The prediction of spontaneous oil-water imbibition in composite capillary

Abstract

In view of the classical Lucas-Washburn equation, which can only describe the spontaneous imbibition of single wetted capillary, a tilted composite capillary model with circular cross section, composed of different wettability capillary wall was established. The model can describe the spontaneous oil-water imbibition of water-wet capillary, oil-wet capillary and mixed wetting capillary. Through numerical solution of the model equation, it is found that the component content of the capillary walls, the capillary radius and the oil-water viscosity ratio have great effects on the spontaneous oil-water imbibition. Effects of capillary inclination angle and inertia force on spontaneous oil-water imbibition are related to the capillary scale. Effects of capillary inclination angle and inertia force can be ignored in small radius capillary, while effects of inclination angle and inertia force can not be ignored in large radius capillary.

Keywords

Non-homogeneous wettability / Composite capillary walls / Spontaneous imbibition / Oil and water / Lucas-Washburn equation

Acknowledgments

Support from Open Fund (PLC20190804) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Chengdu University of Technology), Maoming City Science and Technology Plan Project (2019413 and 2020530), Guangdong Natural Science Fund (2019A1515012235), China National Fund for Studying Abroad (201808440643) are gratefully acknowledged.

Author statements

Under guidance of Yongming He, Lin Wang established the model, derived the equation and performed calculations. Feiying Ma did the drawing and data analysis. Dawei Liu modified the language. All authors read and contributed to the manuscript.

References

[1] R. H Brooks, A.T. Corey,Properties of porous media affecting fluid flow, J. Irrig. Drainage Div. ASCE Proc. 92 (1966) 61-88, https://doi.org/10.1061/JRCEA4.0000425.

[2] L. Susana, F. Campaci, A.C. Santomaso, Wettability of mineral and metallic powders: applicability and limitations of sessile drop method and Washburn's technique, Powder Technol. 226 (2012) 68-77, https://doi.org/10.1016/j.powtec.2012.04.016.

[3] S. Kirdponpattara, M. Phisalaphong, B.M.Z. Newby, Applicability of Washburn capillary rise for determining contact angles of powders/porous materials, J. Colloid. Interf. Sci. 397 (2013) 169-176, https://doi.org/10.1016/j.jcis.2013.01.033.

[4] D. Benavente, P. Lock, M. ángeles, S. García Del Cura, Ordó?Ez, predicting the capillary imbibition of porous rocks from microstructure, Transport Porous Media 49 (1) (2002) 59-76, https://doi.org/10.1023/A:1016047122877.

[5] J. Murison, B. Semin, J.C. Baret, S. Herminghaus, M. Brinkmann, Wetting heterogeneities in porous media control flow dissipation, Phys. Rev. Appl. 2 (3) (2014), 034002, https://doi.org/10.1103/PhysRevApplied.2.034002.

[6] R. Lucas, Rate of capillary ascension of liquids, Kolloid Z. 23 (1918) 15-22, https://doi.org/10.1007/BF01461107.

[7] E.W. Washburn, The dynamics of capillary flow, Phys. Rev. 17 (3) (1921) 273-283, https://doi.org/10.1103/physrev.17.273.

[8] J. Szekely, A.W. Neumann, Y.K. Chuang, The rate of capillary penetration and the applicability of the Washburn Equation, J. Colloid Interf. Sci. 35 (2) (1971) 273-278, https://doi.org/10.1016/0021-9797(71)90120-2.

[9] B.V. Zhmud, F. Tiberg, K. Hallstensson, Dynamics of capillary rise, J. Colloid Interf. Sci. 228 (2000) 263-269, https://doi.org/10.1006/jcis.2000.6951.

[10] N. Fries, M. Dreyer, An analytic solution of capillary rise restrained by gravity, J. Colloid Interf. Sci. 320 (1) (2008) 259-263, https://doi.org/10.1016/j.jcis.2008.01.009.

[11] J. Berthier, D. Gosselin, E. Berthier, A generalization of the LucaseWashburneRideal law to composite microchannels of arbitrary cross section, Microfluid. Nanofluidics 19 (3) (2015) 497-507, https://doi.org/10.1007/s10404-014-1519-3.

[12] P.P. van Lingen, J. Bruining, C.P.J.W. van Kruijsdijk, Capillary entrapment caused by small-scale wettability heterogeneities, SPE Reservoir Eng. 11 (2) (1996) 93-99, https://doi.org/10.2118/30782-PA.

[13] L. Wang, Y.M. He, Y.H. Xiao, H.H. Wang, F.Y. Ma, Spontaneous gas-water imbibition in mixed-wet pores, Petrophysics 61 (2) (2020) 230-238, https://doi.org/10.30632/PJV61N2-2020a8.

[14] A. Habibi, H. Dehghanpour, M. Binazadeh, D. Bryan, G. Uswak, Advances in understanding wettability of tight oil formations: a montney case study, SPE Reservoir Eval. Eng. 19 (4) (2016) 583-603, https://doi.org/10.2118/175157-PA.

[15] A.B.D. Cassie, S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc. 40 (1944) 546-551, https://doi.org/10.1039/tf9444000546.

[16] J.H. Michael, G.K. John, The apparent contact angle for a nearly spherical drop on a heterogeneous surface, Chem. Phys. Lett. 447 (2007) 44-48, https://doi.org/10.1016/j.cplett.2007.08.080.

[17] G. Whyman, E. Bormashenko, T. Stein, The rigorous derivation of Young, Cassie-Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon, Chem. Phys. Lett. 450 (2008) 355-359, https://doi.org/10.1016/j.cplett.2007.11.033.

[18] J. Berthier, K. Brakke, E. Berthier, A general condition for spontaneous capillary flow in uniform cross-section microchannels, Microfluid. Nanofluidics 16 (2014) 779-785, https://doi.org/10.1007/s10404-013-1270-1.

[19] S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1988) 12-49, https://doi.org/10.1016/0021-9991(88)90002-2.

[20] H. Grzybowski, R. Mosdorf, Modelling of two-phase flow in a minichannel using level-set method, J. Phys. Conf. Ser. 530 (2014), 012049, https://doi.org/10.1088/1742-6596/530/1/012049.

[21] P. Jangir, A.K. Jana, CFD simulation of droplet splitting at microfluidic Tjunctions in oil-water two phase flow using conservative level set method, J. Braz. Soc. Mech. Sci. Eng. 41 (2) (2019) 1-16, https://doi.org/10.1007/s40430-019-1569-2.

[22] S. Bashir, J.M. Rees, W.B. Zimmerman, Investigation of pressure profile evolution during confined microdroplet formation using a two-phase level set method, Int. J. Multiphas. Flow 60 (2014) 40-49, https://doi.org/10.1016/j.ijmultiphaseflow.2013.11.012.

[23] G. Mason and N. R. Morrow, Developments in spontaneous imbibition and possibilities for future work, J. Petrol. Sci. Eng. 110(213) 268-293. https://doi. org/10.1016/j.petrol.2013.08.018.

[24] K.W. Li, D.F. Zhang, H.Y. Bian, C. Meng, Y.N. Yang, Criteria for applying the Lucas-Washburn law, SCI. Rep. UK 5 (2015), 14085, https://doi.org/10.1038/srep14085.