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Computer-aided design and control of an activated sludge process
The Chemical Engineering
Journal, 27 (1983)
B13 - B27
B13
Computer-aided Design and Control of an Activated SluQge Process* ROBERT
Department (Received
B. PATERSON+
and MORTON
of Chemical Engineering, July
14, 1982;
M. DENNS
University
of Delaware,
Newark,
DE 19711
(U.S.A.)
.
in final form May 4, 1983)
The activated sludge process for wastewater treatment is studied by use of steady state and dynamic process models. Process constraints fix the steady state with only three designer-selected parameters: the percentage removal of suspended solids in the primary clarifier, the aeration basin suspended solids and the sludge age. A primary clarifier cannot be justified economically. Total plant cost (construction plus operation) is insensitive to the other two design variables over a wide range. The transient analysis enables controllability to be taken into account when making a final design decision between alternatives that are equally attractive economically. In a comparison of designs for a plant processing 20 000 m3 day-’ of medium strength wastewater, it was found that dynamic stability was enhanced by operating with lower aeration basin suspended solids and recycle ratio. Continuous control of dissolved oxygen was shown to be important, and the oxygen control system might require more blower capacity than is indicated by a steady state design.
Design is typically carried out on a steady state basis, and operability under normal diurnal transients is not taken into account. In this paper a set of interactive computer programs that simulate the steady state and transient response of an activated sludge wastewater treatment system is discussed. The steady state program includes construction and operating costs and thus enables rapid economic evaluation of a proposed design. The transient simulation provides an opportunity to incorporate into a final decision the relative controllability of alternative designs that may be equally attractive economically. The model and representative results have been discussed in detail elsewhere [l, 21; some of the major results are summarized here. Because of constraints imposed by the system structure and by effluent requirements, the steady state program will compute the design of a complete plant, for a set of given wastewater characteristics and flow rate, on the basis of three designer inputs: (1) percentage removal of suspended solids in the primary clarifier, (2) aeration basin mixed liquor volatile suspended solids (MLVSSs) and (3) sludge age.
1. INTRODUCTION
2. PROCESS
The optimal design of an activated sludge process for the treatment of municipal wastewater requires an analysis of the interactions between the major unit processes and an evaluation of system performance versus cost.
The process flow sheet is shown in Fig. 1. The aeration basin is assumed to be well mixed, and a circular secondary clarifier has been specified. Multiple aeration basins and clarifiers may be specified by the program as required by the plant flow rate. Brief descriptions of the mathematical models of the individual unit operations are contained in Appendix A. The model of the aeration basin is a fundamental model that is based on mass balances and kinetic information on the growth rates of both carbonaceous and nitrifying bacteria. The model of the thicken-
ABSTRACT
*Paper presented at the Fifty-fourth Annual Water Pollution Control Federation Conference, Detroit, MI, U.S.A., October 4 - 9, 1981. +Present address: Radian Corporation, McLean, VA 22102, U.S.A. *Present address: Department of Chemical Engineering, University of California, Berkeley, CA 94720, U.S.A. 0300-9467/83/$3.00
@ Elsevier Sequoia/Printed
in The Netherlands
B14
Chlorination system
Secondary Settler
Aerotton Basin
Primary Settler
Preliminary Treatment
~nxz
1,
ttttttt Diffused
Primary Sludge wostoge
Air
Underflow
Feed Recycle wastage
Two-Stage Thickener
Polymer Feed
Ancerobic Digester
Solids Centrifuge
------7 1
Return To Sludge Thickener -7
Thickener Underflow
Fig. 1. Schematic
diagram
Final Waste Sludge (To Landf!ll)
of an activated
sludge wastewater
1
Average wastewater composition used in the simulations for medium strength domestic wastewater
Parameter
Concentration (mg 1-l)
Total (BOD)s, 20 “C! Dissolved (BOD)s , 20 “C Suspended (BOD)s , 20 “C
200 70 130
TSSs Volatile suspended solids Fixed suspended solids
200 150 50
Total nitrogen (as N) Ammonia nitrogen (as N) Nitrite nitrogen (as N) Nitrate nitrogen (as N) Organic nitrogen (as N)
40 25 0 0 15
Total phosphorus Dissolved phosphorus Suspended phosphorus
10 7
TABLE
constants
Kinetic
constant
Y
3
2
Kinetic
l-h b K
system.
primary clarifier and the clarification section of the secondary clarifier are described by empirical equations. The steady state simulation program is limited to the unit process arrangement shown in Fig. 1. All plants discussed here have been designed to meet an average effluent quality with a total biochemical oxygen demand over a period of 5 days (( BOD)s) of 20 mg 1-l and total suspended solids (TSSs) of 20 mg 1-l. The average flow rate and the wastewater characteristics are required as input from the user; the characteristics of the medium strength wastewater used in the simulations here are shown in Table 1. The kinetic parameters are also required for the growth rates of the bacteria that degrade (BOD)5 and nitrogen compounds. The carbonaceous bacteria are considered to be a single pseudo-species, and (BOD)5 to be a single pseudo-component. The kinetic parameters in Table 2 are the values used here; these are typical of municipal wastewaters and thus can be used in the simulation program in the absence of wastewater-specific values.
ing section of the secondary clarifier is also fundamental and utilizes the simulation program described by Attir et al. [3]. The
TABLE
treatment
used in the simulations
for carbonaceous
and nitrifying
bacteria
at 20 “C!
Carbonaceous
Nitrosomonas
Nitrobacter
5.0 day-r 0.055 day-’ 100 mg 1-l of (BOD)s 0.50 g of volatile suspended solids per gram of (BOD)s
0.33 day-’ 0.05 day-’ 1.0 mg 1-l of NHa-N 0.05 g of volatile suspended solids per gram of NH4-N -I_
0.80 day-’ 0.05 day-’ 2.1 mg 1-l of N02-N 0.02 g of volatile suspended solids per gram of N02--N __-
B15 3. ECONOMIC EVALUATION
The cost of construction and the annual cost of operation and maintenance (0 & M) for each unit in the plant is determined from the data of Patterson and Banker [4] for wastewater treatment processes. Where comparison is possible, their data are consistent with the process industry cost functions compiled by Woods et al. [ 51. The data were correlated in the conventional power equation form, in which the cost of the unit is expressed as a function of some unit process size characteristic such as the primary clarifier surface area or the recycle pump flow rate. For example, the installed cost of the primary clarifier is estimated from the following equation: construction cost in 1978 U.S. dollars
4. BASE CASE DESIGN
06? = 3355.0
X
(1)
The data were converted to 1978 U.S. dollars using the September 1978 chemical engineering plant cost index; the current value of the index can be used to update the economic base. Data of this type are typically accurate to within *(15% - 30%). For this reason, all unit process costs are automatically rounded off to two significant figures by the program. The plant cost is evaluated on a present worth basis. The present total system cost represents the capital that must be available at time zero to pay construction costs and 0 & M costs over the entire plant lifetime. The present total system cost is calculated as follows: total present total system = capital cost cost
+ PWF
Although we have not done so in our examples, the PWF can be looked on as a design parameter. The PWF plays the role of a Lagrange multiplier in either of two optimal design formulations: (1) the minimization of 0 & M for fixed construction cost or (2) the minimization of construction cost for fixed 0 & M. The first of these could be an attractive formulation if subsidies exist for construction but not for operating costs. The PWF then reflects the sensitivity of the design to cost changes. In that case, a design would be sought that is near the minimum cost over a range of values of PWF, even if the design never represents the absolute minimum cost for any one PWF.
(2)
where the present worth factor (PWF) determines the amount of capital needed at time zero to be able to pay annual 0 & M costs for the entire life of the plant and to have zero capital remaining at the end of the plant life. The sample calculations reported here are based on a net interest rate of 10% and a lifetime of 20 years, corresponding to a present worth factor of 8.6. The PWF varies between zero (infinite interest rates) and the number of years over which 0 & M costs must be paid (zero net interest).
The base case for this study is a plant to treat 20 000 m3 day-l (5.3 X lo6 gal day-‘) of medium strength wastewater with the composition listed in Table 1. There is to be 60% removal of primary solids, a sludge age of 10 days and aeration basin MLVSSs of 2000 mg 1-l. A typical print-out of the detailed design specifications for the secondary clarifier is shown in Table 3. Similar printouts are also generated by the steady state design program for all the other unit processes. The computer-generated cost breakdowns for construction and annual 0 & M for the entire plant are shown in Tables 4 and 5 respectively, and the overall economic summary is shown in Table 6. The present total cost of this plant in 1978 U.S. dollars, using a 10% effective net interest rate, is U.S. $5.3 million. Table 6 also indicates the average treatment cost in U.S. dollars per cubic meter of water treated. For the base case plant the average cost of treatment is 3.6 U.S. & m-‘, which is equivalent to 14 U.S. & per thousand gallons. It is important to note that the average cost of treatment was calculated as the present total system cost divided by the total volume of water treated in 20 years of plant operation. The more common method of calculating average treatment cost is to calculate the annualized plant cost, which is the sum of the annualized cost of capital plus the 0 & M costs, and to divide by the total volume of water treated in 1 year of plant operation.
B16 TABLE
3
Secondary
clarifier
design summary __I__--.-
Total
Concentration (g mP3) Total (BOD)s, 20 “C Dissolved (BOD)s , 20 “C Suspended (BOD)s, 20 “C TSSs Volatile suspended solids Fixed suspended solids
Feed
1811 3.2 1808 2598 2018 520
Total nitrogen NH4-N N02-N NOs-N Organic nitrogen Total phosphorus Dissolved phosphorus Suspended phosphorus
276 0.8 0.5 23.7 251 63 7.0 56.1
Feed flow rate (m3 day-r)
23013
Underflow flow rate (m3 day-‘) Recycle flow rate (m3 day-‘) Effluent flow rate (m3 day-‘) Underflow ratio Recycle ratio Wastage ratio Effluent ratio Overflow rate (m3 me2 day-r) Total area (m2 ) Number of units Settler diameter (m) Construction cost (U.S. $)
3092 3061 19921 0.1549 0.1534 0.0015 0.9985 23.3 855.3 1 33.0 310000
Effluent
Underflow
16.8 3.2 13.6 19.5 15.6 3.9
13374
26.9 0.8 0.5 23.7 1.9 7.4 7.0 0.4
1885
The latter method of calculation leads to an average treatment cost of 8.5 U.S. & mm3 or 32 U.S. & per thousand gallons. Thus these two methods of calculating average treatment cost are not equivalent. There are several interesting points here that bear directly on the economic evaluation of the plant. First, the construction cost and the present value of 20 years’ worth of 0 & M costs are comparable (U.S. $2.9 million uersus U.S. $2.4 million). Thus, design evaluations based only on minimizing construction costs could be seriously in error. Furthermore, the result is very sensitive to the projected interest and inflation rates. If, for example, the effective annual interest rate is reduced from 0.10 to 0.05, then the present worth factor is increased from 8.6 to 12.5, and the present worth of 0 & M costs is increased to U.S. $3.5 million. Hence, lower interest rates will favor capital-cost-intensive plants with low 0 & M costs.
Bottom zone
Zone I
19210 15368 3842
15842 12674 3168
Zone 2
Clarifier zone
-
3.2 13370 19210 15638 3842
334 261 67
19.5 15.6 3.9
0.8 0.5 23.7 1860 422 7.0 415
The air supply system is a major factor in both the construction and the 0 & M costs. It represents most of the plant electrical cost, for example, which is in turn 13% of the total 0 & M cost. The air supply system was sized to meet the oxygen demand at the average wastewater flow rate and (BOD), loading. Dynamic simulations presented later in this paper will show that the air supply system capacity, when sized in this manner, is just adequate to meet peak oxygen demands at periods of high flow and high (BOD), loading, provided that all blowers are in service. Since the situation where at least one blower is out of service is common, it is possible that a more conservative design basis might be employed. For example, the program could instead specify a firm blower capacity adequate to meet the expected daily maximum oxygen demand. Because of the impact of the air system on total costs, such a change could affect the selection of a final design.
B17 TABLE
4
Construction
TABLE
cost (X103
U.S.
Percentage of total
Total
Land (18.6 acres) Engineering Legal, fiscal, administration Interest during construction Total
TABLE
construction
capital
130 350 20 310 290 310 46 2 50 6 39 2 180 140 150 46 290 2362
summary
construction
for an evaluation
capital
(X103
(1978)) Total annual costs per year (X103
$ (1978)) Preliminary treatment Primary clarifier Primary sludge pump Aeration tank Air supply system Secondary settler Recycle pump Wastage pump Chlorination tank Chlorine feed system Sludge thickener Thickener pump Anaerobic digester Solids centrifuge Laboratory facilities Garage and shop Yardwork Total construction cost
6
Final economic 20 years
cost summary
5.5 14.8 0.8 13.1 12.3 13.1 1.9 0.1 2.1 0.3 1.7 0.1 7.6 5.9 6.4 1.9 12.3 100.0
(1978)) Present worth Present worth
$
U.S.
$
factor of 20 years of annual costs
5. PRIMARY
-
of
2910
at 10.0% interest (X103 U.S. $ (1978)) Present total cost (total construction capital and present worth of 20 years’ operation costs) (X103 U.S. $ (1978)) Average treatment cost (U.S. $ (1978) (m3 HzO)-‘)
93 270 35 150 2910
U.S.
period
2797 8.51 2382 5291
0.036
CLARIFIER
The effect of the primary clarifier was studied in detail for sludge ages ranging from 2 to 20 days and MLVSSs in the range 1000 5000 mg 1-l. The plant cost as a function of primary clarifier efficiency is shown in Fig. 2 for a sludge age of 10 days and MLVSSs of 2000 mg 1-l. Results are shown for strong and weak wastewater, as well as for the medium
5
Annual expenses
Cost (X103 U.S. $ (1978) Operation
Preliminary treatment Primary clarifier Primary sludge pump Aeration tank Air supply system Secondary settler Recycle pump Wastage pump Chlorination tank Chlorine feed system Sludge thickener Thickener pump Anaerobic digester Solids centrifuge Laboratory facilities Yardwork Administration and general Indirect labor costs Total Percentage
of annual costs
10
7.6 2.5 0 29 7 2.2 0.4 0 4.8 1.3 0.4 3.1 16 23 0 8.1 16 131.5 47.0
Maintenance
4.9 3.9 0.8 0
6.3 3.6 1.7 0.4 0 0.9 0.7 0.4 2.1 2.3 1.2 9.6 1.7 5.6 45.9 16.4
year-‘)
Material and supply 5.6 3.2 0.7 0 8.2 2.8 0.5 0.01 0 0
0.3 0.01
2.5 9.8 1.3 2.2 6.1 0 45.6 16.3
Electrical
0 0
Chemical
0.04 0 36 0 1.3 0.02 0 0 0 0.03 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 10 0 0 0 9.4 0 0 0 0
37.4 13.4
19.4 6.9
Total
20.5 14.7 4.0 0 79.5 13.4 5.7 0.8 0 18.1 2.3 0.8 7.7 37.5 25.5 11.8 15.9 21.6 279.7 100.0
Percentage of total
7.3 5.3 1.4 0.0 28.4 4.8 2.0 0.3 0.0 6.5 0.8 0.3 2.8 13.4 9.1
4.2 5.7 7.7 100.0
B18
c b = 8
6.0 -
400,
I I
300
.
AtrSupply System
200 50 40 -
Sludge
Thickener
I
Solids
30(1 3.0 0
I IO Percent
1 20 Removal
I 30
k 40
Promary
Fig. 2. Cost as a function
I 50 Suspended
of primary
I 60 Sohds
clarifier
efficiency.
strength wastewater used in the base case. All costs shown in Fig. 2 are for a plant where no polymer is used to enhance settling in the primary clarifier. The minimum cost in all cases occurs with no primary clarifier. The same result was obtained for all sludge ages and MLVSSs studied and for plants that do add polymer to the primary clarifier. The apparent economic trade-offs related to primary settling are clear. Increased primary clarification requires more area, and therefore a more expensive settler. The reduced (BOD)s load to the aeration basin, however, will allow construction of a smaller aeration basin and air supply system. These effects can be seen in Fig. 3, where the individual unit construction costs are plotted for a sludge age of 10 days and MLVSSs of 2000 mg 1-l. The trade-off is roughly even in the intermediate range of 20% - 40% removal, but the large cost associated with the existence of any primary clarifier cannot be offset by savings elsewhere in the process. Some of the non-linearities in the process are also evident in Fig. 3. The required size of the primary clarifier more than doubles for the removal of between 50% and 60% primary solids, and it appears that if primary clarification is to be used for the system studied here it should be designed for no more than 40% or 50% removal. It should be noted that the cost of the sludge thickener does not increase until the removal of primary suspended solids exceeds 50%. Since primary sludge thickens more easily than secondary waste activated sludge, the thickener can accommodate the increases in the amount of primary sludge
200
I
01
100
0
IO Percent
20 Removal
Centrifuge
30 Primary
1
40
50
60
Suspended
Solids
Fig. 3. Construction function of primary
cost of six unit processes clarifier efficiency.
as a
generated without increases in thickener area. For removal of more than 50%, however, the increased mass loading to the thickener dominates the improved sludge settlability, and an increase in thickener area is required. Some previous studies have also concluded that the minimum cost will be obtained without a primary clarifier. Von der Emde [6] reached this conclusion on the basis of an analysis of operating data from full-scale treatment plants with and without primary clarifiers. He noted that a primary clarifier might be justified if the level of TSSs in the influent wastewater was high enough. The calculations in Fig. 2 indicate that the marginal cost of including primary clarification is less with increasing wastewater strength, and it is possible that a non-zero minimum will exist for a sufficiently strong waste. Conclusions regarding the economic justifiability of a primary clarifier are probably also dependent on the kinetic assumption in the design program that the specified growth rate is the same for dissolved (BOD), and suspended ( BOD)s. The limited available data suggest that the rate of utilization of suspended (BOD)S is slower, leading to an increase in required aeration basin volume relative to that needed if all the (BOD), is dissolved, but too little is still known to justify separating dissolved and suspended (BOD), kinetics at
B19
this time. Kuo et al. [7] did include a “masking effect” of solids in the Monod equation for a 12 000 m3 day-’ plant operating on medium strength wastewater. They found the minimum cost plant to include a primary settler with a detention time of 1 h, which corresponds to the removal of about 70% solids with polymer addition. This uncertainty in the kinetics clearly has imporI tant design implications. Despite the increased cost, there may be some motivation to include a primary clarifier. Even with a mean residence time of the order of only 1 h, the primary clarifier will tend to spread the effects of feed variations, and particularly shock loads. In the event of aeration system failure the presence of a primary unit will ensure that at least minimal treatment is provided to the wastewater before it is discharged to the receiving water body.
6. SLUDGE
AGE
VOLATILE
SUSPENDED
AND MIXED
LIQUOR
SOLIDS
The remaining calculations discussed here were carried out without primary clarification, since that represents the minimum cost situation. The cost and recycle ratio are shown in Fig. 4 as a function of aeration basin MLVSSs for a sludge age of 10 days. At large values of MLVSSs the recycle ratios are very large,
;; 6.01,
-4.01 ' ' 1000 2000 Mixed
Liquor
1
' 3000
Volotlle (g vss
'
' 4000
Suspended
1
exceeding unity in some cases. A large recycle rate in a plant with high MLVSSs, and hence a small aeration basin, results in a very short hydraulic residence time in the aeration basin. This could lead to operability problems during transients. Indeed, conventional activated sludge plants do not normally operate with recycle ratios greater than 0.50 [8], and a maximum recycle ratio of 0.50 is included in the current version of the design program. The constrained calculations are also shown in Fig. 4. The decrease in cost as the MLVSSs increase from 1000 to 2500 mg 1-l is a consequence of the reduced volume of the aeration basin, since the basin volume is inversely proportional to MLVSSs. This trend is ultimately offset by the increased capital and operational costs of the air supply system and the recycle pump. The very rapid cost increase for the constrained solution for MLVSSs greater than 4000 mg 1-l is associated with the increased cost of the secondary clarifier. Because of the constrained recycle ratio, a clarifier sized on the basis of effluent suspended solids cannot satisfy the thickening constraints, and the area must be increased in order to pass the required amount of solids back to the aeration basin. The increased area will lead to better clarification as well, so the effluent quality will be better than the required TSSs of 20 mg 1-l on the average, but at the expense of a large cost increase. Plant costs for MLVSSs from 1000 to 5000 mg 1-l and sludge age from 2 to 46 days are summarized in Fig. 6. Since actual plant designs were done for sludge age in increments of 2 days and for MLVSSs in increments of 500 mg l-l, the regions shown in the figure are approximate. It is striking to note the
I 5000
Solids
63)
Fig. 4. Cost and recycle ratio as a function of aeration basin MLVSSs with no primary clarifier (sludge age, 10 days): A, any value of recycle ratio allowed; 0, no value of recycle ratio greater than 0.50 allowed; VSS, volatile suspended solids.
Sludge
Fig. 5. Regions clarification.
of constant
Age
cost
(days)
without
primary
B20
relative insensitivity of the cost over broad changes in design variables. Similar results were obtained by Middleton and Lawrence [ 91 in an earlier study. There are two least-cost designs, both having the same total present system cost of US. $4.3 million. These plants both have MLVSSs of 4000 mg l--i; one has a sludge age of 12 days and the other has a sludge age of 14 days. A very large region, however, including sludge ages from 6 to 36 days and MLVSSs from 2500 to 4500 mg l-i, has a cost of only U.S. $4.4 million, which is certainly within the uncertainty of the calculation. Plants with a total cost that is no more than 10% above the minimum exist for sludge ages from 2 to 38 days and MLVSSs from 1000 to 4500 mg 1-i. The minimum cost plants have particularly high recycle ratios and might therefore be expected to be dynamically more sensitive to disturbances than are adjacent lower recycle designs of slightly higher cost. All the calculations described above were carried out using the sludge-settling data discussed in Appendix A. Comparable calculations were carried out using other sludgesettling functions. In one the initial settling velocity was assumed (unrealistically) to continue to increase with increasing sludge age beyond 15 days. The continuously improving settlability does not result in any further decrease in cost, because the secondary clarifier is sized by clarification requirements for sludge ages greater than 12 days. This result emphasizes the importance of the clarification function in establishing the system design and the fact that there is a point of zero marginal return from improved settling. More details regarding the effect of alternative settling assumptions have been presented elsewhere [ 1, 21.
7. OPTIMAL
DESIGN
As the preceding calculations indicate, the notion of an “optimal” design is somewhat nebulous. The minimum cost designs can be clearly identified, and these must be the standard against which other designs are evaluated. There is a large range of designs with costs just slightly above the minimum, however, as illustrated in Fig. 5, and the cost
difference is probably within the uncertainty even of a calculation with good kinetic and settling data on the sludge system in question. Hence, the designer has considerable flexibility and can use other factors besides cost in making a final selection. Plant controllability should be a primary factor in selecting between alternatives, and the remainder of the paper is concerned with this subject. Two designs have been selected for detailed study, either of which might be considered “optimal” on the basis of the steady state calculations. Since it was shown to result in the least-cost design, both plants have no primary clarifier. Plant A is one of the two least-cost designs. It has a sludge age of 14 days, MLVSSs of 4000 mg l-” and a fairly high recycle ratio value of 0.45. This plant represents a departure from usual practice in both the high concentration of MLVSSs and the large recycle ratio. It was desired to compare the least-cost design with another plant which had a cost slightly higher than the minimum but which might have a superior dynamic stability. Plant B was selected for this comparison. It has a total present system cost of U.S. $4.4 million, only 2% higher than the minimum cost. Plant B has a sludge age of 10 days, MLVSSs of 2500 mg 1-i and a recycle ratio of 0.22. It was thought that the lower MLVSSs and the lower recycle ratio compared with those of plant A should result in a longer aeration basin residence time and thus improved dynamic stability. The costs of both plants are to be contrasted with U.S. $5.3 million for the base case design to treat the same wastewater and to meet the same effluent standards. (A base case design with a primary clarifier designed to remove 40% of primary solids would cost U.S. $4.9 million.) Figure 6 shows the present total system cost as a function of sludge age. Costs are plotted for whichever value of MLVSSs gave the lowest cost at a particular sludge age. The locations of plants A and B are shown in the figure. It should be noted that plant B is the plant with the lowest recycle ratio of all plants with a present total system cost of U.S. $4.4 million. The rapid rise in cost shown in Fig. 6 for plants with sludge ages greater than 32 days is related to a decay in the sludge-settling
B21
0
6
16
24 Sludge
32
40
46
Age(days)
Fig. 6. Minimum total present system cost and recycle ratio as a function of sludge age.
characteristics for high sludge ages [ 1, 21. Thus, although the results indicate that a designer has great flexibility in choosing values of sludge age, there are limitations that should not be exceeded.
8. PROCESS
DYNAMICS
Typical 24 h variations in influent flow rate and wastewater characteristics, adapted from Metcalf and Eddy Inc. [lo], are shown in Fig. 7. These variations could cause changes in micro-organism concentration that would alter the distribution among the several carbonaceous species and hence affect both the rate of substrate utilization and the settling characteristics of the micro-organism
d
6
12 Time
16
24
(h)
Fig. 7. 24 h time series of influent flow rate and wastewater strength. (Adapted from Metcalf and Eddy Inc. [lo].)
floes. The settling characteristics are of particular concern, since altered settling characteristics could lead to poor functioning of the secondary clarifier and increased carryover of solids in the clarified effluent. The governing dynamics are in the aeration basin secondary clarifier loop. Attir and Denn [ 111 have shown that two control objectives must be attained: (1) a small variation in aeration basin MLVSSs and (2) maintenance of the clarifier sludge blanket. Objective (2) is important because the sludge blanket buffers the transmission of disturbances back to the aeration basin and hence reduces the detrimental effect on the process response time of the positive dynamic feedback loop associated with recycle. (For a discussion of the dynamics of recycle processes, see ref. 12.) The two control objectives are not compatible. Maintaining aeration basin MLVSSs requires high sludge recycle rates during periods of high influent flow, but raising the sludge recycle rate tends to lower the sludge blanket. Simulation studies have indicated that ratio control on the clarifier underflow and sludge recycle is effective in achieving both control objectives [ 1,111. Ratio control means that the secondary clarifier underflow flow rate and the sludge recycle flow rate are both kept proportional to the influent flow rate; the ratio of these flows to the influent flow is held constant. The 5 day dynamic response of plant A, the optimal design, with no control (constant clarifier underflow and recycle) is shown in Figs. 8 and 9. The plant experiences wide diurnal variations in both aeration basin cell concentration and sludge blanket height. Figures 10 and 11 illustrate the 5 day dynamic response of plant A when ratio control is used on the secondary clarifier underflow and sludge recycle flow rates. It should be noted that the diurnal variations in both aeration basin cell concentration and sludge blanket height have been reduced considerably. A comparison of the dynamic stabilities of plants A and B should be based on the performance of each plant under ratio control. Figures 12 and 13 show the 5 day dynamic response of plant B, the near-optimal design, using ratio control. The diurnal variations in the aeration basin cell concentrations are
24 Time
(h)
Fig. 8. Aeration basin response for the optimal design (plant A); constant clarifier underflow and recycle.
48
72 Time (hl
120
Fig. 10. Aeration basin response for the optimal design (plant A); ratio control on underflow and recycle.
Underflow
Underflow
96
VSS Concentration
VSS Concentratmn
Sludge
Effluent
0 Trme
Fig. 9. Secondary clarifier design (plant A); constant recycle.
lhl
response clarifier
VSS
significantly less for plant B than for plant A. Similarly, the overall stability of the sludge blanket is superior for plant B. Thus, the dynamic simulations indicate that the minimum cost plant A is dynamically more sensitive, and hence more difficult to control, than the more conventional plant B. Given the small difference in computed cost between the two plants, plant B appears to be a better choice of a final design. The 5 day final effluent quality time series for plant B is shown for the case where no control is used (constant underflow and recycle) in Fig. 14. Figure 15 shows the
Height
Concentration
1
I
I
I
I
24
48
72
96
120
Time
for the optimal underflow and
Blanket
(h)
Fig. 11. Secondary clarifier response for the optimal design (plant A); ratio control on underflow and recycle.
effluent quality when ratio control is used. It should be noted that the effluent quality for both cases is almost identical. The invariance of the effluent quality with and without control emphasizes an important fact: process control in response to diurnal feed variations serves to control the internal variables and to maintain the operability of the process, but it has little or no effect on effluent quality, which is fixed by the design and the mean flows. Thus, transient effluent quality should not be used as a basis of comparison between control systems in a welldesigned plant.
B23
0
0
i4
48
7.2 Time
Ii0 (h)
Fig. 12. Aeration basin response for the near-optimal design (plant B); ratio control on underflow and recycle.
24
48
96
72 Time
120
(h)
Fig. 14. Final effluent quality for the near-optimal design (plant B); constant underflow and recycle.
8
7
low3
P
0
TE .z
N
f -
p
0 Time
(h)
Time
(h)
Fig. 13. Secondary clarifier response for the nearoptimal design (plant B); ratio control on underflow and recycle.
Fig. 15. Final effluent quality for the near-optimal design (plant B); ratio control on underflow and recycle.
9. OXYGEN
essentially the same curve is obtained for plants A and B, with and without ratio control on the underflow and recycle. This is because the rate of oxygen uptake is determined by the conversion rate of (BOD)s, which is essentially the same in all cases. Negative values of the dissolved oxygen concentration, as shown in Fig. 16, serve as an indication of the extent to which the oxygen demand is exceeding the oxygen supply. In an actual plant the dissolved oxygen concentration can obviously never drop below zero. As the dissolved oxygen
CONTROL
The kinetic expressions used in the steady state and transient simulations require that the dissolved oxygen level always be above the minimum value at which kinetics are oxygen independent. The air supply system is sized by the steady state program to ensure that this is true on the average, but the dissolved oxygen concentration will vary during the transient unless control is used. The computed dissolved oxygen concentration during a 24 h transient is shown in Fig. 16;
Dissolved
Oxygen
Recommended
DO
-* -* 0
-N
AT-
“do Time
(h)
Fig. 16. Aeration-basin-dissolved oxygen (DO) with constant air flow rate; plant B with ratio control on underflow and recycle.
Recommended
DO
measurement. (In practice, since the integration scheme uses finite time steps, an oxygen measurement is required about once every 15 min.) The result in Fig. 17 shows the dissolved oxygen concentration for the simulation of plant B when the blower rate is increased or decreased by 10% following each dissolved oxygen measurement in which the concentration is found to be below 2.0 mg 1-l or above 3.0 mg 1-l respectively. This is a simple and effective scheme as long as reliable dissolved oxygen measurements are available. The maximum air flow rate for the control shown in Fig. 17 is approximately twice the design air flow rate (the firm blower capacity). Some small- and medium-sized plants have a maximum blower capacity with all units in service that exceeds the firm blower capacity by a factor of 1.5 - 2.0, so it might be possible to implement the oxygen control with the blowers designed by the steady state program as long as all blowers are usually in a working condition [ 1,4]. A more conservative strategy would be to design the process with a firm blower capacity based on the maximum demand.
ACKNOWLEDGMENT
0
6
12 Time
18
24
(h)
Fig. 17. Aeration-basin-dissolved oxygen with oxygen feedback control; plant B with ratio control on underflow and recycle.
The work on which this paper is based was supported by funds provided by the U.S. Department of the Interior, Office of Water Research and Technology, as authorized under the Water Research and Development Act of 1978, Public Law 95-467.
REFERENCES
concentration approaches zero, the metabolic activity of the bacteria drops off rapidly. This dependence of the (BOD), degradation rate on the dissolved oxygen concentration was not included in the dynamic simulations presented here and thus results in negative dissolved oxygen concentrations. Several alternative dissolved oxygen control strategies have been evaluated using the dynamic model, and the results have been presented elsewhere [ 11. The only successful strategy requires continuous dissolved oxygen
R. B. Paterson and M. M. Denn, Design and control of an activated sludge process for municipal wastewater treatment, Tech. Completion Rep., 1980 (Water Resources Center, University of Delaware, Newark, DE) (Project A-041-DEL). R. B. Paterson and M. M. Denn, Least cost design and design sensitivity of an activated sludge treatment system, Industrial Waste, Proc. 13fk Mid-Atlantic Conf., Ann Arbor Science, Ann Arbor, MI, 1981, p. 189. U. Attir, M. M. Denn and C. A. Petty, Dynamic simulation of continuous sedimentation, AICkE
Symp.
Ser., I67 (73) (1977)
49.
B25
The aeration basin is assumed to be well mixed. The mass balance equations for biochemical oxygen demand over a period of 5 days ((BOD),) and carbonaceous microorganisms are as follows:
to the flow rate of the influent to the aeration basin. The kinetic parameters are given in Table 2. The most important assumption here is that the consumption rates for suspended and dissolved (BOD)5 are the same or, in other words, that the total (BOD), in the influent to the aeration basin can be modeled as if it were all present in the dissolved form. Equations identical with eqn. (A2) are used for the micro-organisms Nitrosomonas and Nitrobacter. The steady state design equations are obtained by setting time derivatives d/dt equal to zero. Each aeration basin is taken to be rectangular, with a width and depth of 6 m and a maximum length of 45 m. The rate of oxygen uptake is computed from an oxygen balance that includes the metabolic rates of the biochemical reactions. The required air flow is determined from the overall mass transfer coefficient needed to maintain the dissolved oxygen concentration at the required level, taken here to be 2 mg l-l, using the correlation of Schmit et al. [Al] for a diffused air system. The thickening section of the secondary clarifier is modeled with the simulation described by Attir et al. [ A2], which reduces to conventional flux theory at steady state. Batch settling data of Dick and Javaheri [ A3], Tracy [ A41 and Munch [ A51 were fitted with the form
VI:
u = u. exp(-4.5
4
W. L. Patterson and R. F. Banker, Estimating costs and manpower requirements for conventional wastewater treatment facilities, Water
Poll&.
Control
Res. Ser. 17090DANl
O/71, 1971
(U.S. Environmental Protection Agency). D. R. Woods, S. J. Anderson and S. L. Norman, Can. J. Chem. Eng., 57 (1979) 385. W. Von der Emde, To what extent are primary tanks required?, Water Res., 6 (1972) 395. M. T. Kuo, L. T. Fan and L. E. Erickson, Effects of suspended solids primary clarifier size optimization, J. Water Pollut. Control Fed., 46 (1974)
2521. 8
9
10 11
12
L. D. Benefield
and C. W. Randall,
Process
for
Design
Wastewater
Biological
Treatment,
Prentice-Hall, Englewood Cliffs, NJ, 1980. A. C. Middleton and A. W. Lawrence, Least cost design of activated sludge systems, J. WaterPollut. Control Fed., 48 (1976) 889. Metcalf and Eddy Inc., Wastewater Engineering, McGraw-Hill, New York, 1972. U. Attir and M. M. Denn, Dynamics and control of the activated sludge wastewater process, AZChE J., 24 (1978) 693. M. M. Denn and R. Lavie, Dynamics of plants with recycle, Chem. Eng. J., 24 (1982) 55.
APPENDIX
A
=Qf(Bf---B)-
;+&X& c
(Al) UC = rQf-L Kdt
X 10m4X)
(A3)
B
- (1 + r)QfX,
X,V,
+
(A3
where B and X, denote the concentrations of dissolved ( BOD)5 and total carbonaceous cells respectively in milligrams per liter; without additional subscripts they represent the concentrations in the aeration basin and in the basin effluent. A subscript f denotes the feed stream to the aeration basin, a subscript a denotes the aeration basin and a subscript u denotes the underflow from the secondary clarifier. V and Q are the volume and volumetric flow rate respectively and r is the ratio of the flow rate of the recycle stream
.where X is the concentration of volatile suspended solids in milligrams per liter. The initial settling velocity u. is taken to depend on sludge age according to the function shown in Fig. Al. The rising portion of the function is based on the data of Bisogni and Lawrence [ A6], while the turndown follows from the limited data of Ford and Eckenfelder [ A7]. Recent work by Wu and Mahmud [ A81 has reinforced the work of these earlier researchers. Two other assumptions regarding the change in sludge-settling characteristics are possible and have been discussed elsewhere [ A9, AlO]. In one, u. was taken to have a constant value of 143 m day-’ and, in the other, u. was identical with the function shown in Fig. Al except that u. continued to rise at the same rate after a sludge age of 15 days.
I326
The primary clarifier area is sized on the basis of the empirical equation 1 -
Ap-
3.82 X 10-3Qf 0.6355 -R/P
+1.99 X 10-4(TSSs)pf (A6)
R is the fractional
Sludge
Fig. Al. Initial settling sludge age.
Age
(days)
velocity
as a function
The mean sludge age is defined 9, =
KXC wQfXcu + (1 - w)QfXce
of
here as (A4)
where w is the ratio of the sludge wastage flow rate to the aeration basin influent flow rate and X,, is the concentration of carbonaceous volatile suspended solids in the effluent from the secondary clarifier. The area required for clarification in the secondary clarifier is determined in terms of the total effluent volatile suspended solids X, using the following equation obtained from the correlation by Rex Chainbelt Inc. [All] : A, =
0.267(1
- w)Qf
X, + 2.7 X 1O-3X, - 15.0
(A5)
where Qf is in cubic meters per day, A, is in cubic meters and X, is the total concentration of mixed liquor volatile suspended solids (MLVSSs) in milligrams per liter. This correlation gives results consistent with the rule-ofthumb values suggested by Kalinske [A12]. The settler area is fixed initially at an integer size in meters by eqn. (A5). The side wall depth is set at 4 m and the center depth at 5 m. The maximum diameter of a single unit is 40 m; if a larger area is required, then two or more units are stipulated. Thickening calculations are then carried out to ensure that the area is adequate for thickening; if additional area is required, the diameter is increased in integral increments until the thickening constraint is satisfied. The settler area will typically be set by thickening requirements when the aeration basin MLVSSs are in excess of about 3500 mg 1-l.
removal of primary suspended solids, (TSSs)pf is the total suspended solids (TSSs) of the influent wastewater and P is an enhancement factor for the addition of anionic polymer. P is linearly dependent on polymer concentration, with a value of 1.5 for a polymer concentration of 1.0 mg 1-l. This equation gives overflow rates and removal efficiencies in the range of the rule-ofthumb values suggested by Metcalf and Eddy Inc. [A13]. Each unit is set at a depth of 3 m, a width of 6 m and a maximum length of 45 m. The chlorine contact system is sized by requiring 15 min of residence time at peak flow, which is taken to be 140% of mean flow, with a length that is at least 40 times the width. The chlorine addition rate is set at 5 mg 1-i. The sludge thickener is sized on the basis of recommended solids loading rates. The overall sludge loading rate is taken as a massflow-weighted average of the recommended primary and secondary values. The diameter is fixed at less than 40 m. Sludge is assumed to be thickened to 90 000 mg 1-i of TSSs. The anaerobic digester is modeled as a well-stirred reactor, using equations analogous to eqns. (Al) and (A2), with r = 0, with the following kinetic parameters at 35 “C: pm = 0.28 day-‘; K = 154 mg 1-l of (BOD)S; b = 0.023 day-‘; Y = 0.04 g of volatile suspended solids per gram of (BOD),. Four times the volume computed for a 60% reduction in volatile suspended solids was typically in the middle of rule-of-thumb loading factors, so this procedure was adopted as the design algorithm, with the second-stage volume taken to be equal to the first. The total underflow suspended solids are taken to be 80 000 mg 1-i. Finally, the solids centrifuge, following Zenz et al. [A14], is assumed to operate at a solids capture rate of 93.2% with a thickened total solids concentration of 200 000 mg 1-l. Final sludge disposal is
accomplished by hauling sanitary landfill.
the sludge to a
References for Appendix A Al
A2
A3
A4
A5
A6
A7
F. L. Schmit, J. D. Wren and D. T. Redman, The effect of tank dimensions and diffuser placement on oxygen transfer, J. Water Poll&. Control Fed., 50 (1978) 1750. U. Attir, M. M. Denn and C. A. Petty, Dynamic simulation of continuous sedimentation, AIChE Symp. Ser., 167 (73) (1977) 49. R. I. Dick and A. R. Javaheri, Continuous thickening of non-ideal suspensions, Res. Rep. 45, 1972 (University of Illinois Water Resources Center, Urbana-Champaign, IL). K. Tracy, Mathematical modeling of unsteadystate thickening of compressible slurries, Ph.D. Thesis, Clemson University, Clemson, SC, 1973. W. L. Munch, Performance of full-scale circular final clarifier for activated sludge, Master’s Thesis, Northwestern University, Evanston, IL, 1976. J. J. Bisogni and A. W. Lawrence, Relationships between biological solids retention time and settling characteristics of activated sludge, Wuter Res., 5 (1971) 753. D. L. Ford and W. W. Eckenfelder, Effect of process variables on sludge floe formation and settling characteristics, J. Water PoNut. Control
Fed., 39 (1967) 1850. A8 Y. C. Wu and Z. Mahmud, Performance of final clarifier as a function of wastewater characteristics, Industrial Waste, Proc. 13th Mid-Atlantic Conf., Ann Arbor Science, Ann Arbor, MI, 1981, p. 370. A9 R. B. Paterson and M. M. Denn, Design and control of an activated sludge process for municipal wastewater treatment, Tech. Completion Rep., 1980 (Waters Resources Center, University of Delaware, Newark, DE) (Project A-041 -DEL). Al0 R. B. Paterson and M. M. Denn, Least cost design and design sensitivity of an activated sludge treatment system, Industrial Waste, Proc. 13th Mid-Atlantic Conf., Ann Arbor Science, Ann Arbor, MI, 1981, p. 189. All Rex Chainbelt Inc., A mathematical model of a final clarifier, Rep., 1972 (U.S. Government Printing Office) (U.S. Environment Protection Agency Project 17090FJW). A12 A. A. Kalinske, Comparison of air and oxygen activated sludge systems, J. Water Pollut. Control Fed., 48 (1976) 2472. Al3 Metcalf and Eddy Inc., Wastewater Engineering, McGraw-Hill, New York, 1972. Al4 D. R. Zenz, B. Sawyer, R. Watkins, C. Lue-Hing and G. Richardson, Evaluation of dewatering equipment for anaerobically digested sludge, J. Water Pollut. Control Fed., 50 (1978) 1965.
Journal, 27 (1983)
B13 - B27
B13
Computer-aided Design and Control of an Activated SluQge Process* ROBERT
Department (Received
B. PATERSON+
and MORTON
of Chemical Engineering, July
14, 1982;
M. DENNS
University
of Delaware,
Newark,
DE 19711
(U.S.A.)
.
in final form May 4, 1983)
The activated sludge process for wastewater treatment is studied by use of steady state and dynamic process models. Process constraints fix the steady state with only three designer-selected parameters: the percentage removal of suspended solids in the primary clarifier, the aeration basin suspended solids and the sludge age. A primary clarifier cannot be justified economically. Total plant cost (construction plus operation) is insensitive to the other two design variables over a wide range. The transient analysis enables controllability to be taken into account when making a final design decision between alternatives that are equally attractive economically. In a comparison of designs for a plant processing 20 000 m3 day-’ of medium strength wastewater, it was found that dynamic stability was enhanced by operating with lower aeration basin suspended solids and recycle ratio. Continuous control of dissolved oxygen was shown to be important, and the oxygen control system might require more blower capacity than is indicated by a steady state design.
Design is typically carried out on a steady state basis, and operability under normal diurnal transients is not taken into account. In this paper a set of interactive computer programs that simulate the steady state and transient response of an activated sludge wastewater treatment system is discussed. The steady state program includes construction and operating costs and thus enables rapid economic evaluation of a proposed design. The transient simulation provides an opportunity to incorporate into a final decision the relative controllability of alternative designs that may be equally attractive economically. The model and representative results have been discussed in detail elsewhere [l, 21; some of the major results are summarized here. Because of constraints imposed by the system structure and by effluent requirements, the steady state program will compute the design of a complete plant, for a set of given wastewater characteristics and flow rate, on the basis of three designer inputs: (1) percentage removal of suspended solids in the primary clarifier, (2) aeration basin mixed liquor volatile suspended solids (MLVSSs) and (3) sludge age.
1. INTRODUCTION
2. PROCESS
The optimal design of an activated sludge process for the treatment of municipal wastewater requires an analysis of the interactions between the major unit processes and an evaluation of system performance versus cost.
The process flow sheet is shown in Fig. 1. The aeration basin is assumed to be well mixed, and a circular secondary clarifier has been specified. Multiple aeration basins and clarifiers may be specified by the program as required by the plant flow rate. Brief descriptions of the mathematical models of the individual unit operations are contained in Appendix A. The model of the aeration basin is a fundamental model that is based on mass balances and kinetic information on the growth rates of both carbonaceous and nitrifying bacteria. The model of the thicken-
ABSTRACT
*Paper presented at the Fifty-fourth Annual Water Pollution Control Federation Conference, Detroit, MI, U.S.A., October 4 - 9, 1981. +Present address: Radian Corporation, McLean, VA 22102, U.S.A. *Present address: Department of Chemical Engineering, University of California, Berkeley, CA 94720, U.S.A. 0300-9467/83/$3.00
@ Elsevier Sequoia/Printed
in The Netherlands
B14
Chlorination system
Secondary Settler
Aerotton Basin
Primary Settler
Preliminary Treatment
~nxz
1,
ttttttt Diffused
Primary Sludge wostoge
Air
Underflow
Feed Recycle wastage
Two-Stage Thickener
Polymer Feed
Ancerobic Digester
Solids Centrifuge
------7 1
Return To Sludge Thickener -7
Thickener Underflow
Fig. 1. Schematic
diagram
Final Waste Sludge (To Landf!ll)
of an activated
sludge wastewater
1
Average wastewater composition used in the simulations for medium strength domestic wastewater
Parameter
Concentration (mg 1-l)
Total (BOD)s, 20 “C! Dissolved (BOD)s , 20 “C Suspended (BOD)s , 20 “C
200 70 130
TSSs Volatile suspended solids Fixed suspended solids
200 150 50
Total nitrogen (as N) Ammonia nitrogen (as N) Nitrite nitrogen (as N) Nitrate nitrogen (as N) Organic nitrogen (as N)
40 25 0 0 15
Total phosphorus Dissolved phosphorus Suspended phosphorus
10 7
TABLE
constants
Kinetic
constant
Y
3
2
Kinetic
l-h b K
system.
primary clarifier and the clarification section of the secondary clarifier are described by empirical equations. The steady state simulation program is limited to the unit process arrangement shown in Fig. 1. All plants discussed here have been designed to meet an average effluent quality with a total biochemical oxygen demand over a period of 5 days (( BOD)s) of 20 mg 1-l and total suspended solids (TSSs) of 20 mg 1-l. The average flow rate and the wastewater characteristics are required as input from the user; the characteristics of the medium strength wastewater used in the simulations here are shown in Table 1. The kinetic parameters are also required for the growth rates of the bacteria that degrade (BOD)5 and nitrogen compounds. The carbonaceous bacteria are considered to be a single pseudo-species, and (BOD)5 to be a single pseudo-component. The kinetic parameters in Table 2 are the values used here; these are typical of municipal wastewaters and thus can be used in the simulation program in the absence of wastewater-specific values.
ing section of the secondary clarifier is also fundamental and utilizes the simulation program described by Attir et al. [3]. The
TABLE
treatment
used in the simulations
for carbonaceous
and nitrifying
bacteria
at 20 “C!
Carbonaceous
Nitrosomonas
Nitrobacter
5.0 day-r 0.055 day-’ 100 mg 1-l of (BOD)s 0.50 g of volatile suspended solids per gram of (BOD)s
0.33 day-’ 0.05 day-’ 1.0 mg 1-l of NHa-N 0.05 g of volatile suspended solids per gram of NH4-N -I_
0.80 day-’ 0.05 day-’ 2.1 mg 1-l of N02-N 0.02 g of volatile suspended solids per gram of N02--N __-
B15 3. ECONOMIC EVALUATION
The cost of construction and the annual cost of operation and maintenance (0 & M) for each unit in the plant is determined from the data of Patterson and Banker [4] for wastewater treatment processes. Where comparison is possible, their data are consistent with the process industry cost functions compiled by Woods et al. [ 51. The data were correlated in the conventional power equation form, in which the cost of the unit is expressed as a function of some unit process size characteristic such as the primary clarifier surface area or the recycle pump flow rate. For example, the installed cost of the primary clarifier is estimated from the following equation: construction cost in 1978 U.S. dollars
4. BASE CASE DESIGN
06? = 3355.0
X
(1)
The data were converted to 1978 U.S. dollars using the September 1978 chemical engineering plant cost index; the current value of the index can be used to update the economic base. Data of this type are typically accurate to within *(15% - 30%). For this reason, all unit process costs are automatically rounded off to two significant figures by the program. The plant cost is evaluated on a present worth basis. The present total system cost represents the capital that must be available at time zero to pay construction costs and 0 & M costs over the entire plant lifetime. The present total system cost is calculated as follows: total present total system = capital cost cost
+ PWF
Although we have not done so in our examples, the PWF can be looked on as a design parameter. The PWF plays the role of a Lagrange multiplier in either of two optimal design formulations: (1) the minimization of 0 & M for fixed construction cost or (2) the minimization of construction cost for fixed 0 & M. The first of these could be an attractive formulation if subsidies exist for construction but not for operating costs. The PWF then reflects the sensitivity of the design to cost changes. In that case, a design would be sought that is near the minimum cost over a range of values of PWF, even if the design never represents the absolute minimum cost for any one PWF.
(2)
where the present worth factor (PWF) determines the amount of capital needed at time zero to be able to pay annual 0 & M costs for the entire life of the plant and to have zero capital remaining at the end of the plant life. The sample calculations reported here are based on a net interest rate of 10% and a lifetime of 20 years, corresponding to a present worth factor of 8.6. The PWF varies between zero (infinite interest rates) and the number of years over which 0 & M costs must be paid (zero net interest).
The base case for this study is a plant to treat 20 000 m3 day-l (5.3 X lo6 gal day-‘) of medium strength wastewater with the composition listed in Table 1. There is to be 60% removal of primary solids, a sludge age of 10 days and aeration basin MLVSSs of 2000 mg 1-l. A typical print-out of the detailed design specifications for the secondary clarifier is shown in Table 3. Similar printouts are also generated by the steady state design program for all the other unit processes. The computer-generated cost breakdowns for construction and annual 0 & M for the entire plant are shown in Tables 4 and 5 respectively, and the overall economic summary is shown in Table 6. The present total cost of this plant in 1978 U.S. dollars, using a 10% effective net interest rate, is U.S. $5.3 million. Table 6 also indicates the average treatment cost in U.S. dollars per cubic meter of water treated. For the base case plant the average cost of treatment is 3.6 U.S. & m-‘, which is equivalent to 14 U.S. & per thousand gallons. It is important to note that the average cost of treatment was calculated as the present total system cost divided by the total volume of water treated in 20 years of plant operation. The more common method of calculating average treatment cost is to calculate the annualized plant cost, which is the sum of the annualized cost of capital plus the 0 & M costs, and to divide by the total volume of water treated in 1 year of plant operation.
B16 TABLE
3
Secondary
clarifier
design summary __I__--.-
Total
Concentration (g mP3) Total (BOD)s, 20 “C Dissolved (BOD)s , 20 “C Suspended (BOD)s, 20 “C TSSs Volatile suspended solids Fixed suspended solids
Feed
1811 3.2 1808 2598 2018 520
Total nitrogen NH4-N N02-N NOs-N Organic nitrogen Total phosphorus Dissolved phosphorus Suspended phosphorus
276 0.8 0.5 23.7 251 63 7.0 56.1
Feed flow rate (m3 day-r)
23013
Underflow flow rate (m3 day-‘) Recycle flow rate (m3 day-‘) Effluent flow rate (m3 day-‘) Underflow ratio Recycle ratio Wastage ratio Effluent ratio Overflow rate (m3 me2 day-r) Total area (m2 ) Number of units Settler diameter (m) Construction cost (U.S. $)
3092 3061 19921 0.1549 0.1534 0.0015 0.9985 23.3 855.3 1 33.0 310000
Effluent
Underflow
16.8 3.2 13.6 19.5 15.6 3.9
13374
26.9 0.8 0.5 23.7 1.9 7.4 7.0 0.4
1885
The latter method of calculation leads to an average treatment cost of 8.5 U.S. & mm3 or 32 U.S. & per thousand gallons. Thus these two methods of calculating average treatment cost are not equivalent. There are several interesting points here that bear directly on the economic evaluation of the plant. First, the construction cost and the present value of 20 years’ worth of 0 & M costs are comparable (U.S. $2.9 million uersus U.S. $2.4 million). Thus, design evaluations based only on minimizing construction costs could be seriously in error. Furthermore, the result is very sensitive to the projected interest and inflation rates. If, for example, the effective annual interest rate is reduced from 0.10 to 0.05, then the present worth factor is increased from 8.6 to 12.5, and the present worth of 0 & M costs is increased to U.S. $3.5 million. Hence, lower interest rates will favor capital-cost-intensive plants with low 0 & M costs.
Bottom zone
Zone I
19210 15368 3842
15842 12674 3168
Zone 2
Clarifier zone
-
3.2 13370 19210 15638 3842
334 261 67
19.5 15.6 3.9
0.8 0.5 23.7 1860 422 7.0 415
The air supply system is a major factor in both the construction and the 0 & M costs. It represents most of the plant electrical cost, for example, which is in turn 13% of the total 0 & M cost. The air supply system was sized to meet the oxygen demand at the average wastewater flow rate and (BOD), loading. Dynamic simulations presented later in this paper will show that the air supply system capacity, when sized in this manner, is just adequate to meet peak oxygen demands at periods of high flow and high (BOD), loading, provided that all blowers are in service. Since the situation where at least one blower is out of service is common, it is possible that a more conservative design basis might be employed. For example, the program could instead specify a firm blower capacity adequate to meet the expected daily maximum oxygen demand. Because of the impact of the air system on total costs, such a change could affect the selection of a final design.
B17 TABLE
4
Construction
TABLE
cost (X103
U.S.
Percentage of total
Total
Land (18.6 acres) Engineering Legal, fiscal, administration Interest during construction Total
TABLE
construction
capital
130 350 20 310 290 310 46 2 50 6 39 2 180 140 150 46 290 2362
summary
construction
for an evaluation
capital
(X103
(1978)) Total annual costs per year (X103
$ (1978)) Preliminary treatment Primary clarifier Primary sludge pump Aeration tank Air supply system Secondary settler Recycle pump Wastage pump Chlorination tank Chlorine feed system Sludge thickener Thickener pump Anaerobic digester Solids centrifuge Laboratory facilities Garage and shop Yardwork Total construction cost
6
Final economic 20 years
cost summary
5.5 14.8 0.8 13.1 12.3 13.1 1.9 0.1 2.1 0.3 1.7 0.1 7.6 5.9 6.4 1.9 12.3 100.0
(1978)) Present worth Present worth
$
U.S.
$
factor of 20 years of annual costs
5. PRIMARY
-
of
2910
at 10.0% interest (X103 U.S. $ (1978)) Present total cost (total construction capital and present worth of 20 years’ operation costs) (X103 U.S. $ (1978)) Average treatment cost (U.S. $ (1978) (m3 HzO)-‘)
93 270 35 150 2910
U.S.
period
2797 8.51 2382 5291
0.036
CLARIFIER
The effect of the primary clarifier was studied in detail for sludge ages ranging from 2 to 20 days and MLVSSs in the range 1000 5000 mg 1-l. The plant cost as a function of primary clarifier efficiency is shown in Fig. 2 for a sludge age of 10 days and MLVSSs of 2000 mg 1-l. Results are shown for strong and weak wastewater, as well as for the medium
5
Annual expenses
Cost (X103 U.S. $ (1978) Operation
Preliminary treatment Primary clarifier Primary sludge pump Aeration tank Air supply system Secondary settler Recycle pump Wastage pump Chlorination tank Chlorine feed system Sludge thickener Thickener pump Anaerobic digester Solids centrifuge Laboratory facilities Yardwork Administration and general Indirect labor costs Total Percentage
of annual costs
10
7.6 2.5 0 29 7 2.2 0.4 0 4.8 1.3 0.4 3.1 16 23 0 8.1 16 131.5 47.0
Maintenance
4.9 3.9 0.8 0
6.3 3.6 1.7 0.4 0 0.9 0.7 0.4 2.1 2.3 1.2 9.6 1.7 5.6 45.9 16.4
year-‘)
Material and supply 5.6 3.2 0.7 0 8.2 2.8 0.5 0.01 0 0
0.3 0.01
2.5 9.8 1.3 2.2 6.1 0 45.6 16.3
Electrical
0 0
Chemical
0.04 0 36 0 1.3 0.02 0 0 0 0.03 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 10 0 0 0 9.4 0 0 0 0
37.4 13.4
19.4 6.9
Total
20.5 14.7 4.0 0 79.5 13.4 5.7 0.8 0 18.1 2.3 0.8 7.7 37.5 25.5 11.8 15.9 21.6 279.7 100.0
Percentage of total
7.3 5.3 1.4 0.0 28.4 4.8 2.0 0.3 0.0 6.5 0.8 0.3 2.8 13.4 9.1
4.2 5.7 7.7 100.0
B18
c b = 8
6.0 -
400,
I I
300
.
AtrSupply System
200 50 40 -
Sludge
Thickener
I
Solids
30(1 3.0 0
I IO Percent
1 20 Removal
I 30
k 40
Promary
Fig. 2. Cost as a function
I 50 Suspended
of primary
I 60 Sohds
clarifier
efficiency.
strength wastewater used in the base case. All costs shown in Fig. 2 are for a plant where no polymer is used to enhance settling in the primary clarifier. The minimum cost in all cases occurs with no primary clarifier. The same result was obtained for all sludge ages and MLVSSs studied and for plants that do add polymer to the primary clarifier. The apparent economic trade-offs related to primary settling are clear. Increased primary clarification requires more area, and therefore a more expensive settler. The reduced (BOD)s load to the aeration basin, however, will allow construction of a smaller aeration basin and air supply system. These effects can be seen in Fig. 3, where the individual unit construction costs are plotted for a sludge age of 10 days and MLVSSs of 2000 mg 1-l. The trade-off is roughly even in the intermediate range of 20% - 40% removal, but the large cost associated with the existence of any primary clarifier cannot be offset by savings elsewhere in the process. Some of the non-linearities in the process are also evident in Fig. 3. The required size of the primary clarifier more than doubles for the removal of between 50% and 60% primary solids, and it appears that if primary clarification is to be used for the system studied here it should be designed for no more than 40% or 50% removal. It should be noted that the cost of the sludge thickener does not increase until the removal of primary suspended solids exceeds 50%. Since primary sludge thickens more easily than secondary waste activated sludge, the thickener can accommodate the increases in the amount of primary sludge
200
I
01
100
0
IO Percent
20 Removal
Centrifuge
30 Primary
1
40
50
60
Suspended
Solids
Fig. 3. Construction function of primary
cost of six unit processes clarifier efficiency.
as a
generated without increases in thickener area. For removal of more than 50%, however, the increased mass loading to the thickener dominates the improved sludge settlability, and an increase in thickener area is required. Some previous studies have also concluded that the minimum cost will be obtained without a primary clarifier. Von der Emde [6] reached this conclusion on the basis of an analysis of operating data from full-scale treatment plants with and without primary clarifiers. He noted that a primary clarifier might be justified if the level of TSSs in the influent wastewater was high enough. The calculations in Fig. 2 indicate that the marginal cost of including primary clarification is less with increasing wastewater strength, and it is possible that a non-zero minimum will exist for a sufficiently strong waste. Conclusions regarding the economic justifiability of a primary clarifier are probably also dependent on the kinetic assumption in the design program that the specified growth rate is the same for dissolved (BOD), and suspended ( BOD)s. The limited available data suggest that the rate of utilization of suspended (BOD)S is slower, leading to an increase in required aeration basin volume relative to that needed if all the (BOD), is dissolved, but too little is still known to justify separating dissolved and suspended (BOD), kinetics at
B19
this time. Kuo et al. [7] did include a “masking effect” of solids in the Monod equation for a 12 000 m3 day-’ plant operating on medium strength wastewater. They found the minimum cost plant to include a primary settler with a detention time of 1 h, which corresponds to the removal of about 70% solids with polymer addition. This uncertainty in the kinetics clearly has imporI tant design implications. Despite the increased cost, there may be some motivation to include a primary clarifier. Even with a mean residence time of the order of only 1 h, the primary clarifier will tend to spread the effects of feed variations, and particularly shock loads. In the event of aeration system failure the presence of a primary unit will ensure that at least minimal treatment is provided to the wastewater before it is discharged to the receiving water body.
6. SLUDGE
AGE
VOLATILE
SUSPENDED
AND MIXED
LIQUOR
SOLIDS
The remaining calculations discussed here were carried out without primary clarification, since that represents the minimum cost situation. The cost and recycle ratio are shown in Fig. 4 as a function of aeration basin MLVSSs for a sludge age of 10 days. At large values of MLVSSs the recycle ratios are very large,
;; 6.01,
-4.01 ' ' 1000 2000 Mixed
Liquor
1
' 3000
Volotlle (g vss
'
' 4000
Suspended
1
exceeding unity in some cases. A large recycle rate in a plant with high MLVSSs, and hence a small aeration basin, results in a very short hydraulic residence time in the aeration basin. This could lead to operability problems during transients. Indeed, conventional activated sludge plants do not normally operate with recycle ratios greater than 0.50 [8], and a maximum recycle ratio of 0.50 is included in the current version of the design program. The constrained calculations are also shown in Fig. 4. The decrease in cost as the MLVSSs increase from 1000 to 2500 mg 1-l is a consequence of the reduced volume of the aeration basin, since the basin volume is inversely proportional to MLVSSs. This trend is ultimately offset by the increased capital and operational costs of the air supply system and the recycle pump. The very rapid cost increase for the constrained solution for MLVSSs greater than 4000 mg 1-l is associated with the increased cost of the secondary clarifier. Because of the constrained recycle ratio, a clarifier sized on the basis of effluent suspended solids cannot satisfy the thickening constraints, and the area must be increased in order to pass the required amount of solids back to the aeration basin. The increased area will lead to better clarification as well, so the effluent quality will be better than the required TSSs of 20 mg 1-l on the average, but at the expense of a large cost increase. Plant costs for MLVSSs from 1000 to 5000 mg 1-l and sludge age from 2 to 46 days are summarized in Fig. 6. Since actual plant designs were done for sludge age in increments of 2 days and for MLVSSs in increments of 500 mg l-l, the regions shown in the figure are approximate. It is striking to note the
I 5000
Solids
63)
Fig. 4. Cost and recycle ratio as a function of aeration basin MLVSSs with no primary clarifier (sludge age, 10 days): A, any value of recycle ratio allowed; 0, no value of recycle ratio greater than 0.50 allowed; VSS, volatile suspended solids.
Sludge
Fig. 5. Regions clarification.
of constant
Age
cost
(days)
without
primary
B20
relative insensitivity of the cost over broad changes in design variables. Similar results were obtained by Middleton and Lawrence [ 91 in an earlier study. There are two least-cost designs, both having the same total present system cost of US. $4.3 million. These plants both have MLVSSs of 4000 mg l--i; one has a sludge age of 12 days and the other has a sludge age of 14 days. A very large region, however, including sludge ages from 6 to 36 days and MLVSSs from 2500 to 4500 mg l-i, has a cost of only U.S. $4.4 million, which is certainly within the uncertainty of the calculation. Plants with a total cost that is no more than 10% above the minimum exist for sludge ages from 2 to 38 days and MLVSSs from 1000 to 4500 mg 1-i. The minimum cost plants have particularly high recycle ratios and might therefore be expected to be dynamically more sensitive to disturbances than are adjacent lower recycle designs of slightly higher cost. All the calculations described above were carried out using the sludge-settling data discussed in Appendix A. Comparable calculations were carried out using other sludgesettling functions. In one the initial settling velocity was assumed (unrealistically) to continue to increase with increasing sludge age beyond 15 days. The continuously improving settlability does not result in any further decrease in cost, because the secondary clarifier is sized by clarification requirements for sludge ages greater than 12 days. This result emphasizes the importance of the clarification function in establishing the system design and the fact that there is a point of zero marginal return from improved settling. More details regarding the effect of alternative settling assumptions have been presented elsewhere [ 1, 21.
7. OPTIMAL
DESIGN
As the preceding calculations indicate, the notion of an “optimal” design is somewhat nebulous. The minimum cost designs can be clearly identified, and these must be the standard against which other designs are evaluated. There is a large range of designs with costs just slightly above the minimum, however, as illustrated in Fig. 5, and the cost
difference is probably within the uncertainty even of a calculation with good kinetic and settling data on the sludge system in question. Hence, the designer has considerable flexibility and can use other factors besides cost in making a final selection. Plant controllability should be a primary factor in selecting between alternatives, and the remainder of the paper is concerned with this subject. Two designs have been selected for detailed study, either of which might be considered “optimal” on the basis of the steady state calculations. Since it was shown to result in the least-cost design, both plants have no primary clarifier. Plant A is one of the two least-cost designs. It has a sludge age of 14 days, MLVSSs of 4000 mg l-” and a fairly high recycle ratio value of 0.45. This plant represents a departure from usual practice in both the high concentration of MLVSSs and the large recycle ratio. It was desired to compare the least-cost design with another plant which had a cost slightly higher than the minimum but which might have a superior dynamic stability. Plant B was selected for this comparison. It has a total present system cost of U.S. $4.4 million, only 2% higher than the minimum cost. Plant B has a sludge age of 10 days, MLVSSs of 2500 mg 1-i and a recycle ratio of 0.22. It was thought that the lower MLVSSs and the lower recycle ratio compared with those of plant A should result in a longer aeration basin residence time and thus improved dynamic stability. The costs of both plants are to be contrasted with U.S. $5.3 million for the base case design to treat the same wastewater and to meet the same effluent standards. (A base case design with a primary clarifier designed to remove 40% of primary solids would cost U.S. $4.9 million.) Figure 6 shows the present total system cost as a function of sludge age. Costs are plotted for whichever value of MLVSSs gave the lowest cost at a particular sludge age. The locations of plants A and B are shown in the figure. It should be noted that plant B is the plant with the lowest recycle ratio of all plants with a present total system cost of U.S. $4.4 million. The rapid rise in cost shown in Fig. 6 for plants with sludge ages greater than 32 days is related to a decay in the sludge-settling
B21
0
6
16
24 Sludge
32
40
46
Age(days)
Fig. 6. Minimum total present system cost and recycle ratio as a function of sludge age.
characteristics for high sludge ages [ 1, 21. Thus, although the results indicate that a designer has great flexibility in choosing values of sludge age, there are limitations that should not be exceeded.
8. PROCESS
DYNAMICS
Typical 24 h variations in influent flow rate and wastewater characteristics, adapted from Metcalf and Eddy Inc. [lo], are shown in Fig. 7. These variations could cause changes in micro-organism concentration that would alter the distribution among the several carbonaceous species and hence affect both the rate of substrate utilization and the settling characteristics of the micro-organism
d
6
12 Time
16
24
(h)
Fig. 7. 24 h time series of influent flow rate and wastewater strength. (Adapted from Metcalf and Eddy Inc. [lo].)
floes. The settling characteristics are of particular concern, since altered settling characteristics could lead to poor functioning of the secondary clarifier and increased carryover of solids in the clarified effluent. The governing dynamics are in the aeration basin secondary clarifier loop. Attir and Denn [ 111 have shown that two control objectives must be attained: (1) a small variation in aeration basin MLVSSs and (2) maintenance of the clarifier sludge blanket. Objective (2) is important because the sludge blanket buffers the transmission of disturbances back to the aeration basin and hence reduces the detrimental effect on the process response time of the positive dynamic feedback loop associated with recycle. (For a discussion of the dynamics of recycle processes, see ref. 12.) The two control objectives are not compatible. Maintaining aeration basin MLVSSs requires high sludge recycle rates during periods of high influent flow, but raising the sludge recycle rate tends to lower the sludge blanket. Simulation studies have indicated that ratio control on the clarifier underflow and sludge recycle is effective in achieving both control objectives [ 1,111. Ratio control means that the secondary clarifier underflow flow rate and the sludge recycle flow rate are both kept proportional to the influent flow rate; the ratio of these flows to the influent flow is held constant. The 5 day dynamic response of plant A, the optimal design, with no control (constant clarifier underflow and recycle) is shown in Figs. 8 and 9. The plant experiences wide diurnal variations in both aeration basin cell concentration and sludge blanket height. Figures 10 and 11 illustrate the 5 day dynamic response of plant A when ratio control is used on the secondary clarifier underflow and sludge recycle flow rates. It should be noted that the diurnal variations in both aeration basin cell concentration and sludge blanket height have been reduced considerably. A comparison of the dynamic stabilities of plants A and B should be based on the performance of each plant under ratio control. Figures 12 and 13 show the 5 day dynamic response of plant B, the near-optimal design, using ratio control. The diurnal variations in the aeration basin cell concentrations are
24 Time
(h)
Fig. 8. Aeration basin response for the optimal design (plant A); constant clarifier underflow and recycle.
48
72 Time (hl
120
Fig. 10. Aeration basin response for the optimal design (plant A); ratio control on underflow and recycle.
Underflow
Underflow
96
VSS Concentration
VSS Concentratmn
Sludge
Effluent
0 Trme
Fig. 9. Secondary clarifier design (plant A); constant recycle.
lhl
response clarifier
VSS
significantly less for plant B than for plant A. Similarly, the overall stability of the sludge blanket is superior for plant B. Thus, the dynamic simulations indicate that the minimum cost plant A is dynamically more sensitive, and hence more difficult to control, than the more conventional plant B. Given the small difference in computed cost between the two plants, plant B appears to be a better choice of a final design. The 5 day final effluent quality time series for plant B is shown for the case where no control is used (constant underflow and recycle) in Fig. 14. Figure 15 shows the
Height
Concentration
1
I
I
I
I
24
48
72
96
120
Time
for the optimal underflow and
Blanket
(h)
Fig. 11. Secondary clarifier response for the optimal design (plant A); ratio control on underflow and recycle.
effluent quality when ratio control is used. It should be noted that the effluent quality for both cases is almost identical. The invariance of the effluent quality with and without control emphasizes an important fact: process control in response to diurnal feed variations serves to control the internal variables and to maintain the operability of the process, but it has little or no effect on effluent quality, which is fixed by the design and the mean flows. Thus, transient effluent quality should not be used as a basis of comparison between control systems in a welldesigned plant.
B23
0
0
i4
48
7.2 Time
Ii0 (h)
Fig. 12. Aeration basin response for the near-optimal design (plant B); ratio control on underflow and recycle.
24
48
96
72 Time
120
(h)
Fig. 14. Final effluent quality for the near-optimal design (plant B); constant underflow and recycle.
8
7
low3
P
0
TE .z
N
f -
p
0 Time
(h)
Time
(h)
Fig. 13. Secondary clarifier response for the nearoptimal design (plant B); ratio control on underflow and recycle.
Fig. 15. Final effluent quality for the near-optimal design (plant B); ratio control on underflow and recycle.
9. OXYGEN
essentially the same curve is obtained for plants A and B, with and without ratio control on the underflow and recycle. This is because the rate of oxygen uptake is determined by the conversion rate of (BOD)s, which is essentially the same in all cases. Negative values of the dissolved oxygen concentration, as shown in Fig. 16, serve as an indication of the extent to which the oxygen demand is exceeding the oxygen supply. In an actual plant the dissolved oxygen concentration can obviously never drop below zero. As the dissolved oxygen
CONTROL
The kinetic expressions used in the steady state and transient simulations require that the dissolved oxygen level always be above the minimum value at which kinetics are oxygen independent. The air supply system is sized by the steady state program to ensure that this is true on the average, but the dissolved oxygen concentration will vary during the transient unless control is used. The computed dissolved oxygen concentration during a 24 h transient is shown in Fig. 16;
Dissolved
Oxygen
Recommended
DO
-* -* 0
-N
AT-
“do Time
(h)
Fig. 16. Aeration-basin-dissolved oxygen (DO) with constant air flow rate; plant B with ratio control on underflow and recycle.
Recommended
DO
measurement. (In practice, since the integration scheme uses finite time steps, an oxygen measurement is required about once every 15 min.) The result in Fig. 17 shows the dissolved oxygen concentration for the simulation of plant B when the blower rate is increased or decreased by 10% following each dissolved oxygen measurement in which the concentration is found to be below 2.0 mg 1-l or above 3.0 mg 1-l respectively. This is a simple and effective scheme as long as reliable dissolved oxygen measurements are available. The maximum air flow rate for the control shown in Fig. 17 is approximately twice the design air flow rate (the firm blower capacity). Some small- and medium-sized plants have a maximum blower capacity with all units in service that exceeds the firm blower capacity by a factor of 1.5 - 2.0, so it might be possible to implement the oxygen control with the blowers designed by the steady state program as long as all blowers are usually in a working condition [ 1,4]. A more conservative strategy would be to design the process with a firm blower capacity based on the maximum demand.
ACKNOWLEDGMENT
0
6
12 Time
18
24
(h)
Fig. 17. Aeration-basin-dissolved oxygen with oxygen feedback control; plant B with ratio control on underflow and recycle.
The work on which this paper is based was supported by funds provided by the U.S. Department of the Interior, Office of Water Research and Technology, as authorized under the Water Research and Development Act of 1978, Public Law 95-467.
REFERENCES
concentration approaches zero, the metabolic activity of the bacteria drops off rapidly. This dependence of the (BOD), degradation rate on the dissolved oxygen concentration was not included in the dynamic simulations presented here and thus results in negative dissolved oxygen concentrations. Several alternative dissolved oxygen control strategies have been evaluated using the dynamic model, and the results have been presented elsewhere [ 11. The only successful strategy requires continuous dissolved oxygen
R. B. Paterson and M. M. Denn, Design and control of an activated sludge process for municipal wastewater treatment, Tech. Completion Rep., 1980 (Water Resources Center, University of Delaware, Newark, DE) (Project A-041-DEL). R. B. Paterson and M. M. Denn, Least cost design and design sensitivity of an activated sludge treatment system, Industrial Waste, Proc. 13fk Mid-Atlantic Conf., Ann Arbor Science, Ann Arbor, MI, 1981, p. 189. U. Attir, M. M. Denn and C. A. Petty, Dynamic simulation of continuous sedimentation, AICkE
Symp.
Ser., I67 (73) (1977)
49.
B25
The aeration basin is assumed to be well mixed. The mass balance equations for biochemical oxygen demand over a period of 5 days ((BOD),) and carbonaceous microorganisms are as follows:
to the flow rate of the influent to the aeration basin. The kinetic parameters are given in Table 2. The most important assumption here is that the consumption rates for suspended and dissolved (BOD)5 are the same or, in other words, that the total (BOD), in the influent to the aeration basin can be modeled as if it were all present in the dissolved form. Equations identical with eqn. (A2) are used for the micro-organisms Nitrosomonas and Nitrobacter. The steady state design equations are obtained by setting time derivatives d/dt equal to zero. Each aeration basin is taken to be rectangular, with a width and depth of 6 m and a maximum length of 45 m. The rate of oxygen uptake is computed from an oxygen balance that includes the metabolic rates of the biochemical reactions. The required air flow is determined from the overall mass transfer coefficient needed to maintain the dissolved oxygen concentration at the required level, taken here to be 2 mg l-l, using the correlation of Schmit et al. [Al] for a diffused air system. The thickening section of the secondary clarifier is modeled with the simulation described by Attir et al. [ A2], which reduces to conventional flux theory at steady state. Batch settling data of Dick and Javaheri [ A3], Tracy [ A41 and Munch [ A51 were fitted with the form
VI:
u = u. exp(-4.5
4
W. L. Patterson and R. F. Banker, Estimating costs and manpower requirements for conventional wastewater treatment facilities, Water
Poll&.
Control
Res. Ser. 17090DANl
O/71, 1971
(U.S. Environmental Protection Agency). D. R. Woods, S. J. Anderson and S. L. Norman, Can. J. Chem. Eng., 57 (1979) 385. W. Von der Emde, To what extent are primary tanks required?, Water Res., 6 (1972) 395. M. T. Kuo, L. T. Fan and L. E. Erickson, Effects of suspended solids primary clarifier size optimization, J. Water Pollut. Control Fed., 46 (1974)
2521. 8
9
10 11
12
L. D. Benefield
and C. W. Randall,
Process
for
Design
Wastewater
Biological
Treatment,
Prentice-Hall, Englewood Cliffs, NJ, 1980. A. C. Middleton and A. W. Lawrence, Least cost design of activated sludge systems, J. WaterPollut. Control Fed., 48 (1976) 889. Metcalf and Eddy Inc., Wastewater Engineering, McGraw-Hill, New York, 1972. U. Attir and M. M. Denn, Dynamics and control of the activated sludge wastewater process, AZChE J., 24 (1978) 693. M. M. Denn and R. Lavie, Dynamics of plants with recycle, Chem. Eng. J., 24 (1982) 55.
APPENDIX
A
=Qf(Bf---B)-
;+&X& c
(Al) UC = rQf-L Kdt
X 10m4X)
(A3)
B
- (1 + r)QfX,
X,V,
+
(A3
where B and X, denote the concentrations of dissolved ( BOD)5 and total carbonaceous cells respectively in milligrams per liter; without additional subscripts they represent the concentrations in the aeration basin and in the basin effluent. A subscript f denotes the feed stream to the aeration basin, a subscript a denotes the aeration basin and a subscript u denotes the underflow from the secondary clarifier. V and Q are the volume and volumetric flow rate respectively and r is the ratio of the flow rate of the recycle stream
.where X is the concentration of volatile suspended solids in milligrams per liter. The initial settling velocity u. is taken to depend on sludge age according to the function shown in Fig. Al. The rising portion of the function is based on the data of Bisogni and Lawrence [ A6], while the turndown follows from the limited data of Ford and Eckenfelder [ A7]. Recent work by Wu and Mahmud [ A81 has reinforced the work of these earlier researchers. Two other assumptions regarding the change in sludge-settling characteristics are possible and have been discussed elsewhere [ A9, AlO]. In one, u. was taken to have a constant value of 143 m day-’ and, in the other, u. was identical with the function shown in Fig. Al except that u. continued to rise at the same rate after a sludge age of 15 days.
I326
The primary clarifier area is sized on the basis of the empirical equation 1 -
Ap-
3.82 X 10-3Qf 0.6355 -R/P
+1.99 X 10-4(TSSs)pf (A6)
R is the fractional
Sludge
Fig. Al. Initial settling sludge age.
Age
(days)
velocity
as a function
The mean sludge age is defined 9, =
KXC wQfXcu + (1 - w)QfXce
of
here as (A4)
where w is the ratio of the sludge wastage flow rate to the aeration basin influent flow rate and X,, is the concentration of carbonaceous volatile suspended solids in the effluent from the secondary clarifier. The area required for clarification in the secondary clarifier is determined in terms of the total effluent volatile suspended solids X, using the following equation obtained from the correlation by Rex Chainbelt Inc. [All] : A, =
0.267(1
- w)Qf
X, + 2.7 X 1O-3X, - 15.0
(A5)
where Qf is in cubic meters per day, A, is in cubic meters and X, is the total concentration of mixed liquor volatile suspended solids (MLVSSs) in milligrams per liter. This correlation gives results consistent with the rule-ofthumb values suggested by Kalinske [A12]. The settler area is fixed initially at an integer size in meters by eqn. (A5). The side wall depth is set at 4 m and the center depth at 5 m. The maximum diameter of a single unit is 40 m; if a larger area is required, then two or more units are stipulated. Thickening calculations are then carried out to ensure that the area is adequate for thickening; if additional area is required, the diameter is increased in integral increments until the thickening constraint is satisfied. The settler area will typically be set by thickening requirements when the aeration basin MLVSSs are in excess of about 3500 mg 1-l.
removal of primary suspended solids, (TSSs)pf is the total suspended solids (TSSs) of the influent wastewater and P is an enhancement factor for the addition of anionic polymer. P is linearly dependent on polymer concentration, with a value of 1.5 for a polymer concentration of 1.0 mg 1-l. This equation gives overflow rates and removal efficiencies in the range of the rule-ofthumb values suggested by Metcalf and Eddy Inc. [A13]. Each unit is set at a depth of 3 m, a width of 6 m and a maximum length of 45 m. The chlorine contact system is sized by requiring 15 min of residence time at peak flow, which is taken to be 140% of mean flow, with a length that is at least 40 times the width. The chlorine addition rate is set at 5 mg 1-i. The sludge thickener is sized on the basis of recommended solids loading rates. The overall sludge loading rate is taken as a massflow-weighted average of the recommended primary and secondary values. The diameter is fixed at less than 40 m. Sludge is assumed to be thickened to 90 000 mg 1-i of TSSs. The anaerobic digester is modeled as a well-stirred reactor, using equations analogous to eqns. (Al) and (A2), with r = 0, with the following kinetic parameters at 35 “C: pm = 0.28 day-‘; K = 154 mg 1-l of (BOD)S; b = 0.023 day-‘; Y = 0.04 g of volatile suspended solids per gram of (BOD),. Four times the volume computed for a 60% reduction in volatile suspended solids was typically in the middle of rule-of-thumb loading factors, so this procedure was adopted as the design algorithm, with the second-stage volume taken to be equal to the first. The total underflow suspended solids are taken to be 80 000 mg 1-i. Finally, the solids centrifuge, following Zenz et al. [A14], is assumed to operate at a solids capture rate of 93.2% with a thickened total solids concentration of 200 000 mg 1-l. Final sludge disposal is
accomplished by hauling sanitary landfill.
the sludge to a
References for Appendix A Al
A2
A3
A4
A5
A6
A7
F. L. Schmit, J. D. Wren and D. T. Redman, The effect of tank dimensions and diffuser placement on oxygen transfer, J. Water Poll&. Control Fed., 50 (1978) 1750. U. Attir, M. M. Denn and C. A. Petty, Dynamic simulation of continuous sedimentation, AIChE Symp. Ser., 167 (73) (1977) 49. R. I. Dick and A. R. Javaheri, Continuous thickening of non-ideal suspensions, Res. Rep. 45, 1972 (University of Illinois Water Resources Center, Urbana-Champaign, IL). K. Tracy, Mathematical modeling of unsteadystate thickening of compressible slurries, Ph.D. Thesis, Clemson University, Clemson, SC, 1973. W. L. Munch, Performance of full-scale circular final clarifier for activated sludge, Master’s Thesis, Northwestern University, Evanston, IL, 1976. J. J. Bisogni and A. W. Lawrence, Relationships between biological solids retention time and settling characteristics of activated sludge, Wuter Res., 5 (1971) 753. D. L. Ford and W. W. Eckenfelder, Effect of process variables on sludge floe formation and settling characteristics, J. Water PoNut. Control
Fed., 39 (1967) 1850. A8 Y. C. Wu and Z. Mahmud, Performance of final clarifier as a function of wastewater characteristics, Industrial Waste, Proc. 13th Mid-Atlantic Conf., Ann Arbor Science, Ann Arbor, MI, 1981, p. 370. A9 R. B. Paterson and M. M. Denn, Design and control of an activated sludge process for municipal wastewater treatment, Tech. Completion Rep., 1980 (Waters Resources Center, University of Delaware, Newark, DE) (Project A-041 -DEL). Al0 R. B. Paterson and M. M. Denn, Least cost design and design sensitivity of an activated sludge treatment system, Industrial Waste, Proc. 13th Mid-Atlantic Conf., Ann Arbor Science, Ann Arbor, MI, 1981, p. 189. All Rex Chainbelt Inc., A mathematical model of a final clarifier, Rep., 1972 (U.S. Government Printing Office) (U.S. Environment Protection Agency Project 17090FJW). A12 A. A. Kalinske, Comparison of air and oxygen activated sludge systems, J. Water Pollut. Control Fed., 48 (1976) 2472. Al3 Metcalf and Eddy Inc., Wastewater Engineering, McGraw-Hill, New York, 1972. Al4 D. R. Zenz, B. Sawyer, R. Watkins, C. Lue-Hing and G. Richardson, Evaluation of dewatering equipment for anaerobically digested sludge, J. Water Pollut. Control Fed., 50 (1978) 1965.