Experimental Study on the Transport Behavior of Micron-Sized Sand Particles in a Wellbore

Abstract

In the process of natural gas hydrate extraction, especially in offshore hydrate extraction, the multiphase flow inside the wellbore is complex and prone to flow difficulties caused by reservoir sand production, leading to pipeline blockage accidents, posing a threat to the safety of hydrate extraction. This paper presents experimental research on the migration characteristics of micrometer-sized sand particles entering the wellbore, detailing the influence of key parameters such as sand particle size, sand ratio, wellbore deviation angle, fluid velocity, and fluid viscosity on the sand bed height. It establishes a predictive model for the deposition height of micrometer-sized sand particles. The model’s predicted results align well with experimental findings, and under the experimental conditions of this study, the model’s average prediction error for the sand bed height is 12.47%, indicating that the proposed model demonstrates a high level of accuracy in predicting the bed height. The research results can serve as a practical basis and engineering guidance for reducing the risk of natural gas hydrate and sand blockages, determining reasonable extraction procedures, and ensuring the safety of wellbore flow.

1. Introduction

Natural gas hydrates possess five significant characteristics: vast reserves, widespread distribution, shallow burial, high energy density, and cleanliness. They are considered the most effective strategic alternative energy source after coalbed methane and shale gas, showing promising development potential [1,2,3,4]. Over 30 countries and regions worldwide are conducting research and exploration surveys on natural gas hydrates, gradually advancing into the exploration and experimental drilling and extraction stages. However, extracting natural gas hydrates presents significant challenges, primarily due to the complex multiphase flow in the wellbore and the potential for sand production [5,6].

Sand production during the trial extraction of natural gas hydrates refers to the process where micrometer-sized sand particles, along with water and hydrocarbon gases produced after hydrate decomposition, enter the wellbore [7,8,9]. Due to the constraints of hydrate phase equilibrium conditions and the formation geothermal gradients, natural gas hydrates are buried relatively shallowly in marine and permafrost reservoirs, having low formation strength and weak cementation effects. Moreover, hydrates in predominantly sandy reservoirs mainly exist in the forms of contact, cementation, and skeletal support [10,11]. Therefore, even a small proportion of hydrate decomposition with initiating cementation and skeletal support can disrupt the reservoir structure, leading to the loss of soil support, reducing the soil strength, and causing sand production in natural gas hydrate reservoirs. Additionally, the gases and water produced during hydrate decomposition accelerate the breakdown of cementation and skeletal support, thereby accelerating sand production.

Unlike conventional oil and gas reservoirs where sand predominates, hydrate reservoirs are primarily composed of clay (<4 μm) and silt (4–63 μm) [12,13]. Particle size analysis of various hydrate reservoirs revealed that the proportion of sand particles with a diameter less than 63 μm is generally above 65%, with some even reaching up to 94%. However, the current limit of sand control methods is around 44 μm. This is because in engineering practice, particles smaller than 44 μm are generally believed not to damage equipment and can be produced through the wellbore. Specifically, in the South China Sea hydrate reservoirs, the silt and clay contents of the sediment can exceed 25%, with the sediment being primarily composed of fine silty sand with a median particle size of 10–15 μm. For hydrate reservoirs, existing sand control technologies are not entirely effective, inevitably leading to the phenomenon of micrometer-sized sand particles bypassing sand control systems and entering the wellbore [14,15]. These micrometer-sized sand particles, which are carried by reservoir fluids into the wellbore, will deposit and form a sand bed, reducing the flow area of the wellbore, increasing frictional pressure loss, and even causing severe incidents like channel blockage [3]. This forces an early termination of natural gas hydrate trial extraction operations.

Sand production in hydrate reservoirs has led to the premature termination of natural gas hydrate trial extraction operations worldwide. This has prompted many scholars to focus on the issue of micrometer-sized sand production within the wellbore during natural gas hydrate trial extractions. Kneafsey et al. [16], utilizing X-ray computed tomography (CT), detected local density changes during hydrate formation and decomposition. They discovered that mineral particles and water could move due to the formation and decomposition of hydrates. Uchida et al. [17] observed significant sand migration into the wellbore during the depressurization method for gas hydrate extraction conducted in the Mackenzie Delta, Canada, in 2007. This directly led to the premature termination of the trial extraction after 24 h, highlighting the importance of sand control in reservoirs. Lee et al. [18], based on data from the 2013 offshore gas hydrate trial extraction in Japan, evaluated the effectiveness of conventional commercial sand screens. They concluded that conventional sand screens could effectively control sand production. However, this conclusion did not align with subsequent sand production results in several natural gas hydrate trial extraction operations. Terao et al. [19] explored the design, testing process, and challenges of the open-graded gravel packing technique employed in the offshore gas hydrate trial extraction in the Nankai Trough, Japan. Sun et al. [20], through a study on the stability of a certain natural gas hydrate reservoir, discovered that sand production is prone to occur at the edges. Hence, careful control of the production pressure drop and sand production rate is necessary. Lu et al. [8] believed that sand production is the process of reservoir sand migrating into the wellbore with the flow of reservoir fluids. Yan et al. [21] used numerical simulation methods to study the characteristics of rock plastic yield and sand production laws in hydrate reservoir exploitation. They found that an increase in the pressure drop during the production process and differences in the horizontal stresses of the reservoir lead to an increased stress concentration around the wellbore, making the reservoir more prone to sand production. Moreover, an increase in the pressure drop during the production process can promote hydrate decomposition and reduce the strength of the rocks around the wellbore, leading to extensive plastic yield of the surrounding rocks, thereby causing sand production. Additionally, an increase in the bottomhole temperature and reservoir permeability accelerates hydrate decomposition, thereby accelerating the reduction in reservoir strength and increasing the volume of sand production.

In summary, the production cost resulting from the micrometer-sized sand transport issue in hydrate production and transportation systems is exceedingly high. Therefore, there is a need for a comprehensive understanding of the transport characteristics of micrometer-sized sand particles within a wellbore. In-depth research on the flow, transport, and deposition patterns of micrometer-sized sand particles entering the wellbore is essential to ensure the safety of wellbore flow and achieve the long-term stable extraction of natural gas hydrates. Therefore, this paper conducts experimental research on the transport characteristics of micrometer-sized sand particles entering a wellbore. It investigates the sand bed height during the transport of micrometer-sized sand particles and proposes a corresponding predictive model. The research results can provide practical evidence and engineering guidance for reducing the risks of natural gas hydrate blockage and sand plugging, determining reasonable extraction work procedures, and ensuring the safety of wellbore flow.

2. Experimental Methodology

2.1. Experimental Setup

In this study, an experimental setup consisting of seven components was designed and utilized, including an experimental stand, transparent acrylic tube, horizontal variable-frequency mud pump, high-precision electromagnetic flowmeter, stainless-steel frame sand mixing tank, variable-frequency control cabinet, and high-speed camera. The average roughness (Ra) of the transparent acrylic tube is approximately 0.01–0.1 µm. A clear observation of the experimental process is ensured by the transparent acrylic tube, and the actual trial extraction conditions are simulated using the horizontal variable-frequency mud pump [22]. Accurate measurements of sand particle transport are provided by the integration of the high-precision electromagnetic flowmeter and the stainless-steel frame sand mixing tank. The experimental parameters are adjusted for better simulation of different conditions by the use of the variable-frequency control cabinet. The detailed process of micrometer-sized sand particle transport is captured with the high-speed camera. The schematic diagram of the entire experimental setup is shown in Figure 1.

2.2. Experimental Materials

Due to the current limit of sand prevention methods being around 44 μm, we use this limit as a standard and consider that the particle size of sand entering the wellbore is below 44 μm. To gain an in-depth understanding of the characteristics of sand particles within this range, we selected three samples with different particle sizes, labeled as A, B, and C. By utilizing the advanced Mastersizer 3000 laser diffraction particle size analyzer (as shown in Figure 2, range: 0.01–3500 μm), we conducted detailed measurements of the particle sizes of samples A, B, and C.

Such a particle size analysis not only aids in understanding the size distribution of sand particles within the wellbore but also provides crucial data to assess the effectiveness of current sand prevention methods across different particle size ranges. In this study, we will delve into the transport characteristics of sand particles of different sizes, aiming to provide strong support for engineering practices during the natural gas hydrate extraction process.

Each sample was measured three times to ensure the accuracy and reliability of the data. Through sand particle size testing, we obtained detailed distribution results, including D10, D50, and D90, as shown in

Table 1. Test results for each sample’s D10, D50, and D90.

Sample Names	Record Number	D10 (μm)	D50 (μm)	D90 (μm)
Case 1	1	2.28	8.14	15.6
	2	2.30	8.17	15.0
	3	2.29	8.17	15.1
Final average value of sample A		2.29	8.16	15.23
Case 2	1	2.61	16.9	31.7
	2	2.61	17.0	32.0
	3	2.61	17.0	32.2
Final average value of sample B		2.61	16.97	31.97
Case 3	1	23.9	40.9	65.5
	2	24.1	40.12	65.7
	3	24.1	42.2	65.6
Final average value of sample C		24.03	41.24	65.60

. To determine the typical particle size of the samples, we chose the average value of D50 from the three measurements. According to this method, we determined the particle sizes of samples A, B, and C to be 8.16 μm, 16.97 μm, and 41.24 μm, respectively.

2.3. Experimental Methodology and Steps

The main steps of the experiment are as follows:

① The pipeline and sand mixing tank should be cleaned and allowed to air dry. ② The volume of micrometer-sized sand particles and water required for the specified sand concentration should be calculated. The volume ratio should be referred to as the ratio of the total volume of particles injected into the wellbore to the volume of fluid. According to the calculation results, the specified volumes of sand and water should be added to the sand mixing tank using measuring sand and water buckets. ③ The frame agitator in the mixing tank should be started, stirred for at least 10 min, and then the valve of the mixing tank should be opened after a uniform mixture of sand and water is achieved. ④ The target flow rate should be input on the control cabinet, and the reading on the electromagnetic flowmeter should be observed. ⑤ When the reading on the electromagnetic flowmeter matches the input target flow rate and remains stable, the accumulated sand bed height should be measured. ⑥ Steps 1–5 should be repeated to measure the transport of micrometer-sized sand particles under different flow rates, different sand particle sizes, different sand concentrations, and different wellbore inclinations.

Furthermore, our experimental setup operates on a smaller scale compared to actual hydrate extraction processes. This scale difference may affect the flow dynamics and particle interactions observed in our experiments. The experiments were conducted under relatively uniform conditions, which may not fully capture the variability in natural wellbore environments, such as variations in the pressure, temperature, and particle size distribution.

The samples were then carefully weighed to create specific sand ratios, with a predefined blend of each particle size group. Each mixture was homogenized to ensure uniformity before being introduced into the experimental setup. To conduct micrometer-sized sand deposition experiments, it is essential to accurately measure the sand bed height inside the wellbore. This height can be calculated based on the geometrical relationship of the wellbore, as illustrated in Figure 3.

Initially, the central angle corresponding to the sand bed is computed:

$$\theta ={\displaystyle \frac{2L}{R_{\mathrm{w}}+2t}}$$

(1)

where θ is the central angle corresponding to the sand bed arc length; L is the sand bed arc length (averaged from multiple measurements); t is the casing wall thickness; and R_w is the wellbore’s inner diameter.

The height of the sand bed surface from the wellbore center is determined:

$$h_{\mathrm{o}}={\displaystyle \frac{1}{2}}{R}_{\mathrm{w}}\cos \left({\displaystyle \frac{\theta }{2}}\right)$$

(2)

where h_o is the height of the sand bed surface from the wellbore center.

The height of the sedimentary sand bed inside the wellbore is determined:

$$h={\displaystyle \frac{R_{\mathrm{w}}}{2}}-h_{\mathrm{o}}$$

(3)

where h is the height of the sedimentary sand bed inside the wellbore.

The sand ratio of micrometer-sized sand particles is primarily controlled by quantitatively adjusting the ratio of micrometer-sized sand particle content to water content while maintaining the overall stability in the experimental process. To achieve this, a stainless-steel frame sand mixing tank was designed, along with measuring sand and water buckets with scales to facilitate the preparation of micrometer-sized sand particles at different volume concentrations.

The procedure for preparing the sand ratio of micrometer-sized sand particles is as follows: ① The target volume concentration of sand particles for the experiment should be determined. ② The required sand particle content at this concentration should be calculated. ③ The required water content at this concentration should be calculated. ④ The determined amounts of sand particles and water should be added into the stainless-steel frame mixing tank using the measuring sand bucket and water bucket with scales. ⑤ The stainless-steel frame mixing tank should be started to uniformly mix the sand particles and water. Since the volume of the sand mixing tank is much larger than the volume of the pipeline, it is approximately assumed that the sedimentation of sand particles in the pipeline does not affect the volume concentration of sand particles in the mixing tank.

Some changes in experimental phenomena are illustrated in Figure 4.

From the experiment, it can be observed that the flow rate required for the complete suspension of sand particles is 12 m³/h or above. When sand particles exhibit linear deposition, the flow rate is 10 m³/h, and at this point, the sand particles still move upward. For plug-like deposition of sand particles, the flow rate is 9 m³/h, and the sand particles continue to move upward. At a flow rate of 8 m³/h, the sand particles form a strip-shaped distribution, and as the flow rate decreases, the spacing becomes smaller, resulting in a denser distribution. When the flow rate is reduced to 7 m³/h, the sand particles begin to slide downward. A further reduction in the flow rate causes the sand particles to gradually connect into a cohesive whole, forming a sand bed.

3. Analysis of Experimental Results on Micrometer-Sized Particle Transport inside the Wellbore

3.1. Impact of Sand Ratio on Sand Bed Height

In this study, the experimental data vividly illustrate the relationship between the sand bed height in the wellbore and the sand ratio under various conditions. The impact of different sand ratios on the sand bed height is depicted in Figure 5, revealing the trends associated with this influence.

From Figure 5, it can be observed that as the sand concentration increases, indicating a higher sand production rate and a larger base, the sedimentation volume of micrometer-sized sand particles inside the wellbore increases. When the sand concentration is relatively low (e.g., below 6), a small amount of micrometer-sized sand particles settling in the wellbore can lead to a substantial increase in the sand sedimentation concentration, with a nearly 684% rise in the sedimentation height. With a higher sand concentration in the reservoir (e.g., greater than 8), a larger sand sedimentation requires more sand particles to settle in the wellbore. The sand bed height in the reservoir increases exponentially with the increase in the sand ratio. This is because a higher sand production concentration implies a greater number of sand particles inside the wellbore, leading to more collisions. In other words, sand particles are more likely to collide with the wellbore walls or with each other. Since these collisions are mostly inelastic, the kinetic energy of the sand particles dissipates in the form of heat during the collision process. Therefore, with a higher sand concentration, more sand particles deposit, resulting in a higher sand bed height.

3.2. Impact of Wellbore Inclination on Sand Bed Height

In this study, the experimental data clearly reveal the relationship between the sand bed height in the wellbore and the wellbore inclination under different conditions. The influence of different wellbore inclinations on the sand bed height is depicted in Figure 6, illustrating the trends associated with this influence.

From Figure 6, it can be observed that the sediment concentration of sand gradually increases with the increase in the wellbore inclination. An interesting phenomenon is that the sand bed height increases with the increasing wellbore inclination, contrary to the conventional pattern in the drilling industry, where the most severe sedimentation of cuttings occurs at wellbore inclinations between 45° and 60° due to the cuttings sliding. The unique behavior observed regarding the increase in the sand bed height with the wellbore inclination may be attributed to the enhanced adhesion between micrometer-sized sand particles and the wellbore wall. Due to their small size and larger surface area, micrometer-sized sand particles are less prone to sliding after deposition, potentially contributing to the gradual increase in the sediment concentration with the wellbore inclination. As the wellbore inclination increases, the rise in the sand bed height may be associated with the finer particles forming a more cohesive and stable structure. This distinctive influence of the wellbore inclination on the sand bed height, in contrast to the traditional cuttings’ sliding patterns, highlights the uniqueness of micrometer-sized sand particles and their crucial role in the deposition process. Therefore, the trends exhibited by micrometer-sized sand particles under varying wellbore inclinations offer a new perspective for understanding the deposition mechanisms in the process of natural gas hydrate trial production.

3.3. Impact of Fluid Flow Velocity on Sand Bed Height

In this study, the experimental data clearly reveal the relationship between the sand bed height in the wellbore and the fluid flow velocity under different conditions, as shown in Figure 7. The results depicted in the figure illustrate the trends of how different fluid flow velocities affect the sand bed height in the wellbore.

From Figure 7, it can be observed that the sand bed height decreases with the increase in the Reynolds number. The reason for this phenomenon is that as the Reynolds number increases, the intensity of turbulence increases, leading to an increase in the lift force that keeps sand particles suspended. Consequently, more micrometer-sized sand particles remain suspended within the main flow and move with it, resulting in a lower sand bed height. Additionally, under the same Reynolds number, larger inclinations of the wellbore lead to higher dimensionless sand bed heights. Furthermore, further experimental observations indicate that with the increase in the Reynolds number, the fluid velocity within the pipeline increases, enhancing the motion capability of the suspended particles. This exacerbates the collisions between the particles in the sand bed, making micrometer-sized sand particles more prone to entering the suspended state. This finding further supports the observed trend of a decreasing sand bed height in the experimental results.

3.4. Impact of Particle Size on Sand Bed Height

In this study, the experimental data clearly reveal the relationship between the bed height of the sediment layers in the wellbore and the particle size under different sand discharge conditions, as shown in Figure 8. The results presented in the figure demonstrate the impact trends of different sand particle sizes on the bed height of sediment layers in the geological formation.

From Figure 8, it can be observed that as the sand particle size increases, the height of the sedimentation bed gradually increases. In other words, with larger particle sizes, sedimentation within the wellbore becomes more pronounced. When the particle size is smaller, the sand particles have a larger surface area and are more likely to remain in a suspended state, resulting in less sedimentation. As the particle size increases, this effect gradually weakens. Larger particle sizes have greater weight, making the sand particles more prone to settling at the wellbore bottom, leading to increased sedimentation height. This sedimentation phenomenon has significant implications for the natural gas hydrate production process, especially as prolonged testing may give rise to various engineering challenges. It is important to note that the increase in sedimentation bed height may elevate resistance in pipelines and wellbores, affecting fluid transport. Additionally, sediment accumulation may lead to wellbore blockages, impacting the efficiency of natural gas hydrate production.

3.5. Impact of Fluid’s Apparent Viscosity on Sand Bed Height

In this study, the experimental data clearly reveal the relationship between the bed height of the sediment layers in the wellbore and the fluid viscosity under different conditions, as shown in Figure 9. The results presented in the figure demonstrate the impact trends of different fluid viscosities on the bed height of sediment layers in the geological formation.

From Figure 9, it is evident that the height of the sedimentation bed formed by reservoir sand production grows exponentially with the apparent viscosity of the fluid. When the fluid’s apparent viscosity is low, the sedimentation bed height is significantly influenced, indicating that the apparent viscosity of the fluid plays a crucial role in controlling the formation of the sedimentation bed. This may be because under low apparent viscosity conditions, the interaction between the fluid and micrometer-scale reservoir sand particles is more pronounced, leading to a more extensive variation in the sedimentation bed height. However, when the apparent viscosity of the fluid is high, the influence of changing the fluid’s apparent viscosity on the sedimentation bed height becomes relatively less apparent. This might suggest that under high-apparent-viscosity conditions, the formation of the sedimentation bed resulting from reservoir sand production is constrained by other factors, and the impact of the fluid’s apparent viscosity is smaller. This observation provides us with a deeper understanding of the mechanisms behind reservoir sand production, emphasizing the complexity of the process under different fluid conditions.

3.6. Sand Bed Height Prediction Model Based on Experimental Results

In this paper, based on the theory of dimensional analysis, we establish a predictive model for the bed height of cuttings. This model is based on the observed distribution trends of the sand bed height under different experimental parameters. We analyzed the specific distribution forms, such as linear, power-law, and logarithmic trends. Finally, we employed nonlinear fitting techniques to establish a model that captures the influence of various parameters on the sand bed height under experimental conditions.

Utilizing dimensional analysis theory, the complex multi-factor problem is transformed into the study of relationships among a few dimensionless variables. The final optimized predictive model for the bed height of sediment in the micrometer-sized sand bed is as follows:

$$H=0.004V^{-1.37}{\left(1+\theta \right)}^{0.72}{\epsilon }^{1.30}{\mu }^{0.17}{d}_p^{1.05}$$

(4)

Using the proposed model, predictions for the bed height are made based on experimental parameters. The calculated model predictions are compared with the experimental values to validate the accuracy of the model results. In this comparison, the experimental values are taken as the horizontal axis and the model-predicted values as the vertical axis, resulting in a scatter plot of bed height experimental values versus predicted values, as shown in Figure 10. From the graph, it can be observed that the scatter points on the graph are predominantly distributed within a range of −20% to +20%, and under the experimental conditions of this study, the model’s average prediction error for the sand bed height is 12.47%, indicating that the proposed model demonstrates a high level of accuracy in predicting the bed height.

4. Conclusions

This study experimentally analyzed the influence of key factors such as the sand particle size, sand ratio, wellbore deviation angle, fluid velocity, and fluid viscosity on the sand bed height, ultimately establishing an effective predictive model for micrometer-sized sand particle deposition height. The model demonstrates strong alignment with experimental findings and provides insight into the complex interactions among these parameters:

• As the subsurface sand concentration intensifies, the sand bed height undergoes exponential growth, intertwined with the augmentation of the sand ratio. The enlargement of the sand particle diameter also manifests a positive correlation with the dimensionless sand bed height increment, highlighting the importance of both the sand ratio and particle size in determining sedimentation patterns.
• The sedimentation concentration gradually increases with the augmentation of the well deviation angle, deviating from the conventional rock debris sedimentation pattern. The increase in the sand particle diameter exhibits a positive correlation with the increment in the sand sedimentation bed height; the greater the particle diameter, the more pronounced the sedimentation.
• The sand bed height resulting from subsurface sand production experiences power function growth with the augmentation of the fluid’s apparent viscosity. Micrometer-sized subsurface sand particles display less sensitivity to fluctuations in the fluid’s apparent viscosity, underscoring the complex relationship between the particle size and fluid properties. In future studies, using larger datasets will be a significant focus for improving model robustness. Moreover, future studies will prioritize the consideration of gas–liquid–solid three-phase flow, which is critical for enhancing the accuracy of wellbore simulations.