OIL SPILL SCIENCE chapter 9 – evaporation modeling

OIL SPILL SCIENCE chapter 9 – evaporation modeling OIL SPILL SCIENCE chapter 9 – evaporation modeling OIL SPILL SCIENCE chapter 9 – evaporation modeling OIL SPILL SCIENCE chapter 9 – evaporation modeling OIL SPILL SCIENCE chapter 9 – evaporation modeling OIL SPILL SCIENCE chapter 9 – evaporation modeling

Diffusion-Regulated Models

2129.4 Complexities to the

Diffusion-Regulated Model

229

9.5 Use of EvaporationEquations in SpillModels

233

9.6 Comparison of ModelApproaches

An important concept in understanding evaporation is to understand themechanisms that regulate evaporation If there were no regulation, evaporationwould proceed nearly instantly Figure 9.1 shows a schematic of the air-boundary-layer regulated mechanism The liquid would evaporate at a veryhigh rate if it was not for the regulation caused by the slow transfer of vaporthrough the air boundary layer The most common example of this type ofregulation is applicable to water, and this concept enters into most people’scommon view of evaporation Evaporation of water can be increased byspreading it out or by increasing the wind speed

Oil Spill Science and Technology DOI: 10.1016/B978-1-85617-943-0.10009-7

Many liquids are not air-boundary-layer regulated primarily because theyevaporate too slowly to have the vapors saturate the air boundary layer abovethem Many mixtures are often regulated by the diffusion of molecules insidethe liquid to the surface of the liquid This situation is illustrated inFigure 9.2.Such a mechanism is true for many slowly evaporating mixtures of compounds,such as oils and fuels Some of the outcomes of this mechanism may seemcounterintuitive to some people in that increasing the area may not increase theevaporation rate except to a small degree if the initial pool is very thick, such asover about 10 to 20 mm Also, and perhaps more importantly, increasing windspeed does not increase evaporation.

Air Air boundary

Scientific and quantitative work on water evaporation is decades old.3,4Thebasis for the oil evaporation work in the literature is water evaporation Thereare several fundamental differences between the evaporation of a pure liquidsuch as water and that of a multicomponent system such as crude oil Mostobviously, the evaporation rate for a single-component liquid such as water is

a constant with respect to time.3,4Evaporative loss, by total weight or volume,

is not linear with time for crude oils and other multicomponent fuel mixtures.5Evaporation of a liquid can be considered as the movement of moleculesfrom the surface into the vapor phase above it The layer of air above theevaporation surface is known as the boundary layer.6The characteristics of thisair layer, or boundary layer, can influence evaporation In the case of water, theboundary layer regulates the evaporation rate Air can hold a variable amount ofwater, depending on temperature, as expressed by the relative humidity Underconditions where the boundary layer is not moving (no wind) or has lowturbulence, the air immediately above the water quickly becomes saturated andevaporation slows or ceases In practice, the actual evaporation of waterproceeds at a small fraction of the possible evaporation rate because of thesaturation of the boundary layer The air-boundary-layer physics are then said

to regulate the evaporation of water This regulation manifests itself in thesensitivity of evaporation to wind or turbulence When turbulence is weak orabsent, evaporation can slow down by orders-of-magnitude The moleculardiffusion of water molecules is at least 103 times slower than turbulentdiffusion.6

Evaporation can be viewed as consisting of two components, fundamentalevaporation and regulation mechanisms Fundamental evaporation is thatprocess consisting of the evaporation of the liquid directly into the vapor phasewithout regulation other than by the thermodynamics of the liquid itself.Regulation mechanisms are those processes that serve to regulate the finalevaporation rate into the environment For water, the main regulation factor isthe air-boundary-layer regulation discussed above Air-boundary-layer regu-lation is manifested by the limited rate of diffusion, both molecular andturbulent diffusion, and by saturation dynamics Molecular diffusion is based

on exchange of molecules over the mean-free path in the gas The rate ofmolecular diffusion for water is about 105slower than the maximum rate ofevaporation possible, purely from thermodynamic considerations.6The rate forturbulent diffusion, the combination of molecular diffusion and movement withturbulent air, is on the order of 102slower than that for maximum evaporation

In fact, in the case of water, maximum evaporation is not known and has onlybeen estimated by experiments in artificial environments or by calculation.3

If the evaporation of oil was like that of water and was air-boundary-layerregulated, one could write the mass-transfer rate in semi-empirical form (also

in generic and unitless form) as:

where E is the evaporation rate in mass per unit area, K is the mass-transferrate of the evaporating liquid, presumed constant for a given set of physicalconditions, sometimes denoted as kg (gas phase mass-transfer coefficient,which may incorporate some of the other parameters noted here), C is theconcentration (mass) of the evaporating fluid as a mass per volume, Tu is

a factor characterizing the relative intensity of turbulence, and S is a factor thatrelates to the saturation of the boundary layer above the evaporating liquid Thesaturation parameter, S, represents the effects of local advection on saturationdynamics If the air is already saturated with the compound in question, theevaporation rate approaches zero This also relates to the scale length of anevaporating pool If one views a large pool over which a wind is blowing, there

is a high probability that the air is saturated downwind and the evaporation rateper unit area is lower than for a smaller pool It should be noted that there manyequivalent ways of expressing this fundamental evaporation equation.Much of the pioneering work for evaporation studies was performed bySutton who proposed an equation based largely on empirical work:7

where Csis the concentration of the evaporating fluid (mass/volume), U is thewind speed, d is the area of the pool, Sc is the Schmidt number, and r is theempirical exponent assigned values from 0 to 2/3 Other parameters are defined

as above The terms in this equation are analogous to the very generic equation,(1), proposed above The turbulence is expressed by a combination of the windspeed, U, and the Schmidt number, Sc The Schmidt number is the ratio ofkinematic viscosity of air (v) to the molecular diffusivity (D) of the diffusinggas in air, that is, a dimensionless expression of the molecular diffusivity of theevaporating substance in air The coefficient of the wind power typifies theturbulence level The value of 0.78 (7/9) as chosen by Sutton, represents

a turbulent wind, whereas a coefficient of 0.5 would represent a wind flow thatwas more laminar The scale length is represented by d and has been given anempirical exponent of1/9 For water, this represents a weak dependence onsize The exponent of the Schmidt number, r, represents the effect of thediffusivity of the particular chemical, and historically was assigned valuesbetween 0 and 2/3.7

This expression for water evaporation was subsequently used by thoseworking on oil spills to predict and describe oil and petroleum evaporation.Much of the literature follows the work of Mackay.8,9Mackay and co workersadapted the equations for hydrocarbons using the evaporation rate of cumene.Data on the evaporation of water and cumene have been used to correlate thegas phase mass-transfer coefficient as a function of wind speed and pool size bythe equation:

K ¼ 0:0292 U0 :78X0:11Sc0:67 (3)

where Kmis the mass-transfer coefficient in units of mass per unit time and X isthe pool diameter or the scale size of evaporating area Stiver and Mackaysubsequently developed this further by adding a second equation:9

where N is the evaporative molar flux (mol/s), kmis the mass-transfer cient at the prevailing wind (m/s), A is the area (m2), P is the vapor pressure ofthe bulk liquid (Pascals), R is the gas constant [8.314 Joules/(mol-K)], and T isthe temperature (K )

coeffi-Thus, boundary-layer regulation was assumed to be the primary regulationmechanism for oil and petroleum evaporation This assumption was neverwell tested by experimentation, as revealed by a literature search.2 Theimplications of these assumptions are that evaporation rate for a given oil isincreased by:

l increasing turbulence

l increasing wind speed

l increasing the surface area of a given mass of oil

These factors can then be verified experimentally to test whether oil isboundary-layer regulated

9.2 REVIEW OF THEORETICAL CONCEPTS

Blokker was the first to develop oil evaporation equations for oil evaporation

at sea.10 His starting basis was theoretical Oil was presumed to be a component liquid The ASTM (American Society for Testing and Materials)distillation data and the average boiling points of successive fractions wereused as the starting point to predict an overall vapor pressure The averagevapor pressure of these fractions was then calculated from the Clausius-Clapeyron equation to yield:

one-logps

p ¼ qM

4:57

1

The term qM/(4.57 Ts) was taken to be nearly constant for hydrocarbons(¼5.0 þ/ 0.2), and thus the expression was simplified to:

From the data obtained, the weathering curve was calculated, assuming thatRaoult’s law is valid for this situation giving qM as a function of the percentage

evaporated Pasquill’s equation10 was applied stepwise, and the total ration time was obtained by summation:

of the component or oil mass Thus the model is partially air-boundary-layerregulated

Blokker constructed a small wind tunnel and tested this equation againstthe evaporation of gasoline and a medium crude oil The observed gasolineevaporation rate was much higher than was predicted, and the crude oil rate wasmuch lower than predicted The times of evaporation, however, were somewhatclose, and the equation was accepted for further use The above equations werethen incorporated into spreading equations to yield equations to predict thesimultaneous spreading and evaporation of oil and petroleum products.Mackay and Matsugu approached the problem by using the classical waterevaporation and experimental work.8 The water evaporation equation wascorrected to hydrocarbons using the evaporation rate of cumene It was notedthat the difference in constants was related to the enthalpy differences betweenwater and cumene Data on the evaporation of water and cumene were used tocorrelate the gas phase mass-transfer coefficient as a function of wind speedand pool size by the equation:

Km ¼ 0:0292 U0 :78X0:11Sc0:67 (8)where Kmis the mass-transfer coefficient in units of mass per unit time and X

is the pool diameter or the scale size of evaporating area Note that theexponent of the wind speed, U, is 0.78, which is equal to the classical waterevaporation-derived coefficient Mackay and Matsugu noted that for hydro-carbon mixtures, the evaporation process is more complex, being dependent

on the liquid diffusion resistance being present Experimental data on line evaporation were compared with computed rates The computed ratesshowed some agreement and suggested the presence of a liquid-phase mass-transfer resistance

gaso-This work was subsequently extended by the same group to show that theevaporative loss of a mass of oil spilled can be estimated using a mass-transfercoefficient, as shown above.11 This approach was investigated with somelaboratory data and tested against some known mass-transfer conditions on thesea The conclusion was that this mass-transfer approach could result inpredictions of evaporation at sea

Butler developed a model to examine evaporation of specific hydrocarboncomponents.12The weathering rate was taken as proportional to the equilib-rium vapor pressure, P, of the compound and to the fraction remaining:

where x is the amount of a particular component of a crude oil at time, t, xoisthe amount of that same component present at the beginning of weathering(t¼ 0), k is an empirical rate coefficient, and P is the vapor pressure of the oilcomponent

Since petroleum is a complicated mixture of compounds, P is not equal tothe vapor pressure of the pure compound, but neither would there be largevariations in the activity coefficient as the weathering process occurs For thisreason, the activity coefficients were subsumed in the empirical rate coefficient

k P and k were taken as independent of the amount, x, for a fairly wide range ofoils The equation was then directly integrated to give the fraction of theoriginal compound remaining after weathering as (similar to Henry’s law):

The vapor pressure of individual components was fit using a regression line

to yield a predictor equation for vapor pressure:

Equation(12)predicts that the fraction weathered is a function of the carbonnumber and decreases at a rate that is faster than predicted from simpleexponential decay If the initial distribution of compounds is essentiallyuniform (xoindependent of N ), then the above equation predicts that the carbonnumber where a constant fraction (e.g., half) of the initial amount has been lost(x ¼ 0.5 xo) is a logarithmic function of the time of weathering:

N1=2 ¼ 10:66 þ 2:17 logðkt=xoÞ (13)where N1/2is half the volume fraction of the oil

The equation was tested using data from some patches of oil on shoreline,whose age was known The equation was able to predict the age of the samplesrelatively well It was suggested that the equation was applicable to open waterspills; however, this was never subsequently applied in models It should benoted that this approach is somewhat similar to the model that will be described

later in this paper and also that it is not air-boundary-layer based but is

a diffusion-like model based partially on empirical values

Yang and Wang developed an equation using the Mackay and Matsugumolecular diffusion process.13 The vapor phase mass-transfer process wasexpressed by:

Die ¼ kmð pi pi NÞ=½RTS (14)where Dieis the vapor phase mass-transfer rate, kmis a coefficient that lumps allthe unknown factors that affect the value of Die, pi is the hydrocarbon vaporpressure of fraction, I, at the interface, piNis the hydrocarbon vapor pressure offraction, I, at infinite altitude of the atmosphere, R is the universal gas constant,and Tsis the absolute temperature of the oil slick

The following functional relationship was proposed:

where A is the slick area, U is the over-water wind speed, and a, q, and g areempirical coefficients This functional relationship was based on the results ofpast investigations, including, for instance, those of MacKay and Matsugu whosuggested the value of g to be in the range from0.025 to 0.055.8Furtherexperiments were performed by Yang and Wang to determine the values of

a and q.13The results were found to be twofold Experiments showed that a filmformed on evaporating oils and that this film severely retarded evaporation.Before the surface film has developed (rt/ro< 1.0078):

Brighton proposed that the standard formulation used by many workersrequired refining.14

E ¼ K CsU7=9d1 =9Scr (18)His starting point for water evaporation was similar to that proposed by Sutton7where E is the mean evaporation rate per unit area, K is an empirically deter-mined constant, Csis the concentration of the evaporation fluid (mass/volume),

d is the area of the square or circular pool, and r is an empirical exponentassigned values from 0 to 2/3

Brighton suggested that this equation does not conform to the basic sionless form involving the parameters U and Zo (wind speed and roughnesslength, respectively), which define the boundary-layer conditions The key factor

dimen-in Brighton’s analysis was to use a ldimen-inear eddy-diffusivity profile This featureimplied that concentration profiles become logarithmic near the surface, which issuspected to be more realistic compared to the more finite values previously used.Using a power profile to provide an estimation of the turbulence, Brighton wasable to substitute the following identities into the classical relationship:

U ¼ u

where u* is the friction velocity, z1is the reference height above the surface, z0

is the roughness length, and n is the power law dimensionless term It should benoted that these are applicable to neutrally stable atmospheres

U

z

z1

dX

dx ¼ ddz

as 0.85)

Brighton subsequently compared his model with several runs of mental evaporation experiments in the field and in the laboratory This includedlaboratory oil evaporation data.15 The model only correlated well with labo-ratory water evaporation data, and the reason given was that other data setswere “noisy.”

experi-The most frequently used work in spill modeling is that of Stiver andMackay.9It is based on some of the earlier work by Mackay and Matsugu, butsignificant additions were made.8Additional information is given in a thesis byStiver.16The formulation was initiated with assumptions about the evaporation

of a liquid If a liquid is spilled, the rate of evaporation is given by:

where N is the evaporative molar flux (mol/s), K is the mass-transfer coefficientunder the prevailing wind (ms1), A is the area (m2), and P is the vapor pressure

of the bulk liquid

This equation was arranged to give:

where Fv is the volume fraction evaporated, v is the liquid’s molar volume(m3/mol), and Vois the initial volume of spilled liquid (m3).

By rearranging, we obtain:

or:

where H is Henry’s law constant and q is the evaporative exposure

The right-hand side of the second to last equation has been separated intotwo dimensionless groups The group, KAdt/Vo, represents the time rate of whathas been termed the “evaporative exposure” and was denoted as dq Theevaporative exposure is a function of time, the spill area and volume (orthickness), and the mass-transfer coefficient (which is dependent on the windspeed) The evaporative exposure can be viewed as the ratio of exposed vaporvolume to the initial liquid volume

The group Pv/(RT) or H is a dimensionless Henry’s law constant or ratio ofthe equilibrium concentration of the substance in the vapor phase [P/(RT)] tothat in the liquid (l/v) H is a function of temperature The productqH is thus theratio of the amount that has evaporated (oil concentration in vapor times vaporvolume) to the amount originally present For a pure liquid, H is independent of

Fvand Equation 2.26 was integrated directly to give:

If K, A, and temperature are constant, the evaporation rate is constant andevaporation is complete (Fvis unity) when q achieves a value of 1/H

If the liquid is a mixture, H depends on Fvand the basic equation can only

be integrated if H is expressed as a function of Fv; that is, the principal variable

of vapor pressure is expressed as a function of composition The evaporationrate slows as evaporation proceeds in such cases

Equation(26)was replaced with a new equation developed using data fromevaporation experiments:

Fv ¼ ðT=K1Þ Inð1 þ K1q=TÞ expðK2 K3=TÞ (27)where Fvis the volume fraction evaporated and K1,2,3are empirical constants

A value for K1was obtained from the slope of the Fvversus log q curve frompan or bubble evaporation experiments For q greater than 104, K1was found to

be approximately 2.3T divided by the slope The expression exp(K2 K3/T)was then calculated, and K2and K3were determined individually from evap-oration curves at two different temperatures Variations of all the aboveequations have been used extensively by many other experimenters and formodel application

Brown and Nicholson studied the weathering of a heavy oil, bitumen.17They compared experimental data using a large-scale weathering tank with two

spill model outputs In the FOOS model, the evaporative exposure concept isused in which the fraction of oil evaporated is given by a variant of the Mackayequation:

where F is the fraction evaporated, C is an empirical constant, and E is

a measure of the evaporative exposure, defined as;

where;

Km ¼ 0:0048 U0 :78Z0:11Sc0 :67 (30)and where Kmis the mass-transfer coefficient, A is the slick area, v is the oilmolar volume, Vois the initial slick volume, Z is the pool size scale factor, and

Sc is the Schmidt number (taken as 2.7)

Brown and Nicholson compared the measured evaporation for a 5 ms1wind at an ambient temperature of 20C, and evaluation was done with theequation above.17 A spill volume of 100 m3was assumed A value of about

105 m3/mol was used for the average molar volume The model generallydescribed the observed evaporation quite well, particularly during the first fewhours Later, however, the model consistently overpredicted the evaporationrate A simple method of correcting the equation was implemented byassuming that the vapor phase Schmidt number decreases slightly as the skin onthe oil thickens In response, the evaporative exposure was modified to:

Km ¼ ð0:0025  0:000021 tÞ U0 :78 (31)The predicted evaporation then compared favorably with the measured values.Bobra conducted laboratory studies on the evaporation of crude oils.18Theevaporation curves for several crude oils and petroleum products weremeasured under several different environmental conditions These data werecompared to the equation developed by Stiver and Mackay.9The equation usedwas:

Fv ¼ In½1 þ BðTG=TÞ q expðA  B To=TÞfT=BTGg (32)where FVis the fraction evaporated, TGis the gradient of the modified distil-lation curve, A and B are dimensionless constants, Tois the initial boiling point

of the oil, and q is the evaporative exposure as previously defined

The comparison by Bobra et al showed that the Stiver and Mackay equationpredicts the evaporation of most oils relatively well until time exceeds about

8 hours; after that it overpredicted the evaporation The “overshoot” can be as much

as 10% evaporative loss at the 24-hour mark This is especially true for very lightoils The Stiver and Mackay equation was also found to underpredict or overpredictthe evaporation of oils in the initial phases In addition, it was found that the basic

assumptions in the bubble experiment as proposed by early researchers, namely,that the air bubbles are saturated with vapor, was not correct.9Bobra also noted thatmost oil evaporation follows a logarithmic curve with time and that a simpleapproach to this was much more accurate than using Equation(32).

9.3 DEVELOPMENT OF NEW DIFFUSION-REGULATED

MODELS

A review of the theoretical work above reveals that air-boundary-layer conceptsare very limited and cannot accurately explain long-term evaporation Fingasconducted a series of experiments over several years to examine the conceptsfurther.19

The results of the boundary-regulation experiments are presented in theorder of the experimental series

9.3.1 Wind Experiments

A major factor in determining whether or not oil evaporation is layer regulated is if the evaporation rate increases with wind as would bepredicted by Equations(2) and (8)above Experiments on the evaporation ofoil with and without wind were conducted with ASMB (Alberta Sweet MixedBlend), gasoline, and water Water formed a baseline data set since much isknown about its evaporation behavior.3 Regressions on the data were per-formed, and the equation parameters calculated Curve coefficients are theconstants from the best fit equation [Evap¼ a ln(t)], t ¼ time in minutes, forlogarithmic equations or Evap¼ a Ot, for the square root equations Oils withfew components evaporating at one time have a tendency to fit square rootcurves.5While data were calculated separately for percentage of weight lostand absolute weight, the latter is usually used because it is more convenient.The plots of wind speed versus the evaporation rate (as a percentage of weightlost) for each oil type are shown inFigures 9.3 to Figure 9.5 These figuresshow that the evaporation rates for oils and even the light product gasoline arenot increased by a significant amount with increasing wind speed In mostcases, there is a small rise from the 0-wind level to the 1-m/s level, but afterthat, the rate remains relatively constant The evaporation rate after the 0-windvalue is nearly identical for all oils This is due to the stirring effect on the oil,which increases the diffusion rate to the surface The oil evaporation data can

air-boundary-be compared to the evaporation of water, as illustrated inFigure 9.5 These datashow the classical relationship of the water evaporation rate correlated with thewind speed (evaporation varies as U0.78, where U is wind speed) This, by itself,indicates that the oils studied here are not boundary-layer-regulated, but

a small effect is seen in moving from 0-wind to 1 m/s, and not thereafter This,

as noted above, is due to the stirring effect of the wind thus increasing thediffusion rate

FIGURE 9.3 Evaporation of ASMB with varying wind velocities This figure shows that there

is little variation with wind velocity except in going from the 0-wind-level up to the others This

is due to the stirring effect of wind and not air-boundary-layer regulation.

FIGURE 9.4 Evaporation

of gasoline with varying windvelocities This figure alsoshows that there is littlevariation with wind velocityexcept in going from the0-wind-level up to the others.This again is due to the stir-ring effect of wind and notair-boundary layer regulation

Figure 9.6shows the rates of evaporation compared to the wind speed for allthe liquids used in this study This figure shows the evaporation rates of all testliquids versus wind speed The lines shown are those calculated by linearregression This clearly shows that water evaporation rate increased, asexpected, with increasing wind velocity The oils, ASMB, and gasoline, do notshow any significant increase with increasing wind speed In any case, they donot show the typical U0.78relationship that water shows.

All the above data show that oil is not boundary-layer-regulated

FIGURE 9.5 Evaporation

of water with varying windvelocities This figure showsdramatic differences in theevaporation rate of water withwind velocity This is typical

of air-boundary-layer tion Compare Figure 9.5

regula-with oil evaporation in

Figures 9.3 and 9.4, which donot show this trend of vari-ance with wind velocity

FCC Heavy Cycle ASMB

FIGURE 9.6 Correlation

of evaporation rates and windvelocity The lines are drawnthrough the data points fromexperimental values Thisclearly shows no correlation

of oil evaporation rates withwind velocity and the strongand expected high correlation

of water with wind velocity.The water evaporation line

is moved to fit on the verticalscale, but otherwise isunaltered

9.3.2 Evaporation Rate and Area

Air-boundary-layer regulated liquids evaporate much faster if one increasesthe area A small spill of water on the kitchen cupboard can be evaporatedquickly by spreading it out on the cupboard A test of this tendency will alsoconfirm the proposition that oil is diffusion regulated ASMB was also used toconduct a series of experiments with varying evaporation area The mass of theoil was kept constant so that the thickness of the oil would also vary However,the greater the area, the less the thickness, and both factors would increase oilevaporation if it were boundary-layer regulated The experiments show nocorrelation between area and evaporation rate One can conclude that evapo-ration rate is not highly correlated with area, and thus the evaporation of oil isnot air-boundary-layer regulated

9.3.3 Study of Mass and Evaporation Rate

Air-boundary-layer liquids show no correlation between the mass of oilevaporated and the evaporation rate; however, diffusion-regulated liquids do.ASMB oil was again used to conduct a series of experiments with volume as themajor variant Alternatively, thickness and area were held constant to ensurethat the strict relationship between these two variables did not affect the finalregression results.Figure 9.7 illustrates the relationship between evaporationrate and volume of evaporation material (also equivalent to mass of evaporatingmaterial) This figure illustrates a strong correlation between oil mass (orvolume) and evaporation rate This again proves that there is no boundary-layerregulation

a direct relationship betweenevaporation rate of oil andmass of oil It indicates thatoil is diffusion regulated

9.3.4 Study of the Evaporation of Pure Hydrocarbonsdwith and Without Wind

A study of the evaporation rate of pure hydrocarbons was conducted to testthe classic boundary-layer evaporation theory as applied to the hydrocarbonconstituents of oils The evaporation rate data are illustrated inFigure 9.8 Thisfigure shows that the evaporation rates of the pure hydrocarbons have a variableresponse to wind Heptane (hydrocarbon number 7) shows a large differencebetween evaporation rate in wind and no wind conditions, indicating boundary-layer regulation Decane (carbon number 10) shows a lesser effect, anddodecane (carbon number 12) shows a negligible difference between the twoexperimental conditions This experiment shows the extent of boundary regu-lation and the reason for the small or negligible degree of boundary regulationshown by crude oils and petroleum products Crude oil contains very littlematerial with carbon numbers less than dodecane, often less than 3% of itscomposition Even the more volatile petroleum products, gasoline and dieselfuel, only have limited amounts of compounds more volatile than decane, andthus are also not strongly boundary-layer regulated, if at all

9.3.5 Other Factors

Another evaluation of evaporation regulation is that of saturation concentration,the maximum concentration soluble in air The saturation concentrations ofwater and several oil components are listed inTable 9.1.20This table shows thatsaturation concentration of water is less than that of many common oilcomponents The saturation concentration of water is, in fact, about two orders

of magnitude less than the saturation concentration of volatile oil componentssuch as pentane This further explains why even light oil components have littleboundary-layer limitation Further, the saturation concentration of water is soregulating that with a high relative humidity, there is little that can be added tothe air

9.3.6 Temperature Variation and Generic Equations Using

equations may be needed for each oil is a significant disadvantage to practicalend use, and a way to accurately predict evaporation using other readily-available data is necessary Findings show that distillation data can be used topredict evaporation Distillation data are very common and are often the onlydata used to characterize oils This is because the data are crucial in operatingrefineries Crudes are sometimes priced on the basis of their distillation data.New procedures to measure distillation data are very simple, fast, andrepeatable.

Further, it was noted that oils and fuels evaporated as two distinct typesdthose that evaporated as a logarithm of time and those that evaporated as asquare root of time.5 Most oils typically evaporated as a logarithm (natural)with time Diesel fuel and similar oils, such as jet fuel, kerosene, and the like,evaporate as a square root of time The reasons for this are simply that dieselfuel and the like have a narrower range of compounds that evaporate at similaryield rates, which are a summation of a square root.5

The empirically measured parameters at 15C were correlated with boththe slopes and the intercepts of the temperature equations Full details of thiscorrelation are given in the literature.22,23For the variation with temperature,the resulting equation is:

Percentage evaporated ¼ ½B þ 0:045ðT  15Þ InðtÞ (33)where B is the equation parameter at 15C, T is temperature in degrees Celsius,and t is the time in minutes

Distillation data were directly correlated to the evaporation rates mined by experimentation The distillation data used were the type that arestated as the temperature at which a fixed amount of material is lost Theoptimal point, or point at which the regression coefficient is maximum, wasfound to be 180C by using peak functions The percent mass distilled at 180degrees was used to calculate the relationship between the distillation valuesand the equation parameters The equations used were derived from correla-tions of the data

deter-The data from those oils that were better fitted with square rootequationsddiesel, Bunker C light, and Fluid Catalytic Cracker (FCC) HeavyCycledwere calculated separately

The equations derived from the regressions are as follows:

For oils that follow a logarithmic equation:

Percentage evaporated ¼ 0:165ð%DÞ InðtÞ (34)For oils that follow a square root equation:

Percentage evaporated ¼ 0:0254ð%DÞpffiffit

(35)where %D is the percentage (by weight) distilled at 180C

These equations can be combined with the equations generated in previouswork as shown in Equation(33)above to account for the temperature variations:For oils that follow a logarithmic equation:

Percentage evaporated ¼ ½:165ð%DÞ þ :045ðT  15Þ lnðtÞ (36)For oils that follow a square root equation:

Percentage evaporated ¼ ½:0254ð%DÞ þ :01ðT  15Þpffiffit

(37)where %D is the percentage (by weight) distilled at 180C

In addition, a large number of experiments were performed on oils todirectly measure their evaporation curves The empirical equations that resultare given inTable 9.2

TABLE 9.2 Equations for Predicting Evaporation

Adgo e long term %Ev ¼ (.68 þ 045T)ln(t)

Alaminos Canyon Block 25 %Ev ¼ (2.01 þ 045T)ln(t)

Alaska North Slope (2002) %Ev ¼ (2.86 þ 045T)ln(t)

Alberta Sweet Mixed Blend %Ev ¼ (3.24 þ 054T)ln(t)

Amauligak e f24 %Ev ¼ (1.91 þ 045T)ln(t)

Anadarko H1A-376 %Ev ¼ (2.66 þ 013T)/t

Arabian Medium %Ev ¼ (1.89 þ 045T)ln(t)

Arabian Light (2001) %Ev ¼ (2.4 þ 045T)ln(t)

ASMB e Standard #5 %Ev ¼ (3.35 þ 045T)ln(t)

ASMB (offshore) %Ev ¼ (2.2 þ 045T)ln(t)

(Continued )

TABLE 9.2 Equations for Predicting Evaporationdcont’d

Aviation Gasoline 100 LL ln(%Ev) ¼ (0.5 þ 045T)ln(t)

Azeri e long term %Ev ¼ (1.3 þ 045T)ln(t)

Azeri e short term %Ev ¼ (0.09 þ 013T)/t

Bent Horn A-02 %Ev ¼ (3.19 þ 045T)ln(t)

Beta e long term %Ev ¼ (0.29 þ 045T)ln(t)

Bunker C e Light (IFO~250) %Ev ¼ (.0035 þ 0026T)/t

Bunker C e long term %Ev ¼ (.21 þ 045T)ln(t)

Bunker C (short term) %Ev ¼ (.35 þ 013T)/t

Bunker C Anchorage %Ev ¼ (0.13 þ 013T)/t

Bunker C Anchorage (long term) %Ev ¼ (0.31 þ 045T)ln(t)

California API 11 %Ev ¼ (0.13 þ 013T)/t

California API 15 %Ev ¼ (0.14 þ 013T)/t

Cat Cracking Feed %Ev ¼ (0.18 þ 013T)/t

Cold Lake Bitumen %Ev ¼ (0.16 þ 013T)/t

Combined Oil/Gas %Ev ¼ (0.08 þ 013T)/t

TABLE 9.2 Equations for Predicting Evaporationdcont’d

Compressor Lube Oil -New %Ev ¼ (0.68 þ 045T)ln(t)

Cook Inlet e Granite Point %Ev ¼ (4.54 þ 045T)ln(t)

Cook Inlet e Swanson River %Ev ¼ (3.58 þ 045T)ln(t)

Cook Inlet New Batch %Ev ¼ (3.1 þ 045T)ln(t)

Cook Inlet Trading Bay %Ev ¼ (3.15 þ 045T)ln(t)

Corrosion Inhibitor Solvent %Ev ¼ (0.02 þ 013T)/t

Delta West Block 97 %Ev ¼ (6.57 þ 045T)ln(t)

Diesel e Anchorage e long term %Ev ¼ (4.54 þ 045T)ln(t)

Diesel e Anchorage e short term %Ev ¼ (.51 þ 013T)/t

Diesel e long term %Ev ¼ (5.8 þ 045T)ln(t)

Diesel Mobile1997 %Ev ¼ (0.03 þ 013T)/t

Diesel (regular stock) %Ev ¼ (.31 þ 018T)/t

Diesel fuel e Southern e long term %Ev ¼ (2.18 þ 045T)ln(t)

Diesel fuel e Southern e short term %Ev ¼ (0.02 þ 013T)/t

Diesel Fuel 2002 %Ev ¼ (5.91 þ 045T)ln(t)

Diesel Fuel 2002 short term %Ev ¼ (0.39 þ 013T)/t

Diesel Mobile 1997 long term %Ev ¼ (0.02 þ 013T)/t

Eugene Is 224-condensate %Ev ¼ (9.53 þ 045T)ln(t)

Eugene Island Block 32 %Ev ¼ (0.77þ 045T)ln(t)

(Continued )