Flow Interference Between Hydraulic Fractures
- Ruud Weijermars (Texas A&M University) | Arnaud van Harmelen (Texas A&M University) | Lihua Zuo (Texas A&M University) | Ibere Nascentes Alves (Texas A&M University) | Wei Yu (Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- November 2018
- Document Type
- Journal Paper
- 942 - 960
- 2018.Society of Petroleum Engineers
- Drainage contours, Stimulated rock volume, Visualization, Flow interference, Streamline
- 20 in the last 30 days
- 325 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
The flow toward hydraulic fractures is visualized at high resolution using a newly developed analytical streamline simulator that is based on complex potentials. Drainage contours show progressive fluid recovery from the stimulated rock volume (SRV). The method plots streamlines, time-of-flight contours, velocity-field contours, and pressure distribution around fractured wells. Independent simulations with a commercial reservoir simulator confirm that visualizations with complex potentials are accurate, and that the latter method provides high-resolution images of the pressure and flow fields around individual fractures. Contours for the drained rock volume (DRV) that are based on particle-velocity tracking outline the actual region drained by a well through its fractures. First, matrix drainage by two-fracture and three-fracture clusters is studied in detail. Flow-separation surfaces between two clustered fractures (with equal length and flux) are always straight, creating planes of symmetry between adjacent drainage regions. Clusters of three fractures develop curved-flow-separation surfaces, convex toward the inner fracture. For fracture spacing less than four times total fracture length, drainage of the central region of the three-fracture clusters slows down because of flow interference, which confirms earlier findings that production gains become insignificant above certain fracture length/spacing ratios. Next, the analysis shows the flow field, drainage contours, velocity contours, and pressure distribution for a horizontal, synthetic well with 11 transversal, kinked fractures. A final section shows a brief example of application to a field case.
|File Size||3 MB||Number of Pages||19|
Cinco-Ley, H. 1974. Unsteady-State Pressure Distributions Created by a Slanted Well, or a Well With an Inclined Fracture. PhD thesis, Stanford University, Stanford, California (January).
Cipolla, C. L. and Wallace, J. 2014. Stimulated Reservoir Volume: A Misapplied Concept? Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 4–6 February. SPE-168596-MS. https://doi.org/10.2118/168596-MS.
Datta-Gupta, A. and King, M. 2007. Streamline Simulation: Theory and Practice, Vol. 11. Richardson, Texas: Textbook Series, Society of Petroleum Engineers.
Duong, A. M. 2011. Rate-Decline Analysis for Fracture-Dominated Shale Reservoirs. SPE Res Eval & Eng 14 (3): 377–387. SPE-137748-PA. https://doi.org/10.2118/137748-PA.
Gringarten, A. C. and Ramey, H. J.Jr 1973. The Use of Source and Green’s Functions in Solving Unsteady-Flow Problems in Reservoirs. SPE J. 13 (5): 285–296. SPE-3818-PA. https://doi.org/10.2118/3818-PA.
Hagoort, J. 2006. Stabilized Productivity of a Hydraulically Fractured Well Producing at Constant Pressure. SPE J. 11 (1): 120–131. SPE-88960-PA. https://doi.org/10.2118/88960-PA.
Khanal, A. and Weijermars, R. 2018. Analysis of Pressure Depletion and Drained Rock Volume (DRV) for Parent and Child Wells (Eagle Ford Formation). Journal of Petroleum Science and Engineering (in press).
Kucuk, F. and Brigham, W. E. 1979. Transient Flow in Elliptical Systems. SPE J. 19 (6): 401–410. SPE-7488-PA. https://doi.org/10.2118/7488-PA.
Lalehrokh, F. and Bouma, J. 2014. Well Spacing Optimization in Eagle Ford. Presented at the SPE/CSUR Unconventional Resources Conference–Canada, Calgary, 30 September–2 October. SPE-171640-MS. https://doi.org/10.2118/171640-MS.
Lim, J., Zuo, L., and King, M. J. 2014. Development of Data Models and Velocity Interpolation Methods for Streamline Trajectories on Unstructured Grids. Proc., 11th World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain, 20–25 July.
MathWorks. 2018. MATLAB, https://www.mathworks.com/products/matlab.html.
Nelson, R., Zuo, L., Weijermars, R. et al. 2018. Outer Boundary Effects in a Petroleum Reservoir (Quitman Field, East Texas): Applying Improved Analytical Methods for Modelling and Visualization of Flood Displacement Fronts. Journal of Petroleum Science and Engineering 166 (July): 1018–1041. https://doi.org/10.1016/j.petrol.2018.03.006.
Olver, P. J. 2012. Introduction to Partial Differential Equations (in preparation). In Complex Analysis and Conformal Mappings, Chapter 7, http://www.math.umn.edu/~olver/pd_/cm.pdf.
Parsegov, S. G., Nandlal, K., Schechter, D. S. et al. 2018. Physics-Driven Optimization of Drained Rock Volume for Multistage Fracturing: Field Example From the Wolfcamp Formation, Midland Basin. Presented at the Unconventional Resources Technology Conference, Houston, 23–25 July. URTEC-2879159-MS. https://doi.org/10.15530/urtec-2018-2879159.
Pollock, D. W. 1988. Semianalytical Computation of Path Lines for Finite-Difference Models. Groundwater 26 (6): 743–750. https://doi.org/10.1111/j.1745-6584.1988.tb00425.x.
Pólya, G. and Latta, G. 1974. Complex Variables. New York: Wiley.
Potter, H. D. P. 2008. On Conformal Mappings and Vector Fields. Senior thesis, Marietta College, Marietta, Ohio.
Sato, K. 2015. Complex Analysis for Practical Engineering. Switzerland: Springer. https://doi.org/10.1007/978-3-319-13063-7.
Weijermars, R. 2014. Visualization of Space Competition and Plume Formation With Complex Potentials for Multiple Source Flows: Some Examples and Novel Application to Chao Lava Flow (Chile). Journal of Geophysical Research 119 (3): 2397–2414. https://doi.org/10.1002/2013JB010608.
Weijermars, R. 2015. Salt Sheet Coalescence in the Walker Ridge Region (Gulf of Mexico): Insights From Analytical Models. Tectonophysics 640–641 (January): 39–52. https://doi.org/10.1016/j.tecto.2014.11.018.
Weijermars, R. and Schmeling, H. 1986. Scaling of Newtonian and Non-Newtonian Fluid Dynamics Without Inertia for Quantitative Modelling of Rock Flow Due To Gravity (Including the Concept of Rheological Similarity). Phys. Earth Planet. Inter. 43 (4): 316–330. https://doi.org/10.1016/0031-9201(86)90021-X.
Weijermars, R. and van Harmelen, A. 2015. Quantifying Velocity, Strain Rate and Stress Distribution in Coalescing Salt Sheets for Safer Drilling. Geophysical Journal International 200 (3): 1483–1502. https://doi.org/10.1093/gji/ggu405.
Weijermars, R. and van Harmelen, A. 2016. Breakdown of Doublet Re-Circulation and Direct Line Drives by Far-Field Flow: Implications for Geothermal and Hydrocarbon Well Placement. Geophysical Journal International 206 (1): 19–47. https://doi.org/10.1093/gij/ggw135.
Weijermars, R. and Van Harmelen, A. 2017. Advancement of Sweep Zones in Waterflooding: Conceptual Insight and Flow Visualizations of Oil-Withdrawal Contours and Waterflood Time-of-Flight Contours Using Complex Potentials. Journal of Petroleum Exploration and Production Technology 7 (3): 785–812. https://doi.org/10.1007/s13202-016-0294-y.
Weijermars, R., and van Harmelen, A. 2018. Shale Reservoir Drainage Visualized for a Wolfcamp Well (Midland Basin, West Texas, USA). Energies 2018 11 (7): 1665. https://doi.org/10.3390/en11071665.
Weijermars, R., Dooley, T. P., Jackson, M. P. A. et al. 2014. Rankine Models for Time-Dependent Gravity Spreading of Terrestrial Source Flows Over Sub-Planar Slopes. Journal of Geophysical Research 119 (9): 7353–7388. https://doi.org/10.1002/2014JB011315.
Weijermars, R., van Harmelen, A., and Zuo, L. 2016. Controlling Flood Displacement Fronts Using a Parallel Analytical Streamline Simulator. Journal of Petroleum Science and Engineering 139 (March): 23–42. https://doi.org/10.1016/j.petrol.2015.12.002.
Weijermars, R., van Harmelen, A., Zuo, L. et al. 2017a. High-Resolution Visualization of Flow Interference Between Frac Clusters (Part 1): Model Verification and Basic Cases. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Austin, Texas, USA, 24–26 July. URTEC-2670073A-MS. https://doi.org/10.15530/URTEC-2017-2670073.
Weijermars, R., van Harmelen, A., and Zuo, L. 2017b. Flow Interference Between Frac Clusters (Part 2): Field Example From the Midland Basin (Wolfcamp Formation, Spraberry Trend Field) With Implications for Hydraulic Fracture Design. Presented at the Unconventional Resources Technology Conference, Austin, Texas, 24–26 July. URTEC-2670073B-MS. https://doi.org/10.15530/URTEC-2017-2670073.
Weijermars, R. and Nascentes Alves, I. 2018. High-Resolution Visualization of Flow Velocities New Frac-Tips and Flow Interferences of Multi-Fracked Eagle Ford Wells, Brazos County, Texas. Journal of Petroleum Science and Engineering 165 (June): 946–961. https://doi.org/10.1015/j.petrol.2018.02.033.
Yu, W. 2015. A Comprehensive Model for Simulation of Gas Transport in Shale Formation With Complex Hydraulic Fracture Geometry. Presented at SPE Annual Technical Conference and Exhibition, Houston, 28–30 September. SPE-178747-STU. https://doi.org/10.2118/178747-STU.
Yu, W., Wu, K., Zuo, L. et al. 2016. Physical Models for Inter-Well Interference in Shale Reservoirs: Relative Impacts of Fracture Hits and Matrix Permeability. Presented at the Unconventional Resources Technology Conference, San Antonio, Texas, 1–3 August 2016. https://doi.org/10.15530/URTEC-2016-2457663.
Zuo, L. and Weijermars, R. 2017. Rules for Flight Paths and Time of Flight for Flows in Porous Media With Heterogeneous Permeability and Porosity. Geofluids 2017, Article ID 5609571, 18 pages. https://doi.org/10.1155/2017/5609571.
Zuo, L., Lim, J., Chen, R. et al. 2016. Efficient Calculation of Flux Conservative Streamline Trajectories on Complex and Unstructured Grids. Presented at the 78th EAGE Conference and Exhibition, 31 May. https://doi.org/10.3997/2214-4609.201600779.