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

Chapter Evaporation Modeling Merv Fingas Chapter Outline 9.1 Introduction 9.2 Review of Theoretical Concepts 9.3 Development of New Diffusion-Regulated Models 9.4 Complexities to the Diffusion-Regulated Model 201 205 212 229 9.5 Use of Evaporation Equations in Spill Models 9.6 Comparison of Model Approaches 9.7 Summary 233 235 240 9.1 INTRODUCTION Evaporation is a very important process for most oil spills In a few days, typical crude oils can lose up to 40% of their volume.1 Most oil spill behavior models include evaporation as a process and in the output of the model Despite the importance of the process, relatively little work has been conducted on the basic physics and chemistry of oil spill evaporation.2 The difficulty with studying oil evaporation is that oil is a mixture of hundreds of compounds and this mixture varies from source to source and even over time Much of the work described in the literature focuses on “calibrating” equations developed for water evaporation.2 Furthermore, very little empirical data on oil evaporation was published until a decade ago An important concept in understanding evaporation is to understand the mechanisms that regulate evaporation If there were no regulation, evaporation would proceed nearly instantly Figure 9.1 shows a schematic of the airboundary-layer regulated mechanism The liquid would evaporate at a very high rate if it was not for the regulation caused by the slow transfer of vapor through the air boundary layer The most common example of this type of regulation is applicable to water, and this concept enters into most people’s common view of evaporation Evaporation of water can be increased by spreading it out or by increasing the wind speed Oil Spill Science and Technology DOI: 10.1016/B978-1-85617-943-0.10009-7 Copyright Ó 2011 Elsevier Inc All rights reserved 201 202 PART | IV Behaviour of Oil in the Environment and Spill Modeling Evaporation limited by diffusion rate into the air therefore air-boundary-layer regulated Air Air boundary layer Liquid FIGURE 9.1 Illustration of the air-boundary-layer regulation mechanism The diffusion into the air layer is the limiting factor and serves to regulate the evaporation rate This rate is affected by turbulence in the air, which will increase the transfer of the molecules across the boundary layer This regulatory mechanism is true for pure liquids that have a high evaporation rate Water is an example of such a liquid and is the most common concept held Many liquids are not air-boundary-layer regulated primarily because they evaporate too slowly to have the vapors saturate the air boundary layer above them Many mixtures are often regulated by the diffusion of molecules inside the liquid to the surface of the liquid This situation is illustrated in Figure 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 seem counterintuitive to some people in that increasing the area may not increase the evaporation rate except to a small degree if the initial pool is very thick, such as over about 10 to 20 mm Also, and perhaps more importantly, increasing wind speed does not increase evaporation Evaporation limited by diffusion rate through liquid and through surface layer-therefore diffusion regulated Air Liquid surface Liquid FIGURE 9.2 Illustration of the diffusion-controlled regulation mechanism The diffusion through the evaporating liquid is the limiting factor and thus the regulation mechanism This mechanism is generally true for oils, fuels, and many other mixtures of liquids that both evaporate more slowly than water and are mixtures Chapter | Evaporation Modeling 203 Scientific and quantitative work on water evaporation is decades old.3,4 The basis for the oil evaporation work in the literature is water evaporation There are several fundamental differences between the evaporation of a pure liquid such as water and that of a multicomponent system such as crude oil Most obviously, the evaporation rate for a single-component liquid such as water is a constant with respect to time.3,4 Evaporative loss, by total weight or volume, is not linear with time for crude oils and other multicomponent fuel mixtures.5 Evaporation of a liquid can be considered as the movement of molecules from the surface into the vapor phase above it The layer of air above the evaporation surface is known as the boundary layer.6 The characteristics of this air layer, or boundary layer, can influence evaporation In the case of water, the boundary layer regulates the evaporation rate Air can hold a variable amount of water, depending on temperature, as expressed by the relative humidity Under conditions where the boundary layer is not moving (no wind) or has low turbulence, the air immediately above the water quickly becomes saturated and evaporation slows or ceases In practice, the actual evaporation of water proceeds at a small fraction of the possible evaporation rate because of the saturation of the boundary layer The air-boundary-layer physics are then said to regulate the evaporation of water This regulation manifests itself in the sensitivity of evaporation to wind or turbulence When turbulence is weak or absent, evaporation can slow down by orders-of-magnitude The molecular diffusion of water molecules is at least 103 times slower than turbulent diffusion.6 Evaporation can be viewed as consisting of two components, fundamental evaporation and regulation mechanisms Fundamental evaporation is that process consisting of the evaporation of the liquid directly into the vapor phase without regulation other than by the thermodynamics of the liquid itself Regulation mechanisms are those processes that serve to regulate the final evaporation rate into the environment For water, the main regulation factor is the air-boundary-layer regulation discussed above Air-boundary-layer regulation is manifested by the limited rate of diffusion, both molecular and turbulent diffusion, and by saturation dynamics Molecular diffusion is based on exchange of molecules over the mean-free path in the gas The rate of molecular diffusion for water is about 105 slower than the maximum rate of evaporation possible, purely from thermodynamic considerations.6 The rate for turbulent diffusion, the combination of molecular diffusion and movement with turbulent air, is on the order of 102 slower than that for maximum evaporation In fact, in the case of water, maximum evaporation is not known and has only been estimated by experiments in artificial environments or by calculation.3 If the evaporation of oil was like that of water and was air-boundary-layer regulated, one could write the mass-transfer rate in semi-empirical form (also in generic and unitless form) as: E ! K C Tu S (1) 204 PART | IV Behaviour of Oil in the Environment and Spill Modeling where E is the evaporation rate in mass per unit area, K is the mass-transfer rate of the evaporating liquid, presumed constant for a given set of physical conditions, sometimes denoted as kg (gas phase mass-transfer coefficient, which may incorporate some of the other parameters noted here), C is the concentration (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 that relates to the saturation of the boundary layer above the evaporating liquid The saturation parameter, S, represents the effects of local advection on saturation dynamics If the air is already saturated with the compound in question, the evaporation rate approaches zero This also relates to the scale length of an evaporating 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 rate per unit area is lower than for a smaller pool It should be noted that there many equivalent ways of expressing this fundamental evaporation equation Much of the pioneering work for evaporation studies was performed by Sutton who proposed an equation based largely on empirical work:7 E ¼ K Cs U 7=9 dÀ1=9 ScÀr (2) where Cs is the concentration of the evaporating fluid (mass/volume), U is the wind speed, d is the area of the pool, Sc is the Schmidt number, and r is the empirical exponent assigned values from 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 wind speed, U, and the Schmidt number, Sc The Schmidt number is the ratio of kinematic viscosity of air (v) to the molecular diffusivity (D) of the diffusing gas in air, that is, a dimensionless expression of the molecular diffusivity of the evaporating substance in air The coefficient of the wind power typifies the turbulence 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 that was more laminar The scale length is represented by d and has been given an empirical exponent of À1/9 For water, this represents a weak dependence on size The exponent of the Schmidt number, r, represents the effect of the diffusivity of the particular chemical, and historically was assigned values between and 2/3.7 This expression for water evaporation was subsequently used by those working on oil spills to predict and describe oil and petroleum evaporation Much of the literature follows the work of Mackay.8,9 Mackay and co workers adapted the equations for hydrocarbons using the evaporation rate of cumene Data on the evaporation of water and cumene have been used to correlate the gas phase mass-transfer coefficient as a function of wind speed and pool size by the equation: Km ¼ 0:0292 U 0:78 X À0:11 ScÀ0:67 (3) Chapter | Evaporation Modeling 205 where Km is the mass-transfer coefficient in units of mass per unit time and X is the pool diameter or the scale size of evaporating area Stiver and Mackay subsequently developed this further by adding a second equation:9 N ¼ km AP=ðRTÞ (4) where N is the evaporative molar flux (mol/s), km is the mass-transfer coefficient at the prevailing wind (m/s), A is the area (m2), P is the vapor pressure of the bulk liquid (Pascals), R is the gas constant [8.314 Joules/(mol-K)], and T is the temperature (K ) Thus, boundary-layer regulation was assumed to be the primary regulation mechanism for oil and petroleum evaporation This assumption was never well tested by experimentation, as revealed by a literature search.2 The implications of these assumptions are that evaporation rate for a given oil is increased by: l l l increasing turbulence increasing wind speed increasing the surface area of a given mass of oil These factors can then be verified experimentally to test whether oil is boundary-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 onecomponent liquid The ASTM (American Society for Testing and Materials) distillation data and the average boiling points of successive fractions were used as the starting point to predict an overall vapor pressure The average vapor pressure of these fractions was then calculated from the ClausiusClapeyron equation to yield: log   ps qM 1 ¼ À p 4:57 T Ts (5) where p is the vapor pressure at the absolute temperature, T, ps is the vapor pressure at the boiling point, Ts (for ps, 760 mm Hg was used), q is the heat of evaporation in cal/g, and M is the molecular weight The term qM/(4.57 Ts) was taken to be nearly constant for hydrocarbons (ẳ5.0 ỵ/ 0.2), and thus the expression was simplified to: log ps =p ẳ 5:0ẵTs TÞ=TŠ (6) From the data obtained, the weathering curve was calculated, assuming that Raoult’s law is valid for this situation giving qM as a function of the percentage 206 PART | IV Behaviour of Oil in the Environment and Spill Modeling evaporated Pasquill’s equation10 was applied stepwise, and the total evaporation time was obtained by summation: t ¼ DhDb X Kev U a PM (7) where t is the total evaporation time in hours, Dh is the decrease in layer thickness in m, D is the diameter of the oil spill, b is a meteorological constant (assigned a value of 0.11), Kev is a constant for atmospheric stability (taken to be 1.2  10À8), a is a meteorological constant (assigned a value of 0.78), P is the vapor pressure at the absolute temperature, T, and M is the molecular weight of the component or oil mass Thus the model is partially air-boundary-layer regulated Blokker constructed a small wind tunnel and tested this equation against the evaporation of gasoline and a medium crude oil The observed gasoline evaporation rate was much higher than was predicted, and the crude oil rate was much lower than predicted The times of evaporation, however, were somewhat close, and the equation was accepted for further use The above equations were then incorporated into spreading equations to yield equations to predict the simultaneous spreading and evaporation of oil and petroleum products Mackay and Matsugu approached the problem by using the classical water evaporation and experimental work.8 The water evaporation equation was corrected to hydrocarbons using the evaporation rate of cumene It was noted that the difference in constants was related to the enthalpy differences between water and cumene Data on the evaporation of water and cumene were used to correlate the gas phase mass-transfer coefficient as a function of wind speed and pool size by the equation: Km ¼ 0:0292 U 0:78 X À0:11 ScÀ0:67 (8) where Km is 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 the exponent of the wind speed, U, is 0.78, which is equal to the classical water evaporation-derived coefficient Mackay and Matsugu noted that for hydrocarbon mixtures, the evaporation process is more complex, being dependent on the liquid diffusion resistance being present Experimental data on gasoline evaporation were compared with computed rates The computed rates showed some agreement and suggested the presence of a liquid-phase masstransfer resistance This work was subsequently extended by the same group to show that the evaporative loss of a mass of oil spilled can be estimated using a mass-transfer coefficient, as shown above.11 This approach was investigated with some laboratory data and tested against some known mass-transfer conditions on the sea The conclusion was that this mass-transfer approach could result in predictions of evaporation at sea Chapter | Evaporation Modeling 207 Butler developed a model to examine evaporation of specific hydrocarbon components.12 The weathering rate was taken as proportional to the equilibrium vapor pressure, P, of the compound and to the fraction remaining: dx=dt ¼ ÀkPðx=xo Þ (9) where x is the amount of a particular component of a crude oil at time, t, xo is the amount of that same component present at the beginning of weathering (t ¼ 0), k is an empirical rate coefficient, and P is the vapor pressure of the oil component Since petroleum is a complicated mixture of compounds, P is not equal to the vapor pressure of the pure compound, but neither would there be large variations in the activity coefficient as the weathering process occurs For this reason, 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 of oils The equation was then directly integrated to give the fraction of the original compound remaining after weathering as (similar to Henry’s law): x=xo ẳ expktP=xo ị (10) The vapor pressure of individual components was fit using a regression line to yield a predictor equation for vapor pressure: P ¼ expð10:94 À 1:06 NÞ (11) where P is the vapor pressure in Torr and N is the carbon number of the compound in question This combined with Equation (10) yielded the following expression: x=xo ẳ expẵkt=xo ịexp10:94 1:06 Nị (12) where x/xo is the fraction of the component left after weathering, k is an empirical constant, xo is the original quantity of the component, and N is the carbon number of the component in question Equation (12) predicts that the fraction weathered is a function of the carbon number and decreases at a rate that is faster than predicted from simple exponential decay If the initial distribution of compounds is essentially uniform (xo independent of N ), then the above equation predicts that the carbon number 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 ẳ 10:66 ỵ 2:17 logkt=xo ị (13) where N1/2 is 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 samples relatively well It was suggested that the equation was applicable to open water spills; however, this was never subsequently applied in models It should be noted that this approach is somewhat similar to the model that will be described 208 PART | IV Behaviour of Oil in the Environment and Spill Modeling 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 Matsugu molecular diffusion process.13 The vapor phase mass-transfer process was expressed by: Die ¼ km ð pi À piN Þ=½RTS Š (14) where Die is the vapor phase mass-transfer rate, km is a coefficient that lumps all the unknown factors that affect the value of Die, pi is the hydrocarbon vapor pressure of fraction, I, at the interface, piN is the hydrocarbon vapor pressure of fraction, I, at infinite altitude of the atmosphere, R is the universal gas constant, and Ts is the absolute temperature of the oil slick The following functional relationship was proposed: km ¼ aAg eqU (15) where A is the slick area, U is the over-water wind speed, and a, q, and g are empirical coefficients This functional relationship was based on the results of past investigations, including, for instance, those of MacKay and Matsugu who suggested the value of g to be in the range from À0.025 to À0.055.8 Further experiments were performed by Yang and Wang to determine the values of a and q.13 The results were found to be twofold Experiments showed that a film formed on evaporating oils and that this film severely retarded evaporation Before the surface film has developed (rt/ro < 1.0078): Kmb ¼ 69Ầ0:0055 e0:42U (16) where Kmb is the coefficient that groups all factors affecting evaporation before the surface film has formed and A is the area After the surface film has developed (rt/ro > 1.0078): Kma ¼ 1=5 kmb (17) where ro is initial oil density, rt is weathered oil density at time t, and Kma is the coefficient that groups all factors affecting evaporation after the surface film has formed The evaporation rate was found to be reduced fivefold after the formation of the surface film Brighton proposed that the standard formulation used by many workers required refining.14 E ¼ K Cs U 7=9 d1=9 ScÀr (18) His starting point for water evaporation was similar to that proposed by Sutton7 where E is the mean evaporation rate per unit area, K is an empirically determined constant, Cs is the concentration of the evaporation fluid (mass/volume), d is the area of the square or circular pool, and r is an empirical exponent assigned values from to 2/3 Chapter | 209 Evaporation Modeling Brighton suggested that this equation does not conform to the basic dimensionless form involving the parameters U and Zo (wind speed and roughness length, respectively), which define the boundary-layer conditions The key factor in Brighton’s analysis was to use a linear eddy-diffusivity profile This feature implied that concentration profiles become logarithmic near the surface, which is suspected to be more realistic compared to the more finite values previously used Using a power profile to provide an estimation of the turbulence, Brighton was able to substitute the following identities into the classical relationship: U ¼ uà n k (19) where u* is the friction velocity, z1 is the reference height above the surface, z0 is the roughness length, and n is the power law dimensionless term It should be noted that these are applicable to neutrally stable atmospheres   z1 (20) n ¼ In z0 The evaporation equation now becomes:     z dX d kuà zdX U ¼ z1 dx dz s dz (21) where z is the height above the surface, X is the concentration of the evaporating compounds, x is the dimension of the evaporating pool, k is given by K/u)z, and is the von Karman constant, and s is the turbulent Schmidt number (taken as 0.85) Brighton subsequently compared his model with several runs of experimental evaporation experiments in the field and in the laboratory This included laboratory oil evaporation data.15 The model only correlated well with laboratory water evaporation data, and the reason given was that other data sets were “noisy.” The most frequently used work in spill modeling is that of Stiver and Mackay.9 It is based on some of the earlier work by Mackay and Matsugu, but significant additions were made.8 Additional information is given in a thesis by Stiver.16 The formulation was initiated with assumptions about the evaporation of a liquid If a liquid is spilled, the rate of evaporation is given by: N ẳ KAP=RTị (22) where N is the evaporative molar flux (mol/s), K is the mass-transfer coefficient under the prevailing wind (msÀ1), A is the area (m2), and P is the vapor pressure of the bulk liquid This equation was arranged to give: dFv =dt ẳ KAPv=Vo RTị (23) 210 PART | IV Behaviour of Oil in the Environment and Spill Modeling where Fv is the volume fraction evaporated, v is the liquid’s molar volume (m3/mol), and Vo is the initial volume of spilled liquid (m3) By rearranging, we obtain: or: dFv ẳ ẵPv=RTịKAdt=Vo ị (24) dFv ẳ Hdq (25) 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 into two dimensionless groups The group, KAdt/Vo, represents the time rate of what has been termed the “evaporative exposure” and was denoted as dq The evaporative exposure is a function of time, the spill area and volume (or thickness), and the mass-transfer coefficient (which is dependent on the wind speed) The evaporative exposure can be viewed as the ratio of exposed vapor volume to the initial liquid volume The group Pv/(RT) or H is a dimensionless Henry’s law constant or ratio of the equilibrium concentration of the substance in the vapor phase [P/(RT)] to that in the liquid (l/v) H is a function of temperature The product qH is thus the ratio of the amount that has evaporated (oil concentration in vapor times vapor volume) to the amount originally present For a pure liquid, H is independent of Fv and Equation 2.26 was integrated directly to give: Fv ¼ Hq (26) If K, A, and temperature are constant, the evaporation rate is constant and evaporation is complete (Fv is unity) when q achieves a value of 1/H If the liquid is a mixture, H depends on Fv and 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 evaporation rate slows as evaporation proceeds in such cases Equation (26) was replaced with a new equation developed using data from evaporation experiments: Fv ẳ T=K1 ị In1 ỵ K1 q=Tị expK2 K3 =TÞ (27) where Fv is the volume fraction evaporated and K1,2,3 are empirical constants A value for K1 was obtained from the slope of the Fv versus log q curve from pan or bubble evaporation experiments For q greater than 104, K1 was found to be approximately 2.3T divided by the slope The expression exp(K2 À K3/T) was then calculated, and K2 and K3 were determined individually from evaporation curves at two different temperatures Variations of all the above equations have been used extensively by many other experimenters and for model application Brown and Nicholson studied the weathering of a heavy oil, bitumen.17 They compared experimental data using a large-scale weathering tank with two 228 PART | IV Behaviour of Oil in the Environment and Spill Modeling root curve.1 Data on a number of oil evaporation rates, gathered experimentally and basic properties of oil were collected, primarily from a previous paper, and also from literature sources.24-26 While it is known that density and viscosity are not necessarily good indicators of other oil properties, these may be the only data available at the site of a spill, at least until some time passes.21,26 The data show that the general trends of correlation of evaporation parameters with density and viscosity are shown, with significant variance that is only captured by specific oil experiments The evaporation equation parameters were measured in specific experiments and often are the result of several repeat experiments The data were correlated with the evaporation parameter in order to derive a simplified model using oil density and viscosity or Saturates, Aromatics, Resins and Asphaltenes (SARA) data.24 The curve-fitting exercise with the logarithmic evaporation data and density and viscosity data resulted in a best-fit simplest equation: Evap ¼ 15:4 À 14:5 density ỵ 2:58=viscosity (39) where Evap is the evaporation equation parameter and as in Equation (33) is Be0.675 to compensate for the temperature parameter as explained above Similarly, the data for those oils that evaporate as a square root with time were correlated with density and viscosity The equation for predicting those oils that evaporate as a square root of time is: Evap ¼ 2:3 À 1:47à density À 0:073à InðviscosityÞ (40) where Evap is the evaporation equation parameter or B in Equation (33), but for the square root equivalent Other data that may be available are SARA data Statistical analysis shows that only the saturate content correlates, and this does not so well (r2 < 0.6) The addition of the other SARA data only marginally assists in the correlation However, an equation for the prediction of the evaporation parameter using SARA data is: Evap ẳ 0:048 S ỵ 0:006 A 0:025 R 0:0003As ỵ 0:27 (41) where Evap is the evaporation equation parameter or Be0.675 as in (33) above: S is the saturate content in percent, A is the aromatic content in percent, R is the resin content in percent, and As is the asphaltene content in percent It is important to understand that such simplified predictions are much less accurate than empirical data such as those shown in Table 9.2 Chapter | 229 Evaporation Modeling 9.4 COMPLEXITIES TO THE DIFFUSION-REGULATED MODEL 9.4.1 Thickness of the Oil Studies show that under diffusion regulation very thick slicks (much more than mm) evaporate slower than other slicks due to the increased path length that volatile components must diffuse in a thicker slick This can certainly be confused with air-boundary-layer regulation Figure 9.10 shows the evaporation rate of various thicknesses of oil by the volume to thickness ratio As can be seen, there is very little difference in this standard presentation However, one can exaggerate the thickness by a volume factor and this is presented in Figure 9.11 This figure shows that there is a small difference beginning at about mm to about 10 mm The difference amounts to about 10% slower at 10 mm compared to the rate at about mm There are few data at very great thicknesses, so this phenomenon requires further investigation In any case, actual slicks at sea would never reach this thickness Figure 9.12 shows the concept of slower evaporation with increased path length, that is, increased oil thickness As noted, there are insufficient data to fully evaluate this at this time, but there is not much motivation as slicks at sea not reach this thickness 9.4.2 The Bottle Effect Another confusing phenomenon encountered in trying to understand evaporation is the bottle effect This effect is illustrated in Figure 9.13 If all the 6.0 Evaporation Rate (%) 5.5 5.0 4.5 4.0 3.5 3.0 2.5 10 15 20 Volume to Thickness Ratio FIGURE 9.10 The relationship of volume over thickness (area) to evaporation rate (given as the equation parameter) for one light crude oil This shows that there is little relationship Volume largely dictates the evaporation rate; however, for very thick slicks of thickness more than about 10 mm, the evaporation rate slows due to the increased diffusion distance through the liquid 230 (Volume/Thickness)/Evaporation Rate PART | IV Behaviour of Oil in the Environment and Spill Modeling 4.5 4.0 3.5 3.0 2.5 2.0 10 Thickness mm FIGURE 9.11 A plot of the exaggerated evaporation rate (equation factor, raised by the volume factor) versus oil thickness for one light crude oil The exaggeration is about an order of magnitude This shows that evaporation slows somewhat after mm and is slowed more at 10 mm The effect is only about 10% at 10 mm This is due to the increased diffusion length through the slick Typical oil spills are much thinner than about mm, and thus this effect would not be important evaporating oil mass is not exposed, such as in a bottle, more oil vapors than can readily diffuse through the air layer at the bottle mouth may yield a partial air-boundary-layer regulation effect This air-boundary-layer regulatory effect may end when the evaporation of the oil mass lowers past the rate at which the vapors can readily diffuse through the opening Such effects could occur in reality in situations such as oil under ice, partially exposed to air or when a thick skin forms over parts of the oil, blocking evaporation During a recent experiment in the Arctic, it was noted that the evaporation rate varied with the amount of exposure to the air.27 This phenomenon was probably caused by a combination of the bottle effect and partially as a result of the increased thickness in the more confined ice situations 9.4.3 Skinning Several workers have noted that some crude oil and petroleum products form “skins” on their surfaces.28,29 These are largely due to the accumulation of compounds such as resins on the surface, some possibly created by photo oxidation These can retard the evaporation of the compounds to a great extent Figure 9.14 shows the results of some evaporation experiments carried out on two oils, Terra Nova crude and Statfjord crude Simultaneous experiments were carried out on the oils, one of which was stirred, the other not.1 As can be seen in Figure 9.14, the stirred oils evaporated to a greater extent than the unstirred oils The relevance of this effect at sea may not be as great as wind and waves Chapter | 231 Evaporation Modeling Evaporation limited by diffusion rate through liquid and through surface layer - therefore diffusion regulated Air Liquid surface Liquid Air Liquid surface In very thick layers, evaporation limited by diffusion rate through liquid but after about 20 to 40 mm, diffusion slows significantly Liquid FIGURE 9.12 An illustration of the effect of very great thicknesses of oil The evaporation rate is slower because of the longer diffusion difference The difference becomes measurable after about to 10 mm of oil thickness This is much greater than typical slicks at sea may accomplish; the stirring and skin formation may thus be prevented or retarded It should be noted that during these experiments, one could see the skin formation on the unstirred oil, and this skin developed more toward the end of the 200-hour experiments Grose used the Mackay and Matsugu equations with some modification and also to account for the skinning factor:30 L ẳ C U 0:78 D0:11 (42) =RKị Pi Sk Mi o 232 PART | IV Behaviour of Oil in the Environment and Spill Modeling More vapor than can easily diffuse through opening - therefore partially air-boundary layer regulated Opening Air Air Liquid surface Evaporation limited by diffusion rate through liquid and through surface layer Liquid FIGURE 9.13 An illustration of the bottle effect If all the evaporating oil mass is not exposed, more oil vapors than can readily diffuse through the air layer at the bottle mouth may yield a partial air-boundary-layer regulation effect This regulatory effect may end when the evaporation of the oil mass lowers past the rate at which the vapors can readily diffuse through the opening stirred 40 Statfjord crude % Evaporated not stirred stirred 30 not stirred Terra Nova crude 20 Terra Nova Terra Nova - stirred Statfjord Statfjord - stirred 10 0 50 100 150 200 Time (Hours) FIGURE 9.14 Results of an experiment to show the effect of “skinning” on oil evaporation The upper curve in each case is the evaporation of the oil shown with stirring, thus preventing or retarding skin formation The lower curve is the evaporation without stirring The effect of skinning for these two oils amounts to several percent differential in evaporation over 200 hours At sea, wind and waves may mix the oil sufficiently to minimize the skinning effect Chapter | Evaporation Modeling 233 where L is the mass of oil evaporated with time (kg/s), C is the environmental transfer constant, U is the wind speed at the surface (m/hr), Do is the diameter of the oiled area (m), K is the oil temperature in Kelvin, Pi is the vapor pressure of the particular component, Sk is the skin factor, and Mi is the molecular-weight equivalent of the particular oil fraction The skin factor, Sk, ranges from 0.1 to and accounts for the effect of skinning (the formation of a semipermeable surface layer) Yang and Wang suggested a value of Sk ¼ 0.2 after the density of their test oils had increased by 0.78%.13 A value of 1.0 was used in testing the model In addition, the massloss rate depends on the vapor pressure, Pi, and the molecular weight, MWi, of each fraction C is a dimensionless environmental transfer constant whose magnitude depends on the units used The value used for C (0.00024) includes the constant 0.015 after Mackay and Matsugu.8 9.4.4 Rises from the 0-Wind Values Experimentation shows that studies of oil evaporation at absolutely no turbulence or air flow show a slight decrease in evaporation rate from those experiments carried out with slight air movement such as are found in an ordinary room.19 This is due to the slight stirring in the oil mass which increases the diffusion rate somewhat Tests of this phenomena show that further increases in evaporation rate not occur with increased air movement or turbulence, thus confirming that this is a phenomenon only at 0-wind or turbulence conditions These are seen only during capped vessel experiments, and the “jump” in the evaporation rate is seen when the restriction is removed 9.5 USE OF EVAPORATION EQUATIONS IN SPILL MODELS Evaporation equations are the prime physical change equations used in spill models This is because evaporation is usually the most significant change that occurs in an oil’s composition Many models after 1984 have used the Stiver and Mackay approach.9 The equations developed by Mackay and co workers can be implemented in a variety of ways Often the difference in models is the manner in which the models are applied Mackay and co workers developed an extensive oil spill model incorporating a number of process equations including evaporation.31 The earlier work of Leinonen and Mackay was used with the modification proposed by Yang and Wang.13,32 The process includes dividing the oil into a number of different fractions and analyzing each fraction for evaporation loss The mass-transfer function used is the familiar one proposed by Mackay and Matsugu.8 These equations can be solved to obtain V and ci as functions of time Solutions were developed by assuming a five-component crude oil that spreads on the water surface according to the correlations for the area 234 PART | IV Behaviour of Oil in the Environment and Spill Modeling Payne and co workers developed an oil spill model using the pseudocomponent approach.33-35 Given the boiling point (1 atm) and API gravity of each cut (or pseudocomponent), the vapor pressure of the cut as a function of temperature was calculated First, the molecular weight and critical temperature of the cut were calculated according to the following correlation: y ¼ C1 þ C2 X1 þ C3 X2 þ C4 X1 X2 þ C5 X12 þ C6 X22 (43) where y is the vapor pressure of the cut, X is the boiling point (oF) at one atmosphere, X2 is the API gravity, and C1À6 are constants empirically determined Similarly, the critical temperature was calculated from the same equation form using the calculated and empirical constant values Next, the equivalent paraffin carbon number, Nc, was calculated according to: Nc ¼ ðM À 2Þ=14 (44) where M is the molecular weight assigned to the particular cut The critical volume, Vc, was then calculated according to: Vc ẳ 1:88 ỵ 2:44Nc ị=0:044 (45) and the critical pressure, Pc, was calculated from: Pc ¼ 20:8 Tc ỵ P0c Vc 8ị (46) where Tc is the critical temperature and Pc0 correction factor for critical pressure The factor Pc0 was set to 10 to correct the critical pressure correlation from a strictly paraffinic mixture to a naphtha-aromatic-paraffin mixture Next the parameter, b, was calculated according to: where: b ¼ b0 À 0:02 (47) b0 ¼ C1 þ C2 Nc þ C3 Nc2 þ C4 Nc3 (48) and the values of the constants C to C were calculated and tables of the values are available.19 A final parameter designated as A is then calculated according to: A ẳ Trb ẵlog10 Prb ị ỵ exp20Trb bÞ2 ފ Trb À (49) where A is an intermediary parameter, Trb is the reduced temperature at the normal boiling point, Prb is the reduced pressure at the normal boiling point, and b is an intermediary parameter determined in (48) above Chapter | Evaporation Modeling 235 The vapor pressure equation that can be used down to 10 mm Hg can be expressed in terms of A and b as: log10 Pr ẳ A1 Tr ị expẵ20Tr bị2 Tr (50) where Pr is the reduced pressure and Tr is the reduced temperature A, b, Tc and Pc were determined from the normal boiling point and API gravity of the cut The temperature at which the vapor pressure is 10 mm Hg was obtained by the root-finding algorithm of Newton-Raphson.34 Below 10 mm Hg, the vapor pressure between two temperatures, Tr1 and Tr2, was calculated according to the Clausius-Clapeyron equation as follows: Z Tr 0:38 ð1 À T Þ P2 lo r dTr (51) In ¼ P1 RTc Tr1 Tr2 where P1 is the vapor pressure at temperature 1, P2 is the vapor pressure at temperature 2, l0 is the heat of vaporization at K, and Tc is the critical temperature This was based on the fact that the ratio of the heat of vaporization, l, to (1 e T )0.38 is a constant at any temperature The latent heat of vaporization was calculated from the slope of the natural log of the vapor pressure equation with respect to the temperature where the vapor pressure is 10 mm Hg Thus, in the above equation, P2 is the 10 mm Hg vapor pressure at the temperature, Tr, previously determined Variations of the Payne model were used in older oil spill models Several models had used the pseudocomponent approach but with the Mackay evaporation method.36 Currently, there are a number of oil spill models using the empirical equations of Fingas.25 9.6 COMPARISON OF MODEL APPROACHES The comparison of air-boundary-layer models with the empirical equations lead to some interesting conclusions on their applicability Figure 9.15 shows a comparison of the prediction of evaporation of diesel fuel using an air-layerboundary model and an empirical curve The 0-wind diesel evaporation calculated using an air-layer-boundary model comes closest to the empirical curve However, prediction is of the wrong curvature The prediction of diesel evaporation using the wind levels shown results in prediction errors as great as 100% over about 200 hours Figure 9.16 shows a comparison of the evaporation of Bunker C using two air-layer-boundary models and an empirical curve The 0-wind evaporation air-boundary-layer prediction comes closest to the empirical curve As most comparisons show, the evaporation rate up to about 10 hours is similar to the empirical curve The prediction of Bunker C evaporation 236 PART | IV Percent Evaporated 80 Behaviour of Oil in the Environment and Spill Modeling Traditional with varying winds 60 Traditional no wind 40 Trad no wind Trad 10 m/s Trad 20 m/s Empirical curve Trad B no wind Trad B 10 m/s Trad B 20 m/s Empirical curve 20 0 20 40 60 80 100 120 140 160 Time in Days FIGURE 9.15 A comparison of the evaporation of diesel fuel using an air-layer-boundary model and an empirical curve The 0-wind diesel evaporation calculated using an air-layer-boundary model comes closest to the empirical curve, but it is of the wrong curvature The prediction of diesel evaporation using the wind levels shows errors as great as 100% over about 200 hours using the wind levels shown results in prediction errors as great as 400% over about 200 hours These high values of Bunker C evaporation as predicted by air-boundary-layer models with wind conditions are completely impossible, as shown by extensive experimentation and field measurements.19 Figure 9.17 shows a comparison of the evaporation of Prudhoe Bay crude using two airlayer-boundary models with an empirical curve The 0-wind evaporation prediction using air-boundary-layer methods comes closest to the empirical curve The evaporation rate calculated by most means up to about 10 hours is similar to the empirical curve The prediction of Prudhoe Bay evaporation using the wind levels shown results in prediction errors as great as 100% over about 200 hours These high values of Prudhoe Bay evaporation as predicted by air-boundary-layer models with wind conditions are not realistic The importance of evaporation modeling can be shown in Figures 9.18 and 9.19 The fate of oil spills is often dictated by evaporation Accurate modeling of evaporation then becomes of key importance to the useful prediction of oil fate Thus there are three major errors resulting from the use of air-boundarylayer models First and most important is that they cannot accurately deal with long-term evaporation; second, the wind factor results in unrealistic values; and finally, they have not been adjusted for the different curvature for diesel-like evaporation Some modelers have adjusted their models using air-boundary-layer models to avoid very high values at long evaporation times Chapter | 237 Evaporation Modeling Trad m/s Trad 10 m/s Trad 20 m/s Trad 40 m/s Trad 80 m/s Empirical Trad B m/s Trad B 10 m/s Trad B 20 m/s Trad B 35 m/s Percent Evaporated 20 15 10 Empirical curve Empirical curve 0 20 40 60 80 100 120 140 Time (Hours) FIGURE 9.16 A comparison of the evaporation of Bunker C using two air-layer-boundary models and an empirical curve The 0-wind evaporation prediction comes closest to the empirical curve The prediction of Bunker C evaporation using the wind levels shown results in prediction errors as great as 400% over about 200 hours These high values of Bunker C evaporation as predicted by air-boundary-layer models with wind conditions are completely impossible As most comparisons show, the evaporation rate calculated by most means up to about 10 hours is similar to the empirical curve by setting a maximum evaporation value This does avoid very unrealistic high values after a point in time, but does so artificially Most models of any type will require that one sets a maximum rate to avoid overprediction or values over 100%, for example This can be best illustrated using a long-term example A spill in northern Alberta of Pembina oil was sampled 30 years after its spill Analysis shows that this was weathered to the extent of 58%.37,38 Figure 9.20 shows the comparison of the actual value, the empirical projection, and the air-boundary-layer predicted value This shows that the air-boundary-predicted value overshoots the estimate by over 60%, despite using only two low wind values of and m/s Use of higher wind values increases the evaporation to well over 100% 238 PART | IV Behaviour of Oil in the Environment and Spill Modeling Percent Evaporated 40 30 Empirical curve 20 Trad m/s Trad 10 m/s Trad 20 m/s Empirical Curve Trad B m/s Trad B 10 m/s Trad B 20 m/s Empirical curve 10 0 50 100 150 200 250 300 Time (Hours) FIGURE 9.17 A comparison of the evaporation of Prudhoe Bay crude using two air-layerboundary models and an empirical curve The 0-wind evaporation prediction using air-boundarylayer methods comes closest to the empirical curve The evaporation rate up to about 10 hours is similar to the empirical curve The prediction of Prudhoe Bay evaporation using the wind levels shown results in prediction errors as great as 100% over about 200 hours These high values of Prudhoe Bay evaporation as predicted by air-boundary-layer models with wind conditions are not realistic FIGURE 9.18 Highly-evaporated oils can form tar balls that typically strand on beaches This shows a typical-size tar ball stranded along with other debris Chapter | 239 Evaporation Modeling FIGURE 9.19 This shows highly evaporated Bunker C oil, which has just arrived on a beach In this case, evaporation is a very important factor dictating how an oil spill can be cleaned up 100 Air-boundary-layer model m/s wind Percent Evaporated 80 Air-boundary-layer model m/s wind 60 Empirical curve Analysis value at 30 years 40 Empircal curve Actual analytical Air-Bound., m.s wind Air-Bound m.s wind 20 year 0.0 5.0e+4 years 1.0e+5 15 years 1.5e+5 2.0e+5 30 years 2.5e+5 Time - Hours FIGURE 9.20 A comparison of the evaporation of Pembina crude using an air-layer-boundary model, an actual analysis after 30 years, and an empirical curve The evaporation rate up to about 100 hours is similar to the empirical curve The prediction of long-term evaporation using even small wind levels shown results in prediction errors as great as 60% over about 10 years These high values of evaporation as predicted by air-boundary-layer models with wind conditions are not realistic 240 PART | IV Behaviour of Oil in the Environment and Spill Modeling 9.7 SUMMARY A review of the physics of oil evaporation shows that oil evaporation is not strictly air-boundary-layer regulated The results of the following experimental series have shown the lack of boundary-layer regulation A study of the evaporation rate of several oils with increasing wind speed shows that the evaporation rate does not change past the 0-level wind Water, known to be boundary-layer regulated, does show the predicted increase with wind speed, U (Ux, where x varies from 0.5 to 0.78, depending on the turbulence level) Increasing area does not change the oil evaporation rate This is directly contrary to the prediction resulting from boundary-layer regulation The volume or mass of oil evaporating correlates with the evaporation rate This is a strong indicator of the lack of boundary-layer regulation because with water, volume (rather than area) and rate not correlate Evaporation of pure hydrocarbons with and without wind (turbulence) shows that compounds larger than nonane and decane are not boundarylayer-regulated Most oil and hydrocarbon products consist of compounds larger than these two and thus would not be expected to be boundarylayer-regulated The fact that oil evaporation is not strictly boundary-layer-regulated implies that a simplistic evaporation equation will suffice to describe the process The following factors not require consideration: wind velocity, turbulence level, area, thickness, and scale size The factors important to evaporation include time and temperature A comparison of the various models used for oil spill evaporation shows that air-boundary-layer models result in erroneous predictions There are three issues: air-boundary-layer models cannot accurately deal with long-term evaporation; second, the wind factor results in unrealistic values; and finally, they have not been adjusted for the different curvature for diesel-like evaporation Modelers have made some effort to adjust air-boundary-layer models to be more realistic for longer-term evaporation, but these may be artificial and result in other errors such as underestimation for long-term prediction A diffusion-regulated model has been presented along with many empirically developed equations for many oils The equations are found to be of the form: Percentage evaporated ẳ ẵB þ 0:045ðT À 15ފ InðtÞ (52) where B is the equation parameter at 15 C, T is temperature in degrees Celsius, and t is the time in minutes It is also noted that with diesel fuel and similar oils, the curve is different and follows a generic curve, such as: p Percentage evaporated ẳ ẵB ỵ 0:01T 15ị t (53) Chapter | 241 Evaporation Modeling The most accurate predictions are carried out using the empirical equations as noted in Table 9.2 If these are not available, the parameters can be estimated using distillation data, such as: For oils that follow a logarithmic equation: Percentage evaporated ẳ ẵ:165%Dị ỵ :045ðT À 15ފlnðtÞ (54) For oils that follow a square root equation: p Percentage evaporated ẳ ẵ:0254%Dị ỵ :01T 15ފ t (55) 180 C, T is the temperature in Celcius, where D is the percentage distilled at and t is the time in minutes Equations are also given that allow estimation of evaporation from density, viscosity, or SARA data; however, these are much less accurate than the direct empirically-derived equations REFERENCES Fingas MF The Evaporation of Oil Spills: Development and Implementation of New Prediction Methodology IOSC 1999;281 Fingas MF A Literature Review of the Physics and Predictive Modelling of Oil Spill Evaporation J Haz Mat 1995;157 Jones FE Evaporation of Water Chelsea, Michigan: Lewis Publishers; 1992 Brutsaert W Evaporation into the Atmosphere Dordrecht, Holland: Reidel Publishing Company; 1982 Fingas MF Studies on the Evaporation of Crude Oil and Petroleum Products: I The Relationship between Evaporation Rate and Time J Haz Mat 1997;227 Monteith JL, Unsworth MH Principles of Environmental Physics London: Hodder and Stoughton; 1990 Sutton OG Wind Structure and Evaporation in a Turbulent Atmosphere P Royal Society of London 1934;701 Mackay D, Matsugu RS Evaporation Rates of Liquid Hydrocarbon Spills on Land and Water Can J Chem Eng 1973;434 Stiver W, Mackay D Evaporation Rate of Spills of Hydrocarbons and Petroleum Mixtures Env Sci Tech 1984;834 10 Blokker PC Spreading and Evaporation of Petroleum Products on Water Proceedings of the Fourth International Harbour Conference, 1964;911 11 Goodwin SR, Mackay D, Shiu WY Characterization of the Evaporation Rates of Complex Hydrocarbon Mixtures under Environmental Conditions Can J Chem Eng 1976;290 12 Butler JN Transfer of Petroleum Residues from Sea to Air: Evaporative Weathering In: Windom HL, Duce RA, editors Marine Pollutant Transfer, 201 Toronto: Lexington Books; 1976 13 Yang WC, Wang H Modelling of Oil Evaporation in Aqueous Environments Water Res 1977;879 14 Brighton PWM Further Verification of a Theory for Mass and Heat Transfer from Evaporating Pools J Haz Mat 1990;215 15 Brighton PWM Evaporation from a Plane Liquid Surface into a Turbulent Boundary Layer J Fluid Mech 1995;323 16 Stiver W Weathering Properties of Crude Oils wWhen Spilled on Water, Master of Applied Science Thesis, Department of Chemical Engineering and Applied Chemistry Toronto: University of Toronto; 1984:4,110,132 242 PART | IV Behaviour of Oil in the Environment and Spill Modeling 17 Brown HM, Nicholson P The Physical-Chemical Properties of Bitumen AMOP 1991;107 18 Bobra M A Study of the Evaporation of Petroleum Oils, Manuscript Report Number EE-135 Ottawa, ON: Environment Canada, 1992 19 Fingas MF Studies on the Evaporation of Crude Oil and Petroleum Products: II Boundary Layer Regulation J Haz Mat 1998;41 20 Ullmann Encyclopedia Hamburg: Ullmann Publishing; 1989-2005 21 Jokuty PS, Whiticar S, Wang Z, Fingas MF, Fieldhouse B, et al Properties of Crude Oils and Oil Products Environment Canada Manuscript Report EE-165, Ottawa, ON 1999 22 Fingas MF The Evaporation of Oil Spills: Prediction of Equations Using Distillation Data Spill Sci Tech Bull 1996;191 23 Fingas MF The Evaporation of Oil Spills: Prediction of Equations Using Distillation Data AMOP 1997;1 24 Fingas MF Estimation of Oil Spill Behaviour Parameters from Readily-Available Oil Properties AMOP 2007;1 25 Fingas MF Modeling Evaporation Using Models That Are Not Boundary-Layer Regulated J Haz Mat 2004;27 26 Oil Catalogue, http://www.etc-cte.ec.gc.ca/databases/spills/oil_prop_e.html, accesssed April, 15 2010 27 Brandvik PJ, Faksness L-G Weathering Processes in Arctic Oil Spills: Meso-Scale Experiments with Different Ice Conditions Cold Reg Sci Technol 2009;160 28 Bobra M, Tennyson EJ Photooxidation of Petroleum AMOP 1989;129 29 Garrett RM, Pickering IJ, Haith CE, Prince RC Photooxidation of Crude Oils Environ Sci Technol 1998;3719 30 Grose PL A Preliminary Model to Predict the Thickness Distribution of Spilled Oil, Proceedings of a Workshop on The Physical Behaviour of Oil in The Marine Environment, Princeton University, 1979 31 Mackay D, Buist I, Mascarenhas R, Paterson S Oil Spill Processes and Models, EE-8 Ottawa, ON: Environment Canada, 1980 32 Leinonen PJ, Mackay D A Mathematical Model of Evaporation and Dissolution from Oil Spills on Ice, Land, Water, and Under Ice, Proceedings Tenth Canadian Symposium 1975: Water Pollution Research Canada, 1975;132 33 Payne JR, McNabb Jr GD, Hachmeister LE, Kirstein BE, Clayton Jr JR, et al Development of a Predictive Model for the Weathering of Oil in the Presence of Sea Ice, Outer Continental Shelf Environmental Assessment Program, vol 59, NOAA, 1988 34 Payne JR, Kirstein BE, McNabb Jr GD, Lambach JL, Redding R, et al Multivariate Analysis of Petroleum Weathering in the Marine EnvironmentdSubarctic, U.S Department of Commerce, NOAA, OCSEAP, vol 21, 1984 35 Payne JR, McNabb Jr GD Weathering of Petroleum in the Marine Environment, Marine Technology Society Journal, Washington, DC, 1984;24:18 36 Buist I, Belore R, Guarino A, Hackenberg D, Dickins D, Wang Z Empirical Weathering Properties of Oil in Ice and Snow AMOP 2009;56 37 Wang Z, Fingas M, Yang C, Hollebone B, Peng X Biomarker Fingerprinting: Applications and Limitations for Source Identification and Correlation of Oils and Petroleum Products AMOP 2004;103 38 McIntyre CP, Harvey PM, Ferguson S, Wressnig AM, Snape I, George SC Determining the Extent of Weathering of Spilled Fuel in Contaminated Soil Using the Diastereomers of Pristane and Phytane Org Geochem 2007;2131 ... Fuel Oil %Ev ẳ (0.12 ỵ 013T)/t Hondo %Ev ẳ (1. 49 ỵ 045T)ln(t) Hout %Ev ẳ (2. 29 ỵ 045T)ln(t) IFO-180 %Ev ẳ (0.12 ỵ 013T)/t Chapter | 223 Evaporation Modeling TABLE 9. 2 Equations for Predicting Evaporationdcont’d... empirical data such as those shown in Table 9. 2 Chapter | 2 29 Evaporation Modeling 9. 4 COMPLEXITIES TO THE DIFFUSION-REGULATED MODEL 9. 4.1 Thickness of the Oil Studies show that under diffusion regulation... compounds in oil are higher than dodecane, the bulk oil would not show air-boundary-regulated behavior Chapter | 217 Evaporation Modeling 9. 3.5 Other Factors Another evaluation of evaporation