Statistics – Computation
Scientific paper
Aug 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989gecoa..53.1955k&link_type=abstract
Geochimica et Cosmochimica Acta, vol. 53, Issue 8, pp.1955-1964
Statistics
Computation
12
Scientific paper
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 m 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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