Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures

Hoteit, Hussein; Firoozabadi, Abbas

doi:10.1016/j.advwatres.2007.06.006

Cited by 267 publications

(238 citation statements)

References 71 publications

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“…The Va formulation has some clear advantages when treating capillary pressure, e.g., Hoteit and Firoozabadi [9], Friis et al [8], Bastian [15]: Apart from convective terms, the need for nonlinear (Newton) iteration is eliminated due to the explicit treatment of capillary pressure in the Va formulation, which is an advantage computationally and from the implementation point of view. The Va formulation also facilitates a much more straightforward CVD-MPFA implementation of the capillary pressure operator.…”

Section: Governing Equations: Va Formulationmentioning

confidence: 99%

“…Two formulations for coupling the pressure equation with fluid transport are presented. The first is based on the classical total velocity Vt fractional flow (Buckley Leverett) formulation and the second is based on a more recent Va formulation, proposed by Karimi-Fard and Firoozabadi [4] and used in [8,9,15]. The CVD-MPFA method is employed here for both Vt and Va formulations.…”

Section: Introductionmentioning

confidence: 99%

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Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids

Xie

Edwards

2017

Comput Geosci

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Novel cell-centred finite-volume formulations are presented for incompressible and immiscible two-phase flow with both gravity and capillary pressure effects on structured and unstructured grids. The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a higher resolution approximation for convective transport. The CVD-MPFA method is used for Darcy-flux approximation involving pressure, gravity, and capillary pressure flux operators. Two IMPES formulations for coupling the pressure equation with fluid transport are presented. The first is based on the classical total velocity Vt fractional flow (Buckley Leverett) formulation, and the second is based on a more recent Va formulation. The CVD-MPFA method is employed for both Vt and Va formulations. The advantages of both coupled formulations are contrasted. The methods are tested on a range of structured and unstructured quadrilateral and triangular grids. The tests show that the resulting methods are found to be comparable for a number of classical cases, including channel flow problems. However, when gravity is present, flow regimes are identified where the Va formulation becomes locally unstable, in contrast to the total velocity formulation. The test cases also show the advantages of the higher resolution method compared to standard first-order single-point upstream weighting.

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Section: Governing Equations: Va Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids

Xie

Edwards

2017

Comput Geosci

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“…Although the Buckley and Leverett (1942) solution is a well-known analytical solution, it cannot be adopted in this verification because it suppresses the capillary drive term and is only suitable for use when externally applied driving forces are large in relation to the gradient of capillary pressure. In common cases, capillary pressure can not be neglected because it has a significant effect on two-phase flow (Hoteit and Firoozabadi 2008). Until now, although there are still problems in purely analytical approaches, the capillary drive has been considered through numerical solution (Yortsos and Fokas 1983;Chen 1988;Van Duijn and De Neef 1998;McWhorter and Sunada 1990).…”

Section: Verification Against a Semi-analytical Solutionmentioning

confidence: 99%

A Numerical Model of Tracer Transport in a Non-isothermal Two-Phase Flow System for $${\text{ CO}}_2$$ Geological Storage Characterization

et al. 2013

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For the purpose of characterizing geologically stored CO 2 including its phase partitioning and migration in deep saline formations, different types of tracers are being developed. Such tracers can be injected with CO 2 or water, and their partitioning and/or reactive transfer from one phase to another can give information on the interactions between the two fluid phases and the development of their interfacial area. Kinetic rock-water interactions and geochemical reactions during two-phase flow of CO 2 and brine have been incorporated in numerical simulators (e.g., Xu et al., TOUGHREACT User's Guide: A Simulation Program for Non-isothermal Multiphase Reactive Geochemical Transport in Variably Saturated Geologic Media. LBNL Report 55460, V.1.2., Berkeley, CA, 2004). However, chemical equilibrium between the fluid phases is typically assumed, and multi-component, multiphase, non-isothermal codes for CO 2 -brine systems that incorporate kinetic mass transfer of tracers between the two fluid phases are not readily available. New models or further developments of existing models are therefore needed to provide the capability for interpreting the signals of novel tracers, including tracers with kinetic/time-dependent interface transfer. This paper presents such new numerical model of tracer transport in a non-isothermal two-phase flow system. The model consists of five different governing equations describing liquid phase (aqueous) flow, gas (CO 2 ) flow, heat transport and the movement of the tracers within the two phases, as well as allowing kinetic transport of the tracers between the two phases. A finite element method is adopted for the spatial discretization and a finite difference approach is used for temporal discretization. Some special technologies and solution strategies are adopted for increasing the convergence, ensuring the numerical stability and eliminating non-physical oscillations. The new numerical model is validated against the code TOUGH2/ECO2N as well as some analytical/semi-analytical solutions. Good agreement between the simulated and analytical results indicates that the model has capability to simulate two-phase flow and

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“…These relatively modest convergence rates are a result of the shock between the two fluids that dominates the overall error. Schmid et al [7] and Hoteit and Firoozabadi [36] applied the Buckley-Leverett problem for various numerical methods. They observed low convergence rates for the Buckley-Leverett problem regardless of the numerical method used, as we see here, because of this sharp separation between the two fluids.…”

Section: Figmentioning

confidence: 99%

Interface control volume finite element method for modelling multi-phase fluid flow in highly heterogeneous and fractured reservoirs

Abushaikha

Blunt

Gosselin

et al. 2015

Journal of Computational Physics

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We present a new control volume finite element method that improves the modelling of multi-phase fluid flow in highly heterogeneous and fractured reservoirs, called the Interface Control Volume Finite Element (ICVFE) method. The method drastically decreases the smearing effects in other CVFE methods, while being mass conservative and numerically consistent. The pressure is computed at the interfaces of elements, and the control volumes are constructed around them, instead of at the elements' vertices. This assures that a control volume straddles, at most, two elements, which decreases the fluid smearing between neighbouring elements when large variations in their material properties are present. Lowest order Raviart-Thomas vectorial basis functions are used for the pressure calculation and first-order Courant basis functions are used to compute fluxes. The method is a combination of Mixed Hybrid Finite Element (MHFE) and CVFE methods. Its accuracy and convergence are tested using three dimensional tetrahedron elements to represent heterogeneous reservoirs. Our new approach is shown to be more accurate than current CVFE methods.

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Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures

Cited by 267 publications

References 71 publications

Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids

Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids

A Numerical Model of Tracer Transport in a Non-isothermal Two-Phase Flow System for $${\text{ CO}}_2$$ Geological Storage Characterization

Interface control volume finite element method for modelling multi-phase fluid flow in highly heterogeneous and fractured reservoirs

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