E
~
~ DESIGN, ~ AND ~ PROCESS ~ DEVELOPMENT ~ ~ ~
ternal circulation and oscillation obtained with larger droplets may compensate for the smrtller total interface. Nomenclature
A,* Cj
= solute concentration throughout droplet after time t,
Ci
= Eolute concentration a t droplet interface-assumed
= mean surface area per drop, sq. em.
gram-moles/cc.
constant, gram-nioles/cc. C, = solute concentration throughout droplet when diffusion begins, gram-moles/cc. = mean drop diameter, em. d, = solute diffusivity in disperse phase, sq. cm./sec. D DI = solute diffusivit,y in cont'inuous phase, sq. cm./sec. = correction factor (15, 1 6 ) J"~ = disperse phase concentration/continnous phase concenH tration at equilibrium = individual effective film coefficient for continuous Dhase, k, cm./sec. = individual effective film coefficient for disperse phase, La em./see. K d = over-all coefficient of mass transfer based on disperse phase, cm./sec. I c d s r p ,, K d t k e o r . = expermental and theoretical values, respectively, of Kd. ?l = an integer number = difference of vapor pressure at surface and in free P stream = drop radius, em. r = gaq-constant R = time of drou formalion or time of f ~ fall, e see t = time of eupi.wi~e= lifc of film, sec. tc = time when drop Ijegins to form to
F. GILL
AND
~ ti
G
,
LO) of detachment of drop from nozzle volume per drop, cc. TV est'raction per drop, ,gram-moles ACl,n = log mean concentration difference between dispersc and continuous phase (continuous phase concentrations Twre converted to equilibrium disperse phase concentrations by use of H ) , gram-moles/cc. = dFnsitp of continuous phase, gr?ms/cc. p = viscosity of continuous phase, poises p V
= time (after = =
Literature Cited (1) Arnold, J. H., J . Am. Chem. Soc., 52, 3937 (1930). (2) Bond, W.N., and Newton, D. A, Phil. Mag., 5, 794 (1928). (3) Coulson, J. M., and Skinner, S.J., Chem. Eng. Sei., 1, 5, 1952. (4) Farmer, W. S., Oak Ridge National Laboratories, Unclassified Rept. 635 (1950). (5) Frossling, Nils, Gerlands. Reitr. Geophys., 52, 170-216 (1938). (6) Garner, F. H., Trans. Inst. Chem. Engrs. (London), 28,88 (1950) (7) Garner. F. H.. and Skelland. A. H. P.. Ibid.. 29. 315 (1951). (8; Geddes, R. L.', Trans. Am. Inst. Chem. Engrs., 42, 79 (1946) (9) Higbie, R., I b i d , 31, 365 (1935). (10) International Critical Tables, Vol. 5, p. 69, New York and London, iCIcGraw-Hill Book Co., 1929. (11) Licht, W., and Conway, J. B., IND.EXG.CHEX.,42, 1151 (1950). (12) Lioht, W., and Pansing, IV. F., Ibid., 45, 1886 (1953). (13) Sherwood, T. K., Evans, J. E., and Longcor, J. V. A,, Ibid., 31, 1146 (1939). (14) Thorvert, J., Ann. phys., 2 , 415 (1914). (15) West, F. B., Herrman, A. J.,Chong, A. T., and Thomas, L E. K , ISD. EXG.CHCM., 44, 625 (1952). (16) J17est, F. B., Robinson, P. A , , Xorgenthaler, A. L., Beck, T. R., and XcGregor, D. K , I b i d , 43, 234 (1951). a
.
RECEIT E D for rei iew M a y 23, 1953.
I
ACCEPTED Januaiy 22, 1954.
R. J. RUSSELL
Anglo-Iranian Oil Co., Itd., Research Station, Sunbury-on-Thumer, Middlesex, England
ISCE the conclusion of the first' ~vorldwar the demand for the gasoline and gas oil fractions of crude has increased more rapidly than the demand for residual fuel oil. To meet this demand it has been necessary to cut more deeply into the crude, to take more of the vacuum gas oil fraction int'o salable gas oil, and so to leave heavicr residues for the fuel oil market. The introduction of cracking, which chiefly uses as feed stock the was distillate fractions of crude, has resulted not only in a considerable increase in the bitumen available but also in the production of m-asy residues for iiiclusioii in fuel oil blends. These factors have resulted in a steady increase oT'er the last 30 years in the general level of the viscosity of residual fuel oils and have also led to a relaxation in the stringency with n-hich the low temperature properties of fuels are controlled in specifications. This second effect has been largely due to the nonavailability of realistic testing procedures for fuel oil pumpability. I t is illustrated by the gradual increase in the specification temperature for viscosity in successive British Admiralty fuel oil specifications (Table I). (Commercial marine fuels are, of course, far more viscous than admiralty fuels-up to 7000 seconds Saybolt Universal a t 1CO O F.)
Table I.
British Admiralty Fuel O i l Specifications of Temperature and Viscosity
D a t e of Specification Before 1944 1944-1940
a
Specification Temp, F. 40
70 100 122 Since 1940 ConiTerted t o equivalent Saybolt units.
1264
Max. Viscositya Allowed a t Specification Temp., Saybolt Sec. 1100 1700 510 3 A0
(Faral)
(Universal) (Universal) (Universal)
At the same time that this has becn taking place because of market pressure, the importance of the 3Iiddle East fields has been increasing, as shown in Table 11.
Table (I. Increasing Importance of Middle East Oil Production
Year 1920 1825 1930 1935 1940 1045 1950
World Production of Crude Oil, BIillion Bbl. 594 922 1220 1117 1813 2295 3150
Total Middle East Production, Million Bbl. 10.9; 28.95 39,80 72.2 86.3 167 533
Per Cent of Total World Production from bliddle East 1.84 3.24 3.25
5.08 4.77 7.40 16.90
Although the crude from a large number of field8 in America and the Far East is very n-axy in type, the production of these fields is normally consumed locally and hence does not have any widespread impact on quality. I n contrast, practically the entire crude production from the Middle East, which is of a relatively waxy type, is exported. Thc rising impnrtancs of thc production of the Middle East has resulted in an increase in the amount of waxy fuel oils marketed in temperate climates, where they tend to gel a t normal R inter ambient temperatures. Either the increase in fuel oil viacosity or the increase in fuel oil gelling tendencies may increase the difficulties of handling fuel oils to a level where existing installations are not adequate to deal with them. Although it is possible to handle any fuel with suitable equipment and although any present difficulties are
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Vol. 46, No. 6
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT largely due to failure to adapt installations to the changed fuel oil situation, it is important to know the low temperature pumpability of fuels so that the user can handle the highest viscosity fuel suitable for his equipment and thereby take full advantage of the price differential in favor of the heavier fuels. In addition, sufficient data should be available to permit the assessment of the economics of changing over to the use of heavier fuels and to enable new refinery and transmission pipeline schemes to be designed. This indicates that, in order to be useful in a practical
way, knowledge of the pumpability properties of fuels must be supplemented by engineering-type information on heat losses from hot oil t o cold lines (which are affected by temperature distribution and convection currents in the oil), effective viscosities and pressure drops, and the relative effectiveness of thermal and pressure boosting. There are also problems concerning the possibility and the speed of starting up cold lines and of mixing and contamination when lighter oils are used to displace heavy oils before shutting down a residual fuel line.
FLOW PROPERTIES AND STALLATION CHARACTERISTICS I n this paper the emphasis is on pumpability as a property of the oil, although the over-all handling of an oil in an installation is also a function of the installation. This has a parallel in terms of straightforward viscosity, as with a wax-free oil-viscosity is a pure physical property of the oil, wholly independent of any installation or equipment, but rate of flow involves installation characteristics. What is required, therefore, is a physical property of the oil which will define its pumpability independent of the installation or measuring equipment, but which can be applied, like viscosity, to any installation in order to derive over-all handling qualities. It is helpful to keep in mind the essential difference between cooling a wax-free and a waxy oil. The former increases in viscosity in a known and simple manner as the temperature falls, but it remains a true liquid-Le., it will flow under a pressure difference, however small. The waxy oil behaves in the same way until some temperature is reached below which the “viscosity” increase is not according to a simple law-the viscosity has become anomalous and, a t some lower temperature, the oil ceases t o behave as a true liquid, because it is able to resist the application of a pressure difference. This state is indicated by the ordinary pour point, but for various reasons the pour point cannot be regarded as any more than a probable indication of the pumpability of the oil. It is therefore necessary to choose some more suitable property of the oil, to define it, to outline a method for measuring it which will be independent of the measuring apparatus, and to examine its correlation with the behavior of oil in large scale equipment. Yield Value and Rate of Shear/Shear Stress Behavior Indicate Pumpability of Oil
The well-known Fanning equation, which is the general equation connecting pressure drop, P , density, p , velocity, vl with line length, L , and diameter, D, may be written
or
F is the friction factor which for streamline flow has the value
V D p ’ where
7 is the absolute viscosity.
Substituting this value
and replacing D by ZR, this equation becomes the Poiseuille equation Q
= 7rR4P
87L
where Q is the rate of flow ( = ?rR*v). The Poiseuille equation may be rewritten as follows: June 1954
This equation assumes that the viscosity, 9, is not a function of the rate of shear. By definition, shearing stress =
-7ateofshear
and, since it is easy to show that
RP - is the shearing stress a t the 2L
4Q represents the corresponding rate of shear. pipe wall, ?rR3 Shearing stress has the dimensions of pressure and is therefore expressed in the units in which the pressure is measured, pounds per square inch or dynes per square em. (1 pound per square inch is equivalent to 69,000 dynes per square cm.). The dimen1 sions of rate of shear are 7 (reciprocal seconds). This unit is time an unfamiliar one but it can always be converted to equivalent rate of flow in a pipe of given size. All the quantities on the right-hand side of Equation 1 can be measured experimentally, and Figure 1 shows the type of plot which is obtained with a waxy fuel oil a t different temperatures. Curve A is obtained a t a temperature well above that a t which wax is precipitated from solution and corresponds to a Newtonian liquid for which the viscosity is constant and independent of rate of shear. At some lower temperature, B , the oil has ceased to be Newtonian and shows a viscosity (slope) which varies with shear rate, while a t a still lower temperature, C, not only is the viscosity anomalous as a t B, but, as shown by point Y , the oil can resist a finite shearing stress since no flow results from the application of a stress not greater than Y . The maximum shearing stress corresponding to Y , which can be applied without producing flow or shear, is the yield value of the oil a t temperature C. At temperature B (or above) the yield value is zero. At temperatures where the viscosity is anomalous, three viscosities may have to be dealt with:
1. The “effective” viscosity, OEIEF, a t any rate of shear or shear stress, P. 2. The “slope” viscosity, DEIEF, for any rate of shear or shearing stress on the linear portion of the curve. 3 . The “initial” viscosity corresponding to the slope of the tangent to the curve a t the lowest rate of shear. The initial viscosity is infinite below the yield value and very large just above it. The shearing stress, RP/2L, a t the pipe wall is the maximum that can be applied in the pipe by a given pressure, P (since R is the pipe radius), and unless the applied stress is greater than the yield value no flow will result. These points are well illustrated by Table 111, which shows some results in full scale pumping trials a t 37 F. of an oil having
INDUSTRIAL AND ENGINEERING CHEMISTRY
1265
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT Table 111.
Installation Transfer of
65" F. Pour Point Oil
(Transfer temp. 37' F.) Applied Line Line Pressure, Rate Shearing of Floir-. Length. Diam., Lb./Sq. Stress, Inch Bbl.iRr. Ft. Inches Lb./Sq. Inch 664 15 13.9 0 0.0063 BO4 15 25.2 Flowjiist 0.0119 starts 664 15 13.9 1457 0,0065 Oil being pumped after flow is started.
Effective Viscositj-, Cs. Undetermined 3620"
I n order to determine the pumpability of a n oil i t is ideally necessary to measure the yield value a t a specific temperature and the rate of shear/shear stress behavior a t one or more temperatures. Pour Point I s Not a Satisfactory Index of Pumpability
Fundamentally, pour point cannot be a satisfactory index of pumpability. It has the nature of a "go/not go" test rather than of a measurement Besides, it does not measure the strength of t'he structure set up a t the pour point', which must be a function of many factors which influence the type and agglomeration of wax crystals. The implication of pour point seems t,o be that it represents the temperature a t or below which the oil cannot be pumped -a-hich is untrue, as oils can be pumped a t much lower temperatures under proper conditions. The shearing stress applied in the pour point test is variable, practically indeterminate, but, very small, whereas it should be measurable, adjustable, and constant. Finally, cases are lcnown of oils which ahow anomalous viscosit,y behavior at, temperatures considerably above the pour point. It, is not a criticism of pour point vis-a-vis yield value that it is dependent on previous thermal history of the oil, because yield value is also subject to this complication. It has been shoivn statistically, however, that the reproducibility of pour point determinations is inferior to yield value determinations.
SUSPENSIOH W I R E
SHEARING
Figure 1.
STRESS
, POINTER
Anomalous Viscosity Behavior of Fuel
Oils
an ASTN (maximum) pour point of 05 O F. and a viscosity of 75 cs. a t 100" F. Table I11 illustrates another interesting point in addition to the existence of a yield value. Once the flow has started, the shearing stress necessary t o maintain it is l o m r than that required to initiate flow. Thus, the effect of breaking the gel structure appears to be equivalent to moving from a lower to a higher temperature curve on Figure 1. This point is further brought out in Table IV, which shows for various fuels and temperatures the throughput rates attainable by applying a pressure which is just sufficient t o causc the oil to vield.
Table IV.
Equilibrium Throughput a t Shearing Stress Just Sufficient to Cause Yielding
(Inside diameter of pipe, 12 inches) Throughput, U. S. Gal./Hour, of Fuel with S.U. S . 4 Viscosity of Temp.. 0 F. 450 570 900 60 74,500 3,000b 30,000 50 60,000 36,000 15.000 40 42,000 30 000 15,000 30 36,000 24 000 ... a Savbolt Cniversal seconds a t 100O F D& to very low yield value a t 6O0 F.
:
1266
1 i E
30,000 30,000 18,000
...
-HOTOR
Figure 2.
SHAFT
Conicylindrical Viscometer
Pour point, under appropriate conditions, is only a guide t o probable pumpability characteristics. It has the virtues of a simple test, and in its modified form, referred to as flow point, has its uses for specification-type testing. It should not, however, be overvalued. Conicylindrical Viscometer I s Used for Rate of Shear/Shear Stress Measurements
I n principle, both yield value and complete rate of shear/ shearing stress curvcs can be determined on a single instrumenta correctly designed rotating cylinder viscometer, as shown diagrammatically in Figure 2.
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
Vol. 46, No. 6
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT ,4n inner cylinder carries a balanced pointer and is suspended from a torsion wire so that it is free to rotate inside an outer cylinder. The annular gap between the two is small so that the ratio of the gap to the radius of the outer cylinder is less than 1 to 5 (actually about 1 t o 10). The cylinders are contained in a lagged controlled-temperature bath through which cooled kerosine circulates, and the outer cylinder is motor driven at adjustable constant speed to give the required range of shear rates. The oil under test is contained in the annular gap, and t o maintain a constant wetted length of cylinder the inner cylinder projects above the top of the outer cylinder, which is fitted with an overflow gallery. The deflection of the pointer as the outer cylinder is driven indicates the torsion of the suspension wire and hence the shearing stress applied.
DRIVE FROM TOP /MOTOR
S P I R A L SPRING
S C A L E O N INNER CYLINDER
EAR CONNECTION
GEARING OUTER CY S C A L E ON OUTER CYLINDER
INNER CYLINDER
OUTER
CYLINDER
T U R 0 l N E VANES
PADDLE
For work at constant shearing stress, the upper gear drive is disconnected and the outer cylinder (mounted in ball races whose drag torque is less than 5% of the torque corresponding to the lowest shearing stress t o be applied) is driven from below by a fluid drive with a high slip coefficient, so that the impeller is always running at high speed (250 to 1000 r.p.m.) compared xvith the driven member or viscometer cylinder (0 to 30 r p.m.). Thus, the torque transmitted to the outer cylinder is independent of its speed of rotation, and constancy of shearing stress (at any one motor speed) is achieved. This represents installation conditions in which either the gravity head or the pump delivery pressure is constant, so that the resulting rate of shear (flow rate) varies with the condition of the oil in the line. The modified viscometer has valuable features like jewel bearings (the upper of which is spring loaded) and accurate centering due to the method of construction. U-Tube Yield Value Apparatus Permits Study of Effects of Heat Treatment
The original stimulus which promoted the development of a U-tube type apparatus for the measurement of yield value arose not from any dissatisfaction with the results obtained from the conicylindrical viscometer but from the thought that if yield value mas to become a specification test an apparatus simpler to operate and suitable for installation routine testing was required. I t was also appreciated that niultitube-type apparatus, in which the
ROTOR
\\ DRIVE FROM BOTTOM MOTOR
Figure 3.
Modified Conicylindrical Viscometer
An alternative method, used for oil which is gelled in the annulus, is to rotate the torsion head against a fixed stop and to measure the L‘recovery’’rate of the pointer as the gel breaks down, while the outer cylinder is fixed. I n this method, although it is useful for determination of yicld value, the shearing stress is not held constant as the torsion wire recovers, and for constant applied shearing dress during gel breakdown, the use of an alternative-type viscometer, described below, is preferable. The conicylindrical feature of both viscometers is based on a design by Mooney and Ewart (4). If the bottom of the inner cylinder is plane, the shearing stress over the base cannot be constant and equal to that in the annular gap. By coning the base of the inner cylinder the effective gap width a t the base can be varied in correct relationship to the increasing radius, so as to reproduce effectively a t all points the rate of shear in the annular gap. The semiangle of the cone in the Sunbury instrument is 83.5” for the cylinder normally used. The wetted length of the inner cylinder is 7 cm. and the inner and outer radii are 0.83 and 0.93 cm., respectively (annular gap = 1 mm.). Figure 3 shows diagrammatically the later type of conicylindrical viscometer designed to maintain a constant shearing etress during gel breakdown so that the resultant rate of shear at constant stress can be followed. Inner and outer cylinders have radii of 2.30 and 2.39 cm., respectively (annular gap = 0.9 mm.), and the wetted length IS 6 cm. The overflow me11 is now part of the inner c?-linder. The conical base is retained (semiangle of cone = 87.7 , based on the smaller annular gap and greater radius compared with those of the earlier model). Certain disadvantages of the torsion wire at very high viscosities are overcome by using a flat spiral (clock-type) spring as the torsion control, but the essential difference between the instruments is in the drive arrangements. For work a t constant rates of shear the outer cylinder is driven from above through a gear train. The rotational deflection of the inner cylinder due to the drag of the oil is indicated by a circular scale attached to its upper end, illuminated and viewed through a window in the lagging jacket; the window carries fiducial marks. June 1954
YIELD VALUE RATIO
Figure 4.
YIELD VALUE FOR
Q /‘
=
300
Variation of Apparent Yield Value with Length/Diameter Ratio 1. 2. 3.
Length/gop ratio = 70 Length/gap ratio = 14 Length/gap ratio = 8.75
oil could be subjected to different heat treatments in equipment separate from the measuring equipment and then transferred without disturbance of the oil structure, would avoid keeping the equipment out of operation during long periods of sample storage and treatment and would allow the effect of various heat treatments on yield value to be determined simultaneously. It mas also felt that the U-tube type of apparatus required less knowledge of the fundamentals of the subject than the viscometer type-an assumption which now appears doubtful.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1267
ENGINEERING, DESIGN, AND PROCESS DEVELQPMENT Initial experiments were made using an adjustable source of air pressure and various types and sizes of tube for the oil column. The yield values were calculated using the expression, RPIBL, froin the pressure, P , required to cause the oil to flow and the tube dimensions, and these results were compared with those for the same oils in the same state derived from a tube having a large LID ratio (300/1). The results of a long series of experiments 0'1 a wide range of fuel oils, in C-tubes with LID ratios from 12/1
U-tube is connected to a short right-angled length of copper tubing which serves to make connection to the pressure line and support the E-tube in the bath. For the measurement of a yield value the oil is loaded into the U-tube and cooled to the requisite temperature of test; precautions are taken to ensure that the E-tube is kept full of oil. After the U-tube is at the temperature of test and mounted in the constant temperature bath, the end of the capillary tube exposed to the atmosphere is wiped clean. Pressure is applied in small increments with a pause at each stage. Yielding of the oil is shoxn by its emergence, usually as a plug, from the exposed end of the capillary, and the yield value is calculated by clubstituting in R P / 2 L the value of the pressure, P , which just causes yielding. installation Shearing Stresses Are Guide ICFuei Oil Properfies Required for Large Scale Handling
I
/+4 _ _ _ _ __ _- _ _ _ J U B U -- T TL L IIY BE ES S CONTAiNmNG
C O N S T A N T TEMPERATLIRE BATH
OiL U Y D E R TEST
Figure 5. Schematic Diagram of Value Apparatus
Yield
to 900/1,are summarized by the curve of Figure 4. As far as could be ascertained, the curvature employed for the U of the Utube had no effect on the yield value determined. The several individual points reproduced and shomn on this curve represent the ratio, conicylindrical viscomcter yield value tube yield value at L,'D = 300 where diffeient viscometer results n ere obtained by using various inner and outer cylinders to alter the annular gap, nith the n-etted length kept constant.
Shearing stresses in viscometers and laboratory tubes have so far been dealt with, and it rvill be useful to quote the maximum shearing stresses available in some typical ship and shore installations. The maximum stresses available are entirely a function of the inst'allation, and they can he calculated froin the geometry and the pressures available. These maximum stresses have noth-. ing to do with the oil itself, but the possibility of pumping and the rate of pumping do depend on the relationship between the maximum stress which can be applied in the installation and the yield value or other characterist'ics of t'he oil. There is nothing in the equation which defines the stress, R P / 2 L , which is limiting .ivith regard to absolute size and, therefore: a small laborat'ory tube of fixed R / L ratio should be equivalent to a large installation line of the same &/Lratio, if factors like differing relative roughness and any effect of the change in material, as from glass t o steel, are ignored. It is well appreciated that considerable large scale checking is required. I n fact, experiments are a t present being designed in the U. K. specifically to investigate correlation between 1-inch tubes and 6-inch pipes, but other factors complicate the issue-notably, factors connected with the sensitivity of oils to heat treatment and different rates of temperature change.
L
Figure 4 shons that a ratio, 5=14OS is about the minimum value necessary for a tube yield value to be independent of LID. Further, since the three viscometer points fall on the curve and since these neie obtained with wetted length/gap ratios, z, of 70, 14, and 8.75, it can be concluded that a wetted lengthjgap ratio of 2 for the visconiPter is equivalent t o an L I D of 22 for the tube. Thus, the viscometer in normal use, with a wetted length to gap ratio of 7 to 0.1 em., is equivalent t o a tube with the mininium LID of 140.-a very fortunate circumstance. It is believed that these ieeults have a physical explanation based on contraction and shearing of the gel on formation and cooling. Evidence for the occurrence of shearing and contraction is given in the second part of this paper, Shearing, as would be expected, n-eakens the structure developed by the gel and thereby reduces the yield values determined in long tubes below those determined in short tubes. The U-tube apparatus based on these preliminary evperiments is sketched in Figures 5 and 6. Figure 5 sliows the general layout of the whole apparatus in schematic form. The U-tubes are contained in a constant temperature bath and connected t o tappings nom a pressurc line. The pressure applied to the oil in the tube is adjustable by means of the system shown on the left. The laboratory air supply is fed through a pressure regulating valve t o a capillary bleed lvhich is necessary for the proper operation of the valve. Further dovmstream is a Bourdon gage for measuring the pressures in the range 5 to 30 pounds per square inch and a mercury manometer for pressures below 5 pounds per square inch. Beyond the gages are two pressure lines, each Kith four points for mounting the Utubes. The U-tubes (Figure 6) consist of a length of capillary tubing, bore approximately 1 mm., scaled into unions One side of the
1268
Figure
6.
Construction of U-Tubes
With regard to correlation between conicylindrical viscometer results and laboratory tube results it has been shown that, with the proper precautions, the results for the yield value of an oil by the two methods are identical, This is not true, hox-ever. of the results for viqcosities measured by the two methods because ~ the conditions of flo~vin a tube and in a viscosity implies f l o and rotating cylinder viscometer are very different. This implies that before the conicvhndrical viscometer viscosities are used for application to flow in a tube or pipe they must have applied to them a correction factor rvhose value is a function of the rate of shear/shearing stress curve determined in the viscometer.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No, 6
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT usually ensures that, except with long gelled lines, difficulty is confined to the suction side. LARGESHOREINSTALLATIONS-SUCTION SIDE Here the maximum pressure ( I 2 Lb./sq. inch pump suction assumed throughout) head is limited to (head of oil Rlin. Temp. for Shear Stress Available Pumping Oil G b pump suction head), and 10-Ft. oil head 20-Ft. oil head (Worst Fluidity the suction head due t o the Empty tank in tank in tank oil Condition), FL Lb./sq. Lb./sq. Lb./sq. to Give 500 No 20-Ft. pump will be of the order of 10 Dynes/ inch X Dynes/ inch X Dynes/ inch X Dynes/Sq. head in head in Instalpounds per square inch. The sq. em. 103 sq. om. 103 sq. om. 103 Ft. tank tank lation 250 3.6 310 4.5 370 5.4 40 37 34 oil head may, of course, be 143 2.1 210 3.0 260 3.8 60 42 39 negative w i t h a n e l e v a t e d ... ... ... ... .. 32 lCA
L
D I S T R IBUTION
a 8 0 F.
85'F
Figure 15.
¶O°F:
P5'F.
IOO'F:
IOS'C
IIO'F.
li5'F.
120°F
Temperature Distribution a t Exit of Pipeline
Input temp. 142' F. Output temp. 105' F.
Flow r o t e 22 U.S. gal./min. Pipe diam. 3 inches
arid Prandll numbers, as shoTvn by Figure 16. The line correlates data from the literature on other cases of natural convection, according t o the equation :
When the temperature distlibution dovn a pipeline is calculatcd (and due allowance is made for the oil to pipe and pipe to atmosphere or pipe i o soil hen5 transfer coefficients) it is possible t o distinguish three regions n-hicli depend on the pumping rate. 1. Aktvery low throughputs, the oil is immediately cooled t o the surrounding soil or atmospheric temperature. 2. At very high throughputs, the temperature of the oil i s not substantially affected. 3. At intermediate throughputs the oil emerges partially cooled; its temperature is dependent on the throughput and the line. 1276
sx
NUSSEL.T
NUMBER
Figure 16. Dependence of Nusselt Number on Product of Grashof and Prandt Numbers in Streamline Flow of Heated Oil
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 6
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
300
-
3
r 0 \
-
Y)
c 0 1200-
O
O
k
-
-
i
Figure 17.
k
+
&
-
&
+ ~ o O T I M E rIOURS
-
Start-up Time for Oil Pumping in 1 1 Mile Line Hump pressure 600 Ib./sq. inch Oil viscosity 1700 S.U.S. at 100' F.
Pressure 800 Ib./sq. inch Ground temp. 40' F.
time has becn developed. In a large number of cases it has been shown that with a buried line sufficient heat is fed into the line by pumping through it a quantity of hot oil equivalent to three times the line capacity. If the oil fed into the line is of a grade for which the available line pressure only just exceeds the hump pressure, starting takes a long time and a period of 4 days, as shown in Figure 17, is not unusual. Use of a low viscosity oil eliminates the long induction period of Figure 17 and a much shorter start-up time results. In many cases it may be desirable to clear heavy fuel oil pipelines with light fuel on shutdown-not on account of any pumpability problem but because of the slow start-up inherent in pumping heavy fuels. However, the change to light fuel oil introduces a further problem, for in streamline flow the forward velocity across the pipe varies greatly. Hence, when the grade of oil being pumped is changed a central core of +he second grade of oil penetrates through the slower moving oil near the walls, and a considerable amount of intermixing of the two grades takes place (Figure 18). The convection currents in heated oil, which adversely affect heat transfer, reduce the pure streamline intermixing to more manageable proportions because the transverse diffusion which they really represent gives conditions intermediate between the streamline and fully turbulent flows of Figure 18. Calculation of the effect of convection on the degree of mixing has shown that it takes a large change in convection to cause an appreciable change in the amount of contaminated oil pumped from the pipe. The calculated figures of Table XIV indicate the total amount of contamination to be expected in most practical circumstances and t,he table also quotes experimental figures determined in a 16-inch diameter line. Turbulent flow a t a Reynolds number of 20,000 and a 1% allonble contamination by the minor component requires that
Table XIV. Mixing of Two Grades of Heated Fuel Oil Pumped Successively in Streamline Flow Allowable Contamination b y bIinor Component,
%
1
5
10
15 20
25
June 1954
Vol. of Contaminated Oil, % of Line Capacity Calcd. from conyeetive Exptl. 16inch line mixing
-
114 84
65 50 39 30
86
73 52 36 29 21
only about 2.5% of the line capacity be discarded as off-specification oil. Cold Gelled Suction Lines. Difficulty in start-up due t o gelled oil is most likely to occur on the suction side of the pump where the maximum stress is limited by the maximum reduction in pressure which can be attained. In order to determine whether blowing a gelled suction line clear by compressed air or by steam was practicable, a small amount of work was done on a line having a length to diameter ratio of 480, in which various proportions of the line were cleared back into a hot oil tank by using various pressures above the minimum necessary to cause yielding of the gel. A 100% line clearance is ideal to rapidly establish full flow rate. Clearing less than 60% of the capacity of the line is not recommended, chiefly because of the long time which is required for the remaining slug of gelled oil to be drawn back into the pump suction. The actual times required to achieve full throughput from the time a t which blowback pressure was applied were shown to be functions of length to diameter ratio and the characteristics of the oil. Two outstandingly striking results were shown : Unless the line is blown 100% clear there is not likely to be any advantage in using blowback pressures much in excess of the minimum pressure required to cause yielding of the oil column. This is explained by the fact that with high excess pressures the oil plug is sheared over a greater thickness extending inwards from the walls of the pipe. With pressures just above the yield pressures the stress is sufficient to shear only a very thin oil layer in close contact with the pipe wall. The result is that the total shear or breakdown expressed in terms of unit volume of oil is actually greater with the low pressure (which results in plug flow) than with the high pressure (which results in a flow approaching more closely the usual parabolic distribution). When the blowback pressure is reduced and replaced by a lower suction pressure from the pump, there is a rebuilding of structure in the sheared part of the gel, so that the final state +CION
OF C O N T A M I N A T I O N
I
I N T E R F A C E IN S T R E A M L I N E F L O W
R E G I O N OF CONTAM I NAT ION
INTERFACE
IN T U R B U L E N T FLOW
Figure 18. Interpretation in Streamline and Turbulent Flow
of the gelled column moving towards the pump is an equilibrium state between shear breakdown and structure rebuilding. The rate of rebuilding is probably a function of the ratio of the total pressure used for breakdown to the minimum pressure required just to cause yielding. Production of Pumpable Fuel Oils Is Basically a Wax Removal Problem
No attempt is made in this paper to discuss fuel oil production methods as they affect the pumpability of the residual fuel. This is a matter for experts on refining. However, Figure 7 shows the correlation between the wax content of the fuel and the Anglo-Iranian Oil Co. maximum pour point which, for present purposes, can be regarded as the ultimate high limit of pour point which the fuel can posjibly (but may not) reach in
INDUSTRIAL AND ENGINEERING CHEMISTRY
1277
€NGINEERING, DESIGN, AND PROCESS DEVELOPMENT storage and, therefore, as the highest possible "stable" pour point. The curve of Figure 7 is based on a wide range of fuels and is independent of all other factors at present known-e.g., light distillate content, hard or soft asphalt content, etc. It includes results on fuels with added wax and added wax plus asphalt. For present purposes, it is better to regard any expedient for producing a lower pour point, such as heat treatment, blending, and the like, as a means for producing only a temporary effect. Assumptions regarding the permissible wax content for satisfactory pumpability can hardly be fixed and immutable sine[, satisfactory pumpability can only be related to conditions of storage and use. HoTTever, in order to view the problem quantitatively, suppose that an absolute maximum stable pour point of 45" F.is specified in order to provide a margin of safety in pumpability (except for unheated storage in the Arctic). T h i ~ pour point corresponds to a wax content of 8% by weight, and the refiner's problem would be to lower the wax content from about 11% by weight (which corresponds to a maximum stable pour point of 75" F.)by removing 3% weight on fuel or around 1 to 1.5 % on crude. Removal of the wax by solvent extraction or dewaxing i q seldom economically feasible, although it mag be considered at particular refineries where local circumstances are favorable I n general terms, however, the process is not very attractive because fuel oil itself is a lovi price product and the wax recovered from atmospheric residue contains microcrystalline as vel1 aq crystalline material and is not easy to refine to marketable grades. Further, Tvax removal involves a viscosity increase in the fuel which must either be accepted or countered by additional cutback. T a x destruction seems to be the only solution and is far more likely to be economic in the U S. A than in the U. K. owing to very different market requirements, noiably in the distillate oil to residual fuel ratio demanded Some of the lighter productq of wax cracking or their equivalent in alternative cutter stock must be blended back into the fuel oil unless the resulting increase in viscosity can be tolerated, and this is bound to reduce the margin from n-hich the wax cracking cost can be met Since this kind of process is already being operated in the U. S.A. it is evident that U. S. refiners are the authorities well qualified to assess the possibilities in the light of their o m circumstances. I n one particular case it was shown that when !Tax ~ a wq moved to the extent of 1% on the fuel oil (all the wax was iemoved from the light wax distillate or v a x y heavy gas oil component of the blend) the result was to allow a threefold increase in viscosity for no change in pumpability, as measured by fixed yield value. Cutting back to the viscosity of the original blend with a wax-free stock would, in effect, give improved pumpability a t a cost, because of the further reduction of R ax content.
Figure i indicates that removal of 1% was corresponds to a drop of 11" to 12' F. in maximum pour point, which agrees closely with the 3% removal to reduce the maximum pour point from 75 ' to 45' F. Acknowledgment
The authors take pleasure in thanking the chairman of the Anglo-Iranian Oil Co. for permission t o publish this series of papers, and they acknowledge with gratitude the work and cooperation of many colleagues on the staff of the company's research station a t Sunbury-on-ThameP, England. Nomenclature
a = coefficient of thermal expansion of oil, 11' F. c = specific heat per unit volume of oil, B.t.u.,'(cu. ft.)(" F.! D = pipe diameter, ft. F = Fanning, friction factor, dimensionless g = acceleration due to gravity, ft./sec.* h = heat transfer coefficient. oil to pipe, B.t.u./(sy. ft.)(' P.) (see.) K = thermal conductivity of oil, (B.t.u.)(ft. thickness) /(sq. it.)(" F.Ksec.) L = line lGngth, ft. P = pressure drop, poundalslsq. ft. Q = rate of flow = 7iR2z',cu. ft./ser. R = pipe radius, f t . v = velocity, ftJsec. z = wetted length /gap ratio e = temperature difference between oil and pipe, O F. M~ = absolute viscosity of oil w-hen at pipe TTall temperature, lb./(ft. )(see.) p = density of oil, lb./cu. f t .
_- = Xusselt number
'a= GraEhof number (PLp)*
' 2= Prandtl number PK
literature Cited (1) Am. Soc. Testing Xaterials. Proc., 31, Pt. 1, 468 (1931). ( 2 ) Kolvoort, E. C. H.. Aloser. F. R., and Verver, C. G., .J. Inst. Petroleum, 23, 735 (1937). (3) Kreulen, D. J. W., Ihid., 24, 441 (1938). (4) Ilooney, M.,and Ewart, R. H., P h y s i c s , 5, 350 (193411. ( 5 ) Iloorbeck, R. H., and Van Reest, A. C.. J . I n s t . Petroleum, 2 1 ,
155 (1935)
(6) Ibid., 21, 174 (1936). (7) . . Rutter. I. R.. and Anderson, H. M , , h m . SOC.Testing hraterials, Pmc., 24, Pt,. 1, 553 (1924). (8) Zimmer. J. C., Davis, G. H. R..and Frolich, P. K., Penn State Coll. Mineral Ind. Expt. Sta., Bull. 12, 57 (1933). RECEIVED f o r reriew M a y 6. 1953. ACCEPTEDJanuary 4, 19.54. Presented a t the meeting of t h e ;Imerican Petroleum Institute, S e n - York, 1953.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 6
