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Application of multi-trial Monte Carlo design simulations to the design of
to produce a final effluent with a required maximum number of faecal coliform bacteria

Download the Monte Carlo design program for WSP design

Read how to enter parameter value ranges and how to do a multi-trial program run

The design equations used for faecal coliform removal in WSP are:

(a) Anaerobic ponds

1. The first-order equation for faecal coliform (FC) removal in a completely mixed reactor:

Ne = Ni/(1 + kB(T)θ)

2. An Arrhenius equation for the variation with temperature of the first-order rate constant for FC removal in anaerobic ponds (Mara, 2004):

kB(T) = 2(1.07)T–20


Ne and Ni are the FC numbers per 100 ml of the anaerobic pond effluent and the raw wastewater, respectively;

kB(T) is the first-order rate constant for FC removal in anaerobic ponds at T , day–1; and

θ is the mean hydraulic retention time in the anaerobic pond, days – defined as the pond volume V in m3 divided by the raw wastewater flow Q into the pond in m3/day.

The retention time θ is determined from the permissible volumetric BOD loading on anaerobic ponds at the design temperature T . Details are given in our on-line Pond Design Manuals.

(b) Facultative and maturation ponds

1. The ‘abbreviated’ Wehner-Wilhelm equation for FC removal in dispersed flow reactors:

Ne  =  Ni[4a/(1 + a)2]exp[(1 – a)/2d]

where a  = ; q = V/Q (ie, the nominal mean hydraulic retention time), days; and d is the pond dispersion number, which is zero for plug-flow reactors and infinity for completely mixed reactors, and thus somewhere between these two extreme values for dispersed flow reactor.

2. The simple equation for d given by von Sperling (2003):

d = (L/B)–1

3. The two equations for kB given by von Sperling (1999):

kB(20) = 0.92D–0.88q–0.33                               

 kB(T) = kB(20)(1.07)T–20                               

where L, B and D are the pond length, breadth and depth, respectively, m; and kB(T)  is now the first-order rate constant for FC removal in a dispersed flow reactor at a design temperature of T , day–1.

The equation for kB(20) was derived by von Sperling from faecal coliform removal data obtained from 33 facultative and maturation pond systems in tropical and subtropical Brazil (latitude 7–24º S).

The retention time in the facultative pond depends on the permissible surface BOD loading at the design temperature T and on the rate of net evaporation, but it should never be lower than a minimum of 4 days. The retention times in the maturation ponds must be less than that in the facultative pond, but never lower than a minimum of 3 days; additionally the surface BOD loading on the first maturation pond must not be greater than 75% of that on the facultative pond. Details are given in our on-line Pond Design Manuals.

The whole design procedure is now done by Monte Carlo simulation as described by von Sperling (1996) for facultative ponds.

The procedure is illustrated by Gawasiri (2003), who compared FC removals in WSP series estimated by this Monte Carlo method (allowing each design parameter to vary by ±20% – but, of course, any percentage could be chosen), with those predicted by the 'classical' Marais design procedure.

Further details of both procedures are given by Mara in Domestic Wastewater Treatment in Developing Countries (Earthscan Publications Ltd, London, 2004).

A detailed discussion of waste stabilisation pond design is given by Chimwemwe Gawasiri in his MSc thesis Modern Design of Waste Stabilization Ponds in Warm Climates: Comparison with Traditional Design Methods (This is a 1.8Mb PDF document containing 138 pages.)

: E-mail either Professor Duncan Mara or, for questions about the Monte Carlo program, Dr Andrew Sleigh.

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