Shipping is a relatively clean transport method with low emissions per ton-mile compared with road transport. However, harmful emissions emitted in coastal areas are a concern, as these affect local air quality and health. To reduce sulphur oxide (SOX ) emissions, the International Maritime Organization (IMO) implemented a global sulphur cap of 0.5 wt% and the 0.1 wt% limit in emission control areas (ECAs). Ship owners can opt for either low sulphur fuels or wet scrubber systems. Wet scrubber systems are a reliable method for reducing SOX emissions with capture rates of up to 98%. These systems may use seawater alkalinity or caustic soda (e.g. closed-loop systems) to neutralise the SOX emissions. However, the dynamic loading of engines can cause large fluctuations in the exhaust flow conditions, and it is unknown how these affect the effectiveness of the scrubber. This study explores the impact of dynamic loads on the SOX removal efficiency of closed-loop wet scrubbers. A dynamic model of a closed-loop wet scrubber utilising fresh water and caustic soda is developed and verified using publicly available data. The model applies the two-film theory to model the gas-liquid interface. Billet and Schultes liquid hold-up theory is used to model the liquid film thickness in the packed bed. Maintaining scrubber efficiency with large load fluctuations or high-frequency fluctuations requires an increased liquid flow. The scrubber control system used a set-point of 75% of the equivalent compliance limit to ensure compliance with the 0.1% ECA limit during load fluctuations. The model and results can be used to develop a more advanced control system for improved scrubber operation and integration with a selective catalytic reduction (SCR) system to demonstrate compliance with the IMO NOX Tier III limit when using high-sulphur heavy fuel oil (HFO).