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

Abstract

Application of the principles of transport theory to studies of magma-hydrothermal systems permits quantitative predictions to be made of the consequences of magma intruding into permeable rocks. Transport processes which redistribute energy, mass, and momentum in these environments can be represented by a set of partial differential equations involving the rate of change of extensive properties in the system. Numerical approximation and computer evaluation of the transport equations effectively simulates the crystallization of magma, cooling of the igneous rocks, advection of chemical components, and chemical and isotopic mass transfer between minerals and aqueous solution. Numerical modeling of the deep portions of the Skaergaard magma-hydrothermal system has produced detailed maps of the temperature, pressure, fluid velocity, integrated fluid flux, δ18O-values in rock and fluid, and extent of nonequilibrium exchange reactions between fluid and rock as a function of time for a two-dimensional cross-section through the pluton. An excellent match was made between calculated δ18O-values and the measured δ18O-values in the three principal rock units, basalt, gabbro, and gneiss, as well as in xenoliths of roof rocks that are now embedded in Layered Series; the latter were evidently depleted in 18O early in the system's cooling history, prior to falling to the bottom of the magma chamber. The best match was realized for a system in which the bulk rock permeabilities were 10−13 cm2 for the intrusion, 10−11 cm2 for basalt, and 10−16 cm2 for gneiss; reaction domain sizes were 0.2 cm in the intrusion and gneiss and 0.01 cm in the basalts, and activation energy for the isotope exchange reaction between fluid and plagioclase was 30 kcal/mole. The calculated thermal history of the Skaergaard system was characterized by extensive fluid circulation that was largely restricted to the permeable basalts and to regions of the pluton stratigraphically above the basalt-gneiss unconformity. Although fluids circulated all around the crystallizing magma, fluid flow paths were deflected around the magma sheet during the initial 130,000 years. At that time, crystallization of the final sheet of magma and fracture of the rock shifted the circulation system toward the center of the intrusion, thereby minimizing the extent of isotope exchange between rocks near the margin of the intrusion at this level. For comparison, similar calculations were also made for pure conductive cooling; it was found that the rate of crystallization of the magma body was not changed. The solidified pluton cooled by a factor of about 2 faster in the presence of a hydrothermal system. Transport rates of thermal energy out of the intrusion and of low-18O fluids into the intrusion controlled the overall isotope exchange process. During the initial 150,000 years, temperatures were high and reaction rates were fast; thus, fluids flowing into the intrusion quickly equilibrated with plagioclase. However, the temperature decreased between 120,000 and 175,000 years and caused a decrease in reaction rates and an increase in the equilibrium fractionation factor between plagioclase and fluid. Consequently, during this time period fluids in the intrusion tended to be out of equilibrium with plagioclase. After 175,000 years temperatures had decreased sufficiently that reaction rates became insignificant, but convection rates were large enough to redistribute fluid and enlarge the regions where fluid and plagioclase were out of equilibrium. By 400,000 years, the pluton had cooled to approximately ambient temperatures, and the final δ18O values were ‘frozen in’. Reactions between hydrothermal fluid and the intrusion occurred over a broad range in temperature, 1000-200 °C, but 75 per cent of the fluid circulated through the intrusion while its average temperature was >480 °C. This relatively high temperature is consistent with the observation that only minor amounts of hydrothermal alteration products were formed in the natural system, even where several per mil shifts in δ18O were detected. The relative quantities of fluid to rock integrated over the entire 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 the entire domain. Almost all of the fluid flowed into the intrusion from the basalt host rocks that occur adjacent to the side contacts of the intrusion. Convection transferred about 20 per cent of the total heat contained in the gabbro upward into the overlying basalts; the remaining 80 per cent of the heat was transferred by conduction.