A practical model for fluid flow in discrete-fracture porous media by using the numerical manifold method

Hu, Mengsu; Rutqvist, Jonny; Wang, Yuan

doi:10.1016/j.advwatres.2016.09.001

Cited by 43 publications

(37 citation statements)

References 42 publications

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“…We consider the fractures as (approximated by) planar objects, following e.g. [37,20,32,2,27]. The extension to curved fractures is possible, but the analysis and the presentation will increase in complexity, see [28,35].…”

Section: Mathematical Modelmentioning

confidence: 99%

Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations

Fumagalli

Keilegavlen

Scialò

2019

Journal of Computational Physics

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Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which explicitly represent flow in fracture surfaces, but ignore the impact of the surrounding host rock. Fracture networks, generated from observations or stochastic simulations, will contain intersections of arbitrary length, and intersection lines can further cross, forming a highly complex geometry. As the flow exchange between fractures, thus in the network, takes place in these intersections, an adequate representation of the geometry is critical for simulation accuracy. In practice, the intersection dynamics must be handled by a combination of the simulation grid, which may or may not resolve the intersection lines, and the numerical methods applied on the grid. In this work, we review different classes of numerical approaches proposed in recent years, covering both methods that conform to the grid, and non-matching cases. Specific methods considered herein include finite element, mixed and virtual finite elements and control volume methods. We expose our methods to an extensive set of test cases, ranging from artificial geometries designed to test difficult configurations, to a network extruded from a real fracture outcrop. The main outcome is guidances for choice of simulation models and numerical discretization with a trade off on the computational cost and solution accuracy.

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Section: Mathematical Modelmentioning

confidence: 99%

Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations

Fumagalli

Keilegavlen

Scialò

2019

Journal of Computational Physics

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“…Aiming at solving these problems, the time-domain random-walk (TDRW) method was firstly implemented into the discrete element method (DEM) in this study. During each time step of hydromechanical calculation, hydraulic aperture of each fracture and fluid pressure on fracture surface were calculated according to (15) and (14) to consider the coupled hydromechanical effect. To present the effect of matrix diffusion on nuclide transport, (24) and (27) were adopted to get the breakthrough curves.…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, water flow process in fractured rock masses should be studied firstly and foremost. Till now, five models have been found in literatures to simulate the water flow in fractured rock masses, that is, continuous model [3][4][5], dual-continuum model [6][7][8], equivalent continuum model [9][10][11], discrete fracture network (DFN) [12][13][14], and hybrid model [15][16][17]. In continuous model, rock masses are treated as continuum porous media with porosity and permeability and continuum-mechanics formulations can be used to describe flow and transport in media.…”

Section: Literature Review About Nuclide Transport Simulationmentioning

confidence: 99%

Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses

Liu

Chan

et al. 2017

Geofluids

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It is essential to study nuclide transport with underground water in fractured rock masses in order to evaluate potential radionuclide leakage in nuclear waste disposal. A time-domain random-walk (TDRW) method was firstly implemented into a discrete element method (DEM), that is, UDEC, in this paper to address the pressing challenges of modelling the nuclide transport in fractured rock masses such as massive fractures and coupled hydromechanical effect. The implementation was then validated against analytical solutions for nuclide transport in a single fracture and a simple fracture network. After that, the proposed implementation was applied to model the nuclide transport in a complex fracture network investigated in the DECOVALEX 2011 project to analyze the effect of matrix diffusion and stress on the nuclide transport in the fractured rock masses. It was concluded that the implementation of the TDRW method into UDEC provided a valuable tool to study the nuclide transport in the fractured rock masses. Moreover, it was found that the total travel time of the nuclide particles in the fractured rock masses with the matrix diffusion and external stress modelled was much longer than that without the matrix diffusion and external stress modelled.

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“…The physical cover is utilized to construct local approximations and define manifold elements on which the weak form of the problem is integrated. NMM has been successfully applied in many fields, such as static and dynamic crack problems, plate and shell bending problems, seismic problems, and seepage problems . For coupled hydromechanical (HM) problems, Zhang conducted the analysis of nonlinear consolidation based on two‐field u‐p model.…”

Section: Introductionmentioning

confidence: 99%

Numerical manifold method for dynamic consolidation of saturated porous media with three‐field formulation

Zheng

Yang

2019

Numerical Meth Engineering

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In terms of the three-field formulation of Biot's dynamic consolidation theory, the numerical manifold method (NMM) is developed, where the same approximation to skeleton displacement (u) and fluid velocity (w) is employed and able to reflect incompressible as well as compressible deformation, but the approximation to pore pressure (p) takes two different types, respectively. The first type of approximation to p is continuous piecewise linear interpolation and the second type assumes that p is a constant within each element. It is verified that using the second type of approximation to p naturally satisfies the inf-sup condition even in the limits of rigid skeleton and very low permeability, avoiding the locking problem accordingly. Energy components done by various forces are calculated to verify the accuracy and stability of the time integration scheme.A mass lumping technique in the NMM framework is employed to effectively reduce the unphysical oscillations and increase computational efficiency, which is another unique advantage of NMM over other numerical methods. A number of numerical tests are conducted to demonstrate the robustness and versatility of the proposed mixed NMM models. KEYWORDSdynamic consolidation, inf-sup condition, mass lumping, numerical manifold method 768 769 u − p models are established. When the liquid in the porous media is deemed compressible, pore pressure p can be eliminated instead of fluid velocity w, leading to the two-field u − w models that are advantageous in dealing with issues of porous mixture induced by earthquake. 1,2 On the other hand, to solve the coupling systems of equations for poroelasticity problems, three approaches are frequently employed, ie, fully implicit, loose or explicit coupling, and iterative coupling schemes. Fully implicit approach generally presents more accurate results but requires more expensive equation solvers in comparison with the loose or explicit coupling and iterative coupling approaches. A fully implicit solving approach is employed in this study and other two efficient implicit solving schemes can be found in the works of Saett and Vitaliani 14 and Zienkiewicz et al. 15 Several effective and commonly used iterative coupling procedures are presented in the works of Mikelić and Wheeler, 16 Both et al, 17 and Kim et al, 18 where their stability and convergence are also demonstrated, which are quite helpful for increasing computational efficiency. For nonlinear analysis of porous media, de Boer and Kowalski 19 presented a plasticity theory of saturated porous mixture and a more general plastic formulation can be found in the work of Zienkiewicz and Shiomi. 1 Besides fully implicit approach, the iterative coupling approach, especially the splitting scheme, 20,21 is also applied to solve the nonlinear Biot model. For more details of the applications of iterative coupling approach in nonlinear Biot model, please see the work of Borregales et al 22 where nonlinear mechanics and nonlinear fluid flow are both considered. Moreover, the splitting schem...

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A practical model for fluid flow in discrete-fracture porous media by using the numerical manifold method

Cited by 43 publications

References 42 publications

Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations

Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations

Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses

Numerical manifold method for dynamic consolidation of saturated porous media with three‐field formulation

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