Three-dimensional numerical investigation of the interaction between multiple hydraulic fractures in horizontal wells

Highlights

• A fully-coupled three-dimensional lattice-spring code is utilized to study the interference among multiple fractures.

• The development of complicated non-planar geometry and branching of hydraulic fractures is captured.

• The effects of the various parameters (i.e., in-situ stresses, Young’s modulus, viscosity, and injection rate) on HF propagation are investigated.

Abstract

Complex, non-planar fracture geometry is often observed in multi-stage hydraulic fracturing. The opening of hydraulic fractures results in a disturbance of local stress, which in turn affects the propagation of the adjacent fractures (stress shadow effect). The interaction between multiple fractures is of major importance in the design of fracturing treatments. In this study, a fully-coupled three-dimensional lattice-spring code is utilized to study the interference among multiple fractures. The results indicate that simultaneous propagating fractures can move towards or away from each other, resulting in complicated non-planar geometry and branching of hydraulic fractures. In an isotropic stress field, continued fracture propagation involves reorientation into a direction normal to the initial fracture plane, leading to an S-shaped fracture geometry. Higher Young's modulus values amplify the interaction of multiple fractures, resulting in more secondary fractures normal to the initial fracture plane and the greater dimension of fracture. Treatments assuming a higher magnitude of fluid viscosity /injection rate induce more branches at the tips of the primary fracture. An adjacent layer with a low modulus restricts the height growth of fractures, whereas the lateral growth and the stress interference will be in contrast relatively enhanced. This study provides further insight into the design and optimization of multiple-stage hydraulic fracturing in horizontal wells.

Introduction

Hydraulic fracturing has been extensively applied to the oil and gas industry [1], Enhanced Geothermal Systems [2], and the mining industry [3]. Complex, non-planar hydraulic fracture (HF) geometry is often observed in multi-stage hydraulic fracturing in horizontal wells. The interaction of multiple HFs is of major importance in the routine design of well completions and treatment strategies. The opening of an HF causes an alteration in the neighboring stress field, which in turn affects the propagation of the adjacent HFs. This phenomenon is referred to as the “stress shadow effect” [1]. Green and Sneddon [4] presented an analytical solution for a pressurized HF opening and the induced stress in an elastic solid. Based on Green and Sneddon's solution, an analysis of the fracture-induced stresses has been given to calculate the stability of reservoirs [5]. A three-dimensional stress solution produced by an elliptical crack has also been developed [6]. However, calculating stress variations induced by the interaction between multiple curved HFs using analytical solutions remains a challenging task.

Stress shadow has been documented for decades from fracture mapping data. Field observation has shown that the maximum increase in compressive stress can be expected to occur at the HF plane, with the stress disturbance radiating into the surrounding rock for hundreds of feet [1]. Laboratory experiments showed that the stress shadow effect is evident with the presence of closely spaced notches [7]. The stress shadow effect may either inhibit the propagation of neighboring HFs or induce a deviation of neighboring HFs. An older HF impact the shape and path of newer HF. The newer HF path curved toward and coalesced with the older HF [8]. Because of experimental limitations, it is difficult to perform a sensitivity study of the stress interference process for multiple fracture propagation under laboratory conditions.

Numerical simulation has been extensively used to study the interaction between multiple HFs. A comprehensive overview of numerical methods for hydraulic fracturing can be found in previous publications [9], [10], [11]. Only a few numerical methods are introduced in this study, including the finite element method (FEM), boundary element method (BEM), displacement discontinuity method (DDM), distinct element method (DEM), and lattice spring method. A finite-element model has been employed to study the interaction between multiple HFs [12]. The results showed that the stress induced by the opening of the HF or the fluid leak-off could alter the magnitudes and orientations of the principal stresses, thereby influencing the pathway of the HF. The 3D multiple-cluster fracturing problems have been investigated using the XFEM-based CZM (cohesive zone model based on the extended FEM) [13]. Results showed that the HF propagation pathway depends on a complex stress distribution (or stress shadowing effect). The interaction between HFs causes HF to coalesce, grow parallel, or diverge depending on cluster spacing. A pseudo-3D model based on the BEM has been utilized to investigate the simultaneous growth of multiple HFs [14]. The simulations showed that the HFs do not always propagate perpendicular to the far-field, minimum principal stress direction. The HF pattern complexity is influenced by the magnitude of the HF net pressure relative to the differential stress. The interaction between multiple neighboring cracks has been investigated using the BEM model [15]. Modeling results showed that the creation of outer cracks could act to either promote or inhibit adjacent cracks propagation depending on the spacing and the loading conditions. A plane strain simulator based on the DDM has been developed for simulating multiple HFs growth [16]. The simulations showed that the HFs can curve toward or away from one another, potentially intersecting. The curving of HFs is associated with a combination of opening and sliding along the previous HF, as well as the disturbance of the local stress field. An HF-propagation model based on the DDM has been presented [17]. Model results indicated that non-planar geometry reduced propagation occurs for interior HFs, resulting in a substantial restriction in HF aperture and a reduction in length. A pseudo 3D-based HF model based on the 3D-DDM has been developed [18]. Model results showed that the height growth may be promoted or suppressed for parallel HFs. The accurate prediction on the HF height and width profile require the incorporation of stress shadow effect.

The DEM has been extensively applied in different practices in rock engineering [19], [20], [21]. Simulations of stress interference among multiple HFs based on the DEM has been presented [22]. Simulation results showed that stress interference might impact the extent of the induced HF and treatment effectiveness. Numerical investigation of the stress shadow effect using the DEM code (both mechanical-only and hydro-mechanical coupled modes) has been presented [23]. The results showed that multiple HFs enhance the increase in minimum principal stress in the inter-fracture zone. Additionally, the increase in minimum principal stress reduces the HF apertures.

In the conventional DEM, discontinuities are regarded as distinct boundaries between blocks. The failure of intact blocks and the propagation of HFs may be simulated by implementing a Voronoi or Trigon tessellation within the intact blocks [24], [25]. Therefore, the HF trajectory is constrained by the geometry of the contacts. Based on Synthetic Rock Mass and Lattice methods, a fully-coupled code, XSite, has been presented, which allows simulating asymmetrical non-planar HF propagation in a full 3D setting [26]. The simulation of non-planar propagation of multiple HFs using XSite has been presented [27]. Simulation results revealed that the propagation of a middle HF is enhanced with an increase in the cluster spacing but decreases for higher in-situ stress difference. The mechanical interference among multiple HFs has been investigated using XSite [28]. The simulation captured the HF front segmentation and asymmetric growth due to the combined influence of the stress shadowing and perforation/in-situ stress misalignment.

In the present study, the lattice simulator, XSite, is employed to study the interference between multiple HFs. The simulator allows sensitivity analyses of the key parameters influencing multiple HFs propagation to be undertaken. Several simulations of simultaneous propagation of multiple HFs are presented, in which the effects of the various parameters (in-situ stresses, Young’s modulus (E), the viscosity of the fluid (μ), and injection rate (Q)) are investigated. Multiple HFs propagation in a layered formation is also simulated.