Group Title: systems approach to financial appraisal of greenhouse heating with power plant cooling water
Title: A systems approach to financial appraisal of greenhouse heating with power plant cooling water
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Title: A systems approach to financial appraisal of greenhouse heating with power plant cooling water
Physical Description: Book
Language: English
Creator: Burch, David W
Copyright Date: 1985
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Bibliographic ID: UF00102785
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: ltuf - ACU3558
oclc - 12741044

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Almighty God, who teaches us
to husband the resources of the Earth


I am deeply grateful to my employer, the Tennessee

Valley Authority, and to four individuals in the organiza-

tion who were especially instrumental in this undertaking.

Dr. Joseph Roetheli spoke the words on my behalf that opened

the opportunity for this dissertation project and was always

an encouragement. Mr. John Shields and Dr. Porter Russ made

the necessary administratative arrangements and enquired of

my progress on every occasion. Dr. James Ransom continual-

ly encouraged me and provided administratative support as


I am sincerely indebted to Dr. Clyde Kiker for his

thoughtful guidance in the organization and preparation of

this manuscript. It was always a pleasant experience to

receive his counsel. Special thanks are also due Dr. W. W.

McPherson for opening the way to resume work for comple-

tion of my degree requirements and for his patient attitude

over the years. Thanks are extended to the other members of

my supervisory committee, Dr. Max R. Langham, Dr. Gary D.

Lynne, and Dr. Richard Fluck, for their reviews and sug-

gestions. The efforts of Mrs. Adele Koehler in the editing

and printing of this manuscript are also appreciated.

- 111 -

The loving support of my family has been a constant

factor in the completion of this project. Thanks are ex-

tended to my wife, Ariete, for her cooperation and for the

sacrifices she has made, and to my three sons, who have been

so anxious to see their father complete his "textbook."

Finally, I want to thank my parents for their many efforts

and sacrifices, material and otherwise, over many years,

that I might reach this point in my education.

- IV -



ACKNOWLEDGMENTS......................... ....... .... ......iii

ABSTRACT................................................................ vii


I INTRODUCTION.......................................1

Problem......................................... ... 6
Objectives................................. .............. .9
Significance....................... ..............11
Organization of the Study.........................16


Status of Commercial Waste Heat
Utilization.................................. 21
Heat Recovery Systems.... .........................30
Systems Concepts..................................37
Context of the Study...............................41


Decision Context of Integrated
Decision Contexts of Combined
Systems.......................................... 66
Conclusion............................................. 83

WASTE HEAT ...................................... 84

Literature Review.................................. 87
Heat Recovery System Models........................97
Conclusion.......................... ............116

HEAT RECOVERY .. ..............................118

Heat Exchanger Performance.......................122
Greenhouse Heating Requirements..................124


Waste Heat System Design
Specification................................... 126
Revenue Potential of Waste Heat.................133

Estimation of Delivery System
Pumping Cost ................................... 136
Financial Feasibility of CCW Delivery............138
Conclusion.... ..................................140

VI RESULTS AND DISCUSSIONS ..........................143

Waste Heat System Design......................... 144
Revenue Potential of Waste Heat..................151
Delivery System Pumping Costs.................... 154
Financial Feasibility of CCW Delivery.............157
Summary and Conclusion .......................... 160

VII SUMMARY AND CONCLUSIONS...........................164

Suggestions for Additional Study.................174
Usefulness of the Study..........................177

GLOSSARY.. ................................................ 179


SYSTEM PERFORMANCE MODELS.....................181

B ALGORITHM OF THE HEX MODEL.......................196


D ALGORITHM OF THE CCWDEL MODEL.................... 204

E FINANCIAL APPRAISAL PROGRAM......................208

MODELS.......... ............................ ...249

MODEL GLW660S FAN COIL UNIT....................255

BIBLIOGRAPHY ... ............ .............................. 270

BIOGRAPHICAL SKETCH .......................................279

- vi -

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



David W. Burch

August 1985

Chairman: Clyde F. Kiker
Major Department: Food and Resource Economics

The low-grade waste heat contained in power plant

condenser cooling water (CCW) is a virtually untapped re-

source with potential for reducing heating costs of the

greenhouse industry. Some commercial development is

occurring, but the lack of a model for valuation and

pricing of heat from CCW is an impediment to commercial-


A framework is needed to assist growers in estimating

what they can afford to pay for reject heat and to assist

utilities in estimating the capital and operating costs

of CCW delivery to greenhouses.

The broad purpose of this study was to examine and

model the factors which determine capital and operating

costs of heat recovery from both grower and utility


perspectives. Waste heat valuation and pricing serve as

the basis for financial appraisals and for the establish-

ment of mutually acceptable contractual agreements between

growers and utilities. Theoretical implications of three

basic pricing alternatives were considered as they relate

to cost-minimizing control of greenhouse heating systems.

Both access and BTU pricing were found to encourage growers

using fan coil heat exchangers to maximize CCW usage and

minimize heat recovery per unit volume of CCW delivered to

greenhouses. Volumetric pricing was found to establish an

incentive to increase heat recovery per unit volume of CCW

delivered for a given greenhouse heating requirement, and

hence, to reduce pumping costs. The modeling effort focused

on the potential role of volumetric pricing as a control

variable which utilities might use to reduce the capital

and operating costs of CCW delivery per acre of greenhouse


A case study based on conditions representative of the

lower Midwest showed that CCW demand schedules of cost-

minimizing growers were inelastic, and that over the range

of volumetric prices examined, CCW price was fairly in-

effective as a means of influencing cost-minimizing design

and control of greenhouse heating systems. It is recom-

mended that heavy reliance on volumetric pricing be avoided,

with perhaps no more than 20 percent of revenues coming from

that source, with the remainder coming from an access or

demand charge.



In the production of electricity at thermoelectric gen-

erating plants, electric generators are turned by steam tur-

bines driven by high pressure steam at one end and a vacuum

at the other. Cooling water pumped through the condensers

creates the vacuum by condensing the steam. Condenser cool-

ing water (CCW) is elevated in temperature as it passes

through the condensers, reflecting the loss of a large por-

tion of the energy input from fuel combustion for steam pro-

duction. The heat lost to CCW is referred to as reject or

waste heat, because it is rejected after it is no longer of

economic value to the process (Olszewski, 1980; Fourcy et

al. 1979). From 47 to 65 percent of the raw fuel energy

input at conventional thermoelectric generating plants is

transferred to CCW and discharged to the environment, along

with another 12 percent or so which is rejected in stack

gases (Effer and Barnstaple, 1979; Kim et al. 1980; Marsh,

1980). Figure 1.1 shows the schematic of a nuclear power

plant steam cycle, where as much as 60 to 65 percent of the

energy input is transferred to CCW.

Rapidly escalating prices of fossil fuels during the

1970's stimulated interest in possibilities for waste heat














e -

tL *,

- 3 -

recovery and commercialization. The regulatory environment

contributed further to this interest. The Federal Water

Pollution Control Act (FWPCA) Amendments of 1972 designated

heat as a pollutant and established a national goal to elim-

inate discharge of pollutants into navigable waters by 1985.

The definition and implementation of Environmental Protec-

tion Agency (EPA) regulations, also during the 1970's, led

to expanding use of cooling towers for heat dissipation with

recirculation of cooling waters (de Pass et al. 1979;

Graham, 1979; Maloney, 1972; Porter, 1979). Compliance re-

sulted in a trend from open-mode to closed-mode cooling

which, in turn, resulted in availabilities of CCW at signi-

ficantly higher temperatures. At the higher temperature

levels of closed-mode cooling systems, technical viability

of waste heat recovery was enhanced and investment and

operating costs of heat recovery systems reduced.

Both industrial and agricultural production processes

have been studied to identify technically and economically

viable applications for waste heat. There appears to be

little potential for industrial applications because of the

relatively low and variable temperatures of CCW, high util-

ization costs, the necessity of locating users near heat

sources, the interruptable nature of the service, and the

possibility of chemical contamination (Kim et al. 1980).

Suggested agricultural uses have included soil warming, warm

water irrigation, greenhouse heating, aquaculture, and bio-

logical recycling of livestock wastes in conjunction with

- 4 -

aquaculture (Balligand et al. 1978; Beall et al. 1977; Berry

and Miller, 1974; Boersma and Rykbost, 1973; Guerra and

Godfriaux, 1976; Hubert and Madewell, 1978; Kawaratani,

1981; Maddox et al. 1982; Witzig and DeWalle, 1978). Com-

mercial development has been largely limited to greenhouse

heating, with about 40 acres of production area in the

United States and Great Britain now relying on power plant

CCW as the primary heat source.

Figure 1.2 presents a schematic of power plant waste

heat recovery from a closed-mode cooling system. In the

diagram, a small portion of CCW bypasses the cooling towers

and is pumped to an adjacent greenhouse complex. Circula-

tion of the water through heat exchangers located in green-

houses accomplishes heat transfer to greenhouse air. The

CCW is subsequently returned to the cooling tower basin for

further cooling, if necessary, before recirculting through


Utilities have for the most part taken a cautious

attitude toward waste heat commercialization. This caution

derives from doubts about economic viability and concern

with the possible reactions of regulators, and in particu-

lar, the reactions of state utilities regulatory commis-

sions. Electric utilities operate as regulated monopolies,

having a mandate to produce electricity at the lowest pos-

sible cost. As such, they are answerable to state regula-

tory commissions which monitor their performance.

- 5 -



plastic tube

fan coil unit, /



Figure 1.2. Use of condenser cooling water for greenhouse

- 6 -

Engagement in waste heat commercialization represents a

departure into unfamiliar territory which raises several re-

gulatory issues. How are capital and operating costs of

generating stations to be allocated between thermal and

electrical energy services? How is waste heat to be priced,

and capital expenditures for commercialization financed? In

the event of adverse cash flows from thermal service, will

electric ratepayers have to subsidize the activity? Atti-

tudes of regulators will be conditioned by their perception

of waste heat as either a joint product or a by-product of

electric energy production. A precedent seems to have been

established for the pricing of waste heat on an incremental

cost basis. Whatever the basis for assignment of costs,

both utilities and regulators want to be satisfied that the

benefits from waste heat recovery can be translated into re-

venue streams which cover the operating costs of CCW deli-

very systems and yield rates of return on investment compa-

rable to those earned on power investments.


Enormous quantities of reject heat could be made avail-

able on a nearly continuous basis at thermoelectric generat-

ing stations, in many locations at temperatures permitting

the use of dry-type heat exchangers capable of providing a

conventional greenhouse environment. Little is known, how-

ever, about the financial feasibility of marketing the waste

heat contained in CCW. Furthermore, little formal attention

7 -

has been given to the pricing problem. What is the basis

for pricing, and what are the implications of alternative

pricing modes. What are the implications of imposing a flat

annual user access fee or a heat recovery charge versus a

volumetric charge on CCW, the medium of conveyance? There

is no framework of analysis even remotely suited for finan-

cial appraisals of proposed waste heat recovery ventures.


The bottom line as in all cases is economic feasi-
bility. Faulty proposals for waste heat utilization
facilities not only ignore utility operating con-
straints but in many cases fail to support the eco-
nomic feasibility of the concept being put forth.
This is a fatal flaw of many of the proposals being
made today. (Cordaro and Gross, 1979, p. 2,441)

A scheme of analysis is needed which is appropriate for

site-specific evaluations, and which can address the viabil-

ity concerns of utilities and regulators. Until such a

framework of analysis is available, utilities can be ex-

pected to remain generally unresponsive to commercialization


What are the factors which influence the costs and ben-

efits of waste heat recovery? Factors affecting costs in-

clude heat content of CCW and greenhouse heat loads, both of

which are subject to continual fluctuations. Additionally,

the design, heat exchange capacity, and control of green-

house heating systems are important determinants of capital

and operating costs of heat recovery systems, all of which

may be influenced to varying degrees by the pricing mode.

- 8 -

Gross benefits include reductions in fossil fuel heating

costs of greenhouses and negligible reductions in cooling

tower operating costs.

The ownership of heat exchange systems is customarily

separate from that of the heat delivery system, with green-

house firms responsible for heat exchange and the utility

responsible for CCW delivery. Under this type of arrange-

ment, the investment and operating costs of CCW delivery

incurred by the utility are largely dependent on the deci-

sions of greenhouse firms relative to design, capacity, and

control of heat exchange systems. The waste heat user rate

structure adopted by the utility must take into account the

value of waste heat as a substitute for fossil fuel and the

relationships which exist between the rate structure itself

and cost-minimizing design, capacity, and control of heat

exchange systems, which in turn influence investment and op-

erating costs of CCW delivery.

Determination of financial feasibility can be logically

viewed as a sequential process of problem solution in which

investment and operating costs of heat exchange and CCW de-

livery systems are estimated within an arbitrarily specified

pricing context. Subsequent to the first stage of analysis,

resolution of the problems of succeeding stages depends on

the results obtained from preceding stages. The first stage

of analysis deals with the problem of identifying the pro-

bable heating system design, the implied peak flow rate, and

the annual CCW usage of greenhouses assuming that growers

- 9 -

operate heating systems so as to minimize operating costs.

Specifically, what are the probable choices of backup and

supplemental heating mode and the level of investment in

heat exchange capacity which minimize the present value of

greenhouse heating costs over an extended period of time?

What are the implications for CCW delivery requirements?

The second stage of analysis deals with the problem of esti-

mating the revenue potential from waste heat, based on capi-

tal and operating costs differences of least-cost waste heat

and conventional heating systems. In a third stage of anal-

lysis, electrical pumping costs of the CCW delivery system

are estimated, based on acreage projections and the least-

cost heating system design identified previously. In the

final stage, financial feasibility of the CCW delivery sys-

tem is examined using revenue and operating cost estimates

obtained previously, and investment costs for CCW delivery

capacity consistent with results obtained in the first stage

of analysis.


Power plant waste heat commercialization depends on the

approval of regulators, and normally depends on investment

decisions of both utilities and greenhouse firms. Regula-

tors and utilities must be satisfied of the financial feasi-

bility of investment in CCW delivery to greenhouses. Finan-

cial feasibility is seen as dependent on capital and operat-

ing costs of CCW delivery systems and the revenues which can

- 10 -

be generated by them. Greenhouse firms must be convinced

that under the terms by which waste heat is offered, total

variable heating costs of waste heat greenhouses, including

backup and supplemental heating, are at least low enough to

justify the incremental capital investment in heating equip-

ment as compared to conventional heating alternatives. The

broad objectives of this study are to develop a framework of

analysis for assessments of financial feasibility of waste

heat commercialization and to use that framework to explore

the theoretical and practical implications of CCW pricing

alternatives. Specific objectives are

1. to estimate the hourly CCW demand process of a
cost-minimizing greenhouse operator, given heat
exchanger design, and to study the effect of
greenhouse heat load and electricity price on

2. to estimate peak CCW flow rates, derive seasonal
CCW demand functions and estimate annual vari-
able heating costs of design alternatives;

3. to determine present values of heating costs of
design alternatives;

4. to identify the least-cost backup and supplemen-
tal heating mode and the least-cost heat ex-
changer design;

5. to determine an annual stream of user charges
which equalizes the present values of heating
costs of least-cost waste heat and conventional
alternatives, and to use these charges to esti-
mate the maximum revenue potential of waste
heat sales by the utility;

6. to estimate annual costs of the CCW delivery
system, given the greenhouse heating require-
ment, acreage levels, and the least-cost waste
heat design;

- 11 -

7. to appraise the overall financial potential of
the CCW delivery system, given the information
obtained in meeting the previous objectives.


Early proposals for beneficial uses of waste heat were

largely motivated by expectations that power plants could

significantly reduce investment and operating costs of heat

dissipation. Initially, applications were sought which

might have the potential to use large quantities of low-

grade heat on a continual basis (Beall and Samuels, 1971;

Boersma and Rykbost, 1973; Olszewski, 1979, p. 797).

Seasonality of heating demand and limited daytime heating

requirements made the greenhouse industry a seemingly poor

candidate for significant reductions in the cost of heat

dissipation. The additional use of CCW as a greenhouse

coolant in summer months was proposed by Price and Peart

(1973) and Williams (1972). Tests conducted by the

Tennessee Valley Authority (TVA) showed, however, that CCW

was an ineffective greenhouse coolant of little practical

value (Pile et al. 1979).

Greenhouse and other applications were investigated

which minimized or eliminated the need for further heat re-

moval by power plants. Cooperative work was conducted on

evaporative pad systems for several years at TVA and the Oak

Ridge National Laboratory (ORNL) because of their effective-

ness as dissipators of heat, in spite of the excessive lev-

els of humidity associated with these systems. Surface

- 12 -

heating was also proposed as a means of cooling large vol-

umes of CCW while concomitantly reducing greenhouse heat

loads and permitting maintainence of a conventional green-

house growing environment. Neither mode of heat exchange

gained acceptance in commercial greenhouse production.

Limited availability of land suitable for development

adjacent to power plants makes greenhouse heating a promis-

ing application, because of the potentially high consumption

of low-grade heat per unit of land area occupied (Iverson et

al. 1976). Another factor favoring greenhouse over other

proposed agricultural production systems is the comparative-

ly high marginal value product of heat in greenhouse produc-

tion. Revenue potential from sales of waste heat to green-

houses appears comparatively high per dollar invested in CCW

delivery capacity, relative to other agricultural production


Census of Agriculture data show that United States

greenhouse acreage expanded 4,764 acres between 1959 and

1979, most of this expansion having occurred after 1970.

While acreage expanded, a significant shift in geographical

distribution took place. Table 1.1 shows the geographical

distribution of acreage in 1959, 1970, and 1979. The Middle

Atlantic and East North Central regions accounted for 52.5

percent of production area in 1959 and only 26.8 percent in


The greenhouse industry was particularly affected by

the rapid escalation of fossil fuel prices during the

- 13 -

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- 14 -

1970's, giving rise to concerns that the future of the in-

dustry was in jeopardy, at least in traditional production

areas of the Midwest and Northwest. Greenhouse heating

costs typically range from 12 to 35 percent of variable pro-

duction costs on an annual basis, depending on location,

structure, heating system, and cropping patterns. Heating

cost may have been the major factor in location of new acre-

ages, since expansion has occurred in regions where heating

requirements are comparatively low. From 1959 to 1979,

California, Florida and Texas had increases of 2,133, 918,

and 333 acres respectively, accounting for 71 percent of the

total increase in acreage. The acreage data suggest that

potential exists for expansion of production area where

heating costs are low.

Reject heat from thermoelectric generating stations is

a virtually untapped resource of potential significance to

the greenhouse industry. For example, each of the two gen-

erating units at TVA's new Watts Bar nuclear plant, sched-

uled for completion in 1987, will have an approximate CCW

flow of 410,000 gallons per minute (GPM) at January tempera-

tures of 93 to 120 degrees F. A planned CCW delivery line

with an ultimate capacity of 100,000 GPM could meet 92 to 94

percent of annual heating requirements for a 275-acre green-

house complex, which would occupy all available land at the


Total capital cost for CCW delivery, heat exchangers,

and backup and supplemental heating and controls is high.

15 -

It is by no means evident that future savings in variable

heating costs can justify the initial capital outlay. Ini-

tial investment cost of the CCW delivery line may seem pro-

hibitive to utilities, particularly in view of the paucity

of data on CCW flow requirements and potential value of the

waste heat contained in CCW. This study makes a significant

contribution to the waste heat commercialization effort by

presenting methodologies for assessing financial feasibility

of waste heat recovery from both the utility and greenhouse

perspectives. As such, the study can be of indirect benefit

to regulators in deciding whether or not to grant approval

of proposed ventures, and of direct benefit to utilities and

greenhouse firms in reaching the investment decisions neces-

sary for implementation.

Commercialization of reject heat from CCW presents some

interesting problems for economic analysis in the areas of

resource valuation and pricing. "The assignment of a price

for reject heat from electricity generating stations is im-

portant in determining the financial viability for subse-

quent uses of the heat" (McBean et al. 1979, p. 690). But

the importance of pricing goes beyond its effect on the via-

bility of subsequent uses. The degree of correlation be-

tween greenhouse heat recovery and CCW usage is partially

dependent on pricing mode. In pricing waste heat, the util-

ity must decide whether the cost to the user will bear some

reasonable economic relationship to CCW delivery cost

(Sjoholm, 1980). The analysis of pricing alternatives as a

- 16 -

means of regulating heat recovery rates is of interest to

utilities. The importance of pricing modes lies in their

influence on heating system design and the operating

strategies of growers, and consequently on CCW delivery re-

quiments to meet greenhouse heat loads.

The heat content of CCW is variable, and heat recovery

rates are also variable and substantially under the discre-

tionary control of greenhouse operators, primarily through

control of CCW flow rates through heat exchangers. While

appealing from the utility perspective, the incorporation of

volumetric pricing of CCW in the user rate structure is ob-

jectionable to growers because variable user costs are not

then highly correlated with heat recovery. Volumetric pric-

ing is therefore a controversial topic. This study contri-

butes to resolution of the controversy by specifically ex-

ploring the implications of volumetric pricing for heating

costs, demonstrating that variability of heating costs need

not be objectionable in itself, as long as variable heating

costs remain well below those of fossil fuel systems.

Organization of the Study

Chapter II begins with a statement on the status of

waste heat commercialization and a brief discussion of heat

exchange technologies, followed by a conceptualization of

the total heat recovery system from an integrated systems

approach. Descriptions of basic physical attributes of the

CCW delivery system and alternative heat exchange

- 17 -

technologies provide background for subsequent discussions

of procedures for design refinements from integrated and

combined systems approaches. A statement on the context of

the study concludes the chapter.

The material of Chapter III establishes decision con-

texts for implementations of waste heat recovery projects

from both integrated and combined systems perspectives, giv-

en the existing regulatory environment. From an integrated

systems approach, the power plant has two outputs: electri-

city and heat. There is a recognized tradeoff between elec-

trical and heat output, with electricity being the higher

value product. Heat is viewed as a by-product whose output

is to be minimized. The objective of the heat recovery sys-

tem is to minimize the present value (PV) of n-year heat re-

covery costs for a given periodic greenhouse heating regime.

Heating requirements can be met from multiple combinations

of investments in CCW delivery and heat exchange capacities

and CCW flow regimes.

Economies resulting from specialization of functions

normally dictate a separation in ownership and management of

the CCW delivery system (utility) from that of heat exchange

systems (greenhouse firms). From a combined systems ap-

proach, separate sections discuss optimization of the CCW

delivery system from a utility perspective and optimization

of the heat exchange system from a greenhouse perspective.

The basis for interrelated operating systems is a scheme of

compensation to the utility for costs incurred in delivery

- 18 -

of heat to greenhouses which allows an acceptable rate of

return on utility investment, while maintaining greenhouse

heating cost at or below that of the least-cost fossil fuel

alternative. Theoretical implications of waste heat pricing

alternatives are considered. A description of the operating

characteristics of water-to-air heat exchangers leads to a

discussion of principles underlying the warm water demand

function of a cost-minimizing greenhouse operator. An in-

depth analysis -of volumetric pricing of CCW is presented in

Chapter III.

Computer models developed to aid in the valuation and

pricing of waste heat are presented in Chapter IV. The

modeling effort of this study focused on a) specification of

heat recovery system performance models to estimate oper-

ating costs of design alternatives and associated CCW pump-

ing costs within a specified pricing context and b) devel-

opment of models to appraise financial feasibility of heat

exchange and CCW delivery systems. The sequential proce-

dure for financial appraisals of waste heat commercializa-

tion on a site-specific basis involves the use of five com-

puter models presented in this chapter.

Chapter V presents assumptions and decision scenarios

for analysis of a location in the lower Midwest to demon-

strate applications of the models of Chapter IV. Assump-

tions and decision scenarios are selected to explore in par-

ticular the implications of volumetric pricing of CCW. A

sequential solution procedure is laid out, in which the

- 19 -

outputs of initial runs of the computer models provide in-

puts for succeeding runs.

Chapter VI contains results and discussions of calcula-

tions based on the representative assumptions and decision

scenarios of Chapter V. Least-cost heating systems of waste

heat and conventional greenhouses are identified, from which

the revenue potential of waste heat is calculated. Delivery

system pumping cost estimates show that variable costs of

CCW delivery are negligible in comparison with fixed cost.

Results of net present value calculations of a 10,800-GPM

delivery system are obtained from estimates of revenue po-

tential and electrical pumping cost. The material in this

chapter provides procedural guidelines for sequential ap-

plication of the models of Chapter IV to the financial

appraisal problem.

Chapter VII summarizes findings and conclusions of the

study and makes recommendations for further work. Optimiza-

tion of CCW delivery system design presents ample material

for further analysis. Optimization of heat exchanger design

within a volumetric pricing context is another promising ar-

ea for further work. A third topic deserving attention is

the design of cost-minimizing control modules for heat ex-

change systems, also within a volumetric pricing context.


Greenhouse utilization of power plant reject heat re-

quires the allocation of resources to site preparation,

pumps, pipeline, heat exchangers, instrumentation, and new

greenhouse acreage. The total capital requirement for waste

heat recovery is substantially greater than for conventional

greenhouse heating systems, particularly considering the

need for backup and supplemental heating. It is unlikely

that the total investment burden will be borne by either

utilities or greenhouse firms. The incremental capital in-

vestment for waste heat recovery relative to conventional

heating and prices of coal or natural gas determine rather

low ceilings for the replacement value of waste heat. De-

sign and management considerations are therefore of crucial

importance to economic viability.

The ownership and management of heat exchanger systems

has generally, in practice, been separated from ownership

and management of warm water delivery systems. Separate

ownership and management of components of the heat recovery

system leads conceptually to optimization criteria for each

component which are antagonistic to optimization criteria

from an integrated system perspective.

- 20 -

- 21 -

This chapter begins with a review of the status of com-

mercial waste heat use by greenhouses and existing institu-

tional arrangements. A description of general characteris-

tics of a heat recovery system follows, including CCW deli-

very and heat exchange. Alternative heat exchange technolo-

gies are covered to provide additional background, since

technologies vary considerably in capital cost, operating

requirements, and the environments which they produce.

Principles of design are then considered from the perspec-

tives of both integrated and combined systems. The chapter

concludes with a statement on the context of the study.

Status of Commercial
Waste Heat Utilization

Approximately 60 acres of commercial greenhouses in the

United States and Great Britain are heated primarily with

power plant reject heat. This is a fairly recent develop-

ment since the first acreage was established in 1977. An

additional 9 acres uses industrial waste heat. Table 2.1

summarizes the status of existing commercial greenhouse ven-


The Archer Daniels Midland Company owns and operates a

9-acre greenhouse range primarily dedicated to lettuce pro-

duction, which is located adjacent to its Decatur, Illinois,

ethanol plant. Hot water discharged from the ethanol plant

at temperatures of 150 to 155 degrees F is circulated

through low-temperature fan coil heat exchangers.

- 22-



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- 23 -

Sufficient waste heat is believed to be available from the

ethanol plant to support a greenhouse complex of at least 12

and possibly up to 20 acres. The company has followed a

program of phased expansion of production area, beginning

with one acre of conventional greenhouse in 1980, and having

added 1.5 acres of waste heat greenhouse in 1982, two acres

in 1984, and 4.5 acres in 1985. The original one-acre

conventional house was converted to waste heat in 1984.

A 20-acre glasshouse complex completed in 1981 is

heated with CCW from the coal-fired Drax power station in

Yorkshire, Great Britain. This greenhouse range produces

tomatoes and is operated as a joint venture between the

Central Electricity Generating Board and Express Dairy

Foods. Winter CCW temperatures are relatively low, normally

ranging in the low to mid eighties (degrees F). Low-temper-

ature fan coil units provide primary heat exchange capacity.

In 1977 the Northern States Power Company initiated the

first commercial waste heat delivery system in the United

States at the Sherco power plant, following one year of op-

eration of a half-acre demonstration facility (Boyd et al.

1978; Hietala and Ashley, 1983). The Sherco plant, located

near Becker, Minnesota, is a two-unit coal-fired station

with a total rated output of approximately 1360 megawatts.

The cooling system is operated in closed-mode with a total

CCW flow of about 500,000 GPM at peak load. Greenhouse pro-

duction area reached 4.25 acres by 1979, but no further ex-

pansion occurred through the end of 1985. About 70 percent


- 24 -

of the acreage is in roses, and the remainder in miscellan-

eous cut flowers and potted plants. The distribution of

condenser cooling water temperatures during the coldest

months tends to be skewed toward the lower end of a range

extending from about 78 to 115 degrees F. A large invest-

ment in greenhouse heat exchange capacity is necessary due

to extreme heat loads and a relatively low CCW temperature


Primary heat exchange capacity is provided by low-tem-

perature fan coil units. A portion of the acreage also has

embedded pipe in the greenhouse floor, through CCW is circu-

lated after discharge from fan coil units. Backup and sup-

plemental heating is required for the eventuality of pipe-

line failure or a simultaneous outage of both power generat-

ing units. Condenser cooling water is normally available

about 97 percent of the time during the heating season, but

may not always be warm enough to meet greenhouse heating

loads. Overhead propane-fired unit heaters are used for

backup and supplemental heating. The Northern States Power


has adopted a philosophy of providing waste heat
on a cost-of-service basis with a return on invest-
ment that is equivalent to the rate of in return for
other utility services provided by the Company. No
portion of the fuel cost of the power station or any
capital investment normally associated with a power
plant is allocated to the cost of serving waste
heat. The cost of serving waste heat is based on
incremental operating costs only. (Ashley, 1978, p.

- 25 -

The user rate structure consists of demand and volumetric

charges, with the demand charge based on peak flow rate and

calculated to amortize capital cost of the delivery system

over a 20-year period (Ashley et al. 1979). A volumetric

charge of $0.01 per thousand gallons was initially levied to

recover costs of pumping and maintenance. The volumetric

charge is subject to annual adjustment and had risen to

$0.0158 by 1985. The annual demand charge in 1985 was

$13.90 per peak GPM.

The largest waste heat greenhouse complex in the United

States is currently under development at Pennsylvania Power

and Light's Montour generating station at Washingtonville,

Pennsylvania. This two-unit coal-fired plant has a total

rated capacity of 1,500 megawatts, each unit having a CCW

flow of 226,000 GPM. The utility has sufficient adjacent

land to accommodate up to 70 acres of greenhouses. Green-

house production began in December, 1980, with completion of

a 2.75-acre range under private ownership producing floral

crops. The entry of a tomato grower in 1983, entry of a

lettuce grower in 1985, and expansions by the first two

growers would bring total production area to 13.56 acres by

late 1985.

January CCW temperatures at Montour (cooling tower

basin) generally range from 90 to 115 degrees F, with the

utility reporting a weighted average temperature of around

100 degrees F over a heating season. The temperature drop

in the CCW delivery line from cooling tower basin to

- 26 -

greenhouses is typically less than two degrees. A flooded

floor system provided primary heating in the initial 2.75-

acre range. Subsequent acreages used hybrid systems com-

bining low-temperature fan coil units and either flooded

floor or embedded pipe systems. Backup and supplemental

heating for all houses is provided by boilers.

The land is leased to growers for a nominal fee by

long-term agreement with renewable options. A flat annual

access fee is based on acreage occupied and is calculated to

amortize pipeline capital cost and provide for operation and

maintenance costs of the delivery system. The annual access

fee is not subject to escalation, remaining fixed at a con-

stant level for the duration of the contract. As production

area has expanded, however, new acreages have been subject

to higher access fees. Apportionment of charges to recover

initial pipeline investment was based on a projected peak

production area of 15 acres. A time path of expected acre-

age expansion was projected to estimate ex ante access fees

necessary for amortization of delivery system capital cost.

Another major Pennsylvania project is 11.5 acres built by a

single grower at Pennsylvania Electric's Homer City

generating station. Condenser cooling water temperatures at

Homer City generally remain above 90 degrees F throughout

the winter. Greenhouse heat exchange capacity consists pri-

marily of embedded pipe, from which over 90 percent of

greenhouse heating needs are meet. Backup and supplemental

heat is provided by overhead propane-fired unit heaters.

- 27 -

The grower, who built five acres in 1984 and added 6.5 acres

in 1985, specializes in bedding plants, flowers, and hanging


The Homer City project differs from others in that CCW

delivery and return lines were installed by the grower. A

nominal annual access fee is charged for the use of CCW as

available. The 24-inch delivery line can accommodate up to

a 30-acre greenhouse range.

A one-acre greenhouse was constructed in 1983 at the

Astoria 6 unit of the Power Authority of the State of New

York. The Astoria 6 unit, located in Queens, is an 800-

megawatt oil-fired generating plant. The greenhouse, which

is privately owned and managed, produces cucumbers, toma-

toes, and lettuce.

The Astoria project differs from other power plant

waste heat recovery ventures in several respects. The heat

source is turbine lubricating oil cooling water (Stipanuk et

al. 1982). Salinity of the cooling water, which normally

ranges in temperature from 105 to 120 degrees F, prevents

direct circulation through the low-temperature fan coil

units installed in the greenhouse. An intermediate heat ex-

changer provided by the utility transfers heat from the sa-

line cooling water to a water loop recirculating within the

greenhouse. Exiting water temperatures on the cool side of

the heat exchanger normally remain at or above 100 degrees


- 28 -

Backup and supplemental heat is provided by the utility

via steam injection into the recirculating greenhouse loop,

obviating the need for a backup heating system in the green-

house. During the first season of operation, a problem was

encountered with the warm water delivery system which forced

use of the steam backup most of the time.

A long-term contract between the utility and the green-

house firm stipulates several components in the user rate

structure. Fees include separate charges for heat recovery,

delivery system repair and maintenance, amortization of the

delivery system and ancillary capital costs, and a steam

charge for backup and supplemental heating. The heat reco-

very charge is subject to a minimum and is escalated 10 per-

cent per annum. Steam and repair and maintenance charges

were predetermined and are subject to 10-percent annual es-

calation beginning in the third year of operation. A flat

annual fee fixed for the life of the contract provides for

amortization of delivery system capital cost and site pre-

paration. The contract provides for possible adjustment of

heat recovery, repair and maintenance, and steam charges

after five years of operation.

The South Carolina Public Service Authority built a

2.5-acre greenhouse in 1984 at the new coal-fired Cross gen-

erating station. The first generating unit scheduled for

completion, rated at 450 megawatts, was expected to supply

warm water at temperatures ranging from 100 to 125 degrees F

during the heating season. The greenhouse is owned and

- 29 -

operated by the utility and will be engaged in production of

roses, tomatoes, mums and snapdragons. Low-temperature fan

coil units were installed for primary heating, with backup

provided by a hot water boiler. The CCW delivery system was

initially sized to accommodate a greenhouse complex of ten

acres. An additional seven acres were scheduled for comple-

tion at the Georgetown generating station in the summer of

1985. The acreage at Georgetown will be privately owned,

and tentative plans are established for a total of 40 acres

at this site.

The only commercial greenhouse which has used CCW from

an open-mode cooling system is located at the Browns Ferry

nuclear plant, near Athens, Alabama (Burch et al. 1982;

Burns et al. 1980). The Browns Ferry nuclear plant has

three generating units with total output of approximately

3,600 megawatts. The open-cycle cooling system has a 1.8

million GPM discharge when operating at full load, with

January CCW temperatures normally ranging from 57 to 70

degrees F at the greenhouse.

The 0.58-acre greenhouse was built by the Tennessee

Valley Authority (TVA) in 1978 as a demonstration facility

and was subsequently licensed to a private grower in 1982.

The structure is divided into three zones of equal size, one

of which is conventionally heated while the other two are

waste heat zones. Due to the low level of CCW temperatures,

direct-contact wet-type heat exchangers (evaporative pads)

were installed in the waste heat zones. Backup heating is

- 30 -

provided by forced-air propane unit heaters. The licensee

pays a flat annual fee subject to 6 percent escalation year-

ly for use of the premises and unlimited access to CCW as

available at the greenhouse.

Heat Recovery Systems

The waste heat recovery system is an extension of the

power plant heat rejection system which is divided into two

component subsystems: the CCW delivery system and the green-

house water-to-air heat exchange system.

Condenser Cooling Water Delivery System

The warm water delivery system consists of the


1. tie-in to the warm water source (normally the
cooling tower basin),

2. CCW supply pumping station,

3. all supply and return lines between the warm
water source and greenhouse heat exchangers, and

4. instrumentation and controls including control
valves, pressure differential controllers, pres-
sure switches, flow meters and temperature indi-

Heat Exchange Systems

Halliday and Resnick give a useful but nonoperational

definition of heat as "that which is transferred between a

system and its surroundings as a result of temperature dif-

ferences only" (1978, p. 475). Heat transfer occurs as the

temperature of warm water exceeds that of the medium with

- 31 -

which it comes in contact. Heat transfer is measured as

Q = m f cdT (2.1)

where Q is heat transfer, T. and T are inlet and outlet

water temperatures respectively, m is water mass and c, the

specific heat of water, is a function of temperature. Over

the interval of water temperatures encountered in waste heat

recovery the specific heat of water varies from about 0.9984

to 1.0008 (Halliday and Resnick, 1978, p. 478). Assuming a

specific heat of 1.0, heat transfer Q (BTU/HR) can be ap-

proximated for a steady state as

Q = 8.333GPM-OT-WTD (2.2)

where GPM is a constant gallons per minute flow rate, OT is

minutes operating time per hour, and WTD is the water tem-

perature drop through the heat exchanger.

Various heat exchanger designs are available for green-

house application. Discussions of design alternatives are

found in Stipanuk et al. (1981), Stipanuk et al. (1982),

Freemyers and Incropera (1979), and Olszewski (1980). In

general, investment and operating costs of all systems are

inversely related to warm water temperature levels, ceteris

paribus. Since conditions vary widely from one location to

another, the appropriate type of heat exchanger design must

be determined in accordance with site characteristics.

- 32 -

Evaporative pad. Evaporative pad heating involves di-

rect contact of warm water and greenhouse air. A pad made

of a fibrous material is mounted at one end of the green-

house, over which warm water is distributed and across which

air is drawn by fans located at the opposite end of the

greenhouse. Evaporative pad systems were first proposed by

Beall and Samuels (1971) as a supplementary year-around heat

removal system capable of reducing net operating costs of

cooling towers. A feasability study of evaporative pad

heating by Trezek and Olszewski (1974) concluded that such

systems could be economically viable at certain locations.

Evaporative pad systems can achieve high rates of heat

recovery at low water temperatures and can be technically

viable where water temperatures remain above about 70 de-

grees F during the heating season. The Tennessee Valley

Authority conducted extensive trials with evaporative pad

systems from 1974 through 1981 (Madewell et al. 1975; Burns

et al. 1976; Pile et al. 1976; Pile et al. 1979; Burns et

al. 1980; Burch et al. 1982).

Excessive levels of humidity associated with direct-

contact water-to-air heat exchange are reported to produce

an unacceptable environment for many crops (Trimmer, 1974;

Boyd et al. 1978; Burns et al. 1980; Burch et al. 1982).

Evaporative pad systems have not achieved commercial accep-

tance for several reasons including excessive levels of hu-

midity and high investment, electrical operating, and repair

and maintenance costs. A further difficulty is the

- 33 -

impracticality of adding supplemental heat from a conven-

tional fuel source as needed. Developmental work with evap-

orative pad designs was abandoned as CCW became available at

winter temperatures above 80 degrees F.

Floor heat. Floor heating systems have been developed

which effectively utilize water at temperatures as low as

the mid-seventies. Floor heating has the benefit of pro-

viding heat to the root zone, where it is most needed for

many crops. At the water temperatures available from

closed-cycle power plants, floor heating can provide the

major part of annual heating requirements, but supplemental

overhead heating is required except in very mild climates.

Floor heating systems are classified into two basic

types: embedded pipe and flooded floor. Embedded pipe sys-

tems provide heat to the root zone by circulating heated

water through pipe buried in the greenhouse soil. The

flooded floor system developed at Rutgers University circu-

lates heated water through a gravel storage area beneath a

porous concrete greenhouse floor. If warm water must be re-

turned at or near the pressure at which it is received,

pressure loss in a flooded floor system can result in a sig-

nificant pumping requirement.

The Ohio State University has conducted crop response

trials on embedded pipe systems in diverse greenhouse soil

media. Work done at Ohio State is described in Roller and

Elwell, 1980; Elwell et al. 1982; and Ahmed et al. 1983.

Results suggest that floor heating can appreciably increase

- 34 -

yields and/or shorten growing cycles of many crops with a

generally reduced heat input. Research at Rutgers Univer-

sity has resulted in design of both embedded pipe and

flooded floor systems (Roberts and Mears, 1980; Manning et

al. 1980; Manning and Mears, 1981; Manning et al. 1983).

Floor heating may be an economically viable alternative to

low-temperature forced-air heat exchangers where water tem-

peratures normally range from 70 to 90 degrees F during


In some commercial applications floor heating has been

preferred to low-temperature forced-air units because of the

reduced level of electrical operating costs. The disadvan-

tages of floor heating systems include their comparatively

high investment costs and supplemental heating requirements.

Loss of water pressure is also a problem where there is a

return pumping requirement. Expected crop yield benefits

and electrical savings must be weighed against higher in-

vestment cost and supplemental fuel requirements in deciding

whether to use floor heating or fan coil units where water

temperatures remain above 90 degrees F.

Surface heat. Surface heating is accomplished by the

distribution of a thin layer of heated water over the green-

house roof and sidewalls, which reduces rates of heat loss

from the structure. Whenever surface-applied water is warm-

er than the greenhouse interior, some heat transfer occurs

from water to air, but the major benefit comes from the

reduction in heating requirements. As mentioned previously,

- 35 -

early interest in surface heating was stimulated by the

potential for increasing power plant heat rejection capacity.

Surface heating may be of interest where CCW tempera-

tures remain typically in the range of 60 to 75 degrees F

and there is no need to maintain water pressure, such as may

be the case at power plants using open cycle cooling. Since

a conventional growing environment can be maintained, sur-

face heating may be a preferred alternative to evaporative

pad heating where water temperatures are low, although water

usage and supplemental fuel requirements of surface heating

are comparatively high.

Surface heating has been practiced for some time in the

Soviet Union (Minasyan et al. 1978) and has been researched

in the United States as a potential application for CCW from

open-cycle power plants (Braden et al. 1982; Walker, 1978;

Walker and Wells, 1980; Walker et al. 1981; Walker et al.

1982). There is some problem of compatibility of surface

heating with the curved-roof inflated double-polyethylene

covers now common in new greenhouse construction. Addi-

tional structural support is needed for the water delivery

line which is centered over the greenhouse roof. Even dis-

tribution of water flow is also difficult to maintain over

an inflated polyethylene cover.

Fan coil. Commercial waste heat utilization from

heated water has been almost exclusively limited to sources

with temperatures generally above 80 degrees F, and fan coil

heat delivery has clearly predominated in these applications.

- 36 -

The fan coil unit is similar in principle to an engine

cooling system, consisting of a coil through which heated

water is circulated, fan(s) and housing to force air across

the coil. Heated air is distributed through a perforated

polyethylene tube which is attached to the air outlet and

which extends the length of the greenhouse.

Discussions of low-temperature fan coil performance un-

der power plant or simulated power plant conditions are

found in Ashley (1978), Boyd et al. (1978), and Badger et

al. (1981). Tiessen (1983) reports on a fan coil system

using heated water from a Canadian oil refinery at tempera-

tures ranging from 80 to 86 degrees F.

Other. Cornell University has conducted research on an

experimental heating system which uses corrugated plastic

panels for both heat delivery and as bench tops (Stipanuk et

al. 1981). Warm water is circulated through flow channels

extending the length of panels, providing bottom heat for

bench-grown plants. Rutgers University has experimented

with vertical curtain heat exchangers made of black poly-

ethylene over which heated water is distributed (Manning et

al. 1980; Rynk and Mears, 1982). Practical considerations

of greenhouse layout appear to limit the potential useful-

ness of either system. Finally, Detroit Edison has tested

the use of heat pumps to recover heat from CCW at winter

temperatures of 55 to 63 degrees F (Rotz et al. 1981).

Investment costs of heat pump systems are extremely high.

- 37 -

Systems Concepts

The approach to design opti ization of components of

the heat recovery system depends on the division of owner-

ship and managerial responsibilities. Conceptually, a num-

ber of institutional arrangements are possible. Under one

form of organizational structure the waste heat supplier is

also the user, owning and operating the greenhouse complex,

as is the case at the Archer Daniels Midland and South

Carolina Public Service Authority projects. Under a slight-

ly different arrangement the supplier could build and own

greenhouses which would be leased to individual growers. A

number of growers have expressed interest in this approach,

which would minimize grower investment. However, construc-

tion costs may be excessively high if greenhouses are built

by utilities, and this cost must ultimately be passed on to

growers. At the Drax power station, greenhouses and the CCW

delivery system are jointly owned by the grower and the

utility, with the grower responsible for greenhouse manage-

ment and the utility responsible for management of CCW deli-

very and return. Another possibility would be for the util-

ity to design, own and manage the entire heat recovery sys-

tem including greenhouse heat exchangers, with growers re-

sponsible only for greenhouse construction and management.

Another alternative would involve the creation of an

independent developmental authority to construct and manage

the waste heat delivery system. Such an authority has been

established to market waste heat from the Department of

- 38 -

Energy's gaseous diffusion plant at Piketon, Ohio. The sale

of tax-exempt bonds to finance construction may be a possi-

bility under this approach. The creation of a separate ad-

ministrative organization may, however, impose a heavy bur-

den of overhead expense on small and medium-scale projects.

Under the prevalent institutional arrangement utilities

deliver heated water to greenhouse sites, with growers re-

sponsible for design, construction and management of green-

houses, including heating systems. This is the approach

taken by Northern States Power, Pennsylvania Power and

Light, and the Power Authority of the State of New York, and

this is the institutional arrangement relevant to this

study. Nevertheless, insight may be gained by first con-

ceptualizing the design problem from the perspective of in-

tegrated ownership and management of the entire heat re-

covery system.

Integrated Systems

Schisler et al. define an integrated system as one

where the size of the components, or their arrangement, or

their operation is chosen to optimize a criterion (1976, p.

6A3). Principal components of the heat recovery system are

pumps, pipeline, heat exchangers, valves, and instrumenta-


Cultural requirements of crops establish minimum

acceptable air temperature settings for day and night

operation respectively, with some leeway for discretionary

control by growers. For a greenhouse structure of given

- 39 -

design and orientation, heat load varies with desired green-

house temperature, ambient temperature, solar insolation,

wind speed and direction, relative humidity, cloud cover,

and latent heat stored in the greenhouse floor and contents.

Although a major portion of annual heating requirements may

be met from CCW, we assume that a fossil fuel backup heating

system sized to design heat load must be installed.

For a given n-year joint distribution of greenhouse

heat loads and CCW temperatures, total n-year operating cost

depends on design and capacity of the waste heat recovery

system, CCW flow rates, and future prices of electricity and

fossil fuel used for backup and supplemental heating. For

any type of heat exchange technology, an inverse relation-

ship is observed to exist between investment in heat trans-

fer capacity and water flow requirement to deliver heat at a

specified rate under a given set of operating conditions

(McBean et al. 1980). Thus, as investment in heat exchange

capacity increases, electrical pumping costs and required

investment in delivery system capacity (pipeline and pumps)

are reduced. The investor faces tradeoffs between invest-

ment and operating costs in sizing heat exchangers. Fur-

thermore, there exist other tradeoffs among investment costs

of system components and among investment and operating

costs of components which need to be considered in the

design process, and which complicate any procedure for

optimization. To achieve a given CCW delivery capacity, for

example, there are multiple configurations of pipeline and

- 40 -

pump designs, each of which may differ in investment and

operating costs.

Design alternatives may be ranked by estimating present

value of greenhouse heating costs over a specified time-

frame. The present value method is a commonly accepted

technique used by the electric utility industry in the com-

parison of investment alternatives and in the justification

of investment decisions to investors and state regulatory


Combined Systems

A combined system is one consisting of two or more in-

dependent components. The heat recovery system is appropri-

ately analyzed as a combined system if ownership and manage-

ment of the CCW delivery system are separate from that of

heat exchange systems. Such is the case if greenhouse firms

are free to design and operate their own heat exchange sys-

tems, with CCW supplied by the utility on demand. Con-

ceivably growers would then want to design their heating

systems and operate them so as to minimize heating costs,

without regard for the capital and operating costs of CCW

delivery. The utility then faces the problems of waste heat

valuation and pricing, and of designing a delivery system to

accommodate an unknown proportion of greenhouse heating re-

quirements for an undetermined acreage, without knowledge of

how individual growers will operate their heating systems.

The customary approach has been to estimate the maximum

acreage and the peak flow requirement per acre based on an

41 -

assumed greenhouse heat exchange capacity, given the set of

design operating conditions specific to a particular site.

Even if maximum acreage is accurately predicted, there

remains uncertainty about heat exchanger design, capacity,

and operational strategies of growers, all of which are

likely to be influenced to some extent by the rate


Context of the Study

This chapter opened with a review of the status of com-

mercial development of low-grade waste heat for greenhouse

heating, in which existing institutional arrangements and

pricing modes were discussed. Basic physical properties of

the heat recovery system were next considered briefly, fol-

lowed by a review of alternative heat exchange technologies.

The final portion of the chapter dealt with systems con-


It was noted in the discussions on systems concepts

that the approach to design optimization of heat recovery

system components and control of heat exchange systems de-

pends on whether the utility designs and operates the entire

heat recovery system as an integrated system. A very dif-

ferent set of problems emerges when greenhouse firms are

free to design and operate their own heating systems. From

an integrated systems perspective, valuation of waste heat

is required for assessments of economic feasibility, but not

pricing. From a combined systems approach, both valuation

- 42 -

and pricing are necessary steps in appraising financial fea-

sibility. The possible influence of pricing on heating sys-

tem design and operating strategies of growers makes pre-

diction of CCW delivery system flow requirements difficult.

While either systems approach presents challenging pro-

blems for economic analysis, the focus of this study will be

on a combined systems approach. Although there are

precedents for an integrated systems approach to waste heat

commercialization (Archer Daniels Midland and South Carolina

Public Service Authority), a combined systems approach has

predominated, wherein the CCW delivery system is under the

domain of the power plant and heat exchange systems are de-

signed, owned, and operated by growers. Work in this area

is therefore expected to apply to a larger audience.

There are two reasons for the prevailing dichotomy of

ownership and management of heat exchange from that of CCW

delivery. First, less investment is required by utilities.

The probability of interference from state regulatory com-

missions is perceived to be directly related to the amount

of utility capital required for the commercialization ven-

ture. Secondly, growers are reluctant to relinquish com-

plete control over design and operation of heating systems.

McBean et al. (1979) have suggested that an inconvenience

cost is associated with the use of CCW from an electric gen-

erating station as opposed to an individually-owned and con-

trolled burner. Any perceived inconvenience cost can be

- 43 -

minimized by allowing maximum freedom to growers in design

and operation of heating systems.

The pricing analysis of Chapter III and subsequent mod-

eling of heat exchanger and heating system control assume

low-temperature fan coil units provide heat exchange capac-

ity. This technology is dominant in practice where CCW

temperatures remain above about 80 degrees F. Analysis of

fan coil heating therefore has a wider audience, and models

of fan coil systems have a greater potential for practical

applications, particularly as increasing volumes of CCW

become available from power plants operating closed-mode

cooling systems.


Involvement of utilities in waste heat recovery on a

commercial scale requires compensation for the delivery of

reject heat to greenhouses. Costs incurred by utilities in

the process are dependent not so much on amounts of heat re-

covered by greenhouses as on design and installed capacity

of heat exchange systems, heat loads, water temperatures,

and heating system control strategies. If ownership and

control of heat exchange systems are separate from that of

the warm water delivery system, the utility is appropriately

viewed as supplier of a commodity--heated water--for which

there exists some sort of demand function. Knowledge of the

demand function is needed to establish delivery system de-

sign criteria and to assess financial feasibility.

Systems analysis techniques may be employed to discover

much about the nature of the warm water demand function and

how it may relate to various economic parameters of the heat

recovery system. Bender et al. define systems analysis as

"a management tool for maximizing profit (or efficiency,

yield, etc.) by minimizing costs and/or optimizing the use

of available resources" (1976, p. 1). Chorafas defines a

system as "a group of interrelated elements acting together

- 44 -

- 45 -

to accomplish a predetermined purpose" (1965, p. 2). Sys-

tems research is used to establish design criteria of new

systems and for the prediction of system behavior. In this

study we are concerned with the specification of design cri-

teria for the heat recovery system and prediction of its be-

havior. McMillan and Gonzalez (1965) delineate a four-step

systems analysis procedure:

1. conceptualization of the system configuration
in terms of components and their relationships.

2. construction of a computer model of the theore-
tical system,

3. specification of inputs like those in the real
system for processing within the framework of
the model, and

4. an attempt to produce outputs from the model
that correspond to the real world.

In the previous chapter a general conceptualization of

a heat recovery system configuration was presented in terms

of components and their relationships. Chapter III first

explores theoretical principles of systems design and opera-

tional criteria from an integrated-systems approach, fol-

lowed by examination from a combined-systems perspective, to

gain insight into the basis for interface of subsystems un-

der separate ownership and control. Essentially the basis

for interface of warm water delivery and heat exchange sys-

tems is a user rate structure acceptable to both utility and

growers. Theoretical implications of pricing alternatives

are therefore discussed, with particular emphasis given to

- 46 -

volumetric pricing of warm water as a control variable or

policy device available to utilities.

Decision Context of Integrated Systems

The reject heat recovery system is itself a subsystem

of the much larger power plant cooling system. Major compo-

nents of the cooling system without heat recovery are the

cooling towers and basin, pipelines connecting condensers

to cooling towers, pumps, valves and instrumentation to

maintain CCW flow rate, pressure, and temperature within

specified tolerance limits.

The upper portion of figure 3.1 shows primary inputs

of the cooling system without heat recovery. The lower

portion of the figure depicts a cooling system with heat

recovery. Heat recovery increases use of electricity for

operation of pumps and fans and requires capital inputs as

outlined in Chapter II. With proper design and instrumen-

tation, labor and management requirements may be met by the

existing work force. Total heat rejection is unchanged from

that of the system without heat recovery, with the amount

rejected from cooling towers reduced by the sum of green-

house use and heat losses along CCW transmission lines.

The upper portion of figure 3.2 depicts conventional

greenhouse heating with fossil fuel as the principal input.

The lower portion of the figure depicts a waste heat system

with conventional fossil fuel backup and supplemental

- 47 -

labor and
repair and

Reject heat

IPower Plant Cooling System
I with Heat Recovery

labor and reject heat
anagementect heat
repair and

electricity 7 / / / / 1

capital / greenhouse heat
equipment (CCW)
labor and /
Management ---------
',or heat recover. y sstem___

Figure 3.1. Schematic of waste heat systems.


-- - -- -------- I__ __ _

- 48 -


labor and

fossil fuel


Waste Heat System with
Fossil Fuel Backup

Figure 3.2. Schematic of greenhouse waste heat

- 49 -

heating. Waste heat, together with increased inputs of

capital, electricity, and labor and management substitute

for most of the fossil fuel heating requirement. In both

cases the amount of heat input into the greenhouse is the


Econonomic and Financial Context

For a known greenhouse acreage and design, assume that

the entire heat recovery system (including greenhouse heat

exchangers) is designed, owned, and operated by the utility,

which delivers heat to growers on demand. There are two fa-

cets to the "optimization" problem: system design and system

control. Objectives are to identify the system design and

operational strategy which minimize total cost of heating,

given known variabilities in greenhouse heat loads and heat

content of CCW. In this context, optimization is not in-

tended in a rigorous sense, but rather as a process of iden-

tifying preferred courses of action through comparisons of a

limited number of plausible alternatives.

Assume as given a CCW delivery system design and capac-

ity, heat exchanger design, periodic heat load and CCW tem-

perature. Heat delivery per unit of time (Q) can be approx-

imated by

f(FR,ETD,Q) = 0


- 50 -

where ETD is the temperature differential between CCW and

greenhouse air entering the heat exchanger and FR is a

periodic flow rate. Figure 3.3 shows a typical heat ex-

changer performance curve (in this case a fan coil unit).

The following conditions are observed to hold for water-to-

air heat exchangers in general,

fl > 0 f11 < 0

f2 > 0 f22 = 0 (3.2)

f12 = 21 > 0

where fl and fll are the first and second partial deriva-

tives of Q with respect to FR, f2 and f22 are the first and

second partial derivatives of Q with respect to ETD, and fl2

and f21 are second cross partial derivatives. The condition

f22 = 0 is assumed to hold over the limited range of values

of ETD encountered in low-grade waste heat recovery, but

does not strictly hold over broader ranges. Setting dQ = 0

and by the implicit function rule,

dETD 1_
d f 0 (3.3)
dFR f

- 51 -

(G(130,/) l11!u1191J!p ajniJBedwue, lo eejbap jed C


- 52 -

By further differentiation of (3.3) and conditions (3.2),

2 2
2 -(f f 2- 2f ff + f f2)
d ETD (fllf2 12 1 f2 22fl)
------ > 0 (3.4)
dFR2 f

(Henderson and Quandt, 1971, p. 400). Equations (3.3) and

(3.4) describe the heat transfer isoquant, i.e., the locus

of all combinations of warm water flow rate and entering

temperature differential which deliver heat at a given rate

under conditions of continuous operation. Three curves from

a family of heat delivery isoquants are shown in figure 3.4.

As the entering temperature differential varies, whether

due to fluctuations in CCW or greenhouse air temperatures,

a constant heat delivery rate can be maintained within

limits by offsetting adjustments of water flow rates.

Now consider a fixed heat load per period of time Q0)

with entering temperature differential ETD(0). Point A of

figure 3.4 corresponds to continuous operation at the min-

imum technically viable flow rate FR(0). Points B and C are

alternatives where instantaneous rates of heat delivery are

increased, allowing the same heat load to be met by inter-

mittent operation of the heat exchanger unit. It is pos-

sible to operate at any flow rate greater than or equal to

FR(0) up to a physical limit imposed by design constraints

with the fraction of time in operation inversely related to

flow rate, ceteris paribus. Admitting the possibility of

- 53 -




&g (0) ET---- -----
) Q(2)

-------------- QM0

0 FR')
water flow rate (FR)

Figure 3.4. Characteristic heat transfer isoquants of
a water-to-air heat exchanger.

- 54 -

intermittent operation, the heat recovery relationship can

be expressed as

f(FR,ETD,OT,Qr) = 0 (3.5)

where ETD is entering temperature differential, FR is the

periodic flow rate while in operation, OT is fractional op-

erating time, and Qr is the periodic heat input requirement

of the greenhouse. It follows that

OT = (3.6)

where Q is the heat delivery rate during operation. Given a

range of technically feasible flow rates at a given ETD,

there is a single flow rate which minimizes periodic opera-

ting cost.

Periodic heat transfer is calculated as

Q = s-V-WTD (3.7)

where s is the specific weight of water, WTD is the water

temperature drop through the heat exchanger, and V, the per-

iodic volume of warm water used is calculated as



- 55 -

A characteristic of water-to-air heat exchangers is that

< 0 (3.9)

which for given periodic heat transfer implies

9V (3.10)
FR > 0


T < 0 (3.11)

For fixed periodic heat load Q(0), the effect of in-
creasing flow rate above FR(0) (figure 3.4) is to increase

the total volume of water used and to reduce elapsed oper-

ating time. What are the implications for periodic operat-

ing cost? As flow rate increases, pump electrical consump-

tion is increased due to increased friction losses through

pumps, pipeline, valves, and heat exchanger coil and also

due to the increased volume of water transported. On the

other hand, fan electrical operating cost, being approxi-

mately proportional to elapsed operating time, is reduced

with increases in flow rate. Figure 3.5 demonstrates these

relationships for a given heat load and entering temperature

- 56 -


o 0
o0 a. U a:



I m

I \0

I \
II -,


L .


- -LL +J

0 4-'
Iso ado poad
/ / \ *)

/ / \ )5 J

(TI)10 6U


- 57 -

differential. Curve F shows fan electrical operating cost

as a function of FR.

Taking the partial derivative of OT with respect to FR

and by conditions (3.2)

OT -Qr f1
R- < 0 (3.12)
aFR 2

Differentiating (3.12) further and again by conditions


(0) 2
20T Q 0 (2f Qf )
> 0 (3.13)

implying the convexity of curve F since periodic fan elec-

trical operating cost is approximately proportional to

elapsed operating time. Also observe that curve P, which is

periodic pump electrical operating cost, is convex

(Henderson and Perry, 1966, p. 105). Curve OC is the sum of

periodic fan and pump electrical operating costs, and as the

sum of two convex functions having opposite first deriva-

tives, is also a convex function, with a unique minimum over

a given range of flow rates (point B of figure 3.5).

For a heat recovery system of given design it is pos-

sible to determine periodic CCW flow and operating cost for

any specified set of operating conditions. Furthermore,

given a known joint probability distribution of greenhouse


- 58 -

heat loads and CCW temperatures over a specified timeframe

(one heating season), heating system operation can be simu-

lated and peak flow rate, total periodic water usage, and

electrical operating cost estimated. Power stations

routinely maintain requisite historical weather data and CCW

temperature records suitable for simulation work.

Operating and capital cost estimates of design alterna-

tives provide inputs for financial evaluations. A commonly

used criterion for ranking of investment alternatives in the

electric utilities industry is present value (PV). Equation

(3.14) provides a framework for comparison of heat recovery

system design alternatives by calculation of n-year after-

tax heating costs

n (1 m) x xt + Pt mdt ct
PV = p + j= (3.14)
t=l (i + 1)


c = investment tax credits utilized.

d = depreciation reported for calculation of income tax.

i = discount rate (decimal fraction).

m = marginal income tax rate (decimal fraction).

n = timeframe of analysis (years).

p = value of equity funds applied to capital expenditures
and debt retirement.

t = year.

- 59 -

x1 = electricity expense.

x2 = fossil fuel expense.

x3 = repair and maintenance expense.

x4 = property tax and insurance expenses.

x5 = interest on long-term indebtedness.

Application of the present value method to evaluations of

energy systems is discussed in Williams and Bloome (1980).

Regulatory issues. Electric utilities are public mo-

nopolies created with the objective of providing electricity

to users at the lowest possible cost, and as such, are ans-

werable to state regulatory commissions which monitor their

performance relative to that objective. Other regulatory

agencies include the United States Environmental Protection

Agency and the Nuclear Regulatory Commission. State regula-

tory commissions limit profits to a maximum percentage of

the "rate base," which in general consists of the net or de-

preciated value of original plant investment. To the return

allowed on the rate base are added the cost of fuel, opera-

tion and maintenance expenses, labor, insurance, and any

taxes paid (Marsh, 1980).

The existing institutional framework of public utili-

ties regulation has been identified as tending to promote

adherence to traditional business practices and to discour-

age innovation in the area of thermal service (Donnelly and

Sewell, 1980, p. 212). The involvement of utilities in

- 60 -

waste heat commercialization tentatively raises several

regulatory issues including

1. proper allocation of costs;

2. the pricing of thermal service;

3. the mechanics of financing waste heat recovery
facilities and;

4. the security of thermoelectric generating sta-

(Donnelly and Sewell, 1980; Kelly, 1980; Reid, 1981).

Electrical ratepayers argue for reductions in electri-

city rates and a transfer of some of the costs of production

over to waste heat users (McBean et al. 1979). Lindsay

contends, however, that if the heat marketed can be con-

sidered a by-product of electricity production, the alloca-

tion of costs to the by-product can be made on an incremen-

tal cost basis (1972). This has been the de facto position

taken by Northern States Power, Pennsylvania Power and

Light, the Power Authority of the State of New York, and the

Tennessee Valley Authority. Ontario Hydro also considered

only incremental costs in the proposed development of the

Bruce Energy Centre (McBean et al. 1979, p. 688). Costs

assignable would accordingly be carrying charges on incre-

mental capital expenditures plus incremental operation and

maintenance expenses. To these costs could be added the

cost of any loss in efficiency of power production and any

other separable costs, and a credit could be allowed for any

avoided costs of heat dissipation.

- 61 -

Kelly suggests that rates might be established based on

value of service, rather than incremental costs or allocated

costs (1980). With value of service pricing, rates are set

as high as the market will bear. A precedent for value-of-

service pricing exists in the determination of telephone


Cash flow considerations give rise to another regula-

tory concern. While present value and internal rate of re-

turn studies may show favorable prospects for long-term suc-

cess, large-scale commercialization projects may initially

experience several years of underutilized capacity and ad-

verse cash flow. Thus, a transitory period is anticipated

during which time electric ratepayers subsidize waste heat

development, raising the issue of future reimbursement of

ratepayers. Even where rate of return estimates indicate

probable recovery of investment at a high rate of return,

regulatory constraints on maximum earning rate could remove

the incentive for commercialization.

Since operating costs of heat recovery are relatively

insignificant and easily recovered, the primary concern of

regulators is with capital cost. The ease with which regu-

latory approval is obtained may be inversely related to the

level of proposed capital investment. Consequently, utili-

ties may be inclined toward minimization of capital invest-

ment, which could be manifested either in a preference for

small-scale projects or in a bias toward minimization of

investment per unit of greenhouse production area. "Under

- 62 -

today's laws, there is no incentive for a utility to spend

capital to utilize waste heat" (Brown, 1980, p. 72).

Technical Context

Power plant cooling system. For a given cooling tow-

er design, CCW temperature varies with ambient meteorologi-

cal conditions, unit load, and CCW system flow rate. Unit

load fluctuates in accordance with customer demand and the

operating status of other generating units in the power sys-

tem. Diurnal, weekly, and seasonal cycles are observed in

electrical demand, which together with seasonal variations

in makeup water temperature, give rise to predictable varia-

tions in CCW temperatures.

Power stations are designed and operated to maximize

electrical energy production relative to fuel consumption

and therefore, to minimize the loss of energy (Iverson et

al. 1976). Condensers and turbines are designed to be

compatible in order to achieve the optimum electrical gen-

eration for the expected range of recirculating water tem-

peratures (Brown, 1980). The efficiency of electricity

generation depends on turbine exhaust pressure, which varies

with the temperature of condenser cooling water. From the

point of view of thermodynamic cycle efficiency, it is de-

sirable to condense steam and reject heat at the lowest

practical temperature (Conrad and Munson, 1982; Marsh,


- 63 -

Since the value of CCW to users is directly related to

temperature, some sacrifice in efficiency of electrical pro-

duction might be justified to achieve more revenue from heat

recovery. Augmentation of heat content in CCW does not,

however, guarantee full utilization of added heat, and only

in the unlikely event of utility control of greenhouse heat

recovery might it be possible to estimate marginal revenue

potential. The value of energy as electricity is substan-

tially greater than the value of energy as low-grade heat,

and heat recovery rates are likely to be variable and diffi-

cult to control. It is therefore unlikely that state regu-

latory agencies will be receptive to proposals for augmenta-

tion. Cordaro and Gross suggest that "the generation of

electricity must come first and any concept which interferes

with that from an efficiency or economic point of view will

not be acceptable (1979, p. 2,441).

Greenhouse waste heat utilization is not expected to

significantly reduce cooling tower operating costs, since

heating demand is intermittent and seasonal, and negligible

volumes of water are needed. Neither can cooling tower ca-

pacity be reduced, given the seasonality of heating demand.

Care must be exercised that operation of the heat recovery

system not interfere with normal operation of the power

plant cooling system. This may require the installation of

special controls, instrumentation and valves to maintain

pressures, direction and rate of flow. A control panel may

be needed in or near the power plant control room which is

- 64 -

connected to all recorders, indicators, and motorized con-

trol valves in the heat recovery system.

CCW delivery system. The delivery system transmits CCW

to greenhouses and returns it to the cooling tower basin. A

minimum flow velocity of one to two feet per second must be

maintained at all times to prevent settling of solids and

formation of air pockets. Flows greater than ten feet per

second can result in excessive loss of pressure and erosion.

Air and vacuum releases are recommended at all potential air

trap points. All low points should be provided with drain

lines. Pipe should be buried, preferably with a gravel,

sand or fly ash backfill. Valves and flanges may be in-

stalled at extreme points for future extension of lines.

Taps are also needed for instruments to monitor water flow

rates, temperatures, and possible heat recovery. One-way

valves control the direction of flow throughout the system.

If existing pumping capacity of the power plant cooling

system is inadequate, additional pumps must be added. At

least three pumps should be installed to assure efficient

operation and reliability. Pressure switches control se-

quencing of pumps as greenhouse demand for CCW fluctuates.

A control valve is needed between the supply and return

headers, controlled by a pressure differential controller,

to maintain the desired pressure differential so that users

at the greatest distance from supply pumps have sufficient

pressure for proper operation of control valves under all


- 65 -

Greenhouse. The primary concern of growers is with

maintenance of desired minimum temperatures. Reliability of

heated water supply is an important consideration. Loss of

heat in the greenhouse, even for a few hours, can be disas-

trous. Loss of heated water can occur as a result of simul-

taneous outages of all power plant generating units, or due

to pump or pipeline failures. There are known probabilities

for occurrences of unscheduled unit outages from which prob-

abilities of heated water availability at any given time can

be calculated. The probability of failure of a well-de-

signed delivery system is remote, but failures have occurr-

ed, due to unforeseen conditions. Delivery system failures

occurred during initial phases of operation at both the

Northern States Power and Power Authority of the State of

New York projects.

However small the probability that warm water will be

unavailable at any given time, a backup and supplementary

fossil fuel heating system is strongly recommended, sized

for 100 percent of design heat load. It is therefore un-

necessary that a heat exchange system be sized for design

heat load, and to do so may result in an unjustifiable du-

plication of heating capacity. For a given design, heat ex-

change capacity is defined in terms of entering temperature

differential and flow rate, and determination of optimum

capacity is appropriately a problem for economic analysis.

- 66 -

Decision Contexts of Combined Systems

Power Plant Perspective

As mentioned earlier, it is more difficult to predict

the CCW flow profile when growers install and operate their

own heating systems. Consequently, greater uncertainty at-

taches to estimates of periodic pumping costs per unit of

greenhouse production area. A volumetric charge on CCW use

may be a means of reducing uncertainty by narrowing the

scope of feasible design alternatives and operating strate-

gies economically attractive to growers. The implications

of volumetric pricing will be discussed in some detail in a

later section.

Allocation of pumping capacity can present problems in

a multiple-user network operating at or near peak flow.

This potential difficulty might be simply avoided by mechan-

ical restriction of peak flow per unit of production area.

As an alternative, the use of demand and/or volumetric

charges is a less restrictive means of allocation which may

be preferable to mechanical flow restriction from a grower


Maintenance of delivery capabilities to all users re-

quires maintenance of specified water pressure differen-

tials. Decentralized operation of heat exchangers compli-

cates control of pressure differentials. Utilities can im-

pose a limitation on allowable water pressure drop through

heat exchangers to maintain required pressure differentials

in the distribution and return network. Imposition of a

- 67 -

pressure drop or head loss constraint may create a modest

pumping requirement for growers, depending on design and

flow rate.

Greenhouse Perspective

Because growers must make a substantial long-term com-

mitment of capital to utilize waste heat, long-term pricing

agreements are expected. Long-term pricing facilitates fi-

nancial evaluation of investments in heat exchange systems.

The price of waste heat may be tied to a price index of a

designated fossil fuel. Savings in heating system operating

cost must be sufficient to justify incremental capital in-

vestment as well as any locational and inconvenience costs

as perceived by growers.

Basis for Combined Systems

The basis for combined systems is a user rate structure

which is acceptable to both utility and growers. The cost

of heating with condenser cooling water needs to be somewhat

below fossil fuel heating cost, with some sort of contrac-

tual guarantee that initial cost relationships will not

shift adversely for a specified period of time. Utilities

must receive sufficient compensation for supply of CCW to

cover delivery system investment and operating costs and

provide a rate of return at or above the rate earned on pow-

er investments.

The usual impasse in waste heat commercialization

schemes is in the elaboration of a pricing mechanism,

- 68 -

without which the heat recovery problem is insufficiently

defined for financial evaluations from either a supplier or

user perspective. Specification of a rate structure is a

crucial preliminary step which gives definition to the pro-

blem. There are basically three pricing alternatives open

to utilities: the flat periodic access fee, the heat

recovery charge, and volumetric pricing of CCW.

Flat access fee. The flat access fee is an annual

user charge levied for use of warm water as available.

Charges may be subject to periodic adjustments as stipulated

by contractual agreement. Other than possible penalties for

exceeding flow rate limitations, charges are not related to

flow rate, and in any event, are not tied to total usage or

amount of heat recovered. Charges may be determined by such

factors as amortization of delivery system investment cost,

recovery of repair and maintenance expenses, and pumping and

administrative costs.

In multi-user networks, access charges can be prorated

according to production area or peak flow. Peak flow

charges can be objectionable since peaks in usage may result

from sudden unexpected drops in CCW temperature. Compared

with other pricing modes, the flat access fee is simple and

easily administered. If used as the sole basis for charges,

growers know approximate total seasonal heating costs in ad-

vance, regardless of CCW temperature profile and seasonal

heat load, and CCW reliability becomes the principal risk


- 69 -

Heat recovery charge. Heat utilization can be esti-

mated by metering devices which monitor water flow rate and

temperature drop through heat exchangers. The heat meter

performs heat recovery calculations approximating the value

of the integral given in equation (2.1)

Q = m fcdT

Total heat recovery (Q) for a billing period divided into n

discreet time intervals can be approximated by

Q = s I FRtWTDt (3.15)

where s is the specific weight of water, FR is periodic warm

water flow and WTD is water temperature drop through the

heat exchange system. As n goes to infinity, the value of

(3.15) approaches the value of the integral.

By pricing on a heat recovery basis, the precise cost

of heat is known and unit cost of heat is invariable with

fluctuations in warm water and greenhouse air temperatures

and water flow rate. Heat recovery pricing facilitates cost

comparisons between waste heat and conventional heating sys-

tems upon which investment decisions are based.

Heat metering may be expensive and difficult, since

volume, flow rate, and temperature must be measured, corre-

lated, and integrated (Olszewski, 1980). Reliability,

initial investment cost, and repair and maintenance costs of

- 70 -

instrumentation should be taken into account in deciding

whether to price on a heat recovery basis.

CCW volumetric pricing. With volumetric pricing us-

ers are billed in proportion to warm water usage without re-

gard for heat content or heat recovery. The argument usu-

ally advanced for volumetric pricing is that a pumping

charge is needed to create a reasonable relationship between

operating costs incurred by the utility and charges to grow-

ers. From the utility perspective, volumetric pricing over-

comes a potential difficulty encountered with both access

and heat recovery pricing. Under typical operating condi-

tions there is a range of possible flow rates at which an

hourly heat load can be met. Users paying either a flat ac-

cess fee or heat recovery charge but no volumetric charge

find that heating system operating costs decline with in-

creases in flow rate, ceteris paribus. This is true with

access and heat recovery pricing because the only variable

cost affected by flow rate is fan operating cost, which is a

decreasing function of flow rate.

Assuming a volumetric charge is levied, the periodic

operating cost function of the fan coil heat exchanger be-


OC = W + F


- 71 -

where W is the cost of CCW and F is electrical operating

cost of the fan(s). Further, we define W and F as

W = P -V (3.17)

F = K-OT (3.18)

where V is the volume of CCW used, P is the volumetric
price of CCW, K is the periodic electrical operating cost of

the fan(s) for continuous operation, and OT is the fraction

of time the heat exchanger is in operation. Differentiating

W with respect to FR gives

W 9V
S P = P *OT > 0 (3.19)
aFR w 9FR w

by (3.8), and differentiating a second time gives

< OT 0 (3.20)
FR2 w FR

by (3.11). Differentiating F with respect to FR gives

RF K 2OT < 0 (3.21)

by (3.11), and differentiating a second time gives

K > 0 (3.22)

- 72 -

by (3.13). As the sum of two convex functions having first

derivatives of opposite signs, OC is therefore a convex

function with a unique minimum over any feasible range of

CCW flow rates. If periodic heat delivery capability ex-

ceeds periodic heat load, OC is minimized where

9OC _W 3F

= P-OT + K 9FR 0 (3.23)

The curves of figure 3.6 depict the cost relationships.

Suppose a CCW price and environmental conditions such that

W(0) and OC(0) are the CCW and total operating cost curves.

Operating cost is minimized at instantaneous flow rate

FR0). Now consider the effect of an increase in P on the
cost-minimizing CCW flow rate. Differentiating (3.23) with

respect to P gives

-P = OT > 0 (3.24)

Curves W and OC are shifted upward to W() and OC The

slope of the new operating cost curve OC(1) at FR(0) is pos-

itive, implying that the new operating cost minimum occurs

to the left of the previous minimum. The new cost-mini-

mizing flow rate becomes FR (). A cost-minimizer responds

to increases in CCW price by reducing flow rates as long as

- 73 -



W ()

FR'' FR(O0
warm water flow rate (FR)

Figure 3.6. The cost-minimizing warm water flow rate is
reduced as volumetric price increases.

- 74 -

it is possible to do so and maintain the desired amount of

heat delivery per period of time.

Figure 3.7 illustrates what occurs as CCW price in-

creases. Starting at the price corresponding to curve OCO)

with optimum flow rate FR(0), successive price increases re-

duce flow rates and increase heat exchanger operating cost.

As this occurs, the amount of heat recovered per volume of

water delivered to the greenhouse is also increased, ceteris

paribus. Flow rate FR(4) corresponds to the minimum level

at which the periodic heat load can be met, and operation is
continuous at FR At all flow rates greater that

FR (4), cost-minimizing flow rate is a decreasing monotonic

function of water price. At point E however, further

increases in price shift the operating cost curve upward but

have no effect on CCW usage. From equation (3.8) it follows

that the periodic volume of warm water (V) used is also a

decreasing monotonic function of water price up to a point.

That point depends on the heat delivery requirement and the

entering temperature differential.

Figure 3.8 shows a representative CCW demand curve, the

location of which, given a heat exchanger design and

electricity price, depends on heat load and entering temper-

ature differential. The perfectly inelastic portion of the

demand curve corresponds to operation at the minimum flow

rate capable of meeting the periodic heating requirement.

Setting a water price at or above P forces continuous

operation of the heat exchanger and maximization of heat

- 75 -

$ OC (5) OC(4)

OC (3)





i I i I I

FR(4) FR(3) FR(2) FR(1)FR(O) FR
warm water flow rate

Figure 3.7. Successive increases in volumetric price lead
to successive reductions in flow rate to deliver a fixed
periodic heat load.


CCW usage per unit of time (V)

Figure 3.8. A characteristic condenser cooling water
demand curve.

- 76 -

- 77 -

recovery per volume of CCW delivered to greenhouses.

Intermittent operation of the heat exchanger occurs at any

price below P and delivery system pumping requirements to

meet the same greenhouse heat load are greater.

Note that with volumetric pricing, CCW operating cost

is strictly proportional to volume of water used, while the

partial derivative of heat recovery with respect to FR is a

concave function.

The concavity of the heat recovery equation implies

convexity of the marginal cost curve,

MC (3.25)

As flow rate is increased in response to an increasing heat

load, the marginal cost of heat from CCW rises at an in-

creasing rate. If the marginal cost of heat from CCW

reaches the cost of heat from the supplementary fossil fuel

system, a cost minimizer responds to further increases in

heat load by operating the supplementary system. Volumetric

price determines the flow rate at which the marginal cost of

waste heat equals fossil fuel heating cost at any given lev-

el of ETD. The horizontal line F of figure 3.9 represents

fossil fuel heating cost. The maximum economically viable

flow rate at a given price and entering temperature dif-

ferential is determined by the intersection of the MC curve

with line F. Since the cross partial derivative of flow

- 78 -


warm water flow rate (FR)

Figure 3.9. The marginal cost of heat from condenser
cooling water as a function of flow rate.

79 -

rate with respect to entering temperature differential is

positive (conditions (3.2)), the effect of an increase in

ETD is to shift the MC curve to the right, increasing maxi-

mum economically viable flow rate. Also observe that an in-

crease in volumetric price shifts the marginal cost curve

upward, since the partial derivative of operating cost with

respect to volumetric price is positive. A price increase

therefore reduces maximum viable flow rate, and potentially

increases reliance on supplemental heating systems.

Investment mix with volumetric pricing. The potential

impact of volumetric pricing on grower investment in heat

exchange capacity needs to be carefully considered in design

of CCW delivery systems. Volumetric pricing conceivably

impacts optimal investment in heat exchange capacity and the

optimal volume of water used to meet any heat load. Higher

prices produce an incentive to economize on water use. From

an operational perspective this translates into reductions

in the volumes of water used to meet periodic heat loads

under specified sets of operating conditions. From the de-

sign perspective, a warm water operating cost advantage is

realized by increasing investment in heat exchange capacity,

which may or may not yield a net operating cost reduction,

depending on fan and pump horsepower requirements and the

price of electricity relative to the water price. Price-in-

duced increases in heat exchange capacity also reduce reli-

ance on supplementary heating, producing the countervailing

effects of increasing peak flow rates and annual usage.

- 80 -

Financial appraisal. A combined systems approach re-

quires analyses of CCW delivery and heat exchange systems

from different perspectives. If growers can be assumed to

approximate cost-minimizing behavior, the use of CCW price

as a policy variable greatly narrows the range of probable

design alternatives and operating strategies, giving defini-

tion to the problem for financial appraisals from both user

and supplier perspectives.

Simulation studies of greenhouse heating systems can

produce estimates of periodic operating costs under differ-

ent investment and pricing scenarios. These estimates pro-

vide inputs for present value studies of CCW delivery and

heat exchange systems from utility and grower perspectives

respectively. Equation (3.26) presents a net present value

(NPV) equation for evaluation of the CCW delivery system

from a utility perspective.

n (l-m) (rt- I xjt) -Pt +mdt +ct
NPV = -p + j=l (3.26)
t=l (1 + i)


c = investment tax credit utilized.

d = depreciation reported for calculation of income tax.

i = discount rate (decimal fraction).

m = marginal income tax rate (decimal fraction).

n = timeframe of analysis (years).

- 81 -

p = value of equity funds applied to capital expenditures
and debt retirement.

r = revenue from growers.

t = year.

x1 = electricity expense.

x2 = repair and maintenance expense.

x3 = property tax and insurance expenses.

x4 = interest on long-term indebtedness.

Alternatives may be evaluated within the framework of

(3.26) with the objective of maximizing n-year after-tax NPV

of the delivery system. Given the cost escalation index for

waste heat charges, the lower bound for compensation is es-

tablished by the base year value of r in (3.26) such that

NPV equals zero.

Equation (3.27) presents a framework for greenhouse

heating system evaluations,

(1 m) Xjt + Pt mdt ct
PV = -p + j=l t (3.27)
t=l (1 + i)


c = investment tax credit utilized.

d = depreciation reported for calculation of income tax.

i = discount rate (decimal fraction).

m = marginal income tax rate (decimal fraction).

n = timeframe of analysis (years).

82 -

p = value of equity funds applied to capital expenditures
and debt retirement.

t = year.

x, = payment for waste heat.

x2 = electricity expense.

x3 = fossil fuel expense.

x4 = repair and maintenance expense.

x5 = property tax and insurance expenses.

x6 = interest on working capital.

x7 = interest on long-term indebtedness.

The waste heat system (including backup and supplemen-

tal heating) is optimized, and comparative evaluations of an

optimized system with conventional heating options are con-

ducted via equation (3.27). If the PV of heating costs of

the optimized waste heat system is less than the least-cost

conventional alternative, time series of payments for waste

heat can be determined which equalize PV's. If there is a

waste heat cost escalation index specified by contractual

agreement, there is a unique solution for the base-year val-

ue of xl in (3.27). The resulting series defined by the

base-year value and the cost escalation index establishes an

upper boundary for revenue potential from waste heat.

Equations (3.26) and (3.27) are used to establish upper

and lower boundaries respectively for compensation for CCW

delivery. A mutually acceptable solution exists if the

upper boundary is above the lower boundary. Determination


- 83 -

of compensation within the feasible range is a matter for



In this chapter volumetric price was introduced as a

variable of potentially strategic importance to design and

operation of heat exchange systems. Study of the implica-

tions of volumetric pricing therefore has relevance to the

delivery system design and financial feasibility problems.

In the next chapter several computer models are presented,

all of which were written to answer specific but related

questions pertaining to financial aspects of waste heat re-

covery from power plant CCW. Outputs of performance models

of a low-temperature heat exchanger, a greenhouse heating

system, and a CCW delivery system yield inputs to financial

appraisal models. Performance models demonstrate the use-

fulness of volumetric pricing as a control variable under

the assumption that growers operate heating systems so as to

minimize variable operating costs.



The financial feasibility of investment in heat waste

recovery is strongly influenced by long-term trends in fos-

sil fuel prices. Operating costs of heat exchange and warm

water delivery systems depend on patterns of joint occur-

rences of greenhouse heat loads and CCW temperatures, design

and capacity of heat exchange systems, and control strate-

gies of growers. Estimation of operating costs, revenue po-

tential, or revenue requirements is impractical by direct

analytical methods.

The physical properties and quantifiable relationships

of a heat recovery system do lend themselves well to simula-

tion as a technique of analysis. Simulation requires the

construction of mathematical models presenting similarity of

properties or relationships with a natural or technological

system under study. Through simulation "we can preoperate a

system without actually having a physical device to work

with and can predecide on the optimization of its character-

istics" (McMillan and Gonzalez, 1965, p. 15).

Simulation is a problem solving technique frequently

resorted to when systems under consideration cannot be ana-

lyzed using direct or formal analytical methods (McMillan

- 84 -

- 85 -

and Gonzalez, 1965, p. 16; Wright, 1971, p. 25). It is es-

sentially a two-phase process consisting of modeling and

experimentation. In the modeling phase a mathematical model

is developed which is a simplified abstraction of the system

and which is suitable for processing on a computer. The an-

alyst seeks to construct a model that is realistic or that

corresponds to reality in at least a few particulars, while

reducing the problem to manageable proportions. "The value

of a model is judged by the contribution it makes to our

understanding of the system it represents" (McMillan and

Gonzalez, 1965, p. 7).

The material of Chapters II and III conceptualized the

heat recovery system and its major components. Principal

environmental variables were identified, and optimization

criteria were discussed from both integrated and combined

systems pespectives. The context of the study was narrowed

to analysis of a combined systems approach, and implications

of waste heat pricing alternatives were explored in Chapter

III. Both access and heat recovery pricing were observed to

create an incentive for growers to maximize CCW flow rates

through greenhouse heat exchangers. Attention was therefore

focused on volumetric pricing as a means of influencing


- 86 -

design and control of heat exchange systems, hence reducing

uncertainty in the prediction of delivery system flow re-


The introduction of volumetric price as a policy vari-

able raises questions about its effectiveness as a control

device which might influence grower behavior. Clearly, the

institution of volumetric pricing creates an incentive to

increase heat recovery from CCW, thereby reducing investment

and operating costs for CCW delivery per unit area of green-

house heated. However, almost nothing is known about the

level at which CCW price might become a significant factor

influencing investment and control decisions of cost-mini-

mizing growers at any given location.

In this chapter five models are introduced in prepara-

tion for experimentation. These models are processed by two

computer programs, one of which deals primarily with estima-

tion of operating costs, and the other with financial ap-

praisals. The use of computer simulation routines greatly

facilitates experimentation. Experimentation is frequently

used to make comparisons between alternative courses of ac-

tion, to estimate responses of systems to changes in the

level of a single input, and to identify input combinations

yielding optimal or near optimal solutions. Points most

sensitive to managerial interference and policies most


- 87 -

appropriate for effective management are discovered through

experimentation (Dent and Anderson, 1971).

Simulation is usually undertaken because we have
raised questions or posed hypotheses about the sys-
tem behavior under various decision rules. We thus
begin with the purpose of sampling behavior or res-
ponse subject to alterations that are feasible but
about which we have only vague notions of the con-
sequences. (McMillan and Gonzalez, 1965, p. 329)

By processing different sets of inputs within the model

we move toward identification of those values of the control

variables which yield the best solution (Bender et al.

1976). We may evaluate, for example, the impact of volu-

metric pricing on cost-minimizing CCW flow rates and optimal

level of heat exchange capacity with the objective of dis-

covering a relationship between price and delivery system

design requirements. We may derive hourly or seasonal CCW

demand curves given a set of assumptions, and determine the

shifts in demand resulting from changes in such factors as

level of installed heat exchange capacity, electricity and

supplemental fossil fuel prices, greenhouse heat load and

CCW temperature.

Literature Review

A search of the waste heat literature was conducted to

discover modeling techniques which might be included in a

comprehensive scheme of financial appraisal of waste heat

commercialization. Most of the feasibility work in waste

heat use has been done by agricultural engineers and

- 88 -

horticulturists. The focus of interest has been on

technical viability, with only cursory economic analyses

found in most studies. Nevertheless, considerable progress

has been made in identifying important linkages between

technical and economic parameters, and most of the economic

issues have been dealt with to some extent, with the excep-

tion of pricing.

Economic appraisals have generally focused on estimates

of potential savings in fossil fuel expenditures or esti-

mates of net reductions in overall heating system operating

costs resulting from the use of waste heat. Solutions de-

pend on estimates of greenhouse heating requirements, and

the coincidence of heating requirements with heat availabil-

ities from CCW. Greenhouse heating requirements depend on

structural design and orientation, covering, outside and in-

side temperatures, outside dewpoint temperature, wind speed,

and solar radiation. Measurement of heat loads is difficult

because of the many factors involved, but engineers have

provided a basis for computer modeling of greenhouses and

heating systems by developing mathematical relationships de-

scribing heat flows. These relationships have been stand-

ardized and published in the ASHRAE Handbook of Fundamentals

(1972), and Badger and Poole (1979). Power plants routinely

keep records of weather data and CCW temperatures from which

heating requirements and heat availabilities can be


- 89 -

Several models are available for simulation of green-

house heat loads from weather data. Walker (1965) developed

mathematical relationships for predicting greenhouse heat

loads as environmental conditions change. Meyer et al.

(1984) prepared a program for microcomputer to simulate the

greenhouse environment based on daily or hourly summary

climatic data. A weather model written by Degelman (1974)

and frequently applied in waste heat work employs a Monte

Carlo technique to simulate hourly weather parameters for

any location from means and standard deviations of monthly

values for each of the parameters.

The Degelman model was used in waste heat feasibility

studies by Rotz and Aldrich (1979) and Rotz et al. (1981) to

simulate conditions of temperature, dew point, solar in-

solation and wind velocity for a full year at locations in

southwestern Pennsylvania and Monroe, Michigan respectively.

Simulations of weather data permitted calculations of hour-

ly greenhouse heat loads to obtain estimates of fuel and

electrical requirements, and possible benefits from substi-

tution of waste heat for fossil fuel. Rotz and Aldrich com-

pared five waste heat system design alternatives with a con-

ventional boiler system to heat a hypothetical 3.2-acre

greenhouse. Economic comparison of systems was based on

calculation of a simple after-tax pay-off ratio. The ratio

for each waste heat alternative was found by dividing the

increase in initial equipment costs relative to a boiler

system by the difference in total annual costs (sum of


- 90 -

energy and annualized equipment costs), again relative to a

boiler system.

Heat availability considerations were specifically ad-

dressed by Manning and Mears (1981), Ashley (1982), and

Freemyers and Incropera (1979). Manning and Mears wrote a

computer program to simulate hourly heat availabilities

based on specified heat exchanger designs and actual CCW

discharge temperatures at the Montour power plant in

Pennsylvania. Hourly heat loads were estimated from actual

ambient temperature readings. If for a specified heat ex-

changer design and CCW temperature the hourly heat avail-

ability was insufficient to match the hourly heat load, the

supplemental heat input to match the load was calculated.

Since solar radiation data were not available for the site,

calculations were performed for nighttime operation only.

One significant conclusion resulting from simulation work

was that a substantial potential benefit existed in develop-

ing a computer based control system for a waste heat green-


Ashley (1982, p. 43) prepared a similar computer pro-

gram to estimate the thermal performance of a proposed waste

heat greenhouse at a North Dakota power station to determine

the cost of heating the structure with low-temperature fan

coil heating units for a typical heating season. The ef-

fects of fluctuations in CCW temperatures and changes in

heat exchanger capacity on electric power and supplemental

heating fuel consumption of greenhouse heating equipment

- 91 -

were studied to discover a least operating cost heating


Freemyers and Incropera combined a model predicting

heat demand from ambient temperature, wind speed and cloud

cover, with a model predicting heat exchanger performance.

Performances of two types of heat exchangers were simulated

with the objective of design optimization. Specifically,

with reference to fin tube designs, Freemyers and Incropera

reported development of an unpublished model providing the

flexibility to vary the number of tube rows and passes, the

length and diameter of individual tubes, fin arrangement,

and the overall volume and frontal area of the exchanger.

Calculations were performed within the simulation routine to

determine for a given design the heat transfer rate, outlet

air and water temperatures, and fan power requirement.

The high capital cost of low-temperature heat exchange

capacity prompted Stipanuk and Friday (1981) to analyze the

problem of capacity optimization at the Astoria greenhouse.

Since a backup system is normally required, it may be uneco-

nomical to install a waste heat system to supply 100 percent

of design heat load. A simplified approach to estimation of

heat loads was proposed, since "in light of all the poten-

tial factors which can result in variations in heating needs

of the greenhouse, the use of a highly detailed greenhouse

heat loss model would appear to be of questionable value"


- 92 -

(Stipanuk and Friday 1981, p. 6). The recommended alter-

native to detailed weather simulation was estimation of the

annual heating requirement using weather data from

Engineering Weather Data (Departments of the Air Force, the

Army, and the Navy, 1978), which reports average wind

velocities and average monthly daytime and nighttime hours

of occurrences of ambient temperatures in five-degree ranges

for many locations.

Annual nighttime hours of occurrences within each five-

degree temperature interval were obtained for a location

near the Astoria greenhouse. For each of 13 five-degree am-

bient temperature intervals below 60 degrees F, an hourly

greenhouse heat load was calculated based on the midpoint of

the ambient temperature interval and an average wind speed.

Heat availability calculations were based on a constant en-

tering temperature differential of 35 degrees F and speci-

fied numbers of fan coil units. For given combinations of

heat exchange capacity and hourly heat loads, the amount of

heat available from CCW was determined, and, if necessary,

additional backup heat input to match the load was calcu-

lated. At each level of fan coil capacity and heat load,

operating costs were calculated as the sum of fan and pump

electrical and supplemental heating oil costs. Due to the

difficulty of estimating solar heat input, calculations were

performed for nighttime operation only. Nighttime totals

were obtained as the sum of products of hourly operating

parameters at the midpoints of the 13 ambient temperature


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