WSRC-TR-2000-00263
Minimum Velocity Required to Transport Solid
Particles from
the 2H-Evaporator to the Tank Farm
Michael R. Poirier
Westinghouse Savannah River Company
Aiken, SC 29808
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Summary
CSTE requested SRTC to determine the requirements for transferring insoluble solids from the evaporator pot to the High Level Waste Tank Farm. SRTC performed the analysis by reviewing available information on the properties of the solids and fluid that need to be transported and by reviewing the technical literature for information on transporting slurries through pipelines.
Solid-liquid horizontal flow can occur in a number of different flow regimes. The common flow regimes are pseudo-homogeneous suspensions, heterogeneous suspensions, heterogeneous suspensions with sliding beds, and stationary beds. Slurries should be transported as heterogeneous suspensions.
The following assumption were made to perform the analysis: All pipelines are either vertical or horizontal, the particle density is 3.93 g/cc, the fluid density is 1.0 g/cc, the particle diameter is 0.1 – 4.0 mm, the fluid viscosity is 1 cp., and the pipe diameter is 2 inches. Based on these parameters, the following transport velocities are predicted:
SRTC makes the following recommendations to CSTE for transporting solid particles from the 2H-evaporator to the Tank Farm:
Introduction
Aluminosilicate forms in the SRS high level waste system by the reaction of aluminum from the Separations Canyons with silica from DWPF recycle. The high temperature of an evaporator accelerates the normally slow reaction. The 2H-evaporator pot contains approximately 3500 kg of solids that include aluminosilicate and slightly enriched uranium (108 kg). SRS High Level Waste proposes to remove the solids by dissolving them with nitric acid, neutralizing the acid solution, and transferring the solution to the tank farm. The transferred solution will contain insoluble solid particles. CSTE requested SRTC to determine the requirements for transferring insoluble solids from the evaporator pot to the High Level Waste Tank Farm.
Analysis
SRTC performed the analysis by reviewing available information on the properties of the solids and fluid that need to be transported and by reviewing the technical literature for information on transporting slurries through pipelines.
The following assumptions were made to perform the analysis:
Vertical Pipelines
One guideline for transporting solid particles in vertical pipelines is for the bulk fluid velocity to be greater than twice the particle settling velocity.^{5,6,7}
where v_{s} is the settling velocity, g is the acceleration due to gravity, s is the ratio of particle and fluid densities (s = particle density/fluid density), d_{p} is the particle diameter, and n is the fluid kinematic viscosity (n = m/r).
To perform the calculation, one assumes a particle Reynolds number, calculates the settling velocity with the appropriate equation, and calculates a new particle the Reynolds number with the calculated settling velocity. If the Reynolds number is in the correct range for the equation used, the calculated settling velocity is correct. If the Reynolds number is not in the correct range for the equation used, use a different equation to calculate the settling velocity. Repeat these steps as necessary. Table 1 shows the calculation results. If the particle size is 4.0 mm, a fluid velocity of 3.86 ft/sec is needed to transport the solid particles through vertical pipelines.
Table 1. Calculated Particle Settling Velocity
Particle Size (mm) |
0.1 mm |
4.0 mm |
Particle density |
3.93 g/cc |
3.93 g/cc |
Fluid density |
1.0 g/cc |
1.0 g/cc |
Viscosity |
1.0 cp. |
1.0 cp. |
s |
3.93 |
3.93 |
Re_{p} |
1.6* |
2359 |
Settling velocity (ft/sec) |
0.052 ft/sec |
1.93 ft/sec |
Transport Velocity (ft/sec) |
0.104 ft/sec |
3.86 ft/sec |
* Settling velocity calculated with equation [1]. Using equation [2] yields a settling velocity of 0.46 ft/sec and a Reynolds number of 1.39.
Horizontal Pipelines
Solid-liquid horizontal flow can occur in a number of different flow regimes.^{9,10,11,12} The primary parameters influencing flow regimes are velocity and particle size. The common flow regimes are pseudo-homogeneous suspensions, heterogeneous suspensions, heterogeneous suspensions with sliding beds, and stationary beds. Pseudo-homogeneous suspensions occur at high velocities with small particles. The particles move at the same velocity as the fluid with a uniform distribution across the pipe. With slower velocities and larger particles, heterogeneous suspensions occur. The concentration of particles across the pipe is not uniform, and the particle velocity is slightly less than the fluid velocity. At low velocities with large particles, a heterogeneous suspension with a sliding bed occurs. Particles in upper part of the pipe are in suspension and move with the liquid, while particles in the bottom of the pipe form a bed of solids which moves at a slower, uniform rate. At very low velocities with large particles, a stationary bed occurs. The upper part of the pipe contains a suspension, while the lower part contains a deposit, the surface layers of which move.
The conditions at which sliding and stationary beds occur are of interest because these conditions are normally undesirable. A sliding bed can cause substantial pipe abrasion. Sliding and stationary beds lead to low transport efficiencies. The transition between a heterogeneous suspension and a heterogeneous suspension with a sliding bed is often called the deposition velocity or re-suspension velocity, depending on whether the velocity is decreasing or increasing.^{9} The axial velocity in a transfer line should be greater than the deposition velocity or re-suspension velocity. Slurry transfers should occur as heterogeneous suspensions.^{7,13}
One correlation frequently employed to calculate minimum transport velocities (i.e. for heterogeneous suspensions) in horizontal pipelines is the Durand equation.^{6,7,14} The correlation was developed for coarse particles, and it does not account for differences in particle size. Equation [5] describes the correlation
v_{t} = F[2g(s-1)D]^{ ½} [5]
where v_{t} is the minimum transport velocity, F is an empirical constant that varies between 0.4 and 1.5, and D is the pipe diameter. Using a value of 1.5 for F, 3.93 for s, and 2 inches for the pipe diameter, the calculated minimum transport velocity is 8.4 ft/sec. This correlation does not enable one to calculate the transition between a heterogeneous suspension with a sliding bed and a stationary bed.
Wasp^{6} added a correction to the Durand equation to account for the influence of particle size (d_{p}). Using this correction, the modified Durand equation is described by equation [6].
v_{t} = F[2g(s-1)D]^{ ½} (d_{p}/D)^{1/6} [6]
Using a value of 1.5 for F, 3.93 for s, 2 inches for the pipe diameter, and 4.0 mm for particle diameter, the calculated transport velocity is 5.5 ft/sec. If the particle size is 0.1 mm, the calculated transport velocity (i.e. for heterogeneous suspensions) is 3.0 ft/sec. This correlation does not enable one to calculate the transition between a heterogeneous suspension with a sliding bed and a stationary bed.
Newitt et. al. investigated flow regimes for transporting solids in pipelines.^{9} They measured the velocity needed to transport solids such as sand and gravel in 1 inch and 6 inch pipelines. The particle density was 1.4 – 2.64 g/cc. The particle diameter was 0.02 – 6.0 mm. By reviewing their graph, the author estimated the minimum transport velocity (i.e., for a heterogeneous suspension) for 0.1 mm diameter particles to be 2.5 ft/sec and the minimum transport velocity for 4.0 mm diameter particles to be 13 ft/sec.
The sodium diuranate particles have a density of 3.93 g/cc, which is outside the range of particle density investigated by Newitt et. al. Turian et. al. reviewed 864 critical transport velocity data to develop a correlation for critical transport velocity.^{15} They found the critical transport velocity to vary with the square root of (s-1). To account for the density of sodium diuranate, the Newwitt data was multiplied by a correction factor of 1.33 (=[2.93/1.64]^{1/2}).Using this correction factor, the predicted minimum transport velocities for 0.1 mm and 4.0 mm particles are 3.3 ft/sec and 17 ft/sec, respectively.
The author used their graph to estimate the minimum velocity for the slurry to move as a heterogeneous suspension with a sliding bed. At velocities of 5.6 – 13 ft/sec, 4.0 mm particles would be transported as a heterogeneous suspension with a sliding bed. The correction factor of 1.33 was applied to the transition between a heterogeneous suspension with a sliding bed and a heterogeneous suspension. At velocities of 7.5 – 17 ft/sec, 4.0 mm sodium diuranate particles would be transported as a heterogeneous suspension with a sliding bed.
Turian and Yuan investigated flow regimes for transporting solids in pipelines.^{16} They measured the velocity needed to transport glass beads in 2.43 and 5.25 cm pipes. The particle density was 2.977 g/cc. The particle diameter was 0.03 – 4.4 mm. By reviewing their graph, the author estimated the minimum transport velocity (i.e., for a heterogeneous suspension) for 0.1 mm diameter particles to be 4.0 ft/sec and the minimum transport velocity for 4.0 mm diameter particles to be 9.9 ft/sec.
To account for the density of sodium diuranate, the Turian and Yuan data was multiplied by a correction factor of 1.22 (=[2.93/1.977]^{1/2}). Using this correction factor, the predicted minimum transport velocities for 0.1 mm and 4.0 mm particles are 4.9 ft/sec and 12 ft/sec, respectively.
The author used their graph to estimate the minimum velocity for the slurry to move as a heterogeneous suspension with a sliding bed. At velocities of 7.4 – 9.9 ft/sec, 4.0 mm particles would be transported as a heterogeneous suspension with a sliding bed. The correction factor of 1.22 was applied to the transition between a heterogeneous suspension with a sliding bed and a heterogeneous suspension. At velocities of 9.0 – 12 ft/sec, 4.0 mm sodium diuranate particles would be transported as a heterogeneous suspension with a sliding bed.
Table 2 summarizes the analysis. For 4.0 mm diameter particles, the calculated minimum transport velocity (i.e., for a heterogeneous suspension) varies between 4.4 and 16 ft/sec. The average transport velocity estimated by the four methods is 9.8 ft/sec for 4.0 mm particles.
Table 2. Calculated Minimum Transport Velocity in Horizontal Pipeline
Reference |
v_{t} (0.1 mm particle) |
v_{t} (4.0 mm particle) |
Durand^{ 6,7,14} |
8.4 ft/sec |
8.4 ft/sec |
Wasp^{6} |
3.0 ft/sec |
5.5 ft/sec |
Newitt et. al.^{ 9} |
3.3 ft/sec |
17 ft/sec |
Turian and Yuan^{ 16} |
4.9 ft/sec |
12 ft/sec |
Average |
4.9 ft/sec |
10.7 ft/sec |
The most conservative approach for determining the minimum transport velocity for a heterogeneous suspension would be to select the maximum value from Table 2 (17 ft/sec). Another approach is to take the average of the four values (10.7 ft/sec) and add 25% conservatism (13.4 ft/sec).^{7} The Turian data is more recent than the Newitt data, and Turian’s experimental conditions more closely resemble the expected conditions in the 2H-evaporator. However, the Turian data was collected with glass spheres, while the Newitt data was collected with irregular shaped sand and gravel particles, which would more closely resemble the aluminosilicate particles. With the information available, the recommended minimum transport velocity would be estimated to be 13 – 17 ft/sec. For conservatism, CSTE should design the transport system to have a minimum velocity of 17 ft/sec in horizontal pipelines.
If the transport velocity is between 9 ft/sec and 17 ft/sec, the slurry could be transported as a heterogeneous suspension with a sliding bed or a heterogeneous suspension. Transporting the slurry as a sliding bed could increase erosion and abrasion of the pipeline.
Since the slurry is composed of a mixture of particle sizes, the fine particles that are easily suspended will reduce the settling rate of the coarse particles and thereby reduce the minimum transport velocity.
The minimum transport velocity could be reduced if the insoluble particle size was reduced. CSTE should investigate methods for reducing the size of insoluble articles in the 2H-evaporator pot.
Recommendations
SRTC makes the following recommendations to CSTE for transporting solid particles from the 2H-evaporator to the Tank Farm:
References