Density‐driven geothermal flow in 3‐D fractured rock is investigated and compared with density‐driven haline flow. For typical matrix and fracture hydraulic conductivities, haline flow tends to be unstable (convecting) while geothermal flow is stable (non‐convecting). Thermal diffusivity is generally three orders of magnitude larger than haline diffusivity and, as a result, large heat conduction diminishes growth of geothermal instabilities while low mass diffusion enables formation of unstable haline ‘fingering’ within fractures. A series of thermal flow simulations is presented to identify stable and unstable conditions for a wide range of hydraulic conductivities for matrix and fractures. The classic Rayleigh stability criterion can be applied to classify these simulations when fracture aperture is very small. However, the Rayleigh criterion is not applicable when the porous matrix hydraulic conductivity is very small, because stabilizing fracture–matrix heat conduction is independent of matrix hydraulic conductivity. In that case, the numerically estimated critical fracture conductivity is nine orders of magnitude larger than the theoretically calculated critical fracture conductivity based on Rayleigh theory. The numerical stability analysis presented here may be used as a guideline to predict if a geothermal system in 3‐D fractured rock is stable or unstable.

INTRODUCTION Arid and semi-arid climates are mainly characterised as those areas where precipitation is less (and often considerably less) than potential evapotranspiration. These climate regions are ideal environments for salt to accumulate in natural soil and groundwater settings since evaporation and transpiration essentially remove freshwater from the system, leaving residual salts behind. Similarly, the characteristically low precipitation rates reduce the potential for salt to be diluted by rainfall. Thus arid and semi-arid regions make ideal ‘salt concentrator’ hydrologic environments. Indeed, salt flats, playas, sabkhas and saline lakes, for example, are ubiquitous features of arid and semi-arid regions throughout the world (Yechieli and Wood,2002). In such settings, variable density flow phenomena are expected to be important, especially where hypersaline brines overlie less dense groundwater at depth. In contrast, seawater intrusion in coastal aquifers is a global phenomenon that is not constrained to only arid and semi-arid regions of the globe and is inherently a variable density flow problem by its very nature. These two examples make it clear that variable density flow problems occur in, but importantly extend beyond, arid and semi-arid regions of the globe. The intention of this chapter is therefore not to limit ourselves to modelling arid zone hydrological systems, but rather to present a more general treatment of variable density groundwater flow and solute transport phenomena and modelling. The concepts presented in this chapter are therefore not climatologically constrained to arid or semi-arid zones of the world, although they do apply equally there.

Groundwater is the most unexplored element of the hydrologic cycle on the Tibetan Plateau (TP) due to harsh climate conditions. This study aims at delineating and characterizing the unexplored Zhanongtang–Ganmanong aquifer, situated in the Zhagu subcatchment of the Nam Co catchment, south-central TP. Multiple hydrogeophysical and lithological in situ field and laboratory methods are applied: depth-to-water-table measurements, grain size analysis, hydraulic empirical and field methods to estimate hydraulic conductivity (K), and analysis of electrical resistivity tomography profiles. Integration of these methods revealed the existence of a Quaternary hydrostratigraphic unit that was found to be unconsolidated, laterally heterogeneous and homogeneous over depth. The results revealed consistent K ranges of three K zones, which is in accordance with local lithology. The K ranges are applicable to other locations within the Nam Co catchment with similar lithology as in the study area without further field experiments. Permafrost was found to be absent in the study area ranging from 4730 m a.s.l. to 5200 m a.s.l. altitude. These results provide insight into the hydrogeological conditions of the TP and are useful for conceptual and numerical groundwater flow modeling to predict future changes of water fluxes and water budgets caused by climatic change, especially in remote areas.

In natural environments, fluid density and viscosity can be affected by spatial and temporal variations of solute concentration, for example, due to saltwater intrusion in coastal aquifers, leachate infiltration from waste disposal sites, and upconing of saline water from deep aquifers. Potentially unstable situations may arise in which a dense fluid overlies a less dense fluid. This situation can produce instabilities manifested by dense plume fingers moving vertically downwards counterbalanced by vertical upward flow of the less dense fluid. The resulting free convection increases solute transport rates over large distances and times relative to constant-density flow. Unstable brine flow is further complicated if the porous medium is variably saturated. The results from a laboratory experiment of variably saturated variable-density flow and solute transport from Simmons et al. (2002) are used as the physical basis to define a new mathematical benchmark. This benchmark aims at realistically reproducing the experimental fingering patterns. Random hydraulic conductivity fields were used in the simulations as a numerical perturbation method to realistically mimic the observed dense plume fingering. The HydroGeoSphere code coupled with PEST are used to calibrate the parameter set that defines the benchmark. A grid convergence analysis is performed to obtain the adequate spatial and temporal discretizations. The new mathematical benchmark is useful for model comparison and testing of variably saturated variable-density flow in porous media. Simmons CT, Pierini ML, Hutson JL (2002) Laboratory investigation of variable-density flow and solute transport in unsaturated–saturated porous media. Transp Porous Media. 47(2): 215–244, 10.1023/A:1015568724369.