Table 3.

Parameters, their definitions, source and values as applied in the proposed model.

Parameter	Definition	Source/Expression	References	Value	Unit
S	Salinity	Calculated based on medium formula	/	61	‰
T	Temperature	Measured	/	293.15	K
K1	Equilibrium constant for H2CO3 dissociation	${10}^{(}{ }^{8.712+9.46\times {10}^{-3}·S-8.56\times {10}^{-5}}·S^2-\frac{1355.1}{T}$ −1.7976·ln(T))	Millero et al., 2002	10−5.864	M
K2	Equilibrium constant for ${\text{HCO}}_3^{-}$ dissociation	$\begin{array}{l}10{(}^{-17.001+0.01259·S+7.9334\times {10}^{-5}}·S^2-\frac{936.291}{T}\\ +1.87354·\ln (T)+2.61471·\frac{S}{T}-0.07479\frac{S^2}{T})\end{array}$	Millero et al., 2002	10−8.893	M
Kw	Solubility product of water	/	DOE, 1994	10−13.5	M2
KTris	Equilibrium constant for Tris deprotonation	Product data sheet (Sigma), ionic strength corrected	Johnson, 1982	10−8.1	M
k+1	Rate constant: $C{O}_2{+H}_{2}O\begin{array}{c}{k}_{+1}\\ \rightleftharpoons \\ k_{-1}\end{array}HC{O}_3^{-}+H^{+}$	$e^{1246.98-\frac{6.19\times 10^4}{T}-183·ln(T)}$	Schulz et al., 2006	0.0238	s−1
k−1		k+1/K1	Eigen, 1964	1.74 × 104	M−1·s−1
k+2	Rate constant: $C{O}_2+O{H}^{-}\begin{array}{c}{k}_{+2}\\ \rightleftharpoons \\ k_{-2}\end{array}HC{O}_3^{-}$	$A·e^{-\frac{90166.83}{R·T}}/K_w$	**	6.74 × 103	M−1·s−1
k−2		k+2·Kw/K1	Schulz et al., 2006	1.56 × 10−4	s−1
$k_{+3}^{H^{+}}$	Rate constant: $C{O}_3^{2-}+H^{+}\begin{array}{c}{k}_{+3}^{H^{+}}\\ \rightleftharpoons \\ k_{-3}^{H^{+}}\end{array}HC{O}_3^{-}$	/	Eigen, 1964	5.00 × 1010	M−1·s−1
$k_{-3}^{H^{+}}$		$k_{+3}^{H^{+}}·K_2$	Schulz et al., 2006	63.96	s−1
$k_{+3}^{O{H}^{-}}$	Rate constant: $HC{O}_3^{-}+O{H}^{-}\begin{array}{c}{k}_{+3}^{O{H}^{-}}\\ \rightleftharpoons \\ k_{-3}^{O{H}^{-}}\end{array}C{O}_3^{2-}{+H}_{2}O$	/	Eigen, 1964	6.00 × 109	M−1·s−1
$k_{-3}^{O{H}^{-}}$		$k_{+3}^{O{H}^{-}}·K_w/K_2$	Schulz et al., 2006	1.48 × 105	s−1
k+4	Rate constant: $H_{2}O\begin{array}{c}{k}_{+4}\\ \rightleftharpoons \\ k_{-4}\end{array}{H}^{+}+O{H}^{-}$	Eigen (1964)	Eigen, 1964	0.014	M·s−1
k−4		k+4/Kw	Schulz et al., 2006	4.43 × 1010	M−1·s−1
k+5	Rate constant: $TrisH\begin{array}{c}{k}_{+5}\\ \rightleftharpoons \\ k_{-5}\end{array}Tri{s}^{-}+H^{+}$	k+5·KTris	Schulz et al., 2006	3.16 × 103	s−1
k−5		${10·k}_{-3}^{H^{+}}$	Schulz et al., 2006	5.00 × 1011	M−1·s−1
υmax, CO2	Maximum CO2 utilization/uptake rate	Artificial value	/	5 × 10−4	M·s−1
KS, CO2	Half saturation constant for CO2 utilization/uptake	Artificial value	/	10−3	M
${\nu }_{max,HC{O}_3^{-}}$	Maximum ${\text{HCO}}_3^{-}$ utilization/uptake rate	Artificial value	/	5 × 10−4	M·s−1
$K_{S,HC{O}_3^{-}}$	Half saturation constant for ${\text{HCO}}_3^{-}$ utilization/uptake	Artificial value	/	10−3	M
${{\rm Y}}_{HC{O}_3^{-},O_2}$	Net ${\text{HCO}}_3^{-}$ bicarbonate utilization rate	Artificial value	/	0.6	/
$F_{eCA}^{*}$	pH independent eCA enhancement factor	Artificial value	***	100	/
FeCA	Enhancement factor for eCA catalysis,	For k+1: $F_{eCA}^{*}\times \frac{10^{-8}}{\left[H^{+}\right]+10^{-8}}$	Steiner et al., 1975	/	/
		For k−1: $F_{eCA}^{*}\times \frac{\left[H^{+}\right]}{\left[H^{+}\right]+10^{-8}}$	Steiner et al., 1975
Lb	Effective thickness of diffusion boundary layer between bulk medium and the surface of the biomass	Estimated	/	20	μm
DO2	Diffusion coefficient of dissolved oxygen	/	Wolf et al., 2007	2.00 × 10−9	m2·s−1
DCO2	Diffusion coefficient of dissolved free CO2	/	Wolf et al., 2007	1.91 × 10−9	m2·s−1
$D_{HC{O}_3^{-}}$	Diffusion coefficient of ${\text{HCO}}_3^{-}$ ion	/	Wolf et al., 2007	1.18 × 10−9	m2·s−1
$D_{C{O}_3^{2-}}$	Diffusion coefficient of ${\text{CO}}_3^{2-}$ ion	/	Wolf et al., 2007	9.14 × 10−10	m2·s−1
DTris	Diffusion coefficient of Tris buffer	Estimated	/	1.0 × 10−10	m2·s−1
$D_{H^{+}}$	Diffusion coefficient of proton	/	Lee and Rasaiah, 2013	6.82 × 10−9	m2·s−1
$D_{O{H}^{-}}$	Diffusion coefficient of hydroxyl ion	/	Lee and Rasaiah, 2013	6.8 × 10−9	m2·s−1

^*Refer to Table 2 and Figure 2; if not specified values shown here were used in the simulation.

^**A = 499002.24·e^{4.2986× 10−4}·S²+5.75499 × 10⁻⁵·S,

R is the universal gas constant, equals 8.31451 J/mol.

^***Higher values indicate stronger eCA activity, a value of 1 indicates no eCA activity.