Research Papers

Poroelastic Effects in Reactivation of a Fingerlike Hydraulic Fracture

[+] Author and Article Information
Erfan Sarvaramini

Department of Civil and Resource Engineering,
Dalhousie University,
1360 Barrington Street,
Halifax, NS B3H 4R2, Canada
e-mail: erfan.sarvaramini@dal.ca

Dmitry I. Garagash

Department of Civil and Resource Engineering,
Dalhousie University,
1360 Barrington Street,
Halifax, NS B3H 4R2, Canada
e-mail: garagash@dal.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 13, 2016; final manuscript received February 25, 2016; published online March 21, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(6), 061011 (Mar 21, 2016) (8 pages) Paper No: JAM-16-1084; doi: 10.1115/1.4032908 History: Received February 13, 2016; Revised February 25, 2016

This paper studies the transient pressurization of a pre-existing, fingerlike crack in a poroelastic, permeable rock due to a fluid injection, the problem previously considered in the nonporoelastic reservoir context in the companion paper (Sarvaramini and Garagash, 2015, “Breakdown of a Pressurized Fingerlike Crack in a Permeable Solid,” J. Appl. Mech., 82(6), p. 061006). Large-scale fluid leak-off from the crack and the associated pore-fluid diffusion within the permeable rock formation lead to dilation of the pore volume, which acts to additionally confine/close the crack. The influence of this so-called “poroelastic backstress” on the evolution of the fluid pressure in the crack and the onset of the fracture propagation are investigated. We first revisit the existing solution to an auxiliary problem of a poroelastic crack subjected to a step pressure increase and generalize it to account for the full-space fluid leak-off diffusion. This solution is then used to formulate the solution to the transient pressurization of the crack due to a constant rate of fluid injection via the Green's function approach. Comparison to the reference solution for a fingerlike crack in a nonporoelastic reservoir shows that the poroelasticity has a minor effect on the fluid pressure evolution in the crack. However, the evolution of the fracture volume and the onset of the fracture propagation are shown to be significantly hindered by the poroelastic backstress at large enough injection time when fluid diffusion becomes fully two- or three-dimensional.

Copyright © 2016 by ASME
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Grahic Jump Location
Fig. 1

Injection into a pre-existing poroelastic fingerlike crack with half-length and height h ( ≫ h)

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Fig. 2

Numerical solution for the normalized leak-off rate in the mode 2 loading, after [15]. The small-time (a) and the large-time asymptotes (b) are contrasted to the general numerical solution. The timescale is t2D = 2/4α.

Grahic Jump Location
Fig. 3

Comparison of the general numerical solution for theinfluence function F(x, t) with its 1D asymptote F1D (t/t1D), given by Eq. (12), for the case with h/ = 0.1. The timescale is t1D = h2/4α.

Grahic Jump Location
Fig. 4

Evolution of (a) the crack-average of the influence function, 〈F〉(t), and (b) the tip value of the influence function, F(x = ±, t), with normalized time for various values of the crack aspect ratio h/. The timescale is t1D = h2/4α.

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Fig. 5

Numerical solution for the normalized cumulative leak-off volume in the mode 2 loading, after [14,15]. The small- and large-time asymptotes [15] are shown by dashed lines for comparison. The timescale is t2D = 2/4α.

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Fig. 6

(a) Evolution of normalized net pressure (p − σ0)/p1 with time t/t1 during transient pressurization for various values of the crack aspect-ratio h/ℓ, SE′=10 and η = 0.3. The 1D (Eq. (30)) and 2D leak-off-dominated (Eq. (31)) asymptotic solutions are shown by dashed lines. The dotted line shows the early-time storage-dominated solution. (b) The ratio of the poroelastic to the nonporoelastic [15] net pressure solutions. The pressure and timescales are p1=Q0E′t1/h2ℓ and t1=(1/SE′)2(h2/4α), respectively.

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Fig. 7

Distribution of the backstress to the net pressure ratio along the crack for h/ = 0.1, SE′=10, and η = 0.3. The small-time (a) and large-time asymptotes (b), shown by dashed lines, are contrasted to the numerical solution. The timescale is t1=(1/SE′)2(h2/4α).

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Fig. 9

Evolution of the normalized poroelastic net-loading at the crack tip p¯(ℓ,t)/p1=(p(t)−σ0−σb(x,t))|x=ℓ/p1 for the injection scenario described in the text, and characterized by h/ = 0.4, SE′=16.9, and η = 0.3. A simplified poroelastic solution using the 1D approximation for the poroelastic influence function (FF1D) and the reference normalized nonporoelastic solution p¯(t)/p1=(p(t)−σ0)np/p1 are also shown for comparison. Predictions of the onset of the fracture propagation (p¯(ℓ,tB)=p¯B) are shown by the indicated sets of points for the full poroelastic solution (points B and B′), the approximate (FF1D) poroelastic solution (points C and C′), and the reference, nonporoelastic solution (points A and A′). The primed points correspond to the doubled fluid injection rate.

Grahic Jump Location
Fig. 8

Evolution of (a) average backstress and (b) backstress at the crack tip (x = ) normalized by the net pressure in the crack with normalized time t/t1 for various crack height to length ratio h/, SE′=10 and η = 0.3. The timescale is t1=(1/SE′)2(h2/4α).




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