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Capillary Number - Christopher Sparages: Difference between revisions
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==Applications== | ==Applications== | ||
[[Image:Capillary graph 1.jpg|thumb|upright=1|right|Figure 3: Shows the normalized bubble suspension viscosity as a function of capillary number in the developed experiment.< | [[Image:Capillary graph 1.jpg|thumb|upright=1|right|Figure 3: Shows the normalized bubble suspension viscosity as a function of capillary number in the developed experiment.<ref name="three">Truby, J. M., Mueller, S. P., Llewellin, E. W., & Mader, H. M. (2014). The rheology of three-phase suspensions at low bubble capillary number. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2173), 20140557-20140557. https://dx.doi.org/10.1098/rspa.2014.0557</ref>]] | ||
===Bubble Suspension=== | ===Bubble Suspension=== | ||
As mentioned above the capillary number is a representation of forces between two immiscible liquids (gas or liquid). In the case of bubble suspension, the interaction is between a liquid and gas. A large reason for studies conducted with bubble suspension is to learn more about to develop models, characterize, and control the flow of the respective gas. In order to achieve these goals, rheology tests are conducted while values for viscosity, velocity, and surface tension are taken see how capillary number effects the behavior of this bubbling. Comparing the bubble viscosity to the capillary number, results can be seen that with an increase in capillary number there is a sigmoidal response in the bubble viscosity (Figure 3).< | As mentioned above the capillary number is a representation of forces between two immiscible liquids (gas or liquid). In the case of bubble suspension, the interaction is between a liquid and gas. A large reason for studies conducted with bubble suspension is to learn more about to develop models, characterize, and control the flow of the respective gas. In order to achieve these goals, rheology tests are conducted while values for viscosity, velocity, and surface tension are taken see how capillary number effects the behavior of this bubbling. Comparing the bubble viscosity to the capillary number, results can be seen that with an increase in capillary number there is a sigmoidal response in the bubble viscosity (Figure 3).<ref name="three" /> | ||
===Chemical Flooding=== | ===Chemical Flooding=== | ||
[[Image:Sandstone_microfluidics.png|thumb|upright=1|left|Figure 4: Schematic diagram of the small sandstone device used in these experiments. The lower image is what the sandstone | [[Image:Sandstone_microfluidics.png|thumb|upright=1|left|Figure 4: Schematic diagram of the small sandstone device used in these experiments. The lower image is what the sandstone | ||
portion looks like when filled with the Miglyol oil dyed with Sudan Blue.<sup>9</sup>]] | portion looks like when filled with the Miglyol oil dyed with Sudan Blue.<sup>9</sup>]] | ||
[[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 .< | [[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. 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.< | 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. 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. | ||
Relative permeability takes into consideration wettability as mentioned above, capillary end effects, geometry of the pore, rock type, and imbibition or drainage. It was found through experimentation by isolating wetting as the independent variable that at low capillary numbers capillary end effects had high influence. As a result, in order to produce consistently successful results for the relative permeability very high capillary numbers were achieved and monitored to ensure the capillary end effects did not become influential. These types of experiments show the just how important capillary number is to chemical flooding, especially when it comes to investigating relative permeability.< | Relative permeability takes into consideration wettability as mentioned above, capillary end effects, geometry of the pore, rock type, and imbibition or drainage. It was found through experimentation by isolating wetting as the independent variable that at low capillary numbers capillary end effects had high influence. As a result, in order to produce consistently successful results for the relative permeability very high capillary numbers were achieved and monitored to ensure the capillary end effects did not become influential. These types of experiments show the just how important capillary number is to chemical flooding, especially when it comes to investigating relative permeability.<ref name="two" /> | ||
===Droplet Microfludics=== | ===Droplet Microfludics=== | ||
