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

The energy balance can be solved assuming local thermal equilibrium (a single lumped gas/solid temperature) or local thermal non-equilibrium (separate gas and solid temperatures) — see the energy balance.

Algebraic Equations

Several algebraic relationships close the system:

• Equilibrium Isotherm - Adsorption equilibrium relationship
• Kinetic Rate Model - Mass transfer kinetics
• Transport Correlations - Axial dispersion, thermal conductivity and heat-transfer coefficients
• Equation of State - Ideal gas law

Numerical Solution

The PDEs are discretised using a finite volume method in space. The resulting system of coupled differential-algebraic equations (DAEs) is integrated in time with a variable-order (BDF), variable-step implicit solver (SUNDIALS IDA). At each step a non-linear system is solved by a Newton iteration. Solver tolerances and step limits are described in Running the Solver.