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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

## Abstract

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 $0.1m≤ℓ≤1m$, 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.

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## Figures

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

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

Fig. 2

Schematic of the problem domain

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.

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.

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.

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

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

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

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.

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

Fig. 12

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

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