Governing Equations

Skarstrom is a one-dimensional adsorption process simulator that uses a finite volume discretisation scheme to solve the governing equations. The governing equations are composed of coupled non-linear partial differential equations (PDEs) and algebraic equations.

Partial Differential Equations (PDEs)

The simulation is based on five conservation equations:

1. Overall Mass Balance - Ensures mass conservation throughout the packed bed
2. Momentum Balance - Describes fluid flow using Darcy's law
3. Component Mass Balance - Accounts for axial dispersion, convection, and adsorption
4. Energy Balance - Thermal balance between gas and adsorbent phases
5. Wall Energy Balance - Heat transfer between wall and surroundings

Algebraic Equations

Three algebraic relationships close the system:

• Equilibrium Isotherm - Adsorption equilibrium relationship
• Kinetic Rate Model - Mass transfer kinetics
• Equation of State - Ideal gas law

Numerical Solution

The PDEs are discretized using a finite volume method with a backwards difference formula as a time-stepping scheme. The resulting non-linear algebraic system is solved iteratively at each time step.