Effects of convective heat transport in modelling the early evolution of conduits in limestone aquifers
Introduction
Meteoric water flowing through a karst aquifer is generally under-saturated with respect to calcite and thus can dissolve the limestone in aquifers (Palmer, 1991). Heterogeneity and hydraulic conductivity of the epigenic karst aquifers increase with time due to the positive feedback loop between the calcite dissolution by chemically aggressive groundwater and the resulting growth in void space, which in turn facilitates higher water flow. Progressively dissolutional widening of rock voids results in the formation of cave conduits in karst aquifers.
The water temperature is the crucial factor that influences both the chemical solution process and water circulation. On one hand, calcite solubility has an inverse relationship with water temperature (Thrailkill, 1968; Dreybrodt, 1988), which affects the flux rate of calcium (Kaufmann and Dreybrodt, 2007). On the other hand, there is a reduction in flow resistance due to the decrease in viscosity with increasing temperature (Ma and Zheng, 2010; Saar, 2011), which controls the flux of water (Worthington, 2001).
In the absence of ground water flow, subsurface temperatures in the geothermal zone, which is situated below a depth of approximately 10 m, normally follow the geothermal gradient (Anderson, 2005). Movement of groundwater creates a systematic pattern of temperature distribution in aquifers due to heat convection. As a result, descending cold water reduces temperatures in recharge areas, and ascending warm water increases temperatures in discharge areas (Toth, 1999). Temperature fluctuations affect water flow patterns by changing the water density and water viscosity. Conversely, flow-induced heat anomalies can be accentuated by increased flow rates (Toth, 1999). As flow rates in karst aquifers are highly heterogeneous and may gradually increase over time, convective heat transport plays an important role in the evolution of karst aquifers.
Numerical models have been used to simulate epigenic conduit evolution in karst aquifers since the 1990s, employing CaCO3 dissolution kinetics (Groves and Howard, 1994; Howard and Groves, 1995). Variations are introduced in these models by different treatment of the flow and/or the chemical dissolution in the porous matrix between fractures (Kaufmann and Braun, 1999, 2000; Bauer et al., 2003; Kaufmann, 2003). Some studies have tested whether or not epigenic karst evolution would qualitatively change if diverse boundary conditions, apertures of initial fractures, or CO2 sources were used (Gabrovšek et al., 2000; Birk et al., 2003; Hubinger and Birk, 2011). Other studies have been applied to predict the location of caves and proto-conduits under artificial and natural conditions (Kaufmann and Romanov, 2008; Gabrovšek and Dreybrodt, 2010). Most simulations set the temperature of groundwater everywhere at a uniform value. If the temperature increases linearly with depth, the effect on conduit dissolution of the increase in flow through deep conduits due to the reduction of viscosity was far outweighed by the decrease in solubility with depth (Kaufmann et al., 2014). The effect of convective heat transfer on modelling conduit evolution has not been discussed in detail previously.
The location of the formation of cave conduits is dependent on geological conditions. Commonly, caves preferentially develop along the water table in host rocks (Swinnerton, 1932; Rhoades and Sinacori, 1941). Structural heterogeneities, such as strike dip prominent faults and dominant bedding partitions, guide the water flow deeper down into the aquifers, which is beneficial for the formation of cave conduits at great depths below the water table (Ford and Williams, 1989; Alexander et al., 2012). Long flow-path lengths (>3 km) favour deep conduit development because the reduction of viscosity with increasing temperature enhances flow at depth (Worthington, 2001, 2005). The impact of variable density and viscosity on modelling increases with the difference in temperature across the domain (Ma and Zheng, 2010). Therefore, the aim of this study is to quantitatively analyse, by a flow-heat-solute coupled karst evolution model, the effect of convective heat transport on the development of cave conduits in three scenarios, using different geological or thermodynamic controls (i.e., long flow-paths, a steeply dipping fault, and larger differences in temperature).
Section snippets
Flow, heat and solute transport
Equivalent porous-medium flow models can simulate regional, long-path groundwater flow in a karst environment because, at a sufficiently large scale, the discontinuities between the fractured and un-fractured parts are blurred, and Darcy flow may be assumed (Thrailkill, 1968; Scanlon et al., 2003). Isotropic porous rocks can be generalized as a bundle of conduits (Bear, 1972; Chen and Lin, 1999), and the hydraulic conductivity, K, is given by:where (-) is the porosity, which rarely
Model setup
The model used is a two-dimensional vertical section with dimensions of 10 km horizontally and 2.5 km vertically (Fig. 1). The right-hand side, the bottom and the lower part of the left-hand side boundaries are assumed to be impermeable. The hydraulic head, H, of the surface of the river is fixed at 2000 m above the zero metre elevation of the bottom of the domain. A recharge of 400 mm/yr is evenly distributed over the surface of the aquifer, with 0 mg/L calcium infiltrating into the aquifer.
Initial homogeneous aquifer
Fig. 2, Fig. 3 show the diameter of the conduits, the water table, the hydraulic head, and the isothermal contours for five successive temporal stages, from the early stage at t = 1000 yr to the time of onset of turbulent flow, occurring in the model with and without convective heat transport. Variations in the maximum (MAX), average (AVG), and standard deviation (SD) value of diameter, d, with time are depicted in Fig. 4. The locations of cave formation and karstification processes in
Discussion
Flow-induced heat transfer accelerates the karstification process in the model without a dipping fault by 3640 years, while it postpones the turbulent flow occurring at the proto-conduit along the fault by 110 years and 6830 years, in Scenario 2 and 3, respectively, as shown in Table 2. Because of the heat convection, the water temperature of the widest conduit decreases in the initial homogeneous aquifer but increases in the initial heterogeneous aquifer. The solubility of calcite in the water
Conclusions
In this paper the effect of convective heat transport on the evolution of epigenic limestone aquifers has been investigated by means of numerical modelling. During the dissolution of limestone coupled with heat convection, conduits are enlarged mainly in regions with decreased temperature and increased flux of water but remain unchanged in regions with increased temperature or decreased flux of water. Although influences of thermal convection on a simulation time scale (the delay of thousands
Acknowledgements
The authors would gratefully like to acknowledge the support provided by the National Key Research and Development Program of China (2017YFB0903700, 2017YFB0903703), the Chinese Postdoctoral Science Foundation (2017M622635), and the Natural Science Fund of Guangdong Province (2017A030310244, 2016A030310345).
References (37)
- et al.
Karstification in unconfined limestone aquifers by mixing of phreatic water with surface water from a local input: a model
J. Hydrol. (Amst)
(2010) A model comparison of karst aquifer evolution for different matrix-flow formulations
J. Hydrol. (Amst)
(2003)- et al.
Calcite dissolution kinetics in the system CaCO3-H2O-CO2 at high undersaturation
Geochim. Cosmochim. Acta
(2007) - et al.
Cave development in the Swabian alb, South-West Germany: a numerical perspective
J. Hydrol. (Amst)
(2008) - et al.
Can we simulate regional groundwater flow in a karst system using equivalent porous media models? Case study, Barton Springs Edwards aquifer, USA
J. Hydrol.
(2003) Karst hydrology: recent developments and open questions
Eng. Geol.
(2002)- et al.
Speleogenetic effects of interaction between deeply derived fracture-conduit flow and intrastratal matrix flow in hypogene karst settings
Int. J. Speleol.
(2012) Heat as a ground water tracer
Ground Water
(2005)- et al.
Modeling of karst aquifer genesis: influence of exchange flow
Water Resour. Res.
(2003) American elesevier publishing Company, New York
Dynamic of Fluids in Porous Media
(1972)
Hydraulic boundary conditions as a controlling factor in karst genesis: a numerical modeling study on artesian conduit development in gypsum
Water Resour. Res.
Dynamics of Groundwater (in Chinese)
Processes in Karst Systems: Physics, Chemistry, and Geology
Karst Geomorphology and Hydrology
Groundwater
A model of early evolution of karst conduits affected by subterranean CO2 sources
Environ. Geol.
Stress‐dependent permeability and the formation of seafloor event plumes
J. Geophys. Res. Solid Earth
Early development of karst systems: 1. Preferential flow path enlargement under laminar flow
Water Resour. Res.
Cited by (2)
A reactive transport approach for modeling scale formation and deposition in water injection wells
2020, Journal of Petroleum Science and Engineering