Group Title: study of the optimum number, sizes, and locations of wastewater treatment facilities in Alachua County, Florida /
Title: A study of the optimum number, sizes, and locations of wastewater treatment facilities in Alachua County, Florida
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 Material Information
Title: A study of the optimum number, sizes, and locations of wastewater treatment facilities in Alachua County, Florida
Physical Description: x, 141 leaves : ill. ; 28 cm.
Language: English
Creator: Lee, Jonq-Ying, 1944-
Publication Date: 1975
Copyright Date: 1975
 Subjects
Subject: Sewage -- Purification   ( lcsh )
Alachua County (Fla.)   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 135-140.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Jonq-Ying Lee.
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Bibliographic ID: UF00097530
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000355573
oclc - 02276790
notis - ABZ3814

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A STUDY OF THE OPFIMUM NUMBER, SIZES, AND LOCATIONS
OF WASTEWATER TREATMENT FACILITIES IN
ALACHUA COUNTY, FLORIDA














PY
JONQ- LNG LEE



























A DJSSEERTA'ION' PRESENTED TO 'ITE CRADUATF COUNCIL OF
THE UNIVERSITY OF FLOvIIDA
IN PARTiAL FULFILLMENI OF T!iE RE.QUIRT.MENIT FOR THE
DECREE OF DOCTOR OF PF0TLOSOP3HY


UNIVERSITY OF FLORIDA
1975
















ACKNOWLEDGMENT


My graduate study has been rewarding and enjoyable. Many people

are responsible and to them I feel a debt of gratitude.

My greatest debt is to Max Langham, Chairman of ny Supervisory

Committee, who has provided academic and technical guidance as well as

criticism in a masterful way, making the preparation of this disserta-

tion both exciting and enjoyable. More than this, he has provided a

warn friendship in trying times. Bobby Eddleman, Frederick Goddard,

and Lloyd B. Baldwin critically reviewed the manuscript. Special

thanks also go to LeAnne VanElburg and Janet Eldred for their help in

typing the preliminary drafts.

Leo Polopolus, the faculty, and my fellow graduate students of

the Department of Food and Resource Economics have contributed greatly

to making this study period significant. My friends on this campus

have done likewise. To all I am grateful.

This study could not have been accomplished without the financial

support of the Center for Community and Rural Development and the

Florida Agricultural Experiment Stations.

To the many unmentioned others, I am grateful.
















TABLE OF CONTENTS


Page

ACKNOWLEDGMENT ii

LIST OF TABLES v

LIST OF FIGURES vii

ABSTRACT viii

CHAPTERS

I. INTRODUCTION 1

The Problem and Objectives 1
Method of Study 3
Area of Study and Source of Data 5

II. RELEVANT ECONOMIC THEORY 8

Cost Minimization with Respect to Output 8
The Theory of Location 14
Multidimentional Utility Analysis 19

III. A GENERAL MODEL FOR REGIONAL WASTEWATER TREATMENT 23

The Model 24
Wastewater Production 27
Cost Functions 28

IV. WASTEWATER TREATMENT SITES 33

General Description of the Area 33
Wastewater Transmission Costs 40
Wastewater Treatment Costs 42
Tertiary Treatments 46
Assumptions about Cost Increases 49
Potential Sites for Wastewater Treatment Plants 50
Concluding Remarks 55


11i









TABLE OF CONTENTS (Continued)


Page

V. CAPACITY EXPANSION SCHEME 57

Investment Over Time 57
Future Service Value of Treatment Facilities 69
Minimum Cost Option for Wastewater Treatment 73

VI. LANDSPREADING SECONDARY EFFLUENT AS A SUBSTITUTE
FOR TERTIARY TREATMENT PROCESSES 89

VII. SUMMANY AND DISCUSSION 115

Summary 115
Discussion 119

APPENDIX 122

I. COMPUTER PROGRAM FOR THIS STUDY 123

BIBLIOGRAPHY 135

BIOGRAPHICAL SKETCH 141















LIST OF TABLES


Table Page

4.1 Estimated Land Uses in Alachua County 35

4.2 A Brief Description of the Incorporated Cities in
Alachua County 37

4.3 Number and Capacities of the Treatment Plants in
Alachua County, December, 1973 38

4.4 Estimated Wastewater Flows in Alachua County, Florida,
by Incorporated Cities for 1975, 1980, and 1990 39

4.5 Cost-Capacity Factors for Municipal Wastewater
Treatment Plants 45

4.6 Cordinates of Municipalities in Alachua County in
Miles 51

4.7 The Potential Sites, Capacities, and Costs of Regional
Treatment Plants and the Cities They Served 54

4.8 Possible Options for Satisfying County's Wastewater
Treatment Demands and Associated Costs, 1975 to 1990 56

5.1 Reference Numbers for Time Options in Alachua County,
Florida, 1975 to 1990 66

5.2 Reference Numbers for Regional Wastewater Treatment
Options in Alachua County, Florida, 1975 to 1990 75

5.3 Present Value of Costs of Alternative Regional
Treatment Plants for Alachua County, Florida, 1975,
1980, and 1990 76

5.4 Present Value of Total Cost of Alachua County
Wastewater Treatment by Time Options and by Regional
Wastewater Treatment Options, 1975 to 1990 79

5.5 Present Value of Secondary Treatment Costs for the
Minimum Cost Option for Alachua County, Florida, 1975
to 1990 84









LIST OF TABLES (Continued)


Table Page

5.6 Present Value of Secondary and Tertiary Treatment
Costs for the Minimum Cost Option for Alachua
County, Florida, 1975 to 1990 85

5.7 Present Value of Wastewater Treatment Costs for Time
Option 5 for Alachua County, Florida, 1975 to 1990 86

5.8 Alternate Plans of Regional Wastewater Utilities in
Alachua County as Suggested by NCFRFC 88

6.1 Estimated Returns and Fertilizer Costs per Acre of
Selected Irrigated Crops on the Deep Sands of North
and West Florida 104

6.2 Nutrient Composition of Secondary Effluent at
Southwest Treatment Plant in Talahassee 105

6.3 Estimated Total Expenses per Acre of Selected
Irrigated Crops on the Deep Sands of North and West
Florida 106

6.4 Estimated Costs of Land Preparation and Irrigation
System 107

6.5 Present Value of Costs of Transmission Pipeline per
Mile, Pumping Station, and Irrigation Systems for
Alachua County, Florida, 1975 to 1990 110

6.6 Break-even Length of Transmission Pipeline for Land
Treatment in Alachua County, Florida, 1975 to 1990 112















LIST OF FIGURES


Figure Page

1.1 Steps in the Development of the Decision Model 4

1.2 Location of Alachua County 6

4.1 Locations of the Incorporated Cities in Alachua County,
Florida 36

4.2 Tertiary Treatment Processes, Lake Tahoe [Slechta and
Culp, 1973] 47

5.1 Long-run Average Construction Cost Curve 60

5.2 Average Operation and Maintenance Cost Curve 60

5.3 Operation and Maintenance Cost over Time 63

5.4 Demand for Wastewater Treatment over Time 65

5.5 Relative Location of Potential Regional Treatment Sites
for Activated Sludge System and the Distances from the
Cities Involved to these Sites 82

5.6 Relative Location of Potential Regional Treatment Site
for Trickling Filter System and the Distances from the
Cities Involved to this Site 83

6.1 Cost Curves of Disposal of Effluent on Land 98

6.2 Examples of Equilibrium and Disequilibrium Conditions 100
















Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy


A STUDY OF OPTIMUM NUMBER, SIZES, AND LOCATIONS
OF WASTEWATER TREATMENT FACILITIES IN
ALACHUA COUNTY, FLORIDA

By

Jonq-Ying Lee

June, 1975

Chairman: Max R. Langham
Major Department: Food and Resource Economics

Economies of scale provide the main incentive for regionalization

of wastewater treatment facilities. The cost of collecting wastewater

increases with the size of plant and serves to offset within plant scale

economies. Two types of secondary treatment and three tertiary treat-

ment processes were considered as feasible alternatives. They were

high-rate trickling filter system, activated sludge system, and two

clarifier lime clarification processes, line recalcination, and ammonia

stripping process, respectively.

The space and time dimensions of regionalization were considered.

In order to find the potential sites of regional treatment plants, a

cost minimization model was used. For the consolidation over time an

exponential objective function was minimized subject to discrete ca-

pacity requirements.

Estimates of construction and operation and maintenance costs were

based upon Environmental Protection Agency (EPA) studies. The rates of


viii









cost increases over time were also estimated from EPA cost indexes as

.12, .10, and .07 per year for force main construction cost, pumping

station and sewage treatment plant construction costs, and operation

and maintenance costs for both force mains and sewage treatment plants,

respectively. Service lives for pumping station and wastewater treat-

ment were taken as 25 years, and for pipelines as 50 years. An inter-

est rate of 5% per year was assumed.

A least cost staging policy to satisfy the wastewater treatment

requirements of the nine cities in Alachua County, Florida for the

years 1975, 1980, and 1990 was determined with the model. The results

were sensitive to the required quality of secondary effluents.

If the required quality of secondary effluent is set at above 80%

removal, activated sludge plants will be required to provide the least

cost method of treating wastewater. The results show that secondary

treatment cost will be minimized if High Springs, Alachua, Archer, and

Newberry cooperate to build a regional treatment plant in 1975 to

satisfy their 1980 demands, and then construct individual plants in

1990 to satisfy the additional demands at that time. The other cities

would satisfy their demands by building individual activated sludge

plants in 1975 to satisfy their 1980 demands with additions being made

in 1990. The minimum tertiary treatment cost combination would require

the construction of two regional treatment plants, one for High Springs,

Alachua, Archer, and Newberry, and one for Waldo and Hawthorne, in 1975

to satisfy the 1980 demands of these six cities. Their additional de-

mands in 1990 would be met with plants added in each city. Gainesville,

LaCrosse, and Micanopy would satisfy their tertiary treatment demands

with individual plants constructed in 1975 with additions in 1990.









If the required quality of secondary effLuent is set at 807 re--

noval, the results show that secondary treatment cost for the county

will be minimized if each city builds a trickling filter plant which

satisfies 1980's wastewater treatment demands in 1975 with additions to

capacity being made in 1990. The minimum tertiary treatment cost com-

bination suggests that there will be regionalization of treatment in

1975 to satisfy the 1980's demands of three cities---Newberry, Archer,

and Alachua. Additional demands in 1990 were satisfied by building in-

dividual treatment plants in these three cities, The other six cities

would satisfy their tertiary treatment with individual plants con-

structed on the same schedule as the trickling filter plants.

The possibility of substituting land spreading for tertiary

treatment is discussed, and the factors which should be considered in

land treatment are analyzed with the aid of an optimization model. The

break-even distances of transmission pipelines for land treatment as a

substitute for tertiary treatment are calculated and presented.
















CHAPTER 1
INTRODUCTION


The Problem and Objectives


The environmental thrust of the 1970's has resulted in regulations

to clean up wastewater from a number of sources including industry,

municipalities, and nuclear power generating stations. Communities

throughout the country faced with meeting the 1985 goal of zero dis-

charge of pollutants into streams encounter both economic and environ-

mental constraints [Public Law 92-500, 1972]. The high costs of

providing primary, secondary, and especially tertiary treatment by con-

ventional methods place an economic burden on communities, especially

on the smaller ones typically found in rural areas.

Several wastewater management alternatives exist, including

(1) advanced biological treatment, (2) physical-chemical treatment, and

(3) land treatment. Communities upgrading their treatment systems must

determine which individual or combination of these treatment methods

has the greatest potential for meeting both economic and environmental

constraints.

The concept of land treatment is receiving increased attention as

an alternative wastewater management approach [Dalton and Murphy, 1973;

Egeland, 1973; Parizek et al., 1967; Sopper and Kardos, 1973; Thomas,

1973; Williams et al., 1969]. Briefly stated, land treatment involves

the use of agricultural land and crops or forest products to absorb and

filter nitrates, phosphates, and other elements from wastewater that









has undergone primary and, usually, secondary treatment. Water filtered

by the soil is then returned to the undergroLnd water supply.

The many issues surrounding the use of land for treatment of muni-

cipal wastewater, and subsequent land reclamation through soil infil-

tration and plant growth, encourages a multidisciplinary planning

approach. Systematic investigation of institutional, economic, and

social issues should be made concurrently with technical and engineering

studies. To date, most attention has focused on technical and engineer-

ing questions. An objective of this study is to articulate some of

these issues and to suggest a framework which social scientists, and

agricultural economists in particular, might use as a starting point

for further inquiry into the socioeconomic aspects of land treatment.

In the planning and design of a wastewater treatment facility for

a city, town, or an area where the requirements for treatment are ex-

pected to increase with time, the initial size of the treatment plant

and the timing of capacity additions and/or replacements over some time

horizon need to be answered in the context of an optimal staging policy.

Such a policy is affected by the wastewater treatment requirements, the

rates of interest and inflation, construction cost, operating costs,

maintenance and repair, service life, and the staging efficiency of the

system to be designed.

Recently, the concept of regionalization of wastewater treatment

has been suggested as an effective means of meeting the water quality

goals at a minimum cost. Although economy of scale provides the pri-

mary incentive for regionalization, a host of other advantages such as

more qualified operating personnel and higher degrees of automation

may be gained through the utilization of this concept.










The recent literature of city planning and regional science con-

tains few analytical studies concerned with facility planning for

public urban systems. However, the management of these systems needs a

coherent framework for planning which deals with facility size, loca-

tion, and timing.

This study develops a decision model to use as a guide in planning

facilities for a specific wastewater treatment system. An optimization

technique will be utilized in selecting the optimum program. The final

plan will include the number of treatment plants needed, treatment

plant capacities, waste sources to be served by each plant, disposal

methods, and plant locations.


Method of Study ,



The selection of an optimal regional plan over time is a complex

problem, the solution of which requires a considerable variety and a

quantity of information, a great expenditure of time, money, and a wide

diversity of expertise. The optimum plan provides the least cost

system of collection, treatment, and disposal of wastewater subject to

the physical, financial, and sociopolitical constraints of the region.

Choosing an optimal plan from among a large number of alternatives

(which involve different construction costs, plant location, facilities

and capacity, and farming programs) is quite difficult without a formal

model that can accommodate a large number of variables that are deter-

mined simultaneously in a dynamic framework. The steps to develop such

a model and the links between them are shown in Figure 1.1. The steps

consist of two sets: (1) the estimation of the form of cost functions

and the values of uncontrolled variables; and (2) the choice of values


























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of decision variables. Decisions deal with sizes, types, locations,

and timing of plants and facilities to be constructed.

In this study, a mathematical optimization model is proposed which

will minimize the present value of total expenses over the planning

horizon subject to the requirements for wastewater treatment and land

availability in the region of interest. Treatment plant facility costs

as functions of capacity, land requirements, wastewater production and

land values as functions of time and population, and information on

zoning and population growth estimates were incorporated in the model

to determine a minimum cost expansion program.


Area of Study and Source of Data


Alachua County, Florida was chosen as the study area. The county

has a total land area of 568,320 acres or 888 square miles. These

figures do not include the large bodies of water representing about

76.4 additional square miles [North Central Florida Regional Planning

Council, 1973]. Figure 1.2 shows the location of Alachua County.

There are nine incorporated cities or population centers in Alachua

County. Only one of these nine incorporated communities has adequate

wastewater collection, treatment, and disposal; the remaining eight

incorporated municipalities have either privies or septic tanks with

the large flow users such as hotels, restaurants, and service stations,

primarily located along major thoroughfares, being served by small

package plants.

Population estimates for this study were obtained from the esti-

mates provided by North Central Florida Regional Planning Council

[1973]. The relationships between capacity and costs, both construction


















































6oe I' ,,


Figure 1.2 Location of Alachua County









and operation and maintainence, were obtained from EPA studies [Michel

and Johnson, 1970; Smith and McMichael, 1969; Smith and Eilers, 1971].

The information about cost increases over time was provided by EPA cost

indexes. Other knowledge required to complete this study was obtained

from journals, textbooks, and miscellaneous publications on wastewater

treatment.

This study developed a procedure to find the optimum number, sizes,

and locations of wastewater treatment facilities in Alachua County.

The time period involved is from 1975 to 1990, and wastewater sources

are only the nine incorporated cities in the county. The concept of

regionalization used in this study was that more than one city might

transfer its waste to a regional treatment facility in some selected

location.
















CHAPTER II
RELEVANT ECONOMIC THEORY


This chapter develops a theoretical framework for structuring

the mathematical optimization model. Cost minimization theory, loca-

tion theory, and multidimensional utility analysis are combined to de-

termine the optimum number, size, and location of wastewater treatment

plants.


Cost Minimization with Respect to Output


Consider a system of equations consisting of a productLcn function

(2.1), a cost equation (2.2), and an expansion path function (2.3):1

q = f(xl, x2) (2.1)

c = r1 x1 + r2 x2 + b (2.2)

o = g(xl, x2) (2.3)


where q is output, xl, x2 are variable inputs, rl and r2 are the re-

spective prices of xI and x2, and b is the cost of the fixed inputs.

This system of three equations in four variables can be reduced to a

single equation in which cost is stated as an explicit function of the

level of output plus the cost of the fixed inputs:

c = t(q) + b (2.4)

The fixed cost must b1 paid regardless of how much the firm produces,

or whether it produces at all. The cost function gives the minimum


This system of equations can be expanded o include more than two
variable inputs. [SeC Ferguson, 1971, pp. 154-168]









cost of producing each output and is derived on the assumption that the

entrepreneur acts rationally.

Let the levels of the entrepreneur's fixed inputs be represented

by a parameter k, which gives the "size of his plant"--the greater the

value of k, the greater the size of his plant. The entrepreneur's

short-run problems concern the optimal utilization of a plant of given

size. In the long-run he is free to vary k to select a plant of optimum

size. The shapes of the entrepreneur's production and cost functions

are given in the short-run and depend upon fixed plant size. In the

long-run he can choose a production function. Once he has selected this

function, i.e., selected a value for k, he is faced with the conven-

tional short-run optimization problems.

Assume that k is continuously variable and introduce it explicitly

into the production function, cost equation, and expansion path

function:

q = f(xl, x2, k) (2.la)

c = r1 x + r2 x2 + q(k) (2.2a)

o = g(xl, x2, k) (2.3a)

d*(k)
Fixed cost is an increasing function of plant size: -- > 0. As
dk
before, total cost may be expressed as a function of output level and

plant size:

c = i(q, k) + '(k) (2.4a)

The entrepreneur's long-run total cost function gives the minimum

cost of producing each level of output as a function of plant size.

This function is the envelope of the short-run functions: it touches

each and intersects none. Write the equation for the family of short-

run cost functions (2.4a) in implicit form:









C 4(q, k) i(k) G(C, q, k) = 0 (2.4))

and set the partial derivative of (2.4b) with respect to k equal to

zero:

Gk(C, q, k) = 0 (2.4c)

The equation of the envelope curve (the long-run cost curve) is obtained

by eliminating k from (2.4b) and (2.4c) by solving for C as a function

of q, i.e.:

C = ((q) (2.4d)

Long-run total cost is a function of output level, given the condition

that each output level is produced in a plant of optimum size.

Since average cost equals total cost divided by output level, the

minimum average cost of producing a particular output level is attained

at the same plant size as the minimum total cost of producing that out-

put level. The long-run average cost curve can be derived by dividing

long-run total cost by output level, or by constructing the envelope of

the short-run average cost curves. The two constructions are equivalent.

Generally, long-run average cost (LAC) is considered as a planning

device, which given the state of the arts would tell an entrepreneur

the plant size which will enable him to produce a desired output level

at the least possible cost per unit. The significance of plant size in

relation to the plant costs results from the nature of the economies of

scale.

The possible existence of substantial scale economies which would

permit relatively large treatment plants to process their wastewater at

lower average cost per unit than relatively smaller treatment plants is

a key factor in stimulating interest in regional wastewater treatment.

The principal basis of scale economies is specialization, or the









division of labor--a phenomenon Adam Smith deemed so central that he de-

voted the first three chapters of Wealth of Nations to it. In Smith's

view, great increases in the productivity of labor (and hence great re-

duction in product cost) were due to three repercussions of the division

of labor: an increase in worker dexterity, the saving of time commonly

lost in "passing from one species of work to another," and "the inves-

tion of a great number of machines which facilitate and abridge labor,

and enable one man to do the work of many."

A somewhat different basis of scale economies is found in the pro-

cess industries such as petroleum refining, chemical production, cement

making, glass manufacturing, and steam generation. The output of a pro-

cessing unit tends within certain physical limits to be roughly propor-

tional to the volume of the unit, other things being equal; while the

amount of materials and fabrication effort (and hence investment cost)

required to construct the unit is more apt to be proportional to the

surface area of the units reaction chambers, storage tanks, connecting

pipes, etc. Since the area of a sphere or cylinder of constant propor-

tions varies as the two-thirds power of volume, the cost of constructing

process industry plants can be expected to rise as the two-thirds power

of their output capacity, at least up to the point where they become so

large that extra structural reinforcement and special fabrication tech-

niques are required. There is considerable empirical support for the

existence of this "two-thirds rule," which is used by engineers in esti-

mating the cost of new process equipment [Haldi and Whitecomh, 1967;

Moore, 1959; Schuman and Alpert, 1960].

Still another benefit of size arises from what E. A. G. Robinson

calls "the economies of massed reserves" [Robinson, 1958, pp. 26-27].









A firm anxious to maintain continuity of production rist hold equipment

in reserve against machine breakdowas. A firm lirge enough to use only

one specialized machine nay be forced to double its capacity if it

insists on hedging against breakdown: the larger firm with numerous ma-

chines can obtain virtually the same degree of protection by holding

only a small proportion of its capacity in reserve. Likewise, the num-

ber of repairmen a company must employ to provide any stipulated amount

of service in the event of random machine failure rises less than pro-

portionately with the number of machines in operation [Whitin and

Peston, 1954].

Two other common arguments are the theory of "perfect divisibility"

promoted by Kaldor [1943] and Lerner [1946, pp. 186-199], and the

theory of "proportionality" developed by Chamberlin [1948]. The theory

of perfect divisibility states that the imperfect divisibility of

factors explains economies of scale and that with perfect divisibility

the economies of scale would be absent. In criticizing the theory of

perfect divisibility, Chamberlin argued that it neglects the effects

of divisibility of the efficiency of factors. Rather, he claimed that

all economies of scale will be explained by the proportion of factors.

The theory of proportionality indicates that there is a certain optimum

proportion of factors, and because factors are obtainable only in dis-

crete units, this optimum proportion can be closely approximated only

when the aggregate of factors is large. In other words, snall scale

production will be relatively inefficient in achieving these optimum

proportions.

It is quite clear that econor ies of scale do exist, and that unit

costs decline with nrass in pant nd firm size, at least










within limits. However, there are several reasons for believing that

scale economies are limited. First, in nearly all production and dis-

tribution operations the realization of scale economies appears to be

subject to diminishing returns. Sooner or later a point is reached at

which all opportunities for making further cost reductions through in-

creased size are exhausted. Second, it is possible that rising unit

costs related to the difficulty of managing an enterprise of increas-

ingly large scale will offset and eventually overwhelm the savings at-

tributable to high-volume production and distributions [Robinson, 1958,

Chapters 3, 10, 12; Coase, 1937; Williamson, 1967]. A third major in-

fluence which may prevent economies of scale from being realized in-

definitely is the cost of transportation.

The theory of the firm implies that, under pure competition,

individual firms tend to operate at equilibrium in the long run, seek-

ing to minimize the long-run cost with respect to output [Leftwich,

1966, pp. 167-177]. The number and size of plants of a given firm are

assumed to be determined within the equilibrium conditions. However,

wastewater treatment in Alachua County is a regulated utility subject

to the control of a single authority. It is a local monopoly and its

size is determined largely by the extend of local demand. The distinc-

tion between perfect competition industries on the one hand and regu-

lated and imperfectly competitive industries on the other is that, in

the former, the size of the market plays no part in determining the

size of firm but merely determines the number that can survive, while

in the public utility type of industry the spatial distribution of de-

mand determines both the number and relative scale of the firms in the

optimal (cost-minimizing) setup.









The Theory of Location


The basic concept of location theory is to incorporate assembly

costs into production costs as the basis for determining the cost mini-

mizing conditions. This combination overcomes the shortcomings of

neglecting the selection of location as a production activity in the

pure theory of the firm. Since the production origins and plants are

generally not at the same location, the assembly costs are incurred

while transferring the raw material from production origins to plants.

Furthermore, the marketing costs incurred while transporting final pro-

ducts from plant site to market should also be included in the analysis.

Assembly costs consist of two parts in this study. The collection

costs, which relate to the process of removing the sewage from the site

of production by small sewer; and the transmission costs, which relate

to transporting the sewage from the small sewers by larger sewers to

the treatment site. Those costs are directly related to the distance

from the site of production to treatment site, the amount of flow trans-

mitted, and the difference in elevation between the two sites to be

joined by sewers.

The pure theory of the firm must be combined with the theory of

location in order to interpret the joint problem with which this study

is concerned. The incorporation of assembly activities into the pro-

duction process makes the goal of the firm one of minimizing the total

combined cost of assembly and production rather than those associated

with production alonf.

While assembly is clearly external to the operations of a particu-

lar plant, both plant operations and transportation are integral parts









of the joint function. In order to minimize the production cost, the

firm seeks to gain the economies of scale by increasing plant size.

However, as the scale of plant increases, there will be accompanying

changes in the magnitude of the required assembly costs of raw materi-

als as well as the required costs of disposing of its final products.2

More specifically, increases in plant size will be associated with ex-

panded supply requirements, and hence, with increased assembly costs

and disposal costs. Therefore, potential economies of scale will

gradually be offset by increases in these costs.

For instance, consider two communities, A and B, which both have a

need for wastewater treatment by means of conventional activated sludge

and associated processes. If neither community has an existing waste-

water treatment plant and each community needs a one mgd (million gal-

lon per day) plant, the two alternatives are for each community to

build and operate its own plant or for some joint effort with one plant.

Assume the costs for a single one mgd plant is 25.5 cents/kgal, 22

cents/kgal for a two mgd plant and pipeline cost of 1.71 cents/kgal/

mile. Under these assumptions, if two communities are more than 4.1
3
miles apart, each community would build a one mgd plant. The same

kind of argument can be expanded to include more than two communities

with different wastewater treatment requirements.


2Disposal costs for an effluent plant are somewhat analogous to
marketing costs for a firm producing consumer goods.

The breakeven length pipeline (L) is calculated by equating the
total daily cost of the two alternatives and solving for the length of
the pipeline at the breakeven point, i.e., to solve (25.5) x 1000 +
25.5 x 1000 = 1.71 L x 1000 + 22.0 x 2000 for L, which gives L = 4.1
miles.









However, the potential location for a plant need not be situited

in a site of demand or supply. The question is how location decisions

are made. In the ideal case they are made with perfect knowledge of

costs and benefits at alternative locations, and they are made so as to

maximize net benefits from operations at the optimal location. Often

in the real world case, perfect knowledge is replaced by error and an

adverse reaction to risk, and the search for optimal locations is re-

duced to a search for a satisfactory location.

Transport systems were built to promote interactions over space,

and prevailing location theory models are largely transportation

oriented. To study the effect of cost of geographic space on the loca-

tion of human activity let us examine the location problem in general

terms rather than in terms of specific industry case studies. We shall

consider only manufacturing activity and will assume that wage, inter-

est, and other prices are equal everywhere. Only transportation charges

which vary with distance are considered in the analytical approaches

presented below.

Problems on location analysis can be classified into two major

structural categories.

A. Location on a plane, which is characterized by

1. an infinite solution space. That is, central facilities

may be located anywhere on the plane and are confined neither to nodes

of the network nor to points on the links between these nodes.

2. distance measurement according to a particular metric.

One example is the Euclidean metric where

dij = ((x x.) + (yi -

d.. = the distance between points i and j,
:j









x., y. = the coordinates in a rectangular system of the
1 1 ith point.

Another example is the metropolitan metric where

dij = Ix. x + iYi y. I

B. Location on a network which is characterized by

1. a solution space consisting of the points on the network

(both nodes and points on the arcs which join the nodes),

2. distance measurement or time measurement along the network,

d.. = the length (time) of the shortest path [Cooper,
13 1967] from node i to node j.

Alfred Weber [1909] pioneered the Location Theory. He considered

the location of an industry between two resources and a single market

where the criterion was minimization of transportation cost. however,

it is only two decades since the advent of mathematical programming and

computer-aided computation that the problem has received real attention

from the standpoint of research.

Werson et al. [1962] presented one of the earliest modern consid-

erations of location problems. They located solid waste disposal sites

to minimize hauling costs in a metropolitan environment. Travel was

assumed to be along the rectangular grid which typifies many American

cities. An optimal single disposal site was determined by linear pro-

gramming to be at the median of the generating sites.

Beginning with the formulation of Cooper [1963] and Kuhn and

Kuenne [1962], interest in location analysis has quickened. Their

work which appeared independently described an iterative process for

solving the generalized Weber problem. The problem is to find the

single point which minimizes the sum of the weighted Euclidean distances

to that point. The objective is








n
minimize z w. d.
1 i
where:

w. the weight attached to the ih point (goods de-
manded, resources sent, population, etc.);

d. = ((xi -_ x) + (y. y) )2, which is the Euclidean
distance from point i to central point;
th
x., y. = the location of the i point relative to some
fixed cartesian coordinate system;

x, y = the unknown coordinates of the central point;

n = the number of points served.

Partial differentiation with respect to x and y yields a pair of

equations that are the first order conditions for a minimum:

3z w.(x. x)
Ix 1 = 0 (2.5)
i d.
1

3z wi (y. y)
= = 0 (2.6)
ay i d

Somewhat more attention has been devoted to problems of locating central

points on a network. The problem of warehouse or plant location has the

following general characteristics. Given a number of demand areas of a

certain product, each with a demand D., and a number of alternative

sites where facilities may be built to satisfy these demands, determine

where the facilities should be placed and which demand areas are to be

served by a given facility. The objective is that the sum of the trans-

portation cost and the amortized facility cost is minimized.

A tradeoff exists between facility and transport costs; clearly,

the greater the number of well-placed facilities, the lower will be the

cost of distribution. But as shipment cost decreases, the investment

in facilities must rise. At so e number of facilities the total cost

should be a minimum. -. that point, Lit cost of adding a facility










exceeds the savings in distribution cost. It is assumed that both the

number of demand areas for products and the number of plant or ware-

house sites are finite.

Maranzana [1964] considered warehouse location where distances are

not Euclidean but are measured on the road network. He also utilized

an heuristic procedure to locate a specified number of warehouses to

serve a region of known demands. His criterion was the minimization of

transport costs. Kuehn and Hamburger [1963] also presented a heuristic

method for warehouse location; their approach was to minimize the sum

of transport and warehousing costs.

ReVelle and Swain [1970] consider a location problem; their objec-

tive was the minimization of average time or distance which people must

travel to the facilities. The problem is constrained by a fixed number

of facilities. The model was structured as a 0-1 mix integer program-

ming problem with facilities restricted to nodes of the network.

In this study, equations (2.5) and (2.6) were used to find the

potential sites for treatment plants. Euclidean metric distance meas-

urement was used to determine the optimal locations for wastewater

treatment facilities. The solution space consists of potential sites

and sources of wastewater treatment demands.


Multidimentional Utility Analysis


Since their inception, cost minimizing models for firm behavior

have certainly not been without their critics. But for the most part

the critics have failed to propose substantive alternatives for theo-

retical use. An approach not directly involving simply cost minimiza-

tion was suggested by Scitovsky [1943]. In particular, he showed that









if an entrepreneur attempts to maximize satisfaction, he will expend

the same amount of effort as if he were attempting to maximize profit

only in the special case in which the marginal rate of substitution

between entrepreneruial activity and money income is independent of

the level of money income. The point of interest is the applicability

of multidimensional utility theory to a certain class of microeconomic

problems.

The theory of multidimensional vector ordering, or what is now

more generally called lexicographic ordering, has the following meaning.

Consider two alternatives, which may be bundles of commodities, combina-

tions of lottery tickets, business objectives, etc., i.e., x0 = (xl,

x0, ..., x0) and x1 = (x, x1 ..., x1). Let u be a preference index
n 1 2' n
function. A regular ordering ranks u(xI) > u(x1) if, and only if, x? >
I -
xl for all i and the strict inequality holds for at least one component.

In a lexicographic ordering a hierachy of wants is recognized; the

components of the vector x are not regarded as equally important. For

convenience, let the elements of each vector be numbered so that xl is

more important than x2, x2 is more important than x 3, etc. Then u(x0) >

u(x1) if x > x1, irrespective of the relationships between x? and xi,
1 1 1 1
for i 2,3, ..., n. Xfx
for i = 2, 3, ..., n. If x1 = x, comparison is based upon the second

component. Thus, u(x0) > u(x1) if xO = xl and xO > x, etc. Proceeding
1 1 2 2'
in this manner, vector elements associated with variables lower in the

hierachy of wants are considered only after the higher order wants are

satisfied [Encarnacion, 1964].

Let us consider a wastewater treatment system in a basin, in which

it is assumed that the policy makers attempt to minimize wastewater

treatment cost for the entire basin subject to maintaining a









satisfactory level of water quality. This model actually has two possi-

ble outcomes. First, if the level of water quality is less than the

satisfactory level, the policy makers disregard the cost minimization

goal and behave as though they were purely radical environmentalists.

Second, if the satisfactory level of water quality is achieved, the

policy makers would seek to minimize wastewater treatment costs for the

entire basin. In the terminology of multidimensional utility analysis,

level of water quality is the dominant component and cost minimizing is

the subordinate one.

Denote the level of water quality by xl and costs by x2. Thus any

situation is represented by the vector x = (x x2). Suppose the satis-

factory level of water quality is xl. According to the description of

the model, further water quality does not enhance the utility or satis-

faction of the policy makers. In other words, if u(x) is the utility

function,

au
S]I = 0
3x xl > x

Thus the optimum vector x is found by selecting the policy that mini-

mizes x2 (costs) subject to xl > xl. In particular, let us compare two

situations x0 = (xa xO) and x1 = (xl1 x1). The former is preferred to
1' 2 1' 2
the latter if, and only if, x i x for i = 0, 1, and x < xa. If this
i *
problem is not feasible, i.e., xl < xl for i = 0, 1, the optimum vector

x is the one whose first component is greater (x1 > x for i # j).

This simple two-variable model can easily be generalized. Suppose

there are M goals xl, x2, ..., x arranged in order of descending
m
importance. Further, let each goal be defined so that


Du ] > 0 and iu ] = 0
Dx. x. < x. .x a x. > x.
1 1 1 1 1 1-









Every possible situation is described by a vector x = (xl, x2, ..., x)

and the optimal vector x is found by selecting the set of policies

which solves the following constrained maximization (or minimization)

problem: maxi-:ize xm subject to x, > x. for i = 1, 2, ..., m-1. If

this problem is unfeasible, the least important goal (x ) is dropped

from consideration. The new problem accordingly becomes: maximize

x1 subject to x. > x. for i = 1, 2, ..., m-2. One thus works in se-
M- 1 I 1
quence until a feasible problem is detennined, all lower ordered goals

being discarded in route. If goal k(
tive for which a feasible problem exists, the vector x0 is the optimal

vector if, and only if, x > x. for i = 1, 2 ..., k-1 and x > xj for
S -k k k
all j # 0.

In this study, treating wastewater is the dominant component and

cost minimizing is the subordinate one. Possible wastewater treatment

methods will be investigated, and their costs will be estimated; a

decision will be made according to the framework of multidimensional

utility analysis.
















CHAPTER III
A GENERAL MODEL FOR
REGIONAL WASTEWATER TREATMENT


Regionalization may consist of the centralization of administra-

tion (separate sewerage systems operated by a single authority) or one

central plant serving several municipalities. There are two ways to

centralize the wastewater treatment for the second case. One sugges-

tion which has been made to control pollution along reaches of a system

is to collect the sewage from all the cities and firms along the stream

and treat it at one central downstream location. Another suggestion

often made is that small outlying cities or villages transport their

waste to a regional treatment facility in a large city. The feasi-

bility of such proposals can be judged by comparing the cost of trans-

porting waste with the treatment savings which can be realized.

In order to meet the condition that the available treatment plant

capacity at any time during the study period is sufficient to meet the

requirement, there are many expansion policies that can be chosen.

Planning an expansion scheme involves the choices of choosing plant

capacity, building site, and treatment facilities (such as land spread-

ing versus integrated biological-chemical systems and the like). Also,

different rates of interest and inflation can change the preferred

ordering of alternative schemes.

In this chapter, a mathematical model is developed for the purpose

of choosing an expansion scheme which minimizes the present value of









investment given conrtiru, iIn costs ano weas -vtcter treatment require

ments over time.


The Model


The primary factors which will be considered in selecting a

regional plan in this study include:

a) waste sources to be served;

b) number and capacities of treatment plants needed;

c) treatment plant locations;

d) desired degrees of treatment;

e) collection system; and

f) cost functions.

Arrangement of outfall structure, cost allocation among partici-

pants, methods of financing, and methods of implementation will not be

considered in the model. The influence of factors (a) (f) on the

selection of an optimal regional wastewater management system is de-

scribed more fully below.

The development of a sound regional wastewater treatment plan

requires a full knowledge of the major existing and potential sources

of wastes. The type of the treatment facility, physical, chemical, or

biological, as well as the design of the collection system, pumping

stations, and treatment depends on the quantity and characteristics of

the wastes. Therefore, characterization and quantification of all the

major sources, both municipal and industrial, within the region may be

considered as one of the most important factors in the development of

an effective wastewater annagenent plan.









The locations of wastewater treatment plants constitute a major

factor in the overall plan for optimization of wastewater management

in a region. Such factors as the water quality criteria, the distribu-

tions of waste sources, cost of treatment facility, cost of pumping

stations, and interceptor sewers must be considered.

A general model is to supply answers regarding the location of

treatment facility, capacities, and the number of treatment plants.

Assume that we have I wastewater sources, J potential regional and/or

individual plant locations, K types of treatment plant, and a planning

horizon from time 1 to T. In the following relations:

i refers to waste source; i = i, ..., I

j to plant location; j = ..., J

k to type of treatment plant; k = 1, ..., K

t to time period; t = 1, ..., T

dit to amount of wastewater generated at source i at time t;

CCjkt to present value of wastewater treatment costs at loca-
tion j for type k facility at time t;

CS.. to present value of wastewater transmission cost from
source i to location j at time t;

RCjkt to required wastewater treatment capacity at location j
for type k facility at time t;

RS.. to required wastewater transmission capacity from
source i to location j at time t;

Cjkt to existing wastewater treatment capacity at location j
for type k facility at time t;

Si. to existing wastewater transmission capacity from
source i to location j at time t;

CXjkt to new wastewater treatment capacity to be built at
location j of type k at time t;

SX.. to new wastewater transmission capacity to be built
from source i to location j at time t; and

Zijt to the amount of waste flow from i to j at time t.









Specifically the iT '1 can be stated as follows:

Mini iize E (CC + CS. ) (3.1)
j ,k, jkt ijt

Subject to the constraints:

J
E Z.. < d for all i and t (3.2)
ijt it
j=1

(waste at each source rust be satisfied)

I K
E Zi. < RCjkt for all j and t (3.3)
i=l k= kt

(the amount of waste flow into location j must be less than or equal to

treatment capacity at location j)

Zijt RSijt for all i, j, and t (3.4)

(the amount of waste flow from source i to location j at time t must be

less than or equal to its required transmission capacity)

RS. Si < SX,. for all i, j, and t (3.5)
jt ijt ijt
(the difference between required capacity and existing capacity for

transmission must be less than or equal to the new capacity to be added

for the waste flow from source i to location j at time t)

RCjkt Cjt < CXk for all j, k, and t (3.6)

(the difference between required capacity and existing capacity for

treatment must be less than or equal to the new capacity to be added

for type k facility at location j at time t)

where CCjk and CSt are functions of CXkt and SX.. respectively.
jkt ijt jkt ijt
This model involves three dimnsions. These are time, space, and

types of facility. In order to solve this model one needs information

about the amount of vaste generated at each source, the cost functions

of treating and tranporting the wIst, and the locations for regional

wastewater treatint pits. In the following sections vw will discuss









briefly how this information was obtained for this study. A brief dis-

cussion will be given on the basic ideas which have been built into

this general model; then a way of solving this model will be introduced

as a preview for the next three chapters.


Wastewater Production


Wastewater comes from four primary sources: municipal sewage, in-

dustrial wastewater, agricultural runoff, and storm water and urban

runoff. Estimation of municipal and industrial wastewater flows and

loadings can be done in one of several ways, based on knowledge of past

and future growth plans for the community, sociological patterns, and

land-use planning.

Municipal and industrial (M&I) water use rates are affected by

variables that may be grouped into two broad categories [Department of

Water Resources, California, 1968]:

1. Climatic factors such as temperature, rainfall, wind speed,

and so on.

2. Man-made factors which further divided into two groups:

a) Residential-related factors such as economic level, educa-

tion, price of water, family size and age, metering and

severing.

b) Other urban related factors such as greenery, kind of com-

munity, changing industrial water requirements, water pro-

duction and use measurements, population served, and other

factors such as worn flow meters and inadequate distribution

systems.









WaLking [1968] points out about the same results in a study of

sociological perspective of water consumers in South Florida households.

An aggregate wastewater production function can be specified by

the following relationship:

dit = f(wit Pit, M it) (3.7)

where:

d. is the amount of wastewater at zone i at time t;
it
wit is the price of water at zone i at time t;

PNi is the population served by the treatment plant at
zone i at time t; and

Mit is the income level at zone i at time t.

In an urban water demand study, Hanke [1968] pointed out that

average household water uses differ little between metered and unmetered

areas, but sprinkling uses and peak demand differ considerably. In

other words, household water uses are price inelastic and sprinkling

uses are price elastic. Since in most cases only household wastewater

which is not sensitive to the price of water goes into sewage system,

equation (3.7) may be simplified as follows:

dt = f (P it, M it (3.8)


Cost Functions


The cost of a regional wastewater treatment network is a function

of a number of variables. Some of these variables are internal to the

technology of the service in question. Others are a function of condi-

tions which are unique to a certain site and life style which the plan-

ner usually accepts as given, while a third set involves factors which

relate to the urban morphology (form and structure). This last set of

factors will be regarded as choice variables front the point of view of








the city planner who is involved in studying the cost implications of

alternative zoning and development policies but will be considered as

given in this study.

Emphasis on regional planning usually centers around optimization

of the collection, treatment and disposal of wastewater in the region

to meet a set water quality goal at a minimum cost to the region. A

host of alternative solutions must be entertained and each alternative

has an associated cost function. These cost functions include cost of

facilities, construction, operation and maintenance of collection, and

final disposal. Although economies of scale provide the main incentive

to a regional wastewater treatment system, it is not always true that a

single large treatment plant for the entire region will provide the

least cost system, nor is it always possible to have a single plant.

This is, of course, due to the fact that the location and the capacity

of the treatment facility can not be independent of other factors such

as waste sources to be served, the topography of the region, length of

interceptors, and locations and number of existing sewage facilities.

The final analysis in the regional plan must, therefore, consider trade-

offs between combining treatment facilities, combining and/or abandoning

transmission facilities, and final disposal methods.

In this study, cost functions of the wastewater treatment facili-

ties will be divided into two categories--cost functions of collection

systems, cost functions of treatment plant facilities (secondary and

advanced). Furthermore, each category of cost functions will be sub-

divided into two subcategories, i.e., construction cost functions and

operation and maintenance cost functions.










Since an optimal staging policy is also affected by the rate of

interest and inflation, one dollar spent today will not be considered

equivalent to one dollar spent at some future date. The decision pro-

blem at hand is a multipoint-input, multipoint-output allocative pro-

blem [Henderson and Quandt, 1958, p. 244] with the demand given for

output treatment capacity at each point of time.

To project year-by-year operating costs for each segment of the

proposed system, a present value of future expenditures scheme was used

in the optimization model. A basic operating cost for the present year

was set for each treatment plant and transmission line. The value was

then inflated at a parameterized rate to reflect increased labor and

maintenance expenditures in the future. The present value of the re-

sulting series of expenditures was then added to the initial cost of

each system component to obtain a present value of costs over the plan-

ning horizon.

Let it be the market rate of interest and yt be the inflation rate

connecting marketing date t-l and t. Then the present value of one
th
dollar payable at the end of t marketing period is

t -1 =
[ (1 + ) (1 + i )-] = V t = 1, ..., T (3.9)
S T T t
T=l

For example, the total present value of costs for a type k treatment

facility at location j at the end of time t is

jkt = (FCjk + ljkt) Vt (3.10)

where FCjkt and FMkt are the construction cost and operation and main-
jkt 3kt
tenance costs for type k facility at location j at time t, respectively.

This same rule will be used to calculate the present value of a trans-

mission system.










In order to solve this general model, we need information about

the potential sites for individual and/or regional t-eatment plants.

Theoretically, a regional treatment plant can serve from two to nine

cities; therefore, for a nine-city problem, such as this study, we end
9 9
up with E ( ) potential sites, where ( ) represents the number of
i=l
combinations of choosing i cities out of nine cities. This study will

be started from the estimation of wastewater production, finding po-

tential sites for regional treatment plants, collection cost data, and

eventually reaching a solution for this general model.

The first dimension to be considered in this study is the con-

solidation of treatment plants over space. This dimension is included

because the existence of scale economies may permit relatively large

treatment plants to process their wastewater at lower average cost per

unit. Thus, the cost for treating wastes from several sources at a

regional plant may be lower than the total cost if wastes were treated

at each source. There is a tradeoff between the gains from scale

economies and the losses incurred by constructing transmission

pipelines.

The second dimension to be considered in this study is the con-

solidation of treatment plants over time. Since the demands for waste-

water treatment increase with time and the inflation rate exceeds the

interest rate there may be a net gain by building a treatment plant

larger than necessary. This is the tradeoff between the gains in econo-

mies of scale, savings in inflation, and the losses in interests and in

operating and maintaining excess capacity,

The third dimension to be considered is the effect of different

types of treatment facilities. In this study, we consider only two





32



types of secondary treatment plant, three tertiary processes, and the

possibility of substituting tertiary treatment by land treatment.

The problem of consolidation of treatment plants over space was

first solved for this problem; the central location model mentioned in

Chapter II was used. Then the consolidation of treatment plants over

time was incorporated with the consolidation over space, and solved

simultaneously. Finally, a feasibility analysis of substituting land

treatment for tertiary treatment is presented.

















CHAPTER IV
WASTEWATER TREATMENT SITES


In order to develop a working model, the following information is

required:

1. potential wastewater sources and potential sites for waste-
water treatment plant,

2. the amount of wastewater produced at each source, and,

3. cost functions of wastewater treatment facilities as well
as cost functions of transmission pipeline from each waste-
water source to the potential sites for wastewater treat-
ment facilities.

This chapter will provide the above information and then compare

the potential treatment sites found in this study with those provided by

North Central Florida Regional Planning Council [1973, pp. 11.1-11.27].


General Description of the Area


Alachua County is located in the North Central section of the

Florida peninsula. The Santa Fe River, on the north, separates Alachua

County from Columbia, Bradford, and Union Counties. Putnam County lies

along most of the Eastern boundary, with Clay County at the north end.

Marion County is at the south end of the east boundary and runs along

roughly two-thirds of the south boundary. Levy County borders Alachua

County to the south and west, and Gilchrist to the west. All of Alachua

County's territory falls within the 29" 25' and 290 57' parallels of

latitude north and the 820 03' and 82 40' meridans of longitude west.









The county i-s a totil la-n area of 568,320 acres or 888 sr,0 re

viles. These figures do not iri ud the large bodies of water re, r-

senting about 76.4 additional square miles [Gorth Central Florida .e-

gional Planning Council, 1973]. Alachua County lies within the central

highlands of the state. The area generally ranges from level or nearly

level to gently sloping. Most ground elevations range between 50 and

210 feet above sea level. Climate in Alachua County is mild, with a

mean annual temperature of 70.2 degrees and an average yearly rainfall

of approximately 52 inches. Precipitation varies from year to year,

particularly in the surer months. Alternating wet and dry cycles of

several years' duration are observed. Most of the rain, an average of

about 36 inches per year, is tropical in nature, falling during the

summer months as thundershowers. About 16 inches of the yearly average

cone as winter rain of the cyclonic or frontal type, usually slow and

drizzly and followed by a drop in temperature.

As a result of the increase in population and its changing charac-

teristics, the way in which land is used in the county has two basic

land use patterns. Agricultural land use has retained its dominance

and is still the primary land use category as it was in the early 1900's.

The Gainesville Urban Area has developed as a major urban center at the

approximate geographic center of the county. Land use in the urban

center is primarily residential and institutional in nature. Co-mercial

land uses, although occupying a relatively smaller number of acres, have

developed to support the agricultural, residential, and institutional

uses. Table 4.1 so r riz s tih estimated rnjor land use categories for

Alachua County in 19 2. i e ost significant changes expected are









Table 4.1 Estimated Land Uses in Alachca County


Nonagriculture Agriculture
Public Developed Water Cropland Pasture Forest Other
Land Land Areas

% of
% of 4.03 9.91 7.71 11.17 20.81 19.16 27.20
Total


Source: North Central Florida Regional Planning Council [1973].



increase in forest lands and urban area, and a decrease in croplands or

cultivated areas.

Alachua, Archer, Hawthorne, High Springs, LaCrosse, Micanopy,

Newberry, and Waldo are the eight incorporated centers of population in

Alachua County exclusive of Gainesville. Their location is shown on

Figure 4.1. Melrose, an unincorporated community is situated on the

boundary line between Alachua and Putnam Counties.

There are many unincorporated towns within Alachua County. The

most important are Arredondo, Campville, Cross Creek, Earleton,

Evinston, Fairbanks, Forest Grove, Grove Park, Hague, Island Grove,

Lochloosa, Monteocha, Orange Heights, Rochelle, Santa Fe, and Windsor.

Most of the rural dwellings are found within the western half of the

county. Table 4.2 provides a brief description of each of the incor-

porated cities.

The city of Gainesville is the only incorporated community with

near adequate wastewater collection, treatment, and disposal. Present

treatment facilities in Gainesville consist of a 5-ngd high-rate trick-

ling filter plant and the recently completed 4.5-mgd contact stabiliza-

tion plant. In addition, the city owns a third treatment plant; this






































































Figure 4.1 Locations of the Incorporated Cities in Alachua County,
Florida

















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So o 3





S ~ C










a-
114
















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is an extended aeration plant with a nom 1al c.npaiity of 55,000 gallon,

per day.

The city of :aldo is the only other city providing public sanitary

facilities; the present wastewater treatment facility is a 40,000 gallon

septic tank, which is grossly inadequate, The remaining eight incorpo-

rated municipalities have either privies or septic tanks with the large

flow users such as hotels, restaurants, and service stations, primarily

located along major thoroughfares, being served by small package plants.

Table 4.3 gives an inventory of the treatment plants in Alachua County

by their capacities.



Table 4.3 Number and Capacities of the Treatment Plants in
Alachua County, December, 1973


Capacity (million gallons per day)

0.01 0.01-0.05 0.05-0.1 0.1-1.0 1.0

Number 8 14 2 3 3
of Plants


Source: A computer output provided by Alachua County Pollu-
tion Control Board.



As mentioned in Chapter III, the amount of wastewater produced may

be estimated as a function of the size of population served, and the in-

come level. However, due to the lack of accurate data on the size of

population served,l this relationship was not estimated. Instead, an


The monthly sewage treatment operation report submitted by each
treatment plant should provide this inforr tion. Iowver, a review of
those reports submitted by the Ireatment plants in Alachua Countyi ndi-
cated incompletenesses as well as inaccuracies which prohibit -rcanin ful
estimation of wastet:ter production function. Therefore, an avie
daily flow per capital estint:e was used.









average daily flow per capital was used to estimate the wastewater pro-

duced at each wastewater source. Assuming a sewage flow of 1352 gallon

per capital per day, Table 4.4 shows the estimates of sewage flow of each

city in Alachua County in year 1975, 1980, and 1990, respectively.



Table 4.4 Estimated Wastewater Flows in Alachua County,
Florida, by Incorporated Cities for 1975, 1980,
and 1990

Wastewater Flows (gal/day)
Name


Alachua

Archer


Gainesville
Urban Area
Hawthorne


High Springs

LaCrosse

Micanopy

Newberry

Waldo


Total


1975


456,975
(3,385)
133,650
(990)
13,729,500
(101,700)
168,750
(1,250)
409,050
(3,030)
58,050
(430)
108,540
(804)
184,275
(1,365)
114,075
(845)

15,362,865
(113,799)


1980


479,250
(3,550)
149,850
(1,110)
16,044,615
(118,849)
177,525
(1,315)
445,500
(3,300)
65,475
(485)
116,100
(860)
201,150
(1,490)
120,825
(895)

17,800,290
(131,854)


1990


600,750
(4,450)
182,250
(1,350)
20,632,185
(152,831)
199,800
(1,480)
532,575
(3,945)
81,000
(600)
120,825
(895)
239,625
(1,775)
134,325
(995)

22,723,875
(168,325)


Remark: The figures in parentheses are estimated population
sizes from North Central Florida Regional Planning
Council [1973].

2
2Which is an average daily flow of 73 cities in 27 states in the
United States [Loehr, 1968].


__


~









After potential was Ltwater sources and the a onnit of wastew-ater

produced by each source were determined, the potential sites for waste-

water treatment facilities were considered. In order to chose it po-

tential sites, the central location model mentioned in Chapter II was
3
used. The number of potential sites is quite large. As a consequence,

the large amount of computer time makes it impractical to find a solu-

tion for each potential site using the model presented in the previous

chapter. To overcome this problem, a computer progr n was developed

(see Appendix I and next chapter for the details of this program ) to

scan through all the potential sites, and eliminate those w:dich have

higher sum of regional treatment and transmission costs than the sam of

individual treatment costs. This computer program used a central loca-

tion model to determine potential sites and to calculate the transmis-

sion costs and the combined treatment costs. The program then compares

the sum of transmission and treatment costs with the sum of the treat-

ment costs if each city involved built its own treatment facilities.


Wastewater Transmission Costs


The cost functions for transmission are as follows:

1. The relationship between flow and the diameter of sewers, which

minimizes the sum of the cost ot frictional power and the debt service

for the pipe, estimated in [Smith and Eilers, 1971] as:

Economic Diameter (inches) = 8.55Q463 (4.1)

where:

Q = designed flow in mgd.

39 9
The total number of potential sit equls t ( ) = 491, where
( ) is defined as 9! i=
(9-i)! (i)!









2. The cost associated with sewers which includes th." amo-tization

cost and a small maintenance cost in terms of October, 1970 dollars was

estimated [Smith and Eilers, 1971] as follows:

Construction costs in dollars per mile =

1540.7(ID + 2.0436)1.37949 (4.2)

where:

ID = inside pipe diameter in inches.

The cost of maintaining the sewer was taken as $40/yr/mile.

3. The construction cost for pumping stations has been estimated

[Smith and Eilers, 1971] as:

Construction cost, $ = 76,300Q682 (4.3)

where:

Q = average flow in mgd.

The operation and maintenance cost for pumping stations has been esti-

mated [Smith and Eilers, 1971] as:

cents/1000 gal. = 1.59Q263 (4.4)

where electrical power was assumed to cost one cent per kw-hr. The

hydraulic efficiency of the pump was taken as 60% and the electrical

efficiency of the driving motor was taken as 80%. All costs were keyed

to October, 1970.

The Ten State Standards [Great Lakes--Upper Mississippi River Board

of State Sanitary Engineers, 1971] require interceptor sewers to be

sized to carry 3.5 times the design flow for the plant. This factor was

used for sizing both the pipelines and the pumping stations, since the

flow of sanitary sewage reaching the treatment plant varies over time,

and the capacity of the sewage facility is fixed over the short run.








Excess capacity (cptt abo e th avern,,, dily f!s,) is neccrsary Lo

collect and treat the se-agc

The collection and transmission of peak flos ray be handled in one

of the three ways: (1) sewers could be built to handle the expected

peak or some greater flow, (2) a holding tank could be installed to

average flows, and (3) some method could be employed which would average

the release of flows. Of these three, engineers consider the first as

the only feasible alternative. Holding tanks have not been used because

there are design problems which engineers feel prevent their use.

Averaging at the source of the flows is an alternative which engineers

avoid completely.


Wastewater Treatment Costs


Treatment of sewage is the process of removing undesirable materi-

als from the water and/or changing them into less objectionable forms.

In the typical plant this is done by a combination of physical and bio-

logical processes. In essence, the treatment process uses a more rapid

version of the same process which would occur if the wastes were re-

leased to the receiving water without treatment.

The selection of a wastewater treatment process or a combination of

processes will depend upon: (1) the characteristics of the wastewater,

(2) the required effluent quality, (3) the costs and availability of

land, and (4) the future upgrading of water quality standards. In this

study, two conventional treatment systems will be considered, i.e.,








4
high-rate trickling filter system and activated sludge system. Since

the high-rate trickling filter systems cannot remove more than about

80% of BOD and SS, most new plants for domestic wastewater treatment are

activated sludge plants.

Of course, there are minor variations in the designs of treatment

plants. For example, there are different ways to circulate the primary

as well as secondary sludge, and there are different designs for re-

turned sludge entering the primary settling tank and the like. However,

the cost variations incurred by these different designs are not large,

hence these differences in cost will not be considered in this study.

There are several ways one can estimate the construction and opera-

tion and maintenance costs of a treatment plant. A cost estimation com-

puter program was developed by Smith [Environmental Protection Agency,

1973b] which allows the consideration of influent waste strength as well

as the different combinations of treatment processes. Such a program

was purchased from National Technical Information Service and adapted to

the IBM 370 system at the University of Florida. However, there were

errors in the program which precluded its use.

EPA [1973a] has estimated cost equations with regression analysis

using data on accepted bids for construction of new municipal wastewater


The differences of design between a high-rate trickling filter sys-
tem and a standard-rate (or low-rate) trickling filter system depend on
their hydraulic loading, 200-1000 gpd per sq. ft. for high-rate opera-
tion, and 25-100 gpd per sq. ft. for standard-rate operation [Fair et al.,
1971].

5Treatment plant design examples provided by National Technical In-
formation Service were used to test the computer program, however, the
computer output showed that during the calculation some logarithm and
exponential functions had illegal arguments. Several attempts have been
made without success to correct these errors, hence the program was not
used in this study.









treatment plants in several states between 1967 and 2969 as a Function

of design flow. Costs were updated to September 1972 dollars by usir,

the EPA Sewage Treatment Plant Construction CosL Ind e. EPA's estimates

provide another means of estimating costs. Their estimates were as

follows:

1. For high-rate trickling filter system:
-.37461
AC = 852049.58 37461 (4.5)

2. For activated sludge system:
-.3544
AC = 699835.09 -3544 (4.6)

where:

AC = average construction cost, and

M = amount of design flow in mgd.

And estimates of operation and maintenance cost collected from re-

ports on 600 plants between 1968 and 1970 in January 1968 dollars have

the following relationships [Michel and Johnson, 1970]:

1. For high-rate trickling filter system:

TC = 31959.50 M6496 (4.7)

2. For activated sludge system:
.6023
TC = 46989.41 M6023 (4.8)

where:

TC = total annual operation and maintenance cost, and

M = amound of design flow in mgd.

A third way of estimating wastewater treatment costs is the appli-

cation of the six-tenths rule [Berthauex, 1972; Williams, 194/; Chilton,

1950; Eckenfelder and Ford, 1969]. Under this rule, the cost-capacity

relationship has the following form:









Cost of Plant A Capacity of Plant A M
Cost of Plant B Capacity of Plant B

or

C C = C/Q (Q'
Ca Cb a /Qb = KQ
where:

C = cost of an item of capacity Q a,
a a
K = base cost factor and equals Cb/Q and

M = measure of the economy of scale.

The name "Six-tenths rule" arose because the exponent M is often about

0.6 for chemical processing plants. The rule not only applies to

scaling-up the costs of an entire plant but shows that the exponent

varies with the type of plant under construction. Some of the estimates

of factor M are shown in Table 4.5.



Table 4.5 Cost-Capacity Factors for Municipal Wastewater
Treatment Plants


Size Factor (M)
Type of Plant
(1) (2)

Activated Sludge 0.77 0.65

Trickling Filter 0.60 0.62


Source: (1) from Berthauex [1972]. (2) from EPA [1973a].



In this study, the estimated equations (4.1) through (4.8) by EPA

were used. All the cost figures were adjusted to September 1974

dollars. Equations (3.9) and (3.10) were used to calculate the present

values of 1975, 1980, and 1990 cost figures in terms of September 1974

dollars.









'TArl. v Irialt intf


Tert ary tre,'arLt n may bi catrgor call dfcined as trc-'L- Ifor

thi removal of pollutants not rc. ov-ed by conavent.io;i a treatriiol pi--

cesses (act lvted sludge, trickling filters, etc.). These pollutants

will ilnlude suspended solids (SS), biochemical oxygen demep, d ( ,),

refractory organic (un:ally reported as chemical oxygen demand (COD)

or eotL;l organic carbon (TOC)), nutrients (nitrog-n and phosp..r-. ), arnd

inorganic salts. In tre United States today, increasing en ph-:,i is

being pl.'ced on the removal of phosphorus and the removal of uno'idl-z'd

nitrogen 'which will exhibit a long-term oxygen demand in the receiving

waters.

'he line clarification process is used primarily for thb refov; l

of phosphorus and suspended organic matter. An additional benefit is

the iocrccsing pH resulting from line addition which makes i:aonia

nitrogen available for removal by air stripping. Even thougn many pro-

blems associated with the use of ammonia stripping processes remain to

be solved, it is presently viewed as the most promising process for re-

moving ammonia nitrogen from wastewater. A process employed in Lake

Tahoe is shown in Figure 4.2. The effluent characteristics are shown in

lower part of the same figure.

The estimated cost equations for three tertiary treatment processes

to be ued in this study from the data provided by [Smith and M:Ilichael,

1969] arc presented below:

1. Two clarifi;r lime clarification process without ri,' iiis:


Tihere is sone evidence that a co.nu ril i aid suc s iron ji ,i( be
required in the second clarifier. Sie the i d ior this ch .l is
not clearly established, it t.wa not in cludied ii the cost.
























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0 0












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0



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V l-I V ,-< V

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Construi ion cost T uiilion dollars)

0.128371Q776102 (4.9)

O&M cost (del ars/dy) = 62.851B8Q692928 (4.10)

2. Lime recalcination plus make up lime for use with limn

clarification:

Construction cost (million dollars)

0.196977Q'508007 (4.11)

O&M cost (dollars/cay) = 49.373Q 7285b4 (4.12)

3. Amnonia stripping of lime clarified wa-tcwater:

Construction cost billionn dollars) =

0.490535Q .10744 (4.13)

O&M cost (dullars/day) = 40.9442Q778987 (4.14)

where Q represents design capacity measured by millions of gallons per

day (mgd).

As pointed out in Chapter II, the long-run cost curve is the

envelope of the short-run cost curves. Cost equations (4.5) through

(4.8) were estimated by regression analysis from cross-section data, and

these cost observations were subject to variations in the age, type, and

cost of equipment, the quality of executives as well as the effects from

spatial variation in factor prices. Cost equations (4.2) through (4.4)

and (4.9) through (4.14) were estimated as the loci of minimum costs by

the engineering approach. Therefore, equations ( .1) through (4.14) as

used in this study to estimate the wastewater treatment costs give

higher cost estimates thin the rnirnim theoretical costs from equation

(2.4d).









Assumptions anout Cost Increases


In order to estimate the rates of cost increases over time to be

used in the calculation of present values, regression analysis was

used. In this analysis, we assume that cost index is a function of time,

i.e.,

Cost index = a + bt + u t = 1966, ..., 1973
t t

where a and b are parameters to be estimated, and ut is the disturbance

term at time t.

Three different kinds of cost indexes were used in this analysis,

they are: sewer construction cost index (SW), sewage treatment plant

construction cost index (ST), and consumer price index for residential

water and sewerage services (SR). All the September cost index figures

from 1966 to 1973 were used for the estimation of parameters a and b,

and the results are as follows:

SW = -23567.0 + 12.0444t R = .9595 (4.15)
(1990.00) (1.0104)
2
ST = -20378.8 + 10.4214t R = .9654 (4.16)
S (1585.40) (0.8050)

2
SR = -14604.9 + 7.4762t R = .9745 (4.17)
t (973.204)(0.4941)

where the "hats" on top of SWt, STt, and SRt represent estimated values,

the figures in the parenthesis are estimated standard errors of the

parameters, and R 's are multiple determination coefficients.

Parameter b represents the effect of one unit change in t on the

corresponding cost index, hence it can be explained as the annual rate

of increase in costs and they were used in equations (3.9) and (3.10).


These three cost indexes were provided by Advanced Waste Treatment
Research Laboratory, Cincinnati, Ohio.








b in (4.15) wUn used in the calcnl t ion of s-wer construction costs, b

in (4.16) was used in the claculation of sewage treatment plant con-

struction cost, and b in (4.17) was used in the calculation of O&M costs

for both sewer and sewage treatment plant. Service lives for pumping

stations and wastewater treatment plants were assumed to be 25 years, and

for transmission pipelines 50 years. Interest rate was assumed to be

5%.


Potential Sites for Wastewater Treatment Plants


In order to reduce the possible number of potential sites, a com-

puter program written in FOXTRIN; IV was developed (Appendix I). This

computer program calculates

1. the coordinates in miles from the origin (290 30' parallel
of latitude north and 82' 37' 30" meridian of longitude
west) for each of the cities of this study (Table 4.6).

2. construction costs and operation and maintenance costs for
wastewater treatment plants, transmission pipelines, and
pumping stations for each city using equations (4.1)
through (4.14), and

3. the transmission cost from each source to the potential
sites obtained using equations (2.5) and (2.6).8 Finally,
the program compares the sum of pumping station costs,
transmission costs, and regional wastewater treatment
costs for each site with the wastewater treatment costs
for a completely disaggregated system (i.e., one in which
each of the nine cities build their own facilities). If
the regional cost is less than or equal to the sum of in-
dividual costs, the program prints out the related cost
figures.


8wi represents transmission pipeline cost per mile from cit. i as
calculated froi equations (4.2) or (4.4).









Table 4.6 Cordinates of Municipalities in Alachua County in
4ilesa

Cordinate
City Number
East(x) North(y)


High Springs 1 1.6190 22.4526

Newberry 2 0.8572 10.0476

Archer 3 6.1428 2.0952

Alachua 4 7.9524 20.2380

Gainesville
Urban Area 5 18.0476 10.4762

LaCrosse 6 13.1904 23.6666

Micanopy 7 20.9524 0.3810

Waldo 8 27.6190 20.0476

Hawthorne 9 32.5714 6.6190


aThese coordinates are calculated from the origin 800 37'
30" longitude West and 29 30' latitude North in miles.

These numbers will be used later to represent the cor-
responding cities.


9
It is assumed that force mains were used as the connecting pipe-

lines between contributing cities and receiving regional plants, and a

raw sewage pumping station has been sized to handle the flow at each

source.


Smith and Eilers [1971] indicate that the cost of constructing
force mains is not significantly different from the cost of constructing
gravity sewers, hence, equation (4.2) may be used to find the construc-
tion cost for force mains. However, by a conversation with Mr. Baldv.in
(Agricultural Engineer), this approach may overestimate the cost of
force mains.









The Newton-Rnphson ri-tLhod was first uud to solve equations (2.5)

and (2.6) simultaneously, but this method required Loo Imany operations

to finish one iteration, hence, it was not used in this study. Instead,

an iterative procedure suggested by Kuhn and Kuenne [1962J and by

Cooper [1963] was used to solve these two equations for x and y in terms

of w., xi, Yi, and d.:
1 1 i 1
w. x. w.
S d. i d (418)
1 1

wi Yi w.
y = E. (4.19)
1 1

di = ((xi x)2 + (i )2) (4.20)

The value of d. is recalculated via (4.20) and the procedure repeated
1

until successive differences between values of x and between values of

y are negligible. In this study, the initial values of x and y for

the calculation of d. are the weighted average of x.'s and i 's,

respectively. As mentioned by ReVelle et al. [1970] this method has

been found to be extremely fast, usually terminating at the global mini-

mum in less than ten iterations, and no problems of lack of convergence

have been reported. Therefore, a maximum number of fifty iterations was

set and a four-digit accuracy was required for the solution of (x, y).

The last (x, y) in the iteration procedure was taken as the solution for

(2.5) and (2.6).

A regional treatment plant in this study is defined as one serving

more than one city. Let R(.) represent a regional treatment plant which

serves the cities represented by the numbers within the parentheses; for

example, R(l, 2) is a regional treatment plant that serves cities 1 and

2 (the number for each city has been assigned in Table 4.6). If there









is one number within the parentheses, it indicates that a treatrient

plant serves only one city.

Assuming that d975, d980, and dl990 were satisfied in years 1975,

1980, and 1990, respectively, Table 4.7 shows the possible sites, capa-

cities, and costs of regional treatment plants, the cities they will

serve, and the years they are to be built. There are regional treatment

plant sites in the southeast corner of Alachua County other than those

presented in Table 4.7 which were not considered because of the lakes

and swamps in that area. These sites involve the following regional

treatment plants: R(6, 7, 8), R(6, 7, 8, 9), R(7, 8, 9), R(2, 3, 4, 5,

6, 7, 8, 9), and R(l, 2, 3, 4, 5, 6, 7, 8, 9).

Based on the population estimates and wastewater production of 135

gallons per person per day [Loehr, 1968], demands for wastewater treat-

ment and the corresponding treatment costs are calculated. The treat-

ment cost figures in column five in Table 4.7 are the future service

values (see next chapter for definition) up to 1990 for the correspond-

ing treatment plants. From these estimates, one finds that (1) high-

rate trickling filter plants are cheaper than activated sludge plants,10

(2) the costs for tertiary treatment processes are higher than the costs

of both high-rate trickling filter plants and activated sludge plants.

Assuming that secondary treatment is adequate to meet the require-

ments, there are several ways to satisfy the demands in the county. If

secondary treatment is adequate to meet the requirements the least cost

method of treatment is for each city to build a high-rate trickling


1Federal regulation requires a 90% removal of BOD's and SS which
high-rate trickling filter plant cannot achieve. However, if tertiary
treatment processes were added to this system, the results of trickling
filter plant from this study are still valuable. Therefore, the results
of trickling filter system were presented and discussed.




















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filter plant to meet its demand (Table 4.8). However, if tertiary

treatment processes are required to meet the requirements, the results

show that High Springs, Newberry, and Archer should cooperate in develop-

ing a regional facility if their objective is to minimize cost. The

potential site has a coordinate of x = 0.88 and y = 10.07, which is in

Newberry, and an estimated regional treatment cost of 4,086,862

September 1974 dollars to satisfy their 1975 demands and to meet their

demands in 1980 and 1990 by building individual plants. The other six

municipalities should build separate treatment plants to meet their

individual demands.


Concluding Remarks


As mentioned in Chapter III, this is a study over time and space.

This chapter discussed the consolidation of waste treatment facilities

over space for specific points in time, i.e., 1975, 1980, and 1990,

respectively. There are other ways that wastewater treatment demands

can be satisfied over time. For example, the estimated treatment de-

mands of High Springs are .4090 mgd, .4455 mgd, and .5236 mgd for years

1975, 1980, and 1990, respectively; these demands could be satisfied by

building a .5326 mgd treatment plant in 1975. Of course, there are

other options. Chapter V brings the time dimension into the optimiza-

tion process and considers the simultaneous determination of costs over

both time and space dimensions.

Since interest is in minimizing costs, combinations over time and

space which lead to greater costs than those presented in Table 4.8 need

not be considered. Therefore, the results of Chapter V help to narrow

the search for an optimal county solution.









Table 4.8 PossLble Options for Satisfying Count, e Enst(;atcr F eat-
w.ant Dneinnds and Associated Costs, 1975 to 1990Q

OpLion Total Cost for CounLy

I. Without Tertiary Processes
i. high-rate trickling filter system
9
E R(i) 12,276,820
i=l
ii. activated sludge system
9
R(l, 2, 3, 4) + Z R(i) 14,464,670
i=5
R(1, 2, 3, 4, 5, 6, 7, 8) + R(9) 14,550,152
II. With Tertiary Processes
i. high-rate trickling filter system
9
R(1, 2, 3) + Z R(i) 44,589,425
1=4
9
R(1) + R(2, 3, 4) + Z R(i) 44,590,757
i=5
9
R(1) + R(2, 3) + E R(i) 44,765,688
i=-4

ii. activated sludge system
7
R(1, 2, 3) + E R(i) + R(8, 9) 46,719,711
i=4
7
R(1) + R(2, 3) + Z R(i) + R(8, 9) 46,986,390
i=4
7
R(l, 2) + 2 R(i) + R(8, 9) 47,015,999
i=3
7
R(1, 2, 3, 4) + Z R(i) + R(8, 9) 45,698,220
1=5
R(l, 2, 3, 4, 5, 6, 7, 8) + R(9) 46,454,733
7
R(1) + R(2, 3, 4) + Z R(1) + R(8, 9) 46,698,720
i=5

aAssuming that d d and d were s n-sfied in years 1975,
1980, and 1990, respei cv y.
















CHAPTER V
CAPACITY EXPANSION SCHEME


Investment Over Time


When a firm experiences a growing demand for its output and makes

investments aimed at increasing its capacity in existing lines of ac-

tivity, the outlays are called induced investments. When, on the other

hand, the firm diversifies into new lines of activity, the capital in-

vestments involved are referred to as autonomous investments [Dernburg

and McDougall, 1968]. This study deals only with induced investments of

wastewater treatment facilities.

The simplest feedback theory of how induced investment takes place

is called the acceleration principle. This principle holds that the

rate at which a firm invests in new, as opposed to replacement, equip-

ment is a linear function of the rate of change of output. Suppose a

wastewater treatment plant has a capacity of 1.0 mgd, and is operating

at that capacity. Assuming that the only way to increase treatment

capacity is to add more capacity, then as demand increases capacity must

be increased in direct proportion.

The acceleration principle assumes that capacity is well defined

and that when it is reached such alternatives as overtime, subcontract-

ing, and back ordering are not available. The principle purports to

explain only new investment or net investment and also assumes that the

firm is able to obtain the funds to finance the indicated expansion.









When demand is constant the fir;n's invc ;trint i"ay be confine to

replacement of its e'Lsting capacity, although if this was not being

fully utilized the firm might actually neglect repl.:' cr it. while the

acceleration principal: provides a first indication, elective imple.en-

tation of an expansion program requires considerably greater insight.

Capacity is not a particularly well-d fined concept in most firms.

There is a gradual growth in unfilled orders and overtime, shifts are

added, and any slack or hidden capacity comes into use. Thus management

has several alternatives to capacity expansion. It can use inventories

as a demand buffer to insulate to sone extent the steady operation of

production facilities from changes in the market. Negative inventories

or back orders are a useful means of meeting what appear to be temporary

increases in demand. The capacity of existing facilities can also be

extended by working overtime or expanding the working force. Sometimes

capacity can be expanded by subcontracting part of the production pro-

cess to others and effectively buying rather than making some of the

required output.

In the planning and designing of a wastewater treatment facility

for a town, city, or an area where wastewater treatment requirements

are expected to increase with time, the questions as to the initial size

of the treatment plant and the timing of capacity additions and/or re-

placements over the period of study or time horizon have to be answered

in the context of an optimal staging policy. Such a policy is affected

by the wastewater treatment requirement and its growth rate; the rates

of interest and inflation; the cost of Lhi treatiynt plant and its

operation and maintenance; th load factor, service life, and e'pecled









salvage value of the treatment plant; and the staging efficiency of the

system to be designed.

Incremental savings in construction and operation and maintenance

costs due to economies of scale make it desirable to bear the cost of

overcapacity until demand catches up. A major decision variable in

public and private wastewater treatment plant staging policy is the

amount of excess capacity to be built initially into a new system and

the staging of capacity additions and/or replacement (as the old plants

become uneconomical to run, being past their useful service life) to

meet demands increasing with time.

For example, the vertical axis in Figure 5.1 represents the long-

run average construction cost for wastewater treatment, and the hori-

zontal axis represents the demand for wastewater treatment capacity.

Q1975 and Q1980 represent the required capacities in 1975 and 1980 re-

spectively; LL is the long-run average construction cost curve. Assume

there are two choices to chose from, i.e., to build a single plant with

capacity Q1980 in 1975, or to build one plant with capacity Q1975 in

1975 and another one with capacity Q1980 1975 in 1980. The differ-

ence in construction costs represented by present value is


(1 + h)
D = ocdj obeh oafg (5.1)
(1 + i)5

where oa = oc ob, A represents rate of inflation in construction cost,

i represents interest rate, and D represents the difference in construc-

tion costs between these two options. If De > 0, then there is a saving

in construction cost, if D < 0, then there is a loss in the two-plant
c

option. However, the choice between a single-plant option and two-plant

option depends not only on construction costs but on operation and

























Q1975 1980


Capacity (ngd)


Figure 5.1 Long-run Average Construction Cost Curve





Cost ($)


b



Q L'
id

1975 1980


Capacity (-nid)


Figure 5.2 AveraeO Operation nd nint'ennce Cost Curv-


Cost ($)









maintenance (O&M) costs also. In Figure 5.2, L'L' represents long-run

average O&M cost curve, which is the envelop of short-run cost curves

fa' fb' fc' for capacities Q1980 Q1975 Q1975 and Q1980, respectively,

od equals the difference between Q1975 and Q1980. The present values of

O&M cost for the two options mentioned above follow.

Single-plant option: D = present value of 980 Qf dQ (5.2)
1 975 c

f1j979
Two-plant option: D2= present value of 979 fb dQ
"1975
+ Odeg (5.3)

where fe and fb are functions of operating capacity Q. Let

D = D D (5.4)
om 1 2

then if D + D is negative, the single-plant option will be chosen,
c om
otherwise the two-plant option will be chosen.

For each potential site the model may be stated as


Model 1

Min


FT97 975) + FT 980 980) + FT (990
1975 1975 1980 1980 1990 1990


s.t. Q >d
t. Q1975 > d1975

1975 + 1980 d1980

1975 + 1980 + Q1990 d1990

1975' 1980' Q1990 > 0

where FT (Qt)'s are total cost functions of treatment facilities in

terms of present value of plants to be built at time t with design capa-

city Qt, and dt's are scalars as demand for wastewater treatment at time

t, where t = 1"75, 1980, and 1990.

As mentioned above, FT (Q ) for t = 1975, 1980, 1990, includes con-

struction costs as well as O&M cost. The O&M cost as mentioned in equa-

tions (5.2) and (5.3) involves short-run cost functions. There are









several points about short-run cost functions th;it should he d iscuss'd.

First, as shown in Figure 5.3, L'L' represents a lon'o-run cost curve,

and f represents a conventional short-run cost curve. To the left of

point g, short-run average cost increases as Q decreases. This may be

explained as the indivisibility of management, production factors, and

the like. The decrease in Q will not decrease the quality of effluent.

However, to the right of point g, can one expand Q without reducing the

quality of effluent? Or, can one expand Q by working overtime, adding

more shifts, or increasing the inventory of raw sewage? The capacity of

a treatment plant is measured by a rate (e.g., million gallons per day)

and the possibility of expanding treatment capacity Q beyond the design

capacity without reducing the quality of effluent may not exist. Hence,

the segment of the short-run cost curve to the right of point g may not

exist if the quality of effluent has to be maintained.

Second, there are very few studies about short-run costs of waste-

water treatment, and therefore it is difficult, if not impossible, to

find short-run cost functions with the capacities needed in this study.

As a proxy, long-run O&M cost functions were used. There are shortcom-

ings with this approach. For example, if a treatment plant is to be

build with capacity Q1980 in 1975, one should use f to estimate the O&M
in 15 o c
costs from 1975 through 1980; however, there is no information abour fe

Therefore, if L'L' is used to estimate O&M cost with capacity Q1980, it

is difficult to determine if the cost has been over- or underestimated

without knowing f since there is no information about the difference

between ojgh and oacd.

In this study, each trentr'int, transmission, or pumping facility

has been assumed to operate at iL, design capacity. The reasons are





63






Cost ($)



S L'
f




d .........


e -------- --------- ..


L'
I .
0 a Capacity (ngd)
Q1975 1980


Figure 5.3 Operation and Maintenance Cost over Time









that 1) there is not enough inforrntion about short-run cost functions,

especially for advanced treatment processes, 2) this study was for plan-

ning purposes and emphasis was placed on the long-run effect, and 3) in

most cities the differences in demands for wastewater treatment over

time are not large; therefore, the differences between long-run cost

estimates under design capacity and short-run cost estimates under capa-

city in use may not be substantial.

In this study, interest is in satisfying the demands for wastewater

treatment in 1975, 1980, and 1990. The demand functions for wastewater

treatment over time can be considered as step functions rather than as

continuous functions. One example is shown in Figure 5.4, where d(t)

represents a continuous function, and d'975 d'980 and d'1990 are

segments of a step function. One of the disadvantages of using step

functions for wastewater treatment demands is that one may underestimate

the quantity of demand toward the end of each time period, but if each

time period is not large, this underestimation will not be serious. The

advantage of using step functions is that it simplifies the staging

process. For example, instead of considering Model 2 in this study, we

consider Model 1 which when compared to Model 2 is easier to solve.

Model 2

Min 1990
E FT(Q)
t=1975

s.t. Q1975 j dl975

t"
E Qt d,, for all L" < 1990
t-1975

Q 1 0, 1990 < t 1975

where FT, Q, and d are as de ined in Model 1.














Capacity (mgd)

















0


d1990
1990


1975 1980


1990


Figure 5.4 Demand for Wastewater Treatment over Time


- time (year)









The difference between Model 1 and Mod l 2 is in inly in the time

variable, t. In Model 2, t is a continuous variable; therefore the two

constraints in the model are not vell defined. Unless one cnn split the

time variable into some finite segments, that is to say t is a step

function rather than a continuous function, one may not be able to solve

Model 2.

Let d < Q975 < d1980 and FT975(x), FT1980(x) be functions in

present value for years 1975 and 1980 respectively, and x be the design

capacity. If one can show that

FT975 1975+ 1980(d980- Q1975
> FT1975 (1980 (5.5)


then the capacities between d and 980 for year 1975 do not have to

be considered. This is to say, it is more expensive to build two treat-

ment plants with capacities Q1975 and d Q1975 in 1975 and 1980,

respectively. If this is true, the problem is simplified to choosing

the minimum cost plan from the following options.



Table 5.1 Reference Numbers for Time Options in Alachua
County, Florida, 1975 to 1990

Demand for Wastewater To Be Satisfied
Options Treatment in Year(s)


1 d975 1975

1980 d7975 1980

d990 d1980 1990
d d 1990
2 d1980 1975


1990 1980 1990
3 d 980 1975

1990 d 0 1980
1990 19b0









Table 5.1 (Cont.)

Demand for Wastewater To Be Satisfied
Options Treatment in Year(s)


4 d975 1975

1990 d1975 1980

5 d990 1975





Now, split FT into construction cost, CC, and Operation and mainte-

nance cost, OC, and consider construction cost only in the following

inequality:

CC1975(Q1975) + CC1980(d1980 Q1975

> CC1975(d1980 (5.6)

where d975 < Q1975 < d980 If inequality (5.6) holds, and if only the

construction cost is considered, it is more economical to build a plant

with capacity d980 in 1975 than any other plan which can meet the treat-

ment requirement, d1980, in 1980. If inequality (5.6) holds, one should

only consider the tradeoff between the savings in capital by meeting

d1980 in 1975 with the losses of O&M cost in excess capacity. In other

words, one only has to consider three capacities, d975 d1980, and

d 990, in year 1975, not a continuum on the interval [d1975, d 990].

The following lemma is used to prove that (5.6) holds

Lemma Suppose f(x) = (1 + x ) (1 + x) is continuous on (0,m),

f'(x) exists at some point xe(O,=), and 0 < 9 < 1, then x > (1 + x) 1.

Proof: f(O) = (i + 0 ) (1 + 0) = 0 = lim f(x)
xl O
f'(x) = PxB- (1 + x)-

K 11-6 1-6
x I+x








1 1-R 1 1-
No" (- ) (I ) > 0, fo aTl x > 0, since x < 1 + x. Thert-

119 1 1- P
for, > --- and i:ce 1 >0, ( > ( ) e
x 1 + x 1 a
f'(x) > 0, which i:plic f( ) is an increasing function ad lir f(x) = 0.
xa0
In other words,

f(x) = ( + x) ( + x) > 0 for x > 0

= 0 for x = 0

where 0 < 9 < 1 and x > 0. Therefore, 1 + x > (1 + x), or x >

(1 + x) 1.

All the construction cost curves except the one for transmission

pipelines are of form
I-
CC(Qt) = at Q9, Q > 0, 0 < 9 < 1, and te[1975, 19901

and a > at, if t > t' because the rate of inflation is greater than the

rate of interest. If (5.6) holds, the following will hold:

al975 1975 +1980 1980 1975

> 1975(d80.7)

Divide both sides of (5.7) by 1975 to obtain,
B B
+ y (d1 Q > ) d>
1975 + d980 1975 > 1980
al980
where y = -- > 1, or
"1975

y(d Q > d Q (5.8)
1980 1975 1980 1975
where d9 > Q1975 > 0, and 0 < B < 1. Inequality (5.8) can he re-

written as:
S1980 d (1980
Y[ .. > -1 (5.9)
1975 1975

Therefore, if [ ] > ( ) 1, inequaliy (5.6) holds.
Q1975 Q1975
By lemn, we hlnve /. > (1 + ) 1 if x > 0, and 0 < 9 < 1,

d9800
lt x ( 980) 1 > 0, thedi-- 1 + x. He1nc y th 1 nm
Q1975 197









inequality (5.9) holds. Therefore, given the estimated cost functions

all one has to do is to choose the minimum cost plan from the five

options mentioned above.


Future Service Value of Treatment Facilities


In this study, the service lives for treatment plants and pumping

stations are assumed to be 25 years, and for transmission pipelines 50

years. The five options mentioned in the previous paragraph involve

building treatment plants with different capacities in different years.

In order to make a comparison among the costs of these five options,

the cost of unused services of each option after 1990 should be sub-

tracted from the total cost.

From an economic point of view, a capital asset is nothing but a

store or reservior of valuable future services, from which alone the

value of the asset derives. ile say "future services" because they can

be used up only over a period of time. They are deferred benefits. If

these services were valued at par, this is to say, at what they will

eventually be worth when realized, the capital value of the asset would,

of course, equal their sum. But a business enterprise does not know-

ingly buy future services at par if profits are to exist. To earn pro-

fits a firm must buy the asset for less than its services will

eventually be worth, the profit over the asset life as a whole being the

excess of these service values over the acquisition and use costs. The

capital value of the asset, in other words, is the discounted value, or

present worth, of these service values, the latter in turn being the

amount available for capital recovery and profit combined.









It is a matter of co..)n observation that the services of capital

assets tend to become less and less valuable ;s tin e goes on. The ma-

jority of the assets require during their service lives a flow of main-

tenance expenditures, which as a rule rises irregularly with age and

use. Most of them suffer a progressive deterioration in the quality or

the adequacy of their service. Moreover, in dynamic technology they are

subject to the competition of improved substitutes, so that the quality

of their service declines relative to the available alternatives even

when it does not deteriorate absolutely.1 All of these factors--rising

operation costs, impaired service quality or adequacy, and improved

alternatives--combine to reduce the value of the service as the asset

ages.

In practice, the future service value of an asset has to be

estimated. Such estimates are quite common in the valuation of real

estate, where annual service values are projected and discounted into

capital value. It must be admitted that they are not much employed in

the valuation of other types of property.

With the exception of land, the productive facilities of industry

are wasting assets and are depreciated with time and use until the capa-

tal embodied in the facilities is exhausted over their productive ser-

vice lives. The worth of the asset to the owner at any given point is

what he could afford to pay for it in competition with the various al-

ternatives then available, if he did not already have it. So long as he

elects to hold the asset, it may be presumed that this worth is above


IThis deterioration in the quality of service, both absolutely and
relative to current alternatives, is reflected in a general tendency to
reduce the intensity or continuity of use of tih asset as time goes on.









resale value. It may also be presumed that the decline therein since

the asset was acquired has been less than the decline from original to

resale value.

Costs make up the depreciation base for purchased assets. In set-

ting up a depreciation schedule a firm must establish a useful life and

salvage value of the asset in question. The most common methods of de-

preciation are straight-line, declining-balance, sum of the digits, and

unit-of-production or service [Dougall, 1973, p. 474]. Since the proba-

ble loss of capital value is decidedly concentrated in the early part of

life, the straight-line writeoff is not a completely satisfactory method

of depreciation for productive equipment. Any realistic allocation pro-

cedure should get rid of at least one half of the initial value over the

first third of the service life and at least two-thirds over the first

half. The straight-line method is perhaps less objectionable for build-

ings and structures than for equipment [Terborgh, 1954, pp. 37, 47].

In this study, wastewater treatment facilities are long-term invest-

ments, and a straight-line method was used to calculate the depreciation

of facilities. The undepreciated balance of the assets was discounted

back to present value for each of the options mentioned above and sub-

tracted from the present value of costs.

Construction costs, less discounted salvage value divided by the

estimated years of life, produced (for each type of fixed asset) a uni-

form depreciation expense each year. The salvage values for treatment

facilities in this study were assumed negligible. The present value of

future costs included both construction and O&M costs.









As mentioned in I TTT, this stuly tries to find the least

cost option to satisfy th wast ,-ter treaiaciint dem i for the ni e

cities in Alachua Cunt, subject to five constrain s.

By inequality (5.6), it is obvious that if cost curves are of for:;

CC (Qt) = at Qt Q > 0, 0 < I < 1, and ts[1975, 1990]

there is no need to transport waste to more than one location for

treatment. All the cost curves used in this study but two--one for

transmission pipelines and one for ammonia stripping--are of this form,

and a study by Smith and Eilers [1971] shows that there are economies of

scale existing in transmission pipeline construction cost, which sug-

gests this cost curve has the sa io form. Ammonia stripping is a very

small part of the total cost for the facilities studied here so no waste

was transported to more than one location for treatment.

A computer program was developed to scan through all the possible

ways of satisfying wastewater treatment demands of the nine cities in

Alachua County. This computer program consists of one main program,

four subroutines, and two functions, they are iMAIN, GRAVTY, TRI, COST,

ZERO, TRM, and PMC, respectively (see Appendix I). Their individual

functions follow:

MAIN: 1. To read city coordinates, population figures, and calcu-
late wastewater treatment demands over time;

2. To calculate construction costs as well as operation and
maintenance costs of pipelines per mile, pumping sta-
tions, and treatment costs (both secondary and tertiary
treat-rnt) for each city and time of interest according
to the needs of each city, and to print out the results.
The printout inc u es wastewater treatment demands,
popul tic figures, and all the needed cost figures over
time;


illation of cities
reriono iization


3. To gei
routi:


d send it to sub
ilysis.









CRAVTY: 1. Using the combination provided by MAI; to find out che
potential site for regional treatment and to calculate
transmission costs for regional treatment;

2. To sum up the individual treatment costs of the cities
in the combination and to calculate regional total cost;

3. To compare the sum of individual treatment cost and
regional total cost. If regional total cost is lower,
print out the coordinates of potential treatment site,
regional treatment costs, transmission costs, pumping
station costs, sum of individual treatment costs, and
the distance from each city in the combination to the
potential site. If the sum of individual costs is
lower, return to step 3 in MAIN to get a new combination,
until all the possible combinations are exhausted.

TRT, TRM, PMG: To provide cost figures of treatment, transmission pipe-
line, and pumping station, respectively, which are re-
quired by MAIN, GRAVTY, and COST.

COST: Using the combination provided by MAIN to screen out the
required information about costs and send it to GRAVTY
for further calculation.

ZERO: To initialize some of the variables in COST.

There are 491 potential sites for each time option, five time op-

tions, two kinds of secondary treatment, and three tertiary treatment

processes. The program is instructed to choose one secondary treatment

with and without tertiary treatment processes, one time option, and one

potential site at a time to calculate cost figures, and give answers to

the feasibility of regional treatment until all the possible combinations

of treatment types, time options, and potential sites are exhausted.

This is a brute-force search for the solution of the optimization model

mentioned in Chapter III.


Minimum Cost Option for Wastewater Treatment


In the last chapter it was shown that if only secondary treatment

facilities are required a regional wastewater treatment plant is not

needed. In this case individual high-rate trickling treatment plants









will give minimuin cost option prtv toid that d 198 an d 199 art
1955' 1980' t990
satisfied in years 1975, 1980, and 1990, respectively. lHowever, under

the same scheme, if tertiary treat :nt processes are required, there is

one regional treatment plant site which has a higher gain in economies

of scale than the losses in pulping and transmission pipelines, and has

a minimum cost anong the nine options under considerations, and this

regional treatment plant has a capacity which satisfies the 1975 d ans

for wastewater treatment of three cities in 1975.

The same procedures in the previous chapter were used to scan

through all the combinations of time, treatment types, and combinations

of cities to meet the demand for each of the time options mentioned in

Table 5.1.

To simplify the discussion, Table 5.2 shows all the possible re-

gionalization options, and a number is assigned to each. In the follow-

ing discussion or representation, instead of repeating the constituents

of these options, reference numbers will be used. For example, regional

option 11 represents the plan which consists of a regional treatment

plant which serves cities 1 through 8 and a single plant serving city 9.

Table 5.3 shows the seven ways of satisfying demands over 1975,

1980, and 1990. Present value of future cost of possible regional

treatment plants, cities to be served, and capacities to be built by

types are also presented. For example, if d1975 is satisfied in 1975,

there are four possible regional high-rate trickling filter regional

plants with tertiary processes, seven possible regional activated sludge

plants with tertiary processes, and two possible regional activated

sludge plants without tertiary treatment processes. Present value of

costs up to 1990 in t cis of Se tem:br 1974 dollars ar s ii srn n coln









Table 5.2 Reference Numbers for Regional 'Wastcwater Tre:atr t Options
in Alachua County, Florida, 1975 to 1990

Regional Wastewater Treatment Options Reference Nunber


9
E R(i) 1
i=l

9
R(1) + R(2,3) + E R(i) 2
i=4

9
R(l, 2, 3) + F R(i) 3
i=4

9
R(1) + R(2, 3, 4) + Z R(i) 4
i=5

9
R(1, 2, 3, 4) + E R(i) 5
i=5

7
R(l, 2) + E R(i) + R(8, 9) 6
i=3

7
R(1) + R(2, 3) + E R(i) + R(8, 9) 7
i=4

7
R(l, 2, 3) + E R(i) + R(8, 9) 8
i=4

7
R(1) + R(2, 3, 4) + E R(i) + R(8, 9) 9
i=5

7
R(i, 2, 3, 4) + E R(i) + R(8, 9) 10
i=5

R(1, 2, 3, 4, 5, 6, 7, 8) + R(9) 11









Table 5.3 Present Volue of Cos-ts of Alternative Regional Treatment
Plants for Alachua County, Florida, 1975, 1980, and I


Regional Treatmeint
Plant


Activated S
System

tertiary pro

with


Iludge High-rate Tr ckli n
Filter System

cesses tertiary processes

without with without


1. d 975 is satisfied in 1975

R(2, 3)
R(1, 2)
R(8, 9)
R(1, 2, 3)
R(2, 3, 4)
R(1, 2, 3, 4)
R(1, 2, 3, 4, 5, 6, 7, 8)


2,232,163
3,603,283
2,216,676
4,336,789
4,550,842
6,171,936
35,550,720


2. d1980 dl975 is satisfied in 1980

R(l, 2, 3) 758,340
R(2, 3, 4) 657,067
R(l, 2, 3, 4) 946,246


3. d1990-

R(1, 2,

4. d1990-

R(2, 3)
R(1, 2,
R(2, 3,
R(1, 2,


is satisfied in 1990


d1980

3, 4)


d980 is satisfied in 1980
1980


3)
4)
3, 4)


5. d980 is satisfied in 1975

R(l, 2)
R(2, 3)
R(8, 9)
R(1, 2, 3)
R(2, 3, 4)
R(1, 2, 3, 4)
R(l, 2, 3, 4, 5, 6, 7, 8)


618,276
1,260,849
1,426,352
1,859,144



3,824,863
2,495,646
2,297,853
4,650,832
4,773,810
6,506,944
'0,885,104


3,422,759
9,605,506


2,147,296


4,086,862
4,261,926
5,816,155


880,555


226,315


235,555




1,273,937

1,742,912


2,301,272

4,357,962
4,474,878
6,137,994


3,558,569









Table 5.3 (Cont.)


Activated Sludge High-rate Trickling
System Filter System
Regional Treatment
Plant tertiary processes tertiary processes

with without with without

6. d990 is satisfied in 1975

R(l, 2) 4,327,626 ---
R(2, 3) 2,830,965 --- 2,617,682
R(8, 9) 2,478,977 ---
R(l, 2, 3) 5,272,472 --- 4,952,246
R(2, 3, 4) 5,516,895 --- 5,185,699 ---
R(l, 2, 3, 4) 7,474,954 4,052,585 7,068,858
R(l, 2, 3, 4, 5, 6, 7, 8) 53,032,960 --- -

7. d990 d1975 is satisfied in 1980
1990 1975
R(I, 2) 1,256,987 ---
R(2, 3) 872,681 -----
R(l, 2, 3) 1,594,391 --- 1,489,681 ---
R(2, 3, 4) 1,681,106 --- 1,571,759 ---
R(l, 2, 3, 4) 2,244,183 --- 2,110,057


in September 1974 dollars.


aAll costs are









2 to 5 in Table 5.3. Other possibilities and their costs up to y ar

1990 are also shown in Table 5.3.

In order to find the least cost combination these cost figures

(Table 5.3) were assembled with other individual treatment costs to

estimate county total costs. All the regional plants shown in Table

5.3 have lower costs than the sum of the costs of individual plants for

the cities each regional plant serves. Therefore, for the five time

options mentioned in Table 5.1, regional treatment plants were chosen

first, and the discrepancies over time and over space were filled by in-

dividual plants.

Table 5.4 shows all the county total cost figures according to time

options and regional wastewater treatment schemes. Cost figures are

discounted present values of all costs up to 1990. From these figures,

one finds that time option 2, i.e., the option to satisfy d1980 in 1975

and d990 d980 in 1990, has the lowest cost for both systems and for

all the treatment schemes. And as before, the activated sludge system

has a higher cost than the high-rate trickling filter system.

Though simpler and cheaper to operate, the typical trickling filter

plant is being used less and less on domestic sewage in North America

due to the fact that it does not achieve the percent removal of organic

material that an activated sludge plant does. The least cost method

thus depends on the required quality of the effluent. Typical effluents

from trickling filter plants trciting domestic wastes have BOD's and SS

usually greater than 20 mg per liter. Typical removal efficiencies for

both BOD and SS are in the area of 80%. Activated sludge plant efflu-

ents have BOD's and SS between 10 and 20 mg per liter and removal ef-

ficiencies in the ara o0 90'.





79





,< o an m co
CN A' c-C ') on -7 a CO 1


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i m c I co coo o (-- co r~,
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0o 4T -
or c ri r r -3 3 n .o
4 r L ) 00 NCn 'N 1 in ) i4 ) n -












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u- ., -I .. 0
So o o o 0o






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r C C l 0
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.0 4r COsM CC0H4 O O^-D NCO 44



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0 HD m o- C hr cN ,-, r--- r o T- ,
c0 H! -) u0 Li i -- Lr Lr u_





iH : cd -:I ow I
Si i i c o t





c z rom c o o oo m --T Ni m Q -
nc (U r, to r o u
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4-C0 a N 0CC - 44- 0 O r.c O '
)o 0N .- IN C C CN c^ O' 1 C7 r' 0
v N m .4Th 0 m0hO 0)< < < < 0


O0 C c- -41 0 C -i --4T N
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En c r o Io oc C I
C ) 4- 0
d o o *-oI l








o r m a v,
00 0H 0 4






U 0 U 0 4 L,
-4-4 4 t -o
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Uu 4 0 00CN COcah- OO-IOc













L1 lu w 0 m m 0
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H CO C C . V 0 ) C









4.4 0. Q) Ci Ci 4
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m 0d 0 C i ->
0 C -H cH 0 Co
OH

D CO 0 4C 0 Px Cz C N 5
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00)- -HO c) *H 0 0 44 0 4 cO O


c~ H C H -H 0.0 *H CO .0.0







co









Hence, if the required qu; ity of secondary effluent is set et 90T

removal, a tricklinG pl:'nt will P etl achieve ti is level. of re-oval, and

an activated sludge plist mould be required to provide thi least cost

method of treating waste:-.ter. The results in Table 5.4 show that if

only secondary treatment is required, the least cost method suggests

that the cities of High Springs, Alachua, Archer, and hewberry should

cooperate to build a regional treatment plant with coordinate x=5.02,

y=18.77 in 1975 to satisfy their 1930 demands. Added der nds in 1990

were satisfied in the solution by the construction of individual plants.

For the other five cities, time option 2 was used to satisfy their de-

mands by building individual activated sludge plants for each. iHowever,

if tertiary treatment processes are required, one would build two

regional activated sludge plants, one for the cities of High Springs,

Alachua, Archer, and Ne-berry with coordinate Y.=5.02, y=18.77, and one

for Waldo and Hawthorne with coordinate x=32.57, y=6.62, in 1975 to sat-

isfy the 1980 demands of the six cities. Added demands in 1990 were

satisfied in the solution by the construction of individual plants. For

the other cities--Gainesville Urban Area, LaCrosse, and Micanopy--time

option 2 and individual activated sludge plants were used to satisfy

demands.

If the required quality of secondary effluent is set at 80% re-

moval, a trickling filter plant will provide the least cost method

(Table 5.4) of treating wastewater. The solution suggests that each

city should built its on;n high-rate trickling filter plant according to

time option 2. How vr if tertiry treatment processor are required,

one would build a re inal hi i-r Le trickling filter 1nt for the

cities of Alaca, Arc, r a ry with cori "tr x:4.02, y-12.03










in 1975 to satisfy the 1930 demands of the three cities. Added demands

for these three cities in 1990 .ere satisfied in the solution by the

construction of individual plants. For the other six cities--High

Springs, the Gainesville Urban Area, LaCrosse, Micanopy, Waldo, and

Hawthorne--time option 2 and high-rate trickling filter plants should

be used to satisfy the demands.

Figure 5.5 shows the locations of the regional activated sludge

treatment plants and the lengths of pipelines from the cities to these

two sites. Figure 5.6 does the same for the regional trickling filter

treatment plant. Tables 5.5 and 5.6 show the details of the minimum cost

schemes for secondary treatment and advanced treatment, respectively.

The figures in parentheses are the corresponding treatment capacities in

mgd to be built. The difference in treatment capacities between second-

ary treatment and tertiary treatment in the Gainesville Urban Area is

due to the fact that the Gainesville Urban Area has secondary treatment

plants with capacity 9.5 mdg, but has no tertiary treatment facilities.

Therefore, if tertiary treatment is required, the facilities should be

large enough to handle all the wastewater generated in this area.

The results shown in Tables 5.5 and 5.6 were calculated under the

assumption that one can build a treatment plant as small as one likes.

However, this assumption may not be realistic. If one suspects that the

capacity, for instance, required for Micanopy in 1990 under time option

2 is too small to be practical, then time option 5 would provide second

best solutions. The present values of cost for each city or regional

plant for both secondary treatment and secondary treatment with tertiary

processes for time option 5 are presented in Table 5.7. The conclusions

are still the same as those from time option 2, except the cost figures





82










AJ









L
Sa)






























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-H O) 1-,





































.41
E .- -



oo 1
















































U)


0




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01 01 L

























































L O





-H
P4 U
4




-H

-H
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*rC C O




C)n
00




U r







-H C











LI V^' "- C)




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I*-. r-1 CC

0)





t'C
F-H

















































































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c-


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0







m
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0






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-l
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&.
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-H


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-H






*r4









Ta;'le 5.5 Present V blu of Secondary Treatment Costs for the HirViiul
Cost Option for Ala hua County, Florida, 1975 to 1990'


Activated Sludge
System


1975


High Springs


Newberry


Archer


Alachua


Gainesville 6,204,332
Urban Area (6.5446)

LaCrosse 366,428
(.0655)

Micanopy 520,765
(.1161)

Waldo 533,672
(.1208

Hawthorne 675,850
(.1775)

R(1, 2, 3, 4) 3,588,569b
(1.2756)


aAll costs are in September


1990


39,059
(.0871)

23,559
(.0385)

21,182
(.0324)

48,008
(.1215)

697,737
(9.0876)

13,438
(.0155)

6,441
(.0047)

12,325
(.0135)

16,799
(.0223)


1974 dollars.


This figure includes pu-ping and transmission costs.


Hi-gh-ratc Trickling
Filter System

1975 1990


969,928 33,919
(.4455) (.0871)

583,362 20,183
(.2011) (.0385)

483,274 18,094
(.1498) (.0324)

1,016,294 41,920
(.4792) (.1215)

5,410,354 652,094
(6.5446) (9.0876)

284,666 11,337
(.0655) (.0155)

410,530 5,324
(.1161) (.0074)

421,134 10,373
(.1208) (.0135)

538,577 14,260
(.1775) (.0223)









Table 5.6 Present Value of Secondary and Tertiary Treatment Costs for
the Minimum Cost Option for Alachua County, Florida, 1975
to 1990a


Activated Sludge
System


City


High-rate Trickling
Filter System

1975 1990


73,790
(.0871)

42,890
(.0385)

38,313
(.0324)

92,373
(.1215)


31,090,496 1,535,004
(16.0446) (4.5876)


High Springs


Newberry


Archer


Alachua


Gainesville
Urban Area

LaCrosse


Micanopy


Waldo


Hawthorne


R(8, 9)


R(2, 3, 4)


R(l, 2, 3, 4)


23,738
(.0155)

11,089
(.0047)

21,690
(0.35)

29,997
(.0223)


2,297,853b
(.2983)




6,506,944b
(1.2756)


2,248,431
(.4455)


68,651
(.0871)

39,514
(.0385)

35,225
(.0324)

86,285
(.1215)


30,296,512 1,489,361
(16.0446) (4.5876)


591,564
(.0655)

876,234
(.3161)

900,693
(.1208)

1,176,076
(.1775)




4,474,878b
(.8301)


21,637
(.0155)

9,972
(.0047)

19,739
(.0135)

27,458
(.0223)


a
All costs are in September 1974 dollars.

This figure includes pumping and transmission costs.


673,327
(.0655)

986,469
(.1161)









Table 5.7 Present Vanue of ',t water r TreaLm(nt Costs for Tioe
Option 5 for Aln-'p: County, Florida, 1975 to 1990a


Activated Sludge
System

tertiary processes


with


wi tout


High-rate Trickling
Filter System

tertiary processes


with


without


High Springs


Newberry


Archer


Alachua


Gainesville
Urban Area

LaCrosse


Micanopy


41,808,368 10,602,925
(20.6322) (15.6322)


775,558
(.0810)

1,013,231
(.1208)


Waldo


Hawthorne


R(3, 9)


R(2, 3, 4)


R(1, 2, 3, 4)


2,478,977b
(.3341)





7,474,954b
(1.5551)


417,534
(.0810)

533,672
(.1208)

569,520
(.1343)

726,721
(.1998)


2,554,474 1,087,224
(.5326) (.5326)

-- 652,435
(.2396)

547,699
(.1822)

-- 1,174,284
(.6007)

40,650,256 9,444,815
(20.6322) (15.6322)


684,164
(.0810)

900,693
(.1208)

969,109
(.1343)

1,277,120
(.1998)




5,185,699b
(1.0225)


326,139
(.0810)

421,134
(.1208)

450.637
(.1343)

580,857
(.1998)


4,052,585b
(1.5551)


aAll costs are i Sept

bThis figure incld 1


1974 dollars.


and tLi-runsssion costs.





87



are different. Again the figures in parentheses under each set of cost

figures are the capacities to be built.

North Central Florida Regional Planning Council [1973] has six al-

ternatives toward supplying wastewater treatment facilities in Alachua

County and these alternatives are shown in Table 5.8. There are differ-

ences between their estimated capacities and those used in this study.

There are also differences in basic assumptions used in consolidations

over space and time, e.g., highway milages were used in NCFRPC's study

instead of a Euclidean distance measurement which was used in this

study. Therefore, a meaningful comparison between their alternatives

and the results of this study is difficult.









Tble 5.8 Alternn ive P7lans o c' ional 1 astcwat Utilities in
Al'chua Count a S :: ted by NCFI C


Alternati ve Regional Plants


9
I E 1(i)
i=1

II R(5, 7, 8, 9) + R(1, 2, 3, 4, 6)

ilI R(l, 2, 3, 4, 6) + R(8, 9) + R(5) + R(7)

9
IV R(1, 4, 6) + R(2, 3) + R(5) + 7 R(i)
i=7

9
V R(1, 2, 4) + R(3) + 7 R(i)
i=5

S9
VI R(I, 4, 5,a 6) + R(2) + R(3) + R(5b) + I R(i)
i=7


aThis regional treatment plan serves only part of the NW section
of Gainesville.

bThis regional treatment plant serves Cainesville except for the
part of N1 Gainesville.

Source: North Central Florida Planning Council [1973].















ClAPTER VI
LANDSPREADING SECONDARY EFFLUENT AS A
SUBSTITUTE FOR TERTIARY TREATMENT PROCESSES


The technology employed in wastewater treatment has not advanced

much in the past several decades. There are several difficulties one

encounters when attempting to remove more than 95% of the BOD and SS

with the standard processes. Greater removals require very large in-

creases in detention times and a corresponding increase in tank sizes.

A second treatment problem is the removal of nutrients. Nitrogen and

phosphorous compounds are more likely to be responsible for excess weed

growth than BOD. Standard processes do not do a good job of removing

these nutrients. These two problems can be handled by tertiary treat-

ment processes; however, the cost for these treatment processes alone

is higher than the cost of conventional treatment processes. Land

treatment is therefore considered as an alternative to tertiary waste

treatment.

Briefly stated, land treatment involves the use of agricultural

land and crops or forest products to absorb and filter nitrates, phos-

phates, and other elements from wastewater that has undergone primary

and, usually, secondary treatment. Excess "purified" water is then

returned to the water course. The methods of applying wastewater to

the land can be identified as infiltration systems, crop irrigation

systems, and spray-runoff systems [Thomas, 1973; Thomas and Law, 1963].

infiltration systems are usually designed to prevent surface runoff.

High loading rotes make evaporative losses relatively insignificant.









and up to 99% of the appliu waLtewater nay be contri ut ed to ground

water as rechar ed [LavrLy et_ l., 1961]. Crop irrt iiton systrs may

or may not control surface runoff. Low loading rates Anlj]O nch of the

applied wastewater to be lost through evapotranspiri ion, and the con-

tribution to ground water is largely dependent on evapotranspiration

losses [Dalton and Murphy, 1973; Craveland and Vickerman, 1972; Parizek

et al., 1967; Sprout and Hopkins, 1972; Young et al., 19721. Spray

runoff systems arc designed tc return 50% or more of the applied wrste-

water as direct surface runoff, evapotranspiration losses are variable

but relevant, and the selection of sites with impermeable soils re-

stricts the contribution to ground water [Law et al., 1970]. 'he appli-

cation of wastewater to land serves the following purposes: promotes

growth of crops, conserves water and nutrients that are normally wasted,

provides economical treatment of the wastewater, and reduces the pollu-

tion load on surface water supplies.

Many researchers have contributed estimates of the fertilizer value

in treated sewage effluent, and the values vary with the study, with the

type of treatment given to the sewage effluent, and with the source of

effluent. Schreiber [1957] reports that the amount of the principal

fertilizer elements in sewage effluents from 15 California cities stud-

ied is 60 to 100 pounds of nitrogen chiefly in the form of ammonia; 20

to 40 pounds of potassium occurring as potassium; and 60 to 100 pounds of

phosphate occurring as phhosphte, par acre-foot of effluent. Schruiber

does not assign a dollar \alue to the fertilizer contained in an acre-

foot of effluent; however, Hlirsch [1959] staLes that t-ic 1969 value of

nitrogen, phosphorus and polassiui fertilizer in an rr -feot of typical

San Diego wasLevator i S 18. A Pcnnsylvani State UnivcrsitL rscarech




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