Modeling of Erosion in a Cyclone and a Novel Separator with Arc-Shaped Elements

: Modeling of the separation of catalyst particles from gas using two devices, a cyclone and a novel separator with arc-shaped elements, was performed for ﬂuidized-bed dehydrogenation of C 4 –C 5 parafﬁns to isooleﬁns as an example. The proposed dust collector allows one to reduce erosive wear by several times (~6.5-fold) in identical regimes and at identical parameters of the process. The effect of particle size on erosive wear was analyzed under near-industrial conditions; the regions most susceptible to wear in the analyzed devices were identiﬁed, as well as the functions describing the dependence between the erosive wear rate and particle diameter for the cyclone and separator with arc-shaped elements, making it possible to predict wear in the devices were obtained.


Introduction
Petrochemical companies are paying much attention to the improvement of equipment reliability, reduction of operating expenses, and equipment maintenance. It is particularly relevant for existing dust collection systems [1][2][3][4][5][6][7][8][9], where the fundamental components are cyclones characterized by relatively high performance, as well as simple operating principle and design. Their drawbacks include the relatively high hydraulic drag and susceptibility to abrasive wear of the walls [5][6][7][8]. Thus, cyclones used for coarse and medium-degree gas purification are commonly used in petrochemistry for production lines performing fluidized-bed dehydrogenation of C 4 -C 5 paraffins to isoolefins. A typical feature of these cyclones is that the contact between particles and cyclone walls alters the fractional size distribution of the catalyst due to particle crushing and abrasion [9][10][11][12].
Erosion affecting the upper inlet section and the lower cone of the cyclones is one of the most common problems related to this type of cyclone. F. Fulchini [13] identified the highest-stress areas in the fluidized bed where mechanical strain causes particle abrasion: gas dispensing nozzles, the bubbling layer, cyclones, and bending sections. They also suggested that each of these abrasion sources should be analyzed individually, as there are different abrasion mechanisms (surface abrasion, chipping, and fragmentation). A combination of particle properties and operating conditions, as well as device geometry, are responsible for the predominating mechanism [14][15][16][17]. J. Werther and J. Reppenhagen [18] mentioned that the cyclone is one of the most significant factors contributing to particle abrasion, especially at high flow rates of the surface gas. J. Werther et al. [19] proposed a model of particle abrasion caused by cyclones under conditions of surface particle abrasion for catalyst particles in fluid catalytic cracking (FCC). An analysis of the results revealed that the abrasion rate depended on the material properties, kinetic energy of the gas, and particle size. J. Reppenhagen et al. [20] tested the model reliability by analyzing  The operating principle of a cyclone is widely known. The dust-laden flow enters the chamber through the inlet (1). The dust-laden medium then moves with a tornado-like helical flow pattern. Centrifugal forces make particles leave the flow and collide with the internal wall of the cylindrical cyclone body. The particles then fall into the hopper through the orifice (2). The purified gas leaves the cyclone through the outlet of the dipleg (3) submerged into the cyclone to a certain depth ( Figure 1).
The separator with arc-shaped elements has a simple design: it consists of several rows of arc-shaped elements (2) enclosed in the body (3) having a rectangular trapezoid shape. The arc-shaped elements inside the SAE are arranged at an angle of 30°, thus ensuring identical flow motion. To prevent loosening of the arc-shaped elements (2) as the gas flow moves, they are attached to the separator body on both sides. In the upper part

Experimental Procedure
A standard device for collecting solid particles, the centrifugal cyclone (TsN-15), that is employed for the dehydrogenation of isoparaffins at petrochemical plants (Figure 1), and the novel separator with arc-shaped elements proposed for replacing the conventional cyclone were used to study the erosive wear ( Figure 2).  The operating principle of a cyclone is widely known. The dust-laden flow enters the chamber through the inlet (1). The dust-laden medium then moves with a tornado-like helical flow pattern. Centrifugal forces make particles leave the flow and collide with the internal wall of the cylindrical cyclone body. The particles then fall into the hopper through the orifice (2). The purified gas leaves the cyclone through the outlet of the dipleg (3) submerged into the cyclone to a certain depth ( Figure 1).
The separator with arc-shaped elements has a simple design: it consists of several rows of arc-shaped elements (2) enclosed in the body (3) having a rectangular trapezoid shape. The arc-shaped elements inside the SAE are arranged at an angle of 30°, thus ensuring identical flow motion. To prevent loosening of the arc-shaped elements (2) as the gas flow moves, they are attached to the separator body on both sides. In the upper part The operating principle of a cyclone is widely known. The dust-laden flow enters the chamber through the inlet (1). The dust-laden medium then moves with a tornado-like helical flow pattern. Centrifugal forces make particles leave the flow and collide with the internal wall of the cylindrical cyclone body. The particles then fall into the hopper through the orifice (2). The purified gas leaves the cyclone through the outlet of the dipleg (3) submerged into the cyclone to a certain depth ( Figure 1).
The separator with arc-shaped elements has a simple design: it consists of several rows of arc-shaped elements (2) enclosed in the body (3) having a rectangular trapezoid shape. The arc-shaped elements inside the SAE are arranged at an angle of 30 • , thus ensuring identical flow motion. To prevent loosening of the arc-shaped elements (2) as the gas flow moves, they are attached to the separator body on both sides. In the upper part of the separator, the arc-shaped elements are inserted into special slots in the internal wall of the separator body (3). In the lower part of the device, they are attached to the grid, where the hopper (4) begins ( Figure 2). The operating principle of SAE is that a wavy structure of dust-laden gas flow is generated, giving rise to a high centrifugal field in which the particles are thrown back to the separator walls and gradually settled in the hopper (4).
Numerical simulation of erosive wear in the separator with arc-shaped elements and the cyclone was performed using the ANSYS Fluent software. The k-w SST turbulence model was used for numerical simulation. When solving this model, partial differential equations (the Navier-Stokes equation) were also set: where ∇ is the Del operator; ∆ is the Laplacian vector operator; t is time, s; v is the coefficient of kinematic viscosity, m 2 /s; ρ is the gas density, kg/m 3 ; p is pressure, Pa; → v is the velocity vector field; and → f is the vector field of bulk forces. The Navier-Stokes equation was supplemented with the continuity equation: The discrete phase model (DPM), taking into account the effect of solid particles on the gas flow, was used for modeling. The following equation was applied: where F D is the drag force, N trajct ; v f is the gas flow rate, m/s; v p is the particle speed, m/s; g is the acceleration due to gravity, m/s 2 ; ρ p is the density of particles, kg/m 3 ; and F x are the additional forces, N trajct . The erosive wear of the devices was calculated using the equation [45]: where G p is the mass flow rate of particles, kg/s; C(dp) is the function of particle diameter; f(α) is the function of collision angle; v is the particle impact rate, m/s; n is the number indicating the particle impact rate; and A face is the surface area of a near-wall cell, m 2 . When building the 3D cyclone model, the geometric parameters were assumed to be as follows: cylindrical body diameter, 800 mm; height, 4000 mm; inlet, 500 × 180 mm, outlet diameter; 480 mm; and lower orifice diameter, 240 mm. The cyclone was made of steel of AISI 321 grade ( Figure 1).
When building the 3D model of the separator with arc-shaped elements, the geometric parameters were assumed to be as follows: device length, 2500 mm; height, 910 mm; width, 900 mm; thickness of the device walls, 10 mm; the size of arc-shaped elements, 76 × 4 mm; the number of rows of arc-shaped elements, 8; the number of elements per row, 6 ( Figure 2). H-shaped elements were studied in refs. [46][47][48]; however, the hydraulic drag of the separator with this type of elements was higher compared to that of the device with arc-shaped elements.
The boundary and initial conditions were closest to those used in industrial-scale dehydrogenation of paraffin hydrocarbons. The volumetric flow rate of gas = 1.7 m 3 /s was set at the device inlet. Pressure of 58,839.9 Pa (0.6 kgf/cm 2 ) was set at the outlet for purified gas and the outlet orifice for the catalyst entering the hopper. The gas flow temperature was assumed to be 550 • C. The standard aluminum-chromium catalyst particles were used. Particle size varied from 20 to 160 µm; particle density was 1400 kg/m 3 . Table 1 shows the mass flow rates of particles depending on their size.

Results and Discussion
To provide the empirical foundations for studying erosion and verify the model, we conducted six experiments with varied sizes of catalyst particles (20-160 µm) and flow rates at a varied (assessed) erosive wear rate (0-1.0; 0-5.0; 0-10.0, and 0-15.0 mm/year). The gas flow rate, pressure, and temperature inside the devices was assumed to be constant upon modeling.
The simulated data are shown in Figures 3-9.

Results and Discussion
To provide the empirical foundations for studying erosion and verify the mod conducted six experiments with varied sizes of catalyst particles (20-160 µ m) an rates at a varied (assessed) erosive wear rate (0-1.0; 0-5.0; 0-10.0, and 0-15.0 mm The gas flow rate, pressure, and temperature inside the devices was assumed to b stant upon modeling.
The simulated data are shown in Figures 3-9.

Results and Discussion
To provide the empirical foundations for studying erosion and verify the model, we conducted six experiments with varied sizes of catalyst particles (20-160 µ m) and flow rates at a varied (assessed) erosive wear rate (0-1.0; 0-5.0; 0-10.0, and 0-15.0 mm/year). The gas flow rate, pressure, and temperature inside the devices was assumed to be constant upon modeling.
The simulated data are shown in Figures 3-9.
(a) (b) (c)         Figures 3 and 4 show the comparative data on the pressure, velocity, and temperature profiles. According to these data, one can see that increased eddy velocities and pressures are generated at the cyclone margin, thus causing turbulent gas flow and increasing hydraulic drag. Elevated temperatures were also observed in the conical section of the cyclone. Most likely, it occurs due to friction of coarse particles exposed to centrifugal force ( Figure 3). Changes in the pressure and velocity profiles for SAE (Figure 4) occur in a regular manner, and no critical deviations were observed. Unlike in the cyclone, the gas flow rate in SAE is stable. Temperature at the device outlet was slightly increased because of centrifugal forces.

Assessing the Velocity, Pressure, and Temperature Profiles
Earlier studies have shown that the turbulent gas flow in cyclones increase the probability of fine particle penetration, thus worsening separation efficiency. The high level of fine particle collection is an advantage of the novel device [44,46].      Figures 3 and 4 show the comparative data on the pressure, velocity, and temperature profiles. According to these data, one can see that increased eddy velocities and pressures are generated at the cyclone margin, thus causing turbulent gas flow and increasing hydraulic drag. Elevated temperatures were also observed in the conical section of the cyclone. Most likely, it occurs due to friction of coarse particles exposed to centrifugal force ( Figure 3). Changes in the pressure and velocity profiles for SAE (Figure 4) occur in a regular manner, and no critical deviations were observed. Unlike in the cyclone, the gas flow rate in SAE is stable. Temperature at the device outlet was slightly increased because of centrifugal forces.

Assessing the Velocity, Pressure, and Temperature Profiles
Earlier studies have shown that the turbulent gas flow in cyclones increase the probability of fine particle penetration, thus worsening separation efficiency. The high level of fine particle collection is an advantage of the novel device [44,46]. W e , mm/year dp, µm Figure 9. The erosive wear rate W e , mm/year as a function of particle diameter for different devices: (1) the cyclone and (2) the separator with arc-shaped elements. Figures 3 and 4 show the comparative data on the pressure, velocity, and temperature profiles. According to these data, one can see that increased eddy velocities and pressures are generated at the cyclone margin, thus causing turbulent gas flow and increasing hydraulic drag. Elevated temperatures were also observed in the conical section of the cyclone. Most likely, it occurs due to friction of coarse particles exposed to centrifugal force ( Figure 3). Changes in the pressure and velocity profiles for SAE (Figure 4) occur in a regular manner, and no critical deviations were observed. Unlike in the cyclone, the gas flow rate in SAE is stable. Temperature at the device outlet was slightly increased because of centrifugal forces.

Assessing the Velocity, Pressure, and Temperature Profiles
Earlier studies have shown that the turbulent gas flow in cyclones increase the probability of fine particle penetration, thus worsening separation efficiency. The high level of fine particle collection is an advantage of the novel device [44,46].

Numerical Investigation of Erosion for the Cyclone
The results of the studies proved that there is significant erosive wear on the cyclone walls in the component of the technological line of paraffin dehydrogenation (>15 mm/year). As a result, holes appear in certain areas of the cyclones, thus increasing catalyst consumption, as well as causing a pressure drop in the technological line and jeopardizing the environment and health of plant employees. Several cyclones arranged in series in a parallel manner (2,4,6, and more cyclones) are most commonly used to increase efficiency of gas purification [48,49]. However, the problem of wear remains as proved by the fact that cyclones are frequently repaired and replaced. The highly loaded first-stage cyclone separators are usually more susceptible to erosive wear in their upper part, starting at the inlet and ending at the lower cylindrical section of the cyclone. The lower part of the cyclone cone is almost not subjected to erosive wear ( Figure 5). The reason for that is the scheme of gas flow in the cyclone. After the solid catalyst particles are knocked out of the swirling flow towards the cyclone walls in the upper part of the device, gravity starts playing the key role. As a result, solid particles quickly fall down to the cyclone bottom and almost do not contact the cyclone cone.
Numerical modeling of the separator with arc-shaped elements has shown that, unlike for the cyclone, the separator walls are much less prone to erosive wear (≤2.31 mm/year). The lower annual erosion rate in the proposed separator compared to that in the cyclone can be attributed to differences in the flow structure. However, separation of particles from the gas occurs in both devices mostly due to centrifugal forces. For the wave-like flow structure, particles are thrown to different areas of the separator walls more chaotically, so the erosive wear rate is reduced. The presence of several rows of arc-shaped elements allows one to replace the worn-out elements when necessary.
It was found experimentally that the erosive wear rate depends on particle diameter in both devices. The erosive wear rate goes up as particle diameter is increased from 20 to 160 µm. Variation of catalyst particle size can alter the erosive wear rate in different cyclone regions. Thus, the inlet area and the upper cylindrical part of the cyclone are most susceptible to erosive wear from particles with a diameter of 20-40 µm. As particle size increases from 40 to 160 µm, erosive wear starts to be observed in the lower cylindrical part of the cyclone as well. It is caused by particle coarseness. After being knocked out of the structured swirling flow, particles fall down, but they are constantly and repeatedly thrown to the device walls due to the eddy existing along the entire length of the cylindrical part of the cyclone. Therefore, pressure applied to the lower cylindrical part of the cyclone and the erosive wear rate increase at larger particle sizes ( Figure 5). Figure 6 shows the wave-like flow structure. The ordered arrangement of the eddy structure without chaotic swirl motion allows one to minimize the pickup of particles previously separated from the flow back into it.

Assessment of the Gas Flow Structure for the Novel Separator with Arc-Shaped Elements
The dust-laden gas flow enters the separator with arc-shaped elements through the inlet (1). The flow runs into the space between the rows of arc-shaped elements (2). The elements are arranged in a checkerboard pattern. Along with the checkerboard pattern of arrangement of arc-shaped element rows (2), there is an important design feature related to their arrangement with respect to each other. In particular, the following condition is met: the elements are arranged in such a manner that it is possible, starting at the central point of the circle (that is equal to two united arc-shaped elements), to draw a circle equal to two of its diameters and running through the central points of the straight outermost margin (the adjacent elements located in the preceding and subsequent rows). The fulfilment of this condition provides the most efficient wave-like structure of gas flow motion, since the centrifugal forces are maximal for this arrangement [41].
The wave-like flow structure is generated as the dust-laden gas goes around the large number of rows of arc-shaped elements (2) arranged in a checkerboard pattern. During the gas motion, there emerge many points of centrifugal forces in each eddy (turn). The high centrifugal forces are caused by the small diameter of semi-circles. Under the centrifugal forces, particles are knocked out of the structured flow towards the walls of the arc-shaped elements (2) and fall down into the hopper (4). The purified gas flow leaves the separator with arc-shaped elements through the outlet (5) (Figure 2). The absence of rectilinear or nearly rectilinear particle motion towards the device walls and further contact with the walls as the dust-laden flow passes through the separator substantially minimizes the erosive wear.

Numerical Investigation of Erosion for the Separator with Arc-Shaped Elements
Numerical modeling of erosive wear in the separator with arc-shaped elements showed that the first two rows of elements were most susceptible to erosion. It was presumably caused by the incompletely formed structure of the dust-laden medium in the proposed device. In particular, the structure became fully wave-like in the zone located within the first two rows of the arc-shaped elements ( Figure 6). However, some particles did not have enough time to be rearranged along with the gas and inertially move in a rectilinear manner towards a certain area of the walls of the first two rows of arc-shaped elements, thus causing greater erosive wear of these elements compared to the other rows (Figures 7 and 8).
An analysis of the erosive wear patterns shown in Figures 7 and 8 (the catalyst particle diameter (d p ) in the gas flow being 20 and 160 µm, respectively) demonstrates that the erosive wear area on the walls of the arc-shaped elements increased with rising particle diameter. It is clearly seen by examining the first two rows of arc-shaped elements. At a particle diameter of 20 µm, the peripheral regions of arc-shaped elements were more susceptible to erosion. At 160 µm, erosion was observed in certain areas of the arc-shaped elements along the entire perimeter. It is also evident by comparing rows 3-5 of the arc-shaped elements at a particle diameter of 20 and 160 µm (Figures 7 and 8).
The maximum erosive wear rates of the rows of elements in the separator with arcshaped elements at particle diameters ranging from 20 to 160 µm were digitized during numerical modeling. In Table 2, the first two columns correspond to the two rows of arc-shaped elements that had undergone the maximum erosion at each analyzed catalyst particle diameter. One can see that in this range of particle diameters (20-160 µm), the first two rows of arc-shaped elements are characterized by the maximum erosion rate, which proves the statement given above. For rows 7 and 8, there is almost no wear of the arc-shaped elements, which may indicate that particle concentration in the gas was relatively low (Table 2).  7 and 8 show that the erosive wear rate of the cyclone was significantly higher than that for separators with arc-shaped elements. Figure 9 shows it in a more systematized manner. As particle diameter increases from 20 to 160 µm, the erosive wear rate of the cyclone is most accurately described by linear function with the mean square deviation of 0.98: W e (TsN − 15) = 0.23d p + 13.46.
The erosive wear rate of the separator with arc-shaped elements is most accurately described by the power-law function with the mean square deviation of 0.93: W e (SAE) = 0.0006d 1.75 p .
Numerical experiments demonstrate that the continuous impact of the high-speed flow of solid catalyst particles on the walls of the devices after the particles were knocked out of the dust-laden medium leads to gradual formation of micro-and macro-defects, which can manifest themselves as roughness, pits, cavities, holes, and other wall defects. As mentioned previously, it increases the catalyst consumption and causes a pressure drop in the technological line and other negative effects.
The study has predicted that using the cyclone for one year for collecting catalyst particles sized 20-160 µm will most likely cause the formation of holes, since erosive wear is more than 15 mm/year. For the wave-like flow structure in the separator with arc-shaped elements, at the volumetric flow rate of 1.7 m 3 /s, the erosive wear rate was no higher than 2.31 mm. For cyclone walls thicker than 3 mm, it is highly likely that arc-shaped elements will remain undamaged.
In the separator with arc-shaped elements, erosive wear affects the elements rather than the separator body; therefore, the probability of erosive wear of the body of the proposed separator and excessive catalyst losses is minimized.

Conclusions
Modeling of the separation of catalyst particles from the gas using two devices (a cyclone and a separator with arc-shaped elements) revealed that the proposed dust collector allows one to reduce the erosive wear by several times (6.5-fold) for identical operating modes and operating parameters (temperature, pressure, particle size and speed, etc.). The lower erosive wear in the novel separator compared to that in a cyclone is caused by the ordered wave-like flow structure at which particles are thrown into different regions of SAE elements with a greater intensity during eddy formation, so the equipment-damaging side processes are mitigated. A unique feature of the SAE compared to other centrifugal separators is that higher-intensity centrifugal forces are generated in it. Many points of eddy formation appear, with eddy radius being relatively small, as the gas passes around the arc-shaped elements, making particle separation from gas flows more efficient.
It has been demonstrated that the wall erosion rate rises with increasing average size of catalyst particles (>40 µm) for both analyzed devices. Whereas in the presence of particles sized up to 40 µm only the upper part of the cyclone was mainly susceptible to erosive wear, at larger particle size, wall erosion starts to be observed both in the upper part and the lower cylindrical part of the cyclone due to particle coarseness and their chaotic collisions with the device body during settling.
In the separation device with arc-shaped elements, the first two rows of elements are most susceptible to erosion. This is caused by the incomplete formation of the structure of the dust-laden medium in the front part of the device. As a result of rectilinear and inertial motion, particles enter into the same zones within the first two rows of the arc-shaped elements. For the proposed separator, arc-shaped elements undergo erosive wear, thus preventing the formation of holes in the device body and catalyst loss.
The functions showing the dependence between the erosive wear rate and particle diameter for the cyclone and the separator with arc-shaped elements have been obtained; these functions allow one to predict wear of the devices. Speaking about the future outlook, the separator with arc-shaped elements can be recommended to be used at petrochemical plants, and in such processes as fluidized-bed dehydrogenation of C 4 -C 5 isoparaffins to isoolefins in particular.