Application of the activated sludge model to aerated lagoons

The lagoon system of wastewater treatment covers a spectrum of clearly definable systems differentiated by the degree of mixing and the method of oxygenation. At the one extreme is the oxidation pond, in which the mixing is totally dependent on natural conditions, mainly the wind, and oxygenation is almost entirely due to photosynthesis. The maximum load on the pond and its response to this is largely dictated by the prevailing environmental conditions. At the other extreme is the suspension mixed aerated lagoon, in which both mixing and oxygenation are provided by technological means which give the greatest degree of control over the system. Both the maximum loading and the response to this can be quantitatively estimated. Intermediate systems are defined by the degree of technological assistance with the mixing and oxygenation. On this basis 5 types of lagoon system can be identified, listed in increasing order of the amount of technological assistance applied for the required mixing and oxygenation: (1) Oxidation ponds (2) Mechanically assisted oxidation ponds (3) Aerated oxidation ponds (4) Facultative lagoons (5) Suspension mixed aerated lagoons


INTRODUCTION
The lagoon system of wastewater treatment covers a spectrum of clearly definable systems differentiated by the degree of mixing and the method of oxygenation.At the one extreme is the oxidation pond, in which the mixing is totally dependent on natural conditions, mainly the wind, and oxygenation is almost entirely due to photosynthesis.The maximum load on the pond and its response to this is largely dictated by the prevailing environmental conditions.At the other extreme is the suspension mixed aerated lagoon, in which both mixing and oxygenation are provided by technological means which give the greatest degree of control over the system.Both the maximum loading and the response to this can be quantitatively estimated.Intermediate systems are defined by the degree of technological assistance with the mixing and oxygenation.On this basis 5 types of lagoon system can be identified, listed in increasing order of the amount of technological assistance applied for the required mixing and oxygenation: (1) Oxidation ponds (2) Mechanically assisted oxidation ponds (3) Aerated oxidation ponds (4) Facultative lagoons (5) Suspension mixed aerated lagoons

LAGOON SYSTEMS
In order to bring some definition to the 5 types of lagoon system, the degree of aeration and mixing assistance in the different systems is briefly reviewed below.

Oxidation pond
The oxidation pond has an extensive literature and it is not the objective to review the design procedure here.This is given by Gloyna (1971) and Marais (1966;1970).Only the factors related to mixing and aeration will be briefly discussed.
When wastewater enters an oxidation pond, the settleable fraction of the organic load settles to the bottom of the pond where it forms a sludge layer.In this sludge layer, anaerobic fermentation takes place.As the sludge layer increases so does the fermentation until the accumulation of sludge in the layer equals the rate of sludge removal by fermentation.In this way, the sludge layer could achieve a steady state if environmental conditions remain unchanged.Fermentation in the sludge layer releases energy from the system in the form of methane gas, which escapes to the atmosphere.In this fashion, fermentation contributes significantly to the removal of energy (COD) from the wastewater.Marais (1966;1970) estimated that approximately 30 to 40% of influent energy leaves the system as methane gas.The depth of the sludge layer depends on the organic load per unit area of pond and the water temperature.The fermentation rate is very temperature dependentincreasing as the temperature increases.Therefore, with seasonal temperature variations, the sludge layer depth also varies, increasing during the cold season (i.e.accumulating energy in the sludge layer) and decreasing during the hot season (reducing the energy in the sludge layer).
In the supernatant (upper) layers of the pond, algae develop, which, with photosynthesis, supply oxygen to the pond to facilitate heterotrophic breakdown of the non-settleable organics.In this way, aerobic conditions are maintained in the upper layers of the pond.The types of algae that grow and their concentrations are crucially affected by the mixing of the pond contents by wind action.If the mixing energy is

ABSTRACT
The different kinds of aerated lagoons, which exclude anaerobic pre-treatment ponds, are described and the design approach for aerated lagoons is explained.This hinges around ensuring that the 1st lagoon is suspension mixed and the second and any additional are facultative.Selection of the retention time for the 1st lagoon is important to ensure complete utilization of the influent biodegradable organics.Minimum retention times to achieve this at 14°C and 22°C were determined with the general activated sludge kinetic simulation model for (i) readily biodegradable soluble organics (BSO) only, (ii) slowly biodegradable particulate organics (BPO) only, (iii) real municipal wastewater (20% BSO and 80% BPO) and (iv) real municipal wastewater with 5% OHO active VSS mass seed.The minimum hydraulic retention times for these four cases are: at 14°C 1.3, 3.0, 2.0 and 1.5 d, respectively, and at 22°C 0.3, 2.0, 1.2 and 1.0 d, respectively.From a comparison of the simulation results with the steady-state model calculations, washout of OHOs takes place at about 75% of these retention times.Approximate equations to estimate the power requirements for aeration by mechanical surface aerators and mixing are given.These equations are combined with those of the steady-state activated sludge lagoon model for calculating the oxygen requirements and the aeration power density (W/m 3 ) in each lagoon.With these equations, it is shown that influent COD concentration needs to be between an upper and lower limit band to ensure that the 1 st lagoon is suspension mixed and the second lagoon is facultative.This COD concentration band decreases as the influent flow increases.The important conclusion arising from this is that if the aerated lagoon system is applied for small rural communities, where land for these large systems is likely to be available, then additional mixing energy above that for aeration will need to be provided to ensure that the 1st lagoon is suspension mixed -this additional aeration cost makes it unlikely that aerated lagoons will be applied for municipal wastewater treatment.Matching mixing and aeration power requirements for industrial organic wastewaters is easier because these usually are significantly stronger than municipal wastewaters.low, stratification develops which prevents non-motile algae in the lower layers from being brought periodically to the photic surface layers.The non-motile algae therefore die out and are supplanted by motile algae which can move in and out of the photic zone independently of mixing.The non-motile algae are good oxygen producers whereas the motile algae are not.Also the density of the non-motile algae is greater than that of the motile algae.Consequently, during stratification, the oxygenation capacity of the pond is severely impaired, resulting in poor non-settleable organic material breakdown by the heterotrophic organisms.During windy and temperate weather, mixing is good and non-motile algae proliferate.This results in good oxygen generation and distribution throughout the water layers of the pond by the mixing action, and hence improved non-settleable organic material breakdown by the heterotrophic organisms.In general, mixing in the pond always has a marked beneficial influence on the ability of the pond to maintain aerobic conditions and sustain higher organic loading rates.Clearly, the sludge layer and mixing conditions of the pond have a crucial effect on the response of the pond under varying natural environmental conditions.

Mechanically assisted oxidation ponds
In order to overcome the adverse effects of (i) stratification on oxygen production, and (ii) increased loading on the pond supernatant by feedback from the sludge during the hot weather, the pond can be assisted to maintain non-motile algae in suspension by artificially augmenting the mixing action.This can be accomplished in small ponds by installing a recirculating pump giving a turnover of the pond volume once or twice per day.For large ponds (> 10 ha) installation of a floating stirrer is preferable.These are similar to floating aerators but the blades are set deep below the pond surface and rotate slowly.The objective is to move large volumes of water at a slow velocity as this allows the mixing action to extend a considerable distance away from the stirrer.The energy requirement is small, ~ 0.1 W/ m 3 pond volume.In Cape Town, a 10 kW floating stirrer on a 16 ha pond of 1 m depth (0.6 W/m 3 ) ensured complete mixing for extended periods over a 200 m radius.Comparison of the stirred pond with an identical unstirred adjacent pond indicated that there were higher oxygen concentrations, higher algal growth and improved visual appearance in the stirred pond.
Installation of stirring does not alter the basic physical/ biological processes in the pond.It only provides greater security for good non-motile algal growth by maintaining a minimum mixing level during those periods when the natural environmental conditions are such that stratification would develop in the pond.The presence and action of the sludge layer is in no way affected.

Aerated oxidation ponds
In this system, the natural oxygenation capacity of the oxidation pond is augmented by installing air pipelines with diffusers at regular intervals along the pond bottom.Sometimes the pipelines are raised above the bottom.The rising bubbles mix the pond contents and augment the oxygen supply, but the main source of oxygen remains algal photosynthesis.The mixing energy is insufficient to prevent settlement of settleable organic material from the influent and a sludge layer forms as in the oxidation pond.By raising the aeration pipes above the pond bottom, the sludge layer is not disturbed and fermentation can proceed unimpeded as in the oxidation pond.
The performance of aerated oxidation ponds has not been widely published in the open literature and design procedures tend to be in the hands of the aeration system manufacturers.

Facultative aerated lagoons
In the facultative aerated lagoon, oxygen is supplied wholly by artificial means, usually floating aerators.Algal photosynthesis plays little or no part in the oxygen supply.However, the mixing energy is insufficient to keep the settleable solids in suspension and a sludge layer forms on the pond bottom.There is relatively little accurate information available defining the level of energy required to ensure that the settleable solids remain in suspension, or to ensure that settlement will take place.Eckenfelder (1966) suggests that facultative conditions can be presumed to be present when the power density in the lagoon is < 2 to 4 W/m 3 and suspension mixing is present at > 20 W/m 3 .There is therefore a wide range of power inputs for which there is uncertainty regarding the type of mixing present in a lagoon.Yet it is important to know whether 'suspension mixed' or 'facultative' conditions are present in a lagoon because this affects the oxygen requirements and effluent quality from the lagoon.
A difficulty reported in the operation of facultative aerated lagoons is that foaming occurs.This tends to happen particularly where facultative lagoons are applied for the treatment of industrial wastewaters with high soluble BOD 5 fractions.The reason for this is low mixing energy, so that the OHO active mass formed settles out with the result that aerobic degradation of organics in the lagoon supernatant layers is slowed.This type of foaming also occurs in activated sludge (AS) plants during start-up, when the organic load to OHO VSS ratio is very high.

Suspension mixed aerated lagoons
In this system, the aeration energy input is so high that no settlement of suspended solids takes place.Provided the lagoon is maintained in an aerobic state, the system is identical to the normal AS system except that (i) no settling tank and (ii) no sludge recycle are provided.Consequently, the sludge age (R s ) is equal to the hydraulic retention time (R h ).The effluent contains organic particulate material, mostly the AS formed from the influent organics, viz., active OHO (X BH ), endogenous (X E ) and unbiodegradable particulate organics from the influent (X I ).From the COD balance, the reduction in COD between the unfiltered influent and effluent COD is equal to the carbonaceous oxygen demand for growth and endogenous respiration per unit influent flow.Generally speaking, this COD reduction is insufficient: The effluent COD is too high for unrestricted discharge to receiving stream and rivers.Additional treatment with the specific objective of removing the settleable solids from the effluent flow without settling tanks is necessary to achieve a reasonably good (though not nitrified) effluent quality.
Additional treatment is usually achieved in one or more oxidation ponds or facultative lagoons.In these second lagoons, the solids settle out to form a sludge layer and a relatively solidsfree effluent is obtained.The sludge in the layer ferments so that a considerable proportion of the influent energy is lost from the system via methane gas.Due to the fermentation, recycling of energy (COD) from the sludge layer to the supernatant layers occurs, imposing an oxygen demand in the supernatant.
Therefore, the behaviour of the second facultative pond or lagoon does not at first sight appear to be different to the system where the suspension mixed lagoon is eliminated and the influent discharged directly to a facultative lagoon.However, there is a major difference.In the suspension mixed lagoon, the soluble and particulate organics are transformed to settleable solids by biological and physical processes such as growth, adsorption and flocculation.Most of the effluent organics are therefore settleable and settle out much more readily and completely in the second pond.The suspension mixed lagoon therefore acts as a biological 'flocculator' , which promotes solid/ liquid separation in the subsequent facultative pond.
The oxygen demand in the suspension mixed lagoon can be calculated with good precision with the steady-state AS model as described in this paper.Also, by making the reasonable assumption that all the influent biodegradable organics are transformed to OHO active mass in the first suspension mixed lagoon, an accurate estimate of the upper limit of the oxygen demand in the subsequent facultative lagoon can also be made.This is done with the aid of the endogenous respiration part of the AS model and by assuming that the facultative pond is suspension mixed.Thus, by making the 1 st lagoon suspension mixed and assuming the second lagoon is also, it is possible to estimate with reasonable accuracy the oxygen demand for the 1 st lagoon and obtain an upper bound for the oxygen demand in the second facultative lagoon.It will be shown that in the 1 st lagoon the energy input from the surface aerator is sufficient to establish suspension mixing conditions whereas in the second lagoon it is not, with the result that facultative conditions are established in the second lagoon.The implications and merits of this approach are below.

APPLICATION OF THE ACTIVATED SLUDGE MODEL TO SUSPENSION MIXED LAGOONS
The design approach is based on two theories, (i) the steadystate activated sludge (AS) model and (ii) energy requirements for mixing.Assuming constant flow and load, and completely mixed conditions in the 1 st and second lagoons, allows application of the steady-state AS model to both.By assuming that all the influent biodegradable organics are utilized and transformed to OHO active VSS in the 1 st lagoon, it behaves very similarly to the single completely mixed AS system and the full growth-endogenous respiration AS model is applied to the design of the 1 st lagoon.With no growth of OHO biomass in the second lagoon, it behaves similarly to the in-series reactor waste activated sludge aerobic digester and only the endogenous respiration part of the AS model is applied to the design of the second (and additional) lagoons.As mentioned above, the energy requirements for suspension mixing and settlement of solids are not well defined, certainly not as well as for the AS model.Due to this uncertainty, it is difficult to specify definitive design criteria that accurately define the type of mixing.The mixing 'theory' included in the approach is based on some early empirical formulae and anecdotal data from the literature.However, the design approach is sound and as mixing 'theories' improve, these can be included in the design approach outlined below.
The aerated lagoon model in terms of COD is presented first, and thereafter in terms of BOD 5 .Recasting the design procedure in terms of BOD 5 allows it to be used with the BOD 5 as the energy measurement parameter.Most of the aerated lagoon performance data available in the literature are in terms of BOD 5.
The design equations are therefore required in terms of BOD 5 to validate the design approach.

COD-BASED STEADY-STATE THEORY The 1 st lagoon
The same steady-state AS model equations of Marais and Ekama (1976) apply to the 1 st lagoon with sludge age (R s ) equal to nominal hydraulic retention time (R h ), i.e., Eqs 1 to 8 below are obtained directly from their Eqs 43,48,53,49,30 and 31,33,32 and  where: 1 = filtered effluent biodegradable COD concentration from the 1 st lagoon.
The remaining symbols are defined in the List of Symbols in Appendix 2. The subscripts 1 or n denote the concentrations from the 1 st or n th lagoon.Because the lagoons are assumed suspension (or completely) mixed, the concentrations in the lagoon and its effluent are equal.
From the above, the unfiltered effluent COD concentration from the 1 st lagoon S t1 is given by: mgCOD/L (9) The filtered effluent COD concentration from the 1 st lagoon S tf1 is given by: mgCOD/L (10) The carbonaceous oxygen demand in the 1 st lagoon (FO c1 , kgO/d flux, Eq. 11) is found from Eq. 38 in Marais and Ekama (1976), i.e. mgO/d (11) where: MX BH1 = mass of OHO VSS in 1 st lagoon X BH1 V 1 kgVSS and V 1 = volume of the 1 st lagoon Rh 1 Q 1 ML (12) With regard to the values of the kinetic (K v and b H ) and stoichiometric (f H , f cv , Y H ) constants, the same values for the AS system can be used.Of these, the only one of uncertain validity is the COD utilization rate K v [L/(mgOHOVSS•d)].It therefore may not give a very accurate estimate of the filtered effluent biodegradable COD concentration (S b1 ) from the 1 st lagoon.However, this does not influence the design of the 1 st lagoon very much because S b1 , being soluble, is likely to be readily biodegradable and therefore very low (Marais and Ekama, 1976).More important is the unutilized biodegradable particulate organics (BPO) concentration to determine the concentration of biodegradable COD utilized in the lagoon.Being slowly biodegradable, this concentration will be significantly greater than S b1 .However, it cannot be measured because it is enmeshed with the AS and therefore part of the VSS concentration.For this reason, the design approach is based on prudent selection of the retention time (see below) to ensure a high soluble and particulate biodegradable COD utilization.Then the resulting carbonaceous oxygen demand (OD) will not be strongly influenced by the unutilized COD concentration.Whether the COD utilization is 95% or 98% in the 1 st lagoon, does not affect the carbonaceous OD very much -only by 3%.If desired, the K v value determined by Marais and Ekama (1976) on AS systems treating municipal wastewater can be used, i.e.: L/(mgOHOVSS•d) (13) where: K v20 = substrate utilization rate at 20°C = 0.07 L/(mgOHOVSS•d) But it is far simpler to just ignore K vT and assume 100% biodegradable COD utilization (i.e. S b1 = 0) provided the hydraulic retention time (R h1 ) is correctly selected (see below).
For industrial wastewaters, the K v value may be significantly different to that for municipal wastewaters but again this will not affect the design of the lagoon system very much, provided the retention time is not selected too low, because it focuses on supplying the correct mass of oxygen per day rather than on the accuracy of the effluent COD concentration.

The 2 nd lagoon
The effluent from the 1 st lagoon, containing S b1 , X I1 , S us1 , X BH1 , X E1 and X v1 , passes to the 2 nd lagoon with retention time R h2 .If 100% utilization of biodegradable COD was not assumed for the 1 st lagoon, then in the 2 nd lagoon, utilization of the influent biodegradable COD will be complete (S b2 = 0).Therefore, the concentrations of the variables in the 2 nd lagoon, and its effluent, are: where: The 3 rd lagoon The effluent from the 2 nd lagoon, containing X I2 , S us2 , X BH2 , X E2 and X v2 , passes to the 3 rd lagoon (if included) with retention time R h3 .In this lagoon, because utilization of biodegradable organics is complete, only endogenous respiration of the AS takes place (utilization of biodegradable organism organics).Therefore, the concentrations of the variables in the 3 rd lagoon, and its effluent (if completely mixed), are: From the above, the unfiltered effluent COD concentration from the 3 rd lagoon S t3 is given by: mgCOD/L (29) The filtered effluent COD concentration from the 3 rd lagoon S tf3 is given by: mgCOD/L (30) The carbonaceous oxygen demand in the 3 rd lagoon (FO c3 , kgO/d flux) is like Eq. 22 but with no biomass growth, i.e.: mgO/d (31) where:

SELECTION OF RETENTION TIME
To determine the effect of retention time on the degradation efficiency of the readily biodegradable soluble organics (BSO) and slowly biodegradable particulate organics (BPO), the general AS model (ASM1, Henze et al., 1987or UCTOLD, Dold et al., 1991) 1, the following can be noted; (1) At both temperatures, the BSO influent has the shortest washout retention time and the BPO influent the longest.The washout retention time for the raw wastewater, which comprises both BSO (25%) and BPO (75%), is (as expected) between the BSO and BPO influents washout retention times.The raw wastewater with the 5% OHO seed does not have a washout retention time because OHOs are fed continuously into the lagoon with the influent resulting in at least some utilization of BSO and BPO depending on the retention time.The washout retention time for the raw wastewater is 1.4 d and 0.5 d at 14°C and 22°C, respectively.
(2) The retention time for approximate equivalence with the steady-state model is longer than the washout retention time.For the BSO, the increase is very small -only 0.2 and 0.1 d at 14°C and 22°C, respectively.For the BPO, the increase is large -1.3 and 0.7 d at 14°C and 22°C, respectively.Hence, the more easily the influent biodegradable organics are degraded, the smaller the difference between the washout and steadystate equivalent retention times.Like for the washout retention times, the steady-state equivalence retention time for the raw wastewater is between the BSO and BPO influent values, i.e., at 2.0 d and 1.2 d at 14°C and 22°C, respectively.The steady-state equivalent retention time for raw wastewater with the 5% OHO seed is somewhat lower at 1.5 and 1.0 d than that for the raw wastewater without OHO seed (2.0 d and 1.2 d).
From the above, it can be seen that if the retention time in the 1 st lagoon is selected longer than 2.0 d at 14°C and 1.2 d at 22°C, virtually complete utilization of influent biodegradable organics will take place.Therefore, at retention times greater than these, the steady-state lagoon model assuming all the biodegradable organics are completely utilized can be applied to municipal wastewater without significant error.For other wastewaters, these minimum retention times may be different, depending on the biodegradability of the organics in the wastewater.

OVERALL LAGOON PERFORMANCE
Even if biodegradation of the influent biodegradable organics is virtually complete in the 1 st lagoon, the COD removal is still low.This is because the AS formed in the 1 st lagoon is part of the unfiltered effluent COD (Eq.9) because the lagoon is suspension mixed.In fact, the power input of the aeration system in the 1 st lagoon, sized to supply the growth and endogenous oxygen demands (Eq.11), is usually sufficient for suspension mixing.The filtered effluent COD is very low because (depending on the wastewater type and retention time) most of the influent biodegradable soluble organics (BSO) are utilized and transformed to OHO VSS mass (Eqs 5 and 6).In most wastewaters, including municipal wastewater, the BSO are readily biodegradable and OHO mass is produced very rapidly from it.This OHO mass accelerates the utilization of the slowly biodegradable particulate organics (BPO), but that not utilized in the retention time of the 1 st lagoon is enmeshed with the AS and so is removable by settlement (or filtration) in the 2 nd lagoon.This is the main purpose of the 2 nd (and 3 rd facultative) lagoon.In fact, the power input of the aeration system in the 2 nd (and 3 rd ) lagoon, sized to supply mainly the endogenous oxygen demand (Eqs 22 and 31), is usually insufficient for suspension mixing, even though the oxygen demand in it is calculated assuming

COD BALANCE OVER THE LAGOON SYSTEM
Each lagoon in the system, as well as the system overall, must conform to the COD balance.The COD balance up to and including the n th lagoon is given by; kgCOD/d (32) where: It should be noted that the COD removal and the COD degraded are equal only for the 1 st lagoon because this is the only lagoon that is suspension mixed.With settlement of AS in the facultative 2 nd (and 3 rd ) lagoons, the COD removal is much greater than the COD degraded, both of which are difficult to estimate because they depend on the environmental conditions in the lagoons.The COD degraded depends on the fermentation rate in the sludge layer and the COD removal on the efficiency of AS settling.

STEADY-STATE MODEL APPLICATION
The theory set out above can be applied to raw municipal wastewater without difficulty.This is because the unbiodegradable soluble and particulate COD fractions (f S'us and f S'up ) are fairly well known (WRC, 1984).When applying the theory to specific industrial wastewaters, the problem is that these wastewater characteristics are not known.To determine these two characteristics for a particular industrial wastewater requires an experimental investigation in which two or more AS systems treating the particular wastewater are operated at different sludge ages for an extensive period (about 6 months).At present, there are not many industrial wastewaters that have been characterized in this way in terms of COD.There is far more operating experience with municipal and industrial wastewater treatment in aerated lagoons in terms of BOD 5 .Therefore, the steady-state aerated lagoon model equations developed above in terms of COD are transformed to BOD 5 units below to give some validation of the model.Interestingly, the use of BOD 5 leads to a simple aerated lagoon design procedure and provides insight into their behaviour because the biological processes in the BOD bottle on an unfiltered effluent from the n th lagoon are the same as in the (n + 1) th lagoon -i.e.mainly endogenous respiration.

BOD 5 -BASED THEORY
The main difference when using the BOD 5 as the wastewater strength parameter instead of the COD, is that the BOD 5 is related, in a non-linear way, only to the oxygen consumed in the utilization of the biodegradable organics through the growth and endogenous respiration processes (see Appendix 1 for detail).
Initially in the BOD test, oxygen is utilized for growth of OHO VSS (catabolism) on the biodegradable organics in the sample and thereafter in the utilization of the biodegradable organics of the OHO VSS via endogenous respiration.
The unfiltered influent BOD 5 is the oxygen utilized for growth of OHO VSS on the biodegradable organics in the influent wastewater and for endogenous respiration of this OHO VSS over 5 d.The BOD 5 gives no indication of the unbiodegradable organics in the effluent, which in some industrial wastewaters can be considerable.From Eq. A13 in Appendix 1, the influent BOD 5 and biodegradable COD (S bi ) are related proportionally for a particular wastewater.If the proportionality factor is γ, then the biodegradable COD (S bi ) from a measured BOD 5 is: The magnitude γ is related to the rate of utilization of the wastewater organics in the BOD 5 test (i.e. the K rate in Eq.A14), which in turn is related to the proportion of BSO in the wastewater.However, if γ values for different wastewaters are known, it is possible to use the BOD 5 parameter in the CODbased design equations developed above.
The BOD 5 in the unfiltered effluent from a suspension mixed lagoon is oxygen utilization due to two effects, i.e. (i) growth of OHO mass on the residual influent biodegradable organics and (ii) endogenous respiration of the OHO VSS in the effluent and that produced in the test.The unfiltered effluent BOD 5 from the 1 st lagoon therefore is similar to the carbonaceous oxygen demand in the 2 nd lagoon (Eq.22).In fact, the biological processes in the BOD 5 test are simply a continuation of those in the 1 st lagoon.
The remaining BSO can be measured on the filtered effluent BOD 5 .However, there is no way of knowing how much of the unfiltered effluent BOD 5 concentration is due to undegraded BPO enmeshed in the AS.Being slowly biodegradable, the BPO concentration can be high at low retention times (< 1 d, see Figs 1e and f).However, it is not necessary to have a very accurate value because it is usually very low for R h > 1.5 d.At R h > 1.5 d, most of the biodegradable organics, whether readily (BSO) or slowly (BPO) biodegradable, will have been utilized and so usually can be neglected without much error in the estimate of the carbonaceous oxygen demand, especially if the influent BOD 5 is high (see Figs 1e and f).
Accepting that the remaining influent biodegradable organics concentration in the lagoon effluent is zero, then from Eq. A9, with S bi = 0 and t = 5d, the unfiltered effluent BOD 5 from the n th lagoon is: Note from Eq. 34 that, even though all the influent biodegradable organics have been utilized, the effluent BOD 5 is not zero.This is because endogenous respiration of the OHO VSS continues in the BOD 5 test.
The 1 st lagoon The BOD 5 utilized, ΔBOD 5 , is the difference between the influent and effluent BOD 5 , i.e .: mgBOD 5 /L (36) and hence from Eq. 6, the active organism concentration is: mgVSS/L (37) where: BOD 5i = influent BOD 5 concentration (mg/L) BOD 5f1 = filtered effluent BOD 5 (mg/L) Equations 35 to 37 are correct for purely soluble organic wastewaters.For wastewaters that include particulate biodegradable organics, these equations are only approximate because ΔBOD 5 does not correctly reflect the influent biodegradable organics utilized -the concentration of unutilized particulate biodegradable organics enmeshed in the VSS solids is not known.
Because the BOD 5 gives no estimate of the influent unbiodegradable particulate organics concentration (UPO, S upi or X Ii ), the VSS concentration in the lagoon cannot be calculated.
The mass of OHO VSS in the 1 st lagoon is given by: kgVSS (38) and hence the carbonaceous oxygen demand in the 1 st lagoon (FO c1 , kgO/d) is found from Eq. 11, i.e.: mgO/d (39) From Eq. 34, the BOD 5 of the unfiltered effluent, BOD 51 , is given by: mgO/L (40) The equations above work best when BOD 5f1 = 0 so that ΔBOD 5 = BOD 5i , and hence it is recommended to select retention times at which there is reasonable certainty that this is so (see Fig 1a to h and Table 1).
With regard to the values of the kinetic (K vB and b H ) and stoichiometric (f H , f cv , Y HB ) constants, only K vB and Y HB are different and the BOD 5 -based values can be calculated from the COD-based values.Converting the filtered effluent biodegradable COD (S b1 , Eq. 5) to BOD 5 (BOD 5f1 , Eq. 35) with Eq.A12 yields: Also, the yield coefficient in terms of BOD 5 is obtained from: where Y HB =yY H and y is the COD/BOD 5 ratio of the influent wastewater.With Y H = 0.45 mgVSS/mgCOD yields Y HB = 0.81 mgVSS/mgBOD5 for γ = 1.8 for municipal wastewater.
Of the Y HB and K vB , K vB is of uncertain validity for the same reasons that K v is uncertain.It therefore may not give accurate estimates of the filtered effluent BOD 5 concentration from the 1 st lagoon.However, like K v , this does not influence the design of the 1 st lagoon very much because (i) a retention time is selected so that the residual soluble and particulate (enmeshed with the VSS) biodegradable organics are very low and (ii) the design approach is based on the carbonaceous OD which is not strongly influenced by the residual biodegradable organics concentration, especially if the influent BOD 5 is high.But, if required, the K vB value, determined from the effluent soluble COD concentration from AS systems treating municipal wastewater, can be used, i.e.: where: K vB20 = substrate utilization rate at 20°C = 0.055 L/(mgVSS•d) For industrial wastewaters, the K vB value may be significantly different to that for municipal wastewaters but again this will not affect the design of the lagoon system very much, because the design focuses on selecting the appropriate retention time and supplying the correct mass of oxygen per day rather than on the accuracy of the residual biodegradable wastewater organics concentration.For R h > 1.0 − 1.5 d, it is easiest to assume that BOD 5f1 = 0 and ΔBOD 5 = BOD 5i .

The 2 nd lagoon
The effluent from the 1 st lagoon, containing BOD 5f1 and X BH1 , passes to the 2 nd lagoon with retention time R h2 .In this lagoon, utilization of the influent biodegradable organics will be complete (BOD 5f2 = 0).Therefore, the unfiltered effluent BOD 5 concentration, BOD 52 from the 2 nd lagoon is: The filtered effluent BOD 5 concentration is 0, i.e.: mg/L (45) and the OHO concentration X BH2 is given by: mgVSS/L (46) The carbonaceous oxygen demand in the 2 nd lagoon (FO c2 , kgO/d) is found from Eq. 39, i.e.: mgO/d (47) where: The VSS concentration cannot be calculated with the BOD 5 as wastewater strength parameter.

The 3 rd lagoon
The effluent from the 2 nd lagoon, containing X BH2 , passes to the 3 rd lagoon (if included) with retention time R h3 .In this lagoon, because utilization of wastewater biodegradable organics is complete, only endogenous respiration of the AS takes place (utilization of biodegradable organism organics).Therefore, the concentrations of the variables in the 3 rd lagoon, and its effluent, are: mg/L (48) mgVSS/L (49) From Eq. 34 the unfiltered effluent BOD 5 concentration from the 3 rd lagoon BOD 53 is: The carbonaceous oxygen demand in the 3 rd lagoon (FO c3 , kgO/d) is found from Eq. 39 with ΔBOD 5 = 0, i.e.

mgO/d (51)
where: As for Lagoons 1 and 2, the VSS concentration in the 3 rd lagoon cannot be calculated with the BOD 5 as wastewater strength parameter because the influent unbiodegradable particulate organics (UPO) concentration (S upi , X Ii ) is unknown.

THE VALUE OF
From an examination of suspension mixed lagoon behaviour treating different industrial wastewaters reported in the literature, values of γ were derived and are listed in Table 2.With the γ values in Table 2, and applying the above equations to assess lagoon performance as reported in the literature, the correlation between the calculated and observed unfiltered effluent BOD 5 concentrations are shown in Fig. 2. In the assessment of each lagoon, the data were taken only where there was reasonable certainty that the system was suspension mixed.
A difficulty in assessing the validity of the steady-state lagoon model is that rarely, if ever, are oxygen utilization rates reported for lagoons.Without this parameter, it is not possible to either (i) give very reliable values for γ or (ii) validate the model better.
Notwithstanding these difficulties, the correlation in Fig. 2 is reasonably good and so the steady-state lagoon model can be accepted as reasonably good.

DESIGN OPTIMIZATION
The 1 st lagoon For design, valuable insights into the relative importance of different facets of the design, such as retention time, oxygen demand, and single versus series lagoons, can be gleaned from the BOD 5 -based steady-state lagoon model.For this discussion, complete utilization of influent wastewater organics in the 1 st lagoon will be accepted, i.e., ΔBOD 5 = BOD 5i .This considerably simplifies the model.
From Eq. 37, the OHO concentration in the 1 st lagoon X BHi , is: where: For most wastewaters, γ = 1.8 and hence Y HB = γY H = 0.81 mgVSS/mgBOD 5 .The unfiltered effluent BOD 5 is given by Eq. 40 with BOD 5f1 = 0 and substituting Eq. 34 into this yields: and so mgBOD 5 /L (54) The carbonaceous oxygen demand in the 1 st lagoon (FO c1 , kgO/d) is found from Eq. 39, i.e.:  4, respectively.Figure 3 shows that an appreciable fraction of the BOD 5 removal is due to growth (catabolism, Eq.A1) given by the difference 100 − 67 = 33% at R h = 0.The minimum retention time for a lagoon is about 1 d, to ensure that the growth process on biodegradable wastewater organics is virtually complete, giving a BOD 5 removal of 46% (Fig 4).At 2 d retention time, only an additional 8.7% BOD 5 removal is obtained.As the retention time increases, the additional BOD 5 removal added decreases with each day added.The same effect is observed in the oxygen demand (Fig. 4).Therefore, the volumetric efficiency of BOD 5 removal decreases as the retention time increases.So as to make the most efficient use of the lagoon volume, the retention time needs to be as short as possible.However, at short retention times the BOD 5 removal is unacceptably low.In-series suspension mixed lagoons have improved compared with single lagoons at the same retention time, but not enough to make a significant difference.This is demonstrated below.

The 2 nd lagoon
From Eq. 46 with BOD 5fi = 0, the OHO concentration in the 2 nd lagoon and its effluent is: The unfiltered effluent BOD 5 is given by Eq. 44 and successively substituting Eq. 56 for X BH2 and Eq.52 for X BH1 into this yields: The carbonaceous oxygen demand in the 2 nd lagoon (FO c2 , kgO/d) is found from Eq. 47, and successively substituting Eq. 56 for X BH2 and Eq.52 for X BH1 into this yields: kgO/d per kgBOD 5 /d (58) If in Eq. 58, R h1 = R h2 , then the ratio of the BOD 5 reduction (due to endogenous respiration) from lagoon to lagoon down the series is the same.In Fig. 3, this is shown by the straight line from 67% at R h = 0, through the BOD 5 remaining at R h1 = 2d (45.3%) and continuing a further 2 d (for the 2 nd lagoon) to 4 d.Therefore, in double lagoon system with 4 d retention time, the BOD 5 remaining is 30.8%whereas in a single lagoon of 4 d retention time, the BOD 5 remaining is 34.2%.This difference is very small, too small to make much difference between single and in-series lagoons.The oxygen demand reflects the same outcome.From Eqs 55 and 58, the ratio of the oxygen demand in the 1 st and 2 nd lagoon is 0.21/0.91= 0.23, making the oxygen demand in the 2 nd lagoon only 23% of that in the 1 st lagoon (see Fig. 4 for an approximate visual difference).Because OD is a direct measure of the BOD removal, it is clear that the removal in the 2 nd lagoon, of equal volume to the 1 st , is only 23% of that in the 1 st .With such a low OD, the aeration power input is insufficient to establish suspension mixing in the second lagoon.
The design approach is therefore to meet the OD required in the 2 nd lagoon but not to supplement the aeration power input with mixing energy to establish suspension mixing, but instead to allow the 2 nd lagoon to be facultative.By being facultative, the 2 nd lagoon achieves far greater BOD 5 removals by sedimentation to a sludge layer and oxidation by anaerobic fermentation than by aerobic oxidation.(With aerobic digestion, multiple reactor digesters do achieve significantly lower effluent active fractions (equivalent to BOD 5 remaining) than the single reactor digester at the same retention time (Ekama et al., 2006).Even though one expects the same outcome for suspension mixed aerated lagoons because the biological process is the same, i.e. endogenous respiration, the reason that it doesn't yield the same outcome is because the retention times in the aerated lagoons are an order of magnitude shorter than in aerobic digesters.) In order to demonstrate that the input by the aeration system establishes suspension mixing and facultative conditions in the 1 st and 2 nd lagoons, respectively, the power requirements for aeration need to be determined.This is presented below.

POWER REQUIREMENTS FOR AERATION
The oxygen transfer rate (OTR) of an aeration device is given by its mass oxygen transfer per unit energy consumption -kgO/kWh -under standard conditions, which are into clean de-oxygenated tap water at STP -standard temperature (20°C) and pressure (1 atm = 760 mm Hg).This OTR value (R std ) is a characteristic of the aeration device and is specified by the manufacturers.The OTR under standard conditions (R std ) needs to be corrected for the site conditions (R act ) where the aeration device is installed.The parameters that are different at the site compared to standard conditions are (i) atmospheric pressure and water temperature, (ii) the oxygen mass transfer coefficient K La and (iii) non-zero water dissolved oxygen (DO) concentration.The saturated DO concentration under STP is corrected for temperature and atmospheric pressure at the site and for impurities in the wastewater (β).The K La coefficient is corrected for temperature (θ) and impurities in the wastewater (α).Details of these corrections are given in WPCF/ ASCE (1988).Combining all the corrections gives the ratio of the OTR under site and standard conditions, i.e.: The effect of temperature and altitude on the R act /R std ratio is shown graphically in Fig. 5.The relationship between altitude and barometric pressure in mmHg can be approximated with mmHg (R 2 = 0.9999) Alt = altitude in m, and the relationship between the saturated vapour pressure of water and temperature between 5 and 35 o C can be approximated with: mmHg (R 2 = 0.9999) (61) where: p 20 = saturated vapour pressure of water at 20°C = 17.51 mmHg From Fig. 5, it can be seen that the effect of temperature and altitude is not very strong on the R act /R std ratio, only 25% between 15 and 30°C and 0 and 3 000 m and decreasing as both temperature and altitude increase.The lowest power requirement for aeration for a particular carbonaceous oxygen demand (OD) therefore will be at sea level and low temperature.As temperature and altitude increase, the power input for a fixed OD increases and therefore increases the power density (W/m 3 ) for mixing in the lagoon.
In Eq. 59, the 1 st and 2 nd terms in front of the β are the saturation DO concentration correction for temperature and pressure, respectively.Accepting an altitude of 1 000 m, which gives a site barometric pressure of about 673 mmHg, maximum and minimum seasonal temperatures of 14 and 22°C, a manufacturer's R std of 2.5 kgO/kWh and a lagoon design DO concentration of 0.5 mgO/L, and α = 0.80 and β = 0.90 gives the R act values for mechanical surface aerators listed in Table 3. Once the actual OTR at the site is known, the power requirements for aeration are calculated from the mass oxygen demand (OD) per day (flux) FO c , i.

MIXING POWER REQUIREMENTS
The power density expressed in W/m 3 is the usual way in which mixing power density in biological reactors is defined.However, this parameter only partially defines the mixing conditions.Other parameters such as surface aerator and mixer design, spacing of aerators, aerator rotational speed and reactor geometry all influence the mixing efficiency at a particular power density.However, the effect of these factors is difficult and complex to define and adds unnecessary detail when the power densities for suspension or facultative mixing regimes are not well known.Very little information is available on the power density required to maintain suspension mixing.According to Von der Emde (1969), Kalbskopf proposed the power densities in Table 4 to maintain AS in suspension.

TABLE 4 Power densities for suspension mixing in AS biological reactors
Reactor volume (V, m 3 ) 500 1 000 2 000 Power density (P d , W/m 3 )w 20 15 10 The power density (P d ) in Fig. 6 can be related to the volume with the following approximate equation: A plot of Eq. 64 is shown in Fig. 6 (solid line).Also shown are the power densities (•) in aerated lagoons which, apparently, behaved kinetically in accordance with the theory for suspension mixed aerated lagoons (data on mixing energies from Beychok, 1971).Although this does not constitute a satisfactory proof that the lagoons were indeed suspension mixed, it does support the implications of Eq. 64 that the power density decreases as volume increases.Only one instance was found which could be used to validate Eq. 64; Balasha and Sperber (1975) operated an aerated lagoon of 14 000 m 3 at a power density of 2.7 W/m 3 and reported no evident sludge deposition (☒).For this volume, the power density from Eq. 64 is 3.8 W/m 3 .Therefore, a somewhat lower power density than estimated by Eq. 64 establishes suspension mixing.Since the objective of Eq. 64 is to establish a minimum lower value in the 1 st lagoon, to ensure suspension mixing, and an upper maximum value for the 2 nd lagoon, to ensure facultative conditions, overestimation by Eq. 64 for suspension mixing conditions is acceptable.Therefore, even though application of Eq. 64 to aerated lagoons extrapolates it way out of the range of AS biological reactor volumes in Table 4, it would appear that Eq. 64 can be applied (with caution) to determine the mixing regime from the power density in large aerated lagoons -provided the actual power density in the 1 st and 2 nd lagoons are significantly above and below that given by Eq. 64, suspension and facultative mixing regimes are likely to be present in the 1 st and 2 nd lagoons, respectively.Knowledge of the minimum power densities for suspension mixed and facultative mixing regimes is of crucial importance in the design of series lagoon systems.In the 1 st lagoon, suspension mixing is essential for rapid transformation into settleable solids by (i) growth of OHO VSS from the influent biodegradable soluble organics and (ii) growth and flocculation of the influent particulate biodegradable and unbiodegradable organics, and in the 2 nd lagoon, facultative conditions are essential to settle out the settleable solids formed in the 1 st lagoon to produce an effluent low in suspended solids.Interestingly, because the oxygen demand in the 1 st lagoon includes the growth oxygen demand, its aeration power input invariably is sufficient for suspension mixing, and because the oxygen demand in the 2 nd lagoon excludes the growth oxygen demand, its aeration power input invariably is insufficient for suspension mixing.This will be demonstrated in a worked example below.
Knowledge of the minimum power density for suspension mixing in different volumes also allows intelligent application by scaling up pilot plant data to full-scale plant design.A pilot plant may have been deliberately operated as a facultative lagoon with a certain power density.If the full-scale plant is designed with the same power density, the lagoon may be suspension mixed and deliver an effluent BOD 5 (COD) very different from that expected from the pilot plant performance.

DESIGN EXAMPLE
To demonstrate the aerated lagoon design procedure based on the steady-state AS model, the example raw wastewater in WRC (1984), i.e. 15 ML/d at 750 mgCOD/L, is treated in a two-inseries aerated lagoon system, the 1 st suspension mixed and the 2 nd facultative.The hydraulic retention time (HRT) in the 1 st lagoon is selected at 1.5 d to ensure near complete utilization of influent biodegradable organics at the minimum temperature of 14°C.The 2 nd lagoon is designed for a retention time of 4 d.Because the oxygen demand is highest at the maximum temperature, the calculations are repeated at 22°C to determine the aeration power requirements, which establishes the mixing conditions in the lagoons.Complete utilization of biodegradable organics in the 1 st lagoon is assumed because HRT selection is based on this (Fig 1).The results of the calculations for the COD and BOD 5 models are given in Table 5.The oxygen transfer rate (OTR) at the site were calculated from the information in Table 3. From Table 5, the following can be noted: (1) The COD-and BOD 5 -based models give identical results.This is because the same γ value of 1.8 was used (i) to calculate the influent BOD 5 concentration, which is 325 mgO/L and (ii) in the BOD 5 model calculations.From Eq. A10, which is based on the AS growth-endogenous

Figure 6
Power density (in W/m 3 ) versus volume (in m 3 ) for estimation of mixing regime (450/V -0.5 , Eq. 64) -suspension mixed above line 500/V -0.5 and facultative below line 400/V -0.5 , between lines mixing regime uncertain respiration model, the γ value is 1.41 yielding an influent BOD 5 concentration of 415 mgO/L.Differences in γ values do not affect the BOD 5 -based model, provided the same value is used to calculate the influent BOD 5 and in the model.If only the influent BOD 5 concentration is known, then it is best to select a γ value on the high end, because this leads a more conservative design, i.e., higher oxygen demand.
(2) The effluent COD and BOD 5 concentrations from the 2 nd lagoon are uncertain.The concentrations given in Table 5 are the lowest and highest possible values.If 100% solids removal is achieved in the 2 nd lagoon, which is unlikely, the unfiltered effluent COD concentration is the unbiodegradable soluble concentration, i.e., 53 mgCOD/L and the BOD 5 is 0. At the other extreme, if the 2 nd lagoon were suspension mixed, the unfiltered effluent COD concentration is the soluble unbiodegradable COD plus the COD of the AS solids, i.e., 354 and 375 mgCOD/L at 22 and 14°C, respectively; the effluent BOD 5 is 79 and 93 mgO/L at 22 and 14°C respectively.From this it can be seen that if settlement of solids in the 2 nd lagoon is good, the lagoon system can achieve very respectable effluent organic concentrations.The disadvantage of lagoons is not their organic removal efficiency, which clearly can be good, but that lagoon systems, due to their low retention times, rarely nitrify.For municipal wastewater with high influent TKN concentrations this is a severe shortcoming.For agroindustrial wastewaters with much lower TKN/COD ratios, the lack of nitrification is not such a serious shortcoming.Indeed, with some agro-industrial wastewaters N and P may have to be dosed to ensure optimal OHO growth.The N and P dosages can be calculated with the AS model equations (Marais and Ekama, 1976;WRC, 1984;Henze et al., 2008).
(3) The power density (P d ) supplied by the aeration system in the 1 st lagoon is 5.38 W/m 3 at 22°C.As a P d > 3 W/m 3 is required for suspension mixing, the 1 st lagoon will be suspension mixed.The power density of the aeration system in the 2 nd lagoon is only 0.82 W/m 3 and, as 1.84 W/m 3 are required for suspension mixing, the lagoon will be facultative.Because the retention time of the 1 st lagoon is generally short (1-2 d) and oxygen demand includes that for growth, it will generally be found that the 1 st lagoon will be suspension mixed, unless the influent COD concentration is low.Furthermore, because the retention time of the 2 nd lagoon usually is longer than the 1 st (3-6 d), and oxygen demand is that for endogenous respiration only, it will be found that the 2 nd lagoon is generally facultative, unless the influent COD is high.
Elaborating on (3) by making the influent flow and COD concentration variables, the power densities for aeration and mixing for the 1 st and 2 nd lagoons are given by: where the LHS of Eqs 65 and 66 are the power densities due to aeration in the 1 st (P d1 ) and 2 nd (P d2 ) lagoons and the RHS the power density limit between suspension mixing (>) and facultative (<) conditions in the lagoons.Note that in Eqs 65 and 66 Q i is in ML/d.From Eq. 65, Figs 7a and b show the minimum raw wastewater, with unbiodegradable soluble organics (USO) COD fraction (f S'us ) = 0.07 and unbiodegradable particulate organics (UPO) COD fraction f S'up = 0.15), influent COD concentration versus the influent flow to achieve suspension mixing in the 1 st lagoon at retention times of 1.0, 1.5, and 2.0 d for 14 (Fig. 7a) and 22°C (Fig. 7b) based on the aeration system characteristics in Table 3.While the positions of the lines change only marginally for different wastewater and aeration system characteristics, the lines in Figs 7a and b show a general trend, i.e.: • For a fixed influent flow, the shorter the HRT of the 1 st lagoon (R h1 ), the lower the influent COD concentration (S ti ) to achieve suspension mixing in the 1 st lagoon.
• At the same HRT, the lower the wastewater temperature, the higher the influent COD concentration for suspension mixing in the 1 st lagoon.
• The higher the influent flow, the larger the lagoon volume at a particular HRT, the lower the power density required for   Because the minimum HRT for the 1 st lagoon is around 1 d at 22°C and 1.5 d at 14°C, the minimum influent COD concentration to establish suspension mixing is about 650 and 830 mgCOD/L at 22 and 14°C for an influent flow of 5 ML/d.At 0.5 ML/d, the concentrations are much higher, i.e., about 2 000 and 2 600 mgCOD/L 22 and 14°C.The pattern here is important to note.The lower the influent flow, the higher the influent COD concentration for suspension mixing by the aeration system alone.For agro-industrial wastewaters, like those from fruit and vegetable processing, the influent COD concentrations are usually high (2 000-3 000 mgCOD/L) and so suspension mixing by the aeration system alone can be achieved even at very low flows of 0.5 ML/d (Figs 7a and b).For municipal wastewater with low per capita water consumption, as is usual for rural areas, the raw wastewater influent COD concentrations are from 1 000-1 200 mgCOD/L (in South Africa), so the influent flow has to be quite high to achieve suspension mixing in the 1 st lagoon, i.e. > 2 ML/d at 22°C and R h1 = 1.0 d at 1 000 mgCOD/L and > 3 ML/d at 14°C and R h1 = 1.5 d at 1 050 mgCOD/L).
Because aerated lagoons are more likely to be applied in rural areas where land is more readily available, town populations are generally low (3 000 to 10 000), too low to generate a high influent flow.For example, a town with a population of 5 000 at 0.1 kgCOD/(person•d) produces an organic load of 500 kgCOD/d.If the water contribution is, say, 100 L/d per person, then the influent COD concentration and flow are 1 000 mgCOD/L and 0.5 ML/d.At a retention time of 1.5 d at 14°C, the minimum influent COD concentration for suspension mixing by the aeration system alone is around 2 600 mgCOD/L.The minimum influent flow at 1 000 mgCOD/L is about 3.0 ML/d at 14°C and R h1 = 1.5 d giving a population of around 30 000.This is not a small town and it is probably better to build a normal AS system for it.Clearly, when treating municipal wastewater from small towns in aerated lagoons, the mixing energy of the aeration system in the 1st lagoon needs to be supplemented to ensure suspension mixing, making it unlikely that it will be applied due to the higher than normal activated sludge energy requirements (Fig 10).
For the 2 nd lagoon, the maximum influent COD concentration versus influent flow for facultative conditions is shown in Fig 8 for 14 and 22°C, altitudes of 0 and 1 000 m and a retention time of 1.5 d in the 1 st lagoon.From Fig. 8 it can be seen that: • The higher the influent flow, the lower the influent COD concentration to ensure facultative conditions in the 2 nd lagoon.
• The higher the temperature and the higher the altitude, the lower the influent COD concentration to ensure facultative conditions in the 2 nd lagoon.An important conclusion from the above is that if high-strength agro-industrial wastewaters are treated in aerated lagoons, the influent flow must be low otherwise facultative conditions will not be achieved in the 2 nd lagoon.Without facultative conditions, settlement of solids will not take place and the effluent will have high COD, BOD 5 and suspended solids concentrations.
Combining the suspension and facultative mixing regime requirements for the 1 st and 2 nd lagoons defines lower and upper bounds for the influent COD concentration at different influent flows.This is shown in Fig. 9 (which is a combination of Figs 7a and 8).Proper operation of the lagoon system requires the influent COD concentrations above the 1 st lagoon lines to ensure suspension mixing in the 1 st lagoon and below the 2 nd lagoon line to ensure facultative conditions in the 2 nd lagoon.Influent COD concentration and flow values that fall midway in this band are best because the higher above the 1 st lagoon lines, the higher the mixing energy for suspension mixing and the lower below the 2 nd lagoon line, the lower the mixing energy for facultative conditions.Figure 9 is valid for 14°C and 1 000 m altitude -higher temperatures and lower altitudes move the relative positions of the lines, but not by very much.However, these figures are not intended to be design charts but only to illustrate the principles involved in aerated lagoon process design.Influent COD concentration and flow combinations for suspension mixing in the 1 st lagoon and facultative conditions in the 2 nd lagoon will be affected significantly by different aeration system parameters to those in Table 3, in particular the standard OTR (R std ) of the aeration device and the impurity correction factors for the oxygen mass transfer coefficient K La (α) and saturated DO concentration (β).While the trends shown in Figs 7 to 9 are general and can be used for establishing the feasibility of treating a particular wastewater in an aerated lagoon system, it is recommended that detailed process design calculations are undertaken for each particular case using the equations developed in this paper.Furthermore, the lower and upper bounds for the influent COD concentration at different influent flows (Fig. 9) are based entirely on the premise that all the mixing energy is supplied by the aeration device.If the aeration mixing energy is supplemented, the lower bound on the 1 st lagoon will fall away.However, the upper bound on the 2 nd lagoon cannot fall away unless the aeration mixing energy can somehow be reduced without reducing the oxygen transfer.Finally, a matter of primary importance in design, but which is not addressed in this paper and therefore left to the expertise and experience of the design engineer, is how the aeration device's mixing energy is most effectively distributed into the lagoon volume -it is well known that different aeration devices have significantly different mixing efficiencies.
An alternative to the facultative lagoon is the facultative oxidation pond.Here it is difficult to determine a retention time.The fact that the pond receives organics (BOD) which are virtually all in a particulate solids form would aid settling of this material to the base of the pond.Probably, a pond of 5 to 7 d retention time, 1.5 m deep would be satisfactory.Balashi and Sperber (1975) report on the behaviour of such oxidation ponds.Effluent from a suspension mixed lagoon with 5 to 11 d retention time was discharged into an oxidation pond which was 60% of the volume of the aerated lagoon.The depth of the pond was 1 m.Although an estimated 170 t VSS mass was discharged to the oxidation pond over a period of 2 years, only 40 t accumulation was measured in the sludge layer.No problems with odour development were noted.Based on this experience, it seems that a facultative pond following suspension mixed lagoons is also an appropriate method of wastewater treatment, particularly where space is not limiting.

CONCLUSION
The different kinds of aerated lagoons, which exclude anaerobic pre-treatment ponds, were described and the design approach for aerated lagoons was explained, viz., ensuring the 1 st lagoon is suspension mixed and the second is facultative.By careful selection of the hydraulic retention time (HRT) of the 1 st lagoon (HRTs calculated with the general activated sludge simulation model are given in the paper), it can be accepted that the influent biodegradable organics are completed utilized and transformed to OHO active VSS in the 1 st lagoon -it behaves very similarly to the single completely mixed AS system and the full growthendogenous respiration AS model is applied to the design of the 1 st lagoon.With no growth of OHO biomass in the 2 nd lagoon, it behaves similarly to the single or in-series reactor waste AS aerobic digester and only the endogenous respiration part of the model is applied to the design of the 2 nd (and additional) lagoons.
Even if biodegradation of the influent biodegradable organics is virtually complete in the 1 st lagoon, the COD removal is still low.This is because the AS formed in the 1 st lagoon is part of the unfiltered effluent COD because the lagoon is suspension mixed.In fact, the power input of the aeration system in the 1 st lagoon, sized to supply the growth and endogenous respiration oxygen demands, is usually sufficient for suspension mixing of high influent COD concentration agro-industry wastewaters.The filtered effluent COD is very low because (depending on the wastewater type and HRT) most of the influent soluble biodegradable organics are utilized and transformed to OHO VSS mass.In most wastewaters, including municipal wastewater, the soluble biodegradable organics are readily biodegradable and OHO mass is produced very rapidly from it.This OHO mass accelerates the utilization of the slowly biodegradable particulate organics, but that not utilized in the HRT of the 1 st lagoon is enmeshed with the AS and so is removable by settlement (or filtration) in the 2 nd lagoon.This is the main purpose of the 2 nd (and 3 rd ) facultative lagoon.In fact, the power input of the aeration system in the 2 nd (and 3 rd ) lagoon, sized to supply mainly the endogenous respiration oxygen demand, is usually insufficient for suspension mixing even though the oxygen demand in it is calculated assuming complete mixing.The unfiltered effluent COD from the 2 nd (and 3 rd ) lagoons is therefore mainly the COD of the remaining non-settleable AS (which is small) and the unbiodegradable soluble COD.The COD of filtered effluent is mainly the unbiodegradable soluble organics (USO).
Because selection of HRT of the 1 st lagoon is important to ensure complete utilization of the influent biodegradable organics, minimum retention times to achieve this at 14°C and 22°C were determined with the general AS kinetic simulation model UCTOLD (Dold et al., 1980(Dold et al., , 1991) ) which gives identical results to Activated Sludge Model No 1 (ASM1, Henze et al., 1987;Dold and Marias, 1986) for (i) readily biodegradable soluble organics (BSO) only, slowly biodegradable particulate organics (BPO) only, real municipal wastewater (20% BSO and 80% BPO) and real municipal wastewater with 5% OHO active VSS mass seed.The minimum hydraulic retention times were found to be at 14°C 1.3, 3.0, 2.0 and 1.5 d, respectively, and at 22°C 0.3, 2.0, 1.2 and 1.0 d, respectively.From a comparison of Approximate equations to estimate the power requirements for aeration by mechanical surface aerators and mixing are given.These equations are combined with those of the steady-state AS model for calculating the oxygen requirements and the aeration power density (W/m 3 ) in each lagoon.With these equations it is shown that influent COD concentration needs to be between an upper and lower limit band to ensure that the 1 st lagoon is suspension mixed and the second lagoon is facultative.This influent COD concentration band decreases as the influent flow increases, e.g., at 0.5 ML/d the influent COD needs to be between 2 600 and 9 000 mg/L, but at 15 ML/d between 500 and 2 000 mg/L.The important conclusion arising from this is that if the aerated lagoon system is applied for small low-flow rural communities, where land for these large systems is likely to be available, then additional mixing energy over and above that required for aeration will need to be provided to ensure that the 1 st lagoon is suspension mixed.Due to the higher than normal activated sludge energy requirements this will necessitate, it is unlikely that aerated lagoons will be applied for treating municipal wastewater from small towns.Matching mixing and aeration power requirements is easier for agro-industrial organic wastewaters which usually have significantly higher influent organic strengths (COD) than municipal wastewaters.
the difference is small: If the BOD u in Fig A3 is 250 mg/L instead of 230 mg/L, the Phelps equation cuts through the experimentally observed BOD 5 = 185 mg/L point (185/250 = 0.74).However, as noted above the steady-state AS model estimates for the BOD 5 /BOD u ratio do give COD/BOD 5 ratios that are higher than observed values (Table 2 in Marais and Ekama, 1976), and those implemented in practice.
3. Figure A2 shows an initial lag in the BOD time response and then a rapid increase with a plateau at ~1.5 d.The general AS model (Fig. A2) shows a similar response.In the model, the initial lag is due to the very low initial seed OHO concentration (3% of total COD).Because growth on readily BSO is rapid, the OHO concentration rapidly increases and causes the sharp increase in BOD.After ~0.65 d, the BSO is all utilized but growth continues on the slowly BPO, which stops at ~1.5 d.Although the specific OHO growth rate on BPO is about 1/10 th of that on BSO, after 0.65 d, the actual BPO utilization rate is reasonably high because the OHO concentration has increased due to the rapid growth on BSO.Therefore, the BOD continues to increase steeply while utilizing the BPO.Once the BPO is completely utilized at  ~1.5 d, OHO growth ceases and the BOD increases much more slowly due to the slow endogenous process.The delay of 1.5 d in complete BPO utilization causes the OUR associated with the endogenous process also to be delayed (shift to the right in Fig. A1), giving a BOD 5 value of about 392 mg/L which is 77% of the BOD u .Thus, the general model BOD 5 /BOD u ratio (0.77) lies between that of the steady-state AS models (0.80) and that of Phelps (0.68), and illustrates the uncertainty in this value.
The above discussion demonstrates that the AS models simulate the BOD time curve reasonably well.While the general model simulates it better than the steady-state model, the latter nevertheless gives a reasonable 1 st estimate of COD/BOD 5 ratio; this can be refined from the BOD 5 /BOD u ratio of Phelps (as demonstrated above), or from that of the general AS model.The relationships developed above therefore can be used when converting from COD to BOD 5 units.
load applied to system (kgCOD/d) S tn = unfiltered COD concentration from the n th lagoon mgCOD/L (Eqs 9, 20 and 29) ∑FO cn = flux OD up to and including the n th lagoon (kgO/d, Eqs 11, 22 and 31).

Figure 2
Figure 2 Correlation between theoretically calculated and experimentally observed BOD5 concentrations of unfiltered effluents from suspension mixed aerated lagoons treating various wastewaters

Figure 3 Figure 4
Figure 3Percentage BOD 5 remaining versus retention time is single and double suspension mixed lagoon at 20°C La correction factor of impurities θ = K La correction factor of temperature = 1.012 for mechanical surface aerators C Sstd = saturation DO concentration under standard conditions = 9.07 mgO/L at STP T = temperature the site (°C) P act = barometric pressure at site (mmHg) P std = standard barometric pressure (mmHg) = 760 mmHg p act = water vapour pressure at site (mmHg) p std = water vapour pressure at standard temperature 20°C (mmHg) = 17.51 mmHg β = C Sstd correction factor of impurities C L = DO concentration in lagoon (mgO/L).
oxygen demand (OD) in kgO/(m 3 •d) in n th lagoon = FO c / V n with FO cn in kgO/d and lagoon volume V n in m 3

Figure 5
Figure 5Actual/standard oxygen transfer rate (OTR) ratio versus altitude at different temperatures

Figure 7
Figure 7Municipal raw WW influent COD concentration versus influent flow for suspension mixing in the 1 st lagoon at retention times of 1.0, 1.5 d and 2.0 d and 1 000 m altitude at 14°C (Fig.7a) and 22°C (Fig.7b).

Figure 8
Figure 8Influent COD concentration versus influent flow for facultative conditions in the 2 nd lagoon at retention times from 2-10 d with the 1 st lagoon retention time at 1.5 d for 14 and 22°C and 0 and 1 000 m altitudes

Figure 9
Figure 9Influent COD concentration versus influent flow for suspension mixed conditions in the 1 st lagoon at retention times of 1.0, 1.5 and 2.0 d and facultative conditions in the 2 nd lagoon at retention times from 2-10 d 14°C and 1 000 m altitude.

Figure 10
Figure 10Population equivalent versus required average influent COD concentration to establish suspension mixing in the 1 st lagoon at 14°C by equating aeration and mixing energy requirements (lines) for 0 m and 1 000 m amsl showing that for small rural populations suspension mixing in the 1 st lagoon requires more energy than aeration.

Figure A3
Figure A3Typical experimental BOD time curve on wastewater sample with heterogeneous seed clearly showing the 'plateau' behaviour after about 1.5 d followed by an increase in oxygen utilized considered to be due to predation(Copcutt, 1983).Nitrification, which can occur from about 5 d unless inhibited by ATU, can cause a second increase in BOD.The theoretical BOD time curve with Phelps' (1944) K= 0.23/d at 20°C also is shown for an ultimate BOD U = 230 mg/L.

Figure
Figure A1 and A2 Cumulative oxygen utilized (BOD)-time curves at 20°C for the example raw wastewater, calculated with the steady-state activated sludge (AS) model assuming OHO growth is (1) instantaneous and (2) takes 48 h, the general AS model and the Phelps (1944) empirical equation (Eq.A15) over 20 d (Fig. A1, top) and 3 d (Fig. A2) to show more detail at the start.
rate (K La ) correction term for impurities β DO saturation concentration correction term for impurities γ COD to BOD 5 conversion factor θ oxygen transfer rate (K La ) correction term for temperature b H OHO endogenous respiration rate.Additional subscript T or 20 denotes T or 20°C BOD 5i influent BOD 5 concentration (mgO/L) 51, respectively, with R s = R h :

TABLE 1 Washout (zero biodegradable COD utilization, R hmin ) and steady-state (SS) model equivalent (100% biodegradable COD utilization (R h SS) hydraulic retention times in days at 14 and 22°C for influents comprising BSO only, BPO only and raw wastewater (WW) with and without OHO (5% as COD) seed.
hmin (d) R h SS (d) R hmin (d) R h SS (d) http://dx.doi.org/10.4314/wsa.v43i2.08Available on website http://www.wrc.org.zaISSN 1816-7950 (Online) = Water SA Vol.43 No. 2 April 2017 Published under a Creative Commons Attribution Licence The unfiltered effluent COD from the 2 nd (and 3 rd ) lagoons is therefore mainly the COD of the remaining nonsettleable AS (which is small) and the unbiodegradable soluble organics (USO) (Eqs 21 or 30).The COD of filtered effluent is mainly the COD of the USO (Eqs 21 or 30).

TABLE 5 Design example calculation results from the COD-and BOD 5 -based steady-state aerated lagoon design equations for a two-in-series lagoon system treating the example raw wastewater at 14 and 22°C. For the BOD 5 -based equations, the γ value selected for the raw wastewater is 1.8, giving an influent BOD 5 of 325 mg/L.
April 2017 Published under a Creative Commons Attribution Licence suspension mixing, and hence the lower the influent COD concentration (S ti ).