simulating advention diffusion reaction of chemical reaction flow with mole increase

[oscarhx]

I am working on simulating chemical reaction flow in a gas phase using Pore Network Modeling. The reaction involves 2 moles of reactant entering and 4 moles of product exiting the system.The challenge is that, in PNM, Stokes flow is typically used to solve for the flow field, but this approach doesn't directly account for varying concentrations.
In my case, the reaction is assumed to follow a simple first-order reaction kernel. Initially, I was considering the iterative coupling approach where:

1. The velocity field Un is solved using the concentration field Cn via Stokes flow equations.
2. The concentration field Cn is updated using the velocity field Un through the advection-diffusion-reaction equation.

However, I realized this approach isn't feasible for my scenario, as the concentration varies across different pores, and the Stokes equation in PNM is calculated using throat hydraulic conductance, which doesn't directly incorporate varying concentrations Cn.

Given this, is there a way to solve my problem? Specifically, if I want to estimate the first-order reaction rate constant k by fitting the PNM model to experimental data (curve of gas inflow rate vs. its conversion ratio), what would be the appropriate approach to couple the flow and reaction dynamics in a way that accounts for the density changes?