Selection Results of Solid Material for Horizontal and Highly-Deviated Well Completion Gravel-Packing: Experiments, Numerical Simulation and Proposal

Abstract

Lightweight and ultra-lightweight solid materials are being used in gravel packing for horizontal wells instead of traditional quartz and ceramsite to decrease the risk of premature plugging and improve packing efficiency. Physical and numerical simulation experiments of gravel packing were conducted to assess the effectiveness of reducing solid material density and investigate its impact on packing and sand control. Packed gravel destabilization experiments highlighted the importance of high-compaction degree packing for effective sand control. Further gravel packing experiments examined the packing performance of different solid materials, revealing that lightweight solids have minimal gravitational deposition effect because their density is similar to the gravel slurry, relying primarily on fluid flow for compaction. The numerical simulation indicated that lightweight ceramsite is unsuitable for horizontal and highly-deviated wells because of its poor compaction degree and sand control, especially with high-viscosity slurry. High-density particles enhance gravitational deposition, improving packing compaction and sand control. Lightweight materials are recommended only when advanced plugging of α wave packing cannot be avoided. In highly-deviated wells, high-density materials significantly improve packing stability and sand control. This study provides clear technical guidelines for selecting solid materials for gravel packing in horizontal and highly-deviated wells.

1. Introduction

Weakly consolidated sandstone reservoirs are one of the main types of hydrocarbon reservoirs that contribute a great amount of natural gas and crude to the energy industry [1,2,3]. Due to the relatively short geological age of this reservoir, the mechanical properties such as bond strength, permeability, and compressive strength of the rock are poor, especially in the development of deep-sea shallow oil and gas wells in this type of reservoir, tend to produce sand along with the fluid when the production parameters achieve a certain critical condition [4,5,6]. For decades, sand control has been the main solution to solve the problem of sand production in weakly-consolidated sandstone reservoirs [7,8,9]. Nowadays, gravel packing has been fully developed as an effective sand control method, not only in vertical wells but also in horizontal and highly-deviated wells, which concerns packing gravel into the annulus between the screen and the open-hole well wall or the perforated casing [10,11,12]. The screen is used to support the packed gravel; meanwhile, the packed gravel mainly undertakes the task of retaining the produced sand from the formation [13,14,15].

As shown in Figure 1, the gravel packing in horizontal wells involves the multiple solid–liquid two-phase coupled flow and sand-bed migration processes under complex conditions, such as inclined wellbore, formation filtration loss, and fluid mass exchange [16,17]. Aiming at the complex flow process, gravel filling mechanism, gravel filling law, and gravel filling design in horizontal wells and large inclined wells, many scholars have carried out a lot of research in the directions of experimental simulation and numerical simulation.

In the physical experimental simulations, Maly et al. found through in-house physical experiments that dunes form in the wellbore when the inclination is greater than 45° [18]. They believed that due to the continuous escape of sand-carrying fluids, the height of the dune gradually increased along the inclined section until the accumulation channel was blocked. They found the phenomenon of sand bridges during gravel filling, but no in-depth study was conducted on the causes and mechanisms of sand bridge formation. Gruesbeck et al. described the gravel-filling process in large inclined wells by carrying out gravel-filling experiments [19], further explained the experimental phenomena found in Maly’s experimental study, and proposed the concept of a ‘balanced dike’ for the first time. Bigna et al. investigated the effects of screen offset, flow rate, and sand content on the equilibrium height of the wave sand layer by using a full-size horizontal well internal circulation gravel filling simulator to address the problems of solid–liquid two-phase flow and sand bed transport under complex conditions during the gravel filling process in horizontal wells or wells with large gradient [20]. Sanders et al. developed an alternative flow path system and verified the feasibility of the alternative flow path concept through small and large-scale experimental tests using equipment ranging in length from 1.524 to 304.8 m [21]. The alternative path allows the slurry to bypass the bridge if one is formed. In wells with low reservoir pressure, the safety window for gravel filling is narrow, and the dynamic pressure during the gravel filling operation can easily overcome the formation fracturing pressure and lead to reservoir fracture. Magalhães et al. proposed a new gravel-filling method by selecting two different proppants for filling [22]. In the α phase, when the filling pressure is low, a conventional density proppant is pumped, and in the β-wave phase, when a larger pressure increase is observed, a lightweight proppant will be pumped. Dong et al. simulated the process of gravel cyclic filling in horizontal wells and large inclined well tubes by using a horizontal well and large inclined well tubes gravel cyclic filling test simulator [23], analyzed the characteristics of α-wave and β-wave filling fronts, and researched the influences of the wellbore inclination angle, screen tubing offsets, flow rate, and sand volume fraction on the filling dynamics and the equilibrium height of the sand bed in α-wave and the mechanism.

Physical modeling studies have significant limitations at the experimental scale and are unable to simulate on-site gravel fill construction conditions accurately. Therefore, many more scholars have devoted great efforts to studying the mathematical description and simulation of the gravel packing process in horizontal wells [24,25,26].

In numerical simulations, since the 1970s, many scholars have begun to study the numerical modeling of gravel filling in horizontal wells. Gruesbeck et al. first put forward the concept of ‘equilibrium dykes’ based on the gravel filling process observed in the indoor test [19] and established a mathematical model for the inclined wells and horizontal wells in the case of complete filling. This model can be used to calculate the equilibrium height of the sand bed in a gravel-filled wellbore/screen tube annulus, but it cannot be used to plug in advance, nor can it simulate the whole filling process. Peden et al. extended the ‘equilibrium sand bed’ theory [27]. The semi-empirical formulae for predicting the filling rate of the screen tube/well simple annulus and shot hole aperture were obtained by using the method of magnitude analysis and fitting of experimental simulation results. The accuracy of the calculation is largely dependent on these experimental data and the limitation of experimental conditions, and the results of the calculation are not stable. A real-time numerical study of gravel filling in horizontal wells was carried out systematically [28]. They established a model for calculating the height of the equilibrium sand bed based on the probabilistic change in the limit state of particle movement on the sand bed surface. According to the theory of water turbulence, a set of theories and methods of stochastic analysis was proposed to study the particle motion state on the sand bed surface and the change rule of sand bed height. A three-dimensional mathematical model for gravel filling was established, considering the difference between gravel particles and sand-carrying liquid when solid–liquid flows in the annulus, and introduced the concept of deposition factor [29,30,31,32]. The model overcomes the shortcomings of one-dimensional and two-dimensional models, fully considers the effect of solid particle deposition when the mortar flows in the annulus, and reasonably predicts the concentration of in-situ gravel during the filling process so that the equilibrium height of the sand bed can be calculated more accurately. Bai et al. established a time-dependent mathematical model describing the α-filling process based on the equations of conservation of mass and momentum of sand and liquid in two independent flow systems of the wellbore and the rinse screen annulus [33] and the flow coupling equations between the systems. The entire filling process can be simulated visually using numerical model development software. Mimouna et al. achieved this by solving the mass and momentum conservation equations for the fluid [34] and gravel by interleaving them, taking into account the well, the downhole tool tubing column structure, the fluid and gravel properties, and the pumping time. The simulation predicts changes in fluid pressure as well as gravel concentration over time. Changes in gravel concentration provide reliable data on filling patterns and operational filling states. Sarraf Shirazi and Frigaard investigated and explained [11] the filling process of α-wave and β-wave by developing a mathematical model of gravel filling. The effects of important parameters such as mud flow rate, average solids concentration, flushing pipe diameter, and leakage rate on gravel filling flow were also investigated. Huang et al. proposed a design calculation method for α–β wave filling length considering the success of α-wave filling and the success of β-wave reverse filling [35]. The corresponding software was prepared to discuss and calculate the quantitative analysis of the factors affecting the α–β wave filling length, such as the density of sand-carrying liquid, gravel density, and wash pipe sieve ratio. Under specific conditions, certain criteria and methods can be used to design and optimize the gravel filling length of horizontal wells. Nie et al. made a detailed analysis of the whole process of gravel filling flow in horizontal wells [36], established a three-dimensional numerical model of gravel filling, and carried out several sets of gravel filling experiments to verify the improved three-dimensional numerical model.

These numerical simulation results enhance the understanding of the law of the influence of pumping parameters on filler performance and filler efficiency. Gravel packing efficiency is a key parameter that significantly affects the effectiveness of gravel packing against sand. However, in horizontal wells and large gradient wells, the high-density gravel material may lead to early sand plugging and reduce the gravel filling compactness because it tends to deposit solid particles in the fluid. Engineers are now gradually applying lightweight or ultra-lightweight gravels in horizontal packings [37,38,39,40], which reduces the risk of premature plugging during operations. The use of lightweight or ultra-lightweight materials as gravel for horizontal good gravel packing has almost become a trend to extend the length of horizontal good gravel packing, widen the safe operating window for gravel packing, and reduce the hazards to the reservoir. However, there is a lack of effective evidence on whether the use of light or ultra-light materials can really improve the effect of gravel packing. Therefore, this paper will study a selection of gravel packing materials for horizontal wells and highly deviated wells.

2. Methodology

This paper adopts a method combining physical experimental simulation and numerical simulation to carry out research. Figure 2 shows the methodology and approach. Numerical simulation experiments overcome the problem of small-scale indoor physical simulation experiments. Indoor physical simulation experiments can supplement and verify the results of numerical simulations and improve the accuracy and reliability of numerical simulation results.

(1)

The density of gravel packing affects the instability morphology of the gravel layer. First, an indoor physical simulation experiment of gravel layer instability is carried out to study the law of gravel layer instability under different gravel packing density conditions.

(2)

However, the density of gravel packing is affected by the type of gravel packing. Therefore, an indoor physical simulation experiment of horizontal well gravel packing is carried out. Based on the results of indoor physical simulation experiments, the type of gravel packing material is preliminarily selected to improve the density of gravel packing.

(3)

The scale of indoor physical simulation experiments is small and cannot simulate the gravel packing process in actual oil wells. Therefore, based on the actual oil wells in a certain oil field, a numerical simulation study of gravel packing is carried out. Based on the results of numerical simulation experiments, the types of gravel filling materials are selected for horizontal wells and highly deviated wells, respectively.

(4)

Finally, the types of gravel filling materials are selected by combining the results of physical experimental simulation and numerical simulation, and construction suggestions are put forward for on-site gravel filling of horizontal wells and highly deviated wells.

3. Packing Gravel Instability Experiment

3.1. Methods and Materials

To accurately replicate the production conditions of gravel-packed wells, a comprehensive visualized gravel-packed production simulation experiment system has been carefully constructed (Jiangsu Tuochuang Technology Co., Ltd., Nantong, China). The experimental system is mainly used to simulate the morphological changes in the gravel layer after filling operation in the production process after being carried by fluid impact, and its flow is shown in Figure 3a. The experimental apparatus comprises a fluid tank, a screw pump, a primary container, as well as a comprehensive data acquisition and control system. The experimental setup can be flexibly assembled with different main containers to conduct different experiments. Containers AB are two different main devices; container A is a simulated vertical wellbore, and container B is a simulated horizontal wellbore. The main container A has an inner diameter of 0.3 m, which can accommodate a short section of the screen with a length of 0.245 m; Unit B, with an inner diameter of 0.22 m, is designed to house a sand-proof screen pipe that is 1 m long and measures 0.1 m diameter. Additionally, a clamping mechanism is installed at both ends to prevent any radial displacement of the screen when it is inserted into the main apparatus.

For the experiments, samples from screens commonly used in oilfield construction were placed into the main device, making sure that both ends of the screen were sealed to both sides of the device. Different types of filler particles were used to fill the cavities formed by the screen and the outer wall of the device (simulated casing) according to the densities set in the experimental conditions. The filling materials used in the experiment are normal quartz sand and ceramsite with a diameter of 0.424–0.85 m. Fluid was injected into multiple inlet ports along the sidewall of the device using the same discharge volume, and the pressure, flow rate, and particle accumulation pattern over time were recorded and photographed in real-time by a data acquisition system to simulate the production process. Based on the equivalent flow rate method, the experimental flow rate is converted into 2 m³/h according to the actual production of the oil well. All test data and images were used for further analysis of the formation process and morphology of the erosion holes in the gravel layer.

3.2. Results and Discussion

Using the above apparatus and methods, the simulation experiments were carried out around the gravel-packed layers formed by different types of particles, and the gravel-packed densities were set to 95%, 96%, 98%, and 100%. Figure 4 and Figure 5 show the erosion and sediment intrusion patterns of the quartz sand and ceramsite particle-filled layer under the impact of local high-flow rate load fluids.

As evident from Figure 4, the degree of filling compactness significantly influences both the stability of the gravel layer and the patterns of intrusion and plugging exhibited by the formation sand when subjected to local high-flow velocity fluid impact conditions. When the compactness is 100%, as shown in Figure 4a, the space for sliding and displacement between quartz sand grains is very limited. The impact and carrying action of the fluid are counteracted by the tightly arranged grains, and only a small portion of the gravel layer is displaced to form holes. When the formation sand intrudes with the fluid, it can only be transported between the pores of the quartz sand body, and no new transport channel can be generated. When the intrusion reaches a certain depth, with a reduction in the sand-carrying capacity of the fluid and the accumulation of sand clogging, resulting in the subsequent strata sand being difficult to intrude further, the intrusion behavior is close to stagnation.

Moreover, with a decrease in filling compactness, as shown in Figure 4b–d, the quartz sand particles are no longer tightly stacked with each other. The particles are displaced by the impact of high-flow fluid, which produces large holes near the inlet, and the holes eventually extend to the screen with the prolongation of production time.

In addition, when the fluid carries the formation of sand intrusion, as the pressure of the intruding fluid increases, when it exceeds the original stabilizing force between the quartz sand grains, the quartz sand grains are disturbed and thus rearranged. The pressure change causes the formation sand to squeeze out new flow channels and allows deeper intrusion, which is why the formation sand is able to contact the screen in Figure 4d–h.

It can be found that the same pattern is observed when ceramsite grains are used as filling materials. It is worth noting that when the fluid carries the formation of sand to invade the packed layer, the fluid always preferentially breaks along the stress weak point of the filling zone. In the experiment shown in Figure 5, the weak stress direction is axial, so the erosion holes along the axial direction formed first. Subsequently, the holes gradually developed radially toward the screen until the edges of the holes contacted the screen and expanded.

Using the main container B in Figure 3 to simulate the gravel-packed layer of a horizontal well to carry out simulation experiments, it can be found that under different inflow angle conditions, the noncompact filling layer produces erosion holes. Figure 6 shows the changes in the erosion cavity of gravel packing layers in horizontal wells under different levels of gravel compaction degree.

The erosion dynamics in the lower and middle part of the simulated wellbore near the lateral inlet are the same as that of the vertical well, which first expands along the weak stress area and then extends in the radial direction after formation. The cavity near the inlet at the top of the simulated wellbore is in the shape of a regular trumpet, which is affected by the gravity effect of ceramsite grains, and it is difficult for the local high-flow rate fluid to break through the gravel layer directly, and the formation sand can still be blocked by the gravel layer after erosion.

4. Gravel-Packing Experiments

4.1. Method and Materials

In order to simulate the dynamic process of gravel packing in horizontal wells and large inclined wells, a large-scale visual gravel packing simulation experiment system was built (Jiangsu Hua’an Technology Co., Ltd., Nantong, China). The experimental system mainly clarifies the transportation and accumulation patterns of different types of particles inside the annular space between the screen and casing, as well as the final filling effect, and its process and device objects are shown in Figure 7. The apparatus mainly includes a liquid storage tank, screw pump, sand filler, sand collector, main device unit, data acquisition and control system, and so on. The simulated wellbore has an inner diameter of 250 mm and a length of 10 m. It is capable of accommodating standard screen tubing actually used in oilfield production sites. In this study, a 5 in screen pipe with a length of 9.5 m and a flushing pipe with an outside diameter of 63 mm and a length of 8.5 m were used to simulate the gravel filling process by allowing the load fluid to enter through an inlet at the root end of the wellbore, located below the screen pipe.

The flow rate is set as 21 m³/h, and the sand-carrying fluid is clean water with a viscosity of 1 mPa·s and a sand ratio of 5% in the gravel packing experimental. The gravel packing simulation is carried out using different types of particles according to the set discharge volume and sand ratio. The gravel particles are carried and mixed uniformly by the experimental fluid into the annulus of the screen sleeve, the gravel particles are blocked by the screen and retained in the annulus, and the liquid is returned to the tank through the wash pipe, forming a cyclic packing process. During the experiment, the movement state and overall morphology of the sand bed formed by gravel deposition were recorded. The experimental pressures and discharges were collected to analyze the filling dynamics of different types of gravels and the final filling effect.

Three types of gravel particles were used in this paper (Beijing Qixiang Ceramic Materials Co., Ltd., Beijing, China), including conventional ceramsite particles (Figure 8a), lightweight ceramsite particles (Figure 8b), and ultra-lightweight ceramsite particles (Figure 8c), with apparent densities of ceramicite particles of 2.76, 1.92, and 1.00 g/cm³, and stacking densities of 1.49, 1.31, and 0.62 g/cm³, respectively. The diameters of the three types of particles were 0.425–0.850 mm (

Table 1. The parameters differences of different packing materials.

Type	Apparent Density/g/cm3	Stacking Density/g/cm3	Diameter/mm
Normal Ceramicite	2.76	1.49	0.425–0.850
Light Ceramicite	1.92	1.31	0.425–0.850
Ultra-Light Ceramicite	1.00	0.62	0.425–0.850

).

4.2. Results and Discussion

4.2.1. Basic Packing Process Analysis

In the simulation experiment of the gravel packing process in horizontal wells, the filling process of conventional and lightweight ceramicite grains all showed obvious α and β waves. During the filling process, the sedimentary sand bed extends along the direction of fluid flow, but the closer the inlet is, the stronger the effect of fluid turbulence is, which leads to the inability of ceramicite grains to accumulate. Therefore, during the α-filling stage, there is a section of unfilled area between the inlet and the sedimentary sand bed, as shown in Figure 9a. The density of lightweight ceramicite grains is closer to that of the load fluid, so they are more easily carried by the load fluid of the same viscosity and displacement during the filling process. The fast transportation speed of the lightweight ceramicite grains α-wave deposited sand bed makes the angle between the front section of the sand bed and the horizontal plane larger, as shown in Figure 9b,d.

Under the same discharge and sand-carrying fluid conditions, the low-density ceramicite grains were transported over a long distance, showing an overall transport but not accumulation filling trend.

Influenced by the density difference between particles and load fluid, more particles are transported or floated into the same filling space during the filling process of lightweight ceramicite grains. A stronger fluid-carrying effect and weaker gravity deposition prevent lightweight ceramicite grains from forming dense deposits during the filling process. In the formation of β-wave filling, the height of the conventional ceramicite grains deposited sand bed is higher, the angle of the β-wave front is small, the backfilling speed is fast, and the fluid impact and compaction effects are strong, which can further enhance the dense degree of gravel packing, as shown in Figure 10c,d. Among them, Figure 10b is the filling state near the end of the β-wave filling, so the sand bed has a larger angle along the front edge, which is not contrary to the above analysis.

Figure 11 shows the changing curves of packing pressure and flow rate during normal ceramsite packing. The test process shows that in the α-wave filling stage, the filling flow rate and filling pressure are relatively stable as the filling sediment bed advances. When entering the β-wave filling stage, as the distal end of the filling port gradually becomes dense, the channel for sand-carrying liquid to return to the bed gradually decreases, and the flow resistance increases, which is manifested as a significant increase in the pressure and a decrease in filling displacement. When the β-wave is about to reach the filling port, in order to prevent the damage of the filling tool caused by excessive pressure and the disturbance of the filled area, the final desanding is achieved by decreasing the displacement, and with an obvious increase in the filling pressure, it is proved that the grains carried by the β-wave have reached the filling port, and the filling test is finished.

In the horizontal well circulation filling process, the load fluid and the filled ceramicite particles enter the annular cavity formed by the screen and the well wall through the filling port and are transported to the outside of the screen. The filled ceramicite particles are blocked by the screen pipe from entering the annular cavity of the screen pipe and wash pipe, while the load fluid without ceramicite particles enters the annular cavity of the screen and wash pipe and finally enters the inlet at the bottom of the wash pipe, and then flows back to the wellhead.

The filling process is generally divided into α-wave filling (Figure 12a) and β-wave filling (Figure 12b). During the α-wave filling, the ceramicite grains preferentially accumulate at the bottom of the annulus between the screen and the well wall and gradually push the sedimentary sand bed along the axial direction toward the end of the well bottom. After the front edge of the sand bed touches the bottom of the well, β-wave filling follows, and the ceramicite particles in this process will fill the cavity between the deposited sand bed and the top portion of the well wall until the end of the desanding pressure is reached when the ceramicite particles pile up in the vicinity of the filling port.

4.2.2. Packing Performance with Different Solid Materials

The apparent density of the filled ceramic grains has a significant effect on the filling effect. As can be seen in Figure 13, taking the α-wave filling process as an example, as the density of the filled ceramic grains decreases, their gravitational deposition effect is relatively weak or even absent, so it takes longer time to reach the closed-loop pressure of the α-wave, which is also confirmed by the pressure curve in Figure 13b. Compared with the conventional ceramic grains with a density of 1.49 g/cm³ that reach the closed-loop pressure of the α-wave in 800 s, the ultralight ceramic grains need a time of 1700 s, which more than doubles the time and reduces the construction efficiency. Especially in the high-viscosity sand-carrying liquid, the ultra-lightweight ceramic particles are easily carried and disturbed, the original filling structure is destroyed, resulting in the filling compactness can not be guaranteed.

Comparing the phenomena during the filling process of the three different densities of vitrified gravel, it can be found that the ultra-lightweight vitrified grains are similar to the density of clear water because the apparent density is close to 1 g/cm³. Therefore, the stratification is obvious in the α-wave filling stage (Figure 14), with a suspended layer at the bottom and a sedimentary layer at the top with a flow zone in the middle, which is opposite to the phenomenon of conventional ceramicite gravel packing.

Since the accumulation of gravel is only supported by the buoyancy of the loaded liquid, and the filling effect cannot be further enhanced by the impact compaction of the liquid and gravity, the accumulation of gravel is less dense than that of the other two densities of gravel. The gravel layer with low density has poor stability and is prone to erosion holes, so the formation sand invades the screen directly, which is not conducive to the stable production and control of sand for a long period of time.

When the filling process of β-waves is carried out, the sedimentary surface of the sand bed of ultra-lightweight ceramicite grains is extremely irregular under the scouring effect of the impact, while the surface of the sand bed of lightweight, conventional ceramicite grains is more regular, which is conducive to the improvement of the final filling and densification degree (Figure 15).

Comparing the phenomena during the filling process of three different densities of vitrified gravel, it can be found that when using normal ceramsite and lightweight ceramsite for gravel filling experiments, the density of ceramsite is greater than the density of water. During the α wave filling process, most of the ceramsite is deposited at the bottom of the wellbore under the action of gravity and gradually forms a sand bed. Under the carrying effect of the mortar, the sand bed gradually moves forward (Figure 14a,b).

The ultra-lightweight vitrified grains are similar to the density of clear water because the apparent density is close to 1 g/cm³. Therefore, the stratification is obvious in the α-wave filling stage (Figure 14c,d), with a suspended layer at the bottom and a sedimentary layer at the top with a flow zone in the middle, which is opposite to the phenomenon of conventional ceramicite gravel packing. Since the accumulation of gravel is only supported by the buoyancy of the loaded liquid, and the filling effect cannot be further enhanced by the impact compaction of the liquid and gravity, the accumulation of gravel is less dense than that of the other two densities of gravel (Figure 16). The gravel layer with low density has poor stability and is prone to erosion holes so that the formation sand directly invades the screen, which is not conducive to the stable production and control of sand for a long period of time.

The dynamic filling process of ultra-lightweight ceramicite is different compared with conventional ceramicite filling because of its weak gravity effect (Figure 17). In the α-wave filling stage, most of the ultra-lightweight particles are in suspension, making it difficult to achieve effective sand control with low-density filling. Only in the β-wave filling stage, under the action of fluid pressure, the reverse accumulation and the accumulation surface are gradually pushed to the filling mouth, showing the full β-wave filling pattern.

5. Numerical Simulation Analysis

5.1. Numerical Model and Simulator

Well A is an open-hole horizontal well in the CB field with a reservoir of loose sandstone that requires a gravel-filled, sand-proof completion. The main borehole size of Well A is 152.4 mm, the drilling depth is 2060 m, and the maximum inclination angle is 91.0°. The starting depth of the filling tool is 1784 m, and the filling length is 276 m. The screen size is 124 mm, and the wash pipe size is 73.0 mm. A circulating gravel filling simulation calculation is carried out for Well A. The filling material is 0.4–0.8 mm ceramic grains, the apparent density is 2.5 g/cm³, the viscosity of load liquid is 1.5 mPa·s, and the density is 1.0 g/cm³. Based on basic data from Well A, the calculation is made by a simulator. Visualization of gravel filling dynamic process in horizontal wells as shown in Figure 18.

The simulation results show that complete filling can be achieved using a combination of ceramicite with an apparent density of 2.5 g/cm³ and 1.5 mPa·s load liquid. No early blockage occurred during the filling process, and the filling rate was 100%.

However, from Figure 18c, it can be found that when the α-wave filling stage is about to end, and the leading edge of the deposited sand bed contacts the bottom of the artificial well, the height of the deposited sand bed is too high, the overall slope of the sand bed is large, and there is a risk of forming an early blockage, and the safety of the filling process is low. In addition, from Figure 18b, it can be found that the formation location of the sedimentary sand bed in the α-wave filling stage is far away from the inlet, about 85 m, which leads to a longer travel time in the final filling stage of the β-wave, as shown in Figure 18e,f. In this stage, the ceramicite is carried by the fluid and impact to complete the filling, and the gravity effect is difficult to play a real role, which hinders the further improvement of the filling degree of compactness. The filling parameters of Well A still need to be optimized.

5.2. Sensitivity Analysis

5.2.1. Solid Material Density

Based on the above calculation results, by changing the apparent density of ceramicite, the filling rate index was analyzed to determine the filling process stability and safety index. A comprehensive analysis was conducted to obtain the comprehensive filling effect evaluation index and establish different filling particle densities under the filling evaluation index plate, as shown in Figure 19.

Packing ratio index: the ratio of the actual filling volume to the theoretical filling space volume, which evaluates the degree of annular filling at the end of filling.

$${\mathsf{\Psi }}_p={\displaystyle \frac{V_A}{V_T}}$$

(1)

where ${\mathsf{\Psi }}_p$ is the packing ratio index, dimensionless; $V_A$ is the actual filling volume, m³; $V_T$ is the theoretical filling volume, m³.

Packing stability index: used to evaluate the safety and stability of the α wave packing process. Specifically, the change in sand bed height per unit length of sedimentary sand bed extension indicates that the higher the safety evaluation index of the filling process, the better the filling effect.

$${\mathsf{\Psi }}_{Hb}=1-{\displaystyle \frac{R_W-H_b}{R_W}}$$

(2)

where ${\mathsf{\Psi }}_{Hb}$ is the packing stability index, dimensionless; $R_W$ is the inner diameter of the casing or wellbore, m; $H_b$ is the final equilibrium height of the sand bed, m.

Comprehensive index: comprehensively evaluates the final effect of gravel packing. It is calculated by weighting the packing process safety and packing rate evaluation indicators.

$$V={\alpha }_{Hb}{\mathsf{\Psi }}_{Hb}+{\alpha }_p{\mathsf{\Psi }}_p$$

(3)

$${\alpha }_p+{\alpha }_{Hb}=1$$

(4)

where $V$ is the comprehensive index, dimensionless; ${\alpha }_{Hb}$ is the weighted coefficient of balanced height evaluation indicators, dimensionless; ${\alpha }_p$ is the weighted coefficient of the filling rate evaluation index, dimensionless.

According to the calculation results, it was found that the filling evaluation indexes decreased when the density was less than 1.4 g/cm³, which indicated that ultra-lightweight ceramicite was not necessary for conventional gravel filling of horizontal wells.

Adjusting the density of ceramicite in a reasonable range enables the formulation of an optimal load fluid to obtain a higher sand control capacity after filling while ensuring the filling effect. Therefore, the optimal density of filled particles is recommended by the platen to be between 1.4 and 2.5 g/cm³.

5.2.2. Fluid Viscosity

The viscosity of the load fluid was taken as the sensitivity factor and the change rule of each index was analyzed.

Through sensitivity analysis, the filling evaluation index plate under the influence of sand-carrying fluid viscosity was established, showing that when the viscosity of sand-carrying fluid is 6~10 mpa·s, the balance between the sand-carrying effect and sand-sedimentation effect is reached, which meets the construction requirements of high filling rate for the long horizontal well section, and the comprehensive filling evaluation effect is the best (Figure 20).

5.2.3. Discussion

Through simulation experiments, the changes in the erosion pattern and the dynamics of intrusion of formation sand particles under the action of local high-flow velocity fluids during the production process of gravel layers of different densities are analyzed. The dynamic process of gravel filling with different densities of ceramicite and its differences are clarified. Based on the experimental results, a numerical model and simulation software were developed to reveal further the sensitivity law of solid and load fluid properties.

In order to obtain a high sand control effect, it is an important condition to improve the compactness of the gravel layer. Under the impact and disturbance of local high-flow velocity fluid, large holes are easily eroded in the uncompacted gravel layer. After the holes are created, the sand particles produced by the formation will invade the screen along the holes quickly, causing serious blockage of the screen, or even pass through the screen directly and produce to the ground with the fluid. The gravel layer with a high degree of compactness, whether it is localized high-flow velocity fluid or low-velocity fluid, can not erode and penetrate the gravel layer, forming large holes. Fluid scouring can only slightly change the accumulation pattern on the surface of the gravel layer, and a small portion of the sand produced from the stratum intrudes into the interior of the gravel layer, while most of the sand particles are blocked on the surface of the gravel layer. The high-density gravel layer maintains a good sand control effect during the whole production process.

For different densities of ceramicite, the filling process of horizontal well gravel is simulated experimentally. For lightweight and conventional ceramicite, there are clear α-wave and β-wave filling processes in the filling process, while this process is not obvious in the experiments of ultra-lightweight ceramicite. In the filling process, the α-wave filling can make full use of the gravity deposition effect to improve the density of the whole filling process, and affected by the density difference between the particles and the load fluid, more particles were transported or floated in the same filling space during the filling process of lightweight and ultra-lightweight ceramicite. The stronger fluid-carrying effect and the weaker gravity deposition effect make the lower-density ceramicite unable to form dense deposition during the filling process. This problem is particularly evident when filling with ultra-lightweight ceramicite, which, at the end of the α-wave filling, differs from other ceramicites in that the ceramicite forms a suspended sand bed. At the β-wave filling stage, the front surface of the sand bed of the ultra-lightweight ceramicite is extremely irregular under the scouring effect of the fluid. In contrast, the sand bed surface of the lightweight, conventional ceramicite was more regular, which was favorable to improving the final filling densification. Under the displacement range of the simulation experiments, the degree of filling compaction decreased with a decrease in ceramicite density.

For high-angle wells, since the wellbore has a certain downward deflection angle, the gravel particles can reach the bottom of the well smoothly with the fluid, and it is almost impossible to form a sedimentary sand bed, and basically, there is no α-wave filling. Early plugging rarely occurs in gravel filling operations in high-angle wells, so the use of gravel with higher density can further enhance the gravel layer densification to obtain a high sand control effect.

Based on the experimental results, a numerical model and simulation software were developed to calculate the process and effect of gravel filling based on data from actual production wells and to analyze the sensitivity between ceramicite density and the viscosity of load fluid. The simulation results show that adjusting the gravel density within a reasonable range can safely and stably complete the gravel filling operation so that the filling rate reaches 100%. The ultra-lightweight ceramicite was not within the recommended range. The use of ultra-lightweight ceramicite is rare and only applies to the situation where premature clogging of α-wave filling cannot be avoided even after all construction parameters are optimized.

Although this article conducted simulations based on data from actual production wells and carried out large-scale physical modeling experiments, the relevant understanding has not yet been validated in actual production. Subsequently, it is necessary to combine filling data from multiple different well types to optimize understanding gradually.

6. Recommendations and Conclusions

In the case of high velocity of inflow from formation to the wellbore, the restructuration destabilization of packed gravel is easy to take place, leading to the form of the cavity, which emasculates the sand retention function of the packing gravel layer. Therefore, how to improve and ensure the compaction degree of packing gravel is absolutely a considerable issue to achieve the desired sand control effect. Through experiments and simulations, the results indicate that:

(1)

For gravel-packing in highly deviated wells, due to the deviated wellbore and direction of downward flow, α wave packing can hardly happen. The premature plugging almost won’t happen during the job. Therefore, the usage of high-density solid material can obviously improve the compaction of packing and help to ensure the stability of the packing layer and the effect of sand retention.

(2)

In horizontal gravel-packing, which involves α and β wave packing, the gravitational effect of solid material really helps to improve the compaction of packing. So, the utilization of high-density particles favors strengthening the effect of gravity deposition obviously and resultantly improves the effect of sand retention during production.

(3)

The density of light or ultra-lightweight solid ceramsite is close to, even smaller than, the density of normal-used carrier fluid. In this case, the effect of gravitational deposition is extremely weak even negligible, which does no favor to the compaction during packing. The compaction degree depends on only the compact of fluid flowing. From the perspective of compaction and sand retention, light and ultra-lightweight ceramsite are not a good choice for horizontal and highly-deviated gravel packing, especially in the case of using high-viscosity fluid. The lightweight solid material will be recommended for use only in one situation, under which the premature plugging of α wave packing can not be avoided under all of the parameters optimization.