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The yield stress of frozen hydrocarbon fuels
The yield stress of frozen hydrocarbon
fuels
Rex A. Neihof Chemistry Division, Naval Research Laboratory, Washington D.C. 20375-5000, (Received 18 August 1988; revised 23 December 1988)
USA
A more complete description of the flow properties of frozen hydrocarbon fuels is necessary to deal with practical problems such as tank drainage and line stoppage. A study has been made of the minimum stress necessary to effect a change in frozen fuels and hydrocarbon mixtures from solid-like to liquid-like behaviour, by measuring the torque required to rotate an immersed vaned rotor. Experimental variables that affect the interpretation of the results as a rheologically defined yield stress were explored. The yield stress was highly dependent on the temperature and the n-alkane composition of the sample. The total n-alkane concentration determined the rate of increase in yield stress with temperature decrease. For a given total n-alkane concentration, the temperature at which a given yield stress was reached increased with the average n-alkane carbon chain length. While yield stress of frozen hydrocarbons is primarily dependent on the total solids present, other mechanisms involving crystal interactions appear to be necessary for interpretation of the results. Information about yield stress of a frozen fuel as a function of temperature provides a precise, rheologically sound basis for formulating improved methods of forecasting field performance. (Keywords:
hydrocarbon;
fuel; physical
bebaviour)
At low temperatures hydrocarbon fuels become more viscous and certain constituents, especially normal paraffins, separate as solid crystals. If the temperature is low enough, the crystal formation may be sufficiently extensive that the entire mass becomes solidified. This behaviour has long been recognized as being important for vehicles and aircraft operating at low ambient temperatures. Filters may become clogged, fuel lines stopped, fuel pump efficiencies reduced, and storage tanks may not drain. The cloud or freeze point tests define the temperature at which solids first appear with cooling or disappear on warming, and the pour point defines the temperature at which the fuel will no longer flow by gravity under specified conditions. The cloud point predicts the temperature at which fuel filters may become plugged and the pour point relates more to line stoppage and tank drainage. The inadequacies of these tests in predicting real service behaviour have been enumerated by Hutton’, Strawson’ and others. Many other tests have been proposed to satisfy the need for improved means of forecasting the low temperature operability limits of middle distillate fuels. It appears that a more complete description of the flow behaviour of solidified fuels at temperatures above and below the pour point, and under stresses other than gravitation, would be useful. Aircraft fuels, in particular, are subjected to stresses different from those present in the pour point test, and fuel flow from a tank may be determined by pumps and tank overpressure as well as the depth of fuel above the outlet. One approach to such a characterization is to apply rheological techniques for measuring yield stress at various temperatures below the freeze point. The yield stress can be considered to be the minimum shear stress necessary to produce a transition in a
0016-2361/89/070843~6$3.00 0 1989 Butterworth & Co. (Publishers)
Ltd
material from solid-like to liquid-like behaviour. Many systems have this property, notably clay and polymer suspensions. Many frozen hydrocarbon fuels containing normal or straight-chain paraffins also appear to display this behaviour, since they exhibit solid-like behaviour below the pour point, but will flow readily after the external stress required to break the coherent network structure of wax crystals has been exceeded. Various approaches have been taken in determining yield stresses. Indirect methods based on interpretations of shear stress-shear rate data using conventional viscometric instruments usually are inadequate because of the difficulty of obtaining data at suhiciently low shear rates. Where the flow follows known relationshps, it may be possible to extrapolate to low shear rates, but frequently the model behaviour is not followed. A direct technique is to measure the torque required to turn a vaned rotor immersed in the sample3-‘. This method has been widely used to characterize yield stresses of soils and clay suspensions but appears also to offer utility for studying frozen fuels. In contrast to devices involving flow-through, small-bore tubing or shearing between concentric cylinders or cone-plate rotors with relatively narrow gaps, the use of a vaned rotor eliminates wall slippage and would not be so likely to crush macroscopic crystals and give anomalously high yield stress*. The applicability of the vaned rotor to the determination of the yield stress of frozen fuels is explored here. When torque is ,applied to a rotor immersed in a material that exhibits a yield stress, the measured stress will increase and little or no rotor movement may be detected until the elastic limit of the material is exceeded. Then the rotor begins to rotate and the stress decreases. The stress exerted at the maximum torque is taken as the yield stress. Calculation of the yield stress is possible from the maximum torque value and the rotor
FUEL, 1989, Vol 68, July
843
The yield
stress of frozen
hydrocarbon
fuels:
R. A. Neihof
dimensions4,‘. It is assumed that the rotor shears a surface described by a cylinder with the diameter D and length H as indicated in Figure I. The torque acting at the cylindrical wall is given by
and the torque on the two ends by I 2(27r t,(r)rdr s0 where 7y is the yield stress at the wall; and 7, is the shear stress at the end surfaces and is a function of the radial distance, r. Making the reasonable assumption that 7, is uniformly distributed over the ends and is equal to ty at the cylindrical wall, then the torque at the ends is
The total torque, T, is the sum of the torque components due to shear stress at the walls and the two end surfaces of the cylinder:
Concern about the uncertainty in the assumption about stress distribution at the ends is reduced by the fact that the contribution of the ends to the total torque is small, provided the length of the vanes is large compared to their width (H/D > 2). EXPERIMENTAL Instrumentation
and procedure
Three rotors with the dimensions shown in Table1 were used to obtain the results reported in this investigation. Each consisted of four identical stainless steel vanes welded at 90” intervals around one end of a stainless steel rod (3.2 mm diameter and 23 cm long) and with a screw fitting at the opposite end for attachment to a torque measuring device. Rotors with varied dimensions and numbers of vanes were used to test the generality of the method. Brookfield digital viscometers, models RVTD (maximum torque 7187 dynecm), HBTD (maximum torque 57496 dynecm), and 5 x HBTD (maximum torque 287 480 dyne cm) were used to apply and measure torque on the rotors. The HBTD and 5 x HBTD models used for most measurements were specially geared to permit rotor motor speeds down to 0.1 rpm. To avoid movement of the viscometer and the attached rotor when turning on the rotor motor, the motor switch was brought outside the viscometer housing with an electrical cord.
Table 1 Effect of rotor dimensions - 18.4”C)
on yield stress (I~) (Fuel 83-99 at -___
_____.
___
Wcm)
Wcm)
~~(Nrn-')
1.00 1.50 1.50
4.oci 4.00 2.00
128 124 133 -__
844
FUEL, 1989, Vol 68, July
.
Figure 1 stress
Schematic
diagram
of vaned rotor for determination
of yield
The hydrocarbon liquid under study was contained in a Pyrex glass cylinder 22cm long and 4.7 cm inside diameter. Four glass rods (4 mm in diameter) were fused longitudinally and at equal intervals along the inside walls of the cylinder to prevent movement of frozen fuel along the cylinder surface when torque was applied to the rotor. The cylinder was tilled with the sample to about 1Ocm depth and immersed in a refrigerated, temperaturecontrolled, methanol bath in a large Dewar flask with windows through the external insulation to allow visual inspection. The bath liquid was 334 cm above the sample level and, to reduce heating from ambient air, was covered by a plastic top with a hole for the rotor shaft. The rotor was suspended about midway between the top
The yield
stress of frozen
hydrocarbon
fuels:
R. A. Neihof
and bottom levels of the fuel. The rotor was rrsually placed in position in the sample before the bath was cooled. Cooling was achieved by vigorous stirring at a rate determined by the refrigerator and immersed cooling probe. The desired bath temperature set point was maintained within <0.2”C by an immersed resistance heater regulated by a solid state controller and platinum resistance thermometer. The yield stress was determined only after the sample had been in the bath at the desired final temperature for at least 3 h. After that time, the interior fuel temperature was usually within 0.2”~ of the bath temperature. The torque was recorded on a strip chart recorder. Rotor movement was detected visually by a pointer fixed to the upper end of the rotor shaft which rotated around a fixed, graduated, circular scale 4.5 cm in diameter. Sample temperature around the rotor was always measured at the conclusion of an experiment with a platinum resistance thermometer. Fuels and ilydrocarbon
mixtures
n-Alkane solutions and model fuel mixtures were made up by weight from pure hydrocarbons (99mol% pure) in a relatively high boiling, low-freezing, narrow cut, isoparafinic solvent (Phillips Soltrol 170). The diesel and aircraft fuels used were analysed for n-alkanes by gas chromatography. Four point, freeze and cioud points were determined by modified ASTM methods. Diesel fuels designated 83-99 and 2059 were straight run distillates with pour points of - 17.5”C (cloud point - 8°C) and - 1S”C (cloud point - 12”C), respectively. The product designated 2060 was a light cycle oil with a pour point of - 25°C. Aircraft fuel 85-3 originated from a West Texas crude and was hydrodesulphurized (freeze point -43°C); 85-7 was a straight run distillate from an Alaskan North Slope crude (freeze point -40°C); 85-5 was a hydrocracked product from an Alaskan North Slope crude (freeze point -49°C).
RESULTS AND DISCUSSION Torque-time
behaviour
The range of torque-time behaviour typified by various hydrocarbon mixtures is indicated in Figure2. The initial rise in the stress refIects the linear rate at which torque is being applied to the rotor. As the maximum is approached, the rotor begins to turn slightly resulting in a decrease in slope. A marked drop in torque usually followed the maximum. Curve A shows typical behaviour lor a fuel with a substantial concentration of n-alkanes at a temperature considerably below the freeze point. The rotor turned only slightly (5” or less) before the maximum torque was reached and then dropped sharply to a low value and remained low even though the rotor speed was increased from 0.1 to 10rpm. This behaviour clearly indicates that a definite yield stress exists for the rigid crystalline mass at a given temperature and that viscosity contributed insignificantly to the stress at the yield point. With samples having low paraffin contents or when the temperature was not much below the freeze point, curves of type B were frequently obtained. Here the maximum was well defined, but the subsequent drop in torque was less abrupt and one or more plateaux were seen before the torque finally dropped to a low value. In other cases, especially where large wax crystals were present as a result of a predominance of one n-alkane,
SECONDS Figure 2 mixtures
Torque-time
behaviour
for selected,
frozen
hydrocarbon
the maximum was less definite and subsequent plateaux or even secondary peaks in the torque-time curve were seen (curve C) before dropping to low values after nearly 90°C rotor rotation. Failure of the torque to drop to a low value after reaching the initial maximum was probably due to a pile-up of crystals in front of the rotor vanes and the pushing aside of individual crystals or crystal aggregates. These features tended to be variable, depending on the rotor dimensions and the number of vanes, but the maxima were remarkably reproducible in most cases. Until a more thorough investigation of these effects is possible, it seems reasonable to attribute the maximum in all cases to a yield stress. There is little or no recovery of stress resistance at constant temperature once the yield stress has been exceeded. The crystal mass must be completely melted and refrozen to repeat reproducibly the yield stress measurement. With some heavier oils such as lube oils, a pour point could be determined but no yield stress was detectable by the vaned rotor method. The torque (shear stress) was simply proportional to the rotor speed (shear rate), i.e., Newtonian viscosity alone controlled flow and there was little or no indication of any structural breakdown. Effect of rotor size Table 1 gives the yield stresses of a frozen diesel fuel measured with each of the three rotors used in obtaining the data presented here. The values are not significantly different and justified the neglect of vane dimensions as a factor in yield stress measurements. An effort was made to choose a rotor which would give the highest measurable torque at the yield stress within the range of the viscometer being used. Measurements with rotors having six and eight vanes indicated that the number of vanes was not an important variable. Effect of varying
the rate of stress application
The rate of increase of stress imposed on a sample could be controlled by changing the speed of the rotor
FUEL, 1989, VoJ 68, July
845
The yield stress of frozen hydrocarbon
fuels: R. A. Neihof A
drive motor. There was a tendency for the yield stress to increase with increasing rate of stress application. For this reason, the lowest viscometer rotor motor speed (0.1 rpm) was always used since low rates of stress increase appear more relevant to practical problems related to fuel tank draining. Low rotational speeds avoid significant contributions to torque from viscous resistance and inertial overshoot.
4000 -
Effect of cooling mode
3000 -
The rate of cooling of the sample was normally determined by the rate at which the refrigeration unit cooled the bath, starting at room temperature. This rate was reproducible, but different for the two baths used. One was cooled at about 0.67”Cmin-’ initially, decreasing to about 0.4”C min- ’ at - 40°C. The second bath cooled at 1.78”C min-’ initially, decreasing to about 0.3”C min- ’ at - 35°C. The sample cooling rates were similar to the bath cooling rates as long as the sample was liquid. Below the freezing point, there was a marked decrease in cooling rate as a result of the heat of crystallization and the loss of convection imposed by the appearance of wax crystals. Variations in yield stress within the range of cooling rates given by the two refrigerated baths, were usually small. However, in the case of solutions of certain pure n-alkanes, large differences in yield stress were obtained with different cooling rates, particularly through the temperature range where crystallization was occurring. Another variation in the cooling regime, which had a pronounced effect on yield stress in some fuels, occurred when the sample was allowed to come to temperature equilibrium at temperatures other than the one at which the yield stress measurement was finally made. Table2 gives examples. Each soak temperature was held constant for 34 h before changing to a different soak temperature or making a yield stress measurement. In the case of the diesel fuel 83-99, a soak temperature at - 15°C made little difference in the yield stress measurements at - 20.5”C, but with a presoak at - 3 1“C, the yield stress was greatly reduced whether an initial presoak at - 21 “C was included or not. Structures formed at -20.5”C were evidently being weakened by lower temperatures. Warming the frozen fuel to - 15°C from a presoak at - 21°C before cooling again to - 20.5”C also greatly reduced the yield stress. At - 31°C a presoak at 10” lower made a less marked percentage reduction in the yield stress than at -20.5”C, presumably because most of the waxes had already solidified at the lower temperature. Exposing aircraft fuel 85-7 to a temperature 10°C
Table 2
Effect of cooling
mode on yield stress
Fuel
Soak temperatures
83-99
-20.5 -15+-20.5 -21-+-31-t-20.7 -21-+-15+-20.5 -31-t -20.8 -30.9 -41+-30.9
236 218 52 92 78 1760 1110
85-7
-55.8 -65+-55 -56-+-51-*-56.2
232 222 290
846
FUEL, 1989, Vol 68, July
(“C)
Yield stress (Nmm2)
ccI E t g zoook! k n ii F
1000 -
t, 0 -60
C,4(3 113) -50
t -40
I -10 -30 -20 TEMPERATURE (“C)
-0
Figure 3 Yield stress-temperature behaviour for solutions of single and of pure n-alkanes (C I 4, C,,, C,,) at 3f and 10% concentrations all three n-alkanes at a total concentration of 10% (3f% of each) using an isoparaffmic solvent
below the measurement temperature or introducing a 5°C degree warming period made relatively little difference in the yield stress result. An explanation of all these results is likely to require a much more complete knowledge of the way wax crystals form, melt, interact and vary with temperature changes and n-alkane composition. The interpretation of flow behaviour results from the field may require this kind of information. Pure n-alkane solutions Figure 3 shows the yield stress-temperature behaviour for three pure n-alkanes at two concentrations and for a mixture of all three at equal concentrations in an iso-paraffrnic solvent (Soltrol 170). With the solutions of single n-alkanes, the rate of increase in the yield stress with temperature reduction was highly dependent on both the concentration and molecular weight. With the lower concentration (3.33 w/w%), the rate of increase of yield stress with temperature decrease was not only much less than at the higher concentrations (lo%), but tended to reach a yield stress plateau at lower temperatures. This is probably due to the complete crystallization of all the n-alkanes available. At a concentration of lo%, the yield stresses of C,, and C,, solutions appear to be approaching a plateau with decreasing temperature, but the yield stress for the CZOsolution is still rising rapidly at the maximum measurable limit of our present instruments. These measurements depended strongly on cooling rate in some cases. Results for C,, at 3.33% were omitted, because of an inability to obtain satisfactory reproducibility, possibly due to small cooling rate variations. The
The yield stress of frozen hydrocarbon
fuels: R. A. Neihof
crystals
Fuels
Model fuel mixtures
The n-alkane compositions of the diesel and aircraft fuels studied are tabulated in Table4. Yield stresstemperature behaviour is shown in Figures5 and 6. The results are consistent with the model studies already presented. The yield stress at a given temperature increases markedly with the total n-alkane content. The slopes of the z,-temperature curves increase with the total n-alkane content. Indeed, the z,-temperature slopes of all the fuels at a given zy can, in general, be ranked according to their total n-alkane contents. The position of the curves on the T axis is, however, considerably different, reflecting the different average n-alkane molecular weights.
of pure n-alkanes were much larger than those in n-alkane mixtures, and it is to be expected that nucleation and temperature dependent crystal growth rate would be important in determining yield stress. The behaviour of the mixtures of equal weight concentrations of the three n-alkanes at a total concentration of 10% differed from that of the single component solutions in showing only a gradual increase in yield stress with temperature decrease at the higher temperatures. At lower temperatures, however, the .rate of increase of yield stress was almost as great as with CZO (lo%), but displaced to lower yield stresses by 3540°C.
Figure4 shows the variation in yield stress with temperature for three different model fuel mixtures (in Soltrol 170) whose n-alkane compositions are shown in Tuble3. The total n-alkane concentration in each was 17% (w/w). The changes in yield stress with temperature follow approximately parallel courses in each case. Displacement along the temperature axis, however, was very marked, especially for mixtures containing a preponderance of n-alkanes with the shortest chain lengths. Thus a relatively small change in the compositional distribution of a hydrocarbon mixture of n-alkanes can result in a very large shift in the temperature dependence of the yield stress.
Errors and precision
The use of a vaned rotor as a valid way of determining yield stress has been established by comparison with other methods for only a few systems e.g. clay suspensions’ and greases4. Frozen hydrocarbon suspensions differ from these systems in having larger solid particles (n-alkane crystals) in suspension. However, the similarity in behaviour of the different systems and the reproducibility of measurements on frozen fuels under a variety of experimental conditions strongly suggests that Table 4
Composition of fuels Aircraft fuels (w/w%)
Diesel fuels (w/w%) Carbon number
83-99
2
d0 Cl1 C12 C13
E::
C16 C17 C18 C19
C 20 C 21 C 22 Total OL
1
-70
,
I
-65
-60
-56 TEMPERATURE
-45
-40
Composition of model fuel mixtures (w/w%) Low molecular weight bias (w/w%)
Cg C 10 C-9
c;;
C L3
C14 C15 C16
1.0 2.0 3.5 5.5 2.5 1.0 0.75 0.5 0.25
Balanced (w/w%) 0.5 1.0 1.5 2.5 6.0 2.5 1.5 1.0 0.5
0.14 0.29 0.52 1.28 0.68 0.63 0.54 0.39 0.23 0.14 0.05
14.58
11.06
4.89
High molecular weight bias (w/w%) 0.25 0.5 0.75 1.0 3.0 5.5 3.0 2.0 1.o
85-7
85-3 0.09 0.56 1.75 4.15 4.57 3.4s 2.37 I.13 0.38 0.17
85-5
0.30 0.71 2.78 2.69 2.17 1.58 1.43 0.87 0.58 0.32 0.13
0.11 0.66 1.56 1.so 1.43 1.29 0.63 0.13 -
13.65
7.61
-
18.65
.4. 93.99
2.5 0 I E i .s
2.0 -
2u
1.5-
2059
F t/Y 2
G
0.03 0.09 0.36 0.78 0.86 1.15 2.12 I s9 1.38 1.00 0.19 0.49 0.29 0.13
3.0 -
Table 3
Carbon number
-
0.23 0.59 1.14 1.37 1.53 1.68 1.96 1.58 1.41 1.08 0.74 0.57 0.39 0.23
-35
(“c)
Figure 4 Yield stress-temperature behaviour for solutions of pure n-alkanes in an isoparafhnic solvent with the compositions shown in
Table 3
0.08
\,
-50
2060
2059
l.O-
F
2060
.
0.50 \\\, -50
-45
-40
-35
-30
TEMPERATURE
-25
- 20
, -15
-10
(*C)
Figure 5 Yield stress-temperature behaviour of selected diesel fuels. N-alkane compositions are given in Table 4
FUEL, 1989, Vol 68, July
847
The yield stress of frozen hydrocarbon fuels: R. A. Neihof
85-3
2.5
TEMPERATURE (“C) Figure 6 Yield stress-temperature behaviour N-alkane compositions are given in Table 4.
of selected aircraft
fuels.
a parameter at least closely related to yield stress, is being determined by the vaned rotor method. Systematic errors and imprecision in the method have been discussed elsewhere6v7. Generally, the greatest sources of imprecision in the measurement of yield stress of frozen hydrocarbon mixtures, involve temperature definition and uniformity and the cooling mode. Fuel 83-99 (Figure5) at - 19”C, for example, showed a yield stress increase of about 40% for a temperature drop of 1°C. The temperature of the cold bath was controlled to less than 0.2”C but the temperature in the interior of the sample around the rotor, even after 34 h, was 0.1 to 0.3”C higher than the bath temperature set point, depending on the number of degrees below the freeze point of the liquid and the position in the sample. An estimate of typical imprecision, obtained from replicate determinations of yield stress of 83-99 diesel fuel at - 19.O”C, gave a coefficient of variation of 4.5%. Yield stress and n-alkane
content
A complete explanation of yield stress-temperature behaviour in terms of n-alkane composition is not yet possible. However, a few observations relevant to this matter can be made from information in the present study and the published literature. Van Winkle et al.* have shown that the n-alkanes in selected diesel and aircraft fuels separate out as solids in a linear fashion with temperature decrease in the early part of the freezing process and up to the point where half or more of the
848
FUEL, 1989, Vol 68, July
total n-alkanes have solidified. The z,-temperature curves for solutions of pure n-alkanes (Figure3) are consistent with this. However, z,-temperature curves for n-alkane mixtures and fuels show a greater negative slope as the temperature decreases, i.e., some mechanism other than amount of solids formed must be contributing to yield stress. Possible factors to consider include crystal intergrowth, van der Waals or other interactions between adjacent crystal surfaces, and mechanical entanglement of crystals. The possibility of crystal intergrowth or co-crystallization by more than one n-alkane has been shown by Holder and Winklerg to occur with long chain paraffins (C,, to C,,) when differences in chain length were small. X-ray analysis showed that crystals from C,, and C,, mixtures were different from crystals of the pure compounds. The tendency to co-crystallize in binary mixtures decreased as the chain length differences became greater. For C,, and C2s mixtures, independent crystallization predominated. The work of Van Winkle et al.* indicated that n-alkanes in typical diesel and jet aircraft fuels crystallize independently, at least near the freezing point. However, there appeared to be an interaction between C, 3 and C,, at the freezing point. Thus, co-crystallization and inter-growth between crystals, may be factors to be considered in interpreting yield stress. The importance of these and other possible mechanisms may become clearer when the results of an ongoing study of flow improvers are available. The yield stress-temperature behaviour of typical jet fuels (Figure 6) shows a strong resemblance to the relation between fuel retention and temperature in refrigerated tanks employed in low temperature rig tests”,“. Work is now in progress to evaluate this apparent relationship, with the aim of developing improved methods of predicting fuel tank drainage in actual practice. ACKNOWLEDGEMENT This work was sponsored Center and David Taylor U.S. Navy Energy R&D n-alkanes were carried out
by the Naval Air Propulsion Research Center, through the Office, OCNR. Analyses for by E. J. Beal and D. Lineman.
REFERENCES I 2 3 4 5 6
Hutton, J. F. J. Inst. Petroleum 1959, 45, 123 Strawson, H. J. Inst. Petroleum 1959, 45, 129 American Society for Testing Materials. ‘Field Vane Shear Test in Cohesive Soil’, ANSI/ASTM 2573-72 Keentok, M. Rheol. Acfa 1982, 21, 325 Dzuy, N. D. and Boger, D. V. J. Rheology 1983,27, 321 Keentok, M., Milthrope, J. F. and O’Donovan, E. J. Non-Newtonian Fluid Mechanics 1985, 17, 23 Neihof, R. U.S. Naval Research Laboratory Letter Report. Ser. 6180-312, 29 November 1988 Van Winkle, T. L., Affens, W. A., Beal, E. J. et al. Fuel 1987, 66, 947 Holder, G. A. and Winkler, J. J. Inst. Petroleum 1965,51,228 Ford, P. T. and Robertson, A. G. Shell Aviation News 1977, 441, 22 Mehta, H. K. and Armstrong, R. S. Final Report-NASA-Lewis Research Center, NASA CR 174938, U.S. National Aeronautics Space Administration 1985
fuels
Rex A. Neihof Chemistry Division, Naval Research Laboratory, Washington D.C. 20375-5000, (Received 18 August 1988; revised 23 December 1988)
USA
A more complete description of the flow properties of frozen hydrocarbon fuels is necessary to deal with practical problems such as tank drainage and line stoppage. A study has been made of the minimum stress necessary to effect a change in frozen fuels and hydrocarbon mixtures from solid-like to liquid-like behaviour, by measuring the torque required to rotate an immersed vaned rotor. Experimental variables that affect the interpretation of the results as a rheologically defined yield stress were explored. The yield stress was highly dependent on the temperature and the n-alkane composition of the sample. The total n-alkane concentration determined the rate of increase in yield stress with temperature decrease. For a given total n-alkane concentration, the temperature at which a given yield stress was reached increased with the average n-alkane carbon chain length. While yield stress of frozen hydrocarbons is primarily dependent on the total solids present, other mechanisms involving crystal interactions appear to be necessary for interpretation of the results. Information about yield stress of a frozen fuel as a function of temperature provides a precise, rheologically sound basis for formulating improved methods of forecasting field performance. (Keywords:
hydrocarbon;
fuel; physical
bebaviour)
At low temperatures hydrocarbon fuels become more viscous and certain constituents, especially normal paraffins, separate as solid crystals. If the temperature is low enough, the crystal formation may be sufficiently extensive that the entire mass becomes solidified. This behaviour has long been recognized as being important for vehicles and aircraft operating at low ambient temperatures. Filters may become clogged, fuel lines stopped, fuel pump efficiencies reduced, and storage tanks may not drain. The cloud or freeze point tests define the temperature at which solids first appear with cooling or disappear on warming, and the pour point defines the temperature at which the fuel will no longer flow by gravity under specified conditions. The cloud point predicts the temperature at which fuel filters may become plugged and the pour point relates more to line stoppage and tank drainage. The inadequacies of these tests in predicting real service behaviour have been enumerated by Hutton’, Strawson’ and others. Many other tests have been proposed to satisfy the need for improved means of forecasting the low temperature operability limits of middle distillate fuels. It appears that a more complete description of the flow behaviour of solidified fuels at temperatures above and below the pour point, and under stresses other than gravitation, would be useful. Aircraft fuels, in particular, are subjected to stresses different from those present in the pour point test, and fuel flow from a tank may be determined by pumps and tank overpressure as well as the depth of fuel above the outlet. One approach to such a characterization is to apply rheological techniques for measuring yield stress at various temperatures below the freeze point. The yield stress can be considered to be the minimum shear stress necessary to produce a transition in a
0016-2361/89/070843~6$3.00 0 1989 Butterworth & Co. (Publishers)
Ltd
material from solid-like to liquid-like behaviour. Many systems have this property, notably clay and polymer suspensions. Many frozen hydrocarbon fuels containing normal or straight-chain paraffins also appear to display this behaviour, since they exhibit solid-like behaviour below the pour point, but will flow readily after the external stress required to break the coherent network structure of wax crystals has been exceeded. Various approaches have been taken in determining yield stresses. Indirect methods based on interpretations of shear stress-shear rate data using conventional viscometric instruments usually are inadequate because of the difficulty of obtaining data at suhiciently low shear rates. Where the flow follows known relationshps, it may be possible to extrapolate to low shear rates, but frequently the model behaviour is not followed. A direct technique is to measure the torque required to turn a vaned rotor immersed in the sample3-‘. This method has been widely used to characterize yield stresses of soils and clay suspensions but appears also to offer utility for studying frozen fuels. In contrast to devices involving flow-through, small-bore tubing or shearing between concentric cylinders or cone-plate rotors with relatively narrow gaps, the use of a vaned rotor eliminates wall slippage and would not be so likely to crush macroscopic crystals and give anomalously high yield stress*. The applicability of the vaned rotor to the determination of the yield stress of frozen fuels is explored here. When torque is ,applied to a rotor immersed in a material that exhibits a yield stress, the measured stress will increase and little or no rotor movement may be detected until the elastic limit of the material is exceeded. Then the rotor begins to rotate and the stress decreases. The stress exerted at the maximum torque is taken as the yield stress. Calculation of the yield stress is possible from the maximum torque value and the rotor
FUEL, 1989, Vol 68, July
843
The yield
stress of frozen
hydrocarbon
fuels:
R. A. Neihof
dimensions4,‘. It is assumed that the rotor shears a surface described by a cylinder with the diameter D and length H as indicated in Figure I. The torque acting at the cylindrical wall is given by
and the torque on the two ends by I 2(27r t,(r)rdr s0 where 7y is the yield stress at the wall; and 7, is the shear stress at the end surfaces and is a function of the radial distance, r. Making the reasonable assumption that 7, is uniformly distributed over the ends and is equal to ty at the cylindrical wall, then the torque at the ends is
The total torque, T, is the sum of the torque components due to shear stress at the walls and the two end surfaces of the cylinder:
Concern about the uncertainty in the assumption about stress distribution at the ends is reduced by the fact that the contribution of the ends to the total torque is small, provided the length of the vanes is large compared to their width (H/D > 2). EXPERIMENTAL Instrumentation
and procedure
Three rotors with the dimensions shown in Table1 were used to obtain the results reported in this investigation. Each consisted of four identical stainless steel vanes welded at 90” intervals around one end of a stainless steel rod (3.2 mm diameter and 23 cm long) and with a screw fitting at the opposite end for attachment to a torque measuring device. Rotors with varied dimensions and numbers of vanes were used to test the generality of the method. Brookfield digital viscometers, models RVTD (maximum torque 7187 dynecm), HBTD (maximum torque 57496 dynecm), and 5 x HBTD (maximum torque 287 480 dyne cm) were used to apply and measure torque on the rotors. The HBTD and 5 x HBTD models used for most measurements were specially geared to permit rotor motor speeds down to 0.1 rpm. To avoid movement of the viscometer and the attached rotor when turning on the rotor motor, the motor switch was brought outside the viscometer housing with an electrical cord.
Table 1 Effect of rotor dimensions - 18.4”C)
on yield stress (I~) (Fuel 83-99 at -___
_____.
___
Wcm)
Wcm)
~~(Nrn-')
1.00 1.50 1.50
4.oci 4.00 2.00
128 124 133 -__
844
FUEL, 1989, Vol 68, July
.
Figure 1 stress
Schematic
diagram
of vaned rotor for determination
of yield
The hydrocarbon liquid under study was contained in a Pyrex glass cylinder 22cm long and 4.7 cm inside diameter. Four glass rods (4 mm in diameter) were fused longitudinally and at equal intervals along the inside walls of the cylinder to prevent movement of frozen fuel along the cylinder surface when torque was applied to the rotor. The cylinder was tilled with the sample to about 1Ocm depth and immersed in a refrigerated, temperaturecontrolled, methanol bath in a large Dewar flask with windows through the external insulation to allow visual inspection. The bath liquid was 334 cm above the sample level and, to reduce heating from ambient air, was covered by a plastic top with a hole for the rotor shaft. The rotor was suspended about midway between the top
The yield
stress of frozen
hydrocarbon
fuels:
R. A. Neihof
and bottom levels of the fuel. The rotor was rrsually placed in position in the sample before the bath was cooled. Cooling was achieved by vigorous stirring at a rate determined by the refrigerator and immersed cooling probe. The desired bath temperature set point was maintained within <0.2”C by an immersed resistance heater regulated by a solid state controller and platinum resistance thermometer. The yield stress was determined only after the sample had been in the bath at the desired final temperature for at least 3 h. After that time, the interior fuel temperature was usually within 0.2”~ of the bath temperature. The torque was recorded on a strip chart recorder. Rotor movement was detected visually by a pointer fixed to the upper end of the rotor shaft which rotated around a fixed, graduated, circular scale 4.5 cm in diameter. Sample temperature around the rotor was always measured at the conclusion of an experiment with a platinum resistance thermometer. Fuels and ilydrocarbon
mixtures
n-Alkane solutions and model fuel mixtures were made up by weight from pure hydrocarbons (99mol% pure) in a relatively high boiling, low-freezing, narrow cut, isoparafinic solvent (Phillips Soltrol 170). The diesel and aircraft fuels used were analysed for n-alkanes by gas chromatography. Four point, freeze and cioud points were determined by modified ASTM methods. Diesel fuels designated 83-99 and 2059 were straight run distillates with pour points of - 17.5”C (cloud point - 8°C) and - 1S”C (cloud point - 12”C), respectively. The product designated 2060 was a light cycle oil with a pour point of - 25°C. Aircraft fuel 85-3 originated from a West Texas crude and was hydrodesulphurized (freeze point -43°C); 85-7 was a straight run distillate from an Alaskan North Slope crude (freeze point -40°C); 85-5 was a hydrocracked product from an Alaskan North Slope crude (freeze point -49°C).
RESULTS AND DISCUSSION Torque-time
behaviour
The range of torque-time behaviour typified by various hydrocarbon mixtures is indicated in Figure2. The initial rise in the stress refIects the linear rate at which torque is being applied to the rotor. As the maximum is approached, the rotor begins to turn slightly resulting in a decrease in slope. A marked drop in torque usually followed the maximum. Curve A shows typical behaviour lor a fuel with a substantial concentration of n-alkanes at a temperature considerably below the freeze point. The rotor turned only slightly (5” or less) before the maximum torque was reached and then dropped sharply to a low value and remained low even though the rotor speed was increased from 0.1 to 10rpm. This behaviour clearly indicates that a definite yield stress exists for the rigid crystalline mass at a given temperature and that viscosity contributed insignificantly to the stress at the yield point. With samples having low paraffin contents or when the temperature was not much below the freeze point, curves of type B were frequently obtained. Here the maximum was well defined, but the subsequent drop in torque was less abrupt and one or more plateaux were seen before the torque finally dropped to a low value. In other cases, especially where large wax crystals were present as a result of a predominance of one n-alkane,
SECONDS Figure 2 mixtures
Torque-time
behaviour
for selected,
frozen
hydrocarbon
the maximum was less definite and subsequent plateaux or even secondary peaks in the torque-time curve were seen (curve C) before dropping to low values after nearly 90°C rotor rotation. Failure of the torque to drop to a low value after reaching the initial maximum was probably due to a pile-up of crystals in front of the rotor vanes and the pushing aside of individual crystals or crystal aggregates. These features tended to be variable, depending on the rotor dimensions and the number of vanes, but the maxima were remarkably reproducible in most cases. Until a more thorough investigation of these effects is possible, it seems reasonable to attribute the maximum in all cases to a yield stress. There is little or no recovery of stress resistance at constant temperature once the yield stress has been exceeded. The crystal mass must be completely melted and refrozen to repeat reproducibly the yield stress measurement. With some heavier oils such as lube oils, a pour point could be determined but no yield stress was detectable by the vaned rotor method. The torque (shear stress) was simply proportional to the rotor speed (shear rate), i.e., Newtonian viscosity alone controlled flow and there was little or no indication of any structural breakdown. Effect of rotor size Table 1 gives the yield stresses of a frozen diesel fuel measured with each of the three rotors used in obtaining the data presented here. The values are not significantly different and justified the neglect of vane dimensions as a factor in yield stress measurements. An effort was made to choose a rotor which would give the highest measurable torque at the yield stress within the range of the viscometer being used. Measurements with rotors having six and eight vanes indicated that the number of vanes was not an important variable. Effect of varying
the rate of stress application
The rate of increase of stress imposed on a sample could be controlled by changing the speed of the rotor
FUEL, 1989, VoJ 68, July
845
The yield stress of frozen hydrocarbon
fuels: R. A. Neihof A
drive motor. There was a tendency for the yield stress to increase with increasing rate of stress application. For this reason, the lowest viscometer rotor motor speed (0.1 rpm) was always used since low rates of stress increase appear more relevant to practical problems related to fuel tank draining. Low rotational speeds avoid significant contributions to torque from viscous resistance and inertial overshoot.
4000 -
Effect of cooling mode
3000 -
The rate of cooling of the sample was normally determined by the rate at which the refrigeration unit cooled the bath, starting at room temperature. This rate was reproducible, but different for the two baths used. One was cooled at about 0.67”Cmin-’ initially, decreasing to about 0.4”C min- ’ at - 40°C. The second bath cooled at 1.78”C min-’ initially, decreasing to about 0.3”C min- ’ at - 35°C. The sample cooling rates were similar to the bath cooling rates as long as the sample was liquid. Below the freezing point, there was a marked decrease in cooling rate as a result of the heat of crystallization and the loss of convection imposed by the appearance of wax crystals. Variations in yield stress within the range of cooling rates given by the two refrigerated baths, were usually small. However, in the case of solutions of certain pure n-alkanes, large differences in yield stress were obtained with different cooling rates, particularly through the temperature range where crystallization was occurring. Another variation in the cooling regime, which had a pronounced effect on yield stress in some fuels, occurred when the sample was allowed to come to temperature equilibrium at temperatures other than the one at which the yield stress measurement was finally made. Table2 gives examples. Each soak temperature was held constant for 34 h before changing to a different soak temperature or making a yield stress measurement. In the case of the diesel fuel 83-99, a soak temperature at - 15°C made little difference in the yield stress measurements at - 20.5”C, but with a presoak at - 3 1“C, the yield stress was greatly reduced whether an initial presoak at - 21 “C was included or not. Structures formed at -20.5”C were evidently being weakened by lower temperatures. Warming the frozen fuel to - 15°C from a presoak at - 21°C before cooling again to - 20.5”C also greatly reduced the yield stress. At - 31°C a presoak at 10” lower made a less marked percentage reduction in the yield stress than at -20.5”C, presumably because most of the waxes had already solidified at the lower temperature. Exposing aircraft fuel 85-7 to a temperature 10°C
Table 2
Effect of cooling
mode on yield stress
Fuel
Soak temperatures
83-99
-20.5 -15+-20.5 -21-+-31-t-20.7 -21-+-15+-20.5 -31-t -20.8 -30.9 -41+-30.9
236 218 52 92 78 1760 1110
85-7
-55.8 -65+-55 -56-+-51-*-56.2
232 222 290
846
FUEL, 1989, Vol 68, July
(“C)
Yield stress (Nmm2)
ccI E t g zoook! k n ii F
1000 -
t, 0 -60
C,4(3 113) -50
t -40
I -10 -30 -20 TEMPERATURE (“C)
-0
Figure 3 Yield stress-temperature behaviour for solutions of single and of pure n-alkanes (C I 4, C,,, C,,) at 3f and 10% concentrations all three n-alkanes at a total concentration of 10% (3f% of each) using an isoparaffmic solvent
below the measurement temperature or introducing a 5°C degree warming period made relatively little difference in the yield stress result. An explanation of all these results is likely to require a much more complete knowledge of the way wax crystals form, melt, interact and vary with temperature changes and n-alkane composition. The interpretation of flow behaviour results from the field may require this kind of information. Pure n-alkane solutions Figure 3 shows the yield stress-temperature behaviour for three pure n-alkanes at two concentrations and for a mixture of all three at equal concentrations in an iso-paraffrnic solvent (Soltrol 170). With the solutions of single n-alkanes, the rate of increase in the yield stress with temperature reduction was highly dependent on both the concentration and molecular weight. With the lower concentration (3.33 w/w%), the rate of increase of yield stress with temperature decrease was not only much less than at the higher concentrations (lo%), but tended to reach a yield stress plateau at lower temperatures. This is probably due to the complete crystallization of all the n-alkanes available. At a concentration of lo%, the yield stresses of C,, and C,, solutions appear to be approaching a plateau with decreasing temperature, but the yield stress for the CZOsolution is still rising rapidly at the maximum measurable limit of our present instruments. These measurements depended strongly on cooling rate in some cases. Results for C,, at 3.33% were omitted, because of an inability to obtain satisfactory reproducibility, possibly due to small cooling rate variations. The
The yield stress of frozen hydrocarbon
fuels: R. A. Neihof
crystals
Fuels
Model fuel mixtures
The n-alkane compositions of the diesel and aircraft fuels studied are tabulated in Table4. Yield stresstemperature behaviour is shown in Figures5 and 6. The results are consistent with the model studies already presented. The yield stress at a given temperature increases markedly with the total n-alkane content. The slopes of the z,-temperature curves increase with the total n-alkane content. Indeed, the z,-temperature slopes of all the fuels at a given zy can, in general, be ranked according to their total n-alkane contents. The position of the curves on the T axis is, however, considerably different, reflecting the different average n-alkane molecular weights.
of pure n-alkanes were much larger than those in n-alkane mixtures, and it is to be expected that nucleation and temperature dependent crystal growth rate would be important in determining yield stress. The behaviour of the mixtures of equal weight concentrations of the three n-alkanes at a total concentration of 10% differed from that of the single component solutions in showing only a gradual increase in yield stress with temperature decrease at the higher temperatures. At lower temperatures, however, the .rate of increase of yield stress was almost as great as with CZO (lo%), but displaced to lower yield stresses by 3540°C.
Figure4 shows the variation in yield stress with temperature for three different model fuel mixtures (in Soltrol 170) whose n-alkane compositions are shown in Tuble3. The total n-alkane concentration in each was 17% (w/w). The changes in yield stress with temperature follow approximately parallel courses in each case. Displacement along the temperature axis, however, was very marked, especially for mixtures containing a preponderance of n-alkanes with the shortest chain lengths. Thus a relatively small change in the compositional distribution of a hydrocarbon mixture of n-alkanes can result in a very large shift in the temperature dependence of the yield stress.
Errors and precision
The use of a vaned rotor as a valid way of determining yield stress has been established by comparison with other methods for only a few systems e.g. clay suspensions’ and greases4. Frozen hydrocarbon suspensions differ from these systems in having larger solid particles (n-alkane crystals) in suspension. However, the similarity in behaviour of the different systems and the reproducibility of measurements on frozen fuels under a variety of experimental conditions strongly suggests that Table 4
Composition of fuels Aircraft fuels (w/w%)
Diesel fuels (w/w%) Carbon number
83-99
2
d0 Cl1 C12 C13
E::
C16 C17 C18 C19
C 20 C 21 C 22 Total OL
1
-70
,
I
-65
-60
-56 TEMPERATURE
-45
-40
Composition of model fuel mixtures (w/w%) Low molecular weight bias (w/w%)
Cg C 10 C-9
c;;
C L3
C14 C15 C16
1.0 2.0 3.5 5.5 2.5 1.0 0.75 0.5 0.25
Balanced (w/w%) 0.5 1.0 1.5 2.5 6.0 2.5 1.5 1.0 0.5
0.14 0.29 0.52 1.28 0.68 0.63 0.54 0.39 0.23 0.14 0.05
14.58
11.06
4.89
High molecular weight bias (w/w%) 0.25 0.5 0.75 1.0 3.0 5.5 3.0 2.0 1.o
85-7
85-3 0.09 0.56 1.75 4.15 4.57 3.4s 2.37 I.13 0.38 0.17
85-5
0.30 0.71 2.78 2.69 2.17 1.58 1.43 0.87 0.58 0.32 0.13
0.11 0.66 1.56 1.so 1.43 1.29 0.63 0.13 -
13.65
7.61
-
18.65
.4. 93.99
2.5 0 I E i .s
2.0 -
2u
1.5-
2059
F t/Y 2
G
0.03 0.09 0.36 0.78 0.86 1.15 2.12 I s9 1.38 1.00 0.19 0.49 0.29 0.13
3.0 -
Table 3
Carbon number
-
0.23 0.59 1.14 1.37 1.53 1.68 1.96 1.58 1.41 1.08 0.74 0.57 0.39 0.23
-35
(“c)
Figure 4 Yield stress-temperature behaviour for solutions of pure n-alkanes in an isoparafhnic solvent with the compositions shown in
Table 3
0.08
\,
-50
2060
2059
l.O-
F
2060
.
0.50 \\\, -50
-45
-40
-35
-30
TEMPERATURE
-25
- 20
, -15
-10
(*C)
Figure 5 Yield stress-temperature behaviour of selected diesel fuels. N-alkane compositions are given in Table 4
FUEL, 1989, Vol 68, July
847
The yield stress of frozen hydrocarbon fuels: R. A. Neihof
85-3
2.5
TEMPERATURE (“C) Figure 6 Yield stress-temperature behaviour N-alkane compositions are given in Table 4.
of selected aircraft
fuels.
a parameter at least closely related to yield stress, is being determined by the vaned rotor method. Systematic errors and imprecision in the method have been discussed elsewhere6v7. Generally, the greatest sources of imprecision in the measurement of yield stress of frozen hydrocarbon mixtures, involve temperature definition and uniformity and the cooling mode. Fuel 83-99 (Figure5) at - 19”C, for example, showed a yield stress increase of about 40% for a temperature drop of 1°C. The temperature of the cold bath was controlled to less than 0.2”C but the temperature in the interior of the sample around the rotor, even after 34 h, was 0.1 to 0.3”C higher than the bath temperature set point, depending on the number of degrees below the freeze point of the liquid and the position in the sample. An estimate of typical imprecision, obtained from replicate determinations of yield stress of 83-99 diesel fuel at - 19.O”C, gave a coefficient of variation of 4.5%. Yield stress and n-alkane
content
A complete explanation of yield stress-temperature behaviour in terms of n-alkane composition is not yet possible. However, a few observations relevant to this matter can be made from information in the present study and the published literature. Van Winkle et al.* have shown that the n-alkanes in selected diesel and aircraft fuels separate out as solids in a linear fashion with temperature decrease in the early part of the freezing process and up to the point where half or more of the
848
FUEL, 1989, Vol 68, July
total n-alkanes have solidified. The z,-temperature curves for solutions of pure n-alkanes (Figure3) are consistent with this. However, z,-temperature curves for n-alkane mixtures and fuels show a greater negative slope as the temperature decreases, i.e., some mechanism other than amount of solids formed must be contributing to yield stress. Possible factors to consider include crystal intergrowth, van der Waals or other interactions between adjacent crystal surfaces, and mechanical entanglement of crystals. The possibility of crystal intergrowth or co-crystallization by more than one n-alkane has been shown by Holder and Winklerg to occur with long chain paraffins (C,, to C,,) when differences in chain length were small. X-ray analysis showed that crystals from C,, and C,, mixtures were different from crystals of the pure compounds. The tendency to co-crystallize in binary mixtures decreased as the chain length differences became greater. For C,, and C2s mixtures, independent crystallization predominated. The work of Van Winkle et al.* indicated that n-alkanes in typical diesel and jet aircraft fuels crystallize independently, at least near the freezing point. However, there appeared to be an interaction between C, 3 and C,, at the freezing point. Thus, co-crystallization and inter-growth between crystals, may be factors to be considered in interpreting yield stress. The importance of these and other possible mechanisms may become clearer when the results of an ongoing study of flow improvers are available. The yield stress-temperature behaviour of typical jet fuels (Figure 6) shows a strong resemblance to the relation between fuel retention and temperature in refrigerated tanks employed in low temperature rig tests”,“. Work is now in progress to evaluate this apparent relationship, with the aim of developing improved methods of predicting fuel tank drainage in actual practice. ACKNOWLEDGEMENT This work was sponsored Center and David Taylor U.S. Navy Energy R&D n-alkanes were carried out
by the Naval Air Propulsion Research Center, through the Office, OCNR. Analyses for by E. J. Beal and D. Lineman.
REFERENCES I 2 3 4 5 6
Hutton, J. F. J. Inst. Petroleum 1959, 45, 123 Strawson, H. J. Inst. Petroleum 1959, 45, 129 American Society for Testing Materials. ‘Field Vane Shear Test in Cohesive Soil’, ANSI/ASTM 2573-72 Keentok, M. Rheol. Acfa 1982, 21, 325 Dzuy, N. D. and Boger, D. V. J. Rheology 1983,27, 321 Keentok, M., Milthrope, J. F. and O’Donovan, E. J. Non-Newtonian Fluid Mechanics 1985, 17, 23 Neihof, R. U.S. Naval Research Laboratory Letter Report. Ser. 6180-312, 29 November 1988 Van Winkle, T. L., Affens, W. A., Beal, E. J. et al. Fuel 1987, 66, 947 Holder, G. A. and Winkler, J. J. Inst. Petroleum 1965,51,228 Ford, P. T. and Robertson, A. G. Shell Aviation News 1977, 441, 22 Mehta, H. K. and Armstrong, R. S. Final Report-NASA-Lewis Research Center, NASA CR 174938, U.S. National Aeronautics Space Administration 1985