Research Papers

Characterizing the Stimulated Reservoir Volume During Hydraulic Fracturing-Connecting the Pressure Fall-Off Phase to the Geomechanics of Fracturing

[+] Author and Article Information
Erfan Sarvaramini

Department of Civil and
Environmental Engineering,
University of Waterloo,
200 University Ave W,
Waterloo, ON N2 L 3G1, Canada
e-mail: esarvaramini@uwaterloo.ca

Maurice B. Dusseault

Earth and Environmental Sciences Department,
University of Waterloo,
200 University Ave W,
Waterloo, ON N2 L 3G1, Canada
e-mail: mauriced@uwaterloo.ca

Robert Gracie

Department of Civil and
Environmental Engineering,
University of Waterloo,
200 University Ave W,
Waterloo, ON N2 L 3G1, Canada
e-mail: rgracie@uwaterloo.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 16, 2018; final manuscript received May 30, 2018; published online July 3, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(10), 101006 (Jul 03, 2018) (11 pages) Paper No: JAM-18-1152; doi: 10.1115/1.4040479 History: Received March 16, 2018; Revised May 30, 2018

Microseismic imaging of the hydraulic fracturing operation in the naturally fractured rocks confirms the existence of a stimulated volume (SV) of enhanced permeability. The simulation and characterization of the SV evolution is uniquely challenging given the uncertainty in the nature of the rock mass fabrics as well as the complex fracturing behavior of shear and tensile nature, irreversible plastic deformation and damage. In this paper, the simulation of the SV evolution is achieved using a nonlocal poromechanical plasticity model. Effects of the natural fracture network are incorporated via a nonlocal plasticity characteristic length, . A nonlocal Drucker–Prager failure model is implemented in the framework of Biot's theory using a new implicit C0 finite element method. First, the behavior of the SV for a two-dimensional (2D) geomechanical injection problem is simulated and the resulting SV is assessed. It is shown that breakdown pressure and stable fracturing pressure are the natural outcomes of the model and both depend upon . Next, the post-shut-in behavior of the SV is analyzed using the pressure and pressure derivative plots. A bilinear flow regime is observed and it is used to estimate the flow capacity of the SV. The results show that the flow capacity of the SV increases as decreases (i.e., as the SV behaves more like a single hydraulic fracture); however, for 0.1m1m, the calculated flow capacity indicates that the conductivity of the SV is finite. Finally, it is observed that as tends to zero, the flow capacity of the SV tends to infinity and the SV behaves like a single infinitely conducting fracture.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Mayerhofer, M. J. , Lolon, E. , Warpinski, N. R. , Cipolla, C. L. , Walse, D. W. , and Rightmire, C. M. , 2010, “ What is Stimulated Reservoir Volume?,” SPE Prod. Oper., 25(1), pp. 89–98.
Dusseault, M. B. , 2013, “ Geomechanical Aspects of Shale Gas Development,” Rock Mech. Resour., Energy Environ., 39, pp. 39–56.
Dusseault, M. B. , McLennan, J. , and Shu, J. , 2011, “ Massive Multi-Stage Hydraulic Fracturing for Oil and Gas Recovery From Low Mobility Reservoirs in China,” Pet. Drilling Tech., 39(3), pp. 6–16. https://www.researchgate.net/publication/288812002_Massive_multi-stage_hydraulic_fracturing_for_oil_and_gas_recovery_from_low_mobility_reservoirs_in_China
Cipolla, C. L. , Warpinski, N. R. , Mayerhofer, M. , Lolon, E. P. , and Vincent, M. , 2010, “ The Relationship Between Fracture Complexity, Reservoir Properties, and Fracture-Treatment Design,” SPE Prod. Oper., 25(4), pp. 1–21.
Maxwell, S. , 2014, Microseismic Imaging Hydraulic Fracturing: Improved Engineering Unconventional Shale Reservoirs, Society of Exploration Geophysicists, Tulsa, OK. [CrossRef]
Boroumand, N. , and Eaton, D. W. , 2012, “ Comparing Energy Calculations-Hydraulic Fracturing and Microseismic Monitoring,” 74th EAGE Conference and Exhibition Incorporating EUROPEC, Copenhagen, Denmark, June 4–7, Paper No. 58979.
Garagash, D. I. , and Detournay, E. , 2000, “ The Tip Region of a Fluid-Driven Fracture in an Elastic Medium,” ASME J. Appl. Mech., 67(1), pp. 183–192. [CrossRef]
Tsai, Y. M. , 1983, “ Transversely Isotropic Thermoelastic Problem of Uniform Heat Flow Distributed by a Penny-Shaped Crack,” J. Therm. Stress, 6(2–4), pp. 379–389. [CrossRef]
Garagash, D. I. , and Detournay, E. , 2005, “ Plane-Strain Propagation of a Fluid-Driven Fracture: Small Toughness Solution,” ASME J. Appl. Mech., 72(6), pp. 916–928. [CrossRef]
Detournay, E. , Adachi, J. I. , and Garagash, D. I. , 2002, “ Asymptotic and Intermediate Asymptotic Behavior Near the Tip of a Fluid-Driven Fracture Propagating in a Permeable Elastic Medium,” Structural Integrity and Fracture, A. V. Dyskin , X. Hu , and E. Sahouryeh , eds., pp. 9–18, Balkema, Lisse, The Netherlands.
Shimizu, H. , Murata, S. , and Ishidab, 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(5), pp. 712–727. [CrossRef]
B., Damjanac , I., Gil , M., Pierce , M., Sanchez , A., Van , As, J. , and McLennan , 2010, “ A New Approach to Hydraulic Fracturing Modeling in Naturally Fractured Reservoirs,” 44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium, Salt Lake City, UT, June 27–30, Paper No. ARMA-10-400 https://www.onepetro.org/conference-paper/ARMA-10-400.
Drucker, D. C. , and Prager, W. , 1952, “ Soil Mechanics and Plastic Analysis or Limit Design,” Q. Appl. Math., 10(2), pp. 157–165. [CrossRef]
Biot, M. A. , 1941, “ General Theory of Three-Dimensional Consolidation,” J. Appl. Phys., 12(2), pp. 155–164. [CrossRef]
De Borst, R. , and Pamin, J. , 1996, “ Some Novel Developments in Finite Element Procedures for Gradient-Dependent Plasticity,” Int. J. Numer. Methods Eng., 39(14), pp. 2477–2505. [CrossRef]
Pamin, J. , and De Borst, R. , 1995, “ A Gradient Plasticity Approach to Finite Element Predictions of Soil Instability,” Arch. Mech., 47, pp. 353–377.
Engelen, R. A. B. , 2005, “ Plasticity-Induced Damage in Metals: Nonlocal Modelling at Finite Strains,” Ph.D. thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands. https://research.tue.nl/en/publications/plasticity-induced-damage-in-metals-nonlocal-modelling-at-finite-
Engelen, R. A. B. , Geers, M. G. D. , and Baaijens, F. P. T. , 2003, “ Nonlocal Implicit Gradient-Enhanced Elasto-Plasticity for the Modelling of Softening Behaviour,” Int. J. Plasticity, 19(4), pp. 403–433. [CrossRef]
Nilson, R. H. , and Griffiths, S. K. , 1983, “ Numerical Analysis of Hydraulically-Driven Fractures,” Comput. Methods Appl. Mech. Eng., 36(3), pp. 359–370. [CrossRef]
Bourdet, D. , Ayoub, J. A. , and Pirard, Y. M. , 1989, “ Use of Pressure Derivative in Well Test Interpretation,” SPE Form. Eval., 4(2), pp. 293–302. [CrossRef]
Sarvaramini, E. , and Garagash, D. I. , 2015, “ Breakdown of a Pressurized Fingerlike Crack in a Permeable Solid,” ASME J. Appl. Mech., 82(6), p. 061006. [CrossRef]
Sarvaramini, E. , and Garagash, D. I. , 2016, “ Poroelastic Effects in Reactivation of a Fingerlike Hydraulic Fracture,” ASME J. Appl. Mech., 83(6), p. 061011. [CrossRef]
Nolte, K. G. , 1979, “ Determination of Fracture Parameters From Fracturing Pressure Decline,” SPE Annual Technical Conference and Exhibition, Las Vegas, NV, Sept. 23–26, SPE Paper No. SPE 8341.
Cinco, L. H. , Samaniego, V. F. , and Dominguez, A. N. , 1978, “ Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture,” AIME Soc. Pet. Eng. J., Trans., 18(4), pp. 253–264. [CrossRef]
Babuška, I. , 1971, “ Error-Bounds for Finite Element Method,” Numerische Math., 16(4), pp. 322–333. [CrossRef]
Flügel, E. , 2013, Microfacies Carbonate Rocks: Analysis, Interpretation Application, Springer Science & Business Media, New York.
Katz, A. J. , and Thompson, A. H. , 1986, “ Quantitative Prediction of Permeability in Porous Rock,” Phys. Rev. B, 34(11), p. 8179. [CrossRef]
Rothenburg, L. , Bathurst, R. J. , and Dusseault, M. B. , 1989, “ Micromechanical Ideas in Constitutive Modelling of Granular Materials,” Powders Grains, 90, pp. 355–363.
Gringarten, A. C. , Ramey , H. J., Jr. , and Raghavan, R. , 1975, “ Applied Pressure Analysis for Fractured Wells,” J. Pet. Technol., 27(7), pp. 887–892. [CrossRef]
Bazant, Z. P. , and Oh, B. H. , 1983, “ Crack Band Theory for Fracture of Concrete,” Mater. Constr., 16(3), pp. 155–177. [CrossRef]
Simo, J. C. , and Hughes, T. J. R. , 2006, Computational Inelasticity, Vol. 7, Springer Science & Business Media, New York.
Djoko, J. K. , Ebobisse, F. , McBride, A. T. , and Reddy, B. D. , 2007, “ A Discontinuous Galerkin Formulation for Classical and Gradient Plasticity—Part 2: Algorithms and Numerical Analysis,” Comput. Methods Appl. Mech. Eng., 197(1–4), pp. 1–21. [CrossRef]


Grahic Jump Location
Fig. 1

(a) The various stimulated zones during injection into a naturally fractured system [2] and (b) equivalent continuum approximation of the stimulated zone controlled by the length scale

Grahic Jump Location
Fig. 2

Schematic of the problem domain

Grahic Jump Location
Fig. 3

Schematic illustrating the injection problem: water is injected at the flow rate of q = 10−4 m2/s at the center of a 200 × 200 m2 square domain whose boundary is fixed and drained (pnet=p−p0=0). The reservoir ambient pressure is p0 ≈ 16 MPa. The initial in situ stress field is σxx(=σmin)=−20 MPa, σyy(=σmax)=−40 MPa, and σzz(=σV)≈−33.6 MPa. The line A−A′ and points a will be used later to demonstrate the accuracy of the numerical results.

Grahic Jump Location
Fig. 10

Evolution of the net-pressure with time at the point a marked in Fig. 3 for three sets of meshing: coarse, midfine, and fine meshing

Grahic Jump Location
Fig. 9

(a) Nonlocal plastic strain and (b) net-pressure along the line shown in Fig. 3 at t = 2000s (shut-in moment) for three sets of meshing: coarse, midfine, and fine meshing

Grahic Jump Location
Fig. 8

Illustration of the discretization scheme; three sets of meshing, (a) coarse, (b) medium-fine, and (c) fine are used for the study of the accuracy of the numerical results. The inner rectangle surface size is 6 m × 34 m. The original domain size is 200 × 200 m2.

Grahic Jump Location
Fig. 7

(a) Net-pressure and (b) pressure derivative type curves for the post-injection shut-in analysis of a SV with the nonlocal length scale of  = 0.45 m

Grahic Jump Location
Fig. 6

Contours of the (a) Drucker-Prager (DP) stress (ΔσDP), and (b) shear stress (Δσxy) at the moment of the shut-in (t = 2000 s) for the injection example problem

Grahic Jump Location
Fig. 5

Evolution of the non-local plastic strain with time for three selected time steps, t = 500 s (on the left), t = 1000 s, and t = 2000s (on the right). The original domain size is 200 × 200 m2.

Grahic Jump Location
Fig. 4

Evolution of the net-pressure contours with time for three selected time steps, t = 500 s (on the left), t = 1000 s, and t = 2000s (on the right). The original domain size is 200 × 200 m2.

Grahic Jump Location
Fig. 11

Comparison of the pressure and pressure derivative types curves for the SV characterized by the nonlocal length scales  = 0.45 m and  = 1 m

Grahic Jump Location
Fig. 12

The evolution of the fracture flow capacity CfD with respect to the nonlocal length scale



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In