Skip to main content
SpringerLink
Log in

Inference of Intermittent Hydraulic Fracture Tip Advancement Through Inversion of Low-Frequency Distributed Acoustic Sensing Data

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

Abstract

Characterizing the fluid-driven fracture-tip advancing process presents a significant challenge due to the difficulty of replicating real-world conditions in laboratory experiments and the lack of precise field measurements. However, recent advances in low-frequency distributed acoustic sensing (LF-DAS) technology offer new opportunities to investigate the dynamics of propagating hydraulic fractures. In this study, we propose an iterative inversion method to characterize fracture-tip advancing behaviors using LF-DAS data. A forward geomechanical model is developed using the three-dimensional displacement discontinuity method, and the optimization is realized by a conjugate gradient method. The performance of the inversion algorithm is demonstrated using a synthetic case, in which the fracture half-length evolution and propagation velocity match well with the reference solutions. In addition, the averaged fracture cross-section area, fracture volume, and fracturing fluid efficiency can also be estimated, showing good agreements with true values of the synthetic case under reasonable assumptions. Then, a field case with a single-cluster hydraulic fracturing treatment from the Hydraulic Fracturing Test Site 2 project (HFTS-2) is studied. Our analysis of the inversion results reveals that the fracture propagates intermittently, as evidenced by the fracture half-length evolution. This unique field evidence can guide modeling efforts to incorporate this important physical behavior into fracture models, and the secondary information gathered from the study, including fracture cross-section area and volume, can help evaluate and optimize fracturing efficiency.

Highlights

  • Low-frequency distributed acoustic sensing provides a unique dataset to characterize the fracture propagation process.

  • A gradient-based inversion algorithm is developed and validated using a synthetic case to estimate the fracture tip advancing process.

  • In the presented field case, fracture propagates continuously in the beginning, followed by an intermittent advancement pattern

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
Fig. 17

Similar content being viewed by others

References

  • Adachi J, Siebrits EM, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44(5):739–757

    Article  Google Scholar 

  • Becker MW, Ciervo C, Cole M, Coleman T, Mondanos M (2017) Fracture hydromechanical response measured by fiber optic distributed acoustic sensing at milliHertz frequencies. Geophys Res Lett 44(14):7295–7302

  • Branch MA, Coleman TF, Li Y (1999) A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems. SIAM J Sci Comput 21(1):1–23

    Article  Google Scholar 

  • Bunger AP, Detournay E (2008) Experimental validation of the tip asymptotics for a fluid-driven crack. J Mech Phys Solids 56(11):3101–3115

    Article  CAS  Google Scholar 

  • Cao TD, Hussain F, Schrefler BA (2018) Porous media fracturing dynamics: stepwise crack advancement and fluid pressure oscillations. J Mech Phys Solids 111:113–133

    Article  Google Scholar 

  • Chen Y, Nagaya Y, Ishida T (2015) Observations of fractures induced by hydraulic fracturing in anisotropic granite. Rock Mech Rock Eng 48:1455–1461

    Article  Google Scholar 

  • Chen B, Barboza BR, Sun Y, Bai J, Thomas HR, Dutko M, Cottrell M et al (2021) A review of hydraulic fracturing simulation. Arch Comput Methods Eng 29:1–58

    Article  CAS  Google Scholar 

  • Ciezobka J (2021) Overview of hydraulic fracturing test site 2 in the Permian Delaware Basin (HFTS-2). In Unconventional Resources Technology Conference, 26–28 July 2021. Unconventional Resources Technology Conference (URTeC), pp. 259–278

  • Cochard T, Svetlizky I, Albertini G, Viesca R, Rubinstein S, Spaepen F, Yuan C, Denolle M, Song YQ, Xiao L, Weitz D (2023) Unexpected dynamics in the propagation of fracture fronts. Nat Phys. https://doi.org/10.1038/s41567-023-02365-0

    Article  Google Scholar 

  • Crouch S (1976) Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution. Int J Numer Methods Eng 10(2):301–343

    Article  Google Scholar 

  • Garagash D, Detournay E (2000) The tip region of a fluid-driven fracture in an elastic medium. J Appl Mech 67(1):183–192

    Article  Google Scholar 

  • Geertsma J, De Klerk F (1969) A rapid method of predicting width and extent of hydraulically induced fractures. J Petrol Technol 21(12):1571–1581

    Article  Google Scholar 

  • Hartog AH (2017) An introduction to distributed optical fibre sensors. CRC press

  • Ichikawa M, Kurosawa I, Uchida S, Kato A, Ito Y, Takagi S de Groot M. et al (2019) Case study of hydraulic fracture monitoring using low-frequency components of DAS data. In SEG Technical Program Expanded Abstracts 2019. Society of Exploration Geophysicists. pp. 948–952

  • Jin G, Roy B (2017) Hydraulic-fracture geometry characterization using low-frequency DAS signal. Lead Edge 36(12):975–980

    Article  Google Scholar 

  • Lecampion B, Desroches J, Jeffrey RG, Bunger AP (2017) Experiments versus theory for the initiation and propagation of radial hydraulic fractures in low-permeability materials. J Geophys Res Solid Earth 122(2):1239–1263

    Article  Google Scholar 

  • 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 

  • Lhomme TP, De Pater CJ, Helfferich PH (2002) Experimental study of hydraulic fracture initiation in Colton sandstone. SPE/ISRM Rock Mech Conf. https://doi.org/10.2118/78187-MS

    Article  Google Scholar 

  • Li X, Zhang J, Grubert M, Laing C, Chavarria A, Cole S, Oukaci Y (2020) Distributed acoustic and temperature sensing applications for hydraulic fracture diagnostics. SPE Hydraul Fract Technol Conf Exhib. OnePetro

  • Lindsey NJ, Rademacher H, Ajo‐Franklin JB (2020) On the broadband instrument response of fiber‐optic DAS arrays. J Geophys Res: Solid Earth, 125(2):p.e2019JB018145

  • Liu D, Lecampion B (2022) Laboratory investigation of hydraulic fracture growth in Zimbabwe gabbro. J Geophys Res Solid Earth 127(11):e2022JB025678

    Article  Google Scholar 

  • Liu Y, Wu K, Jin G, Moridis G (2020) Rock deformation and strain-rate characterization during hydraulic fracturing treatments: Insights for interpretation of low-frequency distributed acoustic-sensing signals. SPE J 25(05):2251–2264

    Article  Google Scholar 

  • Liu Y, Jin G, Wu K, Moridis G (2021a) Hydraulic-fracture-width inversion using low-frequency distributed-acoustic-sensing strain data—part I: algorithm and sensitivity analysis. SPE J 26(01):359–371

    Article  CAS  Google Scholar 

  • Liu Y, Jin G, Wu K, Moridis G (2021b) Hydraulic-fracture-width inversion using low-frequency distributed-acoustic-sensing strain data part II: extension for multifracture and field application. SPE J 26(05):2703–2715

    Article  Google Scholar 

  • Liu Y, Wu K, Jin G, Moridis G, Kerr E, Scofield R, Johnson A (2021c) Fracture-hit detection using LF-DAS signals measured during multifracture propagation in unconventional reservoirs. SPE Reserv Eval Eng 24(03):523–535

    Article  CAS  Google Scholar 

  • Liu Y, Jin G, Wu K, Moridis G (2022) Quantitative hydraulic-fracture-geometry characterization with low-frequency distributed-acoustic-sensing strain data: fracture-height sensitivity and field applications. SPE Prod Oper 37(02):159–168

    CAS  Google Scholar 

  • Liu Y, Liang L, Zeroug S (2024) Stochastic inversion for equivalent hydraulic fracture characterization using low-frequency distributed acoustic sensing data. Int J Rock Mech Min Sci 173:105610

    Article  Google Scholar 

  • Liu Y (2021) Hydraulic fracture geometry characterization using low-frequency distributed acoustic sensing data: forward modeling, inverse modeling, and field applications. Doctoral dissertation, Texas A&M University, College Station, Texas, USA

  • McLennan J, England K, Rose P, Moore J, Barker B (2023) Stimulation of a high-temperature granitic reservoir at the Utah FORGE site. In SPE Hydraulic Fracturing Technology Conference and Exhibition. OnePetro

  • Medlin WL, Masse L (1984) Laboratory experiments in fracture propagation. Soc Petrol Eng J 24(03):256–268

    Article  Google Scholar 

  • Milanese E, Rizzato P, Pesavento F, Secchi S, Schrefler BA (2016a) An explanation for the intermittent crack tip advancement and pressure fluctuations in hydraulic fracturing. Hydraul Fract J 3(2):30–43

    Google Scholar 

  • Milanese E, Yılmaz O, Molinari JF, Schrefler B (2016b) Avalanches in dry and saturated disordered media at fracture. Phys Rev E 93(4):043002

    Article  Google Scholar 

  • Papanastasiou P, Papamichos E, Atkinson C (2016) On the risk of hydraulic fracturing in CO2 geological storage. Int J Numer Anal Meth Geomech 40(10):1472–1484

    Article  Google Scholar 

  • Papanastasiou P, Atkinson C (2015) June. The brittleness index in hydraulic fracturing. In ARMA US Rock Mechanics/Geomechanics Symposium (pp. ARMA-2015). ARMA

  • Peirce A, Detournay E (2008) An implicit level set method for modeling hydraulically driven fractures. Comput Methods Appl Mech Eng 197(33–40):2858–2885

    Article  Google Scholar 

  • Perkins TK, Kern LR (1961) Widths of hydraulic fractures. J Petrol Technol 13(09):937–949

    Article  Google Scholar 

  • Peruzzo C, Simoni L, Schrefler BA (2019) On stepwise advancement of fractures and pressure oscillations in saturated porous media. Eng Fract Mech 215:246–250

    Article  Google Scholar 

  • Pizzocolo F, Huyghe JM, Ito K (2013) Mode I crack propagation in hydrogels is step wise. Eng Fract Mech 97:72–79

  • Schrefler BA, Secchi S, Simoni L (2006) On adaptive refinement techniques in multi-field problems including cohesive fracture. Comput Methods Appl Mech Eng 195(4–6):444–461

    Article  Google Scholar 

  • Secchi S, Schrefler BA (2014) Hydraulic fracturing and its peculiarities. Asia Pac J Comput Eng 1(1):1–21

    Article  Google Scholar 

  • Sherman C, Mellors R, Morris J, Ryerson F (2019) Geomechanical modeling of distributed fiber-optic sensor measurements. Interpretation 7(1):SA21–SA27

    Article  Google Scholar 

  • Shou KJ (1993) A high order three-dimensional displacement discontinuity method with application to bounded half-space problems. PhD dissertation, University of Minnesota, Minneapolis, Minnesota, USA

  • Srinivasan A, Liu Y, Wu K, Jin G, Moridis G (2023a) Geomechanical modeling of fracture-induced vertical strain measured by distributed fiber-optic strain sensing. SPE Prod Oper 38:537–551

    CAS  Google Scholar 

  • Srinivasan A, Mjehovich J, Wang W, Wu K, Jin G, Moridis G (2023b) Evaluation of parent well depletion effects on fracture geometry based on low-frequency distributed acoustic sensing in hydraulic fracture test site-2. SPE Prod Oper 38:418–432

    CAS  Google Scholar 

  • Tan Y, Wang S, Rijken M, Hughes K, Ning ILC, Zhang Z, Fang Z (2021) Geomechanical template for distributed acoustic sensing strain patterns during hydraulic fracturing. SPE J 26(02):627–638

    Article  Google Scholar 

  • Tinni A, Sondergeld C, Chandra R (2019) Hydraulic fracture propagation velocity and implications for hydraulic fracture diagnostics. In 53rd US rock mechanics/geomechanics symposium. OnePetro

  • Ugueto GA, Todea F, Daredia T, Wojtaszek M, Huckabee PT, Reynolds A, Laing C, et al. (2019) Can you feel the strain? DAS strain fronts for fracture geometry in the BC Montney, Groundbirch. In SPE Annual Technical Conference and Exhibition. OnePetro

  • Ugueto GA, Wojtaszek M, Huckabee PT, Savitski AA, Guzik A, Jin G, Chavarria JA, et al. (2021) An integrated view of hydraulic induced fracture geometry in Hydraulic Fracture Test Site 2. In Unconventional Resources Technology Conference, 26–28 July 2021. Unconventional Resources Technology Conference (URTeC), pp. 923–938

  • Wang J, Tan Y, Rijken M, Liu X, Singh A, Li Y (2022) Observations and modeling of fiber optic strain on hydraulic fracture height growth in Hydraulic Fracturing Test Site 2 (HFTS-2). SPE J 27(02):1109–1122

    Article  Google Scholar 

  • Zhang Z, Fang Z, Stefani J, DiSiena J, Bevc D, Ning ILC, Hughes K et al (2020) Modeling of fiber-optic strain responses to hydraulic fracturing. Geophysics 85(6):A45–A50

    Article  Google Scholar 

  • Zhao Y, Bessa F, Sahni V, Pudugramam S, Liu S (2021) Key learnings from Hydraulic Fracturing Test Site-2 (HFTS-2), Delaware Basin. In Unconventional Resources Technology Conference, 26–28 July 2021. Unconventional Resources Technology Conference (URTeC), pp. 1610–1620

Download references

Data availability

The data used in this paper is downloaded from the NETL’s Energy Data eXchange repository (https://edx.netl.doe.gov/group/gti-hfts-2).

Funding

No funding was received for conducting this study.

Author information

Authors and Affiliations

  1. Schlumberger-Doll Research, Cambridge, MA, USA

    Yongzan Liu, Lin Liang & Smaine Zeroug

Authors
  1. Yongzan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lin Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Smaine Zeroug
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongzan Liu.

Ethics declarations

Conflict of interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests. Yongzan Liu, Lin Liang, Smaine Zeroug have patent Inversion Method to Estimate Fracture Propagation Velocity and Fracture Volume with Cross-Well Distributed Fiber-Optic Strain Data before Fracture Hit pending to SLB.

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 (e.g. a society or other partner) 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

Liu, Y., Liang, L. & Zeroug, S. Inference of Intermittent Hydraulic Fracture Tip Advancement Through Inversion of Low-Frequency Distributed Acoustic Sensing Data. Rock Mech Rock Eng (2024). https://doi.org/10.1007/s00603-024-03853-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00603-024-03853-2

Keywords

Search

Navigation