دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات43
تعداد شماره‌ها1,223
تعداد مقالات15,032
تعداد مشاهده مقاله50,506,934
تعداد دریافت فایل اصل مقاله13,608,998
Aliev, Fikret, Jamalbayov, Mahammad, Hasanov, Ilyas, Valiyev, Nazim, Hajiyeva, Nazile. (1402). Mathematical modeling of a nonlinear two-phase flow in a porous medium and the inflow of volatile oil to a well taking into account inertial effects. سامانه مدیریت نشریات علمی, 11(4), 664-675. doi: 10.22034/cmde.2023.48570.2032
Fikret Ahmadali Aliev; Mahammad Jamalbayov; Ilyas Hasanov; Nazim Valiyev; Nazile Hajiyeva. "Mathematical modeling of a nonlinear two-phase flow in a porous medium and the inflow of volatile oil to a well taking into account inertial effects". سامانه مدیریت نشریات علمی, 11, 4, 1402, 664-675. doi: 10.22034/cmde.2023.48570.2032
Aliev, Fikret, Jamalbayov, Mahammad, Hasanov, Ilyas, Valiyev, Nazim, Hajiyeva, Nazile. (1402). 'Mathematical modeling of a nonlinear two-phase flow in a porous medium and the inflow of volatile oil to a well taking into account inertial effects', سامانه مدیریت نشریات علمی, 11(4), pp. 664-675. doi: 10.22034/cmde.2023.48570.2032
Aliev, Fikret, Jamalbayov, Mahammad, Hasanov, Ilyas, Valiyev, Nazim, Hajiyeva, Nazile. Mathematical modeling of a nonlinear two-phase flow in a porous medium and the inflow of volatile oil to a well taking into account inertial effects. سامانه مدیریت نشریات علمی, 1402; 11(4): 664-675. doi: 10.22034/cmde.2023.48570.2032

Mathematical modeling of a nonlinear two-phase flow in a porous medium and the inflow of volatile oil to a well taking into account inertial effects

Computational Methods for Differential Equations
مقاله 1، دوره 11، شماره 4، مهر 2023، صفحه 664-675    اصل مقاله (661.39 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.48570.2032
نویسندگان
Fikret Ahmadali Aliev* 1، 2؛ Mahammad Jamalbayov3؛ Ilyas Hasanov3؛ Nazim Valiyev4؛ Nazile Hajiyeva1
1Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan.
2Institute of Information Technologies of the National Academy of Sciences of Azerbaijan, Baku, Azerbaijan.
3Socar "Oil gas scientific research project" Institute, AZ1122, Hasan Bey Zardabi, Baku, Azerbaijan.
4Socar Head Office
چکیده
This paper discusses a semi-analytic solution for the volatile oil influx into the well on the base of Forchheimer flow law. The solution is developed employing the concept of binary model for the two-phase petroleum hydrocarbon system in view of phase transformations and interphase mass transfer. Algorithms are developed for calculating the volatile oil reservoir key performance indicators by applying the material balance equations, which take into account the compaction behavior of rocks. A computer simulator for the volatile oil reservoir is modeled, proceeding from these algorithms. The inertial effects on the development process of a volatile oil reservoir, the rocks of which are exposed to elastic deformation, are studied by this simulator. In regard thereto, the reservoir development process is simulated in two variants in conformity with the constant depression: in the first case, it is assumed that the filtration occurs according to Darcy's law, while in the second one, the process is considered on the base of Forchheimer equation. A comparison of the results of these options made it possible to demonstrate the nature of the inertial effects on the volatile oil reservoir key performance indicators.
کلیدواژه‌ها
Volatile oil؛ Inertial effects؛ Nonlinear flow؛ Compressibility؛ Deformation
مراجع
  • [1] F. A. Aliev, N. A. Aliyev, N. S. Hajiyeva, and N. I. Mahmudov, Some mathematical problems and their solutions for the oscillating systems with liquid dampers: a review, Appl. Comput. Math., 20(3) (2021), 339-365.
  • [2] F. A. Aliev, M. A. Dzhamalbekov, and M. Kh. Ilyasov, Mathematical simulation and control of gas lift, Journal of Computer and Systems Sciences International, 50 (2011), 805-814.
  • [3] F. A. Aliev, M. A. Jamalbayov, and S. M. Nasibov, Mathematical modeling of the well-bed system under the gaslift operation, TWMS Journal of Pure and Applied Mathematics, 1(1) (2010), 5-13.
  • [4] F. A. Aliev, M. A. Jamalbayov, N. A. Veliev, I. R. Gasanov, and N. A. Alizade, Computer Simulation of Crude Oil Extraction Using a Sucker Rod Pumping Unit in the Oil Well-Resevoir System, International Applied Mechanics, 55(3) (2019), 332-341.
  • [5] T. Antczak, and M. Arana-Jimnez Optimality and Duality Results for new Classes of Nonconvex Quasidifferen- tiable Vector Optimization Problems, Appl. Comput. Math., 21(1) (2022), 21-34.
  • [6] R. D. Barree and M. W. Conway, Beyond beta factors: a complete model for Darcy, Forchheimer, and trans- Forchheimer flow in porous media, SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, 2004.
  • [7] J. Bear, Dynamics of fluids in porous media, Dover Publications, New York, 2013, 764 p.
  • [8] H. A. Belhaj, K. R. Agha, and S. D. Butt, Simulation of non-Darcy flow in porous media including viscous, inertial and frictional effects, SPE International Improved Oil Recovery Conference in Asia Pacific, Kuala Lumpur, Malaysia, 20-21 October, 2003.
  • [9] R. Camacho-Velazquez, R. Padilla-Sixto, and M. Vasquez-Cruz, Inflow performance relationships with inertial effects in the reservoir, SPE Production Operations Symposium, Oklahoma City, Oklahoma, 21-23 March, 1993.
  • [10] K. H. Coats, L. K. Thomas, and R. G. Pierson, Compositional and black oil reservoir simulation, SPE Reservoir Simulation Symposium, San Antonio, Texas, 1995.
  • [11] H. Darcy, Les fontaines publiques de la ville de Dijon, Victor Dalmont, 1856, 647 p.
  • [12] P. Forchheimer, Wasserbewegung durch boden, Z. Ver. Deutsch. Ing., 1901.
  • [13] X. Y. Gao, Y. J. Guo, and W. R. Shan, Similarity reductions for a (3+1)-dimensional generalized Kadomtsev- Petviashvili equation in nonlinear optics, fluid mechanics and plasma physics, Appl. Comput. Math., 20(3) (2021), 421-429.
  • [14] A. Geertsma, Estimating the Coefficient of Inertial Resistance in Fluid Flow Through Porous Media, Society of Petroleum Engineers Journal, 14 (1974), 445-450.
  • [15] A. M. Guliyev and M. A. Jamalbayov, The prediction of the development indicators of creeping reservoirs of light oils, SOCAR Proceedings, (3) (2017), 51-57.
  • [16] A. N. Gurbanov and I. Z. Sardarova, Optimization Problem of Measurements In Experimental Research of Gas-Lift Wells, Appl. Comput. Math., 21(2) (2022), 223-228.
  • [17] T. Gorbunov, Development of anomalous oil reservoirs, Ioscow, Nedra (in Russian), 1981, 237 p..
  • [18] J. Hagoort, Non-Darcy flow near hydraulically fractured wells, SPE Journal, 9(2) (2004), 180-185.
  • [19] S. I. Hamidov, Optimal trajectories in reproduction models of economic dynamics, TWMS J. Pure Appl. Math., 13(1) (2022), 16-24.
  • [20] Z. Huang, X. Zhang, J.Yao, and Y. Wu, Non-Darcy displacement by a non-Newtonian fluid in porous media according to the Barree-Conway model, Adv. Geo-energ. Res., 1 (2017), 74-85.
  • [21] M. A. Jamalbayov and N. A. Veliyev, The Technique Of Early Determination Of Reservoir Drive Of Gas Con- densate And Velotail Oil Deposits On The Basis Of New Diagnosis Indicators, TWMS J. Pure Appl. Math., 8(2) (2017), 236-250.
  • [22] J. M. Lombard, D. G. Longeron, and F. J. M. Kalaydjian, Influence of connate water and condensate saturation on inertial effects in gas/condensate reservoirs, SPE Journal, 5 (2000), 301-308.
  • [23] A. Saeidi and L. L. Handy, Flow and phase behavior of gas condensate and volatile oils in porous media, SPE California Regional Meeting, San Francisco, California, 4-5 April, 1974.
  • [24] Y. Turhan, Analytical treatment of transient non-Darcy flow, SPE Annual Technical Conference and Exhibition- Dallas, Texas, 6-9 October, 1991.
  • [25] I. Makinde and W. John Lee, Production forecasting in shale volatile oil reservoirs, SPE/IAEE Hydrocarbon Economics and Evaluation Symposium, Houston, Texas, USA, 17-18 May, 2016.
  • [26] V. Marinca, R. D. Ene, and B. Marinca Optimal Homotopy Perturbation Method for Nonlinear Problems with Applications, Appl. Comput. Math., 21(2) (2022), 123-136.
  • [27] H. K. Musaev, The Cauchy problem for degenerate parabolic convolution equation, TWMS J. Pure Appl. Math., 12(2) (2021), 278-288.
  • [28] H. Mustapha, L. de Langavant, and Marie Ann Giddins, Darcy and non-Darcy Flows in Fractured Gas Reservoirs, SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, UAE, 14-16 September, 2015.
  • [29] P. S. Pankov, Z. K. Zheentaeva, and T. Shirinov, Asymptotic reduction of solution space dimension for dynamical systems, TWMS J. Pure Appl. Math., 12(2) (2021), 243-253.
  • [30] K. S. Pedersen, P. L. Christensen, and J. A. Shaikh, Phase behavior of petroleum reservoir fluids, CRC Press, 2014, 465 p.
  • [31] J. Spivey, K. Brown, and W. Sawyer, et al. Estimating non-Darcy flow coefficient from buildup-test data with wellbore storage, SPE Reserv. Eval. Eng., 7 (2004), 256-269.
  • [32] Y. S. Wu, B. Lai, J. L. Miskimins, and P. Fakcharoenphol, Analysis of multiphase non-Darcy flow in porous media, Transp. Porous Med., 88 (2011), 205-223.
  • [33] J. C. Xu, R. Z. Jiang, L. Xie, R. H. Wang, L. Shan, and L. Li, Non-Darcy flow numerical simulation for low- permeability reservoirs, SPE Europec/EAGE Annual Conference, Copenhagen, Denmark, 4-7 June, 2012.
  • [34] L. Yang, H. Rui, and Q. Zhao, Investigation of Barree-Conway non-Darcy flow effects on coalbed methane pro- duction, J. Cent. South Univ., 23 (2016), 3322-3331.
  • [35] J. Zare, A. Shateri, Y. T. Beni, and A. A. Nadooshan, Stability Analysis of Initially Imperfect Nanoshells Con- veying Fluid Based on Nonlocal Strain Gradient Theory, Appl. Comput. Math., 21(3) (2022), 292-316.
آمار
تعداد مشاهده مقاله: 294
تعداد دریافت فایل اصل مقاله: 488


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب