EngiMetric Arena / Engineering Trade-off
Choose a recovery rate that the plant can actually run
What you should take away: Evaluate a multi-constraint design decision against explicit limits and accept that a range of answers is correct, rather than searching for a single optimum.
The situation
A brackish-to-seawater RO plant is being set a design basis. The site has fixed two limits: the concentrate stream must stay below a stated salinity ceiling, and the electrical budget per cubic metre of permeate must not be exceeded. Within those limits, several recoveries are acceptable. Specify one.
Given
| Quantity | Value | Unit | Note |
|---|---|---|---|
| Feed flow | 100 | m³/h | Design feed rate. |
| Feed TDS | 35 000 | mg/L | Feed salinity. The rejected salt ends up in the concentrate. |
| Salt rejection | 99.7 | % | Held constant across the range, which is optimistic at high recovery. |
| Feed pressure | 55 | bar | Used by the energy engine for every candidate recovery. |
Constraints
- Membrane elements are supplied whole. A fraction of an element cannot be ordered.
- Pressure vessels are loaded with a whole number of elements — 6 per vessel here.
- Every vessel in the array is filled to the same element count.
Limits this decision must satisfy
| Limit | Requirement | If it is breached |
|---|---|---|
| Concentrate TDS | ≤ 70000 mg/L | Above the site ceiling the concentrate salinity limit is exceeded, which drives scaling risk and typically a recovery reduction. |
| Net specific energy with ERD | ≤ 2.75 kWh/m³ | Above the electrical budget the operating cost and the pump duty exceed what the project has approved. |
More than one recovery or efficiency can satisfy every limit at once. There is no single right number here — find a value that holds all of them.
Your answer
Hints
- There is no single right answer here. Both limits have to hold at once, and each one is evaluated against the engines for the recovery you propose.
- Concentrate salinity rises steeply with recovery, because the same rejected salt ends up in a shrinking stream. Check which of the two limits that pushes against.
- Do not assume the energy budget is the one that binds. Work out what the net specific energy actually does across the range — it may not move the way you expect.
Where that comes from
Each limit, checked
Why
- Two authoritative engines are called for each candidate: the RO mass balance engine, which returns concentrate TDS, and the RO energy engine, which returns net specific energy after the ERD credit.
- Concentrate salinity rises steeply with recovery. Measured against the 70 000 mg/L site ceiling, the boundary sits between 50 % and 51 % recovery: 45 % gives 63 550 mg/L, 49 % gives 68 527, 50 % gives 69 895 — still inside — and 51 % gives 71 319, which is not.
- The energy result moves the opposite way to the intuition. Net specific energy falls as recovery rises, from 2.44 kWh/m³ at 35 % to 2.03 kWh/m³ at 60 %, because the permeate flow grows faster than the power required. So the 2.75 kWh/m³ budget is never the binding constraint here.
- That is itself the useful finding. The feasible set is a band — anything from low recovery up to about 50 % — bounded by concentrate salinity, not by energy, and every value inside it is a defensible choice.
- Choosing the top of the band maximises water production within the approved envelope; choosing lower inside it buys margin against the salinity ceiling for a season of higher feed salinity, which is a commercial decision rather than an error.
- What this does not claim is a universal optimum. A real design would also weigh membrane life, capital cost, intake salinity across a year, and product quality — none of which these two engines model.
What this challenge does not establish
- Salt rejection is held at the stated 99.7 % across the whole range. Real rejection falls as recovery rises, so the concentrate figure is optimistic at the top of the band.
- The energy engine uses a single feed pressure for every candidate; it does not re-derive pressure from the osmotic balance as recovery changes.
- No scaling, fouling or boron/boride assessment is implied. Scaling risk in particular is what usually caps real recovery, and it is not modelled here.
- Feed salinity is a single value, not a seasonal range.