『Abstract
The possibility that gradients in concentration may develop within
single pores and fractures, potentially giving rise to scale-dependent
mineral dissolution rates, was investigated with experimentally
validated reactive transport modeling. Three important subsurface
mineral phases that dissolve at widely different rates, calcite,
plagioclase, and iron hydroxide, were considered. Two models for
analyzing mineral dissolution kinetics within a single pore were
developed: (1) a Poiseuille Flow model that applies laboratory-measured
dissolution kinetics at the pore or fracture wall and couples
this to a rigorous treatment of both advective and diffusive transport
within the pore, and (2) a Well-Mixed Reactor model that assumes
complete mixing within the pore, while maintaining the same reactive
surface area, average flow rate, geometry, and multicomponent
chemistry as the Poiseuille Flow model. For the case of a single
fracture, a 1D Plug Flow Reactor model was also considered to
quantify the effects of longitudinal versus transverse mixing.
Excellent agreement was obtained between results from the Poiseuille
Flow model and microfluidic laboratory experiments in which pH
4 and 5 solutions were flowed through a single 500μm diameter
by 4000μm long cylindrical pore in calcite. The numerical modeling
and time scale analysis indicated that rate discrepancies arise
primarily where concentration gradients develop under two necessary
conditions: (1) comparable rates of reaction and advective transport,
and (2) incomplete mixing via molecular diffusion. For plagioclase
and iron hydroxide, the scaling effects are negligible at the
single pore and fracture scale because of their slow rates. In
the case of calcite, where dissolution rates are rapid, scaling
effects can develop at high flow rates from 0.1 to 1000 cm/s and
for fracture lengths less than 1 cm. Under more normal flow conditions
where flow is usually slower than 0.001 cm/s, however, mixing
via molecular diffusion is effective in homogenizing the concentration
field, thus eliminating any discrepancies between Poiseuille Flow
and Well-Mixed Reactor model. The analysis suggests that concentration
gradients are unlikely to develop within single pores and fractures
under typical geological/hydrologic conditions, implying that
the discrepancy between laboratory and field rates must be attributed
to other factors.』
1. Introduction
2. Reactions and rate laws
2.1. Calcite dissolution
2.2. Plagioclase dissolution
2.3. Dissimilatory dissolution of iron hydroxide
2.4. Incorporation of aqueous speciation
3. Models for single pores and fractures
3.1. Model for a single pore
3.1.1. Poiseuille Flow model
3.1.2. Well-Mixed Reactor model
3.2. Models for a single fracture
3.2.1. Poiseuille Flow model
3.2.2. 1D Plug-Flow Reactor model
3.2.3. Well-Mixed Reactor model
4. Validation and verification of the Poiseuille Flow model
4.1. Verification of transport for a cylindrical pore
4.2. Validation with a microfluidic reactive flow experiment
5. Results
5.1. Development of concentration gradients at the pore scale
5.2. Single pore results
5.3. Single fracture results
5.3.1. Calcite
5.3.2. Plagioclase
5.4. Time scale analysis
6. Discussion
7. Conclusions
Acknowledgments
References