Study on the Behavior and State of Viscous Fractured Leakage Bridging and Plugging Slurry during the Pump-In and Pressurization Process

Abstract

Clarifying the process of bridging and plugging slurry during pumping and squeezing can effectively improve the efficiency and accuracy of fractured leakage treatment while minimizing impacts on safety and the environment. In this paper, computational fluid dynamics (CFD) numerical simulation and experimentation (hydrostatic settling method) are combined to evaluate the dynamic settlement process of different types of plugging slurry through sedimentation changes, sedimentation volume, sedimentation velocity and sedimentation height for factors such as viscosity, particle size, density and concentration of plugging slurry. The formula of particle sedimentation velocity is combined to obtain the following: When the viscosity of plugging slurry is more than 30 mPa·s, the particle diameter is 1.5 mm (particle size is half the fracture width), and the particle density is 2.0–2.6 g/cm³; it shows good dispersion and plugging performance under pumping pressure and while holding and squeezing after lifting the bit. The simulation results show that the particle density should not exceed two times the plugging slurry density, and the particle concentration has little influence on the particle settling volume.

1. Introduction

Lost circulation is one of the major technical challenges in drilling engineering, with a significant portion of the losses being related to fractures. Fracture-induced losses contribute to over 90% of the overall cost of controlling such losses [1]. As the main direction of oil and gas production gradually shifts towards unconventional reservoirs such as tight oil and shale gas with enormous resource potential, the development of fracture systems in these unconventional reservoirs has brought complex situations in controlling fluid-induced fracture losses [2,3]. The existing research on fracture loss mainly focuses on rock anisotropy, stratigraphy and fracture development, but the research on slurry plugging behavior during pumping is relatively limited, resulting in a lack of understanding of the change in slurry plugging in the lost layer [2,3]. The behavior of plugging slurry during static and pumping–squeezing states significantly affects the efficiency and accuracy of fracture sealing and bridging, while the settlement of weighting materials under the influence of gravity can lead to wellbore losses, stuck pipes, well control and cementing operation difficulties [4,5]. Therefore, understanding the behavior of sealing particles in plugging slurry is crucial in solving the problem of fracture sealing [6]. Hanson [7] studied the dynamic settlement of weighing agents in a wellbore and found that the controllability of dynamic settlement is lower than that of static settlement, as well as the occurrence of complex underground accidents. Especially in inclined shafts, the settling rate of the weighing agent increases after settling, leading to a rapid increase in fluid pressure during circulation, which may cause harmful effects such as pipeline blockage and loss. Lin [8] used the improved VST (viscosity stability test) method to comprehensively evaluate the settlement problem of barite weighing agent and combined the particle size of barite with the settlement stability test method. The results showed that adding a certain amount of ultra-fine barite to conventional barite could greatly improve the settlement problem. Furthermore, Wang [9] compared the rheological properties and settlement performance of plugging slurries and found that the higher the dynamic yield stress of the plugging slurry, the better the dynamic settlement stability. However, the dynamic yield stress depends on the composition of the plugging slurry system, and the predictability of its dynamic settling behavior is limited. Most researchers have focused on the settling behavior of solid particles in conventional plugging slurry systems, while there is limited research on the dynamic settling behavior of sealing particles in plugging mud under fracturing and wellbore conditions. The dynamic settling process of particles in plugging slurry is a complex dynamic behavior [10], and at present, the understanding primarily relies on experimental methods to explain the phenomena and mechanisms of particle settling, with limited studies utilizing numerical simulation methods. Based on previous research, the behavior and flow process of suspended particles and settlement characteristics during the pumping and lifting of plugging slurry into formations and the subsequent pumping of plugging slurry are still not well understood, leading to significant uncertainties in subsequent operational processes. Therefore, in-depth research on the behavior of plugging slurry during pumping and squeezing processes is of great significance. Based on the computational fluid dynamics (CFD) method, this paper adopts the ANSYS Fluent 2020 Euler multiphase flow model to explore the behavior state process of plugging slurry pumped into a formation, while lifting the drill bit and pumping plugging slurry under conditions of different material particle size, concentration, density and fluid viscosity, and to block the settling volume of the material within a specific time. The characteristics, influencing factors and mechanism of the behavior state of the plugging slurry during pumping and squeezing are discussed, which can provide a new basis for the treatment of fracture bridging.

2. Mathematical Model of Solid–Liquid Two-Phase Flow

The settling of particles in plugging slurries is a typical multiphase flow phenomenon, which can be effectively modeled using various computational models available in Fluent. The selection of an appropriate computational model is of crucial importance to achieve high computational accuracy. The Eulerian model finds wide application in domains such as bubble column reactors, flow systems, suspended particles and fluidized beds. Due to its computational simplicity and lower computational requirements, the Eulerian multiphase flow model is chosen for numerical simulation in this paper.

2.1. Particle Settling Equation

During the initial settlement of a single particle in plugging slurry, it is accelerated downwards by gravity, and the viscous resistance it experiences continuously increases. The two forces quickly reach a balance, and the settling process enters a steady state known as the free settling velocity. The free settling velocity reflects the suspension stability of the plugging slurry, and the suspension performance of the plugging particles in the plugging slurry has a great impact on the depth of the bridging particles invading lost formations. The bridging particles must have suspension stability in order to be effectively transported to the leakage layer and create conditions for blocking leakage channels. If the suspension stability of bridging particles is poor, under the condition of pumping the plugging slurry, it is very easy for the plugging agent to detach from the plugging slurry, resulting in a significant difference in the content of the plugging slurry before and after. At the same time, accumulation and water loss rapidly form at the crack’s leakage point, forming a “sealing door” at the fracture, making it difficult to effectively seal the fracture [11]. According to the different Reynolds numbers and flow patterns in plugging slurries (i.e., laminar and turbulent), the calculation of the free settling velocity of particles is as follows [12].

$${\mathrm{N}}_{\mathrm{R}\mathrm{e}}=\frac{{\mathrm{d}}_{\mathrm{p}}{\mathrm{v}}_{\mathrm{p}}{\mathsf{\rho }}_1}{\mathsf{\mu }}$$

(1)

When ${\mathrm{N}}_{\mathrm{R}\mathrm{e}}$ ≤ 2, the free settling velocity of a single particle blocking particles is:

$$v_p=\frac{d_p^2({\rho }_p-{\rho }_1)g}{18\mu }$$

(2)

where $v_p$—free settling velocity of single particle blocking particles, m/s; $d_p$—diameter of blocking particles, m; g—gravity acceleration, m/s²; ${\rho }_p$—visual density of blocking particles, kg/m³; ${\rho }_1$—plugging slurry density, kg/m³; $\mu$—viscosity of plugging slurry, pa·s.

2.2. The Euler Multiphase Flow Model

The Euler model is the most complex multiphase flow model in Fluent and establishes a set of equations including n momentum equations and continuity equations to solve each term. The pressure term and interfacial exchange coefficients are coupled together, with the solid–liquid two-phase flow model using a pseudo-fluidization approach for solid-phase particles, treating them as a fluid for computation. This model is commonly used in various fields such as bubble columns, mud flow, particle suspension and settling simulation. In the Euler–Euler method, different phases are treated as interconnected continuous media, and since the volume occupied by one phase cannot be occupied by other phases, the concept of phase volume fraction is introduced. The volume fraction is a continuous function of time and space, and the sum of the volume fractions of all phases is equal to 1 [13].

The controlling equations included in the Euler–Euler model are as follows:

• Volume fraction equation:

  $$V_q={\int }_V{\alpha }_{q}dV$$

  (3)

  where $V_q$ represents the volume of the q phase, and ${\alpha }_q$ represents the phase volume fraction.

The volume fraction represents the spatial occupation of each phase, and each phase individually satisfies the laws of mass and momentum conservation. The derivation of the conservation equations allows for the attainment of a local transient equilibrium for each phase on average.

• Conservation of mass equation: the continuous equation of the q phase is:

  $$\frac{\alpha }{\partial t}({\partial }_q{\rho }_q)+\nabla ·({\partial }_q{\rho }_q\overrightarrow{v})=\sum _{p=1}^n{m}_{pq}$$

  (4)
• Momentum conservation equation: the momentum balance equation of the q phase is:

  $$\frac{\partial }{\partial t}({\partial }_q{\rho }_q{\overrightarrow{v}}_q)+\nabla ·({\partial }_q{\rho }_q{\overrightarrow{v}}_q{\overrightarrow{v}}_q)=-{\alpha }_q\nabla p+\nabla ·{\stackrel{̿}{\tau }}_q+\sum _{p=1}^n{\overrightarrow{(R}}_{pq}+{\dot{m}}_{pq}{\overrightarrow{v}}_{pq})+{\alpha }_q{\rho }_q({\overrightarrow{F}}_q+{\overrightarrow{F}}_{lift,q}+{\overrightarrow{F}}_{V_m·q})$$

  (5)
• In formulas: ${\rho }_q$—density of q phase, kg/m³; ${\overrightarrow{v}}_q$—velocity of q, m/s; $m_{pq}$—mass transfer from p to q; $\nabla$—full differentiation in all directions of space; $p$—pressure shared by all phases, Pa; ${\stackrel{̿}{\tau }}_q$—pressure–strain tensor of the q-th phase; ${\overrightarrow{v}}_{pq}$—velocity between phases, m/s; ${\overrightarrow{R}}_{pq}$—interaction forces between the phases, N;${\overrightarrow{F}}_q$—external volume force, N; ${\overrightarrow{F}}_{lift,q}$—lift force, N; ${\overrightarrow{F}}_{V_m·q}$—virtual quality force, N.

2.3. Physical Model

A circular wellbore, vertical, wedge-shaped, smooth and rigid fracture model can be used to simulate the settlement process of plugging slurry in wellbores and fractures. Figure 1 illustrates the partial bottom drilling of the LS25-1-1 well in the eastern part of the LingShui depression in the deepwater area of the southeast Qiandong Basin. The drill bit size is 212 mm, with a 10% increase in the wellbore size, resulting in a size of 234 mm. The drill string diameter is 149 mm. The length and width of the two cracks at the bottom of the wellbore are 300 mm and 3 mm, respectively. Figure 1a is a schematic diagram of the model before lifting the drill bit. The height of the wellbore is 1300 mm, and the drill bit is set as the inlet for velocity, with the area above the wellbore designated as the outlet for pressure, while the remaining areas represent the wellbore wall. Figure 1b shows the schematic diagram of the model after lifting the drill bit. Before 6 s, the drill bit serves as the velocity inlet, with Outlet 1 above the wellbore acting as the pressure outlet and the remaining areas representing the wellbore wall. After 6 s, Outlet 1 is set as the velocity inlet, the outlet is the pressure outlet, and the wellbore is filled with plugging slurry, excluding any plugging particles.

2.4. Simulated Working Conditions

The simulated experiment refers to Caco₃ parameters, with a density of 2600 kg/m³ and fluid parameters of the plugging slurry parameters used in the bottom drilling of well LS25-1-1 as follows: density—1480 kg/m³; viscosity—30 mPa·s. The simulation parameters are shown in

Table 1. Simulation parameter.

Parameter	Gradient
Plugging slurry viscosity/(mPa·s)	10	20			30		40			50
Particle density/(g·cm3)	1.4	2.0			2.6		3.2			3.8
Particle size/(mm)	0.5		1			1.5			2.0
Particle concentration	10%			15%				20%

.

The choice of particle size in this paper comes from the research mechanism and achievements of scholars at home and abroad, Abrams formed the 1/3 bridge building rule. Luo proposed temporary plugging technologies, namely the 2/3 bridging and 1/2~1/4 filling shielding methods. Kaeuffer put forward the “ideal filling the ory (theory)” of temporary plugging agent particles. According to previous research, the width of the simulated fracture outlet is selected to be about 3 mm. Based on the above sealing theory, the particle sizes were selected as 0.5, 1, 1.5 and 2 mm. The numerical values (boundary conditions) used in the simulation are those plugging slurry parameters used in the drilling process of well LS25-1-1. The viscosity of the plugging slurry in this well is around 30 mPa·s; therefore, in the simulation, the viscosity of the plugging slurry is set to five gradients of 10–50 mPa·s. According to previous research and on-site applications, the solids content in plugging slurry is usually 15%, and calcium carbonate particles, walnut shells, fiber materials, etc., are commonly used as plugging materials, with a density between 1.0–4.0 g·cm³. Therefore, the parameters shown in Figure 1 are selected for the simulation.

3. Numerical Simulation and Discussion

The suspension capacity of the sealing material determines the position of the sealing material at the leak point, that is, the opening, front and tail of the joint, and the suspension capacity and performance of the sealing material are closely related to the performance of the fluid [14]. The following discussion discusses the main factors that affect the viscosity of the plugging slurry, the density, size and concentration of sealing particles and the speed of pumping the plugging slurry.

3.1. Influence of Viscosity of Plugging Slurry

Viscosity is the resistance of a fluid to flow. It affects the suspension of particles by changing the interaction between fluid and particles, thus affecting the sealing performance of fractures. In traditional plugging mud, the solid particles employed are usually calcium carbonate particles. Initially, the density of the plugging slurry is 1.48 g/cm³, the particle density is 2.6 g/cm³, the particle concentration is 15% and the pumping speed of the plugging slurry is 0.7 m/s. The effects of solid particles before and after lifting and pressurization are explored when the viscosity of the plugging slurry is 10, 20, 30, 40 and 50 mPa·s.

Figure 2, Figure 3, Figure 4 and Figure 5 show the simulation results of the plugging slurry model before lifting the drill bit. The simulation cloud map of particle sedimentation in Figure 2 reflects that as the viscosity of the plugging slurry increases, the dispersion of the plugging particles becomes better. Particles are more likely to accumulate at the bottom of the wellbore and at the entrance of the fracture. Sealing particles at 10 mPa·s “seals the throat” of the fracture, while sealing particles at 20–50 mPa·s mostly distribute at the entrance of the fracture. Moreover, the dispersion of particles at 40–50 mPa·s is similar, with only a few particles reaching the bottom of the wellbore. Figure 3 shows the flow resistance along the Y-axis line, which reflects the ability of the sealing slurry to carry particles and the higher the viscosity, the stronger its ability to carry particles and the greater the flow pressure near the bottom due to the inlet being close to the bottom. The flow direction near the bottom of the wellbore changes, and the flow resistance also changes accordingly. The flow resistance direction near the drill bit changes again, due to the influence of gravity on the fluid, which generates partial reflux and a change in flow direction [15].

Figure 4 shows the relationship between the maximum accumulation volume fraction of particles and time. In order to investigate the effect of density on the suspension stability of plugging slurry, particles of equal diameter are used as spheres, and stacking them together produces large voids. Simulation software provides a maximum volume fraction of particles for stacking, equal to 0.63. The maximum stacking volume fraction achieved at 10–50 mPa·s is around 0.6, indicating that the particle stacking effect has greater strength, and the slower the viscosity of the plugging slurry, the less time it takes for complete stacking, particles can sink quickly, and the poorer its dispersibility.

According to the formula for the free settlement rate of a single particle blocking particles, it is observed that the viscosity of the plugging slurry has an inverse relationship with the free settlement rate of a single particle. The velocity of particles is predominantly influenced by fluid resistance, which is directly proportional to the viscosity of the fluid within the low Reynolds number range. During the sedimentation process, the force of gravity overcomes resistance, resulting in particle settling. Consequently, higher resistance hinders particle settlement. Analysis of the particle settlement volume depicted in Figure 5 reveals that lower viscosity leads to reduced carrying capacity of plugging slurry for particles, resulting in an increase in settlement volume. Figure 5 and Figure 6 demonstrate that viscosity can significantly affect the time required for plugging achievement. However, the settlement volume of particles with viscosities between 30~40 mPa·s depicted in Figure 6 appears similar. Nonetheless, when considering increased drilling rates and reducing circulating pressure consumption, it is preferable to minimize mud viscosity. A comprehensive analysis suggests that a plugging slurry viscosity of 30 exhibits high plugging strength and is suitable for adapting to most geological strata.

Figure 6 depicts the simulated cloud image of particle settlement at 6 s after lifting the drill bit. A comparison with the settlement problem prior to lifting the drill bit at the same time reveals that particles are more prone to settling at the bottom of the wellbore after lifting. Additionally, most of the plugging particles accumulate at the fracture inlet, effectively “sealing the door” of the fracture. Few plugging particles enter the fracture itself [16]. The results indicate that as slurry viscosity increases, the settling height of particles decreases, reducing the likelihood of particle settling. However, when the particle settling height reaches a range of 40–50 mPa·s, the difference in settling height becomes insignificant. Figure 7 shows the variation curve of settlement volume with time under different viscosities of plugging slurry after lifting. The settlement volume after lifting is significantly larger than that before lifting. The greater the viscosity, the longer the settlement time. At 6 s, plugging slurry without particles is injected at the wellbore outlet, and the particle settlement volume increases sharply. The plugging particles in the plugging slurry are suddenly compressed and then gather together when the plugging slurry is injected, and the settlement volume fraction increases sharply. With the injection of plugging slurry, the plugging slurry continuously carries plugging particles out of the fracture outlet, and the settlement volume fraction drops sharply. According to the different viscosities of plugging slurry, its ability to carry particles is also different. The settlement volume is almost zero at about 7.2 s at 20–50 mPa·s, and it cannot be completely taken away at 10 mPa·s. Therefore, the viscosity of the plugging slurry at 30 mPa·s is the most appropriate.

3.2. Effect of Plugging Particle Size

Particle size is an important factor affecting particle dispersion; generally the smaller the particle size, the better the dispersion effect. In order to study the effect of particle size on the suspension stability of the plugging slurry, four grades of plugging particles were selected in this simulation according to the particle size matching theory mentioned above, specifically 0.5, 1, 1.5 and 2 mm. In this paper, the sedimentation level observation method and sedimentation volume method are used to carry out experiments. The material concentration of each particle size in the experiment is 15%. The initial density of the slurry is 1.48 g/cm³, the particle density is 2.6 g/cm³ and the pumping speed is 0.7 m/s.

The settlement effect and settlement curve of plugging particles with variable particle size are shown in Figure 8 and Figure 9. Figure 8 is a cloud chart of the settlement effect of different particle sizes at 6 s. When the particle diameter is 0.5 mm, only a small number of particles are evenly dispersed in the wellbore. With an increase in particle size, the height of particles settling at the bottom of the wellbore is higher. When the particle size is 1 mm, the height of settling is equal to the height of the fracture. When the particle size is 1.5~2 mm, the height of particles settling is higher than the height of the fracture, and the distance of particles entering the fracture is continuously extended [17,18,19].

Figure 9 shows the precipitation volume of different particle sizes at 6 s. compared with other particle sizes, the precipitation volume of particles at 0.5 mm is almost negligible, and the particles are evenly dispersed in the wellbore. The precipitation volume is about 18,000 mL at 2 mm, 8000 mL at 1.5 mm and 4000 mL at 1 mm. With a significant increase in particle size, the corresponding precipitation volume increases from stage to stage. It can be observed in the pressure-holding interval that the smaller the particle size, the easier the particles flow into the fracture with the plugging slurry, but when the particle size is less than 1/3 of the fracture width (the particle size is 0.5 or 1 mm), the plugging particles flow out of the fracture with the plugging slurry, which is not enough to achieve the purpose of plugging the fracture. When the particle size is greater than or equal to half of the fracture width, under the continuous influx of plugging slurry, the particles accumulate within the fracture, leading to fracture plugging. However, when the particle size reaches 2 mm, a significant portion of the particles tend to accumulate at the entrance of the fracture, resulting in a limited support effect for fracture plugging. Hence, based on experimental findings, it can be concluded that particles with a size equivalent to half of the fracture width exhibit superior suspension and sealing capabilities [20,21].

3.3. Effect of Plugging Particle Density

The density of particles is an important factor affecting particle dispersion. Sealing particles are mainly affected by gravity and viscous forces when settling and rolling in the plugging slurry. The density of particles has a certain influence on their settling speed and critical flow rate. In order to make a thorough inquiry regarding the effect of density on the suspension stability of plugging slurry, spherical calcium carbonate particles of low, medium and high density (1.4, 2.0, 2.6, 3.2 and 3.8 g/cm³) are selected for this simulation. The method of observing the height of the settlement liquid and the settlement volume is used for the experiment. The material concentration of each particle size in the experiment is 15%. The density of plugging slurry is initially set at 1.4 g/cm³, the particle diameter is 1 mm and the pumping speed of plugging slurry is 0.7 m/s.

It can be clearly seen from the simulated cloud image of particle sedimentation in Figure 10 that particle density has an important impact on particle dispersion in the plugging slurry. When particle density is equal to 1.4 g/cm³, particle density is the same as that of the plugging slurry, particles are evenly distributed in the wellbore and cracks and there is no deposition at the bottom of the wellbore. When particle density is equal to 2.0 g/cm³, plugging particles settle and deposit at the bottom of the wellbore. At a particle density of 3.8 g/cm³, particle settlement reaches its maximum.

Figure 11 shows the effect of particle density on the settling velocity. Before 6 s, the settling velocity of particles is around 0.3 m/s. The higher the density, the faster the settling velocity. However, the effect of density on the settling velocity is not significant. This simulation calculation result is consistent with actual laboratory experiments [22]. However, after 6 s, the injected plugging slurry causes the particles with lower density to settle at a higher rate. Therefore, when pumping a slurry for plugging, particles are primarily affected by their own gravity and the buoyancy of the fluid. The higher the density, the faster the particles settle. When the pump fluid is replaced by plugging slurry (when holding pressure), the buoyancy is proportional to the magnitude of gravity. When the particle density is lower, the impact of the plugging slurry on the particles is relatively greater, and the particles are more likely to deposit. When selecting the density of the plugging slurry, it is not recommended to choose a high density. When the density is between 3.2 and 3.8 g/cm³, particles settle faster, which is not conducive to normal and safe drilling. Although the particle suspension is best when the density is 1.4 g/cm³, considering that the density is too low, it is not conducive to forming a sealing layer in fractures in the subsequent process. When the density is between 2.0 and 2.6 g/cm³, the suspension stability of particles is still good, with only a small amount of sediment at the bottom of the well, and a density of 2.0 to 2.6 g/cm³ can meet most practical operating conditions.

3.4. Effect of Plugging Particle Concentration

In order to investigate the effect of particle concentration on the suspension stability of plugging slurry, three levels of plugging particles, 10%, 15% and 15%, were selected for this simulation. The experiment was conducted by observing the height of the settling liquid surface and the settling volume. The initial density of the plugging slurry is 1.48 g/cm³, the viscosity is 30 mPa·s, the particle density is 2.6 g/cm³ and the pumping speed of the plugging slurry is 0.7 m/s.

A change in particle concentration mainly affects the change in interaction force between particles. With an increase in particle concentration, the probability of interaction between particles also increases, which makes the interaction force between particles larger. A decrease in particle concentration also weakens the interaction between particles and decreases the sedimentation rate of particles. As shown in Figure 12, when the particle concentration increases from 10% to 20%, the particle settlement height at the bottom of the wellbore does not increase significantly. As shown in Figure 13, the particle settlement volume increases with an increase in particle concentration. In 6 s, the particle concentration is 10% and the settling volume is 2500 mL, and the settling volume is 2600 mL when the particle concentration is 15%. When the concentration is 20% and the sedimentation volume is 2800 mL, the velocity of particle sedimentation volume increase is far less than that of particle concentration increase. In terms of sedimentation velocity, two key factors are the viscosity of the plugging slurry and the density of particles. The interaction between particles primarily affects the motion pattern of particles. In the presence of a highly viscous fluid, the trajectory of particle movement generally remains unchanged. Therefore, particle interaction has minimal impact on particle settling speed, and particle concentration has limited influence on particle settling volume.

4. Experimental Validation

4.1. Experimental Reagents and Instruments

4.1.1. Materials

The particles used in the experiment were calcium carbonate particles guard-3000, guard-4000 and guard-5000, walnut shell, plugging material PD-1 and plugging material MT135 as shown in Figure 14.

Reagents used in the experiment: tackifier Xc, bentonite.

4.1.2. Experimental Instruments and Equipment

The instruments and equipment used in this experiment mainly include a 500 mL measuring cylinder, beaker, high stirring cup, bucket, weighing paper, spoon, electronic balance, six-speed rotary viscometer, electric mixer and a variable-frequency high-speed mixer.

4.1.3. Experimental Steps

(1)

A total of 5000 mL of water +2% bentonite was stirred in an electric mixer for 2 h, and the hydration expansion was 24 h;

(2)

We then took 500 mL of solution +0.3% XC and put it into a high-speed mixing cup and mixed it in a variable-frequency high-speed mixer for 15 min (the mixing speed was set to 6000 R/min). We the put the base solution into a six-speed rotary viscometer to measure its viscosity;

(3)

We then took 500 mL of base solution +10% solid particles and put them into a high-speed mixing cup and mixed them in the variable-frequency high-speed mixer for 5 min (the mixing speed was set at 3000 R/min). We then poured it into the measuring cylinder to observe its settlement.

4.1.4. Evaluation Method of Material Suspension Stability

Solid particles undergo sedimentation due to gravitational forces, leading to a vertical stratification in their concentration within a liquid medium. This stratification is characterized by a reduced concentration of particles in the upper regions and an increased concentration in the lower regions of the liquid. Such a gradient in particle concentration drives the movement of particles from areas of higher concentration to those of lower concentration, thereby facilitating the use of gravity sedimentation as a method for assessing the stability of particle suspensions. The dispersion stability of particles within a dispersion medium is quantitatively evaluated by directly measuring the sedimentation volume of solid particles in the liquid. This sedimentation volume is intrinsically linked to the suspension stability of the particles. Generally, superior suspension characteristics are indicated by prolonged settling times and reduced sedimentation heights [23]. In this study, the sedimentation amount refers to the height of the particle layer at the base of the measuring cylinder when the particles attain a dynamic equilibrium, influenced by gravitational forces, liquid buoyancy and surface tension, among other factors. Consequently, the gravity sedimentation method was employed to evaluate the variations in particle sedimentation at the bottom of the cylinder under varying conditions of particle size and slurry viscosity, thereby determining the suspension stability of the solid particles.

4.2. Experimentation

4.2.1. Effect of Particle Size on Suspension Stability

Particle size is an important factor affecting particle dispersion. Generally, the smaller the particle size, the better the dispersion effect. In order to investigate the effect of particle size on suspension stability, three particle size levels of magnetic materials were selected for this experiment, namely guard-3000, guard-4000 and guard-5000. In experimental step 2, the viscosity of the base solution was measured to be 25 mPa·s, and the amount of material used for each particle size in the experiment was 10% (50 g).

The settlement effect and settlement curve of materials with different particle sizes are shown in Figure 14 and Figure 15, with guard-3000, guard-4000 and guard-5000 in sequence from left to right.

Observations from Figure 15 indicate that at 30 s, the guard-3000 particles are uniformly distributed within the base solution, exhibiting negligible sedimentation at the bottom. In contrast, guard-4000 shows a slight accumulation at the bottom of the measuring cylinder. The guard-5000 particles predominantly settle at the cylinder’s base. At the 5 min mark, guard-3000 begins to exhibit partial sedimentation, while guard-4000 remains partially suspended in the mid-region of the cylinder, and guard-5000 is observed to have fully settled. These data suggest that larger particle sizes correlate with increased sedimentation rates. In practical field applications, particle size selection is dynamic: initially, smaller-sized blocking particles are preferable as they can maximally support crack tips. In later stages of construction, larger particles are employed to prevent fracture closure, thereby maintaining high fracture conductivity [24]. The experimental findings corroborate with the outcomes of the simulation outlined in Section 2.2, affirming that smaller particle sizes result in enhanced dispersion effects.

4.2.2. Effect of Viscosity of Plugging Slurry on Suspension Stability

The viscosity of plugging slurry refers to the total internal friction force between liquid molecules, between liquid molecules and solid particles, and between solid particles and solid particles when the plugging slurry is flowing. By changing the fluid particle interaction and the gravity of particles themselves, the suspension of particles is affected, which affects the fracture sealing performance. In order to investigate the effect of viscosity on suspension stability, four viscosity levels of plugging slurries were selected in this experiment, namely clean water, 20 30 and 40 mPa·s. Guard-3000 was selected as the granular material, and the amount of granular material in the plugging slurry at each level of viscosity was 10% (50 g).

As shown in Figure 16, the particles are only affected by gravity, the internal friction force of clean water on the particles is too small to be ignored, the density of the particles is greater than the density of water and complete settlement is reached in about 30 s. With an increase in the viscosity of plugging slurry, the force of the solution on the particles increases. When the gravity of particles and the force of the liquid on the particles reach a balance, the particles no longer settle and are suspended in the plugging slurry. The plugging slurry with a viscosity of 20 mPa·s almost completely settles at 5 min, but the plugging slurry with a viscosity of 30–40 mPa·s still disperses well at this time, with only some settling occurring. The settling volume at 30 min in Figure 16 is smaller than that at 20 min, because when a large number of particles accumulate at the bottom of the measuring cylinder, this disrupts the uniformity of the system, leading to diffusion, where the thicker particles in the lower part move upwards. However, diffusion is evident in solutions with high viscosity, and diffusion is not observed in clean water and in 20 mPa·s plugging slurry. The experimental results are consistent with the simulation results. Among the 30~40 mPa·s plugging slurries with good dispersion, 30 mPa·s should be selected.

4.2.3. Impact of Blocking Particle Density

We investigated the influence of particle density on suspension stability and verified the simulation results of the influence of plugging particle density in Section 2.3. Four materials with different particle densities were used in this experiment: guard (2.6 g/cm³), iron walnut (2.0 g/cm³), plugging material MT135 (1.0 g/cm³) and plugging material PD-1 (0.8 g/cm³). The density of the initially designed plugging slurry is 1.4 g/cm³, and the viscosity is 30 mPa·s. The experimental results are shown in the figures.

The density of particles is an important factor affecting the dispersion of particles, and there are two main factors affecting the silence of plugging particles: gravity and fluid particle interaction. According to Formula (2) describing the free settlement velocity of a single particle blocking particles, it can be seen that the free settlement velocity of particles is directly proportional to the particle density. According to Yao [25] and Bai [26] and others, the smaller the particle density, the greater the buoyancy generated, and the harder it is for solid particles to settle. The simulation results of the influence of plugging particle density in Section 2.3 show that when the plugging slurry is pumped, the particle settling speed increases with an increase in particle density. The experiment depicted in Figure 17 shows that when the particle density is greater than the density of the plugging slurry, the particles more easily settle. When the particle density is twice the density of the plugging slurry, the particles settle rapidly, which is not conducive to subsequent engineering operations. When the particle density is 2.0 g/cm³, the particles begin to settle a small amount at 5 min, and only a small number of particles settle after 30 min, and most of them are still evenly distributed in the plugging slurry. When the particle density is less than or equal to the density of the plugging slurry, the particles are evenly distributed in the plugging slurry and almost no settlement occurs. The experimental results are similar to the simulation results. When selecting the plugging material, the density of the granular material should not exceed twice the density of the plugging slurry.

5. Conclusions

There are many factors that affect the settlement of plugging particles. This paper mainly studies four factors: the viscosity of plugging slurry, the particle size of plugging particles, the density of plugging particles and the concentration of plugging particles.

Viscosity mainly affects the suspension of particles by changing the fluid particle interaction, thus affecting the fracture sealing performance; the smaller the viscosity, the weaker the ability of the plugging slurry to carry particles and the greater the sinking volume. In a pressure-holding state, the higher the viscosity, the stronger the sand carrying capacity, and the easier the particles are taken away.

Through simulation and experimental verification, a set of relatively optimized plugging slurry systems were selected: the viscosity of the plugging slurry was 30 mPa·s, the density of the plugging slurry was 1.4 g/cm³, the particle diameter was 1.5 mm (the most appropriate particle size was half of the fracture width) and the particle density was 2.0~2.6 g/cm³.

Under the action of high-viscosity fluids, the trajectory of particles generally are not changed, so the interaction between particles has little effect on the particle settling velocity, and the particle concentration has little effect on the particle settling volume.

Through comparison, the numerical simulation’s conclusion is basically consistent with the experimental conclusion, and the numerical simulation model can be used to predict more complex working conditions.