$\mathrm{CO2\_o}=\begin{cases}0.00765730077645094 & \text{if $t< 100$}\\ 1.1877 & \text{if $t< 2800$}\\ 0.00765730077645094 & \text{otherwise}\end{cases}\mathrm{rho}=\frac{2}{r}\mathrm{HCO3\_o}=\frac{\mathrm{K\_HA}\mathrm{CO2\_o}}{\mathrm{H\_o}}\mathrm{epsilon}=e^{\frac{-\mathrm{V\_m}F}{RT}}\mathrm{pH\_Lim}=-\lg (1E-3\mathrm{H\_Lim})\mathrm{pH\_i}=-\lg (1E-3\mathrm{H\_i})\mathrm{pH\_o}=-\lg (1E-3\mathrm{H\_o})\mathrm{J\_CO2}=\mathrm{P\_CO2}(\mathrm{CO2\_o}-\mathrm{CO2\_i})\mathrm{J\_HCO3}=\frac{\frac{\mathrm{P\_HCO3}\mathrm{V\_m}F}{RT}(\mathrm{HCO3\_o}-\mathrm{HCO3\_i}\mathrm{epsilon})}{1-\mathrm{epsilon}}\mathrm{J\_H}=\begin{cases}\frac{k}{\mathrm{rho}}(\mathrm{H\_i}-\mathrm{H\_Lim}) & \text{if $\mathrm{pH\_i}< \mathrm{pH\_Lim}$}\\ 0.0 & \text{otherwise}\end{cases}\mathrm{alpha}=\frac{\mathrm{H\_i}}{\mathrm{H\_i}+\mathrm{K\_HA}}\mathrm{CO2\_i}=\mathrm{alpha}\mathrm{TA\_i}\mathrm{HCO3\_i}=(1-\mathrm{alpha})\mathrm{TA\_i}\frac{d \mathrm{TA\_i}}{d t}=\mathrm{rho}(\mathrm{J\_CO2}+\mathrm{J\_HCO3})\frac{d \mathrm{H\_i}}{d t}=\frac{2.303\mathrm{H\_i}}{\mathrm{beta}}\mathrm{rho}((1-\mathrm{alpha})\mathrm{J\_CO2}-\mathrm{alpha}\mathrm{J\_HCO3}-\mathrm{J\_H})$ $\mathrm{Q\_CO2\_o}=\mathrm{K\_CO2\_o}\mathrm{CO2\_o}\mathrm{V\_cell}\mathrm{Q\_CO2\_i}=\mathrm{K\_CO2\_i}\mathrm{CO2\_i}\mathrm{V\_cell}\mathrm{Q\_HCO3\_o}=\mathrm{K\_HCO3\_o}\mathrm{HCO3\_o}\mathrm{V\_cell}\mathrm{Q\_HCO3\_i}=\mathrm{K\_HCO3\_i}\mathrm{HCO3\_i}\mathrm{V\_cell}\mathrm{Q\_H\_o}=\mathrm{K\_H\_o}\mathrm{H\_o}\mathrm{V\_cell}\mathrm{Q\_H\_i}=\mathrm{K\_H\_i}\mathrm{H\_i}\mathrm{V\_cell}$ $\mathrm{v\_CO2\_m}=\mathrm{rho}\mathrm{J\_CO2}\mathrm{V\_cell}\mathrm{v\_HCO3\_m}=\mathrm{rho}\mathrm{J\_HCO3}\mathrm{V\_cell}\mathrm{v\_H\_m}=-\mathrm{rho}\mathrm{J\_H}\mathrm{V\_cell}\mathrm{v\_H2CO3\_i}=\mathrm{rho}((1-\mathrm{alpha})\mathrm{J\_CO2}-\mathrm{alpha}\mathrm{J\_HCO3})\mathrm{V\_cell}$ $\mathrm{PC\_CO2\_o}=-RT\ln \mathrm{Q\_CO2\_o}\mathrm{v\_CO2\_m}\mathrm{PC\_CO2\_i}=RT\ln \mathrm{Q\_CO2\_i}(\mathrm{v\_CO2\_m}-\mathrm{v\_H2CO3\_i})\mathrm{PC\_HCO3\_o}=-RT\ln \mathrm{Q\_HCO3\_o}\mathrm{v\_HCO3\_m}\mathrm{PC\_HCO3\_i}=RT\ln \mathrm{Q\_HCO3\_i}(\mathrm{v\_HCO3\_m}+\mathrm{v\_H2CO3\_i})\mathrm{PC\_H\_o}=-RT\ln \mathrm{Q\_H\_o}\mathrm{v\_H\_m}\mathrm{PC\_H\_i}=RT\ln \mathrm{Q\_H\_i}(\mathrm{v\_H\_m}+\mathrm{v\_H2CO3\_i})\mathrm{PRe\_CO2\_m}=(RT\ln \mathrm{Q\_CO2\_o}-RT\ln \mathrm{Q\_CO2\_i})\mathrm{v\_CO2\_m}\mathrm{PRe\_HCO3\_m}=(RT\ln \mathrm{Q\_HCO3\_o}+F\mathrm{V\_m}-RT\ln \mathrm{Q\_HCO3\_i})\mathrm{v\_HCO3\_m}\mathrm{PRe\_H\_m}=(RT\ln \mathrm{Q\_H\_o}-F\mathrm{V\_m}-RT\ln \mathrm{Q\_H\_i})\mathrm{v\_H\_m}\mathrm{P\_um}=F\mathrm{V\_m}\mathrm{v\_H\_m}-F\mathrm{V\_m}\mathrm{v\_HCO3\_m}\mathrm{PRe\_HCO3\_i}=(RT\ln \mathrm{Q\_CO2\_i}-RT\ln \mathrm{Q\_HCO3\_i}-RT\ln \mathrm{Q\_H\_i})\mathrm{v\_H2CO3\_i}\mathrm{P\_supply}=\mathrm{PC\_CO2\_o}+\mathrm{PC\_HCO3\_o}+\mathrm{PC\_H\_o}+\mathrm{P\_um}\mathrm{P\_absorb}=\mathrm{PC\_CO2\_i}+\mathrm{PC\_HCO3\_i}+\mathrm{PC\_H\_i}+\mathrm{PRe\_CO2\_m}+\mathrm{PRe\_HCO3\_m}+\mathrm{PRe\_H\_m}+\mathrm{PRe\_HCO3\_i}$ $\frac{d \mathrm{AC\_CO2\_o}}{d t}=\left|\mathrm{PC\_CO2\_o}\right|\frac{d \mathrm{AC\_CO2\_i}}{d t}=\left|\mathrm{PC\_CO2\_i}\right|\frac{d \mathrm{AC\_HCO3\_o}}{d t}=\left|\mathrm{PC\_HCO3\_o}\right|\frac{d \mathrm{AC\_HCO3\_i}}{d t}=\left|\mathrm{PC\_HCO3\_i}\right|\frac{d \mathrm{AC\_H\_o}}{d t}=\left|\mathrm{PC\_H\_o}\right|\frac{d \mathrm{AC\_H\_i}}{d t}=\left|\mathrm{PC\_H\_i}\right|\frac{d \mathrm{ARe\_CO2\_m}}{d t}=\left|\mathrm{PRe\_CO2\_m}\right|\frac{d \mathrm{ARe\_HCO3\_m}}{d t}=\left|\mathrm{PRe\_HCO3\_m}\right|\frac{d \mathrm{ARe\_H\_m}}{d t}=\left|\mathrm{PRe\_H\_m}\right|\frac{d \mathrm{A\_um}}{d t}=\left|\mathrm{P\_um}\right|\frac{d \mathrm{ARe\_HCO3\_i}}{d t}=\left|\mathrm{PRe\_HCO3\_i}\right|\frac{d \mathrm{E\_supply}}{d t}=\mathrm{P\_supply}\frac{d \mathrm{E\_absorb}}{d t}=\mathrm{P\_absorb}\frac{d \mathrm{A\_supply}}{d t}=\left|\mathrm{P\_supply}\right|\frac{d \mathrm{A\_absorb}}{d t}=\left|\mathrm{P\_absorb}\right|$