Define the streams and calculation basis
Let P be RO permeate and T the treated water blended with it without passing through RO. With respective flows QP and QT, makeup M is QP + QT and f = QP/M. For species i, Cblend,i = f × CP,i + (1−f) × CT,i. This assumes complete mixing, flows on the same basis and no reaction during blending.
DOE and EPA describe how evaporation concentrates dissolved solids in cooling towers. For a conservative species, the ideal balance allows Crecirculating,i ≈ N × Cblend,i, where N is cycles of concentration. Reactions, chemical dosing, precipitation or external inputs require an expanded balance. Blend pH cannot be calculated as the arithmetic average of the two stream pH values.
Illustrative blend-quality example
The following analyses are our own assumptions, unrelated to an actual installation. Choose f = 0.60: 60% of makeup as permeate and 40% as treated water. Calcium hardness and alkalinity are reported in mg/L as CaCO3, and silica in mg/L as SiO2.
At five cycles, the conservative model gives 390 mg/L chloride and 66 mg/L silica as SiO2, assuming no precipitation or other inputs. The table describes makeup quality but does not calculate scaling risk, which also needs information including pH and temperature. It does not establish microbiological control either.
| Species or measure | Treated water T | Permeate P | Blend: 60% P + 40% T |
|---|---|---|---|
| Chloride, mg/L | 180 | 10 | 78 |
| Silica, mg/L as SiO2 | 30 | 2 | 13.2 |
| Calcium hardness, mg/L as CaCO3 | 200 | 5 | 83 |
| Alkalinity, mg/L as CaCO3 | 160 | 5 | 67 |
Find the species requiring the greatest permeate fraction
Assume, solely for this exercise, recirculating-water maxima of 400 mg/L chloride and 80 mg/L silica as SiO2 at five cycles. These are not recommended tower limits. Makeup concentrations would need to remain at 80 and 16 mg/L respectively.
When CT exceeds CP, the minimum fraction for a species is f = (CT−Ctarget)/(CT−CP). For chloride: (180−80)/(180−10) = 0.588. For silica: (30−16)/(30−2) = 0.50. The more demanding constraint in this exercise requires approximately 58.8% permeate; the table uses 60%. In a real project, variability and operating margin need assessment before setting the blend target.
The physical fraction must remain between 0 and 1. If the target is below CP, these two streams cannot achieve it. If the target equals or exceeds CT, no permeate is required for that constraint. The formula above assumes CT is greater than CP; if they are equal, changing the blend proportion does not change that concentration.
Include RO in the water balance
Assume evaporation E of 10 m³/h, five cycles and negligible drift or leakage. The ideal relationship described by DOE gives blowdown B = E/(N−1) = 2.5 m³/h and makeup M = E + B = 12.5 m³/h. With the selected blend, QP is 7.5 m³/h and QT is 5 m³/h.
Assuming 75% RO recovery, RO feed is 7.5/0.75 = 10 m³/h and concentrate is 2.5 m³/h. Where both branches originate from the same treated water, required flow before the split is 10 + 5 = 15 m³/h. Account separately for RO concentrate and tower blowdown, alongside additional washing streams omitted from this example.
Maintain the proportion as the water changes
Verify analyses of both streams, actual flow in each branch and blended-water quality. A valve-position relationship alone does not establish a volumetric proportion. If the analysis of T or P changes, recalculate the constraints and review both the blend setting and cycles.
DOE recommends metering makeup and blowdown and comparing cycles; conductivity supports monitoring, while species balances retain the reason for each constraint. Integration should define the response to permeate shortages, storage and acceptable transient quality, alongside the tower's treatment programme.