**1. Introduction**

Natural gas hydrate (NGH) has the characteristics of high energy density and huge reserves. It is widely distributed in the world and is regarded as the alternative energy source with the most potential in the 21st century [1–3]. Deep-sea NGH test production has been carried out in many locations around the world, and many laboratories and scholars have conducted research on NGH production technology and professional production tools. At present, the main NGH exploitation methods include the chemical inhibitor injection method [4], decompression method [5], thermal stimulation method [6], and carbon dioxide (CO2) replacement method [7]. However, those above methods have different degrees of disadvantages for the exploitation of non-diagenetic NGH with the following characteristics: buried shallow, poor cementation, and low permeability. The chemical inhibitor injection method is an effective auxiliary method for NGH exploitation, which makes use of chemical inhibitors with different properties to accelerate the decomposition of gas hydrate and the formation of CO2 hydrate or reduce the speed of secondary formation of gas hydrate. However, the main disadvantage of the chemical inhibitor injection method is expensive chemical reagents, high production costs, and the use of large quantities of

**Citation:** Tang, Y.; Zhao, P.; Fang, X.; Wang, G.; Zhong, L.; Li, X. Numerical Simulation on Erosion Wear Law of Pressure-Controlled Injection Tool in Solid Fluidization Exploitation of the Deep-Water Natural Gas Hydrate. *Energies* **2022**, *15*, 5314. https://doi.org/10.3390/ en15155314

Academic Editor: Ingo Pecher

Received: 11 May 2022 Accepted: 14 June 2022 Published: 22 July 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

chemical reagents in gas hydrate reservoirs, which will cause a series of environmental problems. With reference to the decompression method, which harvests methane from hydrates by reducing hydrate reservoir pressure below the hydrate decomposition pressure to separate the hydrate [8], serious wellbore sand production and secondary formation of NGH in the pipeline will block the transportation channel and cause the interruption of the production process. Furthermore, the formation collapse of the goaf is easily caused by the disorderly decomposition of numerous NGHs. With regard to the thermal stimulation method, which extracts methane by heating hydrate reservoirs to decompose solid hydrates, the obvious disadvantage of this method is the inefficient utilization of thermal energy in subsea hydrate reservoirs [8]. Finally, in the CO2 replacement method, carbon dioxide is injected into the hydrate reservoir, and the methane molecules in the hydrate are replaced by carbon dioxide molecules and further released under specific conditions [6]. However, the production cycle is too long due to the extremely low extraction efficiency, thus the method is not suitable for the large-scale commercial exploitation of NGHs [9,10]. Based on the above reasons, an innovative mining method, that is, natural gas hydrate solid-state fluidization exploitation was proposed by Zhou [11]. Figure 1 illustrates the schematic diagram of this method [11–14]. During this process, the uncontrollable decomposition of NGH in the traditional mining method is transformed into controlled water jet fragmentation and decomposition. The application of bottom-hole sediment coarse separation technology and sediment backfill technology in solid-state fluidized exploitation solves the problems of pipeline blockage and geological collapse inherent in traditional mining technology.

**Figure 1.** Solid fluidization exploitation method.

Based on the requirements of crushing and cavity making of the hydrate layer in NGH solid-state fluidized exploitation, Tang Yang et al. [15,16] innovatively designed a pressurecontrolled injection tool (PCIT) that combines the principle of throttling pressure control and the inclined surface guide mechanism. The PCIT integrates the drilling process of horizontal wells and the jet breaking and cavity making process in the solid-state fluidized exploitation and realizes controllable and rapid switching between the two processes by changing the drilling fluid flow rate inside the tool. In the process of horizontal well drilling and cavity making, high-pressure injection of drilling fluid containing solid particles can effectively fragment and drill hydrate formations with soft geology and large porosity. Under the erosion wear of high-pressure drilling fluid with solid particles over time, the opening and closing process of PCIT will be affected, which will further cause the entire production process to be interrupted. Therefore, in order to ensure the long-term stable use of the PCIT, it is necessary to conduct erosion wear analysis.

With the development of computational fluid dynamics simulation software, computational fluid dynamics (CFD) has become a key tool for predicting erosion in complex flows and is a cost-effective way to mitigate erosion wear when designing drilling tools. Many scholars have done some research on fluid erosion behavior. Yi et al. [17] carried out research on the erosion of fracturing elbows in hydraulic fracturing operations and obtained the influence of fracturing fluid parameters such as flow rate, particle size, and density on the erosion rate of fracturing elbows. Huang et al. [18] established the relationship between the erosion of drill pipe and the gas injection rate and mechanical speed in the process of gas drilling through theoretical derivation and laboratory experiments. It was found that erosion will be reduced under the conditions of small gas injection rate and large mechanical speed. Huang et al. [19] carried out numerical simulation on the erosion of the faucet elbow in reverse circulation drilling, predicted the location of the puncture point of the faucet elbow, and obtained the main factors affecting the collision zone. Wang et al. [20] used the discrete phase model (DPM) and the semi-empirical material removal model to predict the mass loss and erosion distribution of drilling choke valves and greatly reduced the erosion wear of choke valves through optimized design. Jafari et al. [21] analyzed and compared the erosion properties of four wear-resistant steel plates and obtained the relationship between material hardness, erosion resistance, and wear resistance by conducting laboratory experiments. Habib et al. [22] analyzed the liquid–solid two-phase erosion problem in the reducer pipe through numerical simulation and found that the inlet liquid-phase velocity, particle size, and surface hardness of the material are the main factors affecting the erosion law of the reducer. These experiments and studies have made a great contribution to the design and application of the oil and gas exploitation tools. Meanwhile, the PCIT is the key equipment in solid fluidization exploitation. However, to the best of our knowledge, no specific study has addressed the erosion wear analysis of this kind of PCIT, which seriously limits the design and application of such tools. In order to meet the requirements of long-term and stable jet breaking and horizontal well drilling in solid fluidization exploitation, it is necessary to study the erosion wear law of this kind of tool. It is hoped that the commercial application of the natural gas hydrate solid-state fluidization process could be promoted with our proposed PCIT.

### **2. Working Mechanism of PCIT**

The design idea of PCIT is to combine the principle of throttling pressure control and the inclined surface guide mechanism. The throttling pressure control principle is that energy loss occurs when the fluid passes through the variable diameter section, and then a pressure drop occurs at the variable section. This pressure drop in turn generates an axial force at the variable cross-section to control the axial movement of the sliding core [15]. The PCIT is mainly composed of an outer hull, a sliding core, a spring, a thrust bearing, an inclined surface guide mechanism, an axial extrusion seal, and 24 jet nozzles, as shown in Figure 2. Its work process can be divided into the following four stages.

**Figure 2.** Structure diagram of PCIT: (**a**) PJCT in closed state, (**b**) PJCT in opend state.

### *2.1. Stage 1: Horizontal Drilling Process*

The PCIT is the part of the downhole tool string in NGH solid fluidization exploitation. In the horizontal drilling process, the jet nozzle must be closed. Under low drilling fluid flow, a smaller pressure drop and small axial force is created in the slide core of the SPIT, so that the slide core does not move. Therefore, the drilling fluid provides power for lower turbine power drilling tools through the sliding core and the axial flow passage.

### *2.2. Stage 2: NGH Crushing and Cavity Making*

When the horizontal well pilot hole drilling is completed, drilling fluid flow is increased by pumping from the offshore drilling platform, so greater pressure drop and axial forces occur inside the sliding core. The sliding core moves axially to compress the spring, and the inclined plane guide mechanism begins to move with the sliding core. When the sliding core moves to the predetermined position, the jet nozzle on the tool is fully opened, and the drilling fluid is ejected from the jet nozzle at a high speed for the NGH crushing and cavity-making operations. In the meantime, the axial channel is completely blocked under the action of the axial extrusion seal, and the inclined plane guide mechanism also enters the locked state, which ensures the stable process of NGH crushing and cavity making. The PCIT was slowly dragged back with the downhole tool string for NGH crushing and cavity making.

### *2.3. Stage 3: Multi-Angle Directional Mining*

When the exploitation of the target reservoir in this horizontal direction is completed, the downhole tool string does not need to be taken out of the well bore. The drilling fluid flow should be reduced to 0 L/min, and then the drilling fluid flow is gradually increased to release the locked state of the inclined plane guide mechanism. The jet nozzle on the PCIT is closed, and the axial channel is reopened. After that, the whole downhole tool will change in another direction at the bottom of the wellbore and repeat Stage 1 and Stage 2 to achieve multi-angle large-scale mining.

### *2.4. Stage 4: Multi-Level Mining*

When the solid-state fluidized exploitation of the target-depth hydrate reservoir has been completed, the whole downhole tool will change to another depth, and repeat Stage 1, Stage 2, and Stage 3 to realize multi-level large-scale mining.

### **3. Governing Equations**

Numerical simulation is a cost-effective way to mitigate erosion when designing downhole tools, and computational fluid dynamics (CFD) is a highly specialized simulation tool for predicting tool erosion wear under complex flow conditions. In this study, the Eulerian–Lagrangian method was used to describe the flow behavior of solid–liquid twophase in which liquid is regarded as the continuous phase governed by the Reynoldsaveraged Navier–Stokes (RANS) equation, and solid particles were considered as the dispersed phase governed by the second law of Newton. Finally, the finite volume method (FVM) was used to solve the governing equations.

### *3.1. Liquid-Phase Governing Equations*

Considering the solid–liquid-phase interaction, the continuous phase flow equation and the momentum equation are [23,24]

$$\frac{\partial \rho}{\partial t} + \frac{\partial \rho \overline{u\_i}}{\partial x\_i} = 0 \tag{1}$$

$$
\rho \frac{\partial \overline{u\_i}}{\partial t} + \rho \frac{\partial \overline{u\_i u\_j}}{\partial x\_j} = -\frac{\partial}{\partial x\_i} + \mu \nabla^2 \overline{u\_i} - \rho \frac{\partial \overline{u\_i' u\_j'}}{\partial x\_j} + \rho g\_i \tag{2}
$$

where *ui* is the (*u*, *v*, *w*) scalar components of the mean-velocity vector, *xi* is the (*x*, *y*, *z*) scalar components of the spatial-coordinates vector, *t* is the time coordinate, *p* is the mean pressure, *u <sup>i</sup>* is the fluctuation velocity component, *τij* is the scalar components of the Reynolds-stress tensor, and *v* is the fluid kinematic viscosity.

During the numerical simulation in this study, the liquid phase is in a turbulent state. In order to accurately simulate the liquid flow state, it is very important to choose an appropriate turbulence calculation model when performing turbulence calculation. The *k* − *ε* turbulence model is suitable for a high Reynolds number, incompressible turbulent flow, which is widely used in engineering applications. Therefore, the *k* − *ε* turbulence model was applied to describe the turbulent properties; the transport equations of *k* and *ε* are, respectively [25,26],

$$\frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho k u\_i)}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_i} \left[ \left( \mu + \frac{\mu\_l}{\sigma\_k} \right) \frac{\partial k}{\partial \mathbf{x}\_j} \right] + \mathbf{G}\_b + \mathbf{G}\_k - \rho \varepsilon \tag{3}$$

$$\begin{array}{ll} \frac{\partial(\rho\varepsilon)}{\partial t} + \frac{\partial(\rho x u\_i)}{\partial x\_i} = & \frac{\partial}{\partial x\_j} \left[ \left( \mu + \frac{\mu\_t}{\sigma\_t} \right) \frac{\partial \varepsilon}{\partial x\_j} \right] + \rho \mathbf{C}\_1 \mathbf{S} \varepsilon \\ & + \frac{(1 - \mathbf{C}\_{3\ell}) \mathbf{C}\_{1\ell} \varepsilon}{k} \mathbf{G}\_b - \mathbf{C}\_{2\ell} \rho \frac{\varepsilon^2}{k + \sqrt{\nu t}} \end{array} \tag{4}$$

where

$$\begin{aligned} \mathcal{C}\_1 &= \max\left(0.43, \frac{\eta}{\eta + 5}\right), \; \eta = S\_\varepsilon^{\frac{k}{\varepsilon}}\\ \mathcal{G}\_k &= -\rho \overline{u\_i' u\_j'} \frac{\partial u\_j}{\partial x\_i}, \; \mathcal{G}\_b = -\mathcal{g}\_i \frac{u\_t}{\mathcal{P} r\_t} \frac{\partial \rho}{\rho \partial x\_i}, u\_t = \rho \mathcal{C}\_\mu \frac{k^2}{\varepsilon} \end{aligned} \tag{5}$$

where *ε* is the turbulent dissipation rate, m2/s3; *k* is the turbulent kinetic energy, *J*; *μ* is the dynamic viscosity, Pa · s; *μ<sup>i</sup>* is the turbulent viscosity, Pa · s; *S* is the strain rate, *Gk* is the production term of the turbulent kinetic energy, *Gb* is the production term of the turbulent kinetic energy due to lift, *Prt* is the Prandtl number taken as 0.85, *C*3*ε*, *C*1*ε*, *C*2, *C<sup>μ</sup>* are constants taken as 0.9, 1.44, 1.9, and 0.09, respectively, and finally, *σ<sup>k</sup>* and *σε* are turbulent Prandtl numbers taken as 1.0 and 1.3, respectively.

The turbulent intensity of the discrete phase is described by the equation of motion of the solid-phase particles. Through this equation, parameters such as the motion trajectory and velocity of the solid-phase particles can be obtained. This particle motion equation is called the DPM model [27]:

$$\frac{du\_p}{dt} = \frac{\mathbb{C}\_D \mathbb{R}\_\varepsilon}{24t} (u - u\_p) + \frac{\mathbb{g}\_x (\rho\_p - \rho)}{\rho\_p} + F\_{\Delta p} + F\_F + F\_v + F\_L \tag{6}$$

$$\begin{array}{c} \mathsf{R}\_{\mathfrak{c}} = \frac{\rho D\_{p} \left| u\_{p} - u \right|}{\mu} \\ \mathsf{C}\_{D} = \frac{24}{\mathsf{R}\_{\mathfrak{c}}} \left( 1 + b\_{1} \mathsf{R}\_{\mathfrak{c}}^{\mathfrak{b}\_{2}} \right) + \frac{b\_{3} \mathsf{R}\_{\mathfrak{c}}}{b\_{4} + \mathsf{R}\_{\mathfrak{c}}} \end{array} \tag{7}$$

where *up* is the velocity of the solid particle, *Cd* is the drag coefficient, *ρ<sup>p</sup>* is the density of the solid particle, *ρ* is the liquid density, *CD* is the drag coefficient, *u* is the liquid-phase velocity, *F*Δ*<sup>P</sup>* is the additional force due to the pressure gradient in the fluid, *FF* is the lifting force generated by the fluid, *FV* is the virtual mass force required to accelerate the fluid surrounding the particle, *FL* is the buoyancy force that includes gravitational and relative density effects, *b*1, *b*2, *b*<sup>3</sup> , *b*<sup>4</sup> are constants related to the solid-phase particles taken as 0.186, 0.653, 0.437, and 7178.741, respectively.

### *3.2. Erosion Model*

The main material of the PCIT is 42CrMo steel. Therefore, the erosion prediction model suitable for the impact of quartz sand on the surface of carbon steel was selected [28].

$$R\_{crossing} = \sum\_{p=1}^{N\_{particle}} \frac{m\_p \mathbb{C}\left(d\_p\right) f(a) \nu^{b(\nu)}}{A\_{face}} \tag{8}$$

where *Rerosion* is the erosion rate, *Nparticle* is the particle impact number, *mp* is the solidphase particle quality, *C dp* is the solid-phase particle diameter function, *ν* is the velocity of solid particles relative to the wall, *b*(*ν*) is the solid-phase particle relative velocity function, *α* is the impact angle of the solid-phase particle path and the wall, *f*(*α*) is the impact angle function, when the impact angle is 0◦, 20◦, 30◦, 45◦, and 90◦, *f*(*α*) is taken as 0, 0.8, 1, 0.5, and 0.4, respectively, *Af ace* is the area of the material surface impacted by particles.

When the solid-phase particles hit the surface of the material at a certain speed, the solid-phase particles will lose part of their energy due to the impact collision, so the solidphase particles will bounce back at a lower speed than the impact speed. The rebound coefficient is used to determine the rebound speed and rebound angle. Determining solidphase particle trajectories requires particle bounce properties and coefficients of restitution, the tangential and normal restitution coefficients of solid particles are [29,30]

$$
\omega\_T = 0.988 - 0.029\alpha\_1 + 6.43 \times 10^{-4} \alpha\_2 - 3.56 \times 10^{-6} \alpha\_3 \tag{9}
$$

$$
\omega\_N = 0.993 - 0.0307\alpha\_1 + 4.75 \times 10^{-4} \alpha\_2 - 2.61 \times 10^{-6} \alpha\_3 \tag{10}
$$

where *eT* is the tangential coefficient of restitution, *eN* is the normal recovery factor.

### *3.3. Erosion Wear Flow Field Geometric Model and Meshing*

According to the structure of the PCIT, the internal flow field calculation area of the PCIT was established, and the unnecessary structures in the flow field calculation domain were simplified. The simplified flow field geometric diagram is shown in Figure 3a, and the result of meshing the flow field is shown in Figure 3b.

**Figure 3.** Flow field meshing: (**a**) the simplified flow field geometric diagram, (**b**) the result of meshing the flow field.

In Figure 3a, area A is the cone of the sliding core, area B is the transition section of the plug, area C is the surface of the plug and the axial flow passage. The above three area meshes are refined.

### *3.4. Simulation Parameters and Boundary Conditions*



**Table 1.** Impact angle function parameters.

### **4. Analysis of Numerical Simulation Results**

*4.1. Prediction of Erosion Location*

The specific erosion location of the PCIT must be determined to pave the way for the study of the factors that affect the erosion law. For this, the diameter of solid particles in the drilling fluid was set to d = 0.2 mm, the density was 1500 kg/m3, the liquid inlet velocity was 10 m/s, and the viscosity was 20 mpa · s for simulation analysis.

Figure 4 shows the distribution of the PCIT's easily eroded areas. There are four main erosion areas in the PCIT as shown in Figure 4: the sliding core cone surface, the transition section of the plug, the surface of the plug, and the axial flow passage. The sliding core cone surface is located in the PCIT inlet section; if the drilling fluid flow rate increases, the cone surface will be seriously eroded by the vertical impact of solid-phase particles in the drilling fluid. The plug is located at the fluid outlet of the PCIT. The surface of the plug is directly impacted by the drilling fluid, and the average erosion rate and the maximum erosion rate are both the largest. After the fluid particles impact the plane of the plug, the particles will move to the sides of the plug. At the same time, due to the sudden shrinkage of the fluid channel and the increase of the drilling fluid flow rate, the erosion of the inner wall of the axial flow channel is also obvious.

**Figure 4.** Erosion location distribution of PCIT.

*4.2. Influence of Drilling Fluid Physical Parameters on Erosion Rate*

4.2.1. Influence of Drilling Fluid Flow on Erosion Rate

The drilling fluid flow rate was set to 200, 300, 400, 500, 600, 700, and 800 L/min, respectively, and the particle diameter, plug position, and mass flow were kept in the same conditions. The maximum erosion rate and the erosion area of the PCIT under different flow rates were obtained as shown in Figures 5 and 6, respectively.

**Figure 5.** The maximum erosion rate changes with drilling fluid flow.

**Figure 6.** Erosion area changes with drilling fluid flow.

As shown in Figure 5, with the increase of the inlet drilling fluid flow, the maximum erosion rate of the plug surface, the plug transition section, and the axial flow passage all increase. In particular, the maximum erosion rate on the plug surface increases exponentially. This occurs because, as the velocity of drilling fluid flow in PCIT increases with the increase of flow rate, the impact kinetic energy of the solid particles gradually increases, and the frequency and the solid particles' impact the surface of the PCIT per unit time increases. Therefore, the erosion rate of the three erosion-prone areas increases. When the drilling fluid flow increases from 200 to 800 L/min, the average maximum erosion rate of the three erosion-prone areas increased by 65.4 times. As shown in Figure 6, the erosion area of the three erosion-prone areas did not change significantly, which indicates that the inlet flow should be controlled as much as possible during the use of the PCIT.

### 4.2.2. Influence of Solid-Phase Particle Mass Flow on Erosion Rate

The mass flow is the mass of fluid flowing through PCIT per unit time. Under a constant drilling fluid flow velocity and solid particles, the influence of different mass concentrations on the erosion law was analyzed. The mass flow was set as 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, and 0.007 kg/s, respectively. The variation law of the maximum erosion rate and the erosion area in the erosion-prone areas in the PCIT are shown in Figures 7 and 8.

**Figure 7.** The maximum erosion rate changes with mass flow.

**Figure 8.** Erosion area changes with mass flow.

As shown in Figure 7, the maximum erosion wear rates of the three erosion-prone regions increase linearly with the increase of the fluid mass flow. The largest erosion rate at the plug surface increased by 6.05 times when the fluid mass flow increased from 0.001 to 0.007 kg/s. Due to the increase in the mass flow rate of the drilling fluid, the number of solid particles entering the PCIT per unit time increased, and the impact frequency of the PCIT by the solid-phase particles increased per unit time. The plug face was directly impacted by the solid-phase particles in the drilling fluid, and the impact angle was around 90◦. Therefore, the maximum erosion rate on the plug face was always the maximum value of the three erosion-prone areas. Meanwhile, it is greatly affected by the change of mass flow. Then the solid-phase particles hitting the plug face bounce back to the plug transition section while losing kinetic energy. Thus, the erosion and wear in the plug transition section is smaller than that in the plug face. The axial flow passage has the same flow direction as the drilling fluid, and only a small amount of solid-phase particles will hit the axial flow passage. Therefore, the erosion and wear in the axial flow passage is the smallest, and it is the least affected by the increase of mass flow. As shown in Figure 8, the erosion area of the three erosion-prone areas of PCIT did not change significantly with the increase in mass flow. Therefore, it should be considered that the mass concentration of solid-phase particles in the drilling fluid can be reduced when the drilling fluid is configured, which can effectively reduce the erosion in the PCIT.

### 4.2.3. Influence of Solid-Phase Particle Diameter on Erosion Rate

According to the actual working conditions, the diameters of the solid-phase particles were set as 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.1 mm, respectively. The inlet velocity and the mass flow of the drilling fluid were kept constant. The relationship between the different diameter of solid particles and the maximum erosion rate is shown in Figures 9 and 10.

**Figure 9.** The maximum erosion rate changes with solid particle diameter.

**Figure 10.** Erosion area changes with solid particle diameter.

As shown in Figure 9, the maximum erosion rates of the erosion-prone regions in the PCIT all increased with the increase in particle diameter. When the particle size diameter of the solid phase increased from 0.1 to 1.1 mm, the average maximum erosion rate of the three erosion-prone regions increased by 63.4 times, but the growth rate of the maximum erosion rate was different in different particle diameter ranges: When the solid-phase particle diameter was between 0 and 0.3 mm, the growth of the erosion rate of the three erosion-prone regions was relatively low. When the solid-phase particle diameter was between 0.3 and 0.7 mm, the erosion rate of the three easily eroded areas increased rapidly, especially the erosion rate on the surface of the plug increased rapidly. When diameter was greater than 0.7 mm, the maximum erosion rate of the axial flow passage decreased with the increasing particle diameter, while the maximum erosion rates of the plug transition and plug surface continued to increase linearly. At the same time, according to the erosion area diagram in Figure 10, the erosion area of the plug surface and the plug transition section gradually increased with the increase of particle diameter. The analysis results show that the diameter of the solid-phase particles in the drilling fluid should preferably be less than 0.3 mm in the actual production process and that a solid-phase particle diameter exceeding 0.7 mm accelerates the erosion damage to the PCIT.

### *4.3. Influence of PCIT Structural Parameters on Erosion*

### 4.3.1. Influence of the Sliding Core Inlet Angle on Erosion Rate

The inlet angle of the sliding core is closely related to the pressure drop inside the sliding core under the same flow rate, but the variation of the erosion law at the sliding core cone caused by the change of the inlet angle cannot be ignored. The inlet velocity and mass flow rate were kept consistent to carry out numerical simulations. The relationship between the different sliding core inlet angle and the maximum erosion rate is shown in Figures 11 and 12.

**Figure 11.** Maximum erosion rate and pressure drop of the sliding core cone change with *θ* value.

**Figure 12.** Erosion area changes with *θ* value.

As shown in Figure 12, the most serious erosion is at the sliding core cone, and the erosion area increases with the inlet angle. As shown in Figure 11, with the increase of the inlet angle, the pressure drop value inside the sliding core and the maximum erosion rate of the sliding core cone gradually increases. When the inlet angle was 10◦, the maximum erosion rate of the sliding core cone was 1.45 × <sup>10</sup>−<sup>5</sup> kg/(m2·s). The maximum erosion rate can reach 2.05 × <sup>10</sup>−<sup>4</sup> kg/(m2·s), when the inlet angle is 120◦, increasing the erosion rate by 17 times. There is a certain reduction in the maximum erosion rate when the inlet angle is greater than 120◦, but the erosion severity does not improve. Therefore, the relationship between the erosion rate, the internal pressure drop, and the inlet angle of the sliding core should be taken into account. Therefore, the axial force is as large as possible under the same conditions and the erosion rate at the sliding core cone is controlled. Preferably, the inlet angle of the sliding core should be set as 30◦, and the erosion rate at the variable section should be kept between 5.98 × <sup>10</sup>−<sup>6</sup> and 1.2 × <sup>10</sup>−<sup>5</sup> kg/(m2·s), and the maximum erosion rate of the entire inlet section will be 1.99 × <sup>10</sup>−<sup>5</sup> kg/(m2·s).

### 4.3.2. Influence of Plug Angle on Erosion Rate

The variation law of the erosion rate of the erosion-prone area in the PCIT was further analyzed focusing on changes in the top angle of the plug. The simulation analysis results are shown in Figures 13 and 14.

**Figure 13.** Maximum erosion rate changes with plug angle.

**Figure 14.** Erosion area changes with plug angle.

As shown in Figure 13, different top angles of the plug had obvious effects on the erosion law of the plug surface, the transition section of the plug, and the axial flow passage. The erosion rate of the plug transition section gradually increased with the gradual increase of the plug top angle, the maximum erosion rate of the plug surface gradually decreased and the maximum erosion rate of the axial flow passage was almost unchanged. When the top angle of the plug is small, the plug has a stronger diversion effect on the drilling fluid. Under the diversion effect of the plug, most of the solid-phase particles in the drilling fluid will flow directly to the axial flow passage. Therefore, it will not cause serious erosion on the plug transition section. When the top angle of the plug is large, the diversion effect on the drilling fluid is weakened, and a considerable amount of solid particles will bounce back to the plug transitional section after hitting the plug surface, thereby causing the plug erosion of excessive segments. As shown in Figure 12, when the top angle of the plug was less than 60◦, almost no erosion occurred in the plug transition section. However, when the top angle of the plug was greater than 60◦, the erosion area of the transition section of the plug gradually increased. Considering that it is easy to strengthen the erosion area of the plug during processing and combining the analysis results of Figures 13 and 14, the plug top angle was set to 60◦. The erosion rate of the plug surface was then relatively low, and the erosion of the plug transition section was significantly improved.

### 4.3.3. Influence of Plug Transition Distance on Erosion Rate

The erosion of the PCIT with the transition distance was analyzed. Figures 15 and 16 show the results of the maximum erosion rate and erosion area variation of the three erosion-prone areas in PCIT.

**Figure 15.** Maximum erosion rate changes with plug transition distance.

**Figure 16.** Erosion area changes with plug transition distance.

As shown in Figure 15, when the distance of the plug transition section was reduced from 55 to 5 mm, the maximum erosion rate of the erosion-prone areas increased by 3.8 times. The maximum erosion rate at the axial flow passage decreased slightly with the increase of the plug transition section distance. The erosion changes on the plug surface and the plug transitional section can be divided into three stages. Stage 1: when the distance of the plug transition section is between 5 and 15 mm, the maximum erosion rate on the plug surface drops sharply. Stage 2: when the distance is between 15 and 30 mm, the maximum erosion rate of the plug transition section continues to decrease. Stage 3: the erosion rate of the three easily eroded areas tends to be stable when the distance of the plug transition section is between 30 and 50 mm, the erosion rate is less affected by the distance of the plug transition section. As the distance of the plug transition section increased, the erosion area of the plug transition section decreased significantly as shown in Figure 16, while the erosion area of the plug surface and the axial flow passage did not change significantly. Therefore, when the PCIT is designed, the distance of the plug transition section should be greater than 30 mm.

### **5. Conclusions**

In order to meet the demand for hydrate reservoir crushing and cavity making in solid fluidized production of natural gas hydrate, the novel pressure-controlled injection tool in this paper was designed. Variations in the law of erosion under different drilling fluid physical parameters and PCIT structure parameters were analyzed by computational fluid software. According to the simulation results and actual working conditions, the optimal design parameters of the PCIT were optimized. From the numerical simulation, the following conclusions were obtained:


0.3 mm, the erosion of each part of the PCIT was better. The particle size of solid particles should be strictly controlled when configuring the drilling fluid, which can significantly reduce erosion.

(3) With the increase of the sliding core inlet angle, the erosion of the sliding core cone is intensified. Therefore, considering the relationship between pressure drop, erosion rate, and inlet angle, the sliding core inlet angle should preferably be set to 30◦. Under the same flow conditions, an inlet angle of 30◦ can cause the largest possible pressure drop while greatly improving the erosion of the sliding core cone. At the same time, the top angle of the plug should be set to 60◦, and the distance of the plug transition section should be greater than 30 mm, so that the erosion rate of the plug surface and the plug transition section can be effectively reduced.

**Author Contributions:** Y.T. and P.Z. designed the simulation model and carried out the simulation of the proposed model; G.W. analyzed the data; Y.T., P.Z. and L.Z. wrote the initial draft of the manuscript; and X.L. and X.F. reviewed and contributed to the final manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is supported by National Key Research and Development Program (grant numbers 2021YFC2800903); the Fund of Southern Marine Science and Engineering Guangdong Laboratory (Zhanjiang) (grant numbers ZJW-2019-03); the National Natural Science Foundation of China (grant numbers 52004235); International Science and Technology Cooperation Project Funding (grant numbers 2020-GH02-00041-HZ); China Postdoctoral Science Foundation (grant numbers 2020M683359); National Science and Technology Major Project (grant numbers 2016ZX05028-001- 006); China Postdoctoral Innovative Talents Support Program (grant numbers BX20190292); Sichuan Province Applied Basic Research Project (grant numbers 2020YJ0152); and the Miaozi Engineering Project of Sichuan Science and Technology Department (No. 2021124).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data and models generated or used during the study appear in the submitted article.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

