Measurements of deformations by using tiltmeters located at large or moderate distances from a hydraulic fracture (HF) have often been used to monitor fracture geometry. The fracture is generally represented as a singular point displacement discontinuity (DD) source, or as a constant DD over a rectangular plane, or as a distributed DD across a fracture plane, and the analytical solution for the induced deformation by a DD in a homogeneous elastic half-space is commonly used directly as a forward model for representing a simple fracture or as a building block for constructing a more complex fracture in mapping the fracture geometry. The mechanical properties of the coal seam in which an HF is placed are typically very different from those of the surrounding rocks. In addition, the poroleastic response associated with fracturing fluid leakoff from the fracture surface into the coal layer may also influence the HF growth and the induced deformation. In order to obtain a correct interpretation of the created fracture geometry and better understanding of the treating pressure behaviour in hydraulic fracturing stimulation of coal to enhance gas production, the mechanical property contrasts and the poroelastic effect induced by fluid leakoff need to be recognised and taken into account. In this paper, a mechanical model based on the concept of eigenstrain and the equivalent inclusion method is presented and applied to the problem of calculating the far-field deformation and stresses induced by a horizontal fracture located in a formation layer with mechanical properties different from those of the surrounding homogeneous elastic half-space. The fracture is modelled as a constant opening DD across the fracture plane, and the corresponding mathematically equivalent eigenstrain is defined based on the fracture opening and formation layer geometry. A simple one-dimensional hydromechanical model has been presented to approximate the fluid leakoff through the surface of a stationary fracture. The analytical solutions allow for estimating the importance of the poroelastic effect associated with an HF in a coal seam. The variation of the pore fluid content due to fracturing fluid leakoff is characterized by the poroelastic eigenstrain. A relationship connecting the induced far-field deformation and stresses with the fracture and formation layer geometry, the fluid leakoff volume, and the mechanical properties has been established. The proposed method offers a simple and computationally efficient forward model to take into account the effect of mechanical property contrasts and poroelasticity on the deformation induced by the fracture when using tiltmeter monitoring to map the geometry of an HF in a coal seam.
展开▼
