Quantitative Simulation of the Hydrothermal Systems of Crystallizing Magmas on the Basis of Transport Theory and Oxygen Isotope Data: An analysis of the Skaergaard Intrusion

Application of the principles of transport theory to studiesof magma-hydrothermal systems permits quantitative predictionsto be made of the consequences of magma intruding into permeablerocks. Transport processes which redistribute energy, mass,and momentum in these environments can be represented by a setof partial differential equations involving the rate of changeof extensive properties in the system. Numerical approximationand computer evaluation of the transport equations effectivelysimulates the crystallization of magma, cooling of the igneousrocks, advection of chemical components, and chemical and isotopicmass transfer between minerals and aqueous solution. Numerical modeling of the deep portions of the Skaergaard magma-hydrothermalsystem has produced detailed maps of the temperature, pressure,fluid velocity, integrated fluid flux, ¹⁸O-values in rock andfluid, and extent of nonequilibrium exchange reactions betweenfluid and rock as a function of time for a two-dimensional cross-sectionthrough the pluton. An excellent match was made between calculated¹⁸O-values and the measured ¹⁸O-values in the three principalrock units, basalt, gabbro, and gneiss, as well as in xenolithsof roof rocks that are now embedded in Layered Series; the latterwere evidently depleted in ¹⁸O early in the system's coolinghistory, prior to falling to the bottom of the magma chamber.The best match was realized for a system in which the bulk rockpermeabilities were 10^–13 cm² for the intrusion, 10^–11cm² for basalt, and 10^–16 cm² for gneiss; reaction domainsizes were 0.2 cm in the intrusion and gneiss and 0.01 cm inthe basalts, and activation energy for the isotope exchangereaction between fluid and plagioclase was 30 kcal/mole. The calculated thermal history of the Skaergaard system wascharacterized by extensive fluid circulation that was largelyrestricted to the permeable basalts and to regions of the plutonstratigraphically above the basalt-gneiss unconformity. Althoughfluids circulated all around the crystallizing magma, fluidflow paths were deflected around the magma sheet during theinitial 130,000 years. At that time, crystallization of thefinal sheet of magma and fracture of the rock shifted the circulationsystem toward the center of the intrusion, thereby minimizingthe extent of isotope exchange between rocks near the marginof the intrusion at this level. For comparison, similar calculationswere also made for pure conductive cooling; it was found thatthe rate of crystallization of the magma body was not changed.The solidified pluton cooled by a factor of about 2 faster inthe presence of a hydrothermal system. Transport rates of thermal energy out of the intrusion and oflow-¹⁸O fluids into the intrusion controlled the overall isotopeexchange process. During the initial 150,000 years, temperatureswere high and reaction rates were fast; thus, fluids flowinginto the intrusion quickly equilibrated with plagioclase. However,the temperature decreased between 120,000 and 175,000 yearsand caused a decrease in reaction rates and an increase in theequilibrium fractionation factor between plagioclase and fluid.Consequently, during this time period fluids in the intrusiontended to be out of equilibrium with plagioclase. After 175,000years temperatures had decreased sufficiently that reactionrates became insignificant, but convection rates were largeenough to redistribute fluid and enlarge the regions where fluidand plagioclase were out of equilibrium. By 400,000 years, thepluton had cooled to approximately ambient temperatures, andthe final ¹⁸O values were ‘frozen in’. Reactionsbetween hydrothermal fluid and the intrusion occurred over abroad range in temperature, 1000-200 °C, but 75 per centof the fluid circulated through the intrusion while its averagetemperature was >480 °C. This relatively high temperatureis consistent with the observation that only minor amounts ofhydrothermal alteration products were formed in the naturalsystem, even where several per mil shifts in ¹⁸O were detected. The relative quantities of fluid to rock integrated over theentire cooling history were 0.52 for the upper part of intrusion,0.88 for the basalt, 0.003 for the gneiss, and 0.41 for theentire domain. Almost all of the fluid flowed into the intrusionfrom the basalt host rocks that occur adjacent to the side contactsof the intrusion. Convection transferred about 20 per cent ofthe total heat contained in the gabbro upward into the overlyingbasalts; the remaining 80 per cent of the heat was transferredby conduction.