Abstract
Description of a disc-shaped geothermal reservoir, pressurized and subject to thermal stresses, is given in terms of notions employed in mechanics of ductile fracture. The reservoir is assumed to extend in an infinite isotropic and impermeable medium. Range of the analysis, however, is extended to include a possibility of quasi-static stable cracking occurring along the reservoir circumference prior to spontaneous fracture. Extensive microcracking occuring in the region adjacent to the crack front prior to the onset of crack growth (and in the presence of high tectonic pressure encountered in a geothermal system) provides a stabilizing effect, similar in its nature to ductility exhibited in metal fracture.
Numerical example given here shows that the theoretical estimate of the upper critical flow rate of the fluid pumped through the reservoir, at which fracture becomes spontaneous, can be considerably increased (as compared with the values obtained within the LEFM framework) when the nonlinear inelastic behavior of rocks containing the reservoir is accounted for. Available data indicate that the rate of crack extension during the early stage of crack growth can be reduced by several orders of magnitude depending on physical and geometrical factors controlling the microcracking, process. Such result implies widening of the safety margin for a hot dry rock geothermal system.
The results given here may also be of use in designing the hydraulic fracturing experiments and in testing various fracturing concepts.
Résumé
On décrit un réservoir géothermique en forme de disque pressurisé et soumis à des contraintes thermiques en termes de notions utilisées en mécanique de rupture ductile. Le réservoir est supposé se trouver dans un milieu infini isotrope et imperméable. L'étendue de l'analyse toutefois est telle qu'elle inclut la possibilité d'une fissuration quasi statique et stable se produisant le long de la circonférence du réservoir avant la rupture spontanée. Un microfissuration intense se produisant dans la région adjacente au front de la fissure avant le démarrage de la croissance de la fissure et en présence des pressions tectoniques élevées rencontrées dans le système géothermique possède un effet stabilisant similaire par sa nature a la ductilité rencontrée dans la rupture des métaux.
L'exemple numérique fourni ici montre que l'estimation théorique du débit critique supérieur de fluide pompé au travers du réservoir auquel la rupture devient spontanée peut être considérablement accrue, quand on le compare aux valeurs obtenues dans le cadre de la mécanique de rupture linéaire élastique, lorsque l'on tient compte du comportement non linéaire inélastique de la roche comportant le réservoir. Les données disponibles indiquent que la vitesse de l'extension de la fissure au cours du stade primaire de la propagation de fissure peut être réduite de plusieurs ordres de grandeur suivant les facteurs physiques et géométriques contrôlant le processus de micro-fissuration. Un tel résultat implique un élargissement de la marge de sécurité dans le cas d'un système géothermique comportant des roches chaudes ou sèches.
Les résultats fournis peuvent également être appliqués dans la conception d'essai de rupture sous condition hydraulique et dans la mise à l'épreuve de divers concepts de rupture.
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Wnuk, M.P., Mura, T. Stability of a disc-shaped geothermal reservoir subjected to hydraulic and thermal loadings. Int J Fract 17, 493–517 (1981). https://doi.org/10.1007/BF00033344
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DOI: https://doi.org/10.1007/BF00033344