Aqueous Transport of Settling Slurries

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Engineering Approaches

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Aqueous Transport of Settling Slurries

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A. HUGHMARK

GORDON

Ethyl Corp., Baton Rouge, La.

This correlation predicts the minimum design velocity for I

preventing solids deposition in a pipeline

(r

TRANSPORT of slurries in a horizontal pipe may be divided into three classes :

T H E AQUEOUS

0 Solid particles less than about 40 microns in diameter can be transported in laminar flow without settling. Solids in the 40-micron to 2-mm. range settle from water in laminar flow but can be transported as a suspension by water in turbulent flow. 0 At normal transport velocities, particles larger than about 2 mm. in diameter are not suspended but bounce and roll along the bottom of the pipe.

Slurries of the second class are considered in this work. In practice, a standard velocity is used as the minimum design velocity for transport of settling slurries in pipelines. Three published correlations predict appreciably different standard velocities, particularly for large pipe sizes. A new correlation procedure is presented here which predicts the standard velocity for aqueous transport

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of settling slurries with an average absolute deviation of 1.2 feet per second. The method is applicable for particle diameters from 40 microns to 2 mm. and pipe diameters of 0.5 to 28 inches. literature Correlations and Data

solids in air were found to fit an extension of the curve for suspensions in water. Durand ( 4 ) derived a correlation for the standard velocity based on experimental data for sand and coal slurries in 1.5- to 28-inch pipes. This correlation is based on a constant

As defined by Spells (72) for settling slurries, a “minimum velocity” of flow is required to maintain all the particles in suspension. At the minimum velocity and for a velocity range above the minimum, frictional head loss is considerably greater than for an equivalent true fluid having a density equal to that of the slurry and viscosity equal to that of water. Spells has then defined the “standard velocity” as the mean velocity of flow at which the pressure gradients for the slurry become identical with those for the equivalent true fluid. This is the standard velocity used as the minimum design velocity for the transport of settling slurries. Spells correlated data from the literature for the minimum and standard velocities with a combination of Froude and Reynolds numbers. T h e Spells correlation has been generally accepted and used as a design method (6). Zenz (75, 76) also correlated data from the literature for the saturation carrying capacity of uniform-size particles in water. This correlation plots vz/ gdpa2 us. W / v p / . Data for suspension of

which depends on the particle size and solids concentration. Durand found that with particles above 1 mm., F L is essentially independent of particle size and concentration. Spells based his correlation on the data of Settle and Parkins (9, 72) for lime slurry, Williams (72, 73) for Modave effluent and boiler ash, and Smith and Carruthers (77, 72), Howard (5),Yufin ( 7 4 , and Blatch (2) for sand slurries. Zenz used the literature data reported by Spells and the data of Ambrose ( 7 ) . Published data of Smith (70), Newitt and others (8),and the extensive data of Murphy, Young, and Burian (7) are included in the data used to obtain the correlation proposed here. Smith reported observed values of the velocity at which settling commenced. Values of the standard velocity were obtained from the pressure drop data of Murphy, Young,and Burian and of Newitt and others with a log-log plot of head loss

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Experimental data for the standard velocity of settling slurries in water are correlated as the Froude number VO1. 53, NO. 5

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MAY 1961

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Table 1.

Data Source

Ref. (1) (1) (2)

(4) (’)

(4) (5)

(7) (7)

(7) (7) (7) (7) ((8) ‘) (9) (10) (10)

(10) (10) (10)

(13) (Is)

(14)

(14)

(14)

Average Absolute Difference between Experimental and Predicted Velocities Good results were obtained with the proposed correlation

Mean Particle Diameter, In.

Particle Densitv.

0.0229 0.00985 0.0637 0.023 0.009 0.04 0.04 0.015 0.020 0.0026 0.0114 0.0314 0.0149 0.0722 0.0505 0.0082 0.0031 0.0070 0.0106 0.0050

165 165 165 162 65.5 163 93.5 162 165 175 178 157 465 473 705 165 125 162 162 162 162 162 125 125 162 162 162

0.0070 0.0106 0.0039 0.0185 0.0098 0.0098 0.0125

Lb./C;. Ft.

Pioe 1Diameter, In. 5.55 5.55 5.55 1.0 6.0 6-28 6-28 4 1.05 0.5 0.5 0.5 0.5 0.5 0.5 1.0

Av. Abs. Diff. betmeen Exptl and Pred. Velocities, Ft./Sec. Proposed correlaSpells Zenz Durand tion 0.6 1.5 2.7 1.6 2.8 39 11.7 2.5 1.3 1.1 1.1 5.0 43 5.2 4.1 0.3 0.9 2.7 1.0 0.8 1.6 0.5 1.7 3.5 3.4 3.6

3.0 3.0

3.0 2.0 2.0 4.0 4.0 9.8 11.7 11.7

... a

0.5 1.0 2.4 0.8 3.4 6.1 3.6 1.7 1.0 0.4 1.5 2.3 3.2 2.1

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Table 11. Proposed Correlation Shows Smallest Absolute Average Deviation and Standard Deviation

0.4 0.3 0.3 0.6 0.4 1.9 0.5 2.1 1.4 1.4 1.2 0.8 2.0 1.7 0.8 1.6 1.1 0.8 0.7 0.9

... ...

3.6 1.7 0.4 0.1 0.5 3.1 0.2

0.9 2.5 3.0 2.5 1.2 3.3 1.0 0.6 2.6 2.2 0.6 3.6 1.9 0.2 3.2 3.4

7.0 2.2 0.5 0.5 0.7 1.2 0.5 0.8 0.3 1.3 7.2 6.6 9.5

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Method Spells (12) Zenz (16,16) Durand (4) Present work

Abs. Av Dev., Ft./Sec.

Std. Dev., Ft./Sec.

5.0 2.2 1.6 1.2

17.1 3.4 2.2 1.55

Table I1 shows the average absolute average deviation and the standard deviation for all data with the four different methods of predicting the standard velocity. Nomenclature

C d

D Fd

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FL

1.9 2.0 0.6 3.2 0 4.5

g pf pe u

TV

Outside range of correlation.

concentration of solids in slurry, vol. yo = particle diameter, ft. = inside pipe diameter, ft. = correction factor for particle diameter = constant in Durand correlation = acceleration of gravity, ft./sec. = density of medium, lb./cu. ft. = density of solid, lb./cu. ft. = mean velocity of flow. ft./sec. = superficial solids mass flow rate at incipient choking, lb./sq. ft./sec. =

Literature Cited

us. velocity.

Minimum velocity at which head loss deviated from a straight line plot was used as the standard velocity. Table I lists the ranges of particle size, particle diameter, and pipe diameter included in the literature data. Correlation far Standard Velocity

Correlation of the experimental data was made with particle diameter, pipe size, liquid and solids density, and solids concentration as variables. The dependent variable is the mean slurry velocity or standard velocity, as defined by Spells. The experimental data indicate that: 0 The standard velocity is independent of pipe diameter between 0.5 and 3 inches. Therefore, a 3-inch diameter applies in the correlation to all diameters between 0.5 and 3 inches. 0 The standard velocity is independent of particle size for the range of particle diameters from 0.0145 to 0.08 inch.

The correlation derived from the experimental data is shown (p. 389) as a smooth curve to give a reasonable fit of the data. Scatter of the data is expected, since the experimental standard velocity is subject to difference in technique and to experimental error. The factor Fd is a Forrection factor for the particle diameter (right). This correction is applicable to all of the different shapes of particles studied by the various investigators. The cor-

390

rection factor is unity for the particle size range of 0.0145 to 0.08 inch, since the data indicate that the standard velocity is independent of particle size in this range. The standard velocity decreases with particle size for particles less than 0.0145 inch. The straight line for this region appears to fit the data. Smith observed standard velocities for sand slurries with a distribution of particle sizes in the slurry. The best fit of these data is obtained by using the mean particle diameter as the diameter of the particle whose surface area is equal to the average surface area of all of the particles. The absolute average deviation between experimental and predicted velocities is shown in Table I for the data given by the different sources.

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Uzbekh. S.S.R.,Ser. Tekh. N a u k . No. 8,

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PARTICLE DIAMETER, FEET Correlating factor, particle size

INDUSTRIAL AND ENGINEERING CHEMISTRY

(1) Ambrose, H. H., Ph.D. thesis, University of Iowa, Iowa City, Iowa, 1952. (2) Blatch, N. S., Trans. Am. SOC. Civil Engrs. 57, 400 (1906). (3) Bond, R. K., Chem. Eng. 64, 249 (October 1957). (4) Durand, R., “Proc. Minnesota Intern. Hydraulics Convention, September 1953,” Pt. I, pp. 89-103, Am. SOC.Civil Engrs., Minneapolis, University of Minresota, 1953. (5) Howard, G. W., Proc. Am. Sac. Cavil Engrs. 64, 1377 (1938). (6) Lowenstein, J. G., Chem. Eng. 66, 133 Jan. 12, (195’9). (7) Murphy, G., Young, D. F., Burian, R. J., U. S. Atomic Energy Commission ISC-474 (1954). (8) Newitt, D. M., Richardson, J. F., Abbott, M., Turtle, R. B., Trans. Inst. Chem. Engrs. (London) 33, No. 2 , 93 (1955). (9) Settle, J. J., Parkins, R., Imperial Chemical Industries, Ltd., General Chemicals Division, Liverpool, England, private communication, 1951. (10) Smith, R. A., Trans. Inst. Chem. Engrs. (London) 33, No. 2, 86 (1955). (11) Smith, R. A., Carruthers, G. A., Imperial Chemical Industries, Ltd., Billingham Division, Billingham, England, private communication, 1951. (12) Spells, K. E., T ~ a n s . Inst. Chem. Engrs. (London) 33, No 2, 79 (1955). (13) Williams, J. C . , Imperial Chemical Industries, Ltd., Billingham Division, Billingham, England, private communication, 1949. (14) Yufin, A. P., Zzvest. Akad. Nauk.

Fd,

is a function of

1146 (1949). (15) Ze& F: A., Petrol. R&er 36, No. 6, 138 (1957). (16) Zenz, F. A., Othmer, D. F., “Fluidization and Fluid-Particle Systems,” p. 326, Reinhold, New York, 1960. RECEIVED for review September 19, 1960 ACCEPTED January 30, 1961