The case study vessel was built in 1998 and typically operates between ports in the southern United States, primarily Miami, and various destinations throughout the Caribbean Sea. This operational profile is particularly relevant, as Miami lies within the North American Emission Control Area (ECA) designated by IMO. ECAs enforce stricter SOX emission limits than the global standard, reducing the permissible sulphur content in marine fuels from 0.5% to 0.1%. The data for the environmental and economic assessments were collected from the ship’s electronic logbook, during the month of April 2024. Although the vessel is aging, company officials intend to keep it in operation for an additional ten years. This projected service lifetime has therefore been adopted as the time horizon for the economic modelling.
2.1. Environmental Assessment
Currently, the assessment of pollutant emissions from marine vessels can be performed by using three different methods: bottom-up, top-down, or a combination of both [
37,
38]. These methods are outlined in the
Emission Inventory Guidebook 2023, published by the European Environment Agency (EEA), more specifically in Chapter 1.A.3.d Navigation (shipping) [
39]. The guidebook, first published in 1996, included a chapter on estimating emissions from navigation starting in 2009. Since then, it has been continuously updated and adopted by numerous scientists, also being referenced in the Fourth IMO Greenhouse Gas Study [
16,
39]. In the literature, these approaches are often referred to as Tier I, Tier II, and Tier III, differing in the emission assessment process and the geographic characterization of the ship [
40].
The complete “bottom-up” method assesses emissions from an individual ship by considering its characteristics, such as type, construction date, cargo, engine power, and fuel consumption under specific load conditions. With this method, it is possible to estimate the near-instantaneous emission production of a vessel, helping to identify the main contributors to the emissions, offering a clear understanding of their impact. Since the method is data intensive, it is also expensive and time consuming [
37,
38].
The “top-down” method takes a broader perspective based on the highly aggregated information of a given shipping activity, relying on generalized factors such as fuel use statistics and engine types across ships to estimate emissions, as there is no information regarding specific circumstance or specific shipping activities. The advantage of the top-down approach, since it requires a small quantity of data, is that it is less expensive and less time consuming than the bottom-up approach [
37,
38].
The present study uses a hybrid method, which is a combination between the bottom-up and the top-down approaches, known also as the Tier III ship movement method. This hybrid method is generally recommended when detailed data on ship operations and technical characteristics (e.g., size, engine technology, installed power, fuel consumption, and operating hours in different activities) are available, as considered in the presented case study. This enables the estimation of emissions during open-sea navigation, port approach maneuvers, and docking [
39]. Compared to Tier I or Tier II, this methodology ensures higher resolution and reliability in emission assessments and is aligned with international standards.
For commercial vessels, Tier III methodology calculates the emissions based on the engine’s installed capacity and fuel consumption. Emissions for a trip are determined by summing the emissions from each segment of the journey [
39].
Based on the data of fuel consumption in the three different navigation phases, cruise, dock, and maneuvering, the emissions can be calculated using specific fuel emission factors for each phase. In this sense, the pollutant emission calculation can be performed based on Equation (2) [
39,
40].
where
represents the emissions during a complete journey (tons);
FC is the fuel consumption (tons);
EF is the emission factor (kg/ton);
is the pollutant type (NO
x, SO
x, CO
2, PM);
is the fuel type (HFO, MDO/MGO);
is the engine type (low, medium, and high speed); and
is the different phases of the journey (cruise, dock, and maneuvering).
For each level and emission calculation algorithm, it is necessary to use specific emission factors. While Tier I and II methodologies use tabulated emission factors, the more complex methodology, Tier III, adopted in the present study, requires the calculation of specific emission factors based on the present case load-dependent emission factors. It is important to note that variations in emission factor calculations can lead to discrepancies of up to 30% in total emissions [
16].
The pollutant emissions (
) were determined using two primary methods. The energy-based approach estimates emissions based on engine power output (
), applying an energy-based emission factor (
) in grams per kilowatt-hour (g/kWh) [
16].
In the present study was obtained from the data collected on the ship.
This method is used for pollutants such as NOx, CH4, CO, N2O, PM, and Non-Methane Volatile Organic Compounds (NMVOCs).
The fuel-based approach calculates emissions by multiplying hourly fuel consumption (
) by a fuel-based emission factor (
), expressed in grams of air pollutant per gram of fuel (g/g); it is used for CO
2 and SO
x emissions.
where
The baseline specific fuel consumption for main engines, auxiliary engines, and boilers represents the minimum specific fuel consumption along the load curve, indicating the point of maximum fuel efficiency for the engine [
41]. In
Table 2, the baseline SFC values used in this study are depicted.
The methodologies and formulas used in this study were initially introduced in the IMO Third Greenhouse Gas Study [
42] and later refined in the Fourth IMO Greenhouse Gas Study [
16]. This revision integrated findings from literature reviews, engine manufacturers, research institutions, academic studies, and classification societies, providing a more accurate and up-to-date framework for emission calculations.
2.1.1. Carbon Dioxide
Based on the IMO proposals in document MEPC.1/Circ.684,
Table 3 represents CO
2 emission factors for HFO and MDO.
The carbon dioxide emissions from the case study cruise vessel were calculated using Equations (4) and (5), which determine the vessel’s total fuel consumption and the corresponding CO2 emissions.
2.1.2. Nitrogen Oxides
Nitrogen oxide emissions result from the high combustion temperatures in the engines, which cause the oxidation of nitrogen present in the intake air as well as nitrogen particles in the fuel. The NO
x emission factor depends on the engine rate speed and the ship’s Tier (i.e., the year when the engine was manufactured). In the present study, NO
x emission factors were based on the engine rotational speed, as referred to in Annex VI of IMO MARPOL Regulation 13.
Table 4 presents the IMO regulatory limits for NO
x emissions, which vary according to the engine’s rated speed.
is the engine rate speed, which for the Wärtsilä Sulzer ZA40S diesel generators installed in the ship assessed, the alternators have a frequency of 60 Hz and 12 poles, which correspond to an engine rate speed of 514 rpm. Applying the Tier I coefficient for this engine category, the NOx emission limit for the case study vessel engines is calculated to be 12.91 gNOx/kWh.
2.1.3. Sulphur Oxides
Sulphur oxide emissions depend on the sulphur content of the fuel used. In this sense, the SO
x emission factor (g SO
x/g of fuel) is calculated as follows [
16]:
where it is considered that 97.753% of the fuel sulphur content is converted to SO
x (with the remainder converted to sulphate/sulfite aerosol and classified as part of the particulate matter). The number “2” reflects the ratio of the molecular weight of SO
2 to sulphur, since the majority of SO
x is released as SO
2. The term
represents the sulphur content of the fuel assessed. In the present study the sulphur content of HFO is considered to be 3.5% and for MDO, it is 0.1% [
45].
2.1.4. Particulate Matter
The emission factors for particulate matter are influenced by the sulphur content of the fuel.
Table 5 presents the equations used to calculate the PM for engines running on heavy fuel oil or marine diesel oil [
16].
The number 7 in the equations represents the molecular weight ratio between the sulphate of the particles and sulphur, while the value 0.02247 reflects the proportion of sulphur in the fuel that is converted to PM sulphate. Again, the term represents the sulphur content of the fuel assessed.
In this study, the Tier III methodology was applied in the following stages:
Onboard data collection: Engine particulars, power output, load profiles, NOx Tier classification, and fuel consumption for each phase (cruise, maneuvering, docking) were obtained from ship logs and manufacturer datasheets.
Determination of SFC of engines based on IMO baseline values corresponding to the engines type and rating.
Calculation of fuel and energy-based emission factors and pollutant emissions:
Fuel-based factors for CO
2 (based on IMO values;
Table 3). Emission factors for HFO and MDO [
44] (
Table 3), along with SO
x (g/gFuel), as defined by Equation (6).
Energy-based factors for NO
x and PM (g/kWh): NO
x emissions were estimated using Tier I coefficients for engines operating within the 130 <
< 1999 rpm range (see
Table 4). PM emissions were calculated based on the equations presented in
Table 5.
Total trip emissions were calculated by summing the three phase emissions: cruise, maneuvering, and docking.
2.2. Economic Assessment
While environmental considerations may justify the investment in the long term, shipowners, operating within the constraints of commercial viability, prioritize profitability and financial sustainability. Consequently, for a greener solution to be adopted within the sector, it must also demonstrate economic feasibility. In the case of scrubbers, their installation involves a substantial retrofit, which requires modifications such as cutting funnel bulkheads and integrating the scrubber units into the exhaust systems of each engine. This results in a significant initial capital investment. In addition to capital expenditure, there are also ongoing operational expenditures related to system operation and maintenance.
Table 6 summarizes the estimated CAPEX and OPEX associated with scrubber installation in US dollars (USD) (data provided by the shipowner).
When deciding whether to switch from HFO to MDO to comply with IMO SOx regulations or to install scrubbers, shipowners must carefully evaluate the primary cost driver: fuel expenditure. Although the CAPEX for scrubber installation approaches USD 2 million, and the associated annual OPEX for scrubber operation and maintenance exceeds USD 108,000, these costs represent only a small fraction of the vessel’s yearly fuel expenses. Based on the fuel consumption data, and assuming average fuel prices of USD 547 per ton for HFO and USD 885 per ton for MDO, the annual fuel costs are estimated at USD 18,394,500.68 for HFO and USD 26,612,116.38 for MDO [
46]. Consequently, the annual differential in fuel costs between operating on MDO versus HFO is USD 8,217,615.69.
Both HFO and MDO are fossil fuels and thus correlated to some extent, but their prices have historically exhibited significant volatility and variable spreads, especially during periods of uncertainty or the introduction of stringent regulations. A notable example is the implementation of the IMO 2020 regulation, which increased the demand for MDO and led to a relative drop in the demand for HFO. Given the substantial impact of fuel prices on the total cost of each compliance strategy and considering that this is a long-term decision intended to span the remaining service life of the vessel, projected at ten years, the decision must be carefully weighed and supported by reliable data.
In this case, the economic assessment is based on the Net Present Value (NPV), to evaluate the long-term economic feasibility, and the Return on Investment (ROI), to measure the profitability of installing scrubbers, as compared to the alternative compliance strategy of switching from HFO to MDO. Additionally, the Internal Rate of Return (IRR) and the Discounted Payback Period (DPP) were calculated to provide a more comprehensive understanding of the investment’s performance.
NPV is calculated using Equation (7):
where
represents the net cash inflow or outflow at time,
is the discount rate, set at 10% in this analysis, and
is the time period, which in this case is set to 10 years, corresponding to the expected remaining operational life of the vessel.
The ROI is obtained using Equation (8):
where
FVI represents the Final Value of the Investment, obtained by adding the initial CAPEX of the scrubber system to the accumulated net cash flows over the evaluation period, while
IVI denotes the Initial Value of the Investment, corresponding to the upfront capital expenditure required for the installation of the scrubbers. The difference between FVI and IVI yields the net cash flows generated by the investment. The denominator of the ROI expression is the Initial Value of the Investment, which represents the total capital initially committed.
The IRR is obtained by setting NPV equal to zero, while DPP is calculated using the previously mentioned discount rate of 10% over a 10-year evaluation period.
While the calculation of NPV and the other aforementioned key economic indicators at a specific point in time, such as when data was collected onboard the case study vessel, may be sufficient to support preliminary decision-making, the significant influence of fuel prices, coupled with the high volatility of fossil fuel markets, requires a more comprehensive assessment. This is especially relevant when considering a long-term investment such as scrubber installation, expected to last for a ten-year period.
To address this, the present study conducted a deterministic grid sweep sensitivity analysis, which involved systematically evaluating combinations of HFO and MDO prices within the historical ranges shown in
Table 7 [
46]. This analysis aimed to assess the economic viability of scrubber installation under different fuel price scenarios by calculating the Net Present Value (NPV) for each price pair. For the scrubber installation to be considered economically viable, the NPV must remain positive. Otherwise, from both economic and environmental perspectives, switching to cleaner MDO fuel is preferred. This method allows for a robust understanding of how fluctuations in fuel prices impact investment decisions over the scrubber’s expected lifetime.
To assess the long-term economic performance of installing scrubbers versus switching to MDO, and given the potential variability in fuel prices over the vessel’s remaining ten-year operational life and consequently in the price spread between HFO and MDO fuels, a risk-based economic assessment was conducted using a Monte Carlo simulation framework. This approach allows for the evaluation of investment feasibility across a wide range of plausible future fuel price scenarios. Fuel price uncertainty was modelled using 100,000 Monte Carlo iterations, based on historical price ranges of HFO and MDO presented in
Table 7. To account for the interdependence between HFO and MDO prices under different market conditions, it was essential to incorporate statistical correlation between fuel types. For this purpose, a Gaussian copula, a statistical tool that models the joint behaviour of correlated variables by separately capturing their individual marginal distributions and their dependence structure (correlation), was employed to accurately represent the joint price dynamics of HFO and MDO. This approach enables the preservation of each fuel’s distinct historical price distribution while realistically simulating their correlated movements under varying market conditions [
47]. This method enables the generation of correlated random samples while maintaining the marginal distributions of HFO and MDO prices. This process involved the following steps:
Sampling from a bivariate standard normal distribution with a specified Pearson correlation coefficient ().
Transforming each marginal using the standard normal cumulative distribution function (CDF) to obtain uniform variables.
Mapping the uniform variables to the historical price ranges of HFO and MDO using the inverse CDF of each fuel’s empirical distribution.
The CDF plays a relevant role in the Gaussian copula framework by enabling the transformation of each variable’s historical price data into uniform variables on the interval (0,1). For a given random variable
, the CDF is defined as follows:
This represents the probability that takes a value less than or equal to . This transformation facilitates the modelling of dependence separately from the marginal distributions. After introducing the desired correlation structure in the transformed space, the inverse CDF is applied to map the correlated uniform variables back to their original price distributions, preserving their historical characteristics while reflecting their joint behaviour.
According to the analysis of fuel prices for the 2021–2025 period, the Pearson correlation coefficient between HFO and MDO prices was found to be approximately ( with a p-value < 0.01. This result suggests a statistically significant, yet weak, negative correlation between the two fuels, indicating that when the price of one tends to increase, the other tends to decrease slightly. Despite its low magnitude, this inverse relationship may reflect underlying regulatory or market-driven dynamics affecting fuel demand. In addition to this observed correlation, two alternative scenarios were also modelled to capture more extreme but plausible market behaviours:
A negative correlation (: This negative correlation reflects regulatory situations, such as IMO 2020 sulphur restrictions, where the demand shifts from HFO to MDO. When one price goes up, the other tends to go down, increasing their price spread.
A moderately positive correlation (: This positive correlation represents normal market conditions where fuel prices generally move together because they share common cost drivers like crude oil prices.
For each iteration, the correlated pair of HFO and MDO prices was used to compute the annual fuel cost differential between the two compliance options. This differential, adjusted for the fixed annual OPEX and amortized CAPEX of the scrubber system, was treated as a constant net cash flow over the vessel’s remaining 10-year operational life. The resulting cash flows were discounted at a rate of 10% and integrated into the Net Present Value (NPV) model, as defined in Equation (8). This probabilistic framework provides a robust basis for investment appraisal by incorporating both fuel price volatility and the statistical dependence between HFO and MDO prices under varying regulatory and market conditions [
48,
49].
To provide a clearer overview of the entire process,
Figure 1 presents a flowchart outlining the methodology followed in this study.