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A reliability assessment for regional water quality management
Compul. & Ops Ra..
Vol. 3, pp. 145-155. Pergamon Press, 1976. Printed in Great Britain
A RELIABILITY ASSESSMENT FOR REGIONAL WATER QUALITY MANAGEMENT* CHIA SHUN SHIH* Division of Environmental Studies, University of Texas at San Antonio, San Antonio, Texas, 78285U.S.A. Seeps and purposoThe stiffening competition between environmental protection on the one hand and economic and energy resource development on the other, underlines the need to devise means of achieving environmental goals which minim& cost. The purpose of this paper is to show how the concept of water quality reliability can be used to economic advantage in regional water quality management to maintain stream quality at miniium costs. The probability methodology presented allows trade-offs to be made for example, between a better water quality standard and the reliability of achieving that standard if there is no change in operating budget. The realism of the probabilistic approach emphasizes the need to specify future water quality standards with associated realiability levels. Abstract-Deterministic criteria have always been employed in establishing managerial goals for urban water quality management. However, the diiferent parameters, such as quantity and quality of waste treatment discharges, irrigation return tlows and urban runoff, that characterize regional water quality are probabilistic in nature. Thus, the attainment of managerial goals will inherently exhibit the characteristics of uncertainty. In this article the concept of reliability of water quality of a stream system is introduced. Reliability is defined herein as the percentage of time that specitic water quality managerial goals can be attained. A simulationoptimization model was developed for decision-making in regional water quality management. Stochastic quadratic programming techniques have been used in optimizing the basin-wide quality control strategy subject to a probabilistic constraint which reflects the desired reliability of the stream system. The optimization scheme facilitates the determination of the best pollution control decisions for each treatment facility while minimizing the total regional annual cost, subject to the quality criteria, and the desired level of reliability. Practical application of the developed model to the San Antonio River Basin, Texas, was analyzed and a sensitivity analysis was conducted based on varying degrees of the system reliability. INTRODUCTION
The techniques leading to the reduction of environmental pollution have been one of the major concerns of our society. In the light of the recent energy “crunch” and economic recession, efficient utilization of our energy and natural resources has also been recognized as an important economic issue. However, the potential conflicts between the environmental protection and economic and energy resource development has forced us to redefine our goals for pollution control. There is, therefore, a great need to devise a methodology for the assessment of risks associated with achievement of these goals in environmental quality management while minimizing the economic burden occurring to the public. In establishing managerial goals for a regional water quality management system, deterministic criteria have been employed. However, the probabilistic nature of different parameters characterizing regional water quality are also well recognized. Consequently, the attainment of goals for regional water quality management often becomes a problem with built-in risks. For example, the quality of a specific river basin is usually regulated based on a predetermined standard and associated components, including wastewater treatment facilities, flow augmentation system, urban runoff control and in-stream aeration, etc., are designed and operated accordingly. As the initial quality for individual components may change randomly, the resultant quality will also deviate randomly from the predetermined standard. Thus, there is a certain fraction of time the resultant water quality will not be satisfactory. But, (a) How can this risk be assessed? (b) To what degree should this risk be incorporated in legal regulations and managerial goals? (c) What type of economic trade-off relationships will be exhibited due to this risk? This paper has attempted to devise a practical approach to search for the answers to some of these questions associated with a regional water quality management system. *Dr. Shih is a consultant with FEA, on leave of absence from the University of Texas where he served as Professor and Director of Environmental Studies. He received his civil epgineering graduate degree from National Cheng-Kung University in Tiawan. He received his MS. and PhD degrees in Environmental Engineering and Operations Research from the University of Texas in 1967. 145
C. S.SHE-I
146
The concepts of reliability which define such risk in regional water quality management and its effects on optimum control strategies are presented. The existing situation in San Antonio River Basin, Texas is analyzed to illustrate the application of developed methodology. CONCEPTOF
WATER QUALITY RELIABILITY
Reliability is defined herein as the relative efficiency for the attainment of specific managerial goals in water quality preservation; that is, the probability that the quality standard may be satisfied, or the percentage of time that the regional water quality requirement can be met during the critical season of a year. Variability of the water quality of the receiving streams is considered to be a serious problem of the water quality management. Besides the tempory qu~itative and quantitative effects of non-point sources, stream water quality variability is mainly attributed to quality variations in the return flow, especially when the fresh water inflow is insi~fic~t. Thus, managerial goals based on deterministic criteria become either inadequate or too simplistic to handle the probabi~sti~ nature of regional water quality. Reliabi~ty analysis is hence suggested for the assessment of the uncertainty associated with the performance of managerial goals achieved for a regional water pollution control system. Through the decade of 1960, system reliability has become increasingly important in the design and implementation of industrial and military systems. During World War II, the importance of reliability was emphasized by analyzing the consequences of unrealiability of military equipment. In both industrial and domestic applications, reliability is closely associated with preference and acceptance of the individual product. Unreliability normally creates consequence in terms of extra cost, more manpower, and inconvenience to industrial and military operations. Similarly, the unreliability associated with pollution abatement should also be the pivotal element in stream quality planning and control. The causes of unreliability lie in the dynamic complexity of the system, the budg&ry restrictions, as well as the organizational and occasional human error. But the reliability can be used to an economic advantage in regional water quality management by operating individual facilities at optimum control levels in terms of both the prescribed standard and the specified or preferred reliability to maintain satisfactory stream quality at m~mum costs. On the other hand, if the reliability of waste treatment operations is ignored and the total time average is used as the basis of operation for individual facilities, some irreparable damage may result to the stream systems due to unsatisfactory operation of waste treatment facilities for an extended period of time. SYSTEMOPTIMIZATION
MODEL
Minimization of total system cost while satisfying the quality standard imposed by regulating agencies and the technological capabilities of the treatment plants in the region are the basic framework of the system optimization model for a regional water quality management. Because of the reliability in satisfying the quality requ~ement for the receiving stream, a special constraint describing the probabilistic nature of the water quality at control point must be included in the modeling consideration. Meanwhile, in order to m~ntain a healthy ecosystem, the m~imum allowable pollutant concentration reflecting the minimum dissolved oxygen (DO) requirement should also be considered. On the other hand, the minimum attainable po~utant concent~tion based on technological and economic feasibility should also be specified. Thus, the optimization model for the regional water quality m~agement should be in such form as, Minimize [total costs of wastewater treatment in the region] subject to the constraints that: 1. the probability of satisfying the prescribed quality standard is larger than the specified reliability, 2. the effluent pollutant concentration must be less than the level determined by minimum DO requirement, and 3. the effluent pollutant concentration must be achievable by economically and technologically feasible means. A quadratic function is used to describe the costs of wastwater treatment and the model can be symbolically described as a stochastic quadratic programming problem, Min. xTDx+ Cx + k
A reliabilityassessmentfor regionalwaterqwalitymanagement
s.t.
147
P~(x,y,Q,d”“Lxl~~
(2)
LZSX~U
(3)
in which, x = random variables defining the effluent quality of wastewater treatment facilities D = coefficients of quadratic terms C = coefficients of linear terms k = constants P [ ] = probability of the event defined by bracket, [ 1 f = functions defining the quality at control point y = random variables defining the stream quality at headwater points q = random variables represent~g the et&rent quantities Q = random variables representing the stream how quantities L - = specified maximum allowable pollutant concentration at control point (Y= specified reliability level U = maximum allowable pollutant concentration in treated-waste eflluent L = minimum attainable pollutant concentration for treated-waste effluent The pollutant can be any quality parameter. Of course, the non-conservative pollutant is more diiIicult to handle than conservative pollutant because of its biodegradability. The function f can be a simulation model based on the distributions of random variables x, y, q and Q and the stream quality routing relationships. The detail for the development of function f can be found in the description of illustrative case study below for San Antonio River Basin The solution for the stochastic quadratic programming problem can be obtained by a parametric simulation~p~i~tion procedure. But, the rate of convergence is too slow because of the difficulty in controlling the stability of the simulated composite distribution of stream quality at the control point. Thus, a ~ne~~tion procedure using linear regression to decompose the chance-constraint into a series of linear constraints is developed. For each reliability level, a unique linear constraint relating the stream quality at the control point to the quality of treated waste e&rent is derived. Therefore, the orignial problem is decomposed into a series of regular quadratic propping problems. SAN ANTONIO
WASTEWATER
TREATMENT
SYSTEM
The site selected for the study was the regional wastewater treatment system in the San Antonio Metropolitan Area. There are four rivers and three major waste treatment facilities in the region, with total design capacity of 112.3 million gallons per day (MGD). The major waste treatment facilities are: Rilling Road Plant, Salado Piant and Leon Plant. The rivers are: San Antonio River, Salado Creek, Medina River and Leon Creek. Elmendorf, a downstream location, was chosen as the control point for the regional water quality management. Figure 1 schematically presents the regional river system under study. Biochemical oxygen demand (BOD) has been used as the characterizing parameter. STREAM
QUALITY
TRANSITION
FUNCTIONS
Quality transition functions are defined as the relationship between water quality variables of two points in a stream. The two points may be separated by a long distance in a stream or may be the points before and after mixing with a tributary stream or waste discharge but separated by a negligible distance. The Texas Water Development Board has developed a practical water quality routine model (QUAL-I) and calibrated for San Antonio River Basin[3,4]. This model is capable of predicting the temporal and spatial distribution of temperature, biochemical oxygen demand (BOD), dissolved oxygen, and conservative minerals within a segment of streams and canals. Thus, the QUAL-I model was applied to develop transition relationship of water quality from one point to another along the direction of river flow. Figure 2 summarizes the data and information used in the development of quality transition functions. The transition fun&ion was developed to economize the computation requirements, because the direct utilization of QUAL-I in quality routing will consume too much computer time in
148 Son Antonlo Rover heOOdtyater II I Y Solado Creek headwater Q-Y,
t3llmg
Rood plant
Leon Creek plant
Elmendorf control point \
Fig. 1. San Antonio river basin. 40.03cfs
il 8.5 hr.
Rilling Road plant
16.6cfs
I I hr.
jlanr
u v =0.224 PO’ D = 1.08 Q”16’ 4.5hr.
v = Mean velocity, ft/sec D= Mean depib, ft Cl = Discharge, cfs
I
“. .._
” = 1.74 Qoo4’ D=O.l47 Qo5 5.5hr. 464.94
2.7hr. v =0.463 D=0.355
cfs
9”“’ Qo44
I Control potnt(Elmendorf
1
Fig. 2. Hydraulic parameters for determining quality transition.
simulation optimization procedures. With finite simulation runs for practical ranges of quality variations, the quality transition between interested points on a stream system can easily be formulated. By successive use of the QUAL-I Model for decay of biodegradable materials and by applying the material balance formula for mixing as the stream meets tributaries and waste discharges from treatment plants, quality transition functions between various points of interest
A reliability assessment for regional water quality management
149
in the San Antonio River Basin were developed. Though only BOD was used as the quality parameter, the same procedures can be applied to any other parameters. grout these quality transition functions, the stream quality at control point , 1uwtrol,can be determined as a function of quantity and quality of stream flows and treated-waste effluents. SIMULATION
OF CHANCE-CONSTRAINT
As described in equation (2), the control point quality is a function of headwater quantities and qualities, the wastewater treatment plan efBuent quantities and qualities. Since ail these are random variables, the control point quality will thus be probabilistic in nature. A simulation procedure was designed to generate a composite probability distribution for the controf point quality as shown in Fig. 3. Based on their statistical distribution in historical records, the stream inflows, the stream qualities, the waste treatment plant discharges, and the waste effluent qualities are randomly generated. It is reasonable to assume that the statistical distribution of specific treated-waste eflluent is varying with the process and equipments involved. For e&rent quality, the empirical distribution of waste effluent quality from each plant is fist normalized by its mean. Thus the st~d~~~~ dist~bution has a mean of 1.0. Based on random observations, corresponding values of the standardized distribution were selected. These values were then multiplied by pre-specified efBuent quality target value to obtain the quality value used in the computation for control point quality. The pre-specified BOD levels for all treatment plants were set at 5.0, 10.0, 15.0, 20.0 and 25.0 mg/l. Thus there are 125 possible combinations of different BOD levels for the three waste treatment plants under consideration. For each of these combinations the entire simulation is performed 100 times and control point quality is computed. Finally, the frequency distribution of the control point quality is determined. Therefore, the chance-constraint describing the probabilistic nature of stream quality maintenance at control point (Elmendorf) can be written as W’(Q1, Qz, Q3t
Q4r
YI,
~2, ~3, ~4,419
qz,
q3,
XI,
~2,
~3)
5
Lna$~
ci
in which, Q1, yl Quantity and BOD of San Antonio River headwater Qz, y2 Quantity and BOD of Salado Creek headwater Efflwnt
quality
Effluent quality
oq3 42
Headwater quality
Headwater quallty
q’l
Quality tronsition function
i
Streom quolity ot control point
x: = Normalized voriobles for effluent quality, i =1,2,3 EFF, = Pre-specified target value for effluent qualitiy,i =1,2,3
Fig. 3. Schematic representation of computation methodology for control point quality.
(4)
c. s. SHIH
150 @, y2 Quantity Q4, y4 Quantity ql, xl Quantity q2, x2 Quantity q3, x3 Quantity
and BOD of Leon Creek headwater and BOD of Medina River headwater and BOD of Rilling Road Treatment Plant and BOD of Salado Treatment Plant and BOD of Leon Treatment Plant
This chance-constraint equation (4) states that the probability of the control point quality being less than or equal to I,, must be greater than or equal to cy.In other words, the control point quality satisfies the limit L mx at least a - 100% of the time. The concept of reliability can further be illustrated using the probab~ity density function (p.d.f.) for the l,,,,r. Figure 4 depicts a hypothetical p.d.f. for the control point quality, I,-). The point L - in Figs. 4 and 5 is chosen as the upper limit of Lwuo,.The hatched area at the right of L, is equal to (1 - ar) which is the risk factor on the upper limit of BOD at Elmendorf. In other words lOO(1 - a) percent of the time the BOD level at Elmendorf may be allowed to rise up above its maximum allowable level L,. Consequently, the control point quality can be considered as a function of the et&rent discharges from the treatment plants in the system, The functional relationship may be written as g(x,,x2,xs)=
q*
6
Lmnx
(5)
where qp = water quality at Elmendorf control point corresponding to a specific reliability 01,(BOD, mSn), and g = function which describes the relationship between treatment plant effluents and control point quality at reliability (r. Using linear regression, series of linear equations were developed for reliability levels of 0.80, 0.85, 0.90 and 0.95. The resulting linear functions are: at reliability = 0.80 qo.rw= 5.64483+ 0.05079x,+ 0.00136~2+ 0.03781~2
Water quality Fii.
at control point,
I,,,+,,
(BOO mg/l)
4. Probabilitydensityof randomvariablel_,,.
Water quality
at control point,
CC,,+,, ( BOD mg/ll
Fig.5. Cumulativeprobabilityof the randomvariableI-,,,+
(6)
A reliabilityassessmentfor regionalwaterqualitymanagement
151
40.85= 5.86297+ 0.05760x,+ 000147x2 + 0.04408~~
(7)
40.90= 5.98727+ 007294x,+ 0.00230x~f 0.05522x:,
(8)
at reliability = 0.85
at reliability = 0.90
and at reliability = 0.95 ~33.95
=
6.15601-b
0.~2~X, +0.00503X2+0.08842X3
(9)
OBJECTIVE FUNCTION AND OTHER CONSTRAINTS FOR SAN ANTONIO RIVER BASIN
As the annual cost of operation, maintenance and amortization will vary with effluent quality desired in each plant, the total annual cost for each plant has been estimated as a function of BOD co~cen~ation in treated efliuent as cited in Table 1. The cost figures for efliuent levels of 10.0, 18.0 and 30.0 mgll were estimated based on the assumption that secondary treatment (activated sludge process) will be used, while the cost figures corresponding to 4.Omg/l were estimated based on the assumption that an advanced waste treatment facility will be used. The values represent total annual operation, maintenance and amortization over 25 years at 6% annual interest. The capital cost for the designed plant was computed based on E~neering Cost Index for San Antonio during 1974[1]. Table 1. Efauentqualityand total annualcost Totalannual cost, x 1000dollars&r. EffluentBOD,mg/l x,,i=l,2,3
Rillingroadplant, G
Saladoplant, Cz
Leonplant, c,
4.0 10.0 18.0 30.0
6028.0 4737.0 4115.0 4067.0
2163.0 1735.0 1571.0 1534.0
1346.0 1019.0 927.0 907.0
Using multiple linear regression, the total annual cost for each plant is expressed as a function of BOD concentration in the effluent, Cl = 2434.42822-81.20744x, + 1.71653~1’
(10)
C2 = 6928.65625- 261.72241~~+5.56689x;
(11)
C,= 1528.11523-59.21742x,+ 1.28210~3
(12)
Thus the objective function for San Antonio River Basin becomes, TC = 1.71653x: + 5.56689~2~f 1.28210~1~- 81.20744~1 - 261.72241~2- 59.21742~3+ 10901.1997
(13)
in which, TC = Total Annual Costs for San Antonio Region C1 = Total Annual Cost for Rilling Road Plant, x 1000dollarslyr C2 = Total Annual Cost for Salado Plant, x 1000dollarslyr Cs = Total Annual Cost for Leon Plant, X1000dollarslyr. The upper lit on the discharged e&rent BOD quality from the waste treatment plant is the maximum BOD that can be allowed to discharge such that the dissolved oxygen does not fall below S.Omg/l in any point throughout the entire system. This limit has been derived by the iterative use of the QUAL-I Model. It was found that the etlluent BOD levels in treated effluent can be as high as 25.0mgf. In view of the technologic~ limitations, BOD levels lower than
152
c. s. SHIH
5.0 mg/l are considered infeasible. Therefore, the upper and lower bounds of BOD concentration in treated e&rents are: 5sXi 525 (14) where i = 1,2,3. RESULTS
OF OPTIMIZATION
Substi~ting the objective functions and constraints developed above into equation (l-3), the optimi~tion model for San Antonio Regional Water Quality Management can be described by equations (13), (4) and (14). Since the chance constraint has been decomposed into a series of linear constraints as described by equations (6-g), the optimization model thus becomes, Min. TC equation (13) s.t. equation (14) and One of the equations (69). The above water quality optimization model for the San Antonio area was solved for reliability levels at 0.80,0.85, 0.90 and 0.95 while the control point BOD standards (I;,,) were varied between 6.0 mg/l and 11 mgll. In Fig. 6 total annual system cost is plotted as a function of re~ability for different Lmx values. Figure 7 presents total annual system cost vs L, results for
1
I
I
I
I
0.80
0.85
0.90
0.95
Regional system reliability,
a
Fig. 6. Total annual costs vs regional system reIiab~ity.
Water quality standard,
L ,,,iSOD
in mgfl
1
Fig.7. Total annual costs vs water quality criteria.
A reliability assessment for regional water quality management
153
= 8-11
I
I
I
I
5
IO
I5
Optimum
effluent
I 20
quality,
25
BODmgll
Fig. 8. Effects of RillingRoad plantefluent quality on system reliability.
I
I
I
I
1
I
5
IO
15
20
25
Optimum
effluent quality, BODmg/l
Fig. 9. Effects of Leon Creek pht etiiuent quality on systemre~ab~~.
different reliability levels. Effects of plant et&rent quality on the system reliability are shown in Figs. 8 and 9. DfSCUSSIONS
AND CONCLUSIONS
As implied in the chance constraint in equation (4), the increasing system reliability will tighten up the feasible region as shown in Figs. 6 and 7. Thus, at 0.90 reliability, water quality can be as good as almost 6.0 mg/l BOD, but at 0.95 reliability the best quality water that can be obtained is about 8.Omg/I BOD. Furthermore, as the reliability imposed on the system is increased the operating cost of the system increases. This is to be expected and shows that the system reacts normally as would any other system subjected to reliability rating. It can also be seen that as the quality standard in the system is tightened, the annual cost for the system also increases. This, too, is not unexpected, and indicates that the system is behaving in a normal fashion, i.e., higher quality standard requires better treatment of the waste water. In addition, as the stream water quality criteria is tightened, the cost curves of Fig. 7 shift upward. The shift increment increases as the BOD level decreases. For instance, at reliability of 0.85, a decrease in BOD from 8.0 and 7.Omg/l corresponds to an increased system cost of $451,183.50per year. At the same reliability a decrease in BOD from 9.0 to 8.0 mg/l will increase system cost only by $22,410.40 per year. The incremental cost of increased reliability is lower at lower reliability level than that at higher reliability level. For instance, to increase system reliability at a quality level of 8.0 mg/l BOD from 0.80 to 0.85 would require only an additional $22,310.40 per year while an increase in system reliability at the same quality level from 0.85 to 0.90 would require an additional $175,747.80 per year. Thus, cost rises at an accelerating rate as system reliability increases. It is interesting to point out that Figs. 6 and 7 can also be used to evaluate economic
154
C. S. SHIH
feasibility. Assume that the regional pollution control authority has budgeted $6.3 million per year to operate the system. This budget constraint is hypothetical only and does not represent any past or present expenditures within the system. The dashed line on Figs. 6 and 7 represents this budget imposed on the system. From Fig. 6 it can be seen that the managerial policy can be any one point on the line which corresponds to a specific reliability and water quality level for the basin. However, the best that the system can perform is to meet minimum water quality standards of 8.0 mg/l only 87.75% of the time. Any higher degree of reliability will cost more than allocated for the system’s operation. However, as we know, the stream flow is not constant year around. All streams have periods of high and low flow seasons. If advantage is taken of this natural phenomenon, the m~agerial autho~ties can vary their operating policies accordingly. For instance, during periods of high flow, predominantly during the winter months, the management could adjust operating policies while meeting minimum quality standards and reliability requirements accordingly. The money saved can then be applied to the system during periods of low flow when the reliability would then be more critical. The effect would be an overall better managerial policy at the same level of expenditure. There is, then, an economic tradeoff between producing a better efIIuent and a lower reliability. Therefore, as the need arises for better eflluent, a tradeoff between water quality and reliability must be recognized if there is no budget change for the system. Thus, this reliability analysis indicates that the regional management authority has a choice as to its emphasis and purpose. By using the models presented herewith, a guide for decisions can be realized and implemented where priorities dictate. Most water pollution control programs are still outlined on a local basis. The regional approach will shed light on the effects of overall regional water quality by individual waste treatment plants. By using this type of analysis, both the economic considerations of the basin as well as the water quality standards may be examined under the premise of optimum managerial goals. This analysis has also indicated the impacts of each treatment facility upon the regional quality as shown in Figs 8 and 9. Meanwhile, the recent findings have shown that the non-point sources would become the major contributor of pollution loads to our streams if only point sources are well controlled. But the control of non-point pollution sources can be a very expensive undertaking. Besides, the impact of non-point sources on regional water quality may be significant but inte~ittent. Thus, the tradeoffs between the effectiveness of non-point pollution control and the investment required must be assessed carefully before any large-scale non-point source control project is attempted. The reliability analysis model presented herewith may be adopted for such assessment while the non-point sources are considered as large pollution loads with impulse-type probability distribution for its occurrence. Finally, it must be pointed out that the existing water quality standards are still deterministic. In view of the reality of regional water quality management, the reliability concepts must be incorporated into the future water quality standards. Perhaps, both deterministic standards as well as reliability levels should be specified simultaneously. NOTATION afalpha) ~lia~ity requirement for the control point quafity Total AMU~ Cost for Rilling Road P&t, Tiou&nd dollars/yr. Total Annual Cost for Salado Plant. Thousand dollarslvr. Total Annual Cost for Leon Plant, Thousand dollars/$. mean depth, ft. functional expression for control point BOD functional relationship between etlluent quality and reliabaity stream quality at Eimendorf Control Point, n&I maximum allowable BOD standard at the control point, mg/l probability quantity of efliuent from Rilling Road Plant, cfs Quantity of etlfuent from Mado Plant, cfs Quantity of effluent from Leon Plant, cfs Headwater flow San Antonio River, cfs Headwater flow Salado Creek, cfs Headwater flow Leon Creek, cfs Headwater flow Medina Creek, cfs Water quality at Ehnendorf control point corresponding to a specific reliability, (I, BOD mg/l discharge, cfs total regional am~ualcost for water tr~tment, Thousand do~a~~~,
A reliability assessment for regionai water qua&y man~ement
15s
mean velocity, ftfsec BOD of Rillii Road Plant effluent, mg/l BOD of Salado Plant efiiuent, mg/i BOD of Leon Plant e&tent, mg/l BOD of San Antonio River Headwater, me/l BOD of Saiado Creek IIeadwater, mg/l BOD of Leon Creek Headwater, n&l BOD of Medina River Headwater, mg/l
AcknowMgements-This study was made possible by a retesrch grant from the U.S. Environmental Protection Agency (2) (Project No. R-gtl%%). The author wishes to thank Mr. Donald II. Lewis and Dr. Roger D. Shtdi of the Agency for their comments, ideas and technical consuhation. RBFERENCES 1. L. Koenig, Private- Consultation, L. Koenig Research, Inc., San Antonio, Texas, 1974. 2. C. S. Shih and S. Hasan, Assessment of Reliability Criteria for EfBuent Standards. Project Report submitted to U.S. Environmctual Protection Agency (Project No. R-MJOS%).1974. 3. Texas Water Development Board: Simulation of Water Quality in Streams and Canals-Program Documentation and Users Mamtal. Texas Water Development Board, Austin, Texas, September 1970. 4. Texas Water Development Board: Simulation of Water Quality in Streams and Canals. Report 128, Texas Water ~v~opment Board, Austin, Texas, May 1971.
Vol. 3, pp. 145-155. Pergamon Press, 1976. Printed in Great Britain
A RELIABILITY ASSESSMENT FOR REGIONAL WATER QUALITY MANAGEMENT* CHIA SHUN SHIH* Division of Environmental Studies, University of Texas at San Antonio, San Antonio, Texas, 78285U.S.A. Seeps and purposoThe stiffening competition between environmental protection on the one hand and economic and energy resource development on the other, underlines the need to devise means of achieving environmental goals which minim& cost. The purpose of this paper is to show how the concept of water quality reliability can be used to economic advantage in regional water quality management to maintain stream quality at miniium costs. The probability methodology presented allows trade-offs to be made for example, between a better water quality standard and the reliability of achieving that standard if there is no change in operating budget. The realism of the probabilistic approach emphasizes the need to specify future water quality standards with associated realiability levels. Abstract-Deterministic criteria have always been employed in establishing managerial goals for urban water quality management. However, the diiferent parameters, such as quantity and quality of waste treatment discharges, irrigation return tlows and urban runoff, that characterize regional water quality are probabilistic in nature. Thus, the attainment of managerial goals will inherently exhibit the characteristics of uncertainty. In this article the concept of reliability of water quality of a stream system is introduced. Reliability is defined herein as the percentage of time that specitic water quality managerial goals can be attained. A simulationoptimization model was developed for decision-making in regional water quality management. Stochastic quadratic programming techniques have been used in optimizing the basin-wide quality control strategy subject to a probabilistic constraint which reflects the desired reliability of the stream system. The optimization scheme facilitates the determination of the best pollution control decisions for each treatment facility while minimizing the total regional annual cost, subject to the quality criteria, and the desired level of reliability. Practical application of the developed model to the San Antonio River Basin, Texas, was analyzed and a sensitivity analysis was conducted based on varying degrees of the system reliability. INTRODUCTION
The techniques leading to the reduction of environmental pollution have been one of the major concerns of our society. In the light of the recent energy “crunch” and economic recession, efficient utilization of our energy and natural resources has also been recognized as an important economic issue. However, the potential conflicts between the environmental protection and economic and energy resource development has forced us to redefine our goals for pollution control. There is, therefore, a great need to devise a methodology for the assessment of risks associated with achievement of these goals in environmental quality management while minimizing the economic burden occurring to the public. In establishing managerial goals for a regional water quality management system, deterministic criteria have been employed. However, the probabilistic nature of different parameters characterizing regional water quality are also well recognized. Consequently, the attainment of goals for regional water quality management often becomes a problem with built-in risks. For example, the quality of a specific river basin is usually regulated based on a predetermined standard and associated components, including wastewater treatment facilities, flow augmentation system, urban runoff control and in-stream aeration, etc., are designed and operated accordingly. As the initial quality for individual components may change randomly, the resultant quality will also deviate randomly from the predetermined standard. Thus, there is a certain fraction of time the resultant water quality will not be satisfactory. But, (a) How can this risk be assessed? (b) To what degree should this risk be incorporated in legal regulations and managerial goals? (c) What type of economic trade-off relationships will be exhibited due to this risk? This paper has attempted to devise a practical approach to search for the answers to some of these questions associated with a regional water quality management system. *Dr. Shih is a consultant with FEA, on leave of absence from the University of Texas where he served as Professor and Director of Environmental Studies. He received his civil epgineering graduate degree from National Cheng-Kung University in Tiawan. He received his MS. and PhD degrees in Environmental Engineering and Operations Research from the University of Texas in 1967. 145
C. S.SHE-I
146
The concepts of reliability which define such risk in regional water quality management and its effects on optimum control strategies are presented. The existing situation in San Antonio River Basin, Texas is analyzed to illustrate the application of developed methodology. CONCEPTOF
WATER QUALITY RELIABILITY
Reliability is defined herein as the relative efficiency for the attainment of specific managerial goals in water quality preservation; that is, the probability that the quality standard may be satisfied, or the percentage of time that the regional water quality requirement can be met during the critical season of a year. Variability of the water quality of the receiving streams is considered to be a serious problem of the water quality management. Besides the tempory qu~itative and quantitative effects of non-point sources, stream water quality variability is mainly attributed to quality variations in the return flow, especially when the fresh water inflow is insi~fic~t. Thus, managerial goals based on deterministic criteria become either inadequate or too simplistic to handle the probabi~sti~ nature of regional water quality. Reliabi~ty analysis is hence suggested for the assessment of the uncertainty associated with the performance of managerial goals achieved for a regional water pollution control system. Through the decade of 1960, system reliability has become increasingly important in the design and implementation of industrial and military systems. During World War II, the importance of reliability was emphasized by analyzing the consequences of unrealiability of military equipment. In both industrial and domestic applications, reliability is closely associated with preference and acceptance of the individual product. Unreliability normally creates consequence in terms of extra cost, more manpower, and inconvenience to industrial and military operations. Similarly, the unreliability associated with pollution abatement should also be the pivotal element in stream quality planning and control. The causes of unreliability lie in the dynamic complexity of the system, the budg&ry restrictions, as well as the organizational and occasional human error. But the reliability can be used to an economic advantage in regional water quality management by operating individual facilities at optimum control levels in terms of both the prescribed standard and the specified or preferred reliability to maintain satisfactory stream quality at m~mum costs. On the other hand, if the reliability of waste treatment operations is ignored and the total time average is used as the basis of operation for individual facilities, some irreparable damage may result to the stream systems due to unsatisfactory operation of waste treatment facilities for an extended period of time. SYSTEMOPTIMIZATION
MODEL
Minimization of total system cost while satisfying the quality standard imposed by regulating agencies and the technological capabilities of the treatment plants in the region are the basic framework of the system optimization model for a regional water quality management. Because of the reliability in satisfying the quality requ~ement for the receiving stream, a special constraint describing the probabilistic nature of the water quality at control point must be included in the modeling consideration. Meanwhile, in order to m~ntain a healthy ecosystem, the m~imum allowable pollutant concentration reflecting the minimum dissolved oxygen (DO) requirement should also be considered. On the other hand, the minimum attainable po~utant concent~tion based on technological and economic feasibility should also be specified. Thus, the optimization model for the regional water quality m~agement should be in such form as, Minimize [total costs of wastewater treatment in the region] subject to the constraints that: 1. the probability of satisfying the prescribed quality standard is larger than the specified reliability, 2. the effluent pollutant concentration must be less than the level determined by minimum DO requirement, and 3. the effluent pollutant concentration must be achievable by economically and technologically feasible means. A quadratic function is used to describe the costs of wastwater treatment and the model can be symbolically described as a stochastic quadratic programming problem, Min. xTDx+ Cx + k
A reliabilityassessmentfor regionalwaterqwalitymanagement
s.t.
147
P~(x,y,Q,d”“Lxl~~
(2)
LZSX~U
(3)
in which, x = random variables defining the effluent quality of wastewater treatment facilities D = coefficients of quadratic terms C = coefficients of linear terms k = constants P [ ] = probability of the event defined by bracket, [ 1 f = functions defining the quality at control point y = random variables defining the stream quality at headwater points q = random variables represent~g the et&rent quantities Q = random variables representing the stream how quantities L - = specified maximum allowable pollutant concentration at control point (Y= specified reliability level U = maximum allowable pollutant concentration in treated-waste eflluent L = minimum attainable pollutant concentration for treated-waste effluent The pollutant can be any quality parameter. Of course, the non-conservative pollutant is more diiIicult to handle than conservative pollutant because of its biodegradability. The function f can be a simulation model based on the distributions of random variables x, y, q and Q and the stream quality routing relationships. The detail for the development of function f can be found in the description of illustrative case study below for San Antonio River Basin The solution for the stochastic quadratic programming problem can be obtained by a parametric simulation~p~i~tion procedure. But, the rate of convergence is too slow because of the difficulty in controlling the stability of the simulated composite distribution of stream quality at the control point. Thus, a ~ne~~tion procedure using linear regression to decompose the chance-constraint into a series of linear constraints is developed. For each reliability level, a unique linear constraint relating the stream quality at the control point to the quality of treated waste e&rent is derived. Therefore, the orignial problem is decomposed into a series of regular quadratic propping problems. SAN ANTONIO
WASTEWATER
TREATMENT
SYSTEM
The site selected for the study was the regional wastewater treatment system in the San Antonio Metropolitan Area. There are four rivers and three major waste treatment facilities in the region, with total design capacity of 112.3 million gallons per day (MGD). The major waste treatment facilities are: Rilling Road Plant, Salado Piant and Leon Plant. The rivers are: San Antonio River, Salado Creek, Medina River and Leon Creek. Elmendorf, a downstream location, was chosen as the control point for the regional water quality management. Figure 1 schematically presents the regional river system under study. Biochemical oxygen demand (BOD) has been used as the characterizing parameter. STREAM
QUALITY
TRANSITION
FUNCTIONS
Quality transition functions are defined as the relationship between water quality variables of two points in a stream. The two points may be separated by a long distance in a stream or may be the points before and after mixing with a tributary stream or waste discharge but separated by a negligible distance. The Texas Water Development Board has developed a practical water quality routine model (QUAL-I) and calibrated for San Antonio River Basin[3,4]. This model is capable of predicting the temporal and spatial distribution of temperature, biochemical oxygen demand (BOD), dissolved oxygen, and conservative minerals within a segment of streams and canals. Thus, the QUAL-I model was applied to develop transition relationship of water quality from one point to another along the direction of river flow. Figure 2 summarizes the data and information used in the development of quality transition functions. The transition fun&ion was developed to economize the computation requirements, because the direct utilization of QUAL-I in quality routing will consume too much computer time in
148 Son Antonlo Rover heOOdtyater II I Y Solado Creek headwater Q-Y,
t3llmg
Rood plant
Leon Creek plant
Elmendorf control point \
Fig. 1. San Antonio river basin. 40.03cfs
il 8.5 hr.
Rilling Road plant
16.6cfs
I I hr.
jlanr
u v =0.224 PO’ D = 1.08 Q”16’ 4.5hr.
v = Mean velocity, ft/sec D= Mean depib, ft Cl = Discharge, cfs
I
“. .._
” = 1.74 Qoo4’ D=O.l47 Qo5 5.5hr. 464.94
2.7hr. v =0.463 D=0.355
cfs
9”“’ Qo44
I Control potnt(Elmendorf
1
Fig. 2. Hydraulic parameters for determining quality transition.
simulation optimization procedures. With finite simulation runs for practical ranges of quality variations, the quality transition between interested points on a stream system can easily be formulated. By successive use of the QUAL-I Model for decay of biodegradable materials and by applying the material balance formula for mixing as the stream meets tributaries and waste discharges from treatment plants, quality transition functions between various points of interest
A reliability assessment for regional water quality management
149
in the San Antonio River Basin were developed. Though only BOD was used as the quality parameter, the same procedures can be applied to any other parameters. grout these quality transition functions, the stream quality at control point , 1uwtrol,can be determined as a function of quantity and quality of stream flows and treated-waste effluents. SIMULATION
OF CHANCE-CONSTRAINT
As described in equation (2), the control point quality is a function of headwater quantities and qualities, the wastewater treatment plan efBuent quantities and qualities. Since ail these are random variables, the control point quality will thus be probabilistic in nature. A simulation procedure was designed to generate a composite probability distribution for the controf point quality as shown in Fig. 3. Based on their statistical distribution in historical records, the stream inflows, the stream qualities, the waste treatment plant discharges, and the waste effluent qualities are randomly generated. It is reasonable to assume that the statistical distribution of specific treated-waste eflluent is varying with the process and equipments involved. For e&rent quality, the empirical distribution of waste effluent quality from each plant is fist normalized by its mean. Thus the st~d~~~~ dist~bution has a mean of 1.0. Based on random observations, corresponding values of the standardized distribution were selected. These values were then multiplied by pre-specified efBuent quality target value to obtain the quality value used in the computation for control point quality. The pre-specified BOD levels for all treatment plants were set at 5.0, 10.0, 15.0, 20.0 and 25.0 mg/l. Thus there are 125 possible combinations of different BOD levels for the three waste treatment plants under consideration. For each of these combinations the entire simulation is performed 100 times and control point quality is computed. Finally, the frequency distribution of the control point quality is determined. Therefore, the chance-constraint describing the probabilistic nature of stream quality maintenance at control point (Elmendorf) can be written as W’(Q1, Qz, Q3t
Q4r
YI,
~2, ~3, ~4,419
qz,
q3,
XI,
~2,
~3)
5
Lna$~
ci
in which, Q1, yl Quantity and BOD of San Antonio River headwater Qz, y2 Quantity and BOD of Salado Creek headwater Efflwnt
quality
Effluent quality
oq3 42
Headwater quality
Headwater quallty
q’l
Quality tronsition function
i
Streom quolity ot control point
x: = Normalized voriobles for effluent quality, i =1,2,3 EFF, = Pre-specified target value for effluent qualitiy,i =1,2,3
Fig. 3. Schematic representation of computation methodology for control point quality.
(4)
c. s. SHIH
150 @, y2 Quantity Q4, y4 Quantity ql, xl Quantity q2, x2 Quantity q3, x3 Quantity
and BOD of Leon Creek headwater and BOD of Medina River headwater and BOD of Rilling Road Treatment Plant and BOD of Salado Treatment Plant and BOD of Leon Treatment Plant
This chance-constraint equation (4) states that the probability of the control point quality being less than or equal to I,, must be greater than or equal to cy.In other words, the control point quality satisfies the limit L mx at least a - 100% of the time. The concept of reliability can further be illustrated using the probab~ity density function (p.d.f.) for the l,,,,r. Figure 4 depicts a hypothetical p.d.f. for the control point quality, I,-). The point L - in Figs. 4 and 5 is chosen as the upper limit of Lwuo,.The hatched area at the right of L, is equal to (1 - ar) which is the risk factor on the upper limit of BOD at Elmendorf. In other words lOO(1 - a) percent of the time the BOD level at Elmendorf may be allowed to rise up above its maximum allowable level L,. Consequently, the control point quality can be considered as a function of the et&rent discharges from the treatment plants in the system, The functional relationship may be written as g(x,,x2,xs)=
q*
6
Lmnx
(5)
where qp = water quality at Elmendorf control point corresponding to a specific reliability 01,(BOD, mSn), and g = function which describes the relationship between treatment plant effluents and control point quality at reliability (r. Using linear regression, series of linear equations were developed for reliability levels of 0.80, 0.85, 0.90 and 0.95. The resulting linear functions are: at reliability = 0.80 qo.rw= 5.64483+ 0.05079x,+ 0.00136~2+ 0.03781~2
Water quality Fii.
at control point,
I,,,+,,
(BOO mg/l)
4. Probabilitydensityof randomvariablel_,,.
Water quality
at control point,
CC,,+,, ( BOD mg/ll
Fig.5. Cumulativeprobabilityof the randomvariableI-,,,+
(6)
A reliabilityassessmentfor regionalwaterqualitymanagement
151
40.85= 5.86297+ 0.05760x,+ 000147x2 + 0.04408~~
(7)
40.90= 5.98727+ 007294x,+ 0.00230x~f 0.05522x:,
(8)
at reliability = 0.85
at reliability = 0.90
and at reliability = 0.95 ~33.95
=
6.15601-b
0.~2~X, +0.00503X2+0.08842X3
(9)
OBJECTIVE FUNCTION AND OTHER CONSTRAINTS FOR SAN ANTONIO RIVER BASIN
As the annual cost of operation, maintenance and amortization will vary with effluent quality desired in each plant, the total annual cost for each plant has been estimated as a function of BOD co~cen~ation in treated efliuent as cited in Table 1. The cost figures for efliuent levels of 10.0, 18.0 and 30.0 mgll were estimated based on the assumption that secondary treatment (activated sludge process) will be used, while the cost figures corresponding to 4.Omg/l were estimated based on the assumption that an advanced waste treatment facility will be used. The values represent total annual operation, maintenance and amortization over 25 years at 6% annual interest. The capital cost for the designed plant was computed based on E~neering Cost Index for San Antonio during 1974[1]. Table 1. Efauentqualityand total annualcost Totalannual cost, x 1000dollars&r. EffluentBOD,mg/l x,,i=l,2,3
Rillingroadplant, G
Saladoplant, Cz
Leonplant, c,
4.0 10.0 18.0 30.0
6028.0 4737.0 4115.0 4067.0
2163.0 1735.0 1571.0 1534.0
1346.0 1019.0 927.0 907.0
Using multiple linear regression, the total annual cost for each plant is expressed as a function of BOD concentration in the effluent, Cl = 2434.42822-81.20744x, + 1.71653~1’
(10)
C2 = 6928.65625- 261.72241~~+5.56689x;
(11)
C,= 1528.11523-59.21742x,+ 1.28210~3
(12)
Thus the objective function for San Antonio River Basin becomes, TC = 1.71653x: + 5.56689~2~f 1.28210~1~- 81.20744~1 - 261.72241~2- 59.21742~3+ 10901.1997
(13)
in which, TC = Total Annual Costs for San Antonio Region C1 = Total Annual Cost for Rilling Road Plant, x 1000dollarslyr C2 = Total Annual Cost for Salado Plant, x 1000dollarslyr Cs = Total Annual Cost for Leon Plant, X1000dollarslyr. The upper lit on the discharged e&rent BOD quality from the waste treatment plant is the maximum BOD that can be allowed to discharge such that the dissolved oxygen does not fall below S.Omg/l in any point throughout the entire system. This limit has been derived by the iterative use of the QUAL-I Model. It was found that the etlluent BOD levels in treated effluent can be as high as 25.0mgf. In view of the technologic~ limitations, BOD levels lower than
152
c. s. SHIH
5.0 mg/l are considered infeasible. Therefore, the upper and lower bounds of BOD concentration in treated e&rents are: 5sXi 525 (14) where i = 1,2,3. RESULTS
OF OPTIMIZATION
Substi~ting the objective functions and constraints developed above into equation (l-3), the optimi~tion model for San Antonio Regional Water Quality Management can be described by equations (13), (4) and (14). Since the chance constraint has been decomposed into a series of linear constraints as described by equations (6-g), the optimization model thus becomes, Min. TC equation (13) s.t. equation (14) and One of the equations (69). The above water quality optimization model for the San Antonio area was solved for reliability levels at 0.80,0.85, 0.90 and 0.95 while the control point BOD standards (I;,,) were varied between 6.0 mg/l and 11 mgll. In Fig. 6 total annual system cost is plotted as a function of re~ability for different Lmx values. Figure 7 presents total annual system cost vs L, results for
1
I
I
I
I
0.80
0.85
0.90
0.95
Regional system reliability,
a
Fig. 6. Total annual costs vs regional system reIiab~ity.
Water quality standard,
L ,,,iSOD
in mgfl
1
Fig.7. Total annual costs vs water quality criteria.
A reliability assessment for regional water quality management
153
= 8-11
I
I
I
I
5
IO
I5
Optimum
effluent
I 20
quality,
25
BODmgll
Fig. 8. Effects of RillingRoad plantefluent quality on system reliability.
I
I
I
I
1
I
5
IO
15
20
25
Optimum
effluent quality, BODmg/l
Fig. 9. Effects of Leon Creek pht etiiuent quality on systemre~ab~~.
different reliability levels. Effects of plant et&rent quality on the system reliability are shown in Figs. 8 and 9. DfSCUSSIONS
AND CONCLUSIONS
As implied in the chance constraint in equation (4), the increasing system reliability will tighten up the feasible region as shown in Figs. 6 and 7. Thus, at 0.90 reliability, water quality can be as good as almost 6.0 mg/l BOD, but at 0.95 reliability the best quality water that can be obtained is about 8.Omg/I BOD. Furthermore, as the reliability imposed on the system is increased the operating cost of the system increases. This is to be expected and shows that the system reacts normally as would any other system subjected to reliability rating. It can also be seen that as the quality standard in the system is tightened, the annual cost for the system also increases. This, too, is not unexpected, and indicates that the system is behaving in a normal fashion, i.e., higher quality standard requires better treatment of the waste water. In addition, as the stream water quality criteria is tightened, the cost curves of Fig. 7 shift upward. The shift increment increases as the BOD level decreases. For instance, at reliability of 0.85, a decrease in BOD from 8.0 and 7.Omg/l corresponds to an increased system cost of $451,183.50per year. At the same reliability a decrease in BOD from 9.0 to 8.0 mg/l will increase system cost only by $22,410.40 per year. The incremental cost of increased reliability is lower at lower reliability level than that at higher reliability level. For instance, to increase system reliability at a quality level of 8.0 mg/l BOD from 0.80 to 0.85 would require only an additional $22,310.40 per year while an increase in system reliability at the same quality level from 0.85 to 0.90 would require an additional $175,747.80 per year. Thus, cost rises at an accelerating rate as system reliability increases. It is interesting to point out that Figs. 6 and 7 can also be used to evaluate economic
154
C. S. SHIH
feasibility. Assume that the regional pollution control authority has budgeted $6.3 million per year to operate the system. This budget constraint is hypothetical only and does not represent any past or present expenditures within the system. The dashed line on Figs. 6 and 7 represents this budget imposed on the system. From Fig. 6 it can be seen that the managerial policy can be any one point on the line which corresponds to a specific reliability and water quality level for the basin. However, the best that the system can perform is to meet minimum water quality standards of 8.0 mg/l only 87.75% of the time. Any higher degree of reliability will cost more than allocated for the system’s operation. However, as we know, the stream flow is not constant year around. All streams have periods of high and low flow seasons. If advantage is taken of this natural phenomenon, the m~agerial autho~ties can vary their operating policies accordingly. For instance, during periods of high flow, predominantly during the winter months, the management could adjust operating policies while meeting minimum quality standards and reliability requirements accordingly. The money saved can then be applied to the system during periods of low flow when the reliability would then be more critical. The effect would be an overall better managerial policy at the same level of expenditure. There is, then, an economic tradeoff between producing a better efIIuent and a lower reliability. Therefore, as the need arises for better eflluent, a tradeoff between water quality and reliability must be recognized if there is no budget change for the system. Thus, this reliability analysis indicates that the regional management authority has a choice as to its emphasis and purpose. By using the models presented herewith, a guide for decisions can be realized and implemented where priorities dictate. Most water pollution control programs are still outlined on a local basis. The regional approach will shed light on the effects of overall regional water quality by individual waste treatment plants. By using this type of analysis, both the economic considerations of the basin as well as the water quality standards may be examined under the premise of optimum managerial goals. This analysis has also indicated the impacts of each treatment facility upon the regional quality as shown in Figs 8 and 9. Meanwhile, the recent findings have shown that the non-point sources would become the major contributor of pollution loads to our streams if only point sources are well controlled. But the control of non-point pollution sources can be a very expensive undertaking. Besides, the impact of non-point sources on regional water quality may be significant but inte~ittent. Thus, the tradeoffs between the effectiveness of non-point pollution control and the investment required must be assessed carefully before any large-scale non-point source control project is attempted. The reliability analysis model presented herewith may be adopted for such assessment while the non-point sources are considered as large pollution loads with impulse-type probability distribution for its occurrence. Finally, it must be pointed out that the existing water quality standards are still deterministic. In view of the reality of regional water quality management, the reliability concepts must be incorporated into the future water quality standards. Perhaps, both deterministic standards as well as reliability levels should be specified simultaneously. NOTATION afalpha) ~lia~ity requirement for the control point quafity Total AMU~ Cost for Rilling Road P&t, Tiou&nd dollars/yr. Total Annual Cost for Salado Plant. Thousand dollarslvr. Total Annual Cost for Leon Plant, Thousand dollars/$. mean depth, ft. functional expression for control point BOD functional relationship between etlluent quality and reliabaity stream quality at Eimendorf Control Point, n&I maximum allowable BOD standard at the control point, mg/l probability quantity of efliuent from Rilling Road Plant, cfs Quantity of etlfuent from Mado Plant, cfs Quantity of effluent from Leon Plant, cfs Headwater flow San Antonio River, cfs Headwater flow Salado Creek, cfs Headwater flow Leon Creek, cfs Headwater flow Medina Creek, cfs Water quality at Ehnendorf control point corresponding to a specific reliability, (I, BOD mg/l discharge, cfs total regional am~ualcost for water tr~tment, Thousand do~a~~~,
A reliability assessment for regionai water qua&y man~ement
15s
mean velocity, ftfsec BOD of Rillii Road Plant effluent, mg/l BOD of Salado Plant efiiuent, mg/i BOD of Leon Plant e&tent, mg/l BOD of San Antonio River Headwater, me/l BOD of Saiado Creek IIeadwater, mg/l BOD of Leon Creek Headwater, n&l BOD of Medina River Headwater, mg/l
AcknowMgements-This study was made possible by a retesrch grant from the U.S. Environmental Protection Agency (2) (Project No. R-gtl%%). The author wishes to thank Mr. Donald II. Lewis and Dr. Roger D. Shtdi of the Agency for their comments, ideas and technical consuhation. RBFERENCES 1. L. Koenig, Private- Consultation, L. Koenig Research, Inc., San Antonio, Texas, 1974. 2. C. S. Shih and S. Hasan, Assessment of Reliability Criteria for EfBuent Standards. Project Report submitted to U.S. Environmctual Protection Agency (Project No. R-MJOS%).1974. 3. Texas Water Development Board: Simulation of Water Quality in Streams and Canals-Program Documentation and Users Mamtal. Texas Water Development Board, Austin, Texas, September 1970. 4. Texas Water Development Board: Simulation of Water Quality in Streams and Canals. Report 128, Texas Water ~v~opment Board, Austin, Texas, May 1971.