Mechanistic simulation of batch acetone–butanol–ethanol (ABE) fermentation with in situ gas stripping using Aspen Plus™

Abstract

Process simulations of batch fermentations with in situ product separation traditionally decouple these interdependent steps by simulating a separate “steady state” continuous fermentation and separation units. In this study, an integrated batch fermentation and separation process was simulated for a model system of acetone–butanol–ethanol (ABE) fermentation with in situ gas stripping, such that the fermentation kinetics are linked in real-time to the gas stripping process. A time-dependent cell growth, substrate utilization, and product production is translated to an Aspen Plus batch reactor. This approach capitalizes on the phase equilibria calculations of Aspen Plus to predict the effect of stripping on the ABE fermentation kinetics. The product profiles of the integrated fermentation and separation are shown to be sensitive to gas flow rate, unlike separate steady state fermentation and separation simulations. This study demonstrates the importance of coupled fermentation and separation simulation approaches for the systematic analyses of unsteady state processes.

Appendices

Appendix A

Ordinary differential equations representation of the fermentation kinetics of a batch culture of Clostridium acetobutylicum [18]:

$$\frac{{{\text{d}}{m_{\text{z}}}}}{{{\text{d}}t}}={k_1}{m_{\text{S}}}\frac{{{K_{\text{I}}}}}{{{K_{\text{I}}}+{m_{\text{B}}}}}{m_{\text{z}}} - 0.56\left( {{m_{\text{z}}} - 1} \right){m_{\text{z}}},$$

(8)

$$\frac{{{\text{d}}{m_{\text{q}}}}}{{{\text{d}}t}}=0.56({m_{\text{z}}} - 1){m_{\text{q}}} - {k_2}{m_{\text{B}}}{m_{\text{q}}},$$

(9)

$$\frac{{{\text{d}}{m_{\text{S}}}}}{{{\text{d}}t}}= - {k_3}{m_{\text{S}}}{m_{\text{q}}} - {k_4}\frac{{{m_{\text{S}}}}}{{{K_{\text{S}}}+{m_{\text{S}}}}}{m_{\text{q}}},$$

(10)

$$\frac{{{\text{d}}{m_{{\text{BA}}}}}}{{{\text{d}}t}}={k_5}{m_{\text{S}}}\frac{{{K_{\text{I}}}}}{{{K_{\text{I}}}+{m_{\text{B}}}}}{m_{\text{q}}} - {k_6}\frac{{{m_{{\text{BA}}}}}}{{{K_{{\text{BA}}}}+{m_{{\text{BA}}}}}}{m_{\text{q}}},$$

(11)

$$\frac{{{\text{d}}{m_{\text{B}}}}}{{{\text{d}}t}}={k_7}{m_{\text{S}}}{m_{\text{q}}} - 0.841\frac{{{\text{d}}{m_{{\text{BA}}}}}}{{{\text{d}}t}},$$

(12)

$$\frac{{{\text{d}}{m_{{\text{AA}}}}}}{{{\text{d}}t}}={k_8}\frac{{{m_S}}}{{{K_{\text{S}}}+{m_{\text{S}}}}}\frac{{{K_{\text{I}}}}}{{{K_{\text{I}}}+{m_{\text{B}}}}}{m_{\text{q}}} - {k_9}\frac{{{m_{{\text{AA}}}}}}{{{K_{{\text{AA}}}}+{m_{{\text{AA}}}}}}\frac{{{m_{\text{S}}}}}{{{K_{\text{S}}}+{m_{\text{S}}}}}{m_{\text{q}}},$$

(13)

$$\frac{{{\text{d}}{m_{\text{A}}}}}{{{\text{d}}t}}={k_{10}}\frac{{{m_{\text{S}}}}}{{{K_{\text{S}}}+{m_{\text{S}}}}}{m_{\text{q}}} - 0.484\frac{{{\text{d}}{m_{{\text{AA}}}}}}{{{\text{d}}t}},$$

(14)

$$\frac{{{\text{d}}{m_{\text{E}}}}}{{{\text{d}}t}}={k_{11}}\frac{{{m_{\text{S}}}}}{{{K_S}+{m_{\text{S}}}}}{m_{\text{q}}},$$

(15)

$$\frac{{{\text{d}}{m_{{\text{C}}{{\text{O}}_2}}}}}{{{\text{d}}t}}={k_{12}}\frac{{{m_{\text{S}}}}}{{{K_{\text{S}}}+{m_{\text{S}}}}}{m_{\text{q}}},$$

(16)

$$\frac{{{\text{d}}{m_{{{\text{H}}_2}}}}}{{{\text{d}}t}}={k_{13}}\frac{{{m_{\text{S}}}}}{{{K_{\text{S}}}+{m_{\text{S}}}}}{m_{\text{q}}}+{k_{14}}{m_{\text{S}}}{m_{\text{q}}}.$$

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Appendix B

Parameter definition for the kinetic model and their respective values

k ₁ :

kinetic constant in Eq. 8, = 0.009 L/g-substrate/h

k ₂ :

kinetic constant in Eq. 9, = 0.0008 L/g-butanol/h

k ₃ :

kinetic constant in Eq. 10, = 0.0255 L/g-biomass/h

k ₄ :

kinetic constant in Eq. 10, = 0.6764 g-substrate/g-biomass/h

k ₅ :

kinetic constant in Eq. 11, = 0.0136 g-butyric acid L/g-substrate/g-biomass/h

k ₆ :

kinetic constant in Eq. 11, = 0.1170 g-butyric acid/g-biomass/h

k ₇ :

kinetic constant in Eq. 12, = 0.0113 g-butanol L/g-substrate/g-biomass/h

k ₈ :

kinetic constant in Eq. 13, = 0.7150 g-acetic acid/g-biomass/h

k ₉ :

kinetic constant in Eq. 13, = 0.1350 g-acetic acid/g-biomass/h

k ₁₀ :

kinetic constant in Eq. 14, = 0.1558 g-acetone/g-biomass/h

k ₁₁ :

kinetic constant in Eq. 15, = 0.0258 g-ethanol/g-biomass/h

k ₁₂ :

kinetic constant in Eq. 16, = 0.6139 g-carbon dioxide/g-biomass/h

k ₁₃ :

kinetic constant in Eq. 17, = 0.0185 g-hydrogen/g-biomass/h

k ₁₄ :

kinetic constant in Eq. 17, = 0.00013 g-hydrogen L /g-substrate/g-biomass/h

K _I :

inhibition constant, = 0.833 g-butanol/L

K _S :

Monod constant, = 2.0 g-substrate/L

K _BA :

saturation constant, = 0.5 g-butyric acid/L

K _AA :

saturation constant, = 0.5 L/g-acetic acid/L

m _A :

acetone concentration, g/L

m _B :

butanol concentration, g/L

m _E :

ethanol concentration, g/L

m _BA :

butyric acid concentration, g/L

m _AA :

acetic acid concentration, g/L

m _S :

glucose concentration, g/L

m _q :

cell biomass concentration, g/L

${m_{{\text{C}}{{\text{O}}_{\text{2}}}}}$ :

carbon dioxide concentration, g/L

${m_{{{\text{H}}_{\text{2}}}}}$ :

hydrogen concentration, g/L

m _z :

marker of the physiological state culture, dimensionless

Appendix C

Stoichiometric equations (Eqs. 18–22) used together with stoichiometric coefficients relative to glucose [13,14,15,16]. The stoichiometric coefficients used in the stoichiometric reactor were 0.319, 0.495, 0.080, 0.120, 0 (mole of product/mole of glucose fed) for acetone, butanol, ethanol, acetic and butyric acids, respectively, calculated from the model of Votruba et al. [18]:

$${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}{{\text{O}}_{\text{6}}} \to {\text{ }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{1}}0}}{\text{O }}\left( {{\text{butanol}}} \right){\text{ }}+{\text{ 2C}}{{\text{O}}_{\text{2}}}+{\text{ }}{{\text{H}}_{\text{2}}}{\text{O,}}$$

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$${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}{{\text{O}}_{\text{6}}}+{\text{ }}{{\text{H}}_{\text{2}}}{\text{O }} \to {\text{ }}{{\text{C}}_{\text{3}}}{{\text{H}}_{\text{6}}}{\text{O }}\left( {{\text{acetone}}} \right){\text{ }}+{\text{ 3C}}{{\text{O}}_{\text{2}}}+{\text{ 4}}{{\text{H}}_{\text{2}}},$$

(19)

$${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}{{\text{O}}_{\text{6}}} \to {\text{ 2}}{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}{\text{O }}\left( {{\text{ethanol}}} \right){\text{ }}+{\text{ 2C}}{{\text{O}}_{\text{2}}}+{\text{ }}{{\text{H}}_{\text{2}}},$$

(20)

$${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}{{\text{O}}_{\text{6}}} \to {\text{ }}{{\text{C}}_{\text{4}}}{{\text{H}}_{\text{8}}}{{\text{O}}_{\text{2}}}\,\left( {{\text{butyric acid}}} \right){\text{ }}+{\text{ 2C}}{{\text{O}}_{\text{2}}}+{\text{ 2}}{{\text{H}}_{\text{2}}},$$

(21)

$${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}{{\text{O}}_{\text{6}}} \to {\text{ 3}}{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{4}}}{{\text{O}}_{\text{2}}}\,\left( {{\text{acetic acid}}} \right).$$

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