Model equation/Mechanism

Parameter estimation

r

MSC

$r=\frac{k_d{K}_A\left[C_A^{g0}\left(1-X\right)C_B^{g0}\right]}{1+K_A{C}_A^{g0}\left(1-X\right)+K_C\left(C_C^{g0}+C_A^{g0}X\right)}$

1a. Glucose adsorption. r.l.s.: surface reaction.

$k_d=2.10$

$K_A=3.32\times {10}^7$

$K_C=4.10\times {10}^7$

0.951

2.264

$r=\frac{k_d{K}_A\left[C_A^{g0}\left(1-X\right)C_B^{g0}\right]}{1+K_A{C}_A^{g0}\left(1-X\right)}$

1b. Glucose adsorption. There is no sorbitol adsorption. r.l.s.: surface reaction.

$k_d=1.02$

$K_A=5.84\times {10}^2$

0.907

1.523

$r_{anA}=\frac{k_{aA}\left(C_A^{g0}\left(1-X\right)\right)}{1+K_C\left(C_C^{g0}+C_A^{g0}X\right)}$

1c. Glucose adsorption. r.l.s.: glucose adsorption.

$k_{aA}=5.60\times {10}^{-1}$

$K_C=1.54\times {10}^2$

0.926

1.811

$r_{anA}=k_{aA}\left(C_A^{g0}\left(1-X\right)\right)$

1d. Glucose adsorption. There is no sorbitol adsorption. r.l.s.: glucose adsorption.

$k_{aA}=7.12\times {10}^{-2}$

0.862

1.615

$r_{dnC}=\frac{k_{aC}}{K_C}$

1e. Glucose adsorption. r.l.s.: sorbitol desorption.

$k_{aC}=1.78\times {10}^{-2}$

$K_C=3.22$

0.907

1.297

$r=\frac{k_d{K}_A{K}_B\left(C_A^{g0}\left(1-X\right)C_B^{g0}\right)}{{\left[1+K_A{C}_A^{g0}\left(1-X\right)+K_B{C}_B^{g0}+K_C\left(C_C^{g0}+C_A^{g0}X\right)\right]}^2}$

2a. Glucose and molecular H₂ adsorption. r.l.s.: surface reaction.

$k_d=4.02\times {10}^{-1}$

$K_A=1.11\times {10}^4$

$K_B=5.45\times {10}^4$

$K_C=7.40\times {10}^3$

0.964

2.531

$r=\frac{k_d{K}_A{K}_B\left(C_A^{g0}\left(1-X\right)C_B^{g0}\right)}{{\left[1+K_A{C}_A^{g0}\left(1-X\right)+K_B{C}_B^{g0}\right]}^2}$

2b. Glucose and molecular H₂ adsorption. There is no sorbitol adsorption. r.l.s.: surface reaction.

$k_d=3.60\times {10}^{-1}$

$K_A=8.54\times {10}^8$

$K_B=2.75\times {10}^9$

0.928

1.468

$r_{anA}=\frac{k_{aA}\left[C_A^{g0}\left(1-X\right)\right]}{1+K_B{C}_B^{g0}+K_C\left(C_C^{g0}+C_A^{g0}X\right)}$

2c Glucose and molecular H₂ adsorption. r.l.s.: glucose adsorption.

$k_{aA}=1.03\times {10}^{-1}$

$K_B=-1.51\times {10}^2$

$K_C=2.36\times {10}^1$

0.928

1.822

$r_{anA}=\frac{k_{aA}\left[C_A^{g0}\left(1-X\right)\right]}{1+K_B{C}_B^{g0}}$

2d. Glucose and molecular H₂ adsorption. There is no sorbitol adsorption. r.l.s.: glucose adsorption.

$k_{aA}=4.32\times {10}^{-2}$

$K_B=-9.32\times {10}^1$

0.870

1.346

$r_{anB}=\frac{k_{aB}{C}_B^{g0}}{1+K_A{C}_A^{g0}\left(1-X\right)+K_C\left(C_C^{g0}+C_A^{g0}X\right)}$

2e. Glucose and molecular H₂ adsorption. r.l.s.: H₂ adsorption.

$k_{aB}=5.15$

$K_A=1.63\times {10}^1$

$K_C=7.46\times {10}^1$

0.955

2.301

$r_{anB}=\frac{k_{aB}{C}_B^{g0}}{1+K_A{C}_A^{g0}\left(1-X\right)}$

2f. Glucose and molecular H₂ adsorption. There is no sorbitol adsorption. r.l.s.: H₂ adsorption.

$k_{aB}=9.38\times {10}^{-1}$

$K_A=-6.07\times {10}^{-1}$

0.907

1.522

$r_{dnC}=\frac{k_{aC}}{K_C}$

2g. Glucose and molecular H₂ adsorption. r.l.s.: sorbitol desorption.

$k_{aC}=1.78\times {10}^{-2}$

$K_C=3.22$

0.907

1.297

$r=\frac{k_d{K}_A\sqrt{K_B}\left(C_A^{g0}\left(1-X\right)\sqrt{C_B^{g0}}\right)}{{\left(1+K_A{C}_A^{g0}\left(1-X\right)+\sqrt{K_B{C}_B^{g0}}+K_C\left(C_C^{g0}+C_A^{g0}X\right)\right)}^2}$

3a. Glucose and dissociative H₂ adsorption. r.l.s.: surface reaction.

$k_d=1.49$

$K_A=7.72\times {10}^1$

$K_B=3.86\times {10}^{-1}$

$K_C=4.75\times {10}^1$

0.968

2.630

$r=\frac{k_d{K}_A\sqrt{K_B}\left(C_A^{g0}\left(1-X\right)\sqrt{\left(C_B^{g0}\right)}\right)}{{\left(1+K_A{C}_A^{g0}\left(1-X\right)+\sqrt{K_B{C}_B^{g0}}\right)}^2}$

3b. Glucose and dissociative H₂ adsorption. There is no sorbitol adsorption. r.l.s.: surface reaction.

$k_d=-6.80\times {10}^1$

$K_A=2.72\times {10}^1$

$K_B=\sqrt{-3.98\times {10}^{-2}}$

0.921

1.638

$r_{anA}=\frac{k_{aA}\left[C_A^{g0}\left(1-X\right)\right]}{1+\sqrt{K_B{C}_B^{g0}}+K_C\left(C_C^{g0}+C_A^{g0}X\right)}$

3c. Glucose and dissociative H₂ adsorption. r.l.s.: glucose adsorption.

$k_{aA}=7.65\times {10}^{-2}$

$K_B=\sqrt{-1.23\times {10}^1}$

$K_C=1.90\times {10}^1$

0.923

1.840

$r_{anA}=\frac{k_{aA}\left[C_A^{g0}\left(1-X\right)\right]}{1+\sqrt{K_B{C}_B^{g0}}}$

3d. Glucose and dissociative H₂ adsorption. There is no sorbitol adsorption. r.l.s.: glucose adsorption.

$k_{aA}=3.18\times {10}^{-2}$

$K_B=\sqrt{-8.62}$

0.869

1.340

$r_{anB}=\frac{k_{aB}{C}_B^{g0}}{{\left(1+K_A{C}_A^{g0}\left(1-X\right)+K_C\left(C_C^{g0}+C_A^{g0}X\right)\right)}^2}$

3e. Glucose and dissociative H₂ adsorption. r.l.s.: H₂ adsorption.

$k_{aB}=2.94$

$K_A=3.00$

$K_C=1.15\times {10}^1$

0.948

2.150

$r_{anB}=\frac{k_{aB}{C}_B^{g0}}{{\left(1+K_A{C}_A^{g0}\left(1-X\right)\right)}^2}$

3f. Glucose and dissociative H₂ adsorption. There is no sorbitol adsorption. r.l.s.: H₂ adsorption.

$k_{aB}=9.36\times {10}^{-1}$

$K_A=-3.10\times {10}^{-1}$

0.907

1.522

$r_{dnC}=k_{aC}$

3g. Glucose and dissociative H₂ adsorption. r.l.s.: sorbitol desorption.

$k_{aC}=5.53\times {10}^{-3}$

0.907

1.323