be unlikely that field studies wouldsample more than a few specimens precisely at the tran-sltron.

For completeness, Figure 6b illustrates predicted iso-topic alteration that would result if down-temperaturemagmatic fluid flow were somehow focused and valuesof q^ > 2000 mol/cm2 were attained. As time-integated

<'tT,l'tt fluid flux increases, the region of '8O-depleted rocks closeto the pluton expands to larger values ofZ. For all valuesof 4*, however, the 9.TVudiscontinuity is retained. Fur-thermore, for values of q^ - l0a mol/cm2, significant '8O

<'lixf,'

t'ilf,:'

<';xxf,'

-'E 24o

vcL

-o 20t'O

.!a

P 1 6E

.9oEP

600' 378'

1000 2000 3000 4000 5000

distance lrom contact, Z (m)flow direction )

(-Fig. 6. Measured and calculated whole-rock O isotope com-

positions of calcareous aryillites as a function of distance fromthe pluton-metasediment contact. Measured distance-dt8O datasame as in Figure l. All calculations consider flow of magmaticHrO fluid (d'EO : 8.5%oo) in the direction of decreasing temper-ature. Temperatures calculated from equation for temperatureprofile in Table 2. (a) Predicted isotopic compositions for time-integrated flux of 2000 moVcm2 and flow from the pluton-meta-sediment contact (thick black curves). (b) Predicted isotopiccompositions for time-integrated fluxes of 2000, 10000, and20000 mol/cm'zand flow from the pluton-metasediment contact.Curves for the three different fluxes superimpose along their pos-itively inclined portions and along their horizontal portions thatlie at 199*. For each value of time-integrated flux, only thatportion ofthe inclined line with positive slope between Z: 0and the point indicated by the appropriately numbered arrowapplies. (c) Predicted whole-rock isotopic compositions if argil-lite perfectly equilibrates with magmatic fluid at 0-400 m fromthe contact and if 900 mol/cm2 HrO fluid with d'EO : 8.5Vqflows down-temperature from a position at 400 m.

rcc)270" 202" 175" 175"

20initialrock=

E 1 8o.L: 1 6o

?14(,o

E12o.Ci 1 0

t"ll'"0'

O measured data

time-integrated flur inmol fluid/cm2 rock

@

@@

@

@

%@3@

Y

@

@

o measured data

equilibration of rock andinput fluld, G400m

time-integrated flux = 900mol fluid/cm2 rock, >400m

586 FERRY AND DIPPLE:MODELS FOR CONTACT METAMORPHISM

enrichment, >2.5Vm, develops in the outer portion of theaureole. For time-integrated flux <2-104 mol/cm2, evenconsidering the effect of diffusion and dispersion insmoothing the discontinuity, all or almost all whole-rock6'80 values ofargillite should either lie along the inclinedl i ne be tween 9 .3Tmat Z :0 and 6 '80 : l 6 .4vua t Z :2460 m (corresponding to perfect equilibration of rockwith magmatic fluid) or be > l9%m (Fig. 6b).

Labotka et al. (1988a) proposed perfect equilibration(by diffusion) of argillite with magmatic fluid in the in-nermost 400 m of the contact aureole and fluid flow awayfrom the pluton with time-integrated fluxes in the range800-1000 mol/cm2 (p. l32l of their article). A secondcase therefore considered the isotopic alteration causedby equilibration of argillite with fluid of d'8O : 8.5Vm atZ : 0-400 m and flow of that same fluid (q- : 900 mol/cm'z) in the direction of decreasing temperature at Z >400 m (computed with Eq. l). Results are illustrated inFigure 6c. A discontinuity in whole-rock d'8O is producedwith one group of values 9.3-10.6V-lying along the in-clined line between Z : 0 and 5l I m and a second groupwith uniform d'8O : 19.3Vm at Z : 5ll-4000 m.

Coupled fluid flow and mineralogical reaction. Themineralogical effects of magmatic fluid flow in the direc-tion of decreasing temperature were simulated by consid-ering flow of pure HrO fluid away from the pluton intothe argillite. Prior to flow the mineral content of the ar-gillite was considered to be that produced by heating therock with a tiny porosity filled with CO,-H2O fluid topeak temperatures in the aureole (i.e., that developed alongthe thick gray shaded path in Fig. 3a). The infiltratingfluid is out of chemical equilibrium with the assemblagecalcite + quartz + anorthite + diopside adjacent to thecontact and will react with it. Reactions driven by infil-tration ofnonequilibrium fluids in rocks produce sharpreaction fronts that propagate downstream (Bickle andBaker, 1990b). For the case of a single decarbonation-dehydration reaction driven by the flow of H,O fluid inthe direction ofdecreasing temperature, the relation be-tween the time-integrated mole fluid flux and the distancethat the reaction front moves downstream from the inlet(z : 0) is

r ' lQ^: frco,

J" ,."Adz - (nro, * n^,o)z (3)

where X"or(z) is the functional dependence between X.o,of fluid in equilibrium with reactants and products anddistance z along the flow path (computed from equationsin Table 2), and n"o, and nH2o are the moles CO, andHrO, respectively, released by the reaction per cm3 rock(Ferry, I 99 I ). For down-temperature magmatic fluid flowinto the aureole, the spatial coordinate z in Equation 3 isparallel to and numerically identical to distance Z mea-sured from the pluton-metasediment contact.

When more than one reaction front occurs along theflow path, however, there is no simple analytical expres-sion that links time-integrated flux to progress of de-

volatilization reactions (except the reaction farthestupstream, whose position is specified by Eq. 3). A finite-element computer code therefore was written to predictthe identity of reactions along the flow path and to cal-culate reaction progress as a function of4-. The programspecifically simulated fluid-rock interaction by dividing a3-km column of argillite with l-cm'?cross-sectionalareaand =lolo fluid-filled porosity into 300 boxes. Tempera-tures at the ends of the column were 600 and 202 "C; auniform temperature was assigned to each box based onthe temperature at its midpoint defined by the equationin Table 2. An increment of HrO fluid corresponding tothe porosity of one box, A4- moles, was considered toenter the column at the high-temperature end. The incre-ment of fluid displaced the fluid from each box to thenext box immediately downstream. The displaced fluideither caused no reaction or drove one of the mineral-fluid reactions illustrated in Figure 3a. If reaction oc-curred, its progress was computed according to

X"or: [(,Y3"rXAqJ * v.or{l/lAq^ * (v"or* t ,n Jt] g)

where Xgo, is the composition of fluid entering the boxand X"o, is the composition of fluid after equilibrium isattained and reaction complete (see Ferry, 1986, 1989, orBickle and Baker, 1990b, for further detail). Values ofX.o, for each reaction at each temperature along the col-umn were taken from equations in Table 2. A new incre-ment of fluid was considered to enter the column and thecalculation repeated until a desired time-integrated fluidflux had passed through the column. Results are sum-maized in Figure 7 and Table l.

The first case considered was simply flow of HrO fluidoutward from the pluton-metasediment contact in the di-rection of decreasing temperature for a range of values ofq^ (Fie.7). For values of time-integrated flux >200 mol/cm2, the initial assemblage close to the pluton, calcite +anorthite + qvartz * diopside, reacts completely to cal-cite + diopside * grossular * wollastonite. With increas-ing distance (Z) from the contact, a sharp wollastonitereaction front is encountered across which the stable min-eral assemblages changes to calcite * grossular + quartz+ diopside. The position of the wollastonite front com-puted from the computer code (Eq. 4) agrees exactly withthe position calculated analytically (Eq. 3). With furtherincreasing Z a gtossular reaction front occurs across whichthe stable assemblage changes to calcite + anorthite +q\artz + diopside. At still greater Z a diopside reactionfront occurs across which the assemblage changes to cal-cite + anorthite * quartz + tremolite. The reaction frontsmigrate outward from the pluton-metasediment contactas a function of time-integrated fluid flux (Fig. 7). Re-gardless of time-integrated flux, tremolite + calcite +qluartz + diopside coexist only across the sharp interfacecorresponding to the diopside reaction front.

A second case simulated mineralogical consequencesofthe flow model oflabotka et al. (1988a) by consideringthat argillite first fully equilibrates with magmatic fluid(pure HrO) in the innermost 400 m of the contact aureole.


Rock therefore is composed of calcite + diopside + gros-sular * wollastonite prior to fluid flow at Z < 400 m andcalcite + quartz + anorthite * tremolite + trace diopsidefarther away from the pluton. A time-integrated flux of900 mol/cm'zHrO fluid then flows outward from a posi-tion at Z: 400 m. Computations were the same as beforebut with a smaller (l m) box size; results are listed inTable l. After flow is complete, calcite + quartz + an-onhite + tremolite have reacted completely to calcite *diopside * grossular + wollastonite between Z : 400and 417 m. At a sharp interface within the box at 417-418 m, calcite + diopside * grossular * wollastonite *quartz coexist. Between Z : 418 and 428 m calcite *quartz + anorthite * tremolite have reacted completelyto calcite + diopside * grossular * qluartz. At a sharpinterface within the box at 428429 m, calcite + diopside* grossular + anorthite + quarlz coexist. Between Z:429 and 588 m calcite + quartz + anorthite * tremolitehave reacted completely to calcite + diopside * anorthite+ quartz. At a sharp interface within the box at 588-589m, calcite + diopside + anorthite + quartz + tremolitecoexist. At Z > 589 m calcite + anorthite + quartz +tremolite remain. After flow is complete the initial stablecoexistence of calcite + qvarlz * anorthite * tremolite+ diopside does not occur over a distance interval but islimited to a sharp interface in the single box at Z: 588-589 m.

DrscussroN

Choice of preferred model of fluid-rock interactionduring contact metamorphism in the Notch Peak aureole

Table I summarizes the isotopic and mineralogicalconsequences of the different models of contact meta-morphic fluid-rock interaction considered in this study.Comparison of calculated isotopic compositions and po-sitions ofisograds with observed values leads to the choiceof a preferred model for metamorphism in the NotchPeak aureole. Models of contact metamorphism that donot involve fluid flow can be summarily dismissed. Suchmodels fail to produce either grossular or wollastoniteand predict virtually no change in whole-rock O isotopecompositions during metamorphism.

Models that involve flow of magmatic fluid outwardfrom the pluton in the direction of decreasing tempera-ture reproduce all observed isograds in the proper orderand maximum whole-rock '8O depletions of the correctmagnitude, =lj%m 6teO. For the range of 4* in Figure 7,0-3.5. l0a mol/cm2, these models, however, predict a di-opside isograd that is much closer to the pluton thanobserved (Z < 900 m). For the range of likely q*,0-2000mol/cm2, the position of the model diopside isograd lieseven closer, <590 m, and the predicted positions of thegrossular and wollastonite isograds are also closer to thepluton than observed (Fig. 7; Table l). Both models ofdown-temperature flow predict a sharp spatial separationof reactants and products of the wollastonite-, grossular-,and diopside-forming reactions. In the case of the wol-

grossular front

0 200 400 600 800 1000

distance trom contact, z (m)

flow direction >

Fig.7 . Positions ofreaction fronts calculated from Equations3 and 4 as a function of time-integrated HrO fluid flux flowingin the direction of decreasing temperature from the pluton-

metasediment contact (see text for details). Mineral abbrevia-tions as in caption to Figure 2. With increasing distance fromthe contact, the disappearance ofwollastonite exactly coincideswith the appearance of quartz, disappearance of grossular coin-cides with the appearance of anorthite, and disappearance ofdiopside coincides v/ith the appearance of tremolite. Tempera-tures calculated from the equation for temperature profile in Ta-ble 2.

lastonite- and grossular-forming reactions, the predicted

reaction fronts are neither confirmed nor refuted by ob-

served field relations (Labotka et al., 1988a, their Table

l). In the case of the diopside-forming reaction, however,

the predicted reaction front deviates greatly from the ob-

served coexistence of tremolite + calcite * quartz * di-

opside in the field over a distance ofat least720 m per-

pendicular to the pluton-metasediment contact.

Models of down-temperature flow predict a bimodal

distribution of whole-rock O isotopic compositions of ar-

gillite in the contact aureole unlike the continuous range

of values observed. The models further predict a naffow

range of whole-rock d'8O values close to the pluton. For

example, models that involve equilibration of aryillite

with magmatic fluid in the innermost 400 m of the au-

reole predict a range of whole-rock 6'80 l7m or less. Con-

trary to prediction, the observed range is =5V* (Figs' 2,

6; Nabelek et al., 1984; Labotka et al., 1988a). Further-

more, regardless of the value of time-integrated fluid flux

and giving consideration to the effect of difiLsion in

smoothing predicted discontinuities, down-temperature

flow fails to explain why most observed whole-rock iso-

topic compositions occur in the region of Figure 6b be-

tween the inclined line (perfect equilibration between ar-

gi l l i te and magmatic f luid) and the init ial isotopic

I

$ sooooN

Ecp.=

E 20000;f

tto6

$ rooooc'ioE

0

I

-.s j#ibei


composition of the rock (l9E@). Models of contact meta-morphism that involve fluid flow in the direction of de-creasing temperature qualitatively explain the first-orderisotopic and mineralogical features of the Notch Peakaureole but provide an unsatisfactory quantitative expla-nation ofthe spatial distribution ofboth whole-rock iso-topic compositions and of mineral reactants and productswithin the aureole.

The model that involves flow of fluid inward towardthe pluton in the direction of increasing temperature alsoreproduces all observed isograds in the proper order andmaximum whole-rock '8O depletions of the correct mag-nitude, =9Vm 6t8O. Moreover, for time-integrated fluxesin the range (1.5-2.5).10a mol/cm2, the predicted posi-tions of all isograds match observed positions in the field.The model of up-temperature flow predicts coexistenceof reactants and products of the wollastonite-, grossular-,and diopside-forming reactions over a range ofdistancein the field. The predicted narrow range ofcoexistence ofreactants + products ofthe wollastonite- and grossular-forming reactions (0.1-0.3 km) is consistent with, but notconfirmed by, observed relations in the field (Labotka etal., 1988a, their Table l). In the case of the diopside-forming reaction, the predicted coexistence of tremolite+ calcite + qtrafiz + diopside in the field over a distanceof =l-2 km is consistent with the observed coexistenceover a distance of at least 0.7 km but not more than 2.1km.

Given the range in values of 4-, (1.5-2.5).10a mol/cm2,the model for fluid flow in the direction of increasingtemperature reproduces 700/o of the measured whole-rockisotopic compositions to within =lEm 6t8O (open circles,Fig. 2). The remaining 300/o of the values could be plau-sibly explained ifless altered argillites were less pernea-ble by a factor of 10. Models of contact metamorphismthat involve fluid flow in the direction of increasing tem-perature explain the first-order isotopic and mineralogicalfeatures of the Notch Peak aureole both qualitatively andquantitatively and are preferred over models of meta-morphism that either do not involve fluid flow or involveflow in the direction of decreasing temperature.

Discussion of preferred rnodel

The numerical simulation of fluid flow, mineral reac-tion, and isotopic alteration during contact metamor-phism in the Notch Peak aureole indicates that both themineral reactions and isotopic shifts can be produced byflow of *2.104 mol/cm2 fluid through the contact aureolein an up-temperature direction. Uncertainties in this val-ue may be evaluated from Figures 2 and 4. If 4- were< 1.104 mol/cm2, (l) maximum predicted whole-rock Oisotopic shifts would be <4V*, less than observed, and(2) quartz-free argillite would not extend further outwardfrom the contact than Z : 300 m, less than generallyobserved. If q^ = 3.10a mol/cmr, (l) predicted isotopicshifts within 0.5 km of the contact would allbe >l}V*,greater than generally observed, and (2) the tremolite-out

isograd would lie further outward from the contact than1.2 km, greater than generally observed.

The up-temperature flow direction is consistent withnumerical simulations of pluton-driven hydrothermalsystems (e.g., Norton and Knight, 1977; Norton and Tay-lor, 1979). The magnitude of the time-integrated massflux (*1.6 ' 105 g/cm'z) is similar to or slightly lower thanvalues predicted for the Skaergaard hydrothermal system(Norton and Taylor, 1979). Because the Notch Peak stockhas a "normal" igneous whole-rock D'8O : 8.57m (Nabe-lek et al., 1986), metamorphic fluids probably did notpenetrate the stock but may have flowed vertically out ofthe aureole along the pluton-metasediment contact.

The preferred model for contact metamorphism in theNotch Peak aureole predicts formation of calc-silicateminerals at =300-450'C in equilibrium with COr-HrOfluids of very low X.o' Although these temperatures arelower than normally associated with prograde metamor-phic mineral reaction, they are in the same range of tem-perature at which diopside, calcium garnet, and wollas-tonite develop during calc-silicate mineralization ingeothermal systems such as Cerro Prieto and Salton Sea(Bird et al., 1984; Schiffman et al., 1984). Furthermore,the aqueous fluids associated with the mineralization arecharacterized by very low f,o, (Bird and Norton, l98l).The inferred T-Xcorconditions for metamorphism in theNotch Peak aureole therefore are not unreasonable andmay in fact have a modern analogue in active geothermalsystems.

The preferred model of fluid flow in the direction ofincreasing temperature produces metamorphosed argil-lite with mineralogical and isotopic composition at orclose to equilibrium with magmatic fluid at Z < E300-500 m (Table l). The preferred model therefore does notrule out the possibility of chemical exchange between ar-gillite and magmatic fluids in the innermost part of thecontact aureole. If interaction between argillite and mag-matic fluid did occur, it would not leave a mineralogicalor isotopic record significantly different from that pro-duced by inward, up-temperature flow of fluids alone.

Calculated results based on the model for fluid flow inthe direction of increasing temperature (Table l; Figs. 2,4) are predicated on a number of assumptions: local min-eral-fluid equilibrium, negligible mass transfer by diffu-sion and dispersion, one-dimensional flow, and a steady-state temperature profile along the flow path. Measuredrates of hydrothermal reactions, observed mineral-fluidequilibrium in active geothermal fields, and fluid inclu-sion studies of metamorphic rocks all suggest that localmineral-fluid equilibrium is probably attained or nearlyso during prograde metamorphism (see Baumgartner andFerry, 1991, or Ferry, 1991, for further discussion).

The assumption of negligible mass transfer by difihsion(used to derive Eqs. l-3) may be quantitatively evalu-ated. For an order-of-magnitude estimate of the lifetimeof the hydrothermal event -5.10o yr (cf. Norton andKnight, 1977;' Labotka et al., 1988a), the average flux

through the aureole was = 3-4' l0 e m3/m2-s. Consideringthe spatial scale of the aureole (l-10 km), the contactmetamorphic event in the Notch Peak aureole plots with-in the field on Figure 6 of Bickle and McKenzie (1987)in which mass transfer by advection dominates over masstransfer by diffusion. The assumption used in the simu-lations therefore appears justified.

Metamorphic fluid flow was radial to the Notch Peakpluton. Radial flow causes time-integrated fluid flux toincrease (up-I flow) or decrease (down-Z flow) along theflow path. The calculated positions of isograds that de-pend on time-integrated flux (Figs. 4, 7) and predictedisotopic alteration associated with plausible models fordown-temperature fluid flow (Fig. 6) all occur within Ikm of the contact. Given the inferred 8-km radius of theNotch Peak pluton (Labotka et al., 1988a, their Table 6),subhorizontal radial flow results in changes of time-in-tegrated flux less than l5o/o within I km of the pluton-metasediment contact. Most isotopic alteration predictedby the preferred model for metamorphic fluid flow occurswithin =2km of the contact. Changes in time-integratedflux caused by radial flow are 20-25o/o within 2 km of thecontact. In the specific case of the Notch Peak aureole,calculated results based on one-dimensional flow there-fore are a good approximation ofresults based on radialflow (had they been computed).

The assumption of a steady-state temperature profilealong the flow path was adopted because there is no sim-ple, general, analytical solution to the coupling of fluidflow with chemical reactions when temperature changesduring flow. In real contact aureoles temperature changeswith time. Heat conduction tends to dampen initially largetemperature gradients. Within the context of the pre-ferred model of fluid flow [Darcy flux : (3-4).10 e m/s],the scale of flow (l-10 km), and a likely value for thermaldiffusivity of rock (10 6 m'?ls), the thermal Peclet numberis 3-40 (Bickle and McKenzie, 1987). Metamorphic fluidflow in the model therefore is a significant transport agentfor heat. (The actual thermal effect of fluid flow, however,would be lessened somewhat by heat conduction fromargillite to interbedded, impermeable limestone.) Specif-ically, up-temperature fluid flow steepens temperaturegradients around the pluton relative to those producedby conduction alone (cf. Figs. 9 and 17 of Norton andTaylor, 1979). The effects ofconduction and up-temper-ature fluid flow therefore tend to offset each other andwill act to stabilize temperature gradients. Furthermore,a steady-state profile based on peak temperatures has agentler slope than the real profile at the early stages ofthemetamorphic event and a steeper slope than the one atlater stages. The profile of peak temperatures may be anadequate time-averaged profile of the entire event. Adop-tion of the steady-state temperature profile in Table 2 asa first approximation therefore is not wholly without jus-tification.

Perhaps the best argument for assuming a steady-statetemperature profile along the flow path is the success of

589

the preferred model in reproducing the first-order petro-logic and isotopic features of the Notch Peak aureole (Figs.2, 4). Nevertheless, the assumption is an obvious over-simplification. Because the real temperature profile dur-ing contact melamorphism evolved from one steeper thanthat in Table 2 to one gentler, however, it is difficult topredict how calculated results would change if a time-varying temperature profile were explicitly considered.An obvious future refinement of our simple models ofcontact metamorphism will be rigorous consideration ofcoupled fluid flow and the thermal evolution of aureoles.

Model of fluid-rock interaction proposed byLabotka et al. (1988a)

Two results from the simulations of contact metamor-phism constitute critical evidence against the model forfluid-rock interaction in the Notch Peak aureole proposedby Labotka et al. (1988a). First, their postulated flow ofHrO fluid in the direction of decreasing temperature wouldproduce a sharp transition between diopside-bearing rocksclose to the pluton and tremolite-bearing rocks fartheraway. The prediction is independent ofthe exact valuesconsidered for the temperature profile and time-integrat-ed flux. Such a sharp transition is inconsistent with theobserved coexistence of diopside * tremolite * calcite+ quarrz over distances of =l-2 km measured radiallyfrom the pluton-metasediment contact. Second, flow of=900 mol HrO fluid/cm'rock with 6180 = 8.57m in thedirection of decreasing temperature into argillite with ini-tial d'8O = lg%n would produce a bimodal distributionof whole-rock isotopic compositions with few or no com-positions represented in the interval l"ll-l97m' Such agap in O isotopic compositions is inconsistent with nu-merous measured compositions in the range ll-lgEm.Considering the mineralogical and isotopic consequencesof this model, outward and down-temperature flow ofmagmatic fluid at distances > *400 m from the pluton-metasediment contact is unlikely.

A second aspect of their model, significant mass trans-fer by diffusion over distances of =400 m during themetamorphic event, may be evaluated both by examiningcurrent knowledge ofdiffusion coefficients and rock po-rosity during metamorphism and by observed field rela-tions in the aureole. The characteristic distance, x, overwhich mass transfer occurs by diffusion in a fluid-satu-rated porous medium is

a = y/@j@ (5)

where 0 is porosity, D, is the coefficient of diffusion inthe fluid, and I is the duration of mass transfer (Putnis

and McConnell, 1980; Bickle and McKenzie, 1987). Theduration of contact metamorphism (l) in the Notch Peakcontact aureole was =5'l0o yr (Labotka et al., 1988a)'Three recent studies have reviewed the value of Dt at theconditions of metamorphism, and all recommend a valueof l0-8 m'zls (Walther and Wood, 1984; Bickle andMcKenzie. 1987: Hacker and Christie, l99l). Published


590

TABLE 3. Characteristic diffusion distances in 5'104 yr

q (m,/s) Porosity Distance (m)


0.12.8

1 340

199

estimates of in situ rock porosity during metamorphismare in the range l0 6 to 5.10-a (Bickle and Baker, 1990a;Ferry and Dipple, l99l). These values imply that (0.D)is in the range l0-'a to 5 . l0 '2 m2ls and that mass transferby diffusion was effective over distances of no more than0. l-3 m during metamorphism in the Notch Peak aure-ole (Table 3). Even if porosity were l0l0, diffusion dis-tances would be no more than 13 m if D.: l0-8 m2ls.Other estimates of (B.Dr), (2-5). l0 r5 m2ls by Baumgart-ner and Valley (1991) and < l0-'5 m2ls for 100 pm grainsby Brady (1983), predict still smaller diffusion distances.Diffusion over distances on the order of 200 m can onlyoccur in 5.10a yr if, as Labotka et al. (1988a) slggested,porosity is =25o/o and Dr is =10-7 m2ls (see Table 3).These values for both p and D, are larger than those es-timated by other published studies. Furthermore, o po-rosity of 250lo is likely unstable at the conditions of meta-morphism and would disappear by compaction on a timescale of x200 yr (Bickle and Baker, 1990b).

Contact metamorphism of siliceous limestones in theNotch Peak aureole provides an independent evaluationof the efficacy of mass transfer by diffusion during themetamorphic event. Contact metamorphosed limestonesclose to the pluton are ElO m thick, contain mineralassemblages that record equilibrium with fluid of X.o, ashigh as 0.8 (Hover-Granath et al., 1983), and have pris-tine and unaltered O isotope compositions (Nabelek etal. 1984). Limestones are interbedded with argillites thatcontain mineral assemblages which record X.o, < 0. I(Hover-Granath et al., 1983; Labotka et al., 1988a). Theargillites exhibit '8O depletions of up to lUVm caused bymetamorphic fluid-rock interaction (Nabelek et al., 1984).If significant mass transfer by diffusion between plutonand metasediment caused the '8O depletion and the lowXco, conditions of metamorphism in the argillites, thenit is unclear why diffusion did not have a correspondingeffect on the interbedded l0-m-thick limestone layers.Even if the porosity of the limestones was much less thanthe argillites (e.g., l0lo), limestones should have thorough-ly equilibrated by diffusion with fluids in the aryillites fora value of D, = l0-7 m2ls (Table 3). In fact, the unalteredO isotopic composition of the limestones and the highvalues of X.o, that minerals in them record are most con-sistent with D. * 1g-e m2/s, B * l0 6 (Table 3).

Consideration of current estimates of in situ porosityand D, during metamorphism and of the mineral contentand O isotopic composition of limestones interbeddedwith argillites in the Notch Peak aureole suggest that masstransfer by diffusion was unimportant during the contact

metamorphic event at scales > I m. Judging from Table3, however, the critical factor in determining the char-acteristic diffusion distance during metamorphism is po-rosity (6). Future work on in situ metamorphic porositywill better resolve whether diffusion in contact aureolesis an effective mechanism for mass transfer over distancesof less than a few meters or over distances of hundredsof meters.

Acxuowr,nncMENTS

Research supported by NSF Division of Earth Sciences gants EAR-8903493 and EAR-9 104084. We thank G.W. Fisher, T.C l-abotka, J.M.Rice, and G.H. Syrnmes for discussion of and comments on earlier draftsof the paper and M.J. Bickle and T.D. Hoisch for thoughtful reviews oflater drafts.

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