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Capillary Number - Christopher Sparages: Difference between revisions
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[[Image:Capillary Number.png|thumb|upright=2.6|right|Figure 1: Shows a series of different forms of the capillary number equation used in literature.<ref name="one">Kantzas, A., Bryan, J., & Taheri, S. (n.d.). Capillary Number | Fundamentals of Fluid Flow in Porous Media. Retrieved February 23, 2018, from http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-2-the-porous-medium/multi-phase-saturated-rock-properties/dominance-capillary-forces-viscous-forces/capillary-number/</ref>]] | [[Image:Capillary Number.png|thumb|upright=2.6|right|Figure 1: Shows a series of different forms of the capillary number equation used in literature.<ref name="one">Kantzas, A., Bryan, J., & Taheri, S. (n.d.). Capillary Number | Fundamentals of Fluid Flow in Porous Media. Retrieved February 23, 2018, from http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-2-the-porous-medium/multi-phase-saturated-rock-properties/dominance-capillary-forces-viscous-forces/capillary-number/</ref>]] | ||
The capillary number (Ca) is a dimensionless number and it represents the relation between viscous forces and capillary forces, which occur between two immiscible liquids. Over the years, the capillary number has been represented by a series of different forms across literature with one of the most common one being the formalism by Saffman and Taylor (Figure 1, No. 6). <ref name="one" /> | The capillary number (Ca) is a dimensionless number and it represents the relation between viscous forces and capillary forces, which occur between two immiscible liquids. Over the years, the capillary number has been represented by a series of different forms across literature with one of the most common one being the formalism by Saffman and Taylor (Figure 1, No. 6).<ref name="one" /> | ||
The Saffman-Taylor definition for capillary number describes the ratio of (vμ)/σ with v as the fluid velocity, μ as the fluid viscosity, and σ as surface tension between the two immiscible liquids or gas and liquid. The capillary number is used to determine which forces dominate in a specific scenario.<ref name="twelve">Squires, T. M., & Quake, S. R. (2005). Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 77(3), 977-1026. https://dx.doi.org/10.1103/revmodphys.77.977</ref> When Ca>>1, surface forces are dominated by the viscous forces. When Ca<<1, surface forces dominate the viscous forces. making the viscous forces negligible. <ref name="one" /> | The Saffman-Taylor definition for capillary number describes the ratio of (vμ)/σ with v as the fluid velocity, μ as the fluid viscosity, and σ as surface tension between the two immiscible liquids or gas and liquid. The capillary number is used to determine which forces dominate in a specific scenario.<ref name="twelve">Squires, T. M., & Quake, S. R. (2005). Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 77(3), 977-1026. https://dx.doi.org/10.1103/revmodphys.77.977</ref> When Ca>>1, surface forces are dominated by the viscous forces. When Ca<<1, surface forces dominate the viscous forces. making the viscous forces negligible.<ref name="one" /> | ||
==Capillary Number Theory== | ==Capillary Number Theory== | ||
[[Image:oil recovery capillary.jpg|thumb|upright=1|left|Figure 2: Shows the use of aquifers on and offshore being used for oil/gas recovery. The blue corresponds to injected carbon dioxide and the red corresponds to the recovered oil/gas.<ref name="five">Gerbis, M., Gunter, W. D., & Harwood, J. (n.d.). Introduction CO2 capture and geological storage in energy and climate policy. Global CCS Institute. Retrieved February 23, 2018.</ref>]] | [[Image:oil recovery capillary.jpg|thumb|upright=1|left|Figure 2: Shows the use of aquifers on and offshore being used for oil/gas recovery. The blue corresponds to injected carbon dioxide and the red corresponds to the recovered oil/gas.<ref name="five">Gerbis, M., Gunter, W. D., & Harwood, J. (n.d.). Introduction CO2 capture and geological storage in energy and climate policy. Global CCS Institute. Retrieved February 23, 2018.</ref>]] | ||
The capillary number theory was originally developed by basing the idea off of capillary tube bundles and Darcy's law.<ref name="two">Guo, H., Dou, M., Hanqing, W., Wang, F., Yuanyuan, G., Yu, Z., | The capillary number theory was originally developed by basing the idea off of capillary tube bundles and Darcy's law.<ref name="two">Guo, H., Dou, M., Hanqing, W., Wang, F., Yuanyuan, G., Yu, Z., Li, Y. (2017). Proper Use of Capillary Number in Chemical Flooding. Journal of Chemistry, 2017, 1-11. https://dx.doi.org/10.1155/2017/4307368</ref> Darcy's law predicts that residual oil will not be able to be moved until it reaches a critical capillary number. The goal of the experiments driving this theoretical discovery was to determine the saturation movement of this residual oil after it is in contact with water forcing imbibition, which is the expansion of solid when it absorbs water.<ref name="four">Ding, M., & Kantzas, A. (2004). Capillary Number Correlations for Gas-Liquid Systems. Canadian International Petroleum Conference, 46(2), 27-32. https://dx.doi.org/10.2118/2004-062 | ||
</ref> Putting this theory to the test through experiments has made it possible for progress to be made in developing enhanced methods to contribute towards gas recovery operations. The capillary number is used for example in chemical flooding situations where a decrease in capillary number corresponds to a decrease in remaining oil saturation.<ref name="two" /> | </ref> Putting this theory to the test through experiments has made it possible for progress to be made in developing enhanced methods to contribute towards gas recovery operations. The capillary number is used for example in chemical flooding situations where a decrease in capillary number corresponds to a decrease in remaining oil saturation.<ref name="two" /> | ||
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[[Image:Capillary_Number_CDC.png|thumb|upright=1|right|Figure 5: Shows a typical capillary desaturation curve with saturation versus the capillary number from a series of different sources .<ref name="two" />]] | [[Image:Capillary_Number_CDC.png|thumb|upright=1|right|Figure 5: Shows a typical capillary desaturation curve with saturation versus the capillary number from a series of different sources .<ref name="two" />]] | ||
The capillary number theory is also used as a basic theory for chemical flooding. Chemical flooding includes things such as oil/gas as mentioned above as well as polymer flooding, alkali-surfactant-polymer flooding, and polymer-surfactant flooding. The capillary number is influential for chemical flooding because it is crucial in determining oil saturation.<ref name="thirteen">Zheng, B., Tice, J. D., & Ismagilov, R. F. (2004). Formation of Droplets of Alternating Composition in Microfluidic Channels and Applications to Indexing of Concentrations in Droplet-Based Assays. Analytical Chemistry, 76(17), 4977-4982. https://dx.doi.org/10.1021/ac0495743</ref> A common way to represent this data is by using a capillary desaturation curve (CDC) (Figure 3). The CDC shows the pore arrangement within the media and fluid distribution within the pores. However, to produce a corresponding CDC to a data set one must first test the wettability effect of the solids involved which has an effect on the overall saturation(Figure 3). Wettability is one of the factors that contributes to relative permeability, which is effected by capillary number within a certain range.<ref name="two" /> | The capillary number theory is also used as a basic theory for chemical flooding. Chemical flooding includes things such as oil/gas as mentioned above as well as polymer flooding, alkali-surfactant-polymer flooding, and polymer-surfactant flooding. The capillary number is influential for chemical flooding because it is crucial in determining oil saturation.<ref name="thirteen">Zheng, B., Tice, J. D., & Ismagilov, R. F. (2004). Formation of Droplets of Alternating Composition in Microfluidic Channels and Applications to Indexing of Concentrations in Droplet-Based Assays. Analytical Chemistry, 76(17), 4977-4982. https://dx.doi.org/10.1021/ac0495743</ref> A common way to represent this data is by using a capillary desaturation curve (CDC) (Figure 3). The CDC shows the pore arrangement within the media and fluid distribution within the pores. However, to produce a corresponding CDC to a data set one must first test the wettability effect of the solids involved which has an effect on the overall saturation (Figure 3). Wettability is one of the factors that contributes to relative permeability, which is effected by capillary number within a certain range.<ref name="two" /> | ||
In terms of a microfluidic device, the use of rock and sand acts in a microfluidic way and can be developed into a controlled device. In the example provided here, uses a PDMS fabricated microfluidic device that was based on the geometry of sandstone. Oil is flooded through the system and in order to increase its contrast with the PDMS has been dyed with Sudan Blue, which is oil-soluble. The percent of oil remaining in the channel is calculated based on the flow rate of fluids such as water being passed through the device to obtain shear rate. This can also be measured as a function of capillary number versus the percent of oil remaining, where the closer capillary number approaches one the closer the percent remaining of oil reaches zero. | In terms of a microfluidic device, the use of rock and sand acts in a microfluidic way and can be developed into a controlled device. In the example provided here, uses a PDMS fabricated microfluidic device that was based on the geometry of sandstone. Oil is flooded through the system and in order to increase its contrast with the PDMS has been dyed with Sudan Blue, which is oil-soluble. The percent of oil remaining in the channel is calculated based on the flow rate of fluids such as water being passed through the device to obtain shear rate. This can also be measured as a function of capillary number versus the percent of oil remaining, where the closer capillary number approaches one the closer the percent remaining of oil reaches zero. | ||
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===Droplet Microfludics=== | ===Droplet Microfludics=== | ||
Droplet formation is controlled by the formation and deformation of the liquid-liquid interface between the two immiscible phases. There are many forces which acts on droplet formation, but the most prominent among them is the capillary number.<ref name="ten">Jeong, S. (2005). Evaluation of the use of capillary numbers for quantifying the removal of DNAPL trapped in a porous medium by surfactant and surfactant foam floods. Journal of Colloid and Interface Science, 282(1), 182-187. https://dx.doi.org/10.1016/j.jcis.2004.08.108</ref> The capillary number represents the ratio of viscosity to interfacial tension and with an increase in capillary number, there is a decrease in droplet diameter.<ref name="fourteen">Tice, J. D., Lyon, A. D., & Ismagilov, R. F. (2004). Effects of viscosity on droplet formation and mixing in microfluidic channels. Analytica Chimica Acta, 507(1), 73-77. https://dx.doi.org/10.1016/j.aca.2003.11.024</ref> To be more specific, spherical droplets form at low capillary values and long liquid plugs at high capillary values ([[Droplet_Microfluidics:_T-Junction_-_Lina_Wu | Droplet Microfluidics: T-Junction]]). | Droplet formation is controlled by the formation and deformation of the liquid-liquid interface between the two immiscible phases. There are many forces which acts on droplet formation, but the most prominent among them is the capillary number.<ref name="ten">Jeong, S. (2005). Evaluation of the use of capillary numbers for quantifying the removal of DNAPL trapped in a porous medium by surfactant and surfactant foam floods. Journal of Colloid and Interface Science, 282(1), 182-187. https://dx.doi.org/10.1016/j.jcis.2004.08.108</ref> The capillary number represents the ratio of viscosity to interfacial tension and with an increase in capillary number, there is a decrease in droplet diameter.<ref name="fourteen">Tice, J. D., Lyon, A. D., & Ismagilov, R. F. (2004). Effects of viscosity on droplet formation and mixing in microfluidic channels. Analytica Chimica Acta, 507(1), 73-77. https://dx.doi.org/10.1016/j.aca.2003.11.024</ref> To be more specific, spherical droplets form at low capillary values and long liquid plugs at high capillary values ([[Droplet_Microfluidics:_T-Junction_-_Lina_Wu | Droplet Microfluidics: T-Junction]]). | ||
Squeezing, dripping, and jetting are other events that occur in droplet microfluidics. In the case of squeezing mode, low capillary numbers are used to produce droplets, in doing so a pressure gradient is formed across the droplet upon being formed. They droplets travel as plugs. In the case of dripping mode, viscous shear stress and interfacial tension compete as the capillary number increases with flow rate and the droplet fluid is broken up along its pathway through the channel. The droplets travel as small drips. Lastly, by increasing the capillary number and forces farther jetting occurs, resulting in droplets traveling as either spheres or plugs ([[Droplet_Microfluidics:_T-Junction_-_Lina_Wu | Droplet Microfluidics: T-Junction]]).<ref name="eight">Ralf Seemann et al 2012 Rep. Prog. Phys. 75 016601. https://dx.doi.org/10.1088/0034-4885/75/1/016601</ref> | Squeezing, dripping, and jetting are other events that occur in droplet microfluidics. In the case of squeezing mode, low capillary numbers are used to produce droplets, in doing so a pressure gradient is formed across the droplet upon being formed. They droplets travel as plugs. In the case of dripping mode, viscous shear stress and interfacial tension compete as the capillary number increases with flow rate and the droplet fluid is broken up along its pathway through the channel. The droplets travel as small drips. Lastly, by increasing the capillary number and forces farther jetting occurs, resulting in droplets traveling as either spheres or plugs ([[Droplet_Microfluidics:_T-Junction_-_Lina_Wu | Droplet Microfluidics: T-Junction]]).<ref name="eight">Ralf Seemann et al 2012 Rep. Prog. Phys. 75 016601. https://dx.doi.org/10.1088/0034-4885/75/1/016601</ref> | ||
