Erosion Modeling in Parallel Gate Valve

Gate valves, which are widely used in oil production and transportation processes, can be eroded by high fluid pressures and sand particles contained in crude oil during operation. This erosion can result in loss of valve thickness and shutdown of the operating system. Erosion is not uniform on valve elements, and it is different depending on the stages of opening the valve. In this paper, flow analysis and erosion rate analysis for the fluid flowing through the valve in different stages of opening were performed by using ANSYS Fluent 19.2. The gate valve model was designed by using AutoCAD, and the geometric dimensions and physical properties of the material required for modeling were determined according to the specifications of the gate valve installed in the oil pipeline. By the Reynolds calculation, it was disclosed that the fluid which flows in the valve has the characteristic of turbulent flow, and based on this calculation, the inlet length of the valve was determined. For the CFD analysis, the Euler method and the method of Lagrange were used. Using the k ε and DPM models according to the fluid characteristics of the turbulent flow, it was predicted the erosion rates of the surface generated by the sand which is the solid phase dispersed in the multiphase fluid. In addition, based on the Von Mises method and the pressure distribution, data obtained by fluid analysis, the process of calculating the stress on the closing elements was presented. The fluid used in the analysis was petroleum with sand particles.


INTRODUCTION
Internationally, energy security is an important issue for the country's economy and stability. As the demand for energy and its production increases, the reliability requirements for the valve, which is an important element in the oil transport process, also increase day by day.
Gate valves, which are widely used in oil production and transport processes, can be eroded by the high pressure of the fluids and by the sand particles contained in them during operation. In particular, erosion by sand particles or liquid jets may occur locally in the part of the gate or seat where fluid flow changes rapidly when the gate is open or closed ( Figure 1).
Such erosion can lead to the loss of the thickness of the parts and can even stop the valve system. Therefore, predicting the degree of erosion and weakness of the valve in advance is an important requirement for increasing the durability of the valve and for ensuring the fluid flow safely.
The position and severity of the erosion of the valve are related to the opening situation of the gate, the speed of the fluid, the material of the valve, the size and distribution of the sand particles and it' s impact angle, [1,2].
In general, the erosion rate can be predicted using the empirical formulas presented at API (American Petroleum Institute) [3] and Erosion / Corrosion Research Center (E / CRC) (McLaury and Shirazi, 1999) [4]. It is difficult to predict the erosion rate changes depending on the solid particle ratio and the rapid changes of the fluid that passes inside the gate valve only by the empirical methods. Many scientists, including Sheldon (1966), Goodwin (1969), Head (1970), Sheldon (1970), Grant (1973), Williams (1974), and Sundararajan (1983) presented a general equation to predict the rates of erosion due to solid particles [5], but the empirical equations presented did not reflect the contents related to the velocity and the angle of impact of the particles. McLaury et al. (1996) presented a model to predict the rate of erosion of the sand particles in water [6] and also Edwards et al. (1998) proposed a model to predict the rates of erosion in polyphase fluids using the CFD method, [7]. Oka et el. (2005) conducted many experiments to reveal the influence of sand particles in the fluid on erosion of the pipe wall and during this process, presented a calculation equation for prediction of the rates of erosion, [8].
On the other hand, G.V. Messa et al. (2017) predicted the rate of erosion of the gate valve by combining with the CFD model and the model of erosion proposed by Oka, and presented a calculation equation to predict the life of the valve using MATLAB E-Code, [9].
Also, Det Norske Veritas(DNV) (2007) presented a calculation equation that considers the velocity and the angle of impact for predicting the rate of erosion in a system of the pipes through which polyphasic fluid flows, [10].
But, despite many studies, none of the empirical equations hasn't predicted the rate of erosion fully and accurately yet. For these reasons, it can be said that the combination of the experimental method and the CFD analysis method is the most effective way for accurate prediction of erosion rate.
The present study presented an analysis model for predicting erosion wear that would occur in a gate valve and the values of stresses for evaluating its structural stability in diferent stages of valve gate opening when the polyphase fluid containing petroleum and sand passes through it.

Design of the geometric shape of the gate valve
The valve model was designed by using AutoCAD according to the standard and operating conditions of type 2 1/16 ̋ -3/5M type gate valve actually installed in the oil pipeline.
The thing we should pay attention to at the design of the geometrical shape of the valve, is the length of the pipe installed on the inlet side of the valve. In general, the valve is installed in the straight portion of the pipe, so when the fluid hits the gate surface of the valve, the fluid usually collides in a fully developed flow state.  In the paper, considering this, the pipe length of the valve inlet was set long enough when designing the valve model. In this case, the inlet length of the pipe was calculated using the Reynolds Number and the diameter of the valve.
In CFD(Computational fluid dynamics) analysis, erosion occurs only on the surface of the model, so the valve body has been replaced with a pipe to reduce the calculation speed. Table 1 presents the geometrical dimensions of the model and other parameters used in the analysis, and Table 2 presents the material list of the valve parts.
Calculation of the Reynolds number: When calculating the Reynolds number for the fluid flowing in the valve, it has turbulent flow characteristics, so the length of the pipe can be determined by using the equations of Muzychka and Yovanovich, [11].
To facilitate the discretization of the model, the length of the pipe at the entrance of the valve was set to 1400 mm.

Discrete composition
To increase the intuition of the model and the calculation speed, the hexagonal discretization method was used.
Since the velocity distribution of the fluid in the gate part changes rapidly and the erosion model being used is a model related to the surface of the valve and the pipe, the mesh size was set from the hydrodynamic point of view.
The height of the surface element was calculated using the y + method (Wall Distance Method), [12].
In the above equation, the y + range is from 30 to 500, but the y + value was chosen as 50 to finely divide to fit the erosion model and the discretization size was calculated ( y = 3.5•10 -3 m).
The discretization form for the erosion model is presented in Figure 2. Was used a 194372 number of cells, with cell size of 3.5mm, 193611 nodes, 1 second time step size, 3600 number of time steps, and 50 max iterations / time step.

Fluid flow modeling
In the paper, the fluid flow characteristics were calculated using ANSYS Fluent 19.2.
In solving the governing equations in hydrodynamics, the continuous phase has been calculated by Euler's method and the dispersed phase has been calculated by the Lagrange method of tracking the individual particles.
For the continuous phase, the oil specified in the list of materials on the computer has been selected, and for the dispersed phase, the sand which was the main cause of erosion has been selected.
It has been assumed that the continuous and kinetic equations of the fluid flowing through the valve are equations (7) and (8), [13].
where [13] Since it is not possible to directly solve the stress tensor, the differential equation is solved by applying the gradient-transfer hypothesis.
These values depend on the type of the k−ε model. In this study, the realizable k−ε model was used for the turbulence model. The realizable k−ε model is a turbulence model for analyzing the action process of a fluid with a relatively high Reynolds number at the wall boundary surface.

Calculation of erosion rate
DPM (Discrete Phase Model) model was used as an erosion model. DPM model can be used in case that the continuous phase acts together with the dispersed phase. In the DPM model, it is assumed that the continuous phase exerts a force on the dispersion phase, but the dispersion phase does not affect the continuous phase.
This assumption is possible when the dispersed phase contained in the fluid is less than 10% and there is no significant effect [6]. In this study, a DPM model can be used because fluid analysis is performed on petroleum with less than 10% sand as impurities.
In the paper, erosion rate was predicted by using the Generic Erosion Model that ANSYS Fluent has. In this case, the particle erosion rate is calculated by equation    Table 3 presents the values of the parameters used in the erosion calculation.

Calculation results and analysis
Based on the model proposed above, the flow characteristics of the fluid and the change of erosion rates were observed, dividing the state of opening and closing of the valve in 4 cases.
In the analysis, the characteristic values of the fluid and particles were given at the inlet, and the relative pressure was taken into account at the outlet by giving the opening condition.
To fit the erosion model, the wall boundary condition of the model was set to the condition of No slip wall, and the operating time of the particle was set to 3600 seconds.
First, the flow characteristics of the fluid and the state of pressure change according to the state of opening and closing of the valve are presented in Figures 3 and 4, and the calculation results are presented in Figures 5 and 6 and in Tables 4 and 5.

1-4 2-4
3-4 4-4  As shown in Figures 5 and 6, it can be seen that the smaller the passage area of the fluid is, the greater the velocity of the fluid and the pressure applied to the valve are.
In the figures above, 1-4 is the valve in which the gate was opened by only about a quarter, 2-4 is the valve in which the gate was opened by only half, 3-4 is the valve in which the gate was opened by only three fourths, 4-4 is the valve in which the gate opened completely.

1-4 2-4 3-4 4-4
In addition, except for the valve in which the gate was opened completely, when it is observed in the same valve, the velocity of a fluid was higher in seat 2 and in the part of the gate in which the direction of fluid flow changes rapidly. In particular, as the passage area of the fluid became smaller, the fluid vortex phenomenon inside and behind the gate appeared more severely. The value of the pressure was also higher in the gate section and gradually decreased as it went to tube 2.
In this case, the maximum pressure appeared on the surface of the wall in front of the gate which is in direct contact with the fluid and, in rare cases, near the contact boundary between the fluid passage surface of the gate and the lower section of the seat. The reason for this is that as the fluid passage area decreases, a vortex is generated inside and behind the gate.
When the valve gate is opened completely, the pressure and velocity of the fluid gradually decreased as it went to tube 2. In this case, there are pressure losses only due to the friction between the fluid and the pipe wall.
Next, the erosion state of the valve and the calculation results are presented in Figures 7 and 8 and in Table 6.
The rate of erosion also increased as the fluid flow area decreased, and the flow characteristics changed rapidly.
In addition, as can be seen in Figure 7, except for the valve in which the gate was fully opened, erosion first occurred on the surface of the tube1 in front of the gate and on the inner surface of the gate, and this was gradually transferred to the back of the gate, as the gate is closed. In particular, erosion was severely generated on the inner surface of the gate and at the boundary between the gate and the seat 2. Further, when the gate was closed by a quarter, most of the erosion occurred near the boundary between the inner surface of the gate and the lower section of the seat 2 and on the inner surface of the tube 2. The reason for this is that a stronger vortex was generated inside the gate and inside the seat 2 and the tube 2 behind the gate, as the fluid passage area is gradually decreased.
In all cases, the erosion rate was recorded as the maximum value on the inner surface of the gate and it was 4.597 •10 -3 kg/(m 2 h) when the valve was opened by only 1/4. In addition, when the valve was fully opened, erosion occurred accidentally along the entire length of the pipe (tubes).

STRESSES CALCULATION ON CLOSING ELEMENTS
Depending on the pressure distribution data obtained by CFD analysis, the stress states of the closing elements were analyzed according to the open state of the valve.   The model of the valve for analysis was designed by using AutoCAD according to the standard and operating conditions of type 21/16 -3/5M type gate valve actually used in the oil pipelines ( Figure 9). For analysis, both surfaces of the valve were fixed and contact conditions between the parts were established. The model used for calculation was designed to be the same as the size of the actual valve, and the Von Mises method was used for stress calculation.
The calculation results are presented in Figures 10  and 11, and in Table 7.  Figure 10 shows, the smaller the fluid passage area is, the bigger the value of the tension on the inner surface of the inlet part of the valve body is, and the tension on the gate wall reaches the maximum value when the valve is completely closed. Of course, in this case, the maximum tension was produced near the boundary between the wall in front of the gate and the valve seat1.
However, given that the maximum value of the calculated stress is 115.05 MPa, which is less than the permissible value of the material (yield stress of gate material = 460 MPa), the valve is considered to be stable in terms of structurally real working conditions.
As can be seen from Table 7, maximum values were generated near the boundary between the gate and the seat 1 or between the gate and the seat 2 as the valve gate gradually is closed. In addition, at the valve in which the gate was fully opened, the value of the stress was reduced as it went to the tube 2, and in this case, the maximum value was produced on the inner surface of the inlet part of the valve body. Of course, the value in this case was 0.075MPa, which was lower than the maximum values obtained in other cases.

CONCLUSION
This research presented the process of evaluating the erosion and the structural stability on the gate valve where the multiphase fluid flows, using Ansys Fluent 19.2. Using the DPM model, the flow characteristics and the change in erosion rates on the valve were calculated, and in this process it was confirmed that the erosion phenomenon appeared most seriously on the inner surface of the gate, where the flowing direction of the fluid changed rapidly.
In addition, using the Von Mises method it is confirmed that the valve is structurally stable even when the valve is under maximum pressure. Of course, it is true that the accuracy of Ansys analysis results should be confirmed by experimental methods, however this method of analysis suggests that the gate, seat, and inner surface of the body behind the gate should be covered with good wear-resistant material to increase the valve durability.
It has also been confirmed again that to reduce the erosion rate we should avoid the fluid swirl by actuating the valve in the condition that the gate is completely opened or closed.