presented and illustrated, the design engineer will obtain a clearer idea of the magnitude of deviations between the reported value and a safe value for design purposes than is afforded by simply using the reported experimental error. Nomenclature
Note. Any consistent set of units may be used. B = second virial coefficient P = pressure P o = vapor pressure R = gas-law constant t = temperature T = absolute temperature specific volume x = liquid phase mole fraction Y = vapor phase mole fraction Y = activity coefficient yo = activity coefficient at infinite dilution 6 = factor defined as 612 = 2B12 - B11 - B22 net error of a vapor-liquid determination in terms c = of subscript on t nonideality factor accounting for pressure effects on both liquid and vapor phases
v =
SUPERSCRIPTS
v L
= vapor phase = liquid phase
SUBSCRIPTS
p,=
calculated expressing net error in terms of pressure
P = calculated expressing net error in terms of vapor pressure
t = calculated expressing net error in terms of temperature x = calculated expressing net error in terms of liquid
phase mole fraction Y = calculated expressing net error in terms of vapor phase mole fraction 1 = component 1 in a mixture 2 = component 2 in a mixture T = absolute temperature P = pressure Literature Cited
Black, Cline, A.1.Ch.E. J . 5, 249 (1959). Erg. Chem. 50, 391 (1958). Black, Cline, Id. Brown, I., Ewald, A. H., Australian J . Sci. Res. 44, 198 (1951). Friend, John, M. S. thesis, University of Nebraska, 1968. Kretschmer, C. D., Nowakowska, Janina, Wiebe, Richard, J . A m . Chem. Soc. 70, 1785 (1948). Prausnitz, J. M., A.1.Ch.E. J . 5, 3 (1959). Scatchard, George, Wood, S. E., Mochel, J. M., J . A m . Chem. Soc. 61, 32 (1939a). Scatchard, George, Wood, S. E., Mochel, J. M., J . Phys. Chem. 43, 119 (193913). Van Ness, H. C., “Classical Thermodynamics of NonElectrolite Solutions,” p. 122, Macmillan, New York, 1964.
c = calculated e = experimental i = component i in a mixture
RECEIVED for review May 14, 1969 ACCEPTED September 12, 1969
SOME PUMPING CHARACTERISTICS OF COAL CHAR SLURRIES M A R T I N
E.
S A C K S ,
M I C H A E L
J .
R O M N E Y ,
A N D
J O H N
F .
J O N E S
Chemical Research and Development Center, FMC Corp., Princeton, N . J . 08540 The transportation of char produced from the pyrolysis of coal in slurries with water and with oil was investigated as a means of reducing the delivered cost of coal-derived energy. Viscometer tests showed that the apparent viscosity of char slurries could be reduced by adding -325-mesh char to the original size consist of the char. The greatest reduction in viscosity occurs when the 48- to 325-mesh fraction is minimized. Char-oil and char-water slurries with up to 5 0 weight % solids were pumped in a I-inch-diameter test pipeline. Pressure drop-velocity data correlated assuming a Bingham-fluid model. Pumping costs of 0.16 cent per ton per mile for a 5 0 weight % char-water slurry were predicted and are comparable to the costs of other commercial slurry pipelines.
ASpart of the program sponsored by the Office of Coal Research for increasing coal markets, Project COED (Char Oil Energy Development) is aimed at developing an economic process for upgrading coal energy by converting coal t o an oil, a gas, and a fuel char, and decreasing the delivered cost of coal energy (Jones et al., 1966). One possible method for lowering the delivered cost of 148
coal energy is to transport the char in a slurry to market. The pumping of solid fuels in a slurry is not new. Consolidation Coal Co. demonstrated the feasibility of pumping coal-water slurries in a 108-mile coal pipeline (Reichl and Thagard, 1962). Char from a COED plant could be conveyed in either a water or oil slurry, or pumped in a water slurry with intermittent slugs of COED Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 1, January 1970
oil. The objective of this study was to obtain preliminary data in order to evaluate the technical feasibility of transporting char in a pipeline as a slurry. The viscosity of char slurries was measured to determine the effects of char loading and size distribution. This survey was followed by extensive testing in an experimental pipeline. Slurry Material
Water and two oils-mineral oil and a petroleum recycle oil-were used as slurry media. The latter oil was used because it was similar to the product oil from a COED plant. The viscosities of mineral oil and petroleum recycle oil are 36 and 8 cp., respectively, a t 100" F. The char used for the slurries was obtained from pyrolysis of Utah A-seam coal in a multistage fluidized-bed process developed under Project COED (Jones et al., 1966). Its properties are listed in Table 1.
Y)
W
200I
0 + W z V
='
too-
u"
9080-
i
y >
70-
c
60-
z
50-
Initial Viscosity Measurements
a
A rotating-spindle viscometer, Brookfield Model RVT, was used. The depth to which the spindle was inserted into the slurry, the time required for the measurement, and the temperature of the slurry were duplicated for each test. Apparent slurry viscosities were determined at 100' F. For char loadings higher than 25 weight %, the apparent viscosities of the two char-oil slurries were nearly the same, although the viscosities of the pure slurry media differed by a factor of 3.5 (Figure 1). The apparent viscosities of the water slurries were lower a t the same solids concentrations. The size consist of the char has a large effect on the observed viscosity of the slurry. Size consists for eight slurries are shown in Table 11. The size distributions have two distinct peaks. One occurs between 16- and 100-mesh, and the other below 325-mesh. The average particle size was changed by varying the relative size of these two peaks. Test 8 is different from the others in that a large proportion of plus 16-mesh char is present with little material between 48- and 325-mesh. This slurry had an apparent viscosity of 184 cp., while the slurry in test 4, which had the same average particle size, had an apparent viscosity of 288 cp. Thus, a size distribution
a
40-
Table 1. Physical Properties of Char
After Pumping
Properties Density Bulk, lb./cu. ft. Packed, lb./cu. ft. Particle, g./cc. Sieve analysis, Tyler Mesh, cum. wt. 5; 14 28 48 100 200 325 Pan Av. particle diameter, inch
Before Pumping 27 31 0.79
Slurry medium Mineral Recycle oil oil
... ...
34 41
...
...
4 27 60 82 95 98 100
1 11 41 68 80 85 100
3 25 58 83 95 99 100
0.009
0.005
0.009
Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 1, January 1970
--
30
-
20
-
- RECYCLE
I
- MINERAL
OIL OIL
MEASUREMENTS AT IOO'F. W I T H A BROOKFIELD
COSIMETER I
1
0
10
I
I
30 40 CHAR CONTENT, WT. %
20
VIS-
MODEL RVT. 50
Figure 1. Effect of char concentration on apparent viscosity of slurries
containing large and small particles, but no intermediate ones, may be desirable. This confirms the conclusions of Moreland (1963) and Reichl (1963). Experimental Pipeline
A sketch of the pipeline used for testing the pumpability of char slurries is shown in Figure 2. The major components are: a centrifugal pump with an open impeller and a 15-hp. motor, a 150-gallon slurry tank with an attached mixer for agitation, a 55-gallon weigh drum for determining volumetric flow rates, about 100 feet of 1-inch schedule 40 pipe arranged for recycle to the weigh tank or slurry tank, and pressure-measuring devices consisting of diaphragm pressure seals, 6-inch dial gages, and mercury manometers. Known weights of char and slurry media were charged to the slurry tank and allowed to mix a t least 1 hour to allow for absorption of the media in the pores of the char before taking measurements. Flow rates in the test section were controlled by bypassing a portion of the flow from the pump back to the slurry tank. Flow rates were determined by diverting the flow from the test section to a weigh tank. Average linear velocities ranged from 1 to 20 feet per second. The pressure drop was measured over a 20-foot section with dial gages and manometers. Pressure drops varied from 1 to 10 p.s.i. over the 20-foot section. Pipeline Results
At low char loadings, the pressure drop obeyed the relationship: 149
Table II. Effect of -325-Mesh Char Content on Apparent Viscosity of Char-Oil Slurries
Char Size Consist, W t . '?a on Tyler Screen 48 IO0 200 325
-325
Al: Particle Diameter, Inch
1.3 1.2 4.0 1.1 0.9 0.8 6.6 1.1
0.9 10.0 17.0 20.0 30.0 40.0 27.5 26.5
0.00739 0.00447 0.00344 0.00323 0.00252 0.00205 0.00245 0.00310
Test No.
16
28
1 2 3 4 5 6 7 8
5.6 5.1 6.0 4.5 4.0 3.4 0.3 31.0
21.2 19.3 19.0 17.1 15.0 12.8 11.0 20.5
36.8 33.4 30.0 29.7 26.0 22.3 26.4 12.0
10.8 9.8 9.0 8.7 7.6 6.5 10.6 2.6
23.4 21.2 14.0 18.9 16.5 14.2 17.6 6.1
Viscosity of 44 W t . %-CharOil Slurry at 1000F., C p . 616 344 328 288 250 180 202 184
I 20' I T O MANOMETER
TO MANOMETER DIAPHRAGM SEAL
TIMER
(1"
n
SCH. 40 P I P E
?
I
MIXER
nl
I
I
/I
I
WATER
I
t' WATER
t DRAIN
J
I CENTRIFUGAL PUMP
Figure 2. Pipeline test system
The exponent was 1.7 for the two oil slurries, and 1.9 for the water slurries. This relation held for concentrations up to 25, 30, and 40 weight %c for the recycle oil, mineral oil, and water slurries, respectively, and for velocities as low as 3 feet per second. The experimental data illustrating this relationship are shown in Figures 3 and 4. At higher concentrations the pressure drop was dependent on a smaller power of the velocity. This is an indication of the transition region between laminar and turbulent flow. However, dilute slurries could not be pumped in the laminar regime and concentrated slurries could not be pumped in the fully turbulent regime with the existing experimental equipment. The effect of particle size on pressure drop was determined for char-water slurries. The addition of large amounts of -325-mesh char caused a marked decrease in the pressure drop, compared to that of a slurry with equal total solids loading but no fine material. Slurries with solids concentrations up to 50 weight "c were easily pumped. The quantitative effect of this fine material is shown in Figure 5 for two velocities a t a total solids loading of 50%. The pressure drop appeared t o be minimized when about one-half the char was -325-mesh.
A RECYCLE OIL
25
Discussion
An initial attempt was made to correlate the pipeline data on a friction factor-Reynolds number plot using the viscosity determined on the Brookfield viscometer. The general shape of these plots was characteristic of the well known correlations for Newtonian fluids. The transition 150
Figure 3. Pressure drop vs. velocity for char-oil slurries with solids concentrations from 5 to 30 weight Yo Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 1, Jonuory 1970
CHAR CONCENTRATION WT. PERCENT
34 35 35 36 39
0 0
w
-du =o dr
0 V 0
T < T >
This equation can be integrated for laminar pipe flow to give
a
If the yield stress is small compared to the wall stress, the last term in the brackets may be neglected. Rearrangement and the insertion of ( A P L ) R / 2 for the wall shear stress transform Equation 3 into
4
w
9
0.1
W
a
0
t
0.02I 2
I
I
I
l
l
l
l
l
10
VELOCITY, f t / sec.
20
Figure 4. Pressure drop vs. velocity for char-water slurries with solids concentrations from 21 to 3 9 weight Yo
"." W
E a
LL
The laminar data for char-water slurries are plotted on the coordinates of pressure drop us. velocity in Figure 6. The resulting curves are in good agreement with Equation 4. Values of the yield stress and the plasticity were calculated from the slopes and intercepts of the curves on Figure 6 and are tabulated in Table 111. Data for the charoil and coal-oil (Berkowitz et d . ,1963) slurries are included. Yield stresses ranged from 0.2 x to 4.9 x lo-' p.s.i. and plasticities ranged from 28 to 104 cp. For char-water slurries in the limited range of char concentrations from 45 to 52 weight % and -325-mesh char concentrations from 28 t o 48 weight % of the total solids, the yield stress was found to be
0
= 3.6 x lo-' p.s.i.
O
a
w a
with an uncertainty of +60% a t the 90% confidence level. The plasticity was correlated to the equation
0.2
q =
w
2.3 CI - 0.8'7 Cp - 44
(6)
with an uncertainty of &25% a t the 99% confidence level. The failure of the friction factor-Reynolds number plot to correlate the data can now be explained. T h e dimensional analysis leading to this correlation was based on only one rheological parameter, the Newtonian viscosity. If the two Bingham parameters are taken into consideration, a third dimensionless group is required (Michiyoshi et al., 1966; Thomas, 1963), the Hedstrom number:
n
d 0
a 0
:: I t 2
(5)
7%
I-
0.1
v)
W
E 30 40 50 60
.O520
MINUS
325-MESH
CONTENT
OF CHAR, W T . %
Figure 5 . Effect of content of -325-mesh char on pressure drop for a 50-50 char-water slurry
-~ Table 111. Rheological Parameters
from laminar t o turbulent flow was readily apparent. However, the quantitative results were not satisfactory. The transition to turbulent flow occurred a t a Reynolds numbe? of 1200 for char-mineral oil slurries and a t 600 for char-water slurries. I n addition, the laminar data for the char-water slurries were not correlated by a single line. There was a definite trend towards higher friction factors with decreasing particle size (increasing -325mesh). A possible non-Newtonian model is the two-parameter Bingham fluid (Bird et al., 1960). This model gives the following relationship between the shear stress and the shear rate: Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 1, January 1970
Solids Concentration, Wt. f i 50.4 char in water 47.4 char in water 48.9 char in water 52.3 char in water 45.4 char in water 38.0 char in recycle oil 55.0 coal in oil
-325- Mesh Char Concentration, Slurry W t . 5; of Total Derwity, Solids Lb./Cu. Ft. 47.5 36.9 34.8 28.6 28.6
76.0 77.0 78.0 78.2 76.5
... ...
... ...
Yield Plasticity Stress, or Limiting Viscosity, T , , P.S.I x 10' 7, CP. 2.9 28 1.8 38 4.9 36 50 3.7 3.8 31
... 0.2
104 57
151
0.31
I
I
o,3,
I
I
I
I
I
1
,VELOCIT:,ft
/snc,
I
1
I
I
I
I
,
,
-0.2 -
54 n
g s w
-
3
201SOLID
W
SYMBOL
0
A
CONCENTRATION! W T 50 4 47 4 I SEE TABLE FOR RHEOLOGICAL PARAMETERS
2
I
0
3
5
4
6
9
8
7
IO
VELOCITY, f t , / s w .
Figure 6. Pressure d r o p vs. velocity for laminar flow of char-water slurries
WT. % CHAR-WATER 38 WT. % CHAR-OIL
45
w r . ye
COAL-OIL
;'b 6
'b'lb00
5s -3
IOILO
I
; h' I
pvD
Re=
'b'hooo
L
I
d
I
l~'lbO,OOO
T
Figure 7. Plot of Hedstrom number-Reynolds number-friction factor
152
Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 1, January 1970
i
/ /
5-A L
other commercial slurry pipelines (Reichl and Thagard, 1962). In the final economic evaluation, several other factors need to be considered. The costs in Figure 8 do not include terminal facilities. These include not only capital investment in pumping stations, but slurry preparation and separation facilities as well. The effect of the extrafine material, which must be added, on product value has not been determined. Acknowledgment
The authors thank the Office of Coal Research, Department of the Interior, and the FMC Corp. for permission to publish this paper, C. R . Allen for performing the initial work, and C. A. Gray for counsel during the investigation.
I . BASED ON 2 0 y r S T R A I G H T - L I N E DEPRECIATION 2. DOES NOT INCLUDE COSTS OF T E R M I N A L FACILI TIES. I
I
I
I
I
I
I
I
I
I
16.1 9.05 580 403 S53 2.78 213 1.7‘25 1.425 l.lS5
Nomenclature
VELOCITY, FT./SEC.
0
4
12 16 20 PIPE INSIDE D I A M E T E R , INCHES
8
24
28
Figure 8. Pipe diameter vs. cost of pipelining for a constant throughput of 11,380 cubic feet per hour
The Reynolds number is now based on the plasticity instead of the Brookfield viscosity:
(8) The data for char-water slurries in laminar flow were plotted using these dimensionless parameters in Figure 7. One set of data for char-oil slurries and a set for coal-oil slurries (Berkowitz et al., 1963) are included. This correlation indicates that the Hedstrom number is about 1000, which is consistent with the value calculated from experimental yield stresses. A significant aspect of this correlation is the predicted suppression of turbulence a t high Hedstrom numbers. Since the Hedstrom number is proportional to the sqoare of the pipe diameter, it becomes increasingly important when attempting scale-up, provided char slurries can be adequately represented by the Bingham fluid model at high Hedstrom numbers. More work is required to extend the data to higher Hedstrom numbers. Economics
From the predictions of the correlation in Figure ‘i and the properties of the slurries studied, a preliminary estimate of pumping costs for char from a 3.5 M M T P Y COED plant in a 50 to 50 slurry with water was obtained. Figure 8 shows the estimated cost on a cents per ton per mile basis as a function of pipe diameter. Only those costs which are dependent on pipe diameter are included. At the diameter corresponding to the minimum in the total cost curve, the pumping cost is 0.16 cent per ton per mile. This is comparable to the operating costs of
Ind. Eng. Chem. Process Der. Develop., Vol. 9, No. 1, January 1970
a = constant defined in Equation 1, dimensionless = total char concentration, weight % C? = -325-mesh char concentration, weight % of total solids D = pipe diameter, ft. k = constant defined in Equation 1 L = pipe length, ft. “e = Hedstrom number = (prD’)/ v i dimensionless Nk, = modified Reynolds number = p D i q dimensionless AP = pressure drop, lb., ft:’ 4 = volumetric flow rate, cu. ft./sec. r = radial distance, ft. R = pipe radius, ft. s = pipe cross-sectional area, sq. ft. u = linear velocity, ft. set.-' duldr = shear rate, set.-' average linear velocity, ft. set.-' B = plasticity defined by Equation 2a, lb., sec. ft.-’ density, lb., ft.-J p = 7 ’ shear stress, lb., ft.-’ T v = shear stress at wall = P ( R ] / L ( S ) lb., , ft.-’ 7 , = yield stress defined by Equation 2a, lb., ft.-’ c 1
v
v =
Literature Cited
Berkowitz, N., Moreland, C., Round, G. F., Can. J . Chem. E%. 41, 116-21 (1963). Bird, R. B., Stewart, W. E., Lightfoot, E . N., “Transport Phenomena,” pp. 48-50, Wiley, New York-London, 1960. Jones, J. F., Eddinger, R. T., Seglin, L., Chem. Eng. Progr. 62 (2), 73-9 (1966). Michiyoshi, I., Matsumoto, R., Mizuno, K., Nakai, W., Intern. Chem. Erg. 6 (2), 383-8 (1966)> Moreland, C., Can. J . Chem. Eng. 41, 24-8 (1963). Reichl, E . H. (to Consolidation Coal Co.), U.S. Patent 3,073,652 (1963). Reichl, E . H., Thagard, W. T., Paper CPA 62-5113, National Power Conference, Baltimore, September 1962. Thomas, D. G., Ind. Eng. Chem. 55 ( l l ) ,18-29 (1963a). Thomas, D. G., Ind. Eng. Chern. 55 (lis), 27-35 (1963b). RECEIVED for review May 5, 1969 ACCEPTED October 6, 1969
153
