American Mineralogist, Volume 76, pages 1081-1091, I99I

Physics of aqueous phase evolution in plutonic environments

hrrr,rp A. C.lNoBr,lLaboratory for Mineral Deposits Research, Department of Geology, University of Maryland,

College Park, Maryland 207 42, U.S.A.

AssrRAcr

Many mineral deposits appear to have been formed by fluids of magmatic-hydrothermalorigin. However, the means of egress of magmatic fluids and the focusing of these fluidsinto sites of alteration and mineralization are not well understood.

High Lewis numbers for HrO imply that HrO will accumulate within a maryinal bound-ary layer or crystallization interval within magma chambers. Three cases are discussed:(l) Magmatic H,O exsolution occurs at <<20o/o crystallization (at high initial magmaticHrO concentrations or low pressures), inducing the rise of plumes laden with bubbles (+crystals). (2) Magmatic HrO exsolution occurs later (at moderate initial magmatic HrOconcentrations or moderate pressures), and vapor bubbles, trapped in an immobile crust,form a spanning cluster at critical percolation through which the magmatic aqueous phasecan advect. (3) Vapor exsolution occurs in an immobile crust but with lower initial HrOconcentrations or at higher pressure, so that the spanning cluster at critical percolation isnot achieved and the magmatic aqueous phase is dispersed through the subsolidus crackingfront.

The likelihood of plume rise (relative to the rise of individual bubbles) can be evaluatedby calculating the characteristic rise time for individual bubbles relative to the character-istic rise time for bubble-laden plumes. For bubbles of r s I cm, plume rise is likely.

Percolation theory indicates that a spanning cluster of the aqueous phase on a simplethree-dimensional lattice is attained when the aqueous phase achieves a volume fractionof iD" : 0.31. Percolation is attained for initial magmatic HrO concentrations >l-2o/o at0.5 kbar and >4-5o/o at2kbar. For lower HrO concentrations and higher pressures, vaporwill be dispersed through a rather diffuse cracking front. This analysis suggests that or-thomagmatic-hydrothermal fluids can be transported and focused to sites of mineral de-position near the apical regions of magma chambers by either bubble-plume rise or ad-vection through spanning clusters ofbubbles.

INrnonucrroN: vAPoR EvoLUTroN rNINTRUSIVE SYSTEMS

The last few decades have seen many advances inchemical modeling of magmatic differentiation processes.More recently, a number of studies have focused onchemical modeling of magmatic aqueous phase exsolu-tion. However, many of the chemical models of mag-matic vapor evolution in ore-forming systems (Candela,1986, 1989, 1990) ignore the physical constraints on thesystems that are being modeled. Whereas significantprogress has been made in understanding ore fluid chem-istry in porphyry, skarn, and related systems, the meansof egress of the magmatic fluids from crystallizing plutonsand the mechanisms by which these ore fluids are focusedin sites of mineralization are not well understood.

The importance of orthomagmatic-hydrothermal flu-ids in porphyry-type and skarn-type deposits has beendebated for many years in the geological literature. Nor-ton (1982) demonstrates convincingly that nonmagmaticHrO can be focused in regions of mineralization, withmagma bodies acting solely as heat engines. The volume

of country rock from which ore metals can be leached bynonmagmatic fluids is obviously much larger than thevolume of the associated pluton. Therefore, if the countryrock is the source of ore substance, there is little problemaccounting for the quantity of ore metals in the anomaly.That meteoric HrO is important in the genesis of thesedeposits is not contested. Conversely, S isotope data,summarized by Ohmoto and Rye (1979), and hydrogenand oxygen isotope data (cf. Sheppard et al., l97l) sug-gest that a magmatic aqueous phase may also be activein ore formation. Further, Cl and Cu concentrations foundin fluid inclusions from porphyry copper and related de-posits (Reynolds and Beane, 1985; Scherkenbach et al.,1985) may easily be accounted for by the evolution of anaqueous phase from arc magmas (Candela and Holland,1986; Candela, 1989). At the Henderson deposit, one ofthe most heavily studied porphyry deposits in the world,

Carten et al. (1988) demonstrate very close links betweenintrusions and ore zones. Differences in the mass of ore,intensity ofalteration, and density ofveins can be directlycorrelated with primary igneous features in the associated

0003-o04x/9 l/0708-1 08 l $02.00 108 I

1082

stocks. Additionally, Hannah and Stein (1985), in isoto-pic studies of the Climax group deposits, show convinc-ingly that Pb and S were not derived from the countryrock but from the ore-related plutons. The intrusive com-plexes associated with the Climax, Urad-Henderson, andMount Emmons-Redwell porphyry Mo deposits wereemplaced in very different host rocks: Precambrian felsicgneisses, amphibolites, and granulites at Climax; a youn-ger Precambrian granite at Henderson; and Cretaceousshales and sandstone at Mount Emmons-Redwell. Thesevariations in host rocks support the contention that coun-try rocks at sites of stock emplacement played no signif-icant chemical role in the mineralization process (Han-nah and Stein, 1985).

Yet the hypothesis that orthomagmatic-hydrothermalprocesses play a dominant role in porphyry ore genesisremains problematic: it fails to account fully for the originof at least some of the ore constituents in porphyry de-posits. Quoting from Carten et al. (1988):

The absence of high temperature veins and associatedhydrothermal alteration in deep cores of stocks, thedistribution of ore about the high levels of stocks, theorientation of veins about the apex of stocks . . . aresuggestive of initially high concentrations of molyb-denum and volatiles in the apex of a stock immediatelyprior to the onset of significant crystallization. . . . As-signment of molybdenum in the ore shell about theSeriate stock to the volume of solid occupied by theapex . . . yields concentration levels in the apical mag-ma of approximately 13,000 ppm molybdenum.

Based on these and other observations, a number offundamental questions may be raised with regard to thephysics of magmatic aqueous phase evolution, such as:(1) Why do some plutons possess focused zones of intensemineralization, whereas others do not? and (2) How canlarge quantities of ore metals be brought to sites of oredeposition, given the orthomagmatic-hydrothermal par-adigm, when only small cupolas are intimately associatedwith mineralization?

As a step toward answering these formidable questions,a general, preliminary physical model has been construct-ed to account for aqueous phase evolution from felsicmagmas. The model, which is based on current physicalmodels of magma chambers, suggests means by whichmagmatic ore fluids may be scavenged from rather largevolumes of magma and delivered to sites of ore deposi-tion, and it provides rationales for discriminating "pro-ductive" from "nonproductive" plutons. Eventually, moresophisticated physical models may be wedded to chemi-cal models, such as those presented in Candela (1986),Candela and Holland (1986), and Candela (1989), to pro-vide a comprehensive model for the evolution of aqueousfluids from epizonal plutons. Thus, this paper is a modestattempt to answer a portion of the question of why mag-matic-hydrothermal mineralization occurs where it does.

The aims of this paper do not include a detailed dis-cussion ofhow fracturing occurs in the apical regions of

CANDELA: PHYSICS OF AQUEOUS PHASE EVOLUTION

magma chambers. That cupolas and apical stocks are thefoci of mineralization is not an issue. Clearly, in somecases, the magmatic aqueous phase is focused toward thesestructures (given a magmatic-hydrothermal paradigm).Knapp and Norton (198 l) show that fracturing resultingfrom both magma pressure and thermal stress is initiatedin the upper regions ofa pluton. Buoyant forces resultingfrom the delivery of copious amounts of fluids to thesezones ensure that repeated fracturing will occur in theseregions (Norton and Cathles, 1973). This subject has beenaddressed in other works (cf. Knapp and Norton, 1981).Rather, the mechanisms by which the aqueous phase isbrought to the upper regions of magma chambers are theobjects ofthis study.

GrNrnlL CRYSTALLIZATIoN MoDEr,s

The primary process in the crystallization of a magmabody is the irreversible loss of heat to the surroundings.Heat passes out of the magma at the margins of the body,and crystallization is localized in these regions. With time,the solidus moves toward the interior of the magmachamber, defining a moving margin.

Langmuir (1989) refers to crystallization that occurs atthe margins of a chamber as in situ and considers twolimiting cases that are pertinent to the present endeavor.In Langmuir's first case, crystallization occurs at an in-terface between solid and liquid. The degree of crystalli-zation as a function ofdistance varies as a steplike func-tion near the interface. The evolved liquid is convectedaway from the rather sharp solidJiquid interface becauseofa (positive or negative) change in its density upon dif-ferentiation (Fig. l). In Langmuir's second case, crystal-lization occurs at the margins in a crystallization intervaloffinite thickness, here defined as the region between 99volo/o and I volo/o crystallization, consistent with Brandeisand Jaupart (1987) (Fig. 2). In this case, the evolved,residual melt within the crystallization interval is trappedin an immobile crust or mush (Marsh, 1988a, 1988b) anddoes not mix with the bulk melt.

The first case is similar to the model presented byMcBirney et al. (1985) and Sparks et al. (1984) and isapplicable to systems where crystals plate (nucleate) onthe walls of a container and where rapid changes in meltdensity occur with crystallization. The diference betweenthe density of the fractionated melt and the surroundingless-fractionated melt may lead to compositionally driv-en side wall convection, which can redistribute some ofthe differentiated melt to other parts of the chamber. Theresiduum may remix with the bulk melt or rise and forma compositionally stratified cap of diferentiated magmaat the top of the chamber.

The second case is a limiting case of a model presentedfor the Hawaiian lava lakes where magmatic differentia-tion is confined mostly to crusts of solid + liquid 1+ gas),which trap nearly all the fractionated liquid (Marsh,1988a, 1988b). These systems cool mainly by conduction(Peck et al., 1977), with convection relegated to a ratherminor role. Experimental simulation of these systems by

CANDELA: PHYSICS OF AQUEOUS PHASE EVOLUTION 1083

F

Fitszc)p oo &

MELT WTTH < 1*CRYSTALS

LIQUID + SOLID

LI9UID + SOLID+ VAPOR

Y I- MECIIANICALCRYSTALLIZED BOUNDARY I.AYER

MAGMAFig. 1. A portion of a rising plume of bubbleJaden melt along

the margins of a magma chamber.

Brandeis and Marsh (1989) supports this interpretation.Apparently, under some conditions, convection in sub-liquidus fluids is inhibited by crystallization. Langmuir(1989) suggests that the chemical trends found in somemafic systems can be explained by chemical processesthat are intermediate between the extremes of cases I and2, with the nearJiquidus butk magma mixing with moreevolved, multiply saturated melts from the crystallizationinterval.

Now that the basic qualitative physical models forcrystallization have been outlined, the modes of vaporsaturation in these systems can be addressed. In the cool-ing of multicomponent liquids that are in homogeneousequilibrium, vapor saturation is the result of either apressure decrease (first boiling) or the crystallization ofanhydrous phases (second, or resurgent, boiling). In thecase of second boiling, HrO saturation will either occurahead ofthe inward-advancing solidus for all x, I or occurlate and in spatially segregated regions (e.g., the core ofthe plutonic complex), with HrO back diffusing from thecrystallization interval into the remaining body of theliquid.

The controls on the rate of crystallization need to bedefined so that the behavior of HrO in the region of crys-tallization can be determined. Given the importance ofconduction relative to convection, summarized above,and the small thermal role attributed to convection forsubliquidus systems (Brandeis and Marsh, 1989) and forsystems not steadily heated from below (Marsh, 1988a,1988b), a conductive model will be adopted here as thecontrolling factor in heat loss. Further, aside from tran-sient effects where nucleation phenomena dominate,

cMcKrNG | =-- cRYsrALLrzATroNERoNT .-.J I.-_ INTERVAL OF THICKNESS I

Fig. 2. Cross section of the margin of a magma chambertraversing (from left to right): country rock, cracked pluton, un-cracked pluton, solidus, crystallization interval with liquid +solid + aqueous fluid(s), and bulk melt. (See text for more de-tails.)

magmatic systems are probably attracted to a steady statecharacterized by a balance between crystal growth andheat loss to the country rocks (Brandeis et al., 1984).Therefore, for all but small times, the rate of advance-ment of the solidus is given by an expression (Jaeger,1968) ofthe form

x : 0 . 2 8 . t t / 2 ( l a )

where x is the position of the solidus (crystallization pro-ceeds in the positive x direction) in centimeters and / istime in seconds. (If x is recast in meters and I in years,the constant in Eq. la is approximately 16.) Equation laassumes a constant Af : 800 "C (temperature of crystal-lization minus the temperature of the country rock farfrom the intrusion) at the contact and assumes a fixedmelting point. However, Equation la does yield a firstorder estimate of the rate of advance of the crystallizationfront. For an order-of-magnitude estimate of the thick-ness of the crystallization interval, 1, an equation has beenextracted from Brandeis and Jaupart (1987) ofthe form

I : 0 . 9 3 . t o 3 1 ( lb)

where 1is in centimeters and / is in seconds. Equationlb assumes a Stephan number (the ratio of the latent heatof crystallization to the heat capacity of the melt times atemperature scale for crystallization) equal to 0.55, andcrystal growth rates and nucleation rates on the order ofl0 '0 cm/s and l0 3 cm 3/s, respectively. These growthand nucleation rates are reasonable estimates for the in-terior ofpluton systems (see Brandeis and Jaupart, 1987,for more details on growth and nucleation rates and back-ground on Eq. lb). In Table l, the position of the solidus(x) and the interval thickness (1) are given as a functionof time for a spherical chamber with a radius of I km

l-;l

wm

1084

TABLE 1. Solidus position, thickness of crystallization interval,and fractional volume change as a function of time

x (meters) , (cm) AVIV x 101 t (s)

0.892.88.9

2889

280885

CANDELA: PHYSICS OF AQUEOUS PHASE EVOLUTION

Nofe: Solidus position, x (x : 0 is the original magma to country rockcontact), thickness of crystallization interval, ,, and fractional volume changeof chamber resulting from vapor exsolution as a function of time, usingEquations 1a, 1b, and 20, respectively.

(volume : 4.19 km3). This hypothetical chamber crys-tallizes in approximately 10" s (=3000 yr). The crystal-lization interval increases in thickness from a centimeterscale early on to tens of meters near the time of completecrystallization.

Given this basic cooling model, the Lewis number (Ze= k/DH2o) for HrO (hereafter referred to simply as Le)can be calculated. Ie indicates whether the rate of diffu-sion of H.O is greater or smaller than the rate of heatdiffusion, the main control on the rate of advance of thecrystallization front into the magma. Either HrO satura-tion is locally achieved (high fe) at the site of crystalli-zation (boundary zone vapor saturation) or HrO back dif-fuses into the rest melt (low Ze). Given the range of HrOdiffusion coefrcients in rhyolites (10-? to l0-8 cm'?ls) andthe thermal diffusivities found in rock systems (7 x lQ-rcm2ls), the Lewis numbers are orders of magnitude aboveunity (log Le : 3.8-4.8). This indicates that the rate ofdiffusion of HrO into the residual melt is insignificantrelative to the rate of crystallization, and either HrO ac-cumulates in the crystallization interval or HrO accu-mulates at the crystal-melt interface. The consequencesofboundary zone vapor saturation will now be addressedin detail.

Clsn 1: vApoR SATURATToN rN A BoUNDARyLAYER DURING SIDE WALL CRYSTALLIZATION

According to the models presented by McBirney et al.(1985) and Sparks et al. (1984), crystals are plated on themagma chamber side wall as crystallization proceeds. TheHrO concentration rises in the boundary layer until theaqueous-phase bubbles nucleate and grow. The mixtureof bubbles and liquid will be referred to as a froth or agas emulsion, depending upon the volume percent gas.According to Bikerman (1973), a foam has less than l0volo/o liquid, and the liquid phase is dominated by surfacerather than by bulk properties. Froth is a rather ill-de-fined term that will be used here to denote the regionbetween <10 volo/o liquid (true foams) and >90 volo/oliquid (gas emulsions). Here, the term froth will includegas emulsions. If crystals nucleate on the wall of thechamber (as in many crystallization experiments), thenvapor bubbles will either rise separately or in plumes ofvapor + liquid + crystals. We can calculate the terminal

velocity of rise of vapor bubbles by a Stokes-like formulaor, more precisely, a Hadamard-Rybczynski (H-R) for-mula (Ramos, 1988). The H-R formulation accounts formotion in the boundary layer of the bubbles by employ-ing a reduced drag coefficient, thus allowing for a morerapid rise of the vapor bubbles. Bubbles of hydrosalinefluid will rise less rapidly, resulting in an increase in theirpopulation in the melt relative to bubbles of vapor. Incase l, the bubbles may gain access to the upper reachesof the magma chamber by H-R bubble rise or by rise ofa plume of bubbles and liquid.

From the H-R formula, the characteristic time for therise of bubbles of radius r in a chamber of characteristicheight h, containing a magma with a dynamic viscosityof p.r, a density difference between melt and vapor : Ap,and an acceleration due to gravity, S, is given by

fouoo , " : 3 ' p ' r ' h / r2 ' g 'Ap ' ( 2 )

For h: I km, r : I cm, &r : 108 poise, g: 980 cm2ls,and Ap : 2 rcm 3, a minimum bubble rise time of 1.5x l0ro s is calculated. For a lower viscosity melt (p : 105poise), the rise time is reduced to 1.53 x l0? s.

If the presence of crystals or bubbles in the mediumsurrounding any given bubble is taken into account, thecalculated viscosity of the medium increases. The rheol-ogy of crystal- and bubble-fluid mixtures has been dis-cussed by Marsh (1981), in part, in an attempt to explainDaly's dichotomy of basaltic extrusions vs. granitic intru-sions. According to Marsh, basalts are rarely seen withmore than about 55 volo/o crystals. Smith (1979) suggeststhat this limit constrains the eruption of silicic ash flowsto those that are less than half crystalline. Apparently, themagma is too viscous to erupt (or in general, too viscousto flow) if a critical crystallinity is exceeded. For graniticmagma (sensu stricto), Marsh suggests that the criticallocking point may be as low as 20 volo/o crystals. Hildreth(1981) presented data that support this general proposi-tion. Marsh and Maxey (1985) present an equation forthe variation in the viscosity of magma as a function ofthe volume fraction of particles. Assuming that the vis-cosity rises steeply as the proportion of crystals * bubbles(,AI) reaches 20o/o by volume, their equation becomes

lllr.otr, : p,/ (exp 2.5' {N/II - (N/0.2)l}). (3)

Therefore, as the proportion ofbubbles increases, the risetime for bubbles of any given diameter will increase.

The characteristic time for vapor + liquid plume riseis calculated using the Stokes formula in a manner similarto that used by Marsh (1988b) to calculate the flow timefor crystal plumes. In this model, vapor bubbles accu-mulate in a boundary layer. The thickness of this bound-ary layer will be given by the difiirsion distance for HrOon the time scale for plume rise: 62 = 4D*' t. The resultingformula is then

/pru-.: vq:E:iB:E:6; pq, ()

where iD.'Ap is the density contrast between the bubble-laden liquid and the bulk melt, and p is the density of the

3dl67

138281c / J

117123

4.59.0

1 73664813.3

10510610'1061 0 e1 0 1 01 0 1 1

RHYOLITE1 TO 6 WT% ITATER

PLUME RISE DOMINANT

INDIVIDUAL BUBBLE RISE DOMINANT

- 4 -3 -2 -10log BUBBLE RADIUS (cm)

Fig. 3. Log of the ratio of the time scale of bubble rise to thetime scale of plume rise vs. bubble diameter. The black bandindicates solutions to Equation 4b for rhyolites with HrO con-tents between I and 6 wto/0. Note that plumes rise faster (i.e.,have smaller characteristic rise times) for bubble radii less thanI cm.

melt surrounding the plume. In the case of a ..deep" epi-zonal felsic magma (p = 2kbat,6 wtolo HrO at saturation,depths on the order of 7-8 km), p : lQs poise (McBirneyand Murase, l97l) and D"ro : l0-? cm2ls (Delaney andKarsten, 198 l). Characteristic times (/","-") for the rise ofa bubbleJaden plume in a deep magma are on the orderof 3.4 x l0? s (l yr) or less. For a "shallow" magma, thelower HrO concentrations result in higher viscosities andlower diffusivities, and plume rise times are on the orderof 0.9 to 3.4 x 10, s (28-109 yr) .

In the case of a deeper epizonal system, the plume risetime is on the same order as the rise time for larye (r -I cm) bubbles. However, most bubbles will have smallerradii and therefore much longer rise times. In Figure 3,the ratio of to"oo," to /pr,.", obtained by dividing Equation2 by Equation 4,

(lo,oo,./to,"-") : (20/ rr). fut. D*. Q,7',, (4b)

is plotted vs. bubble radius (on a logJog ptot) for,D" (withinthe plume) : 0.1. Over a large range of bubble radii, /or-.is much smaller than lo,oo,", indicating that if vapor bub-bles accumulate in a crystal-poor boundary layer, thenthe bubble-laden liquid is apt to rise to the top of thechamber. The density of HrO vapor is reduced upon risebecause of its small bulk modulus; therefore, the buoy-ancy of a plume is further enhanced by positive feedback.This process of bubble-laden plume flow may be a driv-ing force for convection in some magma chambers. Com-mon miarolitic cavities are probably the result of the de-compression of vapor bubbles that were originally smallerthan the crystals growing from the same melt. The ex-pansion of the bubbles probably results from decompres-sion during plume rise. Granitic melts lacking miaroliticcavities should not be interpreted as having been under-saturated with HrO. Rather, those granites with miarolit-

1085

ic cavities may have crystallized under conditions wherethe initial HrO concentration was within 80-900/o of sat-uration. For most melts, this restricts the pressure duringcrystallization to approximately I kbar (=4 wt0/o HrO atsaturation), although melts with higher initial HrO con-centrations, such as those from muscovite-bearing sources,may possess miarolitic cavities at much greater depths.

This boundary layer model differs from other models(e.g., Sparks et al. 1984; Nilson et al., 1985) by explicitlyconsidering the presence of vapor bubbles in promotingcompositional side wall convection. One potentially sig-nificant complication associated with this analysis is thecompetition between the rate of rise of a plume and therate of crystal nucleation and growth due to decompres-sion and loss of vapor. This is similar to the problem ofisothermal undercooling discussed by Westrich et al.(1988). Presumably, plume rise will terminate when thesurrounding melt loses its fluidity. However, the system-atics developed herein seem likely to be operative untilthe plume is adiabatically pressure quenched, as dis-cussed by Norton and Knight (1977), producing a quenchaplite or microgranite in the apical portions of the cham-ber.

Clsn 2: vAPoR sATURATToN rN ACRYSTALLIZATION INTERVAL

As the leading edge of the crystallization interval ad-vances into the magma after the nucleation incubationperiod, the percent crystallization at the wall steadilyclimbs. Crystallization progress is given by .F, which var-ies from I (1000/o liquid) to 0 (1000/o solid). At some time,depending on the depth and the initial HrO concentrationin the melt, a critical fraction of liquid remaining (,F) isreached at the wall such that vapor saturation is achieved.A new progress variable, Z (the vapor exsolution progressvariable), is set equal to unity at the initiation of vaporexsolution; Z progresses toward zero as vapor is exsolved.As crystallization proceeds, the Z: I front advances in-ward behind the ,F : I front. Note that HrO-saturatedmelt is confined to the crystallization interval (see Fig.4). Even though the presence of vapor bubbles reducesthe bulk density of the crystallization interval relative toits surroundings, and although there is no critical Raleighnumber for convection in a horizontal density gradient,a few tens of percent (by volume) of bubbles plus crystalsgreatly reduce the probability of flow of the melt + vapor* crystal mixture because of the increased viscosity. Inthe limiting case of vapor saturation in a crystallizationinterval, vapor bubbles are probably trapped in an im-mobile crust. The aqueous fluid can only be removedfrom the sites ofbubble nucleation through the establish-ment of a three-dimensional critical percolation networkand advection ofaqueous fluids through it or by meansofthe flow offluid through a cracking front that is likelyto form some l0- 100 "C below the solidus.

On a three-dimensional, simple cubic lattice consistingof particles A and B (with number fractions Xo < Xu),critical percolation is said to occur, that is, a spanning

CANDELA: PHYSICS OF AQUEOUS PHASE EVOLUTION

FB11

E6F

. 4 4Flm 2H:-rca0Fat -Z

1086

cluster of A is formed from one end of the lattice to an-other, when approximately 310/o of the lattice points areoccupied by A (Sur er al., 1976 Feder, I 988). This resultwas obtained by Monte Carlo simulations on a 50 x 50x 50 grid and generalized using scaling laws. Ifthe vapor-liquid-crystal region is modeled as a simple cubic latticewith the aqueous fluid as the potentially percolating phase,advection of the fluid upward may be considered possiblewhen the volume fraction of the aqueous phase in thecrystallization interval reaches approximately 0.31. Theflux of HrO at critical percolation may be low; however,as the volume fraction increases beyond the critical per-colation threshold, the advective flux (driven by buoy-ancy and the positive pressure gradient produced by va-por exsolution, and allowed by the ability of the melt andthe vapor to flow into the region vacated by advectingfluid) will increase rapidly (a type of gravitationally driv-en filter pressing ofvapor).

Critical percolation begins at the wall and sweeps in-ward behind the zone ofvapor bubble nucleation (see Fig.4). It is followed by the solidus. The zone of percolationoccurs between the solidus and a surface characterized bythe critical value of the vapor exsolution progress vari-able (Z) at which percolation commences (2."). For anidealized, hypothetical hemispherical magma chamber,this zone of percolation is a hemispherical shell that movesinward and thickens with time, as does the crystallizationinterval (Brandeis and Jaupart, 1987). The rate of in-crease of the volume fraction of vapor is significantly re-

F = Z = O

C R Y S T S + M E T | 3 l

BUBBLES OF AgUEOUS PrcE

Fig. 4. Detailed, idealized illustration of the production of aspanning cluster of vapor bubbles at critical percolation. InitialHrO concentration: 2.5o/o, HrO saturation : 4ol0. Under theseconditions Zcp : 0.093 and lt

" : 0.058. Three stages in the

formation of a crystallization interval upon intrusion are shownin the right portion of the figure: A is the leading edge of thecrystallization interval, B is the leading edge ofthe zone ofaque-ous phase saturation, C is the magma to country rock contact,D is the leading edge of the zone of percolation, and E is thesolidus.

CANDELA: PHYSICS OFAQUEOUS PHASE EVOLUTION

tarded as V"/V,,,exceeds 0.31 because of the upward ad-vection of the vapor from the system. This large volumechange is, of course, not experienced by the whole magmachamber but only by the hemispherical shell of percola-tion, which is centimeters to meters thick.

Below, I present the derivation of the expression forZ.r. ln this derivation, the volume of liquid (V,) andvolume of crystals (2.,) will be expressed as a function ofthe volume of vapor (I/"). The common factor Z, willthen be removed from the right-hand side of the equation

v"".(n: v. + vt + va (5)

(which expresses the volume of the aqueous phase + melt* crystal system for any given value of F) to form anexpression for V"",(F)/V., the reciprocal of which is O" :

V"/V,,(F), the volume fraction of vapor in the system atany time. Embarking on this derivation, let

F = V,/V?. (6)

Also, assuming a constant density for the liquid duringdifferentiatiot, F: M,/Afi. Modeling HrO as a perfectlyincompatible substance (the presence of a few percenthydrous minerals does not affect the substance ofthe ar-gument), the critical F value at HrO saturation is

F = Mi/It4: Vi/Vf : C\o/CV. Q)

The vapor exsolution progress variable, Z, is unity atvapor saturation and zero when F -- 0 at the cessation ofcrystall ization: Z: (C$/C[o'F) or

F : Z , F .

Because V*t = V? - V,,

V * ' / V Y x l - F ' ( 9 )

Combining Equations 6, 8, and 9 yields

v,: vo.lF z/(r - FZ)1. (10)

An expressionfor V*,may be obtained from the definitionof the density of the melt at the commencement of vaporsaturation combined with the volume form of Equation 7:

M i : p , ' F ' V ? . ( l l )

Substituting Equation 8 into Equation 9 and combiningthe result with Equation I I gives

Mi: p, 'F 'V- , / ( l - FZ) . (12)

Given the mass balance of expression M,: Mtf - Mt*and the definitions Z = M'*/M'i and Cf = MV/M\,

M": ( r - z)C' i .Mi . (13)

Combining Equations 12 and 13 to eliminate Mi andsolving for Z-, results in the expression

(8)

Z = lF = O.62

L"H8ffl'L

tl

(14 )

Substituting Equations l0 and 14 into the basic volumeequation for the system (Eq. 5) and letting M": p;V"yields

ZOM OFCruTIW

f PERcoKroN

>_

>_>_

>-

o o " "

o - o

" 'o o

o o

o o

o o 'o o

o oo '

CANDELA: PHYSICS OFAQUEOUS PHASE EVOLUTION I 087

Simplifying Equation 15, substituting the identity fromEquation 7 in the form F : C'f /C'f , and rearrangingglves

Q": V" /V" , " : ( l + {p" / lp , ( l - Z) 'Ctro1y1- t .

Letting O" : 0.31 from percolation theory yields a Zat critical percolation (Z.r) glvenby

'*:(,%-)

(ff)..".:

( 1 5 )

ztrpF

V)

NH

-l

F

z

C\l

10 . 90 . 80 . 70 . 60 . 50 . 40 . 30 . 20 . 1

0(16 )

2., car. be transformed into the critical .iq value, f.", (thecritical value of the crystallization progress variable atpercolation) by multiplying Equation l6 by F, yielding

F." : [Cl;o - 0.45(p"/ p,)]/ Ct;. ( l 7)

The condition of -F." : 0 is a limiting case of Equation17 that indicates the onset ofcritical percolation at l00o/ocrystallization. Setting F." : 0 in Equation 17 yields

0 . 4 0 . 6 0 . 8 r t . 2 1 . 4 1 . 6 1 . 8 2PRESSURE (kbar)

Fig. 5. The curved line indicates, for a given pressure, theminimum ratio of the initial magmatic HrO concentration to themagmatic HrO concentration at saturation [(HrO initial)/(H.Osaturation)l at which a spanning cluster of vapor bubbles willallow the upward advection of magmatic HrO. Further, in arhyolitic system, bubbleJaden plume rise is expected for valuesof the (H,O initial)/(H,O saturation) : 0.8. Arrows indicateregions of graph favoring large-scale upward transport of themagmatic aqueous phase.

or the specific relationship between permeability and po-rosity of the crystallization interval, rather than the con-ceptual features of the physical model.

Given this concept ofcritical percolation, advection ofthe aqueous phase occurs as porous media flow throughthe spanning cluster of vapor bubbles. An illustrative cal-culation can be performed by using data on the relation-ship of permeability to porosity for obsidian reported inEichelberger et al. (1986). At a porosity of 37o/o, the ob-sidian exhibited a permeability on the order of k : l0 ''z

cm2, the lowest permeability measured in their study. Athigher porosities (up to 74o/o), the permeability climbedto almost k : l0 8 cm'. Therefore, calculations from thisstudy provide a minimum estimate for the fluid flux ofan upwardly aqueous phase. The estimate is most accu-rate for porosities close to the iD" ofthe original spanningcluster. Given kinematic viscosities for the aqueous phaseon the order of l0 3 cm2ls at 800 'C and I kbar (Nortonand Knight, 1977), a Darcy fluid flux can be calculatedfrom the equation Q: (Wv)'(Ap/h). After the spanningcluster ofvapor bubbles is achieved, the pressure at anypoint in the column of vapor will be less than that in theadjacent melt by a factor of Lp : g'h' Lp, where g : theacceleration due to gravity, h: characteristic height ofthe magma chamber, and Ap = 2 g'cm-3 is the differencein density between the melt and vapor. In this case,

Q : (Wv) ' s 'Ap . ( le)

This calculation yields a minimum value of Q: t0-u t'em 2/s, which is comparable to the largest fluid fluxes

o.2

0 .45 ' p ,( 1 8 )

C ' i ' p ,

The left-hand side of Equation 18 indicates the minimumratio of the initial HrO concentration in the melt to theHrO concentration at saturation, for a given total pres-sure, at which a spanning cluster of vapor bubbles willform. Spanning clusters will form in the crystallizationintervals of all wetter magmas (higher Cl;O) at the sametotal pressure. Conversely, drier magmas at the same to-tal pressure will not achieve a state ofcritical percolation.With increasing pressure, the density of the aqueous phaseincreases more rapidly than the solubility of HrO in themelt, resulting in an increase in the minimum CLolCf forwhich a spanning cluster of vapor bubbles will form with-in a crystallization interval (see Fig. 5). At magma pres-sures equal to or greater than approximately 1.7 kbar,critical percolation is not achieved at any initial HrO con-centration. If itr

" lies between I and 0, then significant

amounts of fluid can be removed and concentrated beforethe solidus isotherm sweeps through the system. If f." isnegative, critical percolation is never achieved, and HrOis probably pumped out ofthe system through the crack-ing front; this is discussed in the next section ofthis pa-per.

The approach taken here, essentially a "modified massbalance approach" coupled with a phenomenologicalphysical model rooted in elementary percolation theory,obviously neglects some effects, such as the spatial dis-tribution of bubbles on a small scale and nucleation con-trol of bubble size distribution. However, these parame-ters are likely to affect the particular values ofF." or 2."

PLUME RISE

NO PERC

1088

calculated in the convective systems surrounding mag-ma-hydrothermal systems (Norton, 1982). Obviously,these fluxes are sufficient to deliver significant amountsof fluid to upper portions of a magma chamber.

At this point, the effect of the chlorinity of the magmaand the associated aqueous phase may be addressed. Whenthe magmatic aqueous fluid composition is in the two-phase region of the system NaCl-HrO for pressures belowapproximately 1.4 kbar at 800 "C (Bodnar et al., 1985),some fraction of hydrosaline fluid (with a density on theorder of unity) will be present. As a result of its lowerdensity, one might expect the vapor to be fractionatedrelative to the hydrosaline fluid, although both will riseto the top of the chamber. The vapor may, however, risefaster. Whereas the hydrosaline fluid is buoyant withinthe confines of the magmatic system (p-r, > pnyarosarinenuia),it is not buoyant within the surrounding geothermal sys-tem. For example, given that cold ground HrO has a den-sity on the order of unity, vapor-saturated hydrosalineliquids with salinities greater than 500/o NaCl (at 500 barspressure and temperatures greater than approximately 550"C) will not be buoyant within the hydrothermal system.(The interested reader is referred to Henley and McNabb,1978, especially Fig. 4 therein, for further considerationsof this type.) The hydrosaline fluid will tend to pond inthe crystal mush near the roof, possibly creating a stable,stratified deep brine zone (cf. Henley and McNabb, 1978).This may account for the trapping of hydrosaline fluidsas opposed to vapor in inclusions in magmatic mineralsin the upper reaches ofplutonic complexes (Frezzotti andGhezzo,1989).

Although the crystallizing magma experiences volumeincreases on the order of 45o/o [the relative volume change,AV/V = (V" - VJ/V,, is equal to 0.45 when Q" = l/"/(V" + V-t t V^^,) is equal to 0.311, the volume of thecrystallization interval is rather restricted (see Table l).The total volume increase of the magma chamber istherefore rather modest. The value of AV/V can be cal-culated by considering vapor evolution to occur rn aspherical shell bounded by the solidus (at x) and the lead-ing edge of the crystallization interval (at x + I) at anytime such that

A V / V \ - ^ * : 0 . 4 5 . [ ( l - x ) ' - ( l - x - 4 ' 1 Q 0 )

for a magma chamber with a radius of I km. The A,V/Vis tabulated in Table l.

It is not the purpose of this paper to provide a modelfor the fracturing of plutons; however, the crystallizationand vapor saturation model presented here does allowfor the fracturing of a magma chamber by magma pres-sure, and this will be discussed briefly. Given tensilestrengths ofroofrocks on the order of I 00 bars (cf. Suppe,1985), a Mohr circle analysis with a combination Grif-fith-Coulomb failure envelope suggests that pure tension-al failure is indicated for magma overpressures (AP) onthe same order as the tensile strength, with a Mohr circleradius of approximately AP. A crude approximation of

CANDELA: PHYSICS OF AQUEOUS PHASE EVOLUTION

the overpressure produced in a magma chamber, neglect-ing shear deformation of the roof and neglecting volumechanges resulting from crystallization (aside from secondboiling), can be obtained using the coefficient for com-pressibility of the magma. Taking 0 = l0 5 bars-r and AP,v 10'zbars for pure tensile failure yields d'V/V = LP'A= l0 3, suggesting that failure of the chamber occurs witha whole-chamber fractional volume increase on the orderof 0. l. This result is in good agreement with the moresophisticated analysis ofTait et al. (1989), who suggestthat failure occurs with fractional changes in volume of0.2 - 0.8 x l0 3. Inspection of Table I suggests thatfailure occurs early (after about I yr) and continuesthroughout much of the crystallization history of themagma chamber. The whole-chamber volume changesare on the same order as those required to fracture theroof zone of the chamber.

CnrlrroN oF THE MAGMATIc vAPOR-DTSPERSESYSTEM: THE LACK OF CRITICAL PERCOLATION

According to Knapp and Norton (1981), thermalstresses generated by the cooling of a pluton cause rockfailure by brittte fracture. Fracture permeability developsadjacent to the magma-rock interface under conditionswhere the igneous rock fails. Norton and Taylor (1979)modeled fracturing in the Skaergaard system by assumingthat the pluton fractured when the temperature decreasedto 50 "C below the solidus. For porphyry copper systems,Norton (1982) has used a figure of 100'C below the sol-idus for magma-induced fracturing in already-crystallizedportions of the pluton. This latter figure is supported bystress-strain calculations for the no-strain case; with rea-sonable values for Poisson's ratio, the elastic constant,and thermal expansion, AZ on the order of 100 'C yieldseffective stresses on the order of 102 bars, which is on thesame order as the tensile strength of many rocks. In caseswhere the critical Z of percolation is outside the domainof the Z variable in a real system (i.e., negative values ofZ.r),the accumulated aqueous phase will remain in pores,vesicles, or miarolitic cavities until provided egressthrough the cracking front and entrained in the meteoricHrO flow. Even though these packets of fluid may advectupward toward the zone of mineralization, the fluid ex-periences a rather rapid decrease in temperature upon riseand may be diluted by adjacent nonmagmatic fluids (cf.Norton and Knight, 1977). This is clearly different fromthe percolation case wherein fluid advects through themelt under quasi-isothermal conditions to a localized, al-beit downward migrating region. Because of the acceler-ated cooling and dilution of the magmatic fluids upontransport in the absence of critical percolation, this mech-anism is likely to result in scattered shows of mineraliza-tion rather than centralized zones of intense alterationand mineral deposition. This will be termed a magmaticvapor-disperse system because egress ofthe fluid throughthe cracking front results in a much more heavily dis-persed zone of metasomatism from magmatic HrO.

DrscussroN

This paper has described two possible processes bywhich magmatic aqueous fluids may be delivered to theupper regions of felsic magma chambers. Both mecha-nisms, plume rise and critical percolation, may be oper-ative in nature depending on the conditions prevailingupon crystallizalion. Further, a synthesis will be present-ed that unites the two models presented in this paper (i.e.,the formation of a crystallization interval with melt"locked in" vs. side wall compositional convection)through the process ofvapor exsolution. The critical fac-tor determining the behavior of a given system, withinthe framework of the models presented in this paper, lsthe rate of change of the density of the crystal-melt-vaporsystem as crystallization proceeds. This rate is controlledby the timing of vapor evolution (which, in turn, is con-trolled by Ctf /Ctg and by the density of the aqueous phase(which, in turn, is controlled dominantly by pressure andto a lesser extent by temperature). For magmas with highvalues of Ctf /C,i (note that the maximum value for thisratio is unity under equilibrium conditions), vapor satu-ration occurs early (at high F values), and significantbuoyancy is achieved at relatively low viscosity (crystal-linity). In this case, plumes may rise from a subverticalborder zone. Given that the probability of eruption of agranitic melt is significantly decreased for crystallizationgreater Ihan 20o/o, vapor evolution probably must occurat .iq values greater than 0.8 for this mechanism to beoperative. This effect is obviously enhanced at lowerpressures because of the effect of reduced pressure ondensity and, hence, buoyancy. Here, side wall crystalli-zation is seen as a special case of the crystallization in-terval-percolation model, where Clf is sufficiently highand pressure sufficiently low that the presence ofbubblesat low crystallinity on the inner (leading) edge of the in-terval induces plume rise. This might result if, for ex-ample, a magma with few crystals and 3 wto/o HrO in-truded to a depth of approximately l 9 km (equilibriumH,O solubility equal to approximately 3 wto/o). Underthese conditions, a few percent crystallization would in-duce vapor bubble formation and plume rise. If, how-ever, this same magma were to intrude to a depth of 3.5to 4 km, then the first bubbles may not form until ap-proximately 25o/o crystallization occurred. The high vis-cosities realized in felsic systems with greater than 20o/ocrystals (Marsh, 198 l) might preclude plume rise underthese conditions. However, critical percolation is achievedat F :0.2 (i.e., after 800/o crystallization); in this some-what deeper case, the delivery ofvapor to the apical por-tions of a chamber would be by advection through aspanning cluster of vapor bubbles. This percolation in-terval sweeps inward and downward with time throughthe chamber. If this same initial magma were to crystal-lize at a greater depth (e.g., greater than 7-8 km), thenboth plume rise and critical percolation would be pre-cluded. The only means of egress available for the mag-

1089

matic volatile phase(s) under supersolidus conditionswould be by a highly tortuous rise of individual vaporbubbles through a crystal-choked immobile crust withinthe crystallization interval. In this case, bubble rise islikely to experience a much greater drag force than thataccounted for by either Stokes or Hadamard-Rybczynskidrag coefficients. Most likely, this would result in a va-por-disperse system with little focusing of the flow ofmagmatic HrO.

Therefore, boundary-layer second boiling in systemswith high Ie numbers at a variety of Cl;o and pressuresspans the range between systems allowing side wall(plume) fractionation at high C!0 and low pressure, onone hand, and those resulting in low-mobility rest melt+ upwardly percolating vapor at lower Cl;O and high pres-sures, on the other hand. The observable characteristicsof these cases will reflect the mode of vapor transport. Inthe case of plume rise, the quenching of the plumes willresult in aplites, miarolitic granites, and porphyries withfine-grained groundmass. Zones ofintense alteration andmineralization may surround these bodies. In the case ofadvection through a spanning cluster, hydrothermal al-teration may be centered on the apical region of the plu-ton, but strong textural variation is not expected. In thecase of the vapor-disperse system, alteration and miner-alizalion will be dispersed throughout a large volume.When present, concentrated zones will be small in vol-ume and not necessarily concentrated in apical regions.

The discussion in this paper is predicated on the con-dition that HrO is characterized by large Ze numbers inmagmatic systems. There may, however, be magmaticsystems (still not well studied) that possess relatively lowviscosities and high diffusivities. London (1986) andLondon et al. (1989) have discussed the effects ofincreas-ing Li, B, P, F, and H on crystallization and vapor exso-lution in pegmatitic systems. In melts with anomalouslylarge concentrations of these elements, it is possible togenerate melts with low viscosity, high diffusivity, andgreatly enhanced HrO solubility. This combination oflowered l,e numbers and elevated HrO solubilities couldresult in a significant delay in vapor saturation in thesemagmas, and vapor saturation might occur only in re-stricted portions of an intrusion. The style and texture ofcrystallization and the style of vapor evolution would bevery different in such systems. London et al. (1989) havepointed out that the increase of the structure-breakingcomponents Li, B, P, F, and H in felsic systems may leadto a reduction in nucleation rates offeldspar as the short-range structure of the melt deviates significantly from tec-tosilicate-like units. The reduction in nucleation rate leadsto the production of pegmatitic textures. These systemsmay evolve a vapor only from restricted portions of themagma chamber.

CoNcr-usroNs

Simple physical analysis of the crystallization of felsicmagmas in light of recent studies of magma dynamics

CANDELA: PHYSICS OF AQUEOUS PHASE EVOLUTION

1090

suggests that the achievement of critical percolation with-in a crystallization interval is possible if the initial H,Oconcentration of the magma is above a minimum valuefor a given pressure (Fig. 5) and if the system is at apressure of less than 2kbar. Fracturing by second boilingis consistent with this model, and aqueous fluids will ad-vect to the apical portions of magmas without experienc-ing significant cooling or mixing with meteoric or otherHrO. In systems with high enough HrO concentrationsfor a given intrusion pressure or in cases where crystalnucleation occurs dominantly along the walls of thechamber, plumes of bubbleJaden melt may raft to thetop of the magma chamber. These buoyantly rising plumesmay erupt, yielding permeable froths (Eichelberger et al.,1986), or may form apophyses, dikes, or lift cupolas byvirtue of their buoyancy. These models account for thedelivery of magmatic aqueous fluid from large portionsof magma chambers to the upper portions where miner-alized zones are formed. This may explain how largeamounts of magmatic vapor, charged with mineralizingagents such as Mo or Cu are focused into small regions,yielding large concentrations of ore metals that appear tobe genetically related to small apical stocks, such as atthe Henderson mine and related deposits. Therefore, sys-tems that are capable of delivering large volumes of vaporto apical regions by plume flow or advection throughspanning clusters possess a greater probability of devel-oping into productive systems. Plumes rising to the topof a chamber may be pressure quenched, resulting in thecrystallization of the vapor + melt mixture with time.The final product might be an aplite (London et al., 1989)consisting of an intimate mixture of igneous material (e.g.,quartzand feldspar) and hydrothermal material (e.g., mo-lybdenite), as is found in the upper regions of a numberof silicic plutons (Ohlander, 1985). Some of these occur-rences exhibit little alteration, as if only a small degree ofcooling in the presence ofaqueous fluids occurred beforethe aqueous phase was driven from the pluton. However,the molybdenite in these systems has precipitated at ahigh enough temperature to result in its incorporation inthe aplitic granites. This is consistent with the high-pre-cipitation temperatures found for molybdenite in volca-nic gases (Bernard et al., 1990).

In systems that are relatively dry or deep and achieveneither critical percolation nor plume rise, the magmaticaqueous phase is apt to be released from the pluton in amore dispersed state, resulting in diffuse zones of meta-somatism and mineralization. Disseminated molybde-nite (Whalen, 1980) and scheelite or wolframite probablymark the incipient cooling and dilution of dispersed mag-matic fluid and may characteize, at least in some cases,the nonproductive system.

CANDELA: PHYSICS OF AQUEOUS PHASE EVOLUTION

crystallization, probability, and rheology was enlightening. Further com-

ments by Steve Lynton, Dennis Bird, and an anonymous reviewer have

greatly improved the manuscript. Special thanks to Barbara ke for help

with the figures. Mary Ostrowski and A. kdbetter are thanked for pro-

viding additional inspiration. Of course, all errors in this paper are the

responsibility of the author. The support of NSF grants EAR-8706198

and EAR-9004154 and the Magma Energy Project of DOE is gratefully

acknowledged.

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MeNuscnrsr RECETvED Ocronen 16, 1989Mnxuscnrrr AccEprED Arnu- 15, l99l

AppnNorx 1. Svvrnor,sconcentration ofi in phase 4 (in weight fraction)diffusion coefrcientcrystallization progress variableacceleration due to gravitymagma chamber height, measured from the top downthickness of the crystallization intervalcoemcient of thermal diffusivitypermeability(subscript or superscript) liquidLewis numbermass of phase i(subscripr or superscript) value ofvariable in initial meltpressureDarcy fluid fluxradius(superscript) value of variable at water saturation(subscript) systemtime in seconds (s) or years (yr)volume of phase i(subscript) vapor(subscript) waterposition of the solidus relative to the initial contact(subscript) crystalvapor exsolution progress variableZ at citical percolationcoefrcient of compressibilitythickness of the rising boundary layerdynamic viscosityvolume fraction of phase Idensity

CANDELA: PHYSICS OF AQUEOUS PHASE EVOLUTION

D :F :

h :I _

t - -

l . -

l -

L e :M, :

0 :D _

O :

sys :

r / -

x l :Z :zcr:a -

A -

o / :