JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. B1, PAGES 475-496, JANUARY 10, 1995
Experiments on flow focusingin soluble porous media, with applications to melt extraction from the mantle PeterB. Kelemen, • J. A. Whitehead, 2 EinatAharonov, 3 andKelseyA. Jordahl 4 WoodsHole Oceanographic Institution,WoodsHole, Massachusetts
Abstract. We demonstratefinite structuresformed as a consequence of the "reactiveinfiltration instability"(Chadamet al., 1986) in a seriesof laboratoryandnumericalexperimentswith growthof solutionchannelsparallelto the fluid flow direction. Regionswith initially high porosityhavehigh ratiosof fluid volumeto solublesolidsurfaceareaandexhibitmore rapid fluid flow at constantpressure,sothat dissolutionreactionsin theseregionsproducea relatively ..,-.•l A l ........... ',., 11 ß,•pß,• in As channelsgrow,largeonesentrainflow lateraßßy inward and extendrapidly. As a result,smallchannelsare starvedanddisappear.The growthof large channelsis an exponentialfunctionof time, aspredictedby linearstabilityanalysisfor growthof infinitesimalperturbations in porosity. Our experimentsdemonstrate channelgrowthin the presenceof an initial solutionfrontandwithoutan initial solutionfrontwherethereis a gradient in the solubilityof the solidmatrix. In the gradientcase,diffuseflow is unstableeverywhere, channelscan form and grow at anypoint, andchannelsmay extendoverthe lengthscaleof the gradient.As a consequence of the gradientresults,we suggest thatthereactiveinfiltration instabilityis importantin the Earth'smantle,wherepartialmeltsin the mantleascend adiabatically.Mantle peridotitebecomesincreasinglysolubleasthe meltsdecompress. Dissolutionreactionsbetweenmeltsandperidotitewill producean increasein liquid massand lead to formationof porouschannelscomposedof dunite(> 95% olivine). Replaciveduniteis commonlyobservedin the mantlesectionof ophiolites.Focusedflow of polybaricpartialmelts of ascending peridotitewithindunitechannelsmay explainthe observedchemical disequilibriumbetweenshallow,oceanicmantleperidotitesandmid-oceanicridgebasalts (MORB). This hypothesis represents an importantalternativeto MORB extractionin fractures, sincefracturesmay not form in weak,viscouslydeformingasthenospheric mantle. We also briefly considerthe effectsof crystallization, ratherthandissolution reactions,on the morphologyof porousflow via a secondsetof experiments wherefluid becomessupersaturated in a solidphase.Formationof short-livedconduitsparallelto the flow directionoccursrapidly,
andtheneachconduit iseventually choked by•nterior crystallization; fluidflowthenpasses throughthe mostpermeableportionof the wallsto form a new conduit.On longtime scalesand lengthscales,transientformationanddestruction of conduitswill resultin randomanddiffuse flow. Whereliquid coolsasit risesthroughmantletectosphere on a conductivegeotherm,it will becomesaturatedin pyroxeneaswell asolivineanddecreasein mass. This processmay producea seriesof walledconduits,asin our experiments.Developmentof a low-porositycap overlyinghighporosityconduitsmay createhydrostaticoverpressure sufficientto causefracture andmagmatransportto the surfacein dikes. Introduction
channels in partially soluble porous media. These results are relevant to understandingmelt extractionfrom the Earth'supper This paper reports initial results of an experimental and mantle. Stronglyfocusedflow, which limits solid/liquidinteracnumerical study of focusedflow of fluids through dissolution tion duringmelt extraction,is requiredto explainthe localization of magmatismat mid-oceanridgesand the compositionof midoceanridge basaltsand residualperidotites. By contrast,more 1Department ofGeology andGeophysics, Woods HoleOceanographic diffuse flow of liquids combinedwith substantialmantle/magma Institution, Woods Hole, Massachusetts. interaction may be indicatedby the geochemistryof subduction2Department of Physical Oceanography, Woods HoleOceanographic related magmas, within-plate volcanics, and samples of the Institution, Woods Hole, Massachusetts. 3WHOI/MITJointGraduate Program inOceanography, Department of mantletectosphere.Resultsof this studywill alsohave relevance to a variety of otherwork in the Earth sciencesand relatedfields. Earth, Atmospheric,and PlanetarySciences,Massachusetts Instituteof Technology,Cambridge,Massachusetts. For example,they may help to explainthe natureof hydrothermal 4WHOI/MITJointGraduate Program in Oceanography, WoodsHole vents along mid-oceanridges, where stronglyfocuseddischarge Oceanographic Institution,WoodsHole, Massachusetts. of coolingfluid seemsto characterizefluid circulation. The simplestexperimentspresentedhereinvolve flow of water Copyfight1995by theAmerican Geophysical Union. througha mixture of glassballs and salt (NaC1) grainscombined into an approximately homogeneousmixture within a narrow, Papernumber94JB02544. 0148-0227/95 / 94JB-02544 $05.00 rectangularglasschamber.Water is introducedat the opentop of 475
476
KELEMEN
ET AL.: FOCUSED
POROUS
FLOW
AND
MELT
EXTRACTION
this chamber,then flows down throughthe matrixof glassballs and salt, througha layer of foam, and finally exitsthroughsmall
melt in the mantle,and the potentialgeochemicaleffectsof flow focusing in different magmatic-tectonic environments are
outlet holes at the base. The initial interface or "front" between
discussed.
salt-free and salt-bearing glass balls is planar and horizontal, perpendicularto the flow direction of the water flowing down throughthe tank. However, within minutes,this front becomes unstable,resultingin focusedporousflow of water within elongate, salt-freedissolutionchannelsparallel to the flow direction. Our numericalcomputersimulationsof theseexperimentsshow the samequalitativebehavior. Chadamand others[Chadamet al., 1986; Ortolevaet al., 1987] havesuggested a simplemechanism for this instability, which they termedthe "reactiveinfiltration instability": small perturbationsin porosityare amplified due to two positivefeedbackmechanisms:(1) in a high-porosity region, a higher water volume to solid surfacearearatio leadsto lower instantaneoussalinity and more rapid dissolutionof salt, and (2) higher-porosityregions permit more rapid ingressof waterthat is not saturatedin salt,leadingto additionaldissolution of salt. For both thesereasons,initial perturbationsin porosity cause formation of dissolution channels parallel to the flow
Melt Extraction From the Mantle at Mid-Ocean Ridges Recent geochemical investigations suggestthat in some tectonicsettingsand on somelengthscales,porousflow of melt in the mantle is the dominant mode of melt extraction.
The
evidencefor porousflow includesfield observations of replacive dunites [e.g., Boudier and Nicolas, 1977; Dick, 1977; Quick, 1981; Kelemen,1990;Kelemenet al., 1992],experimentalresults [e.g., Watson,1982; Riley and Kohlstedt,1991], and theoretical investigations[e.g., Maaloe and Scheie,1982; McKenzie, 1984]. Experimentshave repeatedlydemonstratedporousflow of melt in mantle lithologies can occur at rates of tens to hundredsof centimetersper year, whereasplate velocities(half spreading rate)areof theorderof 1-10cmyr-1. Extremelydepletedabyssalperidotites,dredgedfrom fracture zonesalongthemid-oceanridges,arethe residuesof partialmeltdirection. ing which formedmid-oceanridgebasalts(MORB), but they are Many workers have observedfeaturesin the upper mantle far from traceelementequilibriumwith aggregateMORB liquids sectionof ophioliteswhich were formed by melt/rock reaction [Johnsonet al., 1990; Johnsonand Dick, 1992]. This has been during focused porous flow of ascendingliquid throughperi- ascribedto a fractionalor incrementalmelting process,in which dotire. The most striking of theseare dunires,rocks composed the aggregateliquid producedis MORB, while the solid residue almostentirely of the mineral olivine. Someduniresin the upper recordsequilibriumwith the last, mostdepletedmelt fractionto mantle form by replacementof surroundingperidotire,as melt be extracted. Since this aggregateliquid is extractedfrom the migrating by intergranular flow dissolvespyroxene minerals sourcein very smallincrements(lessthanonevolumepercentof from the porousmatrix throughwhich it passes(Figure 1). Melt the rock),it mustinitially moveby porousflow. Similarexplanaflow may be focused during formation of replacive dunites tions have been advancedfor large fractionationsof the Sm/Nd becauseduniteis more permeablethansurrounding peridotite,in and Lu/Hf ratiosbetweensourceandliquid whichoccurduring a processanalogousto the focusingof flow in our experiments. extraction of MORB from the mantle [Salters and Hart, 1989]. Formation of dunire "conduits"during reactionbetweenolivine- This chemical evidenceconfirms theoreticalsuggestions that saturated liquid and harzburgite has been experimentally melt mobility due to porousflow permitsefficient extractionof demonstratedon a centimeter scale by Daines and Kohlstedt smallincrementsof partialmelt from mantleperidotiteandthere[1993]. fore favors a near-fractionalmelting process[e.g., McKenzie, The melt/rock reaction processwhich initially forms dunite 1984]. from peridotiremay have profoundeffectson the compositionof Acceptanceof the growingbody of evidencefor porousflow derivativeliquids[e.g., Kelemen,1990]. However,oncea dunite as an important mechanism for melt transportin the shallow channelis formed, focusedflow throughthe channelmay leave mantleraisesa numberof fundamental problemsfor geochemists successiveliquids virtually unchanged. Formation of melt and geophysicistsstudying partial melting in the mantle and conduitsas a resultof chemicaldissolutionrepresentsan impor- accretionof the oceaniccrust. Theseproblemsare summarized tant alternativeto melt extractionby flow throughcracksandthus below: may be particularly important in explaining extractionof mid1. The composition of abyssalperidotitepresents a seeming oceanridge basaltfrom the viscouslydeformingasthenosphere. paradox: Large fractionationsof incompatibletraceelementsin Even where transportthroughmelt-filled cracksis the dominant abyssalperidotitesrequire the continual removal of small melt mode of melt extraction from the mantle, formation of porous incrementsby porousflow. Yet, if porousflow is the dominant conduitsmay be importantin creatinghydrostaticpressuresuffi- mechanismof melt transportbeneaththe mid-oceanridges,then cient to cause fracture. why are the shallowestmantlesamplesunaffectedby interaction This paper is divided into four parts. The introduction with liquidsderivedfromdeeperin thecolumnof decompressing describescurrentproblemsin understanding melt extractionfrom mantle? Small degree melts, derived from partial melting of the mantle,with an emphasison mid-oceanridges,summarizes garnet peridotite at pressuresexceedingabout 2.5 GPa, are the evidencefor porousflow of melt throughperidotirein the upper first increments of melting during decompressionof mantle mantle, and summarizessomeprior work on focusingof fluid beneathmid-oceanridges[e.g., Saltersand Hart, 1989]. Such flow in partiallysolubleporousmedia. In the secondsection,the liquidsare enrichedin light rare earthelementsand otherincomresultsof experimentson water flowing throughsalt are usedto patible elements. If thesemeltstraversedthe overlyingcolumn elucidate the dynamic instability of diffuse porousflow in a of mantleby uniformly distributedporousflow, chemicalintersoluble matrix. In the third section, the results of numerical actionwould returnlight rare earth and otherincompatibletrace experimentsare discussed. These confirm and quantify some elementsto the peridotite, so that shallow mantle peridotites observations from the laboratoryexperimentsandextendthemto would have higher concentrationsof these elementsthan are systemsin which there is a gradient in solubility of the solid observedin abyssalperidotite. matrix, rather than a sharp initial solution front. In the final Spiegelmanand Kenyon[ 1992] attemptedto resolvethisparasection,theseresultsare relatedto the structureof porousflow of dox by suggestingthat melt segregatesinto "veins"or channels
b
Figure 1. (a) Outcropmap of discordantdunitc cuttingmantle peridotitein an ophiolitein the polarUrals,from Nicolas [ 1989], after $avel'yevaet al. [ 1980]. Severalaspectsof the contactrelationshipsbetweenduniteand peridotiteindicatethat the dunites were formedby near constantvolumereplacementof peridotite, as a resultof dissolutionof pyroxene,combinedwith crystallization of olivine, in a liquid migratingby porousflow throughthe mantle. Anastamosing duniteenclosesislandsof relict peridotite whoseoutlineswould not matchthe adjacentwalls if dunitewere removed. Pyroxenitelayersin the peridotiteare locally, selec-
tively replacedby narrowdunites.Pyroxenitelayersin theperidotite are not offset but insteadhave beenreplaced,wherethey intersectdunite at an angle. (b) Sketchof an outcropin the Lanzoperidotite,fromNicolas[ 1989],afterBoudierandNicolas [1977], showingdunite replacingperidotitewith a pyroxenite band. Replacement of the relativelychromerich pyroxeniteby dunite formed a train of relict, chromianspinel in the dunite,
indicatingthat the duniteformedby in situ replacementrather thanas an intrusivedike later filled by olivinecrystals.Both (a) and(b) reprintedby permission of KluwerAcademicPublishers.
478
KELEMEN
ET AL.: FOCUSED
POROUS FLOW AND MELT EXTRACTION
spaced at least 10 cm apart. Following segregation,they no longer interact chemically with their solid matrix. Similarly, Hart [1993] suggestedthat melt extraction occurs along a networkof coalescingtubeswith a fractal structure. Melt moves rapidly through large tubes and is out of equilibrium with surroundingmantleperidotiteafter the melt hasmovedmorethan 1 km from its sourceregion. Nicolas and co-workers [e.g., Nicolas, 1990] proposethat developmentof an interconnected porous melt network, over a 10-km depth interval, leads to magmaticoverpressure, followedby hydrofractureandrapid melt extractionalong cracks. A weaknessof the crackinghypothesis is that partially molten, low-viscosityasthenosphere may not be strongenoughto supportsufficientstressto inducefractures. In the presentstudywe hopeto elucidatethe mechanismswhich can form melt veins or channels,the conditionsunder which they form, and the length scalesand aspectratios of the resulting conduits. Formationof dissolutionchannels,perhapsultimately producingsmall openconduits,may representa viable alternative to the crackinghypothesis. 2. Geophysicalmodels of melting and crustal accretionat mid-oceanridges also involve a paradox: In order to produce observedcrustalcompositions and volumes,upwelling mantle mustpassthroughits solidusovera broadzonebeneathspreading
Cpx
centers, much wider than the zone of active crustal accretion at
the ridges. Why, then,is the activevolcanicandplutoniczoneso narrow? Some models proposefocused asthenosphericflow (much fasterthan plate velocities)directlybeneathridges[e.g., Rabinowiczet al., 1984, 1987; Scottand Stevenson,1989]. Other solutionsinvolve two-phaseflow in the partially molten upper
mantle: Melt flow convergestoward the ridge, while the solid matrix divergesfrom the ridge to form part of the lithosphere [e.g., Spiegelman and McKenzie, 1987]. Some hypotheses presumethat porouschannelsform in the mantle. For instance, Spiegelman[1993] suggestedthat decreasingmelt porositynear the asthenosphere/"lithosphere" boundary (as defined by the mantlepeddotitesolidus)producesplanesof focusedmelt flow in the asthenosphere, parallelto the baseof the lithosphere.The presentstudymay advanceunderstanding of thisprocess. In thispaper,it is suggested that melt extractionfrom the shallow mantle beneath mid-ocean ridges is focused in narrow conduits by the inherent instability of diffuse flow through partially soluble porous media. Additionally, under certain circumstances,conduits for focused flow may develop hydrostatic overpressuresufficient to form melt filled cracksat their tops, as proposedby Nicolas and co-workers [e.g., Nicolas, 1990], or melt-filledpocketsasproposedby Sleep[1988, Produc-
Cpx
Cpx
10kb '••••••
2k
c1ø0m•bøsmi Iøtn
OI SiO2Se5b me(ol+ Opx
OI
Opx
I \x
JX\
\
SiO2
Opx
peridotite solidus basalt liquidus
\Mixx N\\
basalt adiabat
basalt adiabat
basalt solidus N mantle solidus
•
Mb•aEliquidus
L
mantle adiabat
bas•t adi•at _
XI OI+ hq Y :::'":--":• OI + Cpx+ Iiq
A [--] Iiq BI OI+ liq C• Ol+Opx+liq
Z•
D•
0 mantlemeEing: Cpxout
Pmantle melting: Opx out • temperature
OI + Opx+ Cpx+ liq temperature
Ol+Opx+Cpx+liq
temperature
Figure 2. Liquid and solid productsof reactionbetweenascendingmelts and surroundingupper mantle wall rocks are illustratedin thesediagrams. At the top are three schematic,pseudo-ternaryphasediagramson the
planeolivine(O1)- clinopyroxene (Cpx)- silica(SiO2),projected fromspinel,for hydrous silicateliquidsat upper mantle pressures[Kelemenet al., 1992]. (a) The effect of pressurein this system. Decreasingpressure leadsto increasedstabilityof O1relativeto pyroxenes,sothatliquidsin equilibriumwith O1,Cpx, and Opx at a
KELEMEN
ET AL.: FOCUSED
POROUS
tion of veins by magma solitons, submitted to Journal of GeophysicalResearch,1994]. Focusedflow of melt in coalescing conduits and cracks beneath mid-ocean ridges, perhaps convergingbeneath the center of individual ridge segments, would leave muchof the shallowmantleunaffectedby chemical exchangewith liquidsfrom deeperin the meltingcolumn. High melt/rockratiosin theseconduitswould producehighly porous dunites,equilibratedwith ascendingmelt, so that ascending liquids may remain out of equilibrium with mantle peridotite surroundingthe conduits. Mixing in focusedflow zoneswould producea relatively uniform liquid compositionin the mantle, which would then be delivered as aggregateMORB during crustal accretion.
r_,vluence lot r ocuseu lv, e•t Flow in the ...................
Upper Mantle:
Formation of Replacive Dunites
Field studieshave demonstratedthat focusedporousflow of melt has occurred in the upper mantle. The most obvious features formed by focused melt flow are bodies of dunite (composedof >95% olivine). These occur in a variety of morphologies,ranging from large, generally elongate, lensoid bodies, often including concentrationsof "cumulate"chromite,
FLOW
AND MELT
EXTRACTION
479
through smaller, commonly tabular bodies which can often be shown to be replacive of surrounding,pyroxene-bearingperidotite [e.g., Boudier and Nicolas, 1977; Dick, 1977; Quick, 1981; Kelemen, 1990; Kelemen et al., 1992], to small, irregular patches. Some dunites have been consideredto be cumulate dikes,i.e., productsof crystalfractionationfilling cracks,which were initially filled with olivine-saturatedmelt. While this processmay have formedsomedunitebodiesin their entiretyand may contributeto the formation of many others,this discussion will concentrateupon those dunite bodies which have demonstrably formed by replacementprocessesduring porousflow of melt. These replacive bodies of dunite form by dissolutionof pyroxene,combinedwith precipitationof olivine, in decompressing melts infiltrating along grain boundaries. Such duniteshave been shown to be replacive on the basisof their contactrelationships(Figure1). While mantle dunites are best known in the mantle sections of
ophiolites,within the upper 15 km of the mantle beneaththin, oceaniccrust,they are alsofound in peridotitesof deeperprovenance. For example, there are garnet-bearingdunite xenoliths derivedfrom depthsexceeding90 km in Hawaii [Senand Jones, 1990] and Siberia [Sobolevet al., 1973; Pokhilenkoet al., 1977]. Dunitesderivedfrom more than 30-40 km depthare abundantin
high pressurewill be saturatedonly in O1 during coolingat a lower pressure.(b) The effect of decompression from 2 to 0.5 GPa, cooling, and closed-system,crystal fractionationupon a picritic (high Mg basalt) liquid formed by a small degreeof partialmelting of mantlelherzoliteat 2 GPa. The adiabaticallyascendingliquid at point W is initially undersaturated in solids. As it coolsanddivergesfrom an adiabaticPT path,it saturatesfirst in O1. Fractionationof O1drivesthe liquid to saturationin Cpx alongthe vectorlabeledX, after which coprecipitation of O1 + Cpx, andreactionbetweenliquid and O1producingCpx, drivesthe liquid alongthe vectorlabeled Y. Finally, saturationin Opx is reachedat point Z. The liquid compositionat Z will be substantiallydifferent from a partial melt of lherzolite at 0.5 GPa, having a lower Mg/Fe ratio and lower Ni and Cr contentsthan a mantlemelt. (c) Reactionat 2 to 0.5 GPa betweenmantlelherzoliteandthe samepicriticliquid asin Figure 2b. The peridotitereactantis just at its solidustemperatureat 0.5 GPa. Liquid rising adiabaticallyis aboveits liquidustemperature.For this reason,alongpathA, the melt initially dissolvesperidotite. This leadsto olivine saturationin the liquid, whichwill crystallizeO1,andcontinueto dissolvepyroxene.One possibleliquid pathis shownas the vectorlabeledB; this is for relatively rapid reactionand slow cooling,during which liquid mass increases. More rapid cooling,or slower pyroxenedissolution,would producederivative liquid compositions within the shadedregionboundedby B, C, X, andY. Eventually,pathB leadsto saturationof the melt in Opx as well as O1. Continuedreactionand cooling will consumeCpx and a small amountof O1 from peridotitereactants, producingdecreasingliquid mass, Opx + O1 solid assemblages,and derivative liquids along path C. Finally, at D, the liquid will becomesaturatedin Cpx. The liquid compositionat point D will be similarin major
elementcomposition(Mg/Fe, Ni, Cr, SiO2)to a smalldegreemeltof mantlelherzoliteat 0.5 GPa,although its trace elementcharacteristics may preservea "memory"of its open systemprovenance.At bottomare PT plots summarizingthe compositionof liquid and solidproductsof the polybariccrystallizationand reactionprocesses illustratedabove. (d) Generalfeaturesof adiabaticascentpathsfor solidsand liquids in the mantle, relative to the slopeof the mantlesolidusandthe saturationsurfacefor olivinein mantle-derived liquids[e.g., Yoder,1976; McKenzieand Bickle, 1988]. If liquid ascendsto the surfacealongan adiabaticPT pathin a closedsystem,it will remainundersaturated in solids,retainingthe composition of a partialmelt of mantleperidotiteat highpressure. If it ascendsin an open system,it will be capableof dissolvingsolid phasesfrom surroundingperidotite, resultingin a net increasein liquid mass. Where it coolsto temperatureslower than alongthe adiabaticascent path,it will saturatefirst in O1. Adiabaticallyascendingmantleperidotitefollows a lesssteepPT path,due to the energy requirementsof fusion during ascent. The lherzolite solidus has a much shallower PT slope than adiabaticascentpaths. Ascendingmantlelherzolitewill graduallygeneratepartialmelt, consumingpyroxeneas it doesso. Cpx is generallynot completelyconsumedby closedsystempartial melting during adiabaticascent beneathmid-oceanridges[e.g., Dick et al., 1984]. By contrast,reactionwith ascendingliquid can completely dissolveall pyroxenefrom lherzolite. (e) Productsof the polybaric,closedsystemcrystalfractionationpath illustrated in Figure 2b. Liquid mass remains constantover the adiabatic portion of the ascentpath, then decreasesduring conductivecooling. (f) Productsof the polybaric reactionprocessillustratedin Figure 2c. Liquid massincreasesduringthe initial portionof the ascentpathin whichthe liquid is under-saturated in solids and also over part of the path in which the liquid is saturatedonly in olivine. As the liquid continuesto cool, liquid massbeginsto decrease,andthe liquid becomessaturatedin pyroxeneaswell asolivine.
480
KELEMEN
ET AL.' FOCUSED
POROUS
continentalxenolith suites[e.g., Nixon, 1987]. Replacivedunites are found within the Ronda peridotite massif [Remaidi, 1993; Garrido et al., 1993], interpretedto have formed at depthsfrom 40 to 15 km. Replacive dunite bodies,replacingpyroxene-fich peridotitesand pyroxenites,are also observedin crustalrocks, within the ultramafic portionsof many large, mafic layeredintrusions, including the Bushveld intrusionin South Africa [e.g., Stumpfland Rucklidge,1982], the Stillwaterintrusionin Montana [e.g., Raedekeand McCallum, 1984], and the Rhum intrusionin Scotland[e.g., Butcheret al., 1985], as well as in smaller,zoned ultramafic-felsicintrusions[e.g., Aho, 1956;James,1971;Irvine, 1974; Kelemen and Ghiorso, 1986].
Mass and Energy Balance in Formation of ReplaciveDunites
FLOW
AND MELT
EXTRACTION
We used this new version of the solution model to calculate
the solubility of mantle peridotite in basaltic liquids beneatha mid-oceanridge. The resultsare illustratedin Figure 3. Calculations were made for a pressureof 0.2 GPa, usingtwo liquid
compositions (Table 1): (1) a picritic liquid producedat small degrees of melting of mantle lherzolite at about 2 GPa and 1350øC, and (2) a tholeiitic liquid with a magnesianmid-ocean ridge composition,producedby 12% meltingof mantlelherzolite at 1 GPa and 1325øC,closeto the conditionsinferredfor average mid-oceanridgebasalt[e.g., Kinzler and Grove, 1992;Langmuir et al., 1992]. The solid reactant was a depleted peridotite compositiontypicalof abyssalperidotitesdredgedfrom the midoceanridges[e.g., Dick, 1989]. These calculationsincorporatethe effect of temperatureas well as pressure. If partial melts beneath "normal" mid-ocean ridge segments(potentialtemperature< 1400øC)rosein a chemically closedsystem,they would have temperatures rangingfrom more than 1350øCto about 1200øC,dependinguponthe pressure
As noted by Sleep [1975], ascendingpartial melts of mantle peridotite,if they rise adiabatically,will be abovetheir liquidus temperatureat pressureslower than the pressureof melting (Figure2). If they are in contactwith solidphasesin the overlying mantle, these melts will dissolve solids until the combined of melting[e.g., McKenzieand Bickle, 1988], with an average effects of conductive cooling, cooling due to the endothermic closeto 1275øC. The solidmaterialrisingbeneatha ridgeundereffect of dissolutionreactions,and compositionalchangedue to goespartial melting and thereforeis cooledby the endothermic dissolutionreactionsreturnthem to saturationin olivine. Sleep effect of the enthalpyof fusion. It may reachthe top of the adia[1975, also personalcommunication,1994] calculatedthat aver- baticupwellingregime,nearthe baseof the crust,at temperatures age basaltic melts ascendingbeneathspreadingcentersmight ranging from about 1275ø to 1200øC. At any given pressure, dissolveseveralpercent of their massdue to this thermal effect adiabatically ascendingliquids in a closed systemwould be alone. Subsequentto olivine saturation,pyroxenedissolution hotter(up to 100øChotter)thanadiabaticallyascendingperidotite combined with precipitation of a smaller mass of olivine will undergoingpartial melting. Thus melt/rock reactioninvolvesa continueto increasethe liquid massand the porosityin the solid combination of processes' solution of solid phases into superliquidusmagma, dissolutionof pyroxenein olivine-satumatrix. These reactionswere analyzedthermodynamicallyby Kelemen [ 1990], who found that the exothermic effect of olivine rated magma, and conductive cooling of hot liquid passing path for a crystallizationnearly balancesthe endothermiceffect of pyrox- throughcooler solids. A typical pressure-temperature melt might begin at 1350øCand 2 GPa, and end at ene dissolution.Kelemen notedthat the apparentheat of crystal- high-pressure 1300øC and 0.2 GPa, near the base of the crust. An average lization of olivine, per gram, at typical magmatictemperatures is about1.3 timeslargerthan the apparentheatof fusionof pyrox- mid-oceanridge melt interactingwith ascendingperidotitemight enes, so that reactionsat constantpressurebetweenolivine-satu- begin at 1325øCand 1 GPa and end at 1275øCand 0.2 GPa. As can be seenin Figure 3, the solubility of peridotiteunder these rated liquid and pyroxene-bearingsolids increasethe mass of picritic liquid underconditionsof constantenthalpyor constanttempera- conditionsis foundto be about25% in the high-pressure, ture. This prediction has been confirmed experimentally by melt, and 3-15% in the magnesianmid-oceanridge basalt. By Daines and Kohlstedt[1993]. Where pressuredecreases, as for contrast,the solubilityof olivine in theseliquidsin the temperaascendingsolids and liquids beneatha mid-oceanridge, liquid ture rangeof interestis small,sothat reactionwith duniteduring mass will increase still more. ascenthasa comparativelyminor effecton the massof ascending As can be seen in the phasediagramsof Figure 2, the total liquids. The phaseproportionsof the reactionproductsat 1300ø and solubility of pyroxene in olivine-saturated, mantle-derived 1275øC are also illustrated in Figure 3. The high-pressure, magmas is dependent upon their composition and upon the temperatureand pressureof the dissolutionreaction. A simple picritic melt dissolvesenoughpyroxeneto convert 4 times its rule is thatthe largerthe differencebetweenthe pressureof initial massin harzburgiteto pyroxene-freedunite. The lower-pressure, melting and the final pressureof reaction,the largerthe solubility magnesianmid-oceanridge basaltmelt convertsone equivalent of pyroxenein a given liquid [e.g., Stolper, 1980]. Other varimassof harzburgiteto dunite. From thesecalculations,we may ables,suchasthechanging alkaliandH20 contentof theliquid conclude that ascendingmelts beneath mid-ocean ridges are as it reacts,play an importantrole in determiningthe solubility. capableof producingsubstantialadditionalporosityby dissoluFor this reason,it is impossibleto usetwo- andthree-dimensional tion reactionsandcanleavebehinda massof dunitein the upper mantle equivalent to the massof the oceaniccrust. These calcuphasediagramsfor accurateestimationof pyroxenesolubilityin natural, multi-componentmagmas. Kelemen [ 1990] useda ther- lations are for the maximum extent of reaction, since they modynamicsolutionmodel for silicateliquids [e.g., Ghiorsoet presumethat all ascendingmelt reactswith mantleharzburgite. al., 1983; Ghiorso, 1985; Ghiorso and Kelemen, 1987] to calcu- If kinetic factors inhibit reaction, or if melt flow is focused into late melt-rock reactioneffectsin naturalsystems.Thesecalcula- nonreactivedunitechannels,thenlessporositywill be createdby tions were limited, in part, due to the difficulty of accurately reaction and less dunite will be formed. These calculations of the mass of dunite which can be calculating melt compositionsat low melt fractions. A new version of the model [Ghiorso and Sack, 1993, 1994] is now producedby reactionmay be comparedwith observedproporavailable. This new version incorporatesminor components, tionsof dunitein the uppermantlesectionof ophiolites.Lippard estimatesof theproportionof dunitein suchas sodiumand titanium, in solid phasessuchas pyroxenes et al. [ 1986] summarized and oxides and thereforecan predict the equilibriummode and the Oman ophiolite. A varietyof French,British,andAmerican compositionof systemsincludingsmallmelt fractions. workershave estimatedthat dunitecomprisesfrom 5 to 15% of
KELEMEN ET AL.: FOCUSED POROUS FLOW AND MELT EXTRACTION
basalt + peridotite
picrite + peridotite c 30 ._
481
ß
.
,
!
.
.
.
!
.
.
.
!
.
.
.
•
.
,
.
!
.
.
.
•
.
.
.
o
E
25
o
-o
20
E •
15
!
._
temperature(øC) ß
10
I
I
I '-'- •275 I I -.-•250 I I -*-•225 I -15
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
mass fractionbasalt/(basalt+ peridotite)
mass fractionpicrite/(picrite+ peridotite) 0
liquid
OøC 2O
4O
additionalliquid producedby reaction 6O
olivine
8O
0
orthopyroxene
2O
4O
6O
8O
IO0
Figure 3. Resultsof thermodynamicmodelingof reactionbetweenliquidsand mantleperidotiteat 0.2 GPa, on the quartz-magnetite-fayalite oxygenbuffer, usinga solutionmodel for naturalsilicateliquids and coexisting minerals[Ghiorsoand Sack,1993, 1994]. Solid andliquid compositions usedin modelingare givenin Table 1.
Inputrequiredfor themodelis pressure, temperature, oxygenfugacity,andbulkcomposition.Outputincludes the proportionsand compositions of solid and liquid phasespredictedto be presentat equilibrium. Resultsare presentedin two columns,the left-handonefor picriticmagmaplusperidotite,andthe right-handonefor basaltic magmaplusperidotite.The x axisin all diagramsis the massfractionof the magmaticcomponent, varyingfrom pure peridotite(0, on left) to pure picrite or basalt(1, on right). The top two diagramsillustratethe percent changein liquid massdueto isothermalreaction,as a functionof the massfractionof the magmaticcomponent. This valueis calculatedas 100% (1 - mliq/mliq'),wheremliq is the massof liquid calculatedby the modelto be presentin a givenbulk composition at 0.2 GPaanda specifiedtemperature, andmliq' is themassof liquidwhich wouldbe presentin a linearcombinationof the peridotiteandmagmacompositions at the sametemperature• and pressure.The bottomfourdiagramsillustratetheequilibriumproportions of solidandliquidphasespresentasa functionof the massfractionof the magmaticcomponent.A small amount( • (3- F)(1 + F)/[2 (1- F)] where
tions.
Results of Laboratory Experiments Dissolution Experiments This sectionillustrates the results of some initial experiments
the dynamicinstabilityof diffuseporousflow in whichvz isthefluidvelocity, Lxis a measure of thewidthof whichdemonstrate
the systemor betweenadjacentfingers,D is the diffusivity in a solublematrix. Table salt (NaC1)and 0.1 to 2 mm glassballs (includingdispersion dueto porousflow), and• and•c arethe were combined into an approximatelyhomogeneousmixture glasstank58.3 cmhighx 63.5cmlongxl.0 porosityand permeability,with subscriptsi and f indicating withina rectangular valuesbefore and after a dissolutionreaction. As notedby both cmwide(Figure4). Waterwasslowlyfedfromabovethrougha Chadamet al. and Steefl andLasaga,channelinginstabilitiesare pipewith manysmallholesto makethe flow even. Waterwas possiblefor virtuallyany combination of v andD, providedthat maintainedat a constant level abovethe solid matrix. The top of the salt andglassmixturewas approximately planar,parallelto the width of the systemis sufficientlylarge. to theflow direction.The In addition, Steefi and Lasaga [1990] emphasizethe impor- thetop of thetankandperpendicular throughthe saltandglassballs,dissolvingsalt tance of the reaction rate in determining the growth rate and waterdescended morphologyof dissolutionchannels. If reactionrate is much until it becamealmost completelysaturated. At the bottom, slowerthan vz, for example,thensmallinitial variationsin water escapedthrougha 3-cm layer of foam rubberabove 50 smallholesin thebottomof thetank. porositymay not leadto instability.HoefnerandFogler [1988] approximately Porousflow rapidlybecamefocusedalongsalt-freedissolution and Daccord [1987] have done laboratory experiments investigating the combinedinfluenceof dissolution reactionrate channelsparallelto the flow direction(Figure5). Preliminary [Whiteheadand Kelemen,1994] conducted using and flow velocityon the morphologyof dissolutionchannelsin experiments porousmedia composedof natural and syntheticcarbonates. only salt,withoutglassballs,had qualitativelysimilarresults. They foundthat focusingof flow in dissolutionchannelsis most pronounced at intermediatevaluesof the ratio of reactionrateto Vzß
Tait and coworkers[Tait and Jaupart, 1991; Tait et al., 1992] and Bddard et al. [1992] have investigatedfocusing of porous
However, as dissolutionchannelsformed,the top of the dissolv-
ing salt in the tank was gravitationallyunstableand formed slopeswhichquicklyreachedthe angleof reposeof salt. Glass balls of variable size were introducedto hold salt grainsin place
in orderto studythe morphologyof dissolutionchannelsin a by Chadamandcoworkers, flow flow in solidifyingcrustalplutons,with experimentsinvolving morerigidmatrix. As proposed channels becauseinitialperturcompositionalconvectionin a cooling, crystallizing system. is focusedin growingdissolution of salt. Areas Experiments were conductedin tanks filled with aqueous bationsin porosityare magnifiedby dissolution with slightlyhigherthanaverageporosityhavehigherwater/salt ammonium chloride solutions. In these systems,cooled from andhigher below,liquidsderivedfrom crystalfractionation werelessdense ratiosresultingin lowersalinityandrapiddissolution, in thanhotterinitial liquidsandrosebuoyantlyfrom the baseof the permeabilitypermitsfasteringressof water,undersaturated tank. Rising, evolvedfluid was heatedby its surroundings and salt,from higherin the chamber.Boththesefactorsin turnlead
484
KELEMEN
ET AL.: FOCUSED
POROUS
FLOW
AND MELT
EXTRACTION
water reservoir, open at top inlet
tube
dozens holes
with
of small to diffuse
flow
mixture
variable height outlet
of
salt & glass balls
tube
water
water
+
glass balls water + glass balls + salt foam
plexiglass with more
than
outlet
50 small
holes
lO closed
water
reservoir
Figure 4. The tank used in experimentsdescribedin the second section. The outsidewalls and baseare constructedof Plexiglas. Diffuse flow into the tank, more rapid than the out flow, fills a reservoirof water at the top. Excessinput spillsoff the top of the tank. Water insidethe tank runsdownthrougha mixtureof glass balls plus salt and descendsthrough a layer of foam near the base,then throughmany small outlet holes,into a closedreservoir. The only outletfrom thisbasalreservoiris via a tubewhose height can be varied in order to controlthe total pressurein the
•
20
o
40 50
tank.
to morerapiddissolution of saltin andabovetheregionof high porosity, creating a channel with even higher averageporosity, and so on.
The dissolutionfront remainsa sharpboundarythroughoutthe experiments,separatingsalt-absentporousmediacomposedonly of glassballs from salt-richporousmediawith approximately the initial concentrationof salt (as determinedby visual inspection). This suggests that conditionsof local equilibriumare very nearly maintainedalong the dissolutionfront; water flowing acrossthe front becomes saturated in salt over a submillimeter
scale. As the
experimentsprogress,large dissolutionchannelsgrow at the expenseof nearby,smallerones,resultingin formationof a series of regularlyspaced"hills" and "valleys"in the dissolutionfront. With time, the amplitudeof the largerchannelsincreases,andthe numberof channelsdecreases,so that only a few channelsextend to the bottom of the chamberat the end of the experiment. This occurs because relatively high permeability within the large channelsleadsto relatively low hydrostaticpressureat their tops. This, in turn, leadsto lateral flux of water into the topsof larger channels. Additional flux of water throughthe large channels leadsto their continuedgrowth,while decreasedflux in smaller, adjacentchannelsleadsto their disappearance as the dissolution front advancesthroughthe tank. A secondimportantobservationfrom theseexperimentsis that flow lines for fluid in the salt/glassmatrix convergetowarddisso-
Figure 5. Resultsof an experimentin which water runs down through a mixture of glass balls and salt. An initially planar, horizontal interface is presentbetweenthe water reservoirat the top of the tank and the mixture of glassballs and salt. As time progresses,descendingwater dissolvessalt from the porous matrix. Within minutes, the planar dissolutionfront becomes unstable,and elongatedissolutionchannelsparallel to the flow directionbeginto form. In the initial stagesof thisprocess,many shortchannelsform. As time progresses, the longer,wider channels increasein length very rapidly, while the smalleronescease to grow and ultimately disappearas the solutionfront advances. Somecompactionof the mixture of glassballs and salt occursas the salt is removed by dissolution,and compactionis greatest abovethe largestdissolutionchannels. lution channelsnear their upstreamendsand divergefrom dissolution channelsnear their growing,downstreamends(Figure 6). Relatively low hydrostaticpressureat the upstreamend of a highporositydissolutionchannelleadsto lateral influx. High flux
KELEMEN
ET AL.: FOCUSED POROUS FLOW AND MELT EXTRACTION
laboratory experiments growthrate
50
/ /•
A
data
• 30
485
k = 4.60 e.0020t e• R=.98 //
6 ,•,o øc•ø B
?
e- 20
p
•
o•,' o/
•'
lO
'
•
L = 1.67 e .0019t
o• © o o
R = .99
•
0
500
1000
1500
25OO
2000
time, t (sec)
Figure 6. Flow vectorsat one time during the experimentillustratedin Figure 5 Flow lines convergetowarddissolutionchannels near their tops and diverge from the center of dissolution channelsnear their bases. The approximatedirectionandrelative magnitudeof fluid velocity indicatedby the vectorswere determinedby observingthe distributionof dye injectedalongthe top of the tank during the experiment. within the channel,in turn, causeshigh hydrostaticpressureat the downstream end (the channel "tip") where permeability decreases,resultingin lateral dispersionof flow out of the channel. If applicableto the mantle,this observationhasthe potential to resolvethe paradoxnotedby Carlson[ 1992], in which thereis geochemical evidence for flow of magma toward some dunite channels [e.g.,Takahashi, 1992], while other dunite channels showevidenceof outwardflow [e.g., Kelemenet al., 1992]. The lengthof the channels( measuredfrom the upstreamlimit of the dissolutionfront in the tank) canbe fitted as an exponential functionof time (Figure 7). An initial exponentialgrowth rate is in accord with the linear stability analysis of Chadam et al. [1986], who consideredthe channeling instability in a porous medium with a two-dimensionalflow field. Here we presenta simplified version of this stability analysisin order to illustrate some of the essentialphysicsof the process. A liquid flowing uniformly in a porous material encountersa material of lower permeability which it can partially dissolve. The dissolution restoresthe material to the original permeability. The interface between the two materials is initially flat, and extendsat right angles to the flow. The stability of the flat interface, and the spatial distributionsof permeability, porosity, soluteconcentration, and water composition were studied by Chadam et al. [1986] and Ortoleva et al. [1987]. They found that the planar interfaceis unstablewith fastestgrowing wavelengthdetermined by "grain size, initial modal amountof material reactive mineral in the rock, initial porosityand compositionand velocity of the inlet fluid." Essentially,their mathematicalrelation simplifiesto the wavelengthof fastestgrowth being proportionalto thickness of the front, which is determinedby diffusivity divided by fluid velocity (within the "transportcontrolledregime"where reaction rate is almostas large as fluid velocity;for details,seeSteefiand Lasaga [1990]). Since diffusivity of a soluteflowing througha granular material is dominatedby mechanicaldispersion,which is equalto velocity times grain size [Phillips, 1991], this reduces to the simplefact that channelsizeis proportionalto grain size. Here, the essentialsof suchstability analysisare presentedin as simple form as possible. For this purpose, many of the elementsincludedby Chadamand coworkers,suchas grain size,
ß
B,0to1250sec ß j
ß ,1250 to 1700 sec
....
'0....
;0....
....
.... 4'0.... 10....
channel length, L cm
1500 seconds
1200 seconds
Figure 7. Length and aspectratiosof two dissolutionchannelsin an experimentsimilar to that illustratedin Figure 5. Length is measuredfrom the highestpoint on the dissolutionfront to the bottom
of each channel.
Channel
A was the first to reach the
bottomof the tank in this experiment,and B was the last discrete channelto reach the bottom. The growth of the channelscan be fitted with an exponentialfunctionof time, as predictedin linear stability analysisby Chadam et al. [1986], and in the second sectionof this paper. The width of growingchannelsis approximately proportionalto the squareroot of their length. ChannelB showstwo aspectratio regimes,one developedbefore ChannelA reachedthe bottom of the tank, and the other afterward. Steefi and Lasaga [ 1990] noted that growth of channelswith width >
•/2L minimizesthe effectof lateraldiffusionof soluteinto the growing finger. Bottom diagramsshow channelmorphologyin this experimentafter 1200 and 1500 secondshad elapsed.
porosity variation, change in volume of the solute, etc., will be neglected. Let the interface
lie at
rl(x,t)= z
(1)
486
KELEMEN
ET AL.' FOCUSED POROUS FLOW AND MELT EXTRACTION
tion, and the one on the right is due to the perturbation. A boundaryconditionof y is producedusingthe x derivativeof the
and the equationfor the dissolutionof the interfacebe
c)•l(x,t)
•
= •w
(2)
where w is flow velocity and ¾is the ratio of the solubilityto the concentrationof the solutein the solid phaseacrossthe interface. In this model, the interface is immediately dissolvedwith a rate proportionalto the amountof materialflowing into the interface. Let the total vertical velocity w consistof a steady,uniformly moving componentplus a small perturbation,andlet the interface consistof a flat horizontal plane plus a small deviation. These are expressedas
w = wo + w' (x,t). (3)
r/= r/o(t) + r/' (x,t).
pressure change fromequation (9) alongwiththefirstequatiohOf (6), and the fact that
so that
gt= A(t)sin(Ix)e -tz
c•t- ywø
(4)
r/o = •4Vot= z. from this flow
(5) will
A(t) = llwo
(12)
now be
investigated.The equationsgoverningperturbationsto the liquid flow in the porousmaterialare givenby Darcy'slaw:
Using (2) with (4), (6), (8), (11), and (12) resultsin o•N
kn •Pn kn •Pn
(11)
whichproduces with (8) and(10) at Z = 0
c)r/o_
of the deviations
(10)
SinceN is small,this conditionwill be assumedto apply at z=O. A solutionto equation(7) is
The steadyflow andthe flat interfaceare givenby
The behavior
- -3-fx =
•X z=N
•=_7/w ø1_1N=T•Wo klk2 • iW n
(6)
(13)
which has an exponentially growing solution for kl>k2 (upstreampermeabilitygreaterthandownstream),
kl-k2]t
klk2. N o• e 7/wø[
(14)
Equation (14)shows thatthelargerthewavenumber, l, the so
fasterthe growthrate. Therefore,wherewe neglectdiffusionand grain size, very small length scaleperturbationsinitially grow V2•n =0 most rapidly. The more completetheoriesof Chadam et al. (7) [1986] and Ortoleva et al. [1987] have shown that diffusion Here, subscriptn=1,2 denotesthe regionupstreamor downstream processesand grain size limit the magnitudeof the fastestgrowof the interface, respectively. Consider a perturbationto the ing wavenumber,sothat fastestgrowthis scaledby grainsize. In interface accord with this theory, the first wavelengthsobservedin our •1'= N(t) cos(Ix) . (8) laboratoryexperimentsare small,but largerthan grainsize. The disappearanceof the short wavelength channelslater in the We are seeking the lateral pressure variations due to the experimentsis probablya resultof lateral entrainmentof flow perturbed interface.Assumingwo >> w', t = 0 (sotheunper- into the longerwavelenthchannels.
These results, and those of Chadam and coworkers, are for turbedinterfaceis at z = 0) and N(t) is smallerthanthelength scale,2 zr/l, integratethe equationfor w upwardfrom a plane growth at infinitesimallysmall channellengthand not directly normal to the bottomof the perturbedinterfaceat z=-N to a plane applicable to the finite channels measured in experiments
describedhere. Nonetheless,approximatevaluesfrom the experiment in Figure 7 are usedin the following calculation. Given solubility of NaC1 in water at 25øC of about 0.2 (weight units)
normal to the top of the perturbedinterfaceat z=N
/.tI wødz =const p(-N) =-•-• .
(9)
-N
and concentration of NaC1 in the initial solids of about 0.4 (so
that 7 = 0.5), widthof theboxof about50 cm ( l = 2 z;/50),an initial flow velocityof 0.05 crn/s,anda final flow velocityof 0.5
Pressure from perturbation velocityw' is of order w' N andis assumedto be negligible. The term in the left bracketsis the pressurechangethat would be found even without the perturba-
cm/s(suchthat k1 = 10k2), oneobtains
N o•eO'003t
KELEMEN
ET AL.: FOCUSED
POROUS FLOW AND MELT EXTRACTION
487
in surprisinglycloseagreementwith the observedgrowthratesof finite channelsin the experiment. The agreementbetweenthe predictionfor growth of infinitesimally small channelswith our datafor growthof finite channelssuggests thatthe channellength remainsunstablethroughoutthe experiments. Our experimentalresults on growth rate are different from thosein the numericalexperimentsof Steefiand Lasaga [ 1990]. They studieda systemof fixed width,with an initial high-porosity channelabouthalf as wide as the system,and found that the lengthof the channelinitially increasedas an exponentialfunction of time but that the growth rate subsequentlydecreased. Factors which could limit the length of dissolutionchannelsas theygrowinclude(1) lateraldiffusionof the soluteinto thegrowing channeland (2) limitationsto the lateralentrainmentof flow due to fixed systemwidth. In considering(1), it is apparentthat diffusionof saltinto the waterwithin a very long,narrowchannel will eventuallyresultin a decreasing dissolutionrateat the tip of plan view the channel. However, Steefl and Lasaganote that increasing width of growingchannels,so that the squareof the half width is proportional to the length, would preservethe initial ratio of transport time down the channel to diffusion time across the channel,neutralizingthe negativefeedbackeffectof lateraldiffusion in a long, narrow channel. Figure 7 illustratesthat these dimensionswere generallymaintainedduringchannelgrowthin our experiments. This was not possiblein Steefl and Lasaga's simulations,beyonda certainpoint, becauseof the limited width of the system. Factor (2) may also have affectedtheir results. These limitations were unimportantat the flow velocities and cross section lengthscalesof the experiments describedin thispaper,andmay not be presentin any systemwith semi-infinitewidth. Figure 8. Schematicillustrationof resultsof experimentsin which an aqueoussolution, saturatedin ammoniumchloride at room temperature,is injected into a narrow gap betweentwo Crystallization Experiments circular plates,as illustratedin the bottomdiagram. Liquid is This paragraphbriefly describespreliminary experiments injectedat the centerand flows outward,escapingfrom the free investigatingthe morphologyof porousflow whenliquid massis edgeat the perimeterof the plates. The lower plateis maintained decreasing,and solids are precipitated. Water saturatedin at 0øC, which causescoolingof the solutionandcrystallizationof ammoniumchloride,at roomtemperature, wasreleasedthrougha ammoniumchloride. At the top is a "stratigraphic" map of the central hole into a narrow gap (-1.4 mm) between a leveled, distributionof ammoniumchloridecrystalsover time. Later flow circularaluminumplatemaintainedat 0øCandanoverlyingPlex- paths are superimposedon those which formed earlier. In all iglas plate. The ammoniumchloridesolutionflowed radially experiments,initially radial flow of fluid quicklyorganizesitself Outward to thefreeedgesof theplates.As in theporous flow into a singlechannelof focusedflow. This channelis surrounded experimentsdescribedabove,the hydrostaticpressurewas held by porous "walls" of ammoniumchloride crystals. Flow in a constantin theseexperimentsby maintaininga constantlevel in channelpermitsoutwardflow of fluid with a minimumof cooling the reservoirof ammoniumchloridesolution. The solubilityof and crystallization. Eventually,however,interior crystallization ammoniumchloridein wateris stronglytemperaturedependent. "chokes"the channel. Sometimes,increasingpressurein the Upon contactwith the cold aluminumplate,the saturatedsolution channelleadsto crackingin the wall. After the channel"chokes," begancrystallizingammoniumchlorideas it cooledand flowed flow is divertedthrougha high-porosityregionor a crackin the radially outward. Crystals thus began to fill the "porosity" channelwall. Releaseof the fluid into a relatively crystal-poor betweenthe aluminumand Plexiglasplates, restrictingflow. areasis followed by initially diffuse flow, then by formationof Figure 8 schematicallyillustratesthe results. Whereas flow is another walled channel, and so on.
H=O+NHnCl
I inflow (const P)
initiallydiffuseandradial,it veryquicklyis restricted to a single channel, which becomes armored with crystal-rich "walls." Initial flow focusingoccursbecausechannelswith rapid fluid flux cool and crystallize less than fluid undergoingradially dispersiveflow. However, the solutionflowing throughthe initial channelstill coolsas it passesoutwardand so continuesto crystallize. Crystallizationultimately restrictsflow so that the channelis no longerthe mostpermeablepathfor fluid introduced at the centerof the plates. At this point,mostof the flow begins to passthrougha relatively high-porositysectionof the channel wall, forminga new channel.This sequenceof eventsis periodically repeatedthroughoutthe durationof the experiments. In someexperiments,the transitionfrom one channelto anotheris
precipitatedby formation of brittle cracksin the initial channel wall.
Resultsof Numerical Experiments Numerical experimentson formation of dissolutionchannels have been madeusing a modificationof the "latticegas"model first proposedby Frisch et al. [1986]. Lattice gasesare fully discretizedmodelsof moleculardynamics,in which an ordered latticeis populatedby identical,pointlikeparticlespositionedon the nodes. The particlespropagatealongthe latticelinks, "hop"
488
KELEMEN
ET AL.: FOCUSED
POROUS FLOW AND MELT EXTRACTION
one nodeper time step,and interactwith eachotheronly when they meet at a node. Then a collisionoccurs,conservingmass andlinearmomentum.After the collisiontheparticlesareredistributed in the available lattice directions. In the limit of small
velocities,the behaviorof individualparticles,takenas a whole, leads to macroscopicbehavior that resemblesthe flow of fluid.
ExperimentsWith a Gradientin Solubility and No Solution
Front
Theinitialcondition in theexperiments described in theprevious section is one in which there is a concentration front in the
solid matrix. Upstreamof this front, there are no solublesolid
particles. In the mantle, by contrast,the porousmediumis Equationsdescribing the macroscopic behaviorof thelatticegas initially composed of homogeneous peridotite.Partialmeltsare closelyresemblethe incompressible Navier-Stokesequations. initially saturated in all solidphases.As meltsascend,they Latticegasesareespeciallyusefulin treatingcomplicated bound- become undersaturated in solids. This undersaturation will drive
ary conditionssuchas flow throughporousmedia,becauseone neednot solvethe Navier-Stokesequationsat the boundary:one merelylets the particlesbounceoff it [e.g.,Rothrnan,1988]. To simulatea pressuregradient,one increases the probabilitythat particleswill movein a specifieddirection. By controllingthe
collisionrules,onecanalsovary viscosityanddiffusivity[e.g., Henon, 1987; d'Hurnierset al., 1988].
Simulationsin this paperuse a floatingpointanalogof the lattice gas method (the relaxation lattice Boltzmann method of
Qian et al. [1992]), allowing mixtures of miscible fluids [Flekkoy,1993],to whichchemicaldissolution andprecipitation were added[E. Aharonov,manuscript in preparation].In orderto simulatea liquiddissolving theporousmediathroughwhichit is flowing, one givesthe fluid particlesthe abilityto detachsolid particlesfrom a wall uponcollidingwith it. The probabilityof detachinga solidparticleis
dissolutionreactionswhichtendto restoreequilibrium,but at the sametime the dissolutionprocessmay producea channeling instability. If high-permeabilitychannelsform, higher flow velocities will drive liquids away from equilibrium, in turn increasingthe dissolutionrate and leading to faster channel growth.
Figure 11 illustratesthe resultsof a numericalexperimentin which the incomingfluid is saturatedin the solidmatrix phase, but there is a gradientin solubility, so that the equilibrium concentration of the solute in the fluid increases downstream.
Despite the absenceof a solutionfront in this experiment,a channelinginstability is observed. This illustratesthat dissolution channelsmay nucleateand grow in a homogeneous medium (suchas may be foundin the uppermantle),in the absenceof an initial solutionfront. A full linearstabilityanalysisof thisproblem, incorporatingthe effects of compactionin a viscously deformingsolidmatrix, hasrecentlybeencompleted[Aharonov P- (1-C/C•q)[(n - s)/n] et al., 1994, Channelinginstability of upwelling melt in the mantle, submittedto Journal of GeophysicalResearch, 1994]. where C is the concentrationof the solutein the fluid, Ceq is the The analysisconfirmsthat diffuse porousflow of melt in the equilibrium concentrationof the solutein the fluid, and the final adiabaticallyupwellingmantleis unstableand will form highterm is a surfacetensionor chemicalpotentialgradienteffect porositychannelsthat are elongatein the verticaldimension. which prevents"tunneling"into aggregates of solid particles, The numericalexperiments alsoillustrateanotherconsequence whereinn is the total numberof nearestneighborson the lattice of havinga gradientin solubility. Becausea new instabilitycan (6 for the two-dimensional hexagonallattice),ands is thenumber nucleateanywherewithin a continuousporousmedium,in the of solidnearestneighbors.The probabilityof detachinga solid presenceof a gradientwith solubility increasingdownstream, particle decreasesas the concentrationin the fluid rises,until a theremay be no limiting lengthfor growingdissolutionchannels, saturation level is reached and no more dissolution occurs. This even if the width of the systemis limited. Dissolutionchannels numericaltechniqueallowsoneto vary boththe diffusivityand in the mantle could spanregionsin which liquids ascendby the reaction rate, thus probing into the transport-controlled, porousflow along a nearly adiabaticPT gradient. This may diffusion-controlled,and reaction-controlled regimes [e.g., applyto mostof the meltingregimebeneathmid-oceanridges. Hoefher andFogler, 1988;SteefiandLasaga,1990]. Experiments With a Solution Front and No Gradient in Solubility
This sectionis a descriptionof resultsof numericalexperimentscloselyanalogousto our saltdissolutionexperiments.An initially undersaturated "fluid" flows betweenregularlyspaced grains of "salt." Initially, one salt grain in the upper row is missing. As predictedby Chadamet al. [1986] andSteer and Lasaga [1990], no instabilityis observedin theseexperiments until a critical Peclet number is exceeded.
The critical Peclet
Discussion Channels
in the Mantle
Formation
of dissolution channels as a result of the reactive
infiltrationinstabilityis likely duringadiabaticascentof melt in the uppermantle,providedthat advectiveflow ratesare substantially greaterthandiffusionanddispersion in migratingliquidsso that a critical Peclet number is exceeded. The fact that dissolu-
tion channelsare observedasreplacivedunires,at the centimeter to 100-mscalein outcropsof shallowmantleperidotire,indicates
numbermaybe reachedby decreasing thediffusivity,or increas- that this critical Peclet number is exceeded in the mantle at some ing the pressuregradient,andtherebythe initial flow velocity. times and places. The time scalesand length scalesfor the Above the critical Peclet number,an elongatechannelgrows channelingprocessremain uncertain. On the basisof resultsof parallelto the flow direction. Figure9 illustratesthe flow field in the experimentson the channelinginstabilityin a solubility the fluid afterthe channelhaspropagated abouthalfwaythrough gradient,aswell asour recentlycompletedlinearstabilityanalythe experimentalbox. Fluid flows laterallyinto the dissolution sis for this problem, incorporatingthe effects of compaction channelnear the upstreamend and laterally out of the channel [Aharonovet al., 1994, submittedmanuscript,1994],it is inferred near the downstream end, as observed in channels in the water that diffuseporousflow may be unstablethroughoutregionsin and salt experiments described in the second section of this the upper mantle where liquid ascendsalong an adiabaticPT paper. The lengthof the channelcanbe approximately fitted as gradient. In theseregions,the solubilityof mantlesilicatesin the an exponentialfunctionof time, asshownin Figure10. initial liquid increasesalong the ascentpath. Perturbationsin
KELEMEN ET AL.: FOCUSED POROUS FLOW AND MELT EXTRACTION
489
Figure 9. Resultsof a numericalexperimentusinga modifiedrelaxationBoltzmannMethod [Qian et al., 1992; Flekkoy,1993;E. Aharonov,manuscript in preparation, 1994]. Fluid particlesenterthebox at thetop andexit at the bottom. The pressure dropacrossthe box is constant.Opensquaresindicatethe positionof solidparticles. Fluid entersthe top of the box with a soluteconcentrationof zero and graduallydissolvessolids(see text). Arrows illustratethe directionandmagnitudeof fluid velocity. Initially, the box holdsa regularpatternof solid particles,exceptfor onemissingsquaregroupof particlesin the top row. This figureillustratesthe configuration of the systemin an experimentwith high Pecletnumberafter a dissolutionchannelhasgrownabouthalfway down the box. There is lateral flow of fluid into the top of the channel,and lateral flow out of the baseof the channel,asin resultsof experiments on waterflowingthroughmixturesof glassballsandsalt(seeFigure6).
porosityanywherealongsuchan ascentpathmay be sufficientto initiate formationof channelizedflow. The tip of a growing dissolutionchannelwill itself be unstable,and porouschannels should continue to grow throughoutthe region of adiabatic
considered: (1) the effective viscosity of the solid matrix decreases asthe melt fractionincreases, sothatcompaction may proceedmore rapidly in regionsof high porosity,and (2) for a
constantpressuredrop acrossthe system,flow velocity, fluid flux, anddissolution rateall increasein morepermeableareas,so At thisjuncture,the effectof compactionshouldbe addressed. that increasingporositydue to dissolutionreactionswill be more As shown by McKenzie [1984], the rate of extraction of melt rapidin regionsof high porosity. from a porousnetworkis limitedby therateof compaction of the Compactionis unlikely to retardthe initiationand growthof solid matrix. In the mantle, compactionis a ductile process, dissolutionchannelsfor three reasons. First, compactionin limited by the viscosityof the solidphases.During isochemical geologically reasonable times cannot occur over distances compaction,per se, the melt fractionin the systemremainsfixed. smallerthana characteristic "compaction length,"oftenestimated The compactionscenariomustbe modifiedfor systemsin which to be 100 m to 1 km in theuppermantle[e.g.,Spiegelman,1993]. the massof melt is changing. Two opposingfactorsmust be Thus high-porositychannelscan grow to at leasttheselengths ascent.
490
KELEMEN
ET AL.: FOCUSED POROUS FLOW AND MELT EXTRACTION
20
15
numericalexperiments growthrate data o/ /
d
10
L = 1.14 e '011t
R = .99
d'
o
o
a&& L=
I
0
I
50
I
I
100
150
I
200
1,30e R = ,97
.007t
I
250
,
,
•
•
300
time, t Figure 10. Lengthof dissolution channels in numerical experiments, measured fromthehighest remaining solid particleto thebottomthechannel, asa functionof time. Initially,measurement of thelengthis complicated by thewidespacingof the solidparticlesin theverticaldimension.As thegrowthof thechannelproceeds, a more smoothand accuratemeasurement canbe made. As for experimentson waterflowingthroughmixturesof glass
ballsandsalt,the growthof thechannels canbe fittedwith an exponential functionof time,aspredictedin the linearstabilityanalysisof Chadamet al. [1986]andin the secondsectionof thispaper. Fittedvaluesareillustratedas circles,thosewhich wereexcludedfrom the fit are shownas squares.Solid symbolsare for the experimentillustratedin Figure9, in whichthereis aninitialsolutionfrontandno gradientin the saturation concentration of the solutein the fluid. The saturationconcentration was0.05. Opensymbolsare for an otherwiseidenti-
calexperiment in whichthesaturation concentration variedlinearlyasa function of verticalposition, from0.05 at thetopto 0.1 at thebottom. '
withoutbeing "squeezedclosed"by compaction.Second,since compaction of partiallymoltenperidotiteby two phaseflow may proceedlinearly with time under some circumstances[e.g., McKenzie, 1984], it may be slower than exponentialgrowth of
thoughtto be too weak to supportstressessufficientto form cracks. However,decompactioninto melt-filledlenses,as envisionedby Sleep [1988, submittedmanuscript,1994], may be a natural consequenceof increasingporosityand permeability
dissolution channels. In other words, silicate dissolution rates of
within a dissolutionchannel. Once such lensesform, they may
microns to centimeters/day under geologically reasonable conditions [e.g.,KuoandKirkpatrick,1985;BrearleyandScarfe, 1986;Zhanget al., 1989] maybe muchfasterthanviscousflow of solidsin compaction.Third, the presenceof an interconnected columnof liquid, of the orderof onecompaction lengthor more, may lead to magmaticoverpressure near the top of a growing channel and drive decompactionrather than compaction.Our recentlycompleted linearstabilityanalysisof thereactiveinfiltration instabilityin a solubilitygradient,includingthe effectsof compaction,[Aharonov et al., 1994, submittedmanuscript, 1994], demonstratesthat diffuse porous flow of melt in the mantle is unstable - even on length scales greater than a compactionlength - and will break down into long, narrow porouschannels(in two dimensions).
tapmuchof theliquidin the system,removingit fromtheporous flow regimeandforestailingthe continuedgrowthof dissolution features.
There are numerousuncertainties regardingthe long-termfate of dissolutionchannelsoncethey form. Continuingdissolution of mantle olivine, in adiabatically ascendingliquid within a dunitechannel,could,in principle,createopentubesor lenses, filled only with liquid, solely as a resultof dissolutionreactions where the melt/rockratio becomesvery high. Formationof open spacein this mannercouldaccountfor the presenceof "cumulate" chromitite bodies within dunires in shallow mantle peridotire. Becauseof the very limited solubilityof Cr in basaltic magmas,the presenceof chromititesis indicativeof chrome spinelcrystallization from an enormous volumeof basalticliquid Formation of cracks or melt-filled lenses could limit the within a very small spacein the shallowmantle[e.g., Leblanc arelikely growthof channelsundersomeconditions.Brittle fractureof and Ceuleneer,1992]. However,compactionprocesses adiabaticallyupwellingmantleperidotitemay be unlikely,since to play an importantrole in limitingthesizeanddurationof such asthenospheric peridotitedeformsviscouslyand is generally features.
KELEMEN
ET AL.: FOCUSED POROUS FLOW AND MELT EXTRACTION
491
...
,,
tl, ii,ll' l! liii
'11 .ll .11 .!11 ,ii i •
'11 'll '11, •!!" ,!•ii
,•,•,:,:,•,•,•,•,•,:,:,•,i• "ll
"!1'
'! ! I"
:! I I'
''ll'
Ill )
ii !•l' :ll, ![!' ., iii •.
.,i "l" '!l" :!!, ,i ,.1•
.•.• .il '1'
,i
..... :,•,!,• ....... :.•,• ................... '11
"11'
"ll
!111 !
..... !
:! ! I"
,!11•!
i,
..,-i..
':'i'!'
.!•!,
.,!
-','•',
::;i'!;'
i•.
.,,
..,-i-,
..,!,. I; .... :;: ..................................
•.:.,.:.,.y:.:.•::::;•.•.:.•;:.•.y I1
Ii' i i ',1•"
'11 '1 i
,.,., ..... ,., .........
.......... ...............'"'
"" -,'•
''11 '1 i
,(•
','1'! ii.
....
o'•',';
::,i•i•,,,;i:.,•..;i,,;•i;,,,; i!'
,., ...........
,.,.,., ..... ,•,•
".::::;:;::":::t:;•;::'::t:t:;:;:;".::t•i•:"::t:t•;•;:::::•q•;::::tt•
'll ''}'ll '""l'{',•')'• ',1•
'•1'• ,'11',
'•!!'
'ill ,11,
'•1!'..
.....
'!!l':
,.,
.........
..... '
i11 ,11•
•11 .'11,
i1!.
,.,.,
.......
'1 '
!l!':
,.,.,
'!
.........
,.,.,
.•.,. ....., , .,]• •l,.I 'll! ,..... "'"
'1'! ....
'!'!'
;•t•;>;:, ...........
I ! ....
::!3''
[,],
.tl}';
.,I,!,
,!l! •
, .........
I I ....
;ill"
.1111l
I I '
;ill"
.•111 )
''!
I '
''1
.•11J )
•"
,!ill!,
,.,., ....... ,.,.,. ...... ,.,.,. ...... ,-,.,., ..... i.o. '1 i • i'. , "ll!
.i.1.1 '11', '•11' :'ll•,
......
::::"';5!;:':::-•i•i !;.... :ih•iq!'"•;•iq•':' .•,•, :,•,•,• :,•,•,• .,•,•, '!h ,• •,• :•,•:,;...::• '
'
ß•" ,'1' "l ....
:'t•':
')1, '•11 II'
....
'•1]'.
',{• i1' '"if'
"1• '11' 'll'
'*•]1'.
'•1}','
.•11
,.,,....... ,.,...... ,.,........ ,.,,,.
"1•k )'
'"llI I
'• "ll" I •
Ill • );• .... :•,11];..... ;till)
') 'll
I I
'• "'Ill I I
"
'1
'"'i I I"I
;[111);..... ;l(Itl
.
.............. :;:;•;:"................. •.,.,.,.,.,.,.,.,.,.,.,.,., •.•.•.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,
,
Figure 11. Resultsof a numericalexperimentsimilarto that illustratedin Figure9, exceptthat herethe saturation concentrationof the solublematerialin the fluid variesfrom zero at the top of the box to 0.05 at the bottom. Initially, the box held a regularpatternof solid particles,exceptfor one missinggroupof particlesin the ninth row from the top. This figureillustratesthe configurationof the systemsafter a dissolutionchannelhasbegunto grow from the positionof the missingsolidparticle. As in Figure9, squaresshowthe positionof solidparticles, and arrowsindicatethe directionand magnitudeof flow velocity. It is inferredfrom theseresultsthat diffuse fluid flow in a solubleporousmediumis unstableevenin the absenceof an initial solutionfront in the system and will form channelswhere fluid becomesgraduallyundersaturated in solidsdownstream. This result has recentlybeenconfirmedby linear stabilityanalysis [Aharonovet al., 1994, Channelinginstabilityof upwelling melt in the mantle,submittedto Journal of GeophysicalResearch,1994].
Flow of CoolingMelt in Mantle on a ConductiveGeotherm Ancient, subcontinentalmantle "tectosphere"[e.g., Jordan, 1988] is essentiallystatic and must be close to a conductive geothermalgradient. Where melt ascendingby porousflow encounters the tectosphere, it mustbeginto cool. Suchcooling liquidswill becomesaturatedin solid phasesand decreasein mass,but it doesnot follow that they will crystallizewithin a narrowdepthinterval.On thecontrary,volatileandincompatible
elements, suchasH20,CO2,andK20,willbeconcentrated in the graduallycrystallizingliquid, loweringthe solidustemperature and viscosityof the evolving liquid. Whereasthe liquidus
temperatureof a (nearly) anhydrousbasalticmagmaat 2 GPa may be 1400øC,the solidustemperaturefor the last fractionof hydrousliquid derivedby very slow,fractionalcrystallizationof sucha basalticmagmaalonga geothermwith an averageslopeof 5øC/kmmay be lessthan900øC,at a level 10 km higher. Thus extensiveportionsof thetectosphere maybe traversedby cooling magmas,migratingby porousflow and decreasingin massas a result of crystalfractionation. Under thesecircumstances, it is expectedthat transientconduitswill form, armoredby lowpermeabilitywalls formedby crystallization.Porosityin these conduitswill eventuallybe chokedwith newly crystallizedmaterial. When one conduitis choked,focusedflow of magmawill
492
KELEMEN
ET AL.: FOCUSED
POROUS
migrate elsewhere so that on large scalesof time and distance, porousflow of melt in suchsettingswill be essentiallyrandom and diffuse. This hypothesisis supportedby experimentson channelformation in convecting,crystallizingammoniumchloride solutions[Tait and Jaupart, 1991; Tait et al., 1992;B•dard et al., 1992], who observedthat wherefluidsin their experiments are heating and dissolving solids, porous flow is focused, whereas where fluids are cooling and precipitating additional solid material, porousflow is diffuse. An interconnectedmelt network in the asthenosphere, in the zone of focusedflow, may developa substantialhydrostatichead. Above, where the interconnected melt networkbecomesclogged with crystalsdue to magmaticcooling,theremay be a substantial hydrostaticoverpressure.Under thesecircumstances, cracksmay form due to hydrofracture,andmelt may be periodicallyexpelled in dikes,in a processsimilar to that proposedby Nicolas [ 1990]. Similarly, increasing volatile contentsof evolving magmas, combinedwith decreasingpressure,may resultin volatile saturation, expansionof the liquid+gassystem,and hydrofracture.In shallow mantle sectionsin ophiolites, this may explain why dunitesgenerally form anastomosing,replacivefeaturesindicative of melt migrationby porousflow, whereaspyroxenitesand gabbroicrocks,which crystallizefrom coolingmagmas,almost always form narrow, tabular dikes [e.g., Kelemen and Dick, 1994].
FLOW AND MELT
EXTRACTION
the tectosphere, but at shallowerlevels,meltsmustpassthrough conductively cooled mantle. Thermal models of subduction zones indicate that an inverted geothermmust form above the cold, subducting slab [e.g., Peacock, 1991; Davies and Stevenson,1992]. Liquids generatedin or abovethe subducting slab must initially heat as they rise through this inverted geotherm[Kelemen, 1990, 1994; Kelemenet al., 1993]. After liquidspassthroughthe thermalmaximumin the mantlewedge, they mustascendthroughcoolermantleto reachthe surface. Beneath a mid-ocean ridge, liquid mass and porosity will continuallyincreasethroughmost of the mantledecompression path,both by additionof partial meltsfrom decompressing peridotite and as a consequenceof the dissolutionreactionsdiscussed in this paper. If porousflow beginsto organizeinto dissolution channels,this processis likely to run away and to continue almost to the base of the crust. Consequently,melt will flow primarily through dunite conduits, melt/rock ratios within conduitswill be very high, and the chemicaleffectsof melt/rock reaction will be subduedin liquid products which form the oceanic crust. These inferencesare schematicallyillustratedin Figure 13. This mechanismcan explain the developmentof chemically isolated channelsfor rapid melt migration, whose existencehas been postulatedin order to explain the observed disequilibriumbetween mid-oceanicridge basaltsand residual, abyssalperidotites[e.g., Spiegelmanand Kenyon, 1992;Hart, 1993].
Beneathbothhot spotsandarcs,liquidspassinto conductively cooledmantle and will themselvesbegin to cool and crystallize. Very different porousflow morphologyand chemicalconse- The intervalover which suchmagmasmay continueto ascendby quences may be anticipated for melt extraction in different porousflow may be tensof kilometers.Within thisinterval,they geodynamicenvironments. As illustratedin Figure 12, beneath may form, fill, and abandonconduitswith relativelyimpermeable mid-oceanridges,both liquidsandsolidperidotiteascendalonga walls. In this process,they may chokeporosityforming impernearly adiabatic pressure-temperaturetrajectory, almost to the meable caps,hydrostaticoverpressure,and crack formation, as baseof the crust. Beneathhot spotvolcanoes,ascendingmantle illustrated in Figure 14. Such a flow structurewill produce (and partial melt) follows an adiabaticascentpath to the baseof increasingly small melt/rock ratios upsection,maximizing the GeochemicalConsequencesof Flow in Channels
MORB
within plate basalt
arc magmas
dry wet
temperature
temperature
Figure 12. Geothermsandlikely structureof porousflow channelnetworksin differentmagmaticenvironments. Beneathmid-oceanridges,both liquids and solidperidotiteascendalonga nearly adiabaticpressure-temperature trajectory,almostto the baseof the crust. Beneathhot spotvolcanoes,ascendingmantleandpartialmelt follow a nearly adiabaticascentpath to the baseof the tectosphere,but at shallowerlevels, melts must passthrough conductivelycooledmantle. In subductionzones,an invertedgeothermmustform abovethe cold, subducting slab,and liquids generatedin or abovethe slabmustinitially heatas they rise. After liquidspassthrougha thermal maximum they will cool as they continueto rise.
KELEMEN
ET AL.' FOCUSED POROUS FLOW AND MELT EXTRACTION
493
Mm, M/R, •
Mm,M/R,•) C )x
Cpx
peridotite /
dunite • rea•any • •
,i
Olivine
Opx
sio 2
reactant
/
•o ,••I i \
Olivine
temperature
-',.
• M
Opx
Si02
temperature
meltingat "30 kb" reaction from "30" to "10 kb"
Figure 13. Structureof porous flow channelsbeneatha midoceanridge and the geochemicalconsequences of this structure. Top left-handdiagramillustratesthat porousflow will be mainly focusedinto discretedissolutionchannels,composedof porous dunite. Top right showsthat the melt fraction (Mm), melt/rock ratio (M/R), and porosity({) will all increasewithin porousflow channelsalmost to the base of the newly forming oceaniccrust whereliquid mustcool andbeginto crystallize. Phasediagramat bottomright illustratesthe chemicaleffectsof melt/rockreaction within the porousflow channel. The porousflow channelwill be composedmainly of dunite,with which ascendingmagmawill be saturated. There will be little or no compositional difference betweenmagma transportedthroughsucha channeland magma which ascendsin a chemicallyclosedsystem.
Figure 14. Structure of porous flow channels beneath an intraplate hot spot or a subduction-related magmatic arc. Ascendingliquid in a closedsystemwould initially be aboveits liquidustemperature,becauseliquid and solid ascendon a nearly adiabaticpath in a mantle "plume" and becauseinitial liquids in subductionzonesmustheatup as they risebeneatharcs. Higher, liquids passinto colder mantle and will themselvesbegin to cool and crystallize, leading to decreasing melt fraction (Mm), melt/rockratio (M/R), and porosity({). In suchconditions,melt migratingby porousflow may form flow conduits,with "walls" of low porosity. Theseconduitswill graduallyfill with products of magmatic crystallizationand be abandoned,after which new flow
conduits
will
form.
Also
shown
are cracks formed
as a
resultof magmaticoverpressurein the tectosphere.The overall effect of such a flow structureis to produceincreasinglysmall chemical effects of melt/rock reaction on the composition of melt/rock ratios upsection,maximizing the chemicaleffects of migratingliquids. Specifically,meltswill remaincloseto Fe/Mg melt/rock reaction on the composition of migrating liquids. equilibrium with mantle olivine and will retain high Ni and Cr Phase diagram at bottom right shows the chemical effects of concentrations,with increasingconcentrationsof magmaphile slow cooling and rapid melt/rock reaction for an initial, picritic components, suchas H20, CO2, K, and incompatible trace partial melt of the mantle reactingwith mantleperidotitefrom 2 elements[e.g., Kelemen,1986; Kelemenet al., 1992, 1993]. This to 0.5 GPa (as in Figure 2c), labeled M, as well as for ascending is in accordwith the idea that melt/rock reactionis importantin partial melts of subductedcrust, labeled S [e.g., Carroll and producingmagmasin subduction-related arcs [e.g., Kay, 1978; Wyllie, 1989; Kelemen, 1993' Kelemenet al., 1993]. Kelemen, 1986, 1990, 1994; Carroll and Wyllie, 1989; Kelemen et al., 1993] and above mantle hot spots [e.g., Watson 1993; Wagnerand Grove, 1992]. The effectsof melt/rockreactionmay Acknowledgments. We thank Robert Frazel for assistancein also be detectedin samplesof the continentaltectosphere[e.g., constructingthe experimentalapparatus;Greg Hirth, Art Thompson,Dan Menzieset al., 1985; Navon and Stolper, 1987; Kelemenet al., Rothman,Henry Dick, StanHart, Nobu Shimizu,Dan McKenzie, Mark 1992;Rudnicket al., 1993] andin the oceanictectosphere where Spiegelman,AdolpheNicolas,Jean-LouisBodinier,andKarl Helfrichfor it hasbeenmodified by hotspots[e.g., Hauri et al., 1993; Sen et stimulatingdiscussions; Mark Ghiorsofor makingthe new versionof his al. , 1993; Saltersand Zindler, 1994]. silicateliquid solutionmodel availableto us; and Bruce Marsh, Tony ß
494
KELEMEN
ET AL.: FOCUSED POROUS FLOW AND MELT EXTRACTION
Morse, and Claude Jaupartfor encouragingus to presentthis paper. We also thank Alexander McBirney for bringing Chadam and Ortoleva's work to our attentionmanyyearsago. Interdisciplinary discussions in the Keck Geodynamics Seminarat WoodsHole initiatedthisproject. Norm Sleep, Dave Scott and Anne Devaille providedcarefulreviewswhich substantially improvedthe manuscript.Early workwassupported by the Woods Hole/MIT Joint GraduateProgramin Oceanography(Aharonov, Jordahl),NSF grantEAR 9218819 andthe sponsors of the MIT Porous
Flekkoy, E., Lattice BGK modelsfor misciblefluids, Phys.Rev. E, 47, 4247-4257, 1993.
Frisch, U., B. Hasslacher,and Y. Pomeau,Lattice gas automatafor the Navier-Stokesequation,Phys.Rev. Lett., 56, 1505-1508, 1986. Garrido, C.J., M. Remaidi, J.-L. Bodinier, F. Gervilla, J. Torres-Ruiz, and P. Fenoll, Replacive pyroxenitesin the Ronda orogeniclherzolite: Evidencefor km-scalepercolationof calc-alkalinemeltsin the upper mantle, Terra Abstr., 1, 147, 1993.
Ghiorso,M. S., Chemical masstransferin magmaticprocesses,I, TherFlow Project(Aharonov),NSF grantsEAR 9005306,OCE 9217556,a modynamic relations and numerical algorithms, Contrib. Mineral. Mellon IndependentStudyAward from the WoodsHole Oceanographic Petrol., 90, 107-120, 1985. Institution(Kelemen), and EAR 8916857 (Whitehead). More recently, Aharonov,Kelemen, and Whiteheadhavebeensupportedin thisresearch Ghiorso,M.S., and P.B. Kelemen,Evaluatingreactionstoichiometryin magmatic systems evolving under generalized thermodynamic by OCE 9314013.
References
constraints:Examplescomparingisothermaland isenthalpicassimilation, in: Magmatic Processes: Physicochemical Principles,editedby B.O. Mysen,Spec.Pub. Geochem.Soc.,1, (Yoder Volume), 319-336,
1987. Aharonov,E., J.A. Whitehead,and P.B. Kelemen,Channelinginstability of melt flowing through the reactive, decompressingmantle, paper Ghiorso,M.S., and R.O. Sack,MELTS: Softwarefor the thermodynamic presented at the 20th International Conference on Mathematical analysisof phase equilibria in magmatic systems,Geol. Soc. Am. Geophysics, NationalScienceFoundation,VillefranchesurMer, 1994. Abstr.Programs,25, A-96, 1993. Aho, A.E., Geology and genesisof ultrabasicnickel-copper-pyrrhotite Ghiorso, M.S., and R.O. Sack, Chemical mass transfer in magmatic deposits at the Pacific Nickel property, southwestern British processes, IV, Contrib.Mineral. Petrol., in press,1994.
Columbia, Econ. Geol., 51,444-481, 1956. B•dard, J.H., R.C. Kerr, and M.A. Hallworth, Porous sidewall and
sloping floor crystallization experiments using a reactive mush: Implicationsfor the self-channelizationof residualmeltsin cumulates, Earth Planet. Sci. Lett., 111,319-329, 1992.
Boudier,F., and A. Nicolas, Structuralcontrolson partialmeltingin the Lanzo peridotites,in Magma Genesis,editedby H.J.B. Dick, Oreg. Dep. Geol. Miner. Ind. Bull., 96, 63-78, 1977. Brearley,M., andC.M. Scarfe,Dissolutionratesof uppermantleminerals in an alkali basalt melt at high pressure:An experimentalstudy and implications for ultramafic xenolith survival, J. Petrol., 27, 11571182, 1986.
Butcher, A.R., I.M. Young, and J.W. Faithful, Finger structuresin the Rhum complex,Geol. Mag., 122, 491-502, 1985. Carlson,R.W., A matterof give andtake,Nature, 359, 16-17, 1992. Carroll, M.R., andP.J.Wyllie, Experimentalphaserelationsin the system tonalite-peridotite-H20: Implicationsfor assimilationanddifferentiation processesnear the crust-mantleboundary,J. Petrol., 30, 13511382, 1989. Chadam, J., D. Hoff, P. Ortoleva, and A. Sen, Reactive-infiltration insta-
Ghiorso, M. S., I. S. E. Carmichael, M. L. Rivers, and R. O. Sack, The
GibbsFree Energyof mixing of naturalsilicateliquids:An expanded regularsolutionapproximationfor the calculationof magmaticintensive variables, Contrib. Mineral. Petrol., 85, 107-145, 1983.
Hart, S.R., Equilibration during mantle melting: A fractal tree model, Proc. Natl. Acad. Sci. U.S.A., 90, 11,914-11,918, 1993.
Hauri, E.H., N. Shimizu,J.J.Dieu, and S.R. Hart, Evidencefor hotspotrelatedcarbonatitemetasomatism in the oceanicuppermantle,Nature, 365, 221-227, 1993.
Henon,M., Viscosityof latticegases,ComplexSyst.,1,763-789, 1987. Hinch, E. J., and B. S. Bhatt, Stability of an acid front movingthrough porousrock, J. Fluid. Mech., 212, 279-288, 1990. Hirose,K., andI. Kushiro,Partialmeltingof dry peridotitesat highpressures:Determinationof compositionsof melts segregatedfrom peridotiteusingaggregates of diamond,Earth Planet. Sci.Lett., 114, 477489, 1993.
Hoefner, M.L., and H.S. Fogler, Pore evolution and channelformation duringflow andreactionin porousmedia,Am. Inst. Chem.Eng.J., 34, 45-54, 1988.
Irvine, T.N., Petrologyof the Duke Islandultramaficcomplex,southeastem Alaska, Geol. Soc.Am., Mem. 138, 240 pp., 1974. bility, J. Appl. Math., 36, 207-238, 1986. Daccord, G., Chemical dissolutionof a porousmedium by a reactive James,O.B., Origin and emplacementof the ultramaficrocksof the EmigrantGap area,J. Petrol., 12, 523-560, 1971. fluid, Phys.Rev. Lett., 58, 479-482, 1987. Daines, M.J., and F.M. Richter, An experimentalmethodfor directly Johnson,K.T.M., H.J.B. Dick, and N. Shimizu, Melting in the oceanic determiningthe interconnectivityof melt in a partiallymoltensystem, upper mantle: An ion microprobestudy of diopsidesin abyssal Geophys.Res.Lett. , 15, 1459-1462, 1988. peridotites,J. Geophys.Res.,95, 2661-2678, 1990. Daines,M.J., and D.L. Kohlstedt,The transitionfrom porousto channel- Johnson,K.T.M., andH.J.B. Dick, Opensystemmeltingandthetemporal ized flow due to melt/rockreactionduringmelt migration,Geophys. and spatial variation of peridotite and basalt compositionsat the Res. Lett., 21, 145-148, 1993. Atlantis II FractureZone, J. Geophys.Res.,97, 9219-9241, 1992. Davies, J.H., and D.J. Stevenson,Physicalmodel of sourceregion of Jordan,T. H., Structureand formationof the continentaltectosphere, J. subductionzonevolcanics,J. Geophys.Res.,97, 2037-2070, 1992. Petrol., SpecialLithosphereIssue,11-37, 1988. d'Humiers, D., P. Lallemand, J.P. Boon, D. dab, and A. Noullez, Fluid Kay, R.W., Aleutian magnesianandesites:Melts from subductedPacific ocean crust, J. Volcanol. Geotherm. Res., 4, 17-32, 1978. dynamicswith lattice gases,in Chaosand Complexity,editedby R. Kelemen, P.B., Assimilation of ultramafic rock in subduction-related Livi, S. Ruffo, S. Cilberto, and M. Buiatti, pp. 278-301, World ScientificPublishers,Singapore,1988. magmaticarcs,J. Geol., 94, 829-843, 1986. Dick, H.J.B., Evidenceof partial meltingin the Josephine peridotite,in Kelemen, P.B., Reactionbetweenultramaficwall rock and fractionating Magma Genesis,editedby H.J.B. Dick, Oreg.Dept Geol.Miner. Ind. basalticmagma, I, Phaserelations,the origin of calc-alkalinemagma Bull., 96, 63-78, 1977.
Dick, H. J. B,, Abyssalperidotites,very slow spreading ridgesandocean ridgemagmatism,in Magmatismin the OceanBasins,editedby A.D. Saunders,and M. J. Norry, Geol. Soc.Spec.Pub., 42, 71-105, 1989. Dick, H. J. B., R. L. Fisher,and W. B. Bryan, Mineralogicvariabilityof the uppermostmantlealongmid-oceanridges,Earth Planet. Sci. Lett., 69, 88-106, 1984.
Faul, U.H., A.D. Johnston,andH.S. Waff, Melt distributionin partially molten lherzolite, Eos Trans. AGU, 74(43), Fall Meeting suppl.,660, 1993.
series, and the formation of discordant dunite, J. Petrol., 31, 51-98, 1990.
Kelemen, P.B., Genesisof high Mg# andesitesand the continentalcrust, Contrib.Mineral. Petrol., in press,1994. Kelemen, P.B., and H.J.B. Dick, Focused melt flow and localized defor-
mation in the upper mantle: Juxtapositionof replacive dunite and ductile shear zones in the Josephineperidotite, SW Oregon. J. Geophys.Res., in press,1994. Kelemen, P.B., and M.S. Ghiorso, Assimilation of peridotite in zoned calc-alkalineplutoniccomplexes:Evidencefrom the Big Jim complex,
KELEMEN
ET AL.: FOCUSED POROUS FLOW AND MELT EXTRACTION
WashingtonCascades,Contrib.Mineral Petrol., 94, 12-28, 1986.
495
peridotites refractaires - pyroxenites dans le massif de Ronda (Espagne),Ph.D. thesis,Univ. de Montpellier,France,1993.
Kelemen,P.B.,H.J.B.Dick,andJ.E.Quick,Production of harzburgite by pervasivemelt-rockreactionin the uppermantle,Nature, 358, 635-
Riley, G.N., Jr., andD.L. Kohlstedt,Kineticsof melt migrationin upper
641, 1992.
mantletype rocks,Earth Planet. Sci. Lett., 105, 500-521, 1991.
Kelemen,P.B.,N. Shimizu,andJ.T.Dunn,Relativedepletion of niobium Rothman,D.H., Cellular-automaton fluids: A modelfor flow in porous in somearc magmasandthe continental crust:Partitioningof K, Nb, media, Geophysics,53, 509-518, 1988. La andCe duringmelt/rockreactionin the uppermantle,EarthPlanet. Rudnick, R. L., W. F. McDonough, and B. W. Chappell, Carbonatite Sci. Lett., 120, 111-133, 1993. metasomatismin the northernTanzanianmantle:Petrographicand Kinzler, R. J., and T. L. Grove,Primarymagmasof mid-oceanridge geochemicalcharacteristics,Earth Planet. Sci. Lett., 114, 463-475, 1993. basalts2. Applications,J. Geophys.Res.,97, 6907-6926,1992. Kuo, L.-C., and R. J. Kirkpatrick, Kineticsof crystaldissolutionin the Salters,V.J.M., andS.R. Hart, The Hf-paradoxandtherole of garnetin systemdiopside-forsterite-silica, Am. J. Sci.,285, 51-90, 1985. Langmuir,C.H., E.M. Klein, and T. Plank,Petrologicalsystematics of mid-oceanridge basalts:Constraints on melt generationbeneathmid-
the MORB source, Nature, 342, 420-422, 1989.
Salters,V.J.M., andA. Zindler,Extreme176Hf/177Hf in thesub-oceanic
mantleand the origin of high field strengthelementdepletionsin the mantle,Earth Planet. Sci. Lett., in press,1994. Savel'yeva,G.N., S.A. Shcherbakov,and Y.A. Denisova, The role of high-temperaturedeformationin the developmentof dunitebodiesin Leblanc,M., andG. Ceuleneer,Chromitecrystallization in a multicellular harzburgites,Geotectonics,14, 175-182, 1980. magmaflow: Evidencefrom a chromititedikein the Omanophiolite, Scott, D.R., and D.J. Stevenson,A self-consistentmodel of melting, Lithos, 27, 231-257, 1992. magma migrationand buoyancydriven circulationbeneathmid-ocean Lippard,S.J., A.W. Shelton,and I.G. Gass,The Ophioliteof Northern ridges,J. Geophys.Res., 94, 2973-2988, 1989. Oman, 178 pp., Blackwell Scientific,Oxford UK, 1986. Sen,G., and R. E. Jones,Cumulatexenolithin Oahu,Hawaii: ImplicaMaaloe,S., andA. Scheie,The permeabilitycontrolledaccumulation of tions for deep magma chambersand Hawaiian volcanism,Science, primarymagma,Contrib.Mineral PetroL, 81,350-357, 1982. 249, 1154-1157, 1990. McKenzie,D., The generation andcompaction of partiallymoltenrock,J. Sen, G., F. A. Frey, N. Shimizu, and W. P. Leeman, Evolution of the Petrol. 25, 713-765, 1984. lithospherebeneathOahu, Hawaii: Rare earthelementabundances in McKenzie,D., and M.J. Bickle, The volumeand compositionof melt mantle xenoliths, Earth Planet. Sci. Lett., 119, 53-69, 1993. generatedby extensionof the lithosphere,J. Petrol., 29, 625-679, Sleep, N.H., Formation of oceanic crust: Some thermal constraints,J. 1988. Geophys.Res., 80, 4037-4042, 1975. Menzies, M., P. Kempton,and M. Dungan,Interactionof continental Sleep,N.H., Tappingof melt by veinsand dykes,J. Geophys.Res., 93, 10,255-10,272, 1988. lithosphereand aesthenospheric meltsbelowthe GeronimoVolcanic Field, Arizona, U.S.A, J. Petrol., 26, 663-693, 1985. Sobolev, N.V., Y. G. Lavrent'yev, N.P. Pokhilenko, and L.V. Usova, Navon,O., andE. Stolper,Geochemical consequences of melt percolaChrome-richgarnetsfrom the kimbeditesof Yakutiaandtheirparagenesis, Contrib. Mineral. Petrol., 40, 39-52, 1973. tion: The uppermantleas a chromatographic column,J. Geol.,95, ocean ridges, in Mantle Flow and Melt Generation at Mid-Ocean Ridges,editedby J. PhippsMorgan,D.K. Blackman,andJ.M. Sinton, Geophys.Monogr. Ser., vol. 71, 183-280, 1992.
285-307, 1987.
Spiegelman, M., Physicsof melt extraction:Theory,implicationsand
Nicolas, A., Structuresof Ophiolites and Dynamics of Oceanic
applications,Philos.Trans.R. Soc.LondonA, 342, 23-41, 1993. Speigelman,M., andD. McKenzie,Simple2-D modelsfor melt extracNicolas,A., Melt extractionfrommantleperidotites:Hydrofracturing tion at mid-oceanridgesandislandarcs,Earth Planet.Sci.Lett., 83, 137-152, 1987. and porousflow, with consequences for oceanicridge activity,in MagmaTransportandStorage,editedby M.P. Ryan,pp. 159-174,J. Speigelman, M., andP. Kenyon,Therequirements for chemical disequiWiley & Sons,1990. libriumduringmeltmigration, EarthPlanet.Sci.Lett., 109,611-620, 1992. Nixon,P.,MantleXenoliths, 844pp.,JohnWiley,New York, 1987. Lithosphere,367 pp., Kluwer Academic,Norwell, Mass., 1989.
Ortoleva P.,J. Chadam, E. Merino,andA. Sen,Geochemical self-organi- Steefel,C., andA. Lasaga, Evolution of dissolution patterns: Permeability zation,II, The reactive-infiltration instability,Am. J. Sci.,287, 1008changedueto coupledflow andreactions, in Chemical Modelingin 1040, 1987. Aqueous Systems II, editedby D.C. Melchior,andR.L. Bassett, Syrup. Peacock,S.M., Numericalsimulationof subduction zonepressureSer. 416, pp. 212-225,AmericanChemicalSociety,Washington, temperature-timepaths: Constraintson fluid productionand arc magmatism,Philos.Trans.R. Soc.LondonA, 335, 341-353, 1991.
Phillips,O. M., Flow and Reactionsin PermeableRocks,285 pp., CambridgeUniversityPress,New York, 1991. Pokhilenko, N.P., N.V. Sobolev, and Y.G. Larent'ev, Xenoliths of
D.C., 1990.
Stevenson, D., Spontaneous small-scale meltsegregation in partialmelts undergoingdeformation,Geophys.Res.Lett., 9, 1067-1070,1989. Stolper,E., A phasediagramfor mid-ocean ridgebasalts:Preliminary resultsand implicationsfor petrogenesis,Contrib.Mineral. Petrol.,
diamondiferous ultramaficrocksfrom Yakutiankimberlites, paper presented at the Second International Kimberlite Conference, AmericanGeophysicalUnion, SantaFe, N.M., 1977.
74, 13-27, 1980.
Stumpfl,E.F., andJ.C. Rucklidge,The platiniferous dunitepipesof the easternBushveld,Econ. Geol., 77, 1419-1431, 1982.
Qian, Y.H., D d'Humieres,and P. Lallemand.Lattice BGK modelsfor the
Tait, S., andC. Jaupart,Compositional convection in a reactivecrys-
Navier-Stokes equation.Europhys.Lett., 17(6), 479-484, 1992. Quick,J.E.,The originandsignificance of large,tabulardunitebodiesin the Trinity Peridotite,northernCalifornia,Contrib.Mineral. Petrol.,
tallinemushandmelt differentiation, J. Geophys. Res.,97, 6735-6756,
78, 413-422, 1981.
Rabinowicz, M., A. Nicolas,andJ.-L.Vigneresse, A rollingmill effectin aesthenospheric flow beneathoceanicspreading centers, EarthPlanet. Sci. Lett., 67, 97-108, 1984.
Rabinowicz, M., G. Ceuleneer, andA. Nicolas,Melt segregation andflow in mantlediapirsbelow spreadingcenters:Evidencefrom the Oman ophiolites,J. Geophys.Res.,92, 3475-3486, 1987. Raedeke,L.D., and I..S. McCallum, Investigationin the Stillwater Complex,II, Petrologyand petrogenesis of the ultramaficseries,J. Petrol., 25, 395-420, 1984.
1991.
Tait, S., K. Jahding,and C. Jaupart,The planformof compositional convectionin a mushylayer,Nature, 359, 406-408, 1992. Takahashi,N., Evidencefor melt segregationtowardsfracturesin the Horomanmantleperidotitecomplex,Nature,359, 52-55, 1992.
Toramaru,A., and N. Fujii, Connectivityof melt phasein a partially moltenperidotite,J. Geophys.Res.,91, 9239-9252, 1986. Von Bargen,N., andH.S. Waff, Wettingof enstatiteby basalticmelt at 1350øC and 1-25 GPa pressure,J. Geophys.Res., 93, 1153-1158, 1988.
Waft, H.S., and U.H. Faul, Effectsof crystallineanisotropyon fluid distributionin ultramaficpartialmelts,J. Geophys.Res.,97, 9003-
Remaidi,M., l•tudepetrologique et g6ochemique d'uneassociation
9014, 1992.
496
KELEMEN
ET AL.: FOCUSED
POROUS FLOW AND MELT EXTRACTION
Wagner,T.P., and T.L. Grove, Primarymagmasof the Hawaiianplume: Experimental evidence bearing on the plume paradox, Eos Trans. AGU, 73(43), Fall Meeting suppl.,615, 1992. Watson, E.B., Melt infiltration and magmaevolution,Geology,10, 236240, 1982.
Watson, S., Rare earth element inversionsand percolationmodelsfor Hawaii, J. Petrol., 34, 763-783, 1993.
WhiteheadJ.A., and K.R. Helfrich, Instabilityof flow with temperaturedependentviscosity:A modelof magmadynamics,J. Geophys.Res., 96, 4145-4146, 1991. Whitehead, J.A., and P.B. Kelemen, Thermal and chemical corrosion in
partiallymoltenmantle,in MagmaticSystems,editedby M.P. Ryan, pp. 355-379, Academic,SanDiego, Calif., 1994, Yoder,H.S., Generationof BasalticMagmas,264 pp.,NationalAcademy of Sciences,WashingtonDC, 1976. Zhang, Y., D. Walker, and C.E. Lesher,Diffusive crystaldissolution, Contrib. Mineral. Petrol., 102, 492-513, 1989.
E. Aharonov,WHOI/MIT JointGraduateProgramin Oceanography, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Instituteof Technology,Cambridge,MA 02139. (email:
[email protected]). K. A. Jordahl,WHOI/MIT JointGraduateProgramin Oceanography, WoodsHole Oceanographic Institution,WoodsHole, MA 02543. P. B. Kelemen,Departmentof GeologyandGeophysics, WoodsHole Oceanographic Institution, Woods Hole, MA 02543. (email:
[email protected]). J. A. Whitehead,Departmentof PhysicalOceanography, WoodsHole Oceanographic Institution, Woods Hole, MA 02543. (email: j
[email protected]).
(ReceivedFebruary15, 1994;revisedAugust19, 1994; acceptedSeptember22, 1994.)
