Fig. 1 Schematic figure of the unloading system
Fig. 2 Simplified model of the system
It is difficult to treat this part as it is by the method of characteristic, because in using column separation models the cavity length should be small enough compared with the length of computational reaches. Therefore, the computation was done for a simplified model. Figure 2 shows the model. It is assumed that the undersea pipeline (I. D. = 1.2 m) continues to the coupler. The ship side is also assumed to consist of a pipe with the same diameter.
Many kinds of crude oil have been unloaded by this system. A typical vapor pressure of them is 0.025 - 0.05 MPa when the temperature is 20 - 40 ℃. In the computation the vapor pressure is assumed to be 0.03 MPa. The mass density of the oil, ρ, is 850 kg/m3, the bulk modulus of elasticity of the oil, K, is 8.67×107 kg/m2, the modulus of elasticity of the pipeline, E, is 2,1 × 1010 kg/m2, and the wave propagation speed a, is 860 m/s. The friction factor of the pipeline, f, is 0.025.
The initial steady state flow rate is 12,000 m3/hr, which corresponds to the velocity of about 3 m/s.
The method of characteristic [1] - [5] is used for the computation. The method is based on the equation of motion (convection term is omitted) and continuity equation. In order to consider the effect of the gas in the liquid. Discrete Gas Model [6] is used. In the method, the gases distributed in the liquid are assumed to be concentrated at each computational node. It is known the model has good agreement with actual transient phenomena as long as the gas volume is much less than the liquid volume.
In the case of oil, the volume ratio of dissolved air is known to be larger compared with the case of water. However, about 99 % of the pipeline is at the bottom of the sea in this system. The pressure inside the undersea pipeline doesn't go down below atmospheric pressure by more than 20 m oil head even in transient state at the valve closing. The air dissolved in the oil at atmospheric pressure would not evolve in the undersea line. Consequently, the effect of air evolution in transient state is estimated to be relatively small.
When the pressure of the oil goes down below the vapor pressure at some computational nodes, the column separation is assumed to occur.
