Predicting Growth and Decay of Hydraulic-Fracture Width in Porous Media Subjected to Isothermal and Nonisothermal Flow

On the basis of the continuum thermo-poroelastic theory, a new analytical formula of fracture width is developed to quickly predict its transient growth or decay. The effects of the poroelastic stress (also called back stress) and thermal stress are taken into account. The counterbalance between the effects of back stress and thermal stress (in case of injection of cold fluid) is shown to be a function of flow and thermal properties and can be easily demonstrated by the formula developed. The analytical formula of fracture width is not complicated and does not require complex calculations. Different phenomena affecting the magnitude of fracture width are easily examined, such as the presence or absence of leakoff, isothermal or nonisothermal fracturing, and initial effective stress in the formation. Results show that the fracture width continuously decays with time because of the effect of pore pressure when there is leakoff. On the other hand, the fracture width will grow with time by the influence of thermal stress when cold fluid is injected. Unlike cold fluid, when hot fluid is used, the crack may close completely and the speed of the process will depend on the temperature of the injected fluid. Formulae for penetration depths for pressure and temperature are also developed and applied to the crack-width equation so that time-dependent maximum width and crack profiles can be computed. The analytical solution has also been validated by the finite-element (FE) numerical method.