Knudsen-Like Scaling May Be Inappropriate for Gas Shales

Handle URI:
http://hdl.handle.net/10754/625900
Title:
Knudsen-Like Scaling May Be Inappropriate for Gas Shales
Authors:
Patzek, Tadeusz ( 0000-0002-9389-7579 )
Abstract:
Summary We 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, Ross and 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. The generally accepted
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Patzek TW (2017) Knudsen-Like Scaling May Be Inappropriate for Gas Shales. SPE Annual Technical Conference and Exhibition. Available: http://dx.doi.org/10.2118/187068-ms.
Publisher:
Society of Petroleum Engineers
Journal:
SPE Annual Technical Conference and Exhibition
Issue Date:
2-Oct-2017
DOI:
10.2118/187068-ms
Type:
Conference Paper
Additional Links:
https://www.onepetro.org/conference-paper/SPE-187068-MS
Appears in Collections:
Conference Papers; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorPatzek, Tadeuszen
dc.date.accessioned2017-10-18T11:40:59Z-
dc.date.available2017-10-18T11:40:59Z-
dc.date.issued2017-10-02en
dc.identifier.citationPatzek TW (2017) Knudsen-Like Scaling May Be Inappropriate for Gas Shales. SPE Annual Technical Conference and Exhibition. Available: http://dx.doi.org/10.2118/187068-ms.en
dc.identifier.doi10.2118/187068-msen
dc.identifier.urihttp://hdl.handle.net/10754/625900-
dc.description.abstractSummary We 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, Ross and 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. The generally accepteden
dc.publisherSociety of Petroleum Engineersen
dc.relation.urlhttps://www.onepetro.org/conference-paper/SPE-187068-MSen
dc.rightsArchived with thanks to SPE Annual Technical Conference and Exhibitionen
dc.titleKnudsen-Like Scaling May Be Inappropriate for Gas Shalesen
dc.typeConference Paperen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalSPE Annual Technical Conference and Exhibitionen
dc.eprint.versionPost-printen
dc.contributor.institutionAli I. Al-Naimi Petroleum Engineering Research Centeren
kaust.authorPatzek, Tadeuszen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.