Cyclic Steady State

A PSA/TSA process does not reach a steady state in the usual sense — instead it settles into a cyclic steady state (CSS), where every cycle is identical to the one before. Performance metrics such as purity and recovery are only meaningful once CSS is reached, because the first cycles still carry the memory of the (arbitrary) initial condition.

Skarstrom can detect CSS automatically and stop the run early, so you do not have to guess how many cycles are needed. Configure it on the Cycle Design → Cycle Data tab with the CSS Convergence Method drop-down. The Number of Cycles still acts as an upper limit; CSS detection simply stops the run sooner once the criterion is met, and the solver status becomes Cyclic Steady State.

Convergence methods

None

No CSS test — the solver runs the full Number of Cycles. Use this when you want a fixed number of cycles regardless.

Molar Profile

Compares the end-of-cycle total molar-concentration profile of the current cycle with the previous cycle. Convergence is declared when

\lVert \mathbf{c}_{\text{curr}} - \mathbf{c}_{\text{prev}} \rVert \;\le\; \varepsilon_{abs} + \varepsilon_{rel}\,\lVert \mathbf{c}_{\text{curr}} \rVert

where the norm is taken over all cells. You set the Molar profile absolute tolerance $\varepsilon_{abs}$ (default 1×10⁻⁴) and the Molar profile relative tolerance $\varepsilon_{rel}$ (default 1×10⁻⁴). This is a direct, profile-based test of whether the bed state has stopped changing from cycle to cycle.

Mass Balance (Total)

Checks that, over a whole cycle, the moles entering the bed equal the moles leaving:

\frac{\lvert n_{\text{in}} - n_{\text{out}} \rvert}{n_{\text{in}}} \;\le\; \varepsilon_{mb}

summed over all steps and all faces. You set the Mass balance tolerance $\varepsilon_{mb}$ (default 0.005, i.e. 0.5%) and a Minimum cycles count (default 5) before the test is allowed to trigger. At CSS there is no net accumulation, so the closing mass balance is a robust convergence indicator.

Mass Balance (Per-Component)

The same as above but evaluated per component, using the worst-offending component:

\max_i \frac{\lvert n_{\text{in},i} - n_{\text{out},i} \rvert}{n_{\text{in},i}} \;\le\; \varepsilon_{mb}

This is the strictest test and the safest choice when component-level purity and recovery are the outputs you care about.

Practical guidance

Set a generous Number of Cycles (an upper bound) and let a CSS method stop the run when converged.
The Molar Profile method is a good general default; switch to Mass Balance (Per-Component) when you need confidence in component-level KPIs.
If a run reaches the cycle limit without converging, either increase the limit or loosen the tolerance — and check that the cycle actually can close (e.g. that feed, product and purge flows are balanced).
Keep enough cycles logged (Maximum Number of Cycles to Log in the solver settings) to plot the approach to CSS and confirm the last cycles overlay.