Elsevier

Geothermics

Volume 77, January 2019, Pages 383-394
Geothermics

Effects of convective heat transport in modelling the early evolution of conduits in limestone aquifers

https://doi.org/10.1016/j.geothermics.2018.10.010Get rights and content

Highlights

  • Simulating the evolution of conduits in limestone aquifers with different geological settings by a flow-heat-solute coupled model.

  • Calculating the discrepancies of temperature and diameter of conduits in the models with and without convective heat transfer.

  • Quantifying the effect of convective heat transport in modelling the early evolution of conduits in limestone aquifers.

  • Providing accuracy and efficiency for when conduit evolution may be simulated by assuming constant or depth-dependent temperature.

Abstract

Resistance to groundwater flow and temperature-dependent solubility of calcite is affected by the flow-induced heat convection in groundwater flow systems, which impacts the dissolution of limestone. The primary objective of this paper is to quantify the effect of convective heat transport in modelling the early evolution of conduits, using a flow-heat-solute coupled karst evolution model. The results show that the enlargement of conduits induced by convective heat transport occurs mainly in a region with a decreased temperature and a increased flux of water. For the initial homogeneous aquifer with conduits that had a diameter of 1E-5 m (Scenario 1), convective heat transport accelerated the karstification progress by 2.5% (3640 years out of 147470 years) and enlarged the diameter of the evolved cave beneath the water table. For the initially heterogeneous model, which was cut by a steeply dipping fault (Scenario 2), heat convection prolonged the early evolution of conduits by 110 years and pushed the proto-conduit along the fault down by approximately 150 m. The maximum diameter of the proto-conduit was reduced, but the total number of dissolved conduits increased. With an increase in the geothermal gradient by 20 °C/km in the heterogeneous model (Scenario 3), the lag-time caused by the convective heat transport increased to 6830 years, and the depth of the proto-conduit increased by 450 m. Although a delay of thousands of years is negligible for the karstification process over millions of years, differences in diameter and depth of karst formation provide some quantitative guidelines for when conduit evolution may be simulated by assuming a constant or depth-dependent temperature as a reasonable compromise between accuracy and efficiency.

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:K=nd232ρgμwhere n (-) 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).

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