Two-phase filtration conditions study in a porous medium at high Weber numbers

UDK: 532.546.3, 539.383

DOI: 10.24887/0028-2448-2026-7-114-118

Key words: proppant, Reynolds number, Weber number, capillary number, turbulent flow

Authors: A.A. Bykov (Moscow Institute of Physics and Technology, RF, Dolgoprudny); A.A. Tairova1,2 (Moscow Institute of Physics and Technology, RF, Dolgoprudny; Sadovsky Institute of Geosphere Dynamics of the RAS, RF, Moscow); I.R. Safiullin (RN-TECHNOLOGIES LLC, RF, Moscow); N.A. Onegov (RN-TECHNOLOGIES LLC, RF, Moscow); S.S. Tsybin (RN-TECHNOLOGIES LLC, RF, Moscow); M.V. Bereznikova (Moscow Institute of Physics and Technology, RF, Dolgoprudny)

This paper analyzes experimental results obtained using the unique equipment of the Stim-Lab laboratory (USA) and published between 2004 and 2012. It is shown that at high values of phase filtration rates in proppant packs, equality of the average volumetric flow rates of the phases is achieved (at saturation values sufficiently different from one and zero). Also, based on the experimental data, the values of the dynamic pressure in the phases, the average intensity of shear stresses, the Weber number, and the capillary number were determined. It was shown that for gas-liquid flows, the moment of dispersion of one of the phases into small droplets is determined by the Weber number, since it is higher than the obtained capillary numbers, and its critical value is approximately in the range of 0,04-0,27. The analysis also showed that the ratio of the intensities of shear stresses in the phases is proportional to the ratio of the average volumetric velocities, and a model is proposed within which the thickness of the laminar boundary layer in the phases is assumed to be equal to explain the found ratio. Based on the obtained results, recommendation can be given that in the case of gas-liquid flow in a proppant pack and a Weber number value near the critical value, the fluid can be considered homogeneous with an effective viscosity value determined by the gas content value using standard models or correlations.

References

1. Bitao Lai, Miskimins J.L., A new technique for accurately measuring two-phase relative permeability under non-Darcy flow conditions, Journal of petroleum science and engineering, 2015, V. 127, pp. 398–408, DOI: https://doi.org/10.1016/j.petrol.2015.01.034

2. Nigmatulin R.I., Dinamika mnogofaznykh sred (The dynamics of multiphase media), Part 1, Moscow: Nauka Publ., 1987, 464 p.

3. Yihuai Zhang, Branko Bijeljic, Ying Gao et al., Quantification of nonlinear multiphase flow in porous media, Geophysical Research Letters, 2021, V. 48,

DOI: https://doi.org/10.1029/2020GL090477

4. Spurin C., Bultreys T., Bijeljic B. et al., Mechanisms controlling fluid breakup and reconnection during two-phase flow in porous media, Phys. Rev. E 100, 2019, V. 100, No. 4, DOI: https://doi.org/10.1103/PhysRevE.100.043115

5. Bitao Lai, Experimental measurements and numerical modelling of hight velocity multiphase non-darcy flow effects in porous media: PhD Thesis, 2010, Colorado School of mines.

6. Olson K.E., Haidar S., Milton-Tayler D., Olsen E., Multiphase non-Darcy pressure drop in hydraulic fracturing, SPE-90406-MS, 2004,

DOI: https://doi.org/10.2118/90406-MS

7. Volkov M.G., Bykov A.A., Tairova A.A. et al., Model of nonlinear single-phase filtration in a proppant pack at high Reynolds numbers (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2025, No. 7, pp. 94–98, DOI: https://doi.org/10.24887/0028-2448-2025-7-94-98

8. Leybenzon L.S., Dvizheniye prirodnykh zhidkostey i gazov v poristoy srede (Movement of natural liquids and gases in a porous medium), Moscow – Leningrad: Gostekhizdat Publ., 1947, 244 p.