heat generation relationship: An interaction model of fluids with cooling intrusions

Earth and Planetary Science Letters, 27 (1975) 73-78

© Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

LLA

THE HEAT FLOW/HEAT GENERATION RELATIONSHIP: AN INTERACTION MODEL OF FLUIDS WITH COOLING INTRUSIONS FRANCIS ALBAREDE Laboratoire de Gdochimie et Cosmochime, * Institut de Physique du Globe, Universitd de Paris VI and Dbpartement des Sciences de la Terre*, Universitd de Paris VII, Paris (France}

Received June 12, 1975

The linear heat flow/heat generation relationship observed for plutonic rocks has been interpreted by Lachenbruch as requiring an exponential depletion of radioactive elements with depth. The exponential depletion is difficult to interpret in terms of fractional crystallization of cooling magmas. Geochemical investigations and autoradiographic method have shown that an important part of the radioactive elements are in leachable sites in the rocks. A model is proposed in which the redistribution of these elements is achieved by fluid-rock interaction during the crystallisation and subsequent cooling of intrusions. A dissolution-precipitationprocess, mathematically similar to multipass zone refining will result in an exponential distribution of radioactive elements. The geothermal and geochemical implications of the model are discussed.

1. Introduction The heat production by radioactivity in igneous acidic rocks is mainly attributable to uranium (about 40%), thorium (40%), and potassium (20%). Birch et al. [1 ] established a rather surprising linear relationship between heat flow measurements and surface radioactive heat production at various sites of the crystalline basement of New England. The same correlation was found also to hold for plutonic rocks in many other regions of the United States [2,3], Australia [4], and Norway [5]. These observations gave rise [2] to the concept of heat flow provinces (see [6] for review). The geological implications of Birch, R o y and Decker's (BIRD) relationship are far-reaching. Assuming that the continental crust is made up of a pile of one or more discrete layers each with constant heat production, Roy et al. [2] concluded that a same ero* Laboratoire associ6 C.N.R.S. No. 196. Contribution I.P.G.P. No. 149.

sional stability level is attained over large regions. However, Lachenbruch [3] showed that an exponential dependence of heat sources with depth is required for the correlation to hold for different erosion rates. (A more general derivation of Lachenbruch's equation is given in Appendix.) The exponential decrease in heat production with depth is evident but not unambiguously in borehole data [7,8,37]. However there is much indirect evidence for the exponential model [9]. This work discusses the various processes by which an exponential distribution of U, Th and K can be achieved and proposes a quantitative geochemical model based on the role o f late magmatic fluids.

2. The origin of the heat source distribution in rocks Lachenbruch [10] proposed that an exponential distribution of heat sources with depth is achieved during tectogenesis by partial melting followed by upward movement and differentiation o f the melts and fluids.

74 However, it seems very difficult for magmatic processes only, to explain the BiRD relationship for such a large area as a heat flow province, within which the age, the chemical composition, the pluton size, and the geological setting vary greatly. The differentiation process also cannot explain why the BiRD relationship seems to hold for the rocks surrounding the various intrusions [ 1], or why chilled borders of intrusions are enriched in U, Th and K [13] rather than depleted. It thus seems that fractional crystallization alone cannot explain the exponential distribution. Turcotte and Oxburgh [38] advocated an equilibrium exponential distribution of heat sources induced by the gravitational forces, but their model deals with ionic complexes for which speculative assumptions are needed. Smithson and Heier [11] and Smithson and Decker [12] studied two parts of the same intrusion emplaced in the "wet" amphibolite facies and in the "dry" granulite facies and found significant differences in the U, Th, and K concentrations for similar bulk compositions. They stressed the role of water in redistributing U, Th, and K. Such an interaction has been invoked also [14,15] to explain various ~lSo patterns in acidic igneous rocks. The distribution of U and Th in rocks and minerals has long been a well-investigated subject. The autoradiographic method [16-19] has indicated that a complex distribution of a-emitters between major minerals, accessory minerals (zircon, sphene, monazite, uraninite), cracks and grain boundaries existed but much of the a-emitting material is at acid-leachable sites [l 3,20,24]. Ranchin [21,22] noted the occurrence in granites of a late magmatic (deuteric) interstitial microparagenesis involving uraninite surrounded by oxides, carbonates, and sericite. These phases are enriched U, Th, K and account for up to 70% of the total uranium. Brimhall and Adams [23] have reported for the Conway granite - the first area in which the BiRD relationship was established - a profound redistribution of U, Th and K with hydrothermal alteration and quartz-sulphur veins. These experiments point out that uranium is very loosely held in rocks and minerals, being localized either in cracks or boundaries or in easily leachable phases. The behaviour of Th is less clear. This element appears mainly in accessory minerals among which monazite is the most Th-rich [25]. Th is generally believed to be much less mobile than U. However, the observed

Th redistributions in the Conway granite [23], as well as successful leaching experiments on monazite [26] and low-temperature hydrothermal synthesis of this mineral [27] favour a considerable mobility of this element under hydrothermal conditions. Finally, direct observations of fluid-induced migrations of radioactive elements have been made. Richter and Moore [28] have deduced K volatile transfer during the cooling of the Kilauea Iki Lava Lake, while lava heating [29] has produced similar results for K and U. It is such a process that Rosholt et al. [30] advocated for considerable U loss during the crystallisation of some acidic lavas.

3. A model for heat source redistribution during the late magmatic history If the fluid phases play a prominent role in redistributing the radioactive elements in a pluton, the time at which this process is in progress should provide an important restraint on any model. During these redistribution processes, most of the common dating isotopes will be involved, e.g. the Th-Pb, U - P b and likely the R b - S r and K - A r systems. If the redistribution of the parent isotopes occurs a long time after the cooling of the intrusion, the different geochronological results should not be consistent. However, if one excepts U, which is recognized to be mobile even in lowtemperature surface or subsurface conditions [7,24], other chronometers generally give reliable emplacement ages. Any radioactive element redistribution thus should be limited to a short time after the intrusion emplacement. A model is proposed in which water and fluids migrate extensively in the cooling magma and further in the cooling rock (deuteric processes). It is similar to the heat engine proposed by Taylor and Forester [14] in order to explain the very low 6180 values in the Skye Intrusive Complex. As a magmatic chamber cools, water and fluids progressively expelled from the crystallising melt migrate upwards. Also, the water of the surrounding rocks is heated in the vicinity of the intrusion and rises under buoyancy forces. These processes should result in the establishment of a convective system with a return flow at the water-depleted low level of the intrusion (presumably via pre-existent fractures and faults in the country rocks). Extensive hy-

75 drothermal circulation is a prominent characteristic of most volcanically active areas but this model proposes that the circulation extends to the base of the pluton, a depth of up to 10 kin. The formulation developed here is quite similar to that for the zone melting. It differs from chromatographic analysis of infiltration metasomatism by Hoffman [31] in that it assumes that the element redistribution is achieved by repeated discrete fluid layers rising up in the medium. Let us now suppose (Fig. 1) a rock column saturated

at a depth Z below the intrusion top by a fluid layer whose thickness is l. The average volume fraction occupied by the fluid is p. C(Z) is the concentration of a mobile element in the saturated solid, C(Z)/k the concentration in the equilibrated saturating fluid. Many successive fluid layers migrate upwards. Let Cn _ t(Z) be the concentration profile after n - 1 passages. The nth layer proceeds upwards leaving behind a profile Cn(Z ). The variation in the total solute amount in the nfil solid + fluid layer rising up from Z to Z + dZ is given by:

Cn(Z) P)Cn(Z) + p ~ - ]

ldI(1 -

=

4= - ( 1 - p)[C n

4-

4-

÷

4-

_

l(Z - l) - Cn(Z)]

dZ

As the process is repeated, an equilibrium profile is obtained for Cn(Z ) = Cn _ I(Z) = C(Z). The solution may be found in Pfann [32]:

C(Z) = ~ e x p ( - Z / b ) 44-

Cn-l(Z)

where ct is an integration constant and b satisfies: 4-

i:i:i:i!i:i!i!~ii!i!i~i!i!i!i!i!iii!!i!:!:!! .-................................,............ .......................,..................

• ..

::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::

Cn(z) 4-

I I

k(1 - p)

lib

k(1 - p) + p

exp (l/b) - 1

or, providedp < 1 a n d l ~ b :

k-~--

2bp l

Assuming a finite height to the rock column we obtain Lachenbruch's distribution:

4-

C(Z) = C(O)- exp ( - Z / b ) 44-

4-

44-

4-

Fig. 1. Model used for calculations. Crosses: " d r y " crystal mush or plutonic rock. Stippled layer: " w e t " crystal mush or plutonic rock in equilibrium with the rising fluid.

4. Discussion and implications This model assumes that the fluid on the influx current is depleted in radioactive elements relative to the cooling intrusion, which is reasonable because the concentrations of radioactive elements in acidic plutons are high, relative to most groundwaters. The parameter l may be regarded as a mean 'bubble" size of the fluid rising in the crystallising melt or in the cooling rock. One cannot estimate this parameter without knowledge

76 of the partitioning of radioactive elements between volatiles, melt, and crystals. Inserting a tentative value p = 2 × 10 -3 [35], a lO0-m thick fluid layer should result in k = 0.4. Oxygen equilibration temperatures in acidic rocks are commonly lower than the accepted eutectic temperature [33,34], which has been interpreted by Taylor (33) by water-rock interaction a certain time after the completion of crystallisation. The permeabilities of granites [35] are sufficient for the proposed infdtration. These observations as well as geological data concerning deuteric processes give a good support to the proposed rock-fluid interaction well below the crystallisation temperatures. Most of heat flow/heat generation studies concern plutons that are homogeneous in bulk composition. Our model suggests, that the BiRD relationship should hold for some acidic rocks enriched in U, Th, and K such as gneisses and schists, in the vicinity of intrusions, as has been found by Birch et al. [1], Jaeger [4], and Swanberg et al. [5]. The interaction of water with cooling magmas and cooling rocks presumably includes all of the elements

Rb/SrlO

qh

involved in deuteric paragenesis, especially alkali metals and alkali earth metals. The effects can be seen in the exponential dependence predicted between any two such elements. Such a dependence is very common in magmatic rocks. In Fig. 2, Rb/Sr is plotted against Sr for the Neira Granite, northwest Spain (Dupuy and Capdevila [36] and unpublished results), in a log-log diagram, a linear pattern is nicely defined. The classical way to interpret this pattern is to appeal to a differentiation governed by fractional crystallisation. Our model proposes an alternative explanation agreeing with the fact that the bulk compositions of the analysed samples are very similar. Concentration mapping such as the one used by Hawkesworth [9] may be used to choose the relevant model.

Acknowledgements I am grateful to C.J. All6gre, Y. Bottinga, R.D. Hyndman and M. Semet for critical reading of the manuscript. This paper was read in a primitive form at the Summer School of Earth Sciences at Carg6se (Corsica) and it benefitted from many valuable comments. J. Geffroy, B. Giletti, and J. Lancelot are also acknowledged for their discussions. C. Dupuy made his unpublished trace elements data on the Neira granodiorite available. A reviewing by A. Lachenbruch improved the model substantially.

Appendix xo xx

0.5

x xx Xo o

If there is a regional linear relationship between the heat flow Q(0) and the surface radioactive heat production A(0) following Lachenbruch [3], the relation must be obeyed at any depth z below the present surface to survive differential erosion:

NEIRA GRANODIORITE (NW SPAIN ) 0.2

Q(z) = q* + bA(z) 10

I

I

I

I

I

20

$0

!00

200

500 Sr

Fig. 2. Rb/Sr ratio versus Sr concentration in the Neira granodiorite (log-logdiagram). Open squares: red granodiorite; crosses: grey granodiorite. Data are taken from Dupuy and Capdevila ([36] and unpublished results).

where q* and b are constants. It can be rewritten as: dQ(z) = bdA(z) On the other hand, the heat balance equation gives: dQ(z) = -A(z)dz

77 C o m b i n i n g t h e last t w o e q u a t i o n s , a n d i n t e g r a t i n g one obtains:

A(z) = A ( 0 )

exp

(-z/b)

This d e r i v a t i o n is m o r e general t h a n L a c h e n b r u c h ' s original o n e for it does n o t a t t r i b u t e a n y g e o p h y s i c a l significance to t h e p a r a m e t e r s b a n d q * a n d it does n o t involve a n y e s t i m a t i o n o f t h e " r a d i o a c t i v e l a y e r " thickness. It s h o u l d be valid in a m e d i u m , w h e r e t h e first e q u a t i o n is satisfied, as l o n g as t h e h o r i z o n t a l v a r i a t i o n s o f q* are small o n t h e scale o f the h e a t flow province.

References 1 F. Birch, R.F. Roy and E.R. Decker, Heat flow and thermal history in New England and New York, in: Studies of Appalachian Geology, E. An-Zen, ed. (Interscience, New York, 1968) 4 3 7 - 4 5 1 . 2 R.F. Roy, D.D. Blackwell and F. Birch, Heat generation of plutonic rocks and continental heat flow provinces, Earth Planet. Sci. Lett. 5 (1968) 1-12. 3 A. Lachenbruch, Preliminary geothermal model of the Sierra Nevada, J. Geophys. Res. 73 (1968) 6977-6989. 4 J.C. Jaeger, Heat flow and radioactivity in Australia, Earth Planet Sci. Lett. 8 (1970) 285-292. 5 C.S. Swanberg, I~I.D. Chessman, G. Simmons, S.B. Smithson, G. GrOnlie and K.S. Heier, Heat flow-heat generation studies in Norway, Tectonophysics 23 (1974) 3 1 - 4 8 . 6 R.F. Roy, D.B. Blackwell and E.R. Decker, Continental heat flow, in: The Nature of the Solid Earth, E.C. Robertson, ed. (McGraw-Hill, 1972) 506-543. 7 J.J.W. Rogers, J.A.S. Adams and B. Gatlin, Distribution of thorium, uranium and potassium concentrations in three cores from the Conway Granite, New Hampshire, U.S.A., Am. J. Sci. 263 (1965) 817-822. 8 A. Lachenbruch and C.M. Bunker, Vertical gradients of heat production in the continental crust, 2. Some estimates from borehole data, J. Geophys. Res. 76 (1971) 3 8 5 2 3860. 9 C.J. Hawkesworth, Vertical distribution of heat production in the basement of the Eastern Alps, Nature 249 (1974) 4 3 5 - 4 3 6 . 10 A. Lachenbruch, Crustal temperature and heat production: implications of the linear heat flow relation, J. Geophys. Res. 75 (1970) 3291-3300. 11 S.B. Smithson and K.S. Heier, K, U and Th distribution between normal and charnockitic facies of a deep granitic intrusion, Earth Planet. Sci. Lett. 12 (1971) 325-326. 12 S.B. Smithson and E.R. Decker, K, U and Th distribution between dry and wet facies of a syenitic intrusion and the role of fluid content, Earth Planet. Sci. Lett. 19 (1973) 131-134.

13 T.P. Labhart and L. Rybach, Granite und Uranvererzungen in den Schweizer Alpen, Geol. Rundsch. 63 (1974) 1 3 5 147. 14 H.P. Taylor and R.W. Forester, Low lSo igneous rocks from the intrusive complexes of Skye, Mull and Ardnamurchan, western Scotland, J. Petrol. 12 (1971) 4 6 5 - 4 9 7 . 15 B. Turi and H.P. Taylor, An oxygen and hydrogen isotope study of a granodiorite pluton from the Southern California batholith, Geochim. Cosmochim. Acta 35 (1971) 383-406. 16 E. Piccioto, Distribution de la radioactivit6 dans les roches 6ruptives, Soc. Beige G6ol. Pal6ont. Hydrol. 59 (1950) 170-198. 17 R. Coppens, Sur remploi de l'6mulsion photographique pour la d6termination de la radioactivit6 des roches par l'examen des trajectoires des rayons a, J. Phys. Radium, Paris 11 (1950) 2 1 - 3 2 . 18 S. Deutsch and E. Piccioto, Pr6sence d'uraninite dans les min6raux accessoires du granite de Baveno, Experientia 12 (1956) 333-334. 19 P.C. Ragland, Autoradiographic investigations of naturally occurring minerals, in: The Natural Radiation Environment, J.A.S. Adams and W.N. Lowder, eds. (Univ. of Chicago Press, 1964) 129-151. 20 V.I. Baranov, Le-Tien Tu and V.1. Korobkov, Geochemistry of uranium and thorium in the granitic rocks of the Kyzyltan massif (central Kazakhstan), 2. Modes of occurrence of radioactive elements in granitic rocks, Geochemistry 5 (1962) 4 6 9 - 4 8 3 . 21 G. Ranchin, Contribution ~ l'6tude de la r6partition de l'uranium dans les roches granitiques saines. Exemple du massif de St Sylvestre dans le Limousin, Sci. Terre, Nancy 13 (1968) 159-205. 22 G. Ranchin, La g6ochimie de l'uranium et la diff6renciation granitique dans la province uranif6re du Nord Limousin, Unpublished Thesis, Nancy (1970). 23 W.H. Brimhall and J.A.S. Adams, Concentrations changes in thorium, uranium and other metals in hydrothermally altered Conway Granite, New Hampshire, Geochim. Cosmochim. Acta 33 (1969) 1308-1311. 24 J.N. Rosholt, R.E. Zartman and I.T. Nkomo, Lead isotope systematics and uranium depletion in the Granite Mountains, Wyoming, Geol. Soc. Am. Bull. 84 (1973) 989-1002. 25 P.M. Hurley and H.W. Fairbairn, Abundance and distribution of uranium, thorium in zircon, sphene, apatite, epidote and monazite in granitic rocks, Trans. Am. Geophys. Union 38 (1957) 939-944. 26 A.J. Burger, L.O. Nicolaysen and L.H. Ahrens, Controlled leaching of monazites, J. Geophys. Res. 72 (1967) 3585 -3594. 27 J.W. Anthony, Hydrothermal synthesis of monazite, Am. Mineral. 42 (1957) 904. 28 D.H. Richter and J.G. Moore, Petrology of the Kilauea Iki Lava Lake, Hawaii, U.S. Geol. Survey Prof. Papers 537 B (1966) 1-26. 29 J.L. Cheminee, Contribution ~ l'6tude des comportements, du potassium, de l'uranium et du thorium dans l'6volution des magmas, Thesis, Paris (1973).

78 30 J.N. Rosholt, Prijana and D.C. Noble, Mobility of uranium, thorium in glassy and crystallized silicic volcanic rocks, Econ. Geol. 66 (1971) 1061-1069. 31 A. Hofmann, Chromatographic theory of infiltration metasomatism and its application to feldspars, Am. J. Sci. 272 (1972) 69-90. 32 W.G. Pfann, Principles of zone melting, J. Metals 4 (1952) 747-753. 33 H.P. Taylor, The oxygen isotope geochemistry of igneous rocks, Contrib. Mineral. Petrol. 19 (1968) 1-71. 34 Y. Bottinga and M. Javoy, Comments on oxygen isotope geothermometry, Earth Planet. Sci. Lett. 20 (1973) 250-265. 35 W.F. Brace, A.S. Orange and T.R. Maden, The effect of

pressure on the electrical resistivity of water-saturated crystalline rocks, J. Geophys. Res. 70 (1965) 5669-5678. 36 C. Dupuy and R. Capdevila, Sur le fractionnement des ~l~ments en traces alcalins et alcalino-terreux dans le massif granodioritique de Neira (Espagne), C.R. Acad. Sci. Paris 272 (1971) 1727-1730. 37 R.D. Hyndman, I.B. Lambert, K.S. Heier, J.C. Jaeger and A.E. Ringwood, Heat flow and surface radioactivity measurements in the precambrian shield of Western Australia, Phys. Earth Planet. Interiors 1 (1968) 129-135. 38 D.L. Turcotte and E.R. Oxburgh, Statistical thermodynamic model for the distribution of crustal heat sources, Science 176 (1972) 1021-1022.