EngiMetric Arena / Quick Challenge
How many RO elements can you actually buy?
What you should take away: Distinguish the membrane area a design requires from the element count that can actually be installed, and recognise that the installed flux is therefore lower than the design flux.
The situation
A seawater reverse-osmosis plant has to deliver 5 000 m³ of permeate per day at a design flux of 15 LMH, using 37 m² elements loaded six to a vessel. Your procurement package is written against the membrane area the design requires. The supplier can only ship whole elements, in whole pressure vessels. How many elements must the array actually contain?
Given
| Quantity | Value | Unit | Note |
|---|---|---|---|
| Permeate required | 5 000 | m³/day | The plant product duty. |
| Design flux | 15 | LMH | L·m⁻²·h⁻¹. The flux the design assumes when sizing area. |
| Active area per element | 37 | m² | Nominal active membrane area of one element. |
| Elements per pressure vessel | 6 | elements | A vessel is loaded with a whole number of elements. |
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.
Your answer
Hints
- Start with the area, not the elements. Required area is the permeate flow divided by the design flux — but watch the units: the engine wants m³/h and the plant is specified in m³/day.
- Divide that area by the area of one element. That gives the theoretical minimum number of elements. Now ask whether a supplier can deliver that number.
- A pressure vessel is loaded with a whole number of elements. If the minimum does not divide evenly into vessels of six, you must round the vessel count up — and every one of those vessels is filled.
Where that comes from
Each limit, checked
Why
- The required area is permeate flow ÷ design flux: 208.33 m³/h × 1 000 ÷ 15 LMH = 13 888.9 m².
- Dividing by a 37 m² element gives 375.4, so the theoretical minimum is 376 elements. **That number cannot be bought.**
- Vessels hold six elements, so 376 elements need ⌈376 ÷ 6⌉ = 63 vessels. Every one of those vessels is filled, so the array carries 63 × 6 = **378 elements**.
- The installed area is therefore 13 986 m², about 0.7 % more than required, and the plant will run at roughly 14.9 LMH rather than the 15 LMH assumed. The design flux is an input to sizing, not a guarantee of operating flux.
- This is why the installed count, not the required count, is what a procurement package and a bill of quantities have to carry. Sizing to 376 would specify a fraction of a vessel that does not exist.
What this challenge does not establish
- Flux is treated as uniform across the array. Real systems develop a flux profile along the brine path, so the first element runs harder than the last.
- Concentrate-side flow maldistribution and fouling allowance are not modelled here.
- A sizing calculation is preliminary. Membrane selection, pretreatment and the vendor warranty terms govern the final purchase.