Optimization of Spacing and Penetration Ratio for Infinite-Conductivity Fractures in Unconventional Reservoirs: A Section-Based Approach
- Shuai Liu (Texas A&M University) | Peter P. Valkó (Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2017
- Document Type
- Journal Paper
- 1,877 - 1,892
- 2017.Society of Petroleum Engineers
- boundary dominated state, optimal development plan, section-based method, productivity index
- 2 in the last 30 days
- 478 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
In this paper, we consider the development plan of shale gas or tight oil with multiple multistage fractured laterals in a large square drainage area that we call a “section” (usually 640 acres in the US). We propose a convenient section-based optimization of the fracture array with two integer variables, the number of columns (horizontal laterals) and rows (fractures created in a lateral), to provide some general statements regarding spacing of wells and fractures. The approach is dependent on a reliable and efficient productivity-index (PI) calculation for the boundary-dominated state (BDS). The dimensionless PI is obtained by solving a time-independent eigenvalue problem by use of the finite-element method (FEM) combined with the Richardson extrapolation.
The results of the case study demonstrate two decisive factors: the dimensionless total fracture length, related to the total amount of proppant and fracturing fluid available for the section, and the feasible range of actual fracture half-lengths, related to current fracturing-technology limitations. Under the constraint of dimensionless total fracture length, increasing the number of columns (horizontal laterals) increases the total PI but with only diminishing returns, whereas the optimal fracture-penetration ratio decreases somewhat, but is still near unity. When adding the technological constraint of a limited range of fracture half-lengths that can be routinely and reliably created, only a few choices remain admissible, and the optimal decision can be easily made. These general statements for the ideal homogeneous and isotropic formation can serve as a reference in the more-detailed optimization works. In other words, we offer a first-pass method for decision making in early stages when detailed inputs are not yet available. The information derived from the section-based optimization method and the efficient and reliable algorithm for PI calculation should help the design of multistage fracturing in shale-gas or ultralow-permeability oil formations.
|File Size||1 MB||Number of Pages||16|
Boulis, A., Jayakumar, R., and Rai, R. 2013. A New Approach for Well Spacing Optimisation and Its Application to Various Shale Gas Resources. Presented at the International Petroleum Technology Conference, Beijing, 26–28 March. IPTC-17150-MS. https://doi.org/10.2523/IPTC-17150-MS.
Burg, C. and Erwin, T. 2009. Application of Richardson Extrapolation to the Numerical Solution of Partial Differential Equations. Numer. Meth. Part. D. E. 25 (4): 810–832. https://doi.org/10.1002/num.20375.
Chen, C.-C. and Rajagopal, R. 1997. A Multiply-Fractured Horizontal Well in a Rectangular Drainage Region. SPE J. 2 (4): 455–465. SPE-37072-PA. https://doi.org/10.2118/37072-PA.
Cinco Ley, H., Samaniego V., F., and Dominguez A., N. 1978. Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture. SPE J. 18 (4): 253–264. SPE-6014-PA. https://doi.org/10.2118/6014-PA.
Eburi, S., Padmakar, A. S., Wilson, K. et al. 2014. Well Spacing Optimization of Liquid Rich Shale Plays Using Reservoir Simulation. Presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October. SPE-170833-MS. https://doi.org/10.2118/170833-MS.
Fisher, M. K., Heinze, J. R., Harris, C. D. et al. 2004. Optimizing Horizontal Completion Techniques in the Barnett Shale Using Microseismic Fracture Mapping. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 26–29 September. SPE-90051-MS. https://doi.org/10.2118/90051-MS.
Gringarten, A. C., Ramey, H. J., and Raghavan, R. 1974. Unsteady-State Pressure Distributions Created by a Well With a Single Infinite-Conductivity Vertical Fracture. SPE J. 14 (4): 347–360. SPE-4051-PA. https://doi.org/10.2118/4051-PA.
Hagoort, J. 2009. The Productivity of a Well with a Vertical Infinite-Conductivity Fracture in a Rectangular Closed Reservoir. SPE J. 14 (4): 715–720. SPE-112975-PA. https://doi.org/10.2118/112975-PA.
Hagoort, J. 2010. Production Performance of a Constant-Pressure Well in an Orthogonally Fractured Reservoir. SPE Res Eval & Eng 13 (3): 523–537. SPE-120228-PA. https://doi.org/10.2118/120228-PA.
Jahandideh, A. and Jafarpour, B. 2014. Optimization of Hydraulic Fracturing Design Under Spatially Variable Shale Fracability. Presented at the SPE Western North American and Rocky Mountain Joint Meeting, Denver, 17–18 April. SPE-169521-MS. https://doi.org/10.2118/169521-MS.
King, G. E. 2010. Thirty Years of Gas Shale Fracturing: What Have We Learned? Presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September. SPE-133456-MS. https://doi.org/10.2118/133456-MS.
Lin, Q. and Xie, R. F. 1987. Error Expansions for Finite Element Approximations and Their Applications. In Numerical Methods for Partial Differential Equations, ed. Y. Zhu and B. Guo, Chap. 6, 98–112. Berlin: Springer.
Ma, X., Plaksina, T., and Gildin, E. 2013. Optimization of Placement of Hydraulic Fracture Stages in Horizontal Wells Drilled in Shale Gas Reservoirs. Presented at the Unconventional Resources Technology Conference, Denver, 12–14 August. https://doi.org/10.1190/URTEC2013-151.
Meyer, B. R., Bazan, L. W., Jacot, R. H. et al. 2010. Optimization of Multiple Transverse Hydraulic Fractures in Horizontal Wellbores. Presented at the SPE Unconventional Gas Conference, Pittsburgh, Pennsylvania, 23–25 February. SPE-131732-MS. https://doi.org/10.2118/131732-MS.
Moghanloo, R. G., Yuan, B., Ingrahama, N. et al. 2015. Applying Macroscopic Material Balance to Evaluate Interplay Between Dynamic Drainage Volume and Well Performance in Tight Formations. J. Nat. Gas Sci. Eng. 27 (November): 466–478. https://doi.org/10.1016/j.jngse.2015.07.047.
Ozkan, E., Brown, M. L., Raghavan, R. S. et al. 2009. Comparison of Fractured Horizontal-Well Performance in Conventional and Unconventional Reservoirs. Presented at the SPE Western Regional Meeting, San Jose, California, 24–26 March. SPE-121290-MS. https://doi.org/10.2118/121290-MS.
Prats, M. 1961. Effect of Vertical Fractures on Reservoir Behavior-Incompressible Fluid Case. SPE J. 1 (2): 105–118. SPE-1575-G. https://doi.org/10.2118/1575-G.
Raghavan, R. S., Chen, C.-C., and Agarwal, B. 1997. An Analysis of Horizontal Wells Intercepted by Multiple Fractures. SPE J. 2 (3): 235–245. SPE-27652-PA. https://doi.org/10.2118/27652-PA.
Roussel, N. P. and Sharma, M. M. 2011. Optimizing Fracture Spacing and Sequencing in Horizontal-Well Fracturing. SPE Prod & Oper 26 (2): 173–184. SPE-127986-PA. https://doi.org/10.2118/127986-PA.
Russell, D. G. and Truitt, N. E. 1964. Transient Pressure Behavior in Vertically Fractured Reservoirs. J Pet Technol 16 (10): 1159–1170. SPE-967-PA. https://doi.org/10.2118/967-PA.
Soliman, M. Y., Hunt, J. L., and Azari, M. 1999. Fracturing Horizontal Wells in Gas Reservoirs. SPE Prod & Fac 14 (4): 277–283. SPE-59096-PA. https://doi.org/10.2118/59096-PA.
Soroushian, A. 2010. Pseudo Convergence and Its Implementation in Engineering Approximate Computations. Proc., 4th International Conference from Scientific Computing to Computational Engineering, Athens, 7–10 July.
Wattenbarger, R. A., El-Banbi, A. H., Villegas, M. E. et al. 1998. Production Analysis of Linear Flow Into Fractured Tight Gas Wells. Presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, 5–8 April. SPE-39931-MS. https://doi.org/10.2118/39931-MS.
Wilson, K. C. and Durlofsky, L. J. 2013. Optimization of Shale Gas Field Development Using Direct Search Techniques and Reduced-Physics Models. J. Pet. Sci. Eng. 108 (August): 304–315. https://doi.org/10.1016/j.petrol.2013.04.019.
Wolfram Research. 2016. Mathematica, Version 10.4. Champaign, Illinois: Wolfram Research Incorporated.
Yu, W. and Sepehrnoori, K. 2013. Optimization of Multiple Hydraulically Fractured Horizontal Wells in Unconventional Gas Reservoirs. Presented at the SPE Production and Operations Symposium, Oklahoma City, Oklahoma, 23–26 March. SPE-164509-MS. https://doi.org/10.2118/164509-MS.