On the Theory of Filtration Waves of Pressure in a Crack in a Porous Permeable Medium
V. Sh. Shagapov1,2, Z. M. Nagaeva3
1Institute of Mechanics and Engineering, Kazan Scientific Center, Russian Academy of Sciences, Kazan 420111, Russia
2Mavlyutov Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa, 450054 Russia
3Ufa State Oil Technical University, Ufa 450062, Russia
Keywords: гидроразрыв пласта, трещина, волны давления, интегродифференциальное уравнение, дисперсионный анализ, fracturing, crack, pressure waves, integrodifferential equation, variance analysis
Abstract
Pressure filtration waves in cracks in porous permeable medium are studied. The effect of the porosity and permeability of the formation and crack, the crack width, and the rheological properties of the saturating fluid on the dynamics of perturbations in the crack are studied. It is shown that in a porous permeable formation, a crack is a wave channel through which low-frequency pressure fluctuations in wells propagate. Accurate solutions are obtained which describe the evolution of pressure fields in a crack with an instantaneous pressure change in the well by a constant value. Based on these solutions, the corresponding dependences of the fluid flow on time and the pressure at the boundaries are determined.
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