Model Mathematics

CO2_o = \{\begin{matrix} 0 if t < 100 \\ 1.1877 if t < 2800 \\ 0 otherwise \end{matrix} HCO3_o = \frac{K_A CO2_o}{H_o} epsilon = ⅇ^{\frac{- V_m}{RTF}} M_CO2 = P_CO2 (CO2_o - CO2_i) M_HCO3 = \frac{\frac{P_HCO3 V_m}{RTF} (HCO3_o - (HCO3_i epsilon))}{1 - epsilon} pH_Lim = - (\log_{10} (1 e -3 H_Lim)) M_H = \{\begin{matrix} k (H_i - H_Lim) if pH_i < pH_Lim \\ 0 otherwise \end{matrix} pH_i = - (\log_{10} (1 e -3 H_i)) pH_o = - (\log_{10} (1 e -3 H_o)) alpha_i = \frac{H_i}{H_i + K_A} CO2_i = alpha_i TA_i HCO3_i = (1 - alpha_i) TA_i \frac{d}{d t} (TA_i) = rho (M_CO2 + M_HCO3) \frac{d}{d t} (H_i) = \frac{(- 2.303) H_i}{beta} rho ((1 - alpha_i) M_CO2 - (alpha_i M_HCO3) - M_H)