Experimental investigation of mechanisms influencing friction coefficient between lost circulation materials and shale rocks

Journal Pre-proof Experimental investigation of mechanisms influencing friction coefficient between lost circulation materials and shale rocks

Jiping She, Hao Zhang, Kai Han, Yin Feng, Yili Kang, Ying Zhong PII:

S0032-5910(20)30059-0

DOI:

https://doi.org/10.1016/j.powtec.2020.01.047

Reference:

PTEC 15115

To appear in:

Powder Technology

Received date:

27 September 2019

Revised date:

17 January 2020

Accepted date:

18 January 2020

Please cite this article as: J. She, H. Zhang, K. Han, et al., Experimental investigation of mechanisms influencing friction coefficient between lost circulation materials and shale rocks, Powder Technology(2019), https://doi.org/10.1016/j.powtec.2020.01.047

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© 2019 Published by Elsevier.

Journal Pre-proof

Experimental investigation of mechanisms influencing friction coefficient between lost circulation materials and shale rocks Jiping She a, b, Hao Zhanga, b, * , Kai Hana , Yin Fengc, Yili Kangd, Ying Zhonga a. State Key Lab of Oil and Gas Reservoir Geology and Exploitation (Chengdu University of Technology), Chengdu, China, 610059. b. College of Energy, Chengdu University of Technology, Chengdu, Sichuan, China, 610059. c. University of Louisiana at Lafayette, Lafayette, LA, USA 70504. d. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, China, 610500. * Corresponding Author (Hao Zhang): [email protected], Tel: +86 (028) 84079010.

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Abstract

The friction coefficient of lost circulating materials (LCMs) and rock is a key parameter to

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determine the stability of the plugging zone in the lost circulation control. However, the influencing mechanisms of the friction coefficient remain unclear. In this work, factors influencing the

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coefficient were studied via investigating tribological properties . To conclude, the friction

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coefficient increases with the normal force and decreases as the sliding velocity increasing. Tested lubricating fluids can all reduce friction coefficients, but white oil reduces more. The long-term alkali erosion can also lower friction coefficients. Friction coefficients increase with declinations of

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sphericity, but with the increase of surface roughness and size. Additionally, auxiliary materials

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(rubber particles and fibers) can increase the friction coefficient, but this increase effect is weakened under white oil lubrication. This work will reveal the conditions to maximize friction coefficient

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for the lost circulation control.

Key words: friction coefficient; calcium carbonate particles; lost circulation; shale; alkali erosion 1 Introduction

Lost circulation is a situation where less fluid (e.g. drilling fluid, fracturing fluid) is returned from the wellbore than the mount it has been pumped in, which is induced by losses of partial or total fluid through pores, fractures or caves in reservoir (Fig.1) [1-3]. Lost circulation is one of the most troublesome drilling problems, which has introduced great challenges to the exploration and development of fractured reservoirs due to causing great cash expenditures, nonproductive time spent on regaining circulation and severe well control issues, poor hole cleaning and stuck pipe [4-8]. For the lost circulation control in drilling, plugging material systems currently used in the drilling to treat losses can be subdivided into LCMs, settable materials (settable materials usually refer to as materials that are liquid before being pumped into a reservoir, but become solid after 1

Journal Pre-proof entering fractures of reservoir through a settable reaction) or a combination of them [2, 9-11]. These systems can be mixed into the drilling fluid or injected separately into the thief zone (thief zone is a formation with a large number of high-permeability channels, such as fractures and large-sized pores) [12]. LCMs typically consist of particulate matters (such as calcium carbonate, rubber particles, nut hulls and graphite), which can form a seal plugging zone either deep ins ide the fracture or near its mouth by a combination effect of filtration of drilling fluid and bridging of LCMs [10, 13-15]. In addition, LCMs also have the advantages of low cost, good thermal stability and easy deployment [2, 9]. Therefore, LCMs are the most widely used system in the field and usually used to treat losses in porous matrix, natural fracture and induced fracture formations. Settable materials can also build a

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seal in the thief zone by a settable reaction, such as cement and cross-linked polymer [11, 16-17]. Slurries of settable materials can enter a fracture of any width, unlike LCM particles that can only enter fractures with sufficient aperture width for the particles to pass [18-20]. Settable materials are

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mainly used to treat losses in vugular and cavernous formations.

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In the LCM system, high-strength particles, which is also named rigid particles, play the role of bridging through the friction with the fracture surface [2, 10, 21-22], which can withstand in-situ

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stress and transform a fracture into a porous medium by the bridging. Deformable particles, known as elastic particles (e.g. rubber), mainly play a filling role, which can further seal the pores between

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the rigid particles. The fibers have a grid structure, which can improve the plugging efficiency of rigid and elastic particles [2, 18]. The plugging zone is generally composed of rigid particles or a

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combination of rigid particles and other materials. The structural stability of the plugging zone is critical for the successful control of lost circulations and is determined by two key factors. The first

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one is the strength of the plugging zone. As shown in Fig. 2, the particles in the plugging zone contact each other under the in-situ stress. Some force chains can be formed by the contact force between particles, which can affect the stability of the plugging zone [3, 23-24]. The second one is the frictional resistance between the plugging zone and the fracture surface. As shown in Fig. 3, the plugging zone is subjected to a frictional resistance Ff under normal force F N (F N is generated by the in-situ stress, such as minimum horizontal stress). If the frictional resistance (Ff ) is greater than or equal to the force ( △P×A) induced by the drilling pressure difference (Fig. 3a), the plugging zone will keep stable. However, if the frictional resistance is less than the force of drilling pressure difference (Fig. 3b), the shear failure of plugging zone will occur because drilling pressure difference cannot be balanced [18], which can lead to the lost circulation again. For a given formation, the frictional resistance is determined by the friction coefficient μf because the normal force F N usually remains constant. Therefore, the high friction coefficient between the LCMs and rock is beneficial to improve the stability of the plugging zone. 2

Journal Pre-proof Maintaining a high friction coefficient between the rock surface and the LCMs is critical to keep the stability of the plugging zone. To the best of authors’ knowledge, the published research mainly focused on the effect of particle size distribution of the LCMs on the wellbore strengthening. Few research has been conducted to discuss the friction coefficient about the LCMs. Moreover, how to maintain a high friction coefficient is still unclear. This paper took the shale gas reservoirs in the Sichuan Basin of China as an example field case to illustrate the conditions to maximize the friction coefficient. The drilling fluid used in the field inc ludes water-based drilling fluid, oil-based drilling fluid, sulfonated polymer drilling fluids and silicate drilling fluids. As shown in Fig. 4a, the shale gas reservoirs contain a large amount of natural and induced fractures, which results in serious

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lost circulation problems in drilling (Fig. 4b). In this work, calcium carbonate particles, which are the most typical lost circulation materials, were considered in experiments. And a series of experiments were conducted to investigate the effect of normal force, sliding veloc ity, lubrication

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fluid properties (such as fluid types, wettability, pH and soaking time), LCM properties (such as

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particle sphericity, roughness and size distribution) and auxiliary materials (rubber particles and fibers) on the friction coefficient. Consequently, this work reveals the tribological characteristics of

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the interface between the LCMs and the shale, so that the conditions to maximize friction coefficient for the lost circulation control in shale reservoirs are presented.

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2 Experimental materials and method

2.1 Shale samples, lubricating fluids and particle plugging materials

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Shale samples. As shown in Fig. 5, shale samples are selected from the Long-maxi formation in Sichuan Bas in of China, which have a diameter of 25.4mm and a thickness of 5mm. The main

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objective of this study is to investigate the effects of different external factors on the friction coefficient so as to clarify the conditions to maximize friction coefficient. Therefore, in order to compare the effects of different factors (regardless of the roughness of the shale surface), the properties of the shale surface should be kept constant. In this study, the surface of each shale sample is polished using emery papers on the polisher to eliminate the effect of shale surface properties on experimental results. The polished surface is used as the friction surface in the experiments. In addition, as shown in Table 1, the X-ray experiment shows that shale samples are mainly composed of quartz and illite. Dentification and analysis of minerals are performed via the method presented by Duane and Robert [25]. Lubricating fluids. Three lubricating fluids, including 3%KCl solution (97% of the mass is distilled water), white oil and the alkaline solution with a pH value of 11, were used in the experiments to represent the water-based drilling fluid, oil-based drilling fluid and high pH drilling

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Journal Pre-proof fluids (such as sulfonated polymer and silicate drilling fluids), respectively, as adopted in the field case. The properties of three lubricating fluids are listed in Table 2. LCMs. Calcium carbonate particles are the most commonly used LCMs in the lost circulation control. Therefore, in this study, calcium carbonate particles are selected as experimental materials (Fig. 6). In addition, considering that the selected size of particles may vary with the width of the plugged fracture in the lost circulation control, four sizes of calcium carbonate particles are investigated in this study, and their particle sizes are 20~40 mesh (100.0~1700.0μm), 40~60 mesh (1.3~1096.5μm), 60~80 mesh (1.1~724.4μm) and 80~100 mesh (1.3~549.5μm), respectively.

2.2 Experimental method

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As shown Fig. 7, the friction coefficient is tested by the friction coefficient measuring system. This measuring system has maximum displacement of 150mm, and the measuring accuracy and data recording frequency of the tension meter are 0.001N and 100 times per minute, respectively. For

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reliability consideration, each test in the laboratory experiments is repeated at least three times until

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Dry the shale sample and calcium carbonate particles in oven at 60℃ for 48 hrs and

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weigh the mass of the shale sample. 

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result stabilizes. The procedures of the friction coefficient measurement are indicated as follows:

Paste a double-sided tape on the thin plate and stick the dry calcium carbonate particles on

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the thin plate uniformly to have the friction plate (the method of making the friction plate is as follows: one side of the double-sided tape sticks on the surface of the smooth metal

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plate, and the prepared calcium carbonate particles are evenly sprinkled (using sieve screen) on the other side of the double-sided tape until the surface of the friction plate is

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completely occupied by particles. Finally, the calcium carbonate particles that are bonded are compacted to make them adhere firmly on the tape). As shown in Fig. 8, the length and width of the friction plate are 7.0cm and 3.0cm, respectively. 

Place the friction plate on the support and put a shale sample on the left side of the friction plate, and then record the total mass 𝑊𝑁 of the shale sample and poise.



Connect the shale sample to the tension meter and put the poise on the center of the shale sample.

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Inject each lubricating fluid into the tank until the liquid level just exceeds the contact interface between the shale and calcium carbonate particles by less than 0.5mm so that the effect of the buoyancy of the lubricating fluid on the friction force can be ignored.

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Start the motor and control movement at a constant velocity and the friction force 𝐹𝑓 is recorded automatically by the data recording system till the shale sample reaches the right edge of the friction plate. 4

Journal Pre-proof 

Calculate the friction coefficient in dry or lubricated condition using Eq. (1). 𝜇𝑓 =

𝐹𝑓 𝐹𝑁

𝐹𝑓

=𝑊

(1)

𝑁𝑔

where, F N -normal force, N; μf -friction coefficient, fraction; F f -friction force, N; WN -the total mass of shale sample and poise weight, kg; 𝑔- constant, 9.8N/kg.

3 Results and discussion 3.1 Influence of normal force on friction coefficient As shown in Fig. 9, friction theory shows that the friction coefficient is determined not only by the properties of the friction interface, but also by the normal force, sliding velocity and viscosity of

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the lubricating fluid [26-29]. During the plugging process, the normal force that is generated by the in-situ stress of the formation, loads on the LCMs and creates a normal squeezing effect on the interface between the LCMs and the shale. Therefore, it is necessary to evaluate the influence of

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normal force on the friction coefficient.

As shown in Fig. 10a, the friction coefficient curve for calcium carbonate particles shows that

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the friction process consists of static friction and sliding friction stages. The static friction stage

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refers to as the process in which the friction coefficient is gradually increases from zero to the first peak value (the first peak is taken as maximum static friction coefficient, MSFC). When the friction coefficient reaches the MSFC, the friction process turns to the sliding friction stage. In addition,

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when the sliding friction starts, the samples will generate acceleration rates under the tension of the

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tension meter to reach the set sliding velocity (1.94 mm/min). The acceleration rates and durations of the acceleration period under different normal forces are shown in Table 3. The friction coefficient

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on the sliding friction stage is called the sliding friction coefficient (SFC) , and the average sliding friction coefficient (ASFC) is determined from the full range from MSFC to 300 second (including the acceleration period of sample). Fig. 10b shows that the MSFC and average sliding friction coefficient (ASFC) increase with the increase of normal force. In addition, fluctuation amplitude of the SFC is positively correlated with the normal force. The influence mechanism of normal force on friction coefficient includes two aspects. On one hand, as shown in Fig.11, a higher meshing degree can be induced by a higher normal force, which can increase the friction resistance [3]. On the other hand, high normal forces can cause damage of asperities on shale surface (Fig. 12), which is one of the reasons that explains why the fluctuation amplitude of the SFC is positively correlated with the normal force.

3.2 Influence of sliding velocity on friction coefficient Fig. 13a to Fig. 13d demonstrate the friction coefficient versus time for various sliding velocities. As the sliding velocity increases, the duration of static friction stage is much shorter than

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Journal Pre-proof that of the reference velocity value (because a higher sliding velocity means that the static friction force increases faster), and the friction coefficient tends to decrease. As shown in Fig. 13e, both the MSFC and ASFC decline with the increase of the sliding velocity, but the ASCF decreases more than the MSFC, which indicates that the ASFC is more sensitive to the sliding velocity. Fig. 13f shows that the SFC variance in sliding stage decreases with the increase of the sliding velocity, which means that the fluctuation of the SFC is weakened under high sliding velocities. For unlubricated conditions (dry), the gap between the shale and the LCMs tends to zero, which indicates that the friction is a boundary lubrication according to the Stribeck curve (Fig. 9). The friction coefficient under the boundary lubrication has a negative correlation with the sliding

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velocity [27-28, 30]. In addition, as shown in Fig. 14, the SEM images show that the asperities on the shale surface are significantly damaged during high veloc ity sliding processes. The asperity failure reduces the friction coefficient may be explained through two mechanisms. Firstly, the

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contact area of the friction interface can be reduced when the asperities are damaged. Secondly, the

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broken particles formed by the damage can fill the friction surfaces, which may cause rolling friction.

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3.3 Influence of lubrication fluid on friction coefficient 3.3.1 lubrication fluid types

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As shown in Fig. 15, compared to the dry condition, all of the three lubricating fluids can reduce the MSFC and ASFC. However, the reductions of friction coefficient for the lubrication of 3%

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KCl solution and alkali solution with pH=11 are similar, but less than the reduction resulting from the white oil lubrication. In this study, the gap between the friction surfaces tends to zero, which

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indicates that the lubrication mode is boundary lubrication. According to the Stribeck curve, the friction coefficient is negatively correlated with the viscosity of the lubricating fluid for the boundary lubrication and mixed lubrication [31-32]. As shown in Table 2, the viscosity of the white oil is 9.3 times more than that of the 3%KCl solution and alkali solution with pH=11. Therefore, the higher viscosity of the white oil can further reduce the friction coefficient. That explains why the stability of plugging zone is lower when the oil-based fluid is used in the drilling as observed in the field case. 3.3.2 Soaking time of lubrication fluids During the drilling process, the plugging zone is always soaked by drilling fluid until the well is completely drilled. As shown in Fig. 16, compared with the soaking for 5 minutes, the friction coefficient for the 3%KCl solution and white oil hardly change, which indicates that the friction interface properties do not change after soaking for 15 days. However, for the alkaline solution with pH=11, the friction coefficient decreased significantly after soaking for 15 days. As shown in Fig. 6

Journal Pre-proof 17a, compared with soaking for 5 minutes by alkali solution with pH=11, the fluctuation of sliding friction coefficient becomes weaker after soaking for 15 days. Moreover, the SFC variance during the sliding become smaller than that after 5 minutes soaking (Fig. 17b). More detailed experiments were conducted to investigate the mechanism of friction coefficient reduction after soaking for 15 days in the alkali solution with pH=11. As shown in Fig. 18, 3D laser scanning images show that the shale surface became smoother after soaking for 15 days, and the asperities height is reduced by 40μm, which indicates that there is an alkali erosion reaction between the shale and alkali solution during the soaking. As shown in Fig. 19, some white reaction products were attached on the shale surface after 15 days soaking. SEM images show that these snowflake

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shaped reaction products contained some mineral particles. EDS results from the SEM image indicates that two elements (including Si and O) have higher contents compared with other elements in the reaction products (Fig. 20). In addition, ion detection results of alkali solution after soaking

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further indicate that the reaction product consisted mainly of element Si, Al and O (Table 4). Previous

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researches show that the main minerals of rock can react with hydroxide ions to form aluminosilicate precipitations [33-35]. These aluminosilicates are mainly composed of element Si, Al, Ca and O

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[36-39]. Therefore, the white reaction product (shown in Fig. 19) on the shale surface can be proved that it is the aluminosilicate precipitation.

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As shown in Fig. 21a, the lubricating effect is determined by the water film formed by alkaline solution when shale is soaked for 5 minutes because the asperities on the shale does not change after

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soaking in a short reaction time [37-38]. However, if the soaking time is sufficiently long (such as 15 days, Fig. 21b), shale minerals will undergo significant chemical reactions with hydroxide ions [39].

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The chemical reaction can cause the asperities to break and therefore the shale surface becomes smoother. Therefore, the alkali solution with pH=11can lead to a significant reduction of friction coefficient after soaking for 15 days.

3.4 Influence of properties on the friction coefficient 3.4.1 Sphericity of calcium carbonate particles The sphericity is an important parameter for characterizing the shape of irregular particles and is defined as the extent to which irregular particles are close to a sphere [41-42]. The sphericity can be calculated from the equivalent volume and surface area of the particle, which can be derived from Eq. (2) to Eq. (5) [41]. As shown in Table 5, three particles with different shapes (particle A, B and C, with sphericity of 0.094, 0.441 and 0.752, respectively) are used to evaluate the effect of sphericity on the friction coefficient. These particles with different sphericities are all made of the same material (calcium carbonate particles with sizes of 1.3~1096.5μm). 𝐷𝑉 = (6𝑉𝑝 /𝜋)1/3

(2)

𝑆𝑝 = 𝑚𝐴𝑝

(3)

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Journal Pre-proof 𝐷𝑠 = (𝑆𝑝 /𝜋)1/2

(4)

𝐷2

𝜋(6𝑉𝑝 /𝜋)2/3

𝑠

𝑆𝑝

𝛹 = 𝐷𝑉2 =

(5)

where, 𝐷𝑉 is equivalent diameter of irregularly shaped particle based on the particle volume (unit: m), 𝑉𝑝 is particle equivalent volume (unit: m3 ), 𝑆𝑝 is surface area of an irregularly shaped particle (unit: m ), 𝑚 is average mass of a particle (unit: g), 𝐴𝑝 is specific surface area of a 2

particle (unit: m /g), 𝐷𝑠 is equivalent diameter of irregularly shaped particle based on the particle 2

surface (unit: m), 𝑆𝑝 is surface area of an irregularly shaped particle (unit: m ), and 𝛹 is sphericity 2

of particle (unit: fraction). Fig. 22 shows the friction coefficient for the particles with three different sphericities. The friction coefficient decreases with the increase of particle sphericity (Fig. 22a). Furthermore, the

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MSFC, ASFC and SFC variances in the sliding stage present negative correlations with the particle sphericity (Fig. 22b). Therefore, for the lost circulation control, irregular particles with a low sphericity value should be expected under the same material properties (e.g. same surface roughness,

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particle size, etc.). 3.4.2 Surface roughness of calcium carbonate particles

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The surface roughness parameter, Ra , is theoretically defined as the arithmetic average value of filtered roughness profile determined from deviations about the center line within the evaluation

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length, and R z is defined as the maximum height of the assessed profile. These two parameters are important parameters to characterize the smoothness of material surface and affects its friction property [43-46]. As shown in Fig. 23, the roughness for each of three same size (1.3~1096.5μm) calcium carbonate particles was tested based on the 3D confocal microscopy method. Fig. 24a shows

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that the friction coefficient is positively correlated with the surface roughness. The MSFC, ASFC

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and SFC variance in the sliding stage decrease with the reduction of surface roughness (Fig. 24b). Therefore, for the lost circulation control, LCMs with higher roughness should be expected under

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the same material properties (e.g. same sphericity, particle size, etc.). 3.4.3 Particle size distribution of calcium carbonate particles The particle size distribution of the LCMs is a key parameter for the lost circulation control, which depends on the width of the plugged fracture [47-49]. As shown in Fig. 25, four distributions of particle sizes (including 100.0~1700.0μm, 1.3~1096.5μm, 1.1~724.4μm and 1.3~549.5μm) were used to evaluate the effect of the size distribution on the friction coefficient. Fig. 26 shows that the MSFC, ASFC and SFC variance in sliding stage decrease with the reduction of particle sizes. Fig. 27 shows the two roughness parameters (average Ra and Rz) of four friction plates with different particle size distributions, which indicates that the particle size is positively correlated to the average surface roughness of the friction plate. Since a higher roughness means a larger friction coefficient, a larger size particle will thus lead to a higher friction coefficient. It should be noted that particle shape may differ with size although the different size classes are made of the same material, which could contribute to the measured friction values . This mechanism will be discussed in future research. For the lost circulation induced by narrow fractures, because the 8

Journal Pre-proof size of the LCMs used is small, LCMs that can produce a higher friction coefficient should be expected under the same material properties (e.g. same surface roughness, sphericity, etc.).

3.5 Influence of auxiliary materials on the friction coefficient In most cases, only calcium carbonate particles can be used to meet the plugging requirements in the oil field. However, in rare cases, such as plugging wide fractures, some auxiliary materials (such as rubber particles and fibers) are often used to improve the stability of plugging zone. Therefore, in this section, the influences of two typical auxiliary materials (rubber particles and QR-1 fibers, as shown in Fig. 28) on the friction coefficient are discussed by considering three lubrication conditions (including dry, 3%KCl solution and white oil lubrication). The size of the

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rubber particles is 1.3~1096.5μm and the aspect ratio of QR-1 fibers is from 5 to 25. Fig. 29 shows the friction coefficient between the two auxiliary materials and shale under the three lubrication conditions. Firstly, the friction coefficient of the calcium carbonate particles is the

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smallest compared to the two auxiliary materials. Secondly, for the three lubrication conditions, the

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friction coefficient under dry conditions is similar to that under 3%KCl solution lubrication and is significantly greater than that under the white oil lubrication. Thirdly, under dry and 3%KCl solution

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lubrication, the SFC variance of QR-1 fiber is the largest, and the values are similar for calcium carbonate and rubber particles. However, the SFC variances of all three materials are significantly

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reduced and tend to be similar when the white oil is used as lubrication fluid. There are four explanations to the experimental phenomena observed in Fig. 29. Firstly, as

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shown in Fig. 30, calcium carbonate particles have lower elastic deformation rates compared to that of rubber particles and QR-1 fibers. Therefore, the addition of rubber particles and QR-1 fibers can

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increase the contact area between shale and the materials, which means that both the rubber particles and QR-1 fibers can produce greater frictional resistance [18]. Secondly, the fiber material can form a grid structure (Fig. 31), which not only benefits the pores sealing between the calcium carbonate particles, but also assists the embedment of shale surface asperities into the grid structure during the sliding process. This embedding effect can further increase the frictional resistance between the shale and the fibers. Thirdly, for the QR-1 fiber, the high SFC variance may be caused by the tensile failure and irregular packing of fibers. If the tensile stress exceeds the tensile strength of the f iber during the sliding process, the fiber will break, which may result in a higher SFC fluctuation. Additionally, irregular packing of fibers may also cause a higher SFC fluctuation. These two hypotheses will be further proven in subsequent future studies. Fourthly, the white oil can not only reduce the friction coefficient, but also weaken the fluctuation of sliding friction coefficient.

4. Conclusions

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Journal Pre-proof (1) The friction coefficient is positively related to the normal force, but negatively related to the sliding veloc ity. Therefore, maintaining a high normal force, a low sliding veloc ity or both of them is beneficial to maximize the friction coefficient. (2) Compared to white oil lubrication, no lubrication (dry) and water lubrication (3%KCl solution and alkali solution with pH=11) is more beneficial to maximize friction coefficient under short-term soaking (e.g. 5 minutes). However, long-term soaking (e.g. 15 days) of alkali solution with pH=11 is not conducive to maintaining a higher friction coefficient because the alkali erosion reaction of shale minerals can reduce the friction coefficient. (3) The friction coefficient present negative correlations with the particle sphericity but

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positive correlations with the surface roughness of particles. In addition, a larger particle size can result in a higher friction coefficient. Therefore, lower sphericity, higher surface roughness and larger particle size are beneficial to maximize friction coefficient.

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(4) Compared to calcium carbonate particles, QR-1 fibers and rubber particles can result in

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higher friction coefficient under dry and 3%KCl solution lubrication conditions. In addition, similar to the calcium carbonate particles, dry and water lubrication are beneficial to maximize the friction

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coefficient of the QR-1 fibers and rubber particles, while the white oil lubrication is not.

Acknowledgments

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The authors gratefully acknowledge the financial support from the NSFC (National Natural Science Foundation of China) (No. 51704043 and No. 51874052) and Education Department

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Foundations of Sichuan Province (NO. 18ZB0074).

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Z.;

Jiang,

G.;

Yang,

L.;

He,

Y.;

Ni,

X.

Microencapsulation

of

2,2'-Azobis(2-methylpropionamide) Dihydrochloride Initiator Using Acrylonitrile Butadiene Styrene as shell for Application in Lost-Circulation Control. Colloids & Surfaces A: Physicochemical & Engineering Aspects, 2018, 20(553), 134-142. [18] Xu, C.; Kang Y.; You L.; You, Z. Lost-Circulation Control for Formation-Damage Prevention in Naturally Fractured Reservoir: Mathematical Model and Experimental Study, SPE Journal, 2017, 22(5), 1654-1670. [19] Kang, Y.; Tan Q.; You, L.; Zhang, X.; Xu, C.; Lin, C. Experimental investigation on size degradation of bridging material in drilling fluids. Powder Technology, 2019, 342, 54-66. [20] Jiang, G.; Deng, Z.; He, Y.; Li, Z.; Ni, X. Cross-linked polyacrylamide gel as loss circulation materials for combating lost circulation in high temperature well drilling operation. Journal of Petroleum Science and Engineering, 2019, 181, 106-250.

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Journal Pre-proof [21] Yan. X.; You L.; Kang Y.; Li, X.; Xu, C.; She, J. Impact of drilling fluids on friction coefficient of brittle gas shale. International Journal of Rock Mechanics and Mining Sciences, 2018, 106, 144-152. [22] Yan. X.; Kang Y.; You L.; Xu, C.; Lin, C.; Zhang, J. Drill-in fluid loss mechanisms in brittle gas shale: A case study in the Longmaxi Formation, Sichuan Basin, China. Journal of Petroleum Science and Engineering, 2019, 174, 394-405. [23] Antoinette, T.; Shi, J.; Hans, B. M. Noncoaxiality and force chain evolution. International Journal of Engineering Science, 2009, 11-12(47), 1386-1404. [24] Tian, J.; Liu E. Influences of particle shape on evolutions of force-chain and micro-macro parameters at critical state for granular materials. Powder Technology, 2019, 353, 906-921. [25] Duane, M. Moore; Robert, C. Reynolds. X-ray diffraction and the identification and analys is of

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clay minerals (2nd Edition). Oxford [u.a.]: Oxford Univ. Press. ISBN 9780195087130. [26] Lu, X.; Khonsari, M. M.; Gelinck, E. R. The stribeck curve: experimental results and theoretical prediction. J Tribol, 2006, 128, 789-794. wetted surfaces. Wear, 2009, 5-8(267), 1232-1240.

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[27] Kalin, M.; Velkavrh, I.; Vižintin, J. The Stribeck curve and lubrication design for non-fully [28] Zhang, H.; Takahiro,Y.; Kenji, F.; Shintaro, I. Is the trend of Stribeck curves followed by

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nano-lubrication with molecularly thin liquid lubricant films? Tribology International, 2018, 119: 82-87.

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[29] Artur, Wójcik; Jarosław, Frączek; Aldona, K. Wota. The methodical aspects of the friction modeling of plant granular materials. Powder Technology, 2019, 344: 504-513. [30]

Tatsuya,

I.;

Motoyasu,

K.;

Atsushi,

T.

Macroscopic

Frictional

Properties

of

al

Poly(1-(2-methacryloyloxy)ethyl-3-butyl Imidazolium Bis(trifluoromethanesulfonyl)-imide) Brush Surfaces in an Ionic Liquid. ACS Appl. Mater. Interfaces, 2010, 2(4), 1120-1128.

rn

[31] Borruto, A.; Crivellone, G.; Marani, F. Influence of surface wettability on friction and wear tests．Wear, 1998, 222(1), 57-65.

Jo u

[32] Ananth, G. R.; Michael, S. S.; Daniel, B. Liquids with Lower Wettability Can Exhibit Higher Friction on Hexagonal Boron Nitride: The Intriguing Role of Solid–Liquid Electrostatic Interactions. Nano Lett., 2019,19(3),1539-1551. [33] Elert, K.; Sebastian, E.; Valverde, I.; Rodriguez-Navarro, C. Alkaline treatment of clay minerals from the Alhambra Formation: implications for the conservation of earthen architecture. Appl. Clay Sci., 2008, 39 (3), 122-132. [34] Ertani-Gmati, M.; Brahim, K.; Khattech, I.; Jemal, M. Thermochemistry and kinetics of silica dissolution in NaOH solutions: effect of the alkali concentration. Thermochim. Acta, 2014, 594, 58-67. [35] Kazempour, M.; Sundstrom, E.; Alvarado, V. Geochemical modeling and experimental evaluation of high-pH floods: impact of water-rock interactions in sandstone. Fuel, 2012, 92 (1), 216-230. [36] Mohnot, S. M.; Bae, J. H.; Foley, W. L. A study of mineral/alkali reactions. SPE Reserv. Eng., 1987, 2 (4), 653-663. [37] Soler, J. M. Reactive transport modeling of the interaction between a high-pH plume and a fractured marl: the case of Wellenberg. Appl. Geochem., 2003, 18(10), 1555-1571.

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Journal Pre-proof [38] Kim, T.; Olek, J.; Jeong, H. G. Alkalie silica reaction: kinetics of chemistry of pore solution and calcium hydroxide content in cementitious system. Cem. Concr. Res., 2015, 71, 36-45. [39] Kang, Y.; She, J.; Zhang, H.; You, L.; Yu, Y.; Song, M. Alkali erosion of shale by high-pH fluid: Reaction kinetic behaviors and engineering responses. Journal of Natural Gas Science and Engineering, 2016, 29, 201-210. [40] Li, Q.; Chen, W.; Lu, Y.; Xiao, Q. Etched surface morphology analysis experiments under different reaction rates. Journal of Petroleum Science and Engineering, 2019, 172(8): 517-526. [41] Shook, C. A.; Roco, M. C. Slurry flow. Butterworth-Heinemann; 1991. [42] Jamie, T.; Alessandro, G. D.; Yogi, G.; Stefanakos, E.; Chand, J.; Nitin, G. Evaluation of Pressure Drop and Particle Sphericity for an Air-rock Bed Thermal Energy Storage System. Energy Procedia, 2014, 57, 633-642.

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[43] Chen, B.; Zhong, G.; Pola, G.; Zhang, C.; Hans, T.; Santiago, E.; Stephan, H.; John, R. Influence of Packing Density and Surface Roughness of Vertically-Aligned Carbon Nanotubes on Adhes ive Properties of Gecko-Inspired Mimetics. ACS Appl. Mater. Interfaces, 2015, 7(6), 3626-3632.

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[44] Ma, Y.; Liu, Y.; Carlo, M.; Tong, J. Evaluation of Wear Resistance of Friction Materials Prepared by Granulation. ACS Appl. Mater. Interfaces, 2015, 7(41), 22814-22820.

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[45] Robert, E. G. New insights about ice friction obtained from crushing-friction tests on smooth and high-roughness surfaces. International Journal of Naval Architecture and Ocean Engineering,

Pr

2018, 10(3), 361-366.

[46] Magdalena, Niemczewska-Wójcik; Artur, Wójcik. The machining process and multi-sensor measurements of the friction components of total hip joint prosthesis. Measurement, 2018, 116,

al

56-67.

[47] Laura, Peña-Parás; Hongyu, Gao; Demófilo, Maldonado-Cortés; Azhar, Vellore; Patricio,

rn

García-Pineda; Oscar, E. Montemayor; Karen, L. Nava; Ashlie, Martini. Effects of substrate surface roughness and nano/micro particle additive size on friction and wear in lubricated sliding. Tribology

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International, 2018, 119: 88-98.

[48] Amin, M.; Dale, E. J.; Sorin, G. T. Geomechanics of Lost-Circulation Events and Wellbore-Strengthening Operations. SPE Journal, 2015, 20(6), 1305-1316. [49] Eric van, O.; James, E. F.; Toby, P.; John L. Avoiding Losses in Depleted and Weak Zones by Constantly Strengthening Wellbores. SPE Drilling & Completion, 2011, 26(4), 519-530. [50] Arunesh, Kumar; Sharath, Savari; Donald, Whitfill; Dale, E. Jamison. Wellbore Strengthening: The Less-Studied Properties of Lost-Circulation Materials. SPE Annual Technical Conference and Exhibition, 19-22 September, 2010, Florence, Italy.

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e-

pr

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Fig.1 Schematic of lost circulation in fractured reservoir.

w

fracture

Wellbore pressure

al △P× A

Ff FN

Pp

Ff ≥△P× A, plugging zone keeps stable.

Jo u

Pw

b

fracture Pw＞Pp, △P=Pw-Pp

Ff=FN× μ f, A=w × b

rn

Pw

Pw＞Pp, △P=Pw-Pp

Pr

Fig.2 Multi-scale structure of the plugging zone.

Pore pressure

Ff=FN× μ f, A=w × b

Pw

△P× A

Ff FN

Pw

（ a）

Pp

Ff＜△P× A, plugging zone occurs shear failure.

（ b）

Fig. 3 Effect frictional resistance on the stability of plugging zone: (a) F f ≥△P×A, plugging zone keeps stable; (b) F f ＜△P×A, plugging zone occurs shear failure.

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30

(b)

Loss volume Loss frequency

2116.6

Loss volume（ m3）

2000

25 20

1500

1396.4

15 1000

871

796.2

10 624 617.4 597.3

500

511

446.1 440

0

Loss frequency

2500

5 0

J-1 J-2 J-3 J-4 J-5 J-6 J-7 J-8 J-9 J-10 Well No.

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Fig. 4 Developed natural fracture and loss data of shale gas reservoirs in Sichuan Basin of China: (a) developed natural fracture in formation; (b) loss volume and frequency of lost circulation, which are collected from drilling fluid leakage monitoring of shale gas wells in the Sichuan Basin, China, where the loss frequency refers to as the number of loss events that occurred during the drilling of

rn

al

Pr

e-

pr

the shale reservoir.

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Fig. 5 Shale sample polished by emery paper (the right subfigure is the side view of the left one).

Fig. 6 Calcium carbonate particles used in the experiments.

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e-

pr

oo f

Fig. 7 Schematic diagram of friction coefficient measuring system.

Pr

Fig. 8 Friction plates bonded calcium carbonate particles (the right subfigure is the zoomed-in

Jo u

rn

al

image).

Fig. 9 Stribeck curve showing friction coefficient versus lubrication type [28].

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Static friction

Friction coefficient

1.0

lubrication contidtion: Dry Particle size: 1.3~1096.5μm Sliding velocity: 1.94mm/min

1.0

MSFC=0.50

MSFC=0.41

ASFC=0.47

ASFC=0.35

0.4 MSFC=0.23

0.2 0.0

0.8 0.6

50

100

ASFC=0.11

150

200

250

0.47

0.41

0.4

0.0010

0.35 0.23 0.22

0.0005

0.13 0.11

0.0

300

0.0000 0.271

Time (s)

0.0020 0.0015

0.5

0.2

0

0.72

ASFC=0.22

MSFC=0.13

0.0025 0.9

ASFC=0.72

MSFC=0.90

0.0030

MSFC ASFC SFC variance in sliding stage

(b)

0.416N 1.042N

Sliding friction

0.8 0.6

0.271N 0.710N 1.482N

Friction coefficient

(a)

SFC variance in sliding stage

1.2

1.2

0.416

0.710 1.042 Normal force (N)

1.482

Fig. 10 Friction coefficients between shale and calcium carbonate particles under different normal

Pr

e-

pr

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forces: (a) friction coefficient versus time; (b) MSFC, ASFC and SFC variance in the sliding stage.

Fig.11 Schematic of the contact change of asperities with the normal load increase (revised from Xu

Jo u

rn

al

et al. [3]).

Fig. 12 SEM images of the asperities on shale surface: (a) low normal force, F N =0.271N; (b) high normal force, F N =1.042N.

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1.0

1.0

(a)

MSFC=0.83

(b)

ASFC=0.76

MSFC=0.75

0.6 ASFC=0.63

0.4

t=73s Reference (1.94mm/min) 3.18mm/min

t=68s

0.2

0.0

50

100

150

200

250

0.6 ASFC=0.61

0.4

t=73s Reference (1.94mm/min) 4.44mm/min

t=61s

0.2

Particle size: 1.3~1096.5μm lubrication contidtion: Dry Normal force： 1.482N

0

0.0

300

Particle size: 1.3~1096.5μm lubrication contidtion: Dry Normal force： 1.482N

0

50

100

1.0

1.0 MSFC=0.83

(d)

ASFC=0.76

0.8

ASFC=0.57 t=73s

0

50

100

150

200

250

300

Time (s)

1.2

300

ASFC=0.76

ASFC=0.50

0.4 t=73s

Reference (1.94mm/min) 7.69mm/min

t=32s

0.0

0

Particle size: 1.3~1096.5μm lubrication contidtion: Dry Normal force： 1.482N

50

100

150

200

250

300

Time (s)

al

0.0030

1.0 0.83 0.76

0.0020

0.75 0.71 0.63

0.6

0.66 0.61

0.61

0.0015

Jo u

0.57

0.4 0.2 0.0 1.94

0.0025

rn

MSFC ASFC SFC variance in sliding stage

(e)

0.8

0.6

0.2

Particle size: 1.3~1096.5μm lubrication contidtion: Dry Normal force： 1.482N

Pr

0.0

250

MSFC=0.61

e-

Reference (1.94mm/min) 6.67mm/min t=47s

MSFC=0.83

pr

0.6

0.2

Friction coefficient

Friction coefficient

MSFC=0.66

0.4

200

3.18 4.44 6.67 Sliding velocity (mm/min)

0.5

0.0010 0.0005

SFC variance in sliding stage

Friction coefficient

0.8

150 Time (s)

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Time (s)

(c)

ASFC=0.76

MSFC=0.71

0.8 Friction coefficient

Friction coefficient

0.8

MSFC=0.83

0.0000

7.69

Fig. 13 Friction coefficient between shale and calcium carbonate particles under different sliding velocities: (a)~(d) friction coefficient versus time; (e) MSFC, ASFC and SFC variance in the sliding stage.

frictional trace Asperity are destroyed

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Journal Pre-proof Fig. 14 SEM images of the asperities on shale surface under 7.69 mm/min.

1.2

Particle size: 1.3~1096.5μm Sliding velocity: 1.94mm/min Normal force： 1.482N

Friction coefficient

1.0

MSFC ASFC

0.82

0.8

0.75 0.61

0.6

0.71 0.63

0.59

0.58 0.5

0.4 0.2

Reference (Dry)

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0.0 3% KCl solution

pH=10 alkaline solution

white oil

1.2

0.6

e-

0.75

0.71 0.59

Pr

0.8

MSFC(5minutes) ASFC(5minutes) MSFC(15days) ASFC(15days)

0.71

0.6

0.58

0.63

0.61

0.58

0.47

0.4

rn

0.2

0.53

0.5

al

Friction coefficient

1.0

Particle size: 1.3~1096.5μm Sliding velocity: 1.94mm/min Normal force： 1.482N

pr

Fig. 15 MSFC and ASFC for different lubrication fluids.

0.0

Jo u

3% KCl solution

pH=10 alkaline solution

white oil

Fig. 16 MSFC and ASFC after soaking for 5 minutes and 15 days

(a)

1.0

0.005 MSFC ASFC SFC variance in sliding stage

(b)

MSFC=0.71

ASFC=0.58

0.8

MSFC=0.61

0.6

0.4 ASFC=0.47

0.2

0.0

soaking for 5 minutes soaking for 15 days 0

50

0.004

0.71

Friction coefficient

Friction coefficient

0.8

100

150 Time (s)

200

250

300

0.6

0.58

0.61

0.003 0.47

0.4

0.002

0.2

0.001

0.0

SFC variance in sliding stage

1.0

0.000 soaking for 5 minutes

soaking for 15 days

Fig. 17 Friction coefficient for pH=11 alkaline solution lubrication: (a) friction coefficient versus time; (b) MSFC, ASFC and SFC variance in sliding stage after soaking for 5 minutes and 15 days, respectively.

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Fig. 18 3D laser scanning images of shale surface: (a) before soaking; (b) after soaking for 15 days; (c) reduction in asperities height. The color bar implies the shape of shale surface and indicates the height above the reference elevation level. And the details of 3D laser scanning method are given

e-

pr

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by Li et al. [40].

Jo u

rn

al

Pr

Fig. 19 SEM images of reaction product on shale surface .

Fig. 20 EDS results of reaction product on shale surface .

Water film

FN

Reaction product

F

FN

(a) Soaking for 5 minutes

F

(b) Soaking for 15 days

Fig. 21 Schematic of the friction interface change for different soaking time by alkaline solution.

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  

Friction coefficient

1.0

MSFC=0.60

0.8

0.008

(b)

MSFC ASFC SFC variance in sliding stage

1.0

ASFC=0.60 ASFC=0.47

0.6 0.4

0.006

0.82

0.8

0.61

0.6

0.6

0.004 0.47

0.45 0.39

0.4

0.002 MSFC=0.45

0.2 0.0

0

50

100

ASFC=0.39

150 Time (s)

200

0.2

250

0.0

300

0.094

0.441 Sphericity

0.752

SFC variance in sliding stage

1.2

Particle size: 1.3~1096.5μm lubrication contidtion: Dry Sliding velocity: 1.94mm/min MSFC=0.82 Normal force： 1.482N

(a)

Friction coefficient

1.2

0.000

Fig. 22 Friction coefficient for different sphericity particles: (a) friction coefficient versus time; (b) MSFC,

Average Ra= 13.1μm , Rz= 101.0μm

Average Ra= 2.3μm , Rz= 30.2μm

Average Ra= 7.4μm , Rz= 88.2μm

(b)

(c)

Jo u

(a)

rn

al

Pr

e-

pr

oo f

ASFC and SFC variance in sliding stage.

Fig. 23 Surface roughness of three calcium carbonate particles, where the color bar implies the shape of each particle and indicates the height above the reference elevation level.

0.8

MSFC=0.79 ASFC=0.64 MSFC=0.60 0.8

Friction coefficient

0.4 0.2

ASFC=0.43 MSFC=0.51 0

50

100

200

250

0.64 0.6

0.6

0.51

0.51

0.004 0.43

0.4 0.002

Ra=13.1μm, Rz=101.0μm Ra=7.4μm, Rz=88.2μm Ra=2.3μm, Rz=30.2μm

150 Time (s)

0.79

0.006

ASFC=0.51

0.6

0.0

0.008 MSFC ASFC SFC variance in sliding stage

(b)

Sliding velocity: 1.94mm/min; Normal force： 1.482N

1.0 Friction coefficient

1.0

(a) Particle size: 1.3~1096.5μm; lubrication contidtion: Dry

0.2

0.0

300

Ra=13.1μm Rz=101.0μm

Ra=7.4μm Rz=88.2μm

Ra=2.3μm Rz=30.2μm

SFC variance in sliding stage

1.2

0.000

Fig. 24 Friction coefficient for different surface roughness particles: (a) friction coefficient versus time; (b) MSFC, ASFC and SFC variance in sliding stage.

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15

20~40 mesh (100.0~1700.0 μm)

40 D50=670μm

10 20 D90

5 0 10

100

30 60~80 mesh (1.1~724.4 μm)

25

60

20 D50=261μm

15

40

10

20

5 1

10

100 Particle size (μm)

100 Particle size (μm)

0 10000

1000

100 Volume percentage Cumulative volume percentage

35

80 30

80~100 mesh (1.3~549.5 μm)

25 20

60

D50=238 μm

15

40

10

20

5 0

0 10000

1000

10

e-

0

1

pr

80

20

40 Cumulative volume percentage（ %）

Volume percentage（ %）

35

40

10

0

Volume percentage Cumulative volume percentage

D50=452μm

15

5

Volume percentage（ %）

40

60

20

0 10000

100 1000 Particle size (μm)

40~60 mesh (1.3~1096.5 μm)

25

Cumulative volume percentage（ %）

20

60

1

10

100 Particle size (μm)

Cumulative volume percentage (%)

25

80 30

oo f

80 30

Volume percentage Cumulative volume percentage

35

Cumulative volume percentage（ %）

Volume percentage（ %）

35

100

40

100 Volume percentage Cumulative volume percentage

Volume percentage（ %）

40

0 10000

1000

Pr

Fig. 25 Particle size distribution for four size calcium carbonate particles.

MSFC=0.82

rn

0.6 0.4

ASFC=0.61 MSFC=0.63

0.2

ASFC=0.45 ASFC=0.50

100.0-1700.0μm 1.1-724.4μm

0

50

100

0.020

(b)

150

200

0.8 0.6

MSFC ASFC SFC variance in sliding stage

0.94 0.82

ASFC=0.75

0.8

0.0

1.0

Friction coefficient

MSFC=0.81

Jo u

Friction coefficient

1.0

Lubrication contidtion: Dry Sliding velocity: 1.94mm/min Normal force： 1.482N

MSFC=0.94

al

(a)

0.81

0.016

0.75 0.63

0.61

0.012

0.51 0.45

0.4

0.008

0.004

0.2

SFC variance in sliding stage

1.2

1.3-1096.5μm 1.3-549.5μm

0.0 250

300

0.000 300.0~1700.0 1.3~1096.5

1.1~724.4

1.3~549.5

Particle size (μm)

Time (s)

Fig. 26 Friction coefficient for different size calcium carbonate particles: (a) friction coefficient versus time; (b) MSFC, ASFC and SFC variance in sliding stage.

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（ a） Average Ra= 92.6μm , Average Rz= 534μm

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（ b） Average Ra= 91.6μm , Average Rz= 527μm

Pr

e-

pr

（ c） Average Ra= 63.9μm , Average Rz= 302μm

（ d） Average Ra= 57.0μm , Average Rz= 280μm

al

Fig. 27 Surface roughness of friction plate with different size calcium carbonate particles: (a)

Jo u

rn

100.0~1700.0μm; (b) 1.3~1096.5μm; (c) 1.1~724.4μm; (d) 1.3~549.5μm.

Fig. 28 Auxiliary materials used in lost circulation control: (a) rubber particles and (b) QR-1 fibers.

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Calcium carbonate particles & shale QR-1 fiber & shale Rubber particle & shale

MSFC=1.18

1.2

ASFC=0.87

Friction coefficient

1.0 0.8 0.6 0.4 0.2 0.0

Sliding velocity: 1.94mm/min Normal force： 1.482N

0

50

100

150 Time (s)

200

250

MSFC=0.95

0.01

0.00

0.16

(d)

1.4 1.2 Friction coefficient

ASFC=0.84

1.0

MSFC ASFC SFC variance in sliding stage

1.21

pr

1.0 0.8

0.8

0.12 0.95 0.84

0.75

0.72

0.6 0.4

ASFC=0.72

MSFC=0.75 ASFC=0.59

0.2

0.04

0.2

Sliding velocity: 1.94mm/min Normal force： 1.482N

0.0

50

100

150

200

250

Time (s)

Calcium carbonate particles & shale QR-1 fiber & shale Rubber particle & shale

1.4 1.2

MSFC=0.85 MSFC=0.70

1.0

1.4 1.2

Sliding velocity: 1.94mm/min Normal force： 1.482N

Jo u

ASFC=0.73 0.8 0.6 0.4

MSFC=0.63 ASFC=0.50

0.2

0.16 MSFC ASFC SFC variance in sliding stage

(f)

rn

(e)

0.00 Calcium carbonate QR-1 fiber & shale Rubber particle & particle & shale shale

1.6

al

1.6

300

Friction coefficient

0

0.12

1.0 0.85

0.8 0.6

0.73 0.63

0.08

0.7 0.59

0.5

0.4

0.04

0.2

ASFC=0.59

0.0

0

50

100

150 Time (s)

200

250

0.08

0.59

e-

0.6 0.4

0.02

Calcium carbonate QR-1 fiber & shale Rubber particle & particle & shale shale

Pr

Friction coefficient

0.6

0.0

300

Calcium carbonate particles & shale QR-1 fiber & shale Rubber particle & shale

MSFC=1.21

1.2

Friction coefficient

0.72 0.61

1.6

(c)

1.4

0.0

0.87

0.82

0.8

0.2

1.6

0.0

1.0

0.4

ASFC=0.72

MSFC=0.82 ASFC=0.61

0.03

1.04

oo f

Friction coefficient

1.2

1.4

0.04 MSFC ASFC SFC variance in sliding stage 1.18

(b)

SFC variance in sliding stage

1.4

1.6 MSFC=1.04

SFC variance in sliding stage

(a)

SFC variance in sliding stage

1.6

300

0.00 Calcium carbonate QR-1 fiber & shale Rubber particle & particle & shale shale

Fig. 29 Friction coefficient between auxiliary materials (elastic particles and fibers) and shale under different lubrication conditions: (a～b) none lubrication (dry); (c～d) 3%KCl solution lubrication; (e～f) white oil lubrication.

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Journal Pre-proof

Elastic deformation rate (%)

500 R- Calcium carbonate particles E- Rubber particle 406.55 400 F- QR-1 fiber R&F&E- R, F and E are mixed 300 in equal proportions 206.03

200

169.63 111.33

100

0 F

E

R&F&E

oo f

R

Fig. 30 Elastic deformation rate for different LCMs. Details of the testing method are given by Arunesh et al.

Jo u

rn

al

Pr

e-

pr

[50].

Fig. 31 SEM image of QR-1 fibers.

25

Journal Pre-proof Table 1 Property of shale sample based on X-ray testing ( unit: %) Quartz

Calcite

Dolomite

Feldspar

Pyrite

Smectite

Illite

I/S

Kaolinite

Chlorite

45.9

3.5

1.4

7.2

2.7

0.0

33.4

0.9

4.0

1.0

Table 2 Properties of three lubricating fluids (20℃) Lubricating fluids

pH

Viscosity 𝜂 (mPa.s)

Density 𝜌 (g/cm3)

3%KCl solution

7.0

1.0

1.0

alkaline solution

11.0

1.0

1.0

white oil

not known

9.4

0.9

oo f

Table 3 Acceleration parameters of each sample under different normal forces Sliding velocity

Acceleration rate

Normal force (N)

Duration of the acceleration

2

(mm/min)

(m/s )

period (s)

0.271

1.07×10

3

0.416

pr

-5 -6

7

-6

15

-6

20

-6

27

4.57×10 2.13×10

1.94

e-

0.710

1.60×10

1.042

1.19×10

Pr

1.482

Table 4 Ion detection results of alkali solution after soaking for 15 days (unit: mg/L). Al3+

0.83

5.29

M g2+

al

Ca

0.12

rn

2+

Fe

Total Si

CO 32-

0.51

321.34

240.47

Table 5 Sphericity for different shape particles

A B C

Particle volume

Jo u

Average size Particle

Average

Specific surface

Surface area

Sphericity 𝛹

D50 (μm)

Vp (m )

mass m (g)

area Ap (m /g)

Sp (m )

452

4.833×10-11

0.131×10-3

0.0522

6.837×10-6

0.094

440

4.458×10

-11

0.121×10

-3

0.0114

1.377×10

-6

0.441

5.609×10

-11

0.152×10

-3

0.942×10

-6

0.752

475

3

26

2

0.0062

2

Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may

Jo u

rn

al

Pr

e-

pr

oo f

be considered as potential competing interests:

27

Journal Pre-proof fracture

Ff=FN× μ f, A=w × b △P× A

Ff FN

Pp

μ f =？

Ff＜△P× A, plugging zone occurs shear failure.

(a)

（ b）

MSFC=0.71

0.8

ASFC=0.58 MSFC=0.61

0.6

0.4 ASFC=0.47

0.2

soaking for 5 minutes soaking for 15 days 0

50

100

pr

oo f

0.0

e-

（ a）

Pw

Pr

Pore pressure

1.0

△P× A

Ff FN

Ff ≥△P× A, plugging zone keeps stable.

al

Pp

Ff=FN× μ f, A=w × b

Pw

rn

Pw

b

Pw＞Pp, △P=Pw-Pp

Jo u

Pw

fracture

Pw＞Pp, △P=Pw-Pp

Friction coefficient

w Wellbore pressure

28

150 Time (s)

200

250

300

Journal Pre-proof

Normal loading and sliding velocity change the friction- interface properties. The friction mechanisms of particles and fiber are discussed. The alkali corrosion of shale is a key factor affecting coefficient friction.

Jo u

rn

al

Pr

e-

pr

oo f

Conditions for maximizing the friction coefficient of are illustrated.

29