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Abstract Hydraulic fracturing in naturally fractured rocks can potentially generate a complex network of connected fractures. Efficient design of stimulation heavily depends on understanding of the mechanisms of hydraulic and natural fracture interactions and coalescence. Termination or partial propagation of hydraulic fractures might occur in the presence of natural fractures with detrimental effects on the stimulation. Improving fracture design in unconventional reservoirs must be based on a solid understanding of HF-NF interactions in 3D. In this study we cast light on the problem of 3D fracture propagation in naturally fractured rocks and show the potential impact on network design, DFIT interpretation, and proppant transport. Unlike attempts by previous Investigators, we investigate hydraulic fracture propagation in the presence of natural fractures by development and use of a fully 3D coupled model. Our 3D model is based on displacement discontinuity method for the stress analysis and a finite element model for fluid flow calculations. The contact status of natural fractures are determined using contact elements along with the Mohr-Coulomb criterion. The model simulation results show that the normal and shear stress on the natural fracture are affected by the approaching hydraulic fracture. In the case of hydraulic fracture arrest, the hydraulic fracture can propagate in other directions and tends to engulf the natural fracture. It should be emphasized that capturing the engulfing pattern is only possible through using a robust 3D HF-NF model and other 2D and simpler 3D models fail to predict this geometry. Moreover, as a development, we show and discuss the pumping pressure profile for hydraulic fracturing in the presence of natural fractures obtained from a fully 3D model. The results show that stress shadowing causes non-uniform aperture profiles along the NF which impacts the proppant transport. Introduction Economic production of hydrocarbons from unconventional reservoirs relies on the stimulation by hydraulic fracturing. Extensive research has been directed towards understanding of the reservoir response to stimulation, including experimental, theoretical, and numerical modeling (Blanton, 1982; Koshelev and Ghassemi, 2003a, b; Dobroskok and Ghassemi, 2004; Dobrosko et al., 2005; Zhang and Jeffrey, 2006; Dahi-Taleghani and Olson, 2011; Sesetty and Ghassemi, 2012; 2017; Hu et al., 2019; Ye and Ghassemi, 2018; Kumar and Ghassemi, 2018; Kamali and Ghassemi, 2018; Gao and Ghassemi, 2019; Sesetty and Ghassemi, 2018; Zhang et al., 2009).
Abstract Currently, the closure stress is often predicted using the conventional tangent method (i.e., G-function) or the variable compliance method. Both methods use several restrictive assumptions such as a single planar fracture. However, the hydraulic fracture often intersects rock fabric features such as bedding planes and/or natural fractures causing the pressure transient behavior to become drastically different compared to that of a single planar hydraulic fracture. Closure of the intersected natural fractures might precede that of the created HF which impacts the interpretation of the pressure derivate plots and also the closure stress. In this paper we present and use an advanced fracture diagnostic model that can help recognize the signatures of rock fabric features and their impact on estimation of the closure stress. An example field data is used to illustrate the potential impact on closure stress. The new DFIT model consists of a fully coupled 3D hydraulic fracture simulator with the ability to handle the opening, propagation, and closure of natural factures so that the pre- and post-closure stress/deformation of both the hydraulic and natural fractures can be captured. Fracture propagation, HF-NF interaction, fracture intersection, and DFIT model are integrated into one simulator to provide a more realistic view of HF propagation and fracture diagnostics in naturally fractured reservoirs. The current model is developed without any major assumptions concerning the fluid flow, fracture deformation, and propagation path. Rock/fracture deformation is calculated using a boundary element formulation whereas the transport processes are solved using finite elements method. Our results indicate that natural fractures affect the pre- and post- shut-in response of the hydraulic fracture in a number of ways. For example, the fracture propagation path, the pumping pressure profile, and interfering with the post shut-in pressure response. These factors, indeed, impact the estimation of the minimum horizontal stress which is a key parameter obtained from DFIT. Moreover, our results show how the normal stiffness of the fracture surface asperities can impact the minimum stress estimation. Closure of natural fractures is reflected in the slope of the pressure derivative and G-function plots so that correct interpretation of these signatures is essential to accurate extraction of the Shmin. Closure of natural fractures is often viewed as a pressure depdendent leakoff mechanism that is reflected on the Gdp/dG curve. The closure behavior of HF-NF sets is, however, not explicitly modeled in the context of pressure transient analysis. Therefore, it is our objective to study the closure behavior of HF-NF sets using a 3D coupled simulator. This novel model is applied to actual field data to illustrate the potential impact on closure stress and to shed light on the subject of fracture diagnostics in naturally fractured reservoirs. Our results indicate that the closure behavior of hydraulic and natural fractures in a HF-NF set differs from that of an isolated fracture due to the effect of stress shadowing. Although the system stiffness method results in distinct signatures on the diagnostic curves, these signatures are not commonly observed in the field data. The absence of stiffness signatures in the field cases could be interpreted in two ways: 1) the closure mechanism assumed in the stiffness/compliance method differs from the actual fracture closure mechanism or 2) the stiffness of the hydraulic fracture is too low to cause any significant changes in the system stiffness after closure.
A closure model is developed for rough fractures along with a fluid flow model to predict fracture conductivity decline under normal closure stress. The closure model is based on surface asperity and half-space deformation considering the effect of mechanical interaction among asperities and inelastic deformation. Fracture aperture profile that is obtained from the closure model is then used in the fluid flow model to predict fracture conductivity. Hydraulic conductivity of synthetic surface profiles are compared to investigate the impact of surface pattern on conductivity. Simulation results indicate that considering half-space deformation and mechanical interaction among asperities affect conductivity decline behavior. Different aperture averaging methods are found to result in noticeably different conductivity results. Narrower and deeper channels undergo less conductivity decline compared to wider and shallower channels.
Rough fractures tend to close due to farfield stresses acting on the plane of fracture. Quantification of fracture closure is crucial to predicting hydraulic conductivity behavior. It is, therefore, necessary to study the closure mechanisms in rough surfaces. The concepts of fracture closure and contact mechanics can be applied to acid fracturing and unpropped fracturing which are of great interest in the petroleum industry.
Several attempts have been made to investigate the closure of rough surfaces in contact. The problem of rough surface closure is addressed in many analytical (Greenwood & Williamson 1966, Brown & Scholz 1985), numerical (Hopkins 1991, Pyrak-Nolte & Morris 2000), and experimental (Bandis et al. 1983, Marache et al. 2008) works. It is worth mentioning that the literature is mainly concerned with the elastic contact of rough surfaces.
Hydraulic conductivity of rough surfaces is extensively studied because of its important implications in different branches of science and engineering. The hydraulic conductivity of rough fractures is studied in many experimental and analytical works (Witherspoon et al. 1980, Tsang and Witherspoon 1981, Gong et al. 1998). It is our aim to investigate the impact of fracture closure on fracture conductivity and also study the importance of fracture surface pattern in conductivity decline behavior.