Large-Scale Geothermal Field Parameters and Convection Theory

The question of the depth reached by groundwater in natural recharge to a geothermal field is of interest for geothermal development, since it can affect the nature of the recharge regime during withdrawal, and the volume of water within reach during exploitation. Also, useful inferences may be drawn about the large-scale permeability of the system if the groundwater flow regime is understood. Evidence for the presence of thermal convection in the groundwater now appears to be well-established, although topographic effects may also be important (Studt and Thompson 1969, Healy and Hochstein 1973). Two regions which serve particularly well as illustrations are (1) the Imperial Valley of Southern California and (2) the Taupo Volcanic Zone of New Zealand. Both exhibit a number of quite well-defined zones of anomalously high heat flow (geothermal fields), separated by distances of 10 to 15 Km, the intervening areas usually having very low heat flow. In (1) the upper flow boundary is practically impermeable while, in (2), flow through the upper boundary is almost unimpeded. Idealized conditions which correspond approximately to these cases were introduced by Lapwood (1948); these will be designated as boundary conditions 1 and 2 respectively. This paper discusses the magnitudes of convection parameters, extensions of Lapwood’s work, the departure of permeable media in geothermal areas from simple homogeneous isotropic systems, and stability analysis for boundary conditions 1 and 2 from convection theory. 11 refs., 1 fig

Stability criteria for the vertical boundary layer formed by throughflow near the surface of a porous medium

We consider gravitational instability of a saline boundary layer formed by evaporation induced upward throughflow at a horizontal surface of a porous medium. Two paths are followed to analyse stability: the energy method and the method of linearised stability. The energy method requires constraints on saturation and velocity perturbations. The usual constraint is based on the integrated Darcy equation. We give a fairly complete analytical treatment of this case and show that the corresponding stability bound equals the square of the first root of the Bessel function J0. This explains previous numerical investigations by Homsy & Sherwood [1975, 1976]. We also present an alternative energy method using the pointwise Darcy equation as constraint, and we consider the time dependent case of a growing boundary layer. This alternative energy method yields a substantially higher stability bound which is in excellent agreement with the experimental work of Wooding et al. [1997a, b]. The method of linearised stability is discussed for completeness because it exhibits a different stability bound. The theoretical bounds are verified by two-dimensional numerical computations. We also discuss some cases of growing instabilities. The presented results have applications to the theory of stability of salt lakes and the salinization of groundwater