http://www.vliz.be/imisdocs/publications/242609.pdf

Seawater intrusion processes, investigation and management: Recent advances and future challenges

Publisher Summary This chapter discusses the mathematical formulation of the problems of convective heat transfer in geothermal systems. Geothermal reservoirs may have numerous near-vertical faults and relatively impermeable intrusive interspersed in the aquifers. Both theoretical and experimental investigations of heat transfer in geothermal systems are reviewed. A qualitative understanding of the large-scale convection processes in a geothermal reservoir and the prediction of reservoir behavior under production can be obtained by idealizing it as a saturated porous medium. The identification of a viable geothermal reservoir and the estimation of its capacity remain major problems in the utilization of geothermal resources. Thermal anomalies in geothermal areas can be detected by surface manifestations, aerial infrared surveys, geochemical analyses, or exploratory drillings. Many of the analyses are applicable to a wide range of engineering problems whenever they can be idealized as convection in a porous medium. These include the problems of the secondary recovery of oil by thermal methods, the use of fibrous materials for thermal insulations, the design of aquifers as an energy storage system, and the deposition of mineral ore in the subsurface formation. Results from short-duration well testing are used to determine reservoir characteristics.

Heat Transfer in Geothermal Systems

The problem of the onset of convection, induced by buoyancy effects resulting from vertical thermal and solute concentration gradients, in a horizontal layer of a saturated porous medium, is treated by linear perturbation analysis. It is shown that oscillatory instability may be possible when a strongly stabilizing solute gradient is opposed by a destabilizing thermal gradient, but attention is concentrated on monotonic instability. The eigenvalue equation, which involves a thermal Rayleigh number R and an analogous solute Rayleigh number S, is obtained, by a Fourier series method, for a general set of boundary conditions. Numerical solutions are found for some special limiting cases, extending existing results for the thermal problem. When the thermal and solute boundary conditions are formally identical, the net destabilizing effect is expressed by the sum of R and S.

Onset of Thermohaline Convection in a Porous Medium

Evidence from rock microstructures, mass transfer and isotopic exchange indicates that substantial quantities of aqueous fluids are involved in low- and medium-grade regional metamorphism. Similar conclusions are drawn from many retrograde environments, whereas high-grade metamorphic fluids may be melt dominated. The mobile fluids play essential roles in metamorphic reactions, mass transport and deformation processes. These processes are linked by the mechanical consequences of meta- morphic fluid pressures (Pr) generally being greater than or equal to the minimum principal compressive stress. Under such conditions meta- morphic porosity comprises grain boundary tubules and bubbles together with continuously generated (and healed) microfractures. Deform- ation results in significant interconnected porosity and hence enhanced permeability. Lithologically and structurally controlled perme- ability variations may cause effective fluid channelling. Simple Rayleigh-Darcy modelling of a uniformly permeable, crustal slab shows that convective instability of metamorphic fluid is expected at the permeabilities suggested for the high Pf metamorphic conditions. Complex, large- scale convective cells operating in overpressured, but capped systems may provide a satisfactory explanation for the large fluid/rock ratios and extensive mass transport demonstrated for many low- and medium-grade metamorphic environ- ments. Such large-scale fluid circulation may have important consequences for heat transfer in and the thermal evolution of metamorphic

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1525-1314.1983.tb00272.x

The role of the fluid phase during regional metamorphism and deformation

Variable-density flow and transport in porous media: approaches and challenges

This is an experimental and numerical study of steady free convection in a porous medium, a system dominated by a single non-linear process, the advection of heat. The paper presents results on three topics: (1) a system uniformly heated from below, for which the flow is cellular, as in the analogous Benard-Rayleigh flows, (ii) the role of end-effects, and (iii) the role of mass discharge. Measurements of heat transfer are used to establish further the validity of the numerical scheme proposed by the author (1966a), while the other flows allow a more extensive study of the numerical scheme under various boundary conditions. The results are very satisfactory even though only moderately non-linear problems can be treated at present.The main new results are as follows. For the Rayleigh-type flow, above a critical Rayleigh number of about 40, the heat transferred across the layer is proportional to the square of the temperature difference across the layer and is independent of the thermal conductivity of the medium or the depth of the layer. This result is modified when the boundary-layer thickness is comparable to the grain size of the medium. The investigation of end-effects reveals variations in horizontal wave-number and a pronounced hysteresis and suggests an alternative explanation of some observations by Malkus (1954).

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112067000023

J. W. Elder

Papers

Steady free convection in a porous medium heated from below