Spatial and temporal scales of local equilibrium in dynamic fluid-rock systems
The assumption of local equilibria (LEQ) is common when calculating the consequences of chemical interactions between a flowing fluid and host rock. LEQ is a good approximation if an initial disequilibrium condition relaxes to an equilibrium state over a distance and time period that is less than th...
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Veröffentlicht in: | Geochimica et cosmochimica acta 1989-08, Vol.53 (8), p.1955-1964 |
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Sprache: | eng |
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Zusammenfassung: | The assumption of local equilibria (LEQ) is common when calculating the consequences of chemical interactions between a flowing fluid and host rock. LEQ is a good approximation if an initial disequilibrium condition relaxes to an equilibrium state over a distance and time period that is less than the spatial and temporal scales-of-interest. These scales-of-interest depend on the particular problem under investigation and include the hundreds of meters scale for field investigations, the sub-meter scale for laboratory investigations and the sub-crystal scale. The computational step size and grid block size define the scales-of-interest for the computer experimentalist. An equation representing the scale-of-interest and describing advective, diffusive and dispersive transport coupled with irreversible heterogeneous reaction is derived and analytically solved for a single component (silica), monomineralic (quartz), one-dimensional system. The time,
t
eq
, and distance,
l
eq
, required for an impulse of fluid, initially undersaturated with respect to quartz, to relax to equilibrium is calculated for a wide range of reactions rates and transport conditions.
t
eq
and
l
eq
are reaction rate dominated for small scales-of-interest and for reaction rates that are fast relative to advection rates; this occurs in most natural environments with elevated temperatures.
t
eq
and
l
eq
are independent of reaction rate for large scales-of-interest and for slow reactions relative to advection; this is characteristic of sedimentary basins and man-made processes. Typically,
t
eq
≈ 1 year and
l
eq
≈ 10 m for sedimentary basins;
t
eq
≈ 3 days and
l
eq
≈ 10 mm for host rocks in magmahydrothermal systems;
t
eq
≈ 10 hours and
l
eq
= 250 μm for regional metamorphic environments;
t
eq
≈ 1 year and
l
eq
≈ 100 m for injection wells;
t
eq
≈ 700 years and
l
eq
≈ 75 km for laboratory core flow experiments. These values depend on the specifics of each environment and can vary over orders of magnitudes. LEQ is a good approximation if
t
eq
and
l
eq
are less than the scales-of-interest. This analysis, though quantitative, is only approximate because it does not include the effects of competing heterogeneous reactions. These effects result in over-estimation of
t
eq
and
l
eq
for low temperature silicate environments and under-estimation of
t
eq
and
l
eq
for high temperature environments. |
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ISSN: | 0016-7037 1872-9533 |
DOI: | 10.1016/0016-7037(89)90316-5 |