Numerical simulation of oil spills and oil combating techniques

Transcription

1 Numerical simulation of oil spills and oil combating techniques P. Tkalich Tropical Marine Science Institute, The National University of Singapore, Singapore. Abstract A multiphase model of oil spill dynamics has been developed. The model simulates oil slick thickness at the water surface; dissolved, emulsified and particulate oil concentrations in the water column; and dissolved and particulate oil concentrations in the bottom sediments. The oil slick dynamics at the water surface is calculated using the layer-averaged Navier-Stokes equations. A highorder numerical scheme, within the Eulerian approach, ensures accurate transport simulation of the oil phases in the marine environment. Model parameters of oil kinetics are tuned using various empirical data. The model is applicable to a comparable simulation of oil spill combating techniques, such as floating booms and chemical dispersants. The model is used for oil spills simulation in The Singapore Straits. 1 Introduction The rapid economic development in South East Asia has resulted in increasing oil consumption and oil traffic in the region. Oil related industries are crucial for regional economies, but they are also potential threats to the coastal marine environment. A sophisticated oil spill model is required for simulation of oil spills consequences and evaluation of effectiveness of different countermeasures. The accuracy of the model depends on adequate parameterisation of oil kinetics, and advancement of applied numerical techniques. Advantages and disadvantages of Eulerian and Lagrangian approaches for a solution of the mass transport equation have been discussed for a long time, ever since their development. The Lagrangian method is more suitable for tracking of movement of separate particles in a continuous medium; the Eulerian approach is

2 52 Oil and Hydrocarbon Spills II: Modelling, Analysis and Control better for calculation of transport of well-mixed substances. It was considered, among the advantages of the Lagrangian method, that a numerical solution using simple (say, fourth-order in time domain) Runge-Kutta method is more accurate, than conventional (first- or second- order) finite-difference methods, usually applied within the Eulerian approach. In recent years, however, with the development of efficient high-order finite-difference numerical schemes, the enormous improvement and accessibility of powerful computers, this argument is becoming less important. The final decision on what method to choose is often subject to research objectives and the researchers' personal preference. Considering that both methods complement each other, rather then compete, our preference, however, is for the Eulerian approach. Application of the Eulerian method for water quality studies appears to be used more frequently in future because of the increasing need to couple the transport and chemical kinetics equations with (Eulerian) hydrodynamic models. Use of similar solution techniques, computational grids, and even stencils for hydrodynamics and consequent water quality simulation increase accuracy of the entire environmental study. Despite the fact that most recent predictive models of contaminant movement in the marine environment are based on the Eulerian description of the flow, oil spill transport models, adopting the Lagrangian method, have been the exception to this practice (see reviews [1], [6] and [9]). Maybe due-to this long tradition, the Fay's [4], [5] empirical formulas and their later derivatives are still sometimes considered as the state-of-the-art in oil slick modelling literature. Recognizing the great contribution of the simplified formulas for rapid evaluation of the slick movement, existing oil spill models must be updated with modern computational techniques for more accurate prediction of fate of the spilled oil. In this paper a consistent Eulerian approach is applied for modelling of the main stages and phases of typical oil spills. The Multiphase Oil Spill Model (MOSM) (see also Tkalich et al. [10]) takes into account six state variables, namely: oil slick thickness at the water surface; dissolved, emulsified and particulate oil concentrations in the water column; and dissolved and particulate oil concentrations in bottom sediments. MOSM utilizes a high-order numerical scheme for solution of transport equations. The model has been used for the simulation of oil spill combating techniques, such as floating booms and chemical dispersants. Comparing the effectiveness of different techniques in different meteorological and hydrological conditions, one may elaborate better and safer tactics for oil spill combating in real-life situations. Examples of the MOSM application are presented. 2 The mathematical model MOSM simulates the transport of the oil phases in an aquatic environment using the following equations: dt

3 Oil and Hydrocarbon Spills II: Modelling, Analysis and Control 53 9?" F"-" ' (2) Here h is the oil slick thickness; ^ (x,y) = (w*, z/j) is the current velocity in the upper (surface) layer of the water column in the x, and y direction, respectively; r // = 0.03fP is the wind-driven shear stress; W = yv*,w*) is the wind velocity in x and y direction, respectively;/is the water-oilfrictioncoefficient; ES = gpozh* //is the oil slick diffusion coefficient; g is the acceleration due to gravity; s = (p- p^)lp\ p is the density of water; p» is the density of oil; e^ = W/W\ is the unit vector; E^ = E^(W) is the diffusion coefficient for the oil slick spreading due-to the wind/waves action; C = {o,, }^<, ^ is the oil concentration in emulsified, dissolved, and particulate phase, respectively; u (.x,jy,z) = (w", u^j are the horizontal components of current velocity; u*(x,y,z) is the vertical component of current velocity (along z coordinate); v = \y,,\=ed) ^ the buoyant/settling velocities of the oil phases; R^, jr = \R^ }^ ^ ^ are the physical-chemical kinetic terms; V = (d/dx, d/dy). The eqn (1) for the slick dynamics was obtained (for E^ =0,^ =0) [11] from the Navier-Stokes equations, averaged over the thickness of the oil slick. The value of the friction parameter/can be chosen by fitting the model on to the Fay's [4], [5] empirical data (see fig la). -o FAY -^ - 3-rd order M OSM -o 2-nd order -o- 1 -st order M O S M 10 * 10' 10* Time (sec) after the oil spill (a) comparison of MOSM and the Fay model (after Tkalich et al. [10]) (b) experiments of [2] Figure 1: Oil slick spreading rate.

4 54 Oil and Hydrocarbon Spills II: Modelling, Analysis and Control Numerous evidence [2], [8] shows, however, that the original Fay equations are suitable only for description of lateral (relatively to the wind direction) oil slick spreading. The rate of longitudinal spreading of the slick is much higher, and is proportional to the wind speed (see fig Ib). This anisotropy is taken into account in the MOSM by adding the wind-related diffusion terms to the eqn (1). At the interface "oil slick - upper layer of the water column" the oil mass exchange is calculated according to the following kinetics R*=- *«(P. - c,) - b* (c, - c,) - b,h, R. = be,(po-c,), Ra=b*(c.-Ct), Rp*0. (3) Here b^b^ are the stirring parameters (functions of the oil density, the wave height, and the wind speed); Az is the thickness of the upper layer of the water column; Z\ is the oil evaporation rate; C* is the saturation concentration of the oil's light fraction. The total amount of oil in the slick is divided according to properties of three fractions: a heavy fraction k^ that is able to produce an oil-inwater emulsion, a light fraction kj that is likely to evaporate and/or dissolve, and a residual fraction k,. 3 Oil spill modelling The importance of application of an accurate numerical scheme for the oil slick simulation was stated previously [11]. It was shown [10] that schemes only thirdorder accuracy in space, or higher, with the friction coefficient of the order f &Q.Qlkg/m*s, may provide accurate enough solution to mach the Fay's empirical data (see fig la). To solve the set of the eqns (l)-(3) numerically, an efficient algorithm is developed. The three-steps time-splitting method solves initially 2-D horizontal and 1-D vertical transport of the oil phases, and then the oil kinetics is considered. Space derivatives in the transport eqns (1),(2) were approximated with the third-order accuracy for convection terms, and the second-order - for diffusion terms. The method is similar to the UTOPIA algorithm [7], with the fourth-order-approximation terms omitted. 3.1 Test case 1 One of the tests, showing performance of the high-order approximation scheme with a flux limiter, is simulation of rotation of the scalar field, shaped as the rectangular parallelepiped (fig 2). For a pure convection, an ideal numerical scheme does not introduce a distortion into the initial shape, while moving it with the flow.

5 Oil and Hydrocarbon Spills II: Modelling, Analysis and Control 55 (a) initial profile (b) the profile after 5 rotations Figure 2: Simulation of convection of a rectangular column source in a 2-D rotational flow. The idealised 2-D constant-depth domain consists of 201x201 grid cells with the grid size (Ax x Ay) = (1000m x 1000m). The rectangular calculation area is described in the Cartesian coordinates by bottom-left and top-right corners (0,0) and (201 Ax, 201 Ay), respectively. Zero concentrations of the oil phases are assumed at the respective boundaries. The initial non-zero concentration distribution at time / = 0 was located within the grid-cells with bottom-left and top-right corners (44 Ax, 84 Ay) and (78Ax, Ay), respectively (fig 2a). After 5 complete rotations of the shape, the result of the simulation is shown at the (fig 2b). The comparison of the initial and the final profiles demonstrates high accuracy of the numerical algorithm. 3.2 Test case 2 The next test problem of the oil slick dynamics is specified as the following. An idealised seawater basin consists of 110x72 grid cells with the grid size AJC = Ay = 1 000m. At the initial moment t$ = 0, an oil slick having thickness /*(f0) = 0.01/H, occupies a region with bottom-left and top-right corners (loax, 14Ay) and (HAx, 15Ay), respectively (fig 3). The uniform south wind \Qm/s and the west current \rnls are assumed in the test. The chosen parameters for the simulation are: ^ = 979 kg /m\ b^ = 0.7xlO-*m/, = 0.1xlO"V,C, kg lm\ :k,) = (0.3:0.6:0.1), = 0, M* =0, / = kglnfs. s, 5, =(l,0)

6 56 Oil and Hydrocarbon Spills II: Modelling, Analysis and Control concentration of emulsified oil (g/l) Figure 3: Simulation of the oil slick thickness and concentration of the emulsified oil droplets at the upper 3 m layer of the water column after the hypothetical oil spill. The results of the simulation are shown in fig 3 as a time-series with the timestep 0.3 day. Under the combined force of the wind and current, the slick is moving in the northeast direction, while undergoing major physical-chemical reactions, according to the specified kinetics. The simulation reproduces the main features of oil slick behaviour, including rapid extension of the slick in the wind direction (for a comparison with the data [2] see fig Ib). Predicted concentration of emulsified droplets below the slick, in the upper 3m layer of the water column, is shown in fig 3. 4 Simulation of oil combating techniques An ability to evaluate and to rank available counter-measures during the spills is an important feature of an oil spill model. Comparing results of simulation for the different techniques, one may elaborate better and safer tactics for combating real-life oil spills. The MOSM is undergoing rigorous tests to include some of the basic oil combating techniques [10]. According to the tests an open sea channel 500km long, and 60m deep was assumed. The numerical grid size (Ax x Az) is (1000m x 5m). Longitudinal currents have logarithmic vertical profiles with a maximum velocity at the surface of 1 m/s, and minimum near-bottom velocity 0.2 m/s. The wind velocity at 10m above the water surface is taken as 7 m/s. A 28, OOOT of marine fuel oil (p<>=979 kg/m*) is spilled instantly on the water

7 Oil and Hydrocarbon Spills II: Modelling, Analysis and Control 57 surface. Napthalene, anthracene, biphenyl, dodecane, tridecane, pentadecane, heptadecane, octadecane and hexane have been selected as the principle components of fuel oil and weighted average rate constants have been computed. The fuel oil is assumed to consist of 27 % heavy fraction, 31 % light fraction and 42 % residual oilfraction.in the oil combating simulation, the following cleanup alternatives are evaluated (1) recovery of the oil from the sea surface with mechanical devices (boom & skimmer) and (2) dispersion of oil into the water column with chemical dispersants. Neither method is perfect: the booms are environmentally friendly, but effective only for calm seas; the dispersants are less dependent on weather conditions, but some of them may be toxic for marine life when the concentration is high. Computations show that if the countermeasures are not taken, after 1 day about 25% of the total oil is lost by evaporation, 0.5% lost due to hydrolysis, photolysis, oxidation and biodegradation, 5% enters into the water column, and 69.5% of the total oil remains on the water surface. After 2 days about 49% of the total oil remains on water surface, 41% is lost due to evaporation, and 10% remains in the water column. The modelled results are very similar to the data of Cornillon etal.[3]. 4.1 Boom & skimmer system Computations are performed for the two locations of a boom & skimmer system: 10 km and WO km downstream from the oil spill in the open sea channel specified above. The boom characteristics are considered as follows: maximum skimming rate rn/hr, maximum effectiveness - 80% at 5 m/s wind speed, and 60% at 10 m/s wind speed. According to the simulations, at the first scenario after 1 day about 3% of the spilled oil remains on the water surface, 0.5% in the water column, 18.5% lost due to evaporation, and the remaining 78% is recovered by the boom. At the second scenario after 1 day about 5% of total oil remains on the water surface, 3% in the water column, 32% lost due to 9 I c 1 ^^- W ater Surface w ater Column Atmosphere O il recovered > Atmosphere? Water Surface W ater Column Time (days) after the oil spil (a) the boom located 100 km downstream the oil spill Time (days) a ft er the oil spi (b) the dispersant used 1 day after the oil spill Figure 4: Spilled oil mass budget after the countermeasures are applied (after Tkalichetal. [10]).

8 58 Oil and Hydrocarbon Spills II: Modelling, Analysis and Control evaporation, and 60% is recovered by the boom (fig 4a). As early as possible a boom application is obviously more effective for recovery because less time is left for the spilled oil to enter into the water column. 4.2 Oil dispersant application The same open sea channel and the same amount and type of spilled oil was assumed for simulation of the chemical dispersant Finasol OSR-7 application. Two scenarios are considered: (1) the dispersant is applied to the oil slick after 1 hour and (2) after 1 day, following the spill. According to the simulation, in the first scenario, after 2 days about 3% of the spilled oil remains on the water surface, 16% is lost due to evaporation, and 81% enters the water column. In the second scenario (fig 4b), after 2 days about 9% of the spilled oil remains on the water surface, 30% is lost due to evaporation, and 61% enters the water column. It is clear from the simulations that early application of dispersants increases its effectiveness. Comparison of the two methods of oil combating seems easy using the fig 4. It is better to remove oil from the water environment entirely, as in the case of skimmer application, then to "push" it deeper in to the water column, as in the case of dispersant application. However, considering the facts that application of booms is effective only for calm waters, and that oil, stranded on a shoreline, may cause much more damage, then in the case of oil dispersed in an open sea, the final decision has to be made using full-scale cost-benefit analysis. In the analysis more factors have to be taken into account, such as biological exposure, damage of recreational zones, etc. 5 Conclusions A three-dimensional multiphase oil spill model is developed to simulate consequences of accidental oil releases in an ocean environment. The model is powered with a high-order numerical scheme for accurate simulation of the oil slick dynamics, and tested on available empirical data. The test simulations demonstrated that MOSM is able to predict the main features of oil spills, and also to evaluate the effectiveness of different oil combating techniques. 6 Acknowledgments The author would like to thank Mr. K. Huda for computations, Dr. K. Gin for fruitful discussions and modelling support, and Dr. J.K. Candlish for editorial help. The project is partially supported by research grant GR6414. References [1] 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. J.Hydraulic Engineering, 122(11), pp , 1995.

9 Oil and Hydrocarbon Spills II: Modelling, Analysis and Control 59 [2] Cormack, D., Nichols, J.A. & Lynch B. Investigation offactors affecting the fate of North Sea oils discharged at sea, Warren Spring Laboratory Publication: UK, [3] Cornillon, P.C., Spaulding, M.L. & Hansen, K. Oil spill treatment strategy modeling for Georges Bank. Proc. of the 1979 Oil Spill Conference, pp , [4] Fay, J.A. The spread of oil slick on a calm sea. Oil on the Sea, ed D.P. Hoult, Plenum Press, pp.53-63, [5] Fay, J.A. Physical processes in the spread of oil on a water surface. Proc. of the Joint Conf. On the Prevention and Control of Oil Spills, pp , [6] Huang, J.C. A review of the state-of-the-art of oil spill fate/behaviour models. Proc. of the 1983 Oil Spill Conference, American Petroleum Institute, pp , [7] Leonard, B.P., MacVean, M.K. & Lock, A.P. The flux integral method for multidimensional convection and diffusion. Appl Math. Modelling, 19, pp , [8] Reed, M., Johansen, O., Brandvik, P.J., Baling, P., Lewis, A., Fiocco, R., Mackay, D. & Prentki, R. Oil spill modelling toward the close of the 20* century: Overview of the state of the art. Spill Science and Technology Bulletin, 5(1), pp. 3-16, [9] Spaulding, M.L. A state-of-the-art review of oil spill trajectory and fate modelling. Oil and Chemical Pollution, 4, pp , [10] Tkalich, P., Gin, K., & Chan E.S. Numerical simulation of oil spill combating techniques. Proc. of the IIAPEC Workshop on Ocean Models, Beijing, pp. 6A(1-12), [11] Warluzel, A., Benque, J.P. Un modele mathematique de transport et d'etalement d'une nappe d'hydrocarbures, Proc. of Conf. Mechanics of Oil Slicks, Paris, pp , 1981.