A litre of water arriving at a tap on the hundred-and-fiftieth floor of a Gulf tower has been made from seawater, pumped inland, and lifted six hundred metres. By the time it reaches the fixture it carries about six kilowatt-hours per cubic metre on the coast and ten inland — and the tower will evaporate several times that volume off its cooling towers without anyone recording the energy that went into making it. This is the accounting nobody does, because the desalination engineer stops at the plant fence and the building engineer starts at the site boundary.

1 · The chain nobody adds up

Every stage of this journey is well understood in isolation, and each has its own literature, its own specialists and its own conferences. What is missing is the sum.

The reason this matters is not moral. It is that the four terms respond to completely different design decisions, they are not the same size in every city, and the cheapest term to fix is almost never the one being optimised.

2 · What a cubic metre costs to make

Reverse osmosis has to raise the feed above the osmotic pressure of seawater and hold it there. The ideal work is set by that pressure and the recovery ratio, and the real work is that divided by pump efficiency [1]:

\[ E_{RO} \;=\; \frac{P}{36\,R\,\eta}\Big(1 - \varepsilon_{ERD}\,(1-R)\Big) \;+\; E_{aux} \qquad \text{kWh/m}^3 \]

with \(P\) the feed pressure in bar, \(R\) the recovery fraction, \(\eta\) the high-pressure pump efficiency and \(\varepsilon_{ERD}\) the effectiveness of the energy recovery device. The bracket is the whole story of the last thirty years: the brine leaves the membrane at almost full pressure, carrying \((1-R)\) of the feed with it, and a pressure exchanger hands that energy straight back to the incoming stream at around 96 % efficiency.

Why the recovery ratio cuts both ways Raising recovery reduces the volume of brine you have to pressurise, which looks like an energy saving — and it is, if there is no energy recovery device. With a pressure exchanger fitted, that brine energy was coming back anyway, so the saving largely evaporates while the fouling, scaling and osmotic pressure penalties of running at high recovery remain. This is the over-design paradox in another guise: the lever that worked before you fitted the device stops working after you fit it.

3 · Interactive: the specific energy of a litre, stage by stage

Set the plant, the transmission route and the tower. The bars are the four stages of the journey; the marker is the total the fixture actually receives. Then move the site from the coast to the interior and watch which term dominates.

Delivered specific energy, from seawater to the top-floor tap
RO from the equation above. Transmission and building lift both from E = h/(367·η), the same relation used throughout the site for pumping energy. Transmission head is static lift plus friction over the route; the building term is tower height plus a 30 m friction and residual allowance.
Open Pump energy & specific energy as a calculator
Membrane feed pressure. Rises with salinity, temperature and membrane age.
Permeate as a share of feed. Gulf seawater rarely justifies more than about 45 %.
Pressure exchanger effectiveness. Drag to zero to see what this same plant would cost without recovery; the 1990s figure of about ten also carried a lower recovery ratio and worse pumps.
Static lift plus friction from the plant to the site. Coastal ≈ 55 m; Riyadh from the Gulf coast ≈ 1,200 m.
Height the domestic riser has to serve.
Desalination
3.5 kWh/m³
Transmission
0.19 kWh/m³
Lift in the tower
2.45 kWh/m³
At the tap
6.1 kWh/m³
Largest term

At the default — a modern coastal plant, a short transmission route and a 600 m tower — the tap receives water at about 6.1 kWh/m³, of which the building itself is responsible for 2.45. Now drag the transmission head to 1,200 m, which is roughly what it takes to move water from the Gulf coast to the Riyadh plateau: the total becomes 10.1 kWh/m³ and transmission, not desalination, becomes the largest single term in the chain. Two conclusions follow immediately. In a coastal tower the building's own lift is the biggest thing the design team controls, and it is worth the zone-boosting argument that halves it. In an inland tower the building's lift is a detail, and every litre not used is worth far more than the pump energy suggests — which changes the economics of reuse completely.

4 · The part that is evaporated

The domestic water in a tower is the small stream. The large one is condenser water, and it does not leave through a drain — it leaves as vapour. The physics is fixed: rejecting a megawatt of heat by evaporation takes about 1.5 m³ of water an hour, because that is what the latent heat of vaporisation demands. Blowdown adds to it, at a rate set by how many times you are prepared to concentrate the dissolved solids before dumping them:

\[ \dot{V}_{makeup} \;=\; \dot{V}_{evap}\left(1 + \frac{1}{C-1}\right), \qquad \dot{V}_{evap} \approx 1.5\,\dot{Q}_{rej}\ \ \text{m}^3\text{/h per MW} \]

At four cycles of concentration a 50 MW plant needs 100 m³/h, or 2,400 m³ a day. In the Gulf that water is desalinated, because there is no other kind. The tower is therefore boiling desalinated seawater to keep itself cool, and the energy that made that water does not appear in any building energy model, any LEED calculation or any chiller efficiency comparison.

5 · Interactive: the evaporation ledger

This puts the two energies side by side: the electricity the chiller plant consumes, and the embodied energy of the water its cooling towers evaporate. They are not the same order of magnitude — but the second is not a rounding error either, and it is the one nobody counts.

Chiller electricity vs the embodied energy of evaporated water
Makeup from the equation above. Embodied energy is makeup volume × the delivered specific energy from the previous chart. Chiller electricity from the rejected heat, taken as 1.25 × the cooling load, divided by the plant COP.
Total rejection at the towers, including chiller work.
Set by makeup water chemistry and the treatment programme.
From the first chart. Coastal ≈ 6; Riyadh ≈ 10; a gravity-fed mountain city ≈ 0.5.
Chillers plus auxiliaries. A colder wet bulb buys a better number.
Annual operating hours at full rejection.
Makeup
2,400 m³/d
Annual water
400,000
Embodied in that water
2.45 GWh
Chiller electricity
29.1 GWh
Water as % of plant
8.4 %

On the coast the water a 50 MW plant evaporates carries embodied energy equal to about 8 % of what the chillers themselves consume. Move the same building to Riyadh and two things happen at once, in opposite directions: the water becomes more expensive to deliver, pushing the embodied term to roughly 14 %, while the drier air and lower wet bulb make the chillers more efficient, which raises the ratio further still. The inland tower has the cheaper cooling plant and the dearer water, and a design optimisation that sees only the electricity meter will get that trade exactly backwards. This is also the honest answer to a question people expect to be alarming: the embodied water energy is not larger than the chiller load, and anyone claiming otherwise is selling something. It is roughly a tenth of it — consistently, invisibly, and for the life of the building.

6 · Which levers actually move

Once the ledger is written down, the design responses sort themselves by size rather than by fashion.

7 · Interactive: the recovery stack

Start with the makeup a plant needs and take it apart. Each measure removes a slice; what is left is the potable or treated-effluent water you actually have to buy, and the energy that came with it.

What each measure removes from the makeup bill
Cycles from the makeup equation. Condensate from the psychrometrics of the outdoor-air load, at the stated air volume and coil condition. Greywater as a share of the remaining demand. Energy is the residual volume at the delivered specific energy.
What the treatment programme can hold. The base case is four.
Total fresh air across the tower. Sets how much condensate exists to collect.
Realistic capture. Floor-level units are hard to collect from; central plant is easy.
Treated greywater available for non-potable use.
Base makeup
2,400 m³/d
Saved by cycles
240 m³/d
Condensate
20 m³/d
Still to buy
1,900 m³/d
Energy avoided
1.1 GWh/yr

The stack is honest about proportions, and the proportions are the point. At the default, raising the cycles of concentration removes as much water as the entire greywater plant does — and it costs almost nothing in capital. Condensate is small in volume but disproportionately valuable: it is the only stream in the building that arrives cleaner than the mains supply, and capturing it well removes a treatment cost as well as a water cost. Greywater is the biggest recoverable volume and the biggest capital commitment. What remains after all three is still the majority of the bill — which is the realistic conclusion. Reuse does not make a Gulf tower water-neutral. It makes it about a fifth better, for a cost that is justified by the delivered energy behind every cubic metre rather than by the water tariff alone.

8 · What this changes on the drawing

The one-line summary A litre reaching the top floor of a coastal Gulf tower carries about six kilowatt-hours per cubic metre; inland it carries ten, and transmission — not desalination — is the largest term. The building then evaporates several times its own drinking water off the cooling towers, carrying embodied energy equal to roughly a tenth of what the chillers consume, on nobody's energy model. The levers, in order of return, are cycles of concentration, condensate capture, greywater, and finally the pumping energy the MEP engineer usually spends all the effort on — and the order changes between the coast and the interior, which is precisely why the number belongs in the design basis rather than in a sustainability appendix.

References & standards

  1. Voutchkov, N. Desalination Engineering: Planning and Design — specific energy consumption, recovery ratio and energy recovery device performance in seawater reverse osmosis.
  2. ASHRAE Handbook — HVAC Systems and Equipment, Cooling Towers chapter: evaporation rate, drift, blowdown and cycles of concentration.
  3. ASHRAE Handbook — Fundamentals, Psychrometrics chapter: moist-air properties used for the condensate calculation.
  4. International Desalination Association and Global Water Intelligence — published specific energy benchmarks for SWRO plants with and without pressure-exchanger energy recovery.
  5. Saline Water Conversion Corporation (SWCC) — Saudi water transmission system characteristics: coastal plants, inland pumping stages and delivered head to the central region.
  6. ASHRAE Design Guide for Tall, Supertall, and Megatall Building Systems, 2nd ed. — domestic water pumping energy and heat rejection strategy in tall buildings.
  7. Saudi Building Code SBC 501 / SBC 701 — mechanical and plumbing provisions, and Saudi Water Authority guidance on non-potable reuse for cooling tower makeup.
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