$\mathrm{epsilon}=e^{\frac{F\mathrm{u\_e\_m}}{\mathrm{RT}}}$ $\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}0.00765730077645094 & \text{if $t< 100$}\\ 1.1877 & \text{if $t< 2800$}\\ 0.00765730077645094 & \text{otherwise}\end{cases}$ $\mathrm{v\_CO2\_m}=\frac{\mathrm{v\_CO2\_max}(\mathrm{Q\_CO2\_o}-\mathrm{Q\_CO2\_i})}{\frac{2\mathrm{gamma\_CO2}}{1+\mathrm{gamma\_CO2}}+\mathrm{Q\_CO2\_o}+\mathrm{Q\_CO2\_i}+\frac{2}{1+\mathrm{gamma\_CO2}}\mathrm{Q\_CO2\_o}\mathrm{Q\_CO2\_i}}$ $\mathrm{v\_HCO3\_m}=\mathrm{kappa\_HCO3\_m}(\mathrm{Q\_HCO3\_o}\mathrm{epsilon}-\mathrm{Q\_HCO3\_i})$ $\mathrm{v\_H\_m}=\mathrm{kappa\_H\_m}(\mathrm{Q\_H\_o}-\mathrm{Q\_H\_i}\mathrm{epsilon})$ $\mathrm{v\_H2CO3\_o}=\mathrm{kappa\_H2CO3}(\mathrm{Q\_CO2\_o}-\mathrm{Q\_HCO3\_o}\mathrm{Q\_H\_o})\mathrm{v\_H2CO3\_i}=\mathrm{kappa\_H2CO3}(\mathrm{Q\_CO2\_i}-\mathrm{Q\_HCO3\_i}\mathrm{Q\_H\_i})\frac{d \mathrm{q\_CO2\_i}}{d t}=\mathrm{v\_CO2\_m}-\mathrm{v\_H2CO3\_i}\frac{d \mathrm{q\_HCO3\_i}}{d t}=\mathrm{v\_HCO3\_m}+\mathrm{v\_H2CO3\_i}\mathrm{q\_HCO3\_o}=\frac{\mathrm{K\_HA}\mathrm{q\_CO2\_o}}{\mathrm{q\_H\_o}}$ $\mathrm{pH\_i}=-\lg (1E-3\mathrm{q\_H\_i})\mathrm{pH\_o}=-\lg (1E-3\mathrm{q\_H\_o})$ $\mathrm{pH\_Lim}=-\lg (1E-3\mathrm{q\_H\_Lim})\frac{d \mathrm{q\_TA\_i}}{d t}=\mathrm{v\_CO2\_m}+\mathrm{v\_HCO3\_m}\mathrm{alpha}=\frac{\mathrm{q\_H\_i}}{\mathrm{q\_H\_i}+\mathrm{K\_HA}}\frac{d \mathrm{q\_H\_i}}{d t}=\frac{2.303\mathrm{q\_H\_i}}{\mathrm{beta}}(\mathrm{v\_H\_m}+\mathrm{v\_H2CO3\_i})$ $\mathrm{PC\_CO2\_o}=-\mathrm{RT}\ln \mathrm{Q\_CO2\_o}\mathrm{v\_CO2\_m}\mathrm{PC\_CO2\_i}=\mathrm{RT}\ln \mathrm{Q\_CO2\_i}(\mathrm{v\_CO2\_m}-\mathrm{v\_H2CO3\_i})\mathrm{PC\_HCO3\_o}=-\mathrm{RT}\ln \mathrm{Q\_HCO3\_o}\mathrm{v\_HCO3\_m}\mathrm{PC\_HCO3\_i}=\mathrm{RT}\ln \mathrm{Q\_HCO3\_i}(\mathrm{v\_HCO3\_m}+\mathrm{v\_H2CO3\_i})\mathrm{PC\_H\_o}=-\mathrm{RT}\ln \mathrm{Q\_H\_o}\mathrm{v\_H\_m}\mathrm{PC\_H\_i}=\mathrm{RT}\ln \mathrm{Q\_H\_i}(\mathrm{v\_H\_m}+\mathrm{v\_H2CO3\_i})\mathrm{PRe\_CO2\_m}=(\mathrm{RT}\ln \mathrm{Q\_CO2\_o}-\mathrm{RT}\ln \mathrm{Q\_CO2\_i})\mathrm{v\_CO2\_m}\mathrm{PRe\_HCO3\_m}=(\mathrm{RT}\ln \mathrm{Q\_HCO3\_o}+F\mathrm{u\_e\_m}-\mathrm{RT}\ln \mathrm{Q\_HCO3\_i})\mathrm{v\_HCO3\_m}\mathrm{PRe\_H\_m}=(\mathrm{RT}\ln \mathrm{Q\_H\_o}-F\mathrm{u\_e\_m}-\mathrm{RT}\ln \mathrm{Q\_H\_i})\mathrm{v\_H\_m}\mathrm{P\_um}=F\mathrm{u\_e\_m}\mathrm{v\_H\_m}-F\mathrm{u\_e\_m}\mathrm{v\_HCO3\_m}\mathrm{PRe\_HCO3\_i}=(\mathrm{RT}\ln \mathrm{Q\_CO2\_i}-\mathrm{RT}\ln \mathrm{Q\_HCO3\_i}-\mathrm{RT}\ln \mathrm{Q\_H\_i})\mathrm{v\_H2CO3\_i}\mathrm{P\_supply}=\mathrm{PC\_CO2\_o}+\mathrm{PC\_HCO3\_o}+\mathrm{PC\_H\_o}+\mathrm{P\_um}\mathrm{P\_absorb}=\mathrm{PC\_CO2\_i}+\mathrm{PC\_HCO3\_i}+\mathrm{PC\_H\_i}+\mathrm{PRe\_CO2\_m}+\mathrm{PRe\_HCO3\_m}+\mathrm{PRe\_H\_m}+\mathrm{PRe\_HCO3\_i}$ $\frac{d \mathrm{AC\_CO2\_o}}{d t}=\left|\mathrm{PC\_CO2\_o}\right|\frac{d \mathrm{AC\_CO2\_i}}{d t}=\left|\mathrm{PC\_CO2\_i}\right|\frac{d \mathrm{AC\_HCO3\_o}}{d t}=\left|\mathrm{PC\_HCO3\_o}\right|\frac{d \mathrm{AC\_HCO3\_i}}{d t}=\left|\mathrm{PC\_HCO3\_i}\right|\frac{d \mathrm{AC\_H\_o}}{d t}=\left|\mathrm{PC\_H\_o}\right|\frac{d \mathrm{AC\_H\_i}}{d t}=\left|\mathrm{PC\_H\_i}\right|\frac{d \mathrm{ARe\_CO2\_m}}{d t}=\left|\mathrm{PRe\_CO2\_m}\right|\frac{d \mathrm{ARe\_HCO3\_m}}{d t}=\left|\mathrm{PRe\_HCO3\_m}\right|\frac{d \mathrm{ARe\_H\_m}}{d t}=\left|\mathrm{PRe\_H\_m}\right|\frac{d \mathrm{A\_um}}{d t}=\left|\mathrm{P\_um}\right|\frac{d \mathrm{ARe\_HCO3\_i}}{d t}=\left|\mathrm{PRe\_HCO3\_i}\right|\frac{d \mathrm{E\_supply}}{d t}=\mathrm{P\_supply}\frac{d \mathrm{E\_absorb}}{d t}=\mathrm{P\_absorb}\frac{d \mathrm{A\_supply}}{d t}=\left|\mathrm{P\_supply}\right|\frac{d \mathrm{A\_absorb}}{d t}=\left|\mathrm{P\_absorb}\right|$