A simple magma-driven thermal balance model for the formation of volcanogenic massive sulphides

Earth and Planetary Science Letters, 76 (1985/86) 123-134

123

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

[41

A simple magma-driven thermal balance model for the formation of volcanogenic massive sulphides J.R. C a n n 1 M.R. Strens 1 a n d A. Rice 2 i Department of Geology, Universi(v of Newcastle upon 7~vne. NE1 7R U (U. K.) 2 Department of Physics, University of Colorado, Boulder, Colo. (U.S.A.) Received February 4, 1985; revised version received June 27, 1985 A simple model is used to examine the balance of heat, water flow and temperature in a long-lived single-pass hydrothermal system heated by magmatic heat. The geometry of the system is based on mid-ocean ridge observations. Cold water percolates downward to the top of a shallow m a g m a chamber, is heated by conduction through a thin boundary layer, and discharges through a permeable fault zone, modelled as a bundle of narrow rough pipes. As heat input is increased, the model shows a catastrophic temperature transition at an exit water temperature of between 340 and 410°C depending on seafloor pressure, which in nature would probably be represented by surging flow and sudden changes in the specific volume of the circulating fluids. To generate a 3 million tonne sulphide deposit with 70% efficiency of deposition from water at 350°C within 4000 years would require a heat flux of 110 W m 2 from the m a g m a chamber for a mass flow rate of 140 kg s 1 if the plan area of the reacting part of the system is 2 km 2. The total heat input would be 3 × 1019 J. Under these conditions the thickness of the solid boundary layer between liquid m a g m a and circulating water will be about 10 m, and the integrated reactive water-rock ratio over the lifetime of the system will be about 30. Decreasing the water temperature to 250°C would require a heat flux of only 60 W m - 2 but the time to form a 3 million tonne deposit is increased to 33,000 years and the overall heat requirement is more than quadrupled.

1. Introduction This paper describes a new simple model for black smoker hydrothermal circulation which sets out to examine the thermal balance between heat source and water, the flow rates of water under different conditions and the time taken for large ore deposits to form on the ocean floor. The model assumes that, after a short initial period during which hot rock may be important, the main source of heat, while the system is at high temperatures, will be heat from crystallising magma in a shallow m a g m a chamber. The model does not aim to derive a flow geometry, but uses observational constraints to impose a flow regime and examines the thermal consequences of the flow. The active black smokers discovered so far at 21°N and 13°N on the East Pacific Rise are located within the extrusion zone, very close to the ridge axis, which is thought, from seismic evidence, to be underlain by a liquid magma chamber probably at a depth of about 1.5 km [1,2]. The 0012-821X/85/$03.30

~ 1985 Elsevier Science Publishers B.V.

temperature, exit velocity and chemistry of the vent fluids have now been recorded at 13°N [3] as well as at 21°N [4]. The temperature of the 21°N fluid and of the hot end-member components at other sites is about 350°C, the exit velocity is 0.5-5 m s 1 [5,6]. In all cases the upflow is from groups of narrow vents, associated with ridge-crest fissures which clearly become faults when they pass outside the zone of fresh lava flows [7,8]. Similar upflow regions are represented by the stockworks below Cyprus ore deposits, where they are seen to be associated with faults as pipe-like zones, tens of metres across, within which the water must have flowed in a network of interconnected fissures [9]. The target for this model is the production of 3 million tonnes of sulphide, chosen as representing a moderate-sized Cyprus ore deposit. However, the model can readily be extended to larger ore masses, and is limited only by the availability of enough magma to provide the heat for the system. The model itself can be used for any hydrothermal

124 circulation fuelled by magmatic heat, but the resuits derived in Table 1 are specific to the mid-ocean ridgeenvironment. 2. Construction of the model 2.1 Heat

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150 kg s ~ of 350°C water) is far greater than that available on a steady state basis from a short segment of mid-ocean ridge [10]. Heat must thus be extracted from a heat store, and there are two possible types of store, hot rock and magma. Though hot rock can contain considerable reserves of heat, this is unlikely to be readily available for high-temperature systems for two reasons. Firstly the heat must be extracted from the rock at high temperature, and this is only possible for a reasonable length of time if the fluid flows through a small-scale fracture matrix, with a spacing of a metre or less, as modelled by Lister [11]. However, the large ridge-crest-parallel faults form major discontinuities in the permeability of the ocean floor, and cause the flow to be channelled preferentially through these major fractures rather than through the crack matrix if one exists. Fracture flow can remove heat efficiently for a short time, but the fluid temperature will tend to fall rapidly as heat must be conducted to it from a progressively greater distance. Secondly the spacing of the major faults, with their associated circulation systems, at about 1-2 km apart, prevents the build up of large volumes of hot rock. If magma is the heat store, the magma chamber can be inflated gradually, and then the latent heat of crystallisation can be extracted through a conductive boundary layer at its upper contact. Convection within the magma chamber transports the heat very effectively to this upper contact, and will increase in intensity as the heat flux across the upper surface increases. For these reasons we have previously concluded [12] that magma chambers are the most likely source of heat for long-lived black smoker systems, and this alternative is certainly worth exploring further with a new model.

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The first element of the model is thus a liquid m a g m a chamber about 1.5 km below the seafloor (Fig. 1). We include in the model only the latent heat of solidification of the magma and not the heat produced on cooling after solidification for the following reasons. Firstly most of the crystals, which form in the convecting magma, will probably accumulate on the walls and floor of the magma chamber, and will undergo little cooling until the overlying magma solidifies. This may not occur until spreading has carried it well beyond the area covered by axial hydrothermal systems. Secondly if the axial magma chamber itself is episodic one might expect hydrothermal systems to penetrate the newly solidified hot rock. However, there is no geological evidence for high-temperature pervasive alteration of gabbros in ophiolites, and isotopic evidence suggests that the gabbros have reacted with only small volumes of water [13]. This evidence is consistent with the argument above that the flow is likely to be channelled in the major fractures, through which the heat can only be extracted over a long period of time at low temperatures. In our previous modelling of hydrothermal circulation in the ocean crust [14,15] the descending water very rapidly cooled the rock near to the fissure, so that shortly after initiation of convec-

125

tion, the water temperature at the base of the downflow was well below 100°C. For this simple model we have therefore taken the downflow (recharge) part of the system to be at 0°C throughout. The circulating fluid is therefore assumed to acquire all of its heat from the underlying magma, and the total heat input is determined by the volume of magma crystallised. The magnitude of heat input is thus independent of the extent of the downflow, and is not related to the spacing of such circulation systems along the ridge. 2.2. The discharge The fluid in the upflowing limb cools adiabatically as it ascends, the temperature profile in the uplimb being defined by the adiabat. This will follow either an isentrope, if decompression is gradual and reversible, or an isenthalp if decompression is sudden and irreversible. Bischoff and Pitzer [16] consider that the difference between isentropic and isenthalpic decompression is not significant, but suggest that the process is more likely to be isentropic in seafloor systems where abrupt expansion is improbable. We have therefore obtained the vertical temperature profile in the uplimb by calculating the entropy at the exit temperature and seafloor pressure, and have then derived the appropriate temperature for the pressure at each depth increment from the isentrope. Because the upflow pipes have a small diameter, as shown by the Cyprus examples, in relation to the potential area for recharge, upflow velocities are far greater than in the recharge zone, and hydraulic resistance to flow, due to the frictional drag of the rough walls, is predominantly in the upflow limb [15]. This means that the pressure drop due to friction can be defined by applying the turbulent pipe flow equation [17] to the upflow. This also means that the pressure at any given depth in the upflow limb is equal to the cold hydrostatic pressure, assuming uniform vertical distribution of frictional resistance in the uplimb. The pressure at the base of the hot limb is therefore not just the hot hydrostatic pressure, as it would be in a static system, but must also include the pressure difference needed to overcome frictional resistance to flow in the upflow limb. This extra term has been overlooked by Bischoff and Rosenbauer [18] in their calculation of pressure-

depth relationships in hot flowing systems, resulting in an overestimation of the depth for a given pressure, and hence of the maximum circulation depths. 2.3. Properties of seawater The model requires pressure and temperature dependent values of the specific heat capacity, specific volume and entropy of seawater over a P T range which is cut by the two-phase boundary for seawater. This boundary, which follows the critical curve as far as the critical point~ but then continues to higher temperatures and pressures, divides the single-phase field from the P T region in which seawater separates into a low-density fluid and a denser, more saline brine. This boundary has been defined by Bischoff and Rosenbauer [19], and PT-dependent values of seawater properties have been derived for the single phase field by Bischoff and Rosenbauer [18]. The only data that we know of for the two-phase field are adiabats of two-phase mixtures calculated by Bischoff and Pitzer [16]. It seems improbable that high-temperature hydrothermal systems, where the fluid ascends 1-2 km in 10-15 minutes, will be able to achieve equilibrium during upflow, and consequently phase separation is unlikely to occur. The fluid is thus likely to be a metastable single phase for which we also do not know of any density or thermodynamic data.

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126

specific heat capacity. We have compared out data, derived by corresponding states theory, with the data of Bischoff and Rosenbauer [18] for the single phase field and have found that they correspond fairly well. Values derived for integrated specific heat, specific volume and entropy are shown in Figs. 2, 3 and 4 respectively.

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Fig. 3. The specific volume of seawater, derived from pure water data [20] by using corresponding states theory. Contours labelled in m3 kg i The phase boundary is indicated by a solid line as far as the critical point and by a broken line beyond the critical point.

We have overcome this problem by deriving all of the required seawater properties from those of pure water [20,21] by using corresponding states theory. This is based on the principle that substances have the same properties at the same reduced pressure and temperature, where the reduced pressure and temperature are defined as P/P~ and T/T~ °K, and Pc and T are the critical pressure and temperature of the substance. In other words one is assuming that the only effect of the dissolved salt is to move the critical point. Wood and Quint [22] have shown that corresponding states theory is accurate for the calculation of

The model is defined by two steady-state equations. The flow equation equates the buoyancy force, caused by the hydrostatic pressure difference between the cold recharge and hot discharge columns, with the pressure drop due to friction in the discharge limb. Frictional forces in the recharge zone are neglected, since they are low compared with those in the upflow zone, where flow velocities are very much greater. The fluid is heated at the base of the system by an arbitrary heat input, which represents the heat flux through a solid conductive boundary layer between the underlying magma chamber and the hydrothermal fluid.

3.1. Heat balance equation Q = a u p c ( T - To) where Q (watts) is the heat flux from below, a is the cross-sectional area of the upflow, u and p are the mean velocity and density of the upflowing fluid. T is the water temperature at the base of the uplimb, and T0, taken as 0°C, is the temperature at the base of the downlimb. The specific heat capacity, c, is the integrated value over the range 7 " T0 for the pressure at the base of the system,

3.2 Flow equation

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Fig. 4. The entropy of seawater, derived from pure water data [20] by using corresponding states theory, Contours labelled in kJ kg t K ~.

The pressure drop due to friction in the uplimb is obtained from the equation for turbulent pipe flow [17]. This equation is strictly applicable only to incompressible fluids, but we consider that the changes in fluid density with time or any given position will be insignificant. Pressure drop due to friction in uplimb =

4pz f u2 d 2

127

where p is the mean upflow density, z is the depth of circulation, f and d are the friction factor and diameter of the upflow pipes. The friction factor, f, and diameter, d, of the upflow pipes are difficult to evaluate, because we do not know the roughness of the conduits, and reports of vent diameters range from 30 cm at the 21°N vents [10] to 3 cm at 13°N [7]. Since the feeder zones seen beneath Cyprus ore deposits are composed of a network of narrow anastomosing fissures, we have chosen to model the discharge zone as a bundle of narrow rough pipes, so that a = nTrd2/4 where n is the number of pipes comprising the discharge zone. If each pipe is taken to have a diameter of 3 cm and a friction factor (f above) of 0.02, then, at a seafloor pressure of 300 bars and for a discharge temperature of 350°C, it will pass fluid at a linear velocity of 2 m s ~ (the mean velocity observed for black smokers) with a mass flow rate of 1 kg s-1. A pipe of this diameter and roughness thus possesses the hydraulic resistance appropriate to black smoker conditions, and a bundle of 150 such pipes would provide the chosen mass flow rate of 150 kg s 1. The value of f corresponds to a roughness on the walls of the pipe of a few millimetres, which is consistent with geological observation. The flow equation equates the pressure drop due to friction to the hydrostatic pressure difference between the two limbs which drives the flow: U2

( O o - o)gz = 4Oz f T The mean downflow density, Oo, is the only parameter required for the downflow. Values for the flow velocity are not required since it is eliminated on combination of the two equations:

This equation is solved for a range of values of exit temperature, from which values of T, the bottom temperature, are derived by following the isentrope to the required pressure. PT-dependent values of specific heat, specific volume and entropy are used (Figs. 2, 3 and 4). 4. The results from the model

The model determines the relationship between heat input and the resultant hot spring heat out-

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put, We have considered the heat input in terms of a heat flux, and have chosen an area of 2 km 2, since the convective circulation is limited at midocean-ridges by the ridge-crest parallel faults about 1 km from the axis, and is likely to extend for a similar distance along the ridge axis. Choice of another value would affect only the boundary layer thickness in the following analysis. The curves obtained for 2 km deep circulation and a range of seafloor pressures (Fig. 5) show that the relationship between the heat flux and the exit water temperature is complex and non-linear. As the heat flux at the base of the system is increased, the temperature of the outflowing water increases at first steeply, but then more gradually, because of the decreasing density of water (bringing about greater flow velocity and hence greater mass flow) and the increasing specific heat capacity. However, when temperatures reach 340-410°C the curves undergo a sharp inflexion, where the sharpness and the temperature of the in flexion depend on pressure. As a hydrothermal system passes this in flexion it undergoes a catastrophic transition from low to

128 high temperature, as is discussed below. The possible nature of this transition is discussed from three different standpoints. The first assumes, as the model does, that heat input can be varied independently of water temperature. The second considers the possibility that, when rapid changes in heat input or water temperature occur, the thickness of the conductive boundary layer between water and magma cannot change rapidly and will remain constant. The third examines the possibility that the system is no longer steady state, but will move into unstable surging flow.

4.1. Independent heat input The inflexion can be explained by considering the variations in specific volume and specific heat capacity and the form of the isentropes in the PT-field close to the two-phase boundary. For the metastable single phase, which we are considering, this curve is effectively the critical curve and its extrapolation to higher temperatures and pressures. Figs. 2 and 3 show that sudden and large changes occur in specific volume and specific heat as this boundary is crossed. The very high values for heat input at the tip of the inflexion result from the large increase in specific heat capacity and very marked decrease in density as the phase boundary is approached. The tip of the inflexion coincides with the temperature of the phase boundary at the seafloor. This can be explained by examining the form of the isentropes close to the phase boundary in Fig. 4, which shows that when an isentrope, which defines the adiabat of the rising fluid, meets the phase boundary, it ihen follows this boundary up to the seafloor. On the high-temperature side of the phase boundary an increase in the fluid temperature causes the density to drop further, but less rapidly than before, and the specific heat capacity starts to decrease. The declining heat capacity means that the circulatory system can no longer carry the heat load, unless there is a compensatory increase in mass flow requiring higher convection velocities, which in turn require a sufficient drop in density. In the case of seawater the density changes cannot compensate for the decrease in heat capacity, with the result that the system cannot continue to carry the heat load. The curves show that, in theory,

increasing the fluid temperature beyond the inflexion requires a decreasing heat input. Clearly this is physically impossible, and the section of the curve a t temperatures higher than that of the inflexion is not accessible on increasing heat input. Once the inflexion is reached the water temperature will j u m p catastrophically and then drop back, as it attempts to reach a point on the curve at much higher temperatures where the same heat input would be required as at the inflexion. This can happen very suddenly as no additional heat flux is necessary for the water to reach very high temperatures. The magma temperature will limit the maximum temperature attainable by the fluid. The system will therefore show episodic behaviour at this point, with catastrophic transitions between the higher and lower temperature states.

4. 2. Control by' boundary layer thickness The heat flux is conducted from magma to h y d r o t h e r m a l water through a conductive boundary layer of hot rock. The heat flux per unit area, J, will depend on the temperature of the magma, Tm, which will be approximately constant, the thermal conductivity of the rock, K, also nearly constant, the temperature of the water at the base of the circulation, T, and the thickness of the boundary layer, h:

J=K(T m-T) h

Wm

2

For example, for a seafloor pressure of 250 bar and exit temperature of 385°C, where J = 182 W m 2 T = 437°C (derived from isentrope), Tm = l l00°C and K = 2 W m -1 K l, the boundary layer thickness, h, is 7.3 m. A thickness of less than 10 m may seem small, but it is consistent with boundary layer thicknesses between molten lava and cracked rock of less than one metre in lava flows in Iceland [23]. In the model the boundary layer thickness is assumed to be variable, since a value for h corresponds to each pair of values of J and T derived in the model. However during a catastrophic transition, when T rises suddenly, ( T m - T) decreases and J will also decrease unless the boundary layer can thin suddenly to allow the temperature gradient to be maintained. Thinning would be caused by cracking of the upper side of

129

the boundary layer, but a sudden increase in temperature would act to inhibit cracking rather than promote it. Sudden thinning to accommodate a constant heat flux is therefore unlikely to occur. An alternative approach is to suggest that, at times of catastrophic transition, the boundary layer thickness, h, will remain constant rather than be instantly variable, as is assumed in the model and in the discussion so far. The path relating water temperature to heat flux would not then be vertical, but would move rapidly across the figure as the heat flux diminished, along a line of constant h from one part of the steady-state curve to another. Fig. 6 shows that, for 250 bar seafloor pressure, this path intersects the steady-state curve at 465°C exit temperature. The water temperature will thus j u m p catastrophically along the line A B from 385°C to 465°C. The temperature can then drop back along the steady-state curve until it reaches the point at which the boundary layer thickness starts to decrease rapidly (Fig. 7). At this

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point (400°C), a second catastrophic transition will occur along CD (Figs. 6 and 7) to 382°C, again along a path of constant boundary layer thickness. It can be seen in Figs. 6 and 7 that we have a hysteresis loop, with two catastrophic transitions, and that the system it represents will show episodic behaviour as it passes from the low to the high temperature state and back again.

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Boundarylayerthickness(m) Fig. 6. The relationship between heat input and exit water temperature at 250 bar seafloor pressure. The catastrophic transition at A to a higher temperature is represented by the broken vertical line for the ideal condition of steady heat flux. The straight line A B represents the relationship for a constant thickness boundary layer with diminishing heat flux at higher water temperatures. A second catastrophic transition occurs from C to D, thus forming a loop around which the fluid temperature may cycle. Values marked on the curve are of boundary layer thickness in metres.

The calculated curves (Fig. 5) are based on the assumption of steady flow during an episode of hydrothermal circulation. Another possibility for the behaviour that may ensue when the first catastrophic transition is reached is that the flow may become unsteady on a short time scale. Instead of undergoing a smooth, rapid transition to another point on the curve, the system may respond to increased heat input by alternately surging forward, stripping heat from the system, but lowering its temperature, and then slowing down, while the water temperature builds up again. Such surging would be different from the regular cycling

130 of the hysteresis loops d e s c r i b e d above. R a t h e r it w o u l d show a chaotic pulsing of surges and ebbs, with the overall heat i n p u t / w a t e r t e m p e r a t u r e relationship c o r r e s p o n d i n g to a p a i r i n g that does not lie on the a p p r o p r i a t e curve of Fig. 5. Such a system would be difficult to describe in terms of this model, but would be a clear physical possibility, and w o u l d be likely to show very c o m p l e x b e h a v i o u r once,the t e m p e r a t u r e of the c a t a s t r o p h i c transition has been passes.

5. Natural magma-driven systems T h o u g h the model p r o b a b l y describes natural systems r e a s o n a b l y well there is one i m p o r t a n t p o i n t of divergence between the model and n a t u r a l m a g m a - d r i v e n systems. The model treats the water as being c o n t i n u o u s l y well-mixed and as receiving its heat input in a single addition. In n a t u r e the heat transfer and water mixing will be a c o m p l e x process. I n s t e a d of receiving all of its heat directly by c o n d u c t i o n , as in the model, the water will, in nature, be heated to a large extent by small-scale convection of rising p l u m e s of very hot water m i x i n g in with overlying cold water. The very hot water will have been heated directly by c o n d u c tion, but most of the water will, at a n y one time, be receiving its heat by convection mixing. This has the i m p o r t a n t consequence that the water directly in c o n t a c t with the u p p e r surface of the b o u n d a r y layer will be significantly hotter than the bulk water t e m p e r a t u r e at the base of the circulation. The m a g n i t u d e of the t e m p e r a t u r e difference will d e p e n d on the hydrological p r o p e r t i e s of the overlying rock, which are p o o r l y con-

strained. H i g h e r t e m p e r a t u r e s will not only inhibit cracking of rock, b u t m a y also lead to local phase s e p a r a t i o n into highly saline brines and fresh water. Such phase separation, which is much more likely here than in the upflow since the fluid m a y pass t h r o u g h this zone quite slowly, could result in the a c c u m u l a t i o n of local pools of dense brine in the hottest part of the convecting system. The f o r m a t i o n of such h y p e r s a l i n e brines could account for the variable c o m p o s i t i o n s seen in hyd r o t h e r m a l brines [3], as i n d i c a t e d by Bischoff and R o s e n b a u e r [19]. In addition, the very high temp e r a t u r e s in the brines will act to inhibit cracking of the u p p e r part of the b o u n d a r y layer, a n d will thus u l t i m a t e l y limit the t e m p e r a t u r e reached by the bulk water. H y p e r s a l i n e fluid inclusions have been found in deep levels of h y d r o t h e r m a l systems in C y p r u s [24]. In natural systems it is also interesting to ask whether the m a g m a can s u p p l y the heat l o a d required of it. W e envisage heat being t r a n s p o r t e d to the base of the h y d r o t h e r m a l convective system by convection within the m a g m a c h a m b e r accelerated by the lowered t e m p e r a t u r e of the a p p r o p r i a t e p a r t of the m a g m a c h a m b e r roof. Just as convection is accelerated by a heat source at the base of the fluid, so it is also accelerated by a heat sink at the top of the fluid. The heat required for the overlying system would c o m e from the latent heat of fusion of the m a g m a ( a b o u t 10 9 J m 3), released by partial crystallisation as the m a g m a flows p a s t the heat sink. A s s u m i n g 1 5% solidificaiton as the m a g m a passes the heat sink, flow velocities of 1 m m s 1 w o u l d be a d e q u a t e to sustain the heat flux of 2 × 10 5 k W required by the h i g h - t e m p e r a -

TABLE 1 Water flow, heat flux, sulphide deposition, magma crystallisation and water/rock ratio for hydrothermal water temperatures of 200-400°C for the system modelled, at 250 bar seafloor pressure Exit water temp. (°C)

Mass flow rate (kgs-I)

Linear flow velocity (ms 1)

Heat flux Fe conc. for this in fluid mass flow (ppm) rate (kW)

200 250 300 350 400

99 114 128 140 107

1.1 1.3 1.5 1.9 6.5

0.82 )<105 6 1.21 )<105 17 1.67 )<105 45 2.29)<105 115 3.11)<105 305

Water mass for 3 Mt deposit (70% eff.) (kg) 3.3×1014 1.2)<1014 4.4×1013 1.7×1013 6.5 X 1012

Time for 3 Mt deposit (70%elf.) (yr) 105,000 33,000 11,000 4,000 2,000

Total heat required for 3 Mt ore mass (70% eff.) (J) 27 ×1019 13 ×1019 6 XIO 19 3 ×10 ~9 1.9)< 10 ~9

Vol. of Magma magma to cryst, rate supply heat (km kyr-1) (70% eff.) (km3) 270 130 60 30 19

2.6 3.9 5.4 7.5 9.5

Integrated mass W/R (0.2 km~ reaction vol.) 550 200 70 30 10

131 ture hydrothermal flow. Part of the precipitated solid would accrete to the roof of the magma chamber to form the so-called isotropic gabbro section at the upper part of the ophiolitic gabbros, and the rest would be transported away as suspended particles in the magma to be deposited elsewhere in the magma chamber. Just as much of the heat transfer in the overlying water will be by rising hot plumes, so heat transfer in the magma will be accelerated by small-scale convection as drops of cold magma sink into the upper levels of the magma chamber.

6. Formation of sulphide deposits The hydraulic properties of the upflow zone of the model were chosen to give a linear flow velocity of about 2 m s-1 and a mass flow rate of about 150 kg s -1 for an upflow water temperature of 350°C, to be consistent with observations of black smokers (see section 1). Using these hydraulic properties it is possible to use the model equations to calculate mass flow rates and linear flow velocities at different temperatures, although it should be pointed out that these values are model dependent. Table 1 shows that the linear flow velocity varies by a factor of 6 and the mass flow rate by a factor of 1.4 over the temperature range 200-400°C. Similarly the heat flux can be shown to vary from 0.8 to 3.0 × 105 kW over the same temperature range. These figures can be linked to the formation of ore deposits if the concentration of dissolved pyrite (the major component of the sulphide deposits) can be related to water temperature. Consideration of experimental results [25,26] and observations of natural hydrothermal waters [3,5] suggests and exponential relationship in which solubility increases by a factor of rather over 2.5 for each 50°C rise in water temperature. The appropriate solubilities are shown in Table 1. The deposition of sulphide from the hydrothermal solutions will not normally be perfectly efficient. Though the warm springs at the Galapagos spreading centre are the result of subsurface mixing of hot brine and cold seawater [27], so that sulphides are deposited with close to 100% efficiency, the black smokers themselves vent a high proportion of their sulphides to the ocean. Some precipitation occurs in the chimneys and there is

also clearly some subsurface mixing, to judge from the warm water springs closely associated with the black smokers. Unfortunately there has been no assessment of the relative volumes of hot and warm water in black smoker fields which would give a guide to efficiency. For this section, we will assume 70% efficiency in the production of a medium-sized, 3 million tonne sulphide deposit. The values given in Table 1 should be adjusted proportionately if any other value for efficiency is preferred. From the solubility figures and the assumed efficiency of precipitation, the mass of water required to generate a 3 million tonne sulphide deposit can be calculated. Because of the strong variation of sulphide solubility with temperature, 50 times more water is required at 200°C than at 400°C (Table 1). Using the earlier figures for heat flux and mass flow rate of water, the total heat required can be shown to vary by a factor of 14, and the time necessary to form the ore deposit by a factor of 50 over the same temperature range. Clearly if heat supply is limited, it is far more effective to use it at high temperature to generate an ore deposit than to operate at low water temperatures. Since the heat required is derived entirely from crystallisation of m a g m a in the model, the volume of magma required can be calculated, taking latent heat of solidification of magma as 4 × 10 S J kg and density of magma as 2500 kg m 3. On this basis each km 3 of magma yields 10 ~8 J of latent heat. The volume of magma required ranges from 270 km 3 at 200°C water temperature to 19 km 3 at 400°C (Table 1), a factor of 14. The solidification of the magma would not take place solely beneath the hydrothermal system. Removal of heat from the upper surface of the magma chamber by intense hydrothermal circulation will rapidly enhance convection within the magma chamber and transport magma from far away towards the zone in which heat is being extracted. Similarly the crystals forming in the magma will not all be deposited at the site of circulation, but will be spread over a much larger area. Rates of accumulation of crystals will still be rapid. For water temperatures of 3500C magma must crystallise at 7.5 km 3 per 1000 years and if the solid deposit is spread over say 10 km z, this requires the thickness of the deposit to grow by 0.8 m per year, produc-

132 ing an eventual thickness of 3 km in 4000 years. Episodes of such rapid crystallisation would solidify magma far faster than it is supplied on a continuous basis (0.3 km ~ per 1000 years per kilometre of ridge crest at a 1/2-spreading rate of 3 cm yr-1). Episodes of vigorous convection and circulation must thus alternate with periods of quiescence while the magma chamber is replenished. What does the circulation pattern we propose indicate about the water-rock ratio integrated over the lifetime of the hydrothermal system? The whole system contains about 4 km 3 or 12,000 million tonnes of rock, through which, taking the values for 350°C, 17,000 million tonnes of water pass, giving an overall water-rock ratio of 1.4. However, most of that rock will be rapidly cooled by circulating water and will then no longer play any significant part in chemical reactions relevant to ore genesis. Field evidence from Cyprus indicates that it is only in a zone about 100 m thick above the magma chamber that the water becomes heated and reacts with the rock [24]. Here, in the lowest part of the sheeted dyke complex just above the gabbro, which represents the solidified magma chamber, the rock is extensively hydrothermally altered and leached. The mass of rock within which these reactions occur is about 600 million tonnes, and the effective high-temperature waterrock ratio then becomes about 30 for 350°C water, and ranges from 550 to 10 over the temperature range 200-400°C (Table 1). These numbers are much greater than those of 1-5 calculated for black smoker systems from their chemistry [3,27,28], and are consistent with the observations that known black smokers are very young and are associated with very small sulphide deposits. A mature black smoker system associated with major sulphide mineralisation would be expected to have very different chemistry as will be shown elsewhere [29]. 7. Conclusions This simple model is able to describe many of the essential features of the thermal balance of volcanogenic hydrothermal systems when the main source of heat is magma. In the present application the model was tuned hydrogeologically using observations from modern black smokers and the

Cyprus ophiolite, and was calculated using observed sulphide solubility in fluids of seawater salinity, but it could readily be tuned and calculated with other data as appropriate. Essentially the features shown by the model can be divided into those dominant below the inflexion temperature of 340-410°C and those dominant above. In the low temperature region, increasing heat input brings about increasing water temperature, but also a much greater solubility of sulphide in the hydrothermal solution. The result is that a rise in temperature of the water from 200-400°C brings about a fourteen-fold drop in the volume of m a g m a required to produce a 3 million tonne sulphide deposit and a fifty-fold drop in the mass of water needed to carry the sulphide, and in the time needed to form the deposit. All other things being equal, larger deposits are thus much more likely to form in situations where high-temperature circulation is possible: where, for instance, the upflow plumbing has a fair hydraulic resistance, preventing the very rapid flow of large volumes of cool water through the system. Formation of a major ore deposit would be accompanied by crystallisation of a large volume of magma in a very short time (see Table 1). Episodes of such rapid crystallisation would lead to sudden changes in lava composition--either from more basic to more acid or, if the magma chamber became totally crystallised, from any previous composition to very basic as new magma restarted the m a g m a chamber. They would also lead to very rapid accumulation of gabbro in magma c h a m b e r s - - f a r faster than is currently recognised. When the water temperature reaches the inflexion temperature the system undergoes a sudden catastrophic transition. The exact nature of the transition is not clear, but it involves a very rapid increase in temperature of the water in the system. This may lead to a more or less regular cycling, with alternate rising and falling temperature of the outflowing water, or to a more chaotic pattern of surging flow with pulses of hot and less hot water. Cycling or surging will involve sudden changes of specific volume of water and these will lead to pressure pulses that may fracture the surrounding rock. Evidence for the occurrence of catastrophic surging at water temperatures of rather more than

133

400°C should be sought in the rock record. The onset of this complex behaviour marks the upper limit of the exit temperatures that can be attained, this maximum temperature being particularly well defined by the model. The reasons for this are apparent in Figs. 4 and 5. Fig. 4 shows that, close to the phase boundary the isentropes converge from both sides on to the boundary, thus focussing the adiabats, so that similar exit temperatures result from a wide range of bottom temperatures. For example, the exit temperature of 385°C at 250 bar seafloor pressure can result from bottom temperatures ranging from about 405-465°C. This effect is also apparent at temperatures approaching the inflexion temperature in Fig. 5 where a wide range of values of heat input result in a narrow range of exit temperatures. The model thus shows that the maximum exit temperatures are controlled by the physical properties of seawater and are virtually independent of the magnitude of the heat supply and the depth of circulation.

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Acknowledgements This work was supported by N.E.R.C. grant GR3/5073. We would like to thank James L. Bischoff for his help, particularly with the phase relations of seawater. The manuscript was much improved after constructive reviews by Janet L. Morton and Michael J. Mottl. Christine Jeans drew the diagrams, and Elizabeth Walton typed the manuscript.

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References 1 I. Reid, J.A. Orcutt and W.C. Prothero, Seismic evidence for a narrow zone of partial melting underlying the East Pacific Rise at 21°N, Geol. Soc. Am. Bull. 88, 678-682, 1977. 2 B.T.R. Lewis and J.D. Garmany, Constraints on the structure of the East Pacific Rise from seismic refraction data, J. Geophys. Res. 87(B10), 8417-8425, 1982. 3 G. Michard, F. Albar/~de, A. Michard, J.-F. Minister, J.-L Charlou and N. Tan, Chemistry of solutions from the 13°N East Pacific Rise hydrothermal site, Earth Planet. Sci. Lett. 67, 297-307, 1984. 4 J.M. Edmond, K.L. Von Damm, R.E. McDuff and C.I. Measures, Chemistry of hot springs on the East Pacific Rise and their effluent dispersal, Nature 297, 187-191, 1982. 5 J.M. Edmond, Hydrothermal activity at mid-ocean ridge axes, Nature 290, 87-88, 1981. 6 D.R. Converse, H.D. Holland and J.M. Edmond, Flow rates in the axial hot springs of the East Pacific Rise

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