VOCSim

Volatile Organic Compounds Simulation

The main purpose of VOCSim is to simulate the emission of gas from the cargo tanks of crude oil carriers. VOCSim takes into consideration all the main components of the gas mixture that is emitted. There is three main simulation parts in VOCSim:

• the transportation inside the liquid and the gas phases
• the equilibrium at the free surface
• the gas flow out of or into the tanks

 
Sketch of tank with liquid and gas.

Transportation within one phase

The figure above shows a sketch of a cargo tank with some liquid inside it. VOCSim computes the transportation in the vertical direction of individual fluid components both in the liquid and the gas phase within a cargo tank by solving the following one dimensional diffusion/ convection equation for each fluid component i

where C_i is the unknown molar concentration ( kmol/m³) of species i in the mixture, t is time (s), W is vertical velocity (m/s) and z is vertical directions (m).  D_im is the (effective) diffusion coefficient (m²/s) for species i in the mixture, and D_{Unr_Vel} may be looked upon as a diffusion coefficient due to all Unresolved Velocities.  These are velocities typically created by liquid waves inside the tank when the vessel is rolling and pitching, thermal driven circulation in gas and liquid due to temperature differences and impulse from fluid flowing into the tank.

Equation 1 is solved for each of the species of interest by approximating the partial derivatives with finite differences.  100 computational points typically cover the height of the tank. The finite differences grid is adaptive such that there is always one computational point at the free surface in the liquid phase, and likewise one at the free surface in the gas phase.

The species of interest may typically be the following: C1, C2, C3, i-C4, n-C4, i-C5, n-C5, C6, C7, C8, C9, C10+, N₂, CO₂ and O_2. But because most of the emitted VOC gas consists of C1 to C5, the species: C1, C2, C3, i-C4, n-C4, i-C5, n-C5, C6+, N₂, CO₂ and O₂ may also be used.

Equilibrium

At the free surface between the liquid and the gas phases, a local equilibrium is said to exist. VOCSim uses Wilson's modified equation to compute equilibrium factors for each component. In addition the mass transfer of each component is continues across the free surface. 

Flows and temperatures

Loading and discharging rates are usually specified as functions of time through input data to the program. VOCSim computes the gas flow between a tank and the environment and also a neighbouring tank in case of sequential transfer of tank atmospheres, by solving the mass continuity equation in each tank together with an equation of flow for each pipe. Temperature of each phase may be specified as function of time and vertical dimension, or it can be computed in the gas phase.

Input data to VOCSim

Typical input data are as follows:

• geometry of tanks and pipes

• initial composition at each computational points within a tank and initial liquid level

• rate, cargo composition and cargo temperature during loading, and rate during discharging

• data for specification and/or computation of fluid temperature

• values of D_{Unr_Vel} as function of time

Concerning the input data, there are two main challenges for the user of VOCSim. The first one is to find the composition of the crude being representative for the cargo loaded, and to perform any necessary tuning of the equilibrium model.  The other challenge is to find which values to use for D_{Unr_Vel} , because D_{Unr_Vel} is typically a function of ship movement, ship geometry and operational procedures. For the gas phase it will also be a function of the density of gas released from the cargo. But it is not believed to be a function of the cargo for the liquid phase, unless the viscosity of the cargo changes very much.

During several loadings of shuttle tankers offshore, flow rate, composition and temperature of the gas emitted to the atmosphere have been measured. Some of these loadings have also been simulated with VOCSim, and by trial and error, values of D_{Unr_Vel} have been found that produce simulation results in good agreement with the measured ones. As more data from measurements are received, it is possible to find D_{Unr_Vel} values for more typical situations and different types of ships. It is of course very important that as correct characterisation of the cargo as possible is being used during the trial and error procedure to determine D_{Unr_Vel} .

Both the question of oil composition and values of D_{Unr_Vel} are covered in some more details later. 

Results from VOCSim

Simulated results are written on files and can be plotted as function of time by use of commercial graphical programs, e.g. EXCEL, Grapher and SigmaPlot. For emitted gas this data includes flow rate, composition, temperature, molecular weight and accumulated values of VOC, methane and inert gas. For each tank simulated, the composition of the fluid can be shown at 5 chosen levels inside the tank.

Loading of one tank on a shuttle tanker with crude oil type B. Good weather.
A comparison between measured and computed volume fraction VOC in the emitted gas. The agreement is rather good.

Loading of one tank on a shuttle tanker with crude oil type B. Good weather.
The figure compares the measured and simulated molecular weight of the HC gas. The simulated value is a little bit higher than the measured one, but the agreement is regarded to be satisfactory.

Loading of one tank on a shuttle tanker with crude oil type B. Good weather.
Simulated emissions of VOC (including methane), inert gas and methane are compared to measured values. Again the agreement is satisfactory.

This PDF-file gives you a more complementary information about VOCSim.

Contact person at MARINTEK: Ole Oldervik