permeability changes due to mineral diagenesis in...

$: Permeability changes due to mineral diagenesis in ...seismo.berkeley.edu/~manga/fontaine.pdfPermeability changes due to mineral diagenesis in fractured crust: implications for hydrothermal$
Permeability changes due to mineral diagenesis infractured crust: implications for hydrothermal circulation at

mid-ocean ridges

Fabrice Jh. Fontaine a;*, Michel Rabinowicz a, Jacques Boule©gue b

a Laboratoire de Dynamique Terrestre et Planetaire, UMR 5562, Observatoire Midi-Pyrenees, 14 Avenue Edouard Belin, 31400Toulouse, France

b Laboratoire de Geochimie, Physicochimie et Fluides Geologiques, UPMC, UPRESA 7047, 75252 Paris Cedex 05, France

Received 19 April 2000; accepted 26 October 2000

Abstract

The hydrothermal processes at ridge crests have been extensively studied during the last two decades. Nevertheless,the reasons why hydrothermal fields are only occasionally found along some ridge segments remain a matter of debate.In the present study we relate this observation to the mineral precipitation induced by hydrothermal circulation. Ourstudy is based on numerical models of convection inside a porous slot 1.5 km high, 2.25 km long and 120 m wide, whereseawater is free to enter and exit at its top while the bottom is held at a constant temperature of 420³C. Since the fluidcirculation is slow and the fissures in which seawater circulates are narrow, the reactions between seawater and the crustachieve local equilibrium. The rate of mineral precipitation or dissolution is proportional to the total derivative of thetemperature with respect to time. Precipitation of minerals reduces the width of the fissures and thus percolation. Usingconventional permeability versus porosity laws, we evaluate the evolution of the permeability field during thehydrothermal circulation. Our computations begin with a uniform permeability and a conductive thermal profile. Afterimposing a small random perturbation on the initial thermal field, the circulation adopts a finger-like structure, typicalof convection in vertical porous slots thermally influenced by surrounding walls. Due to the strong temperaturedependence of the fluid viscosity and thermal expansion, the hot rising fingers are strongly buoyant and collide with thetop cold stagnant water layer. At the interface of the cold and hot layers, a horizontal boundary layer develops causingmassive precipitation. This precipitation front produces a barrier to the hydrothermal flow. Consequently, the flowbecomes layered on both sides of the front. The fluid temperature at the top of the layer remains quite low: it neverexceeds a temperature of 80³C, well below the exit temperature of hot vent sites observed at black or white `smokers'.We show that the development of this front is independent of the Rayleigh number of the hydrothermal flow, indicatingthat the mineral precipitation causes cold, diffusive vents. Finally, we present a model suggesting that the developmentof smokers is possible when successive tectonic/volcanic events produce a network of new permeable fissures that canovercome the permeability decrease caused by mineral precipitation. Such a model is consistent with recent seismic datashowing hydrothermal vents located at seismologically active ridge segments. ß 2001 Elsevier Science B.V. All rightsreserved.

Keywords: hydrothermal vents; convection; porosity; diagenesis

0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 3 3 2 - 0

* Corresponding author.

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Earth and Planetary Science Letters 184 (2001) 407^425

www.elsevier.com/locate/epsl

1. Introduction

Since the discovery of the ¢rst discharge zoneof hot water along the Mid-Atlantic Ridge(MAR) at the Trans-Atlantic Geotraverse(TAG) site [1], numerous scienti¢c investigationsas well as submersible campaigns (ALVIN) ordrill projects (Ocean Drilling Project) have beenconducted to discover new sites and to under-stand the physical, chemical and biological pro-cesses involved in the development of hydrother-mal activity. The discovery of vent sitesdischarging hot £uids is the best evidence of hothydrothermal activity at ridge crests. The mostspectacular examples, called smokers, exhibit tem-peratures as high as 200^350³C. These smokersare the direct manifestation of £uid venting onthe sea£oor. Seawater penetrates a permeablesystem of ¢ssures maintained open by the con-traction of the surrounding diabase under stressat ridge crest. Below the top cold horizons, seis-mic data reveal the existence of magma chambers[2] that supply the heat transported by the hydro-thermal convection. Along the 3% of the well-mapped global spreading center [4], hot hydro-thermal vent ¢elds are scarce [3]. At slow spread-ing axes, the location of hydrothermal activityseems to be controlled by well-established crustalfractures like at the TAG site. Hydrothermal sitesappear as individual long-lived (103^104 years)`mounds' up to several hundred meters in diame-ter.

The ¢rst investigations of the ridge axis alongthe MAR tended to locate one hydrothermal siteevery 150^175 km [4]. More recent studies [6] onthe active ridge segment at the Azores TripleJunction showed that hydrothermal sites can bemuch more frequent, i.e., one site every 20^30 km,and intimately linked to ridge segmentation. Atfast spreading axes, hydrothermal sites developalong the wall of narrow (about 100 m) axial cal-dera (like at 9³N along the East Paci¢c Rise(EPR)). Their characteristic size is about a fewtens of meters and their separation length is sev-eral meters to several tens of meters. Typically,they last no more than 10^100 years. Neverthe-less, they are numerous (45 between 9³27PN and10³N). Volcanic activity can interact with their

evolution. For example, the shorter-lived sitesare thought to be the result of sill injection [5],while the older ones are associated with shallowdepth of the axial magma chamber. Thus, at fastspreading ridges, hydrothermal activity is inti-mately associated with volcanic activity. At inter-mediate spreading ridges, hydrothermal activityranges from long-lived, fault-bounded, TAG-likehydrothermal systems (e.g., Explorer ridge) toneo-volcanic hydrothermalism (several segmentsof Juan de Fuca Ridge). Furthermore, many sub-marine campaigns reveal a di¡use hydrothermalactivity with very low-temperature emanationsoozing from the crust [5]. When the emanationsare geographically associated with mineral depos-its, we infer that the hydrothermal system hasdied. On the other hand, when no minerals areobserved, the venting £uid has already precipi-tated its dissolved minerals inside the crust be-cause of cooling.

Faced with such complex geological problems,numerical models are very helpful to better under-stand the processes involved. Models assuminghydrothermal £ow in a porous medium with aquasi-isotropic permeability distribution allow es-timates of heat and mass £uxes at the segmentscale [7,8]. Assuming a basal temperature of500³C, Wilcock [9] found asymptotic exit temper-atures consistent with black smokers (sul¢de-rich hydrothermal vents with temperatures be-tween 350 and 400³C). He argued that ventswith exit temperatures lower than those of blacksmokers develop if the £ow crosses low-per-meability crust layers in which the e¡ectivelocal Rayleigh number is reduced. Nevertheless,numerous geological investigations of the sea£oornear vent sites show that their localization is re-lated to precise geological features such as bathy-metric highs [10] or deformed volcanic blocksnear non-transform o¡sets [6]. Some authors lo-cate them at the intersections of fault and ¢ssuresystems [11]. Furthermore, it is well known thatanimal colonies develop near mineral depositslinked to hydrothermal activity. They often occuron top of fault and ¢ssure systems with high per-meability.

Most numerical investigations consider heattransport due to convection in a slot with adia-

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F.J. Fontaine et al. / Earth and Planetary Science Letters 184 (2001) 407^425408

batic walls. Recently, Cherkaoui et al. [12] hy-pothesized that the chronic plume generated dur-ing the 1993 diking event along the Coaxial Seg-ment of the Juan de Fuca Ridge was associatedwith the convective cooling of a 3^5 m wide dikeintruded into a 10311^10312 m2 cold porous layer.This study shows that vertical advection limits thethermal e¡ects of the dike within a few meters ofthe dike margins.

A better approach is to address the modeling ofconvection in a slot surrounded by conductivewalls. Such investigations [13] emphasize the roleplayed by the heat absorbed by the walls. This`horizontal' heat transfer creates a thermal bound-ary layer inside the wall. Its width increases withtime, delaying the onset of convection. Rabino-wicz et al. [14] developed a model of convectionin a porous slot surrounded by conductive imper-meable walls, with realistic equations of state andRayleigh (Ra) numbers, where seawater entersand leaves the porous medium at its top. Convec-tion occurs as narrow ¢ngers [14]. For Ra6 8000,a thick upper thermal boundary layer develops atthe top of the system, while a much thinner onesits on the bottom. Upwelling plumes are able topierce these cold layers for Ras 8000, while theyare bu¡ered for Ra6 8000. The asymptotic exittemperature of 270³C is similar to that found byWilcock [9] with adiabatic walls, assuming a basaltemperature of 420³C.

At slow spreading centers, hydrothermal activ-ity is driven by magmatic intrusions up to severalkilometers in length. The sloping of the basal iso-therm due to the three-dimensional geometry ofthe magmatic intrusions leads to a single-celled£ow pattern with upwelling £uids exiting at370³C. Rabinowicz et al. [14] inferred that blacksmokers are likely to develop where hydrothermalsystems are associated with a tilt of the lowerinterface, while white smokers (sul¢de-poor sili-ca-rich hydrothermal £uids exiting at temperatureof 220^350³C) tend to occur above horizontal sys-tems.

We see that hydrothermal systems can generateeither white or black smokers. This does not ex-plain why high-temperature vents are so rare [3].The physical conditions leading to the cold hydro-thermal vents [5] remain poorly understood. In

the present paper, we show that the sealing ofthe fracture network due to the precipitation ofhydrothermal minerals (anhydrite and sul¢des)can lead to cold vents. In Section 2, we describethe model for hydrothermal convection. We alsogive the equations of state to compute the rate ofmineral precipitation/dissolution during convec-tion and derive rules relating the evolution of per-meability to diagenesis inside the fault. In Section3, we describe the evolution of the £ow, temper-ature, and permeability ¢elds resulting from theresolution of the convective equations in a systemwhere permeability evolves with the diageneticprocess. The modeling suggests that the diagenesisprevents the development of hot vents. We shallshow that this situation is quite general. Signi¢-cantly, it is also independent of the Rayleigh num-ber of the hydrothermal system. Finally we dis-cuss the processes capable of overcoming thedrastic reduction in permeability caused by dia-genesis. Such processes are necessary conditionsfor generation of hot vents.

2. The model

2.1. Physical model

2.1.1. Overall descriptionTo account for the geometry of a kilometer-

high hydrothermal system con¢ned to the sheeteddike complex, we consider a faulted zone parallelto the ridge crest bounded by two walls of mas-sive diabase (Fig. 1). The fault is identi¢ed with a`porous slot' containing a system of ¢ssures par-allel to the fault axis, with a sub-millimeter aper-ture N and separated by meter-scale (spacing f)diabase walls [13,15]. In our model, the xz planeis the fault plane, with the along-strike x axis andthe vertical z axis. The y coordinate represents thedistance to the central plane of the fault. Due tothe symmetry of the system about this central(y = 0) plane, we resolve the equations only inthe half-space yv 0. The height of the slot isH = 1500 m, its length is L = 2250 m and its widthis l = 120 m. This con¢guration determines thee¡ective permeability keff and fracture porosity Oof the network as a function of N and f :

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F.J. Fontaine et al. / Earth and Planetary Science Letters 184 (2001) 407^425 409

keff � N 3

12f�1�

O � Nf

�2�

If N= 0.1 mm and f = 1 m, then keff = 10313 m2

while if N= 1 mm, keff = 10310 m2 ; O ranges be-tween 1034 and 1033. Although the e¡ective per-meability keff is the only free parameter in ourmodel, it is notoriously di¤cult to measure insitu. Nevertheless, this range of e¡ective perme-abilities includes the lower bound of crustal per-meability of 6U10313^6U10312 m2 estimatedfrom a potential £ow model for the Juan deFuca hydrothermal vents [16,17]. Moreover, thee¡ective permeability of diabase is about 10318

m2 [18], i.e., as many as ¢ve orders of magnitudesmaller than for the fracture network. The perme-ability of the meter-thick walls between two adja-cent ¢ssures is thus negligible. Since the ¢ssuresare essentially parallel to the dike plane, the per-colation in the y direction is also negligible. Con-sequently, the circulation is two-dimensional andcon¢ned to the xz plane.

The fracture system probably crosses the pillow

lavas and the sheeted dike complex over a heightof H = 1.5 km. Large cavities that will ultimatelyform the stockwork are likely to exist where thefracture system crosses the volcanic extrusives.According to models and data, the e¡ective per-meability in the discharge zones inside the pillowlavas before the formation of mineral depositsreaches 1039 m2 [9,17]. Consequently we considerthis upper domain to have a quasi-in¢nite iso-tropic permeability.

At the top of the slot, seawater is free to enterat a temperature T of 2³C and to leave with a zerovertical temperature gradient (DT/Dz = 0) [9]. Inour model, the bottom of the slot is held at aconstant temperature of 420³C. This temperatureis close to the maximum paleo-temperatures ofinclusions found in the lower part of the sheeteddike complex which are shown to range between220 and 430³C [15,19]. It is also colder than thetemperature needed to generate a permeable net-work inside diabases [14]. Hydrothermal £ow athigh temperatures in the range 420^600³C areknown to occur at the ridge crest [15], but theyhave been associated with the circulation of crit-ical £uids inside the crack network of the iso-tropic gabbro layer generated during cooling. Ac-cording to Rovetta [18], the permeability of this

Fig. 1. Geometry of the system. Flow and temperature ¢eld are symmetrical on both sides of the y = 0 axial plane. Equations areresolved in the half-space yv0. L = 2.25 km, l = 0.75 km, H = 1.5 km; the thickness of the permeable slot is 120 m.

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layer is about 10318 m2. Thus, the associated hy-drothermal £ow has a low Rayleigh number andthe circulation must be very slow. In the upwell-ing limbs of this hydrothermal £ow, the critical£uid precipitates silica particles [20,21] triggeredby opal colloids [20]. Since the £uid £ow is veryslow in the crack network of the gabbro layer,opal transforms into quartz via agglomerationof the colloids [22]. This occludes the crack net-work and thus destroys the hydrothermal circula-tion. This sealing e¡ect of silica is very e¤cientfor the isotropic gabbro layer [21].

The interaction of this high-temperature hydro-thermal system with that in the sheeted dike com-plex is naturally weak because the critical point ofseawater is about 420³C. At this temperature, twophases coexist : a brine and a fresher component[23]. This is corroborated by the measured saltconcentration of the inclusions at temperaturesbetween 220 and 430³C ranging from 10 up to140 g/l [24]. Due to the relative buoyancy betweenthe two phases, the drops of `fresh water' moveupward, above the interface, and mix with sea-water. Consequently, the region below the inter-face ¢lls completely with brine.

At the interface, surface tension develops be-tween the seawater and the brine. The surfacetension of a liquid cliq enriched or depleted inNaCl as compared to that of seawater csw de-pends on the partial pressure of water above re-spectively the liquid and seawater at a given tem-perature. A good approximation is that of regularsolutions [25]:

c liq3c sw � 13T

T liqc

� �3=2

3 13T

T swc

� �3=2

�3�

where Tliqc and Tsw

c are the critical temperatures ofthe liquid and seawater respectively. For liquidswith salinity higher than seawater, we haveTliq

c sTswc , which leads to cliq scsw. This approx-

imation is valid for interfaces of curvature withradius larger than 10 Wm. There is an inverse pro-portionality between the stresses generated by sur-face tension and the curvature of the interface.Since the curvature of the interface in the direc-tion orthogonal to the sheeted dikes is extremelysmall (i.e., proportional to the ¢ssure width), the

surface tension generates quasi-in¢nite stresses atthe boundary. These stresses inhibit the deforma-tion of both £uids at the interface. Such an e¡ectis equivalent to a step increase of the viscosity ofthe £uids at the interface and yields to a strati¢edconvection [26]. As a result, the 420³C interfacebetween the brine and seawater corresponds to adeep horizon within the sheeted dike complex. Weidentify the bottom of our slot with this 420³Cinterface, but this is not necessarily the bottomof the sheeted dikes.

We assume that the 420³C interface remains ina steady position. This is consistent with the factthat heat is steadily provided by the magmachamber during the early phase of activity ofthe hydrothermal system. Clearly, when this heatsource is exhausted, the transient cooling of thecrust causes the ¢ssure network to propagatedownward as well as the interface betweenseawater and the brine. In that case, the hydro-thermal system evolves in a way which is com-pletely di¡erent from those with a steady bottom[27].

2.1.2. Equations governing convectionIn our model, the magnitude of the Darcy

velocity (U, 0, W) reaches at most 1 m yr31,and the minimum grid spacing dz is about 10 m.The time for the £uid to move up by 10 m isabout 10 years, much larger than the time neces-sary to reach a conductive equilibrium between£uid and rock inside the control volume, sincef2/4U= 3 days with U= 1036 m2 s31. This showsthat the temperatures of the solid and the circu-lating £uid in the ¢ssures are the same. Weinfer that the temperature governing the £uidand the surrounding conductive basalt is de-scribed by:

�bc��DTD t� �bc�f V

!W9!

T � V �9 2T �4�

where (bc)f and (bc)* are the volumetric heat ca-pacity (J m33) of the £uid and the basalt, respec-tively; V* and U= V*/(bc)* are the thermal con-ductivity (J m s31) and thermal di¡usivity (m2

s31) of the basalt.For the £ow, Darcy's law is applicable since the

real velocity Veff /O in the ¢ssure network is slow.

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We write the velocities in the x and z directionsas:

U � 3keff

WD pD x

�5�

W � 3keff

WD pD z� b f g �6�

where p is the pressure, W the £uid viscosity, b the£uid density, and g the gravitational acceleration.The density and viscosity of the £uid are takento be dependent on temperature and pressure.We use the regression of the measured densityof a 30 g/l NaCl solution given at each 10 MPainterval [14]. The top pressure is set to 30 MPa.The densities at 30 and 60 MPa are respective-ly:

b f � 103531415U1034 T32384U1036 T2 �7�

b f � 10493306U1034 T32353U1036 T2 �8�

with T varying between 2 and 420³C.The viscosity W(T) is calculated from [14] :

W � 2:414U1035U10247:8

T�133 �9�

No pressure and salinity dependences have beentaken into account, since their in£uences are weakin the range of temperatures considered [14].

By neglecting the transient variations of bf withtime (Dbf /Dt = 0), we can write the mass conserva-tion equation as:

D �b f U�D x

� D �b f W �D z

� 0 �10�Thus, introducing the stream function 8 forsteady-state solutions of the £ow equation, wecan write :

U � 1b f

D8D z

�11�

W � 31b f

D8D x

�12�

2.2. Nature and solubilities of the mineral phasesinvolved in the seawater^crust interactions

2.2.1. Diagenetic processesThe diagenetic processes are triggered by sur-

face reactions between the circulating £uid andthe rock walls. They are controlled by the di¡u-sion of the species through the ¢ssures. The dif-fusivity of the chemical species in seawater for theconsidered temperatures is about 1038 m2 s31.For a ¢ssure width of 0.1 mm, the di¡usiontime is of the order of 1 s. We will see below (inSection 3) that the thickness of the precipitationfront can be as high as 100 m. Since the Darcyvelocity in the convective model is relatively small(about 1 m yr31), the £uid velocity inside the per-meable network reaches at most 3U1034 m s31.Thus, the time needed for the £uid to cross aprecipitation front of about 100 m is about3U105 s, about six orders of magnitude largerthan the di¡usion time of the chemical speciesinside the ¢ssures. This indicates local equilibriumconditions for the dissolution^precipitation reac-tions between £uid and rock. Here, we also as-sume that the minerals which precipitate do notundergo any other chemical reactions.

Finally, we assume that precipitation is trig-gered when the local concentration exceeds theequilibrium value. Although such a hypothesis isprobably wrong, we will show in Section 4 thatthis simpli¢cation does not change our conclu-sions. Accordingly, at any place in the porousslot, the concentration of any chemical species Cis assumed to be the concentration at equilibrium.Thus C satis¢es:

b fdCdt� dm

dt�13�

where dm/dt is the rate of mass dissolution orprecipitation induced during £ow [28].

The concentration depends on both pressureand temperature. Thus, we can write :

dCdt� DC

DTdTdt� DC

DPdPdt

�14�In Section 2.2.3, we will see that sul¢de and

sulfate minerals predominate as precipitates. Thee¡ect of pressure on the solubilities of sul¢de and

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sulfate minerals has been studied [22,29]. Changesin solubilities due to a variation of pressure of 500bar are in the same range as changes due to avariation of temperature of 20³C. Hence the e¡ectof pressure is negligible. The pressure e¡ects canbe incorporated in the uncertainties of thermody-namic data associated with temperature changes.Therefore:

dCdt� DC

DTdTdt

�15�

Using Eq. 4 we see that the rate of variation ofporosity with time dO/dt veri¢es:

dOdt� 3

b f

b sUDCDT

9 2T �16�

where bs is the mineral density (kg m33).

2.2.2. Mineral speciesAccording to Alt [30], a hydrothermal system

can be divided into three major zones: a rechargezone at the top, a reaction zone at the bottom anda discharge zone at the top. In the recharge zones,2³C seawater penetrates the crest and is warmedduring its descent. At ¢rst, pure seawater androck interact chemically under oxidating condi-tions and at low temperature (50³C). Then anevolved £uid reacts with the wall in a reductiveenvironment and at higher temperature (200³C).

The chemical reactions in recharge zones are:alkaline earth ¢xation in the crust, calcite/aragon-ite precipitation, and anhydrite precipitation.Then the circulation develops in the reactionzones where high-temperature (350^400³C) pro-cesses develop. These include sulfur and metals(Fe, Mn) leached from the rock. The warmesthydrothermal solutions, collected at an exit tem-perature greater than 350³C, are thought to di-rectly come from these zones without any signi¢-cant cooling [30]. They acquire their chemical andisotopic signature in this reaction zone. Finally,the seawater-rich metals and S circulation reachesthe discharge zones where several situations arepossible. If the hydrothermal £uid is su¤cientlychanneled to exit the crust with a low coolingrate, all the mineral content precipitates on thesea£oor. The black smokers, whose temperature

is greater than 350³C, are the £agrant geologicalmanifestation of this channeling. If the £uid coolsinside the crust before exiting, precipitation of thesulfur-bearing minerals (pyrite and chalcopyrite)will happen. When the vent temperature is be-tween 270 and 330³C, white smokers develop. Incase of complete cooling inside the crust, all themineral content of the hydrothermal £uids precip-itates in the crust and the resulting hydrothermalmanifestation does not deposit mineral on the sea-£oor [5].

2.2.3. Chemical reactions and rate of precipitation/dissolution

Our model of precipitation/dissolution is basedon the mineral solubility calculated from speciescontained in seawater. To simplify, we restrict ourstudy to the case of a single retrograde and pro-grade phase. We take anhydrite precipitation/dis-solution as the main chemical reaction occurringduring seawater heating between 50 and 250³C.Bischo¡ and Seyfried [31] noticed that the heatingof 1 kg seawater forms about 1 g anhydrite(CaSO4). Moreover, CaSO4 is often observed inthe oceanic crust samples [30]. Here we considerthat the formation of CaSO4 is bu¡ered by theamount of Ca2� contained in seawater. This isroughly one third of the SO23

4 content. The calcu-lated quantity of CaSO4 is about 1.4 g kg31 sea-water. Considering that the solubility rate ofCaCO3 is one order of magnitude lower thanthat of CaSO4 we neglect the formation of anycalcite or aragonite between 50 and 250³C. Fur-thermore, we assume that DC/bsDT is constant.

Accordingly, we ¢nd that the value of DC/bsDTfor anhydrite at 50^250³C is:

DCb sDT

� �anhydrite

� 34:7U1034 �K31 �17�

Outside the temperature interval 50^250³C we as-sume that (DC/bsDT)anhydrite = 0. The value in Eq.17 is likely to be underestimated. During the rockhydrothermal alteration, additional Ca2� isleached from the rock, such that the concentra-tion of precipitated anhydrite is bu¡ered by theSO23

4 in the seawater. This process increases thevalue of (DC/bsDT)anhydrite by a factor 2, favoring

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diagenesis. This process is partially compensatedby the fact that hydrothermal leaching also in-creases the fracture porosity.

We chose sul¢des as the dominant progrademinerals ¢lling the ¢ssures while the £uid is cool-ing at 350^250³C. The sul¢des are mainly pyriteand chalcopyrite. We assume that the sul¢des pre-cipitate in the ¢ssure network. Indeed, basalticrock contains small quantities of magnetite whichreact during the hydrothermal alteration with the£uid (HS3) to produce pyrite. This process ger-minates in the rock matrix, allowing the sul¢desto precipitate in the ¢ssure network. The esti-mated solubility rate shows that 5 g of sul¢desprecipitate from 1 kg of seawater in the upwelling[32]. We lower this estimation by considering theprecipitation/dissolution of 1 g of sul¢des per kgof seawater, to account for the increase in fractureporosity due to the leaching. Thus, the value ofDC/bsDT for sul¢des at 250^350³C is:

DCb sDT

� �sulfides � 2:4U1034 �K31 �18�

Outside the temperature interval 250^350³C,(DC/bsDT)sulfides is assumed to be zero. Finally,we allow the newly formed minerals to dissolve.This is possible when local inversion of the ther-mal regime between formerly cooling (now warm-ing) and currently warming (now cooling) regionsoccurs. Precipitation of minerals can cause suchan inversion.

We do not consider the formation of silica. Thesolubility of silica is prograde at temperatures be-tween 25 and 320³C and retrograde above 320³C.Consequently, silica precipitates both in the deep-est part of the system, where the £uid is heating,and in upwelling plumes. Silica precipitation oc-curs in the form of very small opal particles about5^10 nm in diameter [22]. Their Stokes velocity isnegligible (6 1 cm yr31) compared to the £uidvelocity in the ¢ssure network. Since opal par-ticles cannot germinate in basaltic rocks, theyare £ushed outside, where their deposition doesnot alter porosity in the fractures [28]. This isconsistent with the observation of much largergraphite particles of 5^100 Wm in size, in hydro-thermal vents [33].

2.3. Numerical methods

To resolve the temperature and £ow equations,we use non-dimensional equations in the numer-ical code. The following scaling factors have beenused. The unit length scale is H = 1500 m. Theunit time is H2/U= 1.25U105 years. The unitDarcy velocity is U/H = 1.2 cm yr31. The dimen-sionless temperature is a= T/vT, with vT = 418³C.The Rayleigh number is de¢ned as:

Ra � vb f Hgkeff

W 0U�19�

where W0 is the viscosity of seawater at 420³C andvbf = 440 kg m33 is the drop in seawater densitybetween 2 and 420³C.

As the e¡ective permeability keff ranges be-tween 10313 and 10310 m2, Ra ranges from1.6U104 to 1.6U107. Due to computational lim-itations, we are only able to run cases at the lowend of this interval.

Using the previous factors, the dimensionlesstemperature equation becomes:

QD aD d� V!0W9!a � 9 2a �20�

where d and VP are the dimensionless time andvelocity, respectively, and Q= (bc)*/(bc)f = 0.75 isthe ratio of the volumetric thermal capacity of thebasalt to that of seawater.

The dimensionless £ow equation is:

1r

� �9 28 0 � 3

DD x0

1r

� �D8 0

D x0� DD z0

1r

� �D8 0

D z0

� ��

RaD M �a �Dx0

� ��21�

where xP, zP are the dimensionless horizontal andvertical coordinates, respectively, and 8P is thedimensionless stream function. The factor r isthe dimensionless hydraulic conductivity, r =R/R0. The hydraulic conductivity is de¢ned asR = keffbf g/W and R0 = k0b0g/W0, where b0 = bf

(420³C) = 590 kg m33 and k0 = keff (xP, yP, zP,d= 0) = 10313 m2. M(a) is a dimensionless functionscaling the variation of the £uid density which

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satis¢es:

b f �a ; z0� � b 0 13vb f

b 0M �a �

� ��22�

The dimensionless rate of variation of porositywith time is :

dOdd� 3BW9 2a �23�

where B is a constant derived from Eqs. 17 and18.

We used equally spaced points in the x, y, zdirections to discretize the equations in the com-puting box. We have computed the stream func-tion and the temperature in ¢ve vertical (xz)planes inside the porous slot while the remain-ing xz planes are used to describe the wall. Forthe experiments shown in Fig. 5, for Ra = 8000and Ra = 12000, we use a set of (256U(5+59)U256) grid points, and a set of (512U(5+59)U512)grid points for Ra = 16000. For the experi-ments with variable permeability (Figs. 2^6) weuse a set of (192U(5+59)U128) grid points. Thenumerical scheme to solve the £ow and tem-perature equations is given in Rabinowicz et al.[14].

For the experiments with variable permeability(see Section 3.1), at each iteration, we calculate(D/Dd)O(xP, yP, zP, d) the transient rate of variationof the fracture porosity due to anhydrite and sul-¢des precipitation/dissolution. The evaluationuses Eqs. 17, 18 and 23. These calculations followthe step by step evolution of the fracture porosity¢eld O(xP, yP, zP, d) inside the permeable slot.Then, using Eqs. 1 and 2, we deduce the perme-ability ¢eld keff (xP, yP, zP, d).

The permeability evolution depending on 92a isa very irregular function. To avoid numerical di-vergence of the code while resolving the £owequation, we apply a conservative linear ¢lter tothe permeability ¢eld. For each discrete value ofkeff , the ¢lter a¡ects the neighbor values, in asquare of dimension 0.03U0.03 (45U45 m).Each of them is weighted with a coe¤cient in-versely proportional to the distance to the centralpoint. This process conserves the mean permeabil-ity on a square of (0.03U0.03). Furthermore, we

¢x a minimum value of k0/1000 for the permeabil-ity, also to prevent divergence.

All the experiments begin with a dimensionlessthermal regime 3(xP, yP, zP) which is a slightlyperturbed conductive pro¢le:

3 �x0; y0; z0� � 13z0 � 2:5U1033 sin�Zz0�A�x0; y0��24�

where A(xP, yP) is a random function with unitamplitude.

3. Results

In this section, we ¢rst investigate the temporalevolution of the permeability and thermal ¢eldsinside the slot while sul¢des and anhydrite precip-itate and dissolve in the ¢ssure network. Then weattempt to draw phenomenological laws to ex-trapolate our results to systems with higher Ranumbers.

3.1. Redistribution of porosity due to mineraldiagenesis during convection

The computational method to track porosityvariations has been described in Section 2.3. TheRayleigh number Ra = 16 000 is consistent with aninitial permeability keff (x, y, x, t = 0) = k0 = 10313

m2 s31 and an initial fracture porosity O(x, y, z,t = 0) = O0 = 1034. At the beginning of the experi-ment (Fig. 2), the circulation along the bottominterface assumes a ¢nger-like structure character-istic of the development of convection in a fault[14]. Such a pattern is expected because of the¢nite width of the permeable slot. A stagnant vol-ume of cold £uid develops at the top of the slotwhile hot buoyant plumes are generated at thebase. These results are speci¢c to numerical ex-periments with £uids with temperature-dependentequations of state.

The evolution of the circulation induces a colli-sion between the upwelling hot ¢nger and theinitial top stagnant cold sheet of water. In thisfront, 92a reaches extremely high values, leadingto the formation of a front of precipitation. Thevertical sheets separating the downwelling and up-

EPSL 5685 20-12-00


welling plumes lead to the formation of con-tact zones where strong values of 92a are alsoubiquitous. In this zone, signi¢cant mineral pre-cipitation (prograde as well as retrograde) alongzones of a gradients occurs. The cores of theascending plumes are not a¡ected since their tem-peratures are high enough to avoid mineral pre-cipitation (see Eqs. 17 and 18 for the temperatureintervals).

At the axis of the fault, zones of precipitationform thin ribbons at the edges of the ascending¢ngers (Fig. 2b). The topology of the precipita-tion domain coupled with the temperature-depen-dent viscosity favors viscous ¢ngering (Fig. 2c).The low-viscosity hot £uid in the ascendingplumes shuns zones where permeability is weakand channels into those where the permeabilityis good. The temperature gradient across the

Fig. 2. Snapshot of the dimensionless thermal and permeability ¢elds at the dimensionless time: 6.28U1034 (80 years). In panelsa are drawn the temperature ¢elds and in panels b the permeability ¢elds at the axial and border planes of the fault, respectively.The permeability is scaled by k0 = 10313 m2 ; here, between two consecutive isolines the permeability decreases or increases by0.2k0. In panels c the 0.3 (125³C) and 0.8 (335³C) isotherms are represented inside the fault and the wall. Note the ¢nger-like cir-culation and the viscous ¢ngering. The stream function of the axial plane is also represented: in grayed areas the £ow turnsclockwise, in white areas the £ow turns anticlockwise.

EPSL 5685 20-12-00


slot generates ¢ngers which are colder close to thelimbs of the fault than on its axis. It also enhancesthe permeability alteration at the edge of thefault, preventing the development of ¢ngeringand weakening the convection. After 80 years,mineral precipitation considerably inhibits the cir-culation in the whole slot. After 350 years, the¢nger-like £ow is replaced by a di¡use circulation(Fig. 3). The permeability ¢eld is strongly reducedin the entire slot, at the axis as well as at the edge

of the slot (Fig. 3a,b). The irreversible cooling ofthe slot generates mineral precipitation every-where in the slot, except in domains where thetemperature is higher than 350³C or lower than50³C, destroying the ¢nger-like pattern. The ther-mal ¢elds in the two extreme planes (Fig. 3a) areroughly the same. After 800 years (Fig. 4), thepermeability alteration (Fig. 4b) causes a com-plete layering of the circulation (Fig. 4c): in thelower part of the system convection takes the

Fig. 3. Same caption and model as in Fig. 2. Snapshot at the dimensionless time: 2.73U1033 (350 years). Venting temperature isabout 0.2 (80³C). Between two successive isolines, the permeability drops by a factor

��10p

. The minimum of the permeability ¢eldis equal to k0/300. Note the complete layering of the circulation.

EPSL 5685 20-12-00


form of several small regular rolls, while abovethe front the circulation is very di¡use.

During the whole 8-century duration of the ex-periment, the venting temperature does not exceed80³C, well below the inferred 270³C of whitesmokers (Figs. 2^4). We ran other simulationswith di¡erent Rayleigh numbers and observedthe same phenomenology. This leads to the con-clusion that there is a con£ict between the growth

of the convective instability and the precipitationof minerals in the ¢ssures.

3.2. In£uence of Rayleigh number

We have seen that the collision between the hot¢ngers and the top cold layer generates a precip-itation front inside the slot. This collision resultsfrom the contrast of buoyancy between hot and

Fig. 4. Same caption and model as in Fig. 2. Snapshot at the dimensionless time: 6.33U1033 (800 years). Dimensionless ventingtemperature is lower than 0.2 (80³C). Between two successive contours, the permeability drops by a factor

��10p

. The minimum ofthe permeability ¢eld is equal to k0/1000.

EPSL 5685 20-12-00


cold £uids: the buoyancy of the layer is propor-tional to its thermal expansion K (K=3(1/b)Db/Da) and to 1/W. The coe¤cient K increases bya factor 30 from 2 to 420³C (see Eqs. 7 and 8) andW decreases by about a factor 15 between 2 and150³C and only by a factor 2 between 150 and420³C (Eq. 9). The interface between the coldand the hot layers corresponds roughly to theinterface between the highly viscous cold layerand the strongly buoyant hot layer. Thus the in-terface remains between 150 and 250³C (Fig. 5b).

In the following part, we study the evolution ofthe thermal front as Ra increases. To investigatephenomenological laws, we consider three runswith Ra numbers of 8000, 12 000, and 16 000, inwhich the permeability of the slot is held constant.At each time step, we compute the maximum pos-itive value of (92a), (92a)max in the 50^250³C tem-perature interval, and the maximum negative val-

ue (92a)min in the 250^350³C interval. Thesevalues determine the maximum rate of precipita-tion of anhydrite and sul¢des, respectively. Theirtemporal evolution is shown in Fig. 5a.

First, we note that (92a)min is nearly alwaysgreater than (92a)max in absolute value. Thisshows that in the boundary layers local coolingof the £uid is greater than heating. The evolutionof (92a)min with time can be divided into twomain domains: a ¢rst one where (92a)min rapidlyincreases linearly and a second one where itstrongly £uctuates. The £uctuations result fromthe unsteady nature of the convective circulation.The maximum of the amplitude of (92a)min aswell as the slope in the linear domain clearly in-crease with Ra. We note that (92a)min increases asa power of Ra (between 1.5 and 2). This maxi-mum occurs well before ¢ngers can completelyerode the cold layer. The dimensionless time

Fig. 5. a: Evolution of (92a)min and (92a)max with time for three constant permeability experiments with Rayleigh numberRa = 8000, 12 000, 16 000, respectively. The vertical line (ts) gives the exit time of the ¢ngers. The signs `3' and `+' refer to(92a)min and (92a)max, respectively. Note that ts exceeds the time when (92a)min and (92a)max reach their maxima. b: Thermal¢eld at the axis of the fault taken when (92a)min reaches its maximum, i.e., 1.3U1033 (160 years), 0.97U1033 (120 years),0.6U1033 (75 years) for Ra = 8000, Ra = 12 000 and Ra = 16 000, respectively. The vertical line gives the location of the line where(92a)min is largest in absolute value. Note the development of the extremely narrow thermal boundary layer between hot ¢ngersand top cold water layer.

EPSL 5685 20-12-00


needed to erode the top cold layers is about1.85U1033 (230 years), 1.2U1033 (150 years)and 8.8U1034 (110 years) for the three caseswhere Ra is 8000, 12 000 and 16 000. It indicatesthat the time needed for the ¢nger to produce hotvents decreases linearly with the Rayleigh num-ber.

As noted in Section 2, the Rayleigh number ofa hydrothermal system is poorly known. Rabino-wicz et al. [14] have shown that the venting £owrates found at experiments with Ra = 16 000 arecompatible with those of hot vents [34]. However,some hydrothermal systems can have Rayleighnumbers three orders of magnitude larger. Theyare associated with fracture porosity of O= 1033

and permeability keff = 10310 m2 [15]. Yet numer-ical modeling of such cases is clearly beyond to-day's computers. For the case with Ra = 16 000and O= 1034, we see that the magnitude of theDarcy velocity reaches 1 m yr31. This correspondsto a £uid velocity VDarcy/O which does not exceed3U1034 mm s31. For Ra numbers up to threeorders of magnitude larger, the porosity increasesby one order of magnitude and the £uid velocitynever exceeds a few 1032 m s31. At this speed, theinertial terms are small, and thus the usual linearversion of Darcy's law still applies (see Eqs. 5 and6). The hypothesis of thermal equilibrium between¢ssure and walls still holds (see Eq. 4) and localchemical equilibrium between rock and seawateralso.

By assuming that the relationship between(92a)min, the exit time of the ¢ngers and Ra stillholds for such high Ra, we can deduce that therate of precipitation of the mineral increases fasterthan the residence time of the ¢nger decreases,since it is proportional to (92a). Accordingly, itis likely that even for Ra numbers up to 1.6U107,the sealing of the ¢ssure network prevents the hot¢ngers from reaching the top of the slot. Thus,the mineral precipitation in the ¢ssures likely pre-vents the formation of hydrothermal vents, what-ever the Ra number is.

4. Discussion

Our conceptual model of hydrothermal circula-

tion at ridge crest consists of a fracture zone ofabout 100 m surrounded by conductive walls in-side the sheeted dike complex. Figs. 2^5 show thatthe temperature remains low (50^100³C) in a largeregion near the top of the slot. Because of thetemperature-dependent viscosity W and thermalexpansion K, this top cold layer is highly viscousand convectively stable. Along the bottom of theslot, the hot buoyant ¢ngers (low-W, high-K) haveto erode the top cold layer before venting hot£uids onto the sea£oor. Yet, this erosion is inhib-ited by the precipitation of anhydrite and sul¢desat the interface between the cold top layer and the¢ngers. This result is obtained assuming a Ranumber of 16 000, and is likely true for Ra upto 107. The calculation assumes that the diagene-sis occurs at equilibrium.

In our modeling, we adopt a power law rela-tionship between permeability and porosity, as-suming that the permeable system consists of per-fectly parallel ¢ssures crossing the whole slot.Nature is clearly more complicated. It is morelikely that the permeable system consists of a setof ¢ssures generated during micro-seismic events,with a relatively large thickness (up to a few milli-meters) [15] and a vertical extent of several me-ters. In that case, the mean fracture porosity canreach a few percent instead of the 1034 consideredhere. As a result, the permeability of these systemsis not controlled by the mean width of the ¢s-sures, but by the e¡ective width of the micro-¢s-sures allowing percolation of seawater from onelarge ¢ssure to the other. Hence, the relationshipbetween permeability and fracture porosity de-pends on the e¡ective width of this macro- andmicro-¢ssure network.

A crucial issue is the location where mineralsprecipitate. If precipitation preferentially occurswithin large ¢ssures, it is the fracture porositydeduced from the mean width of the ¢ssureswhich controls the evolution of permeability dur-ing diagenesis. In this case, our modeling showsthat the time needed to ¢ll the ¢ssures is longenough to generate hydrothermal vents. Such asituation is probably unlikely. Indeed, we haveseen that mineral precipitation is controlled bysurface reactions between rock and hydrothermal£uid, especially for sul¢des which germinate in the

EPSL 5685 20-12-00


walls of the ¢ssures (Section 2.2.3). Moreover,sul¢des precipitate preferentially in constrictedzones where the ratio of water to rock is high,thus in the micro-¢ssures. This localized precipi-tation hardly a¡ects the large ¢ssures but seals themicro-¢ssures. Such a process reduces permeabil-ity as fast as in our models.

Another important point is the need for notablesupersaturation to trigger mineral precipitation,particularly for sul¢des. Supersaturation localizesprecipitation in narrow temperature domains. It

likely accelerates the obstruction of the permeablenetwork, and thus favors the rapid sealing of thesystem. We argue that the seawater hydrothermalsystem in diabases lines micro-¢ssures with min-erals just as cholesterol hardens arteries. Anotherpossibility is that the precipitation triggered bysupersaturation occurs as clots which occludethe micro-¢ssures, as during a heart attack. Inboth cases, the mineral precipitation preventsthe development of hot vents, while a precipita-tion of mineral restricted to the large ¢ssures leads

Fig. 6. Same model and caption as in Fig. 2, but re-initialized with the thermal ¢eld of Fig. 3 and a constant permeability equalto k0. The snapshot is taken at time 4.1U1034 (50 years) after the re-initialization. Between two successive contours, the perme-ability drops by a factor

��10p

. Venting temperature reaches a= 0.7 (295³C).

EPSL 5685 20-12-00


to hot vents. Hence, the occasional occurrence ofhydrothermal vents is a strong argument in favorof rapid occlusion of the permeable network byhydrothermal £ows at ridge axes.

To explain the occurrence of hot vents, weimagine a process generating a new permeablesystem. We run a case beginning with the 350-year-old thermal ¢eld of the model of Figs. 2^4.In this experiment the initial permeability is resetto k0 = 10313 m2, and the Rayleigh number is16 000. After 50 years, the hot ¢ngers bu¡eredat mid depth below the precipitation front rapidlymove upward and exit through the top of the slotwith a temperature of 295³C (Fig. 6). The circu-lation maintains this exit temperature for 50^70years: Thereafter, it slowly decreases by about2³C yr31. Thus, recovering permeability can gen-erate vents.

Several processes can be evoked to explain sucha permeability recovery. A ¢rst hypothesis con-sists of thermo-elastic cracking during the transi-ent cooling of the fracture [35]. We do not thinkthat this process is very e¤cient in our case, be-cause the whole system tends to warm up duringthe short time necessary to form the precipitationfront. This prohibits contraction of the matrix.Nevertheless, thermo-elastic stresses may be e¤-cient once the system is cooling, i.e., as the hydro-thermal process is dying. Contraction may thenopen new pathways to £uid circulation. However,the modeling of hydrothermal systems during thetransient cooling of the crust is too complicated tobe addressed in the present paper, as stated inSection 1.

We also suggest that local seismic events at theridge crest can create a new permeable systemallowing £uid circulation. The ridge crust is hostto a number of dynamic processes that are able tocreate micro-earthquakes. Among them are dikingevents, tectonic faulting, and thermal strain [36].To generate an earthquake, crustal temperaturesmust be low enough to allow brittle deformation,and stresses must exceed the local rock strength.At slow spreading ridges (9 4 cm yr31), seismichypocenters have been located 7^8 km under thesea£oor [37]. This indicates that fault slip can oc-cur over relatively large areas, generating earth-quakes with mb v 4.5 and even teleseismic events

[38]. Many of them are due to normal fault slip[37]. Such seismic events in the vicinity of a sealedhydrothermal system may be responsible for thepermeability recovery of the model of Fig. 6.

Extensive circulation inside the new ¢ssure net-work generates hot vents which vent £uids at 270^290³C over times as long as a century. If the per-meability of this vent is periodically renewed(every 50^100 years), i.e., if the same fault slipsrepeatedly, the vent can exit £uid continuously attemperatures of 270^290³C for as long as a thou-sand years with little variation in the vent exittemperature. Otherwise, the hot discharges (withtemperatures of 220^290³C) last between two andthree centuries. On slow spreading axes, dikingevents occur once every 50^100 years on averageon active segments, for about 8 km of axial valley.Seismic swarms may also re-open the ¢ssures anddrive hydrothermal circulation as described be-fore.

Another way to favor the formation of vent¢eld is to start the convective process from a dif-ferent thermal regime than that considered here.We think that the intrusion of magmatic body,such as sills, in the crust can lead to a `pre-heat-ing' of the slot, which would decrease the thermalshock by reducing the temperature contrast be-tween the fault and the walls. The cooling of ameter-thick intrusion will not contribute to heate¤ciently a 100-m-wide fracture. A particularlysigni¢cant magmatic intrusion, about 10 m thickas possibly at hot spot sites, would be required topromote an appreciable heating of the fracture.

The situation is quite di¡erent on axes spread-ing faster than 10 cm yr31. On the EPR, the depthrange of the micro-earthquakes suggests brittlebehavior restricted to the ¢rst 1^2 km of the crust[36]. This explains why moderate earthquakes(mb v 1) are not observed on fast spreading axes.The small earthquakes appear to be the result ofstresses generated by thermal contraction of thebasalt as it cools [36]. Studies have resolved thestructure of young upper crust at the EPR at9³30PN [39]. The results suggest that dike intru-sions reach within a few hundred meters belowthe sea£oor. Moreover, Haymon et al. [5] postu-lated that hydrothermal activity develops near thetops of these intrusions. More recently, the mod-

EPSL 5685 20-12-00


eling of Rabinowicz et al. [14] indicated that thetime scale required for the development of such100-m-high hydrothermal systems is about a fewyears instead of the 103 years for 1.5-km-highsystems. The characteristics (temperature ¢eldand mass/heat £ux exiting the system) of the cir-culation depend on the Rayleigh number and noton the height of the system. On this basis, Rabi-nowicz et al. [14] infer that the numerous short-lived black and white smokers in the NorthernPaci¢c [40,41] are likely associated with such shal-low intrusions. The characteristics of the model ofFigs. 2^5 apply to such a shallow hydrothermalsystem. Furthermore, these small seismic eventsare several orders of magnitude more frequentthan the more important ones at slow spreadingaxes. These su¤ce to renew permeability in a hy-drothermal system with a height of a few hundredmeters. Thus, we think that the discussion forslow spreading axes also holds for fast spreadingridges, but at a shorter time scale.

The study and observation of seismic activityon ridge crests are recent [42] and the links be-tween hydrothermal system and seismic activityare not well understood yet. Information aboutthe recurrence of diking events on a given pieceof ridge must improve our knowledge of tectonic,volcanic and hydrothermal processes.

5. Conclusion

We have modeled the in£uence of diageneticpermeability changes on hydrothermal circula-tion. Rabinowicz et al. [14] have described theconvective process and thermal regime in a verti-cal slot surrounded by conductive walls assuminga basal temperature of 420³C. In this study, wesimulate the evolution of the permeability ¢eldresulting from the precipitation of anhydrite andsul¢des in the ¢ssure network. We assume localequilibrium between the mineral phases and thecrust. Some 1.4 g of anhydrite and 1 g of sul¢desper kg of seawater are likely to form during aconvective cycle.

The experiments show the development of atransition which transforms the initial conductiveregime in an asymptotic one with ¢nger-like

plumes exiting hot £uids. During this transition,(1) a thermal shock between hot rising ¢ngers andtop cold stagnant water layers induces a front ofprecipitation at notable depth below the top ofthe slot, (2) thereafter, the front gradually thick-ens, and (3) the decrease of the permeability in thefront leads to a layering of the hydrothermal £owon both sides of the front: in the bottom layer thetemperature is too high (s 350³C) and in the toplayer the £uid temperature is too low (6 50³C)for mineral diagenesis to develop. As a conse-quence, venting temperatures are low (6 80³C)and well below the values observed at white orblack smokers.

Our models indicate that the great drop in sea-water viscosity around 150³C coupled with thestrong increase of the thermal expansion withtemperature explains the development of thefront. We show that the rate of precipitation ofminerals increases more rapidly with Ra than thetime needed for the ¢ngers to produce hot ventsdecreases. This suggests that our results can plau-sibly be extended to higher Ra numbers.

We show that if we reset the permeability ¢eldto its initial value, the ¢ngers rapidly reach thetop and generate white smokers. We think thatseismic activity near sealed hydrothermal systemsmay create the permeability recovery necessary todrive the formation of hot vents. Diking eventsmay also favor the formation of hot vents bydecreasing the temperature contrast between thewalls and the fracture, by pre-heating the wholesystem. Recent seismic surveys of ridge crest mustimprove our knowledge of the interactions be-tween hydrothermal systems and volcanic/seismicactivity by determining the periodicity of dikingand microseisms on the same ridge portion.

Acknowledgements

We wish to thank Pierre Genthon for his stim-ulating discussions during this work, Anne Briaisfor helpful information, Kurt Feigl for Englishimprovements and the reviewers Abdellah Cher-kaoui and Frank Spera for their constructive sug-gestions. The computations were supported by theCentre National d'Etudes Spatiales (CNES). This

EPSL 5685 20-12-00


work has been funded by the ECODEV progra-m.[AC]

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