Evaporation of brine water

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Hi. I want to know how to calculate the amount of the evaporation of the brine water from RO system with a TDS of 7400 mg/l.

I want to use this info. for designing the area for the lagoon system for the injected water.

I have the annual rainfall and evaporation in the area under study but I know that the amount of TDS and EC will affect the amount of evaporation?

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1 Answer

  1. Here’s a step-by-step approach to estimate the evaporation and design the lagoon system:

    1. Basic Evaporation Calculation

    Use the following general formula for evaporation:

    E=(P−R)AE = \frac{(P - R)}{A}E=A(P−R)​

    Where:

    • EEE = evaporation rate (m/year)
    • PPP = annual precipitation (m/year)
    • RRR = runoff or additional water losses (m/year)
    • AAA = area of the lagoon (m²)

    2. Correcting Evaporation for High TDS

    High TDS affects evaporation by reducing the vapor pressure at the water surface. The reduction in evaporation can be estimated using empirical factors. For example, a brine with a high salinity (like seawater, around 35,000 mg/L TDS) typically reduces evaporation by 5-10%.

    To estimate the correction for 7400 mg/L TDS, use the following approximation:

    Eadjusted=E×(1−F)E_{adjusted} = E \times (1 - F)Eadjusted​=E×(1−F)

    Where:

    • EadjustedE_{adjusted}Eadjusted​ = evaporation rate adjusted for TDS
    • FFF = salinity correction factor. For TDS of 7400 mg/L, this could be approximately 3-5%.

    3. Relationship between TDS and EC

    The Electrical Conductivity (EC) is roughly proportional to the TDS. The empirical relationship often used is:

    EC(μS/cm)=TDS(mg/L)×0.67EC (\mu S/cm) = TDS (mg/L) \times 0.67EC(μS/cm)=TDS(mg/L)×0.67

    So, for a TDS of 7400 mg/L:

    EC≈7400×0.67=4958 μS/cmEC \approx 7400 \times 0.67 = 4958 \, \mu S/cmEC≈7400×0.67=4958μS/cm

    4. Designing the Lagoon Area

    Once you have the corrected evaporation rate, the lagoon area can be calculated based on the volume of brine produced and the annual water balance in the area.

    The equation for the lagoon area is:

    Alagoon=VbrineEadjustedA_{lagoon} = \frac{V_{brine}}{E_{adjusted}}Alagoon​=Eadjusted​Vbrine​​

    Where:

    • AlagoonA_{lagoon}Alagoon​ = lagoon area (m²)
    • VbrineV_{brine}Vbrine​ = volume of brine water produced annually (m³)
    • EadjustedE_{adjusted}Eadjusted​ = adjusted evaporation rate (m/year)

    Steps to Follow:

    1. Determine the local annual rainfall and evaporation rate.
    2. Calculate the raw evaporation using the basic formula.
    3. Adjust the evaporation rate for TDS using the correction factor (3-5% for 7400 mg/L).
    4. Determine the brine production rate from the RO system.
    5. Calculate the required lagoon area using the adjusted evaporation rate.

    If you provide the specific environmental conditions (temperature, wind speed, etc.) and the volume of brine, I can help refine the calculation further.

    1 Comment

    1. Hi. Thanks for your reply. The info of the situation is: TDS: 7403 mg/l, brine water volume: 286 m3/day, average annual vapor: 51%, ave annual wind speed: 14 km/h, ave annual pressure: 1013 m.bar, average annual temp: 15 C. Thank you in advance

      1 Comment reply

      1. Be careful. The evaporation rate you need is not for 7400 mg/l, but for whatever the saturation value of the pond is. As the water evaporates the TDS will increase. Eventually, the incoming flow will have a low TDS compared to the pond and the dilution achieved by the incoming flow will be negligible. The likely final concentration will be somewhere around 300,000 mg/l, approximately the saturation point of NaCl.