A Model to Predict Rate of Dissolution of Toxic Compounds into Seawater from an Oil Spill

Abstract

In this paper a semianalytical model has been proposed to predict the rate at which oil components dissolve in water when an oil spill occurs in a marine environment. The model breaks the oil into a number of pseudocomponents proportional to the number of compounds originally present in the oil and calculates the rate of dissolution for each component. In addition, the components are divided into paraffinic, naphthenic, and aromatic hydrocarbon types and the amount of dissolution of each pseudocomponent is calculated versus time. In this method the concentration of most toxic components of oil (mainly monoaromatics) is determined. The model considers variable surface area and slick thickness and requires oil specifications (i.e., American Petroleum Institute [API] gravity and boiling point) in addition to air and water temperatures and speeds. The model has been applied to a Kuwaiti crude oil and its products naphtha and kerosene samples at 20°C and 40°C. The results could be useful in selection of an appropriate method for oil spill clean up as well as simulation of environmental impact of oil spill from toxicity points of view.

The fate and behavior of spilled oil depend on the type and the amount of oil as well as environmental conditions such as temperature and wind and water speeds. In general, light petroleum products such as gasoline are more soluble and toxic to marine life. But these products vaporize quickly and do not stay long on the water surface. Heavier oils are less toxic but stay longer in the environment. For example, oil spills after the Persian Gulf war stayed on the coastline years after they occurred. Oil spills have significant environmental impacts on living animals. Killer whales can be poisoned if eat oil or a fish dead by the oil (EPA 1998).

Oil spills can be monitored by geographic information system (GIS), which is a computer system capable of integrating, storing, editing, analyzing, sharing, and displaying geographically referenced information. Oil-spill detection by synthetic aperture radar (SAR) is based on the dampening effect oil has on capillary and short ocean surface waves. The use of SAR permits detection of oil pollution on the sea surface day and night and in most weather conditions (Automatic Oil Spill Detection 1999). SAR image classification can show three different classes for oil spill: spill area in the center surrounded by high pollution area and the outer layers of low pollution area (Mansor, Assilzadeh, and Ibrahim 2006).

Hundreds of oil spills occur every year in Mediterranean Sea, which can be monitored by SAR satellite system as shown by Vogt and Tarchi (2004). The U.S. Environmental Protection Agency (EPA) gives the list of the biggest oil spills occurred so far (EPA 1999). The Gulf War oil spill was one of the worst oil spills in history, resulting from actions taken during the Gulf War in January 23, 1991, and it did considerable damage to wildlife in the Persian Gulf. The exact size of the spill remains unknown; however, the estimate of 6 to 8 millions barrels (about 1 million m³) is most referenced.

On March 24, 1989, some 200,000,000 L (1,250,000 barrels) of crude oil was poured off the coast of Alaska, which covered an area of 1100 miles and is the worst oil spill in U.S. history (EPA 1999). This number was later revised and the latest data indicate that the amount was about 11 million gallons (261,000 barrels), which polluted about 2000 km of coastline (Petroleum Association of Japan 2005). The disaster is estimated to have killed 250,000 seabirds, 2800 sea otters, 300 harbor seals, 250 bald eagles, up to 22 killer whales, and an unknown number of salmon and herring . A court case started in 1994 in San Francisco by more than 32,000 fishermen, native Alaskans, and property owners is one of the longest noncriminal ones in U.S. history, and which has not yet been settled 18 years after the accident occurred (BBC News 2006). In 1978, off the coast of Brittany, France, some 260,000,000 L (1,625,000 barrels) of oil spilled on the sea that covered an area of 400 km and the clean up operations took 8 months. In 1997, an accident near Sharjah in United Arab Emirates split some 40,000 barrels of diesel oil, causing the shutdown of a 20 million gallons–a-day desalination plant in Sharjah that supplies drinking water to some 500,000 people in the region ( Arab Times 1998). Further list of disasters due to oil spills is given in reference (Infoplease Web site 2005).

Fate of a spill is determined by the following physicochemical dynamic processes: spreading, evaporation, dissolution, dispersion, emulsification, and sedimentation degradation processes (Kupier and Van den Brink 1987). Oil rapidly spreads over a large area and breaks up in long narrow slicks with the same direction as the wind. The spreading causes increase in evaporation of the light fractions of the oil, leaving heavier part of oil on water. Emulsification is a process that wave actions mix water into the oil, forming water-in-oil emulsion that may contain up to 80% water and stay up to 100 days. Dissolution is another physical process that water-soluble oil components, especially low-molecular-weight aliphatic and aromatic hydrocarbons, dissolve in water. Dissolution is slower process than evaporation and hydrodynamic and physicochemical conditions in the surface waters strongly affect the rate of the process.

Degradation is decomposition of oil through oxidation and often involve photochemical reactions under the influence of ultraviolet waves of sun. Elements such as vanadium enhance degradation whereas sulfur compounds slow the rate of degradation. The products of oxidation (i.e., phenols, ketones, etc.) usually have higher solubility in water, with higher degree of toxicity than the original components.

Some 10% to 30% of oil may be adsorbed on the suspended material and deposited to the bottom of sea. This mainly happens near the coastal area where particulates may be found. However, in areas that no particulate exists, only oil components heavier than water (specific gravity greater than unity) may deposit. Sedimentation is a very slow process except for very heavy components.

All the above processes can be affected by spreading. Movement of oil on the sea surface occurs under the influence of gravitation forces and it is controlled by oil viscosity and the surface tension of water. Only 10 min after a spill of 1 ton of oil, the oil can disperse over a radius of 50 m, forming a slick 10-mm thick. The slick gets thinner (less than 1 mm) as oil continues to spread, covering an area of up to 12 km² (Patin 1999).

There are a number of different methods that might apparently be used to deal with oil floating on the sea. Some of these methods are burning, to skim it off the surface, to absorb it with something and then remove the absorbent together with the oil, to make it into a gel and then skim it from the surface, to sink it to the bottom, and to emulsify or disperse it (Breuel 1981a, 1981b; Zoebell 1969). In selecting an appropriate clean-up method, prediction of the fate of the oil spill is important. The fate of a spill of crude oil in the marine environment is determined by spreading, evaporation, dissolution, dispersion of oil droplets in water, emulsification, sedimentation, oxidation of oil components (particularly photo-oxidation), advection of slick and water masses, and various degradation processes as discussed by Kuiper and Van den Brink (1987). An ideal model for the oil fate simulates all of the above processes mathematically. All of these processes are time dependent and must be described by dynamic models. State-of-the-art models include some, but not all, of these processes at varying degrees of sophistications. Field or laboratory experiments designed to calibrate or test models usually focus on only one process. For example, Spaulding (1988), Psaltaki and Markatos (2005), Villoria et al. (1991), Nasr and Smith (2006), and Riazi and Alenzi (1999) review and propose some of these models.

Perhaps the cheapest and easiest way to remove an oil spill from seawater is to vaporize and disperse it. Light petroleum fractions such as gasoline or kerosene can be completely vaporized with time. Crude oils, which consist some heavy compounds, may not be completely vaporized. Heavy compounds and residues tend to disperse into water or to sink into the bottom of sea. The rate at which a hydrocarbon dissolves in water is generally lower than the rate of evaporation under the same conditions (Wheeler 1987; Green and Trett 1989; ASCE 1996). It is widely considered that, after volatility, the most significant property of oil components, from the point of view of their behavior in aquatic environments, is their solubility in water (Green and Trett 1989). Riazi et al. (Riazi and Alenzi 1999, 2002, 2005; Riazi and Roomi 2005) showed that the rate of oil dissolution in water is small in comparison with rate of oil evaporation and usually the amount of oil dissolved is less than 1% of original mass of the spill. So the rate of oil dissolution in calculation of the overall rate of oil disappearance may be insignificant and many numerical models developed for oil spill trajectory do not consider this process. But the dissolved concentrations of hydrocarbons in water involve a toxicological viewpoint and it is important to know the exact amount of oil dissolved in water as a result of an oil spill. Aromatic hydrocarbons, especially mono-aromatics such as benzenes, are the most toxic compounds and their amount in water determines the degree of toxicity in water. The physical process of dissolution is well understood, but the description in the case of oil spills is complicated, due to the complex oil composition with hundreds of components and the necessity of describing the dissolution of a single component with component-specific parameters. The component-specific description may be necessary because toxicity is component specific as well. The most soluble oil components are usually the most toxic. Even low concentrations of these toxic compounds could lead to serious effects on biological systems. New studies by the National Marine Fisheries Service show that even very low levels of weathered oil spill are toxic to fish and wildlife (Wxxon Valdez 1999). A comprehensive list of references related to oil spills and clean up methods is provided by Victoria Broje (2005).

Riazi and Alenzi (1999) proposed mathematical relations for rates of oil evaporation and dissolution by introducing two temperature-dependent mass transfer coefficients, one for evaporation and one for the dissolution process with variable slick thickness. They also measured some experimental data on the rate of disappearance of some petroleum products and a crude oil floating on water at different conditions. They also developed a more complete model to consider the rate of sedimentation as well as the multicomponent nature of crude oils, but they did not consider dissolution of various hydrocarbon compounds.

The main objective of this work was to develop a more general and more complete model for the fate of a crude oil spill that includes rate of dissolution of various components, including the most toxic compounds. The model presented here is a completion of the model that has been under development in the past few years as presented in several conferences (Riazi and Alenzi 2002; Riazi and Roomi 2005, 2006). Results presented in this work can be used for better prediction of the fate of crude oil spills on the surface of seawater, especially concentration development of toxic compounds in water versus time. Such information may be used in better selection of an appropriate method for the clean-up of a crude oil spill.

PROPOSED MODEL

The major dynamic processes that an oil spill undergoes once it occurs on the seawater surface are shown in Figure 1. These processes determine the fate of the oil spill. For the Alaska oil spill, the rate of spreading based on published data (Galt, Lehr, and Payton 1991; Leber 1989) is shown in Figure 2. The length of spill was increased from 50 to 500 miles after 2 months. Spreading is an important process that affects rates of evaporation, dissolution, and degradation.

Upon spreading, evaporation, and other dynamic processes shown in Figure 1, the thickness of spill decreases with time. In our proposed model, we consider slick thickness as a time-variable parameter. Consider an oil spill floating on seawater surface and has initial volume of V _o and initial surface area of A _o in which the subscript “_o” indicates an initial value at time zero. We assume the oil is a mixture of Ncomponent/pseudocomponents, each specified by “i.” Then at any time t after the occurrence of spill, the volume (V ), area (A), and the thickness (y) of the pill are given as follows:

$$\text{V}=\sum _{i=1}^N{V}_i,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{A}=\sum _{i=1}^N{A}_i,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{y}=\frac{V}{A}$$[1]

For each component, the volume fraction disappeared after time t is defined as F_Vi = (V _oi − V _i)/V _oi. In the mathematical model, we choose a time step of Δt and a semianalytical approach is used to formulate the model. During each time step, it is assumed that slick thickness is constant. The volume fraction of each component x _vi is calculated from V _i and V as x _vi = V _i /V . Volume of each component V _i can be converted to mass (m _i) through its density ρ _i (m _i = V _i ×ρ _i). The total mass of oil at any time is calculated from mass of individual components: m = ∑m _i. Schematic of the model is shown in Figure 3 where the oil is assumed as a mixture of N components. Component 1 is the lightest whereas N is the heaviest component in the oil. Components with specific gravity SG_i (=ρ _i/ρ _water) greater than unity sink to the bottom of the sea immediately. It is assumed that all components heavier than water sink in the first time step. Based on the remaining components, new slick thickness can be determined.

The total volume fraction of oil disappeared at time t is calculated from

$${\text{F}}_{\text{V}}=\sum _{i=1}^N{x}_{vi}{F}_{Vi}$$[2]

The volume fraction disappeared due to dissolution of oil (F _Vi ^dis ) during each time step Δt is calculated from the following relation:

$$F_{Vi}^{dis}=1-\text{exp}(-Q_i^{dis}\mathrm{\Delta }t)\text{where\hspace{0.17em}}{\text{Q}}_i^{dis}=\frac{K_i^{dis}{C}_{si}}{y_i{\rho }_{mi}}$$[3]

In the above equation, ρ _mi is liquid molar density and C _si is the molar solubility of component “i” in water at water temperature and K _i ^dis is the mass transfer coefficient due to dissolution given by the following relation derived specifically for Kuwait oils:

$${\text{K}}_i^{dis}=\frac{4.18\times {10}^{-9}{T}^{0.67}}{V_{Ai}^{0.4}{A}_i^{0.1}}$$[4]

in which K _i ^dis is in m/s, T is in K, V _Ai is the molar volume of component “i ” at its normal boiling point in m³/gmol. A _i is the surface area of component “i” in m².

M _i is the molecular weight of component “i” and U is the wind speed in m/s. Solubility of component “i ” in water (C _si ) is calculated from the following relation in terms of molecular weight, temperature, and salt concentration in water:

$$C_{si}=\text{exp}[(4.6-0.0036M_i)+(0.1-0.0018M_i)S_w-4250/T]$$[5]

in which C _si is in mol/L, T is the absolute temperature of water in K, and S _w is the salt concentration in water in weight%. The above relations were derived from data on solubility of various oils in water at different salt concentrations and temperature (Riazi and Alenzi 1999). Once volume fraction of each component dissolved is calculated from Equation 3, mass of each component dissolved (m _i ^dis ) may be calculated through the following relation:

$$m_i{}^{dis}={\rho }_i{F}_{Vi}{}^{dis}{V}_{oi}$$[6]

Total mass of spill disappeared after time t is then calculated through sum of masses disappeared due to evaporation, dissolution, and sedimentation for all components. Total amount dissolved can be calculated as m ^dis = ∑ _{i =1} ^N m _i ^dis . Calculation of basic parameters are discussed in the next section. After each time step, similar calculations are repeated, beginning with a new value of slick thickness calculated from previous calculations.

In our model, we consider an oil spill as a mixture of different real and pseudocomponents. These pseudocomponents are treated separately and those components that are heavier than water, with specific gravities greater than 1, would immediately sink into water. Although sedimentation of oil into water is a time-dependent process, in the proposed model we consider it as an instant process for the sake of mathematical simplicity. So at the beginning of the calculations, if density of component “i ” is greater than water density at the same temperature, then the component sinks into the water and it does not enter into the subsequent calculations for the rates of evaporation and dissolution.

Calculation of Basic Parameters

Composition of a crude oil is normally represented through mole fraction of pure light components such as ethane (C₂), propane (C₃), isobutane (iC₄), n-butane (nC₄), isopentane (iC₅), n-pentane (nC₅), and lumped heavier compounds such as hexanes (C₆) and heptane-plus fraction (C₇₊ ). Wheras C₆ is a narrow-cut hydrocarbon mixture, C₇₊ is a wide hydrocarbon mixture containing hydrocarbons from heptane and heavier. In addition to mole fraction of these compounds, usually molecular weight and specific gravity of heptane-plus fraction (M₇₊, SG₇₊) are also known from laboratory data. Because treatment of the whole crude oil as a single component leads to significant errors in estimation of its properties, a probability density function (PDF) can be used to generate a certain number of pseudocomponents for the C₇₊ fraction. A C₇₊ characterization scheme based on the following probability density function is used in this work (Riazi 2005):

$$F(P^{*})=\frac{B^2}{A}{P}^{{*}^{B-1}}\text{exp}\left(-\frac{B}{A}{P}^{{*}^B}\right)$$[7]

where P is a property such as absolute boiling point (T _b ), molecular weight (M), or specific gravity (SG). In this equation, P ^* is a dimensionless form of parameter P (P ^* = (P −P _o )/P _o , in which P _o is a parameter specific for each property [T _o , M _o , SG _o ] and each mixture). P _o is in fact value of P for the lightest component in the C₇₊ fraction. A and B in Equation 7 are two parameters specific for each property and each mixture.

Boiling point of each pseudocomponent can be estimated from molecular weight and specific gravity through the American Petroleum Institute (API) methods as given in ASTM Manual 50 (Riazi 2005). Therefore, a crude oil can be represented by a mixture of known composition with a set of pure compounds and pseudocomponents with known boiling point (T _b ) and specific gravity (SG). These two parameters are sufficient to estimate all necessary physical properties needed for the proposed model.

For the C₆ and the C₇₊ pseudocomponents (C_{7+ (1)}, C₇₊₍₂₎, C₇₊₍₃₎,. . . .), the PNA (paraffins, naphthenes, and various families of aromatics) composition can be estimated from the API methods proposed by Riazi and Daubert as given in ASTM Manual (Riazi 2005). According to these methods, fraction of paraffins, naphthenes, monoaromatics, and polyaromatics are determined from specific gravity, molecular weight, and refractive index of each pseudocomponent. The relation for estimation of monoaromatics is

$$X_{MA}=-62.8245+59.9081R_i-0.0248335m$$[8]

where X _MA is the fraction of monoaromatics, R _i = n − d/2 and m = M(n− 1.475) in which n and d are refractive index and density, respectively, both at 20°C. Once each C₇₊ fraction group is divided into three subgroups (P, N, and A), required physical properties of these pseudocomponents can be estimated from the methods in reference (Riazi 2005). A summary of calculation scheme is shown in Figure 4.

RESULTS AND DISCUSSION

To show application of the proposed model, a set of data on the rate of disappearance of a Kuwaiti crude oil for export and its products measured and reported by Riazi and Alenzi (1999) are used in this work. The crude composition in terms of mole% is as follows: 0.2 (C₂), 2 (C₃), 2.4 (iC₄), 4.2 (nC₄), 2.4 (iC₅), 4.1 (nC₅), 5.3 (C₆), and 79.4 mol% (C₇₊), with M ₇₊ = 266.6 and SG₇₊ = 0.891.

The experiment was conducted at 40°C, where average wind speed was 5 m/s. Initial volume of the oil spill was 500 ml (cm³) and the initial area was 3116 cm². Total volume of oil dissolved in water after 174 h was 0.76 cm³. Salt concentration of water was 3% by weight, which was taken from Maseela Beach off the coast of Kuwait. Model prediction and experimental data for the mass of the crude oil spill remaining on water surface versus time at temperature of 40°C is shown in Figure 5. Predicted amount of dissolved hydrocarbons in water is shown in Figure 6. Amount of aromatics and monoaromatics dissolved in water versus time are shown in Figures 7 and 8 for temperatures 20°C and 40°C, respectively. As seen in these figures, the amount of dissolved hydrocarbons increases with increase in temperature. Calculated dissolved oil at 40°C after 174 h is 0.8 g versus measured value of 0.72 g. For the slick thickness, calculated value was reduced from 1.6 to 0.75 mm whereas measure values showed reduction from 1.6 to 0.78 mm, confirming validity of calculations for crude oil sample.

In addition to crude oil, for two derived products, naphtha and kerosene, the rate of dissolved aromatics and monoaromatics have been determined at 20°C for two different salt concentrations and are presented in Figures 9 and 10. As shown in these figures, the presence of salt causes a decrease in the amount of hydrocarbon dissolution. For light crude oil products such as naphtha, the oil spill can be completely vaporized within a few hours and the amount of dissolved compounds remain constant after complete disappearance of oil spill due to rapid vaporization process.

In summary, in this paper a model is proposed to calculate the rate at which toxic components (such as monoaromatics) dissolve in seawater from an oil spill floated on the water surface. The result could be helpful in the selection of an appropriate method for clean-up operations. The oil considered could be a crude oil (with wide boiling range of more than 500°C) or products derived from a crude oil such as gasoline, naphtha, kerosene, diesel fuel, gas oil, etc., with boiling range of less than 100°C. The oil is considered as a mixtures of several components from different hydrocarbon families, including mono- and polyaromatics. As it is seen from the results shown in Figures 5 to 10, the amount of dissolved hydrocarbons is small because of low solubility of hydrocarbons in water, but knowledge of this concentration is important from an environmental point of view, especially the amount of aromatics in water because of the toxic nature of these compounds. The proposed model predicts the rate of oil disappearance and concentration of different hydrocarbons as well as monoaromatics in water versus time. The amount of dissolved compounds from heavier oils is greater than the amount dissolved from light petroleum products. Heavier products also have less tendency to vaporize and stay on the water surface longer. Furthermore, salt concentration in water also has impact on the rate of dissolution of hydrocarbon compounds into sweater. With higher salt concentration, the amount of hydrocarbon dissolution decreases. The effect of temperature was also considered in the model as temperature increases the amount of dissolution also increases.

In the proposed model, the change of thickness of oil spill and its surface area due to spreading, evaporation, or sedimentation are considered. However the model has its limitations, most importantly it does not consider dynamic processes such as emulsification and biodegradation. Such processes, if occur, may influence the outcome of the model, especially in later times. Although evaporation, dissolution, and sedimentation processes are mainly important at early stages after an oil spill occurs, other processes may become important at later stages. The model presented in this paper has been evaluated with experimental data obtained in a laboratory scale where temperature variation was from 20°C to 40°C and on a stagnant water surface without waves. In actual cases, such conditions may vary and appropriate modifications should be investigated when these conditions prevail.