The onset of natural convection in vertical fault planes:consequences for the thermal regime in crystalline basementsand for heat recovery experiments

Details The onset of natural convection in vertical fault planes:consequences for the thermal regime in crystalline basementsand for heat recovery experiments The onset of natural convection in vertical fault planes:consequences for the thermal regime in crystalline basementsand for heat recovery experiments

Mar 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000geoji.140..500t&link_type=abstract

Geophysical Journal International, Volume 140, Issue 3, pp. 500-508.

Physics

Fluid Dynamics

4

Convection, Fault Model, Fluid Dynamics, Fractures, Geothermics, Heat Flow

Scientific paper

Very few results are available on free convection in fractured zones, although this is a major mechanism for heat and mass transfer in crystalline rocks. Murphy (1979) has shown, using analytical stability analysis, that the critical Rayleigh number for the onset of free convection in a fracture greatly exceeds the value of 4π2, which is the value for an infinite porous medium, and, even for a subcritical Rayleigh number, convection may occur after a time delay. Murphy proposed that this delayed convection results from a blanketing effect of the fracture induced by the progressive development of a thermal skin inside the fracture walls. The present paper extends Murphy's results by means of numerical modelling. Our numerical method involves a 2-D computation of convection in the fracture plane, and a 3-D solution of the conduction problem inside the fracture wall. The coupling of the codes is achieved by imposing a common temperature at the mid-fracture plane, together with the conservation of energy at the fracture-wall interface. We use two kinds of initial perturbation, which are assumed to constitute end-members for natural or application cases. For an A-type initial condition the thermal field is disrupted in the fracture only, while for a B-type initial condition the perturbation is introduced in the fracture and in the walls. For a given perturbation wavenumber, three distinct domains can be defined according to the Rayleigh number (R). In the first domain, convection takes place immediately; in the second one, convection starts after a delay; and in the third one, convection is damped. These three domains are therefore termed the instantaneous convection (R>Rs), delayed convection (Rd

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