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Vinasse is a sulfate-rich liquid substrate, from which high levels of hydrogen sulfide in biogas can be obtained due to the sulfate reduction process under anaerobic conditions. Hydrogen sulfide is corrosive and toxic and must be removed for any utilization of the biogas. Mathematical models have been developed to study separately sulfate reduction in anaerobic digestion and sulfide removal from biogas streams. However, the levels of hydrogen sulfide produced in the anaerobic digestion stage have an effect on the sulfide removal processes in the next stage. As a method to study both processes and their interaction, a new approach is introduced and reviewed in the present article: the sulfur chain in biogas production. The necessity of studying the sulfate reduction processes in vinasse as a typical sulfate-rich substrate to predict hydrogen sulfide concentrations in the gas phase, as well as the best model approach to that aim are established here. In addition, the approaches to model sulfide removal based on direct conversion processes, the models' capability to predict the removal of hydrogen sulfide from the biogas (at levels between 20 000 and 30 000 ppm v ) as well as the concentration profile of the reactants in this removal processes are discussed.•Equilibrium Equation (9) (m 3 kmol −1 ) •Equilibrium Equation (10) (−) K 100 Concentration of H 2 S or pH at which the uptake rate is decreased 100 times (kmol m −3 ) K 2 Concentration of H 2 S or pH at which the uptake rate is decreased twice (kmol m −3 ) K a, acid Acid-base equilibrium coefficient (kmol m −3 ) K A/B Acid-base kinetic parameter (m 3 kmol −1 d −1 ) K H Henry's law coefficient (kmol m −3 bar −1 ) K I Inhibition coefficient by undissociated H 2 S (kmol m −3 ) K P2 Competitive product inhibition coefficient in Equation (30) (kg m −3 ) K S Half saturation value (kg COD_S i · m −3 ) K S * Half saturation value in absence of inhibitor in Equation (30) kg m −3 K SO4 Half saturation value for sulfates (kmol m −3 ) EL Barrera et al. K W Water equilibrium constant (kmol m −3 ) L n− Organic ligand (−) p H2S Hydrogen sulfide partial pressure (bar) pH LL Lower pH limits where the groups of microorganism are 50% inhibited (−) pH UL Upper pH limits where the groups of microorganism are 50% inhibited (−) pH 0 pH of the maximum growth rate of Thiobacillus ferrooxidans (−) r Reaction rate (kmol m −3 s −1 ) S Concentration of soluble components (for hydrogen ions, sulfates, sulfides and its ionized forms units are in kmol m −3 ) (kg COD_S i m −3 ) S I Inhibitor concentration (undissociated H 2 S) (kmol m −3 ) T Temperature ( • C) t Time (s) X Particulate component (kg VSS m −3 ) x Distance from gas-liquid interface (m) Y Yield of biomass on the substrate (kg VSS kg COD_S i −1 ) Greek letters α LL-α UL Positive values which affect the steepness of the curve (−) ρ A Acid-base kinetic rate (kmol m −3 d −1 ) ρ uptake Kinetic rate of substrate uptake (kg COD_S i m −3 d −1 ) ρ growth Kinetic rate of bacterial growth (kg VSS m −3 d −1 ) ρ decay Kinetic rate of bacterial ...

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