Process to Produce Isothermal Deep Supersaturation Conditions for

Department of Chemistry, Kansas State University, Manhattan, Kansas 66502, United States. Ind. Eng. Chem. Res. , 2014, 53 (28), pp 11320–11325. DOI:...
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Process to Produce Isothermal Deep Supersaturation Conditions for Wax Solvent Crystallization Kinetics or Related Studies Dale L. Schruben,*,†,‡ Horacio A. Duarte,† and Robert M. Hammaker‡,§ †

Department of Chemical and Natural Gas Engineering, Texas A&M University-Kingsville, Kingsville, Texas 78363, United States Department of Chemistry, Kansas State University, Manhattan, Kansas 66502, United States

‡

ABSTRACT: Fast cooling to deep supersaturation for solvent crystallization seems to have two major components. One involves mainly the thermodynamics or phase equilibrium chemical thermodynamics of deep supersaturation. The other component focuses on the fast-cooling or heat-transfer aspect. All previous related crystallization work known to us involves a cooling process coupled with crystallization. This method does the cooling quickly to supersaturated conditions, so the cooling does not couple or interfere with the subsequent isothermal crystallization at supersaturation. Although adiabatic cooling and isothermal crystallization are well-known individually, their combination here with proper choice of liquid and cooling ballast temperatures can achieve supercritical conditions uniquely.

1. INTRODUCTION

2. THERMODYNAMIC THEORETICAL FRAMEWORK FOR FAST COOLING TO DEEP SUPERSATURATION It is helpful to introduce a T−x partial phase diagram from classical phase equilibrium thermodynamics (Figure 1).

Petroleum waxes can cause problems wherever they appear in crude and processed petroleum products. Pumps, filters, and piping suffer in cold zones or in temperate zones during cold snaps as waxes crystallize, precipitate out, and foul these processing pieces. Interest here is particularly in mid-distillates. To deal with these issues, wax crystallization kinetics are needed, but the majority of wax studies are on topics such as solid phases and their morphologies. The works of Chevallier et al.1 and Durand et al.2 and the references derived therein run into the hundreds. A few studies have concerned wax crystallization kinetics,3,4 Field difficulties with waxes in the petroleum enterprise most often involve a solvent (or solution) crystallization situation, rather than melt crystallization. In the few available studies on wax crystallization kinetics,3,4 differential scanning calorimetry (DSC) has been the study technique of choice. Gradual (or differential, as its name implies) changes in temperature and heat effects are noted. The differential cooling aspect can make it difficult to drive DSC samples into deep supersaturation and to probe nature far beyond saturation. Many field conditions in the petroleum industry involve slow cooling, making these DSC studies relevant. However, other events involve flash cooling such as quantity movement in terminal handling situations during cold snaps in the temperate zone or various operations under arctic conditions. That catastrophic consequences can occur is seen with the North Sea Staffa platform blockage and its hundred million dollar loss.5 Because the consequences are so severe, kinetics data for a high degree of supersaturation achieved quickly are appropriate. If wax solvent crystallization kinetics or other data are to be pursued for deep supersaturation under isothermal conditions, then techniques to achieve that state, and to achieve it quickly, must be developed. Mastering that task is the main goal of this work. © 2014 American Chemical Society

Figure 1. Partial idealized binary phase diagram. Solute at the desired mole fraction xS will reach supersaturation when the system is cooled from Thi to TS.

In terms of Figure 1, sufficient solute in the solvent must be heated to Thi so that the solution has the equilibrium mole fraction of solute at Thi, designated as xS. Let CS be the solute concentration associated with xS and Csat be the saturated or equilibrium solute concentration associated with xeq. When the solution at Thi is cooled to TS, it will be in a state of supersaturation, S, where S = C/Csat = CS/Csat. This is indicated where the dotted lines cross in Figure 1. (The definition of Received: Revised: Accepted: Published: 11320

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symbol S is of some endurance,4,6 and the subscript S is generally used to indicate association with supersaturation.) Some analysis will make the above discussion more specific. Let the number of moles of solvent and the number of moles of solute be designated as Msolvent and Msolute, respectively. Then, in any binary solution of solute mole fraction x Msolute = xMsolvent /(1 − x)

of experiments. In that case, pure solvent is the cooling ballast, and the exact solute mass to generate supersaturated composition must be determined prior to mixing. The thermodynamic states that give a process for preparing a supersaturated state and then holding that state at constant temperature have been given. They constitute a benchmark against which isothermal processes at supersaturation can be studied. This benchmark was designed and developed in the context of petroleum wax crystallization, but many other related processes requiring isothermal supersaturated conditions could also be studied by the methods developed in this work.

(1)

which follows from the definition of x = Msolute/(Msolute + Msolvent). Consider this number of moles of solvent, Msolvent, to have the same volume, V, at either Thi or TS irrespective of the solute conditions. The numbers of moles of solute in solution at Thi and TS are designated Msolute,hi and Msolute,eq, respectively. (To be sure, these mole amounts represent the equilibrium amounts at the respective temperatures. The higher number of moles of, Msolute,hi, will still be in solution when cooled to TS, and the instability of their natural tendency to crystallize is the quasi-equilibrium state called supersaturation.) Return to the definition of S S = CS/Csat =

Msolute,hi /V Msolute,eq /V

= Msolute,hi /Msolute,eq

3. EXPERIMENTAL ASPECTS INCLUDING FAST HEAT TRANSFER A theoretical framework has been given for producing arbitrary supersaturation S at a supersaturation temperature of choice, TS. Of course, one need not begin by choosing only these variables because they are interrelated to others that could serve as starting variables. However, typically S and TS are of highest interest. Because the thermodynamic theoretical aspects have been described, it might seem appropriate to give the transport theoretical aspects involved with the process next. However, by proceeding at this time with the straightforward steps suggested by the thermodynamic theory, the impact of the transport and heat-transfer aspects will be highlighted. This approach will be as useful to appreciating this process as constructing a problem description is to teaching heat transfer. The experimental steps and attendant heat-transfer issues will be discovered, and we will then turn to a transport theoretical framework to resolve these issues. Let cold ballast be prepared through contact with a relevant reservoir. The warmed solution is thermally contacted with the cold ballast (below TS), and that combination of ballast and solution is thermally contacted with another reservoir at a temperature TS that is the same temperature as the mixing temperature of the ballast and solution. It will be shown how, by using extraordinary measures, warmed solution and cold ballast reach TS in a matter of seconds. Because the system is surrounded by and in contact with a reservoir at TS, it remains thereafter at TS as isothermal crystallization occurs. The first experiments deal with the basic idea of mixing a warm solute with a cold solvent to reach a supersaturated solution. The warming mentioned is necessary to ensure a liquid state for the solute. Then, the question becomes how one can mix a solvent with it to achieve cold temperatures of deep supersaturation. The answer is by cooling the solvent sufficiently below the target supersaturation temperature to ensure that, when the solute and solvent are mixed, the temperature of the resulting mixture is at the target supersaturation temperature. In implementation of the previous paragraph, some issues at the outset can be considered or at least identified if the system prepared under the thermodynamic theoretical framework above is to be used for crystallization kinetics studies. Supersaturation must be reached quickly; otherwise, the satellite crystallization occurring during cooling will deposit crystal mass that will subsequently be confused with the crystal mass generated by the isothermal supersaturated crystallization. This is an obvious problem if isothermal supersaturated crystallizations kinetics are pursued. A related view emerges from considering concentration upsets. What little kinetic action there is during the short cooling interval can still result in some crystallization. The solute pulled out of solution during

(2)

With eqs 1 and 2, S can be written as S = CS/Csat = Msolute,hi /Msolute,eq = [xhi /(1 − xhi)]/[xeq /(1 − xeq)] → invert for xhi xhi = S /[(1 − xeq)/xeq + S] = xS (3)

Apology is offered for the dual nomenclature: xhi = xS, but the use of both symbols seems to promote overall comprehension of the system and process. The recipe for preparing the proper solution for cooling appears. Specifically, the experimenter would select S and TS as desired. TS, in conjunction with the van’t Hoff equation, would give xeq. Then, the chosen S value, in conjunction with eq 3, would give xhi, which could be inverted by means of the van’t Hoff equation for Thi. The number of moles of solute required is given by Msolute = xhiMsolvent/(1 − xhi) once Msolvent is selected (by the experimenter’s choice of a convenient volume with which to work and knowledge of solvent molecular weight and density). That number of moles of solute will lead to a solute mass, again through the molecular weight. That mass will be combined with the solvent, and the admix will be gently warmed until reaching Thi, as in the Figure 1 diagram. As the solid solute disappears in the warmed solvent, this is a properly prepared solution for cooling to generate a supersaturation value of S at TS, as the experimenter desires. A simpler way to prepare the proper solution is to take the volume of solvent selected by the experimenter and add excess solute. Heat this mixture to Thi and hold until equilibrium is assured. Then, decant solution for the cooling run after assuring that excess solute was indeed present at Thi and that some was indeed left behind in the mother mixture after decantation. This assures phase equilibrium. If the solute disappeared during the temperature hold, then more solute needs to be added until at least some of it does not disappear or dissolve into the solution. Equilibrium-phase thermodynamics dictates that xhi = xS will be the solute mole fraction in the solution. Savings in effort by this simpler method are obvious. However, this technique will, of course, not be possible in what elsewhere are called the first set 11321

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A liquid stream of tetracosane, C24, at its melting point was poured into a stream of toluene chilled to a temperature such that, when mixed with the hot wax, the final temperature was the supersaturated-state temperature, or the room temperature in this case. Returning to Figure 2, the streams appear to comingle in the combined stream as clear liquids before hitting the watch glass. Liquid appearances quickly disappear within 2 s as the strems continue to mix on the watch glass. Lumpy solids form in a somewhat cloudy solvent. Simple theories of fluid and partial mixing could have predicted this outcome. Evidently, a domain of hot wax will meet and be cooled by a domain of chilled toluene. The quickly cooled wax domains form lumps before molecular-scale mixing with the toluene solvent can occur. The approach might still work if the domains could be made into a spray of nanoscale droplets. Mixing competes with heat transfer, but the latter dominates before mixing is complete. Runs were performed identically save only that S = 1.1 with similar results. The second set of experiments was initiated from the calamities of the first set. Mixing must precede cooling to avoid domination by heat transfer. However, that leaves the situation without a cooling driver. That driver had been the cold toluene, but now the cold toluene is consumed in preparing the solution. The next logical choice for the cooling driver would be the watch glass itself. The watch glass is thin and has a large surface area facing the solvent. The solution spread on the watch glass will also be thin and have a large surface area facing the watch glass. This will lead to good heat transfer between the solution and watch glass [although not as good as if two liquids (molten solute and cold solvent) were mixed, as in the original experiments]. This is an important variation of the technique. The much longer crystallization times for waxes, compared to the heat-transfer characteristic times (to be explored later in a transport theoretical framework), mean that the heat-transfer issues have been largely met for the thermodynamic theoretical framework described earlier. To test the variation, a warmed tetracosane/toluene solution was poured onto a chilled watch glass (Figure 3). (To be sure, in this variation, instead of the cold driver being the solution, now it is the crystallizer watch glass.) The switch of cooling ballast from the solvent to the watch glass is a crucial augmentation that allows a true molecular-scale mixed solution

fast cooling might alter the concentration significantly from what the experimenter desired. Again, this detraction is minimized the shorter the cooling interval. These issues are resolved with fast cooling, a clear goal of this research. It is desired to take fuel samples quickly to cold temperatures. Experimental techniques to do that will need to involve high heat transfer and low final temperatures. One of the highest modes of heat transfer between two liquids occurs when they are simply mixed together. This implies that the wax should be in a molten liquid state for the high heat transfer we seek. The solvent with which it is to be mixed is typically in a liquid state at standard conditions. The cold final temperature desired could then be achieved by precooling the solvent to a very low temperature such that, when the solvent and molten solute are mixed, the final temperature obtained will be indeed the desired cold supersaturation temperature. The simple equations that set the solute, solvent, and final mixture temperatures involve heat capacities and balances of heat before and after mixing. We sought to prepare a system as described above in deep supersaturation with S = 1.6. The cooling and heating were all within ranges routinely handled in wet-chemistry and unitoperation laboratories at universities. The attainment of deep supersaturation is a relatively simple reality, one might suppose. Fundamental experimental barriers exist to this end. Figure 2

Figure 2. S = 1.6. In less than 2 s, lumpy wax appears when a liquid stream of tetracosane at its melting point is poured into a stream of cold toluene. (Given that the actual toluene amount was 25 mL, masses and temperatures of member masses can be easily if tediously worked out or are available from the authors.) Similar runs with S = 1.1 gave the same results.

represents multiple experimental cooling runs with molten wax and very cold solvent such that S = 1.6 would be obtained in the final room-temperature supersaturated state. It should be emphasized that, although subambient temperatures will typically be desired for the temperature of the supersaturated state, here, a final temperature or supersaturation temperature of room temperature was selected. The goal was to develop the technique and not pursue a particular cold supersaturation temperature. With the technique developed, different (lower) supersaturation temperatures could be attained with a suitable cold-temperature reservoir such as used in the baseline AMK NASA study.7 Heat-of-crystallization effects are typically dwarfed by the reservoir mass and are arrested before they can upset the isothermal crystallization following the fast cooling.

Figure 3. S = 1.1. Appearance in 30 s after the experiment starts. Warmed tetracosane/toluene solution is poured onto the chilled watch glass, and room temperature is reached, TS. Evidence of smooth crystallization appears with the experiment variation technique. 11322

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Figure 4. Temperature history in a typical run. The heat capacity of the ballast is about half that of the solution, so TB needs to traverse a change of roughly twice that of the solution starting at Thi.

Thi, of either the pure solute in the first set of experiments or the solution in the second set. Note that, in the former, xS = 1.0 in Figure 1. The system is assumed to be surrounded by and in contact with a reservoir at TS and to remain thereafter at TS as isothermal crystallization proceeds. The last temperature mentioned here is the temperature of the reservoir used to deliver the cold ballast at its cold temperature, TB. Little is lost in analysis if this reservoir and ballast are both assumed to have a temperature of TB. These temperatures must bear the relationship TB < TS < Thi. The heat balance

to be prepared rapidly at low supersaturation temperatures. Crystals are just starting to form (Figure 3) in the bulk and on the surface of the solution 30 s after the system was adiabatically (that term to be clarified) prepared at near-room temperature in a little longer than 2 s. (This time required to thermally equilibrate cold watch glass and hot wax solution is only slightly longer than the time required to equilibrate hot wax solute and cold solvent as in the first experiments.) Nearroom temperatures prevail (again, here, room temperature is the supersaturation temperature, the desired temperature of study), and crystallization continues isothermally. As a check against the heat-capacity calculations of the watch glass, the run involved many watch glasses, each retained slightly longer in the cold reservoir than the previous one. The solution temperature, just warm enough to ensure solution, was the same each time. The watch glass that gave the desired room temperature (supersaturation temperature) for the solution after it was poured onto the watch glass was the one selected, as shown in Figure 3. Equipment to chill the watch glass to a set cold temperature and to confirm the temperature of the watch glass was not available to us, as it had been previously.7 Thus, watch glasses with a range of chilled temperatures were employed. What has been described is called the adiabatic cooling to supersaturation, isothermal crystallization (ASIC) technique. Here, the term adiabatic refers to heat transfer external to the experiment members [be they solute and cold solvent or solution and cold ballast (watch glass)]. Heat transfer is high between the two members, of course, and thus, the process is highly nonadiabatic within the system.

TS(MsoluteC hi + MsolventC B) = (MsoluteC hiThi + MsolventC BTB)

(4)

can be inverted for TB because Thi and TS are known. Known as well are the numbers of moles of solute and solvent and respective molar heat capacities. Selecting S and TS in turn sets Thi, as stated earlier. Now, eq 4 can set TB. To validate the assumption of constant heat capacities, the temperature range considered could be restricted by choosing the ballast temperature as a reference temperature. Then, the temperatures in eq 4 would be deltas with respect to that ballast temperature. All temperatures are known. It is time to examine the transitions between these temperatures. These temperature−time behaviors need to be compared with those of the wax crystallization kinetics, given by dC /dt = k(C − Csat)

or

d(C − Csat)/dt = k(C − Csat)

4. TRANSPORT THEORETICAL FRAMEWORK FOR FAST COOLING TO DEEP SUPERSATURATION The theoretical exploration of the heat transfer involved in the experiments will offer some of the best support for understanding the results. For example, the cooling time of a few seconds as observed experimentally can be made an order of magnitude more precise with the transport theoretics of heat transfer. There are several relevant temperatures in these experiments. The most important is the desired supersaturation temperature, TS. The next most often mentioned is the high temperature,

(5)

Because Csat can be taken as constant at a given saturation temperature, its time derivative will be zero. Both left-hand forms of eq 5 are correct. It is useful to render eq 5 in dimensionless form by choosing a characteristic concentration difference and dividing (C − Csat) by it so that it becomes (C − Csat)*, a dimensionless quantity. A dimensionless time can be formed as t* = tk. Equation 5 thus becomes d(C − Csat)*/dt * = (C − Csat)* 11323

(6)

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available data have been collected. The y axis is a dimensionless degree of supersaturation, S − 1, where again S = C/Csat.

Although k can be found from the methods herein (to be published), the carefully constructed and highly acclaimed article by Paso et al.4 will be used to extract values for k in the Appendix. This will show k = 1 min−1 approximately, a value in agreement with our own findings. The basic heat balance for the operation shown in Figure 4 is Q = mCp(Thi − TS) =

∫ Ah(T − TS) dt

= Ah(Thi − TS)t /2

(7)

The total heat removed from the solutions is equal the heat removed by convection during the course of the cooling run. The second equality reflects the rough assumption that the effective temperature difference during the run is roughly onehalf the maximum temperature difference. The mass m of the solution is m = ρV = ρAd, where d is recognized as some depth of the solution in the watch glass and A is the interfacial area for heat transfer. What can be considered as a dimensionless time can be constructed from eq 7 as Ah(t/2)/ρAdCp. The ratio of the dimensionless time from kinetic considerations can be divided by this time from transport considerations. The real time t during the experiment applies to both kinetics and transport and is divided out

Figure 5. Degrees of supersaturation in some recent studies.

Although these studies scan the molecular weight range of C20−C50, they do not cover the vast range of deep supersaturation. With the technique described herein demonstrated for one S value and one TS value, the way is open, in principle, for system preparation at arbitrary S and TS values. The extraordinary heat-transfer rates allow the system to be quickly prepared and held isothermal for crystallization kinetics studies or other studies to proceed.

■

time ratio, kinetics/transport = k 2ρCpd /h

APPENDIX Consider the possibility of extracting k from the article by Paso et al.4 The governing equation for k for their DSC-enabled sample cooling is

(60/h)(2)(50 lb m/ft 3)[0.4 B/(lb m F)](0.026 ft) = [64 B/(h ft2 F)] ≈ 1, but 1−10 in broad view given variable h

(8)

k=

All of the data in eq 8 came from a classic heat-transfer text.8 The kinetic eq 6 can be solved for the time. The concentration difference from Csat is one-tenth of its initial difference as a quantitative indication of time scales for kinetic changes. The time scale for the removal of the necessary amount of heat can also be found, about 10 s. The kinetic-to-transport ratio of these time scales is on the order of 10, providing support for the conclusions of eq 8. The h values used above came from the assumption that the solution dropped a height of 3 in. as it loaded the watch glass. The velocity gained by the fluid was assumed to be altered into motion in the plane by the curvature of the watch glass and thereafter circulated as turbulent flow. Well-known Nusselt number correlations then lead to h (eq 6-67 on p 314 of ref 8). Use of that correlation within a wide range of assumptions still leaves the time-scale conclusions unchanged. Further, use of this value of h leads to cooling times of about 10 s, as stated. This is longer than the experimental times of a few seconds mentioned earlier. This crude turbulent-flow model does not suffice and suggests that the true cooling process has some mixing-cup type of phenomena included in the flow. However, this turbulent model is superior to a conduction model that predicts cooling times on the order of 100 s. Quantification has been provided that the wax crystallization kinetics are much slower than the preparation times of the method herein for preparing supersaturated solutions. The method should facilitate working in deep supersaturation. The cold processing situations in the field mentioned in the Introduction are typically far removed from nucleation and well into crystallization in deep supersaturation (high-S regime; see below). Yet, look in Figure 5 at the regimes in which the scant

(dC /dt )max (S − 1)Csat

(5)

where eq 1 is written in a form closer to their work. Their Figure 74 gives crystallization rates in mass fraction per minute (dX/dt) for cases of 4%, 1%, and 0.5% n-C36 in Coray-15 solvent as the y axis. The x axis of their Figure 74 is the temperature of the system at various stages, and from it, we can gather the temperature at (dX/dt)max. That leads to (dC/dt)max with the help of other information given. Their Figure 64 guides us to interpret the coincidence of the maximum of dX/dt in their Figure 74 as being in the center of the “supersaturation growth regime” as they describe it, the region of our interest. This then is the item carried to our Table 1 below the heading “from their Figure 7”. The next item noted is S, or S − 1. Their Figure 34 gives supersaturation information as S − 1 at nucleation for two of the three cases 4%, 1%, and 0.5%. A footnote in Table 1 tells how we were able to extrapolate to obtain S − 1 for the 0.5% case as well. According to their Figure 6,4 nucleation precedes supersaturation crystal growth, but only slightly (slight uncertainty). Supersaturation at nucleation might be expected to be different than at “supersaturated crystal growth” as they call it, but perhaps not by much, and so their Figure 34 value is taken as the best estimate (and the only possible estimate from their article) that can be made of (S − 1) under the conditions implied by the companion entries under “given” in Table 1. To be clear, these include (dX/dt)max from the previous paragraph and the temperature when it occurred from the discussion following. Enough detail from ref 4 has been given so that the reader should be convinced of the plausibility of the construction in Table 1. 11324

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Table 1. Kinetics Data from Figures 3, 6, and 7 of Ref 4 given from their Figure 3

a

case

S−1

4% 1% 0.5%

0.15 0.46 0.59a

from their Figure 7 −1

(dX/dt)max (min ) 0.0102 0.0032 0.0023

at 40C at 27C at 21C

extracted Csat (mol/L)

(dC/dt)max

k (min−1) = (dC/dt)max(S − 1)Csat

0.051 758 0.008 838 0.003 727

0.019 144 0.006 154 0.004 423

2.5 1.5 2.0

An extrapolation was made assuming that the 0.5% behavior relative to the next lower 1% behavior curve in Figure 4 prevails in Figure 3 as well.

A scan of Table 1 shows thet generating “extracted” quantities is the next step. Csat can be obtained from the temperatures indicated, through the van’t Hoff equation. Note that there are some details in generating (dC/dt)max from (dX/ dt)max, and these are available from the authors. The elements of the table are filled, and k works out as 2.5 min−1 for the 4% case. Instead of starting with (dX/dt)max, it might be more realistic to deal with a suitable average. One certainly would not want the maximum rate, if the rate value were to be used in an effort such as crystallization modeling. In that case, a rate value over an interval would be used instead of the maximum at a point. Use of dX/dt at half-maximum is an approximation to the average from Figures 6 and 7 in ref 4. The half-maximum value yields k ≈ 1 min−1, the value taken herein and one that agrees with our own.

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(8) Kreith, F. Principles of Heat Transfer; International Textbook Co.: Scranton, PA, 1965; pp 149, 261−318, 592−598.

AUTHOR INFORMATION

Corresponding Author

*Tel.: 785-537-0073. E-mail: [email protected]. Notes

The authors declare no competing financial interest. § Emeritus.

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ACKNOWLEDGMENTS We acknowledge the service of facilities at Texas A&M University-Kingsville and Kansas State University. Larry Erickson, Jennifer Anthony, and Jasmine Patel at KSU were helpful. Kristofer Paso and H. Scott Fogler at the University of Michigan helped interpret their referenced work.

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REFERENCES

(1) Chevallier, V.; Bouroukba, M.; Petitjean, D.; Barth, D.; Dupuis, P.; Dirand, M. Temperatures and Enthalpies of Solid−Solid and Melting Transitions of the Odd-Numbered n-Alkanes. J. Chem. Eng. Data 2001, 46, 1114−1122; 2002, 47, 115−143. (2) Dirand, M.; Chevallier, V.; Provost, E.; Bouroukba, M.; Petitjean, D. Multicomponent Paraffin Waxes and Petroleum Solid Deposits: Structural and Thermodynamic State. Fuel 1998, 77, 1253−1260. (3) Hammami, A.; Mehrotra, A. K. Non-Isothermal Crystallization Kinetics of Binary Mixtures of n-Alkanes: Ideal Eutectic and Isomorphous Systems. Fuel 1996, 75, 500−508. (4) Paso, K.; Senra, M. Y.; Sastry, A. Y.; Fogler, H. S. Paraffin Polydispersity Facilitates Mechanical Gelation. Ind. Eng. Chem. Res. 2005, 44, 7242−7254. (5) Paso, K. G. Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, 2005; pp 6−7. (6) Mullin, J. W. Crystallization; Butterworths: London, 1961; p 28. (7) Schruben, D. L. Measurement and Correlation of Jet Fuel Viscosities at Low Temperature; NASA Contractor Report 174911; NASA Lewis (Glenn) Research Center: Cleveland, OH, Aug 1985. Anti-mist kerosene (AMK) was once seen as a post-crash fire retardant. The airline industry and fuel suppliers needed impartial testers as they worked through such issues, and this task fell to NASA. 11325

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