- Email: [email protected]
Design of facultative ponds based on uncertainty analysis
~
Wa/, SCI, T~ch, Vol, 33. No, 7. pp, 41-47. 1996, Copynghl@ 1996IAWQ.Publlshed by Elsevier ScIence Lid Pnnled In Oreal 8riI31O, All nghls reserved.
Perganaon
PH: S0273-1223(96)OO338-1
0273-1223/96 SIHJO + (}OO
DESIGN OF FACULTATIVE PONDS BASED ON UNCERTAINTY ANALYSIS Marcos von Sperling Depanment ofSanitary and Environmental Engineering. Federal University ofMinas Gerais. Av. Contorno 842 - 'P andar. 30110-060 Belo Horizonte. Brazil
ABSTRACf The paper presents a methodology for the utilisation of the Uncertainty analysis based on Monte Carlo simulations for the design of wastewater treatment systems, The specIal and important case of facultauveponds design is exemplified. The design is carried out a large number of times. each run with different values of the inputs. randomly selected from uniform distributions within ranges which define the designer's uncertainty with the data. The results are interpreted statistically. giving elemenls for the selection of more or less conservative designs. according to the resulting effiuent quality. The procedure for undertaking a Sensitivity Analysis IS also described and exemplified, allowing the deSigner to concentrate more efforts on a more accurate determination of those inputs found to be significantly important. Copyrighl © 1996 lAWQ. Published by ElseVier Science Ltd.
KEYWORDS Design: facultative ponds; Monte Carlo sinaulation; uncertainty analysis; waste stabilization ponds: wastewater treatnlent. INTRODUCfION The procedure usually adopted for the design of wastewater treatnaent plants assunaes thilt there is no doubt about the values of all the input data. even though all designers recognise, inaplicitly, that there is a variable degree of uncertainty in the data utilised. As a result of this deterministic approach, the output data (areas, volumes, effluent concentrations) are treated as single values, not taking into account their expected variability. In order to reduce the risks of failure, the designer frequently adopts safety factors in the design. In the case of facultative-ponds design, it is known that there is uncertainty in the main model coefficients. In the simpler naodels, these coefficients are the BOD renaoval coefficient K and the tcnaperature coefficient. However, the uncertainty is in reality much more widespread: apart from the coefficients, precise values of other design data are not known. The design population, per capita flowrate, per capita BOD load and liquid temperature are typical examples of variables around which there is uncertainty. This is especially the case in developing countries, where high population growth rates and lack of basic information are predominant. Even though the designer naight accept the existence of this uncertainty, the current design routines very seldona incorporate any naeans of treating it in a naore formal way. The result is either underdesigned systems, naturally prone to failure, or overdesigned systenas, unavoidably naore expensive in order to give 41
.t2
M. VON SPERLING
allowance to safety factors. When the lalter approach is adopted. the safety factors are gross numbers following sometimes sophisticated design routines. usually incorporated without much criterion or reasoning. PROPOSED :v1ETHODOLOGY The paper proposes the utilisation of the Uncertainty Analysis based on Monte Carlo simulations in order to give support to a more realistic design. In parallel. a Sensitivity Analysis can optionally be done. aiming at highlighting the relative imporlance of each input data on the main output data. For the inputs found to be significantly important. more efforts can be concentrated on a more accurate determination. as compared to the other inputs. The proposed procedure can be used for the design of any wastewater treatment systems. but it is exemplified in the present paper for the simple and important case of facultative-pond design.
Uncertainty analysis. The uncertainly is introduced by specifying the design input data (coefficients and variables) according to distributions covering a particular range of values (and not point values). In the present case. uniform distributions for the inputs have been assumed. For instance. the per capita wastewater flow rate could be assumed to vary uniformly between 110 and 130 l/head.d. instead of having the design based on the unique intermediate value of 120 l/head.d. A large number of model runs (say. 100. 500 or 1000) is then carried out. each time with a different set of inputs randomly selected from the specified distributions. This characterises the so-called Monte Carlo simulation. The final result of the design based on the Monte Carlo simulations is to have the outputs presented as distributions instead of single values. As an example. the required pond area could be calculated to vary between 2.0 and 3.0 ha. according to some distribution. instead of having the single intermediate value of 2.5 ha calculated by a conventional design. Each value of the distribution. is of course. associated with a different risk of failure/success and also cost. The procedure for the Monte Carlo simulation is illustrated in Fig. I. Further general descriptions of the method can be found in von Sperling (1990. 1993a. 1993b. 1994) and Campos and von Sperling ( 1994). MONTE CARLO SIMULATION
Figure I. Procedure for [he Monle Carlo simulation.
Sensitivity analysis. The result of each run can be also interpreted by a classification algorithm. which incorporates the input values in a class of '/ower i'll/lies' (input values of a run which led to an outpUI lower than its medianl and in a class of 'higher values' (input value~ of a run which resulted in an output higher than its median). After all the runs hav~ been I:arried out a statistical analysis is conducted. comparing the distributions of each of the parameter values in both classes. The test u~ed is usually a non-parametric twosample test. such as the Kolmogorov-Smirnov or the Mann-Whitney-Wikoxon. because these tests are not dependent upon the distribution of the samples. If the two distribution~ arc significantly different. the input
4.'
is considered to he important for the output. that is. the design is sensitive to the input values. If the distrihutions are not significantly dilTerenl. then the inplll is taken as non-important (under the specified range and distrihution). The use of the generalised sensitivity analysis has been reported hy many authors. incluJing Spear and Hornberger (19ROl, Hornberger and Spear (19K3). Buckley (1985). Tomlin (1986). Lumhers ( 1987). Jaffe l't al. (19liS). van Straten and Keesman {1991 l. von Sperling (1990. 1993a. 1993b. 1993c). The procedure for the Sensitivity Analysis is illustrated in Fig. 2.
SENSmvrrv ANALYSIS
1lWf_
~2·_
HOHEIt
Figure 2. Procedure for the Sensitivity Analysis.
APPLICATION TO A CASE STUDY The paper presents a Montc Carlo simulation for the design of a facultative pond. The design procedure is purposely simple, in order to facilitate the understanding of the overall proposed procedure. The design is based on the calculation of the required surface area utilising the concept of the BOD surface load (kgBOD/ha.d) and the estimation of the effluent BOD concentration according to the complete-mix model. In the Monte Carlo simulation. 500 runs of the facultative pond design were undertaken, each with different values of the input data. randomly generated within a range, according to a uniform distribution. The range width was approximately fixed as: lower value = mean - 10'70 of mean: upper value = mean + 10% of mean. The mean can be understood here as the value which would be adopted by the designer if the concept of the Uncertainty Analysis were not being adopted. The uncertainty off 10% can be considered to be even small, since in many designs a higher level of uncertainty is very frequent. The ranges considered were: population: 9000 to 11000 inhabitants: per capita wastewater tlowrate: 110 to 130 IIhead.d: per capita BODs load: 45 to 55 glhead.d: liquid temperalure: 19 to 21°C; BOD removal coefficient K: 0.27 to 0.33 d- I: temperature coefficient 6: 1.04 to 1.06. The main design criteria, which depend upon the designer's choice, were adopted as fixed values: BOD surface loall : 200 kgBODSlha.d; liquid depth: 2.0 m. RESULTS rROM THE MONTE CARLO SIMULATION The summary statistics of the r.lain design results (effluent BOD concentration S and required surface area A) are presented in Table I.
M. VON SPERLING
Table I. Summary statistics of the output data from the Monte Carlo simulation (500 runs)
Surface area (ha)
Emuent BOD (mg/l) 27 36 31 2 31
Statistics Minimum Maximum Mean Standard deviation Median
2.0
3.0 2.5 2.1 2.5
Even with all the combined variation in the inputs, the effluent BOD concentration varied within the relatively narrow range of 27 to 36 mgt!, suggesting that the design is likely to produce a reasonable effluent quality. However, the required surface area varied within a broad range, from 2.0 to 3.0 ha. The practical and economical implications of this wide variation are obvious. Frequency distribution graphs (simple and cumulative) of S and A are presented in Figs 3 and 4. Based on this distribution and the probabilities behind it, the designer can decide upon whether to adopt a more conservative or a more risky design.
EFFLUENT BOD CONCENTRATION Frequency dstribution 50
45 ~ 40 ~ 35 ~ 30 .:: 25 ~ 20
~ :~
100,00'11.
V-~· ~
oJJ ~
iol
90,00% 60,00'11. ~ 70,00'11. ~ 60,00'11. CI> 50,00'11. 40,00'11. li
.z
nn ln
II I o5 1-.-.... _=,J-l,J-l,J-l,J...-l,,J...-l,,J...-l,.L..J,.L..J,.L..J,.L..J,LJ,JLJ,JW,JLJ,J'-4-<,=>,)
~~:::~
10,00'11. 0,00%
~~~~re~~~~g~~~~~~~i~~~ Effluent BOD concentration (mgI1)
FIgure J. Frequency distribution (simple and cumulative) of the emuent BOD.
REQUIRED SURFACE AREA Frequency dstribution 60
---"'-''-'"
100,00% 90,00'11. ~ 80,00% ~ 70,00% CI>
.z
60,00% 50,00% c 40,00% ~ 30,00% ~ 20,00% 10,00% o ....,lal;;I!!l,J...J..LJ,J-4I-4l-4L-4l-.J.,J....J,l-.l,J....4WL,JW,J...J.,J...-l,.w,l...J,Jw..=>.j 0,00'"
Required area (m2)
Figure 4. Frequency distribution (simple and cumulative) of the required surface area.
The percentage of compliance to different standards is presented in Table 2. It is seen that, for stringent standards. the percentage of compliance is relatively low, whereas for less strict ones. the standards can be
45
Facultative ponds unccrtalllly analy"'I'"
fully satisfied. It is important to mention that in this design only the effluent soluble BOD is taken into account, amI the algae bIOmass is not considered to generate BOD in the effluent. Table 2. Percentage of compliance to different BOD standards BOD standard (mgll)
Percentage of compliance (%)
o
20 30 40 50
41 100 100 100
60
RESULTS FROM THE SENSITIVITY ANALYSIS The Sensitivity Analysis of the input variables on the effluent BOD concentration was based on a subdivision of the results into two samples: one sample with the results from the simulations in which the effluent BOD was less than or equal to the BOD median of 31 mg/1. and the other sample with the results from the simulations in which the BOD was greater than the median of 31 mg/1. The two-sample test adopted was the non-parametric test of Kolmogorov-Smirnov. The results of the test and their interpretation are presented in Table 3. The only critical variables were the liquid temperature and the BOD removal coefficient K. Table 3. Results from the Kolmogorov-Smirnov two-sample test for the Sensitivity Analysis on the effluent BOD concentration
Variable
Two-sided probability (a) of the samples being not dilTerent
Interpretation: variable important?
Population Per capita flow Per capita BOD Temperature Coefficient K Coefficient
0.519 0.828 0.074 0.000 0.000 0.052
unimportant unimportant important
a :>; 0.0 I: critical
0.01; 0.10: important
e
critical critical important
a > 0.10: unimportant
The Sensitivity Analysis of the input variables on the required surface area was undertaken in a similar way as the one adopted for BOD. One sample was with the results from the simulations in which the area was less than or equal to the median (2.5 hal, and the other sample with the results from the simulations in which the area was greater than the median. The results of the test and their interpretation are presented in Table 4. The only critical variables were the population and per capita BOD. Given the structure of the formula for calculating the required area, this was entirely expected, since the area is derived from the applied BOD load. However, in more complex designs, the relationships might not be so apparent, and the Sensitivity Analysis may be an important tool to decide upon those inputs on which to concentrate more efforts for a more accurate determination.
M. VON SPERLING
46
Table 4. Results from the Kolmogorov-$mimov two-sample test for the Sensitivity Analysison the required surface area
Variable Populatkm Per capita flow Per capita BOD Temperature Coefficient K Coefficient a
Two-sided probability (a) of the samples being Dot different 0.000 0.200 0.000 0.200 0.888 0.936
a :s; 0,0): critical
0.01
Interpretation: variable important! critical unimportant critical unimportant unimportant unimportant a> 0.10: unimportant
The frequency distributions of the mputs and outputs are presented in Fig. 5, together with the scatter plots between each input and each output (500 points in each graph). The stronger relationships between the outputs and the variables found to be significantly important are clear from the scatter plots. In the other cases, the scattering of the data points IS suhstantial. HISTOGRAMS AND SeATTER-PLOTS INPUTS
OUTPUTS
Figure S. Histograms of the inputs anu ,IUtputS. and scatter-plols of the relationships belween inpuls and outputs. Inputs: population. per capita flowrate. per capita BOD. lemperature. coefficient K and temperature coefficient. Outt>uts: effluent BOD and reqUired area.
CONCLUSIONS The design based on the Uncertaimy Analysis is a simple and efficient method for incorporating the uncertainties usually overlooked in the normal designs. The procedure exemplified in the paper may be adopted in the designs of other treatment systems. and not only for the case offacultative ponds.
Facultative ponds uncertainty analysis
47
The designer can decide upon the acceptabh safety to be adopted in the design for the compliance with the effluent standards (and the related costs), instead of the simple incorporation of safety factors or overconservative criteria. The Sensitivity Analysis may help the designer in the selection of those inputs in which it is justifiable to spend more time and/or money in a more accurate determination. The effluent BOD seems to be relatively less influenced by the uncertainty in the data, whereas the required area shows a wider variation. In the example shown, the uitical inputs for the effluent BOD were found to be the BOD removal coefficient and the liquid temperature. For the required area, the critical inputs were the population and the per capita BOD load. REFERENCES Buckley, J. M. (1985). A generalized sensitivity alialysIs of the kinetics of the activated sludge process (with particular reference to dissolved oxygen control). M.Sc. Di:;,ertatlOn, Imperial College, Umversity of London. Campos. M. C. S. and Von Sperling, M. (1994). Modelagem e avalia~ao da qualidade da agua de rIOS da Regiao Metropolttana de Belo Horizonte, ulilizando a Analtse da Incerteza. In: VI SILUBESA . SimposlO Luso-Brasileiro de Engenharia Sanitaria e Ambiental. Florian6polis-SC, 12-16 Junho 1994. Torno II, pp. 89-97. Hornberger, G. M. and Spear, R. C. (1983). An approach to the analysis of behaviour andsensitivity in environmental systems. In: Beck. M. B. and Van Straten, G. (cds). Uncertainty and forecasting of water quality. Sprmger-Verlag, pp. 101-116. Jaffe, P. R., Paniconi, C. and Wood, E. F. (1988). Model calibration based on random environmentailluctuation. Journal of the Environmental Engineering Division. ASCE, 114 (EE5). 1136-1145. Lumbers, J. P. (1987). Rotating biological contactors: mechanisms, modelling and design. Ph.D. Thesis, Imperial College, University of London, London. Spear, R. C. and Hornberger, G. M. (1980). Eutrophication in Peel Inlet: II. Identification of Critical uncertainties via generalized sensitivity analySIS. Water Researc/. 14 41-49. Tomlin, S. (1986) The development of a dynamic mode. for an activated sludge sewage treatment process. M.Sc. DIssertation, Imperial College, Umversity of London. Van Straten, G. and Keesman, K. J. (1991). Uncertainty propagation and speculation in projective forecasts of environmental change: a lake-eutrophication example. Journal of Forecasting, 10, 163-190. Von Sperling, M. (1990). Optimal management of the oxidation ditch process. Ph.D. Thesis, Imperial College, University of London, London. Von Sperling, M. (1993a). Parameter estimation and sensitIvity analysis of an activated sludge model using Monte Carlo simulation and the analyst'S involvement. lVat. SCI. Tech., 28(1 1-12), 219-229. Von Sperling, M. (I993b). Analise da incerteza em estudos ambientais. Aplica~ao na modelagem da qualidade da agua de rios. Bio Engenharia Sanitdria e Ambiental. Encarte Tecnico, Ano II, No. I, 2-10. Von Sperltng, M. (1993c). Caltbra~do e analise de sensibilidade de modelos ambientals com base em simula~ao Monte Carlo. In: I Simp6sio de Recursos Hfdricos do Cone Sui: Simposio Brasileiro de Recursos Hfdricos, Gramado-RS, 7-12 Novembro 1993, Vol. I, pp. 556-565. Von Sperling, M. (1994) Calibrauun of poorly identifiable systems. Application to an activated sludge model. Journal of the Environmental Engineering Division, ASCE. 120(3), May/June 1994,625·644.
Wa/, SCI, T~ch, Vol, 33. No, 7. pp, 41-47. 1996, Copynghl@ 1996IAWQ.Publlshed by Elsevier ScIence Lid Pnnled In Oreal 8riI31O, All nghls reserved.
Perganaon
PH: S0273-1223(96)OO338-1
0273-1223/96 SIHJO + (}OO
DESIGN OF FACULTATIVE PONDS BASED ON UNCERTAINTY ANALYSIS Marcos von Sperling Depanment ofSanitary and Environmental Engineering. Federal University ofMinas Gerais. Av. Contorno 842 - 'P andar. 30110-060 Belo Horizonte. Brazil
ABSTRACf The paper presents a methodology for the utilisation of the Uncertainty analysis based on Monte Carlo simulations for the design of wastewater treatment systems, The specIal and important case of facultauveponds design is exemplified. The design is carried out a large number of times. each run with different values of the inputs. randomly selected from uniform distributions within ranges which define the designer's uncertainty with the data. The results are interpreted statistically. giving elemenls for the selection of more or less conservative designs. according to the resulting effiuent quality. The procedure for undertaking a Sensitivity Analysis IS also described and exemplified, allowing the deSigner to concentrate more efforts on a more accurate determination of those inputs found to be significantly important. Copyrighl © 1996 lAWQ. Published by ElseVier Science Ltd.
KEYWORDS Design: facultative ponds; Monte Carlo sinaulation; uncertainty analysis; waste stabilization ponds: wastewater treatnlent. INTRODUCfION The procedure usually adopted for the design of wastewater treatnaent plants assunaes thilt there is no doubt about the values of all the input data. even though all designers recognise, inaplicitly, that there is a variable degree of uncertainty in the data utilised. As a result of this deterministic approach, the output data (areas, volumes, effluent concentrations) are treated as single values, not taking into account their expected variability. In order to reduce the risks of failure, the designer frequently adopts safety factors in the design. In the case of facultative-ponds design, it is known that there is uncertainty in the main model coefficients. In the simpler naodels, these coefficients are the BOD renaoval coefficient K and the tcnaperature coefficient. However, the uncertainty is in reality much more widespread: apart from the coefficients, precise values of other design data are not known. The design population, per capita flowrate, per capita BOD load and liquid temperature are typical examples of variables around which there is uncertainty. This is especially the case in developing countries, where high population growth rates and lack of basic information are predominant. Even though the designer naight accept the existence of this uncertainty, the current design routines very seldona incorporate any naeans of treating it in a naore formal way. The result is either underdesigned systems, naturally prone to failure, or overdesigned systenas, unavoidably naore expensive in order to give 41
.t2
M. VON SPERLING
allowance to safety factors. When the lalter approach is adopted. the safety factors are gross numbers following sometimes sophisticated design routines. usually incorporated without much criterion or reasoning. PROPOSED :v1ETHODOLOGY The paper proposes the utilisation of the Uncertainty Analysis based on Monte Carlo simulations in order to give support to a more realistic design. In parallel. a Sensitivity Analysis can optionally be done. aiming at highlighting the relative imporlance of each input data on the main output data. For the inputs found to be significantly important. more efforts can be concentrated on a more accurate determination. as compared to the other inputs. The proposed procedure can be used for the design of any wastewater treatment systems. but it is exemplified in the present paper for the simple and important case of facultative-pond design.
Uncertainty analysis. The uncertainly is introduced by specifying the design input data (coefficients and variables) according to distributions covering a particular range of values (and not point values). In the present case. uniform distributions for the inputs have been assumed. For instance. the per capita wastewater flow rate could be assumed to vary uniformly between 110 and 130 l/head.d. instead of having the design based on the unique intermediate value of 120 l/head.d. A large number of model runs (say. 100. 500 or 1000) is then carried out. each time with a different set of inputs randomly selected from the specified distributions. This characterises the so-called Monte Carlo simulation. The final result of the design based on the Monte Carlo simulations is to have the outputs presented as distributions instead of single values. As an example. the required pond area could be calculated to vary between 2.0 and 3.0 ha. according to some distribution. instead of having the single intermediate value of 2.5 ha calculated by a conventional design. Each value of the distribution. is of course. associated with a different risk of failure/success and also cost. The procedure for the Monte Carlo simulation is illustrated in Fig. I. Further general descriptions of the method can be found in von Sperling (1990. 1993a. 1993b. 1994) and Campos and von Sperling ( 1994). MONTE CARLO SIMULATION
Figure I. Procedure for [he Monle Carlo simulation.
Sensitivity analysis. The result of each run can be also interpreted by a classification algorithm. which incorporates the input values in a class of '/ower i'll/lies' (input values of a run which led to an outpUI lower than its medianl and in a class of 'higher values' (input value~ of a run which resulted in an output higher than its median). After all the runs hav~ been I:arried out a statistical analysis is conducted. comparing the distributions of each of the parameter values in both classes. The test u~ed is usually a non-parametric twosample test. such as the Kolmogorov-Smirnov or the Mann-Whitney-Wikoxon. because these tests are not dependent upon the distribution of the samples. If the two distribution~ arc significantly different. the input
4.'
is considered to he important for the output. that is. the design is sensitive to the input values. If the distrihutions are not significantly dilTerenl. then the inplll is taken as non-important (under the specified range and distrihution). The use of the generalised sensitivity analysis has been reported hy many authors. incluJing Spear and Hornberger (19ROl, Hornberger and Spear (19K3). Buckley (1985). Tomlin (1986). Lumhers ( 1987). Jaffe l't al. (19liS). van Straten and Keesman {1991 l. von Sperling (1990. 1993a. 1993b. 1993c). The procedure for the Sensitivity Analysis is illustrated in Fig. 2.
SENSmvrrv ANALYSIS
1lWf_
~2·_
HOHEIt
Figure 2. Procedure for the Sensitivity Analysis.
APPLICATION TO A CASE STUDY The paper presents a Montc Carlo simulation for the design of a facultative pond. The design procedure is purposely simple, in order to facilitate the understanding of the overall proposed procedure. The design is based on the calculation of the required surface area utilising the concept of the BOD surface load (kgBOD/ha.d) and the estimation of the effluent BOD concentration according to the complete-mix model. In the Monte Carlo simulation. 500 runs of the facultative pond design were undertaken, each with different values of the input data. randomly generated within a range, according to a uniform distribution. The range width was approximately fixed as: lower value = mean - 10'70 of mean: upper value = mean + 10% of mean. The mean can be understood here as the value which would be adopted by the designer if the concept of the Uncertainty Analysis were not being adopted. The uncertainty off 10% can be considered to be even small, since in many designs a higher level of uncertainty is very frequent. The ranges considered were: population: 9000 to 11000 inhabitants: per capita wastewater tlowrate: 110 to 130 IIhead.d: per capita BODs load: 45 to 55 glhead.d: liquid temperalure: 19 to 21°C; BOD removal coefficient K: 0.27 to 0.33 d- I: temperature coefficient 6: 1.04 to 1.06. The main design criteria, which depend upon the designer's choice, were adopted as fixed values: BOD surface loall : 200 kgBODSlha.d; liquid depth: 2.0 m. RESULTS rROM THE MONTE CARLO SIMULATION The summary statistics of the r.lain design results (effluent BOD concentration S and required surface area A) are presented in Table I.
M. VON SPERLING
Table I. Summary statistics of the output data from the Monte Carlo simulation (500 runs)
Surface area (ha)
Emuent BOD (mg/l) 27 36 31 2 31
Statistics Minimum Maximum Mean Standard deviation Median
2.0
3.0 2.5 2.1 2.5
Even with all the combined variation in the inputs, the effluent BOD concentration varied within the relatively narrow range of 27 to 36 mgt!, suggesting that the design is likely to produce a reasonable effluent quality. However, the required surface area varied within a broad range, from 2.0 to 3.0 ha. The practical and economical implications of this wide variation are obvious. Frequency distribution graphs (simple and cumulative) of S and A are presented in Figs 3 and 4. Based on this distribution and the probabilities behind it, the designer can decide upon whether to adopt a more conservative or a more risky design.
EFFLUENT BOD CONCENTRATION Frequency dstribution 50
45 ~ 40 ~ 35 ~ 30 .:: 25 ~ 20
~ :~
100,00'11.
V-~· ~
oJJ ~
iol
90,00% 60,00'11. ~ 70,00'11. ~ 60,00'11. CI> 50,00'11. 40,00'11. li
.z
nn ln
II I o5 1-.-.... _=,J-l,J-l,J-l,J...-l,,J...-l,,J...-l,.L..J,.L..J,.L..J,.L..J,LJ,JLJ,JW,JLJ,J'-4-<,=>,)
~~:::~
10,00'11. 0,00%
~~~~re~~~~g~~~~~~~i~~~ Effluent BOD concentration (mgI1)
FIgure J. Frequency distribution (simple and cumulative) of the emuent BOD.
REQUIRED SURFACE AREA Frequency dstribution 60
---"'-''-'"
100,00% 90,00'11. ~ 80,00% ~ 70,00% CI>
.z
60,00% 50,00% c 40,00% ~ 30,00% ~ 20,00% 10,00% o ....,lal;;I!!l,J...J..LJ,J-4I-4l-4L-4l-.J.,J....J,l-.l,J....4WL,JW,J...J.,J...-l,.w,l...J,Jw..=>.j 0,00'"
Required area (m2)
Figure 4. Frequency distribution (simple and cumulative) of the required surface area.
The percentage of compliance to different standards is presented in Table 2. It is seen that, for stringent standards. the percentage of compliance is relatively low, whereas for less strict ones. the standards can be
45
Facultative ponds unccrtalllly analy"'I'"
fully satisfied. It is important to mention that in this design only the effluent soluble BOD is taken into account, amI the algae bIOmass is not considered to generate BOD in the effluent. Table 2. Percentage of compliance to different BOD standards BOD standard (mgll)
Percentage of compliance (%)
o
20 30 40 50
41 100 100 100
60
RESULTS FROM THE SENSITIVITY ANALYSIS The Sensitivity Analysis of the input variables on the effluent BOD concentration was based on a subdivision of the results into two samples: one sample with the results from the simulations in which the effluent BOD was less than or equal to the BOD median of 31 mg/1. and the other sample with the results from the simulations in which the BOD was greater than the median of 31 mg/1. The two-sample test adopted was the non-parametric test of Kolmogorov-Smirnov. The results of the test and their interpretation are presented in Table 3. The only critical variables were the liquid temperature and the BOD removal coefficient K. Table 3. Results from the Kolmogorov-Smirnov two-sample test for the Sensitivity Analysis on the effluent BOD concentration
Variable
Two-sided probability (a) of the samples being not dilTerent
Interpretation: variable important?
Population Per capita flow Per capita BOD Temperature Coefficient K Coefficient
0.519 0.828 0.074 0.000 0.000 0.052
unimportant unimportant important
a :>; 0.0 I: critical
0.01
e
critical critical important
a > 0.10: unimportant
The Sensitivity Analysis of the input variables on the required surface area was undertaken in a similar way as the one adopted for BOD. One sample was with the results from the simulations in which the area was less than or equal to the median (2.5 hal, and the other sample with the results from the simulations in which the area was greater than the median. The results of the test and their interpretation are presented in Table 4. The only critical variables were the population and per capita BOD. Given the structure of the formula for calculating the required area, this was entirely expected, since the area is derived from the applied BOD load. However, in more complex designs, the relationships might not be so apparent, and the Sensitivity Analysis may be an important tool to decide upon those inputs on which to concentrate more efforts for a more accurate determination.
M. VON SPERLING
46
Table 4. Results from the Kolmogorov-$mimov two-sample test for the Sensitivity Analysison the required surface area
Variable Populatkm Per capita flow Per capita BOD Temperature Coefficient K Coefficient a
Two-sided probability (a) of the samples being Dot different 0.000 0.200 0.000 0.200 0.888 0.936
a :s; 0,0): critical
0.01
Interpretation: variable important! critical unimportant critical unimportant unimportant unimportant a> 0.10: unimportant
The frequency distributions of the mputs and outputs are presented in Fig. 5, together with the scatter plots between each input and each output (500 points in each graph). The stronger relationships between the outputs and the variables found to be significantly important are clear from the scatter plots. In the other cases, the scattering of the data points IS suhstantial. HISTOGRAMS AND SeATTER-PLOTS INPUTS
OUTPUTS
Figure S. Histograms of the inputs anu ,IUtputS. and scatter-plols of the relationships belween inpuls and outputs. Inputs: population. per capita flowrate. per capita BOD. lemperature. coefficient K and temperature coefficient. Outt>uts: effluent BOD and reqUired area.
CONCLUSIONS The design based on the Uncertaimy Analysis is a simple and efficient method for incorporating the uncertainties usually overlooked in the normal designs. The procedure exemplified in the paper may be adopted in the designs of other treatment systems. and not only for the case offacultative ponds.
Facultative ponds uncertainty analysis
47
The designer can decide upon the acceptabh safety to be adopted in the design for the compliance with the effluent standards (and the related costs), instead of the simple incorporation of safety factors or overconservative criteria. The Sensitivity Analysis may help the designer in the selection of those inputs in which it is justifiable to spend more time and/or money in a more accurate determination. The effluent BOD seems to be relatively less influenced by the uncertainty in the data, whereas the required area shows a wider variation. In the example shown, the uitical inputs for the effluent BOD were found to be the BOD removal coefficient and the liquid temperature. For the required area, the critical inputs were the population and the per capita BOD load. REFERENCES Buckley, J. M. (1985). A generalized sensitivity alialysIs of the kinetics of the activated sludge process (with particular reference to dissolved oxygen control). M.Sc. Di:;,ertatlOn, Imperial College, Umversity of London. Campos. M. C. S. and Von Sperling, M. (1994). Modelagem e avalia~ao da qualidade da agua de rIOS da Regiao Metropolttana de Belo Horizonte, ulilizando a Analtse da Incerteza. In: VI SILUBESA . SimposlO Luso-Brasileiro de Engenharia Sanitaria e Ambiental. Florian6polis-SC, 12-16 Junho 1994. Torno II, pp. 89-97. Hornberger, G. M. and Spear, R. C. (1983). An approach to the analysis of behaviour andsensitivity in environmental systems. In: Beck. M. B. and Van Straten, G. (cds). Uncertainty and forecasting of water quality. Sprmger-Verlag, pp. 101-116. Jaffe, P. R., Paniconi, C. and Wood, E. F. (1988). Model calibration based on random environmentailluctuation. Journal of the Environmental Engineering Division. ASCE, 114 (EE5). 1136-1145. Lumbers, J. P. (1987). Rotating biological contactors: mechanisms, modelling and design. Ph.D. Thesis, Imperial College, University of London, London. Spear, R. C. and Hornberger, G. M. (1980). Eutrophication in Peel Inlet: II. Identification of Critical uncertainties via generalized sensitivity analySIS. Water Researc/. 14 41-49. Tomlin, S. (1986) The development of a dynamic mode. for an activated sludge sewage treatment process. M.Sc. DIssertation, Imperial College, Umversity of London. Van Straten, G. and Keesman, K. J. (1991). Uncertainty propagation and speculation in projective forecasts of environmental change: a lake-eutrophication example. Journal of Forecasting, 10, 163-190. Von Sperling, M. (1990). Optimal management of the oxidation ditch process. Ph.D. Thesis, Imperial College, University of London, London. Von Sperling, M. (1993a). Parameter estimation and sensitIvity analysis of an activated sludge model using Monte Carlo simulation and the analyst'S involvement. lVat. SCI. Tech., 28(1 1-12), 219-229. Von Sperling, M. (I993b). Analise da incerteza em estudos ambientais. Aplica~ao na modelagem da qualidade da agua de rios. Bio Engenharia Sanitdria e Ambiental. Encarte Tecnico, Ano II, No. I, 2-10. Von Sperltng, M. (1993c). Caltbra~do e analise de sensibilidade de modelos ambientals com base em simula~ao Monte Carlo. In: I Simp6sio de Recursos Hfdricos do Cone Sui: Simposio Brasileiro de Recursos Hfdricos, Gramado-RS, 7-12 Novembro 1993, Vol. I, pp. 556-565. Von Sperling, M. (1994) Calibrauun of poorly identifiable systems. Application to an activated sludge model. Journal of the Environmental Engineering Division, ASCE. 120(3), May/June 1994,625·644.