SIMULATION OF THE OIL SLICK MOVEMENT IN TIDAL WATERWAYS*

WU Zhao-chun

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

School of Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai 200235, China, E-mail: sh_wzc@126.com

WANG Dao-zeng

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

(Received November 8, 2009, Revised December 21, 2009)

SIMULATION OF THE OIL SLICK MOVEMENT IN TIDAL WATERWAYS*

WU Zhao-chun

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

School of Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai 200235, China, E-mail: sh_wzc@126.com

WANG Dao-zeng

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

(Received November 8, 2009, Revised December 21, 2009)

Based on particle approach and tidal flow model this article studies the behavior of the oil slick on the water surface in the Huangpu River, a tidal waterway in Shanghai. In order to track the oil slick motion, a two-dimensional oil trajectory model is used. The dynamical properties of spilled oil characterized by advection, oil spreading and turbulent diffusion are considered in the model. The simulation results consistent with the flume experimental data show that the model is applicable. Both simulation and experiment illustrate that the tidal flow has a great influence on the oil slick motion. The calculated results can be used as a reference for the response to oil spill accidents in rivers.

particle approach, track of oil slick, numerical simulation

1. Introduction

The growing demand for crude oils and the shipping boom have led to a significant increase in oil spill accidents caused by operational discharges of ship and tanker collisions. The oil spill accident is very harmful to the aquatic environment and the health of mankind. Therefore, in recent years there has been an increasing concern over the research on the transport and fate of spilled oil.

Oil pollution at sea has been receiving particular attention over the past years from scientists and governments as the consequence of a number of serious accidents involving the release of large amounts of oil at sea. However, the study of the behavior of the spilled oil in rivers, especially in tidal waterways is relatively limited.

In China there are a lot of inland waterways. Many of them are tidal waterways, such as the Yangtze River, Pearl River and the Huangpu River. As heavy traffic waterways, the oil spill accident happening in these rivers is increasing rapidly and has caused great impact on the environment and industry activities. Two examples can be mentioned: the oil spill accisent of the tanker “DaQing 243” in 1997 in the Yangtze River, releasing thousands of tons of crude oil, and more recent accident of the vesse“ChangYang” in 2003, which spilled 85 t of fuel in the Huangpu River.

Generally, the transport and fate of spilled oil can be affected by the physical, chemical and biological processes. In this study, as a short-term forecasting, we concentrate mainly on the oil slick movement on the water surface, therefore, only the dynamical features of the oil slick are considered.

2. Mathematic models and computing methods

2.1 Tidal flow models

The fluid flow pattern on the water surface is important in the oil slick movement. In most cases, the flow in natural tidal waterways may be described as the shallow water flow for the water depth is much less than the other two dimensions of the flow domain. With the shallow water assumption the depthaveraged 2-D shallow water equations[1-3]in Cartesian coordinates are

where h is the water depth,zb=f( x, y) is river bed elevation, ζ=h+zb,ζ is the water lever, εtis the viscosity coefficient, g is the acceleration due to gravity, t is the time, n is the roughness factor, uand v are the depth averaged velocity components of the water current along the x and y directions, respectively.

The initial and boundary conditions are given as follows:

(1) The initial velocity V0and the water depth h0are given.

(2) On the channel wall, V=0 and ?h/?n =0, where n denotes the normal direction of wall.

(4) On the upstream open boundary:u=uinlet(t) and?h/?n=0.

The viscosity coefficienttε in Eqs.(2)-(3) is approximated by the following expression which is widely used in engineering[4]

Many algorithms[5-14]have been developed to solve Eqs.(1)-(3). Among them, the ADI-QUICK method, water level correction algorithm, FEM and FAM are the main schemes used to solve the above equations. The authors presented a new combined scheme in Ref.[15], i.e., the combined MacCormack-finite analysis scheme. In this scheme, a single mesh FAM was used to solve momentum equations, while the MacCormack technique was used to treat the continuity equation. The numerical examples showed its good convergence. The hydraulic simulation for a section of the Huangpu River estuary was carried out to show its efficiency and applicability. The more details can be found in Ref.[15] and the numerical results of the flow field in the Huangpu River will be quoted from it directly and will be applied to the simulation of the oil slick motion.

2.2 Track of oil slick movement on water surface

According to the particle approach[16,17], the oil slick is divided into a number of small grids based on the quantity and initial area, and a set of plane coordinates are assigned to each grid. It is assumed that these grids spread following Fay’s model[18], advect with the surrounding water column and diffuse as a result of turbulence. By the above assumptions, the grid coordinates can be calculated at every time step, and then the shape and track of the oil slick can be determined.

(1) Advection

The advection velocity of each grid UPcan be calculated by the following express:

where Utis the surface flow velocity, Uwis wind velocity at 10 m above the water surface,Ktis the current factor, taken as 1.0, Kwis the wind drift factor, usually adopted as 0.03.

(2) Horizontal turbulent diffusion

Table 1 Fay’s empirical formulas for instant and continuous oil spill

is the turbulent diffusivity, h is water depth, V is the volume of oil spill,δt is the time step, Rnis the random number in the interval 0-1. The directional angle θ′ is assumed to be a uniformly distributed random angle in the interval 0π-2π:

(3) Surface spreading

According to Fay’s spread model, the second stage, known as the gravity-viscous spreading, is primary. Therefore, Fay’s spread model in the second stage is used. Uniform spreading velocity is assumed and is denoted as Uk. The initial shape of the oil slick is assumed to be circular and the final diameter in the first stage is taken as the initial diameter for the numerical process. Some empirical formulas[20]for instant and continuous oil spill in calm water are listed in Table 1.

(4) Displacement of every grid point

The displacement of each grid point at every time step can be expressed as

where r0is initial location vector of each grid point. In the present article, the tracking grid number is 1000.

3. The simulation for instant oil spill process

Instant oil spill caused by vessels accident happens often by faulty operation or illegal emissions, so the leakage quantity in such an accident is relatively small. We take the Ekofisk crude oil[21]as an sample, and 500 Kg, 1000 Kg and 1500 Kg oil are respectively spilled to simulate the oil slick motion. As a short-term forecasting, the behavior of the spilled oil within initial hours is mainly considered, thus the computing time is 2 h.

The numerical results for different tidal processes in the case of 500 Kg of spilled oil are demonstrated as follow.

(1) The track of the oil slick motion during ebb tide

The origin of the coordinate system and oil spill spot are chosen to be located in the middle of the upstream waterway. The time step is Δt =60s. The numerical results are demonstrated in Figs.1-5.

Fig.1 Upstream velocity hydrograph

Fig.2 Shape of oil slick after 1.5 h

Fig.3 Shape of oil slick after 2 h

Fig.4 Variation of.long axis of oil slick versus time

Fig.5 The trajectory of oil slick during ebb tide

From Figs.2-3 we can see that the oil slick is elongated into an oval shape under the action of water current. The oil slick drifts a distance of 3860 m during the ebb tide. A narrow-band elliptic shape is finally formed. Figure 5 shows the trajectory of the oil slick at different instants

(2) The track of the oil slick motion during slack tide and rising tide

Besides different tidal processes, other conditions are the same as above. The numerical results are demonstrated in Fig.6-10.

Fig.6 Upstream velocity hydrograph

Fig.7 Shape of oil slick after 1.5 h

Fig.8 Shape of oil slick after 2 h

Fig.9 Variation of. long axis of oil slick versus time

Fig.10 Trajectory of oil slick during slack tide and rising tide

The flow characteristic during the tidal process is the change of the velocity direction of the water current. In this case, the long axis of the oil slick experiences the elongation-compression-elongation process (see Fig.9). Oil spill drifts totally a distance of 2050 m. Because the oil slick goes back to upstream when the velocity of water current changes into negative one (see Figs.6 and10), the drafting distance of the oil spill between the beginning and the end is only 440 m.

(3) The comparison of different leakage quantities

For different amounts of spilled oil, due to similar hydrodynamics condition and the spreading model used in simulation, it is only just different inthe size of the oil slick (Figs.11-12). The calculation results show that the drifting distance is roughly the same.

Fig.11 Variation of long axis with different leakage quantities during ebb tide

Fig.12 Variation of long axis with different leakage quantities during slack tide and rising tide

4. Simulation for continuous oil spill

The leakage quantity of continuous oil spill depends on the damage in vessel accident. The maximum amount of oil released in the Huangpu River was about 200 t, but no accurate time period of spill accident was recorded. So an averaged leakage quantity is adopted in this study. 100 t/h, 50 t/h and 25 t/h of spilled oil are taken in the simulation examples respectively.

According to the experimental research[16,20], there exist also three spreading stages during continuous oil spill. The oil spreading is quickly marched from the first stage into the second stage that lasts for a relatively long time. Therefore, Fay’s spread model in the second stage can also be used.

Some numerical results for different combination of leakage quantity and tides are shown as follow:

(1) Leakage quantity Q=100t/h during ebb tide.

The calculation results show that (Fig.13), a narrow oil slick with 3900 m in length and 20 m-25 m in width is formed. The original diameter is 43 m for this example.

Fig.13 Trajectory of the oil slick in 2 h during ebb tide

(2) Leakage quantity Q=50t/h during slack tide and rising tide.

A narrow oil band with a total 2060 m in length (including retraced segment) and 25 m in width is formed. Retracing process of the oil slick is demonstrated in Fig.14.

Fig.14 Trajectory of oil slick in 2 h during slack tide and rising tide

(3) Leakage quantity Q=25t/h during maximum ebb.

The total length of the oil slick is about 6600 m long. Because of the existence of centrifugal force induced by the curvature of the waterway the process that oil slick moves to the shoreline is showed in Fig.15.

Fig.15 Trajectory of oil slick in 2 h during maximum ebb

5. The comparison of simulation with the flume experiment

To study the behavior of the oil spill influenced by the tides in the Huangpu River, the flume experimental research[22,23]has been carried out in the Experomental Center of Fluis Mechanics at Shanghai University. The experimental leakage quantities for instant and continuous oil spill are respectively taken as 1 ml and 0.01 ml/s, corresponding real amount of spilled oil 100 m3and 0.01 m3/s.

(1) The comparison during instant oil spill process

The comparison of numerical results and experimental data are shown in Fig.16, in which T isthe tidal period, indicating that both the maximum scale of the oil slick and the pattern of the oil spreading are in good agreement. There exists only certain time deviation in corresponding moment when the largest size of the oil slick turns up. The cause of the error is that certain phase error for upstream velocity hydrograph between experiment and simulation exists.

Fig.16 Comparison of numerical results with experimental data

Different from the oil spreading in calm water, tidal processes have a great influence on the variation in the shape and size of the oil slick. In the initial time when the spilled oil enters into the water, the oil slick spreads rapidly under the action of gravity. As the film thickness decreases, the spreading under the action of gravity is abated and then gravity extension turns into shearing one. In this stage, the viscous force between water surface and the bottom of the oil slick becomes gradually the main driving force for the oil spreading. The oil slick experiences stretching and contracting periods during ebb slack and flood slack processes. Thus an oscillation phenomenon of the film size happens.

(2) The comparison analysis during Continuous oil spill process

Fig.17 Comparison of numerical results with experimental data

The comparison made is shown in Fig.17. The similar reason mentioned above leads to a time deviation. Figure 17 shows that the film size is much larger than that in the case of instant oil spill. The main reason is that the oil spill which enters into the water column later will fill in water surface vacancy left by the oil slick drifted away early. At the same time, the surface spreading will be interacted between preceding and later spilled oil.

6. Conclusion

Based on the oil particles approach and tidal flow model, the oil slick movement on the water surface in the Huangpu River has been simulated. The good consistency between numerical results and the experimental data indicates that the presented hydrodynamic and spill model can replicate the behavior of the spilled oil motion on the water surface. Both the numerical results and the experimental data show that the tidal process has a great influence on the oil slick motion, e.g., the oil slick will contract during flood tide, and retracing process of the water current will lead to diminish pollution zone. Conversely, the oil slick will stretch during ebb tide to expand the scope of oil pollution. Therefore, various emergent responses to the oil spill accidents should be taken in regard to different tides. The numerical model combined with corresponding algorithms can effectively predict the track of the oil slick and its variation in the shape and size, and therefore the numerical results can be used as a reference for planning suitable response to spill accidents.

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10.1016/S1001-6058(09)60033-0

* Project supported by the National Natural Science Foundation of China (Grant No. 10972134), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20050280008).

Biography: WU Zhao-chun (1958-), Male, Ph. D. Candidate, Professor

WANG Dao-zeng,

E-mail: dzwang@staff.shu.edu.cn