Using an Experiment/Simulation-Integrated Approach To Investigate Fracture-Conductivity Evolution and Non-Darcy Flow in a Proppant-Supported Hydraulic Fracture
- Ming Fan (Virginia Polytechnic Institute and State University (Virginia Tech)) | James McClure (Virginia Polytechnic Institute and State University (Virginia Tech)) | Yanhui Han (Aramco Research Center–Houston) | Nino Ripepi (Virginia Polytechnic Institute and State University (Virginia Tech)) | Erik Westman (Virginia Polytechnic Institute and State University (Virginia Tech)) | Ming Gu (West Virginia University) | Cheng Chen (Virginia Polytechnic Institute and State University (Virginia Tech))
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- August 2019
- Document Type
- Journal Paper
- 1,912 - 1,928
- 2019.Society of Petroleum Engineers
- discrete element method, non-Darcy, lattice Boltzmann, fracture conductivity, proppant
- 17 in the last 30 days
- 254 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Optimizing proppant-pack conductivity in a hydraulic fracture is of critical importance to sustaining effective and economical production of petroleum hydrocarbons. In this study, a hybrid, experiment/simulation-integrated workflow, which combines the discrete element method (DEM) and the lattice Boltzmann (LB) method with laboratory-measured load-embedment correlations, was developed to advance the understanding of fracture-conductivity evolution from partial-monolayer to multilayer concentrations. The influence of compressive stress and proppant-diameter heterogeneity on non-Darcy flow behaviors was also investigated. The DEM method was used to simulate effective-stress increase and the resultant proppant-particle compaction and rearrangement. Proppant-embedment distance was then determined using an empirical correlation obtained by fitting experimental data. The final pore structure of the proppant pack was imported into the LB simulator as interior boundary conditions of fluid-flow modeling in the calculation of time-dependent permeability of the proppant pack. To validate the integrated workflow, proppant-pack conductivity as a function of increasing proppant concentration was simulated and then compared with laboratory data. Good agreement was observed between the workflow-derived and laboratory-measured fracture-conductivity vs. proppant-concentration curves. Furthermore, the role of proppant size, size heterogeneity, and closure pressure on the optimal partial-monolayer proppant concentration was investigated. The optimal partial-monolayer proppant concentration has important engineering implications, because one can achieve a considerable fracture conductivity using a partial-monolayer proppant structure, which has much lower material costs compared with the conventional multilayer proppant structures. To investigate the effect of non-Darcy flow on fracture conductivity, three proppant packs with the same average diameter but different diameter distributions were generated. Specifically, the coefficient of variation (COV) of diameter, defined as the ratio of standard deviation of diameter to mean diameter, was used to characterize the heterogeneity of particle size. The results of this research provide fundamental insights into the multiphysics processes regulating the conductivity evolution of a proppant-supported hydraulic fracture, as well as the role of compressive stress and proppant-size heterogeneity in non-Darcy flows.
|File Size||1 MB||Number of Pages||17|
Aven, N. K., Weaver, J., Loghry, R. et al. 2013. Long-Term Dynamic Flow Testing of Proppants and Effect of Coatings. Presented at the SPE European Formation Damage Conference & Exhibition, Noordwijk, The Netherlands, 5–7 June. SPE-165118-MS. https://doi.org/10.2118/165118-MS.
Balhoff, M. T. and Wheeler, M. F. 2009. A Predictive Pore-Scale Model for Non-Darcy Flow in Porous Media. SPE J. 14 (4): 1–9. SPE-110838-PA. https://doi.org/10.2118/110838-PA.
Barree, R. D., Cox, S. A., Barree, V. L. et al. 2003. Realistic Assessment of Proppant Pack Conductivity for Material Selection. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 5–8 October. SPE-84306-MS. https://doi.org/10.2118/84306-MS.
Bestaoui-Spurr, N. and Hudson, H. 2017. Ultra-Light Weight Proppant and Pumping Design Lead to Greater Conductive Fracture Area in Unconventional Reservoirs. Presented at the SPE Oil and Gas India Conference and Exhibition, Mumbai, India, 4–6 April. SPE-185435-MS. https://doi.org/10.2118/185435-MS.
Bolintineanu, D. S., Rao, R. R., Lechman, J. B. et al. 2017. Simulations of the Effects of Proppant Placement on the Conductivity and Mechanical Stability of Hydraulic Fractures. Int J Rock Mech Min Sci 100:188–198. https://doi.org/10.1016/j.ijrmms.2017.10.014.
Brannon, H. D., Malone, M. R., Rickards, A. R. et al. 2004. Maximizing Fracture Conductivity With Proppant Partial Monolayers: Theoretical Curiosity or Highly Productive Reality? Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 26–29 September. SPE-90698-MS. https://doi.org/10.2118/90698-MS.
Chen, H., Chen, S., and Matthaeus, W. H. 1992. Recovery of the Navier–Stokes Equations Using a Lattice-Gas Boltzmann Method. Phys Rev A 45 (8): R5339–R5342. https://doi.org/10.1103/PhysRevA.45.R5339.
Chen, S. and Doolen, G. D. 1998. Lattice Boltzmann Method for Fluid Flows. Annu Rev Fluid Mech 30: 329–364. https://doi.org/10.1146/annurev.fluid.30.1.329.
Chen, C., Hu, D., Westacott, D. et al. 2013. Nanometer-Scale Characterization of Microscopic Pores in Shale Kerogen by Image Analysis and Pore-Scale Modeling. Geochem Geophys Geosyst 14 (10): 4066–4075. https://doi.org/10.1002/ggge.20254.
Chen, C., Lau, B. L. T., Gaillard, J. F. et al. 2009a. Temporal Evolution of Pore Geometry, Fluid Flow, and Solute Transport Resulting From Colloid Deposition. Water Resour Res 45 (6): W06416. https://doi.org/10.1029/2008WR007252.
Chen, C., Martysevich, V., O’Connell, P. et al. 2015. Temporal Evolution of the Geometrical and Transport Properties of a Fracture/Proppant System Under Increasing Effective Stress. SPE J. 20 (3): 527–535. SPE-171572-PA. https://doi.org/10.2118/171572-PA.
Chen, C., Packman, A. I., and Gaillard, J. F. 2008. Pore-Scale Analysis of Permeability Reduction Resulting From Colloid Deposition. Geophys Res Lett 35 (7): L07404. https://doi.org/10.1029/2007GL033077.
Chen, C., Packman, A. I., and Gaillard, J. F. 2009b. Using X-ray Micro-Tomography and Pore-Scale Modeling to Quantify Sediment Mixing and Fluid Flow in a Developing Streambed. Geophys Res Lett 36: L08403 https://doi.org/10.1029/2009GL037157.
Chen, C., Wang, Z., Majeti, D. et al. 2016. Optimization of Lattice Boltzmann Simulation With Graphics-Processing-Unit Parallel Computing and the Application in Reservoir Characterization. SPE J. 21 (4): 1425–1435. SPE-179733-PA. https://doi.org/10.2118/179733-PA.
Cundall, P. A. 1971. A Computer Model for Simulating Progressive Large-Scale Movements in Blocky Rock Systems. Presented at the Symposium of the International Society for Rock Mechanics, Society for Rock Mechanics, France.
Cundall, P. A. and Strack, O. D. L. 1979. A Discrete Numerical Model for Granular Assemblies. Geotechnique 29 (1): 47–65. https://doi.org/10.1680/geot.19188.8.131.52.
Darin, S. R. and Huitt, J. L. 1960. Effect of a Partial Monolayer of Propping Agent on Fracture Flow Capacity. In Petroleum Transactions, AIME, Vol. 219, 31–37, SPE-1291-G. Richardson, Texas: Society of Petroleum Engineers.
Dye, A. L., McClure, J. E., Miller, C. T. et al. 2013. Description of Non-Darcy Flows in Porous Medium Systems. Phys Rev E 87 (3): 033012. https://doi.org/10.1103/PhysRevE.87.033012.
Economides, M. and Nolte, K. 2000. Reservoir Stimulation, third edition. Hoboken, New Jersey: John Wiley and Sons.
Fan, M., Han, Y., McClure, J. et al. 2017a. Hydraulic Fracture Conductivity as a Function of Proppant Concentration Under Various Effective Stresses: From Partial Monolayer to Multilayer Proppants. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Austin, Texas, USA, 24–26 July. URTEC-2693347-MS. https://doi.org/10.15530/URTEC-2017-2693347.
Fan, M., McClure, J., Han, Y. et al. 2017b. Interaction Between Proppant Packing, Reservoir Depletion, and Fluid Flow in Hydraulic Fractures. Presented at the Offshore Technology Conference, Houston, Texas, 1–4 May. OTC-27907-MS. https://doi.org/10.4043/27907-MS.
Fan, M., McClure, J., Han, Y. et al. 2018. Interaction Between Proppant Compaction and Single-/Multiphase Flows in a Hydraulic Fracture. SPE J. 23 (4): 1–14. SPE-189985-PA. https://doi.org/10.2118/189985-PA.
Forchheimer, P. 1901. Wasserbewegung Durch Boden. Zeit Ver Deutsch Ing 45: 1781–1788.
Gaurav, A., Dao, E. K., and Mohanty, K. K. 2010. Ultra-Lightweight Proppants for Shale Gas Fracturing. Presented at the Tight Gas Completions Conference, San Antonio, Texas, 2–3 November. SPE-138319-MS. https://doi.org/10.2118/138319-MS.
Ginzburg, I. 2008. Consistent Lattice Boltzmann Schemes for the Brinkman Model of Porous Flow and Infinite Chapman–Enskog Expansion. Phys Rev E 77: 066704. https://doi.org/10.1103/PhysRevE.77.066704.
Ginzburg, I., d’Humieres, D., and Kuzmin, A. 2010. Optimal Stability of Advection-Diffusion Lattice Boltzmann Models With Two Relaxation Times for Positive/Negative Equilibrium. J Stat Phys 139 (6): 1090–1143. https://doi.org/10.1007/s10955-010-9969-9.
Grunau, D., Chen, S., and Eggert, K. 1993. A Lattice Boltzmann Model for Multiphase Fluid Flows. Phys Fluids A 5: 2557–2562. https://doi.org/10.1063/1.858769.
Gu, M., Dao, E., and Mohanty, K. K. 2015. Investigation of Ultra-Light Weight Proppant Application in Shale Fracturing. Fuel 150: 191–201. https://doi.org/10.1016/j.fuel.2015.02.019.
Gu, M., Fan, M., and Chen, C. 2017. Proppant Optimization for Foam Fracturing in Shale and Tight Reservoirs. Presented at the SPE Unconventional Resources Conference, Calgary, Alberta, Canada, 15–16 February. SPE-185071-MS. https://doi.org/10.2118/185071-MS.
Gu, M. and Mohanty, K. K. 2014. Effect of Foam Quality on Effectiveness of Hydraulic Fracturing in Shales. Int J Rock Mech Min Sci 70: 273–285. https://doi.org/10.1016/j.ijrmms.2014.05.013.
Guo, J. C., Lu, C., Zhao, J. et al. 2008. Experimental Research on Proppant Embedment. J China Coal Soc 33 (6): 661–664.
Han, Y. and Cundall, P. A. 2011. Lattice Boltzmann Modeling of Pore-Scale Fluid Flow Through Idealized Porous Media. Int J Numer Methods Fluids 67 (11): 1720–1734. https://doi.org/10.1002/fld.2443.
Han, Y. and Cundall, P. A. 2013. LBM-DEM Modeling of Fluid-Solid Interaction in Porous Media. Int J Numer Anal Meth Geomech 37 (10): 1391–1407. https://doi.org/10.1002/nag.2096.
Howard, G. C. and Fast, C. R. 1970. Hydraulic Fracturing. Richardson, Texas: Society of Petroleum Engineers, Inc.
Huitt, J. L. and McGlothlin, B. B. 1958. The Propping of Fractures in Formations Susceptible to Propping-Sand Embedment. Drill & Prod Prac 115–123. API-58-115.
Inamuro, T., Yoshino, M., and Ogino, F. 1999. Lattice Boltzmann Simulation of Flows in a Three-Dimensional Porous Structure. Int J Numer Methods Fluids 29 (7): 737–748. https://doi.org/10.1002/(SICI)1097-0363(19990415)29:7<737::AID-FLD813>3.0.CO;2-H.
Itasca Consulting Group, Inc. 2008. PFC3D – Particle Flow Code in 3 Dimensions, Version 4.0 User’s Manual. Minneapolis: Itasca.
Lacy, L. L., Rickards, A. R., and Bilden, D. M. 1998. Fracture Width and Embedment Testing in Soft Reservoir Sandstone. SPE Drill & Compl 13 (1): 1–5. SPE-36421-PA. https://doi.org/10.2118/36421-PA.
Li, K. W., Gao, Y. P., Lyu, Y. C. et al. 2015. New Mathematical Models for Calculating Proppant Embedment and Fracture Conductivity. SPE J. 20 (3): 496–507. SPE-155954-PA. https://doi.org/10.2118/155954-PA.
Li, Y. and Huang, P. 2008. A Coupled Lattice Boltzmann Model for Advection and Anisotropic Dispersion Problem in Shallow Water. Adv Water Resour 31 (12): 1719–1730. https://doi.org/10.1016/j.advwatres.2008.08.008.
Liang, F., Sayed, M., Al-Muntasheri, G. A. et al. 2016. A Comprehensive Review on Proppant Technologies. Petroleum 2 (1): 26–39. https://doi.org/10.1016/j.petlm.2015.11.001.
Macini, P., Mesini, E. N., and Viola, R. 2008. Non-Darcy Flow: Laboratory Measurements in Unconsolidated Porous Media. Presented at the Europe/EAGE Conference and Exhibition, Rome Italy, 9–12 June. SPE-113772-MS. https://doi.org/10.2118/113772-MS.
McClure, J. E., Prins, J. F., and Miller, C. T. 2014. A Novel Heterogeneous Algorithm to Simulate Multiphase Flow in Porous Media on Multicore CPUGPU Systems. Comput Phys Commun 185 (7): 1865–1874. https://doi.org/10.1016/j.cpc.2014.03.012.
Milton-Tayler, D. 1993. Non-Darcy Gas Flow: From Laboratory Data to Field Prediction. Presented at the SPE Gas Technology Symposium, Calgary, Alberta, Canada, 28–30 June. SPE-26146-MS. https://doi.org/10.2118/26146-MS.
Miskimins, J. L., Lopez, H. D. J., and Barree, R. D. 2005. Non-Darcy Flow in Hydraulic Fractures: Does It Really Matter? Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 9–12 October. SPE-96389-MS. https://doi.org/10.2118/96389-MS.
Newman, M. S. and Yin, X. 2013. Lattice Boltzmann Simulation of Non-Darcy Flow in Stochastically Generated 2D Porous Media Geometries. SPE J. 18 (1): 1–15. SPE-146689-PA. https://doi.org/10.2118/146689-PA.
Palisch, T. T., Duenckel, R. J., Bazan, L. W. et al. 2007. Determining Realistic Fracture Conductivity and Understanding Its Impact on Well Performance—Theory and Field Examples. Presented at the SPE Hydraulic Fracturing Technology Conference, Texas, 29–31 January. SPE-106391-MS. https://doi.org/10.2118/106301-MS.
Parker, M. A., Ramurthy, K., and Sanchez, P. W. 2012. New Proppant for Hydraulic Fracturing Improves Well Performance and Decreases Environmental Impact of Hydraulic Fracturing Operations. Presented at the SPE Eastern Regional Meeting, Lexington, Kentucky, 3–5 October. SPE-161344-MS. https://doi.org/10.2118/161344-MS.
Raysoni, N. and Weaver, J. 2013. Long-Term Hydrothermal Proppant Performance. SPE Prod & Oper 28 (4): 1–13. SPE-150669-PA. https://doi.org/10.2118/150669-PA.
Schubarth, S. and Milton-Tayler, D. 2004. Investigating How Proppant Packs Change Under Stress. Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 26–29 September. SPE-90562-MS. https://doi.org/10.2118/90562-MS.
Succi, S. 2001. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. New York: Oxford University Press.
Succi, S., Benzi, R., and Higuera, F. 1991. The Lattice Boltzmann Equation: A New Tool for Computational Fluid-Dynamics. Physica D 47: 219–230. https://doi.org/10.1016/0167-2789(91)90292-H.
Volk, L. J., Raible, C. J., Carroll, H. B. et al. 1981. Embedment of High Strength Proppant Into Low-Permeability Reservoir Rock. Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado, 27–29 May. SPE-9867-MS. https://doi.org/10.2118/9867-MS.
Weaver, J. D., Rickman, R. D., Luo, H., et al. 2009. A Study of Proppant Formation Reactions. Presented at the International Symposium on Oilfield Chemistry, The Woodlands, Texas, 20–22 April. SPE-121465-MS. https://doi.org/10.2118/121465-MS.
Ye, Z. and Ghassemi, A. 2016. Deformation Properties of Saw-Cut Fractures in Barnett, Mancos and Pierre Shales. Presented at the 50th US Rock Mechanics/Geomechanics Symposium, Houston, Texas. ARMA-2016-420.
Zeng, Z. and Grigg, R. 2006. A Criterion for Non-Darcy Flow in Porous Media. Transp Porous Media 63 (1): 57–69. https://doi.org/10.1007/s11242-005-2720-3.
Zhang, F., Zhu, H., Zhou, H. at al. 2017. Discrete-Element Method/Computational-Fluid-Dynamics Coupling Simulation of Proppant Embedment and Fracture Conductivity After Hydraulic Fracturing. SPE J. 22 (2): 1–13. SPE-185172. https://doi.org/10.2118/185172-PA.