Carbon isotope fraction ODEs obtained from the model
\(\dot{f_a} =\left(f_i-f_a\right)\frac{r_p}{c_a}-\left(f_{a,p}-f_a\right)\frac{r_e}{c_a}\)
\(\dot{f_{a,s}}=\left(f_{a,p}-f_{a,s}\right)\frac{r_s}{c_{a,s}}\)
\(\dot{f_{a,p}}=\left(f_i-f_{a,p}\right)\frac{r_p}{c_{a,p}}\)
\(\dot{f_b}=\left(X\ f_i+\left(1-X\right)\ f_o-f_b\right)\frac{r_u}{c_b}\)
\(\dot{f_o}=\left(f_{a,p}-f_o\right)\frac{r_e}{c_o}\)
\(\dot{f_i}=\left(f_b-f_i\right)\frac{r_r}{c_i}\)