Skip to main content

Effect of Foliation and Fluid Viscosity on Hydraulic Fracturing Tests in Mica Schists Investigated Using Distinct Element Modeling and Field Data


Several hydraulic fracturing tests were performed in boreholes located in central Hungary in order to determine the in-situ stress for a geological site investigation. At a depth of about 540 m, the observed pressure versus time curves in mica schist with low dip angle foliation shows atypical pressure versus time results. After each pressurization cycle, the fracture breakdown pressure in the first fracturing cycle is lower than the refracturing or reopening pressure in the subsequent pressurizations. It is assumed that the viscosity of the drilling mud and observed foliation of the mica schist have a significant influence on the pressure values. In order to study this problem, numerical modeling was performed using the distinct element code particle flow code, which has been proven to be a valuable tool to investigate rock engineering problems such as hydraulic fracturing. The two-dimensional version of the code applied in this study can simulate hydro-mechanically coupled fluid flow in crystalline rock with low porosity and pre-existing fractures. In this study, the effect of foliation angle and fluid viscosity on the peak pressure is tested. The atypical characteristics of the pressure behaviour are interpreted so that mud with higher viscosity penetrates the sub-horizontal foliation plane, blocks the plane of weakness and makes the partly opened fracture tight and increase the pore pressure which decreases slowly with time. We see this viscous blocking effect as one explanation for the observed increase in fracture reopening pressure in subsequent pressurization cycles.

This is a preview of subscription content, access via your institution.

Fig. 1

(after ÁKMI 2016). (Color figure online)

Fig. 2

(after Lemon et al. 2016)

Fig. 3
Fig. 4

(after Lemon et al. 2016). (Color figure online)

Fig. 5

(after Lemon et al. 2016). (Color figure online)

Fig. 6

(after Lemon et al. 2016)

Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16



Hydraulic fracturing


Leak-off test


Extended leak-off test


Fracture breakdown pressure


Nuclear power plant


Refracturing pressure or reopening pressure


Shut-in pressure


Instantaneous shut-in pressure


Derivative shut-in pressure


Jacking pressure

P f :

Fluid pressure

σ 3 :

Minimum principal stress

σ 1 :

Maximum principal stress

σn :

Normal stress

Sv :

Vertical stress

S hmin :

Minimum horizontal stress

S Hmax :

Maximum horizontal stress

Sxx :

Stress parallel to axis x

Szz :

Stress parallel to axis z


Uniaxial compressive strength


Brazilian tensile strength


Tensile strength of the rock


Flow rate


Hydraulic aperture

e 0 :

Hydraulic aperture at zero normal stress

e inf :

Hydraulic aperture at infinite normal stress

α :

Coefficient of decay

η :

Dynamic fluid viscosity

R :

Particle radius

m :

Particle mass

a :


K c :

Contact stiffness

K b :

Bond stiffness

U :

Particle overlap

V inj :

Injected fluid volume


  • ÁKMI Ltd (2016) Conduction of geological research program required for Paks II site permit. Final report of the geological research program. Document ID: MÁ/PA2-16-FT-14 V2 (Paks II Telephelyengedélyének Megszerzéséhez Szükséges Földtani Kutatás Végrehajtása. Földtani Kutatási Program Zárójelentése, in Hungarian), Pécs, Hungary

  • Amadei B, Stephansson O (1997) Rock stress and its measurement. Chapman & Hall, London

    Book  Google Scholar 

  • Doe TW, Korbin GE (1987) A comparison of hydraulic fracturing and hydraulic jacking stress measurements, 28th US Symp on Rock Mech, Tuscon, pp 283–290

  • Haimson BC, Cornet FH (2003) ISRM Suggested Methods for rock stress estimation—part 3: hydraulic fracturing (HF) and/or hydraulic testing of pre-existing fractures (HTPF). Int J Rock Mech Min Sci 40:1011–1020

    Article  Google Scholar 

  • Hazzard JF, Young RP, Oates SJ (2002) Numerical modeling of seismicity induced by fluid injection in a fractured reservoir, In: Proceedings of the 5th North American rock mechanics symposium mining and tunnel innovation and opportunity, Toronto, ON, Canada, 7–10 July 2002, pp 1023–1030

  • Healy JH, Zoback MD (1988) Hydraulic fracturing in-situ stress measurements to 2.1 km depth at Cajon Pass, California. Geophys Res Let 15:1005–1008

    Article  Google Scholar 

  • Hickman SH, Zoback MD (1983) The interpretation of hydraulic fracturing pressure-time data for in-situ stress determination. In: Zoback MD, Haimson BC (eds) Hydraulic fracturing measurements. National Academy Press, Washington D.C., pp 44–54

    Google Scholar 

  • Hökmark H, Lönnqvist M, Fälth B (2010) THM-issues in repository rock. Thermal, mechanical, thermo-mechanical and hydro-mechanical evolution of the rock at the Forsmark and Laxemar sites. Technical report, TR-10-23, SKB Publications, 2010, updated 2011–10

  • Itasca Consulting Group Inc (2008) PFC2D version 4.0 manual (Particle flow code in 2 dimensions), Minneapolis, USA

  • Itasca Consulting Group Inc (2012) Technical memorandum to PFC2D (Particle Flow Code in 2 dimensions) version 4.0–5.0. Parallel bond enhancement, Minneapolis, USA

  • Labuz J, Zang A (2012) ISRM suggested methods for rock failure. Mohr–Coulomb failure criteria. Rock Mech Rock Eng 45:975–979

    Article  Google Scholar 

  • Lavrov A, Larsen I, Bauer A (2016) Numerical modelling of extended leak-off test with a pre-existing fracture. Rock Mech Rock Eng 49:1359–1368

    Article  Google Scholar 

  • Lemon M, Farkas MP, Korpai F, Dankó G (2016) Technical report of hydraulic fracturing tests. Conduction of geological research program required for paks II site permit, Golder Associates Hungary, Budapest, Hungary

  • Lin C, He J, Li X, Wan X, Zheng B (2017) An experimental investigation into the effects of the anisotropy of shale on hydraulic fracture propagation. Rock Mech Rock Eng 50:543–554

    Article  Google Scholar 

  • Mas Ivars D, Potyondy DO, Pierce M, Cundall PA (2008) The smoot-joint contact model. In: Proceedings of the 8th World Congress on computational mechanics—5th European Congress on computation mechanics and applied science and engineering, Venice, Italy, 2008

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364

    Article  Google Scholar 

  • Shimizu H, Murata S, Ishida T (2011) The distinct element analysis for hydraulic fracturing in hard rock considering fluid viscosity and particle size distribution. Int J Rock Mech Min Sci 48:712–727

    Article  Google Scholar 

  • Stephansson O, Zang A (2012) ISRM suggested methods for rock stress estimation—part 5: establishing a model for the in-situ stress at a given site. Rock Mech Rock Eng 45:955–969

    Article  Google Scholar 

  • Yoon JS, Zang A, Stephansson O (2014) Numerical investigation on optimized stimulation of intact and naturally fractured deep geothermal reservoirs using hydro-mechanical coupled discrete particles joints model. Geothermics 52:165–184

    Article  Google Scholar 

  • Yoon JS, Zang A, Stephansson O, Hofmann H, Zimmermann G (2017) Discrete element modelling of hydraulic fracture propagation and dynamic interaction with natural fractures in hard rock. Proc Eng 191:1023–1031

    Article  Google Scholar 

  • Zang A, Berckhemer H (1993) Classification of crystalline drill cores from the KTB deep well based on strain, velocity and fracture experiments. Int J Rock Mech Min Sci 30(4):331–342

    Article  Google Scholar 

  • Zang A, Stephansson O (2010) Stress field of the Earth’s crust. Springer, Dordrecht

    Book  Google Scholar 

  • Zang A, Stephansson O, Heidbach O, Janouschkowetz S (2012) World stress map data base as a resource for rock mechanics and rock engineering. Geotech Geol Eng 30(3):625–646

    Article  Google Scholar 

  • Zhou J, Zhang L, Braun A, Han Z (2016a) Numerical modeling and investigation of fluid-driven fracture propagation in reservoirs based on a modified fluid-mechanically coupled model in two-dimensional particle flow code. Energies 9(9):699

    Article  Google Scholar 

  • Zhou L, Ding L, Guo Q (2016b) Indoor experiments on the effect of the slurry on the in-situ stress measurement results, In: Johansson E, Raasakka V (eds) Symposium proceedings, 7th international symposium on in-situ stress, Tampere, Finland, May 10–12, 2016, pp 235–246

  • Zoback MD (2010) Reservoir geomechanics. Cambridge University Press, Cambridge

    Google Scholar 

Download references


The authors would like to thank Golder Associates Hungary for the financial support provided to this research.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Márton Pál Farkas.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Farkas, M.P., Yoon, J.S., Zang, A. et al. Effect of Foliation and Fluid Viscosity on Hydraulic Fracturing Tests in Mica Schists Investigated Using Distinct Element Modeling and Field Data. Rock Mech Rock Eng 52, 555–574 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Hydraulic fracturing
  • Stress measurement
  • Particle flow code
  • Hydro-mechanical coupling
  • Microcrack
  • Viscous blocking