Contributions to Mineralogyand Petrology
Contrib Mineral Petrol (1982) 79:252-257
9 Springer-Verlag 1982
Volatile Production and Transport in Regional Metamorphism John V. Walther ~ and Philip M. Orville 2, 1 Department of Geological Sciences, Northwestern University, Evanston, Illinois 60201, USA 2 Dcpartment of Geology and Gcophysics, Yale University, New Haven, Connecticut 06520, USA
Abstract. Calculations show that H20 and CO~ produced during devolatilization of an average pelite will occupy 12vol. % of the rock at 500~ and 5 kb. Because the tensional strength of well foliated rock at metamorphic conditions is vanishingly small, such a volume of fluid having any vertical extent will fracture the rock and escape upward owing to its lower density. In a simplified model of a sudden increase of heat flow from 0.8 to 2.5 H.F.U., the average pelitic rock will have a rate of fluid production averaging ~9.4 x 10 ~0 g cm 2 s- ~ between 400~ and 600~ The escape of this fluid can be accomodated by a single fracture 1 cm long and 0.21a wide per cm 2 of rock. If the fracture is reduced to 0.02~t then 1,000 cm of fracture per cm 2 would be required. This width is the minimum original width as calculated from the volume of fluid observed in fluid inclusions trapped along annealed fractures within quartz in metamorphic terrains. Fluid flow will be laminar if the fracture is <0.025 cm wide. Additional calculations show that grain boundary diffusion is not an effective means of fluid transport in regional metamorphism. The commonly observed quartz segregations in pelitic terrains appear to mark the site of major channelways for fluid escape. In this case the bulk of escaping fluid is not able to react pervasively with rocks higher in the metamorphisc pile. Regionally metamorphosed rocks will have a discrete fluid phase only when devolatization reactions are actually taking place. At other times only an absorbed surface monolayer of volatiles on the minerals will be present.
During the earliest stages of burial this volatile phase generally consisting primarily of H 2 0 and dissolved salts, is under "hydrostatic" pressure derived from the weight of the fluid in interconnected pores above. The solid mineral phases will be under a greater "lithostatic" pressure owing to their greater density. This difference in pressure is maintained by the effective crushing strength of the mineral phases. Because the effective crushing strength of the solids decreases with increasing temperature (depth), pores will close and the fluid pressure will approach rock pressure. This process generally occurs over an interval from ~100 meters to several kilometers and can begin at depths of 1 to 10 km depending on a variety of factors. Above the depth at which pores become closed the fluid phase can circulate through thc rock driven by gradients in density caused by local contrasts in temperature and/or salinity. This circulation allows fluid from above to be transported downward. In contrast, below the transition zone where fluid pressure equals rock pressure the large density contrast between fluid and rock inhibits downward fluid flow. If fluid is transported at all it must be unidirectional flow towards the earth's surface. It is under the condition of fluid pressure equal to rock pressure that devolatization of minerals during regional progressive metamorphism occurs. This communication addresses the production and transport of volatiles during progressive regional metamorphism. Loss of Volatiles During Metamorphism of an "Average Pelite"
Introduction While it has long been recognized that both H 2 0 and CO 2 are given off with the burial of a section of sedimentary rock, few investigations have focused on the problem of volatile release past the early diagenetic processes of expulsion of pore fluid during compaction. In addition to the escape of the original pore fluid during burial of sedimentary rocks, volatiles are derived from minerals during their progressive metamorphism. For example, analyses of pelitic sediments show significant concentrations of volatiles which consist mainly of H~O and COz with minor concentrations of sulfur and carbonaceous constituents, bound as components of mineral phases in the rock. During regional metamorphism the sedimentary minerals in pelites react to form mineral assemblages poorer in volatiles. * Died April 2, 1980
0010-7999/82/0079/0252/$01.20
While there is considerable variability in the chemical composition of pelitic rocks, the average bulk compositions of unmetamorphosed and high grade metamorphic pelitic rocks differ significantly only in volatile content (Shaw 1956; Clarke 1924). Shown in column A of Table 1 is Shaw's (1956) average of low grade pelitic rocks and column B is that of Clarke (1924). Shaw's average was determined from 85 analyses, eleven of which are themselves averages of analyses of composites of a number of samples. Included in these analyses are two groups of samples, 6 taken from Wells (1937) and 10 from Simonen (1953) that are actually high-grade metamorphic pelites. The average volatile concentration of these sixteen analyses (H20 =1.99wt.% and C O z = 0 . 1 5 w t . ~ ) is less than Shaw's average for metamorphosed pelite. Consequently the analyses from Clarke (1924) are used in the calculations reported below.
253
Table 1. Chemical analyses of average pelites given in weight percent. Column A and B are averages of low grade pelites taken from Shaw (1956) and Clarke (1924), respectively. Column C is Shaw's average high grade pelitic rock A SiO 2 TiO 2 AlzO 3 F%O 3 FeO MgO CaO Na;O K20 H20 CO 2 Total
B
Table 2. Enthalpy of reaction per mole of released H20 + CO 2 calculated at 5 kb and 500~ for various devolitization reactions. Computed from data given by Helgeson et al. (1978) and Flowers (1979) Pyrophyllite = Andalusite + 3QTZ + H20
14.3 Kcal
C
Muscovite + QTZ = K-Feldspar + Kyanite + H 20
14.4 Kcal
Margarite + QTZ = Anorthite + Kyanite + H20
14.7 Kcal
3Tremolite + 5Calcite = 11 Diopside + 2 Forsterite + 5CO 2+ 3H 20
17.6 Kcal
Muscovite + Calcite + 2 QTZ = K-Spar + Anorthite + CO ~+ H20
19.0 KcaI
59.93 0.85 16.62 3.03 3.18 2.63 2.18 1.73 3.54 4.34 2.31
58.38 0.65 15.47 4.03 2.46 2.45 3.12 1.31 3.25 5.02 2.64
63.5I 0.79 17.35 2.00 4.71 2.31 1.24 1.96 3.35 2.42 0.22
100.48
98.78
99.86
In column C of Table 1 is shown Shaw's (1956) average high grade pelitic rock. Comparison of columns B and C in Table l shows a total loss of about 5wt.% of volatiles (2.60wt. % H 2 0 and 2.42wt. % COa) during regional metamorphism. Hence, progressive metamorphic devolatilization leads to losses per kg of "average pelite" of 1.44 moles of H 2 0 and 0.55 moles of CO 2. This amount of volatiles would occupy 12 volume percent of the rock at 500~ C and 5 kilobars. In contrast, the total porosity of pelitic schists is seldom more than a few tenths of a volume percent. Although the present porosity of these rocks is not necessarily indicative of the porosity during metamorphism, the relatively small amount of retrograde hydration and carbonation observed in most highgrade metamorphic rocks indicates that nearly all volatiles produced as temperature increased were able to leave the rock and presumably make their way upward before temperature decreased appreciably below its maximum value.
Rate of Metamorphism The rate at which volatiles are produced depends upon the rate at which heat can be supplied to the rocks undergoing devolatilization. Enthalpy changes for a number of devolatilization reactions are given in Table 2. While the enthalpy change per mole of volatile differs somewhat according to how strongly it is bonded in the crystal structure, approximately 20kcal are required to release one mole of HaO or CO 2. Therefore 40kcal are required for the release of the 2moles of volatiles within each kilogram of average pelite undergoing progressive metamorphism. Possible sources of this heat are (1) conductive transfer along the geothermal gradient, (2) advection by a fluid (silicate magma or a volatile rich phase), (3) radioactive heat production within each rock volume. The average heat capacities of quartz, micas and feldspars are approximately 0.25 cal/g~ over the temperature range 400-600 ~ C. Hence 250 calories must be supplied to increase the temperature of one kilogram of rock I ~ in the absence of devolatilization reactions. If most volatiles are lost from the average pelite over an interval of 200 ~ for example 400-600 ~ C, then the total heat required to metamorphose an average pelite is 90kcal per kg of rock, 40kcal of which is consumed by devolatilization reactions. Disregard of enthalpy
Calcite + QTZ = Wollasonite + CO 2
20.6 Kcal
4 Zoisite + QTZ = Grossular + 5Anorthite + 2H 20
25.6 Kcal
changes in devolatilization reactions produce an error of a factor of 2 in thermal models of progressive metamorphism. The rate of metamorphism can be defined as the rate at which isotherms and devolatilization isograds advance through a column of rock which is undergoing regional metamorphism. A zero rate of metamorphism (and hence volatile production) corresponds to steady-state heat flow along a static geothermal gradient, which requires the temperature of each rock volume to remain constant. The rate of metamorphism is determined by the enthalpy of reaction, heat capacity and net heat input of the metamorphic pile. The net heat input is the difference between the sum of the heat entering the system and that generated within the metamorphic pile and the amount of heat that leaves by conduction or advection. An advance of isotherms leading to the regional metamorphism of a large volume of rock may be brought about in a number of different ways, but mechanisms based upon crustal thickening with normal heat flux can be contrasted with those which call upon an increase in the regional heat flux. 1. Rapid thickening of crust by overthrusting, obduction, or rapid sedimentation, first produces a lower geothermal gradient which is then slowly increased as the crustal section relaxes to a steady stage geotherm determined by the flux of heat from below and that derived internal radioactive heat production. 2. An increase in regional heat flux induced by conduction of heat from the upper mantle or by intrusion of magma into the lower crust. The calculation to be made here is based on a very simple model of the second type, which deliberately maximizes the amount of heat available for advancement of isotherms and devolatilization isograds and therefore gives an estimate of maximum rates of metamorphism and volatile production. In this model we will assume that all loss of HzO and CO z from the "average pelite" occurs between 400 and 600~ without distinguishing the individual discontinuous or continuous isograd reactions which produce volatiles within that temperature interval. The maximum amount of heat available for metamorphism will be taken as the difference between heat flows characteristic of the highest and lowest heat flow provinces. The highest regional heat flows are about 2.5H.F.U. (gcal cm 2 s-~), characteristic of the most actively spreading midocean ridges (East Pacific Rise) or behind arc basins (Sea of Japan). The lowest regional heat flows are about 0.8 H.F.U. and are characteristic of oceanic trenches and ancient shield areas of the continental craton.
254 In this simplified model we will assume that an initial steady state geotherm has been established in a section of continental crust in which 0.8 H.F.U. enter from the base of the crust and 0.8 H.F.U. plus radioactive heat generated within the column exit at the surface. A sudden increase in heat flow from below to 2.5H.F.U. will result in heating of the column as heat flow at the surface gradually increases from the initial steady state value to a new steady state of 2.5 H.F.U. plus radioactive heat generated within the column. In order to calculate the maximum rate of isograd advance and volatile production we will assume that the entire increase in heat flow of 1.7H.F.U. is consumed within the column of rock between the 600~ and 400~ isotherms and that the heat flux leaving the column at the 400~ isotherm remains at 0.8 H.F.U. plus radioactive heat generated within the column. As a further simplification, rather than calculating the change in the actual temperature profile, all isotherms between 600 and 400 ~ will be assumed to advance at the same rate. The heat necessary to advance all isotherms and devolatilization isograds through l k g / c m 2 of average shale amounts to 90kcal/cm z. Assuming a density of 2.6g/cm 3, 1 kg/cm z of average shale corresponds to 380 cm thickness of shale and the maximum rate of metamorphism produced by 1.7 H.F.U. calculating per cm 2 will be 1.7 x 10-~ cal s -1 9380 cm kg- : =7.18 x 10 .9 cm/s 90 x 103 cal kg- 1
(1)
which corresponds to 2.3 mm in one year or 2.3kin in one million years. The metamorphism of a 10kilometer section of this same average shale would therefore require a minimum of 4.3 m.y. A somewhat lower maximum value of heat available for metamorphism and lower rate of advance of isotherms is obtained if one assumes tectonic thickening of the crust in combination with a "normal" continental crust heat flow (type 1 model). The minimum rate of metamorphism can be taken somewhat arbitrarily as one tenth that of the maximum calculated above. This lower limit for an "event" of prograde regional metamorphism would require more than 40 m.y. to metamorphose 10 km of average pelitic rock.
Rate of Volatile Production A maximum heat absorption of 1.7 H,F.U. by a section of average pelitic rock corresponds to a maximum rate of volatile production per cm 2 of 1.7 x 10-~ cals -1 90 x 10a cal kg_l x 50 g volatile kg- 1 =9.4 x 10-:~ g s - :
(2)
or 3.7x10 -11 moles c m - 2 s -1 which is equivalent to 30mg cm 2 in one year or 30 kg per cm 2 in one million years. On the average, this amount of volatiles must pass through each cm 2 of crust overlying the 400~ isotherm at the maximum rate of metamorphism and one tenth this amount at the minimum rate of regional metamorphism as defined above.
Mechanism of Volatile Escape At very low rates of dehydration and decarbonation it may be possible for volatiles to escape in the absence of a discrete fluid phase by diffusion through a volatile-rich layer adsorbed
on grain boundaries. At some higher rate of volatile production, the "equilibrium pressure" of the volatiles should approach or even slightly exceed lithostatic pressure; existing isolated pores may then expand and coalesce, fluid-filled fractures may form, and volatiles can then escape by flow of the fluid phase. Fluid inclusions in many metamorphic rocks occur along planes within crystals which are presumed to form when fluid-filled fractures heal and trap some portion of the fluid in secondary fluid inclusions. Such occurrences leave little doubt that fracturing in the presence of a fluid phase does occur during metamorphism. The volume of fluid presently trapped in inclusions along a plane sets a lower limit on the width of the fracture prior to annealing. Such calculations made from fluid inclusions occurring along planes in quartz crystals from a variety of metamorphic terrains give a minimum fracture width of 0.02 gin. H 2 0 exhibits a small solubility in nominally anhydrous minerals such as quartz. Exsolution of HzO from quartz could contribute to the volume of fluid within fluid inclusions. It seems unlikely, however, that this HaO which occurs as isolated OH ions in oxygen sites associated with charge imbalance or vacancies in cation sites (Wilkins and Sabine 1973) could readily diffuse from a large enough volume to make a significant contribution. Two other observations suggest exsolution is not important. First, the densities of large and small inclusions along a single annealed fracture plane are similar. Second, calculations using CO z dominant inclusions also give fracture widths of ~0.02 gin. If volatiles which escape upward from a column of rock undergoing devolatilization reactions move as a fluid phase along discrete planar fractures, then the volatile flux for laminar steady state flow is given by
(%
d3, q=i'~g Oz
viscous
(3)
where q is the volume flux of volatiles in cm 3 s- :, d and l are the width (distance between parallel walls) and length, respectively, of the crack in cm, # is the viscosity in poise (gm-1 s-1) and OP/Oz viscous is the viscous pressure gradient in the fluid in dyne cm-3 With z increasing downward. The viscous pressure gradient, or effective pressure gradient, is the difference between the total pressure gradient acting on the fluid phase and the hydrostatic pressure gradient, which would be observed in a stagnant column of fluid. It should be noted here that it is not a pressure gradient per se which is responsible for fluid flow. A standing column of fluid is subject to a hydrostatic gradient in the vertical direction determined by fluid density. The gradient which drives fluid flow in the vertical direction is the pressure gradient in excess of the hydrostatic gradient. We have assumed that during the process of progressive regional metamorphism the pressure of a fluid phase (PI) will be equal to or closely approach rock pressure (P~). Neglecting possible non-uniform lithostatic pressure, open fractures will form if fluid pressure exceeds rock pressure by a very small amount since the tensional strength of well foliated rock at metamorphic conditions will be vanishingly small. As shown below the condition PI=P~ can be maintained at all points in a fracture with significant vertical extent only if upward flow of the fluid takes place. Figure 1 represents fractures filled with a static and flowing fluid phase. PI is assumed to be equal to P~ at Zo, or
255 FL( ~WING
STATIC z-
H20
I
4
pfo = pot a t Z~
]
30O/km
20
0.20/
/
/
-
/
/
Z+ Fig. l. Fractures filled with a static and flowing fluid phase
p o =p,o
,
(4) i
where the superscript 0 indicates the Z o position. At some value of Z (Z increasing in the downward direction), the change in P, is given by:
8-C~
(5)
00
I
I
100
I
i
200
I
I
300
I
i
400
I
i
500
600
TEMPERATURE, ~
Fig. 2. Isopleths of viscosity in centipoise of H20 as a function of pressure and temperature. Dashes indicate values are extrapolated. Calculated from data reported by Dudziak and Frank (1966). Also shown are lithostatic gradients for 20~ and 30~ per km
where p and g equal the density and acceleration of gravity respectively. The vertical gradient in P~ is: 5
a8
(6)
OZ - P ' g '
m
,
i
,
i I
|
602
,
w/,
,1,
20~ /
/ / i ' 30O/krn
.3/ , -
4
the change in static fluid pressure with z is: m
v~-P2 =p,(Z-Zo)g,
(7)
~ 3 0,15
and the vertical gradient in Pf is:
afz_ OZ
(8)
PYg"
~Z - 3Z ~- ~Z-
viscous
(9)
where the subscripts f f and s f stand for the flowing and static fluid respectively. Ps can remain exactly equal to P~ at all values of Z if (10)
9Z
which by substitution of Eqs. (6), (2) and (4) with (5) gives
(~Z) visc~176
~ 2
0.10/
Because Pr is greater than Ps, PJ will be greater than P, at all points above Z o and less than P~ at all points below Z o. For wall rock with vanishingly small strength, this is a mechanically unstable situation and the fluid filled fracture will propagate upward by wedging open at the top and closing at the bottom. The vertical pressure gradient in a steady state flowing fluid is
9Z
tf f
f)g"
(11)
Assuming average values of fluid and rock densities of 0.9 and 2.8 grams cm-3, respectively, and g equal to 980.7 cm s -2, the viscous pressure gradient which maintains fluid pressure just equal to rock pressure is 1.9 x 103 dynes c m - 3.
1 0
I
I 100
f
I i I r I 200 300 400 TEMPERATURE, 'C
r
I 500
r
600
Fig. 3. [sopleths of viscosity in centipoise of CO 2 as a function of pressure and temperature. Dashes indicate values are extrapolated. Calculated from a supercritical fluid corresponding states diagram given by Bird et al. (1960). Also shown are lithostatic gradients for 20~ and 30~ per km
The viscosity (ix) of relatively dense supercritical fluids at high temperature and pressure is not very sensitive to changes in temperature and pressure. Figure 2 shows viscosities for H 2 0 based on experimental determinations of Dudziak and Frank (1966). Figure 3 shows viscosities of CO 2 calculated on the basis of a supercritical fluid corresponding states diagram given by Bird et al. (1960; Fig. 1.3-2). It can be seen that the extreme range of viscosities for both H 2 0 and CO 2 in the temperature range 400-600~ at pressures appropriate to average geotherms 15~ to 45~ in the crust fall between 0.1 and 0.2 centipoise. No significant error will be introduced if we assume that the viscosity of a H 2 0 - C O 2 supercritical fluid under metamorphic conditions is 0.15 centipoise. ~P The values stated above for ~ viscous and # together
256 -4
I
'
I /'
A
/
--6
7
O
--
Qt II:
E - 10 O
~='
/ / /
-12 (.9 O "~ - 1 4 -
/
/
o
//
/
/
/
/ // /
-16~-/
/
I
'
I
-1 /
,
dI J, .4
/ /
i
/
i
/
//
/
/
/
'
/
) G41 / / 1G 6 / /
/
O
I/
/
,'%o /
/
-8-
'1
o
102-
/
LAMINAR FLOW
FLOWj
TURBULENT-t
/
/ / I//,
I f I ~ I , I , I t .1 /I I -5 -4 -3 -2 -1 0 -6 1OOpm .0 l p m LOG d, cm Fig. 4. Isopleths of fracture length in cm per cm2 as a function of volume flux (q) and fracture width (d). Hatched area indicates region of diagram appropriate to regional metamorphism (see text) -18
-8
-7
with Eq. (3) can be used to calculate the volume flux per cm 2 as a function of fracture thickness and length. The results are plotted in Fig. 4. This calculation is valid for steady state flow of supercritical C O 2 - H 2 0 fluid within the range of conditions where fluid flow is laminar and where the thickness of the fluid layer strongly adsorbed at the walls of the fracture is small compared to the total thickness of the fluid-filled fracture. Flow changes from laminar to turbulent when the Reynolds number (Re) exceeds about 2,300. For flow in a tabular fracture
2vd
Re=-#
(12)
where v is the average velocity of the fluid which can be expressed in terms of quantities already defined or calculated as:
0
(13)
dl Substitution of Eq.(12) and Eq. (13) into Eq.(3) and rearranging to solve for d, the fracture width, gives:
[
.
\1/3
d = \6# 2 Re ~zOP vzscous]
.
(14)
The value of d, critical for the transition from laminar to turbulent flow for the pressure gradient and viscosity used previously, is 0.025 cm and is shown as a vertical line on the right side of Fig. 4. At high temperature supercritical conditions, molecules of a volatile substance which form strong chemical bonds with the underlying substate may form a strongly adsorbed monomolecular layer. Bonding of additional volatile molecules to form a multimolecular adsorbed layer depends upon relatively weak bonds no stronger than those acting between molecules of the volatile substance in its crystalline state. At temperatures far above the stability of the volatile substance in its crystalline state, no multimolecular adsorbed layer is
possible and the maximum thickness of an adsorbed volatile layer is that of a monomolecular layer. In the case of H 2 0 and CO 2 the dimensions of the molecules are about 5• (5 x 10-s cm). The total thickness of strongly adsorbed volatiles on both surfaces of a fracture would then be no more than about 10 -7 cm or 0.001 gm and would have no appreciable effect on calculated fluid flow in fractures I0 - ~ cm or greater. Since viscosity of a strongly adsorbed molecular layer will be greater than that of bulk fluid, fluid flow calculated from Eq. (3) and shown in Fig. 4 will set a maximum limit for actual flow, even within the range of fracture widths where this volume proportion of absorbed surface layer is important. The results shown in Fig. 4 can be combined with the previous estimate of maximum volatile flux per unit area during metamorphism to arrive at the total length of crack per unit area which will accomodate this flux. The entire maximum volatile flux of 9 x 10-10 gs-1 through the average cm 2 cross section could be accomodated by a single fracture of 1 cm length and 0.2 lam (2 x 10 5 cm) width. If the average fracture width is increased to 2 microns ( 2 x l 0 - g c m ) the same average flux could be accomodated by one fracture 100cm long cutting through a column of rock i m on each side (equal to 10 -2 cm of fracture for each cm 2 area of rock). If the fracture width is reduced to 0.02 gin, a typical value deduced for the minimum original width of an annealed fi'acture plane, then 1,000cm of fracture per cmz would be required. If discrete fractures do not form in the rock, the grain boundary surfaces available for flow or diffusion of volatiles per cm z is given approximately by:
where r is the average grain size in cm. For an average grain size of 0.01 cm, a reasonable minimum grain size for a greenschist facies pelitic schist, the grain boundaries amount to 200cm per cm 2. If each grain boundary has a volatile-rich layer of approximately 10A (10 -7 cm) thickness consisting of a double monomolecular layer of adsorbed volatiles then the flux which can be accomodated by flow through this film by use of Eq.(3) with a viscosity of 0.15 ceptipoise is 2 x10-14cm3/s. This is 1/3,000 the average minimum flux estimated for regional metamorphism of pelite. Because the viscosity of the adsorbed volatiles is likely higher than that in a free volatile phase the computed flux is a maximum.
Volatile Escape and Quartz Precipitation One can imagine two endmember cases for fluid transport. First, the volatiles may flow along fractures whose spacing is on the order of grain size. In this case all rocks above the site of volatile production will come in contact with the escaping volatiles. Under such conditions retrograde reaction could occur. The other possibility is that the bulk of volatile flux is through widely spaced major channelways. Under this condition the bulk of the rock above the site of volatile production will not be in contact with the escaping volatiles and retrograde reaction would not be expected to occur. From the standpoint of energy considerations one might predict a coalescing of fractures as the volatiles flow towards the earth's surface. This hydraulic system would be similar in morphology to a stream basin in its dendritic pattern. It is not clear, however, to what extent fracturing is controlled or influenced by regional stresses, or is associated with distinct
257 episodes in the deformation history of the rock. Tuttle (1949), in the only published study of its kind, found strong regional trends in the orientations of fluid inclusion planes in metamorphic rocks over several hundred square miles in the vicinity of Washington, D.C. He was not able to relate these orientations to foliation, joints, or quartz fabrics, but it is possible that they may be related to large-scale features not recognized by Tuttle. If such a drainage system for the volatiles exists it should be possible to observe some of its major features, It can be anticipated that the fluid released during the progressive metamorphic event is saturated or close to saturation with respect to quartz. Because quartz solubility decreases with decreasing temperature and pressure the fluid will precipitate quartz as it moves towards the earth's surface. We propose that the quartz "segregation" veins commonly observed in metamorphic terrains have been the major channelways for the passage of volatiles, the quartz being deposited from the volatiles that pass through and to some degree represent the cumulative trace of the volatile pathways. The very large grain size of quartz and other minerals within and at the boundaries of these veins compared to the same minerals in the matrix rock and the greater abundance of fluid inclusion planes within the veins are both consistent with this suggestion. Durney and Ramsay (1974) have demonstrated that those veins which show fiber textures normal to the wall probably form as a result of continued fluid flow and gradual accretion of vein material. Once established, the monomineralic quartz veins are conducive to fracture propagation. Volatiles flowing along fractures with quartz segregation that enter the rock surrounding the veins will quickly hydrate the minerals. Because of the positive volume change of hydration these fractures will be quickly sealed by the volatiles. Rims of hydrous minerals on the order of millimeters typically surround metamorphic quartz segregations. Quartz within the segregations contain fluid inclusions oriented along planes which often intersect each other. Compositions and densities of inclusions vary widely from plane to plane. These observations suggest the quartz within the segregations has fractured and annealed many times during the metamorphic event, trapping volatiles produced under a variety of pressure and temperature conditions. If the schist has no effective tensile strength, no volatile phase (except an adsorbed monolayer) will be present within the pelite except when reaction is taking place. While the volatile composition will reflect the conditions at the time of reaction, buffering of the volatiles along isobaric univariant equilibrium phase boundaries will not occur. If the schist has a small but finite tensile strength, volatiles produced during a devolatilization reaction can remain buffered in the local rock volume until the fluid attains a vertical extent that is great enough to fracture the overlying shist and release the volatiles. This process may occur many times during the devolatilization history of the schist. Buffering of the volatiles along isobaric univariant equilibrium boundaries will be segmented. Because volatile escape is in effect a distillation process there should be consequent carbon, oxygen, and hydrogen isotopic systematics as a function of metamorphic grade. Such systematic decrease in 6180 and cs~ac for calcites of increasing metamorphic grade have been observed and interpreted as a continuous loss of CO 2 by Lattanzi, Rye, and Rice (t980).
Conclusions The heat necessary to release the 2 moles of volatiles within each kilogram of an average pelite undergoing progressive metamorphism is significant and must be taken into account in thermal models of progressive metamorphism. Fracturing takes place because permeability of the unfractured rock is not sufficient to accomodate the flux of volatiles produced by prograde metamorphism. The volatiles appear to escape along discrete fractures between 0.1 and 10gin in width. The gradient which drives volatile flow along the fractures in the vertical direction is the pressure gradient in excess of the hydrostatic gradient. Because the volatiles are close to quartz saturated, paths of volatile escape are marked by quartz segregations. These segregations have formed from additions of SiO 2 from the passing volatiles. The system of channels is probably dendritic in pattern. Buffering of fluid compositions along isobaric univariant equilibria will occur in segments. The length of the segment determined by the ability of the rock volume to contain volatiles produced by reaction. Acknowledgements. This study owes its origin to field studies by both authors of progressive metamorphism in the Lepontine Alps. Financial support was contributed in part by the J. Williard Gibbs fund of Yale University (to J.V.W) and NSF grants EAR79-04892 and EAR80-24146. It is a pleasure to acknowledge the assistance through discussion of M. Frey, V. Trommsdorff, J. Rice, D. Rye and others of our friends and colleagues. J.V.W would like to acknowledge the encouragement, inspiration, and support of his coauthor, the late Philip M. Orville. References Bird RB, Stewart WE, Lightfoot EN (1960) Transport Phenomena, John Wiley and Sons, New York Clarke FW (1924) Data of geochemistry. Bull US Geol Surv 770 Dudziak KH, Franck EU (1966) Messungen der Viskosit~.t des Wassers bis 560~ und 3500 bar. Ber Bunsenges Phys Chem 70:1120-1128 Durney DA, Ramsay JG (1974) Incremental strains measured by syntectonic crystal growth. In: Gravity and Tectonics, Wiley Interscience, pp 6%96 Flowers GC (1979) Correction of Holloway's (1977) adaptation of the modified Redlich-Kwong equation of state for calculation of the fugacities of molecular species in supercritical fluids of geologic interest. Contrib Mineral Petrol 69:315-318 Helgeson HC, Delany JM, Nesbitt HW, Bird DK (1978) Summary and critique of the thermodynamic properties of minerals. Am J Sci 278A:1-229 Lattanzi P, Rye DM, Rice JM (1980) Behavior of 13C and isO in carbonates during contact metamorphism at Marysville, Montana: Implications for isotope systematics in impure dolomitic limestones. Am J Sci 280:890-906 Shaw DM (1956) Geochemistry of pelite rocks. Part III: Major elements and general geochemistry. Bull Geol Soc Am 67:919934 Simonen A (1953) Stratigraphy and sedimentation of the Succofennidic early Archean supracrustal rocks in southwestern Finland. Comm G6ol Finlande Bull no 160 Tuttle OF (1949) Structural petrology of planes of liquid inclusions. J Geol 57:331-356 Wells RC (1937) Analyses of rocks and minerals. US Geol Surv Bull 878 Wilkins RWT, Sabine W (1973) Water content of some nominally anhydrous silicates. Am Mineral 58:508-516 Received October 8, 1981; Accepted in revised form March 9, 1982