Skip to main content
SpringerLink
Log in

Validation and Application of a Three-Dimensional Model for Simulating Proppant Transport and Fracture Conductivity

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

Hydraulically fractured well productivity greatly depends on fracture conductivity, which itself is dictated by proppant transport and placement. To guide engineering design and evaluate performance of proppant placement, a full understanding of the underlying physics and robust numerical models are needed. This paper introduces a continuum approach for simulating the transport of multiple fluids and proppant particles within hydraulic fractures. To achieve computational efficiency, this proppant model is developed based on the assumption of multi-component single phase flow and captures proppant settling, hindering effects, proppant-bed erosion and transport. Inter-particle stresses and collisions are not numerically calculated but represented through empirical correlations to include the effects of particle clustering and hindered settling. This model couples the fluid phase and particle phase through the slip velocity, which is governed by particle settling, particle–particle interaction and fluid-particle drag forces. The presented proppant model is validated by comparing numerical results with experimental data. With the calibrated simulation, the modeling capabilities on fracturing treatment design are demonstrated through sensitivity analysis and field-scale applications. Moreover, based on proppant placement and deformation, a generic model is applied to forecast fracture conductivity in different scenarios. As illustrated in this study, this coupled three-dimensional model is capable of simulating proppant placement and fracture conductivity under various operational conditions. This model can be broadly applied to improve fracturing design in various formations, including tight sandstone, shale, coal bed methane and carbonate reservoirs.

Highlights

  • To achieve computational efficiency, we introduce a continuum approach for simulating the transport of multiple fluids and proppant particles.

  • In this new model, several underlying mechanisms are considered to highlight the coupling between proppant transport and fluid flow.

  • The modelling predictions on proppant transport and distribution show a good agreement with the reported experimental data.

  • Using the model calibrated to lab tests, the modeling capability is demonstrated and controlling parameters on proppant transport are identified.

  • This model works for field-scale hydraulic fracturing simulations to model proppant transport and fracture conductivity evolution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig.1
Fig.2
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
Fig.8
Fig.9
Fig.10
Fig.11
Fig.12
Fig.13
Fig.14
Fig.15
Fig.16

Similar content being viewed by others

References

  • Abass HH, Al-Mulhem AA, Alqam MH, Khan MR (2006) Acid Fracturing or Proppant Fracturing in Carbonate Formation? A Rock Mechanics View. In: SPE Annual Technical Conference and Exhibition, San Antonio, Texas, SPE-102590-MS

  • Adachi J, Siebrits E, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44:739–757. https://doi.org/10.1016/j.ijrmms.2006.11.006

    Article  Google Scholar 

  • Aften C (2018) Analysis of Various High Viscosity Friction Reducers and Brine Ranges Effectiveness on Proppant Transport. In: SPE/AAPG Eastern Regional Meeting, Pittsburgh, Pennsylvania

  • Almulhim A, Kebert B, Miskimins J, Hunter W, Soehner G (2020) Field-Scale Computational Fluid Dynamics CFD Modeling of Proppant Transport and Distribution Within a Horizontal Hydraulic Fracturing Stage. In: SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas

  • Alotaibi MA, Miskimins JL (2018) Slickwater proppant transport in hydraulic fractures: new experimental findings and scalable correlation. SPE Prod & Oper 33:164–178. https://doi.org/10.2118/174828-PA

    Article  Google Scholar 

  • Andrews MJ, O’Rourke PJ (1996) The multiphase particle-in-cell (MP-PIC) method for dense particulate flows. Int J Multiph Flow 22:379–402

    Article  Google Scholar 

  • Ba Geri M, Imqam A, Flori R (2019) A Critical Review of Using High Viscosity Friction Reducers as Fracturing Fluids for Hydraulic Fracturing Applications. In: SPE Oklahoma City Oil and Gas Symposium, Oklahoma City, Oklahoma

  • Babcock RE, Prokop CL, Kehle RO (1967) Distribution of propping Agent in vertical Fractures. In: Drilling and Production Practice, New York, New York

  • Baihly JD, Malpani R, Altman R, Lindsay G, Clayton R (2015) Shale Gas Production Decline Trend Comparison Over Time and Basins—Revisited. In: Unconventional Resources Technology Conference, San Antonio, Texas

  • Barree RD, Conway MW (1995) Experimental and numerical modeling of convective proppant transport (includes associated papers 31036 and 31068). J Pet Technol 47:216–222. https://doi.org/10.2118/28564-PA

    Article  Google Scholar 

  • Barree RD, Miskimins JL, Conway MW, Duenckel R (2017) Generic correlations for proppant-pack conductivity. SPE Prod & Oper 33:509–521. https://doi.org/10.2118/179135-PA

    Article  Google Scholar 

  • Biot MA, Medlin WL (1985) Theory of Sand Transport in Thin Fluids. In: SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada

  • Blyton CAJ, Gala DP, Sharma MM (2018) A study of proppant transport with fluid flow in a hydraulic fracture. SPE Drill Complet 33:307–323

    Article  Google Scholar 

  • Carman PC (1937) Fluid flow through granular beds. Trans Inst Chem Eng 15:150–166

    Google Scholar 

  • Chun T, Li Y, Wu K (2020) Comprehensive experimental study of proppant transport in an inclined fracture. J Petrol Sci Eng 184:106523. https://doi.org/10.1016/j.petrol.2019.106523

    Article  Google Scholar 

  • Clark PE, Quadir JA (1981) Prop Transport In Hydraulic Fractures: A Critical Review Of Particle Settling Velocity Equations. In: SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado

  • Cleary MP, Fonseca A (1992) Proppant convection and encapsulation in hydraulic fracturing: practical implications of computer and laboratory simulations. In: SPE annual technical conference and exhibition, Washington, D.C.

  • Cohen CE, Abad C, Weng X, England K, Phatak A, Kresse O, Nevvonen O, Laffite V, Abivin P (2013) Analysis on the impact of fracturing treatment design and reservoir properties on production from shale gas reservoirs. In: International Petroleum Technology Conference, Beijing, China

  • Dontsov EV, Peirce AP (2014) Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures. J Fluid Mech 760:567–590

    Article  Google Scholar 

  • Dontsov EV, Peirce AP (2015a) A Lagrangian approach to modelling proppant transport with tip screen-out in KGD hydraulic fractures. Rock Mech Rock Eng 48:2541–2550

    Article  Google Scholar 

  • Dontsov EV, Peirce AP (2015b) Proppant transport in hydraulic fracturing: crack tip screen-out in KGD and P3D models. Int J Solids Struct 63:206–218

    Article  Google Scholar 

  • Dunand A, Soucemarianadin A (1985) Concentration effects on the settling velocities of proppant slurries. In: SPE annual technical conference and exhibition, Las Vegas, Nevada

  • Gadde PB, Liu Y, Norman J, Bonnecaze R, Sharma MM (2004) Modeling proppant settling in Water-Fracs. In: SPE annual technical conference and exhibition, Houston, Texas

  • Garagash IA, Osiptsov AA, Boronin SA (2019) Dynamic bridging of proppant particles in a hydraulic fracture. Int J Eng Sci 135:86–101

    Article  Google Scholar 

  • Gomaa AM, Gupta DV, Carman P (2015) Proppant transport? Viscosity is not all it's cracked up to be. In: SPE hydraulic fracturing technology Conference, The Woodlands, Texas

  • Gu M, Mohanty KK (2014) Effect of foam quality on effectiveness of hydraulic fracturing in shales. Int J Rock Mech Min Sci 70:273–285

    Article  Google Scholar 

  • Guo Y, Wang L, Chang X, Zhou J, Zhang X (2020) Study on fracture morphological characteristics of refracturing for longmaxi shale formation. Geofluids 2020

  • Hosseini N, Khoei AR (2020) Numerical simulation of proppant transport and tip screen-out in hydraulic fracturing with the extended finite element method. Int J Rock Mech Min Sci 128:104247

    Article  Google Scholar 

  • Hryb D, Archimio A, Badessich M, Ejofodomi E, Diaz A, Cavazzoli G, Zalazar F, Lagarrigue E, Pichon S (2014) Unlocking the True Potential of the Vaca Muerta Shale via an Integrated Completion Optimization Approach. In: SPE Annual technical conference and exhibition. Amsterdam, The Netherlands

  • Hu X, Wu K, Song X, Yu W, Tang J, Li G, Shen Z (2018) A new model for simulating particle transport in a low-viscosity fluid for fluid-driven fracturing. AIChE J 64:3542–3552

    Article  Google Scholar 

  • Hu YT, Popeney C, Gilmer C, Kurian P (2019) Quantification of Dynamic Sand Settling Velocity in High-Viscosity Friction Reducers and Correlation with Rheology. In: SPE/AAPG/SEG Unconventional Resources Technology Conference, Denver, Colorado

  • Huang J, Deshpande KM, Safari R, Fragachan F, Ma X, Smith C, Mutlu U (2015) Clustered Proppant Design Optimization Utilizing Advanced Geomechanics-Flow-Reservoir Modeling. In: SPE Liquids-Rich Basins Conference - North America, Midland, Texas

  • Huang J, Perez O, Huang T, Safari R, Fragachan FE (2018) Using engineered low viscosity fluid in hydraulic fracturing to enhance proppant placement. In: SPE International Hydraulic Fracturing Technology Conference and Exhibition, Muscat, Oman

  • Huang J, Safari R, Perez O, Fragachan FE (2019) Reservoir Depletion-Induced Proppant Embedment and Dynamic Fracture Closure. In: SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain

  • Huang J, Ghassemi A (2015) A poroelastic model for evolution of fractured reservoirs during gas production. J Petrol Sci Eng 135:626–644. https://doi.org/10.1016/j.petrol.2015.10.007

    Article  Google Scholar 

  • Isah A, Hiba M, Al-Azani K, Aljawad MS, Mahmoud M (2021) A comprehensive review of proppant transport in fractured reservoirs: Experimental, numerical, and field aspects. J Nat Gas Sci Eng 88:103832. https://doi.org/10.1016/j.jngse.2021.103832

    Article  Google Scholar 

  • Jia P, Ma M, Cheng L, Clarkson CR (2020) A semi-analytical model for capturing dynamic behavior of hydraulic fractures during flowback period in tight oil reservoir. Energy Sci Eng 8:3415–3440. https://doi.org/10.1002/ese3.769

    Article  Google Scholar 

  • Keck RG, Nehmer WL, Strumolo GS (1992) A new method for predicting friction pressures and rheology of proppant-laden fracturing fluids. SPE Prod Eng 7:21–28. https://doi.org/10.2118/19771-PA

    Article  Google Scholar 

  • Kern LR, Perkins TK, Wyant RE (1959) The mechanics of sand movement in fracturing. J Pet Technol 11:55–57. https://doi.org/10.2118/1108-G

    Article  Google Scholar 

  • Kong X, McAndrew J (2017) A Computational Fluid Dynamics Study of Proppant Placement in Hydraulic Fracture Networks. In: SPE Unconventional Resources Conference, Calgary, Alberta, Canada

  • Kou R, Moridis GJ, Blasingame TA (2018) Analysis and Modeling of Proppant Transport in Inclined Hydraulic Fractures. In: SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas

  • Kumar D, Gonzalez RA, Ghassemi A (2019) The Role of Micro-Proppants in Conductive Fracture Network Development. In: SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas

  • Lecampion B, Bunger A, Zhang X (2018) Numerical methods for hydraulic fracture propagation: a review of recent trends. J Nat Gas Sci Eng 49:66–83

    Article  Google Scholar 

  • Lee HP, Olson JE, Holder J, Gale JFW, Myers RD (2015) The interaction of propagating opening mode fractures with preexisting discontinuities in shale. J Geophys Res: Sol Earth 120:169–181

    Article  Google Scholar 

  • Liang F, Sayed M, Al-Muntasheri GA, Chang FF, Li L (2016) A comprehensive review on proppant technologies. Petroleum 2:26–39. https://doi.org/10.1016/j.petlm.2015.11.001

    Article  Google Scholar 

  • Liu Y, Sharma MM (2005) Effect of Fracture Width and Fluid Rheology on Proppant Settling and Retardation: An Experimental Study. In: SPE Annual Technical Conference and Exhibition, Dallas, Texas

  • Liu Y (2006) Settling and hydrodynamic retardation of proppants in hydraulic fractures. Ph.D. Dissertation, The University of Texas at Austin

  • Loveless D, Holtsclaw J, Saini R, Harris P, Fleming J (2011) Fracturing Fluid Comprised of Components Sourced Solely from the Food Industry Provides Superior Proppant Transport. In: SPE Annual Technical Conference and Exhibition, Denver, Colorado

  • Lu Y, Agrawal M (2014) A computational-fluid-dynamics-based Eulerian-granular approach for characterization of sand erosion in multiphase-flow systems. SPE J 19:586–597

    Article  Google Scholar 

  • Mack M, Sun J, Khadilkar C (2014) Quantifying Proppant Transport in Thin Fluids - Theory and Experiments. In: SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas

  • Mao S, Siddhamshetty P, Zhang Z, Yu W, Chun T, Kwon JS-I, Wu K (2021) Impact of proppant pumping schedule on well production for slickwater fracturing. SPE J 26:342–358

    Article  Google Scholar 

  • McClure M (2018) Bed load proppant transport during slickwater hydraulic fracturing: Insights from comparisons between published laboratory data and correlations for sediment and pipeline slurry transport. J Petrol Sci Eng 161:599–610. https://doi.org/10.1016/j.petrol.2017.11.043

    Article  Google Scholar 

  • McMechan DE, Shah SN (1991) Static proppant-settling characteristics of non-newtonian fracturing fluids in a large-scale test model. SPE Prod Eng 6:305–312. https://doi.org/10.2118/19735-PA

    Article  Google Scholar 

  • Miller MC, McCave IN, Komar PD (1977) Threshold of sediment motion under unidirectional currents. Sedimentology 24:507–527. https://doi.org/10.1111/j.1365-3091.1977.tb00136.x

    Article  Google Scholar 

  • Montgomery C (2013) Fracturing Fluids. In: ISRM International Conference for Effective and Sustainable Hydraulic Fracturing, Brisbane, Australia

  • Novotny EJ (1977) Proppant Transport. In: SPE Annual Fall Technical Conference and Exhibition, Denver, Colorado

  • Osiptsov AA (2017) Fluid mechanics of hydraulic fracturing: a review. J Petrol Sci Eng 156:513–535. https://doi.org/10.1016/j.petrol.2017.05.019

    Article  Google Scholar 

  • Patankar NA, Joseph DD (2001) Lagrangian numerical simulation of particulate flows. Int J Multiph Flow 27:1685–1706

    Article  Google Scholar 

  • Patankar NA, Joseph DD, Wang J, Barree RD, Conway M, Asadi M (2002) Power law correlations for sediment transport in pressure driven channel flows. Int J Multiph Flow 28:1269–1292. https://doi.org/10.1016/S0301-9322(02)00030-7

    Article  Google Scholar 

  • Raterman KT, Farrell HE, Mora OS, Janssen AL, Gomez GA, Busetti S, McEwen J, Friehauf K, Rutherford J, Reid R, Jin G, Roy B, Warren M (2018) Sampling a stimulated rock volume: an eagle ford example. SPE Res Eval & Eng 21:927–941. https://doi.org/10.2118/191375-PA

    Article  Google Scholar 

  • Ray B, Lewis C, Martysevich V, Shetty DA, Walters HG, Bai J, Ma J (2017) An Investigation into Proppant Dynamics in Hydraulic Fracturing. In: SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas

  • Roostaei M, Nouri A, Hosseini SA, Soroush M, Velayati A, Mahmoudi M, Ghalambor A, Fattahpour V (2020) A Concise Review of Experimental Works on Proppant Transport and Slurry Flow. In: SPE International Conference and Exhibition on Formation Damage Control, Lafayette, Louisiana

  • Sanders M, Felling K, Thomson S, Wright S, Thorpe R (2016) Dry Polyacrylamide Friction Reducer: Not Just for Slick Water. In: SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas

  • Shah SN (1982) Proppant settling correlations for non-newtonian fluids under static and dynamic conditions. SPE J 22:164–170. https://doi.org/10.2118/9330-PA

    Article  Google Scholar 

  • Shahri MP, Huang J, Smith CS, Fragachán FE (2017) An Engineered Approach to Design Biodegradables Solid Particulate Diverters: Jamming and Plugging. In: SPE Annual Technical Conference and Exhibition, San Antonio, Texas

  • Shen L, Vigderman L, Heller D, Fu D (2018) Can Friction Reducers Transport Sand During Fracturing Treatment? In: SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas

  • Shiozawa S, McClure M (2016) Simulation of proppant transport with gravitational settling and fracture closure in a three-dimensional hydraulic fracturing simulator. J Petrol Sci Eng 138:298–314. https://doi.org/10.1016/j.petrol.2016.01.002

    Article  Google Scholar 

  • Shrivastava K, Sharma MM (2018) Proppant Transport in Complex Fracture Networks. In: SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas

  • Siddhamshetty P, Mao S, Wu K, Kwon JS-I (2020) Multi-size proppant pumping schedule of hydraulic fracturing: Application to a MP-PIC model of unconventional reservoir for enhanced gas production. Processes 8:570

    Article  Google Scholar 

  • Su K, Torres J, Perl YS, Barlet P, Onaisi A, Vidal-Gilbert S (2017) Tests of Fracture Water and Gas Permeability on Vaca Muerta Gas Shale. In: SPE/AAPG/SEG Unconventional Resources Technology Conference, Austin, Texas

  • Su K, Santacoloma M, Estrada S, Barlet P, Pourpak H (2019) Experimental Study of Fracture Permeability With or Without Proppants on Vaca Muerta Gas Shale. In: SPE/AAPG/SEG Unconventional Resources Technology Conference, Denver, Colorado

  • Tong S, Mohanty KK (2016) Proppant transport study in fractures with intersections. Fuel 181:463–477. https://doi.org/10.1016/j.fuel.2016.04.144

    Article  Google Scholar 

  • Tong S, Gu M, Singh R, Mohanty KK (2019) Proppant transport in foam fracturing fluid during hydraulic fracturing. J Petrol Sci Eng 182:106279. https://doi.org/10.1016/j.petrol.2019.106279

    Article  Google Scholar 

  • van Domelen M, Cutrer W, Collins S, Ruegamer M (2017) Applications of Viscosity-Building Friction Reducers as Fracturing Fluids. In: SPE Oklahoma City Oil and Gas Symposium, Oklahoma City, Oklahoma

  • Wang J, Elsworth D (2018) Role of proppant distribution on the evolution of hydraulic fracture conductivity. J Petrol Sci Eng 166:249–262. https://doi.org/10.1016/j.petrol.2018.03.040

    Article  Google Scholar 

  • Wang J, Elsworth D (2020) Fracture penetration and proppant transport in gas- and foam-fracturing. J Nat Gas Sci Eng 77:103269. https://doi.org/10.1016/j.jngse.2020.103269

    Article  Google Scholar 

  • Wang J, Joseph D, Patankar N, Conway M, Barree R (2003) Bi-power law correlations for sediment transport in pressure driven channel flows. Int J Multiph Flow 29:475–494. https://doi.org/10.1016/S0301-9322(02)00152-0

    Article  Google Scholar 

  • Wang J, Elsworth D, Denison MK (2019) Proppant Transport in a Propagating Hydraulic Fracture and the Evolution of Transport Properties. In: the 53rd U.S. Rock Mechanics/Geomechanics Symposium, New York City, New York

  • Warpinski NR (2010) Stress amplification and arch dimensions in proppant beds deposited by waterfracs. SPE Prod & Oper 25:461–471. https://doi.org/10.2118/119350-PA

    Article  Google Scholar 

  • Weng X, Kresse O, Cohen C, Wu R, Gu H (2011) Modeling of hydraulic-fracture-network propagation in a naturally fractured formation. SPE Prod & Oper 26:368–380. https://doi.org/10.2118/140253-PA

    Article  Google Scholar 

  • Wiberg PL, Dungan SJ (1989) Model for calculating bed load transport of sediment. J Hydraul Eng 115:101–123. https://doi.org/10.1061/(ASCE)0733-9429(1989)115:1(101)

    Article  Google Scholar 

  • Wright CA, Davis EJ, Minner WA, Ward JF, Weijers L, Schell EJ, Hunter SP (1998) Surface Tiltmeter Fracture Mapping Reaches New Depths - 10,000 Feet and Beyond? In: SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, Colorado

  • Wu C-H, Sharma MM (2016) Effect of Perforation Geometry and Orientation on Proppant Placement in Perforation Clusters in a Horizontal Well. In: SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas

  • Xu L, Ogle J, Collier T, French J, Nichols R, Simmons B (2019a) Elastic Friction Reducer Facilitates Proppant Transport and FR Residual Analysis Provides Insight into Potential Formation Damage. In: SPE Oklahoma City Oil and Gas Symposium, Oklahoma City, Oklahoma

  • Xu T, Zheng W, Baihly J, Dwivedi P, Shan D, Utech R, Miller G (2019b) Permian Basin Production Performance Comparison Over Time and the Parent-Child Well Study. In: SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas

  • Zeng J, Li H, Zhang D (2019) Numerical simulation of proppant transport in propagating fractures with the multi-phase particle-in-cell method. Fuel 245:316–335

    Article  Google Scholar 

  • Zhang G, Gutierrez M, Li M (2017a) A coupled CFD-DEM approach to model particle-fluid mixture transport between two parallel plates to improve understanding of proppant micromechanics in hydraulic fractures. Powder Technol 308:235–248

    Article  Google Scholar 

  • Zhang G, Li M, Gutierrez M (2017b) Simulation of the transport and placement of multi-sized proppant in hydraulic fractures using a coupled CFD-DEM approach. Adv Powder Technol 28:1704–1718

    Article  Google Scholar 

  • Zhou L, Hou MZ, Gou Y, Li M (2014) Numerical investigation of a low-efficient hydraulic fracturing operation in a tight gas reservoir in the North German Basin. J Petrol Sci Eng 120:119–129

    Article  Google Scholar 

  • Zhou L, Chen J, Gou Y, Feng W (2017) Numerical investigation of the time-dependent and the proppant dominated stress shadow effects in a transverse multiple fracture system and optimization. Energies 10:83

    Article  Google Scholar 

Download references

Acknowledgements

Funding for YH, RRS, JAW and HG was provided by TotalEnergies through the FC-MAELSTROM project. Portions of this work were performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Author information

Authors and Affiliations

  1. TotalEnergies E&P Research & Technology, Houston, TX, 77002, USA

    Jian Huang, Khalid Mateen & Herve Gross

  2. Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA

    Yue Hao, Randolph R. Settgast & Joshua A. White

Authors
  1. Jian Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yue Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Randolph R. Settgast
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Joshua A. White
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Khalid Mateen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Herve Gross
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian Huang.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, J., Hao, Y., Settgast, R.R. et al. Validation and Application of a Three-Dimensional Model for Simulating Proppant Transport and Fracture Conductivity. Rock Mech Rock Eng 56, 7091–7113 (2023). https://doi.org/10.1007/s00603-022-03092-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-022-03092-3

Keywords

Search

Navigation