Productivity of Multi-Stage Hydraulic Fractured Horizontal Wells and Methods for Its Estimation
https://doi.org/10.18599/grs.2025.4.6
Abstract
A multi-parameter quantitative analysis of horizontal well productivity with multistage hydraulic fracturing under steady-state flow conditions was performed, based on a high-precision numerical solution of the 3D problem on a detailed finite-volume grid. The conditions justifying the application of multistage fracturing were identified along with the interrelationship of the main system parameters to achieve a target well productivity level. An analytical expression for an approximate criterion was proposed for the case when the inflow to the wellbore is negligible compared to that to the hydraulic fractures. The accuracy and limits of applicability of the most substantiated simplified analytical models for productivity calculation were evaluated.
Keywords
horizontal wells,
multistage hydraulic fracturing,
steady-state flow,
well productivity,
analytical models,
numerical simulation,
empirical formulas
Supporting agencies: Scientific Research Center “Kurchatov Institute” within the framework of the government assignment (project no. FNEF-2024-0016)
About the Authors
M. R. Khamidullin
National Research Centre “Kurchatov Institute”;
Kazan (Volga Region) Federal University
Russian Federation
Russian Federation
Marsel R. Khamidullin – Junior Research Assistant, National Research Centre “Kurchatov Institute”; Researcher, Kazan (Volga Region) Federal University
35 Kremlevskya st., Kazan, 420008
K. A. Potashev
Kazan (Volga Region) Federal University;
Kazan State Power Engineering University
Russian Federation
Russian Federation
Konstantin A. Potashev – Dr. Sci. (Physics and Mathematics), Associate Professor, Head of the Fluid Mechanics Department at the Lobachevsky Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University
35 Kremlevskya st., Kazan, 420008
A. B. Mazo
Kazan (Volga Region) Federal University
Russian Federation
Russian Federation
Alexander B. Mazo – Dr. Sci. (Physics and Mathematics), Professor
35 Kremlevskya st., Kazan, 420008
References
1. Barenblatt G.I., Entov V.M., Ryzhik V.M. (1984). Movement of Liquids and Gases in Natural Reservoirs. Moscow: Nedra, 211 p. (In Russ.)
2. Butler R., Suprunowicz R. (1996). The effect of vertical fractures upon the performance of horizontal wells when coning can occur. Journal of Canadian Petroleum Technology, 35(2), pp. 45–54. https://doi.org/10.2118/96-05-05
3. Economides M., Oligney R., Valkó P. (2001). Unified Fracture Design: Bridging the Gap Between Theory and Practice. Orsa Press, 262 p.
4. Economides M., Hill, A. Ehlig-Economides C. (1994). Petroleum Production System. New Jercy: Prentice Hall, 624 p.
5. Elkin S.V., Aleroev A.A., Veremko N.A., Chertenkov M. V. (2016). Accounting for dimensionless conductivity in express calculation of flow-rate in a well after multi-stage hydraulic fracturing. Neftyanoe khozyaystvo = Oil Industry, 12, pp. 110–113. (In Russ.)
6. Frih N., Martin V., Roberts J.E, Saâda A. (2012). Modeling fractures as interfaces with nonmatching grids. Computer Geosciences, 16, pp. 1043–1060. https://doi.org/10.1007/s10596-012-9302-6
7. Gidley J., Holditch S, Nierode D., Veatch R. (1989). Recent Advances in Hydraulic Fracturing. Society of Petroleum Engineers, 318 p.
8. Giger F., Reiss L., Jourdan A. (1984). The Reservoir Engineering Aspects of Horizontal Drilling. Paper SPE 13024 presented at SPE Annual Technical Conference and Exhibition, Houston. https://doi.org/10.2118/13024-MS
9. Guo B. Schechter D. (1997). A Simple and Rigorous Mathematical Model for Estimating Inflow Performance of Wells Intersecting Long Fractures. Paper SPE 38104 presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Kuala Lumpur. https://doi.org/10.2118/38104-MS
10. Guo B., Yu X., Khoshgahdam M. (2009). Simple Analytical Model for Predicting Productivity of Multifractured Horizontal Wells. SPE Reservoir Evaluation & Engineering, 12(06), pp. 879–885. https://doi.org/10.2118/114452-PA
11. Hyman J., Karra S., Makedonska N., Gabel C., Painter S., Viswanathan H. (2015). dfnWorks: A discrete Fracture network framework for modeling subsurface flow and transport. Computers & Geoscience, 84, pp. 10–19. https://doi.org/10.1016/j.cageo.2015.08.001
12. Joshi S. (1988). Augmentation of Well Productivity With Slant and Horizontal Wells. Journal of Petroleum Technology, 75, pp. 729–739. https://doi.org/10.2118/15375-PA
13. Kanevskaya R.D. (1999). Mathematical Modeling of Oil and Gas Field Development Using Hydraulic Fracturing. Moscow: Nedra, 204 p. (In Russ.)
14. Khamidullin M.R. (2016). Numerical simulation of one-phase flow to multi-stage hydraulically fractured horizontal well. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 158(2), pp. 287–301. (In Russ.)
15. Khamidullin M.R., Potashev K.A., Mazo A.B. (2025). FlowPorousMedia. MSHF. Productivity. Calculation of Horizontal Well Productivity with Multistage Hydraulic Fracturing. Computer software. Certificate of State Registration of Computer Program No. 2025685868. (In Russ.)
16. Khristianovich S.A., Mikhlina S.G., Devison B.B. (1938). Some new problems of continuum mechanics. Moscow: Publishing House of the USSR Academy of Sciences, 407 p. (In Russ.)
17. Li H., Jia Zh., Wei Zh. (1996). A New Method to Predict Performance of Fractured Horizontal Wells. International Conference on Horizontal Well Technology, Calgary, Alberta, Canada. https://doi.org/10.2118/37051-MS
18. Lie K.-A. (2019). An Introduction to Reservoir Simulation Using MATLAB/GNU Octave User Guide for the MATLAB Reservoir Simulation Toolbox (MRST). Cambridge University Press, 678 p. https://doi.org/10.1017/9781108591416
19. Long J., Remer J., Wilson C., Witherspoon P. (1982). Porous Media Equivalents for Networks of Discontinuous Fractures. Water Resources Research, 18, pp. 645–658. https://doi.org/10.1029/WR018i003p00645
20. Mazo A.B., Potashev K.A., Khamidullin M.R. (2015). Filtration model of fluid inflow to a horizontal well with multi-stage hydraulic fracturing. Uchenye Zapiski Kazanskogo Universiteta. Seriya Estestvennye Nauki, 157(4), pp. 133–148. (In Russ.)
21. Mazo, A.B., Khamidullin, M.R. (2017). Explicit-implicit algorithms for accelerating the calculation of two-phase inflow to a horizontal well with multi-stage hydraulic fracturing. Vychislitel’nye Metody i Programmirovanie, 18(3), pp. 204–213. (In Russ.) https://doi.org/10.26089/NumMet.v18r318
22. Mazo A., Khamidullin M., Potashev K. (2017). Numerical simulation of a one-phase steady flow towards a multistage fractured horizontal well. Lobachevskii Journal of Mathematics, 38, pp. 818–826. https://doi.org/10.1134/S1995080217050183
23. Mazo A., Potashev K., Khamidullin M. (2019). Simplified Model to Estimate Productivity of Horizontal Well with Multistage Hydraulic Fracturing. Lobachevskii Journal of Mathematics, 40(8), pp. 1186–1193. https://doi.org/10.1134/S199508021908016X
24. Mazo A., Khamidullin M., Potashev K., Uraimov A. (2024). Mathematical Model of Water- and Oil-Soluble Tracers Transfer in Studying Multistage Hydraulic Fracturing. Fluid Dynamics, 59(3), pp. 427–443. https://doi.org/10.1134/S0015462824600287
25. Mukherjee H., Economides M. (1991). A Parametric Comparison of Horizontal and Vertical Well Performance. SPE Formation Evaluation, 6(02), pp. 209–216. https://doi.org/10.2118/18303-pa
26. Ozkan E., Brown M., Raghavan R., Kazemi H. (2009). Comparison of fractured horizontal-well performance in conventional and unconventional reservoirs. Paper presented at the SPE Western Regional Meeting, San Jose, California, pp. 345–360. https://doi.org/10.2118/121290-MS
27. Potashev K., Mazo A., Mukhina M., Uraimov A., Maklakov D., Khamidullin M. (2024). High-speed algorithm for computing the inflow to multiple-fractured horizontal wells using stream tubes. Comput Geosci, 28, pp. 1389–1411. https://doi.org/10.1007/s10596-024-10322-w
28. Prats M. (1961). Effect of Vertical Fractures on Reservoir Behavior Incompressible Fluid Case. Society of Petroleum Engineers Journal, pp. 105–118. https://doi.org/10.2118/1575-G
29. Prismotrov K.V., Varavva A.I., Voroninskaya Ya.G. (2023) Multi-stage hydraulic fracturing simulation methodology at the wells of the gas condensate field X. Georesursy = Georesources, 25(4), pp. 82–91. (In Russ.) https://doi.org/10.18599/grs.2023.4.5
30. Raghavan R., Joshi S. (1993). Productivity of Multiple Drainholes or Fractured Horizontal Wells. SPE Formation Evaluation, 8(01), pp. 11–16. https://doi.org/10.2118/21263-PA
31. Robinson P. (1984). Connectivity, flow and transport in network models of fractured media. PhD thesis. University of Oxford.
32. Simonov M.V., Roshchktaev A.P. (2017). Model pritochka k gorizontal’noy skvazhine s mnogostadiynym gidrorazryvom plasta dlya rascheta debita slantsevogo gaza i nefti. PRONEFT’. Professional’no o nefti, pp. 25–30. (In Russ.)
33. Tan X.-H., Jiang L., Li X.-P., Zhang B.-J., Li X.-C. (2018). Flow model of a multi-stage hydraulic fractured horizontal well based on tree-shaped fractal fracture networks. Journal of Petroleum Science and Engineering, 169, pp. 494–503. https://doi.org/10.1016/j.petrol.2018.06.008
34. Wei Y., Economides, M.J. (2005). Transverse hydraulic fractures from a horizontal well. Proceedings. Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, https://doi.org/10.2118/94671-MS
35. Xing F., Masson R., Lopez S. (2017). Parallel vertex approximate gradient discretization of hybrid dimensional Darcy flow and transport in discrete fracture networks. Computer Geoscience, 21, pp. 595–617. https://doi.org/10.1007/s10596-016-9606-z
36. Yuan H., Zhou D. (2010). A New Model for Predicting Inflow Performance of Fractured Horizontal Wells. SPE Western Regional Meeting, Anaheim, California, USA. https://doi.org/10.2118/133610-MS
37. Zhang H., Han G., Houeto F., Lessard R., Wang W., Li J. (2012). New Methods to Predict Inflow Performance of Multiply Fractured Horizontal Wells under Two-Phase Condition and Optimize Number of Fracture Stages. North Africa Technical Conference and Exhibition, Cairo, Egypt. https://doi.org/10.2118/152837-MS
Review
For citations:
Khamidullin M.R., Potashev K.A., Mazo A.B. Productivity of Multi-Stage Hydraulic Fractured Horizontal Wells and Methods for Its Estimation. Georesursy = Georesources. 2025;27(4):263-275. (In Russ.) https://doi.org/10.18599/grs.2025.4.6
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