Digital core: modeling the temperature field in the hollow space of the rock
https://doi.org/10.31660/0445-0108-2022-6-41-55
Abstract
This article considers the problem associated with conducting experiments in computational fluid dynamics, the solution of which is the application of the equations of incompressible fluid flow and the introduction of vortex flow functions.
The aim of this work is to simulate the temperature viscous flow with a set Reynolds number inside a porous medium enclosed in the rock material to further describe the thermal front of motion in the form of a system of equations, with the choice of the most likely suitable system with differentiated equations for each segment of the thermal simulation (along the cube axes), the final cross-correlation, spread in the identified physical field of confusers/diffusers.
Scientific novelty of the performed work is due to the original approach to the development and interpretation of the results of the algorithm for predicting the temperature field in the textural configuration of the confusers/diffusers of rocks.
About the Authors
Yu. E. KatanovRussian Federation
Yuri E. Katanov, Candidate of Geology and Mineralogy, Associate Professor, Leading Researcher at Well Workover Technology and Production Stimulation Laboratory, Leading Researcher at the Laboratory for Digital Research in the Oil and Gas Industry
Tyumen
A. I. Aristov
Russian Federation
Artyom I. Aristov, Assistant at the Laboratory of Digital Research in the Oil and Gas Industry
Tyumen
Yu. V. Vaganov
Russian Federation
Yuriy V. Vaganov, Candidate of Engineering, Associate Professor, Pro-rector for Research and Innovation
Tyumen
A. G. Klenskih
Russian Federation
Anton G. Klenskih, Junior Researcher at the Well Workover Technology and Production Stimulation Laboratory
Tyumen
References
1. Saeedpanah, I. (2017). A MLPG Meshless Method for Numerical Simulation of Unsteady Incompressible Flows. Journal of Applied Fluid Mechanics, 10(1), pp. 421-432. (In English). DOI: 10.18869/ACADPUB.JAFM.73.238.25895
2. Cao, J., & Kitanidis, P. K. (1998). Adaptive finite element simulation of Stokes flow in porous media. Advances in Water Resources, 22(1), pp. 17-31. (In English). DOI: 10.1016/S0309-1708(97)00040-7
3. Li, P.-W., Fan, C. M., Yu, Y. Z., & Song, L. (2016). A Meshless Generalized Finite Difference Scheme for the Streamfunction Formulation of the Naiver-Stokes Equations. (In English). Available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4230475
4. Bhardwaj, S., & Dalal, A. (2013). Analysis of Natural Convection Heat Transfer and Entropy Generation inside Porous Right-angled Triangular Enclosure. International Journal of Heat and Mass Transfer, 65, pp. 500-513. (In English).
5. Pakdee, W., Utaivorawit, N., & Hussein, A. K. (2015). Mathematical model in the form of vorticity-stream function for porous premixed combustion. Songklanakarin Journal of Science & Technology, 37(5), pp. 595-600. (In English).
6. Pandit, S. K., Chattopadhyay, A., & Oztop, H. F. (2016). A fourth order compact scheme for heat transfer problem in porous media. Computers & Mathematics with Applications, 71(3), pp. 805-832. (In English). DOI: 10.1016/j.camwa.2015.12.037
7. Bagai, S., Kumar, M., & Patel, A. (2020). Mixed convection in four-sided lid-driven sinusoidally heated porous cavity using stream function-vorticity formulation. SN Applied Sciences, 2(12). (In English). Available at: https://doi.org/10.1007/s42452-020-03815-7
8. Comini, G., Manzan, M., & Cortella, G. (1997). Open boundary conditions for the streamfunction-vorticity formulation of unsteady laminar convection. Numerical Heat Transfer, Part B: Fundamentals, 31(2), pp. 217-234. (In English). DOI: 10.1080/10407799708915106
9. Calhoun, D. (2002). A Cartesian Grid Method for Solving the TwoDimensional Streamfunction-Vorticity Equations in Irregular Regions. Journal of Computational Physics, 176(2), рр. 231-245. (In English). DOI: 10.1006/jcph.2001.6970
10. Borah, A. K. (2011). Computational Study of Streamfunction-Vorticity Formulation of Incompressible Flow and Heat Transfer Problems. Applied Mechanics and Materials, (52-54), pp. 511-516. (In English). DOI: 10.4028/www.scientific.net/AMM.52-54.511
11. Wang, C. A., Sadat, H., & Prax, C. (2012). A new meshless approach for three dimensional fluid flow and related heat transfer problems. Computers & Fluids, 69, рр. 136-146. (In English). DOI: 10.1016/j.compfluid.2012.08.017
12. Sousa, A. C. M. (2004). Heat transfer distribution for a free/porous system with forced convection and heat generation - a numerical study. Proceeding of Thermal Sciences 2004. Proceedings of the ASME - ZSIS International Thermal Science Seminar II. Bled, Slovenia, June, 13-16, 2004. (In English). Available at: https://doi.org/10.1615/ICHMT.2004.IntThermSciSemin.1150
13. d'Hueppe, A. (2011). Heat transfer modeling at an interface between a porous medium and a free region. Doctoral dissertation. Paris, 188 p. (In English).
14. Akhter, S., & Ashraf, M. (2021). Numerical study of flow and heat transfer in a porous medium between two stretchable disks using quasi-linearization method. Thermal Science, 25(2(Part A)), pp. 989-1000. (In English).
15. Loukopoulos, V. C., & Karahalios, G. T. (2009). A Stream Function‐ Vorticity Formulation Numerical Method for the Unsteady Flow in the Presence of Natural Convection. In AIP Conference Proceedings, 1148(1), pp. 558-561. (In English). DOI: 10.1063/1.3225374
16. Tian, Z., & Ge, Y. (2003). A fourth‐order compact finite difference scheme for the steady stream function-vorticity formulation of the Navier-Stokes/Boussinesq equations. International Journal for Numerical Methods in Fluids, 41(5), pp. 495-518. (In English). DOI: 10.1002/fld.444
17. Katanov, Yu. E. (2021). A probabilistic and statistical model of rock deformation. E3S Web of Conferences, 266. (In English). Available at: https://doi.org/10.1051/e3sconf/202126603011
18. Katanov, Yu. E., Aleksandrov, V. M., & Yagafarov, A. K. (2020). Geological and mathematical analogy of reservoir and polymer structures. TEST Engineering & Management, 82, pp. 6977-6991. (In English).
19. Katanov, Yu., Vaganov, Yu., & Cheymetov, M. (2021). Neural simulationbased analysis of the well wall stability while productive seam penetrating. Mining of Mineral deposits, 15(4), pp. 91-98. (In English). DOI: 10.33271/MINING15.04.091
20. Katanov, Yu. E., Vaganov, Yu. V., & Listak, M. V. (2020). Geological and mathematical description of the rocks strain during behavior of the producing solid mass in compression (Tension). Journal of Mines, Metals & Fuels, 68(9), pp. 285-293. (In English). DOI: 10.33271/mining15.04.091
21. Yan, Ye., Yan, J., Zou, S., Wang, S., & Lu, R. (2008). A new laboratory method for evaluating formation damage in fractured carbonate reservoirs. Petroleum Science, (5), pp. 45-51. (In English). DOI: 10.1007/s12182-008-0007-3
22. Mackey, G. N., Horton, B. K., & Milliken, K. L. (2012). Provenance of Paleocene-Eocene Wilcox group western Gulf of Mexico basin: Evidence for integrated drainage of the southern Laramide rocky mountains and cordilleran arc. Geological Society of America Bulletin, 124, pp. 1007-1024. (In English). DOI: 10.1130/B30458.1
23. Day-Stirrat, R. J., Milliken, K. L., Dutton, S. P., Loucks, R. G., Hillier, S., Aplin, A. C., & Schleicher, A. M. (2010). Open-system chemical behavior in deep Wilcox group mudstones, Texas Gulf Coast, USA. Marine and Petroleum Geology, 27(9), pp. 1804-1818. (In English). DOI: 10.1016/j.marpetgeo.2010.08.006
24. Aleksandrov, V. M., Morozov, A. V., Popov, I. P., Lebedeva, R. G., & Bulgakova, I. A. (2018). Detailization of the facial conditions for sedimentation of the (formula presented) productive layer with the purpose of specificating features of the geological structure. Journal of Environmental Management and Tourism, 9(5(29)), pp. 932-946. (In English).
25. Nesterov, I. I., Smirnov, P. V., Konstantinov, A. O., & Gursky, H.-J. (2021). Types, features, and resource potential of Palaeocene-Eocene siliceous rock deposits of the West Siberian Province: a review. International Geology Review, 63(4), pp. 504-525. (In English). DOI: 10.1080/00206814.2020.1719370
26. Khan, W., Yousafzai, F., Chohan, M. I., Zeb, A., Zaman, G., & Jung, I. H. (2014). Exact solutions of Navier Stokes equations in porous media. International Journal of Pure and Applied Mathematics, 96(2), pp. 235-247. (In English). DOI: 10.12732/ijpam.v96i2.7
Review
For citations:
Katanov Yu.E., Aristov A.I., Vaganov Yu.V., Klenskih A.G. Digital core: modeling the temperature field in the hollow space of the rock. Oil and Gas Studies. 2022;(6):41-55. (In Russ.) https://doi.org/10.31660/0445-0108-2022-6-41-55