Numerical investigation of the process and flow ...

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tank with nitrogen. Hongjun Zhu ⁎, Qinghua Han, Jian Wang, Siyuan He, Dong Wang. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, ...
Powder Technology 275 (2015) 12–24

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Numerical investigation of the process and flow erosion of flushing oil tank with nitrogen Hongjun Zhu ⁎, Qinghua Han, Jian Wang, Siyuan He, Dong Wang State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China

a r t i c l e

i n f o

Article history: Received 14 September 2014 Received in revised form 31 December 2014 Accepted 27 January 2015 Available online 3 February 2015 Keywords: Flow erosion CFD Oil tank DPM VOF

a b s t r a c t A computational fluid dynamic (CFD) model coupling with volume of fluid (VOF) method and discrete phase model (DPM) has been used to predict the flow erosion rate in an oil tank and blowdown pipe during the process of gas flushing. An initialization method by injecting particles from a tank wall is developed to construct the initialization distribution of residue particles. The flow field distribution of oil–gas–water flow and the erosion rate on the wall surface during emptying process can be captured under different operating conditions with different fluid parameters. The applicability of the approach is verified by comparing the simulated results with the measurements. The effects of fluid parameters such as gas inlet rate, oil density and viscosity, as well as the operating parameters such as residual oil level and residue particle diameter, are evaluated. In general, the required flushing time and erosion rate are all sensitive to fluid parameter changes and operating condition changes. It is found that the flow erosion is related to the emptying process of oil, which has a sharp rise in the end of the process. High inlet speed, large oil density, small oil viscosity, high oil level and large particle diameter can result in severe erosion. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In the oil processing and storage, the separator and oil tank are the key equipments, which frequently require cleaning after a specified interval of time. Because of the structural complexity and to meet safe and efficient cleaning, inert gas (nitrogen) flushing is a common method used in actual operations. However, residual oil and residue particles, such as sand and catalyst, usually remain in the bottom of the tank or accumulate at the tank wall. In the flushing process, residue particles carried by fluid may result in undesired superficial erosion on the tank and blowdown pipe wall. If an eroded hole appears, some catastrophic consequences, such as oil spill, as well as considerable economic loss and liability to the oil company [1], may be brought about. Therefore, it is imperative to find the severe erosion spots in the flushing process and predict the erosion rate to estimate the service life of the tank or blowdown pipe. Flow erosion, as a hot issue in industrial operations, has attracted many investigators to conduct physical or numerical modeling [2–5]. Since the early 1990s, with the purpose of saving time and resources and avoiding potential risks, computational fluid dynamics (CFD) as a reliable tool has been widely used for particle erosion prediction in pipe bends, elbows, ducts, tees and related geometries [6–11]. Numerical simulations have been conducted by Gabriel et al. [7] to predict the erosion due to particles in an elbow pipe with a 90° curvature angle. ⁎ Corresponding author. Tel.: +86 28 83032206. E-mail address: [email protected] (H. Zhu).

http://dx.doi.org/10.1016/j.powtec.2015.01.062 0032-5910/© 2015 Elsevier B.V. All rights reserved.

They found that the Oka model can give relatively accurate predictions. Stack and Abdelrahman [3] have evaluated the effects of particle concentration on the erosion of the inner surfaces of a circular pipe with a 90° bend using a commercial CFD code. Derrick and Michael [6] also used a CFD code to model particle-laden flow and predict erosion in four different 90° square cross-section bends. Zhang et al. [4] have investigated the effects of slurry velocity, bend orientation and angle of the elbow on the location of maximum erosive wear damage by CFD combined with discrete element method (DEM). Tan et al. [9] also used a CFD and DEM model to capture the key features of solid–fluid multi-phase flow and predict the location of maximum erosive wear damage. In our previous work, effects of operation, structure and fluid parameters on erosion of needle valve [8] and erosion of drill pipe [10] due to particle-laden gas flow have been studied by a CFD and DPM model. The flow erosion rates were also predicted by an erosion model. More recently, Zeng et al. [2] have performed an experimental and numerical investigation on erosion behavior of X65 pipeline elbow. The erosion rates at different locations of the elbow were quantified by using array electrodes. And the numerical results of the erosion rate were in good accordance with the test. It was found that change in hydrodynamics is the main reason for the variation of the erosion rate at different locations. Besides, anti-erosion methods were proposed and studied by several investigators. Chen et al. [5] have carried out both physical and numerical modeling of the relative erosion severity between plugged tees and elbows in dilute gas/solid two-phase flow. The erosion effects in three 90° duct bend gas–solid flows with different ribs are numerically evaluated by Fan et al. [11].

H. Zhu et al. / Powder Technology 275 (2015) 12–24

Erosion caused by gas–solid or liquid–solid two-phase flow is the concern of these studies. Few researchers have paid attention to particle erosion resulting from gas–liquid–solid three-phase flow. However, there are residual oil remains in the bottom of the tank, resulting in gas–liquid two-phase for continuous phase. Whether flow erosion is related to the emptying process of residual oil, is a key problem for estimating the service life of the tank and pipe systems. Moreover, most previous studies focus on the flow erosion of steady flow, while it is an apparent unstable flow for gas flushing. Furthermore, in the above simulation researches, particles as discrete phase are injected at the same inlet boundary with fluid flow. However, the residue particles that accumulated at the tank wall are not carried by nitrogen from the gas inlet. So a new initialization method is required to form the residue particles before the simulation of gas flushing process. In this study, the volume of fluid (VOF) method coupling with discrete phase model (DPM), as a Eulerian–Lagrangian approach, is used to capture the continuous phase flow and discrete particles, respectively. And an initialization method by injecting particles from the tank wall is developed to construct the initialization distribution of residue particles. The flow field distribution in the process of gas flushing and the flow erosion varied with the emptying process of residual oil are obtained by a series of non-steady simulations. The effects of gas inlet rate, residual oil density, residual oil viscosity, residual oil level, and residue particle diameter are discussed successively.

2. Problem description In practice, oil tanks have a variety of sizes. The heights of the vast majority of tanks are more than 10 m. In order to facilitate experiments, the experimental tank size is a reduced scale of an actual one. And the numerical simulation of the tank in the current study is conducted in the same geometry size as the test for comparison. Fig. 1 shows the diagram of the computational domain, and the detailed sizes are marked on the figure. The internal space of the oil tank is composed of a cylinder

13

and a hemisphere, which is a rotation axisymmetric construction. So a two-dimensional geometric model is established. At the bottom of the oil tank, a blowdown branch composed of two bends connects the tank to the blowdown main pipe. The lengths of vertical straight pipe sections connecting the tank and blowdown main pipe are 0.2 m and 0.5 m, respectively. And the curvature and diameter ratios of two elbows are both 3. Connecting the two elbows is a horizontal tube with a length of 0.2 m. The length of the horizontal blowdown main pipe is 4 m. And the connection point of the branch pipe and main pipe just sits at the middle of the main pipe. Velocity inlet boundary conditions are used for the gas inlet at the top of the tank and water inlet at the left of the blowdown main pipe. The size of the gas inlet setting in the center of the tank top is 0.05 m. Outflow boundary condition is employed for the outlet of computational domain (the right of the blowdown main pipe). The gas inlet velocity is set to 0.5 m/s, 1.0 m/s, 1.5 m/s, 2.0 m/s or 2.5 m/s, in order to observe the effect of inlet rate. However, the water inlet velocity is fixed at 2.0 m/s and the pressure at water inlet is fixed at 0.5 MPa, in order to facilitate comparative analysis. No slip boundary conditions are assumed for both the tank and pipe wall. As shown in Fig. 1, the residual oil level is calculated from the top wall of the main pipe, which is a variable in different simulation cases in order to observe the effect of liquid level. The height of residual oil is usually no more than 40% of the height of an oil tank. Therefore, five different residual oil levels, 1.1 m, 1.2 m, 1.3 m, 1.4 m and 1.5 m, are selected in the simulations. Twenty-one cases listed in Table 1 are modeled and analyzed in this paper to compare the different influences among different gas inlet rates, oil densities, oil viscosities, residual oil levels and residual particle diameters. Besides liquid level, gas inlet rate, oil density, oil viscosity and particle diameter are chosen as variables. In practice, the gas inlet rate ranges from 0.5 m/s to 3.0 m/s. For analyzing the effect of the inlet rate, five rates, 0.5 m/s, 1.0 m/s, 1.5 m/s, 2.0 m/s and 2.5 m/s, are adopted. The range of oil density is from 700 kg/m3 to 980 kg/m3, in which 700 kg/m3, 750 kg/m3, 800 kg/m3, 850 kg/m3 and 900 kg/m3 are used in this study. Oil viscosity

Fig. 1. Schematic diagram of oil tank and boundary conditions.

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H. Zhu et al. / Powder Technology 275 (2015) 12–24

Table 1 Simulation cases. Case

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Gas inlet rate (m/s) 2.0 0.5 1.0 1.5 2.5 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0

Oil density (kg/m3) 850 850 850 850 850 700 750 800 900 850 850 850 850 850 850 850 850 850 850 850 850

Oil viscosity (Pa·s)

Residual oil level (m)

0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 3.00 5.00 10.00 30.00 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85

1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.1 1.2 1.3 1.4 1.5 1.5 1.5 1.5

Residue particle diameter (mm) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.1 0.5 1.5 2.0

mainly ranges from 0.1 Pa·s to 30 Pa·s, so five classical viscosities are chosen to identify its effect. By field measurements, residue particle diameter mainly ranges from 0.1 mm to 5.0 mm. Therefore, we have selected five particle diameters in this range to conduct simulations. Among the 21 cases, Case 1 is the standard case. One main parameter is changed in other cases in order to evaluate the effect of the changed parameter. Such as in Cases 2, 3, 4 and 5, only the gas inlet rate is changed. Table 2 lists the physical properties of the fluid (oil, water and nitrogen) and solid particle used in the simulation.

3. Governing equations and numerical method 3.1. Governing equations Three main steps are involved in this CFD-based process and erosion modeling: particle initial injection, fluid flow modeling and particle tracking, and flow erosion calculation. A Eulerian–Lagrangian approach is applied to analyze the continuum phase and particle tracking for solid particles [12,13]. Firstly, solid particles are treated as spherical particles with uniform diameter added into residual oil as discrete phase, which are captured by discrete phase model (DPM). Then, fluid flow is treated as the continuum phase valuated by the Reynolds-Averaged Navier– Stokes (RANS) equations based on the Eulerian approach. Meanwhile, the particle dynamics are treated in a Lagrangian framework according to the particle equation of motion, including the trajectory of particles, the attack angle and velocity perturbation [14]. At last, the erosion rate can be determined by the mass transfer rate of magnetite on the metal surface [15]. Because of the flushing process operating at low pressures, all fluids are treated as incompressible flow, including oil, water and nitrogen. In the low-pressure operating condition, there is no phase change. And the four phases (oil–gas–water three fluid phases and solid phase) are

mutually insoluble in the process. Therefore, no mass transfer between continuous phase and particle phase is assumed. The RANS equations used to solve the continuum phase are written as follows [16–18]: ∂ui ¼0 ∂xi

ð1Þ 0

0

∂ui u j ∂ui ∂ui u j 1 ∂p 2 ¼− þ υ∇ ui − þ gi þ ρ ∂xi ∂t ∂x j ∂x j

ð2Þ

where ui represents instantaneous velocity component in i direction, for example u and v are velocity in x and y direction, respectively, while ui′ is fluctuation velocity component in i direction, xi is space coordinate in i direction, gi is gravitational acceleration in i direction, t is time, p is pressure and ρ and υ are density and kinematic viscosity, respectively. The volume of fluid (VOF) approach is based on the solution of one momentum equation for the mixture of the phases, and one equation for the volume fraction of fluid. Therefore, the volume of fluid functions Fw, Fo and Fg is introduced to define the water region, oil region and gas region respectively. The physical meaning of the F function is the fractional volume of a cell occupied by the fluid phase [1,19,20]. For example, a unit value of Fw corresponds to a cell full of water, while a zero value indicates that the cell contains no water. The fraction functions Fw, Fo and Fg are described as follows [21,22]: Fw ¼

Vw Vc

ð3Þ

Fo ¼

Vo Vc

ð4Þ

Fg ¼

Vg Vc

ð5Þ

where Fw, Fo and Fg are water, oil and gas fractional function, respectively, Vc, Vw, Vo and Vg represent volume of a cell, volume of water inside the cell, volume of oil inside the cell and volume of gas inside the cell, respectively. The 2D transport equations for the fractional functions are given by [1]: ∂F w ∂u F w ∂v F w þ þ ¼0 ∂t ∂x ∂y

ð6Þ

∂F o ∂uF o ∂vF o þ þ ¼0 ∂t ∂x ∂y

ð7Þ

∂F g ∂t

þ

∂uF g ∂x

þ

∂vF g ∂y

¼ 0:

ð8Þ

And the mixture fluid density and viscosity can be expressed in following equations [1]: ρ ¼ F w ρw þ F o ρo þ F g ρg

ð9Þ

υ ¼ F w υw þ F o υo þ F g υg

ð10Þ

where subscript w, o and g represent water, oil and gas, respectively.

Table 2 Physical properties of fluid and solid particles.

Density (kg/m3) Dynamic viscosity (Pa·s) Particle size (mm)

Oil

Water

Nitrogen

Solid particle

Variable (700, 750, 800, 850, 900) Variable (0.85, 3, 5, 10, 30)

1000 0.001003

1.138 1.663 × 10−5

2046 Variable (0.1, 0.5, 1.0, 1.5, 2.0)

H. Zhu et al. / Powder Technology 275 (2015) 12–24

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corresponding to turbulent kinetic energy and Prandtl number corresponding to turbulent kinetic energy dissipation rate respectively, Gk is production term of turbulent kinetic energy due to the average velocity gradient, Gb is production term of turbulent kinetic energy due to lift, YM is impact of compressible turbulence inflation on the total dissipation rate, υ is molecule kinetic viscosity and C1ε, C2 and C3ε are empirical constants taken as 1.44, 1.9 and 0.09 respectively. Solid particle motion equation is specified as [10,14]: dvs C D Reds g ðρs −ρÞ ρ dðv−vs Þ ¼ ðv−vs Þ þ þ 0:5 dt 24τ t ρs ρs dt

point 1

ð16Þ

point 2 in which, 2

τt ¼

ρs d s 18μ

ð17Þ

Fig. 2. Diagram of injection wall for preliminary calculation of residue particles.

Reds ¼ The above equations are closed using the realizable k-ε turbulence model [8,23–26]: " #  ∂ðρkÞ ∂ðρkvi Þ ∂ μ t ∂k þ Gk þ Gb −ρε−Y M ¼ μþ þ σ k ∂x j ∂t ∂xi ∂x j " #  2 ∂ðρε Þ ∂ðρεvi Þ ∂ μ t ∂ε ε pffiffiffiffiffiffi þ ρC 1 Sε−ρC 2 ¼ μþ þ σ ε ∂x j ∂t ∂xi ∂x j k þ υε ε þ C 1ε C 3ε Gb k

CD ¼ ð11Þ

ð12Þ

in which,  C 1 ¼ max 0:43;

 η ηþ5

 1=2 k η ¼ 2Si j  Si j ε 1 ∂vi ∂v j Si j ¼ þ 2 ∂x j ∂xi

ρds jvs −vj μ

ð18Þ

 24  b Re b 1 þ b1 Reds2 þ 3 ds b4 þ Reds Reds

ð19Þ

where vs is velocity of particle, ρs is density of particle, CD is drag coefficient, Reds is particle equivalent Reynolds number, τt is particle relaxation time, ds is diameter of particle, b1, b2, b3 and b4 are empirical constants taken as 0.186, 0.653, 0.437 and 7178.741, respectively [27–29]. Finally, erosion rate is defined as the mass of removed material per unit of area per unit time, which is calculated on the walls by accumulating the damage each particle causes when colliding against the surface. It is given by [8,10]:

ð13Þ

N sd X ms er Af sd¼1 

e¼ ð14Þ

ð20Þ

in which,

! ð15Þ

where the subscripts i and j are indices for coordinate axes, k and ε refer to turbulent kinetic energy and turbulent kinetic energy dissipation rate per unit mass respectively, σk and σε represent Prandtl number

n

er ¼ K F s f ðα Þðvs Þ

f ðα Þ ¼

8 > < K 1 α 2 þ K 2 α; > : K 3 cos2 α sin α þ K 4 sin2 α þ K 5 ;

close-up view

Fig. 3. Employed grids of the computational domain.

ð21Þ π 12 π αN 12

α≤

ð22Þ

16

H. Zhu et al. / Powder Technology 275 (2015) 12–24

Table 3 Grid independency tests. Mesh

Number of elements

The maximum erosion rate (kg·m−2·s−1)

M1 M2 M3 M4 M5

10,438 15,670 20,314 25,956 31,302

1.004 × 10−7 1.118 × 10−7 (11.35%) 1.172 × 10−7 (4.83%) 1.190 × 10−7 (1.54%) 1.191 × 10−7 (0.08%)

where Af is projected area of particles in the wall, ṁs is the particle mass flow rate represented by each computational particle that collides with face, Nsd is number of particles, er is the erosion ratio [6,7], K is a material-dependent constant, which has taken the value 2.17 × 10−7 for carbon steel [6,30], n is an empirical coefficient taken as 2.41 [31], Fs is the particle sharpness factor, Fs = 0.2 is used since spherical particles are assumed in this study [6,7], f(α) is the angle function, Ki for i = 1–5 are empirical constants, equal to − 0.334, 0.179, 0.01239, −0.01192 and 0.02167, respectively [32].

Fig. 5. Comparison between simulation result and actual measurement value.

3.2. Numerical method Finite volume method (FVM) is employed to discretize the above equations. All the simulations are conducted using a commercial software package FLUENT 15.0, in which VOF is used to capture oil–gas– water three-phase flow field based on the Eulerian approach and DPM is adopted to track discrete phase based on Lagrangian approach. Segregated SIMPLE algorithm is employed to couple pressure and velocity. And second-order upwind scheme and second-order centraldifferencing scheme are used for convective terms and diffusion terms, respectively. The convergent criteria for all calculations are set in such a way that the residual in the control volume for each parameter is smaller than 10−5. 3.3. Particles' initialization method The significant difference between this erosion issue and other flow erosion problems is that solid particles are not carried by fluid flow from the inlet. Instead, they stay in a position of the computational domain initially. Therefore, we have developed a particles' initialization method. Firstly, residual oil is defined by region filling way (setting Fo as 1.0 in the specified region). Then, residue particles should be added to the residual oil. At this time, DPM is enabled. As shown in Fig. 2, the tank bottom wall is defined as an injection wall. The vertical height of the injection wall is 0.25 m, half of the height of the bottom hemisphere. The particles' injecting direction is perpendicular to the injection wall. And enough time is given so that enough particles are injected into

nitrogen source

oil source

the computational domain from the injection wall. In this paper, the time used to inject particles is two seconds. In order to ensure that the injection particles are settling on the tank bottom wall, reasonable injection velocity and mass flow rate are defined. Especially, the injection velocity should be small enough so that the kinetic energy of injection particles is small. Then, under the combined effect of gravity and oil resistance, the particles will be deposited in the wall surface. The injection velocity and mass flow rate are set as 0.0001 m/s and 0.1 kg/s, respectively. For Case 1, the total number of injection particles is 2 × 106. After residue particles are arranged, the circumstance is defined as the initial condition for gas flushing process simulation. As shown in Fig. 2, two points corresponding to the lateral wall of the two elbows in the blowdown branch are selected to conduct erosion monitoring experiments. The test values are compared with simulation results to validate this model.

3.4. Computational mesh GAMBIT 2.4.6 mesh-generator is employed to perform all geometry generation and meshing. Fig. 3 shows the grid distribution of computational domain, which is divided into three blocks. Rectangular cells are employed in the tank cylinder and main pipe region, while hybrid cells (rectangular cells and irregular quadrilateral cells) are adopted in the tank bottom and blowdown branch region. A suitable grid density

pressure gauge

pump

particles inlet

flowmeter compressor pressure gauge

oil tank

flowmeter computer elbow specimen water source

pressure gauge pump

flowmeter

cyclone separator drain

Fig. 4. Schematic of erosion test facility.

H. Zhu et al. / Powder Technology 275 (2015) 12–24

is reached by repeating computations until a satisfactory independent grid is found. Five different grid densities are used to conduct grid resolution tests, in order to investigate the grid independency. The mesh generation parameters and the maximum calculated erosion rate for Case 1 at oil emptying time are given in Table 3, in which the percentage changes are indicated inside the parentheses. The percentage difference in the maximum erosion rate reduces with the increase in number of grids. Passing from M4 to M5 grid systems, the value is just 0.08%. The simulations are executed using Intel® Xeon® with specifications of CPU E5-2620 2.0 GHz and 64 GB RAM with Windows 7 platform. Simulations consumed typically 120.4 and 150.1 CPU hours for M4 and M5 grids, respectively. The CPU time undergoes an increase of 24.67% while numerical results undergo a maximum variation of only 0.08%. Therefore, M4 grid system can give a good compromise between precision and calculation time and is sufficient for carrying out numerical simulations in this study.

4. Experimental procedure The test data available for erosion resulting from solid particles in a multiphase carrier fluid is very limited [33]. And most of the tests rely on mass loss measurements and thickness loss measurements, which can only reflect erosion of specimens after a period of flushing. However, monitoring erosion rate varying with time is the concern in this study. Therefore, electric resistance probe sensor is employed to obtain cumulative erosion rate, which is reflected by the change of resistance. The resistance is equal to voltage divided by electric current. By applying a constant current, the voltage change is observed, and then the resistance change can be obtained. A schematic of the testing facility is shown in Fig. 4. The two elbows of the blowdown branch are the erosion test sections. A representative elbow test cell is also shown in Fig. 4. The electric resistance probe sensor is installed at the lateral wall of the elbow. Oil and nitrogen are used as the carrier fluid, and the operating conditions and fluid parameters

pressure (Pa) 600000 595862 591724 587586 583448 579310 575172 571034 566897 562759 558621 554483 550345 546207 542069 537931 533793 529655 525517 521379 517241 513103 508966 504828 500690 496552 492414 488276 484138 480000

t=1s

t=2s

t=3s

t=4s

t=5s

t=6s

t=7s

t=8s

t=9s

t=10s

t=11s

t=12s

t=13s

17

t=14s

Fig. 6. Hydraulic pressure distribution profile at different times.

18

H. Zhu et al. / Powder Technology 275 (2015) 12–24

are the same as Case 13. First of all, the oil tank and pipelines were flushed with nitrogen. Then the bottom valve of the oil tank was closed and solid particles were injected from the particles inlet attached on the top of tank. The total mass of injected particles is 2.14 kg and the particle size is uniform with diameter of 1 mm. After that, the bottom valve was opened, and oil was injected into the tank until the liquid level reached the required residual oil level. Then the water pump began to work so that water starts to flow in the blowdown main pipe. After a while, the gas flushing started, and the sensor began to monitor the erosion

rate. The flushing process and test lasted until the residual oil was completely drained. 5. Numerical results and discussion 5.1. Validation of simulation results To validate the approach in this study, the erosion rate in two points at the lateral wall of the elbows are monitored. Fig. 5 shows the

velocity (m/s)

t=1s

t=2s

t=4s

t=5s

t=7s

t=8s

t=9s

t=11s

t=12s

t=10s

t=13s

t=3s

t=6s

t=14s

Fig. 7. Distribution of velocity vectors and streamlines of flow changing over time.

H. Zhu et al. / Powder Technology 275 (2015) 12–24

comparison of measured and predicted erosion rate. It can be seen that, the simulated erosion rates agree well with the measurement data at both points. The average error of simulation result is under 5%. Therefore, the numerical model used in this work can provide reasonable results. 5.2. Process of gas flushing Case 13 has a long emptying time (14 s), which is selected to analyze the variation of flow field and erosion rate. The hydraulic pressure distribution profile at different times is shown in Fig. 6. Pressure in the computational domain has a significant change with time. Initially, because of the presence of residual oil, there is a greater pressure difference in oil tank. Gas needs enough pressure to flush the residual oil. The pressure difference decreases with the discharge of residual oil,

19

which reduces from 0.380 MPa at t = 1 s to 0.013 MPa at t = 14 s. This means that the pressure needed for gas flushing decreases as residual oil is reduced. Fig. 7 shows the distribution of velocity vectors and streamlines of flow changing over time. It can be seen that a pair of symmetrical swirls is formed in the oil tank. When there is residual oil in the tank, the swirls appear at the top of the tank. The reason is that the injected gas encounters the blocking of residual oil. Besides gas pushing forward the oil flowing out from tank into blowdown branch, part of gas is forced to do cyclotron motion above the liquid level. With the gradual outflow of residual oil, the swirl size increases gradually until the height of the tank. There is a significant jet trajectory from gas inlet. When the entrance of blowdown branch is exposed to gaseous environment, jet trajectory has been fully developed. Streamlines become dense in the blowdown branch. Because oil–gas flow is carried by water in the

Fig. 8. Time history of clean-up (reflected by oil volume fraction).

20

H. Zhu et al. / Powder Technology 275 (2015) 12–24

erosion rate (kg·m-2·s-1) 5.2E-09 4.93684E-09 4.67368E-09 4.41053E-09 4.14737E-09 3.88421E-09 3.62105E-09 3.35789E-09 3.09474E-09 2.83158E-09 2.56842E-09 2.30526E-09 2.04211E-09 1.77895E-09 1.51579E-09 1.25263E-09 9.89474E-10 7.26316E-10 4.63158E-10 2E-10

t=1s

t=2s

t=6s

t=7s

t=11s

t=3s

t=8s

t=12s

t=13s

t=4s

t=5s

t=9s

t=10s

t=14s

Fig. 9. Time-varying erosion rate on oil tank surface and blowdown pipe wall.

main pipe and water has a larger density, the streamlines of oil and gas flow are gathering near the top of the main pipe in the downstream of junction.

The oil emptying process is shown in Fig. 8, in which the variation of oil volume fraction is employed to reflect the time history of clean-up. The loss process of residual oil in the tank can be clearly seen from

Fig. 10. Variation of the maximum erosion rate with time for different gas inlet velocities.

H. Zhu et al. / Powder Technology 275 (2015) 12–24

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Fig. 11. Variation of the maximum erosion rate with time for different oil densities.

Fig. 8. The intermediate liquid level has a faster drop rate, forming concave meniscus. When the majority of residual oil has been driven out from the tank, there is a layer of oil film still adhering to the tank surface because of oil viscosity. Therefore, gas flushing should continue until the oil film is thin enough. The erosion location and erosion rate on the oil tank surface and blowdown pipe wall during the flushing process are visible from Fig. 9. In the initial few seconds, residual oil is driven into the blowdown branch and the particles are carried by oil flow. As a consequence of lower velocity of oil flow and greater viscosity of oil, the erosion rate is relatively small and the erosion locations mainly appear in the injection wall and the first half of the branch pipe. Four seconds later, the majority of residual oil has flowed out from the tank. And the carrying fluid entering the branch pipe has been transformed into oil–gas two-phase flow. Moreover, gas occupies a major component of oil–gas flow, while oil appears in the form of liquid droplets. Because of the higher speed of gas flow, particles received more collision kinetic energy, resulting in more severe erosion. At the last moment, almost the entire branch pipe

presents the flow erosion. It can be noticed that the maximum erosion rate occurs at the entrance of the branch pipe, because the rapid change of flow area and flow direction in the connection of the tank and branch pipe allows particles impacting in that region of the flow as the particles deviating from the fluid flow. 5.3. Effect of gas inlet rate Fig. 10 presents the variation of the maximum erosion rate with time for different gas inlet rates. It clearly reveals that the time required for oil emptying is closely related to gas inlet velocity. The time increases with decreasing the gas speed, which increases nearly four times as gas inlet rate decreased from 2.5 m/s to 0.5 m/s. The five curves have a common feature that the erosion rate has a sharp rise in the end of emptying process. It can be explained that with increasing process time, fluid in the branch pipe transforms from oil flow into oil–gas two-phase flow, and then transforms into almost pure gas flow, which results in a rise in the particles-carrying fluid rate. Especially when the

Fig. 12. Variation of the maximum erosion rate with time for different oil viscosities.

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H. Zhu et al. / Powder Technology 275 (2015) 12–24

Fig. 13. Variation of the maximum erosion rate with time for different residual oil levels.

majority of residual oil has been discharged, particles carried by highspeed gas flow have more impact inertia striking on pipe wall, which caused the rapid increase in erosion rate. Fig. 10 also indicates that the maximum erosion rate at the end of the flushing process increases as the gas inlet rate increases. For an inlet rate of 2.5 m/s, the maximum erosion rate is 1.97 times that for the inlet rate of 0.5 m/s.

is the gravity of oil flow, which results in shorter time required for oil to be released from the tank. It is seen that the maximum erosion rate for high-density residual oil has a greater value at the same time (t = 6 s). The reason is that the sooner the oil is driven out, the longer is the exposure time of the surface in particle-carrying gas flow impact.

5.4. Effect of residual oil density

5.5. Effect of residual oil viscosity

The time-varying erosion rate for different oil densities is shown in Fig. 11. The five curves also have a significant turning point as stated above. However, the turning points do not occur at the same time. For a density of 900 kg/m3, the starting point of a sharp increase in erosion rate appears at a time of 5.26 s. While for a density of 700 kg/m3, the starting point appears at a time of 5.71 s. This starting point of erosion rate's sharp rise indicates that the fluid in computational domain is transformed into gas-dominated flow, and also indicates that it is close to the end of emptying. The greater the density of oil, the greater

Fig. 12 displays the variation of the maximum erosion rate with time for different oil viscosities. Greater shear stresses acting on highviscosity oil make oil adhere to the wall strongly. It is difficult to drive high-viscosity oil out from the tank. So the time consumed for emptying oil with viscosity of 30 Pa·s is the longest one, which is 14 s, 2.33 times that required for oil with 0.85 Pa·s. The smaller the oil viscosity, the smaller is the viscous resistance subjected by particle motion. Thus, the greater the collision impact on the wall, the larger is the erosion rate. For a viscosity of 0.85 Pa·s, the maximum erosion

Fig. 14. Variation of the maximum erosion rate with time for different particle diameters.

H. Zhu et al. / Powder Technology 275 (2015) 12–24

rate reaches at 1.19 × 10− 7 kg·m− 2·s− 1. However, the value is just 5.2 × 10− 9 kg·m− 2·s− 1 for a viscosity of 30 Pa·s.

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decreasing erosion. Longer flushing time is required for higher liquid level, resulting in more severe erosion.

5.6. Effect of residual oil level Acknowledgments The time history of changes in erosion rate for different residual oil levels are presented in Fig. 13. The required flushing time increases with increasing the residual oil level. For a level of 1.1 m, just 1.86 s is needed, while it becomes 6 s for a level of 1.5 m. There is not much difference in the maximum erosion rate at the end time among the levels of 1.1 m, 1.2 m and 1.3 m. However, the maximum erosion rate has a significant rise for levels of 1.4 m and 1.5 m. Especially, the erosion rate for 1.5 m has reached the maximum value. The long flushing time is the main reason for this erosion result. 5.7. Effect of residue particle diameter Fig. 14 shows the variation of the maximum erosion rate with time for different particle diameters. Small-diameter particles are easily carried away by fluid flow. Thus, the probability of impinging on the wall is less, resulting in small erosion rate. In contrast, large-diameter particles have great inertia, leading to more severe erosion. The maximum erosion rate increases with the increase of particle diameter. However, the growth rate of erosion rate is decreasing. There is no obvious difference in the maximum erosion rate between particle diameter of 1.5 mm and particle diameter of 2.0 mm. Particle motion and resulting erosion in both the tank and pipe wall are primarily determined by two mechanisms: drag force and particle inertia. Although the particle inertia increases as the diameter rises, the drag force exerted on particles is also increasing. So the erosion rate is the result of the combined effects of particle inertia and drag force. 6. Conclusions A numerical approach based on CFD coupling with VOF and DPM has been conducted to study the process and flow erosion of flushing oil tank with nitrogen. It is shown that the model can satisfactorily capture the changes in flow field and predict the location and extent of erosion. And the simulation results show that the erosion rate in the wall surface well agrees with the corresponding test data. According to the result analysis, the following conclusions can be drawn: (1) A particles' initialization method is developed by injecting particles from the injection wall within a sufficient time. The injection velocity is small enough so that particles can be deposited in the wall surface under the combined effect of gravity and oil resistance. After residue particles are arranged, the circumstance is defined as the initial condition for flushing process simulation. (2) Flow field and erosion rate are sensitive to inlet condition changes, fluid parameter changes and operating condition changes. The required flushing time increases with the increase of oil viscosity or oil level, while decreases as gas inlet rate increases. (3) Flow erosion is related to the emptying process of oil. The erosion rate increases slowly in the initial few seconds, while it has a sharp rise at the end of the emptying process due to the particle-carrying fluid being transformed into gas-dominated flow. The maximum erosion rate occurs at the entrance of the branch pipe, because of the rapid change in flow area and flow direction. (4) Erosion rate is the result of the combined effects of particle inertia and drag force. Particle inertia dominates the particle motion with high-speed carrying flow, and low density and viscosity fluid (e.g. gas-dominated flow), resulting in rise in erosion rate. When oil viscosity increases, the drag force exerted on particles by the carrying fluid has greater effect on particle motion. Consequently, fewer particles impinge the wall, which results in

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