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Flow Formulae for Reed Beds

REED BED performance for industrial wastewaters is based on the following parameters;

  • inlet BOD (Cin) and outlet BOD (Cout) concentrations
  • volumetric flow rate (Q)
  • area (A)
  • depth (h)
  • detention time

BOD is Biological Oxygen Demand and is a measure of the oxygen consumed during bacterial breakdown of organic matter in water.

Established first-order flow models have been extensively used for design of constructed wetlands in the past, however more complex models have come to be used in recent times. These complex models require large amounts of data, and this may not be available for particular tasks.

Therefore, outlined below is the simple approach that will yield appropriate results.

Flow Performance

Whilst steady flow is assumed through the reed bed, the actual performance can vary significantly and can be affected by;

  • fluctuations in input flow
  • changes in BOD, pH, and other parameter concentrations (e.g. Phosphorous, Nitrogen, Suspended Solids) 
  • changes to internal storage due to plant root development and debris build-up
  • weather (i.e. temperature, rainfall, and evaporation)
  • reed bed ecosystem factors

Operation and maintenance routines can ameliorate some of these dynamic aspects. Nevertheless, plug flow (i.e. linear flow along the reed bed cell itself) is assumed to occur.

Design Parameters

Hydraulic parameters

The hydraulic regime of a reed bed will be controlled by the permeability of the media and the hydraulic gradient.

Flow in the reed bed is governed by Darcy’s Law and can be expressed by the equation …

Q = k A i    …where 

Q = wastewater average flow rate (m3/day) 

k = hydraulic conductivity of the medium (m3 /(

A = cross-sectional area (m2)

i = hydraulic gradient

kf= hydraulic conductivity (m/day) = 12,600 Dp1.90 

Dp is media particle size 

kf is an estimate of the clean bed hydraulic conductivity, but this will not occur in practice because of the deposition of fine solids and the taking up of pore space with plant roots. If 1/3 of the pore space is blocked, there will be a 10% decrease in hydraulic conductivity. 

To account for headloss through the reed bed, assume water slope approximates bed slope and is 0.2% (i.e. 1 in 500).

Choose a nominal width W of the reed bed.

Flow capacity -> Qd (m3 / day) = kf x W x h x i 

Biological parameters

Using Kickuth’s equation … As  = Q(ln Cin - ln Cout) / kBOD5

where As = surface area of reed bed

Cout = effluent BOD (20 mg/l - the target concentration)

Cin = influent BOD (from measurements mg/l)

kBOD5 = area-based BOD rate constant = 0.1 (for domestic sewage)

This is a first-order kinetics rate model where it is assumed that the oxygen uptake (BOD exertion) is a function of the BOD remaining, and the rate of BOD removed at any time is proportional to the amount of BOD present in the system at the time.

Remaining oxygen demand Ct at any time is expressed by…… Ct = C0 x 10-kt

where C0 is the ultimate oxygen demand at time t = 0

The measured BOD is the difference between the ultimate and remaining oxygen demands, and is given by … BODt = C0 (1 - 10-kt) 

Hydraulic residence time check

With reed bed systems the general detention time is targeted for a minimum of 5 days.

This is checked from the following formula.

Nominal detention time is the volume of free water in the reed bed divided by the volumetric flow rate of water through it.

HRT (t) = e L W h / Qd

where … e = porosity     L = length     W = width     h = wetland water depth 

Source ;  IWA Specialist Group on Use of Macrophytes in Water Pollution Control, (2001), “Constructed Wetlands for Pollution Control”, IWA Publishing, London

More on Reed Bed Wastewater Treatment Systems



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