Modeling Tankers’ Optimal Speed and Emissions

Abstract

With the increased quest for greener shipping, reducing the speed of ships has obtained an important role as one of the measures to be applied toward that end. Already speed has been important for economic reasons, as it is a key determinant of fuel cost, a significant component of the operating cost of ships. However, as emissions are directly proportional to fuel consumed, speed is also very much connected with the environmental dimension of shipping. So when shipping markets are in a depressed state and “slow- steaming” is the prevalent practice for economic reasons, an important side benefit is reduced emissions. Emissions estimation models typically assume fixed ship speeds. However, ships do not trade at predetermined speeds. Those who pay for the fuel may choose an operating speed as a function of the freight rate and bunker price, among others. Assuming a fixed speed may thus seriously miscalculate emissions. This paper incorporates ship speed into the analysis, and goes one step further by investigating the impact of optimizing speed on ship emissions. The study of the paper focuses on Very Large Crude Carriers (VLCCs), but some analysis for the Suezmax, and Aframax crude tanker segments is also presented, and some results for Panamax/Product, LPG, and LNG tankers are also reported. The paper’s modeling approach has two goals: (a) the determination of the optimal operational speeds (laden and ballast) of a tanker as a function of fuel price, freight rate and other parameters, and (b) the estimation, among other outputs, of the emissions of the global fleet of a specific tanker segment. The modeling task comprises two steps. The first one optimizes the laden and ballast leg sailing speeds over reference trade routes for a specific (single) tanker. In a second step, we estimate annual emissions, and other operational attributes (e.g. fuel consumption) for the tanker fleet segment, based on the output of the previous optimization. Other outputs such as CO2 , SO2, NOx and PM emissions are also produced. The policy implications of our work are finally discussed.

Speed Optimization for Container Ship Fleet Deployment Considering Fuel Consumption

“…Ignoring the payload may lead to significant fuel consumption estimation errors. Research by Gkonis and Psaraftis [23] showed that at the same speed, ship fuel consumption was different between laden and ballast. The difference is approximately 25-30%.…”

“…Constraint (9) ensures that each route deployed only one type of ship; Constraints (10) and (11) indicate that the number of ships configured for each route can meet the service demand in the weekly plan, 168 represents the number of hours in a week, set M 1 and M 2 to 9999; Constraints (12) and ( 13) define the relationship between variables, M 3 and M 4 set to 9999; in Constraint (14) the container transportation volume of each leg cannot exceed the ship's carrying capacity; and Constraint (15) represents the flow of conservation. The carrying capacity before berthing at port i, plus the amount of containers loading and subtract the amount of unloading, is equal to the shipping capacity leaving the port; Constraint (16) ensures that all container transportation needs between ports are served; Constraint (17) indicates containers from the port o will not be shipped back to the port o; Constraint (18) indicates containers from the port o will not be unloaded at the port o; Constraint (19) indicates conservation of the number of ships; Constraint (20) indicates that the number of chartered ships cannot exceed the upper limit; Constraint (21) indicates the weight of ballast water required to ensure the stability of the ship's navigation; Constraint (22) is that for safety or other purposes, the ship's payload should be within the range; Constraint (23) the weight of ballast water needed to ensure the stability of ship navigation; and Constraint (24) is the range of ship speed.…”