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Pulsated flow regime in fractures: a possible explanation of local temperature gradients in hydrothermal systems
Geothermics, Vol. 19, No. 4, pp. 32%339, 1990. Printed in Great Britain.
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P U L S A T E D F L O W R E G I M E IN F R A C T U R E S : A POSSIBLE E X P L A N A T I O N OF L O C A L T E M P E R A T U R E G R A D I E N T S IN H Y D R O T H E R M A L SYSTEMS P I E R R E - O L I V I E R GRIMAUD,* G E R A R D T O U C H A R D , * D A N I E L B E A U F O R T ? and ALAIN MEUNIER? * Laboratoire de Physique et M~canique des Fluides U.A. 191 du C.N.R.S., 40 Avenue du Recteut Pineau, 86022 Poitiers, France, and t Laboratoire de P(trologie des Alterations Hydrothermales U.A. 721 du C.N.R.S., 40 Avenue du Recteur Pineau, 86022 Poitiers, France (Received March 1989; accepted for publication April 1990) Abstract--Several petrological studies of hydrothermal systems suggest the existence of temperature gradients in wall-rock adjacent to fractures. On the basis of a vein alteration system, in which a thermal gradient has been identified at a pluricentimetric scale, we propose a theoretical model of the thermal conditions of the wall-rock alteration: these results are then used to constrain the nature of the fracture flow regime. Knowing that phenomena of dissolution-recrystallization cannot occur if the temperature gradient appears for only a short time (for instance, less than one minute), we show that only a pulsated flow regime can explain such a phenomenon. Moreover, the conditions on the values of minimum crystallization temperature of the observed minerals imply that this pulsated regime cannot be described by a sinusoidal function but rather by a Fourier's series.
I N T R O D U CT IO N Zoned alteration patterns of wall-rock around vein deposits were frequently observed in fossil and active hydrothermal systems (see compilations from Meyer and Hemley, 1967 and Titley, 1982). These mineral zonations are considered to result from chemical rather than from thermal gradients because thermal equilibrium between the fluids and the surrounding rocks is reached in a very short time (Lovering, 1949). Nevertheless, Bonorino (1959) stated that the existence of thermal gradients cannot be excluded. They are subordinate factors in the formation of alteration zoning because they enhance chemical gradients. Temperature may affect the position of the fronts or the width of the alteration halo. Most often, the external zones contain expandable clay minerals whose stability field is not compatible with the micas or feldspars or sulfides that constitute the inner zones or the vein deposits. Page and Wenk (1979) considered that the expandable phases are metastable and transitional to stable ones, mainly kaolinite and muscovite (2M1 polytype) in the studied case. The smectite is produced faster than it can be altered to muscovite by the increase of K + activity. However, the kinetics of the dissolutionprecipitation of these minerals are not known with enough confidence to be sure that they are the controlling factor of the front migration. In spite of the fact that clear evidence of a thermal gradient is difficult to obtain, several studies demonstrate their effects on the surroundings of mineral veins (Beaufort and Meunier, 1983; Horton, 1985; Sharaa, 1986). These data raise the problem of the heat source: what regime of fluid flow in the fracture allows the stabilization of the thermal gradients that control zoned alteration patterns at local scale? As a consequence, what must be the conditions when the isothermal processes are working? As little is known of the hydrodynamics of natural systems, we investigated the conditions of fluid flow necessary for the formation and stabilization of a thermal gradient in the vicinity of 329
P.-O. (;rimaud ctal.
33(I
millimetric veins. The phyllitc vein described by Beaufort and Meunier (1983) has been sclcctcd because the fine-grained rock is convenient for the experimental measure of physical parameters, particularly the rock permeability, which must be determined in order to calculate the flow regime inside the fracture.
DESCRIPTION OF T H E PHYLLIC VEIN The Sibert porphyry granite (Rh6ne, France) is crosscut by a network of phyllite veins (muscovite + quartz + pyrite deposit). A mineralogical study of the phyllosilicates, with emphasis on microprobe analysis, shows a zoned wall-rock alteration. Three zones were distinguished. 1. In the nearest zone (10 mm width), all the pre-existing minerals (quartz excepted) are totally transformed into muscovite. 2. In the intermediate zone (9 mm width) the primary minerals are still recognizable. The stable secondary assemblage is phengite + phlogopite. 3. In the farthest zone (10 mm width), only a small proportion of pre-existing biotites and plagioclases are altered. The stable assemblage is illite + chlorite + corrensite + K-feldspar. In this case the isothermal model cannot explain the simultaneous formation of the different secondary assemblages. Compositions of white micas and phase relationships outline the incompatibility of high-temperature assemblages: muscovite and phengite-phlogopite (350°C) and low-temperature assemblage: illite-chlorite-corrensite-K-feldspar (280°C). So, if these temperatures are significant, a temperature gradient of about 75°C was established on a thickness of about 30 mm in the wall-rock of the phyllite vein (this corresponds to a temperature gradient of 2500°C/m) during a period of time sufficiently long for the mineral reactions to proceed. Such a period was calculated for a comparable hydrothermal alteration of a finegrained granite (Turpault, 1989). The width of the altered wall-rock around a phengite vein (340°C) attains 16 mm after about 100 years. Figure 1 gives the three-dimensional model deduced from the petrographic analysis.
THEORETICAL FORMULATION General equations
Let us consider a rock sample of heat capacity (pc)s (Wohlenberg, 1982) and conductivity 2~ (Cermak and Rybach, 1982) characterized by porosity e (Schopper, 1982) and permeability K. The fluid that saturated the rock has heat capacity (pc)f, conductivity 2t, thermal expansivity fi and viscosity v. The porous medium thus defined has a heat capacity (pc)* = ~(pc)t. + (1 - e)(pc)~ and conductivity 2* = 2f. 2~1--') (Combarnous and Bories, 1975). If the thermal gradient is considered to be established in the same way in each part of the fracture, the problem can be reduced to a one-dimensional model. So, using the Boussinesq approximation (Gray and Giorgini, 1976) and assuming the fluid to be incompressible, the equations governing the phenomenon may be written, for a steady state, in a one-dimensional form: c')//
Ox
-0
u =-
(1) 0g-
(2)
331
Pulsated Flow Regime in Fractures (pc)* OT
)~, (32T
OT
(3)
where u is the fluid filtration velocity in the considered direction, p -- pv is the dynamic viscosity of the fluid, g is the gravitational acceleration in the considered direction and P is the pressure. It will be solved for different cases of fluid flow. We shall first assume a constant flow regime to evaluate the time magnitude order during which the t e m p e r a t u r e gradient is established; a sinusoidal flow regime and a pulsative one will then be considered and discussed.
Constant flow regime In order to have a more general solution, we transform equations (1)-(3) in a dimensionless form using the following reference quantities: h, (pc)*h2/2 *, 2*/h(pc)f, ~*~/K(pc)f, T r for length, time, velocity, pressure and t e m p e r a t u r e , respectively. We thus obtain:
t-bo
:Li
2 - :.: i'". ---
4 4-~
° ~--:'..... 0 0
_
-
ry granlte farthest zone intermediate zone nearest intensely altered zone central vein deposit
chlorite unaltered
rack
I
corr~nsite
illit°
I p.entito I
phlo~opite
muscovite
i 0 cm
9 cm
9 cm
pyrite II
Fig. 1. Schematicrepresentation of a phyllite vein in Sibert porphyry copper after Beaufort and Meunier (1983) and of it,~ reduction to a one-dimensional system.
332
P.-O. (;rimaud et al.
T
('C)
300 " - I &T
=40 "C I
200
_
I00
± (S) o 0
l
I
100
200
(
>
I
>
300
&t ~" 20 s
Fig. 2. Temperature variation with time, at a distance x = 3 cm from the vein; K = l,N. 1(I w me; ~ p = 2.10"~ Pa: T, = 100°C.
Ou+ _ 0
(4)
Ox+
Ra*T+ = OP._~+ u+
(5)
Ox+ aT+ _ OCT+ at+
.
~
ax+
aT+ u+
- -
ax,
(6)
where Ra* = ga(pc)fKh Trh,2* is the filtration Rayleigh n u m b e r (all dimensionless quantities are sub-indexed +). Considering the value of the permeability K, always very small in such kinds of material (see Appendix), we can show that the filtration Rayleigh n u m b e r makes the first term of m o m e n t u m equation (5) nearly negligible. Our problem is finally solved by equation (6). A Fortran program, using a finite-difference method, solves it. The boundary conditions are, in dimensionless form: T+(O, t) = 350/T,.
(7)
T+(h, O) = T,/T,
(8)
where Ti is the initial t e m p e r a t u r e of the porous medium. Figure 2 shows the evolution of t e m p e r a t u r e in terms of time, at a distance x = 3 cm from the vein. If we consider that the transformations observed need a temperature of 280°C __+ 20°C, then the duration At of such a transformation must have been of about 20 s. The evolution of t e m p e r a t u r e in terms of the distance from the vein is plotted in Fig. 3, at different times. Once again, we can see that the duration At during which the t e m p e r a t u r e is within an interval of 40°C around the given value, is often less than 30 s.
Pulsated Flow Regime in Fractures
333
The results shown in these two figures have been obtained for K = 1.8.10-19 m 2, p = 2.105 Pa and Ti = 100°C, but a set of computations, made for various values of these three parameters, always gives the same kind of results: the time during which the t e m p e r a t u r e is within an interval of 40°C around the m e a n value is less than 30 s. T i = 100°C, in particular, is an average value, but whatever the value of this initial t e m p e r a t u r e , the results do not change. Such conditions of fluid flow are not possible, as the duration of t e m p e r a t u r e must be far longer than that obtained with this model. Let us now consider the case of a periodic flow regime.
Periodic regime Because of the very low value of the permeability K, the convective term in energy equation (3) is always much smaller than the conductive term. In order to simplify the fundamental system of equations (1)-(3), we can therefore reduce it as follows:
02T_ 10T Ox2 a Ot
(9)
where a = ;t*/(pc)* is the thermal diffusivity of the porous medium and T = T(x, t) is a periodic function of the distance from the vein x and of the time t. In the first approach, a sinusoidal pulsative regime is considered (Fig. 4); although this regime can explain the establishment of a gradient of m a x i m u m temperatures, it does entail an opposite gradient of minimum temperatures, whose value, in some cases, might greatly compromise growth of the observed minerals. Although the pulsative regime might not then be in question, the sinusoidal form of the pulsations certainly does not square with the reality of the p h e n o m e n o n . The minimum temperatures would have to be higher than those provided with the sinusoidal regime, and observation of the pulsative regime in geothermal research has shown that the evolution of flow vs time would be better described by Fourier's series (Fig. 5). It is from this last assumption that we approach our new model.
/
350
--
280
--
175
T (°C) .
.
.
.
.
--
= 20s 180s ~ = 120s = 60s
x (IO'~) )
o 0
I I
I 2
I 3
Fig. 3. Temperature variation with the distance from the vein, at different times t; K = 1.8.10-19 m2; AP = 2.10~ Pa; ~ = 100°C; . . . . : average temperature to obtain the transformations observed.
P.-O. (;rimaud et al.
334
x,t
s
J
210 •
Fig. 4. Sinusoidal regime: evolution of Tas a function ofx and t.
If T~ is the m e a n value a r o u n d which the t e m p e r a t u r e oscillates, T M a n d T m are respectively the m a x i m u m a n d m i n i m u m t e m p e r a t u r e values, r is the period of the oscillations a n d r~ is the time d u r i n g which the t e m p e r a t u r e is m a x i m u m , we can write the e q u a t i o n : Ts = ctT M + (1 - a ) T m
(10)
where a is the coefficient that relates r~ to r: rl = c z r
(0
(11)
Figure 5 shows the case a = 0.1. A t x = 0, the f u n c t i o n can be d e v e l o p e d in F o u r i e r ' s series form:
T~
TS T~
I'n/2
~2
Fig. 5. Fourier's series: evolution of temperature as a function of time.
Pulsated Flow Regime in Fractures
335
(jnmt)
(12)
~c
T(O, t) = T s+ y ,
Cn exp
n=l
with: 1
cn = -
Ir/2
[T(0, ~) - T~] exp (-jn~o~) d~
(13)
T J-r~2
where ~0 = 2:r/r is the pulsation of the oscillations. From equations (9) and (12), using the Fourier's method, we obtain the general expression of temperature: ~c
T(x, t) = T~ + ~, Tn(x, t)
(14)
n=l
with:
Tn(x, t) = c~ exp ( - ~ x )
cos (nwt -
n~X/nw/2aw/x). 2a
(15)
For TM = 350°C and TS = 280°C, a Fortran program computed the maximum and minimum values of T in terms of x for different values of r and a. Numerical solutions of equation (14) are given in Fig. 6 for different values of the period (150, 600, 2400, 76800 s) and two values of a = 0.1 and a = 0.5. For a = 0.5, the maxima and minima temperature curve vs distance from the vein are symmetrical around the 280°C isotherm line. The consequences are the same as with the sinusoidal model: the temperature minima are well below the muscovite conditions of crystallization inside the fracture and the nearest wall-rock. These minima temperature curves can approach the 280°C isothermal line if a is much smaller. For instance, for a = 0.1, the minima curve is always above 270°C (Fig. 7) and does not seem to be significantly affected by the value of the period. This solution certainly comes closer to the real conditions of fluid flowing in the fracture since temperature varies inside the stability field of muscovite. Despite the fact that the role of temperature fluctuations around a mean value has not yet been studied in geological systems, it is a well-known p h e n o m e n o n in preparative chemistry, where commercial crystallizers use temperature cycling to improve ripening (Baronnet, 1980). Considering that ct = 0.1 is a realistic hypothesis, it is possible to determine the influence of the period. Although the minima temperature curve does not vary significantly with the period, the shape of the maxima curve is strongly dependent on this parameter. The gradient is very steep for short periods; its amplitude diminishes with increasing period. The range of acceptable values for the period could be limited by the presence of corrensite in the farthest wall-rock, excluding temperatures up to 300°C, which means that the period cannot exceed 4800 s. As temperatures are only estimated and not directly measured, these values cannot represent more than an order of magnitude. They are, however, not unrealistic since the eruption period of geysers are similar. The eruption period of the " G r e a t Wairakei Geyser" (New Zealand) for example, varied from 10 s before 1931 to 10 hr after that date (Elder, 1981). The period could be determined with greater accuracy if temperature were measured at an intermediate point between the fracture and the unaltered rock. The direct consequence of pulsated flow is that the physico-chemical conditions imposed on fluid-rock interactions are not constant as expected in the isothermal interpretation of vein zoning. They must fluctuate with the periodical injection of hot fluid in the fracture. These fluctuations were suspected because of their effects on the isotopic compositions of rocks
P.-O. (;rimamt
336
350.
35C
r = 150s ~ O I
r
n
150 s 5
~::O
D o
280 ~_ 270-
I
el al.
Im
280 2
5
x ~cm)
210-
350- \
2ao~
F-- 2 7 0 [
ssc-~
T :600s
I
280
I
2
3
"
r
I
: 600 s
i
;
•
x (cm) 210 ,
sso L
r : 2400 s
i
= 2400 s a=O, 5
550'
~-~
,:
cm)
280
[
r
•
!
!
I
2
5
x (cm)
210,
550-
350
G
o
r = 76800 a=Ol
s
I .........
'
2
3
F-
"r = 7 6 8 0 0 s a:05
? p-
280 270"
I i
280
I I
I 2
! 3
x lcm)
x (cm)
2!o,
Fig. 6. Numerical solutions in the case of a Fourier's series: temperature variation with distance from the vein a
Pulsated Flow Regime in Fractures
iiii
337
"\
Fig. 7. Schematicdiagramof the apparatus: 1--stainlesssteel block, 2--rock sample,3--piston, 4--pole, 5--intake of pressure, 6--safetyvalve. (Barton etal., 1977) and because of zoned minerals deposition in fractures (Marignac, 1988). By means of fluid inclusion studies and accurate chemical analyses of zoning in epidotes, Marignac showed the oscillation of the following parameters: pH, fOe and temperature. Each oscillation involves two events: injection of hot fluid whose chemical properties are controlled by the source region (active during a short time) and equilibration with the host rock during a longer residence time. The question is now to determine what process can stabilize a pulsated flowing during a period of time long enough to produce the alterations observed around the fractures. The effects of seismic pumping (Sibson et al., 1975) involve only large-scale active faults and provide a possible explanation for episodic mineralization events in complex hydrothermal vein deposits, but not for the short period fluctuations studied here. On the contrary, the overpressure mechanism resulting from local boiling, which explains the periodic eruptions of geysers, can be considered a realistic hypothesis since geysers erupt regularly over a thousand year period or more (Elder, 1981). These life times are comparable with those necessary for the formation of a centrimetric alteration zone around a phengitic vein (Turpault, 1989). CONCLUSIONS The isothermal interpretation of vein-zoning based on the assumption that physico-chemical parameters are constant over long periods of time may be considered as very speculative from the fluid mechanics point of view. Natural environments with the conditions required for the stability of such a system must be very rare. A pulsated fluid flow could, however, be stabilized for long enough to produce the chemical transfers and mineral reactions observed in the altered wall-rock. In that case, thermal gradients may develop at a very local scale within the rock surrounding the fracture and may control variations in the degree of alteration vs distance from the fracture and the sequence of secondary parageneses. The period of the pulsations cannot be described by simple sinusoidal functions, but by
338
I ' . - 0 . ( ; r i m a u d ct hi.
F o u r i e r ' s series. T h e d u r a t i o n of hot fluid i n j e c t i o n m u s t be o n e o r d e r s h o r t e r t h a n t h a t o l the r e s i d e n c e t i m e . T h i s can be o b s e r v e d in g e y s e r s ; the W a i r a k e i g e y s e r , for e x a m p l e , has an e r u p t i o n t i m e o f 100 s w h i l e its retilling t i m e is 400 s. T h i s is a n e c e s s a r y c o n d i t i o n to c o m e closc to t h e l o w e s t g r a d i e n t v a l u e . T h e e x a c t w t l u e o f t h e p e r i o d can be d e t e r m i n e d if the t e m p e r a t u r e is k n o w n at an i n t e r m e d i a t e p o i n t b e t w e e n t h e f r a c t u r e a n d t h e u n a l t e r e d rock. T h e q u e s t i o n n o w is w h e t h e r t h e p u l s a t e d f l o w i n g m o d e l r e p r e s e n t s a g e n e r a l i n t e r p r e t a t i o n f o r m o s t o f t h e f l u i d - r o c k i n t e r a c t i o n s o b s e r v e d in n a t u r a l e n v i r o n m e n t s . A s z o n e d a l t e r e d wallr o c k a r o u n d h y d r o t h e r m a l v e i n s are f r e q u e n t l y d e s c r i b e d , w e s u s p e c t t h a t p u l s a t e d fluid flow is m o r e w i d e s p r e a d i n s i d e t h e d e e p p a r t o f g e o t h e r m a l s y s t e m s t h a n a r e g e y s e r s at t h e s u r f a c e . Q u a n t i t a t i v e s t u d i e s o f f l u i d - r o c k i n t e r a c t i o n s in t h e d i f f e r e n t z o n e s s h o u l d b e a b l e to p r o v i d e an a n s w e r to this q u e s t i o n . Acknowledgements--Financial support of this study was provided by the "Programme Intcrdisciplinaire de Recherche sur les Sciences pour I'Energie et les Mati6res premieres".
REFERENCES Baronnet, A. (1980) Polytypism in micas: a survey with emphasis on the crystal growth aspect. In: Current Topics in Material Science, 5 (Edited by Kaldis, E.), pp. 447-548, North-Holland, Amsterdam. Barton, P. B., Bethke, P. M. and Roedder, E. (1977) Environment of ore deposition in the Creede Mining District, San Juan Mountains, Colorado: Part III. Progress toward interpretation of the chemistry of ore-forming fluid for the OH vein. Econ. Geol. 72, 1-24. Beaufort, D. and Meunier, A. (1983) A petrographic study of phyllite alteration superimposed on potassic alteration: The Sibert porphyry deposit (Rb6ne, France). Econ. Geol. 78, 1514-1527. Bonorino, F. G. (1959) Hydrothermal alteration in the Front Range Mineral Belt, Colorado. Bull. Geol. Soc. Am. 70, 53-90. Cermak, V. and Rybach, L. (1982) Thermal conductivity and specific heat of minerals and rocks. In: Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, V/1A (Edited by Angenheister, G.), pp. 320, Springer, Heidelberg. Combarnous, M. and Bories, S. (1975) Hydrothermal convection in saturated porous medium. Adv. Hydrosci. 10,231307. Elder, J. (1981) Geothermal Systems. Academic Press, London, 508 pp. Gray, D. D. and Giorgini, A. (1976) The validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer 19, 545-551. Horton, D. G. (1985) Mixed-layer illite/smectite as a paleotemperature indicator in the Amethyst vein system, Creede district, Colorado, U.S.A. Contrib. Mineral Petrol. 91,171-179. Lovering, T. S. (1949) Rock alteration as a guide to ore-East Tintic district, Utah. Econ. Geology Mon. 1., 65 pp. Marignac, C. (1988) Composition des min6raux et 6volution des phases fluides: le cas des filons polymdtalliques d'Ain Barbar (AlgErie). Bull. Mineral. 111, 183-206. Meyer, C. and Hemley, J. J. (1967) Wall-rock alteration. In: Geochemistry o f Hydrothermal Ore Deposits (Edited by Barnes, H. L.), pp. 166-235. Holt, Rinehart and Winston, New York. Page, R. and Wenk, H. R. (1979) Phyllosilieate alteration of plagioclase studied by transmission electron microscopy. Geology 7,393-397. Schopper, J. R. (1982) Porosity of rocks. In: Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, V/1A (Edited by Angenheister, G.), p. 260. Springer, Heidelberg. Sharaa (AI), M. (1986) Etude g6ochimique ct m6tallog6nique des min6ralisations (U-Ba) du nord du massif dcs Palanges (Aveyron, France). Doctoral Thesis, University of Paris VI, 174 pp. Sibson, R. H., McM. Moorc, J. and Rankin, A. H. (1975) Seismic pumping--a hydrothermal fluid transport mechanism. 1. Geol. Soc. Lond. 131,653~59. Titley, S. R. (1982) Advances in Geology of the Porphyry Copper Deposits. University of Arizona Press, Vol. 1,560 pp. Turpault, M. P. (1989) Etude des m6canismes des alt6rat!ons hydrothermales dans les granites fractur6s. Doctoral Thesis, University of Poitiers, 117 pp. Wohlenbcrg, J. (1982) Density of rocks. In: Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, V/I A (Edited by Angenheister, G.), p. 114. Springer, Heidelberg.
APPENDIX:
EXPERIMENTS
AND RESULTS
The values of rock permeability are strongly dependent on pressure-temperature conditions prevailing in natural geothermal environments. We may first consider that the pressure of fluids inside the fracture is controlled by saturating
Pulsated Flow R e g i m e in Fractures K
2
339
(I0-I~)
_
f
I _
T (*C) '1' 100
"
I 200
>
Fig. 8. Rock permeability as a function of temperature (AP = 2.105 Pa). vapor pressure at the temperature considered, and secondly that the difference in fluid pressure between the fracture and the rock cannot exceed a few bars. A special cell was built to reproduce these conditions (Fig. 7). The block of stainless steel contains three cylindrical cavities: the rock sample (35 mm diameter and 3 mm thickness) is placed inside the largest cavity, the other two are perpendicular and contain a piston. These cavities are filled with water. The two pistons are linked by a pole in order to apply a difference in pressure between the two parts of the cell without changing the total volume of water. Piston movement is measured by a comparator. The speed of the movement gives the water filtration velocity through the sample. The permeability K is obtained by the following relation:
K = k~ue/AP where/~ is the dynamic viscosity of the water, e is the thickness of the sample, u is the fluid filtration velocity, and AP is the differential pressure. The cell is set in a drying oven at varying temperatures (20-220°C). Permeability is calculated as a function of temperature for fixed differential pressure. The results are plotted in Fig. 8. Permeability is seen to increase with temperature, but the order of magnitude seems to go no further than 10-1Vm 2.
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P U L S A T E D F L O W R E G I M E IN F R A C T U R E S : A POSSIBLE E X P L A N A T I O N OF L O C A L T E M P E R A T U R E G R A D I E N T S IN H Y D R O T H E R M A L SYSTEMS P I E R R E - O L I V I E R GRIMAUD,* G E R A R D T O U C H A R D , * D A N I E L B E A U F O R T ? and ALAIN MEUNIER? * Laboratoire de Physique et M~canique des Fluides U.A. 191 du C.N.R.S., 40 Avenue du Recteut Pineau, 86022 Poitiers, France, and t Laboratoire de P(trologie des Alterations Hydrothermales U.A. 721 du C.N.R.S., 40 Avenue du Recteur Pineau, 86022 Poitiers, France (Received March 1989; accepted for publication April 1990) Abstract--Several petrological studies of hydrothermal systems suggest the existence of temperature gradients in wall-rock adjacent to fractures. On the basis of a vein alteration system, in which a thermal gradient has been identified at a pluricentimetric scale, we propose a theoretical model of the thermal conditions of the wall-rock alteration: these results are then used to constrain the nature of the fracture flow regime. Knowing that phenomena of dissolution-recrystallization cannot occur if the temperature gradient appears for only a short time (for instance, less than one minute), we show that only a pulsated flow regime can explain such a phenomenon. Moreover, the conditions on the values of minimum crystallization temperature of the observed minerals imply that this pulsated regime cannot be described by a sinusoidal function but rather by a Fourier's series.
I N T R O D U CT IO N Zoned alteration patterns of wall-rock around vein deposits were frequently observed in fossil and active hydrothermal systems (see compilations from Meyer and Hemley, 1967 and Titley, 1982). These mineral zonations are considered to result from chemical rather than from thermal gradients because thermal equilibrium between the fluids and the surrounding rocks is reached in a very short time (Lovering, 1949). Nevertheless, Bonorino (1959) stated that the existence of thermal gradients cannot be excluded. They are subordinate factors in the formation of alteration zoning because they enhance chemical gradients. Temperature may affect the position of the fronts or the width of the alteration halo. Most often, the external zones contain expandable clay minerals whose stability field is not compatible with the micas or feldspars or sulfides that constitute the inner zones or the vein deposits. Page and Wenk (1979) considered that the expandable phases are metastable and transitional to stable ones, mainly kaolinite and muscovite (2M1 polytype) in the studied case. The smectite is produced faster than it can be altered to muscovite by the increase of K + activity. However, the kinetics of the dissolutionprecipitation of these minerals are not known with enough confidence to be sure that they are the controlling factor of the front migration. In spite of the fact that clear evidence of a thermal gradient is difficult to obtain, several studies demonstrate their effects on the surroundings of mineral veins (Beaufort and Meunier, 1983; Horton, 1985; Sharaa, 1986). These data raise the problem of the heat source: what regime of fluid flow in the fracture allows the stabilization of the thermal gradients that control zoned alteration patterns at local scale? As a consequence, what must be the conditions when the isothermal processes are working? As little is known of the hydrodynamics of natural systems, we investigated the conditions of fluid flow necessary for the formation and stabilization of a thermal gradient in the vicinity of 329
P.-O. (;rimaud ctal.
33(I
millimetric veins. The phyllitc vein described by Beaufort and Meunier (1983) has been sclcctcd because the fine-grained rock is convenient for the experimental measure of physical parameters, particularly the rock permeability, which must be determined in order to calculate the flow regime inside the fracture.
DESCRIPTION OF T H E PHYLLIC VEIN The Sibert porphyry granite (Rh6ne, France) is crosscut by a network of phyllite veins (muscovite + quartz + pyrite deposit). A mineralogical study of the phyllosilicates, with emphasis on microprobe analysis, shows a zoned wall-rock alteration. Three zones were distinguished. 1. In the nearest zone (10 mm width), all the pre-existing minerals (quartz excepted) are totally transformed into muscovite. 2. In the intermediate zone (9 mm width) the primary minerals are still recognizable. The stable secondary assemblage is phengite + phlogopite. 3. In the farthest zone (10 mm width), only a small proportion of pre-existing biotites and plagioclases are altered. The stable assemblage is illite + chlorite + corrensite + K-feldspar. In this case the isothermal model cannot explain the simultaneous formation of the different secondary assemblages. Compositions of white micas and phase relationships outline the incompatibility of high-temperature assemblages: muscovite and phengite-phlogopite (350°C) and low-temperature assemblage: illite-chlorite-corrensite-K-feldspar (280°C). So, if these temperatures are significant, a temperature gradient of about 75°C was established on a thickness of about 30 mm in the wall-rock of the phyllite vein (this corresponds to a temperature gradient of 2500°C/m) during a period of time sufficiently long for the mineral reactions to proceed. Such a period was calculated for a comparable hydrothermal alteration of a finegrained granite (Turpault, 1989). The width of the altered wall-rock around a phengite vein (340°C) attains 16 mm after about 100 years. Figure 1 gives the three-dimensional model deduced from the petrographic analysis.
THEORETICAL FORMULATION General equations
Let us consider a rock sample of heat capacity (pc)s (Wohlenberg, 1982) and conductivity 2~ (Cermak and Rybach, 1982) characterized by porosity e (Schopper, 1982) and permeability K. The fluid that saturated the rock has heat capacity (pc)f, conductivity 2t, thermal expansivity fi and viscosity v. The porous medium thus defined has a heat capacity (pc)* = ~(pc)t. + (1 - e)(pc)~ and conductivity 2* = 2f. 2~1--') (Combarnous and Bories, 1975). If the thermal gradient is considered to be established in the same way in each part of the fracture, the problem can be reduced to a one-dimensional model. So, using the Boussinesq approximation (Gray and Giorgini, 1976) and assuming the fluid to be incompressible, the equations governing the phenomenon may be written, for a steady state, in a one-dimensional form: c')//
Ox
-0
u =-
(1) 0g-
(2)
331
Pulsated Flow Regime in Fractures (pc)* OT
)~, (32T
OT
(3)
where u is the fluid filtration velocity in the considered direction, p -- pv is the dynamic viscosity of the fluid, g is the gravitational acceleration in the considered direction and P is the pressure. It will be solved for different cases of fluid flow. We shall first assume a constant flow regime to evaluate the time magnitude order during which the t e m p e r a t u r e gradient is established; a sinusoidal flow regime and a pulsative one will then be considered and discussed.
Constant flow regime In order to have a more general solution, we transform equations (1)-(3) in a dimensionless form using the following reference quantities: h, (pc)*h2/2 *, 2*/h(pc)f, ~*~/K(pc)f, T r for length, time, velocity, pressure and t e m p e r a t u r e , respectively. We thus obtain:
t-bo
:Li
2 - :.: i'". ---
4 4-~
° ~--:'..... 0 0
_
-
ry granlte farthest zone intermediate zone nearest intensely altered zone central vein deposit
chlorite unaltered
rack
I
corr~nsite
illit°
I p.entito I
phlo~opite
muscovite
i 0 cm
9 cm
9 cm
pyrite II
Fig. 1. Schematicrepresentation of a phyllite vein in Sibert porphyry copper after Beaufort and Meunier (1983) and of it,~ reduction to a one-dimensional system.
332
P.-O. (;rimaud et al.
T
('C)
300 " - I &T
=40 "C I
200
_
I00
± (S) o 0
l
I
100
200
(
>
I
>
300
&t ~" 20 s
Fig. 2. Temperature variation with time, at a distance x = 3 cm from the vein; K = l,N. 1(I w me; ~ p = 2.10"~ Pa: T, = 100°C.
Ou+ _ 0
(4)
Ox+
Ra*T+ = OP._~+ u+
(5)
Ox+ aT+ _ OCT+ at+
.
~
ax+
aT+ u+
- -
ax,
(6)
where Ra* = ga(pc)fKh Trh,2* is the filtration Rayleigh n u m b e r (all dimensionless quantities are sub-indexed +). Considering the value of the permeability K, always very small in such kinds of material (see Appendix), we can show that the filtration Rayleigh n u m b e r makes the first term of m o m e n t u m equation (5) nearly negligible. Our problem is finally solved by equation (6). A Fortran program, using a finite-difference method, solves it. The boundary conditions are, in dimensionless form: T+(O, t) = 350/T,.
(7)
T+(h, O) = T,/T,
(8)
where Ti is the initial t e m p e r a t u r e of the porous medium. Figure 2 shows the evolution of t e m p e r a t u r e in terms of time, at a distance x = 3 cm from the vein. If we consider that the transformations observed need a temperature of 280°C __+ 20°C, then the duration At of such a transformation must have been of about 20 s. The evolution of t e m p e r a t u r e in terms of the distance from the vein is plotted in Fig. 3, at different times. Once again, we can see that the duration At during which the t e m p e r a t u r e is within an interval of 40°C around the given value, is often less than 30 s.
Pulsated Flow Regime in Fractures
333
The results shown in these two figures have been obtained for K = 1.8.10-19 m 2, p = 2.105 Pa and Ti = 100°C, but a set of computations, made for various values of these three parameters, always gives the same kind of results: the time during which the t e m p e r a t u r e is within an interval of 40°C around the m e a n value is less than 30 s. T i = 100°C, in particular, is an average value, but whatever the value of this initial t e m p e r a t u r e , the results do not change. Such conditions of fluid flow are not possible, as the duration of t e m p e r a t u r e must be far longer than that obtained with this model. Let us now consider the case of a periodic flow regime.
Periodic regime Because of the very low value of the permeability K, the convective term in energy equation (3) is always much smaller than the conductive term. In order to simplify the fundamental system of equations (1)-(3), we can therefore reduce it as follows:
02T_ 10T Ox2 a Ot
(9)
where a = ;t*/(pc)* is the thermal diffusivity of the porous medium and T = T(x, t) is a periodic function of the distance from the vein x and of the time t. In the first approach, a sinusoidal pulsative regime is considered (Fig. 4); although this regime can explain the establishment of a gradient of m a x i m u m temperatures, it does entail an opposite gradient of minimum temperatures, whose value, in some cases, might greatly compromise growth of the observed minerals. Although the pulsative regime might not then be in question, the sinusoidal form of the pulsations certainly does not square with the reality of the p h e n o m e n o n . The minimum temperatures would have to be higher than those provided with the sinusoidal regime, and observation of the pulsative regime in geothermal research has shown that the evolution of flow vs time would be better described by Fourier's series (Fig. 5). It is from this last assumption that we approach our new model.
/
350
--
280
--
175
T (°C) .
.
.
.
.
--
= 20s 180s ~ = 120s = 60s
x (IO'~) )
o 0
I I
I 2
I 3
Fig. 3. Temperature variation with the distance from the vein, at different times t; K = 1.8.10-19 m2; AP = 2.10~ Pa; ~ = 100°C; . . . . : average temperature to obtain the transformations observed.
P.-O. (;rimaud et al.
334
x,t
s
J
210 •
Fig. 4. Sinusoidal regime: evolution of Tas a function ofx and t.
If T~ is the m e a n value a r o u n d which the t e m p e r a t u r e oscillates, T M a n d T m are respectively the m a x i m u m a n d m i n i m u m t e m p e r a t u r e values, r is the period of the oscillations a n d r~ is the time d u r i n g which the t e m p e r a t u r e is m a x i m u m , we can write the e q u a t i o n : Ts = ctT M + (1 - a ) T m
(10)
where a is the coefficient that relates r~ to r: rl = c z r
(0
(11)
Figure 5 shows the case a = 0.1. A t x = 0, the f u n c t i o n can be d e v e l o p e d in F o u r i e r ' s series form:
T~
TS T~
I'n/2
~2
Fig. 5. Fourier's series: evolution of temperature as a function of time.
Pulsated Flow Regime in Fractures
335
(jnmt)
(12)
~c
T(O, t) = T s+ y ,
Cn exp
n=l
with: 1
cn = -
Ir/2
[T(0, ~) - T~] exp (-jn~o~) d~
(13)
T J-r~2
where ~0 = 2:r/r is the pulsation of the oscillations. From equations (9) and (12), using the Fourier's method, we obtain the general expression of temperature: ~c
T(x, t) = T~ + ~, Tn(x, t)
(14)
n=l
with:
Tn(x, t) = c~ exp ( - ~ x )
cos (nwt -
n~X/nw/2aw/x). 2a
(15)
For TM = 350°C and TS = 280°C, a Fortran program computed the maximum and minimum values of T in terms of x for different values of r and a. Numerical solutions of equation (14) are given in Fig. 6 for different values of the period (150, 600, 2400, 76800 s) and two values of a = 0.1 and a = 0.5. For a = 0.5, the maxima and minima temperature curve vs distance from the vein are symmetrical around the 280°C isotherm line. The consequences are the same as with the sinusoidal model: the temperature minima are well below the muscovite conditions of crystallization inside the fracture and the nearest wall-rock. These minima temperature curves can approach the 280°C isothermal line if a is much smaller. For instance, for a = 0.1, the minima curve is always above 270°C (Fig. 7) and does not seem to be significantly affected by the value of the period. This solution certainly comes closer to the real conditions of fluid flowing in the fracture since temperature varies inside the stability field of muscovite. Despite the fact that the role of temperature fluctuations around a mean value has not yet been studied in geological systems, it is a well-known p h e n o m e n o n in preparative chemistry, where commercial crystallizers use temperature cycling to improve ripening (Baronnet, 1980). Considering that ct = 0.1 is a realistic hypothesis, it is possible to determine the influence of the period. Although the minima temperature curve does not vary significantly with the period, the shape of the maxima curve is strongly dependent on this parameter. The gradient is very steep for short periods; its amplitude diminishes with increasing period. The range of acceptable values for the period could be limited by the presence of corrensite in the farthest wall-rock, excluding temperatures up to 300°C, which means that the period cannot exceed 4800 s. As temperatures are only estimated and not directly measured, these values cannot represent more than an order of magnitude. They are, however, not unrealistic since the eruption period of geysers are similar. The eruption period of the " G r e a t Wairakei Geyser" (New Zealand) for example, varied from 10 s before 1931 to 10 hr after that date (Elder, 1981). The period could be determined with greater accuracy if temperature were measured at an intermediate point between the fracture and the unaltered rock. The direct consequence of pulsated flow is that the physico-chemical conditions imposed on fluid-rock interactions are not constant as expected in the isothermal interpretation of vein zoning. They must fluctuate with the periodical injection of hot fluid in the fracture. These fluctuations were suspected because of their effects on the isotopic compositions of rocks
P.-O. (;rimamt
336
350.
35C
r = 150s ~ O I
r
n
150 s 5
~::O
D o
280 ~_ 270-
I
el al.
Im
280 2
5
x ~cm)
210-
350- \
2ao~
F-- 2 7 0 [
ssc-~
T :600s
I
280
I
2
3
"
r
I
: 600 s
i
;
•
x (cm) 210 ,
sso L
r : 2400 s
i
= 2400 s a=O, 5
550'
~-~
,:
cm)
280
[
r
•
!
!
I
2
5
x (cm)
210,
550-
350
G
o
r = 76800 a=Ol
s
I .........
'
2
3
F-
"r = 7 6 8 0 0 s a:05
? p-
280 270"
I i
280
I I
I 2
! 3
x lcm)
x (cm)
2!o,
Fig. 6. Numerical solutions in the case of a Fourier's series: temperature variation with distance from the vein a
Pulsated Flow Regime in Fractures
iiii
337
"\
Fig. 7. Schematicdiagramof the apparatus: 1--stainlesssteel block, 2--rock sample,3--piston, 4--pole, 5--intake of pressure, 6--safetyvalve. (Barton etal., 1977) and because of zoned minerals deposition in fractures (Marignac, 1988). By means of fluid inclusion studies and accurate chemical analyses of zoning in epidotes, Marignac showed the oscillation of the following parameters: pH, fOe and temperature. Each oscillation involves two events: injection of hot fluid whose chemical properties are controlled by the source region (active during a short time) and equilibration with the host rock during a longer residence time. The question is now to determine what process can stabilize a pulsated flowing during a period of time long enough to produce the alterations observed around the fractures. The effects of seismic pumping (Sibson et al., 1975) involve only large-scale active faults and provide a possible explanation for episodic mineralization events in complex hydrothermal vein deposits, but not for the short period fluctuations studied here. On the contrary, the overpressure mechanism resulting from local boiling, which explains the periodic eruptions of geysers, can be considered a realistic hypothesis since geysers erupt regularly over a thousand year period or more (Elder, 1981). These life times are comparable with those necessary for the formation of a centrimetric alteration zone around a phengitic vein (Turpault, 1989). CONCLUSIONS The isothermal interpretation of vein-zoning based on the assumption that physico-chemical parameters are constant over long periods of time may be considered as very speculative from the fluid mechanics point of view. Natural environments with the conditions required for the stability of such a system must be very rare. A pulsated fluid flow could, however, be stabilized for long enough to produce the chemical transfers and mineral reactions observed in the altered wall-rock. In that case, thermal gradients may develop at a very local scale within the rock surrounding the fracture and may control variations in the degree of alteration vs distance from the fracture and the sequence of secondary parageneses. The period of the pulsations cannot be described by simple sinusoidal functions, but by
338
I ' . - 0 . ( ; r i m a u d ct hi.
F o u r i e r ' s series. T h e d u r a t i o n of hot fluid i n j e c t i o n m u s t be o n e o r d e r s h o r t e r t h a n t h a t o l the r e s i d e n c e t i m e . T h i s can be o b s e r v e d in g e y s e r s ; the W a i r a k e i g e y s e r , for e x a m p l e , has an e r u p t i o n t i m e o f 100 s w h i l e its retilling t i m e is 400 s. T h i s is a n e c e s s a r y c o n d i t i o n to c o m e closc to t h e l o w e s t g r a d i e n t v a l u e . T h e e x a c t w t l u e o f t h e p e r i o d can be d e t e r m i n e d if the t e m p e r a t u r e is k n o w n at an i n t e r m e d i a t e p o i n t b e t w e e n t h e f r a c t u r e a n d t h e u n a l t e r e d rock. T h e q u e s t i o n n o w is w h e t h e r t h e p u l s a t e d f l o w i n g m o d e l r e p r e s e n t s a g e n e r a l i n t e r p r e t a t i o n f o r m o s t o f t h e f l u i d - r o c k i n t e r a c t i o n s o b s e r v e d in n a t u r a l e n v i r o n m e n t s . A s z o n e d a l t e r e d wallr o c k a r o u n d h y d r o t h e r m a l v e i n s are f r e q u e n t l y d e s c r i b e d , w e s u s p e c t t h a t p u l s a t e d fluid flow is m o r e w i d e s p r e a d i n s i d e t h e d e e p p a r t o f g e o t h e r m a l s y s t e m s t h a n a r e g e y s e r s at t h e s u r f a c e . Q u a n t i t a t i v e s t u d i e s o f f l u i d - r o c k i n t e r a c t i o n s in t h e d i f f e r e n t z o n e s s h o u l d b e a b l e to p r o v i d e an a n s w e r to this q u e s t i o n . Acknowledgements--Financial support of this study was provided by the "Programme Intcrdisciplinaire de Recherche sur les Sciences pour I'Energie et les Mati6res premieres".
REFERENCES Baronnet, A. (1980) Polytypism in micas: a survey with emphasis on the crystal growth aspect. In: Current Topics in Material Science, 5 (Edited by Kaldis, E.), pp. 447-548, North-Holland, Amsterdam. Barton, P. B., Bethke, P. M. and Roedder, E. (1977) Environment of ore deposition in the Creede Mining District, San Juan Mountains, Colorado: Part III. Progress toward interpretation of the chemistry of ore-forming fluid for the OH vein. Econ. Geol. 72, 1-24. Beaufort, D. and Meunier, A. (1983) A petrographic study of phyllite alteration superimposed on potassic alteration: The Sibert porphyry deposit (Rb6ne, France). Econ. Geol. 78, 1514-1527. Bonorino, F. G. (1959) Hydrothermal alteration in the Front Range Mineral Belt, Colorado. Bull. Geol. Soc. Am. 70, 53-90. Cermak, V. and Rybach, L. (1982) Thermal conductivity and specific heat of minerals and rocks. In: Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, V/1A (Edited by Angenheister, G.), pp. 320, Springer, Heidelberg. Combarnous, M. and Bories, S. (1975) Hydrothermal convection in saturated porous medium. Adv. Hydrosci. 10,231307. Elder, J. (1981) Geothermal Systems. Academic Press, London, 508 pp. Gray, D. D. and Giorgini, A. (1976) The validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer 19, 545-551. Horton, D. G. (1985) Mixed-layer illite/smectite as a paleotemperature indicator in the Amethyst vein system, Creede district, Colorado, U.S.A. Contrib. Mineral Petrol. 91,171-179. Lovering, T. S. (1949) Rock alteration as a guide to ore-East Tintic district, Utah. Econ. Geology Mon. 1., 65 pp. Marignac, C. (1988) Composition des min6raux et 6volution des phases fluides: le cas des filons polymdtalliques d'Ain Barbar (AlgErie). Bull. Mineral. 111, 183-206. Meyer, C. and Hemley, J. J. (1967) Wall-rock alteration. In: Geochemistry o f Hydrothermal Ore Deposits (Edited by Barnes, H. L.), pp. 166-235. Holt, Rinehart and Winston, New York. Page, R. and Wenk, H. R. (1979) Phyllosilieate alteration of plagioclase studied by transmission electron microscopy. Geology 7,393-397. Schopper, J. R. (1982) Porosity of rocks. In: Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, V/1A (Edited by Angenheister, G.), p. 260. Springer, Heidelberg. Sharaa (AI), M. (1986) Etude g6ochimique ct m6tallog6nique des min6ralisations (U-Ba) du nord du massif dcs Palanges (Aveyron, France). Doctoral Thesis, University of Paris VI, 174 pp. Sibson, R. H., McM. Moorc, J. and Rankin, A. H. (1975) Seismic pumping--a hydrothermal fluid transport mechanism. 1. Geol. Soc. Lond. 131,653~59. Titley, S. R. (1982) Advances in Geology of the Porphyry Copper Deposits. University of Arizona Press, Vol. 1,560 pp. Turpault, M. P. (1989) Etude des m6canismes des alt6rat!ons hydrothermales dans les granites fractur6s. Doctoral Thesis, University of Poitiers, 117 pp. Wohlenbcrg, J. (1982) Density of rocks. In: Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, V/I A (Edited by Angenheister, G.), p. 114. Springer, Heidelberg.
APPENDIX:
EXPERIMENTS
AND RESULTS
The values of rock permeability are strongly dependent on pressure-temperature conditions prevailing in natural geothermal environments. We may first consider that the pressure of fluids inside the fracture is controlled by saturating
Pulsated Flow R e g i m e in Fractures K
2
339
(I0-I~)
_
f
I _
T (*C) '1' 100
"
I 200
>
Fig. 8. Rock permeability as a function of temperature (AP = 2.105 Pa). vapor pressure at the temperature considered, and secondly that the difference in fluid pressure between the fracture and the rock cannot exceed a few bars. A special cell was built to reproduce these conditions (Fig. 7). The block of stainless steel contains three cylindrical cavities: the rock sample (35 mm diameter and 3 mm thickness) is placed inside the largest cavity, the other two are perpendicular and contain a piston. These cavities are filled with water. The two pistons are linked by a pole in order to apply a difference in pressure between the two parts of the cell without changing the total volume of water. Piston movement is measured by a comparator. The speed of the movement gives the water filtration velocity through the sample. The permeability K is obtained by the following relation:
K = k~ue/AP where/~ is the dynamic viscosity of the water, e is the thickness of the sample, u is the fluid filtration velocity, and AP is the differential pressure. The cell is set in a drying oven at varying temperatures (20-220°C). Permeability is calculated as a function of temperature for fixed differential pressure. The results are plotted in Fig. 8. Permeability is seen to increase with temperature, but the order of magnitude seems to go no further than 10-1Vm 2.