Mathematical filtration model with capillary forces in a multipore medium
Abstract
This paper proposes a modification of a one-dimensional model of fluid filtration in an oil-saturated reservoir under the action of capillary forces to take into account the additional injection pressure gradient. This model was verified through a series of flow experiments on core, and agreement with actual data was obtained at the initial stage of filtration. A deviation of the model in the final sections was also noted, which is associated with the averaging of rock properties and its representation as a set of identical capillary tubes. Therefore, it was proposed to use a dual-poro model, in which the reservoir is decomposed into two media with different properties. This made it possible to reproduce the change in filtration dynamics associated with the flow of liquid through pores of various sizes, but the impregnation curve deviated greatly from the experimental data. To increase accuracy, mass transfer between two media was introduced into the model, and a system of first-order differential equations was obtained that describes the filtration of water and oil in the reservoir rock. This approach made it possible to reproduce the experimental imbibition curves with high accuracy at stages 1 and 2. The introduction of a third medium with the smallest pores into the model helped to describe the third stage, when the increase in the accumulated mass of the imbibition is minimal.
The proposed model was used to conduct a series of numerical experiments. It has been determined that in natural multipore systems, the rate of capillary impregnation increases with increasing radius of the pore channel, despite the decrease in capillary pressure. Moreover, in small channels, imbibition makes a greater contribution to filtration than the external pressure gradient.
Full Text:
PDF (Russian)References
Tsykunov O.I., Kaeshkov I.S. Research and application experience of water Huff and Puff technology on low-permeability oil field. PROneft’. Proffessional’no o nefti, 2021, vol. 6, Iss. 3, pp. 114–120. https://doi.org/10.51890/2587-7399-2021-6-3-114-120
Milad M., Junin R., Sidek A., Imqam A., Tarhuni M. Huff-n-Puff technology for enhanced oil recovery in shale/tight oil reservoirs: progress, gaps, and perspectives. Energy & Fuels American Chemical Society (ACS), 2021, vol. 35, Iss. 21, pp. 17279–17333. Available at: https://doi.org/10.1021/acs.energyfuels.1c02561
Qin G., Dai X., Wu M., Zheng Y., Qing Y., Li W. Study of massive water huff-n-puff technology in tight oil field and its field application. Journal of Petroleum Science and Engineering, 2020, pp. 1–31. Available at: https://doi.org/10.1016/j.petrol.2020.107514
Sheng J.J. Critical review of field EOR projects in shale and tight reservoirs. Journal of Petroleum Science and Engineering, 2017, vol. 159, pp. 654–665. Available at: https://doi.org/10.1016/j.petrol.2017.09.022
Xiaoyan Wang, Kun Xie, Jie Zhang, Yong Zhang, Yang Zhang, Wei Wang, Xi Yan, Fengxiang Zhao. Study on the key influential factors on water Huff-n-Puff in ultralow-permeability reservoir. Geofluids, 2021, vol. 2021, Article ID 5885366, pp. 1–8. Available at: https://doi.org/10.1155/2021/5885366
Li, Z., Qu, X., Liu, W., Lei, Q., Sun, H., & He, Y. (2015). Development modes of Triassic Yanchang Formation Chang 7 Member tight oil in Ordos Basin, NW China. In Petroleum Exploration and Development (Vol. 42, Issue 2, pp. 241–246). Elsevier BV. https://doi.org/10.1016/s1876-3804(15)30011-2
Bourbiaux, B. J., & Kalaydjian, F. J. (1990). Experimental Study of Cocurrent and Countercurrent Flows in Natural Porous Media. In SPE Reservoir Engineering (Vol. 5, Issue 03, pp. 361–368). Society of Petroleum Engineers (SPE). https://doi.org/10.2118/18283-pa
Hatiboglu, C. U., & Babadagli, T. (2004). Experimental Analysis of Primary and Secondary Oil Recovery from Matrix by Counter-Current Diffusion and Spontaneous Imbibition. In All Days. SPE Annual Technical Conference and Exhibition. SPE. https://doi.org/10.2118/90312-ms
Zhang, X., Morrow, N. R., & Ma, S. (1996). Experimental Verification of a Modified Scaling Group for Spontaneous Imbibition. In SPE Reservoir Engineering (Vol. 11, Issue 04, pp. 280–285). Society of Petroleum Engineers (SPE). https://doi.org/10.2118/30762-pa
Zhou, X., Morrow, N. R., & Ma, S. (2000). Interrelationship of Wettability, Initial Water Saturation, Aging Time, and Oil Recovery by Spontaneous Imbibition and Waterflooding. In SPE Journal (Vol. 5, Issue 02, pp. 199–207). Society of Petroleum Engineers (SPE). https://doi.org/10.2118/62507-pa
Tang, G.-Q., & Firoozabadi, A. (2001). Effect of Pressure Gradient and Initial Water Saturation on Water Injection in Water-Wet and Mixed-Wet Fractured Porous Media. In SPE Reservoir Evaluation & Engineering (Vol. 4, Issue 06, pp. 516–524). Society of Petroleum Engineers (SPE). https://doi.org/10.2118/74711-pa
Wang, X., Xie, K., Zhang, J., Zhang, Y., Zhang, Y., Wang, W., Yan, X., & Zhao, F. (2021). Study on the Key Influential Factors on Water Huff-n-Puff in Ultralow-Permeability Reservoir. In W. Shen (Ed.), Geofluids (Vol. 2021, pp. 1–8). Hindawi Limited. https://doi.org/10.1155/2021/5885366
Chen, T.; Yang, Z.; Ding, Y.; Luo, Y.; Qi, D.; Lin, W.; Zhao, X. Waterflooding Huff-n-puff in Tight Oil Cores Using Online Nuclear Magnetic Resonance. Energies 2018, 11, 1524. https://doi.org/10.3390/en11061524
Du, D., Shen, Y., Lv, W., Li, C., Jia, N., Song, X., Wang, X., & Li, Y. (2021). Laboratory study on oil recovery characteristics of carbonated water huff-n-puff process in tight cores under reservoir condition. In Arabian Journal of Chemistry (Vol. 14, Issue 6, p. 103192). Elsevier BV. https://doi.org/10.1016/j.arabjc.2021.103192
Li, S., Yang, S., Dong, W., Yang, K., Shen, B., & Yu, J. (2022). Influence of Water Injection Pressure and Method on Oil Recovery of Water Injection Huff and Puff in Tight Volcanic Oil Reservoirs. In ACS Omega (Vol. 7, Issue 25, pp. 21595–21607). American Chemical Society (ACS). https://doi.org/10.1021/acsomega.2c01448
Cao, B., Wei, P., Tian, F., Yan, Y., Xie, K., Cao, W., Liu, X., Lu, X., Li, Y., & Li, H. (2021). Experimental Investigation on Cyclic Huff-n-Puff with Surfactants Based on Complex Fracture Networks in Water-Wet Oil Reservoirs with Extralow Permeability. In W. Shen (Ed.), Geofluids (Vol. 2021, pp. 1–10). Hindawi Limited. https://doi.org/10.1155/2021/6898581
Li, S., Yang, S., Gao, X., Wang, M., & Yu, J. (2022). Experimental study on liquid production law, oil recovery mechanism, and influencing factors of water huff-n-puff in the tight sedimentary tuff oil reservoir. In Journal of Petroleum Science and Engineering (Vol. 208, p. 109721). Elsevier BV. https://doi.org/10.1016/j.petrol.2021.109721
Babchin, A. J., Bentsen, R., Faybishenko, B., & Geilikman, M. B. (2016). On the capillary pressure function in porous media based on relative permeabilities of two immiscible fluids: Application of capillary bundle models and validation using experimental data. In Advances in Colloid and Interface Science (Vol. 233, pp. 176–185). Elsevier BV. https://doi.org/10.1016/j.cis.2015.07.001
Cai, J., Perfect, E., Cheng, C.-L., & Hu, X. (2014). Generalized Modeling of Spontaneous Imbibition Based on Hagen–Poiseuille Flow in Tortuous Capillaries with Variably Shaped Apertures. In Langmuir (Vol. 30, Issue 18, pp. 5142–5151). American Chemical Society (ACS). https://doi.org/10.1021/la5007204
Schmid, K. S., Alyafei, N., Geiger, S. ., & Blunt, M. J. (2016). Analytical Solutions for Spontaneous Imbibition: Fractional-Flow Theory and Experimental Analysis. In SPE Journal (Vol. 21, Issue 06, pp. 2308–2316). Society of Petroleum Engineers (SPE). https://doi.org/10.2118/184393-pa
Franken, A. C. M., Nolten, J. A. M., Mulder, M. H. V., Bargeman, D., & Smolders, C. A. (1987). Wetting criteria for the applicability of membrane distillation. In Journal of Membrane Science (Vol. 33, Issue 3, pp. 315–328). Elsevier BV. https://doi.org/10.1016/s0376-7388(00)80288-4
Li, K., & Horne, R. N. (2001). Characterization of Spontaneous Water Imbibition Into Gas-Saturated Rocks. In SPE Journal (Vol. 6, Issue 04, pp. 375–384). Society of Petroleum Engineers (SPE). https://doi.org/10.2118/74703-pa
Lugumanov, T. (2018). To Modeling of Dual-Porosity Reservoirs. In Day 3 Wed, October 17, 2018. SPE Russian Petroleum Technology Conference. SPE. https://doi.org/10.2118/191740-18rptc-ms
Kjøsnes, Vegard Aleksander Amundse. “Effects of Fracture Capillary Pressure and non-straight Relative Permeability Lines.” (2012).
Chen, T., Yang, Z., Ding, Y., Luo, Y., Qi, D., Lin, W., & Zhao, X. (2018). Waterflooding Huff-n-puff in Tight Oil Cores Using Online Nuclear Magnetic Resonance. In Energies (Vol. 11, Issue 6, p. 1524). MDPI AG. https://doi.org/10.3390/en11061524
Wang, M., Zhang, S., Zhang, F., Liu, Y., Guan, H., LI, J., Shao, L., Yang, S., & She, Y. (2015). Quantitative research on tight oil microscopic state of Chang 7 Member of Triassic Yanchang Formation in Ordos Basin, NW China. In Petroleum Exploration and Development (Vol. 42, Issue 6, pp. 827–832). Elsevier BV. https://doi.org/10.1016/s1876-3804(15)30079-3
Wang, X., Peng, X., Zhang, S., Du, Z., & Zeng, F. (2018). Characteristics of oil distributions in forced and spontaneous imbibition of tight oil reservoir. In Fuel (Vol. 224, pp. 280–288). Elsevier BV. https://doi.org/10.1016/j.fuel.2018.03.104
Refbacks
- There are currently no refbacks.
Abava Кибербезопасность IT Congress 2024
ISSN: 2307-8162