Capillary Number - Christopher Sparages: Difference between revisions

[[Image:Capillary graph 1.jpg|thumb|upright=1|right|Figure 2: Shows the normalized bubble suspension viscosity as a function of capillary number in the developed experiment. Reproduced from The rheology of three-phase suspensions at low bubble capillary number by J. M. Truby, S. P. Mueller, E. W. Llewellin and H. M. Mader as Unrestricted Use from Creative Commons Licensing. <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), 40557-40643.  https://dx.doi.org/10.1098/rspa.2014.0557</ref>]]

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.<ref name="nine">Ramakrishnan, T. S., & Wasan, D. T. (1986). The Relative Permeability Function for Two-Phase Flow in Porous Media: Effect of Capillary Number. Proceedings of SPE Enhanced Oil Recovery Symposium, 48(2). https://dx.doi.org/10.2523/12693-ms</ref> 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 2).<ref name="three" />

[[Image:Sandstone_microfluidics.png|thumb|upright=1|left|Figure 3: Schematic diagram of the small sandstone device used in these experiments. The lower image is what the sandstone

[[Image:Capillary_Number_CDC.png|thumb|upright=1|right|Figure 4: Shows a typical capillary desaturation curve with saturation versus the capillary number from a series of different sources. Reproduced from Proper Use of Capillary Number in Chemical Flooding by Hu Guo, Ma Dou, Wang Hanqing, Fuyong Wang, Gu Yuanyuan, Zhaoyan Yu, Wang Yansheng, and Yiqiang Li as Unrestricted Use from Creative Commons Licensing.<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 2). 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 2). Wettability is one of the factors that contributes to relative permeability, which is effected by capillary number within a certain range.<ref name="two" />