Shape Factor and Hydraulic Conductance in Noncircular Capillaries

Patzek, Tadeusz W; Silin, Dmitriy

doi:10.1006/jcis.2000.7413

Cited by 195 publications

(123 citation statements)

References 10 publications

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“…The numerical simulations presented in section 3 indicate that setting alpha=1/2 is indeed appropriate for the spheres geometries considered in this investigation. We observe that the values of α obtained analytically vary in a moderately wide range of values for compact throats sections (Patzek and Silin 2001). It is also worth noting that, the factor α being the same for all throats, modifying this value will not modify the pressure distribution in the boundary value problems presented below (mixed Neumann-Dirichlet), and consequently it would not affect the values of forces applied on the particles.…”

Section: Local Conductancementioning

confidence: 62%

“…Pore-network models have been most commonly developed to predict the permeability of materials from microstructural geometry (Bryant et al 1993;Thompson and Fogler 1997;Bakke and Øren 1997;Patzek and Silin 2001;Hilpert et al 2003;Abichou et al 2004), but have also been extended to include multiphase flow effects (e.g., air bubbles, immiscible two-phase flow) (Bryant and Blunt 1992;Øren et al 1998;Bryant and Johnson 2003;Piri and Blunt 2005). Crucial for their success is an adequate definition of how fluids are exchanged between pores in term of the local pore geometry.…”

Section: Pore-network Modelingmentioning

confidence: 99%

“…Even though these variables are found in most of the papers cited above, there is no general agreement on their definition for pore-network modeling of arbitrary microstructural geometry. A detailed analysis of the effect of non-circular cross-sections with variable constriction along the flow path can be found in Patzek andSilin 2001 andMortensen et al (2005), while Thompson and Fogler (1997), Bakke and Øren (1997), and Bryant et al (1993) focused specifically on triangulated sphere packings. Some of these models, however, do not clearly define a partition of the void space, and as such they need ad-hoc corrections for L i j to ensure that the same pore volumes are not accounted for multiple times in different cells (Bryant et al 1993).…”

Section: Local Conductancementioning

confidence: 99%

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Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

et al. 2012

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We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients.

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Section: Local Conductancementioning

confidence: 62%

Section: Pore-network Modelingmentioning

confidence: 99%

Section: Local Conductancementioning

confidence: 99%

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Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

et al. 2012

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“…Analytical expressions for equilateral triangles and squares can also be developed [Patzek and Silin, 2001] with k being 3/5 and 0.5623 respectively. From numerical simulations, Øren et al [1998] found that the conductance for an irregular triangle was closely approximated by equation (19), using the same constant k as for an equilateral triangle, 3/5.…”

Section: Calculation Of Transport Propertiesmentioning

confidence: 99%

Predictive pore‐scale modeling of two‐phase flow in mixed wet media

Valvatne

Blunt

2004

Water Resources Research

655

591

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[1] We show how to predict flow properties for a variety of porous media using pore-scale modeling with geologically realistic networks. Starting with a network representation of Berea sandstone, the pore size distribution is adjusted to match capillary pressure for different media, keeping the rank order of pore sizes and the network topology fixed. Then predictions of single and multiphase properties are made with no further adjustment of the model. We successfully predict relative permeability and oil recovery for water wet, oil wet, and mixed wet data sets. For water flooding we introduce a method for assigning contact angles to match measured wettability indices. The aim of this work is not simply to match experiments but to use easily acquired data to predict difficult to measure properties. Furthermore, the variation of these properties in the field, due to wettability trends and different pore structures, can now be predicted reliably.

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“…The same parameters must also be known for each pore throat connecting this pore body to other pores. It is well-known that the slit-like, angular capillaries can have hydraulic conductances that are much smaller than those of circular cylinders, Patzek and Silin (2001). A multiscale topological description of volumetric rock images with a hierarchy of inscribed spheres, Silin and Patzek (2006), allows one to perform direct lattice Boltzmann calculations of fluid flow, Jin et al (2004).…”

Section: Resultsmentioning

confidence: 99%

Knudsen-Like Scaling May Be Inappropriate for Gas Shales

Patzek

2017

Day 3 Wed, October 11, 2017

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SummaryWe assert that a classification of gas flow regimes in shales that is widely accepted in the petroleum industry, may be inconsistent with the physics of high-pressure gas flow in capillaries. This classification follows from the 1946 work by Brown et al. (1946) that deals with the flow of gases in large industrial metal pipes, elbows and orifices under vacuum, with gas pressures of the order of 1 mm Hg or less. In another pioneering paper that year, Tsien (1946) analyzed the hypersonic flight of rockets in the thermosphere (above 50 miles of altitude), and established the widely accepted Knudsen flow regimes for the high-Reynolds, high-Mach flow of rarified gases. We show why both these papers are not quite applicable to flow of compressed gas in the hot, high-pressure shale pores with rough surfaces. In addition, it may be inappropriate to use the capillary tube metaphor to describe shale micropores or microcracks, simply because each is fed with gas by dozens or hundreds of intricately connected nanopores, which themselves may be slits rather than circular cylinders, and are charged with the dense, liquid-like gas.In the small-scale, low-velocity flows of gases, failure of the standard Navier-Stokes description (the standard Darcy law in petroleum engineering) can be quantified by the Knudsen number, ratio of the mean free path, λ, of gas molecules at the reservoir pressure and temperature to the characteristic pore radius, R. We carefully enumerate the multiple restrictive conditions that must hold for the slip-flow boundary condition to emerge. We also describe the dependence of the slip correction factor on the gas pressure and temperature, as well as the median pore size and rock roughness. In the derivation, we revisit the original approaches of Helmholtz and von Piotrowski (1860) and Maxwell, Niven (1890), which were somehow lost in the multiple translations from physics to petroleum engineering.For example, in Barnett mudrocks, naturally occurring pores are predominantly associated with organic matter and pyrite framboids. In organic matter, the median pore length is 100 nm, Loucks et al. (2009), and the pore radii are likely to be between 1 and 10 nm, Clarkson et al. (2013). Other thermally mature mudrocks may be similar, Bustin (2009), or not, Clarkson et al. (2013). With R = 50 nm, the ratio of λ/R is less than 0.1 for pressures exceeding 60 bars. When we compare the actual slip-flow correction with the accepted classification of gas flow regimes, there is an order of magnitude discrepancy. It appears that our new classification is conservative for pores larger than 5 nm in radius. Therefore, unless the fraction of gas molecules that are bounced off diffusively from the rough pore walls is very low, slip flow is unlikely to dominate in shales. SPE 187068-MSThe generally accepted "Knudsen-diffusion" in shales is based on a mistranslation of the flow physics and may give theoretically unsound predictions of the increased permeability of shales to gas flow. This increase of permeability is real...

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Shape Factor and Hydraulic Conductance in Noncircular Capillaries

Cited by 195 publications

References 10 publications

Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

Predictive pore‐scale modeling of two‐phase flow in mixed wet media

Knudsen-Like Scaling May Be Inappropriate for Gas Shales

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