Lost circulation often occurs in fractured formations, which was a main technological problem during drilling. Conventional lost circulation material (LCM) was often used to form a plugging zone to prevent fluid loss during drilling. The formed seal was a granular material system composed of LCMs. This paper presented the physical mechanism of the force chain within the plugging zone. The seal performance is related to the properties of LCMs. A device for testing seal performance of LCMs with long fracture was developed. The effects of LCM performance on seal integrity were investigated using a plugging device with long fracture. The results showed that the wide particle size distribution (PSD) of LCMs tended to form a strong force chain network structure within the sealing zone. Increasing the stiffness and roughness of LCMs resulted in higher breaking pressure. The addition of fiber with high length-diameter ratio could improve the shear strength of the sealing zone and form a strong force chain network structure, and it can reduce fluid loss.

Lost circulation is defined as drilling fluid loss into the fracture or void in formation during drilling, which is one of the major technological problems during drilling [1]. Because of the existence of fractures, drilling fluid loss into fractured formation is frequent. The drilling fluid loss in fractured formation is divided into natural fractured loss and induced fractured loss.

The addition of conventional LCMs to drilling fluid was the most common method to deal with loss. The sealing zone is formed by bridging, filling, and sealing of LCMs [2]. It is a typical granular material system composed of LCMs. The LCM particles interact and compress with each other to form a force chain. The strength of chain force influences the stability of the formed seal. The sealing strength of chain force is also related to the properties of LCMs. In order to optimize the lost circulation treatments, the concentration, type, particle size distribution (PSD), resiliency, and crush resistance of LCMs were studied [35]. Kang et al. proposed that the strength of the force chain within the formed seal was related to the properties of LCMs and has an obvious impact on the strength of the sealing zone [6]. The technical indices such as particle strength, elasticity, and surface friction coefficient were proposed to evaluate LCM performance [7]. However, the effect of the force chain on seal integrity by plugging experiment was not investigated.

A plugging device with fractures is used to test the plugging performance of the LCMs in the laboratory. The high-pressure high-temperature plugging device and particle plugging device (PPA) with discs are often used to test the plugging performance of the LCMs [810]. The LCM performance is evaluated by a low-pressure device and a high-pressure device [11]. In order to simulate fractures in the formation, the slots are developed. But there is not enough depth within the slots. Therefore, in order to be similar to the reality of the fractured formation, the plugging device with a long fracture slot is required.

The objective of the study is to investigate the factors that affect the strength of the force chain in the plugging zone and the effect of LCM performance on withstanding pressure capacity and fluid loss. To investigate the effect of force chain on seal integrity by plugging experiment, the plugging device with long fracture was developed. The fluid loss values and sealing breaking pressure were the index for evaluating the performance of the LCMs. The position and composition of the formed seal were also investigated. Finally, the LCM treatments based on the sealing mechanism were proposed for the oil field.

The sealing zone is a typical granular material system composed of LCMs [12]. The compression between particles forms the contact force under external load. Contact forces form a network along particle propagation. The transmission path is usually a quasilinear chain structure. It is called the force chain network structure [13]. There is large contact stress between some particles, and it can withstand a large portion of the external load. It forms a strong force chain. Instead, it will form a weak force chain. The strength of the formed seal is determined by the strong force chain. The weak force chain is evenly distributed within the particle system, which helps to reconstruct the strong force chain after the rupture. The more the number of strong force chains, the more stable the sealing zone.

There are three factors which influence the strength of the force chain [14]. (1) Contact number of particles. It defines the number of particles in contact with neighbor particles. In the larger contact number, particles accumulate together compactly. Therefore, the probability of forming a strong force chain increases. (2) Normal contact stress between particles. The greater the normal contact force, the stronger the force chain. (3) Shear strength between particles. The force chain can break easily along the shear plane under small external loads when shear strength is small, thus affecting the structural strength of the particle system.

Particles gradually bridge and fill to form the sealing zone on the macroscale. As the wellbore pressure increases, the local damage occurs within the seal. The sealing strength of chain force is also related to the properties of LCMs and further has a significant effect on the stability of the formed seal.

3.1. Experimental Device

The plugging device is used to investigate the seal integrity of LCMs. In order to be similar to the reality of the fractured formation and research the formed seal, a plugging experiment device with long fracture was developed (Figure 1). We used stainless steel to build the device and the fracture. This material prevents corrosion and can withstand higher pressure. The long fracture contains two symmetrical parts. The fracture channel was assembled by two parts combined. The core gripper was used to place the long fracture. Drilling fluid with LCMs was poured into the test cell. Then, the core gripper and test cell were assembled together. After the experiment, the core gripper was removed from the test cell; then, the plugging fluid was poured out through the entrance. The schematic diagram of the plugging experiment device with a long fracture slot is shown in Figure 1.

Figures 2 and 3 show the schematic and pictures of the tapered fracture, respectively. There is a groove in the steel plates as shown in Figure 3(a). The fracture channel is assembled by two parts combined as shown in Figure 3(b). After the test, we remove the fracture slot from the cell, then take down two hoops and open the fracture. The thickness, composition, and structure of the seal are investigated. Figure 4 is the physical map of the long tapered fracture slot. The specifications of the fracture slot are shown in Table 1.

3.2. Lost Circulation Materials

Calcium carbonate (CC), walnut shell (WS), rubber (RUB), and polypropylene fiber (PF) were selected to test the plugging integrity. The length of the PF is 6000 microns, and the diameter is 20 microns. Figure 5 shows the microscopy photos of the selected LCMs.

3.3. Drilling Fluid

The 4% by weight bentonite mud included sodium carboxymethyl cellulose with high viscosity (CMC-HV) and xanthan (XC). CMC-HV and XC were 0.2% and 0.2% by weight, respectively. When the shear rate was 1022 s-1, the apparent viscosity and plastic viscosity were 48.0 mPa·s and 28.0 mPa·s, respectively.

3.4. Experimental Methodology

The formed seal has a high strength that can withstand higher wellbore pressure [15, 16]. The formed seal would have to remain stable under higher wellbore pressures. A new method of plugging test was developed. Plug breaking pressure (PBP) was introduced to evaluate the performance of LCMs [17]. The experimental principle is shown in Figure 6. The experimental process is as follows [18]:

  • (i)

    As in Figure 6(a), slowly pressurize to push the LCMs through the fracture. Apply the flowing pressure in increments of 1 MPa and 2-minute intervals. Final pressurize to 3.5 MPa. If the loss stops when the pressure reached 3.5 MPa, maintain 5 min and note the loss volume

  • (ii)

    The drilling fluid containing LCMs is completely replaced with the drilling fluids

  • (iii)

    As shown in Figure 6(b), apply the pressure from the bottom side in increments of 1 MPa. When the seal breaks and fluids lost through the exit, note the pressure as breaking pressure

The indexes for evaluating the sealing integrity are proposed: breaking pressure, fluid loss before forming the seal, and position of the plugged zone.

For investigating the effect of PSD, stiffness, roughness, and combinations of LCMs on seal performance, the fracture aperture of 2 mm and tip size of 1 mm were selected.

The PSD of particles was determined by sieve analysis tests. D10, D50, and D90 mean the value of the particle diameter at 10%, 50%, and 90% in the cumulative size distribution, respectively. Table 2 shows the testing results for LCM treatments. The volume concentration was 10% of drilling fluid for the particles such as CC, WS, and RUB. The mass concentration of fiber was 0.3% by weight of drilling fluid. CC-1, CC-2, and CC-3 were three kinds of calcium carbonate with different friction coefficients. Total loss meant the fluid loss volume was 1500 mL and the plugging failed.

Based on the mechanism of the force chain structure in the plugging zone and testing results using long fracture slots, we discussed the factors that influence the strength of the force chain within the plugging zone.

5.1. Effect of Particle Size Distribution

Comparing the experimental results of 1# and 2# in Table 2, blend 1# had a narrow PSD. D10 was 600 microns, and D90 was 1300 microns. The fracture was bridged by the coarse particles, and there were voids between the coarse particles. The fluids could have total loss through the voids. Propagation of pressure through the void spaces pushes the LCM accumulation inside the fracture. So, the long sealing zone from 57 to 96 cm was formed (Figure 7(a)). The permeable seal results in low-pressure bearing capacity (Figure 8(a)). Blend 2# has a wide PSD, and there are enough fine particles. The coarse particles bridged in the fracture slot firstly; then, the small particles filled in the void spaces promptly. The thin plugging zone was formed from 90 to 93 cm (Figure 7(b)). Small particles come close to form the tense sealing zone when the PSD was wide. Thus, increasing the contact numbers of particles leads to a stronger force chain in the formed seal. Therefore, breaking pressure increases to 7.23 MPa, and the fluid loss is 420 mL (Figure 8(b)).

5.2. Effect of Elastic Modulus

The experimental results of 2#, 5#, and 6# are compared in Table 2. With the same concentration and PSD, breaking pressure is varying with the LCM type. As shown in Figure 9, calcium carbonate exhibited higher breaking pressure (7.23 MPa) than walnut shell (5.38 MPa). The total loss occurred during sealing, and breaking pressure is 0 MPa for rubber. The stronger the normal force between particles, the more likely it is to form a strong force chain. Based on the Hertz contact theory [19], the larger the elastic modulus and the greater the contact force between particles, the stronger the force chain network structure. The elastic modulus of CC is 45 GPa, WS is 15 GPa, and RUB is 0.01 GPa. LCM does not deform easily under compression with higher stiffness. The force chain structure is stronger inside the formed seal.

The stiffness coefficient of calcium carbonate was larger compared to walnut shell, so smaller deformation occurred between particles. There was also deformation between the fracture wall and bridging particles. The particles cannot match the fracture width because of the deformation of particles. The sealing zone moved through the tip and did not withstand high wellbore pressure. The stiffness of RUB was too small. The sealing zone had a void and high permeability. RUB particles accumulated in the fracture as injection and total loss occurred.

5.3. Effect of Friction Coefficient

We use a grinder to polish the particles. It was made sure that the PSD of particles is the same, and the influence of the friction coefficient of particles on the seal integrity was researched. The experimental results of 2#, 3#, and 4# are compared in Table 2. Figure 10 shows the influence of increasing the friction coefficient of particles on breaking pressure. Breaking pressure is higher by increasing the friction coefficient of the particle. Rougher particles will give rise to higher shear strength between particles. It helped to form a strong force chain network structure, and the shear strength of the formed seal was higher, which leads to higher breaking pressure.

Discrete element simulation shows the internal force chain distribution of different friction coefficient particles [20] (Figure 11). Mostly, there are weak force chains (light gray lines) and very few strong force chains (black lines) in particle systems when the friction coefficient is 0. There are more strong force chains and the length becomes longer when the friction coefficient is 0.75. Greater roughness of the particles will give rise to higher shear strength. When the material surface is rough, it helps to form a strong force chain network structure, and the shear strength of the formed seal is higher. In addition, the friction is increased between the fracture wall and the formed seal.

5.4. Effect of LCM Combination

When the particles were used during plugging, tangential stress was small between particles. The weak force chain structure is often formed between the particles. The fiber reinforcement technique can effectively improve the shear strength of traditional concrete [21]. We test the shear strength of the particles and the composite of particles and fibers. The results showed that the shear strength of the sealing zone was increased with the addition of fibers and a strong force chain was formed within the sealing.

The results of 2# and 7# are compared in Table 2. The sealing breaking pressure increased from 7.23 to 11.73 MPa, and the fluid loss volume reduced from 420 mL to 190 mL after adding the PF. When calcium carbonate was used individually, the pressure curve (Figure 12(a)) shows that the pressure drops sharply and then rises during plugging. The cell pressure dropped down and rose frequently from 3 to 4 min, 5 to 5.2 min, 6 to 6.8 min, 7.4 to 7.5 min, and 10.8 to 11.2 min during the plugging process. The fluid is lost through the outlet at these moments. There was small tangential stress between particles when the particle LCMs were used only. The seal will be broken with increasing pressure. When calcium carbonate and fiber combinations were tested, the frequency of pressure fluctuations is less (Figure 12(b)). 3D strengthening effect of fiber nets improved the shear strength of the sealing zone and helped to form a strong force chain structure. Figure 13 shows the sealing zone of calcium carbonate and fiber blends. The particles and fibers are evenly distributed and synergistically formed the sealing zone. The fibers can easily fill the voids and improve the tightness of the sealing zone because of the high length-diameter ratio. The fluid loss is reduced.

The shear strength of the sealing zone was increased by the addition of fibers. Shear strength of particles and fiber blends was tested by the direct shear device. Figure 14 shows that the cohesion force of the particles and fiber blends was increased with the increase of fiber content. The fiber networks within the sealing zone could support particles under external load. 3D strengthening effect of fiber nets improved the shear strength of the sealing zone and helped to form a strong force chain structure. The breaking pressure was effectively improved.

5.5. Sealing Mechanism Applied to LCM Treatment in the Field

The sealing zone is composed of LCMs, and it is a typical granular material system. Strength of chain force in the plugging zone influences macroscopic stability of the plugging zone. The effect of LCM type, PSD, roughness, and combination influences the strength of chain force within the plugging zone. In the field, the engineers can select the LCMs based on their property. The stiffness of the LCMs should be taken into consideration during plugging, and the mineral particles with larger stiffness should be selected. The friction coefficient of the LCM particles was tested, and the rough particles were chosen. The particle size distribution of LCM particles was optimized. Coarse, medium, and fine particles are used in combination. The polypropylene fiber was not ignored, the breaking pressure was improved, and the fluid loss was reduced.

  • (1)

    There was a force chain network structure within the plugging zone. The sealing zone was stable with the increased strong force chains

  • (2)

    In order to be similar to the reality of the long fracture in formation, a plugging device with long fracture was developed. The thickness and composition of the sealing zone were investigated

  • (3)

    Wide PSD of LCM tended to form a strong force chain structure within the sealing zone and improve the sealing efficiency. Increasing the stiffness and roughness of LCM resulted in a strong force chain within the sealing zone and higher breaking pressure. The addition of polypropylene fibers could improve the shear strength of the sealing zone and form a strong force chain structure, and the breaking pressure was improved and the fluid loss was reduced

All the data has been presented in the manuscript.

The authors declare that they have no conflicts of interest.

This work is funded by the Research Foundation of Chongqing University of Science and Technology, project No. ckrc2021030, National Natural Science Foundation of China (51604052 and 51974354), and Natural Science Foundation of Chongqing, China (cstc2019jcyj-msxmX0064).

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