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This paper presents a first-principles model for the recovery of dissolved gases from liquids using a sidestream hollow-fiber membrane module. The model avoids the use of new empirical coefficients, thus providing a parametric understanding of the process behavior for future design and optimization of membrane modules. This type of first-principles model could be particularly useful when gas recovery is beneficial to biological or chemical reactions of interest, such as the acetogenesis reactions in two-stage anaerobic digesters. The steady-state behavior of the model was validated against both new experimental data for the recovery of H2, CH4 and H2–CH4 mixtures from pure water, as well as existing published data. The modeled gas recovery predictions agreed with experimental data to an absolute average error of 13%, and an average R value of 0.98. Parametric analysis of mixed-gas recovery suggests possible key transition points in the composition of the recovered gases. For example, at 40 °C, increasing trans-membrane pressure while keeping hydraulic residence time (HRT) under 0.5 s will result in an increase in the ratio of H2 to CH4 recovered. Otherwise, increasing trans-membrane pressure will instead decrease the ratio of H2 to CH4 recovered. The model has potential to be extended to transient analysis, but has yet to be validated with transient experimental data. This model was successfully implemented in both Python and MATLAB, and provides valuable insights for future net-energy optimization for anaerobic digestion systems with in-situ gas recovery.