This paper presents a predictive mathematical model of high-pressure membrane contactor, with a view to developing a plant-wide model of natural gas sweetening including amine regeneration. We build upon an existing model of high-pressure membrane contactor by Quek et al. [Chem Eng Res Des 132:1005–1019, 2018], which uses a combination of 1-d and 2-d mass-balance equations to predict the CO2 absorption flux and membrane wetting under lean solvent operation. For the first time, quantitative predictions of the CO2 absorption flux can be made under both lean and semi-lean operations. A 1-d energy balance that accounts for the solvent evaporative losses and the exothermic CO2 absorption into the amine is solved alongside the mass-balance equations, in order to predict the solvent temperature profile inside the contactor. The evaporative losses of water and amines can be quantified separately, as well as the absorptive losses of light hydrocarbons with the amine solvent. The model’s predictive capability is tested against data from a lab-scale module and a pilot-scale module that is operated under industrially relevant conditions at a natural gas processing facility in Malaysia. A close agreement between model predictions and measurements of the CO2 absorption flux, solvent temperature profile, and hydrocarbon loss is observed for a wide range of gas and solvent flowrates and compositions, thereby validating the modeling assumptions. The contactor model is combined in a plant-wide model of natural gas sweetening in the companion paper, where it is used for process integration and analysis.