Study on the Discharge Process and Mechanism of Anti-Corrosion Pill Particles in the Oil and Gas Field Wellbore Casing Annulus Based on the Discrete Element Method

Abstract

This research studies the discharge process and its mechanism using the discrete element method (DEM) with self-developed annular corrosion pill particles and the discharge device as an example in order to optimize the oil and gas field wellbore casing annular corrosion process. The object of study was chosen from four different grid numbers and four different grid widths, and EDEM software was utilized to simulate and assess the pill particle discharge process based on preliminary experimental research. Under five different pill wheel rotation speeds, the effects of the grid number and grid width on the filling amount, filling density, discharge variation coefficient, and compressive force of pill particles were investigated from macroscopic and microscopic viewpoints. The findings reveal that the grid number, grid width, and rotation speed all have a significant impact on pill filling and discharge performance. As a result, the discharge wheel’s structure and operating characteristics were optimized. The discharge wheel performs best when the grid number is 8, the grid width is 75 mm, and the rotation speed is 15 rpm; the pill filling density is 692.26 kg/m³, the discharge variation coefficient is 0.022, and the maximum compressive force is 188 N. This study establishes the groundwork for enhancing wellbore integrity management in oil and gas fields by providing a reference for the optimal design of wellbore casing annular corrosion prevention devices in oil and gas fields.

1. Introduction

The conventional oil and gas field wellbore casing annulus corrosion prevention fluid filling procedure, while necessary for wellbore integrity maintenance, has major drawbacks, including a time-consuming construction process and a high cost [1,2,3]. As a result, our business produced a solid corrosion-inhibiting and anti-corrosion pill on its own, with the goal of developing a novel procedure for protecting the casing in offshore oil and gas wells against corrosion [4]. However, due to a number of constraints, such as the pill’s fragility and small casing, the creation of a high-performance discharge mechanism that allows pill particles to enter the casing annulus in a uniform and stable manner has become a critical technical bottleneck that must be addressed.

The influence law of the fundamental design parameters of the pill wheel on the discharge process becomes a precondition and is crucial to improving the discharge device’s functioning quality [5,6]. The grid number, grid width, and rotation speed of the discharge wheel are the main factors that govern the kinematics and dynamics of the pill particles throughout the discharge process [7,8,9,10]. As a result, in order to increase the pill discharge device’s operation quality, the ideal combination of the pill discharge wheel’s design parameter values must be improved.

The main issue in the optimal design of the parameters of the pill discharge wheel is obtaining precise observation and analysis of the kinematic and kinetic states of the pill particle population during the discharge operation [11]. Empirical and experimental procedures are currently the most often utilized research methods [12,13,14,15]. However, the approaches described above rely on a significant number of experiments, which are both time- and money-consuming and not general. In recent years, researchers have begun to investigate the use of DEM in the industrial and agricultural production domains for high precision numerical simulation of particle population dynamics states [16,17,18]. Most numerical simulations based on DEM to achieve accurate emission processes of particulate materials are now focused on agricultural products such as seeds and fertilizers [19,20,21,22,23]. However, the shape, size, and composition of the anti-corrosion pill particles analyzed in this work differ greatly from agricultural materials. As a result, the dynamics of the pill particle population and the high-precision simulation of the pill discharge device’s working process must be thoroughly investigated.

In summary, the Hertz–Mindlin contact mechanics model was used to simulate the contact mechanics behavior between the pill particles and the discharge device in this research using EDEM simulation software. The flow process of the pill particle population was simulated using the well-established DEM numerical model of pill particles. The impacts of the structural and operating parameters of the discharge wheel on the performance of the pill filling amount, filling density, discharge variation coefficient, and compressive force of the pill particles were disclosed. Finally, the discharge wheel’s structure and operating characteristics were optimized.

2. Models and Methods

2.1. Model of Pill Discharge Device

This paper independently designed a wheel-type pill discharge device, which included the main working parts, such as the material box, pill wheel, motor, frame, and frame and fluid conveyer, as shown in Figure 1a, in order to make the pill particles evenly and stably placed into the casing annulus of an oil and gas field wellbore.

The material box used galvanized steel as the contact material to increase the stability of the pill particle flow process and reduce adhesion between the pill powder and the material box, and the half angle of the conical top was designed according to the friction characteristics of the pill particles. The discharge wheel was composed of ABS plastic as the contact material and consisted of a set number of wheel grids to promote uniformity and prevent pill particle breakage during the filling process. The wheel drive shaft was composed of steel and was tightly attached to the frame and motor to ensure that the mechanical strength of the mechanism drive process did not fluctuate. The upper discharge pills were transported to the annular flange of the oil field gas well through a tee pipe using fluid conveying in order to minimize pill particle damage during the conveying operation. The behavior of fluid transportation and particle settlement were significantly influenced by the discharge procedure and performance. In order to obtain the ideal working state, this research focused primarily on the discharge device, its functioning, and its influencing mechanisms.

The lower arc of the trough wheel grid was tangential to the inner circle to maximize particle filling efficiency. As the discharge wheel revolved, the granules filled the grid uniformly and were discharged steadily at the outlet. The number and width of the grids have a big influence on particle filling efficiency and discharge stability. As a result, four grid numbers (6, 8, 10, and 12) and four grid widths (75, 100, 125, and 150 mm) were chosen for the study, as shown in Figure 1b, to evaluate the influence of the discharge wheel’s shape and dimensional parameters on the discharge process’ performance.

2.2. Model of Pill Particle

The research object in this work was self-developed pill particles. Depending on the geometrical features of the particles, the particles were divided into three groups based on their height, namely 5.4, 5.8, and 6.2 mm. In the particle population, the mass ratios of pill particles A, B, and C were 35%, 35%, and 30%, respectively. As a consequence, a strategy for modeling the population of pill particles based on DEM is presented, as well as numerical models of the three pill particles based on the 12-sphere model [4], as illustrated in Figure 2a.

Based on an examination of the physical characteristics of the pill particles, parameters such as density, modulus of elasticity, and coefficient of static friction were calculated [24,25,26,27]. The coefficient of rolling friction was calibrated using the angle of repose tests, as shown in Figure 2b.

2.3. Simulation Contact Model and Parameters

To simulate the pill particle discharge process simulation test, the EDEM software Hertz–Mindlin contact mechanics model was employed [28,29,30,31]. According to the following model, the normal contact forces between the particles were estimated [20].

$$F_{ij}^n=\left(\frac{4}{3}{E}^{\ast }\sqrt{R^{\ast }}{\delta }_n^{\frac{3}{2}}-2\sqrt{\frac{5}{6}}\beta \sqrt{S_n{m}^{\ast }}(v_{ij}\cdot {\widehat{n}}_{ij})\right){\widehat{n}}_{ij}$$

(1)

where the equivalent Young’s Modulus $E^{\ast }$ and the equivalent radius $R^{\ast }$ are defined as $E^{\ast }={\left[\left(1-{\upsilon }_i^2\right)/E_i+(1-{\upsilon }_j^2)/E_j\right]}^{-1}$ and $R^{\ast }={\left[1/R_i+1/R_j\right]}^{-1}$, with $E_i$, ${\upsilon }_i$, and $R_i$ and $E_j$, ${\upsilon }_j$, and $R_j$ being the Young’s Modulus, Poisson ratio, and Radius of particles $i$ and $j$, respectively; ${\delta }_n$ is the normal overlap; the damping factor $\beta$, the normal stiffness $S_n$, and the equivalent mass $m^{\ast }$ are given by $\beta =-\ln e/\sqrt{{\ln }^{2}e+{\pi }^2}$, $S_n=2E^{\ast }\sqrt{R^{\ast }{\delta }_n}$, and $m^{\ast }={\left[1/m_i+1/m_j\right]}^{-1}$, with $e$, $m_i$, and $m_j$ being the coefficient of restitution and the mass of each particle in contact; $v_{ij}$ is the relative velocity between particle i and $j$; the unit vector ${\widehat{n}}_{ij}$ is calculated as ${\widehat{n}}_{ij}=\left(R_i-R_j\right)/\left|R_i-R_j\right|$.

The Coulomb Moore friction theory was used to compute the tangential contact forces between the particles, which were derived using the following model.

$$F_{ij}^s=\min \left(-S_t{\delta }_t-2\sqrt{\frac{5}{6}}\beta \sqrt{S_t{m}^{\ast }}(v_{ij}\cdot {\widehat{s}}_{ij}),{\mu }_s{F}_{ij}^n\right){\widehat{s}}_{ij}$$

(2)

where the tangential stiffness $S_t$ is given by $S_t=8G^{\ast }\sqrt{R^{\ast }{\delta }_n}$, with G^* being the equivalent shear modulus; ${\delta }_t$ is the tangential overlap; ${\mu }_s$ is the coefficient of static friction; ${\widehat{s}}_{ij}$ is the unit tangent vector.

Newton’s second law was used to calculate particle translation:

$$m_i\frac{d{v}_i}{dt}={\displaystyle \sum _j(F_{ij}^n+F_{ij}^s)}+m_{i}g$$

(3)

where $v_i$ is the translational velocity of particle $i$; $g$ is the gravitational acceleration.

Euler’s equation was used to compute particle rotation:

$$I_i\frac{d{\omega }_i}{dt}={\displaystyle \sum _j(R_i\times F_{ij}^s-{\mu }_r{R}_i\left|F_{ij}^n\right|{\widehat{\omega }}_i)}$$

(4)

where ${\omega }_i$ and $I_i$ are the angular velocity and moment of inertia of particle $i$, respectively. $R_i$ is a vector running from the center of the particle to the contact point, with its magnitude equal to particle radius $R_i$. ${\mu }_r$ is the coefficient of rolling friction.

The parameters selected for the simulation of the pill discharge process are shown in

Table 1. Parameter selection for simulation.

Parameters	Pill Particle	ABS Plastic	Galvanized Steel
Density ρ, kg/m3	1380	1050	7865
Poisson’s ratio υ	0.350	0.394	0.300
Elastic modulus E, Pa	1.100 × 108	3.189 × 109	7.900 × 1010
Restitution coefficient e	0.201	0.299	0.305
Coefficient of static friction μs	0.466	0.577	0.511
Coefficient of rolling friction μr	0.080	0.120	0.070

. The elastic modulus was appropriately constricted and adjusted to 79 GPa to reduce simulation time consumption without impacting calculation accuracy. Other parameters were calibrated on this basis [4].

2.4. Test and Simulation Methods

This research was divided into two sections: simulation model and parameter accuracy calibration, and discharge process simulation. The simulation model and parameter accuracy calibration test involved both a bench test and a simulation analysis of the discharge process. The simulation model and parameters were calibrated and validated by comparing the experiment data to the simulation results for various rotation speeds of the discharge wheel with the cumulative value of pill discharge.

With the grid number, grid width, and rotation speed of the discharge wheel as test factors and the pill particle filling amount, filling density, discharge variation coefficient, and compressive force as evaluation indicators, simulation tests of the discharge process were conducted using the calibrated and validated simulation model.

Table 2. Components and levels of the simulation tests.

	Grid Number	Grid Width, mm	Rotation Speed, rpm
1	6	75	10
2	8	100	15
3	10	125	20
4	12	150	25
5			30

shows the components and levels of the simulation tests, which each included 40 sets and three repetitions. Finally, the mechanical behavior of the pill particles was observed and calculated, as well as the results of the discharge simulation experiments. The influence of the groove wheel’s structural and operational properties on discharge performance was also disclosed, as was the ideal parameter combination.

The following was the formula for calculating the discharge variation coefficient:

$$CV=\frac{\sqrt{{\displaystyle \sum _1^n\left(M_i-\overline{M}\right)}/n}}{\overline{M}}$$

(5)

where $M_i$ is the total mass of pill particles discharged per 0.5 s, and $\overline{M}$ is the average mass of each sample.

Using EDEM 2018 software, the Hertz–Mindlin (no-slip) contact model and the parameters provided in Table 1 were used to simulate the pill particle discharge processes. In proportions of 35%, 35%, and 30%, respectively, the particle models of the 12-sphere pills A, B, and C were used. The particle factory was first set up as a box area with dimensions of 400-mm-long by 150-mm-wide, with 5 mm above the top of the work bin. Second, the particle factory created 10 kg of almost 60,000 pill particles, which were then progressively accumulated in the hopper. The pill wheel began to spin as soon as the pill particles stabilized. Finally, a calculation was made to determine the assessment indications for the discharge process within 10 s.

3. Results and Discussion

3.1. Simulation Model and Parameter Validation

The width was 100 mm, and the number of grids was eight. The operating procedure of the discharge wheel was studied using an experiment and a simulation at 10 and 15 rpm.

The simulation and testing findings for pill discharge at various rotation speeds increased approximately linearly with time, as shown in Figure 3. When the speed of the discharge wheel was increased from 10 to 15 rpm, the linear deviation of the discharge test results decreased, showing that increasing the speed at lower rates improved the uniformity and stability of the pill-dispensing process. The simulation model and settings utilized in this research could accurately simulate the discharge process of pill particles, as shown by the comparison of simulation and experiment findings.

3.2. Simulation Analysis of the Discharge Process

Figure 4 depicts a simulation examination of the pill discharge wheel’s functioning procedure. The analysis of particle velocity is shown in Figure 4a. During the rotation of the discharge wheel, the pill particles could be split into three zones, with area I being the quasi-static zone, where the pill particles remained moderately static, gradually falling as the filling process continued. Area II was the driving zone, which was influenced by the dispensing wheel’s rotation and had a particular relative velocity with the groove wheel, which had a significant impact on the agent’s filling process. Area III was the filling zone, where particles collected in the grid due to gravity and were impacted by the grid’s shape and size.

The examination of the particles’ compressive force is shown in Figure 4b. The particles were prone to tight contact and jamming between the wheel and the outside wall during the rotation of the discharge wheel, resulting in a significant compressive force and particle breakage. The results reveal that the structure and operating factors, such as grid design and size, as well as the speed of wheel rotation, had a significant impact on the particle loading and discharge process and performance.

3.3. Effect of the Grid Number

The working process of the discharge wheel was researched for four grid numbers and five rotation speeds at a grid width of 100 mm in order to study the effect of the grid number on the discharge process and performance. Figure 5 depicts the simulation findings.

3.3.1. Effect on Filling Process

For varied grid numbers, Figure 5a demonstrates how the simulation results of the pill filling amount varied with the rotation speed of the discharge wheel. As the grid number grew, the average filling amount dropped from 0.34 to 0.13 kg, and the filling amount reduced as the rotation speed increased for different grid numbers. The filling capacity decreased as the grid numbers increased, but the total difference was minor.

Figure 5b depicts the relationship between filling density and discharge wheel rotation speed for various grid numbers. The change in filling density and the filling amount of the pill were essentially the same, as shown in the figure. For various grid numbers, the filling density fell as the rotation speed increased. When the number of grids was increased from 10 to 30 and the rotation speed was increased from 10 to 30 rpm, the filling density was reduced the most, from 674.78 to 607.31 kg/m³.

3.3.2. Effect on Discharge Process

For varied grid numbers, Figure 5c demonstrates how the discharge variation coefficient varied with the rotation speed of the discharge wheel. When the number of grids was increased from 6 to 8, the variation coefficient lowered from 0.029 to 0.024, and when the number of grids was extended from 8 to 12, the variation coefficient decreased from 0.024 to 0.026. When a result, as the grid numbers increased, the stability of pill ejection increased and then declined.

3.3.3. Effect on Compressive Force

Figure 5d demonstrates how the compressive force of the particles varied with the rotation speed of the discharge wheel for various grid numbers. The average value of the compressive force increased from 574.20 to 787.24 N when the grid number was increased from 6 to 12. At various grid numbers, the compressive force of the particles increased dramatically as the rotation speed increased. When the number of grids was 12 and the discharge wheel rotation speed was 30 rpm, the maximum particle compressive force was 1407.50 N.

3.3.4. Discussion of Grid Number

The grid number in the discharge wheel was directly related to the shape and volume of the grid, according to the filling process study. As the grid number increased, the volume of the grids decreased, making it easier for the particles to form an arch, lowering the filling amount and density. The relative speed between the particles and the wheel increased as the rotation speed increased, affecting the filling process. As a result, the filling process and performance were affected by both the grid number and the rotation speed of the discharge wheel.

A critical factor for evaluating the discharge process was the consistency and consistency of particle discharge. When looking at the discharge findings, it can be seen that the rotation speed had a greater impact than the grid number. The pill particles could be ejected constantly and steadily once the rotation speed reached a specified range.

The impact of the discharge wheel’s speed on the compressive force of the pill particles was stronger, according to the investigation. When the speed exceeded 15 rpm, the particles tended to become trapped between the trough wheel and the outer wall, resulting in a greater compressive force. Particle entrapment was more likely when the number of grids was large.

The results of the preceding investigation reveal that when the number of grids was 8, the discharge wheel filling and discharge process was improved, and the agent particles were less likely to break down at lower speeds.

3.4. Effect of the Grid Width

Based on the findings of the previous study, the working process and performance of the discharge wheel with a grid number of 8 were investigated for four grid widths and five rotation speeds, as shown in Figure 6.

3.4.1. Effect on Filling Process

Figure 6a demonstrates how the filling amount varied with rotation speed for various grid widths. As can be seen in the graph, the filling amount increased when the grid width grew; for example, as the grid width went from 75 to 150 mm, the average filling amount increased from 0.16 to 0.36 kg. For various grid widths, the filling amount dropped gradually as the rotation speed increased.

Figure 6b depicts the change in the pill filling density simulation results as a function of rotation speed for various grid widths. The average filling density increased in the order of 75, 150, 100, and 125 mm as the grid number increased in the figure, and the average filling density progressively increased from 666.35 to 726.88 kg/m³. For varied grid widths, the filling density fell as the rotation speed increased. When the rotation speed was increased from 10 to 30 rpm at a trough wheel width of 75 mm, the filling density decreased the most, from 708.46 to 619.39 kg/m³.

3.4.2. Effect on Discharge Process

Figure 6c depicts the variation coefficient as a function of discharge wheel rotation speed for various grid widths. The variation coefficient rose from 0.0214 to 0.0342 as the grid width increased. For grid widths of 75 and 100 mm, the variation coefficient dropped and subsequently climbed, reaching its lowest value at 15 rpm. For grid widths of 125 and 150 mm, the variation coefficient was lower, and it alternated with rotation speed, reaching a minimum at 30 rpm.

3.4.3. Effect on Compressive Force

For varying grid widths, Figure 6d shows how the compressive force of pill particles varied with the rotation speed of the discharge wheel. With the increase in grid width and rotation speed, the average compressive force of the particles increased steadily from 528.2 to 634.4 N. At a grid width of 125 mm and a rotation speed of 30 rpm, the maximum particle compressive force was 1456.24 N.

3.4.4. Discussion of Grid Number

When the number of grids was 8, the filling density increases with the grid width, but this effect gradually diminished as the grid width went to a particular range, according to the filling process study. The filling density reduced as the wheel rotated faster, and this impact grew as the wheel rotated faster.

The variation coefficient was low, and the pill discharge was more uniform when the grid number was 8 and the grid widths were 75 and 100 mm, according to the results of the discharge process. The pill discharge process performed best when the rotation speed was between 10 and 15 rpm, which corresponds to the existing structural specifications of the discharge wheel. As a result, the grid width had a bigger influence on the total pill dispensing procedure.

The compressive force of the pill particles was calculated to illustrate that as the grid width rose, the possibility of the pill particles becoming trapped between the wheel and the outer wall increased, resulting in a higher compressive force. As a result, increasing the grid width increased the risk of pill particle fracture.

The performance of the filling amount, filling density, discharge variation coefficient, and compressive force of the particles during the operation of the discharge wheel was optimal when the grid number was 8, the grid width was 75 mm, and the rotation speed of the discharge wheel was 15 rpm, according to a comprehensive analysis of the effects of the grid number and width.

4. Conclusions

This research presented a simulation analysis of the working performance of the pill discharge device and the mechanical behavior of the pill particles during the pill discharge process using DEM in order to optimize the process of casing annular corrosion in oil and gas fields. The Hertz–Mindlin contact mechanics model was used to study the working process of the discharge device, analyze the contact between pill particles and the discharge device, and analyze the flow process and mechanical behavior of pill particles, due to the non-adhesive characteristics of pill particles. We discovered that the model accurately reproduced the dynamic properties of the pill particle population during discharge device operation. The simulation model and its parameters could more correctly mimic and anticipate the operating process and performance of the discharge device when compared to the actual test results.

In this paper, it was discovered that increasing the number of grids and decreasing the grid width of the discharge wheel, while having a minor effect on the filling amount and filling density, could reduce the time of a single discharge in the discharge process, lowering the variation coefficient of the pill discharge and ensuring that the pill was discharged uniformly and steadily. The discharge variation coefficient tended to drop and then increase as the rotation speed of the discharge wheel increased, and the compressive force of the pill particles gradually increased. As a result, lowering the rotation speed of the discharge wheel could increase pill discharge stability while also reducing particle breakage. The study’s findings revealed that the best combination of grid number, grid width, and discharge wheel rotation speed was 8, 75 mm, and 15 rpm.

The findings of this research can be used to develop novel simulation models, design theories, and parametric guidance for future wellbore casing annular hollow corrosion protection agent addition devices in oil and gas fields, considerably simplifying the design process. It offers the groundwork for quickening the process of changing the way oil and gas field wellbore casing annular hollow corrosion protection is handled, as well as increasing oil and gas field wellbore integrity management capabilities, among other things.