Static iteration, stabilization and physical consistency
Finishing a calculation and obtaining a credible steady-state result are different conditions. Recycle circuits make the distinction especially important.
A calculation depends on a complete process description
The earlier lessons defined material, feed, equipment inputs and connections. The static calculation brings these parts together. Components, densities and size classes establish the material basis; feed quantities and distributions establish the entering material; models and ports determine how it passes through the circuit.
A routing point cannot supply a missing connection or perform a split or mix. Likewise, a numerical output cannot resolve an input whose unit or meaning is unclear. Establishing the model’s basis before the run makes a later balance or product comparison interpretable.
Why a recycle introduces repeated calculation
In an open circuit, material passes from the feed through downstream models. A recycle creates a dependency on material returning from a downstream result. The current estimate of that returning material influences the next calculation pass, which in turn can change the returning result.
DPSIM’s static solver performs the configured number of iterations. A completion message establishes that those passes finished; it does not by itself establish numerical convergence. The relevant question is whether the quantities needed by the study have stabilized sufficiently.
The interface reports the progress of the configured passes
Static Run selects the calculation mode, and Simulate starts the configured iterations. Simulation → Run Static Simulation provides the corresponding menu command. The status area indicates progress and completion, after which calculated stream values can be inspected.
The elapsed time displayed in the capture belongs to that calculation. It does not specify how long another circuit will require, nor is it an acceptance criterion for the numerical result.
Stabilization is judged using quantities relevant to the study
The number of passes needed and an appropriate acceptance tolerance depend on the circuit, selected models, data and engineering purpose. A product flow alone may appear stable while a recycle, size characteristic or component distribution still changes.
| Quantity to compare | What it helps reveal |
|---|---|
| Recycle and product dry-solids flows | Stabilization of circulating material and final output. |
| Water flow and percent solids | Changes in the slurry condition as well as the dry-solids balance. |
| Product P80 and component grades | Stabilization of product characteristics rather than total flow alone. |
A comparison at a larger iteration count is informative only if the process inputs remain unchanged. Otherwise, a result difference could be a response to a changed assumption rather than incomplete settling of the same calculation.
Numerical stabilization does not replace physical interpretation
A stable result can still reflect an incorrect connection, input basis or model assumption. Balances and the expected direction of separation provide a different kind of check. Starting with one unit operation makes the feed and product relationships easier to explain than starting with every stream in the plant.
| Relationship | Interpretation |
|---|---|
| Dry-solids balance | For a unit without solids creation or loss, the product solids should account for its feed solids. |
| Water balance | Water in feeds and added to the unit should appear in the relevant products. |
| Component balance | The component entering the unit should be traceable to its destination products. |
| Size transformation | The distributions should be consistent with the selected model’s action. |
| Separation direction | The connected feed, oversize/undersize or overflow/underflow ports should match the intended process. |
Consistent physical bases are essential: water volume flow cannot be added directly to solids mass flow. An apparently unexplained imbalance may instead be a comparison between quantities with different units or definitions.
Exercise: distinguish an unfinished solution from a changed process
- Confirm the material, feed, connections and model inputs in the saved simple circuit. Select Static Run and start Simulate, or use Simulation → Run Static Simulation. Wait for completion.
- Record quantities relevant to the study, including a recycle stream if present. Keep the same units and definitions for the comparison.
- In Settings… → Static Simulation Iterations, choose a larger count and calculate again without changing process inputs. Compare the recorded quantities.
- If changes are still significant for the study, investigate the setup and continue checking. If a result is missing or physically unexpected, trace the circuit from the feed: connection direction, feed units, size-class order, composition and model inputs. A simpler circuit can help locate the first unexpected output.
- Once the important quantities are adequately stable, inspect one unit’s solids, water and component balances and the expected product behavior.