Comparison of Three FE-FV Numerical Schemes for Single- and Two-Phase Flow Simulation of Fractured Porous Media

Nick, Hamidreza M.; Matthäi, Stephan

doi:10.1007/s11242-011-9793-y

Cited by 84 publications

(38 citation statements)

References 30 publications

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“…Natural fractures may significantly impact subsurface fluid flow patterns, either positively or negatively [Nelson, 2001;Narr et al, 2006]. The contribution of flow through fractures to total reservoir flow is difficult to quantify, as it requires an understanding of the 3-D fracture network geometry, including length, spacing, orientation, and aperture distributions.…”

Section: Introductionmentioning

confidence: 99%

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

2016

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Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length‐aperture scaling), and experiments (Barton‐Bandis conductive shearing). Each method predicts heterogeneous apertures, even along single fractures (i.e., intrafracture variations), but most fractured reservoir models imply constant apertures for single fractures. We compare the relative differences in aperture and permeability predicted by three aperture methods, where permeability is modeled in explicit fracture networks with coupled fracture‐matrix flow. Aperture varies along single fractures, and geomechanical relations are used to identify which fractures are critically stressed. The aperture models are applied to real‐world large‐scale fracture networks. (Sub)linear length scaling predicts the largest average aperture and equivalent permeability. Barton‐Bandis aperture is smaller, predicting on average a sixfold increase compared to matrix permeability. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton‐Bandis peak shear. The impact of the fracture network on equivalent permeability depends on the matrix hydraulic properties, as in a low‐permeable matrix, intrafracture connectivity, i.e., the opening along a single fracture, controls equivalent permeability, whereas for a more permeable matrix, absolute apertures have a larger impact. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on aperture variations within fractures.

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Section: Introductionmentioning

confidence: 99%

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

2016

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“…Finally, there is little known about the relationships between the dynamic relative permeability and dynamic capillary pressure effects. Indeed the scale dependency and methods for upscaling of P c -S w , K r -S w and s-S w relationships had been the subjects of intense study in the literature [7,[51][52][53][54][55][56]. Barker and Thibeau [51] and Renard and De Marsily [54] suggested that the constitutive relationship should be used at the same scale as that of a predictive model but the practicality would only be attained with upscaling.…”

Section: Introductionmentioning

confidence: 99%

Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

et al. 2016

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Capillary pressure-saturation-relative permeability relationships (P c -S w -K r ) are functions of importance in modeling and simulations of the hydrodynamics of two-phase flow in porous media. These relationships are found to be affected by porous medium and fluid properties but the manner in which they are affected is a topic of intense discussion. For example, reported trends in fluid viscosity and boundary conditions effects have been found to be contrary to each other in different studies. In this work, we determine the dependency of dynamic K r -S w relationships (averaged data) on domain scale in addition to investigating the effects of fluid viscosity and boundary pressure using silicone oil (i.e. 200 and 1000 cSt) and water as the respective non-wetting and wetting fluids with a view to eliminating some of the uncertainties reported in the literature. Water relative permeability, K rw , was found to increase with increasing wetting phase saturation but decreases with the increase in viscosity ratio. On the other hand, the oil relative permeability, K rnw , was found to increase with the increasing non-wetting phase saturation in addition to the increase in viscosity ratio. Also, it was found that with the increasing boundary pressure K rw decreases while K rnw increases. The influence of scale on relative permeability was slightly indicated in the non-wetting phase with K rnw decreasing as domain size increases. Effect of measurement location on dynamic relative permeability was explored which is rarely found in the literature. Comparison was also made between K r -S w relationships obtained under static and dynamic condition. Finally, mobility ratio (m) and dynamic coefficient (s) were plotted as a function of water saturation (S w ), which showed that m decreases as s increases at a given saturation, or vice versa.

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“…In general, experimental determination of the capillary pressure relationship is easier than measurement of relative permeability. For this reason, empirical relationships, such as those of Brooks and Corey [1964] and Van Genuchten [1980], are often used to model the dependence of relative permeability on capillary pressure or saturation [e.g., Nick and Matthai , 2011].…”

Section: Introductionmentioning

confidence: 99%

A new formulation for pore‐network modeling of two‐phase flow

Raoof

Hassanizadeh

2012

Water Resources Research

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[1] Pore network models of two-phase flow in porous media are widely used to investigate constitutive relationships between saturation and relative permeability as well as capillary pressure. However, results of many studies show a discrepancy between calculated relative permeability and corresponding measured values. Often, calculated values overestimate the measured values. An important feature of almost all pore network models is that the resistance to flow is assumed to come from pore throats only; i.e., the resistance of pore bodies to the flow is considered to be negligible compare to the resistance of pore throats. We contend that this simplification may considerably affect the results for relative permeability curves. In this study, we present a new formulation for pore network modeling of two-phase flow, which allows for the calculation of wetting phase fluxes in the edges of (partially) drained pores. In a quantitative investigation, we have shown the significance of this effect. The pore space is represented by cubic pore bodies and parallelepiped pore throats in a Multi-Directional Pore Network model. This model allows for a distribution of coordination numbers ranging between 1 and 26. This topological property, together with geometrical distributions of pore sizes, is used to mimic the microstructure of real porous media. In the presence of the nonwetting phase, the wetting fluid is considered to fill only spaces along edges of cubic pore bodies. We show that the resistance to the flow of the wetting phase within these filaments of fluids are comparable to the resistance to the wetting phase flow within pore throats. Resulting saturation-relative permeability relationships show very good agreement with measured curves. Explicit representation of wetting phase filaments and calculation of different fluxes within pore bodies may also lead to improved predictions of transport properties such as dispersivities and mass transfer coefficients.Citation: Raoof, A., and S. M. Hassanizadeh (2012), A new formulation for pore-network modeling of two-phase flow, Water Resour.

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Comparison of Three FE-FV Numerical Schemes for Single- and Two-Phase Flow Simulation of Fractured Porous Media

Cited by 84 publications

References 30 publications

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

A new formulation for pore‐network modeling of two‐phase flow

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