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Background Pressurised anaerobic digestion allows the production of biogas with a high content of methane and, at the same time, avoid the energy costs for the biogas upgrading and injection into the distribution grid. The technology carries potential, but the research faces practical constraints by a.o. the capital investment needed in high-pressure reactors and sensors and associated sampling limitations. In this work, the kinetic model of an autogenerative high-pressure anaerobic digestion of acetate, as the representative compound of the aceticlastic methanogenesis route, in batch configuration, is proposed to predict the dynamic performance of pressurised digesters and support future experimental work. The modelling of autogenerative high-pressure anaerobic digestion in batch configuration, which is not extensively studied and simulated in the present literature, was developed, calibrated, and validated by using experimental results available from the literature. Results Under high-pressure conditions, the assessment of the Monod maximum specific uptake rate, the half-saturation constant and the first-order decay rate was carried out, and the values of 5.9 kg COD kg COD−1 d−1, 0.05 kg COD m−3 and 0.02 d−1 were determined, respectively. By using the predicted values, excellent fittings of the final pressure, the CH4 molar fraction and the specific methanogenic yield calculation were obtained. Likewise, the variation in the gas–liquid mass transfer coefficient by several orders of magnitude showed negligible effects on the model predictive values in terms of methane molar fraction of the produced biogas, while the final pressure seemed to be slightly influenced. Conclusions The proposed model allowed to estimate the Monod maximum specific uptake rate for acetate, the half-saturation rate for acetate and the first-order decay rate constant, which were comparable with literature values reported for well-studied methanogens under anaerobic digestion at atmospheric pressure. The methane molar fraction and the final pressure predicted by the model showed different responses towards the variation of the gas–liquid mass transfer coefficient since the former seemed not to be affected by the variation of the gas–liquid mass transfer coefficient; in contrast, the final pressure seemed to be slightly influenced. The proposed approach may also allow to potentially identify the methanogens species able to be predominant at high pressure.