Proppant Trapping and Washout in Rough Hydraulic Fractures

Proppant Trapping and Washout in Rough Hydraulic Fractures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Method Article Proppant Trapping and Washout in Rough Hydraulic Fractures Serhii Kryvenko This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7601974/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This work introduces an extension to the proppant trapping model proposed by McClure et al. ( 2020 ) by incorporating a washout term that accounts for localized bed-load transport processes within rough hydraulic fractures. The extended formulation enables remobilization of previously trapped proppant when local fluid velocity exceeds a critical threshold derived from Shields theory. By incorporating dependencies on particle size and density, fluid properties, and fracture roughness, the model offers a scalable framework for simulating proppant behavior under dynamic flow conditions. Petroleum Engineering hydraulic fracturing proppant transport proppant trapping Introduction Predictive modeling of proppant placement is critical for optimizing hydraulic fracturing treatments and maximizing asset value through informed development strategies (Shirley et al., 2025 ). Proppant distribution within fractures is influenced by several interacting mechanisms, including viscous drag, gravitational and hindered settling, proppant bridging, etc. (Dontsov and Peirce, 2014 ). Singh et al. (2025) emphasize that proppant immobilization—or trapping—caused by fracture roughness is a key determinant of the propped length. This concept, introduced by McClure et al. ( 2020 ), describes the process by which proppant becomes lodged within asperities on fracture surfaces, limiting further transport. Hai et al. (2017) demonstrated that the proppant-transport behavior in the rough vertical fracture was observed to be totally different from that in the smooth fracture. Core-through experiments and fracture characterization by Gale et al. ( 2018 ) provided direct evidence of trapped proppant due to rough fracture surface. According to McClure et al. ( 2020 ), proppant trapping can be modeled using the following equation: $$\:\frac{d{m}_{i,imm}}{dt}={K}_{imm}{m}_{i,m}$$ 1 where \(\:{m}_{i,imm}\) is immobile mass per area of proppant i (kg/m 2 ), \(\:{m}_{i,m}\) is mobile mass per area of proppant i ( kg/m 2 ), \(\:\text{a}\text{n}\text{d}\:{K}_{imm}\) is immobilization rate constant (s − 1 ) Without accounting for proppant trapping, fracturing models predict that proppant settles to the bottom of the fracture within several hours after a well is shut-in, resulting in poor near-wellbore conductivity—an outcome inconsistent with field diagnostic observations (Ge et al., 2018). However, the formulation by McClure et al. ( 2020 ) treats proppant trapping as an irreversible process and does not incorporate proppant-specific properties, thereby requiring empirical calibration for each proppant type (Singh et al., 2024). Washout Model I propose an extension to the trapping equation introduced by McClure et al. ( 2020 ) by incorporating a washout term that captures the influence of localized bed-load transport processes within rough hydraulic fractures. Unlike traditional sediment transport models that assume a single bed at the fracture base, this formulation conceptualizes proppant interaction with a distributed network of micro-scale “beds” formed by surface asperities and geometric irregularities throughout the fracture height. Once proppant settles onto these ledges, it may be remobilized if local fluid velocity exceeds a critical threshold, initiating transport mechanisms such as saltation or turbulent suspension. These patch-scale processes operate independently and collectively enable proppant to bypass trapping points and redistribute within the fracture. This framework introduces a scalable mechanism that reflects the spatial complexity of fracture roughness and provides a more nuanced basis for modeling proppant behavior under dynamic flow conditions. The proposed formulation modifies Eq. 1 as follows: $$\:\frac{d{m}_{i,imm}}{dt}={K}_{imm}{m}_{i,m}-{K}_{washout}{\left({u}_{D}\right)}^{2}{m}_{i,imm}$$ 2 where: \(\:{u}_{D}=u/{u}_{c}\) , \(\:{K}_{washout}\) is the washout rate constant (s −1 ), \(\:u\) is the superficial velocity (m/s), \(\:{u}_{c}\) is the critical superficial velocity (m/s). The initiation of proppant remobilization is governed by the Shields criterion (Shields, 1936 ), which defines the critical condition for particle motion in a fluid. The Shields number ( \(\:{N}_{Sh}\) ) is a dimensionless parameter that represents the ratio of fluid-induced shear forces to the gravitational force on a particle of sediment (Biot and Medlin, 1985 ): $$\:{N}_{Sh}=\frac{\tau\:}{{d}_{p}g({\rho\:}_{p}-{\rho\:}_{f})}$$ 3 where \(\:\tau\:\) is wall shear stress (Pa), \(\:{d}_{p}\) is particle diameter (m), \(\:g\) is gravitational constant (9.81 m/s²), and \(\:{\rho\:}_{p}\) and \(\:{\rho\:}_{f}\) are particle and fluid densities (kg/m³), respectively. Proppant remobilization or “washout” occurs when \(\:{N}_{Sh}\:\ge\:{N}_{sh,\:cr}\) . The corresponding critical shear wall stress is $$\:{\tau\:}_{c}={N}_{sh,cr\:}{d}_{p}g({\rho\:}_{p}-{\rho\:}_{f})$$ 4 The critical wall shear stress is related to superficial velocity using the Darcy–Weisbach formulation: $$\:{\tau\:}_{c}=0.125f{\rho\:}_{f}{u}_{c}^{2}$$ 5 where \(\:f\) is the Darcy friction factor. The friction factor depends on flow regime and fracture wall roughness, with correlations varying for laminar versus turbulent flow and for smooth versus rough surfaces. Combining Eqs. 4 and 5 gives the relationship for critical velocity: $$\:{u}_{c}=\sqrt{\frac{8{\tau\:}_{c}}{f{\rho\:}_{f}}}=\sqrt{\frac{8{N}_{sh,cr\:}{d}_{p}g({\rho\:}_{p}-{\rho\:}_{f})}{f{\rho\:}_{f}}}$$ 6 This relationship highlights that critical velocity—and therefore both washout potential and the resulting immobilized proppant mass—is strongly influenced by particle size, particle density, fluid density, and fracture surface roughness. These factors must be explicitly considered in hydraulic fracturing numerical models to accurately capture proppant transport dynamics. The model indicates that lower-density proppants are more prone to washout, resulting in a smaller immobilized mass under dynamic flow conditions, meaning they travel longer distances within the fracture before becoming immobilized. Similarly, and consistent with the findings of Singh et al. (2025), larger diameter particles tend to be trapped more than smaller ones, resulting in greater accumulation near the wellbore. Conclusions and Future Work This work introduces a novel extension to the proppant trapping model proposed by McClure et al. ( 2020 ), by incorporating a washout term that captures localized bed load transport processes within rough hydraulic fractures. This addition enables the model to simulate the remobilization of previously trapped proppant when local fluid velocities exceed a critical threshold. Importantly, the extended trapping formulation now incorporates dependencies on fluid and proppant properties. To advance the model further, future efforts should prioritize conducting experimental slot flow tests with controlled roughness to investigate the onset of washout and remobilization dynamics, integrating the model into commercial hydraulic fracturing simulators to support predictive proppant placement modeling, and performing sensitivity analyses to assess the impact of fluid and proppant properties on trapping and washout behavior. Declarations Acknowledgements The author extends sincere appreciation to ExxonMobil for permission to publish this material. References Biot, M.A., and Medlin, W.L. 1985. Theory of Sand Transport in Thin Fluids. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, USA, 22–25 September. SPE-14468-MS. https://doi.org/10.2118/14468-MS Dontsov, E.V., and Peirce, A.P. 2014. Slurry Flow, Gravitational Settling and a Proppant Transport Model for Hydraulic Fractures. Journal of Fluid Mechanics 760: 567–590. https://doi.org/10.1017/jfm.2014.606 Gale, J.F.W., Elliott, S.J., and Laubach, S.E. 2018. Hydraulic Fractures in Core From Stimulated Reservoirs: Core Fracture Description of HFTS Slant Core, Midland Basin, West Texas. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, 23–25 July. URTEC-2902624-MS. https://doi.org/10.15530/URTEC-2018-2902624 Ge, S., Kintzing, M., Jin, M., et al. 2022. Time-Lapse Monitoring of Inter-Well Communication and Drainage Frac Height Using Geochemical Fingerprinting Technology with Case Studies in the Midland Basin. Presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, 1–3 February. SPE-209145-MS. https://doi.org/10.2118/209145-MS Huang, H., Babadagli, T., and Li, H.A. 2017. A Quantitative and Visual Experimental Study: Effect of Fracture Roughness on Proppant Transport in a Vertical Fracture. Presented at the SPE Eastern Regional Meeting, Lexington, Kentucky, USA, 3–5 October. SPE-187520-MS. https://doi.org/10.2118/187520-MS McClure, M., Picone, M., Fowler, G., Ratcliff, D., Kang, C., Medam, S., and Frantz, J. 2020. Nuances and Frequently Asked Questions in Field-Scale Hydraulic Fracture Modeling. Presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, 4–6 February. SPE-199726-MS. https://doi.org/10.2118/199726-MS Shields, A. 1936. Application of Similarity Principles and Turbulence Research to Bed-Load Movement. Mitteilungen der Preußischen Versuchsanstalt für Wasserbau, Berlin. Shirley, R., Spiecker, P.M., Brown, J.S., Benish, T., Jin, X., Kulkarni, M.G., Kao, C.-S., Gordon, P.A., Moffett, T.J., Kumar, S.D., and Staus, G. 2025. Development of a Novel, Patented Fracturing Technology Based on Low-Cost Petroleum Coke Light Weight Proppant from Lab-Scale Evaluation to Field-Scale Pilots: Case Studies in the Midland and Delaware Basins. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, 16–18 June. URTEC-4264319-MS. https://doi.org/10.15530/urtec-2025-4264319 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7601974","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":514305231,"identity":"ea9bfefb-7507-442d-9017-ace71cc7033d","order_by":0,"name":"Serhii Kryvenko","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABG0lEQVRIiWNgGAWjYHACNoYEAwYDCPsAgxxMOIGNnUgtxggtzHi0AAFcS2IDTAsDDi3y7b3PHjwoYDA2n5Fj+LjgjE16vwSQUZhjk8fHzMD44WMOhhaDM8fNDYAOM5O5kWNsPONGWu7MnmPJxjO3pRUDHcYsOXMbphaJNDYJoBYbCYm0NGmeD4dzNxxvPibNu+1wYhszAxszL6YW+fnP4FrSfwO1pNsfZmzDq4XhBhtYi5mERPIxZp4bhxMM2AnYYnAG7DAJYwmex4elec6kGc44A/QLL9gvjM3Y/CLffoxN8scfG8MZ7ImNn3mO2cjzg4KOd5tNnnx788EPH7E4DAIkGBgEEjBEGRtwqYcA/gP45UfBKBgFo2DkAgDxYGAvI8oxQgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0006-6948-9192","institution":"ExxonMobil Upstream Oil and Gas","correspondingAuthor":true,"prefix":"","firstName":"Serhii","middleName":"","lastName":"Kryvenko","suffix":""}],"badges":[],"createdAt":"2025-09-12 15:36:16","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7601974/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7601974/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91336057,"identity":"45fb45e9-5719-41f2-8d22-fafda90cc2ed","added_by":"auto","created_at":"2025-09-15 12:06:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":230811,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7601974/v1/98cd1f9c-9f68-4e90-ad46-efca1b9e5dbe.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eProppant Trapping and Washout in Rough Hydraulic Fractures\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePredictive modeling of proppant placement is critical for optimizing hydraulic fracturing treatments and maximizing asset value through informed development strategies (Shirley et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Proppant distribution within fractures is influenced by several interacting mechanisms, including viscous drag, gravitational and hindered settling, proppant bridging, etc. (Dontsov and Peirce, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Singh et al. (2025) emphasize that proppant immobilization\u0026mdash;or trapping\u0026mdash;caused by fracture roughness is a key determinant of the propped length. This concept, introduced by McClure et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), describes the process by which proppant becomes lodged within asperities on fracture surfaces, limiting further transport. Hai et al. (2017) demonstrated that the proppant-transport behavior in the rough vertical fracture was observed to be totally different from that in the smooth fracture. Core-through experiments and fracture characterization by Gale et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) provided direct evidence of trapped proppant due to rough fracture surface.\u003c/p\u003e\u003cp\u003eAccording to McClure et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), proppant trapping can be modeled using the following equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\frac{d{m}_{i,imm}}{dt}={K}_{imm}{m}_{i,m}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{i,imm}\\)\u003c/span\u003e\u003c/span\u003e is immobile mass per area of proppant \u003cem\u003ei\u003c/em\u003e (kg/m\u003csup\u003e2\u003c/sup\u003e), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{i,m}\\)\u003c/span\u003e\u003c/span\u003e is mobile mass per area of proppant \u003cem\u003ei (\u003c/em\u003ekg/m\u003csup\u003e2\u003c/sup\u003e), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{a}\\text{n}\\text{d}\\:{K}_{imm}\\)\u003c/span\u003e\u003c/span\u003e is immobilization rate constant (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e\u003cp\u003eWithout accounting for proppant trapping, fracturing models predict that proppant settles to the bottom of the fracture within several hours after a well is shut-in, resulting in poor near-wellbore conductivity\u0026mdash;an outcome inconsistent with field diagnostic observations (Ge et al., 2018). However, the formulation by McClure et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) treats proppant trapping as an irreversible process and does not incorporate proppant-specific properties, thereby requiring empirical calibration for each proppant type (Singh et al., 2024).\u003c/p\u003e"},{"header":"Washout Model","content":"\u003cp\u003eI propose an extension to the trapping equation introduced by McClure et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) by incorporating a washout term that captures the influence of localized bed-load transport processes within rough hydraulic fractures. Unlike traditional sediment transport models that assume a single bed at the fracture base, this formulation conceptualizes proppant interaction with a distributed network of micro-scale “beds” formed by surface asperities and geometric irregularities throughout the fracture height. Once proppant settles onto these ledges, it may be remobilized if local fluid velocity exceeds a critical threshold, initiating transport mechanisms such as saltation or turbulent suspension. These patch-scale processes operate independently and collectively enable proppant to bypass trapping points and redistribute within the fracture. This framework introduces a scalable mechanism that reflects the spatial complexity of fracture roughness and provides a more nuanced basis for modeling proppant behavior under dynamic flow conditions.\u003c/p\u003e\u003cp\u003eThe proposed formulation modifies Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e as follows:\u003c/p\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\frac{d{m}_{i,imm}}{dt}={K}_{imm}{m}_{i,m}-{K}_{washout}{\\left({u}_{D}\\right)}^{2}{m}_{i,imm}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003ewhere: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{D}=u/{u}_{c}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{K}_{washout}\\)\u003c/span\u003e\u003c/span\u003e is the washout rate constant (s\u003csup\u003e−1\u003c/sup\u003e), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:u\\)\u003c/span\u003e\u003c/span\u003e is the superficial velocity (m/s), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{c}\\)\u003c/span\u003e\u003c/span\u003e is the critical superficial velocity (m/s).\u003c/p\u003e\u003cp\u003eThe initiation of proppant remobilization is governed by the Shields criterion (Shields, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1936\u003c/span\u003e), which defines the critical condition for particle motion in a fluid. The Shields number (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{Sh}\\)\u003c/span\u003e\u003c/span\u003e) is a dimensionless parameter that represents the ratio of fluid-induced shear forces to the gravitational force on a particle of sediment (Biot and Medlin, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1985\u003c/span\u003e):\u003c/p\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{N}_{Sh}=\\frac{\\tau\\:}{{d}_{p}g({\\rho\\:}_{p}-{\\rho\\:}_{f})}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\tau\\:\\)\u003c/span\u003e\u003c/span\u003e is wall shear stress (Pa), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{p}\\)\u003c/span\u003e\u003c/span\u003e is particle diameter (m), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:g\\)\u003c/span\u003e\u003c/span\u003e is gravitational constant (9.81 m/s²), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{p}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{f}\\)\u003c/span\u003e\u003c/span\u003e are particle and fluid densities (kg/m³), respectively.\u003c/p\u003e\u003cp\u003eProppant remobilization or “washout” occurs when \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{Sh}\\:\\ge\\:{N}_{sh,\\:cr}\\)\u003c/span\u003e\u003c/span\u003e. The corresponding critical shear wall stress is\u003c/p\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\tau\\:}_{c}={N}_{sh,cr\\:}{d}_{p}g({\\rho\\:}_{p}-{\\rho\\:}_{f})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe critical wall shear stress is related to superficial velocity using the Darcy–Weisbach formulation:\u003c/p\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\tau\\:}_{c}=0.125f{\\rho\\:}_{f}{u}_{c}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f\\)\u003c/span\u003e\u003c/span\u003e is the Darcy friction factor. The friction factor depends on flow regime and fracture wall roughness, with correlations varying for laminar versus turbulent flow and for smooth versus rough surfaces. Combining Eqs.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e gives the relationship for critical velocity:\u003c/p\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{u}_{c}=\\sqrt{\\frac{8{\\tau\\:}_{c}}{f{\\rho\\:}_{f}}}=\\sqrt{\\frac{8{N}_{sh,cr\\:}{d}_{p}g({\\rho\\:}_{p}-{\\rho\\:}_{f})}{f{\\rho\\:}_{f}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThis relationship highlights that critical velocity—and therefore both washout potential and the resulting immobilized proppant mass—is strongly influenced by particle size, particle density, fluid density, and fracture surface roughness. These factors must be explicitly considered in hydraulic fracturing numerical models to accurately capture proppant transport dynamics. The model indicates that lower-density proppants are more prone to washout, resulting in a smaller immobilized mass under dynamic flow conditions, meaning they travel longer distances within the fracture before becoming immobilized. Similarly, and consistent with the findings of Singh et al. (2025), larger diameter particles tend to be trapped more than smaller ones, resulting in greater accumulation near the wellbore.\u003c/p\u003e"},{"header":"Conclusions and Future Work","content":"\u003cp\u003eThis work introduces a novel extension to the proppant trapping model proposed by McClure et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), by incorporating a washout term that captures localized bed load transport processes within rough hydraulic fractures. This addition enables the model to simulate the remobilization of previously trapped proppant when local fluid velocities exceed a critical threshold. Importantly, the extended trapping formulation now incorporates dependencies on fluid and proppant properties.\u003c/p\u003e\u003cp\u003eTo advance the model further, future efforts should prioritize conducting experimental slot flow tests with controlled roughness to investigate the onset of washout and remobilization dynamics, integrating the model into commercial hydraulic fracturing simulators to support predictive proppant placement modeling, and performing sensitivity analyses to assess the impact of fluid and proppant properties on trapping and washout behavior.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgements\u003c/h2\u003e\u003cp\u003eThe author extends sincere appreciation to ExxonMobil for permission to publish this material.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBiot, M.A., and Medlin, W.L. 1985. Theory of Sand Transport in Thin Fluids. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, USA, 22\u0026ndash;25 September. SPE-14468-MS. https://doi.org/10.2118/14468-MS\u003c/li\u003e\n\u003cli\u003eDontsov, E.V., and Peirce, A.P. 2014. Slurry Flow, Gravitational Settling and a Proppant Transport Model for Hydraulic Fractures. Journal of Fluid Mechanics 760: 567\u0026ndash;590. https://doi.org/10.1017/jfm.2014.606\u003c/li\u003e\n\u003cli\u003eGale, J.F.W., Elliott, S.J., and Laubach, S.E. 2018. Hydraulic Fractures in Core From Stimulated Reservoirs: Core Fracture Description of HFTS Slant Core, Midland Basin, West Texas. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, 23\u0026ndash;25 July. URTEC-2902624-MS. https://doi.org/10.15530/URTEC-2018-2902624\u003c/li\u003e\n\u003cli\u003eGe, S., Kintzing, M., Jin, M., et al. 2022. Time-Lapse Monitoring of Inter-Well Communication and Drainage Frac Height Using Geochemical Fingerprinting Technology with Case Studies in the Midland Basin. Presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, 1\u0026ndash;3 February. SPE-209145-MS. https://doi.org/10.2118/209145-MS\u003c/li\u003e\n\u003cli\u003eHuang, H., Babadagli, T., and Li, H.A. 2017. A Quantitative and Visual Experimental Study: Effect of Fracture Roughness on Proppant Transport in a Vertical Fracture. Presented at the SPE Eastern Regional Meeting, Lexington, Kentucky, USA, 3\u0026ndash;5 October. SPE-187520-MS. https://doi.org/10.2118/187520-MS\u003c/li\u003e\n\u003cli\u003eMcClure, M., Picone, M., Fowler, G., Ratcliff, D., Kang, C., Medam, S., and Frantz, J. 2020. Nuances and Frequently Asked Questions in Field-Scale Hydraulic Fracture Modeling. Presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, 4\u0026ndash;6 February. SPE-199726-MS. https://doi.org/10.2118/199726-MS\u003c/li\u003e\n\u003cli\u003eShields, A. 1936. Application of Similarity Principles and Turbulence Research to Bed-Load Movement. Mitteilungen der Preu\u0026szlig;ischen Versuchsanstalt f\u0026uuml;r Wasserbau, Berlin.\u003c/li\u003e\n\u003cli\u003eShirley, R., Spiecker, P.M., Brown, J.S., Benish, T., Jin, X., Kulkarni, M.G., Kao, C.-S., Gordon, P.A., Moffett, T.J., Kumar, S.D., and Staus, G. 2025. Development of a Novel, Patented Fracturing Technology Based on Low-Cost Petroleum Coke Light Weight Proppant from Lab-Scale Evaluation to Field-Scale Pilots: Case Studies in the Midland and Delaware Basins. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, 16\u0026ndash;18 June. URTEC-4264319-MS. https://doi.org/10.15530/urtec-2025-4264319\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"ExxonMobil (United States)","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"hydraulic fracturing, proppant transport, proppant trapping","lastPublishedDoi":"10.21203/rs.3.rs-7601974/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7601974/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work introduces an extension to the proppant trapping model proposed by McClure et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) by incorporating a washout term that accounts for localized bed-load transport processes within rough hydraulic fractures. The extended formulation enables remobilization of previously trapped proppant when local fluid velocity exceeds a critical threshold derived from Shields theory. By incorporating dependencies on particle size and density, fluid properties, and fracture roughness, the model offers a scalable framework for simulating proppant behavior under dynamic flow conditions.\u003c/p\u003e","manuscriptTitle":"Proppant Trapping and Washout in Rough Hydraulic Fractures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-15 11:50:10","doi":"10.21203/rs.3.rs-7601974/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9fc722b4-0247-47d7-ad19-6d33cdf0c460","owner":[],"postedDate":"September 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":54642949,"name":"Petroleum Engineering"}],"tags":[],"updatedAt":"2025-09-15T11:50:10+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-15 11:50:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7601974","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7601974","identity":"rs-7601974","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}