## Combined Hydrodynamic and Thermodynamic Model of a Convective
Hydrothermal System.

1. The Marker Method of Modeling

### (C) 1997 A. V. Tutubalin, D. V. Grichuk

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Moscow State University

Department of Geology

Vorob'evy gory, Moscow, 119899 Russia

A combined model of a convective hydrothermal system in a
mid-ocean ridge was developed. The modeling technique includes
two stages of calculations. At the first stage, paths
are calculated for the motion of markers (point-sized portions
of the solution with the given initial coordinates);
temperatures, pressures, and filtration rates are found for
each part of these paths. At the second stage,
compositions of metasomatic mineral associations are
calculated within each part of the marker paths, as well as the
composition of the equilibrium hydrothermal solution.
Temperature and pressure data are directly included in the
thermodynamic calculations, whereas the information concerning
filtration rates is used to estimate the intensity of
interaction between the solution and the host rock.
Calculations within the hydrodynamic part of the model were
based on a numerical solution of the Darcy and heat transfer
equations by the finite elements method. At the thermodynamic
stage, the technique of a flow-type stepwise reactor was used,
and the local equilibrium between the solution and the rock was
calculated at each step of this reactor.

The results of modeling showed that the hydrothermal system is
characterized by formation of a convective cell with a wide
region of descending motion and narrow region of ascending flow in
the fracture zone above the intrusive body. Near the upward
branch, a region of circular flow appears; however, this region
is nonstationary and degenerates with time. The position of
isotherms in the system is subparallel to the contact with a
magma chamber. The rock--water ratios increase in the
contact part of the system and reach maximum values above the
top of the magma chamber. The calculated distribution
of metasomatic minerals agrees with the one observed for
ophiolites. The time required for a portion of sea water to
pass through the convective system was estimated: for a system
as a whole, it is of the order of 1000 years; for the part with
an active water--rock interaction, it amounts to tens of
years.

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