Table 6 Simplified reaction network, kinetic equations and mass balances of the kinetic model proposed

\({\text{CO}} + {\text{H}}_{2} {\text{O}} \to {\text{CO}}_{{2}} + {\text{H}}_{2} ;\; r_{1}\)

2

\(r_{1} = \frac{{K_{1} \cdot p_{{{\text{CO}}}}^{{{\text{OUT}}}} \cdot C_{{\text{X}}} }}{{K_{2} \cdot K_{{{\text{H}}, {\text{CO}}}} \cdot C_{{\text{X}}} + p_{{{\text{CO}}}}^{{{\text{OUT}}}} }}\)

6

\(\vartheta_{{{\text{A}}/{\text{PHB}}}} \cdot {\text{A}} \to {\text{PHB}};\; r_{2}\)

3

\(r_{2} = K_{{\text{P}}} \cdot C_{{\text{X}}}\)

7

\({\text{If}}\;p_{{{\text{CO}}}}^{{{\text{IN}}}} \le 0.10 \;{\text{atm}}: \vartheta_{{{\text{A}}/{\text{X}}}} \cdot {\text{A}} \to {\text{X}}; r_{3}\)

4

\(r_{3} = K_{{{\text{X}}, {\text{A}}}} \cdot C_{{\text{A}}}\)

8

\({\text{If}}\;p_{{{\text{CO}}}}^{{{\text{IN}}}} > 0.10\;{\text{ atm}}: \vartheta_{{{\text{CO}}_{2} /{\text{X}}}} \cdot {\text{CO}}_{2} + \vartheta_{{{\text{A}}/{\text{X}}}} \cdot {\text{A}} \to {\text{X}}; \;r_{4}\)

5

\(r_{4} = K_{{{\text{X}}, {\text{CO}}_{2} }} \cdot \left( {\frac{{p_{{{\text{CO}}_{{2}} }}^{{{\text{OUT}}}} }}{{K_{{{\text{H}}, {\text{CO}}_{2} }} }}} \right)\)

9

CO

\(\frac{1}{R \cdot T}\left( {\frac{{{\text{d}}p_{{{\text{CO}}}}^{{{\text{OUT}}}} }}{{{\text{d}}t}}} \right) = \frac{{{\text{k}}_{{\text{L}}} {\text{a}}^{{{\text{CO}}}} }}{{K_{{{\text{H}},{\text{ CO}}}} }} \cdot \left( {p_{{{\text{CO}}}}^{{{\text{IN}}}} - p_{{{\text{CO}}}}^{{{\text{OUT}}}} } \right) - r_{1}\)

10

H₂

\(\frac{1}{R \cdot T}\left( {\frac{{{\text{d}}p_{{{\text{H}}_{2} }}^{{{\text{OUT}}}} }}{{{\text{d}}t}}} \right) = - \frac{{{\text{k}}_{{\text{L}}} {\text{a}}^{{{\text{H}}_{2} }} }}{{K_{{{\text{H}}, {\text{H}}_{2} }} }} \cdot \left( {p_{{{\text{H}}_{2} }}^{{{\text{OUT}}}} - p_{{{\text{H}}_{2} }}^{*} } \right) + r_{1}\)

11

CO₂

\({\text{If}}\;p_{{{\text{CO}}}}^{{{\text{IN}}}} \le 0.10 \;{\text{atm}}:\frac{1}{R \cdot T}\left( {\frac{{{\text{d}}p_{{{\text{CO}}_{2} }}^{{{\text{OUT}}}} }}{{{\text{d}}t}}} \right) = - \frac{{{\text{k}}_{{\text{L}}} {\text{a}}^{{{\text{CO}}_{2} }} }}{{K_{{{\text{H}}, {\text{CO}}_{2} }} }} \cdot \left( {p_{{{\text{CO}}_{2} }}^{{{\text{OUT}}}} - p_{{{\text{CO}}_{2} }}^{*} } \right) + r_{1}\)

12

\({\text{If}}\;p_{{{\text{CO}}}}^{{{\text{IN}}}} > 0.10 \;{\text{atm}}:\frac{1}{R \cdot T}\left( {\frac{{{\text{d}}p_{{{\text{CO}}_{2} }}^{{{\text{OUT}}}} }}{{{\text{d}}t}}} \right) = - \frac{{{\text{k}}_{{\text{L}}} {\text{a}}^{{{\text{CO}}_{2} }} }}{{K_{{{\text{H}}, {\text{CO}}_{2} }} }} \cdot \left( {p_{{{\text{CO}}_{2} }}^{{{\text{OUT}}}} - p_{{{\text{CO}}_{2} }}^{*} } \right) + r_{1} - \vartheta_{{{\text{CO}}_{2} /{\text{X}}}} \cdot r_{4}\)

13

Residual biomass (X)

\({\text{If}}\;p_{{{\text{CO}}}}^{{{\text{IN}}}} \le 0.10 \;{\text{atm}}: \frac{{{\text{d}}C_{{\text{X}}} }}{{{\text{d}}t}} = r_{3}\)

14

\({\text{If}}\;p_{{{\text{CO}}}}^{{{\text{IN}}}} > 0.10\;{\text{ atm}}: \frac{{{\text{d}}C_{{\text{X}}} }}{{{\text{d}}t}} = r_{4}\)

15

PHB

\(\frac{{{\text{d}}C_{{{\text{PHB}}}} }}{{{\text{d}}t}} = r_{2}\)

16

Acetate (A)

\({\text{If}}\;p_{{{\text{CO}}}}^{{{\text{IN}}}} \le 0.10\;{\text{ atm}}: \frac{{{\text{d}}C_{{\text{A}}} }}{{{\text{d}}t}} = - \vartheta_{{{\text{A}}/{\text{PHB}}}} \cdot r_{2} - \vartheta_{{{\text{A}}/{\text{X}}}} \cdot r_{3}\)

17

\({\text{If}}\;p_{{{\text{CO}}}}^{{{\text{IN}}}} > 0.10\;{\text{ atm}}: \frac{{{\text{d}}C_{{\text{A}}} }}{{{\text{d}}t}} = - \vartheta_{{{\text{A}}/{\text{PHB}}}} \cdot r_{2} - \vartheta_{{{\text{A}}/{\text{X}}}} \cdot r_{4}\)

18