scholarly journals Application of Tempered-Stable Time Fractional-Derivative Model to Upscale Subdiffusion for Pollutant Transport in Field-Scale Discrete Fracture Networks

Mathematics ◽  
2018 ◽  
Vol 6 (1) ◽  
pp. 5 ◽  
Author(s):  
Bingqing Lu ◽  
Yong Zhang ◽  
Donald Reeves ◽  
HongGuang Sun ◽  
Chunmiao Zheng
Keyword(s):  
Fractional Derivative ◽  
Pollutant Transport ◽  
Fracture Networks ◽  
Field Scale ◽  
Fractional Derivative Model ◽  
Discrete Fracture Networks ◽  
Discrete Fracture ◽  
Time Fractional Derivative

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.

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in 3D Discrete-Fracture Networks

SPE Journal ◽  
2016 ◽  
Vol 21 (04) ◽  
pp. 1302-1320 ◽  
Author(s):  
Mark W. McClure ◽  
Mohsen Babazadeh ◽  
Sogo Shiozawa ◽  
Jian Huang
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Fluid Pressure ◽  
Hydraulic Fractures ◽  
Fracture Aperture ◽  
Natural Fractures ◽  
Fracture Networks ◽  
Field Scale ◽  
Discrete Fracture Networks ◽  
Discrete Fracture

Summary We developed a hydraulic-fracturing simulator that implicitly couples fluid flow with the stresses induced by fracture deformation in large, complex, 3D discrete-fracture networks (DFNs). The code is efficient enough to perform field-scale simulations of hydraulic fracturing in DFNs containing thousands of fractures, without relying on distributed-memory parallelization. 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 equations are used to relate normal stress, fracture opening, and fracture sliding to fracture aperture and transmissivity. Fluid leakoff is treated with a semianalytical 1D leakoff model that accounts for changing pressure in the fracture over time. Fracture propagation is modeled with linear-elastic fracture mechanics. The Forchheimer equation (Forchheimer 1901) is used to simulate non-Darcy pressure drop in the fractures because of high flow rate. 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. 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 that 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.

scholarly journals Identifying Non-Darcian Flow and Non-Fickian Pressure Propagation in Field-Scale Discrete Fracture Networks

2018 ◽  
Vol 06 (05) ◽  
pp. 59-69
Author(s):  
Bingqing Lu ◽  
Yong Zhang ◽  
Yuan Xia ◽  
Donald M. Reeves ◽  
Hongguang Sun ◽  
...  
Keyword(s):  
Fracture Networks ◽  
Field Scale ◽  
Discrete Fracture Networks ◽  
Discrete Fracture ◽  
Pressure Propagation

An efficient algorithm for computing nearest medium approximations to an arbitrary anisotropic stiffness tensor

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. C81-C90 ◽  
Author(s):  
Lennert D. den Boer
Keyword(s):  
Large Field ◽  
Stiffness Tensor ◽  
Fracture Networks ◽  
Field Scale ◽  
Higher Symmetry ◽  
Discrete Fracture Networks ◽  
Discrete Fracture ◽  
Transverse Isotropic ◽  
Problem Instances ◽  
Anisotropic Stiffness

The problem of reducing a fully anisotropic (triclinic) stiffness tensor comprised of 21 distinct components to a higher symmetry form having fewer distinct elements is of interest in many geophysical applications, where assuming a particular type of symmetry is often necessary to sufficiently reduce computational complexity to allow practical solutions. In addition, recent advances in the upscaling of realistically large field-scale discrete fracture networks have led to the need for an efficient way to derive a very large number of nearest medium approximations to the triclinic stiffness tensors obtained. Owing to rotational symmetries and nonlinearity, the problem of efficiently finding such approximations is generally nontrivial because optimal orientations are intrinsically nonunique. An algorithm proposed by Dellinger computes nearest orthotropic and transverse isotropic approximations for a given stiffness tensor, using the Federov norm as an objective function to iteratively minimize the fit error. Although this method is appropriate for computing solutions to single problem instances, the implementation is too inefficient for production situations, where a very large number of invocations of the algorithm is required. The enhanced algorithm proposed here is accurate, efficient, and general, allowing nearest medium approximations to be determined for arbitrary symmetry types, including isotropic, cubic, transverse isotropic, orthotropic, and monoclinic.

"Gas migration in discrete fracture networks

1990 ◽  
Vol 26 (10) ◽  
pp. 2425-2434 ◽  
Author(s):  
Roger Thunvik
Keyword(s):  
Gas Migration ◽  
Fracture Networks ◽  
Discrete Fracture Networks ◽  
Discrete Fracture

Can a Time Fractional-Derivative Model Capture Scale-Dependent Dispersion in Saturated Soils?

Ground Water ◽  
2017 ◽  
Vol 55 (6) ◽  
pp. 857-870 ◽  
Author(s):  
Rhiannon M. Garrard ◽  
Yong Zhang ◽  
Song Wei ◽  
HongGuang Sun ◽  
Jiazhong Qian
Keyword(s):  
Fractional Derivative ◽  
Saturated Soils ◽  
Fractional Derivative Model ◽  
Time Fractional Derivative
Sign in / Sign up

Export Citation Format

Share Document