$\mathrm{epsilon}=e^{\frac{F\mathrm{u\_e\_m}}{\mathrm{RT}}}$ $\mathrm{Q\_CO2\_o}=\mathrm{K\_CO2\_o}\mathrm{q\_CO2\_o}\mathrm{Q\_CO2\_i}=\mathrm{K\_CO2\_i}\mathrm{q\_CO2\_i}\mathrm{Q\_HCO3\_o}=\mathrm{K\_HCO3\_o}\mathrm{q\_HCO3\_o}\mathrm{Q\_HCO3\_i}=\mathrm{K\_HCO3\_i}\mathrm{q\_HCO3\_i}\mathrm{Q\_H\_o}=\mathrm{K\_H\_o}\mathrm{q\_H\_o}\mathrm{Q\_H\_i}=\mathrm{K\_H\_i}\mathrm{q\_H\_i}\mathrm{q\_CO2\_o}=\begin{cases}0 & \text{if $t< 100$}\\ 1.1877 & \text{if $t< 2800$}\\ 0 & \text{otherwise}\end{cases}$ $\mathrm{v\_CO2\_m}=\frac{\mathrm{v\_CO2\_max}(1+\mathrm{gamma\_CO2})(\mathrm{Q\_CO2\_o}-\mathrm{Q\_CO2\_i})}{2\mathrm{gamma\_CO2}+\mathrm{Q\_CO2\_o}+\mathrm{Q\_CO2\_i}+2\mathrm{Q\_CO2\_o}\mathrm{Q\_CO2\_i}}$ $\mathrm{v\_HCO3\_m}=\mathrm{kappa\_HCO3\_m}(\mathrm{Q\_HCO3\_o}\mathrm{epsilon}-\mathrm{Q\_HCO3\_i})$ $\mathrm{v\_H\_m}=\mathrm{kappa\_H\_m}(\mathrm{Q\_H\_o}\mathrm{epsilon}-\mathrm{Q\_H\_i})$ $\mathrm{v\_H2CO3\_o}=\mathrm{kappa\_H2CO3}(\mathrm{Q\_CO2\_o}-\mathrm{Q\_HCO3\_o}\mathrm{Q\_H\_o})\mathrm{v\_H2CO3\_i}=\mathrm{kappa\_H2CO3}(\mathrm{Q\_CO2\_i}-\mathrm{Q\_HCO3\_i}\mathrm{Q\_H\_i})\frac{d \mathrm{q\_CO2\_i}}{d t}=\mathrm{v\_CO2\_m}-\mathrm{v\_H2CO3\_i}\frac{d \mathrm{q\_HCO3\_o}}{d t}=-\mathrm{v\_HCO3\_m}+\mathrm{v\_H2CO3\_o}\frac{d \mathrm{q\_HCO3\_i}}{d t}=\mathrm{v\_HCO3\_m}+\mathrm{v\_H2CO3\_i}\frac{d \mathrm{q\_H\_i}}{d t}=\mathrm{v\_H\_m}+\mathrm{v\_H2CO3\_i}$ $\mathrm{pH\_i}=-\lg (1E-3\mathrm{q\_H\_i})\mathrm{pH\_o}=-\lg (1E-3\mathrm{q\_H\_o})$