Bisection Method for the Heavy Fuel Oil Tank Filling Problem at a Liquefied Natural Gas Carrier

The commingling of the two types of heavy fuel oils (fuel remaining in the tanks and fuel loaded) is determined by the company's guidance and safety management system. Remained heavy fuel oil must be distributed in the heavy fuel oil tanks before bunkering efficiently, in order to obtain maximum bunker loading. This paper proposes the use of the bisection method to calculate the distribution of the remaining fuel in heavy fuel oil tanks on the liquefied natural gas carrier. The use of this method is illustrated by three examples. The first and second examples show that the iterations converge quickly to the solution. It is found that maximum tank filling with fuel commingling is achievable if the bunker intervals satisfy the company policy of 10% as a lower limit of tank filling, and 90% to 100% as an upper limit. The third example illustrates a situation when the proposed mathematical model does not allow maximization of the total tank capacity without risk assessment. The mathematical spectrum of the possible tank filling solution is presented. Despite its limitations, the bisection method is suitable for onboard applications because it is simple and fast, and can be easily programmed.