Article
Materials Science, Multidisciplinary
E. Dontsov
Summary: This study addresses the computation of poroelastic stresses caused by fluid leak-off in a permeable formation during hydraulic fracture propagation. By simplifying the problem, an efficient solution is presented to better understand the influence of leak-off induced stresses on large scale hydraulic fracture propagation. The study also discusses how leak-off induced stresses can be represented and applied to various fracture configurations.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Mathematics, Applied
Victor A. Kovtunenko
Summary: A new class of unilateral variational models is introduced and studied in the field of poroelasticity. The fully coupled poroelastic system under the unilateral constraint is analyzed, and the well-posedness of the corresponding variational inequality is established. A non-linear complementarity problem formulation is given for solving the non-penetration conditions, which provides an effective numerical solution strategy.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Environmental Sciences
Shuaifang Guo, Yunxing Cao, Li Wang, Xinsheng Zhang, Wenying Zhang, Haixiao Lin, Zhengzheng Cao, Bingbing Meng
Summary: A model for evaluating the confining stress response in hydraulic fracturing was proposed in this study. The results demonstrated that the confinement of the stress response depends on the characteristic parameters of rock breakdown, volumetric opening, and fluid flow regimes. The study also showed that the confinement of the stress response is influenced by the different fracturing regimes and has an impact on fluid pressure.
Article
Geochemistry & Geophysics
A. Yehya, J. Basbous, E. Maalouf
Summary: This study examines the response of nearby faults to hydraulic fracturing (HF) operations and identifies the hydrogeological factors that affect their stability and response. The study highlights the importance of pore pressure, fault location and architecture, and injection rate in inducing seismicity. The findings emphasize the need to carefully consider fault characteristics and reduce injection rates to mitigate induced seismicity from HF operations.
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH
(2022)
Article
Engineering, Geological
Nghia Quoc Trinh, Simon Alexander Hagen, Helene Stromsvik, Trond Larsen, Eivind Grov
Summary: Hydraulic fracturing is commonly used to determine in situ rock stress, and the interpretation of shut-in pressure is a key aspect of this method. SINTEF has developed two practical methods, zero flow and water hammer, for defining shut-in pressure based on singular events in the pressure/flow development. In this study, 12 existing methods were compared with the two SINTEF methods through laboratory tests and a field test. The SINTEF methods are mainly applicable in hard rock environments with low permeability and have been used in hydroelectric power, tunneling, cavern projects, and mineral mining, but not in deep petroleum applications in porous rock.
ROCK MECHANICS AND ROCK ENGINEERING
(2023)
Article
Mechanics
Aleksandra Peshcherenko, Dimitry Chuprakov
Summary: A new ultrafast simulator for hydraulic fracture growth in layered rock has been developed, significantly increasing computational speed while maintaining accuracy. Comparisons with commercial models demonstrate the model's reliability in predicting fracture height growth.
ENGINEERING FRACTURE MECHANICS
(2021)
Article
Engineering, Multidisciplinary
A. Jafari, M. Vahab, N. Khalili
Summary: A novel fully coupled hydro-mechanical model is used to assess the effect of fluid loss on the efficiency of fracturing treatment within saturated porous media. The model incorporates the formation of a cake layer, effects of filtrate, and independent pressure degrees of freedom. Numerical simulations demonstrate the framework's ability to model hydraulic fracturing in medium to low permeability formations.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
R. Altmann, R. Maier, B. Unger
Summary: The study demonstrates the first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for weakly coupled elliptic-parabolic problems. The decoupling of the system improves computational efficiency without affecting convergence rates. The convergence proof is based on interpreting the scheme as an implicit method applied to a constrained partial differential equation with a delay term.
MATHEMATICS OF COMPUTATION
(2021)
Article
Energy & Fuels
Junchao Chen, Zhenglu Che, Xiaopeng Su, Lei Zhou, Xiaofei Liu, Liang Zhang
Summary: The flow behaviors in created fracture complexity strongly affect the productivity of wells after hydraulic fracturing. Gas flow tests were conducted in both splitting fractures induced by Brazilian splitting and hydraulic fractures created by hydraulic fracturing, and the nonlinear fluid flow behaviors in rough fractures were studied. The results show that splitting fractures have higher transmissivity and are more prone to nonlinearity, while hydraulic fractures have smaller roughness indices and aperture sizes. Therefore, hydraulic fractures should be fully considered for more accurate evaluation in engineering practice.
GEOMECHANICS AND GEOPHYSICS FOR GEO-ENERGY AND GEO-RESOURCES
(2023)
Article
Materials Science, Multidisciplinary
Alexandre Guevel, Yue Meng, Christian Peco, Ruben Juanes, John E. Dolbow
Summary: A Darcy-Cahn-Hilliard model coupled with damage is developed to describe multiphase-flow and fluid-driven fracturing in porous media. The model is calibrated against experimental results, recovering a phase diagram differentiating different flow regimes and suggesting a new flow regime.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Engineering, Chemical
Qinghu Fan, Yonggui Ma, Junping Wang, Liang Chen, Zhiquan Ye, Yajun Xu, Huan Li, Bo Wang
Summary: Through field testing and comparative analysis, the optimal perforation number per cluster in the Mahu conglomerate reservoir was determined to be eight, which is of great significance for the efficient development of the reservoir through horizontal well multi-stage fracturing.
Article
Energy & Fuels
Jie Bai, Xiao-Qiong Wang, Hong-Kui Ge, Hu Meng, Ye-Qun Wen
Summary: Unconventional reservoirs often contain weak surfaces such as faults, laminae, and natural fractures, which can greatly improve extraction efficiency when effectively activated and utilized. This study calculates the hydraulic fracturing-induced stress field and establishes a stability model for natural fractures. Parametric studies are conducted to investigate the impact of each parameter on fracture stability. The validity of the model is verified by comparing it with data from the X-well 150-155 formation in the Songliao Basin. The study suggests connecting natural fractures with hydraulic fractures and then activating the natural fractures to effectively utilize them and form a complex fracture network.
Article
Mathematics, Applied
Muhammad Arshad, Eun-Jae Park, Dongwook Shin
Summary: This paper considers the approximation of nonlinear parabolic partial differential equations using a multiscale mortar mixed method, which decomposes the domain into subregions separated by interfaces with the Dirichlet pressure boundary condition. The method solves local problems on a fine scale and enforces weak continuity of flux across mortar interfaces on a coarse scale. Optimal error estimates for scalar and flux unknowns, as well as mortar pressure, are derived and supported with numerical results.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Tao You, Keita Yoshioka
Summary: This study explores different formulations of degraded poroelastic strain energy in hydraulic fracture models and proposes a new form derived from micromechanical analyses. Unlike previous models, our proposed model depends on both the phase-field variable (damage) and the type of strain energy decomposition. Comparisons with closed form solutions demonstrate that our model accurately recovers crack opening displacement, regardless of Biot's coefficient or pore-pressure distribution. Finally, the model's ability to handle complex hydraulic fracture interactions with pre-existing natural fractures is demonstrated.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Thermodynamics
Lei Hou, Derek Elsworth, Fengshou Zhang, Zhiyuan Wang, Jianbo Zhang
Summary: This study proposes a new data-driven workflow, combining numerical models and ensemble learning algorithm, to predict the proportion of proppant-filled fractures in the reservoir. The algorithm performance is improved using variable importance measure and a backward elimination strategy. The predicted proppant filling index quantitatively evaluates the proppant injection and reveals any mismatch between proppant injection and underground fractures.
Article
Mathematics, Applied
Mostafa Abbaszadeh, Mehdi Dehghan, Amirreza Khodadadian, Thomas Wick
Summary: In this work, we developed a Legendre spectral element method (LSEM) for solving stochastic nonlinear advection-reaction-diffusion models. The basis functions used in this method are based on a class of Legendre functions, with tridiagonal mass and diagonal diffusion matrices. We discretized the temporal variable using a Crank-Nicolson finite-difference formulation, and introduced a random variable W based on the Q-Wiener process for the stochastic direction. We validated the convergence rate and unconditional stability of the semi-discrete formulation, and then extended it to a full-discrete scheme using the Legendre spectral element technique. The error estimation of the numerical scheme was substantiated based on the energy method, and the numerical results confirmed the theoretical analysis.
APPLICABLE ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Meng Fan, Yan Jin, Thomas Wick
Summary: A mixed-mode phase-field fracture model is developed in this work, utilizing a parallel-adaptive quasi-monolithic framework. The model is tested and compared with existing models on rock-like and masonry-like materials, demonstrating numerical robustness and physical soundness.
ENGINEERING WITH COMPUTERS
(2022)
Review
Mathematics, Interdisciplinary Applications
Patrick Diehl, Robert Lipton, Thomas Wick, Mayank Tyagi
Summary: Computational modeling of complex fracture is crucial in engineering fracture mechanics. This review focuses on phase-field and peridynamic models as promising approaches for this class of problems. The basic concepts, including constitutive models, failure criteria, discretization schemes, and numerical analysis, are summarized for both models. Validation against experimental data is essential for all computational methods.
COMPUTATIONAL MECHANICS
(2022)
Article
Multidisciplinary Sciences
Julian Roth, Max Schroeder, Thomas Wick
Summary: This work focuses on neural network guided goal-oriented a posteriori error estimation and adaptivity using the dual weighted residual method. The adjoint problem is solved using a feedforward neural network with two or three hidden layers to explore alternatives for reducing the numerical cost of solving the adjoint problem. The proposed algorithm is applicable to both linear and nonlinear stationary partial differential equations and goal functionals, and is substantiated with numerical experiments.
SN APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Gregoire Allaire, Robert Brizzi, Christophe Labbez, Andro Mikelic
Summary: This paper studies the partial differential equation describing the charge distribution of an electrolyte in a porous medium. Realistic non-ideal effects are considered using the mean spherical approximation (MSA) model, which takes into account finite size ions and screening effects. The main novelty lies in the non-constant surface charge density on the pore walls, modeled using a chemical equilibrium reaction. The resulting system is a new variant of the Poisson-Boltzmann equation with a monotone structure under certain physical parameter assumptions. The MSA model introduces additional non-linearities in the non-ideal case, breaking down the monotone structure of the system. Existence and sometimes uniqueness of solutions are proven, and numerical experiments are conducted to compare the model with a constant surface charge in 2D.
APPLICABLE ANALYSIS
(2022)
Article
Engineering, Multidisciplinary
Vahid Mohammadi, Mehdi Dehghan, Amirreza Khodadadian, Nima Noii, Thomas Wick
Summary: This study focuses on the growth of local prostate tumors in two-dimensional spaces, using asymptotic analysis and simulations to demonstrate the formation of diffuse interfaces. The developed meshless method has advantages such as not requiring a background mesh for approximation and not needing to be combined with adaptive techniques. Results show that the proposed method effectively captures the evolving interface between the tumor and neighboring healthy tissue.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Applied
V. Kosin, S. Beuchler, T. Wick
Summary: In this paper, a new mixed method proposed by Rafetseder and Zulehner is investigated for Kirchhoff plates and applied to fourth order eigenvalue problems. This new mixed method uses two auxiliary variables to require only H(1) regularity for the displacement and the auxiliary variables, without the demand of a convex domain. A direct comparison is provided to the C-0-IPG method and Ciarlet-Raviart's mixed method, specifically in view of convergence orders, for vibration problems with clamped and simply supported plates. Numerical experiments are conducted using the open-source finite element library deal.II and incorporating non-trivial boundary conditions with the coupling of finite elements with elements on the boundary.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Julian Roth, Jan Philipp Thiele, Uwe Koecher, Thomas Wick
Summary: In this work, the dual-weighted residual method is applied to a space-time formulation of nonstationary Stokes and Navier-Stokes flow. Tensor-product space-time finite elements are used for discretization with discontinuous Galerkin finite elements in time and inf-sup stable Taylor-Hood finite element pairs in space. To estimate the error and drive adaptive refinement, a partition-of-unity based error localization is developed using the dual-weighted residual method. The methodology is validated on 2D benchmark problems from computational fluid mechanics.
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Philipp Junker, Thomas Wick
Summary: In this article, we propose a variational material modeling method in a space-time context. By applying the Hamilton principle and considering various thermodynamic variables, we establish thermo-mechanically coupled models. We demonstrate the effectiveness of this approach through a numerical simulation.
COMPUTATIONAL MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Leon Kolditz, Katrin Mang, Thomas Wick
Summary: In this study, a numerical phase-field fracture framework is analyzed using a primal-dual active set method and a linearization in the degradation function to improve numerical stability. The formulation is derived from a complementarity system and a modified active-set Newton approach is proposed. Efficiency improvements are suggested for the active-set iterations. The algorithms are implemented and performance studies are conducted with benchmark examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Henry von Wahl, Thomas Wick
Summary: This work studied the interaction between a Stokes flow in a deformable fracture and a linear elastic medium. The crack dynamics were approximated using a phase-field model, which captures the interface by a smeared zone. The main objective was to construct a robust framework that first computes the crack path using the phase-field method and then does an interface-tracking reconstruction. Various approaches for reconstructing the open crack domain were discussed, including unfitted approaches and remeshing. Numerical examples based on Sneddon's benchmark were used to substantiate the approach.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Operations Research & Management Science
Denis Khimin, Marc Christian Steinbach, Thomas Wick
Summary: This work investigates the space-time formulations and Galerkin discretizations for phase-field fracture optimal control problems. The fracture irreversibility constraint is regularized on the time-continuous level using penalization. The optimization scheme is solved using a Newton method and the state, adjoint, tangent, and adjoint Hessian equations are derived. The key focus is on designing appropriate function spaces and rigorously justifying all Fréchet derivatives.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Mario Fuest, Shahin Heydari, Petr Knobloch, Johannes Lankeit, Thomas Wick
Summary: In this paper, a cancer invasion model is studied both theoretically and numerically. The model consists of three coupled partial differential equations that describe the motion of cancer cells, degradation of the extracellular matrix, and certain enzymes. Global classical solutions are established in bounded domains of both two and three dimensions, despite the lack of diffusion of the matrix-degrading enzymes and corresponding regularizing effects. Finite difference and finite element methods are used for spatial discretization, and a fixed-point iteration scheme is employed for the overall algorithm. The theory and numerical developments are demonstrated through simulations in two and three dimensions.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2023)
Article
Computer Science, Information Systems
Shahrzad Shashaani, Mohammad Teshnehlab, Amirreza Khodadadian, Maryam Parvizi, Thomas Wick, Nima Noii
Summary: A recently developed application of computer vision is pathfinding in self-driving cars, which involves semantic scene understanding and semantic segmentation. Deep learning methods and large sample datasets are used for training accurate and robust models for pathfinding. The proposed learning method, called layer-wise training, is evaluated on the efficient neural network (ENet) structure, and compared with classic learning approaches on two RGB image datasets for road and off-road paths.
Article
Engineering, Multidisciplinary
Nima Noii, Amirreza Khodadadian, Thomas Wick
Summary: In this work, Bayesian inversion is used for parameter estimation in fractured media. A nonintrusive global-local approach is employed to reduce the computational costs of the forward model, and a predictor-corrector mesh refinement approach is adopted for dynamic adjustment. Numerical tests using phase-field descriptions of hydraulic fractures confirm the effectiveness of the global-local approach, which achieves the same accuracy as the full approach but with significantly reduced computational time.
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING
(2022)
