J. Cent. South Univ. (2016) 23: 3256-3261

DOI: 10.1007/s11771-016-3391-7

Coupled effects of stress damage and drilling fluid on strength of hard brittle shale

WANG Wei(汪伟), DENG Jin-gen(邓金根), YU Bao-hua(蔚宝华),

ZHENG Xiao-jin(郑小锦), YAN Chuan-liang(闫传梁), DENG Yue(邓月)

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China

Central South University Press and Springer-Verlag Berlin Heidelberg 2016

Abstract: During well drilling process, original stress state of hard brittle shale will be changed due to stress redistribution and concentration, which leads to stress damage phenomenon around the borehole. Consequently, drilling fluid will invade into formation along the tiny cracks induced by stress damage, and then weaken the strength of hard brittle shale. Based on this problem, a theoretical model was set up to discuss damage level of shale under uniaxial compression tests using acoustic velocity data. And specifically, considering the coupled effect of stress damage and drilling fluid, the relationship between hard brittle shale strength and elapsed time was analyzed.

Key words: hard brittle shale; stress damage; drilling fluid; time effect; strength

1 Introduction

Wellbore instability is most likely to occur in shale formation during drilling operation, with an accident rate as high as seventy percentages. Among them, hard brittle shale formation accounts for two thirds of the total shale accidents, most of which bring about severe consequences [1]. Common accepted theory is that wellbore instability is the combined results under the influence of both rock mechanics and drilling fluid chemistry. For the reason that there are small contents of water sensitivity minerals in hard brittle shale, the effect of hydrate swelling on borehole instability is usually neglected [2-5]. In fact, deeply buried formation has been compressed by original crustal stress before drilling [6-9]. When drilling fluid pressure takes the place of the support of that rock formation, stress around the wellbore will be redistributed and stress concentration will occur, which leads to the emergence of stress damage [10-12].

So, the coupled effects of stress damage and drilling fluids on the strength of hard brittle shale are analyzed. Using stress-damaged rock samples from oil field, we conduct several soaking tests to clarify drilling fluids’ effects on shale strength, and build a model to consider the relationship between shale strength and two controlling variables: the extent of stress damage and the time for soaking. The main tests results about wellbore instability mechanism are provided in the following chapter.

2 Model building

2.1 Measurement of stress damage

During loading process, the velocity of acoustic wave in rock formation changes. Based on such rules, wave velocity is often used as a parameter to decide the formation strength and stress damage. Generally, according to the elastic modulus method proposed in continuum mechanics, damage factor is defined as [13]

                                  (1)

where E_D and E are the elastic modulus after and before stress damage, separately.

We also know that the relation of P-wave velocity and elastic parameters, which can be represented as

                         (2)

where v is Poisson ratio and ρ is material density.

Then substitute Eq. (2) into Eq. (1), we get that

                             (3)

where D is the damage factor of material, V_p is the velocity of P-wave in actual material, and V_f is the velocity of P-wave in undamaged material. So, P-wave velocity could be used as a convenient parameter to decide the stress damage [14].

2.2 Coupling of stress damage and drilling fluids

Rock failure is caused by continuing accumulation of fractures under stress. Stress damage often produces tiny cracks, which grow and connect with each other with the development of stress damage. Then, sealed pores are connected and porosity of communicating pores increases. Although stress damage may not exert significant effects on the total porosity, it will greatly increase the permeability of shale rock [15-16]. The more serious stress damage is, the more substantially permeability will increase, and the more probably that drilling fluids will invade into the formation.

For core sample of hard brittle shale under no loading or low loading stress, drilling fluids only permeate into some preexisting fractures and interact with several infilling minerals or cementing agents. Because of its weak water sensitivity, core sample hardly reacts with drilling fluids, and we could expect that strength of hard brittle shale sample will not be reduced to a large extent.

But for core sample under high loading stress, especially when loading is greater than the dilation point of the core, there will be many tiny cracks in the rock sample. After soaking in the drilling fluids, drilling fluids will invade into these cracks and affect the roughness of fracture surface, the consequence of which is to make stress more easily propagate to the crack tip, and activate the growth of fractures. Moreover, drilling fluids will increase the pore pressure, lower the normal stress on the fracture surface and further decrease the frictional strength of the core. Therefore, the effect of drilling fluids onto the stress-damaged rock sample after high loading will be much more serious than those without stress damage.

2.3 Calculation of overall stress intensity factor

Stress concentration around the borehole will lead to the stress damage of wellbore rock. With the passage of time, the physical mechanics of cracks induced by stress damage changes. When stress intensity factor at the crack tip is higher than fracture toughness of shale, these cracks will expand toward surrounding area. After cracks connect with each other, the whole rock strength will decrease dramatically, and then wellbore collapses.

When discussing the coupled effect of stress damage and drilling fluids on the fracture extension, the key problem is to calculate the stress intensity factor (SIF) at the fracture tip. Here, SIF is affected by crustal stress, fluid pressure in the fracture and interfacial tension. In order to simplify the question, we assume that crustal stress and inner fracture pressure are homogeneous and interfacial tension only confines to fracture tip [17]. Detailed stress decomposition is shown in Fig. 1.

Fig. 1 Stress decomposition on fracture surface

In Fig. 1, fracture length is 2H, and the height of fluid medium is l; σ_insitu is preexisting crustal stress on the fracture surface; β is the angle between the center line of the capillary force and the crack wall; F is the capillary force produced on the fracture surface; and P_fluid is inner fracture fluid pressure played on the fracture surface.

In plane strain state, according to fracture mechanics theory [18-19], SIF of type-I crack based on the fracture mechanics theory could be expressed as

                  (4)

where p(y) is the stress on the fracture surface.

Then substitute each stress into Eq. (4), we could get the following fracture tip SIF under different stresses.

1) SIF produced by original crustal stress σ_insitu at the fracture tip is

   (5)

2) SIF produced by inner fracture fluid pressure P_fluid is

     (6)

3) Tiny cracks induced by stress damage resemble capillary tubes, so there will be capillary pressure to occur at the fracture tip. The corresponding SIF produced by capillary pressure can be expressed as

          (7)

where θ=a+blnt; θ usually decreases with the increase of soaking time [20]; a and b are the constants about formation properties and mud physical chemistry properties; γ is interfacial tension of drilling fluid; and w is fracture width.

Then, after superposition of these three kinds of SIF, we get the overall SIF at the fracture tip. Its expression is

          (8)

Applying the expression above, we calculate the SIF under different soaking time, as shown in Fig. 2. We could see that the core is soaking in the drilling fluids for a longer time, SIF will be larger. In addition, the invasion of drilling fluids will lead to the decease of fracture toughness, which results in crack propagation and the final macro collapse. This is the key issue when analyzing the effect of drilling fluids on the shale strength.

Fig. 2 Effect of soaking time on SIF

3 Experimental study

3.1 Experimental process

In order to analyze the effect of drilling fluids on the hard brittle shale strength under different stress damage conditions, the cores were divided into five groups. The cores of each group were taken from one big rock sample from Sichuan Basin. The mineral contents of the rock samples were tested, and the results are shown in the Tables 1 and 2. A set of cores were soaked in the drilling fluid directly, while the other four groups, which were under uniaxial compression conditions, were firstly loaded up to 30%, 60%, 80% and 95% of the Uniaxial Compression Strength (UCS), respectively. After this process, these four groups are unloaded, and then soaked in the drilling fluid. The drilling fluid used in this experiment is water-based, and we do not consider other kinds of drilling fluid in this paper. The UCS of each core under different soaking time was tested. As shown in Fig. 3, different loading stress can lead to different stress damage degree.

Before the experiment, acoustic P-wave velocity tests were applied on cores under the same conditions, in order to select cores with similar velocity. After soaking samples in drilling fluids for 48, 96 and 168 h, we measure each UCS of core groups respectively. The experimental results are shown in Table 3. Comparison of UCS of hard brittle shale after soaked in drilling fluid is shown in Fig. 4.

According to the experimental results, conclusions can be drawn that with the increase of the drilling fluid soaking time, the strength of hard brittle shale gradually decreases, and the longer the time of the core soaked is, the greater the strength reduction will be. At first, the reduction rate is at its maximum, and then gradually reduces, eventually is flatten out. After soaking in the drilling fluid for more than one week, the strength of hard brittle shale is basically not be influenced by the soaking time.

Table 1 Mineral contents of hard brittle shale

Table 2 Relative contents of clay mineral in hard brittle shale

Fig. 3 Relationship of loading stress and stress damage factor

Table 3 Experimental results of UCS after soaked in drilling fluid

Fig. 4 Comparison of UCS after soaked in drilling fluids

The effect of drilling fluids on different cores, which have various extent of stress damage, will be different. The more serious the stress damage is, the greater the reduction core strength will have. For unloaded core, the UCS decreases by 12% after soaking for 7 d. This relative small reduction could result from hard brittle shale’s average water sensitivity, which keeps it from being greatly influenced by drilling fluids. For cores loaded up to 30%, 60%, 80% and 60% of its UCS, the UCS decreases by 14%, 18%, 29% and 18%, respectively. Therefore, if loading stress is low, the effect of stress damage on the strength reduction will be insignificant. But once loading stress exceeds a certain limit, strength reduction will increase rapidly.

3.2 Fitting of experimental results

After stress damage occurs, drilling fluid, which is driven by chemical potential, capillary force and other physical chemistry effect, will filtrate into the rock along tiny cracks and lower the formation strength. When saturation is reached, shale formation stops water absorption and strength reduction slows down. From the discussion above, we know that strength reduction is affected by both the soaking time and the stress state before soaking (i.e. stress damage degree). These variables could be expressed in the formula as

           (9)

where

                         (10)

                                   (11)

where c and e are the constants about formation properties and mud physical chemistry properties; D_d is the stress damage factor when drilling fluids contact formation; D_f is the stress damage factor when stress reaches its peak; D is the normalized stress damage factor and t is the time for drilling fluid contacting formation.

Combined with these equations and experimental results, we make a fitting of UCS and soaking time with different stress damage degree. The fitting results are shown in Fig. 5. According to the figure, we can see that it fits quite well no matter the degree of stress damage.

According to the experiment results, the rule of hard brittle shale strength changing with the drilling fluid immersion time can be expressed as

  (12)

where UCS(t) is the formation strength after borehole has been drilled for t hours; and UCS_I is the original formation strength before drilling.

Applying Eq. (12), we can get the curves in Fig. 6. It shows that under different stress damage conditions, the influences of drilling fluids on shale strength vary significantly, and this difference increases with the increase of soaking time. For formation without stress damage, drilling fluids will have little impact on the formation strength and stress reduction is not obvious. But with the increase of damage factor, strength reduction amplitude gradually increases. Moreover, in the same soaking time, strength reduction amplitude under different damage state has little difference when damage factor is small, while this difference becomes larger when damage factor increases.

Fig. 5 Relationship of UCS and soaking time (unloaded) (a), relationship of UCS and soaking time (loaded to 30% UCS) (b), relationship of UCS and soaking time (loaded to 60% UCS) (c), relationship of UCS and soaking time (loaded to 80% UCS) (d) and relationship of UCS and soaking time (loaded to 95% UCS) (e)

Fig. 6 Influence of stress damage and mud soaking on UCS

4 Conclusions

1) Stress damage will produce tiny cracks in the formation, along which drilling fluids invade into the formation and change physical mechanics of formation. Then, intensity factor at the crack tip increases and crack will more easily propagate to the surroundings areas, and formation strength decreases.

2) Moreover, with the increase of soaking time, wetting angle on the fracture surface will decrease gradually, which leads to greater capillary stress and greater stress intensity factor, and as a result, there is weaker formation strength.

3) The influence of drilling fluids on core samples with different stress damage degree will be different. The more serious the core is damaged, the greater the strength will be lowered to after soaking in the drilling fluids.

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(Edited by DENG Lü-xiang)

Foundation item: Project(U262201) supported by National Natural Science Foundation of China

Received date: 2015-08-17; Accepted date: 2016-03-17

Corresponding author: DENG Jin-gen, Professor, PhD; Tel: +86-10-89733155; E-mail: dengjg@cup.edu.cn