Summary:

Crank-Nicholson Solution

The article describes the Crank-Nicholson solution used to solve equation (2.25.1) for the mass balance. The fully explicit decomposition of the equation is given in (2.25.15), which is solved for gaseous and aqueous concentrations above and below the water table, respectively. 

The Crank-Nicholson solution combines fully explicit and implicit representations, resulting in equation (2.25.16). This equation is solved using a standard tridiagonal solver, as shown in (2.25.17).

The article also mentions that two methane balance checks are performed at each timestep to ensure strict conservation of methane molecules (except for production minus consumption) and carbon atoms.