Updated model of the batch acetone-butanol fermentation

Summary The recent models of the Acetone-Butanol fermentation did not adequately describe the culture inhibition by the accumulating metabolites and were unable to simulate the acidogenic culture dynamics at elevated pH levels. The present updated modification of the model features a generalised inhibition term and a pH dependent terms for intracellular conversion of undissociated acids into solvent products. The culture dynamics predictions by the developed model compared well with experimental results from an unconventional acidogenic fermentation ofC. acetobutylicum.Nomenclature A acetone concentration in the fermentation broth, [g/L] - AA total concentration of dissociated and undissociated acetic acid, [g/L] - AA_undiss concentration of undissociated acetic acid, [g/L] - APS Absolute Parameter Sensitivity - AT acetoin concentration in the fermentation broth, [g/L] - B butanol concentration in the fermentation broth, [g/L] - BA total concentration of dissociated and undissociated butyric acid, [g/L] - BA_undiss concentration of undissociated butyric acid, [g/L] - E ethanol concentration in the fermentation broth, [g/L] - f(T) inhibition function as defined in Equation (2) - k₁ constant in Equation (4), [g substrate/g biomass] - k₂ constant in Equation (4), [g substrate/(g biomass.h)] - k₁ constant in Equation (5), [g substrate/(g biomass] - k₂ constant in Equation (5), [g substrate/(g biomass.h)] - k₃ constant in Equation (6), [g butyric acid/g substrate] - k₄ constant in Equation (6), [g butyric acid/(g biomass.h)] - k₅ constant in Equation (7), [g butanol/g substrate] - k₆ constant in Equation (8), [g acetic acid/g substrate] - k₇ constant in Equation (8), [g acetic acid/(g biomass.h)] - k₈ constant in Equation (9), [g acetone/g substrate] - k₉ constant in Equation (10), [g ethanol/g substrate] - k₁₀ constant in Equation (11), [g acetoin/g substrate] - k₁₁ constant in Equation (12), [g lactic acid/g substrate] - K_I Inhibition constant, [g inhibitory products/L] - ke maintenance energy requirement for the cell, [g substrate/(g biomass.h)] - K_AA acetic acid saturation constant, [g acetic acid/L] - K_BA butyric acid saturation constant, [g butyric acid/L] - K_S Monod's saturation constant, [g substrate/L] - LA lactic acid concentration in the fermentation broth, [g/L] - m_i,n_i constants in Equation (14) - n empirical constant, dependent on degree of inhibition. - P concentration of inhibitory products (B+BA+AA), [g/L] - P_max maximum value of product concentration to inhibit the fermentation, [g/L] - pK_a equilibrium constant - r_A rate of acetone production, [g acetone/L.h] - r_AA rate of acetic acid production, [g acetic acid/L.h] - r_AT rate of acetoin production, [g acetoin/L.h] - r_B rate of butanol production, [g butanol/L.h] - r_BA rate of butyric acid production, [g butyric acid/L.h] - r_E rate of ethanol production, [g ethanol/L.h] - RPS Relative Parameter Sensitivity - r_LA rate of lactic acid production, [g lactic acid/L.h] - r_S dS/dt=total substrate consumption rate, [g substrate/L.h] - r_S substrate utilization rate, [g substrate/L.h] - S substrate concentration in the fermentation broth, [g substrate/L] - S₀ initial substrate concentration, [substrate/L] - t time, [h] - X biomass concentration, [g/L] - Y_X yield of biomass with respect to substrate, [g biomass/g substrate] - Y_Pi yield of metabolic product with respect to substrate, [g product/g substrate]Derivatives dX/dt rate of biomass production, [g biomass/L.h] - dP_i/dt rate of product formation, [g product/L.h]Greek letters specific growth rate of the culture, [h^–1] - I specific growth rate of the culture in the presence of the inhibitory products, [h^–1] - µ_max maximum specific growth rate of the culture, [h^–1]