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Time delay effect due to pore pressure changes and existence of cleats on borehole stability in coal seam
International Journal of Coal Geology 85 (2011) 212–218
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International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o
Time delay effect due to pore pressure changes and existence of cleats on borehole stability in coal seam Ping Qu a,b,⁎, Ruichen Shen a, Li Fu a,b, Zijian Wang b a b
CNPC Drilling Research Institute, Beijing, China Research Institute Of Petrochina, Beijing, China
a r t i c l e
i n f o
Article history: Received 12 August 2010 Received in revised form 28 October 2010 Accepted 28 October 2010 Available online 4 November 2010 Keywords: Pore pressure Borehole stability Time delay effect Fluid–solid coupling Fracture mechanics Coal seam
a b s t r a c t When horizontal wells are drilled underbalanced in coal seam, it was found that borehole which kept stable at the beginning would probably collapse in some time. The phenomenon was called as time delay effect. In order to clarify the concept of time delay effect, the influence of pore pressure on stresses of cleats was analyzed based on the characteristic that cleats are abundant in coal seam, indicating that pore pressure influences the normal stresses of cleat surface while it has no impact on the tangential stresses. Using the data from field production in a CBM well, the influence of pore pressure changes on stability of coal rock was analyzed, indicating that contents of coal fines in drained water increases as pore pressure decreases. Pore pressure changes due to seepage in underbalanced drilling or overbalanced drilling were analyzed. This study above demonstrates that the time delay effect exists absolutely in borehole stability in coal seams during underbalanced drilling. The pore pressure changes are the main factor on the time delay effect, while cleats are the internal cause. In order to analyze further time delay effect quantitatively, the fluid–solid coupling during underbalanced drilling was numerically simulated, and the relationship between pore pressure and time was fitted, and the equation for computing the delaying time was posed by means of borehole stability theory in fracture mechanics. The analysis of the time delay effect can guide the field drilling operation and avoid the instability caused by pore pressure changes. The delaying time can be altered through adjusting bottom hole pressure in order to supply sufficient time for drilling operation. © 2010 Elsevier B.V. All rights reserved.
1. Introduction During production/injection pore pressure changes, because of influx or efflux, lead to changes in effective stress which in turn lead to changes in the conditions for borehole stability. (Gu and Chalaturnyk, 2005; Deisman et al, 2010). In fact, during drilling, pore pressure changes is also likely to happen because BHP can't keep the same as pore pressure all the time. Changes in effective stress which in turn lead to changes in the stresses acting on cleats which in turn make cleats propagate or fail or keep stable. Propagation, failure, or stability of cleats have an important influence on borehole stability. Hence, when pore pressures vary in time, borehole stability in coal seam will change over time. Large numbers of facts have proved the inference above. 1.1. Study objective Horizontal wells have been used extensively in the Qinshui Basin for CBM development. However, the technologies have not been as ⁎ Corresponding author. CNPC Drilling Research Institute, Beijing, China. Tel.: +86 010 52781873; fax: +86 010 52781890. E-mail address: [email protected] (P. Qu). 0166-5162/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2010.10.013
successful as originally expected (Gentzis et al., 2007). Several drilled horizontal well produced less than 10,000 m3 gas per day and even zero, for example, Zheng Ping 1-1 well, Wu M1-1 well (Lei Qiao et al., 2007) and so on. The lower production may be attributed to borehole instability after drilling which can clog the wellbore or shear failure which may cause generation of coal fines, again clogging the cleats. (Deisman et al., 2008; Moschovidis et al., 2005). When horizontal wells are drilled underbalanced in coal seam, it was found that borehole which kept stable at the beginning would collapse in some time. The phenomenon was defined as time delay effect. It can be concluded from the inference above that time delay effect is mainly tied up with pore pressure changes and existences of cleats. It is also discovered through lots of researches that pore pressure changes is the main factor in time delay effect and cleats in coal seam is the internal cause. There isn't time delay effect without cleats. However, pore pressure changes cause directly the generation of time delay effect. In all, the study objective is to analyze time delay effect and calculate the delaying time during underbalanced horizontal drilling. Firstly, the influence of pore pressure on borehole stability is analyzed so as to analyze time delay effect qualitatively. Secondly, fluid–solid coupling effect is numerically simulated in order to establish the relationship of pore pressure changes over time. In the end, the
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delaying time is calculated by means of borehole stability theory in fracture mechanics.
pressure, if the normal stresses acting on the two surfaces are tensile stress, the normal stresses are
1.2. Study area
σ = σ ðx′Þ + p
At present, CBM development in China is mainly concentrated in Qinshui basin, Shanxi province. Qinshui basin is the very study area which lies in the southeast of ShanXi province, 120 km wide from east to west, north–south 333 km long, and with an area of about 30,000 km2, where CBM resource is quite rich. Coal seams in the basin belong to Taiyuan Formation of Upper Carboniferous and Shanxi Formation of Low Permian, 1.2–23.6 m thick, with the buried depth of less than 1500 m. The primary coal seam containing CBM is NO.3 coal seam of Shanxi Formation and NO.15 coal seam of Taiyuan Formation. Now, CBM in NO.3 coal seam is mainly exploited. NO.3 coal seam of Shanxi Formation is 5.7–6.4 m thick, with gas contents ranging 22.0 to 27.2 cm3/g, formation pressure of 5.24 MPa and permeability of 0.51 μm2 (Lei Qiao et al., 2008). 2. The influence of pore pressure on borehole stability in coal seam 2.1. The influence of pore pressure on the stress of cracks There often exists pore water in coal formation. Pore water can generate pore pressure, which is called formation pressure too. When considering pore pressure, the effective stress concept in intact rock, originally introduced by Terzaghi in 1923 (Terzaghi, 1943; Erling et al., 1992), is used extensively. According to Terzaghi's theory, all normal components of stress tensor of arbitrary point is to decrease due to the effect of pore pressure, Mohr circle is to move left and rock material keeps closer to failure envelope. Hudson and Harrison (2005) argued that the influence of pore pressure on rock should be classified as intact block and discontinuous contact. The intact blocks can be analyzed by effective stress concept, while the discontinuous contacts need new theory to interpret. In this paper, fracture mechanics is employed for analyzing the influence on discontinuous contacts. The stresses of crack are illustrated by Fig. 1, indicating that pore pressure can change normal stresses acting on the two surfaces of crack while it has no influence on shear stresses. Considering pore
ð1Þ
It is seen from Eq. (1) that pore pressure produces an increase in the normal stresses. Hence, model I stress intensity factor (SIFI) of the crack is to increase, so the crack is easier to propagate and fail. If the normal stresses acting on the two surfaces are compressive stress, the normal stresses are σ = −σ ðx′Þ + p
ð2Þ
It is seen from Eq. (2) that if p b σ (x′), pore pressure produces a decrease in the normal stresses. Hence, SIFI of the crack is to decrease, so the crack becomes steadier. If p = σ (x′) the normal stresses equal zero, so SIFI equal zero. If p N σ (x′), the normal stresses are altered from compressive stresses to tensile stresses, so SIFI is to increase on the contrary. In addition, pore pressure has no influence on shear stresses, so it also has no influence on model II stress intensity factor. 2.2. The influence of pore pressure on cleats in coal seam Coal rock contains a large number of cleats, and the cleats can be attributed to internal crack (Laubach et al, 1998). In general, cracks in formation are compression-shear crack, and cleats in coal seam are also compression-shear crack. According to analysis in the last paragraph, if pore pressure is lower than compressive stresses acting on the surface of crack, pore pressure is to alleviate the compressive effect acting on cleats; if pore pressure exceeds the compressive stresses, pore pressure is to convert the compressive effect into tensile effect. As a usual, pore pressure is impossible to exceed the compressive stresses except when fracturing in coal formation. Therefore, the influence of pore pressure on borehole stability in coal seam is different from the influence on borehole stability in sandstone. For coal seam which is abundant in cleats, pore pressure reduction can cause an increase of stresses acting on cleats and furthermore make cleats propagate or fail much more easily. However, for sandstone, pore pressure reduction makes borehole more stable. During drilling in coal seam and production in CBM well, pore pressure is to change. During drilling, if bottom hole pressure (BHP) is more than or less than pore pressure, the influx of drilling fluid or the efflux of formation fluid can lead to changes in pore pressure. That formation fluid is drained persistently can also result in pore pressure reduction during gas production by draining water. 2.3. The effect of pore pressure changes during gas production by draining water
Fig. 1. Schematic illustration of stresses acting on crack.
During gas production by draining water, formation fluid is to flow out persistently and therefore pore pressure near borehole is to reduce gradually. Pore pressure reductions not only influence borehole stability, but also cause local shear failure in coal rock and consequently cause coal fines production and make cleats closed and plugged(Palmer et al., 2005; Gentzis et al., 2009; Gentzis, 2009). Using production data in Zheng Ping 1-1 well, the influences of pore pressure changes on coal rock stability are analyzed qualitatively. Zheng Ping 1-1 well is a multi-horizontal well with total footages of 5090 m and horizontal footages of 4400 m. The target formation is NO.3 coal seam, about 550–560 m deep. The diameter of wellbore in coal seam is 152.44 mm. The well depth of the main wellbore is 1600 m. The pore pressure is predicted to be 4.9–5.0 MPa. Zheng Ping 1-1 well drained formation water from 27, April, 2009, to 10, October, 2009. The relationship between BHP and time is illustrated in Fig. 2. It can be seen that the curve can be divided into two stages: ① the stage of BHP reduction; ② the stage of BHP increase.
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Bottom Hole Pressure/MPa
4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0
7
14
21
28
35
42
49
56
63
70
77
84
91
98 105 112 119 126 133 140 147 154 161
Draining Days/d Fig. 2. Casing pressure vs. time in Zheng Ping 1-1 well.
The relationship between contents of coal fine in drained water and time is illustrated in Fig. 3. Notice that contents of coal fine in drained water are classified into four ranks: black, dark grey, light grey, transparent. “black” is represented by “4”; “dark grey” by “3”; “light grey” by “2”; “transparent” by “1”. The relationship between casing pressure and time is illustrated in Fig. 4. As is seen from Fig. 3, the changes of contents of coal fine can be divided into 8 stages. It is well-known that a large number of drilling cuttings must be left after drilling. When draining formation water, the cutting would be taken to the ground. Therefore the content of coal fine should be much higher at first and decrease gradually up to clean water. Coal fines which appeared at stage 1 S1 and stage 2 (S2) should be the drilling cuttings left during drilling. At stage 3 the cutting left in well bore had been drained completely so the drained water is nearly clean. At this stage, BHP is about 2 MPa–3 MPa. At stage 4 as BHP continued to decrease, coal rock near the borehole would produce shear failure. Therefore, the contents have a gradual increase. At this stage, BHP is about 1.7 MPa–2 MPa. At stage 5, coal rock near the borehole would produce much more shear failure and even parts of borehole collapsed due to a further decrease in BHP. Therefore, the contents had a sharp increase and the drained water showed dark grey. At this stage, BHP is about 0.4 MPa–1.7 MPa. At stage 6, BHP decreased from 0.4 MPa to 0 MPa. At this moment, cleats were closed entirely due to excess stress concentration. Therefore, coal fine and CBM could be locked in the coal reservoir. Consequently, the contents of coal fine and the output of CBM were to decrease. It can be seen from Fig. 4, casing pressure decrease instead of increasing
2.4. The effect of pore pressure changes during drilling During drilling, pore pressure changes can make cleats propagate or fail or keep stable, and therefore have great influences on borehole stability. Moreover, pore pressure changes are related to permeability of borehole wall. If borehole wall is impermeable, pore pressure can't be interfered by BHP. However, if borehole wall is permeable, pore
S1
4
Ranks of contents of coal fine
at this moment. It also confirmed that the closure of cleats must cause a decrease in CBM. At stage 7, BHP went up rapidly from 0 MPa to 0.7 MPa. Cleats could be opened again and the coal fines accumulated at the stage 6 was vented, so the contents increased sharply. At stage 8, BHP went up from 0.7 MPa to 2.2 MPa. The contents went down gradually again because the stress concentration was alleviated. In addition, compared Fig. 2 with Fig. 4, when BHP decreased to 1.3 MPa, casing pressure began to appear. When BHP was about 1 MPa, casing pressure reached the maximum. However, when BHP was less than 1 MPa, casing pressure went down rapidly. This showed that cleats were closed gradually and meanwhile lots of coal rock produced local shear failure and coal fine was formed, when BHP was less than 1 MPa. The coal fine would plug the cleats. Accordingly, the desorbed CBM was shut in coal reservoir. In a word, according to the analysis of production of Zheng Ping 11 well, it proves to be that pore pressure has a great influence on borehole stability, local shear failure of coal rock, and closure and opening of cleats.
S5
S7
3
S4
S2
2
S6
S8
S3 1 0
7
14
21
28
35
42
49
56
63
70
77
84
91
98 105 112 119 126 133 140 147 154 161
Draining Days/d Fig. 3. Contents of coal fine vs. time in Zheng Ping 1-1 well.
P. Qu et al. / International Journal of Coal Geology 85 (2011) 212–218
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1.2
Casing Pressure/MPa
1
0.8
0.6
0.4
0.2
0
0
7
14
21
28
35
42
49
56
63
70
77
84
91
98 105 112 119 126 133 140 147 154 161
Draining Days/d Fig. 4. Bottom pressure vs. time in Zheng Ping 1-1 well.
pressure near borehole must be interfered by BHP, no matter whether in underbalanced drilling or overbalanced drilling. In underbalanced drilling, there is a difference between BHP and pore pressure, commonly called as underbalance pressure value. Under underbalanced condition, the formation water adjacent to borehole is to seep into borehole while the formation water away from borehole is to seep into the belt near borehole. However, to seep into borehole is much quicker than to seep in formation, so the pore pressure is to decrease to BHP gradually. In overbalanced drilling, BHP is more than pore pressure. Hence, the drilling fluid must seep into the formation. So pore pressure is to go up gradually till BHP(Ping Qu et al., 2007). According to the analysis in Section 2.2, the cleats near borehole are compression-shear crack. In underbalanced drilling, the pore pressure is to decrease to BHP gradually as time elapses. According to Eq. (2), the normal stresses of cleat surfaces are to increase, so the probability of cleat propagation is to go up. Therefore, if pore pressure is less than critical valuep1 min, the cleats is to change from keeping stable to propagation or compression-shear failure as time elapses. In overbalanced drilling, the pore pressure is to go up gradually till BHP. If BHP ≤ σ(x′), the normal stresses are to decrease and therefore the probability of cleat propagation is to go down. However, if BHP N σ(x′), the compressive cracks are converted into tensile cracks due to the pore pressure. Hence, if pore pressure is more than critical value p1 max, the cleats is to change from keeping stable to propagation or tension-shear failure as time elapses. It can be concluded that if BHP lies on the intervals of [0 p1 min] or [p1 max + ∞], the propagation of cracks near borehole has the time delay effect, that is, the cracks which should have kept stable is to propagate as time elapses and moreover the crack propagation is to cause the borehole instability. The time delay effect is quite important for drilling horizontal well, and especially multi-branch horizontal well, due to the large footage in the same formation and long drill cycle. For instance, for one CBM multi-branch horizontal well in Shan Xi province, China, its horizontal footage amounts to more than 5000 m and its drill cycle amounts to 20 days. If BHP lies at the intervals of [0 p1 min] or [p1 max + ∞] it is likely that the stable borehole becomes unstable one, and even collapse.
3. Fluid–solid coupling numerical simulation According to the above analysis, pore pressure changes have great influence on borehole stability and are the main factor in the time delay effect. Therefore, fluid–solid module in flac3d (Itasca Consulting
Group, 2006.) is used for analyzing the changes of formation pore pressure. 3.1. Fluid–solid coupling in drilling According to seepage mechanics, the seepage flow of formation water into borehole or the seepage flow of drilling fluid into formation can be divided into unsteady seepage flow, pseudo-steady seepage flow and steady seepage flow. The seepage flow in drilling process can be considered as unsteady seepage flow (XiangYan Kong, 1999). Pore pressure changes in production and these influences on borehole stability have been analyzed in the above paragraph. However, seepage flow in drilling has some differences from the seepage in production. BHP keeps a fixed value for the former while BHP is variational for the latter. In oil production, pore pressure is often computed by well testing or numerical simulation. However, insitu stress changes are often not considered when analyzing the pore pressure changes and some large numerical simulation software is required, for example, Eclipse. Hence, Flac3d is selected for simulating the fluid–solid coupling (Ivars, 2006). In addition, according to the above analysis of pore pressure changes in underbalanced drilling and overbalance drilling, it can be found that the seepage flow in overbalance drilling mainly has great influence on the reservoir pollution while the seepage flow in underbalanced drilling has great influence on borehole stability. Therefore, only the seepage in underbalanced drilling will be analyzed in view of paper space. 3.2. Numerical model The formation model is 5 m × 1 m × 5 m (the corresponding axis is x, y and z, z is gravity direction). Well is designed as a horizontal well, located at the centre of the model, and parallel to axis x. Well diameter is 0.2 m and well length is 5 m. The in-situ stress is 10 MPa, 12 MPa and 15 MPa respectively (The max is in the gravity direction). All parameters come from the experimental data of NO.3 coal rock in Qin Shui basin, Shan Xi province. (i) The petrophysical parameters: permeability is 1 md, porosity is 4%, and pore pressure is 5 MPa. (ii) Mechanical parameters: bulk modulus is 4100 MPa, shear modulus is 3100 MPa, cohesion is 6.25 MPa, dilatational angle is 33.72, friction angle is 33.72 and the tensile strength is 1.8 MPa. The Mohr–Coulomb (M–C) criterion is selected as rock mechanical strength criteria. Suppose that BHP is 3 MPa. The principle of
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supposition is that borehole must keep stable if borehole were not impermeable. 3.3. Result and analysis Contour of pore pressure changes at 500 s, 5000 s and 50,000 s are illustrated in Fig. 4. It can be seen that the area of pore pressure drops enlarges gradually and pore pressure of arbitrary point within the area become smaller as time increases. When time equals 50,000 s, boundary of the area is 1 m away from borehole. The radius of the boundary of the area where pore pressure drops just now is called as front radius. The function of front radius and time is illustrated in Fig. 5. As is seen that front radius increase more and more slowly as time go by. Front radius at 100,000 s is about 1.6 m. On the basis of numerical results, the function is fitted: Fr = −1:0974 × 10
−10 2
−5
t + 2:3292 × 10
t + 0:3401
ð3Þ Fig. 6. Radius of pore pressure drop area.
Where: Fris front radius, m, and t is time, s. 4.1. Model of cleats in coal seam 4. Calculating the delaying time The delaying time is a time span in which borehole changes from stability to instability due to time delay effect. In this chapter, borehole stability theory in fracture mechanics is used for establishing the computing equation of the delaying time. FLAC3D 3.10
The model of cracks near well bore is illustrated in Fig. 6. The length of cracks is 0.2 cm, the obliquity is 45°, the coordinate of the tip of cracks xAand yA both are 0.78 m. Other parameters are referred in the chapter 3.2. It is to be regretted that there is not any field data about cracks in NO.3 coal seam. FLAC3D 3.10 ?006 Itasca Consulting Group, Inc.
?006 Itasca Consulting Group, Inc. Step 11394 Model Perspective 10:49:44 Sat Oct 09 2010
Step 101890 Model Perspective 10:53:37 Sat Oct 09 2010
Center: X: 6.467e-001 Y: 0.000e+000 Z: 5.113e-001 Dist: 1.433e+001
Center: X: 6.344e-001 Y: 0.000e+000 Z: 5.120e-001 Dist: 1.433e+001
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 4.77 Ang.: 22.500
Contour of Pore Pressure
Contour of Pore Pressure Magfac = 0.000e+000 Live mech zones shown 3.0000e+006 to 3.2500e+006 3.2500e+006 to 3.5000e+006 3.5000e+006 to 3.7500e+006 3.7500e+006 to 4.0000e+006 4.0000e+006 to 4.2500e+006 4.2500e+006 to 4.5000e+006 4.5000e+006 to 4.7500e+006 4.7500e+006 to 5.0000e+006 5.0000e+006 to 5.2500e+006 5.2500e+006 to 5.5000e+006 5.5000e+006 to 5.5651e+006 Interval = 2.5e+005
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 4.77 Ang.: 22.500
t=500s
Magfac = 0.000e+000 Live mech zones shown 3.0000e+006 to 3.2500e+006 3.2500e+006 to 3.5000e+006 3.5000e+006 to 3.7500e+006 3.7500e+006 to 4.0000e+006 4.0000e+006 to 4.2500e+006 4.2500e+006 to 4.5000e+006 4.5000e+006 to 4.7500e+006 4.7500e+006 to 5.0000e+006 5.0000e+006 to 5.0817e+006 Interval = 2.5e+005
FLAC3D 3.10 ?006 Itasca Consulting Group, Inc. Step 1006648 Model Perspective 10:43:50 Sat Oct 09 2010 Center: X: 6.402e-001 Y: 0.000e+000 Z: 5.139e-001 Dist: 1.433e+001
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 4.77 Ang.: 22.500
t=50000s
Contour of Pore Pressure Magfac = 0.000e+000 Live mech zones shown 3.0000e+006 to 3.2000e+006 3.2000e+006 to 3.4000e+006 3.4000e+006 to 3.6000e+006 3.6000e+006 to 3.8000e+006 3.8000e+006 to 4.0000e+006 4.0000e+006 to 4.2000e+006 4.2000e+006 to 4.4000e+006 4.4000e+006 to 4.6000e+006 4.6000e+006 to 4.8000e+006 4.8000e+006 to 4.9783e+006 Interval = 2.0e+005
Fig. 5. Contour of pore pressure changes near well bore.
t=5000s
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4.2. Failure criteria based on fracture mechanics For the coal seam containing cleats illustrated in (Fig. 7), the failure criteria of borehole instability based on fracture mechanics is (Ping et al., 2009):
h
VOJ =
( sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi θ 3θ θ 2 θ 2 +4 cos2 ½KI sinθ+KII ð3 cosθ−1Þ 2KI cos ð1− cosθÞ+ KII 3 sin − sin 2 2 2 2 o θ θ θ θ fϕ −16v KI cos −KII sin + 4ð1 + 2vÞ KI cos −KII sin 2 2 2 2
i
KIC i −c × h 8 ð1 + 2vÞfϕ −4v
ð4Þ
Where: v is Poisson ration, θ is crack initiation angle,(°), KIC is 1 fracture toughness, MPa⋅m2 , KI and KII are mode I and mode II stress intensity factor, respectively c is cohesion, fϕ = (cos ϕ + sin ϕ tan ϕ − tan ϕ), ϕ is friction angle, and VOJ(value of judgment) is value of failure judgment. IfVOJ ≥ 0, crack propagation is to result in borehole instability. IfVOJ b 0, borehole is to keep stable. The computing equation of KI and KII (Eq. 4) is 8 rffiffiffiffiffiffiffiffiffiffiffiffiffiffi a > 1 a + x′ > > p ffiffiffiffiffiffiffi ½ ð Þ−p = ∫ f x′ K dx′ > I i < a−x′ π a −a rffiffiffiffiffiffiffiffiffiffiffiffiffiffi > a > 1 a + x′ > > dx′ : KII = pffiffiffiffiffiffiffi ∫ g ðx′Þ a−x′ π a −a
ð5Þ
Fig. 8. Relation between pore pressure and failure criteria.
According to the previous conditions, based on the numerical results of fluid-coupling, the function of value of judgment vs. time is fitted. VOJ = 9:475 × 10
−6
−6 −6 exp 5:372 × 10 t −0:03479 exp −4:472 × 10 t
ð6Þ
Where: a is half of crack length, pi is pore pressure, x′ is local coordinate of crack, f(x′) and g(x′) is function of x′ (Ping Qu et al., 2009). It is seen from Eq. (5) that mode I stress intensity factor is tied up with pore pressure. Pore pressure changes must be reflected directly in the value of mode I stress intensity factor.
The square of correlation R2=0.9912, showing that the fitted results are highly consistent with the actual results (Fig. 9). In Fig. 9, blue points are the actual calculated result while the red curve is the fitted curve. According to Eq. (6), when VOJ = 0,t = 8.3 × 105 s, about 9.6 days, that is, borehole in this formation will become unstable from being stable in 9.6 days.
4.3. Result and analysis 5. Conclusions and suggestions According to the failure criteria, the quantitative relation between pore pressure and borehole stability can be analyzed (Fig. 8). It is seen from Fig. 8 that if pore pressure is equal to 4.4 MPa, value of failure criteria is zero and therefore borehole stability is under critical state. If pore pressure is less than 4.4 MPa, borehole becomes unstable. BHP is 3 MPa, less than 5 MPa, value of the pore pressure, so it is in underbalanced drilling. Hence, the formation water is to seep into borehole and pore pressure of the areas will be less than 4.4 MPa. Especially the pore pressure in the cracks will be less than 4.4 MPa. The time span in which pore pressure in the cracks decreases from 5 MPa to 4.4 MPa is the delaying time of borehole stability in coal seam. When time reaches the delaying time at the beginning of drilling, borehole begins to fail.
(i) Pore pressure has a great influence on the normal stress acting on the cracks surface while has no influence on the tangential stress. In coal seam which is full of a large number of cleats, pore pressure changes cause an increase or decrease in the normal stresses and moreover result in cleats propagation or even failure. (ii) The influence of pore pressure on borehole stability in coal seam is different from the influence on borehole stability in sandstone. For coal seam which is abundant in cleats, pore
σv
2a yA
σh
rw
xA
Fig. 7. Schematic illustration of model of cracks near well bore.
Fig. 9. Relation between pore pressure and failure criteria.
218
(iii)
(iv)
(v)
(vi)
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pressure reduction can cause an increase of stresses acting on cleats and furthermore make cleats propagate or fail much more easily. However, for sandstone, pore pressure reduction makes borehole more stable. Pore pressure is tied up with the contents of coal fines and has a great influence on borehole stability, local shear failure of coal rock, and the closure and opening of the cleats during production by draining water. If borehole wall is permeable, pore pressure near borehole must be interfered by BHP, no matter whether in underbalanced drilling or overbalanced drilling. There exists time delay effect in borehole stability in coal seam full of a large number of cleats. Pore pressure changes is the main factor in time delay effect and the cleats in coal seam is the internal cause. The analysis of the time delay effect can guide the field drilling operation and avoid the instability caused by pore pressure changes. The delaying time can be altered through adjusting bottom hole pressure in order to supply sufficient time for drilling operation.
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Gentzis, T., Deisman, N., Chalaturnyk, R.J., 2007. Geomechanical properties and permeability of coals from the Foothills and Mountain regions of western Canada. International Journal of Coal Geology 69 (3), 153–164. Gentzis, T., Deisman, N., Richard, 2009. A method to predict geomechanical properties and model well stability in horizontal boreholes. International Journal of Coal Geology 78, 149–160. Gu, F., Chalaturnyk, R.J., 2005. Analysis of coalbed methane production by reservoir and geomechanical coupling. Journal of Canandian Petroleum Technology 44 (10), 33–42. Hudson, J.A., Harrison, J.P., 2005. Engineering Rock Mechanics (An Introduction to the Principles). Pergamon Press, pp. 159–160. Itasca Consulting Group, 2006. FLAC3D-Fluid-Mechanical interaction.Ver.3.1.PreRelease, Minneapolis, USA, pp. 30–100. Ivars, D.M., 2006. Water inflow into excavations in fractured rock—a three-dimensional hydro-mechanical numerical study. International Journal of Rock Mechanics and Mining Sciences 43, 705–725. Laubach, S.E., Marrett, R.A., Olson, J.E., et al., 1998. Characteristics and origins of coal cleat: a review. International Journal of Coal Geology 35, 175–207. Lei, Qiao, RuiChen, Shen, ChunHong, Huang, 2007. A preliminary study on drilling technique of Wu M1-1 CBM multi-branched horizontal well. Coal geology & exploration. Coal geology & exploration 35 (1), 34–36. Lei, Qiao, RuiChen, Shen, ChunHong, Huang, 2008. Low-cost drilling and completion techniques for coalbed methane in southern Qinshui Basin, Central China. Petroleum exploration and development 35 (4), 482–486. Moschovidis, Z.A., Cameron, J.R., Palmer, I.D., 2005. Methodology and examples of wellbore stability in coalbed methane wells. Paper No. 517. International Coalbed Methane Symposium, Tuscaloosa, AL, U.S.A. Palmer, I., Technologies, H., Moschovidis, Z., et al, 2005. Coal Failure and Consequences for Coalbed Methane Wells. The 2005 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, U.S.A., 9 – 12 October 2005. Ping, Qiao, RuiChen, Shen, et al., 2007. Research on Stress Sensitivity of Coal Cleat. Petroleum Drilling Techniques 35 (5), 68–71. Ping, Qiao, RuiChen, Shen, Jingcui, Li, et al., 2009. Evaluation Model of Borehole Stability in Coal Seam. Acta Petrolei Sinica 30 (3), 456–459. Terzaghi, K., 1943. Theoretical soil mechanics. Wiley, New York. XiangYan, Kong, 1999. Advanced mechanics of fluid flow in porous media. University of Science and Technology of China Press, An Hui, China, pp. 50–150.
Contents lists available at ScienceDirect
International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o
Time delay effect due to pore pressure changes and existence of cleats on borehole stability in coal seam Ping Qu a,b,⁎, Ruichen Shen a, Li Fu a,b, Zijian Wang b a b
CNPC Drilling Research Institute, Beijing, China Research Institute Of Petrochina, Beijing, China
a r t i c l e
i n f o
Article history: Received 12 August 2010 Received in revised form 28 October 2010 Accepted 28 October 2010 Available online 4 November 2010 Keywords: Pore pressure Borehole stability Time delay effect Fluid–solid coupling Fracture mechanics Coal seam
a b s t r a c t When horizontal wells are drilled underbalanced in coal seam, it was found that borehole which kept stable at the beginning would probably collapse in some time. The phenomenon was called as time delay effect. In order to clarify the concept of time delay effect, the influence of pore pressure on stresses of cleats was analyzed based on the characteristic that cleats are abundant in coal seam, indicating that pore pressure influences the normal stresses of cleat surface while it has no impact on the tangential stresses. Using the data from field production in a CBM well, the influence of pore pressure changes on stability of coal rock was analyzed, indicating that contents of coal fines in drained water increases as pore pressure decreases. Pore pressure changes due to seepage in underbalanced drilling or overbalanced drilling were analyzed. This study above demonstrates that the time delay effect exists absolutely in borehole stability in coal seams during underbalanced drilling. The pore pressure changes are the main factor on the time delay effect, while cleats are the internal cause. In order to analyze further time delay effect quantitatively, the fluid–solid coupling during underbalanced drilling was numerically simulated, and the relationship between pore pressure and time was fitted, and the equation for computing the delaying time was posed by means of borehole stability theory in fracture mechanics. The analysis of the time delay effect can guide the field drilling operation and avoid the instability caused by pore pressure changes. The delaying time can be altered through adjusting bottom hole pressure in order to supply sufficient time for drilling operation. © 2010 Elsevier B.V. All rights reserved.
1. Introduction During production/injection pore pressure changes, because of influx or efflux, lead to changes in effective stress which in turn lead to changes in the conditions for borehole stability. (Gu and Chalaturnyk, 2005; Deisman et al, 2010). In fact, during drilling, pore pressure changes is also likely to happen because BHP can't keep the same as pore pressure all the time. Changes in effective stress which in turn lead to changes in the stresses acting on cleats which in turn make cleats propagate or fail or keep stable. Propagation, failure, or stability of cleats have an important influence on borehole stability. Hence, when pore pressures vary in time, borehole stability in coal seam will change over time. Large numbers of facts have proved the inference above. 1.1. Study objective Horizontal wells have been used extensively in the Qinshui Basin for CBM development. However, the technologies have not been as ⁎ Corresponding author. CNPC Drilling Research Institute, Beijing, China. Tel.: +86 010 52781873; fax: +86 010 52781890. E-mail address: [email protected] (P. Qu). 0166-5162/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2010.10.013
successful as originally expected (Gentzis et al., 2007). Several drilled horizontal well produced less than 10,000 m3 gas per day and even zero, for example, Zheng Ping 1-1 well, Wu M1-1 well (Lei Qiao et al., 2007) and so on. The lower production may be attributed to borehole instability after drilling which can clog the wellbore or shear failure which may cause generation of coal fines, again clogging the cleats. (Deisman et al., 2008; Moschovidis et al., 2005). When horizontal wells are drilled underbalanced in coal seam, it was found that borehole which kept stable at the beginning would collapse in some time. The phenomenon was defined as time delay effect. It can be concluded from the inference above that time delay effect is mainly tied up with pore pressure changes and existences of cleats. It is also discovered through lots of researches that pore pressure changes is the main factor in time delay effect and cleats in coal seam is the internal cause. There isn't time delay effect without cleats. However, pore pressure changes cause directly the generation of time delay effect. In all, the study objective is to analyze time delay effect and calculate the delaying time during underbalanced horizontal drilling. Firstly, the influence of pore pressure on borehole stability is analyzed so as to analyze time delay effect qualitatively. Secondly, fluid–solid coupling effect is numerically simulated in order to establish the relationship of pore pressure changes over time. In the end, the
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delaying time is calculated by means of borehole stability theory in fracture mechanics.
pressure, if the normal stresses acting on the two surfaces are tensile stress, the normal stresses are
1.2. Study area
σ = σ ðx′Þ + p
At present, CBM development in China is mainly concentrated in Qinshui basin, Shanxi province. Qinshui basin is the very study area which lies in the southeast of ShanXi province, 120 km wide from east to west, north–south 333 km long, and with an area of about 30,000 km2, where CBM resource is quite rich. Coal seams in the basin belong to Taiyuan Formation of Upper Carboniferous and Shanxi Formation of Low Permian, 1.2–23.6 m thick, with the buried depth of less than 1500 m. The primary coal seam containing CBM is NO.3 coal seam of Shanxi Formation and NO.15 coal seam of Taiyuan Formation. Now, CBM in NO.3 coal seam is mainly exploited. NO.3 coal seam of Shanxi Formation is 5.7–6.4 m thick, with gas contents ranging 22.0 to 27.2 cm3/g, formation pressure of 5.24 MPa and permeability of 0.51 μm2 (Lei Qiao et al., 2008). 2. The influence of pore pressure on borehole stability in coal seam 2.1. The influence of pore pressure on the stress of cracks There often exists pore water in coal formation. Pore water can generate pore pressure, which is called formation pressure too. When considering pore pressure, the effective stress concept in intact rock, originally introduced by Terzaghi in 1923 (Terzaghi, 1943; Erling et al., 1992), is used extensively. According to Terzaghi's theory, all normal components of stress tensor of arbitrary point is to decrease due to the effect of pore pressure, Mohr circle is to move left and rock material keeps closer to failure envelope. Hudson and Harrison (2005) argued that the influence of pore pressure on rock should be classified as intact block and discontinuous contact. The intact blocks can be analyzed by effective stress concept, while the discontinuous contacts need new theory to interpret. In this paper, fracture mechanics is employed for analyzing the influence on discontinuous contacts. The stresses of crack are illustrated by Fig. 1, indicating that pore pressure can change normal stresses acting on the two surfaces of crack while it has no influence on shear stresses. Considering pore
ð1Þ
It is seen from Eq. (1) that pore pressure produces an increase in the normal stresses. Hence, model I stress intensity factor (SIFI) of the crack is to increase, so the crack is easier to propagate and fail. If the normal stresses acting on the two surfaces are compressive stress, the normal stresses are σ = −σ ðx′Þ + p
ð2Þ
It is seen from Eq. (2) that if p b σ (x′), pore pressure produces a decrease in the normal stresses. Hence, SIFI of the crack is to decrease, so the crack becomes steadier. If p = σ (x′) the normal stresses equal zero, so SIFI equal zero. If p N σ (x′), the normal stresses are altered from compressive stresses to tensile stresses, so SIFI is to increase on the contrary. In addition, pore pressure has no influence on shear stresses, so it also has no influence on model II stress intensity factor. 2.2. The influence of pore pressure on cleats in coal seam Coal rock contains a large number of cleats, and the cleats can be attributed to internal crack (Laubach et al, 1998). In general, cracks in formation are compression-shear crack, and cleats in coal seam are also compression-shear crack. According to analysis in the last paragraph, if pore pressure is lower than compressive stresses acting on the surface of crack, pore pressure is to alleviate the compressive effect acting on cleats; if pore pressure exceeds the compressive stresses, pore pressure is to convert the compressive effect into tensile effect. As a usual, pore pressure is impossible to exceed the compressive stresses except when fracturing in coal formation. Therefore, the influence of pore pressure on borehole stability in coal seam is different from the influence on borehole stability in sandstone. For coal seam which is abundant in cleats, pore pressure reduction can cause an increase of stresses acting on cleats and furthermore make cleats propagate or fail much more easily. However, for sandstone, pore pressure reduction makes borehole more stable. During drilling in coal seam and production in CBM well, pore pressure is to change. During drilling, if bottom hole pressure (BHP) is more than or less than pore pressure, the influx of drilling fluid or the efflux of formation fluid can lead to changes in pore pressure. That formation fluid is drained persistently can also result in pore pressure reduction during gas production by draining water. 2.3. The effect of pore pressure changes during gas production by draining water
Fig. 1. Schematic illustration of stresses acting on crack.
During gas production by draining water, formation fluid is to flow out persistently and therefore pore pressure near borehole is to reduce gradually. Pore pressure reductions not only influence borehole stability, but also cause local shear failure in coal rock and consequently cause coal fines production and make cleats closed and plugged(Palmer et al., 2005; Gentzis et al., 2009; Gentzis, 2009). Using production data in Zheng Ping 1-1 well, the influences of pore pressure changes on coal rock stability are analyzed qualitatively. Zheng Ping 1-1 well is a multi-horizontal well with total footages of 5090 m and horizontal footages of 4400 m. The target formation is NO.3 coal seam, about 550–560 m deep. The diameter of wellbore in coal seam is 152.44 mm. The well depth of the main wellbore is 1600 m. The pore pressure is predicted to be 4.9–5.0 MPa. Zheng Ping 1-1 well drained formation water from 27, April, 2009, to 10, October, 2009. The relationship between BHP and time is illustrated in Fig. 2. It can be seen that the curve can be divided into two stages: ① the stage of BHP reduction; ② the stage of BHP increase.
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Bottom Hole Pressure/MPa
4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0
7
14
21
28
35
42
49
56
63
70
77
84
91
98 105 112 119 126 133 140 147 154 161
Draining Days/d Fig. 2. Casing pressure vs. time in Zheng Ping 1-1 well.
The relationship between contents of coal fine in drained water and time is illustrated in Fig. 3. Notice that contents of coal fine in drained water are classified into four ranks: black, dark grey, light grey, transparent. “black” is represented by “4”; “dark grey” by “3”; “light grey” by “2”; “transparent” by “1”. The relationship between casing pressure and time is illustrated in Fig. 4. As is seen from Fig. 3, the changes of contents of coal fine can be divided into 8 stages. It is well-known that a large number of drilling cuttings must be left after drilling. When draining formation water, the cutting would be taken to the ground. Therefore the content of coal fine should be much higher at first and decrease gradually up to clean water. Coal fines which appeared at stage 1 S1 and stage 2 (S2) should be the drilling cuttings left during drilling. At stage 3 the cutting left in well bore had been drained completely so the drained water is nearly clean. At this stage, BHP is about 2 MPa–3 MPa. At stage 4 as BHP continued to decrease, coal rock near the borehole would produce shear failure. Therefore, the contents have a gradual increase. At this stage, BHP is about 1.7 MPa–2 MPa. At stage 5, coal rock near the borehole would produce much more shear failure and even parts of borehole collapsed due to a further decrease in BHP. Therefore, the contents had a sharp increase and the drained water showed dark grey. At this stage, BHP is about 0.4 MPa–1.7 MPa. At stage 6, BHP decreased from 0.4 MPa to 0 MPa. At this moment, cleats were closed entirely due to excess stress concentration. Therefore, coal fine and CBM could be locked in the coal reservoir. Consequently, the contents of coal fine and the output of CBM were to decrease. It can be seen from Fig. 4, casing pressure decrease instead of increasing
2.4. The effect of pore pressure changes during drilling During drilling, pore pressure changes can make cleats propagate or fail or keep stable, and therefore have great influences on borehole stability. Moreover, pore pressure changes are related to permeability of borehole wall. If borehole wall is impermeable, pore pressure can't be interfered by BHP. However, if borehole wall is permeable, pore
S1
4
Ranks of contents of coal fine
at this moment. It also confirmed that the closure of cleats must cause a decrease in CBM. At stage 7, BHP went up rapidly from 0 MPa to 0.7 MPa. Cleats could be opened again and the coal fines accumulated at the stage 6 was vented, so the contents increased sharply. At stage 8, BHP went up from 0.7 MPa to 2.2 MPa. The contents went down gradually again because the stress concentration was alleviated. In addition, compared Fig. 2 with Fig. 4, when BHP decreased to 1.3 MPa, casing pressure began to appear. When BHP was about 1 MPa, casing pressure reached the maximum. However, when BHP was less than 1 MPa, casing pressure went down rapidly. This showed that cleats were closed gradually and meanwhile lots of coal rock produced local shear failure and coal fine was formed, when BHP was less than 1 MPa. The coal fine would plug the cleats. Accordingly, the desorbed CBM was shut in coal reservoir. In a word, according to the analysis of production of Zheng Ping 11 well, it proves to be that pore pressure has a great influence on borehole stability, local shear failure of coal rock, and closure and opening of cleats.
S5
S7
3
S4
S2
2
S6
S8
S3 1 0
7
14
21
28
35
42
49
56
63
70
77
84
91
98 105 112 119 126 133 140 147 154 161
Draining Days/d Fig. 3. Contents of coal fine vs. time in Zheng Ping 1-1 well.
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1.2
Casing Pressure/MPa
1
0.8
0.6
0.4
0.2
0
0
7
14
21
28
35
42
49
56
63
70
77
84
91
98 105 112 119 126 133 140 147 154 161
Draining Days/d Fig. 4. Bottom pressure vs. time in Zheng Ping 1-1 well.
pressure near borehole must be interfered by BHP, no matter whether in underbalanced drilling or overbalanced drilling. In underbalanced drilling, there is a difference between BHP and pore pressure, commonly called as underbalance pressure value. Under underbalanced condition, the formation water adjacent to borehole is to seep into borehole while the formation water away from borehole is to seep into the belt near borehole. However, to seep into borehole is much quicker than to seep in formation, so the pore pressure is to decrease to BHP gradually. In overbalanced drilling, BHP is more than pore pressure. Hence, the drilling fluid must seep into the formation. So pore pressure is to go up gradually till BHP(Ping Qu et al., 2007). According to the analysis in Section 2.2, the cleats near borehole are compression-shear crack. In underbalanced drilling, the pore pressure is to decrease to BHP gradually as time elapses. According to Eq. (2), the normal stresses of cleat surfaces are to increase, so the probability of cleat propagation is to go up. Therefore, if pore pressure is less than critical valuep1 min, the cleats is to change from keeping stable to propagation or compression-shear failure as time elapses. In overbalanced drilling, the pore pressure is to go up gradually till BHP. If BHP ≤ σ(x′), the normal stresses are to decrease and therefore the probability of cleat propagation is to go down. However, if BHP N σ(x′), the compressive cracks are converted into tensile cracks due to the pore pressure. Hence, if pore pressure is more than critical value p1 max, the cleats is to change from keeping stable to propagation or tension-shear failure as time elapses. It can be concluded that if BHP lies on the intervals of [0 p1 min] or [p1 max + ∞], the propagation of cracks near borehole has the time delay effect, that is, the cracks which should have kept stable is to propagate as time elapses and moreover the crack propagation is to cause the borehole instability. The time delay effect is quite important for drilling horizontal well, and especially multi-branch horizontal well, due to the large footage in the same formation and long drill cycle. For instance, for one CBM multi-branch horizontal well in Shan Xi province, China, its horizontal footage amounts to more than 5000 m and its drill cycle amounts to 20 days. If BHP lies at the intervals of [0 p1 min] or [p1 max + ∞] it is likely that the stable borehole becomes unstable one, and even collapse.
3. Fluid–solid coupling numerical simulation According to the above analysis, pore pressure changes have great influence on borehole stability and are the main factor in the time delay effect. Therefore, fluid–solid module in flac3d (Itasca Consulting
Group, 2006.) is used for analyzing the changes of formation pore pressure. 3.1. Fluid–solid coupling in drilling According to seepage mechanics, the seepage flow of formation water into borehole or the seepage flow of drilling fluid into formation can be divided into unsteady seepage flow, pseudo-steady seepage flow and steady seepage flow. The seepage flow in drilling process can be considered as unsteady seepage flow (XiangYan Kong, 1999). Pore pressure changes in production and these influences on borehole stability have been analyzed in the above paragraph. However, seepage flow in drilling has some differences from the seepage in production. BHP keeps a fixed value for the former while BHP is variational for the latter. In oil production, pore pressure is often computed by well testing or numerical simulation. However, insitu stress changes are often not considered when analyzing the pore pressure changes and some large numerical simulation software is required, for example, Eclipse. Hence, Flac3d is selected for simulating the fluid–solid coupling (Ivars, 2006). In addition, according to the above analysis of pore pressure changes in underbalanced drilling and overbalance drilling, it can be found that the seepage flow in overbalance drilling mainly has great influence on the reservoir pollution while the seepage flow in underbalanced drilling has great influence on borehole stability. Therefore, only the seepage in underbalanced drilling will be analyzed in view of paper space. 3.2. Numerical model The formation model is 5 m × 1 m × 5 m (the corresponding axis is x, y and z, z is gravity direction). Well is designed as a horizontal well, located at the centre of the model, and parallel to axis x. Well diameter is 0.2 m and well length is 5 m. The in-situ stress is 10 MPa, 12 MPa and 15 MPa respectively (The max is in the gravity direction). All parameters come from the experimental data of NO.3 coal rock in Qin Shui basin, Shan Xi province. (i) The petrophysical parameters: permeability is 1 md, porosity is 4%, and pore pressure is 5 MPa. (ii) Mechanical parameters: bulk modulus is 4100 MPa, shear modulus is 3100 MPa, cohesion is 6.25 MPa, dilatational angle is 33.72, friction angle is 33.72 and the tensile strength is 1.8 MPa. The Mohr–Coulomb (M–C) criterion is selected as rock mechanical strength criteria. Suppose that BHP is 3 MPa. The principle of
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supposition is that borehole must keep stable if borehole were not impermeable. 3.3. Result and analysis Contour of pore pressure changes at 500 s, 5000 s and 50,000 s are illustrated in Fig. 4. It can be seen that the area of pore pressure drops enlarges gradually and pore pressure of arbitrary point within the area become smaller as time increases. When time equals 50,000 s, boundary of the area is 1 m away from borehole. The radius of the boundary of the area where pore pressure drops just now is called as front radius. The function of front radius and time is illustrated in Fig. 5. As is seen that front radius increase more and more slowly as time go by. Front radius at 100,000 s is about 1.6 m. On the basis of numerical results, the function is fitted: Fr = −1:0974 × 10
−10 2
−5
t + 2:3292 × 10
t + 0:3401
ð3Þ Fig. 6. Radius of pore pressure drop area.
Where: Fris front radius, m, and t is time, s. 4.1. Model of cleats in coal seam 4. Calculating the delaying time The delaying time is a time span in which borehole changes from stability to instability due to time delay effect. In this chapter, borehole stability theory in fracture mechanics is used for establishing the computing equation of the delaying time. FLAC3D 3.10
The model of cracks near well bore is illustrated in Fig. 6. The length of cracks is 0.2 cm, the obliquity is 45°, the coordinate of the tip of cracks xAand yA both are 0.78 m. Other parameters are referred in the chapter 3.2. It is to be regretted that there is not any field data about cracks in NO.3 coal seam. FLAC3D 3.10 ?006 Itasca Consulting Group, Inc.
?006 Itasca Consulting Group, Inc. Step 11394 Model Perspective 10:49:44 Sat Oct 09 2010
Step 101890 Model Perspective 10:53:37 Sat Oct 09 2010
Center: X: 6.467e-001 Y: 0.000e+000 Z: 5.113e-001 Dist: 1.433e+001
Center: X: 6.344e-001 Y: 0.000e+000 Z: 5.120e-001 Dist: 1.433e+001
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 4.77 Ang.: 22.500
Contour of Pore Pressure
Contour of Pore Pressure Magfac = 0.000e+000 Live mech zones shown 3.0000e+006 to 3.2500e+006 3.2500e+006 to 3.5000e+006 3.5000e+006 to 3.7500e+006 3.7500e+006 to 4.0000e+006 4.0000e+006 to 4.2500e+006 4.2500e+006 to 4.5000e+006 4.5000e+006 to 4.7500e+006 4.7500e+006 to 5.0000e+006 5.0000e+006 to 5.2500e+006 5.2500e+006 to 5.5000e+006 5.5000e+006 to 5.5651e+006 Interval = 2.5e+005
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 4.77 Ang.: 22.500
t=500s
Magfac = 0.000e+000 Live mech zones shown 3.0000e+006 to 3.2500e+006 3.2500e+006 to 3.5000e+006 3.5000e+006 to 3.7500e+006 3.7500e+006 to 4.0000e+006 4.0000e+006 to 4.2500e+006 4.2500e+006 to 4.5000e+006 4.5000e+006 to 4.7500e+006 4.7500e+006 to 5.0000e+006 5.0000e+006 to 5.0817e+006 Interval = 2.5e+005
FLAC3D 3.10 ?006 Itasca Consulting Group, Inc. Step 1006648 Model Perspective 10:43:50 Sat Oct 09 2010 Center: X: 6.402e-001 Y: 0.000e+000 Z: 5.139e-001 Dist: 1.433e+001
Rotation: X: 0.000 Y: 0.000 Z: 0.000 Mag.: 4.77 Ang.: 22.500
t=50000s
Contour of Pore Pressure Magfac = 0.000e+000 Live mech zones shown 3.0000e+006 to 3.2000e+006 3.2000e+006 to 3.4000e+006 3.4000e+006 to 3.6000e+006 3.6000e+006 to 3.8000e+006 3.8000e+006 to 4.0000e+006 4.0000e+006 to 4.2000e+006 4.2000e+006 to 4.4000e+006 4.4000e+006 to 4.6000e+006 4.6000e+006 to 4.8000e+006 4.8000e+006 to 4.9783e+006 Interval = 2.0e+005
Fig. 5. Contour of pore pressure changes near well bore.
t=5000s
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217
4.2. Failure criteria based on fracture mechanics For the coal seam containing cleats illustrated in (Fig. 7), the failure criteria of borehole instability based on fracture mechanics is (Ping et al., 2009):
h
VOJ =
( sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi θ 3θ θ 2 θ 2 +4 cos2 ½KI sinθ+KII ð3 cosθ−1Þ 2KI cos ð1− cosθÞ+ KII 3 sin − sin 2 2 2 2 o θ θ θ θ fϕ −16v KI cos −KII sin + 4ð1 + 2vÞ KI cos −KII sin 2 2 2 2
i
KIC i −c × h 8 ð1 + 2vÞfϕ −4v
ð4Þ
Where: v is Poisson ration, θ is crack initiation angle,(°), KIC is 1 fracture toughness, MPa⋅m2 , KI and KII are mode I and mode II stress intensity factor, respectively c is cohesion, fϕ = (cos ϕ + sin ϕ tan ϕ − tan ϕ), ϕ is friction angle, and VOJ(value of judgment) is value of failure judgment. IfVOJ ≥ 0, crack propagation is to result in borehole instability. IfVOJ b 0, borehole is to keep stable. The computing equation of KI and KII (Eq. 4) is 8 rffiffiffiffiffiffiffiffiffiffiffiffiffiffi a > 1 a + x′ > > p ffiffiffiffiffiffiffi ½ ð Þ−p = ∫ f x′ K dx′ > I i < a−x′ π a −a rffiffiffiffiffiffiffiffiffiffiffiffiffiffi > a > 1 a + x′ > > dx′ : KII = pffiffiffiffiffiffiffi ∫ g ðx′Þ a−x′ π a −a
ð5Þ
Fig. 8. Relation between pore pressure and failure criteria.
According to the previous conditions, based on the numerical results of fluid-coupling, the function of value of judgment vs. time is fitted. VOJ = 9:475 × 10
−6
−6 −6 exp 5:372 × 10 t −0:03479 exp −4:472 × 10 t
ð6Þ
Where: a is half of crack length, pi is pore pressure, x′ is local coordinate of crack, f(x′) and g(x′) is function of x′ (Ping Qu et al., 2009). It is seen from Eq. (5) that mode I stress intensity factor is tied up with pore pressure. Pore pressure changes must be reflected directly in the value of mode I stress intensity factor.
The square of correlation R2=0.9912, showing that the fitted results are highly consistent with the actual results (Fig. 9). In Fig. 9, blue points are the actual calculated result while the red curve is the fitted curve. According to Eq. (6), when VOJ = 0,t = 8.3 × 105 s, about 9.6 days, that is, borehole in this formation will become unstable from being stable in 9.6 days.
4.3. Result and analysis 5. Conclusions and suggestions According to the failure criteria, the quantitative relation between pore pressure and borehole stability can be analyzed (Fig. 8). It is seen from Fig. 8 that if pore pressure is equal to 4.4 MPa, value of failure criteria is zero and therefore borehole stability is under critical state. If pore pressure is less than 4.4 MPa, borehole becomes unstable. BHP is 3 MPa, less than 5 MPa, value of the pore pressure, so it is in underbalanced drilling. Hence, the formation water is to seep into borehole and pore pressure of the areas will be less than 4.4 MPa. Especially the pore pressure in the cracks will be less than 4.4 MPa. The time span in which pore pressure in the cracks decreases from 5 MPa to 4.4 MPa is the delaying time of borehole stability in coal seam. When time reaches the delaying time at the beginning of drilling, borehole begins to fail.
(i) Pore pressure has a great influence on the normal stress acting on the cracks surface while has no influence on the tangential stress. In coal seam which is full of a large number of cleats, pore pressure changes cause an increase or decrease in the normal stresses and moreover result in cleats propagation or even failure. (ii) The influence of pore pressure on borehole stability in coal seam is different from the influence on borehole stability in sandstone. For coal seam which is abundant in cleats, pore
σv
2a yA
σh
rw
xA
Fig. 7. Schematic illustration of model of cracks near well bore.
Fig. 9. Relation between pore pressure and failure criteria.
218
(iii)
(iv)
(v)
(vi)
P. Qu et al. / International Journal of Coal Geology 85 (2011) 212–218
pressure reduction can cause an increase of stresses acting on cleats and furthermore make cleats propagate or fail much more easily. However, for sandstone, pore pressure reduction makes borehole more stable. Pore pressure is tied up with the contents of coal fines and has a great influence on borehole stability, local shear failure of coal rock, and the closure and opening of the cleats during production by draining water. If borehole wall is permeable, pore pressure near borehole must be interfered by BHP, no matter whether in underbalanced drilling or overbalanced drilling. There exists time delay effect in borehole stability in coal seam full of a large number of cleats. Pore pressure changes is the main factor in time delay effect and the cleats in coal seam is the internal cause. The analysis of the time delay effect can guide the field drilling operation and avoid the instability caused by pore pressure changes. The delaying time can be altered through adjusting bottom hole pressure in order to supply sufficient time for drilling operation.
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