In a typical test of the hydraulic fracturing (HF) method, fluid is injected into a wellbore until the initial cracks around the wellbore begin to develop. After that, the injection is stopped and the fluid pressure starts to decline. This stage is called shut-in. The common graph of the HF test is the wellbore pressure versus time that is used for estimating the in-situ stresses. A significant point in this curve, which is associated with the minimum horizontal in-situ stress, is the shut-in pressure. In this paper, a plane strain numerical model is used for simulating the injection and shut-in stages of hydraulic fracturing. This model considers wellbore effects, compressibility of injection system and fluid viscosity. Based on numerical results, increasing of fluid viscosity decreases the duration of the shut-in stage and length of initial notch is ineffective in the shut-in pressure.


Hydraulic fracturing (HF) test has been a rather old method for enhancing the efficiency of oil wells, but the developing this method in recent decades has caused that it has become a technique for designing the huge underground projects such as tunnels, mines, oil and gas wells, etc. (Howard and Fast, 1970, Haimson, 1968, Cornet, 1982, Tsukahara et al., 1996). One of the results obtained from the HF test is the graph of wellbore pressure versus time that is separated to three distinct stages. The first stage that is injection phase, the fluid is pumped into the wellbore and the pressure increases until pre-existing cracks in the rock mass start to propagate. After this stage, the fluid injection stops and then the fluid occupies throughout the crack length (shut-in stage). Finally, the cracks begin to close owing to the residual strength of the rock mass. The fluid withdraws from the wellbore during the phase known as flowback (Fig. 1).

For estimation of in-situ stresses, two vital points have been introduced in the wellbore pressure versus time graph: The breakdown pressure that is the peak pressure and the shut-in pressure is measured during the shut-in stage. According to the H-W (Hubbert and Willis, 1957) and H-F (Haimson and Fairhurst, 1967) criteria, the breakdown pressure is related to the horizontal in-situ stresses. Furthermore, it has been suggested that the shut-in pressure is equal to the minimum in-situ stress (Gronseth and Kry, 1982).

There are many ambiguities and arguments about the shut-in curve and the most of these issues may be attributed to the shut-in stage instability. Although in the shut-in stage the injection ceases but the energy required for propagating cracks exists, then the fluid pressure drops and becomes approximately uniform in the crack. Various factors affect the closure process after the shut-in.

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