A criterion for identifying hydraulic fractures crossing natural fractures in 3D space

PETROLEUM EXPLORATION AND DEVELOPMENT Volume 41, Issue 3, June 2014 Online English edition of the Chinese language journal Cite this article as: PETROL. EXPLOR. DEVELOP., 2014, 41(3): 371–376.

RESEARCH PAPER

A criterion for identifying hydraulic fractures crossing natural fractures in 3D space CHENG Wan1, 2,*, JIN Yan1, 2, CHEN Mian1, 2, XU Tong1, 2, ZHANG Yakun1, 2, DIAO Ce1, 2 1. College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China; 2. State Key Laboratory of Petroleum Resources and Prospecting, Beijing 102249, China

Abstract: Based on the analysis of the stress fields near the hydraulic fracture tip and on the natural fracture surface, a criterion for identifying hydraulic fractures crossing natural fractures was proposed. A series of hydraulic fracturing tests were conducted to investigate the influences of natural fractures occurrence and horizontal stress contrast on hydraulic fracture propagation using large scale tri-axial fracturing system. The experiment results showed that the crossing happens in the region with high approaching angle and strike angle, large horizontal stresses and horizontal stress difference coefficient. Horizontal stress contrast has a critical value, only when it is above the critical value, may the hydraulic fracture cross the natural fracture. These experimental results agree with the predictions of this criterion well. It is predicted by this criterion that the hydraulic fracture of a test well in the Longmaxi shale formation, Sichuan Basin, can’t cross the natural fracture, which agrees with the micro-seismic monitoring results. Key words: shale; hydraulic fracturing; natural fracture; hydraulic fracture; occurrence

Introduction Large scale hydraulic fracturing is commonly used to stimulate the reservoir in the development of unconventional oil and gas reservoirs [1−4]. The complexity of hydraulic fracture network depends on the intersection between hydraulic and natural fractures. Experiments conducted by Norman [5] et al and Daneshy [6] et al proved that the strength of weak plane, its azimuth, and the horizontal stress difference are key factors affecting the intersection between hydraulic and natural fractures. In order to predict whether a natural fracture opens or shear slips [7], a variety of criteria have been proposed, such as Warpinski criterion [8], Renshaw criterion [9] and Zhou criterion [10-11]. These criteria were further used to judge the intersection between hydraulic and natural fractures [12−15]. However, focusing on the interaction between two vertical fracture planes, all these criteria and experiments only considers the effect of natural fracture strike angle but neglect the effect of dip angle on the intersection of hydraulic and natural fractures. Therefore, in 3D space, a new criterion to identify intersection of hydraulic fractures and natural fractures was proposed in this paper, and a series of large scale tri-axial fracturing tests were conducted to prove the validity of this new criterion. Then, this criterion was used in predicting whether the hydraulic fracture of a test

well in Longmaxi shale formation, Sichuan basin, could cross the natural fracture.

1 Intersection criterion of hydraulic and natural fractures Taking the directions of three principal stresses ( σ 1 > σ 2 > σ 3 ,where σ V =σ 1 ,σ H =σ 2 ,σ h =σ 3 ) as coordinate axes, a spatial coordinate system (1,2,3) is built (Fig.1), in which the normal vector of the natural fracture (NF) is

Fig. 1

Spatial schematic of a natural and hydraulic fracture

Received date: 22 Aug. 2013; Revised date: 15 Jan. 2014. * Corresponding author. E-mail: [email protected] Foundation item: Supported by China Natural Science Foundation (51174217; 51234006). Copyright © 2014, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.

CHENG Wan et al. / Petroleum Exploration and Development, 2014, 41(3): 371–376

uuuv nNF = (l1 , l2 , l3 ) . The hydraulic fracture generally propagates perpendicularly to the minimum pricinple stress at high stress uuuv difference. Thus, its normal vector is nHF = (0, 0, 1) . The angle between the natural and hydraulic fracture named as approaching angle, is expressed as: uuuv uuuv θ = arccos nHF ⋅ nNF (1)

(

)

If the natural fracture is a plane, the normal stress and shear stress acting on the plane by the remote in-situ stresses are given by:

⎧σin =σ l + σ l + σ l ⎪ ⎨ 2 2 2 2 2 2 2 2 2 2 ⎪⎩τin = σ1 l1 + σ 2 l2 + σ3 l3 − (σ1l1 + σ 2l2 + σ3l3 ) 2 11

2 2 2

2 33

(2)

The direction of the shear stress is expressed as

uuuv ⎛ σ − σ in σ 2 − σ in σ 3 − σ in ⎞ nτ in = ⎜ 1 l1 , l2 , l3 ⎟ τ in τ in ⎝ τ in ⎠

(3)

A special plane, which is perpendicular to the natural and hydraulic fracture, satisfies plane strain (Fig. 2). The angle ϖ between σ1 and the intersection line of hydraulic and natural fracture satisfies the relationship: uuuv uuuv ϖ = arccos ⎡⎣ nHF × nNF ⋅ (1, 0, 0 ) ⎤⎦ (4) Therefore, σ 4 = σ 2 cos 2 ϖ + σ 1 sin 2 ϖ (5)

(

)

The linear superposition of stress field and remote in-situ stress at hydraulic fracture tip is expressed as: ⎧ KΙ ϑ⎛ ϑ 3ϑ ⎞ cos ⎜ 1 − sin sin ⎟ ⎪σ x = − σ 4 + 2 2 2 ⎠ 2π r ⎝ ⎪ ⎪ KΙ ϑ⎛ ϑ 3ϑ ⎞ (6) cos ⎜1+sin sin ⎟ ⎨σ y = −σ 3 + 2 2 2 ⎠ 2π r ⎝ ⎪ ⎪ KΙ ϑ ϑ 3ϑ sin cos cos ⎪τ xy = 2 2 2 2πr ⎩ Fracture mechanics assumes that material yield at fracture process zone (r
Fig. 2 Schematic of hydraulic fracture approaching natural fracture at non-orthogonal angles

σ y ϑ =0 =

KⅠ −σ3 2πrc

(7)

A hydraulic fracture must meet tow conditions to cross a natural fracture: (1) The maximum tensile stress at the hydraulic fracture tip is equal to the tensile strength of the rock on the opposite side of the natural fracture; (2) No shear slippage occurs in the natural fracture surface. These two conditions can be expressed as:

σ y ϑ =0 = T0

(8-1)

τ θ < τ 0 − μσ θ

(8-2)

The normal and shear stress acting on the right wing ( ϑ = − θ ) of the natural fracture by the hydraulic fracture tip stress field can be expressed as: ⎧ 3θ ⎪⎪σ t , －θ = (σ 3 +T0 ) cos 2 (9) ⎨ θ 2θ ⎪τ = σ － + T sin cos ( ) 3 0 ⎪⎩ t , －θ 2 2 The normal and shear stress acting on the left wing ( ϑ =π − θ ) of the natural fracture by the hydraulic fracture tip stress field can be written as ⎧ 3θ ⎪⎪σ t , π－θ = (σ 3 +T0 ) sin 2 (10) ⎨ θ 2θ ⎪τ = σ + T cos sin ( ) 3 0 ⎪⎩ t , π－θ 2 2 Superposing Eqs. (9)-(10) and (2) respectively, the total normal and shear stress at the right and left wing of the natural fracture can be obtained. The hydraulic fracture crosses the natural fracture when these two groups of stresses satisfy Eq. (8). When the direction of σ1 is parallel with the natural fracture, this criterion is similar to the Gu [15] criterion. When the direction of σ1 is parallel with the natural fracture and θ=90°, τ0=0, stress state is shown in Fig. 3. The comparison (Fig. 4) between this criterion and Renshaw [9] criterion, Gu [15] criterion indicates there are some minor differences between the three curves, which is caused by the intersection condition of Eq. (8-1). The tensile stress at ϑ =90° is compared with tensile strength of rock in Renshaw criterion, which is not reasonable because this direction is 90° different from the tip propagation.

Fig. 3 Schematic of hydraulic fracture approaching natural fracture at orthogonal angle

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CHENG Wan et al. / Petroleum Exploration and Development, 2014, 41(3): 371–376

2-O-3 is defined as β (0<β<90º). According to spatial geometry, the approaching angle can be given by: θ = arccos ( sin α cos β ) (11) To make it easier to investigate the effect of natural fracture occurrence on hydraulic fracture propagation, these experiments assumed that the coordinate system (1, 2, 3) was the same as the earth coordinate system (U, N, E). 2.2

Fig. 4

Comparison of the three criteria

The principal stress at the fracture tip is compared with tensile strength of rock in Gu criterion. The tensile stress at ϑ =0° is compared with tensile strength of rock in Eq. (8-1), which is more reasonable than Gu and Renshaw criterion. This criterion can be used to judge whether a hydraulic fracture can cross a natural fracture. And it can also be used in investigating the effect of in-situ stresses, and natural fracture occurrence etc. on the intersection between hydraulic and natural fractures, and in simulating hydraulic fracture propagation in a natural fractured formation and predicting the fracture network.

2

Experimental verification

2.1

Introduction of pre-fracture occurrence

The angle between the normal vector of pre-existing fracture and σ1 is defined as α (0<α<90º). The angle between σ2 and the intersection line of pre-existing fracture and plane Table 1 Groups

1

2

3

4

Experimental scheme and results

Fracturing tests on cement blocks with pre-existing fractures were conducted by using tri-axial fracturing simulation system. The cement blocks 300 mm×300 mm×300 mm in size, had a mass ratio of cement (P.S32.5) and quartz sand (40-80mesh) of 1:1, an elastic modulus of 8.4 GPa, a Possion’s ratio of 0.23, an unconfined compressive strength of 28.34 MPa, a coefficient of internal friction of 0.75, a tensile strength of 2.55 MPa. The simulated wellbore was casted into the blocks, and a piece of white paper of 200 mm×150 mm×0.1 mm, was spread and casted into the block to simulate the natural fracture in the rock. The natural fracture had a tensile strength and cohesion of zero, and the friction coefficient of 0.65. A gel solution with yellow tracer and a viscosity of 135mPa·s (600 r/min), without proppant, was used as fracturing fluid, which was injected at the flow rate of 0.326 ml/s in the experiment. Three-dimensional confinined pressure were servo controled to simulate three principal insitu stresses which satisfied the relationship of σ 1 > σ 2 > σ 3 , where, σ V =σ 1 , σ H =σ 2 , σ h =σ 3 . Pre-existing fracture occurrence, in-situ stresses and the experimental results are shown in Table 1. The experiments in

Experimental parameters and results No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

α/(º) 60 60 60 30 30 60 60 60 30 30 90 90 90 90 90 90 90 90 90 90 90 90 90 90

β/(º) 90 60 30 90 60 90 60 30 90 60 90 30 90 60 30 60 30 60 90 90 75 75 45 45

θ/(º) 90.0 64.3 47.0 90.0 75.5 90.0 64.3 41.4 90.0 75.5 90.0 30.0 90.0 60.0 30.0 60.0 30.0 60.0 90.0 90.0 75.0 75.0 45.0 45.0

σ1/MPa 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 27.7 27.7 27.7 27.7 27.7 27.7

σ2/MPa 14.0 14.0 14.0 14.0 14.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 8.0 13.0 13.0 8.0 13.8 7.6 17.6 8.3 17.2 8.3

Note: C—Crossing; A—No-crossing.

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σ3/MPa 4.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 3.0 3.0 5.0 3.0 3.0 5.0 6.9 6.9 6.9 6.9 6.9 6.9

Ψ 2.50 2.50 2.50 2.50 2.50 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.33 2.33 0.60 3.33 3.33 0.60 1.00 0.10 1.55 0.20 1.49 0.20

Δσ/MPa 10.0 10.0 10.0 10.0 10.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 3.0 10.0 10.0 3.0 6.9 0.7 10.7 1.4 10.3 1.4

Test results C C A C C A A A A A A A C C A C A A C A C A A A

This criterion C C A C C C A A C A A A C A A C A A C A C A A A

CHENG Wan et al. / Petroleum Exploration and Development, 2014, 41(3): 371–376

group 1 and group 2 were conducted by the author of this paper, the data in group 3 and group 4 are from literatures [10] and [15] respectively. As shown in Table 1, 21 tests out of the 24 tests under different parameters agree with the prediction using this new criterion. The discrepancy in experiment results may be caused by the frictional coefficient of fractures and tensile strength of blocks, which are affected by many uncontrollable factors, such as temperature, humidity in the laboratory etc. 2.3

Experimental analyses

The influences of approaching angle θ, dip angle α, strike angle β, horizontal in-situ stress difference ( Δσ =σ 2 − σ 3 ) and horizontal in-situ stress difference coefficient [10] (Ψ =(σ 2 − σ 3 ) / σ 3 ) on hydraulic fracture propagation can be figured out by statistics of the data in Table 1. As shown in Fig. 5a, the intersection of hydraulic fracture and naturals occurs mainly in the region with high θ and large Ψ. As shown in Fig. 5b, this intersection happened in the region with high θ and large Δσ, and a critical value of Δσ can be identified. Only when Δσ is above this critical value, can hydraulic fracture cross the natural fracture, otherwise the hydraulic fracture can not cross the natural fracture. It is believed that this critical value can help identify the interference between hydraulic and natural fractures in field preliminarily. According to the drawing method in Fig. 5, a similar pattern of the influence of strike angle on hydraulic fracture propagation can be recognized. A computer program has been coded based on this criterion. At a given dip angle, the minimum strike angle for the hydraulic fracture to cross the natural fracture can be easily cal-

Fig. 5

culated based on the three-dimensional stresses in Table 1. When this program has a solution, the boundary line (yellow dotted line) is plotted in Fig. 5, in which a boundary line can distinguish the crossing from no-crossing. The interference between hydraulic and natural fractures can usually be divided into three types: crossing, arrest, and deflecting. It is very difficult to distinguish arrest from deflecting with a naked eye because fracturing liquid will leak off along the natural fracture in both cases. However, they both display the same behavior, i.e., no-crossing, thus, this paper only distinguish crossing (Fig. 6a) from no-crossing (Fig. 6b) in these experiments.

3

Case study

There developed black shale with bedding fractures in lower Silurian Longmaxi Formation of Sichuan basin, where the burial depth of shale gas reservoir is 2 400−2 525 m. The overburden stress gradient is 2.0 MPa/100 m, the minimum horizontal stress gradient is 1.9 MPa/100 m, the maximum horizontal stress gradient is 2.3 MPa/100 m. The basic mechanical properties of this shale mass and bedding plane were obtained from experiment, for shale mass: elastic modulus of 36.5 GPa; Possion’s ratio of 0.21; coefficient of internal friction of 0.7; tensile strength of 6.5 MPa; For bedding plane: coefficient friction of 0.61; cohesion of 2 MPa; tensile strength of 1.9 MPa. The direction of the maximum principal stress of a test well in Longmaxi formation is NWW-SEE 115º. The formation dip angle is about 9º. The strike angle is about NEE-SWW 25º and parallel with the minimum horizontal principal stress but perpendicular to the intermediate principal stress. Transforming

Influence of approaching angle on fracture propagation

Fig. 6

Photos of experimental result

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CHENG Wan et al. / Petroleum Exploration and Development, 2014, 41(3): 371–376

Fig. 7 Side view of microseismic crack monitoring of a well in Longmaxi Formation shale

Fig. 8 Top view of microseismic crack monitoring of a well in Longmaxi Formation shale

the coordinate system (U,N,E) into (1,2,3), α=81º, β=90º. It was predicted the hydraulic fracture wouldn’t cross the natural fracture by using the criterion presented in this paper. Divided into 10 stages, the hydraulic fracturing stimulation in this test well was monitored by micro-seismic monitoring, as shown in Fig.7 and Fig.8. Micro-seismic events mainly distribute in a horizontal plane but not in a plane perpendicular to the minimum in-situ stress, which indicates that the hydraulic fractures propagated along the natural fracture and didn’t cross it, consistent with the prediction of this criterion.

4

Conclusions

(1) A new criterion for judging whether the hydraulic fracture can cross the natural fracture in three-dimensional space was proposed. And large scale tri-axial fracturing experiments have proved the validity of this criterion. (2) The intersection of hydraulic fractures and natural fractures happened in the region with high approaching and strike angle, large horizontal stress difference and horizontal stress difference coefficient. A critical value of Δσ can be identified. Only when Δσ is above this critical value, can the hydraulic fracture cross the natural fracture, otherwise, hydraulic fracture can not cross the natural fracture. This critical value will be useful to judge the interaction between hydraulic and natural fracture in field. (3) It was predicted by this criterion that the hydraulic fracture wouldn’t cross the natural fracture in a test well in shale gas reservoir in lower Silurian Longmaxi Formation of Sichuan basin, which agrees with the results of micro-seismic monitoring.

σH— Horizontal maximum principal stress, MPa; σh— Horizontal minimum principal stress, MPa; σ1— Maximum principal stress, MPa; σ2— Intermediate principal stress, MPa; σ3— Minimum principal stress, MPa; θ— Approaching angle, rad; α— Dip angle, (°) ; β— Strike angle, (°) ; σin— Normal stress of remote in-situ stress acting on natural fracture, MPa; τin— Shear stress of remote in-situ stress acting on natural fracture, MPa; l1, l2, l3— The normal vector of the natural fracture, dimensionless; σ4— Stress component which is parallel to the hydraulic fracture interface under plane strain elasticity, MPa; ϖ— The angle between σ1 and the intersection line of hydraulic and natural fracture, rad; σx, σy— x and y direction stress component acting at hydraulic fracture tip, MPa; τxy— Shear stress component acting at hydraulic fracture tip, MPa; KⅠ— Stress intensity factor of ModelⅠfracture, MPa·m0.5; r, ϑ — Polar coordinate system with the origin at fracture tip; rc— The radius of process zone around fracture tip, m; T0— Rock mass tensile strength, MPa; τ0— Cohesion of natural fracture surface, MPa; σθ— Total normal stress acting at natural fracture surface, MPa; τθ— Total shear stress acting at natural fracture surface, MPa; σt,－θ, σt, π－θ— Normal stress component acting at right and left wing of the natural fracture surface when the approaching angle is θ, MPa; τt,－θ, τt, π－θ— Shear stress component acting at right and left wing of the natural fracture surface when the approaching angle is θ, MPa; Ψ— Horizontal stress difference coefficient, dimensionless; Δσ— Horizontal stress difference, MPa; μ—Natural fracture surface friction coefficient, dimensionless.

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