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1 Serial No Author 1 University of Nigeria Virtual Library AGUNWAMBA, J.C Author 2 Author 3 Title Desludging Interval in a Waste Stabilization Pond Keywords Description Category Desludging Interval in a Waste Stabilization Pond Engineering Publisher Publication Date 1992 Signature

2 Journal of Environmental Management (1993) 38, Desludging Interval in Approach J. C. Agunwamba Department of Civil Engineering, University of Nigeria, Nsukka, Nigeria Received 3 June 1992 The nature of sludge deposits and their effects on pond performance are discussed. A cost-objective function is minimized to obtain an equation for the optimal.desludging interval. The objective function is formulated in terms of the waste stabilization treatment cost incurred at every level of maintenance and the total cost of desludging. The desludging and treatment costs are functions of the underlying finite states, while the optimization criterion is the expected average cost per unit time period. Transition to the terminal state is both gradual and sudden ("catastrophic") depending on the efficiency of the maintenance adopted in the pond. The results obtained are discussed and compared with the conventional desludging interval. Keywords: Markov process, waste stabilization pond, optimal desludging interval, cost of desludging. 1. Introduction A waste stabilization.pond (WSP) is an efficient treatment system used to remove su:pehded matter and pathogenic bacteria from wastewaters. Pond maintenance is a very important aspect of waste stabilization pond management (Mara and Pearson, 1986), and, when neglected, affects its efficiency (Hill et al., 1979). An important aspect of pond maintenance and operation is desludging. It is recommended that anaerobic ponds be desludged when they are half full of sludge (Mara and Pearson, 1987). This occurs every n years in which: where V is the volume of the pond (m3, P is the population served and S is the sludge accumulation rate (m3/person/year). S is usually taken as 0.1 m3/person/year and may also be obtained in m3/hectare/year since the pond area (in hectares or ha) is related to the population being served. The motivation, for this study comes from the state of the waste stabilization pond system at the University of Nigeria, Nsukka, Nigeria. The system, which consists of two facultative ponds in series and treats domestic wastewater effluent from an Imhoff tank, Q 1993 Academic Press Limited

3 290 Desludging intervals " has remained poorly maintained for years. Preliminary investigations carried out show that there is a higher sediment build-up in the ponds than the usual rate could permit. The average normal accumulation rate in terms of pond surface area for an anaerobic pond is m3/ha/year. Hence, for a secondary facultative pond the rate is m3/ ha/year (Mara and Pearson, 1986). With an initial pond area of 8094 m2, and a period of 20 years (between 1971 and 199 I), the expected depth of deposit is 20(0.0105)/ m (i.e. 0.26m). However, the depth obtained by actual measurement was 0.85 m. This higher sediment build-up is caused by the deposition of materials eroded from the farms in the area into the pond. Hence, the assumption of constant rate of sludge accumulation is one of the limitations in using equation (I) to obtain the desludging interval. Equation (I) ignores erosion of sediments from exposed surrounding soils into the pond, which is possible in poorly-maintained ponds, and results in faster accumulation of deposits than the rate usually assumed. There seems to be no simple way of finding a standardized desludging interval. Anaerobic ponds are desludged every 1 to 3 years by local farmers in Bavaria (Mara and Pearson, 1987). Using their own equipment, they do this even before the ponds are half full. In France, desludging of primary facultative ponds is required about every 10 years. This paper, therefore, aims at determining the optimal desludging interval by minimizing a cost function formulated in terms of treatment cost and desludging cost. A Markov process approach, which incorporates environmental factors (e.g. erosion) in addition to the natural-waste degradation that could lead to accumulation of deposits, is presented. Before the above problem is solved, however, background knowledge on the nature of sludge deposits and their effects on pond performance is discussed. 2. Sludge deposits Wastewater particles are always deposited on the bed of an anaerobic and primary facultative pond. This deposition may also occur in secondary facultative ponds, but at a - % very low rate: An anaerobic pond is one that receives raw wastewater with strong wastes and a heavy load of suspended solids (SS). Usually, the pond is devoid of dissolved oxygen, and the SS settle to the bottom of the pond where they undergo vigorous anaerobic digestion at temperatures greater than 15 C. A primary facultative pond receives raw (unsettled) wastewaters and thus has a sludge layer which is responsible, through anaerobic methane fermentation, for up to 30% of the biological oxygen demand (BOD) removal occuring in the pond (Marais, 1974). The pond is such that both aerobic and anaerobic conditions exist in it. A secondary facultative pond receives settled wastewaters such as the effluent from Imhoff tanks and anaerobic ponds. Hence, the rate of accumulation of deposits will depend on the type of pond FORMATION AND COMPOSITION OF THE SLUDGE LAYER The sludge'layer is composed of sediments eroded from the soil around the pond as well as the sludge resulting from the processes taking place in the pond. Such processes include methanogenesis, precipitation of heavy metal ions and sedimentation of algal biomasses. A portion of this sedimentation is non-biodegradable, and the nitrogen it contains remains immobilized in the sediment. The proportion of the sludge that is from solid deposits depends on the degree of vegetative cover around the pond, land slope, nature of soil, etc.

4 J. C. Agunwamba 291 Methanogenesis is a very important mechanism for BOD removal in anaerobic and primary facultative ponds. It is known to be responsible for % removal of BOD in some pilot-scale anaerobic ponds in north-east Brazil (Mara et a]., 1983). This process leads to an increase in the sludge layer. Other constituents of the sludge layer are suspended solids, dissolved organic compounds, oil and greases, etc EFFECTS OF THE SLUDGE LAYER 2.2. I. Efluetrr quality Density currents and other disturbances may cause the upturning of the pond content such that some of the deposits enter the mainstream. This disturbance will lead to a poorer effluent quality. However, for newly-constructed anaerobic ponds, the deeper the sludge layer, the higher the BOD removal efficiency (Parker and Skerry, 1968; Parker, 1979) " Release of gases Odour problems may also increase as the layer increases. The offensive odours released in ponds are the product of anaerobic decomposition at the bottom leading to the production of hydrogen sulphide. Proteolytic microbes in the anoxic sediments release H,S from amino acids as they degrade proteins and amino acids to ammonia. H,S is also produced in the anaerobic sediments by the sulphate-reducing bacteria depending on the temperature, organic loading and influent sulphate concentrations. Odour release from ponds can affect the economic viability, health and population of a given locality and should always be controlled effectively. Odour is usually controlled by spreading nitrate salt on the pond. Hence, the cost of damage by odours released may be estimated as the amount of money spent on nitrates. Apart from H,S, another gas that is evolved is methane. At temperatures greater thh 23"C, the evolution of methane gas is sufficiently rapid to buoy sludge particles up to the surface, where drifting sludge mats are formed. The sludge mats prevent the penetration of light into the photic zone and reduce surface aeration. Hence, while these mats are disadvantageous for facultative ponds and therefore should be removed, they aid the processes of decomposition in anaerobic ponds (Mara and Pearson, 1987). However, they form a suitable habitat for mosquitoes and flies, cause other floating debris and particles to catch and facilitate the sedimentation of particles Danger of over-ow and overflooding Freeboard is usually allowed in ponds to prevent waves generated by the wind from overtopping the embankment. The higher the depth of the sludge layer, the greater the risk of overflow and overflooding of the pond, especially during periods of heavy rainfall. Flooding of the pond may cause the pollution of adjacent land areas and streams, and cover walk ways and roads with scum and debris. In order to avoid these problems, it may be necessary to adjust the flow such that the velocity is increased as the sludge layer increases. This adjustment will help maintain the overall water depth constant. However, the effective water depth and the detention time will reduce. Reduction in detention time will lead to poorer effluent quality.

5 292 Desludging intervals 3. Desludging and sludge disposal A pond may be desludged by using a raft-mounted sludge pump (Mara and Pearson, 1987). The sludge is disposed in accordance with regulations governing sludge disposal (Council of the European Communities, 1986). The sludge may be discharged into lagoons, landfill sites or conveyed to a central sludge treatment facility and treated before disposal. Disposal of the untreated desludged material in streams will reduce the water quality. It may lead to a temporary loss of natural habitat for benthic invertebrates and fish because of increase in BOD and heavy metals. Fish in these receiving streams may be rendered unfit for human consumption if untreated sludges from toxic industrial wastewater ponds are discharged into them. The effects of the sludge deposits were discussed above. There is the need to desludge at the most appropriate period and the least cost with a minimum interference with the ponds efficiency. A technique for achieving these objectives is presented below. " 4. Markov approach The depths of sludge in the pond over the years is classified into a finite number of states 1, 2,..., n. States 1 and n are the initial and terminal states, respectively. While no accumulation has taken place in state 1, the pond is full in state n. The intermediate states, 2, 3,..., n-i, are ordered to show their relative depth of sludge accumulation. The pond in the initial state, if left untouched, will go to a less desirable state in the next transition and eventually reach the terminal state. The following assumptions are made: 1. When the system reaches state i (i= 1,2,..., n-i), the probability that it will move to a less desirable state j (j= i+ 1,..., n) in the next transition is P,. For i= 1, 2,..., n-i, P,=O, where j<i and q:j+, Po= 1. That is, sludge keeps on accumu- lating unless it is desludged. 2. When the system reaches the terminal state, it is desludged, i.e. P,,, = I. 3. There is a gradual sludge accumulation (i.e. transition to less desirable states) and "catastrophic" accumulation of sediments in the pond (i.e. direct transition to the terminal state). The first case is due to transition by the normal waste stabilization pond processes. The second might result from poor management. For example, farming around the pond and the consequent erosion and silting of the pond by runoff. It will be interesting to know whether or not it is more economical to desludge the pond before state n is reached. The sections below deal with this problem TRANSITION PROBABILITIES It is expected that the pond will be filled completely in 15 years. The probability that it will be filled in a particular m-year period is given by (see Wilson, 1981, for a similar application in the design of hydraulic structures): This is used in computing the "catastrophic" transition probability. The probability of transition from state i to any state j can generally be written as:

6 J. C. Agunwamba PI,, Figure I. Transition diagram for gradual and sudden pond filling. Desludging is expected as soon as the pond is in state n. The gradual transitional probabilities are found such that the sum of the probabilities in each row is equal to 1.. From Figure 1, the transition probability matrix is The following points are noted about equation (4) and Figure (1): 1. P,, where j= i+ 1 and 1 < i <n - 1 are the gradual transition probabilities. They depend on the natural rate of sludge accumulation. 2. P,, where j# i+ 1 and j> i, 1 < i <n - 1 are the sudden transitions where one or more states are jumped. Their occurence will depend on rainfall intensity, erosion characteristics of the area, etc. 3. P,, where 2 i j< n represent the probability of transition from any other state to 1. It depends on when it is decided to desludge. p.. =

7 TABLE I. Variation of 0, K and cost with desludging depth Desludging Treatment Desludging Total 0 K frequency x x x 1 u, (days) 1 /day E H(m) per year $10' $104 $lo4 Cost

8 J. C. Agunwamba A - High treatment cost (Cz = $10 000) M Moderate treatment cost (Cp = $5000) 0-0 Low treatment cost (Ce = $1000) ---- Without treatment cost (Cp = 0) -.- Without desludging cost (C2 = $10 000) Fractional desludging pond depth Figure 2. Variation of cost with desludging depth - > From the above, for n=6, the matrix of the transition probabilities is: p..= The interest here is on the transient behaviour of the system. The expected first-passage time from i to j is (Chapman et al., 1987):

9 296 Desludging intervals where U,,.= expected first-passage time from k to j. P, = the probability of moving from state i to k. The equations generated from equation (5) are solved simultaneously to obtain the first-passage times between desludging, i.e. U6,= This is the desludging interval if desludging is done when the pond is full. For the purpose of comparison, the desludging interval when the pond is Sth,. $th, +th and 4th full are also obtained by setting up corresponding probability matrices and solving to obtain Uii for i=2, 3, 4 and 5, respectively. The whole result is: 4.3. OPERATING COST FUNCTION The cost function is formulated as: - 3 in which: a, =treatment cost of a pond with efficiency 0.1 below Em ($); A =pond surface area (mz); C= total operating cost; C, =cost of bringing desludging machine to the site ($); C2 = desludging cost per unit volume ($/m3); E = actual pond efficiency; Em = minimum efficiency to be satisfied by the pond; H=depth of deposits in the pond (m). C consists of the cost of desludging and the total expenses incurred while the pond is in a particular state of desludging. The total expenses incurred is the cost of treatment required to upgrade the effluent quality to the standard (Em). The pond is expected to achieve a certain minimum efficiency (Em) corresponding to a particular level of reuse. Below this value, the pond needs additional treatment before it is discharged. Otherwise, the effluent discharge standard is violated. The associated health hazard is simply quantified as the treatment cost required to increase the efficiency to Em. The treatment cost is proportional to Em- E, where E is expressed as (Agunwamba, 1991): in which No and N are the influent and effluent bacteria number (or BOD); K is the firstorder rate constant; and 8 is the detention time. K and 8 are given, respectively, by (Sarikaya and Saatci, 1987; Sarikaya et al., 1987; Mayo, 1989): and wheref, is a constant, f, is a coefficient dependent on solar radiation, h is the effective water depth in the pond, V is the pond volume and Q is the flow rate.

10 J. C. Agunwamba 2W The problem presented in this research involves finding the desludging interval that will minimize the above cost function using the values of 17,. 2 < i< 6. In order to proceed further, this approach is illustrated with an example and then compared with the conventional method. 5. Application Find the desludging interval of two 200 m x 50 m x 1.5 m dimensioned waste stabilization ponds in series. The flow rate (Q) is 1500 m3/day while the average solar radiation So= 550 cal/cm2 day. Other constants are: C, = $ lo4, C2 = $100/m3, Em = 0.943, population = 8000 and a,= $lo3. The rate constant equation is (Mayo, 1989): where h is the water depth, and efficiency: for two ponds in series MARKOV SOLUTION The water depth state enables their corresponding 0 and K values to be obtained using equations (1 1) and (13), respectively. From these values E is evaluated from equation (14). The values of 0, K and cost at various desludging depths are given in Table 1. The average cost of desludging at i is total cost/uii. If desludging is once every 15 yeags, then the frequehcy of desludging at 3-year intervals is 5, at 6 years is 1516, etc. The graph of total cost versus fractional sludge depth is shown in Figure 2. Graphs are also drawn for other treatment costs (a3=$5000 and $1000) to know how sensitive the minimum cost is to the treatment cost in relation to the desludging cost (Figure 2) CONVENTIONAL METHOD The formula is given by equation (1). From the above data: 6. Discussion Figure 2 shows that the minimum cost occurs when the pond is 0.6H and 0-8H full of sludge, irrespective of the treatment cost, provided it is not negligible. If local conditions permit the discharge of effluent of any quality whatsoever into the environment, then the cost will decrease as H increases, which implies that the pond should be desludged when

11 298 Desludging intervals it is full. This solution, however, should be avoided because of some operational problems. Figure 2 also shows that desludging should be done approximately every 11.2 years if the treatment cost with respect to desludging cost cannot be neglected. If the desludging cost is ignored, the minimum cost shifts to the left, i.e. the pond should be desludged at a greater frequency. For instance, Figure 2 shows for the case C,= $10 000, the optimum depth of sludge is 0.6H. The desludging interval is then 9 years. The Markov approach, unlike the conventional method, incorporates the maintenance structure and efficiency, effluent discharge standard and the rate of degradation in the pond. All these factors affect the rate of sludge accumulation. For instance, particle deposition could be minimized by a proper pond maintenance policy. If pond workers are so ignorant of pond operation that they farm around it, then there will be increased tendency for "catastrophic" filling of the pond. If, on the other hand, the pond is well maintained, the transition into the final state will be gradual and longer. 7. Conclusion., Using the conventional formula to compute the interval for desludging may not always be appropriate, especially when other environmental processes (e.g. erosion), other than natural sludge deposition, contribute to pond filling. Also, waste stabilization ponds should be desludged at the interval period that minimizes the cost while satisfying the effluent discharge standard. Hence, an approach for obtaining the optimal desludging interval of the pond is presented. It involves a Markovian formulation in which the deterioration of the pond, as indicated by the change in the underlying state, is represented by the transition probability matrix of a Markov process. The objective is to find the interval that minimizes the operation cost. It is found that desludging should be done when the pond is between 315th and 415th full, as against the current method of desludging when it is half-full. References Agunwamba, J. C. (1991). Simplified optimal design of the waste stabilization pond. Wafer, Air and Soil Pollufion 59(3/4), Chapman, C. B.. Cooper, D. F. and Page. M. J. (1987). Managemenfjbr Engineers, pp Chichester: J. Wiley & Sons. Council of the European Communities. (1986). On the protection of the environment, and in particular of the soil, when sewage sludge is used in agriculture (86/278/EEC). Oficial Journal ojthe European Communities L181, 6-12 [L181(86:7.4)]. Hill, W. R., Regan, T. M. and Zickefoose, C. S. (1979). Operation and maintenance of water pollutioncontrol facilities: a WPCF white page. Journal offhe Wafer Pollution Confrol Federation 51, Mara, D. D. and Pearson, H. W. (1986). Artificial freshwater environment: waste stabilization ponds. In Biotechnology, Vol. 8 (H. J. Rehn and G. Reed, eds), p Weinheim: VCH VerlagsgeselIschaft. Mara, D. D. and Pearson, H. W. (1987). Wasre Sfabilization Ponds: Design ManualJor Mediferranean Europe. pp University of Liverpool. Mara, D. D., Pearson. H. W. and Silva (1983). Brazilian stabilization pond research suggests low cost urban applications. World Water 6(7), Marais, G. V. R. (1974). Fecal bacterial kinetics in stabilization ponds. Journal of the Environmental Engineering Division of the ASCE 100, Mayo, A. W. (1989). Efkt of pond depth of bacterial mortality rate. JournaloJthe Environmenfal Engineering Division ojthe ASCE 115, Parker, C. D. (1979). Biological mechanisms in lagoons. Progress in Water Technology 11, Parker, C. D. and Skerry, G. P. (1968). Function of solids in anaerobic lagoon treatment of wastewater. Journal ojthc Water Pollution Control Federation 40,

12 J. C. Agunwamba 299 Sarikaya, H. 2. and Saatci, A. M. (1987). Bacterial die-off in waste stabilization ponds. Journal of the Environmen~al Engineering Division of the ASCE 113, Sarikaya, H. Z., Saatci, A. M. and Abdulfattah, A. F. (1987). Effect of pond depth on bacterial die-off. Journal of the Environmental Engineering Division of the ASCE 113, Wilson, E. M. (1981). Engineering Hydrology, pp London: Macmillan.

KEY WORDS Anaerobic lagoons ; reaction constant ; operation ; per capita sludge ; loading rate.

KEY WORDS Anaerobic lagoons ; reaction constant ; operation ; per capita sludge ; loading rate. The Operation of Anaerobic Lagoons A. Gheisari : Lecturer Mohajer Technical School, and senior Scientist, Water & Wastewater Consulting Engineers, Isfahan, Iran M.A. Kazemi: Executive Manager, Water &