Determine rate equations for entire kinetic scheme
The Biomass-equation is:
$$\frac{\mathrm d B}{\mathrm d t} = -(k_1 + k_2) B$$
The (volatile + gases)$_1$ equation is:
$$\frac{\mathrm d VG_1}{\mathrm d t} = k_1 B$$
The (volatile + gases)$_2$ equation is equal to equation for (Char)$_2$:
$$\frac{\mathrm d VG_2}{\mathrm d t} = \frac{\mathrm d C_2}{\mathrm d t} = k_3 C_1$$
(It might be that it needs to be multiplied by 1/2.)

And the equation for (char)$_1$ is this:
$$\frac{\mathrm d C_1}{\mathrm d t} = k_2 B-k_3 C_1$$

The equations for the complete set of (char)s and (volatile+gases)s are then the sums of the solutions for $C_1$ and $C_2$ resp. $VG_1$ and $VG_2$.



For initial concentration of $B(0)=1$ and everything else $f(0)=0$, as well as $k_1=2$, $k_2=10$ and $k_3=3$, you should get something similar to this: