Numerical simulations of sand‐screen performance in unconsolidated prepacked gravel screen

This work addresses the ongoing challenge of optimizing sand control screens, attributed to a limited understanding of screen blocking. A novel one‐way computational fluid dynamics and discrete element method (CFD–DEM) coupling technique is presented to analyze the structural parameters of unconsolidated prepacked gravel screens (PPGS). CFD–DEM involves systematically investigating the width of the punched slot on the outer protective screen, the size of the gravel, and the efficiency of gravel packing to improve the antiblocking capability of unconsolidated PPGS. Results from numerical simulations reveal that under conditions of effective sand control, the amount of sand entering the gravel layer to the bridge (referred to as the sand pass rate) is positively correlated with the antilocking ability (referred to as oil productivity index) for unconsolidated PPGS. The efficiency of gravel packing has the most substantial effect on the antilocking performance of unconsolidated PPGS. The data suggest that appropriately reducing the efficiency of gravel packing can enhance the antilocking capability of unconsolidated PPGS. To design an unconsolidated PPGS with enhanced antilocking capability, the efficiency of gravel packing be determined first. Then, the gravel size is designed based on this efficiency, and the width relative to the gravel size is decided. This contemporary design principle diverges considerably from previous design principles for gravel‐packed sand control screens. Supporting validation experiments agree with simulation outcomes, suggesting the established one‐way CFD–DEM coupling method in this paper is suitable for analyzing the plugging mechanism of unconsolidated PPGS. Thus, the CFD–DEM coupling method improves the design of such screens for improved antiblocking performance.

Sand production refers to the engineering geological phenomenon in which the sediment particles in the formation detach from the original formation skeleton and migrate with the fluid in the formation or enter the production well/pipeline.Sand production adversely affects the continuous, stable production of energy sources. 1 The problem of sand production initially appeared in conventional loose sandstone oil and gas reservoirs. 2 In recent years, as geological energy development has increased, sand generation issues have also been observed in natural gas hydrate reservoirs, 3 underground gas storage, 4 geothermal exploitation wells, 5 and tight oil and gas reservoirs modified by fracturing 6 or perforation. 7Particularly for high-rate gas wells, sanding is a major safety issue, and the produced solids can plug tubing, casing, flowlines, and surface vessels (Figure 1).Sand production can also cause erosion of equipment, leading to loss of well control or unwanted fluid emissions. 1Consequently, sand control is essential in mining operations.
Gravel packing sand control methods have shown effectiveness in managing sand, particularly in reservoirs with a high montmorillonite content. 8,9However, their use can be restricted due to their complex operational process, high risk, and elevated costs. 10Consequently, mechanical screens have become one of the most extensively utilized downhole sand control tools in the oil industry.Currently, the common types of mechanical sand screens include slotted liners (SL), 11 wire-wrapped screens (WWS), prepacked gravel screens (PPGS), and premium screens. 12Among these, SL screens are favored for their simplicity and cost effectiveness, whereas WWS screens provide superior sand control capabilities due to their high overflow area, reduced pressure drop, and corrosion resistance. 13,14PPGS resembles WWS but uses gravel media as filtering media, which may or may not be resin coated. 15The thickness and size of the packing layer vary based on well requirements, such as formation sand size, flow rate, and hole size. 16,17A PPGS consists of two concentric screens with a layer of prepacked gravel placed between them.The high permeability of the gravel packed within the screen results in a minimal pressure drop across the screen, owing to the substantial inflow area provided by the wire-wrapped layers. 18PPGS is used worldwide for open-and cased-hole gravelpacked or standalone completions. 15In these systems, the stability of sand particles is maintained due to the pore throats within the gravel layer, which create narrow openings.The gravel's fixed position achieved with epoxy resin plays a crucial role in this process.However, this condition can lead to rapid blockage of PPGS.The reduction in flow space initiated by the presence of gravel in the punched slots can inhibit optimal operation.This limitation makes monitoring and managing these systems essential to ensure their continued performance and longevity.
Compared with the mechanical sand control method, the gravel pack sand control method has the advantages of a large flow area and unfixed pores in the medium.This process can result in some silt-sized particles passing through the bridge zone along with the fluid, thus reducing blockages.Previous studies showed that the bridging position of formation sand within the gravel layer plays a crucial role in the antiblocking efficiency of PPGS. 19To achieve optimal antiblocking ability for PPGS, more formation sand must be allowed to enter the unconsolidated gravel layer and create a sand bridge.This paper introduces an unconsolidated PPGS, meaning the prepacked gravel is not bonded by adhesives such as epoxy resins.The major advantage of unconsolidated PPGS is the ability for gravel particles to move slightly due to fluid drag forces as it flows through the prepacked gravel pores.This movement causes the sand bridge between the retention medium to break, enabling fine clay particles to be carried away by the fluid (Figure 2).Leveraging this mechanism, the plugging degree of unconsolidated PPGS can be delayed, particularly during early production stages.
In addition, selecting the most cost-effective, safe, and efficient sand control method requires engineers to Causes and problems of sand production, Chen et al. 1 consider various reservoir characteristics thoroughly.These characteristics include sanding laws, particle size distribution within the formation, crude oil viscosity, and the type and content of clay minerals.These characteristics remarkably influence the performance of different sand control techniques.Traditionally, the selection of mechanical sand screens relies on experimental data, general rules, or correlations. 202][23] SRT tests are classified into three main groups: slurry SRT tests, prepacked SRT tests, and full-scale SRT tests.
5][26] In prepacked SRT tests, [24][25][26] a sand specimen is prefilled around screens, while confining or overburden stress is applied to the sand specimen.Most prepacked SRT or slurry SRT tests refer to linear flow conditions.However, the actual flow near the screen should be radial, creating a discrepancy between testing conditions and real-world applications.8][29] However, conducting a full-scale experiment can be quite costly and time consuming.Consequently, such tests are used less frequently due to these factors.
With the advancement of technology, the advanced computational fluid dynamics and discrete element method (CFD-DEM) coupling method has emerged for analyzing interactions between particles and fluids as well as particle-to-particle dynamics. 30This numerical simulation approach replicates experiments under controlled laboratory conditions.This approach enables the in-depth observation of particle trajectories, enhancing our understanding of their movements and interactions. 31,32Most importantly, quantitative analysis of the results becomes feasible upon the completion of a CFD-DEM simulation.Recently, the use of CFD-DEM methods has been increasingly recognized within the field of petroleum engineering.Notable applications include drilling cutting cleaning, lost circulation control during drilling, hydraulic fracturing, and sand production during extraction.The following discussion provides an overview of the recent literature on the application of the CFD-DEM method in sand production.Prominent examples from recent literature illustrate the use of CFD-DEM in sand production analysis.
Wu demonstrated that sand production increases with the rise in flow velocity and fracture width and decreases with the increase of solid-phase concentration. 33Shaffee revealed that increased particle adhesion results in reduced porosity and pressure drop within the sand layer on the screen. 34Zhang studied the process of fine particles passing through a sand column comprising large particles and found that fine particles can freely pass through the entire sand column with a minimal effect on sand column permeability when D15/d85 = 6. 35oor Ilyana Ismail studied the effects of the width-toparticle size ratio of WWS and wetting fluid (including gas and crude oil); they concluded that an increased particle size ratio escalates sand production, and the presence of fluid further intensifies this effect. 36These studies showed the CFD-DEM method is valuable for studying sand retention and observing migration trajectories of particles within sand-retaining media systems.However, the drawback of the CFD-DEM method lies in its high computational costs.Given the substantial number of solid particles involved in the sand control experiment and the small particle size, applying the CFD-DEM method in the sand control design is unrealistic.A more feasible alternative is one-way CFD-DEM coupling, which considers only the effect of fluid force on particles and ignores the particles' influence on the fluid.This one-way coupled CFD-DEM approach remains unaffected by the ratio of CFD element size to particle size and has demonstrated effective performance in simulations involving small particles, such as sand. 37onfronting the anticlogging issue of unconsolidated PPGS through the lens of understanding sand retention positioning can streamline the parameter design.Given this issue, the one-way CFD-DEM coupling method is perfectly suited for examining the dynamics of formation sand retention inside and outside unconsolidated PPGS under fluid influence.To demonstrate the feasibility of the one-way CFD-DEM coupling method for studying the plugging behavior of unconsolidated PPGS, this paper introduces the method to analyze the physical parameters of unconsolidated PPGS, structured closely to real-world engineering scenarios.Three research groups are engaged to explore these parameters: • The first group explores the effect of gravel packing efficiency by modifying the quantity of packed gravel.• The second group assesses the effect of gravel size on operations by adjusting the ratio of gravel median size to sand median size (D50/d50).• The third group investigates the influence of punched slot width in the outer protective shroud by varying the ratio of punched slot width to gravel median size (W/D50).
In addition, a small-sized sand control simulator is introduced to corroborate the relationship between the retaining law and the antiblocking performance of the unconsolidated PPGS.This approach integrates numerical simulation and practical verification, offering comprehensive insights into tackling the anticlogging challenge in unconsolidated PPGS.

| UNCONSOLIDATED PPGS
Unconsolidated PPGS comprises an outer protective shroud, prepacked gravel, and a slotted base pipe, as shown in Figure 3. Fluids carrying sand primarily flow through the punched outer protective shroud, followed by the filter jacket, and eventually through the innermost slotted base pipe into the wellbore.During sand control, sand particles may be obstructed at various positions, allowing oil to flow through the blocked zone.The functions of each component of the unconsolidated PPGS are summarized below: • Outer protective shroud: This part is often designed as a bridge-slotted screen and protects the filled gravel during deployment and support under reverse pressurization.• Filter jacket: This part is the central element of the unconsolidated PPGS's sand control mechanism, designed to meet filtering requirements, and typically comprises gravel of varied sizes that filters crude oil.• Base pipe: This slotted pipe is constructed in adherence to API standards and is designed to optimize flow and prevent gravel leaks while maintaining its structural integrity.However, this pipe is not studied in this context because the slots on the base pipe often cannot be plugged according to practical engineering scenarios.
During sand control, sand particles can be retained at various positions, and oil can flow through the blocking zone.According to the relationship between sand particle size and pore size in unconsolidated PPGS, blocking may occur in various positions (Figure 4).The blockage position is related to the packing efficiency of the gravel layer.As the gravel packing efficiency increases, the sand retention position moves closer to the surface of the outer protective shroud.When the gravel packing efficiency reaches the maximum, the sand retention is likely only in positions 1 and 2. Because the punched slot on the outer protective shroud is fixed, unconsolidated PPGS is prone to permanent blockage in this case.By contrast, the gravel layer is unconsolidated, allowing for micromovements between the gravel.As previously mentioned, unconsolidated PPGS exhibits a certain self-deblocking function under these conditions (Figure 2).If the sand is trapped in position 3 shown in Figure 4, sand retention has a slight effect on the flow capacity of the prepacked screen.Therefore, the primary focus of this paper is to examine the variation law of sand retention position under different structural parameters of unconsolidated PPGS.

| One-way coupled CFD-DEM method
In this paper, a one-way coupled CFD-DEM model was employed to simulate unconsolidated PPGS, as illustrated in Figure 5. First, the mesh and defining boundary conditions on the geometry were constructed, and the  F I G U R E 5 Simulation procedure based on the one-way coupled CFD-DEM method. 38CFD, computational fluid dynamics; DEM, discrete element method.flow field information was resolved using the CFD solver.Next, parameters such as gravel packing efficiency, gravel sizes, and punched slot width for unconsolidated PPGS were determined and utilized as input data for the DEM model.Then, the flow field information was incorporated into the DEM solver via a customdeveloped interface code written in C++.Next, the blocking of unconsolidated PPGS was directly simulated using a DEM software package. 35,39Finally, the blocking position of unconsolidated PPGS was observed using the postprocessing module within the DEM software package.In the context of one-way coupling, the particle motion was linked with the initial fluid condition because the flow was not solved.Therefore, only the influence of fluid flow on particles was considered while disregarding the effect of particles on fluid flow.

| DEM
DEM 40 first proposed by P. A. Cundall in 1971 is a numerical method for analyzing discrete granular materials.The advantage of DEM is that it can accurately calculate and monitor the position, velocity, collision force distribution, and other information of each particle at each time step. 41In the DEM model, Newton's and Euler's equations ( 1) and ( 2) describe the movement of each particle, including translational motion and rotational motion. 42dv (1) where m p , v p , ω p , and I p are the mass, translational velocity, angular velocity, and inertia moment of the particle, respectively; F p and T p are the total force and torque acting on the particle, respectively; and g is the gravitational acceleration.Total force F p applied on a particle p is the sum of forces on its element spheres as follows: where ns is the total number of element-spheres in particle p, and F ps is the force of sphere s in particle p.
where cs is the total number of contact points on each sphere at the current time step.
The total torque 43 acting on particle p can be calculated as follows: where T tps is the tangential force applied to each element sphere, T nps is the normal force, T rps is the torque generated due to rolling friction, r psc is the vector running from the center of element sphere i of particle p to contact point c, and d ps is the relative position vector between the centroid of particle p and the center of the element spheres.

| CFD
CFD is the use of computers and numerical methods to solve mathematical equations that control fluid motion, for example, mass, momentum, and energy conservation equations. 44CFD can also be used to predict different phenomena related to fluid flow, such as heat transfer, mass transfer, and chemical reactions. 45CFD's continuity and momentum conservation equations 46 are as follows: where ε ρ , f f are the volume fraction of solid and the fluid density, respectively; u u , f p are the fluid velocity and the solid velocity, respectively; p Δ represents the pressure; K fp is the momentum exchange coefficient between fluid and particle diameter; τ g , are the fluid stress tensor and gravity, respectively.

| Numerical model setup
Figure 6 illustrates the simplified process from the real unconsolidated PPGS to the simulation model.The fluid domain was meshed with 9000 grid cells using a commercial software package, ANSYS ICEM, as shown in Figure 7.For fluid flow, a constant velocity was set at the inlet, and no-slip boundary conditions were applied to the walls.Figure 8 shows the flow field information incorporated into the DEM solver.In the CFD solver, fluid parameters with a certain viscosity are defined.Previous studies reported increased computational costs in DEM calculations when the quantity of small particle size increases or the size of small particles decreases. 47Emulating field conditions is not feasible under existing constraints.On the basis of previous analysis, bridging location also serves as a critical indicator for assessing the anticlogging ability of unconsolidated PPGS.Therefore, only homogeneous particles were used for gravel particles and formation sand particles in this paper.The open flow area of the sand control screen in the simulation was only 1/12 of that of the sand control screen in the experiment.][50][51] Therefore, Young's modulus two orders of magnitude smaller is commonly used instead of a larger Young's modulus to decrease computational cost.On the basis of the above assumptions, the simulation parameters were set for this study, as shown in Table 1.
The packing efficiency of the gravel is an essential parameter in unconsolidated PPGS. 52A packing efficiency approaching the theoretical upper limit as closely as possible is preferred.However, a high packing efficiency can easily lead to a greater contact between the gravel and the outer protective shroud according to previous analysis.This condition substantially reduces the overall flow capacity of the new PPGS.Figure 9 shows the gravel packing efficiency influences the interaction between the gravel and the outer protective shroud, which in turn affects the filtration accuracy of the screen.The higher the filling rate of the gravel layer is, the stronger its interaction with the exterior.Consequently, the flow area on the outer protective cover is considerably reduced.To explore the influence of gravel layer filling rate on sand retention position, DEM software can adjust the vibration amplitude and frequency of the geometry to achieve different gravel filling effects in the annular space.A packing efficiency of 100% is assumed at the maximum gravel mass that can be accommodated by the annular space.On the basis of this assumption, the mass of the packed gravel is altered to adjust the packing efficiency.Details of how the vibration parameters of the geometry influence the filling efficiency, as demonstrated by the research process and results, are available in another article. 19The maximum packing percentage can be calculated by the following formula: where δ ε , are the packing efficiency and voidage, respectively.ε can be tested directly in DEM software.

| Evaluation criterion
According to the previous analysis, this paper explores the variation of the retention position of formation sand particles inside and outside unconsolidated PPGS under the influence of fluid by introducing a concept of sand passing rate (R).In Figure 11, R represents the proportion of bridging particles that pass through the punched slot relative to the total number of bridging particles.A larger R value indicates a greater likelihood of formation sand being retained in the gravel layer, and vice versa.Drawing from previous theoretical analyses, a higher probability of formation sand retention in the gravel layer corresponds to stronger self-unblocking ability of the unconsolidated PPGS.This outcome implies the screen exhibits superior resistance to plugging.The relationship between these elements is confirmed through an experiment, which is conducted toward the end of this study.To validate the reliability of the one-way CFD-DEM coupling method and corroborate the relationship between the sand-retaining position and the antiblocking performance of the unconsolidated PPGS, a compact sand control apparatus was employed to investigate the influences of several factors on the obstruction of the unconsolidated PPGS.Although certain preliminary assumptions were made in numerical simulations to reduce computational expenses, the principles of sand control within the simulation remained aligned with those in the experimental process.This alignment ensured the numerical and experimental results accurately represent the genuine sand control.To facilitate a comparison between the numerical simulation outcomes and the experimental findings, the data from both sources were normalized.This approach facilitated a coherent evaluation and assessment.The specific experimental process unfolds as follows.

| Experimental method
A small-sized sand control simulator (Figure 12) was introduced to determine the pressure drop through the sand control screen during the SRT test.Figure 13 shows the schematic diagram of the experimental setup.The apparatus comprises five main parts: (1) clean fluid (oil) injection systems, (2) sand slurry mixed systems, (3) SRT cells, (4) measurements and data acquisition systems, and (5) fluid and solid collection and separation systems.This facility, designed to withstand a maximum pressure of 5 MPa, was constructed from transparent perspex featuring an internal diameter of 60 mm, an external diameter of 80 mm, and a length of 40 mm.This facility can accommodate a screen with an effective diameter of 40 mm.For pressure drop measurements, three high-precision pressure transducers (Figure 13), sourced from Jiangsu Abbreviations: CFD, computational fluid dynamics; DEM, discrete element method.
F I G U R E 9 Experimental model of unconsolidated prepacked gravel screens under different packing rates.
MA ET AL.
| 991 Lianyou Scientific Research Instrument Co., Ltd., were used throughout the test.The small-sized sand control simulator features three pressure points.The first pressure point is on the external surface of the protective screen.The second pressure point is placed on the internal surface of the outer protective screen.These two pressure points are designed to measure the pressure drop due to the plugging of the outer protective screen over time.The third pressure point is set on the surface of basis pipe.The last two pressure measurement points are used to determine the pressure drop caused by the blockage of the sand-retaining medium.The combination of these three pressure points facilitates the analysis of the plugging position and calculation of the permeability coefficient of the sand-retaining media.More detailed information on the facility and experimental procedures are discussed in the authors' previous publication. 53

| Test specimen processing
Careful handling of the test specimen is crucial for the success of the characterization work in the laboratory.In this study, a small-scale SRT cell (Figure 14) was processed.
The screen area of the small-scale SRT cell is 28.26 cm 2 .Figure 14 shows that a mechanical vibration device was used to fill gravel at different filling rates in the sand control unit by varying the frequency and amplitude (Figure 15).Additionally, five sand samples and one gravel sample were used in the experiment.The particle size distribution of sand and gravel is also illustrated in Figure 16.
F I G U R E 10 Sand migration in unconsolidated prepacked gravel screens.

| Calculation of the oil recovery index
The oil-production index (OPI) is an essential parameter for evaluating the antiblocking performance of the sand control screens in the SRT test. 53During the slurry SRT test, parameters such as fluid flow rate, cumulative sand production, and pressure difference across the sandretaining medium are determined over time.Subsequently, the OPI can be calculated according to the following formula: where OPI is the oil-production index per area, m 3 /(m d MPa); Q is the fluid flow rate, m 3 /d; h is the length of the sand control screen, m; ΔР is the production pressure difference, MPa.

| Data processing
In the given context, OPI and R serve as metrics for evaluating a screen's capacity to sustain oil production under conditions of sand production and blockage.OPI provides a quantitative measure where higher values indicate better antiblocking performance, meaning screens with higher OPI values are more efficient at preventing blockages caused by sand production, thus maintaining oil flow.Similarly, in the simulation, R represents the ability of bridging within the gravel layer.A higher R value implies stronger antiblocking performance, whereas a lower R value signifies the punched slot becomes bridged faster, indicating more formation sand particles are trapped on its surface within a brief period.This outcome suggests a stronger sand control performance and weaker the antiblocking ability.To compare the experimental and simulated results, a nondimensional analysis method was employed to compare data in these two distinct units.Nondimensionalization is a valuable tool for comparing data in different units and contexts because it enables the rescaling of variables using their "typical" or representative values.This process facilitates comparing various terms in equations without resorting to specific units.The focus instead shifts toward nondimensional groups such as Reynolds and Prandtl numbers, which are widely recognized and used across a variety of scientific fields.The mathematical method used for nondimensionalization can be represented with the following equation:   Six packing efficiency tests, specifically at 100%, 97.7%, 95.7%, 93.7%, 91.4%, and 85.2%, were conducted to investigate the effect of the gravel packing efficiency on the blocking performance of unconsolidated PPGS.All other test conditions remained constant throughout the DEM simulations.Figure 17 shows the quantity of bridging particles decreases progressively with the increasing packing efficiency of gravel.When the packing efficiency reaches 100%, the percentage of bridging particles migrating into the gravel layer accounts for only about 24%.This result indicates enhancing the packing efficiency of gravel may reduce the size of composite pores formed by gravel and punched slots, leading to the premature bridging of the unconsolidated PPGS.Consequently, silty particles struggle to pass through the blocking zone, especially during the initial stages of production.Conversely, lower packing efficiencies of gravel result in an increase in the number of bridging particles and bridge area within the gravel layer.However, a hole is in the gravel layer when the packing efficiency of gravel reaches 85.2% (Figure 18).This condition leads to an increase in bridge particles migrating toward the model's outlet, thereby escalating the risk of sand production.Controlling sand production is vital to prevent the flow of formation sand into the wellbore.Failure to manage this can lead to problems such as sand jams, sand burial, pump jams, and casing damage.These issues can considerably hinder operations, cause equipment damage, and even result in nonproductive time.Therefore, balancing the packing efficiency of gravel is crucial to ensuring effective sand control while preventing undue blockages or migration of sand particles.On the basis of the above analysis, unconsolidated PPGS displays optimal sand control effects and excellent anticlogging ability when the packing efficiency of gravel remains between 91.4% and 97.7%.The productivity of the oil well using the optimal unconsolidated PPGS can be sustained at an elevated level.The primary mechanism involves slight movement of the gravel when particles are loosely filled into the gravel layer, leading to the destruction of the formed bridge and enabling silty particles to slip away.This phenomenon is referred to as the self-deblocking of unconsolidated PPGS within this paper.

| Effect of D50/d50 on the antiblocking ability of unconsolidated PPGS
Previous studies showed the permeability of the blocking zone is high when the D50/d50 ratio falls within the range of 5-6. 54However, this design principle is inappropriate for unconsolidated PPGS due to differences in screen structure.The sand-retaining accuracy of unconsolidated PPGS can be affected by packing efficiency given its unique structure.To gain a more profound understanding of the internal mechanism, two numerical models of packing efficiency were selected for further analysis.
Figures 19 and 20 illustrate the R and area of bridging within the gravel layer increase as the ratio D50/d50 increases.However, Figure 20B shows when the D50/d50 ratio exceeds 10 and the packing efficiency is at 95.7%, no bridge formation occurs.By contrast, when the ratio D50/d50 is 4, all bridge particles are effectively obstructed on the outer protective shroud, resulting in the retention of nearly all silty particles near the punched slot.On the basis of these observations, the optimal range for the ratio D50/d50 is between 6 and 8 when the packing efficiency of gravel is at 95.7%.This finding suggests the design principle for packed gravel size should be adjusted according to the packing efficiency of gravel, differentiating it from the standard principle used for packing gravel sand control.This crucial conclusion, presented for the first time in this paper, underscores the need for a shift in the design approach when dealing with unconsolidated PPGS.

| Effect of punched slot width on the antiblocking ability of unconsolidated PPGS
As an essential component of the mechanical screen, the outer protective shroud primarily safeguards the sand control medium.The form of the outer protective shroud varies based on the type of sand control medium (Figure 21). Figure 22 shows the flow direction of the fluid dynamically changes in 3D space.This consistent shift of flow direction helps avoid direct influence on the sand medium, thereby preventing fluid erosion.Research indicates particles are less likely to plug the opening when the opening size exceeds twice the particle size. 56,57However, when one side of the outer protective shroud is filled with gravel particles, part of the volume of these particles occupies the punched slot's space.This occupancy leads to a substantial reduction in the slot's flow area.Furthermore, the outer protective shroud is designed to stop gravel leaks, necessitating a punched slot width smaller than the gravel particles' minimum diameter.In conclusion, the size of the punched slot is influenced by several factors, including the size of the sand and gravel and the efficiency of gravel packing.
To examine solely the relationship between sand particle size and gravel size, one side of the outer protective shroud was deliberately left unfilled with gravel.Figure 23 shows that as the ratio of the punching width to median sand size (W/d50) ratio increases, the R curve follows a trend of rising initially and then stabilizing.When the W/d50 is within the range of 1.5-2.6,R shows a substantial growth trend with the increase in W/d50.When W/d50 reaches or exceeds 3, R stabilizes at around 80%. R represents the rate at which a punched slot is bridged.The faster the punched slot is bridged, the more formation sand particles are trapped on its surface within a brief period.Therefore, when the W/d50 falls between 1.5 and 2.6, the bridging rate of the punched slot remarkably changes.A smaller W/d50 indicates a faster bridging of the punched slot, resulting in a larger quantity of simulated sand trapped on the surface within a brief period.However, when W/d50 reaches or exceeds 3, the punched slot size has virtually no effect on R.This outcome signifies that sand particles cannot bridge the punched slot when W/d50 reaches or exceeds 3.In such circumstances, R is primarily influenced by the parameters of the internal gravel.
On the basis of research, a further examination of the impact influence of gravel parameters on R was conducted.Figure 24 shows the R curve exhibits a trend of initially increasing and subsequently decreasing as W/D50 increases.R peaks at W/D50 = 1/2, which can be attributed to two primary factors: • Some gravel particles become embedded within the punched slot when the fracture width exceeds 0.5 times the median value of the gravel particle, resulting in a reduced effective flow space.
F I G U R E 21 Different types of stand control screens: (A, B, H) are premium screens with multiple layers, (D) is a wire-wrapped screen, (E) is a basic screen, (F) is a slotted liner, and (G) is a prepacked screen. 55I G U R E 22 Basic structure of precisely punched screens. 14 The available space between the gravel and punched slot is constrained when W is less than 0.5 times the median value of the gravel particle.
The composite pore size is at its maximum when W equals 0.5 times the median gravel particle value.Moreover, although R peaks when W/D50 = 0.5, it only reaches 55%.In conjunction with Figure 25, the dimensions of the unconsolidated PPGS's external protective shroud are also influenced by the packing efficiency.A higher gravel packing efficiency results in a stronger interaction between the gravel and the punched slot, leading to a larger reduction in the punched slot area.As a result, the sand retention accuracy of unconsolidated PPGS drastically decreases when the packing efficiency is set at 100%.
In conclusion, the width of punched slots in the bridge's outer protective shroud depends on several factors: the size of the sand particles, the size of the gravel used, and the efficiency of the gravel packing process.Moreover, this finding highlights the importance of packing efficiency in determining the overall performance of unconsolidated PPGS.Therefore, to achieve optimal sand control in downhole operations, minimizing gravel packing inefficiencies while still meeting necessary requirements is crucial.

| Verification result
Figures 26-28 display the numerical results regarding the effect of the packing efficiency, the width of the punched slot on the outer protective shroud, and the D50/d50 ratio under a 100% packing efficiency on unconsolidated PPGS performance agree with the experimental results.A strong positive correlation exists between the OPI obtained by experiment and the R obtained by numerical simulation at 100% packing rate.For unconsolidated PPGS, the sand retention location can reflect the anticlogging ability of unconsolidated PPGS.Nonetheless, a substantial discrepancy is observed between the numerical and experimental results when the packing efficiency reaches 95.7%, as demonstrated in Figure 29.The simulation suggests that once D50/d50 exceeds 8, forming stable sand bridges within the gravels becomes challenging for bridging particles, leading to the production of some bridging particles.The preliminary condition that the sand retention position can reflect the anticlogging ability of the PPGS is that the formation sand must be prevented in the first place.When D50/d50 exceeds 8, unconsolidated PPGS does not stop the formation sand.Therefore, the data rule after 8 cannot reflect the anticlogging ability of unconsolidated PPGS.The premise of studying the anticlogging performance of the unconsolidated PPGS is that the unconsolidated PPGS can effectively control sand.When D50/d50 surpasses 8, even if more bridging particles infiltrate the gravel layer, substantial blockage occurs within the gravel, resulting in decreased permeability of the unconsolidated PPGS.This outcome is primarily attributed to the small size of the formation sand particles, which substantially reduces the flow capacity of the bridge layer generated when D50/d50 exceeds 8.This conclusion is similar to F I G U R E 24 Effect of W/d50 on the R of unconsolidated prepacked gravel screens with packing rate 100%.
Saucier's law. 54However, Saucier's law does not apply to PPGS due to differences in sand control principles.
To verify the correlation between the OPI and R of the unconsolidated PPGS in the range of D50/d50 less than 8, experimental and numerical simulation data in this range were selected.Figure 30 shows a strong agreement between the simulation and experimental results after making the data for D50/d50 ≤ 8 dimensionless.This finding further implies that introducing more bridging particles into the gravel layer can be beneficial for mitigating clogging effects when D50/d50 is less than 8.The experimental findings validate that the one-way CFD-DEM coupling approach developed in this paper is effective for analyzing the plugging mechanism of sand control screens.Furthermore, the numerical results are consistent with the experimental data.Simultaneously, these findings suggest the bridge depth or range of formation sand within the gravel layer can serve as a reliable indicator of anticlogging capabilities for unconsolidated PPGS when the gravel-to-sand size ratio falls within a certain threshold (i.e., D50/d50 ≤ 8).To manage plugging issues of unconsolidated PPGS effectively, encouraging more formation of sand is crucial to establishing the sand bridge within the gravel layer whenever possible.

| CONCLUSIONS
The structural parameters of unconsolidated analyzed by a one-way CFD-DEM coupling method to investigate the effects of gravel packing efficiency, the ratio of gravel diameter to sand size, and the ratio of slot width to sand size or gravel size on the antiblocking performance of unconsolidated PPGS.The major conclusions can be summarized as follows: • Lowering the gravel packing efficiency can increase the contact area between the bridging particle and the gravel.This approach enables more formation sand to bridge in the gravel layer, causing silty particles to slip away from the plugging zone and reduce the degree of plugging of the unconsolidated PPGS.Consequently, the selfdeblocking ability of unconsolidated PPGS gradually improves with decreasing gravel packing efficiency.• The design principle of gravel size for unconsolidated PPGS differs from the previous design principle of gravel size in the gravel-packed sand control method.The gravel size used in unconsolidated PPGS must be designed considering the specific packed efficiency of gravel.• Unlike other mechanical screens, the antiblocking performance of unconsolidated PPGS is also influenced by the punched slot on the outer protective shroud.When the slot width is approximately 0.5 times the median value of the gravel particle and 2.6 times more than the median particle size of formation sand, it has the least influence on the flow ability of unconsolidated PPGS.
Physical picture of the unconsolidated prepacked gravel screens.

F I G U R E 4
Prepacked gravel screens sand retention location diagram (red particle represents the sand particles).

F I G U R E 6
Numerical model of the new prepacked gravel screens.F I G U R E 7 Geometry and mesh representation of the computational domain.

Figure 10
Figure 10 illustrates the motion of the bridging particles driven by the fluid, which subsequently become lodged in various locations within the unconsolidated PPGS due to the relationship between the diameters of the bridging particles and gravel particles.Time intervals t1-t2 depict the migration of bridging particles along with the fluid flow.In Figure 10, yellow particles symbolize the gravel particles, whereas purple particles signify the bridging particles.For clear visualization of the bridging particles' position, only the purple particles are displayed during postprocessing.

F I G U R E 8
Fluid flow information in DEM solver.DEM, discrete element method.

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Photo of sand distribution inside and outside punched slot.F I G U R E 12 Physical diagram of sand control simulator. 53MA ET AL. | 993 F I G U R E 13 Schematic diagram of sand control simulator.1, High-pressure plunger pump (LP1010) manufactured from Shanghai Sanwei Scientific Instrument Co., Ltd.; 2, liquid storage tank; 3, vacuum pump; 4, data acquisition systems; 5, slurry mixing device; 6, sanding; 7, sand control simulation unit; 8, measurement system of the outflow with flow ranging from 0 1 to 1 L and accuracy of +0.015%; 9, pressure measuring systems.F I G U R E 14 Processing of the small-scale sand retention test cell.

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Effect of packing efficiency of gravel on the antiblocking of unconsolidated PPGS

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I G U R E 15 Gravel pack vibrator.F I G U R E 16 Particle size distribution of formation sand and gravel.F I U R E 17 Effect of packing efficiency on R.

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I G U R E 18 Position of bridging particles versus packing efficiency.

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I G U R E 19 Effect of D50/d50 on the R of prepacked gravel screens.F I G U R E 20 (A) Sand retention position of the unconsolidated PPGS with 100% filling rate.(B) Sand retention position of the unconsolidated PPGS with 95.7% filling rate.PPGS, prepacked gravel screens.

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Effect of W/d50 on the R of unconsolidated prepacked gravel screens.

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I G U R E 25 Comparison diagram of the interaction between gravel prepack and punched slots at different packing efficiencies.F I G U R E 26 Effect of W/d50 on the antiblocking ability prepacked gravel screens with 100% filling rate.F I G U 27 Effect of packing efficiency on the antiblocking ability of unconsolidated prepacked gravel screens.
Simulation parameters of CFD-DEM.
• The experimental results demonstrate the one-way CFD-DEM coupling method established in this paper F I G U E 28 Effect of D50/d50 on the antiblocking ability of unconsolidated prepacked gravel screens with 100% filling rate.F I G U R E 29 Effect of D50/d50 on the plugging of unconsolidated prepacked gravel screens with 95.7% filling rate.I E 30 of D50/d50 on the plugging of unconsolidated prepacked gravel screens with 95.7% filling rate.