Interaction Between Proppant Compaction and Single-/Multiphase Flows in a Hydraulic Fracture
- Ming Fan (Virginia Tech) | James McClure (Virginia Tech) | Yanhui Han (Aramco Research Center—Houston) | Zhe Li (Australia National University) | Cheng Chen (Virginia Tech)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- August 2018
- Document Type
- Journal Paper
- 1,290 - 1,303
- 2018.Society of Petroleum Engineers
- Discrete Element, Hydraulic Fracturing, Proppant, Multiphase Flow, Lattice Boltzmann
- 7 in the last 30 days
- 342 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Understanding proppant-transport and -deposition patterns in a hydraulic fracture is vital for effective and economical production of petroleum hydrocarbons. In this research, a numerical-modeling approach, combining the discrete-element method (DEM) with single-/multiphase lattice Boltzmann (LB) simulation, was adopted to advance understanding of the interaction between reservoir depletion, proppant-particle compaction, and single-/multiphase flows in a hydraulic fracture. DEM was used to simulate effective-stress increase and the resultant proppant-particle movement and rearrangement during the process of reservoir depletion caused by hydrocarbon production. Simulated pore structure of the proppant pack was extracted and used as boundary conditions in the LB simulation to calculate the time-dependent permeability of the proppant pack. We first validated the DEM-LB numerical work flow, and the simulated proppant-pack permeabilities as functions of effective stress were in good agreement with laboratory measurements. Furthermore, three proppant packs with the same average particle diameter but different diameter distributions were generated to study the role of proppant-size heterogeneity (variation in particle diameter). Specifically, we used the coefficient of variation (COV) of diameter, defined as the ratio of standard deviation of diameter to mean diameter, to characterize the heterogeneity of particle size. We obtained proppant-pack porosity, permeability, and fracture-width reduction (closure distance) as functions of effective stress. Under the same effective stress, a proppant pack with a higher diameter COV had lower porosity and permeability and larger fracture-width reduction. This was because the high diameter COV gave rise to a wider diameter distribution of proppant particles; smaller particles were compressed into the pore space between larger particles with increasing stress, leading to larger closure distance and lower porosity and permeability. With multiphase LB simulation, relative permeability curves were obtained, which are critical for larger-scale reservoir simulations under various effective stresses. The relative permeability of the oil phase was more sensitive to changes in geometry and stress, compared with the wetting phase. This was because the oil phase occupied larger pores; compaction of the proppant pack affected the structure of the pores, because the pores were farther from the grain contacts and thus more susceptible to collapse. It is also interesting to note that when effective stress increased continuously, oil relative permeability increased first and then decreased. This nonmonotonic behavior was the result of the nonmonotonic development of pore structure and oil connectivity under increasing stress.
|File Size||1 MB||Number of Pages||14|
Armstrong, R T., McClure, J. E., Berrill, M. A. et al. 2016. Beyond Darcy’s Law: The Role of Phase Topology and Ganglion Dynamics for Two-Fluid Flow. Physical Review E 94 (4): 043113. https://doi.org/10.1103/PhysReveE.94.043113.
Armstrong, R. T., McClure, J. E., Berill, M. A. et al. 2017. Flow Regimes During Immiscible Displacement. Petrophysics 58 (1): 10–18. SPWLA-2017-v58n1a1.
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, 5–8 October. SPE-84306-MS. https://doi.org/10.2118/84306-MS.
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, 26–29 September. SPE-90698-MS. https://doi.org/10.2118/90698-MS.
CARBOHSP Technical Data Sheet. 2015. CARBO Ceramics Inc. http://www.carboceramics.com/getattachment/c14298e6-f68a-4f27-821a-cab71f9fa061.
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., Packman, A. I., and Gaillard, J. F. 2008. Pore-Scale Analysis of Permeability Reduction Resulting From Colloid Deposition. Geophysical Research Letters 35: L07404. https://doi.org/10.1029/2007GL033077.
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 Resources Research 45: W06416. https://doi.org/10.1029/2008WR007252.
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. Geophysical Research Letters 36: L08403. https://doi.org/10.1029/2009GL037157.
Chen, C., Zeng, L., and Shi, L. 2013a. Continuum-Scale Convective Mixing in Geological CO2 Sequestration in Anisotropic and Heterogeneous Saline Aquifers. Advances in Water Resources 53: 175–187. https://doi.org/10.1016/j.advwatres.2012.10.012.
Chen, C., Hu, D., Westacott, D. et al. 2013b. Nanometer-Scale Characterization of Microscopic Pores in Shale Kerogen by Image Analysis and Pore-Scale Modeling. Geochemistry, Geophysics, Geosystems 14 (10): 4066-4075. https://doi.org/10.1002/ggge.20254.
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., 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 ComputerModel for Simulating Progressive Large-ScaleMovements in Blocky Rock Systems. In Proc. Int. Symp. Int. RockMech. 2 (8).
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.19126.96.36.199.
Daneshy A. 2009. Factors Controlling the Vertical Growth of Hydraulic Fractures. Presented at the SPE Hydraulic-Fracturing Technology Conference, The Woodlands, Texas. 19–21 January. SPE-118789-MS. https://doi.org/10.2118/118789-MS.
Darin, S. R. and Huitt, J. L. 1960. Effect of a Partial Monolayer of Propping Agent on Fracture Flow Capacity. Trans. of the American Institute of Mining and Metallurgical Engineers. 219 (3): 31–37.
Dong, H. and Blunt, M. J. 2009. Pore-Network Extraction From Micro-Computerized-Tomography Images. Phys. Rev. E 80 (3): 036307. https://doi.org/10.1103/PhyRevE.80.036307.
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.
Gaurav, A., Dao, E. K., and Mohanty, K. K. 2012. Evaluation of Ultralight-Weight Proppants for Shale Fracturing. J. Petrol. Sci. Eng. 92: 82–88. https://doi.org/10.1016/j.petrol.2012.06.010.
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., Fan, M., and Chen, C. 2017. Proppant Optimization for Foam Fracturing in Shale and Tight Reservoirs. Presented at the SPE Canada Unconventional Resources Conference, Calgary, 15–16 February. SPE-185071-MS. https://doi.org/10.2118/185071-MS.
Gustensen, A. K., Rothman, D. H., Zaleski, S. et al. 1991. Lattice Boltzmann Model of Immiscible Fluids. Physical Review A 43: 4320–4327. https://doi.org/10.1103/PhysRevA.43.4320.
Han, Y. and Cundall, P. A. 2011. Lattice Boltzmann Modeling of Pore-Scale Fluid Flow Through Idealized Porous Media. Int. J. Num. Meth. 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.
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: 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 Three Dimensions, Version 4.0 User’s Manual. Minneapolis: Itasca.
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.
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. Computer Physics Communications 185 (7): 1865–1874. https://doi.org/10.1016.j.cpc.2014.03.012.
Pan, C., Luo, L., and Miller, C.T. 2006. An Evaluation of Lattice Boltzmann Schemes for Porous Medium Flow Simulation. Computers and Fluids 35 (8): 898–909. https://doi.org/10.1016/j.compfluid.2005.03.008.
Ramstad, T., Idowu, N., Nardi, C. et al. 2012. Relative Permeability Calculations From Two-Phase Flow Simulations Directly on Digital Images of Porous Rocks. Transport in Porous Media 94 (2): 487–504. https://doi.org/10.1007/s11242-011-9877-8.
Sheppard, A. P., Sok, R. M., and Averdunk, H. 2005. Improved Pore Network Extraction Methods. Presented at the International Symposium of the Society of Core Analysts, Toronto, Canada, 21–25 August. SCA2005-20.
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.
Succi, S. 2001. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. New York: Oxford University Press.
Terracina, J. M., Turner, J. M., Collins, D. H. et al. 2010. Proppant Selection and Its Effect on the Results of Fracturing Treatments Performed in Shale Formations. Presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September. SPE-135502-MS. https://doi.org/10.2118/135502-MS.
Yang, F., Hingerl, F., Xiao, X. et al. 2015. Extraction of Pore-Morphology and Capillary Pressure Curves of Porous Media From Synchrotron-Based Tomography Data. Sci. Rep. 5: 10635. https://doi.org/10.1038/srep10635.
Zhang, D., Zhang, R., Chen, S. et al. 2000. Pore Scale Study of Flow in Porous Media: Scale Dependency, REV, and Statistical REV. Geophys. Res. Lett. 27 (8): 1195–1198. https://doi.org/10.1029/1999GL011101.
Zhang, F., Zhu, H., Zhou, H. et al. 2017. Discrete-Element-Method/Computational-Fluid-Dynamics Coupling Simulation of Proppant Embedment and Fracture Conductivity After Hydraulic Fracturing. SPE J. 22 (2): 632–644. SPE-185172-PA. https://doi.org/10.2118/185172-PA.