Transactions on Ecology and the Environment vol 20, 1998 WIT Press, ISSN

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1 Assessment of the risk of shore contamination by offshore oil spills: model formulation A.N Findikakis*, A.W.K. Lav/ & Y. Papadimitrakis^ ^Bechtel National Inc., San Francisco com ^Nanyang Technological University, Singapore sg ^National Technical University ofathens, Greece ntua.gr Abstract A stochastic simulation model has been developed to support the assessment of the risk of shore contamination by offshore oil spills. The model simulates the trajectory and evolution of offshore oil spills, accounting for advection by surface currents, spreading, hydrodynamic dispersion, and evaporation. The model uses wind transition matrices to account for the uncertainty in the wind direction and speed that may affect the movement of an oil slick and its point of contact with the shoreline. After the first contact with the shoreline, the model simulates the deformation of the oil slick as it approaches the shore, estimates the mass of oil that comes within the wave breaking zone, and, based on the characteristics of the shore, the oil deposited on it, and accounts for oil transport along the coast due to longshore currents. The latter may result in a much larger portion of the shore impacted than that affected by the initial contact of the oil spill with the shoreline. Risk estimates are made by performing Monte Carlo simulations.

2 210 Oil & Hydrocarbon Spills, Modelling, Analysis & Control 1 Introduction Computer simulation models have long been used to estimate the probability of shoreline contact by accidental oil spills from offshore platforms, pipelines, or tankers along frequently traveled routes. The simplest oil slick models simulate the trajectory of the centroid of the slick, ignoring size changes due to spreading, and losses due to evaporation, sinking, etc. In these models, the velocity of the centroid is estimated by adding geostrophic, tidal and wind driven currents. The emphasis in many of these models is on the estimation of the wind driven currents, which in most cases are the dominant factor that determines the oil slick trajectory. An example of such a model is the model developed by the United States Geological Survey [1, 2]. Oil spill trajectory models have been used for both deterministic and probabilistic predictions. The latter are made by treating the wind vector as a stochastic variable and performing a series of Monte Carlo simulations. A typical application of such simulations is in the prediction of the risk of shore pollution associated with offshore oil production. An example is the work of [3], who estimated the probability that different parts of the California coastline may be affected by potential accidental oil spills associated with a proposed offshore oil development program. In that work, an oil spill was represented by a single point whose movement was simulated until it reached the shoreline. Another type of models are those that estimate the spreading and weathering of an oil slick. These models are based on solutions of the continuity and momentum equations for the oil slick. The simplest of these models are in the form of algebraic expressions representing solutions of simplified versions of the complete flow equations. One of the common simplifying assumptions, in these models, is that the shape of the oil slick is circular. Stolzenbach et al. [4] presented a review of several models in this category. Models that describe the growth of an oil slick accounting for the combined effect of inertial, gravitational, viscous and surface tension forces are usually referred to as spreading models. These models are based on the assumption that some of the forces acting on an oil slick are dominant, during some time period, and that all other forces can be neglected. The forces that dominate the spreading of an oil slick differ during different stages of its development. Another type of models are those that calculate the spreading of oil slicks in the sea due to hydrodynamic dispersion, and the dispersion of surface oil due to the breakup of the initially coherent oil slick into small droplets and the spread and diffusion of the droplets in the water column. A summary of the dispersion models can be found in [4, 5]. An example of a model combining simple relationships for spreading and hydrodynamic dispersion with expressions for evaporation losses, and

3 Oil & Hydrocarbon Spills, Modelling, Analysis & Control 211 emulsification is the model presented by [6]. This model accounts for different oil components, and includes a heat budget calculation for estimating the temperature of the oil which is used in turn to estimate the density, viscosity and surface tension of the oil slick, taking into account the oil composition. Spreading and weathering models, which are based on the assumption of a circular oil slick, can be combined with trajectory models. An example of such a model is the MIT model which accounts for drift, hydrodynamic dispersion, evaporation, biodegradation, photo-oxidation and sedimentation [7]. Accounting for the spreading of an oil slick without making the assumption that the slick is circular, requires the solution of the mass balance and momentum equations for the oil. This was performed by Hess and Kerr who formulated the equations for two-dimensional spreading of oil on a calm water surface, and solved them with an Eulerian finite difference scheme [8]. A different approach was followed by some investigators who described the growth and motion of an oil slick by solving the two-dimensional advection-diffusion equation for oil concentration, neglecting mechanical spreading [e.g. 9]. Another approach to oil slick transport simulation is the use of particle tracking methods. Gait et al. used 10,000 particles to represent the Exxon Valdez spill in Alaska [10]. In this type of model each individual particle is described in terms of several attributes, including its location, time since release, and status flags indicating if it has reached the coastline or if it has evaporated, etc. Yapa et al. presented a model based on the advection-diffusion equations for a two-layer system to describe the fate of oil spills in rivers [11]. The model equations are solved with a Lagrangian discrete-parcel algorithm, using a random walk method to represent diffusion. The model presented in this paper uses a stochastic approach to simulate the trajectory and evolution of an offshore oil spill, accounting for the effects of advection by surface currents, spreading, hydrodynamic dispersion, and evaporation of individual oil components. The present model is referred to by the acronym OSM-A (Oil Spill Model - Assessment). It estimates the changes in size an thickness of an oil slick during its offshore movement, and determines at every time step of the simulation whether the oil slick has contacted the shoreline. For this purpose OSM-A considers both the shape, size and thickness of the slick and the geometry of the coastline, and accounts for longshore transport of the slick within the wave breaking zone, which may result in a larger portion of the shore(line) impacted than that affected by the initial shoreline contact of the oil slick. The treatment of the interaction of the oil slick with the shore(line) is discussed in detail in the second part of

4 212 Oil & Hydrocarbon Spills, Modelling, Analysis & Control this paper [12]. 2 The Oil Spill Simulation Model Physical processes affecting the fate of oil spills include hydrodynamic transport (advection, spreading, dispersion), evaporation, dissolution, emulsification, auto- and photo-oxidation, biodegradation, sinking, uptake by sediments and aquatic plants, and ingestion by aquatic life. The model accounts for the first four processes, which are treated independently of each other. At each simulation step the model first computes the change in the size of the oil slick, assumed to be circular, due to spreading and dispersion. Then it computes the evaporation losses and adjusts the thickness to account for the evaporated mass. 2.1 Advection Advection is accounted for by simulating the movement of the centroid of the circular oil slick due to the hydrodynamic circulation, and tidal and wind-induced currents. Advection due to the combined effect of wind drift, hydrodynamic circulation and tidal currents is described by their vector sum. The wind velocity is represented as a first-order Markov process, simulated using three-hour probability transition matrices. The structure of the probability transition matrices is similar to those used in the USGS oil spill model [1]. Each matrix contains 41 states, five wind speeds for each of eight different wind directions and a calm state. Each element of the transition matrix gives the probability that a wind of given speed and direction, three hours later may be succeeded by a wind of a different speed and direction. The wind-induced surface current velocity, Us, is estimated in terms of the wind speed [/ at 10 m above the water surface as: U,=C.U. (1) where the empirical constant C,< is estimated from data developed analyzed by [13, 14] as: and C,, =0.01exp( UJ (2) The wind drift vector is rotated by an angle 9 to account for the Coriolis effect. The deflection angle 9 can be estimated as a function of the wind speed using the empirical expression proposed by [2]:

5 Oil & Hydrocarbon Spills, Modelling, Analysis & Control 213 (3) where g is the acceleration of gravity and v is the kinematic viscosity of the water. The deflection angle decreases rapidly for wind speeds between 5 to 10 m/s. Wind induced currents become practically parallel to the wind vector for winds greater than 1 5 m/s. The general circulation and tidal currents contributing to the advective transport of an oil slick may be estimated either from data or from a hydrodynamic model. They are treated as input to the oil spill model. 2.2 Spreading An oil slick tends to spread first due to gravity forces and later due to surface tension forces at the oil-air and oil-water interface. Immediately after the occurrence of an oil spill the edge of the slick is accelerated under the influence of gravity. The accelerating phase is followed by a phase during which the gravity force is balanced by the dynamic pressure at the edge of the slick due to the motion of the slick relative to the water. The principal force balancing the gravity force during the next phase of spreading is the viscous shear at the bottom of the slick. Finally, when the slick has become very thin, the spreading is primarily due to surface tension forces balanced by the viscous shear at the bottom of the slick. The rate of spreading is estimated using the following assumptions: a. the oil slick is circular b. the oil is a homogenous mixture c. only motions relative to the centroid of the oil slick are considered. Based on these assumptions the balance of gravity, surface tension, viscous and inertial forces for a circular oil slick leads to the equation: where R is the radius and h the thickness of the oil slick, / is the time from the start of oil release, p is the density of the mixture, p^ and v^ are the density and kinematic viscosity of water, / is the net surface tension, per unit length, of the slick boundary computed as the difference between the surface tension at the air-oil and water-oil interfaces. Based on the mean values of the constants proposed by several investigators,

6 214 Oil & Hydrocarbon Spills, Modelling, Analysis & Control Stolzenbach et al. suggested that the constants /?? fa, fa can be taken equal to: 0.42, 1.64 and 0.86, respectively [4]. 2.3 Dispersion The rate of growth due solely to hydrodynamic dispersion is estimated based on the assumption that the second moment of mass concentration, a; is proportional to a given power of time, /, i.e. cr = af" (5) where a and n are constants. Data from dye studies off the California Coast suggest that n = 2.3 [15]. For a circular oil slick, the rate of growth due to hydrodynamic dispersion can then be expressed as: f) - ^ where k is a dimensional constant.. In the OSM-A model Eq. (6) is approximated by: = 6'Z" (7) where in the open sea the length scale L may be taken equal to the radius R, k' is a dimensional constant taken equal to 0.01, and n' is another constant equal to After contact with the shoreline the scale L is assumed to be proportional to the height of the breaking waves. 2.4 Evaporation Evaporation losses affect primarily the lighter oil components. The evaporation of each component is estimated as: 6 =*,(/>/- A- K (8) where $ is the rate of mass loss due to the evaporation of component /, A/ is a constant, p\,pai are the effective vapor pressure of the oil component / in a mixture of several components and the vapor pressure of the same component in the air above the slick, and [/ is the wind speed at 10 m above the water surface. The constant A, is of the order of 10"^ (for $ in gm/cm^-s, Ua in cm/s, and p\ and Pa\ in dyne/cm^). The effective vapor pressure, p\, of the oil component / is estimated by:

7 Oil & Hydrocarbon Spills, Modelling, Analysis & Control p',=x,p, and Xt=->- (9) i wm, where X^ C, _ M and /?, are the mole fraction, concentration, molecular weight and vapor pressure respectively of component /, and m is the total number of components in the oil mixture. The model keeps track of the mass of individual oil components and estimates their concentration by dividing their mass by the volume of the oil slick. The concentrations of the individual oil components are also used to estimate the density of the oil mixture, as follows: 00) 3 Probability of Shoreline Contact As the model simulates the movement of the oil slick and its change in size and thickness, it also determines at every time step whether the periphery of the oil slick has contacted the shoreline. The length of the shoreline affected by an oil spill depends on the size of the oil slick, on the wind direction after the initial shore contact, as well as on longhshore currents that may cause further migration of the oil slick along the shoreline. For example, if the wind continues in a direction normal to the shoreline, then the affected length of the shoreline will be at least equal to the diameter of the oil slick at the time of initial contact. If, however, after the initial contact the wind reverses direction and blows offshore, then the affected length of the shoreline may be less than the diameter of the oil slick. Also, an oil slick that contacts the shoreline, and then moves away towards the deeper waters due to the reversal of wind direction, may drift in these waters for a while and later contact the shoreline at another location. To account for these effects the simulation of the oil slick movement and spreading continues beyond the time of the initial contact with the shoreline. After contact with the shoreline, the model changes progressively the shape of the oil slick from a circle to an ellipse, which becomes more and more elongated as the oil slick is pushed against the shore. It also estimates the mass of oil that comes within the wave breaking (surf) zone, and accounts for its eventual potential longshore transport. This subject is discussed in more detail in the second part of this work [12].

8 216 Oil & Hydrocarbon Spills, Modelling, Analysis & Control The probability of shoreline contact of an oil spill caused by a specific type of event can be predicted by performing Monte Carlo simulations of the oil slick trajectories originating from the point of the event. The primary stochastic variables in these simulations are the wind speed and direction. Each simulation is based on a synthetic wind speed record generated using a wind transition matrix, developed from actual wind velocity data. Besides the wind, other parameters of the simulation can also be treated as stochastic variables. For example, in assessing the probability of shore contamination by accidental oil releases from tankers on frequently traveled routes, the location of the accidental oil release can be selected randomly along the route under consideration. The size and rate of release can also be treated as stochastic variables. 4 Illustrative Simulation Example To illustrate the use of the OSM-A model for the assessment of the risk of shore contamination by offshore oil spills, we present estimates of the probability of shoreline contact from a hypothetical oil spill originated approximately 12 km offshore. The simulations were made for a spill of 320 m^ of crude oil consisting of four components ranging in molecular weight from 140 to 1200, and in density from 780 to 1070 kg/nf. These estimates of the probability of shoreline contact were produced by dividing the coastline into 8-km segments, and performing a series of Monte Carlo simulations. The results of these simulations were then analyzed to estimate the frequency of each shoreline segment being impacted by the oil slick. Figure 1 shows the simulated trajectories for two different realizations of the wind field. Figure 2 shows the spatial distribution of the probability of shoreline contact within 3 days, after a hypothetical accidental oil spill at the given location. It is noted that Figure 2 gives the nominal probability of shoreline contact after an oil spill has occurred. To find the actual probability of this event, the nominal values given in this figure must be multiplied by the probability of an oil spill occurring at the particular location. 5 Continuing Work The development of OSM-A continues in order to incorporate the description of emulsification, auto- and photo-oxidation, biodegradation, the spreading and deformation of general shape oil slicks, the effect of waves on transport and spreading (including non-hydrodynamic dispersion), and further development of the description of oil deposition on the shore. The present model is being used to assess the probability of

9 Oil & Hydrocarbon Spills, Modelling, Analysis & Control 217 shoreline contamination by potential accidental oil releases by tankers and other ships in Greek seas, and more specifically in the Gulf of Saronikos and in the Gulf of Kavala, where an oil production platform exist. In this application OSM-A is used in conjunction with the Princeton Ocean Model [16] which is used to simulate surface currents and undercurrents associated with the general circulation in Saronikos and in the Gulf of Kavala, under a variety of external forcing conditions. Shoreline contact after 67 hours JV t Oil Spill Location Shoreline contact after 46 hours m lies l.4_l-.j_]_j~j km shoreline Note: A - assumed accidental oil release on March 16, 1982 B - assumed accidental oil release on April 10, 1982 Figure 1. Simulated trajectories of an oil slick originating at an offshore location using wind data from two actual historic storms.

10 218 Oil & Hydrocarbon Spills, Modelling, Analysis & Control t I I..I!._... I m iles L._l.._l... L L_J_J km Notes: 1. The number on each circle represents the probability that a spill, 72 hours after its release, will be offshore within the corresponding circle. 2. The first number at the top of each bar represents the probability (%) that an oil spill may contact the corresponding 8-km shoreline segment. 3. The number in parenthesis represents the minimum contact Figure 2. Probability map of oil slick location, and distribution of probability of shoreline contact (based on 200 simulated trajectories). Acknowledgments The authors would like to acknowledge the contributions of Mr. Chee Siang Toh at Nanyang Technical University in Singapore, and Miss E. Kehagia, Dr. G. Kantzios and Mr. A. Papadopolis-Detzorgis at the National Technical University of Athens, Greece, who work on different aspects of this program. Also, the first and the last author would like to acknowledge the Secretariat of Research and Technology of Greece for its support. The funding support to the second author through the Academic Research Fund from the Nanyang Technological University is also appreciated. References [1] Smith, R.A., Slack, J.R., Wyant, T. and Lanfear, K.J., The Oil Spill Risk Analysis Model of the U.S. Geological Survey, U.S. ^ 107, 1982.

11 Oil & Hydrocarbon Spills, Modelling, Analysis & Control 219 [2] Samuels, W.B., Huang N.E. and Amstutz, D.E., An Oil Spill Trajectory Analysis Model with Variable Wind Deflection Angle, Ocean Engineering, Vol. 9, No. 4, pp , [3] LaBelle, R.P., Lanfear, K.J., Banks A.D. and Karpas, R.M., An Oil Spill Risk Analysis for the Southern California Lease Offering, Minerals Management Service, Environmental Modeling Group, U.S. Geological Survey, Open File Report # , [4] Stolzenbach, K.D., Madsen, O.S, Adams, E.E., Pollack, A.M. and Cooper, C.K., A Review and Evaluation of Basic Techniques for Predicting the Behavior of Surface Oil Slicks, MIT Sea Grant Program, Report No. MITSG 77-8, Massachusetts Institute of Technology, Cambridge, Massachusetts, [5] ASCE Task Committee on Modeling of Oil Spills of the Water Resources Engineering Division, State-of-the-Art Review of Modeling Transport and Fate of Oil Spills, Journal of Hydraulic Engineering, Vol. 122, No. 11, pp , November [6] Rasmussen, D., Oil Spill Modeling-A tool for Cleanup Operations, Proceedings of the 1985 Oil Spill Conference, American Petroleum Institute, Washington, D.C., pp , [7] Psaraftis, H.N., Nyhart, J.D. and Betts, D.A., First Experiences with Massachusetts Institute of Technology Oil Spill Model, Proceedings of the 1983 Oil Spill Conference, American Petroleum Institute, pp , [8] Hess, K.W. and Kerr, C.L., A Model to Forecast the Motion of Oil in the Sea, Proceedings of the 1979 Oil Spill Conference, American Petroleum Institute, Washington, D.C., pp , [9] Kollmeyer, R.C. and Thompson, M.E., New York Harbor Oil Drift Prediction Model, Proceedings of the 1977 Oil Spill Conference, American Petroleum Institute, Washington, D.C., pp , [10] Gait, J.A., Watabayashi, G.Y., Payton D.L. and Peterson, J.C., Trajectory Analysis for the Exxon Valdez: Hindcast Study, Proceedings of the 1991 Oil Spill Conference, American Petroleum Institute, Washington, D.C., pp , [ll]yapa, P.D., Shen, H.T., Daly, S.F. and Hung, S.C., Oil Spill Simulation in Rivers, Proceedings of the 1991 Oil Spill Conference, American Petroleum Institute, pp , 1991.

12 220 Oil & Hydrocarbon Spills, Modelling, Analysis & Control [12] Law, A.W.K, A. N. Findikakis and Papadimitrakis, Y., Assessment of the Risk of Shore Contamination by Offshore Oil Spills. Simulation of Nearshore Transport. To be presented. [13] Wu, J., Wind Induced Drift Currents, J. Fluid Mechanics, 68, pp , [14] Wu, J., Wind-Stress Coefficients over Sea-Surface near Neutral Conditions - A Revisit, J. Phys. Oceanography, 10, pp , [15] Okubo, A., A Review of Theoretical Models of Turbulent Diffusion in the Sea, Chesapeake Bay Institute, John Hopkins University, Technical Report No. 30, [16] Blumberg, A.F. and Mellor, G.L., A Description of a Three- Dimensional Coastal Ocean Circulation Model, Three-Dimensional MxM?, ed. N. Heaps, AGU, pp. 208, 1987.