EPA/600/2-78/114
tates
lental Protection
Municipal Environmental Research
Laboratory
Cincinnati OH 45268
and Development
of Solar Energy
to Heat Anaerobic
Digesters
Part I Technical
and Economic
Feasibility Study
Part II Economic
Feasibility
Throughout the
United States
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RESEARCH REPORTING SERIES
Research reports o* tht; Ott;;e o* R^'ji^r ,', i ~o De.elopment, U S Environmenta;
Protection Agency, have bee1 grouped r,:: n -e series These nine broad ca-e-
gones were established to facilitate furth ?\ development and application of en
vironmental technology Elimination c; tradit:onal grouping was consciously
planned to foster technology transfer and a maximum interface in related fields
The nine series are
1 Environmental Health Effects Research
2 Environmental Protection Technology
3 Ecological Research
4 Environmental Monitoring
5 Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
8 "Special1' Reports
9 Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL PROTECTION TECH-
NOLOGY series This series describes research performed to develop and dem-
onstrate instrumentation equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution This work
provides the new or improved technology required for the control and treatment
of pollution sources to meet environmental quality standards
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161
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EPA-600/2-78-114
July 1978
USE OF SOLAR ENERGY
TO HEAT ANAEROBIC DIGESTERS
Part I
Technical and Economic Feasibility Study
Part II
Economic Feasibility Throughout
the United States
by
ff David E. Cassel
t"^. Environmental Systems, Incorporated
0^
•y
(V)
T
Jess W. Malcolm
David E. Cassel
tal Systems, In
Annapolis, Maryland 21401
Part I: Contract No. 68-03-2356
Part II: Order No. CA-6-99-3499-A
Project Officer
R. V. Villiers
Wastewater Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
This report has been reviewed by the Municipal Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publicationj
Approval does not signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor does mention of
trade names or commercial products constitute endorsement or recommendation
for use.
11
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FOREWORD
The Environmental Protection Agency was created because of increasing
public and government concern about the dangers of pollution to the health
and welfare of the American people. Noxious air, foul water, and spoiled
land are tragic testimony to the deterioration of our natural environment.
The complexity of that environment and the interplay between its components
require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in problem solu-
tion and it involves defining the problem, measuring its impact, and
searching for solutions. The Municipal Environmental Research Laboratory
develops new and improved technology and systems for the prevention, treat-
ment, and management of wastewater and solid and hazardous waste pollutant
discharges from municipal and community sources, for the preservation and
treatment of public drinking water supplies, and to minimize the adverse
economic, social, health, and aesthetic effects of pollution. This publi-
cation is one of the products of that research; a most vital communications
link between the researcher and the user community.
This report contains the results of two studies in which the use of
solar energy to heat anaerobic digesters was proven to be technically and
economically feasible at Annapolis, Maryland and economically feasible at all
other locations in the United States. Economic justification for using solar
heat for anaerobic digestion was based on the value of the methane gas
produced.
Francis T. Mayo
Director
Municipal Environmental Research
Laboratory - Cincinnati
111
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ABSTRACT
Part I of this report was prepared as a result of a study based on the
premise that heat requirements for anaerobic sludge digestion represent a
large proportion of the energy used in most conventional wastewater treat-
ment plants.
Digester gas, consisting principally of methane, is commonly used as
fuel for digester heating. Recognizing that if solar energy could be sub-
stituted as the prime heat source for anaerobic digestion, then the methane
produced could be freed for higher grade energy requirements elsewhere.
The technical and economic feasibility of providing this alternative heat
source was evaluated by Environmental Systems, Incorporated. Detailed plans
and specifications were also prepared for the addition of a solar heating
system to the municipal wastewater treatment plant at Annapolis, Maryland.
To optimize the design, a computer program simulated the operation of
the digester heating requirements over the annual cycle. The inclusion of
all operating parameters and economic factors allowed precise determination
of both the size and specific design of the solar heating system. The pre-
sent worth of the solar heating system over the 25-year project life was
compared with the present worth of the digester gas conserved over the same
period. The system size and design were chosen as those which would provide
the maximum value of gas conserved relative to the cost of the solar heat.
For an anaerobic digester maintained between 32 and 38 degrees Celsius,
at Annapolis, Maryland, the optimum size of the solar heating system is
that which will supply approximately 90 percent of the annual heat load.
Flat-plate solar heat collectors having two glass covers proved to be the
most cost-effective for this digester temperature range and location.
Part I of the report was submitted in fulfillment of Contract Number
68-03-2356, by Environmental Systems, Incorporated, under the sponsorship of
the U.S. Environmental Protection Agency. Work was completed as of June 1976.
Part II of this report was prepared as the result of a study to apply
the principles developed in Part I to other locations throughout the United
States.
Solar digester heating is economically feasible at all locations in the
nation. The degree of economic attractiveness at any given location is
directly proportional to the average annual solar radiation multiplied by
the difference between the digester design operating temperature (35°C) and
the average annual air temperature.
IV
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The study shows that optimum-sized flat plate solar collectors can
provide from 82 to 97 percent of the total annual digester heat load, the
higher percentages being applicable to areas of higher solar radiation in-
tensity. Specific guidelines are given for determining the optimum size
and design of solar heating system for any size of sludge digester at any
location.
Part II of this report was submitted in fulfillment of Order Number
CA-6-99-3499-A by Environmental Systems, Incorporated, under the sponsorship
of the U.S. Environmental Protection Agency. Work was completed as of
December 1976.
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CONTENTS
Foreword, . .............................. iii
Abstract ................................ iv
Figures , .............................. viii
Tables ................................. x
Acknowledgement ............................ xi
Pa,rt I: Technical and Feasibility Study ............... 1
1. Introduction, Conclusions and Recommendations ........ 2
2, Description of Solar Heating System ......... .... 4
3f System Design ........................ 11
Preliminary Design Considerations ......... ... 11
Design Conceptualization ................ 19
Heat Storage and Transfer ................ 24
Control System ..................... 25
Computer Simulation ................... 27
Solar Collector and Structure .............. 31
Solar Collector Piping and Pump ............. 38
Economic Analysis .................... 41
Part II:Economic Feasibility of Solar Digester Heating
Throughout the United States ................ 47
4. Introduction, Conclusions and Recommendations ........ 48
5. Guidelines .......................... 50
General. .... .................... 50
Specific ........................ 50
Scaling to Plant Size .................. 58
6. Assumptions ................ . . . , ..... 60
7, Cpmputer Model ........................ 62
Computer Program .................... 62
Specific Modifications . , ............... 63
Program Changes for Collection, Design and Location, . . 65
8. Results
........................ , ...... 75
Appendices
A. Computer Programs SOL 4 and SOL 5 ............ , , 76
B. Computer Program SOL 6 ................. ... 84
VII
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FIGURES
Number • Page
1 Operation of 90% Solar Heating System over Annual Cycle •. 7
2 Temperature Curves for the System . : 8
3 Efficiency of Solar Heat Collector versus Time of Year 9
4 Determination of Optimum Solar Collector Angle for Winter
Heating, Annapolis, Maryland 23
5 Schematic Diagram of Automatic Control System 26
6 Digestion Time versus Digester Temperature 28
7 Efficiencies of Solar Collectors Evaluated in this Study 33
8 Solar Collector Area Required to Supply Given Percent of
Annual Heat Load, With and Without Horizontal Reflector. . . . '. 34
9 Effective Collector Area versus Percent Solar Heat 36
10 Cost of Collectors, Delivered to Annapolis 37
11 Solar Collector Mounting Arrangement 39
12 Collector Efficiency and Temperature Rise through Collector
versus Flow Rage ."•. ... 40
13 Economic Analysis 43
14 Wholesale Price, Natural Gas 1960-75 44
15- Determination of Optimum Size Solar Heating Systen Given
Latitude of Location 51
16' Determination of Cost of Optimum-Size Solar Heating System
Given Effective Collector Area ..... 52
17 Determination of Optimum Percent Solar Heat Given Average
Solar Radiation 54
Vlll
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Number Page
18 Determination of Savings Due to Solar Heat Given Average
Solar Radiation and Average Annual Air Temperature 57
19 Optimum Collector and Reflector Angles for Three Latitudes
(Cross Section View Looking West) 59
20 Comparison of Measured Average Monthly Solar Radiation and
Derived Curve for Use in this Study, Two Typical Locations ... 64
21 Solar Collector Efficiency Curves Used in this Study (Taken
from Published Research or Manufacturers' Collector
Efficiency Data) 66
22 Savings versus Collector Area for Three Collector Types,
Phoenix, Arizona 70
23 Savings versus Collector Area for Three Collector Types,
Seattle, Washington 71
IX
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TABLES
Number Page
1 Characteristics of Raw Sludge 13
2 Temperature in Soil Outside Digester , 14
3 Average Monthly Power Required to Supply All Heat for
One Digester 15
4 Average Mass Flow Rates Into and Out of Digester , . . , 18
5 General Data Sheet , J9
6 Data for Derivation of Empirical Equation for Incident
Solar Radiation 30
7 Horizontal Reflector for Solar Panels 32
8 Cost of Solar Collectors per Square Meter of Effective
Area (Costs as of Spring 1976) 35
9 Summary of Solar Heating Costs (Present Worth of all Costs). ... 42
10 Current Prices of Natural Gas and Other Fuels 46
11 Average Annual Solar Energy Received on a Horizontal Surface ... 55
12 Variables in Computer Program that Change with Collector Design. . 67
13 Variables in Computer Program that Change with Location , 67
14 Example of Computer Printout Data Obtained for Each Location
and Collector Type 69
15 Summary of Computer Results , . . . . 72
16 List of Eighteen Tested Locations in Order of Decreasing
Economic Feasibility of Solar-Heated Digester. . . , 74
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ACKNOWLEDGEMENTS
The authors wish to thank officials of the City of Annapolis, particu-
'.-•ciy William R. Jackson, former Director of Public Works, for records,
lans, data and access to the Annapolis Wastewater Treatment Plant, without
n Part I of this study could not have been conducted.
Special acknowledgement is extended to Dr. Bringham H. Van Dyke, Jr.
, :; V'-in Dyke Associates, for aid in design of solar collector supply and
. (.1;:.r. manifolds and collector mounting arrangment; Arnold F. Richter, for
assistance and structural steel design and conceptulization of solar heat
.-ilecticr system; James Pluzinski of National Computer Network, for use
•;-'". nis time-sharing computer terminal and aid in programming; Dr. J. Taylor
Dcard of the University of Virginia, for providing advance performance data
the Solaris collector panels; Dr. Daniel Lufkin, Solar Consultant, for
.",: ice regarding solar collector designs; Daniel Fisher of the Carolina
''ii Equipment Company, for the loan of a model Solaris collector panel;
i T-;S Mazzullo of Solar Heating Services, Incorporated, for demonstration of
:.evere collector panel; Dr. William McEver of Intertechnology Corporation,
*."', inspection of the Fauquier High School solar energy system, Warrenton,
;-rginia; James Larrimore of Polytech, Incorporated, for advice and specifi-
c^iions regarding insulation for the solar heat storage tank; Leon Slavon
- ; the Federal Power Commission, for information on natural gas prices, and
JonA H. Koehnlein, Jr. of the Portland Cement Association for concrete re-
\ v.,::or design information.
XI
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PART I
TECHNICAL AND ECONOMIC FEASIBILITY STUDY
by
Jess W. Malcolm
David E. Cassel
Environmental Systems, Incorporated
Annapolis, Maryland 21401
Contract No. 68-03-2356
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SECTION 1
INTRODUCTION, CONCLUSIONS, AND RECOMMENDATIONS
INTRODUCTION
Anaerobic sewage sludge digesters are usually heated by burning digest
er gas, and in some cases by burning another fuel such as oil. To present
an alternative to this use of "high grade" fuels, and to free the digester
gas for other purposes, a six-month technical and economic feasibility
study was performed to evaluate the use of solar energy for heating anaerc
bic digesters. There are many facets of energy use and conservation associ-
ated with sewage treatment, but this study is limited to analyzing direct
solar heat as a heat source for the digesters.
CONCLUSIONS
It is technologically and economically feasible to heat digesters vith
solar energy. All of the necessary components are available as "off-the-
shelf" items. Solar heat collector technology is changing rapidly, but
there are collectors now available that are quite adequate.
Under the requirement of this study, that is, maintaining the dige~' -,-
temperature in the upper mesophilic range (32-38°C) year round and for
weather conditions similar to those at Annapolis, Maryland, the lowest-cost
method of heating the digester is to supply about 90 percent of the annual
heat load with solar energy.
RECOMMENDATIONS
As a result of this feasibility study, we make the following recom-
mendations:
1. The research plan contained herein should be carried out to
positively demonstrate that the solar heating system will work
as expected;
2. A further study should be undertaken, using the computer
techniques and equations developed herein, to evaluate solar
digester heating under different weather conditions for
application throughout the United States; and
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3. The rOle of solar energy in wastewater treatment should be
evaluated as a source of energy for other processes (for
example, sludg6 drying). The cost-effectiveness of solar
energy should be compared with that of other energy con-
servation measures such as insulation.
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SECTION 2
DESCRIPTION OF SOLAR HEATING SYSTEM
PRINCIPLES OF OPERATION
Solar Sludge Preheater
The solar heating system for the anaerobic digester is essentially a
solar preheater for the raw sludge. Raw sludge from the primary clarifiers
passes through the solar heat storage tank/heat exchanger whe.re it is
warmed before entering the digester. The sludge is preheated to the temper-
ature required to provide all of the digester heat whenever possible. Any
additional heat input to the digester enters via the conventional heating
coils, which will be called the auxiliary heating system for the solar
heated digester.
Heat Storage Tank/Heat Exchanger
The combination solar heat storage tank and sludge preheater consists
of a tank of solar-heated water through which the raw sludge pipe passes.
The water in the tank is kept as hot as possible in the winter, but the
temperature of the water is limited in the summer to avoid overheating the
raw sludge.
Solar Heat Collection System
When the solar collector control system calls for heat, the solar
collector pump pumps water from the bottom of the heat storage tank to the
flat-plate solar heat collectors, which are at a higher elevation than the
tank. The water runs through the collectors and drains by gravity to the
top of the tank. When the pump turns off, all water drains back into the
tank.
Control System
The control system is completely automatic and very simple. Tempera-
tures are sensed at three places in the system to control the on/off condi-
tion of the solar collector pump: 1) in one of the solar collectors; 2) at
the heat storage tank; and, 3) in the digester. A differential thermostat
turns the collector pump on when the temperature of the collectors is a
set number of degrees above that in the heat storage tank. A high-limit
thermostat prevents the collector pump from operating when the temperature
in the digester reaches a set high temperature during summer operation. If
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the temperature in the digester reaches a set low limit, the auxiliary heat
system adds heat directly to the digester.
DETAILED DESCRIPTION
Solar Heat Collection
The solar collector panels are commercially available flat-plate panels.
They have two layers of tempered glass over the copper absorber sheet. This
copper sheet has soldered to it copper tubes through which the water passes.
The tubes are joined at top and bottom by larger tubes running horizontally.
Inlet and outlet tubes join these tubes and penetrate the panel casing. The
copper absorber sheet is backed by insulation. The panels are individually
encased and are each self-contained units.
One hundred and thirty panels, comprising an effective collector area
of about 230 square meters, are arranged in two planes facing seven degrees
west of south, at an angle of 60 degrees from the horizontal. Each plane
is two collector panels high. A reflector, consisting of a horizontal con-
crete slab painted white, equal in width to the height of the panels, is
positioned at the base of and parallel to each array of panels. The concrete
reflectors substantially increase the solar radiation on the panels during
the critical winter period.
Pre-insulated plastic pipe carries the water from the heat storage tank
to the collectors and back again. This piping consists generally of sched-
ule 80 PVC or CPVC pipe plus a layer of urethane foam (rigid) insulation,
with an outer shell of PVC pipe. Sections of this pipe run along the top
and bottom of each collector plane as supply and return manifolds. Pipe
nipples are tapped into the manifold for each connection to the collector
panels. Steel frameworks with concrete footings support each row of panels.
The solar collector pump is a close-coupled centrifugal pump with a
nominal 3/4 horsepower (560 W) electric motor. Water can flow back through
the pump freely when it is not operating.
A filter in the discharge line of the pump prevents any solid particles
from reaching the collectors. A pressure gage at the pump discharge indicates
whether the pump is operating normally.
Solar Heat Storage and Heat Transfer
The solar heat storage tank is a 75 m3 (20,000 gallon) steel tank. The
tank is placed horizontally. It is 9.45 m (31 feet) long and 3.2 m (10.5
feet) in diameter. For convenience at the Annapolis plant, the tank is
placed in the empty Number Three digester, previously a floating-cover di-
gester from which the cover has been removed. The nominal six-inch diameter
steel sludge pipe enters near the bottom of one end of the tank, makes five
full-length passes through the tank, and exits near the top of the other end.
From there, it enters the Number Two digester through the digester wall. The
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warmed sludge is introduced into Digester Number Two in the center near the
bottom. The five passes of six-inch steel pipe within the heat storage tank
are supported by vertical steel rods welded to the pipe and tank.
The tank is insulated with sprayed-on urethane foam insulation to a
thickness of 6.4 cm (2% inches). A coating of hydrocide elastomeric roofing
(HER) is sprayed onto the urethane for waterproofing and to protect the
urethane from the sun's rays. This coating is 1.5 mm (0.060 inch) thick.
A sight glass is supplied with the tank to give a visual indication of
the water level. Water can be added via a manual valve when necessary. The
water level should be within 10 cm of the top of the tank when the pump is
not operating.
A sump pump is placed under the tank in the bottom of the Number Three
digester to remove any accumulated rainwater or seepage from the ground.
Control System
The differential thermostat and high-limit controller are located near
the solar collector pump in the pump room adjacent to the Number Three di-
gester. Wires run to the solar collector, the heat storage tank, and to the
temperature sensor in the digester. The dual element temperature-sensing
resistance bulb is located in a well in the digester wall. A #14 gage solid
copper wire connects one element of the bulb to a controller in the pump room.
The other element of the bulb is used to send a signal to the other controller
for the auxiliary heat system. Rho Sigma model 106 differential thermostat
and Rho Sigma model STH sensors will be used. Honeywell Model HP7E11-20-3A
dual element resistance bulb with stainless steel well and housing will serve
to measure digester temperature. The controllers will be Honeywell model
7351 Dialatrol.
Auxiliary Heat System
No additional components will be required for the auxiliary heat system
since the solar heating design is completely independent of that system. The
existing system will not be operated at all in the summer, and only at a
fraction of its normal capacity in the winter. One optional control may be
used with the auxiliary heating system to turn on the boiler when the digest-
er temperature lowers to near the point where auxiliary heat may be needed.
This is not necessary for adequate operation, however, and is not included
in this design.
DETAILED OPERATION
Heat transfer rates (power) for various parts of the system over an
annual cycle are shown graphically in Figure 1. Corresponding temperatures
at various points are shown in Figure 2. All of the assumptions underlying
these graphs will be explained in a later section of this report, but basi-
cally they represent average and typical conditions. The power given in
Figure 1 can be considered to be five-day averages for typical conditions.
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60
•SOLAR RADIATION INTERCEPTED
BY COLLECTOR
50
a;
w
O
DH
CO
^
O
u
H
CO
40
-AVAILABLE SOLAR HEAT
(collector input x collector efficiency)
30
DIGESTER HEAT REQUIREMENT
20
UXILIARY
HEAT
REQUIRE
SOLAR
HEAT
WASTED
SOLAR
HEAT
WASTED
SOLAR HEAT COLLECTED
10
HEAT LOSSES
FROM SOLAR
HEAT STORAGE
TANK—I
•AUXILIARY HEAT
REQUIREMENT
AS ONDJ FMAM
TIME OF YEAR, MIDDLE OF MONTH
Figure 1. Operation of 90% solar heating
system over annual cycle
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50
40
U
o
30
H
C£
!=)
H
W
PL.
H
20
10
DESIRED RAW
SLUDGE TEMPER-
ATURE ENTERING
DIGESTER
HEAT STORAGE TANK
TEMPERATURE
I TEMPERATURE OF RAW SLUDGE
MEAN
MONTHLY AIR
TEMPERATURE
ASONDIFMAM
TIME OF YEAR, MIDDLE OF MONTH
Figure 2. Temperature curves for the system
I I
Starting at the top graph in Figure 1, the solar radiation intercepted
by the collector is given. Multiplying this by the collector efficiency for
each time of year (Figure 3) gives the available solar power. From about
the middle of March through the middle of October, not all of the available
energy is transferred to the heat storage tank because it is not needed.
From October through March, however, all of the available solar energy from
the collector is transferred to the heat storage tank. The total digester
heat requirement varies approximately sinusoidally over the annual cycle,
reaching the maximum of 31.6 kW in the middle of the winter.
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65
60
c
Q)
o
V-.
CD
a
O
£
w
i—i
O
i—i
ix,
ix,
w
55
50
(SUNWORKS DOUBLE-
GLAZED COLLECTOR)
IAS ONDJ FMAMJ J
TIME OF YEAR, MIDDLE OF MONTH
Figure 3. Efficiency of solar heat collector
versus time of year
Auxiliary heat is required from October through March when the digester
heat requirement exceeds the available solar energy. Maximum rate of
auxiliary heat occurs in December, at 8.6 kW. Heat losses from solar heat
storage tank are faily constant throughout the year, but they are slightly
higher in winter than in summer. The rate of heat input to the heat storage
tank any given time is approximately equal to the sum of the heat losses
from the tank plus heat transferred to the sludge. When the temperature of
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the tank is changing, these rates differ slightly, but by not more than
about 1 kW at most.
The average monthly ambient air temperature and raw sludge temperature
vary approximately sinusoidally throughout the year, as shown in Figure 2.
The temperature to which the sludge would have to be preheated to sat-
isfy the total digester heat requirement reaches a maximum in, the winter.
The heat storage temperature, however, cannot be maintained at that temper-
ature during the winter, and dips severely from October through March, reach-
ing a minimum of 39.5°C in December. It is assumed that the sludge exiting
from the heat transfer tank will be at the average temperature of the water
in the tank. It is planned that sludge will be pumped steadily during
twenty minutes out of each hour. The volume of sludge pumped during each
pumping cycle is equal in amount to that required for one complete replace-
ment of sludge in the heat exchanger.
The digester temperature is shown as a constant 35°C. Again, these
graphs represent average and typical conditions. In actual practice, the
digester temperature would vary between 32 and 38°C, still well within the
upper mesophilic digestion range.
The areas under the power curves of Figure 1 represent total annual
energy consumed or transferred. The area under the auxiliary heat curve,
for example, represents the total annual auxiliary heat used, which is about
tern percent of the area under the "digest heat requirement" curve. Similarly,
the area between the "available solar power" curve and the "solar heat
storage input" curve represents solar heat wasted.
10
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SECTION 3
SYSTEM DESIGN
PRELIMINARY DESIGN CONSIDERATIONS
Approach
It is impossible to separate the technical design from economic consi-
deration. The process of technical design consists of optimizing the system
design; that is, finding the most economical hardware to do the job. The
overall approach is to express the total present worth of the cost of the
solar heating system as a function of percent solar heat (total annual heat
supplied to the digester from the solar heating system divided by total
annual heat required, expressed as a percentage), and to compare it with the
present worth of digester gas saved, also as a function of percent solar
heat. It is only after examining the cost data in this way that the most
economical size solar heating system can be established.
Characteristics of the Raw Sludge
3
The total wastewater flow rate into the plant will average 0.197 m /s
(4.5 mgd). Because half of the raw sludge will enter each of the two digest-
ers, and only one digester will be heated by solar energy, all calculations
will be based on a wastewater flow rate of half of the total, or 0.0985 m /s
(2.25 mgd).
Average suspended solids content of the wastewater will be 0.160 kg/m
(160 mg/1). Additional suspended solids in the form of ferric chloride
(Fe C13) will be added at the rate of 0.040 kg/m . The total suspended
solids concentration of the wastewater entering the clarifiers will therefore
be 0.200 kg/m . About 90 percent of the suspended solids are expected to be
removed in the clarifiers, giving, per digester, a mass flow rate of solid
material in the sludge of:
(0.200 kg/m3) x (0.0985 m3/s) x 0.90 = 0.0177 kg/s.
The raw sludge will be about 7.5 percent solids by mass. Therefore, the mass
flow rate of the sludge is:
(0.0177 kg/s) / 0.075 = 0.236 kg/s.
equations on pages 582 - 583 of Met<
specific gravity of sludge having 7.5 percent solids, with one third of the
Using the equations on pages 582 - 583 of Metcalf and Eddy^ , the
11
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solid mass fixed and the other two-thirds volatile, is 1.02. This corre-
sponds to a density of 1,020 kg/m . The average volumetric flow rate of the
sludge to each digester is:
(0.236 kg/s) x (m3/l,020 kg) = 2.31 x 10"4 m3/s (3.66 gpm).
The temperature of the raw sludge at the Annapolis plant varies from a
low of about 16°C in January to a high of 22°C in July, the average annual
temperature being 19°C.
The five-day biochemical oxygen demand (BOD,--20 C) of the influent
wastewater will be about 0.190 kg/m . On a mass flow basis, this is:
(0.190 kg/m3) x (0.0985 m3/s) = 0.0187 kg/s.
About 60 percent of the BOD will be removed by the clarifiers and become
part of the sludge:
0.0187 kg/s x 0.60 = 0.0112 kg/s.
Or, on a volumetric basis, the BOD content of raw sludge is:
(0.112 kg BOD/s) x (s/2.31 x 10"4 m3) = 48.5 kg BOD/m3.
Characteristics of the raw sludge are summarized in Table 1.
Digester Heat Requirements
The heat requirement of the anaerobic digester can be considered to
consist of two parts: 1) heat necessary to raise the temperature of the in-
coming sludge to 35°C; and, 2) heat necessary to offset heat lost from the
digester to the surrounding ground.
The average annual temperature of the raw sludge is 19 C, and the flow
into one digester is 2.31 x 10~4 m /s. The heat capacity of sludge will be
assumed to be the same as that of water, 4.19 x 10^ J/m^-C. The average
annual power required is therefore:
(2.31 x 10~4 m3/s) x (4.19 x 106J/m3 °C) x (35 - 19)°C
= 15,500 J/s = 15,500 W, or 15.5 kW.
The power required in July when the incoming sludge temperature is 22 C is:
(2.31 x 10~4 m3/s) x (4.19 x 106 J/m3 °C) x (35 - 22)°C = 12.6 kW.
The power required in January when the incoming sludge temperature is 16 C is:
(2.31 x 10"4 m3/s) x (4.19 x 106J/m3 °C) x (35 - 16)°C = 18.4 kW.
The annual variation is sinusoidal.
12
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Table 1. CHARACTERISTICS OF RAW SLUDGE
Flow rate, m3/s (each digester) 2.31 x 10
Flow rate, kg/s (each digester) 0.236
Density, kg/m3 1,020
Percent solids by mass 7.5
Percent water by mass 92 .5
Volatile solids, % by mass of total solids 67
Fixed solids, % by mass of total solids 33
Temperature, °C: Max. (July) 22
Min. (January) 16
Ave. annual 19
BOD content (BOD5 - 20°C), kg/m3 48.5
BOD (BOD5 - 20°C) mass flow rate, kg/s 0.0112
Density of fixed solids , kg/m3 2,500
o
Density of volatile solids, kg/m 1,000
The digester is of approximately cylindrical shape, 12.2 m (40 feet) in
diameter and 6.1 m (20 feet) high, and is surrounded on all sides by earth.
The wall areas are as follows:
Roof area = ir(6.1 m)2 = 117 m2
Side area = Tr(12.2 m^ (6.1 m) = 234 nu
Floor area = ir(6.1 m) = 117 m
Heat transfer coefficients (overall) are approximately as follows:
Roof U = 1.9 W/m2C
Concrete walls below grade,
dry earth U = 0.68 W/m C
Floor, concrete in contact
with moist earth U = 0.77 W/m C.
Temperatures in the soil outside the roof, side, and floor of the di-
gester are assumed to be as in Table 2.
13
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Table 2. TEMPERATURE IN SOIL OUTSIDE DIGESTER
(degrees Celsius)
January
luly
Ave. annual
Roof
6
20
13
Sides
7
19
13
Floor
10
16
13
Heat transfer rates out of the digester are calculated using the
following equation:
q = UA (AT)
where q = heat transfer rate, W 2
U = overall heat transfer coefficient, W/m C
AT = temperature differential, C
January:
roof q = (1.9) (117) (35 - 6) = 6.4 kW
sides q = (0.68) (234) (35 - 7) = 4.5
floor q = (0.77) (117) (35 - 10)= 2.3
Total 13.2 kW
July:
roof q = (1.9) (117) (35 - 20) = 3.3 kW
sides q = (0.68) (234) (35 - 19)= 2.6
floor q = (0.77) (117) (35 - 16)= 1.7
Total 7.6 kW
Average annual:
roof q = (1.9) (117) (35 - 13) = 4.9 kW
sides q = (0.68) (234) (35 - 13)= 3.5
floor q = (0.77) (117) (35 - 13)=_2_.0
Total 10.4 kW
The annual variation is sinusoidal.
The total power needed to supply the digester heat requirement is the sum of
that required to preheat the sludge and that required to offset losses from
the digester. It varies sinusoidally over a year's time from a low of 20.2
kW in July to a high of 31.6 kW in January. The average annual power re-
quired is 25.9 kW. The total energy required to heat the digester for one
year is:
(25.9 x 103 J/s) x (3.15 x 10? s) = 816 x 109 J = 816 GJ.
14
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The variation of total digester heat requirements over a year's time can
be expressed by the following equation:
p = 25.9 + 5.7 sin (t - 210)
where p = average monthly power required, kW
t = time of year, degrees (March = 0, April = 30, etc.).
The average required to supply the total heat requirements of one di-
gester for each month is shown in Table 3.
Table 3. AVERAGE MONTHLY POWER REQUIRED
TO SUPPLY ALL HEAT FOR ONE DIGESTER
Month
January
February
March
April
May
June
Power, kW
31.6
30.8
28.8
25.9
23.1
21.0
Month
July
August
September
October
November
December
Power, kW
20.2
21.0
23.1
25.9
28.8
30.8
Total = 311
Total annual heat = 311 kW x 2.63 x 106s = 8.18 x 1011 I
Digester Gas Production
Digester gas is composed of about 65 percent methane (CH^) and 35 per-
cent carbon dioxide (CC^) by volume, or 40 percent methane and 60 percent
carbon dioxide by mass. Any gas under standard conditions occupies a volume
of 22,4 m per kg-mole. Hence, the density of CH4 at standard conditions
(0°c and 1.01 x 105 Pa) is 16/22.4 = 0.714 kg/m3, and that of C02 is 44/22.4
= 1.96 kg/m3. Since digester gas is 65 percent CH4 and 35 percent C02 by
volume, the density of digester gas is:
(0.714) (0.65) + (1.96) (0.35) = 1.15 kg/m3
Air at standard conditons has a density of 1.29 kg/m3, so that the
specific gravity of digester gas is 1.15/1.29, or 0.89 relative to air.
15
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Because the density of gases changes appreciably with temperature and pres-
sure, rates of gas production will be calculated on a mass rather than a
volumetric basis.
Digester gas production can be estimated from volatile solids loading.
Metcalf and Eddyl, p. 606, give a typical value of 0.62 m^ of digester gas
produced per kg of volatile solids added, at standard conditions. (This is
also equal to 0.93 m-^ of digester gas per kg of volatile solids destroyed,
assuming that on the average 2/3 of the volatile solids added are destroyed.)
The mass of digester gas per unit mass of volatile solids added is:
0.62 m x (1.15 kg/m ) = 0.713 kg gas per kg volatile solids added.
The mass flow rate of the raw sludge is 0.236 kg/s. The raw sludge is
about 7.5 percent solids, and about 2/3 of the mass of the solids is volatile.
Therefore, the volatile solids flow rate is:
0.0236 x 0.075 x 0.67 = 0.0119 kg/s.
The digester gas production rate is, therefore,
0.0119 kg/s x 0.713 kg gas/kg volatile solids = 0.00849 kg/s.
This is 3.60 percent of the mass flow rate of the raw sludge.
Digester gas production can also be estimated on the basis of population.
Metcalf and Eddy, p. 606, state that in secondary treatment plants digester
gas production can be estimated to be about 3.28 x 10-7 m /s (1.0 ft-Vday)
per person at standard conditions. For the City of Annapolis, therefore,
with a population of about 35,000 people, the estimated digester gas pro-
duction rate is 0.0115 m-Vs. Since one half of the sludge enters each di-
gester, the production rate of each digester is 0.0115/2, or 5.75 x 10~3m3/s,
which is equal to 0.00661 kg/s. This is slightly lower than the rate based
on volatile solids reduction. The chemical treatment process at Annapolis
probably warrants the higher figure of 8.49 x 10"^ kg/s.
Since 40 percent of the mass of the digester gas is methane, the produc-
tion rate of CH4 is (0.40) x (0.00849 kg/s) = 0.00340 kg/s. The low heating
value of methane is 49.9 x 10" J/kg. Therefore, energy is being produced
in the form of burnable methane gas at the rate of (0.00340 kg/s) x (49.9 x
10^ J/kg) = 170 kW. Assuming a combustion efficiency of 66 percent, 112 kW
would be available for digester heating. This is 112/25.9, or 4.32 times
the average power required to heat one digester, and 112/31.6, or 3.54 times
the maximum power requirement of one digester in January. Twenty-three per-
cent (1/4.32) of the total annual gas produced would be required to supply
100 percent of the digester heating requirements. Thus 23 percent of the gas
produced would be conserved by using a 100 percent solar heating system.
Mass Flow Rates Into And Out Of Digester
Bacteria in the anaerobic digester convert a large percentage of the
16
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volatile (organic) solids to liquid (supernatant) and digester gas. It is
desirable to know how much digested sludge, supernatant, and gas are produced
per inlet flow rate of raw sludge. The following assumptions will be made
in addition to those concerning the characteristics of the raw sludge pre-
viously mentioned:
1. Sixty-seven percent of the volatile solids are destroyed during
anaerobic digestion;
2. The absolute mass flow rate of the fixed solids out of the digester
(in the digested sludge) is equal to that into the digester (in the
raw sludge);
3. The digested sludge contains 12 percent solids by mass; and
4. The density of the supernatant is the same as that of water,
1,000 kg/mS.
The following calculations will be based on a batch of raw sludge having
a total mass of 1,000 kg. Of this, 75 kg are solid material and 925 kg are
water. Of the solids, (0.67) (75), or 50.2 kg are volatile (organic) and
24.8 kg are fixed.
After digestion, the remaining mass of volatile solids is (0.33) (50.2),
or 16.6 kg. The percent that the volatile solids are of the total solids
is therefore:
16.6 kg / (16.6 kg + 24.8 kg) = 40.1%.
The density of the fixed solids remains 2,5000 kg/m , which corresponds
to a specific volume of 4 x 10"^ m /kg. The density of the volatile solids
is 1,000 kg/m^, or a specific volume of 10"^ m^/kg. The average specific
volume of all the solids in the digested sludge is:
(0.401) (10~3) + (0.599) (4 x 10"4) = 6.41 x 10~4 m3/kg.
The average density of all the solids is 1/(6.41 x 10~ ), or 1,560 kg/m .
Since the digested sludge is 12 percent solids by mass, its specific volume
is:
(0.12) (6.41 x 10"4) + (0.88) (10~3) = 9.57 x 10"4 m3/kg.
-4 3
The average density of the digested sludge is I/(9.57 x 10 ), or 1,040 kg/m .
The mass of the digested sludge is equal to the total mass of the solids
divided by the percent solids:
(16.6 kg + 24.8 kg) / 0.12 = 345 kg.
This is 34.5 percent of the mass of the raw sludge.
The mass flow rate of digester gas was calculated previously to be 8.49
x 10~3 kg/s, or 3.60 percent of the mass flow rate of the raw sludge. The
17
-------
balance is assumed to be supernatant. These results are summarized in
Table 4.
Table 4. AVERAGE MASS FLOW RATES
INTO AND OUT OF DIGESTER
Mass flow rate, kg/s Percent by mass of total
Raw sludge 0.236 100.0
Digested sludge
Supernatant
Digester gas
0.814
0.146
0.00849
34.5
61.9
3.6
Alternate Energy Considerations
The scope of this study was limited to the technical and economic fea-
sibility of substituting solar heat for digester gas to heat anaerobic di-
gesters. Other energy considerations have been brought up in the course of
this study, however, which should be mentioned at this time.
Considering the cost of all energy, including solar, consideration
should be given to insulating the digester as well as practical, thus re-
ducing the heat losses to the surrounding ground, which for the Annapolis
Plant amount to 40 percent of the total digester heat requirement.
Depending on what is to be done with the supernatant and digested sludge,
much heat could be extracted from them. The mass of the supernatant is 62
percent of the mass of the incoming raw sludge. It is theoretically possi-
ble> therefore, to supply 62 percent of the digester heating requirements
simply by efficient heat exchange to reduce the temperature of the super-
natant to that of the raw sludge. Similarly, the digested sludge is 35 per-
cent by mass of the raw sludge. If this digested sludge were to be trucked
away, a large percentage of the digester heat requirement could be fulfilled
by transferring heat from the digested sludge to the cold, raw sludge.
Due to the small mass of digester gas produced and low heat transfer
coefficients for gas, less than one percent of the digester heat requirements
could be fulfilled by cooling the gas from 35 to 20°C. Extracting sensible
heat from the digester gas is therefore impractical.
General Data Sheet
Some of the more important values and constants used throughout this
study are summarized in Table 5.
18
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Table 5 . GENERAL DATA SHEET
Heat capacity of water
Density of water
Density of air
Heat capacity of digester gas
Density of methane gas
Density of carbon dioxide
gas
(20°C, 105 Pa)
(0°C, 105 Pa)
(20°C, 105 Pa)
(0°C, 105 Pa)
(20°C, 105 Pa)
Heat capacity of methane
Heat capacity of carbon dioxide
Low heat value of methane (0°C, 10 Pa)
Composition of digester gas by volume:
by mass:
Average raw sludge flow rate (per digester)
Average wastewater flow rate, total
Influent suspended solids
Ferric Chloride feeding rate
Suspended solids reduction in clarifiers
BOD reduction in clarifiers
Raw sludge, percent solids
Volume of one digester
4.19 x 106 J/m3C
4.19 x 103 J/kg C
1,000 kg/m3
1.29 kg/m3
1,510 J/kg C
0.714 kg/m3
0.668 kg/m3
1.96 kg/m3
1.83 kg/m3
2,480 J/kg C
859 J/kg C
33.6 x 10b 1/m6
49.9 x 106 J/kg
65% methane
35% carbon dioxide
40% methane
60% carbon dioxide
0.236 kg/s
2.31 x 10"4
0.197 m3/s
0.160 kg/m3
0.40 kg/m6
90%
60%
7.5%
679 m3
m
Ys
DESIGN CONCEPTUALIZATION
Additon of Solar Heat to Digester
Many methods were considered for adding the solar heat to the digester.
Sludge, either raw or digesting, could be pumped through a solar collector
to be heated directly. Solar-heated water could be circulated in coils with-
in the digester. The cold, raw sludge could be preheated by passing it
through a. solar heat exchanger before it enters the digester. Sludge could
be recycled from the digester to a. solar heat exchanger. Or, any combination
of the above methods could be used. The criteria used to evaluate the
various alternatives were as follows:
1. Efficiency of solar heat collection - solar heat must be collected
quickly when available and stored for future use. The temperature
of the solar heat storage unit must be as low as possible for max-
imum collection efficiency;
19
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2. Cost - expensive valves or controls should be avoided;
3. Temperature shock - the bacteria should not be exposed to extremes
of temperature or rapid changes between temperature ranges;
4. Operation of system during periods of little or no sunlight;
5. Ease of operation and ability to control conditions positively;
and
6. Adequacy to adapt to changing sludge rates, temperatures, and
weather conditions.
Preheating the raw sludge was chosen based on the above criteria.
Heating the sludge directly by passing it through a solar collector would
overheat it or require costly controls. Circulating solar-heated water
through coils in the digester would be inefficient due to the desired low
temperature of that water. Also, this would tend to promote uneven tempera-
tures in the digester. Recycling hot, digesting sludge through a solar heat
exchanger would be less efficient than passing cold, raw sludge through the
same heat exchanger. Recycling of digesting sludge through the solar heat
exchanger in addition to preheating the raw sludge would not be advantageous
because this would only lower the temperature of the solar heat storage unit,
reducing the amount of heat available for preheating the raw sludge.
There are additional advantages of sludge preheating as the sole means
of adding solar heat to the digester. This method would work equally well
for stratified or for high-rate, mixed digesters. The solar heating system
is kept completely separate from the auxiliary heat system, desirable for
two reasons: 1) adding solar heat to existing digesters is simplified; and
2) conventional heating systems can be used as auxiliary heat, operating in-
dependently of the solar heating system.
If sludge pre-heating is used as the sole method of digester heating,
the sludge must be heated to a temperature greater than the design tempera-
ture of the digester, 35° C. The additional temperature rise required above
35°C must compensate for the heat lost from the digester to the surrounding
ground. The sludge flow rate per digester is 0.236 kg/s and the heat capac-
ity of the sludge is assumed to be equal to that of water, 4.19 x 1(P J/kg -
°C. In January, when the heat loss from the digester is 13.3 kW, the
additional temperature rise is:
(13.3 x 103 J/s) x (kg - °C/4.19 x 103J) x (s/0.236 kg) = 13.5°C.
Therefore, the sludge must be preheated in January to 35 + 13.5, or 48.5 C.
In July, when the heat loss from the digester is 7.6 kW, the additonal
temperature rise is:
(7.6 x 103 J/s) x (kg - °C/4.19 x 103J) x (s/0.236 kg) = 7.7°C.
20
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The sludge must be preheated in July to 35 + 7.7, or 42.7 C (see Figure 2).
When the solar heat storage tank cannot be maintained at or above these
temperatures, as will be the case during the critical winter period, auxil-
iary heat must be added to the digester.
Type of Solar Collectors
The temperatures required for heating the sludge are in the range of
those produced efficiently by standard flat-plate solar heat collectors.
Therefore, this is the basic type of collector considered for this appli-
cation.
Heat Storage
Plain water has proven to be the most economical and most easily used
medium for both solar heat collection and storage. The heat storage tank
was placed at a lower elevation than the collectors to allow draining of the
collectors when not in use. This has the dual advantages of preventing
freezing (and not requiring antifreeze") and of keeping the heat capacity of
the collectors low. Rocks, which are sometimes used for transfer of solar
heat to air, were ruled out. Air as a heat-collection fluid is less efficient
than water.
System Operation
Simplicity was attained by using water as both heat collection and
storage medium. To make the system very simple to operate, a single centrif-
ugal pump was used to circulate water from heat storage to collectors. The
differential thermostat pump control for selecting the operating times of the
pump is widely used in solar building heating systems. This system was used
with the addition of another thermostat in series with the differential
thermostat to limit the amount of solar heat transferred to the storage tank
in the summer.
The other option that was considered was to collect solar heat year
round, allowing the temperature of the stored water to increase very high in
the summer and to drop down to a reasonable level in the winter. This would
perhaps increase the percent solar heat for a given size solar heating
system, storing surplus heat in the summer for use in the winter. This was
considered impractical for the following reasons. If the temperature of the
solar heat storage were to increase higher than necessary in the summer, the
heat transfer rate between solar heat storage and sludge would have to be
decreased during that period. In fact, means would have to be provided to
very the heat transfer rate depending on the temperature of the stored water
and the requirements of the digester. This would involve either valving,
changing flow rates, or providing auxiliary heat exchangers outside of the
solar heat storage tank. Sophisticated, expensive control systems would be
required. Storing heat at such high temperatures would increase heat losses
from the storage tank, decreasing the efficiency of the system. Also, the
higher the temperature of the heat storage, the lower the collector
efficiency, so that less heat would be collected than may be expected based
21
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on normal collector efficiencies. The potential difference between year-
round collection and storage of surplus heat and "wasting" excess heat in the
summer is only about 11 percent. (This is partly due to the orientation of
the collectors and use of reflector, both of which maximize solar heat col-
lection when needed most: in the winter.) Collector inefficiencies and
greater heat losses reduce the amount considerably.
Sensing the temperature of the digester and limiting the collection of
solar heat when not required (when the digester temperature increases to a
given value) provides the most practical and economical summertime control
system.
Collector Orientation
Flat-plate, stationary solar heat collectors are normally positioned
facing south at an angle from the horizontal. The physical arrangement of
the Annapolis plant allows placing the collectors parallel to a fence, fac-
ing them seven degrees west of due south. This is ideal because facing the
collectors west of south allows maximum heat collection in early afternoon
when ambient temperatures are usually highest, promoting the highest possi-
ble collector efficiencies at that time.
If the collector angle could be changed during the year to allow maxi-
mum heat collection at all times, the collector angles (for Annapolis, Mary-
land, 39 N Latitude) would be as shown in Figure 4. Figure 4 also gives
monthly normals of temperature at Annapolis, Maryland, averaged from 1941
through 1970. The coldest day of the year occurs in mid-January. Heat losses
from the digester would be greatest then, and raw sludge temperatures would
be lowest. Also, collector efficiency would be lowest at that time. The
collector angle that allows maximum heat collection when needed most is 60
degress from the horizontal. As Figure 1 shows, even at this angle excess
solar heat is available in June. Therefore, the collector angle was chosen
as 60 degress from the horizontal.
In January with the collector 60 degrees from the horizontal and the
sun's rays normal to the collector at 30 degrees from the horizontal, the
amount of radiation incident on the collector can be increased by using a
horizontal reflector in front of the collector. The cost of the reflector
per unit area is a small fraction of the cost of the collector. Wind load
considerations prohibited additonal reflector above the collectors.
Method of Adding Auxiliary Heat
Several methods were considered for adding auxiliary heat to the digester.
A heat pump could be used to "pump" heat from the relatively cool solar heat
storage tank to the digester. This method was discarded because cooling the
solar heat storage tank would reduce the heat available for preheating sludge.
In addition, it is wasteful to use electricity for partial auxiliary heat
when digester gas is available. Either digester gas or other fuels could be
used to add heat either directly to the digester or to the solar heat storage
tank. It is desirable to keep the temperature of the solar heat storage tank
22
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(0
4-)
o
N
-rH
i-i
O
B
o
O)
0)
0)
>-
en
0)
Q
•*
0)
• — i
Cn
C
O
0)
I — I
1 — I
o
O
90
80
70
60
50
40
30
20
10
Average Monthly Air Temperature
Annapolis, Maryland,
1941-1970
•Angle of Collector
Perpendicular to Sun's
Rays at Noon Each
Month
25
20
O
o
15 g
•3
10 s
CD
CX
5 g
H
0
ASONDJFMA
Time of Year (Middle of Month)
M J I
Figure 4. Determination of Optimum Solar Collector Angle
for Winter Heating, Annapolis, Maryland
as low as possible, so the auxiliary heat should be added directly to the
digester. This is most easily done by using the existing digester heating
system at a lower capacity to provide the auxiliary heat. Either preheating
the raw sludge after it is first preheated by solar energy, recycling di-
gesting sludge through external heat exchangers, or circulating hot water in
23
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heating coils within the digester would be satisfactory methods of adding
the auxiliary heat. At Annapolis, the heating coils are already in place,
so the method chosen was to heat water by burning digester gas and circulate
the hot water in the coils within the digester.
HEAT STORAGE AND TRANSFER
Size of Solar Heat Storage Tank
The size of the solar heat storage tank is not critical. Unlike the
effective solar collector area, the size of heat storage has virtually no
direct relationship to the annual percent solar heat. It does, however,
affect the system stability, that is to say temperature variations in the di-
gester and heat storage tank.
The parameter R {the ratio of volume of water stored in m to area of
solar collectors in m ) was varied from 0.1 to 1.5 as a variable in one of
the earlier computer programs of this study. It was found that the annual
percent solar heat was independent of R for all R's over 0.2. Under 0.2 the
system became unstable with fluctuating temperatures in the heat storage tank.
These results were based on heat inputs and withdrawals from the tank every
five days. For a collector area of 400 m^ (proposed at that time, based on
less efficient collectors than those of the final design) a storage volume
of 80 m-5 appeared to be optimum. The standard size steel tank of 75 m^
(20,000 gal) was chosen. The value of R was kept at 0.2 for all subsequent
computer runs.
Heat Capacities Within the System
3
The heat capacity of the 75-m heat storage tank is 11 percent of that
of the 680-m^ digester. The allowable temperature range of the digester is
from 32 to 38°C, six degrees Celsius. With no heat input to the digester
in the winter when the total heat requirement is at the rate of 3.16 kW, the
digester temperature would drop 0.91 C each day, giving about 6% days' heat
storage within the digester itself. Using the same temperature drop in the
heat storage tank, less than one additional day's storage would be available
from that tank. When heat must be stored and not added to the digester dur-
ing the winter, the 75-m tank of water could store about 4% days' worth of
heat input from the sun, assuming a 30-degree Celsius temperature rise:
75 m3 x (4.19 x 106 J/m3'C) x 30°C x (1/25 kW) = 377 ks (4.36 days).
Heat Transfer Unit
Various methods of construction were considered for the combination
solar heat storage and heat transfer unit. Of the more common materials
(wood, concrete, steel, and plastic), steel was chosen because of cost, ease
of construction, and availability. The tank could be buried in the ground
or supported above ground. Number three digester at the Annapolis plant
was convenient for the tank, located between the solar collector site and the
digester to be heated by solar energy. Sprayed-on urethane insulation with
24
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a sprayed-on protective coating of hydrocide elastomeric roofing (HER) was
the easiest and least expensive method of insulating the tank.
Unfortunately, the heat transfer rate between the solar-heated water
and raw sludge is very low due to the laminar flow of the sludge. Therefore,
the volume within the sludge pipe in the storage tank was made equal to the
volume of sludge pumped during each pumping cycle, 20 minutes out of each
hour. The volume pumped during each cycle is:
(2.31 x 10~4m3/s) x 3 x 1200 s = 0.832 m3.
The volume contained within five passes of 6-inch pipe is:
(3.14 x (0.152)2/4 x 9.45 m x 5 = 0.857 m5.
The raw sludge will remain in the heat storage tank for more than 40 minutes,
so that it should be at virtually the same temperature as the tank upon en-
tering the digester.
CONTROL SYSTEM
Figure 5 is a schematic diagram of the control system. Several control
systems were proposed, but the one shown proved to be the best and simplest,
and the lowest in cost. There are two different operating periods during
the year: winter and summer. At the beginning of the winter period, about
mid-October, the auxiliary gas boiler is fired up, and it remains on until
no more auxiliary heat is needed, about the end of March. Turning the boiler
on once a year is the only manual operation. As much solar heat is collec-
ted as possible except when the digester temperature exceeds 37 C. When the
temperature of the digester is about 37 C, the solar collector pump is pre-
vented from operating.
When the digester temperature is below 37 C, the collector pump is
turned on when the temperature on the surface of the copper plate in one of
the collectors rises to about 11 degrees Celsius above the temperature at the
bottom of the heat storage tank. When the temperature of the collector is
reduced to about 1.7 degrees Celsius above the storage temperature, the
pump is turned off. These on/off temperature differentials are adjustable
on the differential thermostat to provide optimum system operation, that is,
minimum cycling of the pump and maximum solar heat collected.
If the digester temperature falls to 33 C, the auxiliary heat circulat-
ing pump is turned on until the digester temperature rises above 33°C.
Three cases of adverse conditions will be described to demonstrate the
pperation of the automatic control system.
1. During summer operation when the digester temperature is 37°C and
when the temperature of the heat storage tank is very high (50 C),
will the digester overheat? The collector pump will be off, so no
heat will enter the heat storage tank. If the sludge were heated
to the storage temperature of 50 C, after one day, the digester
25
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Solar heat collectors
©
Collector pump
P.nlH
L!
Solar heat storage tank
Collector pump on when:
1. T, greater than 1 and
2. T3 less than 37C
Digester
©
Auxiliary heat
circulating pump
Auxiliary heat circulating pump on when:
T less than 33°C ~~
Boiler
tank
Auxiliary
gas boiler
Figure 5. Schematic diagram of automatic control system
26
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temperature would increase to 37.2 C. The storage temperature
would drop to 43°C. After the second day, the digester temperature
would still be at 37.2 C because heat losses would equal heat added
via the raw sludge. The temperature of the storage would be 37 C.
After the third day, the digester temperature would drop to 37.0 C.
and the storage temperature would be 33 C. Therefore, the digester
will not overheat in the summer with this control system.
2. During the critical winter period, what would happen if the solar
input became zero for five days and then returned to "normal" for
the next five days, starting with the digester at 33 C, heat storage
at 35 C, and heat losses of 32 kW? This is a severe test because
if the solar input were zero for five days it should be twice normal
for the next five days. Results of the calculations show that the
temperature of the heat storage would decrease from 35 C to 18.3 C
on the fifth day and increase to 35.1 C by the tenth day. The di-
gester temperature would remain at about 33 C throughout the 10-
day period. Auxiliary heat input would increase to a maximum of
about 29 kW on the fifth day, and then decrease to 15 kW by the
tenth day. During winter conditions such as this, the auxiliary
heating system would operate continually to maintain 33 C in the
digester, the solar heat storage temperature would vary depending
on the amount of solar radiation available, and the raw sludge
would be preheated to the temperature of the heat storage at any
given time.
3. During the summer, with the digester temperature at 37 C, the heat
storage at 43 C, and if solar radiation stopped for five days, the
digester temperature would drop to between 34 and 35 C after the
fifth day, and no auxiliary heat would be needed.
The control system is adequate to maintain the digester temperature
between 32 and 38 C during all days of all seasons of the year. As shown
by Figure 6, the curve of digestion period versus digester temperature is
very flat within this range. Note that this is the upper part of the meso-
phillic temperature range, which extends from about 10 to 38 C.
COMPUTER SIMULATION
Need for Computer Simulation
Two essential parameters, the efficiency of the solar heat collectors,
and the amount of heat transferred from the solar heat storage tank to the
raw sludge, depend on the temperature of the heat storage tank. Heat losses
from the tank, less important but significant, also depend on the temperature
of the heat storage tank. Heat inputs and outputs from the tank, however,
determine its temperature at any given time. The only way to determine the
system operation, therefore, is to actually simulate the system operation
over the annual cycle using equations for the various heat transfers, heat
losses, and efficiencies that contain heat storage temperature and time of
year as independent variables.
-------
w
O
i—i
H
CO
W
O
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PH
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CO
a
80
70
60
50
40
30
20
10
Source: Metcalf & Eddy, p. 605
DESIGN
35°C
-MESCPHILIC-
-THERMOPHILIC —
10 20 30 40
DIGESTER TEMPERATURE, °C
50
60
Figure 6. Digestion time versus digester temperature
Description of the Computer Program
The final form of the basic computer program used in this study, desig-
nated "SOL 4," is given in the appendix of this report. This program simu-
lates operation of the digester heating system on a daily basis over the
annual cycle, and prints an annual summary of all significant parameters. A
modification of this program, designated "SOL 5," also found in the appendix,
prints all heat transfer rates and temperatures every five days throughout
the year, as well as the annual summary. Both programs were written in
28
-------
standard FORTRAN IV computer language and were run on the Honeywell 1648
Series time-sharing computers of National Computer Network of Chicago, Inc.,
via teletype from Annapolis, Maryland.
The programs were run separately for each solar collector design. The
annual summary allowed plotting percent solar heat versus effective collector
area. Multiplying by cost of collectors per unit effective collector area
gave curves of collector cost versus percent solar heat. Thus the most
cost-effective collectors for this particular heating application could be
chosen.
For any given set of conditions, the computer program runs through all
calculations for one year without printing any results. This assures that
the system has been completely stablized for that particular set of conditions.
Values are recorded during simulation of the second year.
The computer program is centered around heat inputs to and outputs from
the solar heat storage tank. After each day of heat transfers, a new heat
storage temperature is calculated for use in determining heat transfers for
the next day.
Results are recorded with and without the horizontal reflector to eval-
uate the benefit of the reflector.
Equations for Use in Computer Program
Equations for most parameters were expressed as a lunction of time of
year, heat storage temperature, collector area, or some combination of these
variables. Parameters expressed as a function of time of year generally
very sinusoidally over the annual cycle. The variable "TY," time of year
in radians, starting with TY as zero at the spring equinox, was used in all
such equations.
Several sources of solar radiation data were analyzed for completeness,
accuracy, and capability of expression in the form required. The final equa-
tion used was derived from data given in the 1975 EI§I Associates guide,
"Determining the Availability of Solar Energy within the Continguous United
States."2 The variable F is an empirical factor that, when plotted versus
time of year, follows approximately a sine curve:
F = 0.725 + 0.175 *SIN (TY - 3.1416).
It is defined by the following equation:
F = CI/(SEXH*COS(DA))
where CI = Average terrestrial solar energy received on south-
facing surface (60 degree angle from horizontal), W/m
SEXH = Average extraterrestrial solar energy received on a
horizontal surface, W/m
29
-------
DA = Deviation angle = absolute value of difference between
angle of collector perpendicular to sun's rays at solar
noon and collector 60 degrees from horizontal, radians.
The fact that F and SEXH vary approximately sinusoidally over the annual
cycle allows CI to be expressed mathematically as a function of TY. Data
for the calculations are given in Table 6.
Table 6. DATA FOR DERIVATION OF EMPIRICAL EQUATION
FOR INCIDENT SOLAR RADIATION
Month
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
SEH
W/m2
262
227
185
142
92
75
85
118
165
203
236
270
SEXH
W/m2
466
418
342
258
189
157
174
235
313
396
454
478
RA
(Dimen-
sionless)
0.76
1.00
1.13
1.44
1.67
1.93
1.81
1.57
1.24
0.96
0.82
0.76
CI
W/m2
199
227
209
205
153
145
153
185
205
195
194
205
DA,
degrees
41.4
32.8
21.0
9.2
0.6
2.5
0.6
9.2
21.0
32.8
41.4
44.5
F
(Dimen-
sionless|
0.569
0.645
0.655
0.804
0.809
0.924
0.879
0.797
0.702
0.586
0.569
0.601
SEH = Average terrestrial solar energy received on a horizontal surface,
Annapolis, Md. (Table 2 of Ref. 2).
SEXH ^Average extraterrestrial solar energy received on a horizontal
surface, latitude 40°N (Table 1 of Ref. 2).
RA = CI/SEH ratio, derived from Figure lOc of Ref. 2, given latitude,
month, and SEH/SEXH ratio.
CI = (SEH) x (RA)
DA,F see text
30
-------
Computations for the effect of the horizontal concrete reflector are
given in Table 7. The following equation, used only when TY is greater than
3.1416, was derived as a best fit to the reflector data of Table 7.
REFL = 1.0 + 0.36 * SIN (TY - 3.1416).
The factor REFL is multiplied by CI to obtain the total radiation on the
collector when the reflector is used.
The equations for the efficiencies of the various solar collectors com-
pared in this study are equations for the best straight-line fit of data for
the collectors as shown in Figure 7. Where the experimental data points or
curves given by the manufacturers did not follow a straight line closely, the
best fit was chosen in the range of solar radiation and temperatures ex-
pected in this application.
SOLAR COLLECTOR AND STRUCTURE
Benefit of Reflector
The effective collector area required versus percent solar heat is
plotted in Figure 8 with and without the reflector. The effect of the refec-
tor is to increase the radiation incident on the collector during the critical
winter period, and therefore to reduce the amount of auxiliary heat required.
As can be seen in the graph, the reflector becomes increasingly more effective
as the percent solar heat increases. At 50 percent solar heat, for example,
the reflector eliminates the need for about 10 square meters of collector area.
At 100 percent solar heat, the reflector replaces about 240 square meters of
collector area.
The cost of the collectors, structure, and manifolds, including instal-
lation, is about $195 per square meter of effective collector area. The cost
of the reflector, however, is only about $15 per square meter of effective
collector area (the area of reflector is equal to the gross area of collector).
For an installation supplying 90 percent solar heat, 220 square meters of re-
flector, costing $3,300, would eliminate the need for 70 square meters of col-
lectors and associated structure and piping, costing $13,700. The net savings
would be $10,400.
White concrete was found to be unavailable, so it was decided to use a
slab of regular concrete with a very smooth surface painted brilliant white.
Selection of Collector
Costs per unit effective collector area for five collector designs are
given in Table 8. Effective collector area is the "aperture area," or area of
glass exclusive of the supporting framework. This is the area upon which
collector efficiencies were calculated in all cases except for the Solaris
collector for which only gross area data were available. Cost includes cost
of delivery to Annapolis, Maryland, which was estimated in some cases.
31
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RANGE OF (T - Ta)/I
EXPECTED FOR
MESOPHILIC DIGESTER
HEATING
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
(T - Ta)/I, °C - m2/W
Collector efficiency = a - b(T~ - Ta)/I
1. Solaris (trickle-type)
2 . Sunworks , single-glaze
3. Revere, double-glaze, 4 tubes
per 2-ft panel
4. PPG, double-glaze
5. Sunworks, double-glaze
0.85 13.5
0.75 6.14
0.69 4.14
0.73 4.31
0.72 4.00
Figure 7. Efficiencies of solar collectors evaluated in this study
(Derived from published test data)
33
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500
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400 I—
300 I—
200 h-
100 |—
SUNVvORKS DOUBLE-GLAZED COLLECTORS
WITHOUT REFLECTOR
WITH REFLECTOR
30 40 50 60 70
PERCENT SOLAR HEAT
90 100
Figure 8. Solar collector area required to supply given percent of
annual heat load, with and without horizontal reflector
Figure 9 shows graphs of effective collector area required versus per-
cent solar heat for five collector designs. Multiplying the required areas
by the cost per unit area of Table 8 gives, in Figure 10, the curves which
show the cost of the delivered collectors versus percent solar heat.
34
-------
Table 8. COST OF SOLAR COLLECTORS PER SQUARE METER
OF EFFECTIVE AREA
(Costs as of spring 1976)
Solar Collector Delivered Effective Cost per
cost per area per effective
panel, $ panel, m2 area, $/m2
Sunworks, single-glaze 185 1.75 106
Sunworks, double-glaze 215 1.75 123
Revere, 4 tubes per 2-ft 200 1.62 124
panel, double-glaze
PPG, copper, double- 211 1.50 140
glaze
Solaris (efficiency cal- 315 4.46 71
culated on basis of gross
area)
Up to about 84 percent solar heat, the Solaris collectors are the least
expensive, although the collector array would be larger (Figure 9), requiring
greater piping and structure cost. Above 84 percent solar heat, the Sun-
works collectors are least expensive. As will be shown later in this report,
solar sludge heating at Annapolis appears most economical at about 90 per-
cent solar heat. Therefore, the collector design will tentatively be chosen
based on this value.
The cost of the Sunworks double-glazed collectors for a 90 percent solar
heating system is about $800 more than the cost of the Sunworks single-
glazed collectors. The cost of the structure, manifolds, reflector, and
other components whose cost is directly proportional to the collector area
is about $88 per square meter of effective collector area. Since 242 square
meters of collector area are required for the single-glazed collectors, and
215 square meters are required for the double-glazed collectors, there is a
total net savings of about $1,600 if double-glazed rather than the single-
glazed collectors are used for a 90 percent system. As the percent solar
heat is increased above 90 percent, the savings become greater. Therefore,
as will be shown by the analyses which follow, the collector design that is
most economical for this application is the Sunworks double-glazed collector.
35
-------
450
400 —
350 —
w
2 300
O
H
O
H
O
O
W
O
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250 —
200 —
150 —
100
SUN WORKS
SINGLE-
GLAZE
SUN WORKS
DOUBLE-GLAZE
50
60 70 80
PERCENT SOLAR HEAT
90
100
Figure 9. Effective collector area versus percent solar heat
36
-------
40
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(0
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30
25
REVERE
20
15
10
— SUNWORKS, DOUBLE
GLAZE
SUNWORKS, SINGLE
GLAZE
50
60 70 80
PERCENT SOLAR HEAT
90
100
Figure 10. Cost of collectors, delivered to Annapolis
37
-------
Solar Collector Mounting
Of the various considerations that entered into the choice of collector
mounting arrangement, structural and manifold costs were prime considerations.
Another design constraint was the fact that an access roadway had to be main-
tained through the construction site. Therefore, the chosen arrangment con-
sists of two structures, each containing 65 panels in two rows. Each steel
structure is 30 meters (100 feet) long and the maximum height of each is 4
meters (13 feet). Figure 11 is a sketch of the mounting arrangment. The
entire plane is graded at a one percent slope so that all water in the supply
and return manifolds drains toward the heat storage tank when the solar col-
lector pump is off.
SOLAR COLLECTOR PIPING AND PUMP
Flow Rate Through Collectors
The flow rate through the collectors should be optimum for winter condi-
tions when it is important that the solar heating system operate most effi-
ciently. If the flow rate is very high, the average collector temperature
approaches the heat storage temperature, resulting in the highest possible
collector efficiency. The cost of the pump and piping, however, would be
high. If the flow rate is very low, the average collector temperature is
much higher than the heat storage temperature, producing low collector effi-
ency.
Figure 12 is a graph of collector efficiency and temperature rise
through the collector versus flow rate, based on typical winter conditions
and a typical double-glazed, flat-plat,solar collector efficiency curve. The
optimum flow rate is about 10 x 10_ m /s per m of effective collector area.
For the design consisting of 230 m of collector panels, the total optimum
flow rate would be 0.0023 m /s (36.5 gpm).
Piping
The size of the inside manifold pipe was chosen as nominal 2-inch
schedule 80 plastic pipe for the top, supply manifold and 3-inch for the
bottom, return manifold. The flow will be reasonably well distributed to
all panels. The pressure drop through each supply manifold will be less than
6000 Pa (2 feet), and the pressure drop through each set of two panels in
series has been calculated to be about 10,000 Pa (3.3 feet). Float-actuated
air vents at the highest point of each supply manifold will purge the system
of air upon filling and allow air to enter when draining.
The total head of the pump will be about 120kPa (40 feet), including
pressure drop through the supply piping, filter, and collectors, and eleva-
tion head. Using a pump efficiency of 60 percent and an electric motor
efficiency of 90 percent, the input power to the pump motor is as follows:
Input power = 120,000 Pa x 0.0023 m3/s (0.60 x 0.90) = 511 W (0.69 hp).
38
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COLLECTOR EFFICIENCY
TEMPERATURE RISE THROUGH
COLLECTOR
5 10 15 20
FLOW RATE x 106, m3/s/m? OF COLLECTOR AREA
January conditions
SOL = 8?5 W/m2
TA = 6°C
T = 40°C
CE = 0.69 - 4.14(TC - TA)/SOL
TC
= T +
AT
Figure 12. Collector efficiency and temperature rise
through collector versus flow rate
40
-------
A pump room is conveniently located adjacent to the Number Three digest-
er in which the heat storage tank is located. It was decided to place a
centrifugal pump, close-coupled to a 560-watt (3/4 hp) electric motor, in
the pump room. The pump will be flooded at all times. An ordinary enclosed-
impeller, single-volute type centrifugal pump will be used so that water can
easily drain backwards through the pump when the pump is turned off. Back-
flow of water through the filter will present no problem.
ECONOMIC ANALYSIS
Cost of Solar Heating System
All costs associated with the solar heating system were categorized as
to either fixed costs (independent of size of solar heating system) or
variable costs (proportional to the size of solar heating system). The
variable costs are expressed in terms of dollars per square meter of effec-
tive collector area. Because the solar heating system is completely auto-
matic, operator costs were assumed to be zero. Maintenance costs consist
primarily of repainting the reflector, structure, and heat storage tank; the
present worth of these costs over the project life of 25 years was included.
The cost of operating the solar collector pump (about $20 per year) was
neglected. The total present worth of all costs associated with the solar
heating system is summarized in Table 9. The cost of the solar heating
system versus percent solar heat is shown graphically in Figure 13.
Cost of Auxiliar>
The present worth of the amount of gas necessary to fulfill 100 percent
of the digester heat requirements over the project life of 25 years was
calculated as follows. According to the U.S. Department of Commerce publi-
cation, "United States Energy Through the Year 2000,"4 the price of all fuels
will rise faster than other commodity prices. In addition, the rate of price
increase for gaseous fuels is expected to be about 2.0 times the rate ex-
pected for coal. Using a rate of inflation of 6.0 percent per year, a con-
servative estimate for the rate of increase in the price of gas would be 12
percent per year.
Wholesale natural gas prices from 1960 through 1975 are plotted in
Figure 14. These data conform very closely with the continuous interest
equation:
r -v rn
p(n) = e
where p(n) = price in any year n
r = annual interest rate
n = year number
e = exponential constant, 2.71828....
41
-------
Table 9. SUMMARY OF SOLAR HEATING COSTS
(Present worth of all costs)
Item
Solar heat storage
tank, heat ex-
change, insula-
tion, paint
Filter
Pump
Sump pump
Sludge pipe
Digester pipe support
Controls
Supply, return pipe,
valves
Installation labor
Manifolds
Reflector
Structure
Site grading
Solar collectors
Maintenance
Fixed
cost
$
5,000
50
50
200
200
500
950
1,000
2,000
Variable
$/m2 of
collector area
49.10
1.10
1.10
5.57
23.70
19.70
14.70
27.90
2.10
123.00
28.30
costs
For 230 m2
collector area, $
11,300
250
250
1,280
5,450
4,530
3,380
6,420
500
28,300
6,500
Total
9,950
296.00
68,200
Present worth of total solar system = $9,950 + $296 (CA)
where CA = effective collector area, m2
A least-squares analysis has been made for two time periods, 1968--1975
and 1971--1975:
1. 1968--1975
2. 1971 — 1975
10.6% with a coefficient of deter-
mination of 0.877
16.52% with a coefficient of deter-
mination of 0.931
It is understood that the second figure may be reduced somewhat if the
OPEC monopoly can be broken, but that is a contingency that, from a con-
servative point of view, should not be anticipated. In any event, as
42
-------
C/3
J-i
to
(0
en
p
O
140
130
120
110
100
90
80
PRESENT WORTH OF GAS CONSERVED
PRESENT WORTH OF
TOTAL COST OF SOLAR
HEATING SYSTEM •
o 70
U3
60
50
40
30
20
10
OPTIMUM RANGE
SAVINGS DUE TO SOLAR HEAT
10 20 30 40 50 60 70 80 90 100
PERCENT SOLAR HEAT
Figure 13. Economic analysis
43
-------
2?0
200
180
x
0)
0)
u
-.— (
i_
CL,
CU
• — i
(0
160
140
120
100
80
Wholesale Price Indexes, by
Commodities 1960-1975, Statistical
Abstract 1975, U.S. Department of
Commerce, Bureau of Statistics, p. 418
1960
O
1965 1970 1975
Year
Figure 14. Wholesale Price, Natural Gas 1960-75
44
-------
petroleum reserves on shore and at shallow depth are exhausted, the real
costs of exploration can be expected to rise exponentially. An assumption
of 12.0 percent increase in prices is not unreasonable for fossil fuels in
general, and gas in particular.
The price of gas in any year n will be a factor of (1.12) times the
present price. The present worth of the cost in year n, using an inflation
rate of 6.0 percent, is (1.06) times the cost in year n. Summing for
values of n from 1 to 25 gives a factor, which, multiplied by the present
annual cost of gas, will give the total present worth of gas heating costs
over the 25-year period:
25 _ 25
Factor = JT (1.12)n x (1.06) " = 21 (i-O57)" = 55.3.
n=l n=l
The total annual heat requirement of the digester is 8.18 x 10 J.
Assuming a combustion efficiency of 66 percent, an amount of gas having a
net heating value of 8.18 x 101* J/0.66, or 1.24 x 1012 J would be required
annually.
Current prices of natural gas and other fuels are given in Table 10
along with the corresponding present annual cost of gas to fulfill 100 per-
cent of the digester heat requirement. The prices for natural gas at the
well-head and at the "city gate" are averages of the Federal Power Commission
regulated prices, which are well below fair market prices. If the interstate
gas prices are deregulated it is expected that the price of natural gas would
be equivalent to that of fuel oil at the present time. Considering the long-
term projections used herein, the most realistic present price of natural
gas would be the fair market value of $2.00/GJ, not an artificially low re-
gulated price. This is equivalent to a present cost for digester heating
of $2,480 per year. Multiplying by the factor 55.3 gives a present worth
for 100 percent gas heating of the digester over 25 years of $137,000. The
straight line on the graph (Figure 13) indicates the present worth of di-
gester gas saved versus percent solar heat.
Optimum Size Solar Heating System
Subtracting the solar heating cost of Figure 13 from the auxiliary heat
cost gives the present worth of the total savings as a result of using the
solar heating system. The maximum savings occurs at 85 percent solar heat
and is equal to about $50,000. The savings is within 5 percent of this
amount from values of percent solar heat from 80 to 94 percent. The solar
digester heating system for the Annapolis wastewater treatment plant will be
based on approximately 90 percent solar heat.
45
-------
Table 10. CURRENT PRICES OF NATURAL GAS AND OTHER FUELS
Fuel source
Gas, wellhead, Jan. '76a
Gas, "city gate," Jan. '76
Gas, intrastate, 1975°
Gas from solid waste
Fuel oil
Q
Gas, home heating
Gasoline
Price ,
$/GJ
0.364
0.837
1.80
1.97
2.45
2.53
4.98
Annual cost of 100% heating
one digester, $
450
1,040
2,230
2,440
3,040
3,140
6,170
o
Federal Power Commission, interstate, average 34 major pipeline
companies.
Federal Power Commission, interstate, average 34 major pipeline
companies.
Q
Standard 5 Poors Industry Surveys - Oil (Ref. 5), p. 71.
Fuel Gas Production from Solid Waste (Ref. 6).
Baltimore Gas § Electric Company residential gas rate, November,
1975 (Ref. 7).
46
-------
PART II
ECONOMIC FEASIBILITY OF SOLAR
DIGESTER HEATING THROUGHOUT
THE UNITED STATES
by
David E. Cassel
Environmental Sytems, Incorporated
Annapolis, Maryland 21401
Order No. CA-6-99-3499-A
47
-------
SECTION 4
INTRODUCTION, CONCLUSIONS AND RECOMMENDATIONS
INTRODUCTION
The use of solar energy to heat anaerobic sludge digesters was deter-
mined to be technically and economically feasible for Annapolis, Maryland.
The results of this study were reported in Part I of this report. This
nationwide study was undertaken to determine the economic feasibility of this
concept at all locations in the United States. In addition, it was desirable
to develop specific guidelines for sizing the most economical solar heating
system at any given location.
The solar heating system considered for use throughout the country is
identical to that described in detail in Part I for Annapolis, except as
modified for other locations according to the guidelines presented in Part II,
CONCLUSIONS
Solar heating of anaerobic digesters is economically feasible at all
locations in the United States. Areas of the country showing the greatest
economic attractiveness include Alaska, the central northwest states of
Montana, North Dakota, Nevada and southward to New Mexico, and also the east-
ern state of Maine. Least attractive areas include the southeastern United
States, especially Florida and southern Texas, and the northwest Pacific
coast. The degree of economic attractiveness of solar digester heating is,
generally speaking, proportional to the average annual solar radiation in-
tensity multiplied by the difference between digester temperature (35 C) and
average annual air temperature.
The optimum-size solar heating system, expressed as solar heat input to
the digester as a percentage of the total annual heat load, varies with
location from about 82 to 97 percent. In general, within this range, the
optimum percent solar heat for a given location varies in direct proportion
to the average annual solar radiation intensity. The optimum-size solar
heating system, in terms of solar collector area and total cost, is higher
for higher latitudes and lower for lower latitudes. However, since the di-
gester heating requirements are greater at the higher latitudes, economic
gains are also greater due to the comparatively low cost of solar heat com-
pared to the higher cost of heating with conventional fuels.
Of the three principal types of liquid flat-plate solar collector de-
signs evaluated, the most economical design for virtually all locations in
the United States consists of copper tubes attached to copper sheet with
48
-------
selective, high energy absorbing black coating, covered with two layers of
glass. Of the locations studies, a collector of the same design, but with
only one glass cover, proved to be marginally economical only at Miami,
Florida. The black coated, corrugated-aluminum, trickle-type collector with
one glass cover is shown to be the least economical design for digester heat-
ing an any of the locations evaluated.
RECOMMENDATIONS
All existing anaerobic sludge digesters in the United States should be
fitted with solar heating systems wherever it is physically possible to con-
struct the system. New wastewater treatment plants should be planned to
allow incorporation of solar-heated digesters as well as other energy con-
servation measures. Special effort should be made to use solar heat in areas
where it is most economically attractive.
Before construction of a solar digester heating system at a particular
location, the computer program contained herein should be run for that loca-
tion, to determine the optimum solar heating system, using the most accurate
design parameters available.
49
-------
SECTION 5
GUIDELINES
GENERAL
The following guidelines constitute modifications of the Annapolis de-
sign for heating anaerobic digesters with solar heat at any location in the
United States. The recommended procedure is to determine all major design
factors, in the order given, for a sludge flow rate equal to that used at
Annapolis (and in the computer model for all locations) and then scale cer-
tain factors to the given wastewater treatment plant size.
SPECIFIC GUIDELINES
Solar Collector Area
The optimum size of the solar heating system curve shown in Figure 15
is a function of the effective, or net solar collector only. The actual
gross, or total collector area required would be about ten percent greater
than the "net" surface area represented by the curve.
To estimate the optimum collector area for any location between 25 and
50 degrees north latitude in the United States, the following equation can
be used:
CA = S.O(Lat) - 110
2
where CA = effective collector area, m
Lat = north latitude, degrees
At locations greater than 50 degrees north latitude, use of the above
equation results in larger collector size than actually required for optimum
operation. It is for this reason that a data point for Fairbanks, Alaska,
also evaluated as part of the nationwide study, does not appear in Figure 15.
Cost of Solar Heating System
The cost of the solar heating system is proportional to the effective
solar collector area, according to the following equation (see Figure 16):
Cost = 9,950 + 296(CA)
50
-------
400
300 —
O
H
w 200
O
O
H
u
fc 100
w
CA - S.O(Lat) - 110
20
30 40 50
NORTH LATITUDE, degrees
60
1. Miami, FL
2. Corpus Christi, TX
3. Dallas, TX
4. Phoenix, AZ
5 . Los Angeles , CA
6 . Albuquerque , NM
7. Nashville, TN
8 . Annapolis , MD
9. Topeka, KS
10. Grand Junction, CO
11. Reno, NV
12. Salt Lake City, UT
13. Madison, WI
14. Portland, ME
15. Bismark, ND
16. Great Falls, MT
17. Seattle, WA
18. Fairbanks, AK
Figure 15. Determination of optimum size solar heating system
given latitude of loaction
51
-------
t/J
S-i
rO
i—i
"o
13
T3
C
(0
w
H
CO
CQ
O
I—I
H
W
ffi
o
CO
P-,
O
H
CO
O
O
130
120
110
100
90
80
70
60
50
40
30
20
10
Cost = $9,950 + $296(CA)
100
200
EFFECTIVE COLLECTOR AREA, m
300
2
400
Figure 16. Determination of cost of optimum-size solar heating system
given effective collector area
52
-------
where Cost = present worth of total cost of solar heating system,
dollars
2
CA = effective collector area, m
This represents the present worth of equipment, installation, operation and
maintenance costs over the 25-year project life. Immediate cash outlay
would amount to about 90 percent of the total cost.
Percent Solar Heat
Optimum percent solar heat, as shown in Figure 17, for a given location
can be estimated by the equation:
PSOL = 0.138(SEH) + 65
where PSOL = optimum percent solar heat, %
SEH = average annual solar energy on a horizontal surface,
W/m
Average annual solar energy for 125 cities in the United States is given
in Table 11, condensed from Reference 2.
The size of solar heating system that was determined from latitude
(Figure 15) should automatically provide the percent solar heat given by the
above equation. By knowing the value of percent solar heat for the optimum
design then the percent of the total annual heat load, and therefore the value
of the digester gas conserved can be determined.
Savings Due to Solar Heat
The savings due to solar heat are representative of the economic attrac-
tiveness of a solar heated digester at any given location. "Savings" is de-
fined as present worth of gas conserved, less present worth of the cost of
the solar heating system, both over the project life of 25 years. As shown
in Figure 18, savings can be estimated for a given location as follows:
Savings = 15.7(SEH)(35 - AMT) - 4,290
where Savings = present worth of savings due to optimum-size solar
heating system, $
2
SEH = average annual solar radiation, W/m
AAT = average annual air temperature, C.
Collector Angle
The flat-plate solar collectors should face approximately due south,
tilted at an angle of latitude plus 20 degrees from the horizontal as shown
in Figure 19.
53
-------
100
w
ffi
O
CO
W
O
OS
W
O,
H
OH
O
95
90
85
80
75
10,11
14 16
O O
O O4
PSOL = 0. 138(SEH) + 65
.13
120 140 160 180 200 220 240
AVERAGE ANNUAL HORIZONTAL RADIATION, W/m2
260
Figure 17. Determination of optimum percent solar heat
given average solar radiation
54
-------
Table 11. AVERAGE ANNUAL SOLAR ENERGY RECEIVED
ON A HORIZONTAL SURFACE
State City
Solar energy,
W/m2
State City
Solar energy,
W/m2
AK
AR
AZ
CA
CO
DC
FL
Annette
Barrow
Bethel
Fairbanks
Matanuska
Little Rock
Page
Phoenix
Tucson
Yuma
Davis
Eureka
Fresno
Inyokern
La Jolla
Los Angeles-
WBAS
Los Angeles-
WBO
Pasadena
Riverside
San Mateo
Santa Maria
Soda Springs
Boulder
Grand Junc-
tion
Grand Lake
Washington
Aplachicola
Belle Isle
Gainesville
Jacksonville
Key West
Miami
Pensacola
Tallahassee
Tampa
121
100
113
108
108
186
240
252
251
245
210
152
216
280
184
216
211
212
227
192
233
222
178
221
201
161
215
192
209
196
219
219
201
201
219
GA
HI
ID
IL
IN
IA
KS
KY
LA
MA
MD
ME
MI
MN
MO
MT
Atlanta
Griffin
Honolulu
Pearl Harbor
Boise
Twin Falls
Chicago
Lemont
Moline
Indianapolis
Ames
Dodge City
Kansas City
Manhattan
Topeka
Lexington
Louisville
Lake Charles
New Orleans
Shreveport
Blue Hill
Boston
Cambridge
East Ware-
ham
Lynn
Annapolis
Silver Hill
Caribou
Portland
East Lansing
Sault Ste
Marie
St. Cloud
Columbia
Glasgow
Great Falls
Summit
191
201
250
234
191
183
132
166
170
167
167
216
184
180
180
199
174
200
193
194
159
151
156
156
153
172
174
153
170
151
161
168
184
188
177
151
55
-------
Table 11 (continued).
State
NB
ND
/
NC
NT
NM
NV
NY
OH
OK
OR
PA
RI
SC
SD
TN
T^
City Solar energy, State City Solar energy,
W/m2 W/m2
Lincoln 176
North Omaha 183
North Platte 190
Bismarck 179
Cape Hat-
teras 216
Greensboro 185
Sea Brook 165
Trenton 172
Albuquerque 248
Ely 226
Las Vegas 246
Reno 232
Ithaca 146
New York 157
Sayville 170
Schenectady 136
Upton 172
Cleveland 155
Columbus 165
Put in Bay 161
Oklahoma
City 211
Stillwater 196
Astoria 146
Medford 136
Philadelphia 172
State College 162
Newport 164
Charleston 197
Rapid City 190
Oak Ridge 176
Memphis 192
Nashville 179
Brownsville 211
Corpus
Chris ti 211
Dallas 199
El Paso
Fort Worth
Midland
San Antonio
259
231
226
214
UT Flaming Gorge 2 06
Salt Lake
City
VA Norfolk
VT Burlington
WA Friday Harbor
Pullman
Prosser
Seattle
Spokane
Tacoma
WI Greenbay
Madison
Milwaukee
WY Lander
Laramie
191
185
153
155
180
193
132
175
145
158
157
167
214
198
56
-------
H
H
CO
O
H
-------
Reflector
Also as shown in Figure 19, the reflector should be positioned such that
the included angle between collector and reflector is 120 degrees. Reflector
width, "x" in Figure 19 should be equal to the length of the collector panels.
Collector Pump
A standard volute-type centrifugal pump should be used to circulate
water from the solar heat storage tank to the collectors. Pump total head
should be equal to the difference in elevation between the top of the col-
lectors and water level in the storage tank plus friction loss through the
supply piping and collectors. Flow rate through the collector should be
about 10-b m3/s (0.16 gallons per minute) for each square meter of collector
area.
Heat Storage Tank
Solar heat storage tank size is not critical, but the larger the better.
The suggested minimum tank size in cubic meters is obtained by multiplying
the solar collector area in square meters by 0.20.
SCALING TO PLANT SIZE
The optimum percent solar heat, collector angle, and reflector configura-
tion are independent of the size of the wastewater treatment plant or sludge
flow rate. Collector area, cost of the solar heating system, savings, pump
size, and solar heat storage tank size are all proportional to the sludge flow
rate. These five factors can be adjusted for plant size by multiplying the
values obtained from "Specific Guidelines" above by the ratio of the actual
average raw sludge flow rate divided by 0.236 kg/s. Alternately, they can
be multiplied by the number of persons served by the plant divided by 17,500.
58
-------
o
Latitude =60 N
Horizontal
Reflector
Collector
Latitude = 40° N
Horizontal
Collector
120
Reflector J
x
,o
Latitude = 20 N
Reflector
Horizontal
Collector
Figure 19. Optimum collector and reflector angles for three latitudes
(Cross section view looking west)
59
-------
SECTION 6
ASSUMPTIONS
ASSUMPTIONS USED IN ANNAPOLIS STUDY
Plant Operation
It is assumed that the raw sludge flow rate is an average of 0.236
with a heat capacity equal to that of water. A constant temperature of 35 C
is maintained in the digester. Digester gas consists of 40 percent methane
and 60 percent carbon dioxide by mass. The low heating value of methane is
used with a combustion efficiency of 66 percent. Heat loss from the digester
varies sinusoidally throughout the year with a maximum heat loss in January
and minimum in July.
Solar Heat Collection
Solar radiation varies gradually throughout the year based on monthly
averages. Radiation intensity is constant throughout the period of avail-
ability each day. Air temperature during solar heat collection is equal to
average daily temperature plus five degrees Celsius. Solar collector
efficiency curves are straight-line approximations of published data.
Economic Factors
Present cost of methane is estimated to be $2.00/GJ for all areas of
the United States, increasing at the rate of 12 percent per year throughout
the project life of 25 years. The inflationary rate is constant at 6 per-
cent per year. Cost of solar collectors is based on cost per unit effective
area for all collectors.
ADDITIONAL NATIONWIDE ASSUMPTIONS
It was necessary to include the following additional assumptions to ex-
pand the Annapolis study for nationwide application.
Plant Operation
Based on known raw sludge temperatures for two cities, Annapolis and
Boston^, the raw sludge temperature for all locations is expressed as a
function of ambient air temperature. Average annual sludge temperature was
assumed to be five degrees Celsius higher than the average annual air
60
-------
temperature, with an annual variation amplitude equal to one-third of the
air temperature variation. Annual variation in air temperature is sinusoidal,
with maximum in July and minimum in January, the curve of each location
approximating published monthly averages.
Heat loss from the digester walls was assumed to have the same absolute
value at all locations as at Annapolis. This requires only slightly more in-
sulation in colder climates, and less in warmer climates. Heat loss from the
solar heat storage tank, however, will vary according to air temperature for
different regions, because the same value of thermal resistance of the tank
insulation is used for all locations.
Solar Heat Collection
Average solar radiation on a horizontal surface varies sinusoidally
throughout the year, with maximum radiation on June 21 and minimum on
December 21. This value of radiation is adjusted by dividing by the cosine
of the angle of the collector perpendicular to the sun's rays at solar noon
for any given day, and multiplying by the cosine of the angle that the
collector deviates from that theoretical perpendicular collector. Solar
radiation intensity during collection is equal to the total energy received
by the collector during the day divided by both the collector area and one-
half the time between sunrise and sunset. The temperature of the water in
the collector is calculated assuming steady-state heat-transfer conditions
based on prevailing solar radiation intensity, water flow rate, and heat
storage temperature.
61
-------
SECTION 7
COMPUTER MODEL
COMPUTER PROGRAM
The computer program for this study, designated "SOL 6," is similar to
that used for the Annapolis study. The computer program is given in
Appendix B. Several modifications and improvements were made to the previ-
ous program "SOL 4" to facilitate input of data for various locations. The
basic logic is described in the following steps:
1. Set values of constants, set initial values of variables.
2. Collector area = 20 m .
3. Set initial values of maximum and minimum heat storage temperatures.
4. Set cumulative annual heat transfers to zero.
5. Calculate temperatures of air and raw sludge, digester heat re-
quired, and heat loss, for given day.
6. Calculate actual heat transferred to sludge from solar heat storage,
and auxiliary heat used, for given day.
7. Calculate solar heat storage temperature after heat is transferred
to sludge, but before solar input from collectors.
8. Calculate available solar energy input to heat storage for given
day.
9. Calculate heat storage temperature assuming all available solar
energy is collected.
10. Reduce solar heat storage input to amount required by digester if
necessary (summer operation); revise storage temperature.
11. Add all daily heat transfers to cumulative total to date.
12. Update maximum and minimum storage temperatures and their day of
occurrence.
13. If not last day of year, increment TY (time of year) for next day
and return to step #5; if last day of year, proceed to step #14.
62
-------
14. If this was first time through year, return to step #3; if second
time through year, proceed to step #15.
15. Calculate total annual percent solar heat.
16. Calculate present worth of total savings due to using given per-
cent solar heat over 25-year period.
17. Print out collector area, percent solar heat, and savings.
18. Update values of all parameters at optimum percent solar heat.
2
19. If collector area is less that 400 m , increase collector area by
20 m and return to step #3; if collector area = 400 m^, proceed
to step #20.
20. Print out annual summary of all parameters at optimum percent solar
heat.
SPECIFIC MODIFICATIONS
Several of the more important modifications of "SOL 4" to produce "SOL 6"
for this study are given below.
Addition of Economic Analysis
For each collector type and location, the revised computer program deter-
mines the most economical size of solar heating system. After running through
the year's calculations for a given collector area, the percent solar heat,
present worth of gas conserved, present worth of cost of solar heating system,
and savings are calculated. If the savings are greater than for the greatest
savings previously found, values for all annual summary parameters are revised
to reflect the new optimum size heating system. Incorporating the economic
analysis into the computer program allows quick and accurate analyses for all
locations.
Solar Heat Collection
The horizontal solar radiation equation is expressed in the following
form:
SEH = a + b * SIN(TY)
where SEH = average daily terrestrial solar radiation on a horizontal
surface, W/nr
2
a = average annual value, W/m
2
b = amplitude of variation throughout year, W/m
TY = time of year, radians, starting at spring equinox.
63
-------
The value of "a" is taken as the average of the maximum and minimum
monthly values from Table 12 of Reference 2. Figure 20 shows the average
monthly values of "SEH" together with the smooth curve derived from the maxi-
mum and minimum values only for two typical locations evaluated in this study.
400
w
O
<
PH
a;
ID
CO
O
O
CO
350 —
300 —
250 <£—
g 200
ffi
I »«
O
a 100
50
O - average monthly values from
Reference 2
derived curve
A
O N D J F M
MIDDLE OF MONTH
AMIJ
Figure 20. Comparison of measured average monthly solar radiation
and derived curve for use in this study, two typical locations
64
-------
Total solar energy input to the collectors during each day is expressed by:
CI = SEH * COS(DA) * P * CA/COS(PERP)
where Cl = total solar energy intercepted by collector during day, J
SEH = average daily terrestrial solar radiation on a horizontal
surface, W/nr
DA = deviation angle between actual fixed collector and one
that would be perpendicular to sun's rays at solar noon
each day, rad
P = period, equal to 86,400s (one day)
2
CA = effective collector area, m
PERP = angle of collector (from horizontal) that would be perpen-
dicular to sun's rays at solar noon each day, rad
The intensity of the solar radiation during collection is given by:
SOL = 2.0 * CI/(DAYL * CA)
where SOL = intensity of solar radiation during collection, W/m
CI = total energy intercepted by collector during day, J
DAYL = time between sunrise and sunset, s
2
CA = effective collector area, m .
The factor of 2.0 in the equation results from considering the solar radiation
to be constant over one-half of the time from sunrise to sunset. Length of
day is calculated each day based on latitude and time of year.
PROGRAM CHANGES FOR COLLECTOR DESIGN AND LOCATION
Collector Design
Three basic types of liquid flat-plate solar heat collectors were evalu-
ated at each location. The efficiency curves for each type are shown in
Figure 21. The specific variables in the program that were changed for each
collector type are given in Table 12.
Location
Table 13 gives the computer program variables that were changed before
running the program for each location. The locations were chosen to include
all of the climatic regions of the TRW studylO plus additional cities to cover
all geographical regions of the United States. Temperature data were taken
from World Climatic Data^.
65
-------
w
O
0)
o
>_
cu
a
100
90
80
70
60
50
o
§ 40
I—I
O
!—1
& 3°
20
10
0.0
Collector type:
1. CE = 0.85
2. CE = 0.75
3. CE = 0.72
13.5 *
6.14
4.00
(TC
* (TC
* (TC
TA)/SOL
TA)/SOL
TA)/SOL
0.02
0.04
0.06
0.08
0.10
(TC - TA)/SOL, C - m2/W
1. Solaris, trickle-type, single-glaze
2. Sunworks, tube-on-sheet, single-glaze
3. Sunworks, tube-on-sheet, double-glaze
Figure 21. Solar collector efficiency curves used in this study
(Taken from published research or manufacturers' collector
efficiency data)
66
-------
Table 12. VARIABLES IN COMPUTER PROGRAM
THAT CHANGE WITH COLLECTOR DESIGN
Collector Trade
type name
1
2
3
Solaris
Sun works
Sun works
Design
Trickle type, single-glaze
Tube-on-sheet, single-glaze
Tube-on-sheet, double-glaze
CE C in PWS
a b equation
0
0
0
.85
.75
.72
13
6
4
.50
.14
.00
244
279
296
CE = collector efficiency = a - b * (TC - TA)/SOL
PWS = present worth of cost of solar heating system, $ = 9,950 + c * CA
Table 13. VARIABLES IN COMPUTER PROGRAM
THAT CHANGE WITH LOCATION
Location City State
number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
AAAT
TAMPL
SEE
Miami
Corpus Christi
Dallas
Phoenix
Los Angeles
Albuquerque
Nashville
Annapolis
Topeka
Grand Junction
Reno
Salt Lake City
Madison
Portland
Bis mark
Great Falls
Seattle
Fairbanks
= average annual air
FL
TX
TX
AZ
CA
NM
TN
MD
KS
CO
NV
UT
WI
ME
ND
MT
WA
AK
AAAT
°C
23.9
22.4
18.8
20.6
16.6
13.7
15.6
13.1
12.5
11.4
9.6
10.5
7.9
7.2
5.7
7.4
10.6
-3.6
TAMPL SEH
°C
4.
8.
11.
10.
4.
12.
11.
11.
14.
14.
9.
13.
15.
12.
17.
12.
7.
20.
6
2
0
7
2
0
2
7
7
4
9
2
8
9
9
6
1
3
a
211
210
198
247
203
243
176
173
174
223
223
186
157
170
179
182
136
124
b
56
94
91
111
86
109
98
98
94
120
122
115
101
102
119
128
107
121
CLAT
Deg.
25
27
32
33
34
35
36
39
39
39
39
40
43
43
46
47
47
64
.8
.9
.6
.5
.0
.0
.2
.0
.0
.2
.5
.9
.1
.6
.8
.5
.7
.9
Rad.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
1.
451
486
573
585
593
611
631
681
681
684
689
713
817
762
817
829
832
132
temperature
= amplitude of annual air
= solar radiation on
temperature
variation
horizontal surface
(a = annual average, b
CLAT
= north latitude
= amplitude
, W/m2
of variation throughout
year)
67
-------
SECTION 8
RESULTS
An example of the computer print-out data obtained for each location and
collector design is given in Table 14. Each line of collector area, percent
solar heat, and savings is printed after simulation of operation of the
heating system for that particular collector area. The annual summary shows
values of various temperatures, heat transfers, dates, costs, etc. for the
optimum size system.
Graphs of savings versus effective collector area are plotted for the
three collector types for two locations in Figures 22 and 23. At Phoenix,
Arizona, the three collector types give almost the same maximum savings,
whereas at Seattle, Washington, the difference is much greater. These two
locations represent widely varying climatic conditions.
A summary of the results for all locations and collector types is given
in Table 15. These results apply to the optimum-size solar heating system
in each case.
The eighteen tested locations are listed in Table 16 in order of de-
creasing economic feasibility of solar digester heating. The most economical
locations have both high solar radiation and large heat demand. A good cor-
relation was found between savings and average annual solar radiation multi-
plied by difference between digester temperature (35 C) and average annual
air temperature (Figure 18).
68
-------
Table 14. EXAMPLE OF COMPUTER PRINTOUT DATA OBTAINED
FOR EACH LOCATION AND COLLECTOR TYPE
(Annapolis, Maryland, Collector type # 3)
Collector Percent Savings,
o
area, m solar heat $
CAO
PSOLO
VO
TMAXO
TYMAXO
TMINO
TYMINO
TOP
SHDTO
SHATO
HLTO
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
Annual Summary for
= 220 m2
= 90.2%
- 44.0 m3
- 46.02°C
= 216° (October 27th)
= 40.68°C
= 0° (March 21st)
= 40.74°C
- 844 GJ
= 761 GJ
= 25.8 GJ
11.6
21.0
30.3
39.6
48.5
57.1
65.3
73.2
80.2
85.8
90.2
93.7
96.6
98.8
99.9
99.9
99.9
99.9
99.9
99.9
Most
500
7,900
15,200
22,400
29,000
35,200
41,000
46,200
50,200
52,200
52,500
51,500
49,700
46,900
42,600
36,700
30,700
24,800
18,900
13,000
Economical Size
CITA
HSITO
HSOTO
AUXTA
K
PWSO
PWGCO
SAVO
SOL
DAYL
System
= 1,500 GJ
= 787 GJ
= 787 GJ
= 82.5 GJ
= 365
= $75,100
- $127,600
- $52,500
= 842 W/m2
= 43,040s (11.96
hours)
69
-------
i-H
a
i—i
,—i
o
<+-<
o
(0
en
O
CO
50
40
30
20
10
COLLECTOR TYPE #3
COLLECTOR TYPE #2
COLLECTOR TYPE #1
100 200
EFFECTIVE COLLECTOR AREA, m
300
2
400
Figure 22. Savings versus collector area for three collector types,
Phoenix, Arizona
70
-------
50
IQ
fO
i—i
i—i
O
-o
13
C
(0
w
a
o
co
O
CO
40
30
20
10
COLLECTOR TYPE
COLLECTOR TYPE #2
COLLECTOR TYPE #1
100 200 300
EFFECTIVE COLLECTOR AREA, m?
400
Figure 25. Savings versus collector area for three collector types,
Seattle, Washington
71
-------
Table 15. SUMMARY OF COMPUTER RESULTS
Location City State Collector PSOLO
number type %
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Miami
Corpus Christi
Dallas
Phoenix
Los Angeles
Albuquerque
Nashville
Annapolis
Topeka
Grand Junction
Reno
Salt Lake City
Madison
Portland
FL 1
2
3
TX 1
2
3
TX 1
2
3
AR 1
2
3
CA 1
2
3
NM 1
2
3
TN 1
2
3
MD 1
2
3
KS 1
2
3
CO 1
2
3
NV 1
2
3
UT 1
2
3
WI 1
2
3
ME 1
92
95
96
81
91
94
80
88
92
89
93
95
90
96
94
88
96
96
69
84
88
69
85
90
68
84
89
82
93
97
87
96
96
68
84
89
55
77
83
63
.9
.2
.9
.1
.5
.5
.6
.6
.3
.7
.1
.6
.3
.0
.8
.8
.9
.0
.8
.1
.6
.1
3
.2
.9
.5
.6
.7
.1
.0
.2
.2
.6
.7
.2
.0
.4
.8
.8
.7
CAO
m2
140
120
120
140
140
140
180
160
160
140
120
120
220
180
160
200
180
160
200
200
200
220
220
220
220
220
220
220
200
200
260
220
200
220
220
220
220
260
260
240
PWSO
$
44,
43,
45,
44,
49,
51,
53,
54,
57,
44,
43,
45,
63,
60,
57,
58,
60,
57,
58,
65,
69,
63,
71,
75,
63,
71,
75,
63,
65,
69,
73,
71,
69,
63,
71,
75,
63,
82,
86,
68,
100
400
500
100
000
400
900
600
300
100
400
500
600
200
300
800
200
300
800
800
200
600
300
100
600
300
100
600
800
200
400
300
200
600
300
100
600
500
900
500
SAVO
$
36,
38,
38,
32,
36,
37,
36,
44,
46,
48,
52,
53,
47,
58,
59,
64,
73,
75,
31,
42,
44,
34,
49,
52,
35,
50,
54,
60,
74,
76,
65,
81,
84,
42,
58,
62,
29,
48,
53,
40,
000
600
100
000
800
300
600
800
300
300
500
100
900
400
800
100
900
600
000
400
800
100
300
500
900
700
300
500
000
400
600
900
700
700
900
600
,500
200
,900
,700
72
-------
Table 15 (continuedj .
Location City State Collector PSOLO CAO
number type % m^
2
3
15 Bismark ND 1
2
3
16 Great Falls MT 1
2
3
17 Seattle WA 1
2
3
18 Fairbanks AK 1
2
3
89
91
69
86
88
73
87
92
46
75
81
72
85
91
.1
.7
.7
.5
.5
.7
.6
.3
.7
.5
.8
.8
.9
.1
280
260
260
260
240
260
240
240
180
260
260
340
300
300
PWSO
$
88
86
73
82
81
73
76
81
53
82
86
92
93
98
,100
,900
,400
,500
,000
,400
,900
,000
,900
,500
,900
,900
,700
,800
SAVO
$
64,
70,
51,
72,
77,
52,
72,
76,
18,
33,
39,
72,
101,
107,
700
500
500
500
600
400
500
400
200
900
200
300
100
900
Collector type:
1. Solaris, trickle type, single-glaze
2. Sunworks, tube-on-sheet, single-glaze
3. Sunworks, tube-on-sheet, double-glaze
PSOLO = percent solar heat at optimum size solar heating system
CAO = collector area for optimum size solar heating system
PWSO = Present worth of cost of optimum size solar heating system
SAVO = present worth of gas conserved less present worth of cost of
solar heat, for optimum size solar heating system (greatest
savings).
73
-------
Table 16. LIST OF EIGHTEEN TESTED LOCATIONS IN ORDER OF DECREASING
ECONOMIC FEASIBILITY OF SOLAR-HEATED DIGESTER
Location
City
Fairbanks
Reno
Bis mark
Great Falls
Grand Junction
Albuquerque
Portland
Salt Lake City
Los Angeles
State
AK
NV
ND
MT
CO
NM
ME
UT
CA
SAVO,
$
107,900
84,700
77,600
76,400
76,400
75,600
70,500
62,600
59,800
Location
City
Topeka
Madison
Phoenix
Annapolis
Dallas
Nashville
Seattle
Miami
Corpus Christi
State
KS
WI
AR
MD
TX
TN
WA
FL
TX
SAVO,
$
54,300
53,900
53,100
52,500
46,300
44,800
39,200
38,100
37,300
SAVO = present worth of gas conserved less present worth of cost of
optimum-size solar heating system, over 25-year project life
74
-------
REFERENCES
1. Metcalf and Eddy, Inc., Wastewater Engineering, McGraw-Hill Book Co.,
New York (1972).
2. El § I Associates, Determining the Availability of Solar Energy
within the Contiguous United States (1975).
3. American Society of Heating, Refrigerating and Air-Conditioning
Engineers, Inc., ASHRAE Handbook of Fundamentals, New York (1972).
4. Dupree, Walter G. Jr. and James A. West, United States Energy through
the Year 2000, Federal Stock No. 2400-00775, U.S. Department of the
Interior (December 1972).
5. Standard § Poors Industry Surveys - Oil, Section 2, p. 71 (June 26, 1975).
6. Dynatech R/D Company, Fuel Gas Production from Solid Waste, Cambridge,
Massachusetts, report for NSF/RANN (July 31, 1974).
7. Baltimore Gas S Electric Company Residential Gas Rate (November 1975).
8. Dynatech R/D Company, Fuel Gas from Solid Waste, Cambridge, Massachusetts,
report for NSF/RANN (July 31, 1974).
9. Frederick L. Wernstedt, World Climatic Data, Climatic Data Press,
Lemont, Pennsylvania 16851 (1972).
10. Solar Heating and Cooling of Buildings (Phase 0), prepared by TRW for
the National Science Foundation, report #NSF-RA-N-022A (May 1974).
75
-------
APPENDIX A
COMPUTER PROGRAMS
Definition of Symbols, SOL 4
M
P
XK
HC
SFR
T
R
CA
V
N
K
TY
TMAX
TYMAX
TMIN
counter (M = 1 without reflector, M = 2 with reflector)
period = 86,400s (1 day), calculation interval
thermal conductivity of storage tank insulation, assuming
4" thick fiberglass, = 0.353 W/m2C
heat capacity of water and sludge = 4.19 x 10 J/m C
sludge flow rate, m /s
temperature (vertical average) of water in solar heat
storage tank, C
3 2
ratio of storage volume, m , to collector area, m
collector area, m
3
volume of solar heat storage tank, m
counter, year number of iterations (values of heat inputs,
etc. are recorded only for N = 2)
counter, day number, should equal 365 at end of year
time of year, radians, varies from 0 on March 21st to
2 IT one year later
maximum temperature reached in heat storage tank during
year, C
time of year of occurrence of maximum temperature in heat
storage tank, degrees (March 21 = 0, April 21 = 30, etc.)
minimum temperature reached in heat storage during year,
76
-------
TYMIN
SHOT
SHAT
HLT
HSOT
time of year (degrees) of occurrence of minimum temperature
in heat storage tank
sludge heat desired total = total annual heat input to
digestr, J
sludge heat actual total = total annual heat actually trans-
ferred from solar heat storage tank to raw sludge, J
heat loss total = total annual heat loss from heat storage
tank to surrounding air, J
heat storage output total = total annual heat output from
heat storage tank, J
CIT
collector input total = total annual solar radiation incident
on collector, J
AUXT
HSIT
auxiliary heat total = total annual auxiliary heat used, J
heat storage input total = total annual heat input to solar
heat storage tank, J
SLIT
SHD
SLOTD
sludge inlet temperature = temperature of raw, cold sludge
as it enters solar preheater, C
sludge heat desired = required heat input to digester during
period P, J
sludge outlet temperature desired - temperature of raw sludge
as it exits solar preheater so that no auxiliary heat is
needed, C
TAM
temperature ambient mean = average daily outdoor temperature,
A
HL
SHA
AUX
HSO
TI
area = surface area of heat storage tank, m
heat loss = heat loss from storage tank to surrounding air
during period P, J
sludge heat actual = actual heat transferred from solar heat
storage tank to raw, cold sludge during period P, J
auxiliary heat input to digester during period P, J
heat storage output = heat output of storage tank during
period P, J
temperature of heat storage after heat is removed, but before
heat is added, C (for system simulation purposes only)
77
-------
SEXH
PERP
DA
CI
REFL
TA
TC
SOL
CE
HSI
PSOL
factor = empirical factor relating horizontal e^trater-
restrial and terrestrial solar radiation, dimensionless
solar energy extraterrestrial horizontal = average daily ex-
traterrestrial solar energy received on a horizontal surface,
W/m (Annapolis, Maryland)
angle of collector perpendicular to sun's rays at solar noon,
radians
deviation angle = absolute value of difference between 60
collector angle and angle of collector perpendicular to the
sun's rays at solar noon, radians
collector input = total radiation incident on collector dur-
ing perido P, J
reflector = factor representing increased incident radiation
on collector due to reflector, dimensionless
ambient temperature during collection of solar energy, C
average temperature of collector during collection of solar
energy, C
2
solar insolation during collection, W/m
collection efficiency of collectors, dimensionless
heat storage input = heat input to storage tank during
period P, J
percent solar = total annual solar heat actually transferred
to sludge divided by total annual heat required by digester,
dimensionless
Additional Symbols Used in SOL 5
SHD5
HL5
CIS
HSI 5
SHA5
AUX5
HS05
PERP5
DAS
counter that triggers printout every 5 days, dimensionless
heat transfer rates,
W, printed every
5 days
angles, degrees,
printed every 5 days
78
-------
7LIST SOL4
90 M = 1
100 P = 86400.
HO XK = 0.353
120 HC = 4190000.
130 SFR = 0.000231
140 T = 35.
150 H = 0.20
160 10 CA = 50.
170 15 V = CA*K
180 N = 1
190 20 K =1
200 TY = 0.
210 TMAX = 0.
220 TYMAX = 500.
230 TMIN = 150.
240 TYMIN = 500.
250 SHUT = 0.
260 SHAT = 0.
270 HLT = 0.
280 HbOT = 0.
290 CIT = 0.
300 AUXT = 0.
310 HSIT = 0.
320 25 SLIT = 19. + 3.*SIN(TY-.5236)
330 SHD = (25900. + 5700. * SIN(TY-3.665))*P
340 SLOTD = SLIT + SHD/(SFR*HC*P)
350 TAM = 13.1 -«• 11.7 * SIN (TY-0.5236)
360 A = 6.2*V**0.6667
370 HL = XK*A*(T-TAM)*P
380 IF (T.LT.SLIT) GO TO 30
390 SHA = n-SLIT)*HC*SFR*P
400 IF(SHA.LT.SHU) GO TO 40
410 SHA = SHD
420 GO TO 40
430 30 SHA = 0.
440 40 AUX = oHD-SHA
450 HSO = SHA + HL
460 Tl = T - HSO/(HC*V)
470 F = 0.725 + 0.175*SIN(TY-3.1416)
480 SEXH = 318. + 160.*SIM(TY)
490 PERP = 0.6807 - 0.4102*SIN(TY)
500 DA = ABSU.047-PERP)
510 CI = F*SEXH*COS(DA)*P*CA
520 IF (M.EQ.2) GO TO 42
530 GO TO 45
540 42 IF (TY.LT.3.1416) GO TO 45
79
-------
SOL 4, continued
550 REFL = I.0 + 0.36*SIN(TY-3.1416)
b60 CI = CI * REFL
570 45 TA = 18. + 11.7 * SINCTY-0.5236)
580 TC = T + 3.0
590 SOL = CI * 4.0/(P*CA)
600 CE = 0.73 - 4.31 * (TC-TA)XSOL
610 HSI = CI*CE
620 T = Tl + HSI/(HC*V)
630 IF (T.LT.SLOTD) GO TO 50
640 T = SLOTD
650 HSI = (SLOTD-T1)*HC*V
660 50 SHOT = SHOT + SHD
670 SHAT = SHAT + SHA
680 HLT = HLT + HL
690 HSOT = hSOT + HSO
700 CIT = CIT + CI
710 AUXT = AUXT + AUX
720 HSIT = HSIT + HSI
730 IF (T.LT.TMAX) GO TO 60
740 TMAX = T
750 TYMAX = TY*57.2958
760 60 IF (T.GT.TMIN) GO TO 70
770 TMIN = T
780 TYMIN = TY*57.2958
790 70 IFCTY.GT.6.2574) GO TO 80
800 TY = TY + 0.0172142
810 K = K + 1
820 GO TO 25
830 80 IKN.EQ.2) GO TO 90
840 N = N + 1
850 GO TO 20
860 90 PSOL = SHAT/SHDT
870 WRITE (9,92) CA,PSOL,V,TMAX,TYMAX
880 WRITE (9,92) TMIN, TYMIN, T,SHDT, SHAT
890 WRITE (9,92) HLT, CIT, HSIT, HSOT, AUXT, K,M
900 92 FORMAT (5E11.4,216)
910 IFCCA.GT.580.0) GO TO 95
920 CA = CA + 50.
930 GO TO 15
940 95 IKM.EQ.2) GO TO 97
950 M = M + 1
960 GO TO 10
970 97 STOP
980 END
80
-------
?LlbT bOL5
90 ,/, = 1
100 F = 86400.
110 XK = 0.3b3
120 HC = 4190000.
130 b>R = 0.000231
140 T = 35.
150 R = 0.20
160 10 CA = 230.
170 15 V = 75.
180 N = 1
190 20 K = 1
195 J = 1
200 TV = 0.
210 TfoAX = 0.
220 T'K.'iAX = bOO.
230 TmIN = 150.
240 TY.ViIN = 500.
250 SHUT = 0.
2oO 6 HAT = 0.
270 HLT = 0.
280 hbOT = 0.
290 C1T = 0.
300 AUXT = 0.
310 hbIT = 0.
320 25 SLIT = 19. + 3.*b'IN(TY-.:J236)
330 bhu = (25900. + 5700. * SIN(TV-3.662))*P
340 SLOTD = SLIT + bHD/(SFR*HC*P)
3^0 TAM = 13.1 + 11.7 * bi;
-------
SCL 5, continued
525
D30
540
550
D60
570
b80
590
600
610
620
630
640
£00
660
670
680
o90
700
710
720
730
740
750
760
770
772
774
776
778
780
782
784
786
788
790
792
794
796
798
800
802
804
806
808
810
812
814
HEFL = 100.
GO TO 4i)
42 IF (TY.LT.3. 1416) GO TO 45
REFL = 1.0 + 0.36*bLHTY-3.14l6
CI = CI * RtirL
45 TA = 18. + 11.7 * bLJ(TY-0.5236
TC = T + 3.0
SOL = CI * 4.0/(P*CA)
CE = 0.72 -4.00*(TC-TA)/bOL
rib I = C1*CE
T = Tl + rib I/ ( HO V)
IF (T.LT.SLOTD) GO TO 50
T = b'LOTD
Hbl = (SLOTLJ-T1 )*HOV
50 b'HUT = SHUT + bHD
biiAT = bhAT + SHA
HLT = nLT + HL
HSOT = HbOT + HbO
C1T = CIT + CI
AUXT = AUXT -i- AUX
HbIT = rib IT + Hbl
Ih (T.LT.TMAX) GO TO 60
T/viAX = T
TYMAX = TY*57.2958
60 IF (T.GT.TMIN) GO TO 62
TM11J = T
TYMIN = TY*57.2958
62 Ih (N.EQ.2) GO TO 63
GO TO 70
63 IF (J.hQ.b) GO TO 65
GO TO 70
65 brlUS = SHb/F
MLt> = iiL/P
CI5 = Cl/P
HbI5 = ribl/P
bi4A5 = bhA/P
AUXb = AUX/P
Hb05 = HbO/P
PEHPb = PERP*57.3
DA5 = UA*57.3
riHlTH (9,67) 3HlJ5,hL5,bHAb,AUX5
WklTE (9,67) HbObtCI5TH5I5tF,CE
HklTfci (9,67) bEXH,b()L,PERP5,DAb
rtHITE (9,67) bLOTD, b'LIT, TAM,
J = 0
67 FORMAT (5F1 1 .4, 216)
70 IF(TY.GT.6.2b74) GO TO 80
T* = TY + 0.0172142
)
)
,T,K,M
,REFL
TA, TC
82
-------
SCL 5, continued
816 K = K + 1
818 J = J + 1
820 GO TO 25
830 80 IKH.EQ.2) GO TO 90
840 rJ = N + I
850 GO TO 20
860 90 PbOL = SHAT/bHUT
870 WHITE (9,92) CA,PSOL,V,TMAX,TYMAX
880 WHITE (9,92) TMIN, TYMIN, T,SHDT, SHAT
890 H'klTE (9,92) HLT, CIT, HSIT, HSOT, AUXT, K,M
900 92 FORMAT (5E 11.4,216)
940 95 IHM.EQ.2) GO TO 97
950 M = M + 1
960 GO TO 10
970 97 STOP
980 EMU
83
-------
APPENDIX B
Computer Program "SOL 6" Symbols
The following list of symbols contains only those used in computer pro-
gram "SOL 6" that did not appear in the previous computer program "SOL 4" of
the Annapolis study. The number given is the computer program line number
in which the symbol first appears.
160 SAVO
330 AAAT
340 TAMPL
350 SLITM
360 SLITAM
380 HLD
390 SLTH
540 SEH
550 CLAT
630 D
640 X
650 Y
660 ANG
670 DAYL
690 Q
Present worth of gas conserved less percent worth of
cost of solar heating system, for optimum-size solar
heating system, $
Average annual air temperature, C
Amplitude of variation of air temperature throughout the
year, C
Average annual raw sludge temperature, C
Amplitude of variation of raw sludge temperature through-
year, C
Rate of heat loss from digester to surrounding ground
or air, W
Rate of heat input to raise temperature of raw sludge to
35°C, W
2
Solar energy received on a horizontal surface, W/m
Latitude, rad
Earth's declination angle from sun-earth plane, rad
Argument of arcos (arc cosine) in daylight equation
Subroutine for arcos
Subroutine for ARCOS "X"
Time between sunrise and sunset, s
Water flow rate through collectors per unit collector
area, m /s • m^
84
-------
990 PWS
1000 EFF
1010 PPRICE
1020 FAC
1030 PWGC
1040 SAVING
1080 PSOLO
1090 CAO
1100 VO
1110 TMAXO
1120 TYMAXO
1130 TMINO
1140 TYMINO
1150 TOP
1160 SHDTO
1170 SHATO
1180 HLTO
1190 CITA
1200 HSITO
1210 HSOTO
1220 AUXTA
1230 PWSO
1240 PWGCO
Present worth of cost of solar heating system, $
Efficiency of combustion of methane, dimensionless
Present price of methane based on low heating value, $/J
Factor which, when multiplied by present annual cost of
gas, will give the total present worth of gas heating
costs over the 25-year period, dimensionless
Present worth of gas conserved, $
Present worth of gas conserved less present worth of
solar heating system, $
Line numbers 1080 through 1240:
These symbols ending in "0" (or in some cases "A" or
"OP") have the same meaning as corresponding, in the
Annapolis study, parameters without the suffic; these
symbols, however, refer to the value for the optimum-
size solar heating system.
85
-------
VLlbT bOL6
100 F = 86400.
110 XK = 0.353
12C HC = 4190000.
130 bt;R = 0.000231
140 T = 3o.
IbO ii = 0.20
160 bAVO = 0.
170 10 CA = 20.
180 15 V = CA*R
190 N = 1
200 20 K =1
210 TV = 0.
220 TmAX = 0.
230 TYMAX = 500.
240 Tiv,ii4 = 150.
2^0 TY,..i;4 = 300.
260 onlJT = 0.
270 bHAT = 0.
280 HLT = 0.
290 HbOT = 0.
300 CIT = 0.
310 AUXT = 0.
320 MbIT = 0.
330 AMI = 12.5
340 TA^FL = 14. /
350 bLITrt = AAAT + o.0
360 6LITAM = TAMPL/3.0
370 25 bLIT = b'LIT.i + bLITAM*SIN(TY - 0.5236)
380 nLu = 10400. + 2800.*b'IH(TY - 3.665)
390 bLTH = bM-i * HC * (35.0 - bLIT)
400 bhU = (riLD + SLTH)*F
410 bLOTL) = bLIT + bHD/ (bF^*HC*P)
420 TAM = AAAT + TAMPL*bIN(TY - 0.5236)
430 A = 6.2*V**0.6667
440 HL = XKxA*(T-TAM)*P
4^0 Ih (T.LT.bLIT) GO TO 30
460 bhA = Ci-5LIT)*HC*bi-rf*F
4/0 Ih(bHA.LT.bhD) GO TO 40
480 bHA = bhL
490 GO TO 40
500 30 bhA = 0.
510 40 AUX = bHL-bHA
520 i4b() = bHA + HL
530 Tl = T - Hb()/(HC*V)
540 bHH = 174. + 94.*bIN(TY)
5DO CLAT = 0.681
86
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SCL 6, continued
b60 PEi?P = CLAT - 0.4102*5irt(TY)
b/0 DA = Ai3b(0.3491 + 0.41 02*SIrI ("i'Y ))
580 CI = 5EH*COb(uA)*P*CA/C()S(PE«P)
590 42 Ii- (TY.LT.3. I 416) GO TO 4o
000 r^ErL = 1.0 + 0.3o*bIN(TY-3.l416)
oiO CI = Ci -A- REFL
620 45 TA = TA..1 + 5.0
630 L) = 0.410*COb(TY-l.571)
04C X = (-b 1 ;•,'( CLAT )/COb< CLAT)) * (oln*( D) /C0b( J )
650 Y = bQl-Tf(1.0 - X*X)
660 ANG = ATAN2(Y,X)
670 UA¥L = 27500. * ANG
080 bOL = 2.0*CI/(uAYL * CA)
ov'O J = 0.000010
100 TC = T + b'()L/(HC*(j*2.0)
710 CE = O./i? - 6.14*(TC-TA)/b'OL
720 Hbl = CI-A-CE
/30 T = Tl + H3i/(riOV)
740 1'r (T.LT.5LCJTD) GO TO 50
750 T = bL'JTL
760 Hbl = (bLOTL-Tl)*HC*V
770 bO Sr-iOT = biiDT + 5HD
780 b'hiAT = ShAT + bHA
790 HLT = nLT + HL
800 hbOT = HbOT + rib()
810 CIT = CIT + CI
820 All XT = AUXT + AUX
530 HbIT = HbIT + ij,bl
840 If (T.LT.TMAX) GO TO 60
8DO TMAX = T
800 TYi-lAX = TY*57.29D8
870 60 If (T.GT.TMIiO GO TO 70
880 TMIi^ = T
890 THilN = TY*57.2958
900 70 IhCTy.GT.6.2574) GO TO 80
910 TV = TY + 0.0172142
920 K = K -»• 1
930 GO TO 25
940 80 Ir(il.EQ.2) GO TO 90
950 N = N + 1
960 GO TO 20
970 90 PbOL = bHAT/bHDT
980 91 HOHMAT(7h CA = ,f-5.0,9H PbOL = tF5.3,llri
bAVI/,G = ,E 1 1 ,4;
990 Pub = 9950. + 279.*CA
100G EH-' = 0.66
1010 PPRICE = 0.000000002
1020 FAC = 05.3
1030 PhGC = (bHDT/EFf-)*PPRICE*FAC*PSC)L
87
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SOL 6, continued
1040 SAVING = Pi'-JGC - Pnb
1050 k'JKITE(9,9 1)CA,PSOL,SAVING
1060 Ii- (SAVING.LT.SAVO) GO TO 94
1070 SAVO = SAVING
1080 PSOLO = PSOL
1090 CAO = CA
1100 VO = V
1110 Ti.tAXO = I'M AX
1 120 TYMAXO = TYMAX
1 130 TMINO = TMIN
1140 TY.alNO = TYMIN
1150 TOP = T
1 160 ShDTO = SHOT
1 170 SHATO = SHAT
1 180 HLTO = fiLT
1 190 CITA = CIT
1200 MS I TO = hb'IT
1210 Hb'OTO = HSOT
1220 AUXTA = AUXT
1230 PliS'O = PuS
1240 Pl.GCO = P.JGC
1250 94 IKCA.GT.390,) GO TO 95
1260 CA = CA + 20.
1270 GO TO 15
1280 95 i.'RITE (9,96) CAO, PSOLO, VO, TMAXO, TYMAXO
1290 »-JHiTE(9,96) TlMIHO,TYMINO,TOP ,SiiDTO,SHATO
1 300 h'RI TH (9 ,96) i .LT(), C1TA , HSI TO, HSuTO, AU XTA, K
1310 ;»!kITE(9t96)PWSO,Pl';GCO,SAVO,SOL,DAYL
1320 96 FORMATC5E11.4,216)
1330 SIOP
1340 END
88
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-78-114
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
USE OF SOLAR ENERGY TO HEAT ANAEROBIC
DIGESTERS; Part I - Technical and Economic Feasibility
Study; Part II - Economic Feasibility Throughout the
United States
5. REPORT DATE
July 1978 (Issuing Date)
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Jess W. Malcolm and David E. Cassel
8. PERFORMING ORGANIZATION REPORT NO,
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Systems, Incorporated
150 South Street
Annapolis, Maryland 21401
10. PROGRAM ELEMENT NO.
1BC611
11. CONTRACT/GRANT NO.
Part IrContract No.68-03-2356
Partll: Order No. CA-6-99-3499-A
12. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research Laboratory--Cin.,OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
Feasibility studyll/5/75-6/1/76
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
Project Officer: R. V. Villiers (513) 684-7664
16. ABSTRACT
Two distinct, yet related studies were conducted to determine the technical and
economic feasibility of using solar energy as the source of heat for the anaerobic
digestion process. Retrofitting a solar energy collection and heat transfer system to
a digester at Annapolis, Maryland was proven feasible in the first part of the study
and the concept of using solar energy for digester heating throughout the United States,
including Fairbanks, Alaska, was shown to be economically feasible in the second part
of the study.
The Part I study compared five (5) types of flat plate collectors and selected the
cost effective design to supply approximately 90 percent of the heat load to maintain
digester operating temperatures of 32 to 38 degrees Celsius. Three flat plate collec-
tors of varying efficiencies were evaluated for use at numerous locations in the
United States. The study showed that optimum-sized flat plate collectors can provide
from 82 to 97 percent of the total annual digester heat, the higher percentages being
applicable to areas of higher solar radiation.
The Part II study developed specific guidelines for determining the optimum size
and conceptual design for a solar heating system for any size sludge digester at any
location.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
Solar Heating
Sludge Digestion
Solar Energy
Waste Treatment
Economic Analysis
Solar System Engineering
Solar Heated Anaerobic
Digesters
Solar Energy Economy
Design Guidelines
13B
18. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
101
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (Rev. 4-77)
89
»US GOVERNMENT PRINTING OFFICE 1978—757-140/1438
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