Three-dimensional lattice simulation of hydraulic fracture interaction with natural fractures

2019 ◽  
Vol 107 ◽  
pp. 214-234 ◽  
Author(s):  
Wei Fu ◽  
Alexei A. Savitski ◽  
Branko Damjanac ◽  
Andrew P. Bunger
Keyword(s):  
Hydraulic Fracture ◽  
Three Dimensional ◽  
Natural Fractures ◽  
Lattice Simulation ◽  
Dimensional Lattice ◽  
Fracture Interaction

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in Three-Dimensional Discrete Fracture Networks

2015 ◽  
Author(s):  
Mark W. McClure ◽  
Mohsen Babazadeh ◽  
Sogo Shiozawa ◽  
Jian Huang
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Three Dimensional ◽  
Hydraulic Fractures ◽  
Fracture Aperture ◽  
Natural Fractures ◽  
Fracture Networks ◽  
Field Scale ◽  
Discrete Fracture Networks ◽  
Discrete Fracture

Abstract We developed a hydraulic fracturing simulator that implicitly couples fluid flow with the stresses induced by fracture deformation in large, complex, three-dimensional discrete fracture networks. The simulator can describe propagation of hydraulic fractures and opening and shear stimulation of natural fractures. Fracture elements can open or slide, depending on their stress state, fluid pressure, and mechanical properties. Fracture sliding occurs in the direction of maximum resolved shear stress. Nonlinear empirical relations are used to relate normal stress, fracture opening, and fracture sliding to fracture aperture and transmissivity. Fluid leakoff is treated with a semianalytical one-dimensional leakoff model that accounts for changing pressure in the fracture over time. Fracture propagation is treated with linear elastic fracture mechanics. Non-Darcy pressure drop in the fractures due to high flow rate is simulated using Forchheimer's equation. A crossing criterion is implemented that predicts whether propagating hydraulic fractures will cross natural fractures or terminate against them, depending on orientation and stress anisotropy. Height containment of propagating hydraulic fractures between bedding layers can be modeled with a vertically heterogeneous stress field or by explicitly imposing hydraulic fracture height containment as a model assumption. The code is efficient enough to perform field-scale simulations of hydraulic fracturing with a discrete fracture network containing thousands of fractures, using only a single compute node. Limitations of the model are that all fractures must be vertical, the mechanical calculations assume a linearly elastic and homogeneous medium, proppant transport is not included, and the locations of potentially forming hydraulic fractures must be specified in advance. Simulations were performed of a single propagating hydraulic fracture with and without leakoff to validate the code against classical analytical solutions. Field-scale simulations were performed of hydraulic fracturing in a densely naturally fractured formation. The simulations demonstrate how interaction with natural fractures in the formation can help explain the high net pressures, relatively short fracture lengths, and broad regions of microseismicity that are often observed in the field during stimulation in low permeability formations, and which are not predicted by classical hydraulic fracturing models. Depending on input parameters, our simulations predicted a variety of stimulation behaviors, from long hydraulic fractures with minimal leakoff into surrounding fractures to broad regions of dense fracturing with a branching network of many natural and newly formed fractures.

High-Resolution 3D Structural Geomechanics Modeling for Hydraulic Fracturing

2015 ◽  
Author(s):  
T.. Bérard ◽  
J.. Desroches ◽  
Y.. Yang ◽  
X.. Weng ◽  
K.. Olson
Keyword(s):  
High Resolution ◽  
Stress Field ◽  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Three Dimensional ◽  
Image Data ◽  
Natural Fractures ◽  
Fracture Length ◽  
3D Space ◽  
Wellbore Pressure

Abstract Three-dimensional (3D) geomechanical models built at reservoir scale lack resolution at the well sector scale (e.g., hydraulic fracture scale), at least laterally. One-dimensional (1D) geomechanical models, on the other hand, have log resolution along the wellbore but no penetration away from it—along the fracture length for instance. Combining borehole structural geology based on image data and finite elements (FE) geomechanics, we constructed and calibrated a 3D, high-resolution geomechanical model, including subseismic faults and natural fractures, over a 1,500- × 5,200- × 300-ft3 sector around a vertical pilot and a 3,700-ft lateral in the Fayetteville shale play. Compared to a 1D approach, we obtained a properly equilibrated stress field in 3D space, in which the effect of the structure, combined with that of material anisotropy and heterogeneity, are accounted for. These effects were observed to be significant on the stress field, both laterally and local to the faults and natural fractures. The model was used to derive and map in 3D space a series of geomechanically based attributes potentially indicative of hydraulic fracturing performance and risks, including stress barriers, fracture geometry attributes, near-well tortuosity, and the level of stress anisotropy. An interesting match was observed between some of the derived attributes and fracturing data—near-wellbore pressure drop and overall ease and difficulty to place a treatment—encouraging their use for perforation and stage placement or placement of the next nearby lateral. The model was also used to simulate hydraulic fracturing, taking advantage of such a 3D structural and geomechanical representation. It was shown that the structure and heterogeneity captured by the model had a significant impact on hydraulic fracture final geometry.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals A numerical investigation on the performance of hydraulic fracturing in naturally fractured gas reservoirs based on stimulated rock volume

2020 ◽  
Vol 10 (8) ◽  
pp. 3333-3345
Author(s):  
Ali Al-Rubaie ◽  
Hisham Khaled Ben Mahmud
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Natural Fracture ◽  
Shear Stresses ◽  
Individual Element ◽  
Natural Fractures ◽  
Gas Reservoirs ◽  
Stimulated Reservoir Volume ◽  
Reservoir Volume ◽  
Naturally Fractured

Abstract All reservoirs are fractured to some degree. Depending on the density, dimension, orientation and the cementation of natural fractures and the location where the hydraulic fracturing is done, preexisting natural fractures can impact hydraulic fracture propagation and the associated flow capacity. Understanding the interactions between hydraulic fracture and natural fractures is crucial in estimating fracture complexity, stimulated reservoir volume, drained reservoir volume and completion efficiency. However, because of the presence of natural fractures with diffuse penetration and different orientations, the operation is complicated in naturally fractured gas reservoirs. For this purpose, two numerical methods are proposed for simulating the hydraulic fracture in a naturally fractured gas reservoir. However, what hydraulic fracture looks like in the subsurface, especially in unconventional reservoirs, remain elusive, and many times, field observations contradict our common beliefs. In this study, the hydraulic fracture model is considered in terms of the state of tensions, on the interaction between the hydraulic fracture and the natural fracture (45°), and the effect of length and height of hydraulic fracture developed and how to distribute induced stress around the well. In order to determine the direction in which the hydraulic fracture is formed strikethrough, the finite difference method and the individual element for numerical solution are used and simulated. The results indicate that the optimum hydraulic fracture time was when the hydraulic fracture is able to connect natural fractures with large streams and connected to the well, and there is a fundamental difference between the tensile and shear opening. The analysis indicates that the growing hydraulic fracture, the tensile and shear stresses applied to the natural fracture.

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