Quartz deposition in a fracture
Section 26.2 of Bethke (2007) describes quartz deposition in a hydrothermal fracture. The setup is similar to quartz dissolution but with a different form of the reaction rate. The reaction is with rate It is assumed that:
there is 1kg of water;
the initial temperature is 300C and this steadily reduces to 25C over the course of 1 year;
the mineral quartz is used instead of SiO(aq) in the basis initially while quartz is an equilibrium mineral (before it is kinetically-controlled);
initially 400g (6.657313mol) of quartz is added to the water;
the specific surface area is cm/g(quartz);
the activation energy is J.mol;
all other silica-containing minerals are prevented from precipitating.
MOOSE input file: stage 1
The MOOSE simulation is in 2 stages. The first determines the molality of SiO2(aq) that is in equilibrium with the quartz. This is necessary because the problem description assumes that the water has had enough time to equilibrate with the quartz mineral at 300C, and in this stage the quartz mineral is not governed by a kinetic rate.
The system described in the input file also includes very small amounts of Na and Cl. These do not impact the results but are necessary because the geochemistry
module requires a charge-balance species to be defined.
The output of this simulation is that the molality of SiO2(aq) is 0.009723mol.
MOOSE input file: stage 2
The second stage uses this molality and performs the time-dependent simulation, as the temperature is reduced. The GeochemistryKineticRate is defined:
(moose/modules/geochemistry/test/tests/kinetics/quartz_deposition.i)The TimeDependentReactionSolver defines the free molality of SiO2(aq) at the initial time, the initial mole number of quartz and that the temperature is controlled using the temp_controller
AuxVariable
:
The temperature controller is:
(moose/modules/geochemistry/test/tests/kinetics/quartz_deposition.i)with time defined through:
(moose/modules/geochemistry/test/tests/kinetics/quartz_deposition.i)The figures below were generated using a time-step of 0.001yr. A set of AuxVariables
and Postprocessors
define the desired output using the mg_per_kg_SiO2(aq)
variable automatically included by the TimeDependentReactionSolver:
GWB input file
The equivalent Geochemists Workbench file is
(moose/modules/geochemistry/test/tests/kinetics/quartz_deposition.rea)Results
Bethke (2007) presents results in Figures 26.3 and 26.4, which look like:
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Figure 1: Change in free mass of SiO2(aq) as fluid flows through a fracture, changing temperature as it does so. Compare with Bethke's Figure 26.3
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Figure 2: Quartz reaction rate as fluid flows through a fracture, changing temperature as it does so. Compare with Bethke's Figure 26.4
The accuracy of the geochemistry
simulation depends on the time-step size. The above figures were generated using a step size of 0.001yr.
References
- Craig M. Bethke.
Geochemical and Biogeochemical Reaction Modeling.
Cambridge University Press, 2 edition, 2007.
doi:10.1017/CBO9780511619670.[BibTeX]