Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media

Mostaghimi, Peyman; Percival, James; Pavlidis, Dimitrios; Ferrier, Richard J.; Gomes, Jefferson L. M. A.; Gorman, Gerard J.; Jackson, Matthew D.; Neethling, S.J.; Pain, Christopher C.

doi:10.1007/s11004-014-9579-1

Cited by 46 publications

(27 citation statements)

References 35 publications

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“…The relative permeability functions are recalculated based on the local recalculated saturation similar to that of commercial simulator with fixed grids. Further discussions relating to the significance of dynamic mesh adaptivity in improving the numerical dispersion error for prediction of saturation can be found in Pain et al (2001) and Mostaghimi et al (2015).…”

Section: Dynamic Mesh Adaptivitymentioning

confidence: 99%

“…The adaptive mesh required only 234 seconds, which is much lower than that required by the high resolution model whilst offering similar accuracy. Mostaghimi et al (2015) has provided further more test cases for validation of the developed CVFE method and Mostaghimi et al (2014) demonstrated that the static mesh CVFE discretization has a linear order of convergence.…”

Section: Stable Displacementmentioning

confidence: 99%

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Adaptive Mesh Optimization for Simulation of Immiscible Viscous Fingering

et al. 2016

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Viscous fingering can be a major concern when waterflooding heavy oil reservoirs. Most commercial reservoir simulators employ low-order finite volume/difference methods on structured grids to resolve this phenomenon. However, this approach suffers from a significant numerical dispersion error due to insufficient mesh resolution which smears out some important features of the flow. We simulate immiscible incompressible two-phase displacements and propose the use of unstructured control volume finite element (CVFE) methods for capturing viscous fingering in porous media. Our approach uses anisotropic mesh adaptation where the mesh resolution is optimized based on the evolving features of flow. The adaptive algorithm uses a metric tensor field based on solution interpolation error estimates to locally control the size and shape of elements in the metric. The mesh optimization generates an unstructured finer mesh in areas of the domain where flow properties change more quickly and a coarser mesh in other regions where properties do not vary so rapidly. We analyze the computational cost of mesh adaptivity on unstructured mesh and compare its results with those obtained by a commercial reservoir simulator based on the finite volume methods.

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Section: Dynamic Mesh Adaptivitymentioning

confidence: 99%

Section: Stable Displacementmentioning

confidence: 99%

Adaptive Mesh Optimization for Simulation of Immiscible Viscous Fingering

et al. 2016

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“…We hope instead that there will be continued development and adoption of new spatial and temporal discretization schemes. Following trends of maturing computational fields, we expect to see improved, adaptive algorithms driven by solution dynamics and a posteriori error estimates (Mostaghimi et al, 2015;Baron et al, 2017). Moreover, approaches are needed that consider entire solution error and dynamics-for example, joint space-time discretization and error control (Solin and Kuraz, 2011) rather than just a MOL approach with temporal adaptivity but static spatial approximation (Farthing et al, 2003b).…”

Section: Discussion and Alternativesmentioning

confidence: 99%

“…There is a traditional rule of thumb that large angles (hence aspect ratios) negatively impact approximation accuracy (Shewchuk, 2002). On the other hand, it is also possible through mesh optimization techniques to exploit solution behavior and gain higher accuracy through the appropriate use of element anisotropy (Pain et al, 2001;Mostaghimi et al, 2015).…”

Section: Spatial Discretizationmentioning

confidence: 99%

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Farthing

Ogden

2017

Soil Science Soc of Amer J

261

138

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The flow of water in partially saturated porous media is of importance in fields such as hydrology, agriculture, environment and waste management. It is also one of the most complex flows in nature. The Richards' equation describes the flow of water in an unsaturated porous medium due to the actions of gravity and capillarity neglecting the flow of the non-wetting phase, usually air. Analytical solutions of Richards' equation exist only for simplified cases, so most practical situations require a numerical solution in one-two-or threedimensions, depending on the problem and complexity of the flow situation. Despite the fact that the first reasonably complete conservative numerical solution method was published in the early 1990s, the numerical solution of the Richards' equation remains computationally expensive and in certain circumstances, unreliable. A universally robust and accurate solution methodology has not yet been identified that is applicable across the range of soils, initial and boundary conditions found in practice. Existing solution codes have been modified over years to attempt to increase robustness. Despite theoretical results on the existence of solutions given sufficiently regular data and constitutive relations, our numerical methods often fail to demonstrate reliable convergence behavior in practice, especially for higher-order methods. Because of robustness, the lack of higher-order accuracy and computational expense, alternative solution approaches or methods are needed. There is also a need for better documentation of improved solution methodologies and benchmark test problems to facilitate consistent advances and avoid re-inventing of the wheel.T his review paper is intended to serve as a touchstone on the state of the science of calculating the flow of water through unsaturated porous media. As active researchers we believe it is good to occasionally take stock in what has been accomplished up to date, where things may be headed, and what important issues remain. This review concentrates on computational modeling of flow through the unsaturated zone via Richards' equation.This effort can help provide some focus to the research community and serve to help propel new research forward, particularly by those just joining the field. There are many practical problems that require calculation of one-, two-, and threedimensional fluxes in the unsaturated zone. For a much broader review of modeling soil processes, we recommend the recent paper from Vereecken et al. (2016). A detailed review of mathematical models of infiltration can be found (Assouline, 2013), while Paniconi and Putti (2015) provide historical perspective and an overview of modeling Richards' equation in the context of catchment hydrology.The equation attributed to Richards (1931) that describes the flow of water through unsaturated porous media under the action of capillarity and gravity was first published by the English mathematician and physicist Lewis Fry Richardson in 1922(Richardson, 1922. Therefore, the equation would r...

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“…Computational fluid dynamics (CFD) technologies have enabled more complex multi-phase transport in the modelling of the heap leaching process [17][18][19][20][21][22] with much of this work focusing on capturing the kinetics in one-dimensional columns or two-dimensional slices. Mostaghimi et al [23,24] applied CFD technology to capturing flow in a three-dimensional heap. McBride et al [25][26][27] coupled flow-solid-gas and chemical interactions within a CFD model and applied the model to a three-dimensional heterogeneous heap with variable permeability, saturated conditions and solution traveling through preferential pathways.…”

Section: Introductionmentioning

confidence: 99%

Heap Leaching: Modelling and Forecasting Using CFD Technology

McBride

Gebhardt²,

Croft

et al. 2018

Minerals

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Heap leach operations typically employ some form of modelling and forecasting tools to predict cash flow margins and project viability. However, these vary from simple spreadsheets to phenomenological models, with more complex models not commonly employed as they require the greatest amount of time and effort. Yet, accurate production modelling and forecasting are essential for managing production and potentially critical for successful operation of a complex heap, time and effort spent in setting up modelling tools initially may increase profitability in the long term. A brief overview of various modelling approaches is presented, but this paper focuses on the capabilities of a computational fluid dynamics (CFD) model. Advances in computational capability allow for complex CFD models, coupled with leach kinetic models, to be applied to complex ore bodies. In this paper a comprehensive hydrodynamic CFD model is described and applied to chalcopyrite dissolution under heap operating conditions. The model is parameterized against experimental data and validated against a range of experimental leach tests under different thermal conditions. A three-dimensional 'virtual' heap, under fluctuating meteorological conditions, is simulated. Continuous and intermittent irrigation is investigated, showing copper recovery per unit volume of applied leach solution to be slightly increased for pulse irrigation.

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Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media

Cited by 46 publications

References 35 publications

Adaptive Mesh Optimization for Simulation of Immiscible Viscous Fingering

Adaptive Mesh Optimization for Simulation of Immiscible Viscous Fingering

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Heap Leaching: Modelling and Forecasting Using CFD Technology

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