GROUND WATER EVALUATION AND COOLING BEFORE UTILIZATION FOR WADI ZAMZAM, LIBYA by
GROUND WATER EVALUATION AND COOLING BEFORE
UTILIZATION FOR WADI ZAMZAM, LIBYA by
Omar Ali Jarroud
A Thesis Submitted to the Faculty of the
DEPARTMENT OF HYDROLOGY AND WATER RESOURCES
In Partial Fulfillment of the Requirements
For the Degree of
MASTER OF SCIENCE
WITH A MAJOR IN HYDROLOGY
In the Graduate College
THE UNIVERSITY OF ARIZONA
1977
STATEMENT BY AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made.
Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship.
In all other instances, however, permission must be obtained from the author.
SIGNED:
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
D. D. EVANS
Professor of Hydrology and
Water Resources
Date
To my mother
ACKNOWLEDGMENTS
I am deeply thankful to my family, their constant encouragement and moral support have made this thesis a reality.
I am grateful to
Dr.
Daniel D. Evans, who supervised my graduate work, for his encouragement, patience, and advice.
Dr.
Rocco A. Fazzolare generously gave of his time to advise me on various aspects of my thesis. I wish to thank
Dr.
K. James
DeCook and
Dr.
Simon Ince, members of my committee, for their interest in the progress and subject matter of my thesis.
Special thanks are given to Non i Esbak and the Libyan General
Water Authority staff for their assistance in collecting data by supplying valuable information and equipment.
I wish to extend thanks to the Wadi ZamZam
Project Authority for the gracious hospitality expressed while allowing me to collect essential measurements.
Special appreciation is given to Christine C.
Milsud for suggestions in improving the manuscript and plotting some graphs.
iv
TABLE OF CONTENTS
LIST OF ILLUSTRATIONS
LIST OF TABLES
ABSTRACT
I.
INTRODUCTION
The
Problem
Scope of the Investigation
2. GROUND WATER EVALUATION
Background
Location and
Extent of the
Area
Climate
Topography
Natural Resources and Population
Previous Investigation
Geology
Quaternary
Eocene
Paleocene
Cretaceous
Ground Water
Aquifers
Characterization of
Chicle Sandstone Aquifer
Extent of the
Aquifer
Discharge and
Movement
Recharge to Ground Water
Transmissivity and
Storage
Coefficient
Interference Effect within the
Well
Field
Piezometric
Head
Well Specifications
Artesian
Head and
Discharge
Well Spacing
Well
Design
Estimating
Head
Losses Inside the
Well
Water Quality for the
Chicle Sandstone Aquifer
Chemical Analysis
Corrosion
Tendency
Page vii xi
xii
2
3
4
30
38
38
4o
42
45
45
45
48
9
9
12
14
15
15
20
20
22
22
24
24
25
26
26
28
6
4
4
1
v i
TABLE OF
CONTENTSContinued
Page
Conclusions and Recommendations of
Ground Water
Evaluation
First Aquifer
Second
Aquifer
Third Aquifer
3. GROUND WATER COOLING
Introduction
Evaporative Cooling  Heat
Dissipation
Cooling
Pond
Completely Mixed
Pond
Energy
Budget
ShortWave Solar
Radiation
Atmospheric LongWave
Radiation
Reflected Atmospheric
Radiation,
(p ab
Reflected Solar
Radiation,
(Psb
Back
Radiation
(
1
5 br
Energy
Flux Due to Evaporation,
(p e
Convection,
(p
c
Methods of
Calculation
Results and Discussion
Spray Pond
Cooling Tower
Theory of
Heat Transfer in
Counterflow Evaporative
Cooling
Theory of
Heat Transfer in
Cooling Towers
Solutions of
Equations (3.44) and
(3.45)
Pressure Drops in
Cooling Towers
Mechanical Draft Tower Costs
Computation Procedure
Results and Discussion
Conclusions and
Recommendations
Conclusions
Recommendations
APPENDIX
A:
DEFINITION
OF
SYMBOLS
APPENDIX B:
COMPUTER
PROGRAM
REFERENCES
58
61
64
65
69
70
70
71
71
72
74
75
79
91
93
52
55
55
56
58
95
96
106
110
112
116
122
132
132
134
138
143
1148
LIST OF ILLUSTRATIONS
Figure
2.1
Project Area
Topographical Map of
Wadi
ZamZam Drainage
Area
. • •
2.2
2.3
2.4
Annual
Air
Temperature in
Wadi
ZamZam
Region
. • •
Mean Annual Rainfall
Region
Distribution in
Wadi
ZamZam
2.5
2.6
2.7
Photograph of Barren
Soil
Surface (a) with the
Exception of
Small Scattered
Plants
Growing in the
Wadi
Bed
(b)
Wadi
ZamZam
GroundWater Well
Location
Map
Hydrogeological CrossSection along Wadi
ZamZam .
2.8
2.9
Geological
CrossSection
Surface
Geological
Map of
Wadi
ZamZam and
Its
Tributaries
2.10
Cone of
Depression for ZZ8 after
48Hour Flow
Period at
50 1/sec Flow Rate
.
2.11
Specific
Drawdown vs.
Distance
Relationship Induced by
One
Well
2.12
Piezometric Head Contours for Wadi
ZamZam in 1974 .
.
2.13
Projected
Piezometric
Decline Produced by
13 Wells in the Chicla
Aquifer after
10
Years of
Development
2.14
The
Relationship between Well
Discharge and
Pressure Head
2.15
Proposed Well
Design for the Chicla
Sandstone
Aquifer
.
Page in pocket
8
10
13
16
17
5
7
19
29
31
35
37
39
44 vii
viii
LIST OF ILLUSTRATIONSContinued
Figure
3.1
Small Water
Tank Used for Cooling Well Water (a), and Irrigation
Water after Being Cooled
Transported by
Truck to the Field
(b)
3.2
Water Flowing through
Long Ditches for Cooling the
Irrigation Water
3.3 Heat Flow in Evaporative Cooling as a Result of
Combined Effects of Heat and Mass
Transfer
. . • •
3.4
Heat Exchange Mechanism at the Pond Surface
3.5
3.6
The
Effect of the Pond
Discharging and Equilibrium
Temperatures on the
Approach
Effect of
Well Discharge Temperature on Pond
Required Area over Various Cooling Ranges for
Average
Summer
Conditions
3.7 The
Effect of Well Discharge Temperature on
Evaporation Rate for
Summer Design Conditions
. .
3.8
The
Effect of Cooling Range (AT) on
Evaporation
Rate over the
Year at Well Discharge
Temperature
57.8
°
C
3.9 The
Effect of
Cooling Range (AT) on the Pond
Evaporation Rate over Various Well Discharge
Temperatures for
Summer Design Conditions
3.10
Effect of Pond
Temperature on
Evaporation
Rate over
Various Cooling Demands for Average
Summer
Design
Conditions
3.11
The Relation between the
Annual Evaporation and
Cooling
Range for Average
Summer Design
Conditions
3.12
Effect of Pond
Intake Temperature on the Total Cost for
Summer Average
Design over Various Cooling
Ranges
3.13
Heat Transfer with Water Temperature above DryBulb
Temperature
Page
63
66
82
59
60
83
85
86
87
89
90
92
97
i x
LIST OF
ILLUSTRATIONSContinued
Figure
3.14
Heat Transfer with Water Temperature below DryBulb
Temperature, but above WetBulb Temperature
. . .
3.15
Water Droplet for Heat and
MassTransfer
Simulation
3.16
The Effect of Temperature and Different Enthalpies between the Air Flowing through the Tower and
Saturated
Enthalpy of the Air at Local Water
Temperature
3.17
The Approximation of Tower Characteristic by the
Relation between
1/(H"  H) and Local Water
Temperature
3.18
Method for Approximating
Enthalpy
Line by Straight
Line to Simplify the Tower Characteristic
Calculation
3.19
The Effect of Hot Water Discharge Temperature on
Tower Characteristic for Various Deck Fills
. . • •
3.20
Cooling Factor as a Function of Temperature Ranges and the Approach
3.21
The Relationship between the WetBulb Temperature and WetBulb Coefficient
3.22
The Effect of Cooling Demand on Evaporation Rate from Mechanical Draft Tower for Average Summer
Design
3.23
Variation of Evaporation Rate over the Year in
Percentage of Flow Rate for Various Cooling
Ranges (AT) at
57.8
°
C
Well Discharge Temperature
3.24
The Relationship between the WetBulb Temperature and Relative Humidity
3.25
The Effect of Cooling Demand on Tower Annual
Evaporation Losses over Various Well Discharge
Temperatures
3.26
The Relationship between Approach and the Packing
Height of the Tower over Various Cooling Ranges
. .
Page
98
100
105
107
125
126
127
109
111
113
114
129
130
LIST OF
ILLUSTRATIONSContinued
Figure
3.27
Relation between Well Discharge Temperature and
Tower Cost Designed for
25 Years Life and for
Average
Summer
Design Conditions
X
Page
131
LIST OF TABLES
Table
Page
2.1
Hydraulic Parameter of
Chicla
Sandstone Aquifer as
Determined by StepFlow Test
27
2.2
Specific
Drawdown in the Middle of the Well Field
(ZZ8)
Induced by
13
Wells
2.3
Specific
Drawdown, D/Q e
,
Induced by
13
Wells in the
Extremity of the Well Field
32
33
2.4
Estimated
Drawdown
Induced by Each Well in the
Chicla
Sandstone Aquifer for Well
ZZ4
2.5
Field Analysis of Ground Water in
Chicla
Sandstone
2.6
Chemical Constituents of Ground Water in
Chicla
Sandstone
Aquifer
36
46
47
2.7
Corrosion Effects on Casing in Deep Closed Wells
50
2.8
Corrosion Index Analysis in Wadi
ZamZam
Deep Flowing Wells
51
3.1
The Statistical Results of
45
Years of Climatological Records
81
3.2
Tower Evaporation Rate in Terms of Well Discharge
Percentage for Summer Design Conditions
124
3.3
Comparison between the Tower Cooling Pond of
57.8
Discharge Temperature and
20
°
C
°
C
Cooling per Well Range
. .
135
3.4
Evaporation Rate of
57.8
°
C
Discharge Temperature and
20
°
C
Cooling Range
135 xi
ABSTRACT
Agricultural development through irrigation is a major effort in
Libya. One of the areas being developed is the Wadi
ZamZam.
The
ZamZam project water supply is entirely deep ground water with essentially no local recharge. The supply aquifer is artesian with an average pressure head of
65 m above land surface and a temperature of
56
°
C.
The water must be cooled before application to crops.
In order to maintain sufficient pressure to keep a constant supply, the number of wells and discharge must be limited. Other ground water aquifers may be developed to supply an additional resource to fulfill agricultural needs. Water quality analysis indicates that corrosion should not be a problem other than perhaps steady corrosion when the wells are closed. Considering the total dissolved solids and other criteria, water quality can be classified as good for irrigation.
Water temperatures can be lowered by cooling ponds or cooling towers. An unlined cooling pond is less expensive than a cooling tower, but requires higher water consumption. Therefore, based on design assumptions, a mechanical draught tower may be considered more efficient than a cooling pond.
xii
CHAPTER
1
INTRODUCTION
The agricultural development in the Wadi
ZamZam area of the
Libyan
Arab
Republic is entirely dependent on ground water for its water supply. Most of the water being pumped is derived from large, underground artesian reservoirs composed of different layers of sandstone, collectively called Nubian sandstone.
The Wadi
ZamZam project intends to develop an agricultural irrigation project to allow nomads to settle where they used to come after the rainy season seeking a good range for their animals. To manage such a valuable resource effectively, it is important to determine how withdrawals will affect the aquifer and its level in the future. The artesian water has a temperature average of
56
°
C (135
°
F); consequently, the direct use of ground water for irrigation and other purposes is restricted. These and other factors may affect future development and management of water resources in the project area.
Water temperature has a significant effect on plant growth.
Plant growth increases as the root temperature increases up to a specific temperature which varies according to the species (Pasternak et al.,
1975).
However, research has not provided the maximum root temperature limits for each species. It is assumed that temperatures above
37
°
C retard and weaken most plant growth, thereby reducing productivity. Its
1
effect on soil chemistry reduces the absorption of essential minerals by plant roots
(Boersma,
Barlow, and Rykbost, 1972).
2
The Problem
The agricultural developments in the Libyan
Arab
Republic essentially depend on ground water which generally is mined. Therefore, special attention has to be given in developing the ground water to conserve this vital resource. Unfortunately, this matter does not now receive adequate concern from Libyan top officials.
In Wadi
ZamZam, 99 percent of the agricultural development will depend on ground water. According to the project authority, plans are to develop 3500 ha. The amount of the water that is needed to irrigate such an area is estimated by the General Water Authority to be
31.5 x 10
6 m
3
/year (9,000 m 3 /ha/yr). Until now, all existing wells discharge from one artesian aquifer.
In addition to hot water, after a well is reopened following a pause in abstraction, the water has a brown tinge. This creates a possibility of corrosive water that may suggest future well problems.
Therefore, the problems that relate to water development which are to be discussed are summarized as follows:
I. Ground water conditions in the area.
2.
Effect of well flow on artesian head.
3.
Appropriate well specification.
4.
Effect of water quality on well construction.
5.
Appropriate method for cooling the ground water.
Scope of the Investigation
The present study is based primarily on the experience of the author with the development of the Wadi
ZamZam
agricultural project.
The study will examine the present situation of ground water in the area.
With limited available information, together with field data collected by
3 the author, the study will examine the possible effects of present and future developments on ground water conditions. Appropriate well specifications will be determined to reduce well interference and to ensure enough artesian pressure to maintain nearly constant discharge for the next ten years. The quality of the water developed by wells will be analyzed to determine its effect on well construction.
In addition, the study will examine various cooling systems that have been used to cool condensed water discharge in power plants as possible techniques for cooling the well water before application to crops. It will attempt to recommend the best system with respect to economic and water conservation considerations.
CHAPTER
2
GROUND WATER EVALUATION
Background
Location and Extent of the Area
Wadi
ZamZam
1 is located south of the
Tawargha region in the western portion of the central region of the Libyan
Arab
Republic. It runs from the southwest to the northeast; the drainage area of the Wadi originates from the east flank of the Hamada El Hamra mountains
(350 km south of Tripoli) and discharges into
Tawargha Sobkha, a depression below sea level (see Fig.
2.1 in the pocket).
Wadi
ZamZam is considered to be the largest drainage system in the west part of the central region of the country. The center of the
Wadi
ZamZam project area is located
30 km upstream of the
Fazzan
Road and the project area extends from
30
0
44' to
30 °
47'N and
14
0
50' to
14
°
53 1
E
(Fig.
2.2).
The two larger tributaries that join with Wadi
ZamZam are Wadi
Taysah and Wadi
Qurayrah.
The conjunction of these two tributaries with
Wadi
ZamZam is located downstream,
10 km southwest of the
Fazzan
Road.
The drainage area of Wadi
ZamZam and its tributaries is roughly
1.
A wadi is a very broad, usually dry, river bed lying between distinct banks.
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rectangular with an area of approximately 4,000 km
2
(Fig.
2.2).
The approximate length of the main stream is 70 km.
An agricultural project extending along the Wadi main stream was
6 started in
1572 and is operated by the Libyan Ministry of Agriculture and supervised by the Libyan Army.
Climate
The climate in the Wadi
ZamZam region is similar to most warm desert climates. It is extremely hot in summer with a drastic change in temperature between day and night. The average daily temperature is
38°C
(the maximum temperature occurs in June;
44
°
C) and it drops to an average low in December of
4
°
C (Fig.
2.3).
The mean annual precipitation is roughly
52 mm.
Rainfall occurs infrequently with random distribution and as shower activities, and is negligible during the summer season. Within
15 years of recorded rainfall, there were only two significant storms that caused some runoff into the Wadi and its tributaries. The mean annual precipitation distribution is shown in Fig.
2.4.
The rainy season normally begins during the second half of October and continues with few scattered showers until April. December and February have the highest rainfall.
Hot winds with high velocities are common phenomena in the Wadi
ZamZam region. These winds act effectively in transporting sand. Sandstorms are wellknown in the area; sand and dust are lifted and conveyed by wind in sufficient volume to blacken the sky at times. This wind is locally known as
Kibli and it blows from the south. The wind is a very
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active factor, causing high evaporation and transportation of sand, forming sand dunes of different sizes and shapes.
The relative humidity is very low in summer, not exceeding
20 percent. Fog frequently occurs in the early morning with high density, but disappears a few hours after sunrise. In the winter, cold winds usually blow from the north with an average speed of
15 km/hr, resulting in an average daily relative humidity of about
44 percent.
9
Topography
Topographically, the Wadi area consists chiefly of sand dunes with gentle slopes generated by wind, and surrounded by a broad desert.
Downstream, the banks of the Wadi slope steeply. Alluvial fans cut the banks here and there with increasing frequency downstream. Generally, the profile of the Wadi from upstream to downstream slopes gently, with an average slope along the valley bed of
2 m/km.
The maximum elevation is about
250 m (msl) upstream and the lowest elevation is
4 m (msl) at the mouth of the Wadi (Fig.
2.2).
Natural Resources and Population
Earlier, agricultural activity in the area was entirely dependent on the occasional rainfall during the fall and winter seasons. Unless there was rainfall, the land was barren except for small scattered shrubs and shallowrooted plants (Fig.
2.5). These plants were considered the main food source for the regional animals. Handdug wells, scattered along the Wadi, with an average depth of
25 meters, were used for domestic supply and animal watering. These wells are limited in yield
( b)
Fig.
2.5 Photograph of Barren
Soil
Surface (a) with the Exception of
Small Scattered
Plants Growing in the
Wadi Bed (6).
10
to less than
1.5 m
3
/hr and yield water of poor quality. When flooding occurred (about once every
10 years), the Wadi bed was seeded to grains,
11 such as wheat and barley, and the edges of the hills were used for raising the animals.
The chief towns in the project area are
Bogran and
Kedahia, which are downstream with small populations of less than
1500 each. The major occupation of the people in the two cities is business.
Bogran serves as a commercial service station on the road between Tripoli and Benghazi, which are the major cities in Libya.
Bogran also provides some governmental employment.
Kedahia serves as a commercial station also, on the
Fazzan
Road. Residents of these two towns did own the land in the Wadi
ZamZam and its vicinity, but it is now controlled by the government.
Also, some nomads come to the area after the rainy season.
In late
1972, the agricultural project was initiated, dependent on deeper ground water in the area. The primary purpose was to settle the nomads and to provide them with a more stable food and water supply.
The plan allots
25 ha to a family and fruits are the principal crops to be grown.
Surface soil in the Wadi, which averages
1/2 km in width, is alluvial and appears homogeneous with only small variations in grain size. The surface soil is underlain by subsoil which is normally compacted and cemented with lime in some places. Upstream, the surface soil has been eroded away and subsoil appears on the surface. Shallow, rocky soils occur in a few small, isolated areas and near the mountains.
The only sizable water resource available in the area is ground water. Since 1972, hydrological investigations have been carried out in
12 an attempt to develop the ground water and thirteen deep wells (1,000 m) have been drilled along the valley (Fig. 2.6).
All of these wells tap an artesian aquifer and have an average yield of about
50 1/sec and an average static pressure of about 6.5 atm
(65 m above the land surface).
At present, 1,400 ha are reclaimed and are being planted with selected varieties of olive trees, almond trees, and table grapes. The process of development is continuous and there are plans now to develop a total of
3,500 ha and to drill eight additional deep wells.
At present, the main problem is the ground water temperature which averages
56
° c. In addition, there is not enough information on the aquifer that is already under development concerning recharge, discharge, areal extent, leakage, etc.
Previous Investigation
This report is based not only on the published information, but also on unpublished works and personal knowledge of the area and personal interpretation of the available data and information that were obtained in the field by the author.
To date there has been no detailed study carried out on the area.
Most of the previous studies were regional, referring very briefly to the project area. Jones
(1964) briefly described the ground water hydrology in the
Tawargha area and
Hungraben, referring briefly to the ground water in the
ZamZam area.
Gaudrazi (1972) reported on the surface geology of the central part of Libya and described very briefly the surface geology
1 3
14 in Wadi
ZamZam.
The
GEFL group (1972) reported on the ground water hydrology in the
Sirtica area (the central part of the country). In a reconnaissance ground water study in Libya, the General Water Authority
(1972) was the first agency to drill the first well in the valley in order to obtain geohydrological information on the area and to help prepare a hydrological scheme for water development. At present, a detailed hydrogeological study is being carried out by the
ENERGOPROJECT Company.
Existing information is not sufficient to provide an accurate analysts for developing the ground water in the valley, but an attempt is made to describe the ground water systems as completely as possible with information available through
1975.
Geology
Geological information is important in ground water assessment.
A knowledge of different geological strata and their arrangements give an indication of the direction of ground water movements, the sources of recharge and discharge, the areal extent of the aquifer, and the occurrence of ground water. Also, the geological structure is an important factor in determining ground water quality. Faults and folds are important in ground water migration. Knowledge of subsurface structural conditions and various controls which determine the presence and movement of water within geological formations is the key to understanding ground water as a potential developable natural resource.
The geology of the Wadi
ZamZam area has been little studied.
There have been no geophysical studies and no detailed studies have been made on the geological structure for the valley. All of the following
15 interpretations are based on welllog information for the wells along the
Wadi and on surface observations. Information from well logs for wells
ZZ1 and
ZZ2 is shown graphically in Fig.
2.7.
Figures
2.8a and
2.8b, showing geological sections of the middle and upstream of the Wadi, respectively, were prepared by the author with the help of the
ENERGOPROJECT staff.
Quaternary
Alluvial deposits of Quaternary age form the land surface along the Wadi. The alluvial formation was deposited either by wind or water, or by a combination of both. The thickness of the alluvial layer changes from place to place, ranging from zero upstream
(40 km from
Fazzan
Road) to
30 m downstream. The alluvial material consists of sand and silt uncemented at the surface to about
2 m and cemented with lime below that level.
Eocene
Sedimentary rocks of Eocene age, locally known as the
Jabel Wadan formation, underlie the alluvial deposits and form the structure of the drainage area of Wadi
ZamZam and its tributaries. They consist of chalky limestone which is locally known as the
Zamam formation. Also, these formations include the Bir
Zidan formation, which is mainly shelly limestone and marl or many limestone. This formation outcrops upstream, forming low permeable layers. Some scattered volcanic rocks are downstream where there are extrusive volcanic rocks, chiefly basalt and olivine, mostly from the Tertiary age (see Fig.
2.9).
O
—
100
—200
—300
100
NMI=
IMINMEN
Limestone
1101111211113
C11311131
Cli1111111111
nosrisin
1311:1111131
Clay Limestone
Chalky Limestone
msomm
WARM
Dolomite
Marl
Fine Sandstone
9
SCALE
10km
16

T500
—700
—800
—900
Fig. 2.7 Hydrogeological CrossSection along Wadi
ZamZam.
AIN
T08 81
135
N 30° 46
• E 14° 50' 15"
Vertical Scale 1500
/AMA
MINEMMIN,
MI NM.
1111/411111
n
011111WVIAL
=MOM
I I II WA I FA I
1
I I MiT
ROUGA CHALK
75
VANNIMMIAMMIA
n
?...:
Waal
Chalky limestone
•
vl
NIA
Dolomitic limestone
(a) Middlestream
Fig. 2.8
Geological
CrossSection.
_44111/
AMINIEVANIONM
AREI=IMMOMMEMM
Slope debris
17
160
N 30
0
40' 30"
E
14° 54'
16"
Vertical
Scale
1:100
Chalky limestone
1112•111111A
Dolomitic limestone
%WA
; 0 
° 0 0 • cr
, • •• • • •
Slope debris
4/1111111/411111111•1
.AIINVAIIIIII
411111•1111/4111111
155
Fig. 2.8,
Continued.
(h)
Upstream
18
1 9
20
The elevation of the bottom of the Eocene formation, referred to mean sea level (msl), ranges from
100 m upstream to
50 m at
ZZ2 downstream. The thickness of the formation ranges from 200 m at well ZZ1 to
80 m at well
ZZ2
(Fig.
2.7) and averages 150 m.
Paleocene
The Paleocene formation of the Tertiary age is not present at the surface in any part of the Wadi. This formation, under the Eocene formation, consists of marl, shell, and marly limestone which is locally fossiliferous.
The upper part of the formation includes the
Zamam formation which is of late Cretaceous age. The formation deepens approximately
1.5 m/km toward the northwest (see Fig.
2.7). The top of the formation is
100 m (msl) at ZZ1 and
50 m (msl) at
ZZ2, with an average thickness of
110 m.
Cretaceous
Mizda Formation.
The
Mizda formation of the upper Cretaceous age lies under the Paleocene formation. It consists of alternating layers of chalkly limestone, marl, and clay limestone.
It appears in all well profiles along the Wadi at an average depth of
300 m (msl) (Fig.
2.7) and has roughly a constant thickness of
170 m. This formation is characterized by a low potential water yield of less than
10 m
3
/hr. Mizda limestone is locally fractured, which makes it difficult to penetrate by rotary drill because of a loss of circulation problem.
Tigrina Formation.
The
Tigrina formation of the upper Cretaceous age was penetrated by all the drilled wells in the area to a depth
ranging from 450 m (msl) at ZZ1 to 390 m (msl) at ZZ2. The
Tigrina formation consists of marl, many limestone, clay limestone, small local
21 layers of sandstone, limestone, and dolomite (see Fig.
2.7). South of the Wadi
ZamZam area, the Tigrina formation contains an aquifer of moderate potential yield. This formation could have a high potential where it is intercepted by faults.
Yefrin
and
Gharian
Formations.
Yefrin and
Gharian lime was penetrated by most of the deep wells drilled in the west and central part of the country. These formations consist chiefly of chalky limestone and clay limestone with locally dolomitic limestone and manly limestone. The average thickness of these formations in Wadi
ZamZam is about
170 m
(GEFL, 1972). The
YefrinGharian formation of the lower Cretaceous formation outcrops at
Jabel Nefusa, 300 km west of the valley and is a source of many springs in that region. This formation is intercepted by a series of faults in many places and by intensity fractures crossing the formation which produce a moderate aquifer potential yield.
Chicla
Sandstone.
Chicla sandstone is the upper part of the continental series which belongs to the lower Cretaceous and upper Paleozoic ages and extends over
50 percent of Libya. This series of sandstones is known as Nubian sandstone. The formation was penetrated by deep wells in the Wadi at depths from
800 m to
850 m (msl) (see Fig.
2.7). The average thickness of the formation is about
80 m without significant changes along the Wadi.
It is chiefly sand and silt, generally weakly cemented, and intercepted locally by thin layers of clay and marl. There
is no significant information on the lateral extension of the formation in Wadi
ZamZam.
This formation is a high potential artesian aquifer.
22
Ground Water
As mentioned earlier, surface water in Wadi
ZamZam is essentially negligible. Therefore, the ground water that has accumulated over a period of centuries is the most important water resource in the area.
Ground water in Wadi
ZamZam area is either fossilized water or comes from regional aquifers that do not receive local recharge.
Aquifers
Four different aquifers have been identified during the reconnaissance phase. The water in these aquifers varies in quality and quantity. The deepest (fourth) aquifer is the most important one for developing in Wadi
ZamZam. The other three aquifers will be discussed only briefly.
First Aquifer.
The first aquifer is alluvial and the deeper chalkly limestone and calcarenites of Eocene age. The fill probably belongs to the Tertiary period and is very heterogeneous.
The depth to the water table varies from
30 m to
120 m below the surface.
The thickness of the first aquifer is approximately
100150 m.
There is no available information concerning the water stored in this reservoir. The water contains
3,0003,500 ppm of total dissolved solids.
The aquifer is locally recharged by occasional rainfall which is usually very small. Numerous dug wells tapping this reservoir along the
Wadi were used for livestock watering and domestic supply. Camels were
2
3 used to withdraw water from these wells at small rates which do not exceed
1.5 m
3
/hr.
Generally, this aquifer provides low yields and water of poor quality. However, when broken by numerous faults crossing Wadi
ZamZam, this aquifer may have good hydraulic characteristics. At present, there is no information available on the hydraulic parameters of this aquifer.
Second
Aquifer.
The second aquifer is made of dolomitic limestone, calcarenite, and chalky limestone belonging to the
Mizda formation. It reaches to
200 m (msl) at
ZZ2 upstream and
270 m at
ZZ1
(see Fig.
2.7).
Its thickness is approximately
160 m.
The second aquifer is separated from the first one by very thick, continuous layers of dark marl approximately
200 m thick. The water in this aquifer occurs under artesian conditions. The water level in the wells stands close to land surface
(+4 m at
ZZ2 and
12 m at ZZ1).
The hydraulic characteristics of this aquifer seem to be poor according to short tests conducted at
ZZ2.
The total dissolved solids content is approximately
3,300 ppm. The water temperature is approximately
40
°
C.
Third Aquifer.
The third aquifer is made of chalky limestone and dolomitic limestone belonging to the
Gharian formation. The top of the aquifer is about
650 m (msl) at
ZZ1 and
580 m (msl) at
ZZ2 (see
Fig.
2.7). Its thickness is approximately
80 m. The water in this aquifer occurs under artesian conditions. The aquifer is overlain by confined layers made of marl, marly limestone, and clay limestone with an
24 average thickness of
180 m. The water level in the wells stands at
50 m above land surface.
There is no information available on well yield from this aquifer, but the hydraulic parameters of the aquifer seem to be good, as was shown by a short test conducted at
ZZ2. The water quality of this aquifer seems to be relatively good
(TDS = 1,300 ppm) and the water temperature is roughly
54
°
C. A detailed study will be carried out to determine the possibility of developing this aquifer with others for agricultural purposes.
Fourth Aquifer. The fourth aquifer is mainly
Chicla formation with dolomitic limestone at the top belonging to the
Aintobi formation.
The top of the formation is roughly at
800 m (msl). The thickness of the aquifer is approximately
200250 m. The water in this aquifer occurs under artesian conditions and the potentiometric surface in all wells tapped from this aquifer stands at an average of
65 m above land surface.
A confining bed overlies the aquifer made of clayey limestone, marl, and many limestone intercepted by thin layers of hard dolomites belonging to the
Yefrin formation of an average thickness of
120 m. This aquifer is described in greater detail in the next section.
Characterization of
Chicla
Sandstone Aquifer
Extent of the Aquifer
The aquifer is the upper part of the continental series belonging to the lower Cretaceous and the upper Paleozoic periods and extends over more than
50 percent of Libya. This series is usually called Nubian
25 sandstone, which is also welldeveloped in Algeria, Egypt, and the Sudan.
This aquifer is considered the most important one when dealing with water recources of Wadi ZamZam.
Discharge and Movement
Discharge from the aquifer in Wadi
ZamZam is increasing every year by the increased number of wells tapping the aquifer. There is no obvious natural discharge from the aquifer in the study area or its vicinity. Thirteen wells have been drilled along the Wadi and eight more wells will be drilled according to present plans. The General Water
Authority has estimated the volume of water from each well to be
50 1/sec
(180 m
3
/hr).
The project plans call for the development of
3,500 ha.
The amount of irrigation water required per hectare is estimated at
9,000 m
3
/ha/yr. This leads to the total amount of water required of
31.5 x 10
6
m
3
/yr. The General Water Authority estimated that the maximum discharge from the
Chicla sandstone aquifer should be
20 x 10
6 m
3
/yr.
A rough estimation of the hydraulic gradient along the Wadi is
5 x 10

4
towards the northeast. Therefore, the natural flow was estimated to be
1.8 x 10
1
1/secm
2 of front, which is negligible by assuming an average thickness of
100 m and a transmissivity of 1.8 x 10
2 m
2
/sec.
Nevertheless, if new information showed this value to be underestimated, it would only increase the water resources available. Consequently, the main part of the water available from the deep aquifer in the
Wadi will come from storage.
26
Recharge to Ground Water
Most of the ground water in the area is either fossilized water or recharged at large distances from the Wadi. Surface flow is essentially absent and only occurs occasionally. Water from occasional flood runoff flows slowly along the Wadi bed and results in some recharge to the shallow aquifer. The shallow ground water in the area is characterized by perched water bodies along the Wadi which overlie the regional ground water. There has been no study done on the amount of water recharged to the shallow aquifer.
On the other hand, the total annual recharge to the Nubian sandstone aquifer was estimated by
Ezzat (1977) to be an average of 26 m
3
/sec.
This recharge is occurring at present at the south and the southeast
Libyan desert where the rainfall intensity increases enough on Tibesti and
Ewinat mountains to create runoff water which percolates into the aquifer.
Transmissivity and Storage Coefficient
The hydraulic parameters of
Chicla sandstone aquifer have been determined by stepflowing and recovery tests carried out by the General
Water Authority on wells
ZZ2, ZZ3, ZZ4, ZZ5, ZZ6, ZZ7, ZZ9, and
ZZ13.
The results are rather consistent, with values of transmissivity ranging from
10
2
to
2 x 10
2
m
2
/sec (see Table
2.1).
The aquifer tapped in Wadi
ZamZam is wellknown from numerous oil wells drilled in various areas. The geometric characteristics of this reservoir are rather homogeneous and extend over several thousand
Table
2.1
Hydraulic Parameter of
Chicla
Sandstone Aquifer as
Determined by StepFlow Test.
Well
No.
Date of
Operation
Transmissivity
(m 2 /sec)
Storage
Coefficient
Estimated
Average
Discharge
Rate
(1/sec)
ZZ1
ZZ2
ZZ3
ZZ4
June
1973
March
1973
January 1975
January
1975
1.2 x 10
2
1.55 x 10
2
4o
1.88 x
10

2
2 x 10 4 *
30
60
2.1 x 10
2
70
2.2 x 10
2
60
ZZ5
ZZ6
ZZ7 zz8
ZZ9
zzio
ZZ11
ZZ12
ZZ13
February
1975
February
1975
June
June
July
1975
1975
1975
August
1975
June
1975
September
1975
March
1975
1.26 x
60
1.44 x 10
2
4o
1.8 x 10

2
50
.85 x 10
2
.88 x 10
2
2.3 x 10
2
30
50
6
0
1.6 x
10 
2
1.88 x
10

2
6
0
30
Average
1.88 x 10
2
*The storage coefficient was only determined with
ZZ4 flowing and
ZZ3 as an observation well.
2 7
28 square kilometers. Therefore, there is no reason to imagine important changes in behavior of this aquifer except over longer periods of time.
The cone of depression for ZZ8 after
48 hours of flow is shown in Fig.
2.10.
The piezometric decline was determined by measuring the pressure decline at
ZZ7, ZZ12, and
ZZ4 while ZZ8 was flowing and calculating the line of equal piezometric head decline assuming a homogeneous aquifer.
The values of transmissivity and storage coefficient that will be used for calculating the effect of well discharge on the piezometric head are as follows:
T = 1.8 x 10
2
m
2
/sec and
S = 2 x 10
4
.
As no lateral boundary is expected to affect the longterm behavior of the aquifer, results using these parameters can be considered as minimum values and would increase with the contribution from the overor underlying strata, which can occur after a certain period of time.
Interference Effect within the Well Field
The size, shape, and the growth rate of the cone of depression resulting from discharge are essentially determined by the transmissivity and storage coefficient. The rate of discharge is affected by the depth of the cone of depression. The coefficient of transmissivity is proportional to the thickness of the aquifer.
In order not to depend on the yield of each well for drawdown, the interference of different wells has been calculated in terms of specific drawdown, DiQ
e
. The specific drawdown is the drawdown per unit of discharge and does not depend on Q. The specific drawdown is
2 9
calculated on the basis of an assumed
100 percent well efficiency using
Theis' equation (Theis,
1935):
30
D/Q = e
1.9
T
W(u) u —
1.87 r
2
S
Tt
(2.1
)
(2.2) where
D
= drawdown, m;
Q e
= well discharge, m 3 /hr;
T = transmissivity, m
2
/day;
W(u) = well function of u; r = well radius, m;
S = storage coefficient; and t = time, days;
Figure
2.11 shows the relation between specific drawdown and distance for the considered
5
days,
10 years, and
50 years. Knowing the distance between the wells, information from Fig.
2.11 is then used to calculate the specific drawdown induced by all the wells:
1) in the middle of the well field (Table
2.2); and
2) on one extremity of the well field (Table
2.3).
Piezometric
Head
As a result of continuous flow from drilled wells, the pressure in the artesian aquifer decreases and that reduces the discharge from the
0
CD
0
0
C
n
J
09
S/
1

1

1
/
11
•
19
0/ 0 NMOON1V0 01.d103ciS
31
Interfering
Well
Total
ZZ9 zzto zzti
ZZ12
ZZ13
ZZ1
ZZ2 zz3 zz4 zz5
ZZ5
ZZ7
ZZ8
Table
2.2 Specific
Drawdown in the Middle of the Well
Field (ZZ8) Induced by 13 Wells.
Distance to
ZZ8
(m)
17,400
12,400
10,60
0
8,
000
15,90
0
14,000
3,100
3,6
00
7,40
0
16,10
0
1
10,700
19,600
Specific
Drawdown in
ZZ8
(m/m
3
/sec)
24
26.7
28
30.5
24.5
25.5
39
110.5
37.5
31
24.5
28
22.5
4 52.2
32
Interfering
Well zzi
ZZ6
ZZ7
ZZ8
ZZ9
ZZIO
ZZ11
ZZ12
ZZ13
Total
ZZ2
ZZ3
ZZ4
ZZ5
Table
2.3 Specific
Drawdown, D/Q
e
,
Induced by
13 Wells in the Extremity of the Well Field.
Distance to
ZZ13
(m)
4,400
31,000
9,600
12,100
8,700
6,700
16,700
19,600
23,100
26,600
34,900
28,500
1
Specific
Drawdown in
ZZ13
(m/m
3
/sec)
35.6
19
29
27
30
32
24.2
22.5
21.5
20
17.8
19.5
110.5
408.6
33
34 aquifer. The measured piezometric level of
Chicla sandstone expressed in mean sea level for
1974 is shown in Fig.
2.12.
Taking into consideration the well field including the wells planned in the near future
(ZZ14,
ZZ15, ZZ16, ZZ17, ZZ18, ZZ19, and
ZZ20) and assuming the values of the hydraulic parameters
(T, S) that were obtained from the flow test
(T = 1.8 x 10 2 m2 /sec and
S = 2 x 10
4 ), it is possible to calculate the effect after
5
days,
10 years, and
50 years. it is assumed for the calculation that each well will flow at an average continuous yield of
50 1/sec; therefore, the piezometric level decline in the
Chicla aquifer will be calculated using Fig.
2.11.
On the other hand, the analysis of the stepflow test data concludes that the piezometric decline produced by the flowing well can be expressed as a function of the discharge:
(2.3)
D
= 500 Qe where D is the water level decline (in meters), and
Q e
is the discharge
(in m 3 /sec).
The drawdown induced by all wells at
ZZ4 is shown in
Table
2.4 for the three time periods.
The drawdowns after
10 years of exploitation (Fig.
2.13), ranging from
17.3 to
19.0 m, are still acceptable. Nevertheless, it has to be noted that specific capacity, and consequently the artesian yield, of the wells would decrease in the future not only because of the normal water level decline, but also because of the increase of friction losses inside the wells due to corrosion of the pipe.
There have been no continuous measurements made of drawdown for existing wells except measurements were taken on
ZZ4 after one year and
Cr)
LI.
35
Distance
(in) o too
200
300
4
00
500
600
700
800
1,000
1,400
I,8
00
2,000
3,000
4,000
5,
000
6,
000
7,000
8,
000
9,
000
10,00
0
20,000
30,00
0
Table
2.4 Estimated Drawdown
Induced by Each Well in the
Chicla
Sandstone Aquifer for
Well ZZ4.
Drawdown after
5 days
(m)
4.o6
1.85
1.6
1.4
1.3
1.2
.50
.4
0
.33
.285
.2
.185
.11
.1
.
0
8
.
0
6
1.15
1.1
1.05
.95
.835
.735
.695
Drawdown after 10 yrs.
(n)
4.
0
5
3.5
3.19
3.
0
2.89
2.79
2.70
2.62
2.585
2.49
2.3
2.2
2.15
1.995
1.85
1.75
1.685
1.6
1.55
1.5
1.45
1.15
.95
Drawdown after
50 yrs.
(m)
2.05
1.99
1.9
1.88
1.8
1.5
1.3
4.05
3.85
3.01
2.25
2.85
2.7
2.6
3.78
3.4
3.29
3.14
3.1
2.55
2.38
2.24
2.13
36
ce1
Cs
IJ
C7)
37
4 months with four wells operating. The drawdown for that well was
6 m, which is close to a calculated value of
5.6 m. The true value was prob
38 ably a little higher because the time of recovery was very short.
Well Specifications
Artesian Head and Discharge
Thirteen wells already have been drilled and tapped from the
Chicla formation. All of these wells are artesian with pressures at the surface ranging from
55 to
70 m
(static). The average pressure is
65 m above the ground surface.
From the flowtest data analysis, which is shown in Fig.
2.14, the following equation was derived to express the relation between the pressure and the yield:
P = 65  100 Q e
 4,500 Q e
2
(2.4) where
P is the piezometric head above the surface (in meters), and
Q e
is the well discharge (in m
3
/sec).
Therefore, the problem is to fix
Q such that the corresponding pressure at the head of the well is equal to the sum of the following terms:
1.
The pressure,
P o required for operation of the irrigation system
(P
0
= 15 m).
2.
The water level decline in order to keep the yield constant for
10 years (D).
o co
Cc
H
0 w
Cr
Z
0_ w
o
u
ct r t
O
w
( f)
—
L
Li
0 cri o_3
o c o
]H.1. ui) ONISVO
JO dal.
9N18è:GA]è:i LIFISSL1c:1 112M u
39
1
+
0
3.
The interference from the nearby Wadis which are located at the west of the area and are expected to be developed soon
(I
).
This interference is assumed to be
10 m.
Hence:
P = P o
+ D +
I
(
2.5
) where D is expressed by equation
(2.3).
Therefore:
P = 15 + 500 Q
e
+ 10
(2.6)
Then, the combination of equations
(2.4) and
(2.6) gives:
900 Q
2
= 120 Q 
8 = 0
This equation has only one positive solution:
(2.7)
Q = .05 m
3
/sec
Therefore, in order to keep enough artesian pressure to maintain a constant well discharge for the next
10 years, the well discharge should not exceed
180 m
3
/hr.
Well Spacing
Under artesian conditions, water released from storage is entirely due to the compressibility of the aquifer material and that of the water. Therefore, the losses in hydraulic head caused by the flow from each well will propagate very fast. In addition, the hydraulic conductivity of the aquifer is
fairly high
(10 m/day). Then the depression
41 cone induced by discharging will be wide and flat. As a result of these two factors, the drawdown induced by each well will cover a great distance.
When wells are spaced close together, their cones of depression may overlap and additional drawdown results. The wells should be placed at desirable distances to reduce the overlapping between wells as much as possible to keep high well efficiency. Well spacing involves hydraulic factors as well as economic factors. Cost of pipe installation and maintenance of the pipe system will increase in the space between wells.
The optimum space was determined by Theis' equation for determining the optimum well spacing in a simple case of two wells pumping at the same rate (Campbell and Lehr,
1973): r = 9.09 x 10
5
CQe2
MT
(2 .8) where r = optimum well spacing,
C = cost of operation (pipe and auxiliaries),
Qe = flow rate
(m 3 /min),
M = capital cost (drilling and construction of the well), and
T = transmissivity (m
2
/day).
It is assumed for the calculation that the well flow is
3 m
3
/min and the capital and operations costs were
10
5
and
6.6 x 10
4
Libyan pounds, respectively.
42
Therefore, the desirable space between wells is recommended to be
3.5
km. This space could produce 1.9 m drawdown in the discharging well due to the neighboring wells, after ten years of continuous discharge.
Well
Design
Well design for water production involves selecting the proper dimensions for the diameter and depth of the well and the proper materials to be used. Proper design aimed at protecting the well assures long life and good performance.
Cost and hydraulic characteristics are the two main factors that control well design; these two factors should be analyzed properly and accurately. The hydraulic factor is involved when designing the well for highest production and
efficiency
in
terms
of
specific
capacity. The cost factor includes the cost for drilling, materials, installation, and cost of operations, maintenance, and replacement.
A large well diameter will increase well efficiency and probably increase the yield. But, as the well diameter increases, the cost will increase too. Therefore, cost and technical factors must be properly analyzed.
Under artesian conditions, well structure consists of two elements. One is the casing which serves as a conduit through which the flow occurs from the aquifer to the land surface. The other is the screen or the intake portion of the well where the water enters from the waterbearing formation to the well.
Under natural flow from an artesian aquifer, the main factors that control well construction are head losses produced inside the well
43 which control the pressure at the surface and the cost. The pressure at the top of the aquifer is proportional to the head loss. Therefore, the diameter of both the casing and the screen must be large enough to assure good hydraulic efficiency for the well.
In Wadi
ZamZam, the well yield is estimated as
50 1/sec (180 m
3
/hr).
Based on Johnson Division's
(1972) criteria and drilling sample analysis by the General Water Authority, coupled with the author's experience, the following program is recommended for well design in the
Wadi (Fig.
2.15):
1.
Installation and cementation of
45.5 cm conductor tube down to approximately
20 m.
2.
Drilling with
44.5 cm diameter down to
250 m.
3.
Setting down and total cementation of a
34 cm casing
(H40).
4.
Drilling with
31.1 cm diameter down to
1,000 m.
5.
Geophysical logging, consisting of a conventional electrical log only.
6.
Setting down and total cementation of a
24.5 cm casing
(H40 or
J55) from
34 cm casing shoe down to the top of the waterbearing formation.
7.
Setting down of screens, stainless steel, bridge slotted slot
60
(15 mm), 15.4 cm diameter,
6 mm wall thickness as a minimum.
8.
Developing for
48 hours, or as needed.
9.
Flow test for
72 hours minimum.
100
L.S.S.
(Lithological)
QUATERNARY : . ALLUVIAL
EOCENE
IN
MEN=
MO
UM—
=NM
LIMESTONE
200
PALEOCENE
•
MARL
300
400
500
=NM
=1•111•11
1•11E111•2 moms
MIZDA
FORMATION
1—
600
700
800
900
CRETAEOUS
=CB
GHAR1AN
LIMESTONE
MMUM
111:311.
YAFREN FORMATION
ammo
CLAY
=MU
MN
LIMESTONE
CH I
'
CLA
SANDSTONE
/,
1000 —
41
1
11
%
CEMENT
BORE HOLE
44 5/11 cm
CASING
33 35/36cm
BORE HOLE
31 1/10 cm
CASING
24 5/11 cm
CENTRALIZER
CASING
17 7/8cm
SCREEN
15 5/12 cm
SEDIMENT
TUBE
15 5/12 cm
Fig.
2.15
Proposed Well
Design
for
the
Chicla Sandstone Aquifer.
44
45
Estimating Head losses Inside the Well
The average yield of the wells in
Chicla sandstone aquifer is
50 1/sec.
The friction losses corresponding to this yield will range from
8
to
13 m according to the well. This friction loss was determined from the manual provided by the manufacturer of the screen and casing and distributed as follows:
34 cm
24.5 cm
15.4 cm casing casing screen
1 m
58 m
24 m
The only way to decrease the friction loss would be to use a larger diameter of casing and screen. Unfortunately, this would double the cost of the well while the capacity still is limited to
50 1/sec in order to keep the artesian yield nearly constant for at least
10 years.
Water Quality
for the
Chicle Sandstone Aquifer
Chemical Analysis
Since all wells tap the same aquifer, chemical analyses were carried out by the author for eight selected wells. Immediate analysis was done in the field using Hach and conductivity meter to obtain dependable results because the composition of the sample may change before arriving in the laboratory. The results are shown in Table
2.5.
Certain chemical analyses were also made in the laboratory from samples collected from the same wells. The results of these analyses are shown in Table
2.6.
They indicate that the water quality for the aquifer
Table
2.5 Field Analysis of Ground Water in
Chicla
Sandstone.
Well
ZZ2
ZZ4
ZZ5
ZZ6
ZZ7
ZZ8
ZZ13
ZZ1
Average
Temp.
(°C)
55
57
57
56
55
55
56
55
56 pH
7.3
6.3
7.2
7.1
7.4
6.9
7.2
6.6
6.6
Cond.
(25°C)
2.32
2.42
2.52
2.49
2.28
2.14
2.60
2.38
2.39
353
384
353
390
335
360
366
335
359
HCO
3
(mg/1)
Total CO
2
(mg/1)
75.9
73.0
68.9
92.9
86.0
82.8
70.9
83.9
79.3
0
2
(mg/1) nil nil nil nil nil nil nil nil nil
H
2
S
(mg/ 1
)
.59
.76
.85
.96
1.09
0.81
.59
.85
.76
1+6
0 ln
••n
CNI a
NO
•
•••n .•
(NJ
1"
CNJ
CO
•••T C ...
4 %.,0 ...
LI\ r•••• .
1"
n
N C71 0 0

`, .
‘.0 N.0 . 1

C C•r") Cs4 0
LrN
,

..c c c c
0 . 0 .
0 In

1

c
. CNI re\
CY1
In
N.0 CNI CO
co
NO
CC)

CNJ
. .
Lnoc).coo— N.
C4
CO 04 Q
N. Q
N
1..r\
C c.1 4
a\
Ce1
CYN
1
0

1 C C C
•••nn
., nnn
fr1
CNI CNI
CNI
• • • •
Lr%
cr,•oo
C
N.
CO
o r
..0
,
.
N.
•
,
.•••
..0 o ix\ c cs, re n
.0
CNI rel M M
I' N
c...i — . .0 / o r
0
,
•
c4 o o o .
in . NO
gI•MP
••n ..•n •nn
1" 0
• • pm.. en
CV
•
.. 1
C'n Cs/ . 0 0
— .0
N.
C C C
0'1 C CO
N.0
0 T
co id, o
CNJ
NO Lfl
.11•••,
1.1"1
• •
CNI
NC) 0 s.0
L.r.\ (=>
L/1
N.0
C C C
1•••
0
•
CD 0
,
CY\
. • v.')
‘.0
C
0 In r•••
NO
CN1
CNI C
1
1
• •
1n• •n• .n••
N 0 0 0
N.
0
CT% N. N
CO 4
C) Lf1 C
1.11 P N. C C C
••
n
 CNI
V\ CY\
.1"
11•n• 1••••
CO
T
CO
• • • •••••
'.0
C
Lr\
C•4
CO
••n•
CO NO CNI
N. Lc% cD i.r c:
0.4 r
, r1
0
LC\ CO
CO ‘.0 0
Cs.1
P
1n•••• e•`n •••.
• •
T
CT%
CV LC\ 0
In m m
N. Q N.
c: c:
C
M
Lr
n
.
0
.1,•• nn
N
CO CO
Cn
• • I••••
•
•
Lr‘ 
.T 0 c:
CO
%ID
LI

N
• N
CV

• •
I•••• re\ CT\
Ls%
C cs) re1
LIN r

,
C CNI
CT\
..01.4"\NCCC
NO
N.
Cs4
CO
• •
• n
•••
ffl
•
1••••
 .0 0
C
N.0
• N
NO
C'1 C\
• •
CNI CNI
Cs.)
•
In CO NO
C Q T
CO
411
0,1
NO

0 r•
n
..••••
••
0 0 0
• •
•
C C C
C
CO
C•4
.
0
LI\ CO
0
.•
Ln
•
1••••
S..0
CO '.0
• ln 0 C71
N. CV CO
Cs4 0
1"

••• N.0 CD ...T C N.0
CNI rel tn
N ce%
• •
1" , NO C C C
CNI rel .1

Ln ,
,•••
NO
0
Im••
•n•
1...
•
•
C'NI C•4
. • 1" CNI
• • ••••
0 m
•
N.
. 00
C
0
N.
47
csrl
O (...)
=
•
C
(r)
0 2 0 0 cr)
cr
.
) rm.
L)
I—
cr2
V) 2 0
CD I) •• CI.)
< <
Q
m
cf*,
0 a:1
is relatively uniform. The small variation could be related to the interbedded shale layers, or experimental error.
The chemical analysis of the ground water indicates that the water is acceptable for irrigation usage
(Israelsen and Hansen,
1962)
The electrical conductivity is slightly high. The total hardness ranges from 675 to 720 mg/1, which is very high, or approximately
50 percent of total dissolved solids.
Corrosion Tendency
Well water of Wadi
ZamZam was studied to determine the corrosivity of the water for pipes used as well casing. Metallic corrosion occurs when a metal reacts with its environment, whether it is a solid, gaseous, or aqueous liquid. Water corrosion takes place when some factors are favorable. As a principle, the corrosion constituents of natural water are: a low pH and dissolved gases (oxygen, carbon dioxide, and hydrogen sulfide), acidity, alkalinity, a high salinity, a high stability index, and a low saturation index
(Zarazzer, 1975).
All these determinations were studied to determine possible corrosion of the installed casing.
The ground water of Wadi
ZamZam is free from oxygen. This element is usually a dominant factor in corrosion when it is present in water.
The amount of free carbon dioxide found in the water ranged between
68.9 and
92.8 mg/l.
This amount is itself not a factor of corrosion by water containing or saturated with dissolved oxygen.
The CO
2
content reacts like an acid by increasing the acidity of water.
In our
49 case, the measured pH in the field is between
6.3 and
7.25. A pH of
6.0 to
8.0 will increase the CO
2
content of water, but has practically no effect on corrosion rate, especially when the water is free of oxygen.
The main effect of dissolved carbon dioxide seems to be its influence on the solubility of calcium and magnesium carbonate.
Acidity accelerates corrosion. The chief characteristic of iron corrosion in acid water is that it proceeds with the evolution of a considerable amount of hydrogen without the formation of an insoluble coating. At pH
5.5
and lower, a rapid hydrogen gas evolution starts and corrosion is accelerated. This condition does not occur in Wadi
ZamZam water.
Hydrogen sulfide is produced by sulfate reduction. Its amount is very low
 0.59 to
1.09 mg/1 expressed as
H
2
S. In the laboratory, water was tested qualitatively by lead acetate paper and a smell was noted.
However, this test is not precise at low concentrations. Hydrogen sulfide dissolved in water acts as an acid and produces corrosion on iron, forming iron sulfide and hydrogen. This corrosion can be accelerated by the presence of free oxygen. This condition is not present in the ground water.
Both carbon dioxide and hydrogen sulfide act as an acid in water.
It means that the pH of water should be very low.
A pH between
6.3 and
7.25 is not a low pH, because it is a common pH of natural water. The effect of corrosion of these two gases is too small to cause a serious corrosion on casing pipes. On the other hand, if this ground water contains free dissolved oxygen, corrosion of casing may be more serious.
50
Table
2.7 shows the corrosion effects in casing by other indices.
As indicated, all samples had a low Fe ion concentration, indicating little corrosive activity. Additional interpretation of the data is given as follows.
Well No.
5
7
8
13
1
2
4
Table
2.7
Corrosion Effects on Casing in Deep Closed Wells.
Saturation
Index
0.05
0.3
o.3

0
.
0
5
o.8
0.2
0.9
Stability
Index
7.3
8.0
7.5
7.2
8.2
7.8
8.1
Total
Iron
(mg/1)
7.2
22.0
4.8
6.8
32.0
9.2
40.0
Saturation Index.
The saturation index indicates the degree of instability with respect to calcium carbonate deposits.
A positive value indicates the tendency for calcium carbonate deposits.
A "zero" saturation index denotes that the water is exactly at equilibrium with respect to calcium carbonate. All ground water samples have a negative index value; that is, there is no tendency for calcium carbonate deposition.
Stability
Index.
The stability index indicates a quantitative
In this case, all values measure of calcium carbonate scale formation. are positive:
1.
A value less than
6.0 or
6.0 indicates scale formation.
2.
A value between
6.0 and
7.0 indicates an equilibrium.
3.
A value between
7.0 and
8.0 indicates no protective coating of calcium carbonate.
4. A value higher than
8.0 indicates corrosion.
51
Ground waters are on an average between
7.1 and
7.8 for flowing wells which means very low corrosion. For wells not flowing, the stability index is higher than
8.0. This type of corrosion is static corrosion resulting from long contact of water/casing (see Table
2.8).
Table
2.8 Corrosion Index Analysis in Wadi
ZamZam Deep Flowing
Wells.
4 6 5
Well
Number
7
8
2 1
13
Fe
(mg/1)
Saturation
Index
Stability
Index
4.8
3.0
6.0
0.7
6.8
0.05
7.2
0.05
9.2
0.2
22.0
0.3
32
40
0.8
0.9
7.5
7.1
7.0
7.3
7.0
8.0
8.2
8.1

In the report written by
Branko and
Brikish (1974): 1) the water is corrosive because of
H
2
S and CO
2
content; and
2) the well will be obsolete in
5 years.
These arguments cannot be taken into consideration.
Corrosive gases, marble test, and pH do not indicate an excessive corrosion sufficient to limit the age of a well to
5 years.
It is too difficult to make
52 a prognostication for the working life of wells; nobody can say if their life is limited for
15 or for
30 years.
The appearance of red water is not necessarily a measure of the degree of corrosion, but from the static condition of the well this appearance can be greater or smaller depending on the static time of the well water/casing contact.
All ground waters contain variable amounts of iron, and iron is abundant in the earth's crust and may be in the
Chicla formation. It means that the presence of this element in water flowing normally, as in wells
ZZ1, ZZ3, ZZ4, ZZ5, and
ZZ6, may arise from two sources: ground water and/or casing.
In order to identify the source of this iron, it is necessary to determine the iron content in different levels of
Chicla formation.
Conclusions and Recommendations of
Ground Water Evaluation
The field data were not enough to make an accurate assessment.
There is no information available on the other three reservoirs that could help to evaluate the ground water system in the valley.
Most of the pumping test data were recorded in the flowing wells and there are not many records of any observation wells.
The maximum flowing test duration was five days.
However, in the light of the data available from the field and the data being calculated, the following assessments can be made:
1.
The results of the primary test conducted by the General Water
Authority
(1973) indicate a similarity in temperature, pressure
53 head, and total dissolved solids between the Gharian limestone formation and the Chicla sandstone aquifer. This indicates strongly that there is a possibility of a hydraulic connection between the two aquifers.
2.
The variation in transmissivity along the valley is mainly related to the variation in the thickness of the aquifer and the impurities (marl, clay, dolomite, limestone) that intercept locally Chicla sandstone (Fig. 2.7).
3.
The spatial change in the transmissivity is related to the change in pressure head. The lower the transmissivity, the higher the formation losses and, consequently, the lower the pressure head.
4.
The pressure head gradient is sloping toward the northeast with an approximate value of
5 x 10
5 and the flow is estimated to be
1.8
1/secm
2
toward the northeast.
5.
The calculated drawdown after ten years of operation shows that there will be extensive drawdown in the center of the valley.
This is essentially because of small spacing between wells (well interference).
6. Water level decline in water wells during the flowing test showed roughly a steadystate condition a few hours after the flow started. This is mainly a result of the large areal extent of the waterbearing formation and the high uniformity of aquifer parameters.
In order to evaluate ground water resources in the valley and to make the best interpretation, more field data are needed, especially in
the other aquifer parameters, and water level measurement in the different wells.
The conservation of the water resources and the proper use of this expensive and limited commodity make it necessary to adopt a hydraulic scheme which takes into consideration:
54
I. The specific characteristics of each well (pressure and artesian yield).
2.
The total yearly water production which must not exceed
20 x 10
6
3 which can be exploited from
13 wells.
3.
The high temperature of the water.
4
• The possible additional resources from the shallow aquifers during the period of peak requirements.
5.
The actual distribution of soils, and consequently the crops, which will determine the best irrigation system.
At present, the hydraulic system in use in the project makes any control of water production and water use impossible.
Thus, it is urgent to reorganize the water management properly.
The proper amount of water from the
Chicla formation is estimated as
20 x 10
6
m
3
; the annual water resource which can be exploited from
13 wells which are already drilled
(50 1/sec).
This amount of water will provide irrigation water for
2,500 hectares. Up to this point, it is recommended that no more wells should be drilled in the same aquifer.
ln order to guarantee a constant artesian yield for each well and the pressure required for irrigation for the next
10 years, the following recommendations could be taken into consideration:
55
1.
The total number of wells has to be limited to 13 (50 1/sec).
2.
Distance between wells must be
3.5 km as an average.
3.
The total discharge of the 13 wells should be limited to
20 x 10
6 m
3
/year.
L. The average yield of each well should be limited to
50 1/sec.
Considering the actual area that the Wadi
ZamZam project plans to plant and the water requirements of certain periods of the year, as in summer, consideration should be given to develop other aquifers to provide additional water.
First Aquifer
The characteristics of the first aquifer are not known at present. A program of necessary geophysical surveying should be performed to investigate the first
200 m. At the same time, the project or any other agency could undertake the drilling of some shallow wells to check the water quality and the capacity of this reservoir, even though it is not expected to have high capacity.
Second Aquifer
At present, the development of the second aquifer is not recommended for both the bad quality of the water and for the poor hydraulic characteristics of the formation. However, it is important to drill two or three wells in order to check these two factors.
56
Third Aquifer
If the same hydraulic parameters of Chicla sandstone aquifer are assumed for the third aquifer of
Gharian chalky limestone, an additional well could be proposed to tap this aquifer in order to supply additional water
(250 1/sec).
There is no detailed study being made concerning the
Gharian chalky limestone in relation to
Chicla sandstone, but initial results indicate a hydraulic connection between the two aquifers. The temperature of the water is roughly the same as the fourth aquifer (55
°
C) and the chemical properties are also similar
 approximately
1,300 ppm for
TDS.
Therefore, before any development of ground water from the third aquifer, it is necessary that this relation should be studied very carefully.
This evaluation of the water resources has to be a primary consideration and it should be reviewed as soon as possible according to the present condition in the Wadi. The following data should be collected:
I. The quantity of water extracted each month or year (by reading the water meter installed on each well).
2.
The water level in each well should be measured each month.
These measurements should be made after the well has been closed for a few days so the steadystate condition may be observed.
3.
The water level in the well during pumping and a measurement of rate of discharge of the well at the same time.
This proposed program of ground water development could provide the agricultural project with
900 1/sec (28 x 10
6
m
3
/year) for a first approximation.
57
Since the water requirements are much higher during summer, the following solutions are recommended to meet the requirements during the whole year:
1.
The deep artesian well will flow at the same rate during the whole year supplying approximately
650 1/sec continuously to meet the water requirements during the winter.
2.
During the summer, wells from other aquifers
(Gharian and alluvial) supply additional amounts of water required. This solution will have two advantages: a.
Shallow water will cool down the hot water from the artesian aquifer.
b.
Fresh water coming from the artesian aquifer will reduce the brackish water from the shallow aquifer.
CHAPTER
3
GROUND WATER COOLING
Introduction
As mentioned in Chapter
2 of this report, the ground water temperature averages
56
°
C
(Table
2.5).
For irrigation purposes, this temperature is detrimental to crop production. The
ZamZam project authority has no specific cooling policy. Sometimes the irrigation water flows from the well to a water tank cooled to near ambient temperature, then the water is transported by tank truck to the field (Fig.
3.1).
Sometimes they use water directly from the well without cooling for irrigation so the applied water has an extreme temperature. Another way they use for cooling the irrigation water is for the irrigation water to flow through long
(1/2 km) ditches where the water temperature is lowered by
510
°
C
(Fig.
3.2). These methods are not satisfactory for technical or economic reasons.
The construction cost of the small cooling tanks
(150 m
3
) is an average of
$2,000 each. The time needed for cooling the irrigation water in tanks to an acceptable temperature averages
48 hours. In addition, the method of water transportation by tank trucks from the cooling tanks to the field is entirely uneconomical and impractical.
in the area of well
ZZ3, where the water was used directly, the measured temperature of the water near the crop was
48
°
C when the ambient temperature was
28°C.
This temperature is too extreme for most
58
(b)
Fig.
3.1
Small Water
Tank
Used for
Cooling Well Water
(a), and
Irrigation Water after Being Cooled Transported by
Truck to the
Field
(b).
59
Fig. 3.2 Water Flowing through Long Ditches for Cooling the Irrigation
Water.
6
0
crops. Using water tanks for cooling purposes is not economical and is ineffective. Flowing of irrigation water through ditches causes high
61 water losses through seepage and evaporation, without adequate cooling.
There are no established guidelines for maximum irrigation water temperature, but high temperature in the root zone may reduce plant growth, and modify the soil by increasing the rate of chemical reaction between the soil compounds and chemical constitution of the soil water
(Zarazzer,
1975).
Since soil temperature affects seedling emergence, growth rate and time of maturity, these three factors affect directly crop production.
In this part of the study, results of an investigation of cooling methods that have been used frequently in cooling of water in power plants will be represented. The three methods are cooling ponds, spray ponds, and cooling towers. The study will examine these methods economically and with respect to water consumption.
Evaporative Cooling

Heat
Dissipation
Evaporative cooling is cooling of liquid (water) by three combined energy transport processes which physically differ. The three processes are:
1.
Latent heat or heat of evaporation, heat transfer by mass diffusion and convection
(4)
e
)
2.
Sensible heat transfer, through contact by conduction and convection ((pc).
3.
Heat transfer by radiation, which is important only in cooling ponds or open reservoirs. In other types of cooling systems, heat transfer by radiation may be neglected.
62
Energy flux due to evaporation plays a major role in the total heat dissipation from a water surface. It is a function of the vapor pressure gradient regardless of the temperature difference at the airwater interface and goes mainly to the atmosphere. In contrast, heat transfer through contact depends on the temperature difference between the water
(T
s
) and the air
(T
a
) and flows either to or from the water body.
Both processes are related and affect each other. The combined effect of the heat ((p
c
) and mass transfer ((p
a
) on the water surface heat exchange is shown in Fig.
3.3
for different conditions. When T
s
>
T a , the heat flux from the water body,
(p
n
, equals the sum of both processes:
' r
(1) c
(1) e
As a result, the water surface temperature continues to fall. When
T
s
< T
a
, the heat flux from the water surface becomes:
4) n =
4) e 
4) c
As the temperature of the water surface continues to fall, it increases the cp
c
and decreases the (I)
e
.
Dynamic equilibrium is reached when cp
c
= 'e and the net energy flux from the water's surface equals zero, or:
63
a
On
1
C
Oe
C
Pc
T = E
Fig.
3.3
Heat Flow in Evaporative Cooling as a Result of Combined
Effects of Heat and Mass Transfer.

From Berman
(1961).
T s
=E
(see Appendix A for definition of symbols) which is the hypothetical point at which heat flow from the water body equals heat flow to the water surface.
Cooling
Pond
A cooling pond is defined as an open water body whose function is to dissipate unwanted heat from a thermal source as well as the natural heat input. A cooling pond receives hot water from one end and discharges cooled water from the other end.
A cooling pond is most acceptable for evaporative cooling in regions where land is inexpensive. Compared with other cooling systems, i.e., towers, cooling ponds require a larger area of water surface for heat dissipation to reduce water temperatures to desirable limits.
A cooling pond has the advantage of Tow maintenance and pumping costs. However, it has higher water consumption than other systems and its design is sensitive to site conditions (Scofield and
Fazzolare,
1971). Cooling pond design depends on accurate calculation of the heat flux dissipated from the water surface to the atmosphere. A small error in prediction of heat flux may lead to a large pond surface area which may reject the cooling pond as an economical heat dissipator.
Detention time is determined by the design. In a good design, detention time should be less than twentyfour hours; some designs may require several days detention time.
65
In this study, the time frame to be used is long enough for monthly meteorological parameters to be adequate to predict the heat flux and evaporation rate from the water surface. A completely mixed pond is assumed for analysis.
Completely Mixed Pond Energy Budget
A completely mixed cooling pond (no vertical water temperature gradient) may be approximated because of the pond design, wind, turbulent flow, instantaneous differences in vertical temperature, and water flow rate.
The significant components of the energy balance for a pond completely mixed are shown in Fig.
3.4.
The water surface receives energy by:
1.
Shortwave solar radiation.
2.
Atmospheric longwave radiation.
3.
Waste thermal discharge.
The water surface dissipates energy by:
1.
Longwave back radiation.
2.
Mass transfer (evaporation) or latent heat.
3.
Sensible heat, or convection and conduction.
4.
Seepage from the bottom and sides of the pond. This term can be usually neglected because it is small compared to the other terms.
Many studies have been carried out on the process of heat exchange between water surface and the atmosphere.
The process can be
66
Long Wave
Atmospheric

Radiation
Ys
Short Wave Solar
Radiation
Heat Load from
1.
P
Thermal Resource
14)P1)
Other Energy
Input
Reflected
Atmospheric
Radiation
(t) a b
Reflected
Solar Energy
(sb
Back Radiation cl)b
30
Fig.
3.4
Heat Exchange Mechanism at the Pond Surface.

From Hogan,
•
Ltepins, and
Reed (1970).
67 identified and evaluated fairly accurately. One of the earliest discussions on the concept of heat dissipation from a pond was presented by
Cummings and Richardson (1927).
Lima (1936) developed a set of empirical curves to determine the overall heat transfer coefficient. These curves were used to predict the mean pond temperature (without the effect of the longitudinal or vertical temperature gradient). Lima was one of the first to compare actual pond temperatures with those predicted.
Throne
(1951) developed empirical curves by using an empirical technique based on the energy budget in natural water bodies (no thermal load) and equilibrium temperature measurements.
LeBosquet (1946) presented an analytical technique to determine the cooling capacity of natural ponds. This technique was expanded by
Langhaar (1953). Langhaar's empirical technique is based on the energy balance of natural water. It takes into account the effect of the vertical and longitudinal temperature gradients.
Langhaar's work was modified by
Velz and Cannon
(1960) for a water body receiving thermal waste discharge. Data used were collected from Shreveport, Louisiana, and rivers in Michigan.
The most comprehensive work on energy budgets appeared in the
Lake
Hafner study as reported by Anderson
(1952). Ediger and Geyer
(1965) and Brady, Grave, and Geyer
(1969) presented a comprehensive study of the energy balance technique. They provided charts and tables for most cases of the heat dissipation process for different water bodies
(lakes, rivers, wellmixed, steady, unsteady, etc.).
The mass balance equation for a cooling pond at dynamic equilibrium condition can be expressed as (Hogan et al.,
1970):
Q
[Q
I
+
QPP
Q
R
(dQ
G
Q
0 a
)]
=
T
E
 (
Yv) = 0
The energy balance equation can be written as:
C
P
[Q
I
T
!
+ Q
PP
T
PP
+
Q
R
T
R
Q
G
T
G
 QoTo] H v dQ
(3.1)
68
A4 s
(1)
.9
(1) sb 4) ab
] =
Ti
fff
yC p TdV (3.2)
Since the temperature of a completely mixed pond at any given instant is the same everywhere, therefore: a
7
.
Iff
yC pTdV = a
(yCpTV) = CT Tt
(y11)
+ C pyV
DT
(3.3)
Since
9
C — (11/) = 0, therefore equation
(3.3) becomes:
P Dt
D
Iff
yC p TdV = C yV
P
31.
Dt
Neglecting the terms
Qpp, Q R , and
QG
in
(3.2) will yield:
(3.4)
(I) p
N

E(l'e
(
I
) c
]
= CI
V DT
(3.5
) where
4)
N =
(4
's
(I) a 
4)
56
4) ab
)
69 and
(PID
= (fi
7
Each term of equation
(3.5) will be discussed separately.
According to Stefani's law, all bodies radiate energy by electromagnetic waves and do so at a rate proportional to the fourth power of their absolute temperature. The wavelength of the radiation is given by
Wien's law:
X m
=
C
I
IT where T is the absolute temperature of the body radiation energy, and C
I is a constant. Therefore, the hotter the body, the shorter the wavelength and vice versa.
ShortWave Solar Radiation
The magnitude of solar radiation is a function of the time of day, altitude, season, and cloud cover. It can be calculated with undue difficulty. Marciano and
Harbeck
(1954) evaluated two empirical formulas that could be used to compute cp s
as functions of the sun's altitude and cloud cover. Kennedy's equation (Marciano and
Harbeck,
1954) evaluated solar radiation of a clear sky at the exterior of the earth's atmosphere and the length of the actual path of solar beams to the path through the
Zenith ratio. As a result of the complexity that is involved in computing solar radiation transmitted to the surface, it is easier to measure it. A pyranometer is the instrument commonly used. Solar radiation can be estimated from charts (Hogan et al.,
1970).
Atmospheric LongWave Radiation
In contrast to solar radiation, atmospheric longwave radiation
70 is easier to calculate than to measure. Several empirical equations have been developed (Hutchinson,
1957;
Koberg, 1963).
Brunt's formula as described by
Koberg (1963) has been used extensively for evaluating atmospheric radiation:
(1) .a
= 4.4 x 10

8 (T a + 273.15)
4
[C B +
.031(P)
112
]
(3.6)
The value of
C
B can be determined from the air temperature and the ratio of measured solar radiation at the surface to clear sky solar radiation (Brady et al.,
1969).
Atmospheric radiation also can be measured directly at night by the
GierDunkle flat plate radiometer or by the
Thornthwaite net radiometer.
Reflected Atmospheric Radiation,
(p ab
The reflected atmospheric, longwave radiation energy by the water's surface can be estimated by the reflectivity coefficient
(R s
):
R s
= ab hp a
(3.6a) and is relatively constant at
.03 as reported by Hutchinson
(1957).
Therefore, the reflected atmospheric radiation by the water's surface may be taken as:
7 1 l 'ab = . 03 (l'a
W/m
2 where
W
(watt)
= 14.34 cal/min.
(3.60
Reflected Solar Radiation,
(1I'sb
As for reflected atmospheric radiation, the reflectivity coefficient 4sb/(1)s) of the water surface to solar radiation can be used to determine reflected solar radiation. The reflectivity ratio is a function of solar altitude and the amount and type of clouds. Empirical curves which show the reflectivity ratio as a function of the above were developed in the Lake
Hafner study.
At particular sites, there is no need to measure all four terms.
It is more convenient to measure a combination of these terms by
Cummings' Radiation Integrator which gives the net absorbed radiation:
W/m
2
(3.6c)
(1)
NI = ci a + (1's  4) ab  sb
Bear in mind that neither solar radiation nor atmospheric radiation depend on water surface temperature.
The rate of heat emitted by back radiation from the water surface can be calculated from
StefanBoltzman's law: br
=
ea(T
s
+
273.15)
4 cp br
=
5
'
5 x 10
8
(T
5
+ 273
•
15)
4
W/m
2
(3.7
)
(3.7a)
which gives a good prediction, usually within
85% accuracy (Marciano and
72
Harbeck, 1954).
In contrast to other radiation terms, energy flux by back radiation is constant on both clear and cloudy nights.
Energy Flux Due to Evaporation, cp e
In view of the fact that evaporation plays an important part in heat transfer from the pond surface, it is very important to make an optimum estimation of evaporation rate. There are two terms that determine the energy flux resulting from evaporation: specific flux per kilogram of water leaving the airwater interface, and the rate of mass transfer at the airwater interface.
Many empirical methods to estimate evaporation have been developed. Most of them are derived by using the theories of momentum and mass transfer. The most notable analytical work is that of Sverdrup
(193738). The most comprehensive study on water budget was undertaken at Lake Hefner (Marciano and
Harbeck, 1954). Meyer (as reported by
Linsley, Kohler, and
Paulhus, 1958), as well as
Koberg, Harbeck, and
Hughs (1959) for Lake Colorado, have also developed important equations.
In addition to those already mentioned, similar equations have been developed by many others.
Most experimental data for large bodies of water are limited to the natural body where the difference between the surface water temperature and the equilibrium water temperature is very small. Limited work has been undertaken on water bodies receiving waste thermal discharge where the temperature differences are great. Therefore, most empirical
equations used for natural water bodies cannot be applied to provide an accurate prediction of evaporation rate where heated effluent is being discharged.
73
Vapor movement from an evaporative surface is a combination of two forces, free convection bouyancy force and forcrd convection (wind action). Most of the derived empirical formulas have underestimated evaporation by neglecting the free convection force. Therefore, most of these equations performed poorly when tested in the Lake
Hafner study.
A simple expression found for estimating the rate of evaporation was given for artificially heated water by Meyer (as reported by
Velz and
Cannon,
1960), as well as
Koberg et al.
(1959) for Lake Colorado, who have also developed important equations:
(3.8
)
4) e = f(w
2
)(P s 
P a
)
The equation expresses evaporation as a function of vapor pressure difference times a wind function. Wind function has been subjected to many field studies.
It can be expressed as a function (Brady,
1970): f(w
2
)
= a l a
2 w
2 a
3 w
2 2
(3.8a)
The Meyer equation performed satisfactorily for Lake
Hafner and Lake
Eucombeen in Australia.
For artificially heated ponds, Brady et al.
(1969) estimated the wind function value from field data from lakes in Texas and Louisiana:
74 f(w2) = a
4. bw
2
2
(3.8b)
Equation
(3.8) can be expressed as a function of temperature instead of pressure difference (Brady et al.,
1969):
(1) e
= Ww)(T s
 T d
)
(3.9) where
=
(P s
 P a
)/(T s
 T d
)
Convection,
(1) c
Energy flux by convection from water to air is a function of the temperature gradient near the airwater interface. It is similar to the energy flux by evaporation. Bowen
(1926) is among the first to derive an expressed ratio between energy flux by convection and evaporation using the diffusion theory:
R
=
(I)
=
.00k76
T s
Ta
q5e
(Ps
)
p
765
(3.10)
(3.11)
(P c
= d
'e
Y e
By substituting
(3.10) into
(3.11):
= B'f(w)(T s
 T d
)
(3.12)
where
B' is the Bowen ratio which is approximated as
.47 (mm Hg/
°
C); therefore:
75
(P c = .47(T s
T a
)f(w)
W/m2 (3.12a)
Methods of Calculation
The computation procedure of various cooling pond design parameters begins with computing the design and equilibrium temperature from the ambient meteorological data. The heat exchange coefficient (the time rate exchangeable heat per unit area per unit temperature gradient) and the pond area are then computed for each specific criterion. The surface water temperature is then computed. With the pond area known, the average monthly evaporation rate is then determined.
Substituting equations
(3.7a), (3.9), and
(3.12) into equation
(3.5) gives the general energy balance equation for completely mixed ponds: r
V 9T
'P Y
3t =
A
P
NI
306 
4.48 T
s
 .025 T s 2
 S(T s
 T d
)f(w)  .47(T s
 T a
)f(w)
W/m
2
(3.13)
At dynamic equilibrium conditions,
(3.13) can be written for isolated water bodies as:
0 = (1)
N
 306 
4.48
E  .025 E
2
 $E(E  T d
)f(w)

.47(E  Ta)f(w) wim2
(3.
1
4)
The rate of
heat transfer
in
natural
ponds (no thermal
water
input)
can be expressed
as (Brady,
1965):
dl
n dt

K(E  T n
)/yC
P h (3.15)
which can be written
as:
4 =
AK(E 
T s )
(3.16)
Under dynamic
conditions,
equation
(3.16)
is similar to equation
(3.5).
Substituting
(3.16)
into
(3.13)
yields:
(
Pp
4 = + K(E 
A
T)
(3.
1
7
)
The
heat exchange
coefficient,
K,
can be derived by subtracting
(3.14)
from
(3.13)
after substituting
(3.17)
into
(3.13) and
assuming
= :
E4) =
(
Pp
+
4.48(E 
T s )
+ .025(E
2

T
2
)
76
+
+
.47)(E  T s
)f(w)
W/m2
(3.18)
77
The cooling demand can be expressed by Newton's law:
(I)p = KA(T s
 E)
(3.19)
Subtracting
(3.17) from
(3.18) gives (Brady et al.,
1969):
K = 4.48 + 0.025(E +
T s
)
+ + .47)f(w) w
_ m
2_
0c
1
(3.20)
The second term of
(3.20) can be neglected (Brady et al.,
1969) and the heat exchange coefficient can be expressed as:
K = 4.48 +
(a
4. .47)f(w)
(3.21)
The wind function has been determined from field observations
(Brady et al.,
1969) as: f(w) = 9.2 + .46 w
2
W/m
2
mm Hg
(3.22)
The value of
$ is defined as the pertinent slope of the chord between the points representing T s and
T d on the saturated vapor pressure curve providing there is exact convergency and not approximation (Brady et al.,
1969): a
0.35 + .015 T m
+ .00012 T m
2
mm Hg/°C where
T m
= (T d
+ E)/2
78
Therefore, the equilibrium temperature can be computed from the ambient meteorological data by using
(3.14) for solving
E and defining the heat exchange coefficient
K in
(3.21) as the equilibrium exchange coefficient
(K
E
) yielding (Scofield and
Fazzolare, 1971):
E =  K
E
+K
E
2
 .4N  306 +
(Td
+ •47T a
)f(w)]
(3.23)
The pond area required to dissipate heat can be determined explicitly. Rearranging equation
(3.16) for temperature distribution in a recirculating flowthrough completely mixed pond gives:
KA
= Q
In
[(T d
 E)/(T s
 E)]
(3.24)
The equilibrium temperature and the heat exchange coefficient are coupled. Both depend on water temperature and meteorological conditions.
Therefore, an iterative technique can be used to avoid the solution of quadratic expressions in equation
(3.16).
The exchange coefficient is computed by using
(3.20) in terms of
T s
, when
T s and the value of a are known. The area of the pond is then computed using equation
(3.24). This method provides accuracy and simplification as the value of
T s differs from one case to another. The combination of equations
(3.24) and
(3.19) results in the surface temperature expression:
T s
=E+Q /Q
In
[(T
1
 E)/(T s
 E)]
(3
.2
5)
Knowing the pond surface area, the operating surface temperature
79 necessary to dissipate the cooling demand is then computed by equations
(3.20) and
(3.25).
An iteration technique is used to avoid the solution of the quadratic expression for the two values of the effective surface temperature and heat exchange coefficient.
The total heat of evaporation rate is computed by multiplying equation
(3.9) by the surface area:
(pc
= af(w)(T s
 T d
)A
(3.26)
Therefore, the evaporation rate can be computed by dividing equation
(3.24) by the heat of evaporation
(H
)
:
Q e
= 1235[Bf(w)(T s
 T a
)A/H v
] kg/hr (3.27) where
H v
= 597.3 + .56(T s
 32.2) kcal/kg
A computer program developed to accomplish the calculation is listed in
Appendix B.
Results and Discussion
Climatological data from
1925 to
1970 were obtained from the
Libyan Weather Bureau for the city of Hon.
The difference between the climatological data of Hon and Wadi
ZamZam was considered negligible.
These data were analyzed to determine annual, monthly, and summer (June,
July, August,
September) statistical parameters; results are shown in
80
Table
3.1.
Final pond design criteria were set for an average summer to consider peak water demands.
Computation of average monthly parameters is based on well discharge temperatures ranging from
48.8 to
60
°
C. Consideration is given for a water temperature lowering (AT) of
16.7 to
22.2
°
C.
A constant well discharge of
50 1/sec was used and a completely mixed pond was assumed.
The computed equilibrium temperatures compared with the approach
(difference between pond discharge temperature and water equilibrium temperature) are shown in Fig.
3.5.
As weather data were studied, monthly variation in drybulb temperatures became apparent. Summer months exhibit the highest drybulb and equilibrium temperatures. This results in the lowest sensible heat transfer from the water surface for any given cooling demand.
For well discharge temperatures of
48.9 to
50
°
C and AT
= 22.2
°
C, the summer drybulb temperature exceeds that of pond discharge temperature and the approach reaches its minimum. Under the conditions considered, heat flow from the atmosphere to the water surface through contact is counteracted by latent heat which becomes the major process of cooling the water body.
As illustrated in Fig.
3.6, the required area for a given cooling demand decreases exponentially, with increase in well water temperature.
Additional cooling demands necessitate larger areas.
It is clear that surface area is affected by a combination of the approach and the well discharge temperature. Sensible heat flux is considered the major factor in this relationship. Because of higher equilibrium and drybulb
81
Table
3.1
The
Statistical Results of
45 Years of
Climatological
Records.
Month
January
February
March
April
May
June
July
August
September
October
November
December
Annual
Average
Summer
Average
Temperature (
°
C)
Dry
Bulb
Wet
Bulb
Dew
Point
11.1
13.0
16.1
20.7
23.9
28.3
27.8
27.8
27.2
21.7
16.7
12.2
22.2
27.8
109
12.2
11.7
12.9
11.3
7.7
2.2
2.5
2.8
4.2
6.4
8.3
7.2
15.0
15.6
15.6
16.1
15.0
10.6
15.0
6.3
6.8
8.6
11.1
13.3
12.8
15.6
12.2
Relative
Humidity
(%)
47.00
41.
00
33.
00
28.0
0
27.00
24.00
26.00
26.00
31.00
35.00
43.
00
35.00
35.00
25.00
Radiation
(4/m 2 )
324.7
377.9
429.5
482.1
536.6
568.7
565.8
542.8
504.3
424.5
359.5
323.0
476.9
564.6
6.7
Wind
Velocity
(m/sec)
4.3
5.3
5.3
6.4
6.4
6.4
7.4
6.4
6.4
5.3
4.3
4.3
5.7
o.
/
1
/
/
/
/ / d
/
/
.7/
/
0
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•
1
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ill
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82
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cs c a.
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cO re) a) 1:1
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E 0
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LE
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V) ti)
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cn
co
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0 4

0 o
co
CO

(
1
1) a.muoiadwai Aolui puod n cs
Crs
83
84 temperatures, the surface area required for summer months is greater than that needed the rest of the year.
Figure
3.7 presents a family of curves showing the evaporation rate treated as the percentage of water flow through a cooling pond designed to dissipate from
2.5 x 10
6 to
3.27 x 10
6 kcal/hr heat load. It is obvious when equilibrium temperatures are high, with a small approach, the evaporation loss is high and air convective heat transfer capability is low. On the other hand, when equilibrium temperatures are low and the approach is high, evaporation loss is low and air convective heat gained is at its highest. Exponential decreases in evaporation losses and surface area are coupled. This is related to the fact that evaporation loss is proportional to area for a given heat capacity. However, there is a comparable reduction in evaporation rate for each discharge temperature because of a resulting increase of surface temperature. For similar reasons, the effect of the operating temperature range is relatively significant.
The monthly evaporation rate for various cooling ranges (AT) exhibit a maximum in June and minimum in
January and December. Monthly evaporation rate for a
57.8
°
C well discharge temperature with AT ranging from
16.7 to
22.2
°
C varies from
1.85 to
4.15% as displayed in Fig.
3.8.
For summer design criteria, the evaporation rate changes only slightly over different well discharge temperatures for a given cooling range (see
Fig.
3.5).
However, for a given well discharge temperature, the evaporation rate approximates a linear relationship over various cooling ranges.
CT)
cD
0
4—
.....
.••
az
.....
a,
serige
— zz
.2°
CC
0 C
1•
....
o
o
o.
a
.............
am .....
.
......
• • aba ra•
.°.
‘e
• r
a• au•
17.86C
163
am.
•
•
co*
o
1
1
44,
1
10
3 0
(II) ainpladulaj. amolui puod
1
1 o
In
C
0
0 .
—
U.
(II
L
.
0
0
Cl.
(1:1
>
LU
..
0
C
0
(1.1
c
0
L
=
...
>
LO a)
Cl.
E a)
I
0")
L.
C
— ca
4
O
41
OC a)
0
4
4
.L.)
LU
a
CO
Cr)
8 5
Dec.
Aug.
July
o
2 June
Nov.
Oct.
Sept.
May
Apr.
Mar.
Feb.
Jan.
2.0
3.0 4.0
Evaporation Rate
(% of Flow)
5.0
Fig.
3.8 The
Effect
of
Cooling
Range (AT) on
Evaporation
Rate
over
the
Year at Well Discharge Temperature
57.8
°
C.
86
0
\
N.
0
n ...
.
\
' e r•
n
v %.
Se
....
Se
J
.... s.».
`S.
s„.
...
ss
\
\
—s.

... se.
s.
S.
%,„,
....
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,
....
••••.
q oo.
..., o.
...
s
••,.
...,
••••
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N.
87
88
It is evident that water surface temperatures linearly affect the depth of daily evaporation over various ranges (AT) with a slope of
.0914
m/day
°
C
(Fig.
3.10).
One can see that the depth of evaporation in
Fig.
3.10 decreases with the pond cooling range (AT). This is due to the fact that evaporation from the water surface is a function of the internal energy of water molecules which is related here to water surface temperature. This indicates that, for a given heat load, the depth of evaporation loss per day will be greater at higher surface temperatures.
However, the evaporation rate of the cooling pond will be greater at lower outlet temperatures mainly because of the effect of the water surface temperature together with the approach on the heat exchange coefficient of the water surface. Therefore, for a summer cooling design, it is essential to consider the two aforementioned factors: evaporation loss and depth of evaporation per day.
The computed annual evaporation losses for various design criteria, represented in Fig.
3.11, increase over the range for any given discharge temperature. Also, the annual evaporation losses for a given heat load slightly change over various pond intake temperatures.
One should note that, for a given heat load, annual evaporation increases as discharge temperatures decrease.
As with the evaporation rate, this is mainly because of the change in the heat exchange coefficient of the cooling pond surface which is affected by water surface temperature together with the approach. Therefore, optimum estimation of evaporation should be based on annual evaporation rather than that occurring at any of the particular design criteria.
Variation in the evaporation rate
re)
o o
•
\
•
•
•
• •
•
•
•
•
N
N •
N
N
s.
N •
N N •
N
\ N N •
N
°di
•
N a
\
°
•,?.
n
N
0'
0
:1...
°/
;ee,N
N
\ cNN
'NC
N
04T,N
411
N •
N
••••
•
1
4j
0
N
N
N
•
se
,
N
N
N
•• %
.% •
\ N
N
o c5
89
•
o
'C cp.
\
•
\
'...
\ \
'b.
•
\
• ‘
•
\
• •
fi

0
‘ ‘‘
N.,
N
0
v
N.,
\
‘,, ''
n
O
%
N ‘ ro, \
•
•
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•
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•
\
\ \
\ •
•
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0
VI
CO
9 0
91 over different times of the year, as indicated in Fig.
3.8, is not only a result of the heat load but also a result of natural evaporation. This was considered in all calculations.
The economic evaluation of cooling ponds must consider pond size.
The major cost in cooling pond construction is land cost. Figure
3.12
represents the cost of a pond for various design criteria of average summer months. It is assumed that pond cost equals land cost; plus operation cost which will not exceed
.2% of the capital cost. The capital cost of the cooling pond was evaluated as the cost of the area multiplied by the cost of the land which is assumed to be
$.2
1 m
2
. Therefore, capital cost is the major aspect in the economic analysis of cooling ponds.
Spray Pond
A spray pond usually contains spray nozzles arranged at
610 feet above the water surface. As the hot water ejects through the nozzle, it breaks up into small drops, increasing the airwater interface. In addition to wind action and free convection, there is air movement to some extent by the ejection action. The existence of water from several nozzles crossing the wind stream reduces the horizontal air velocity.
Subsequently, the vertical velocity of the air along with the humidity of the air participating in the heat exchange process is increased. The heat and mass transfer coefficient increases as a result of the increasing airwater interface. The heat dissipation by spray ponds over cooling ponds may be as high as
3500 percent (Scofield and
Fazzolare,
1971).
0
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. '•
.  
. •••
.
. .
...
.. .
''
_......••
.... —
.
.
. ''
.
.
_
0
17; o
C.)
4

)
0
Ia)
.c
41
a) a)
o
(c. o)
in
œ
In to
O
ICJ
U
rn
ul
IA
10
0
0
(
I
) aJn4o.iedulai
in
puod
92
The spray pond performance depends on the contact time between the water droplets and air. In contrast to the cooling pond, the heat exchange coefficient does not depend on the absolute air velocity. The spray pond depends on the relative velocity of the air and water drop
93 lets. Therefore, increasing the velocity of the water droplets by increasing the nozzle pressure affects the relative velocity which affects the heat transfer mechanism. This indicates that the spray pond performance depends mainly on the design of the spray system.
This additional complexity of the spray pond makes it more complicated to find sufficient methods of estimating the amount of heat dissipation. There have been several attempts made to find such a solution. Badger and McCabe
(1936) found that the spray pond could cool
0.6 to
0.8 m
3 of
43.3 to
48.9
°
C water per hour per square meter to
21.1
°
C.
Scofield and
Fazzolare (1971) tried to use a spray pond to cool part of the water flowing to the pond using constant water and air flow rates. They treated the spray performance as a cooling tower, neglecting the effect of the climate ambient condition.
Therefore, field experimentation is required i
n order to evaluate spray pond design. For this reason, further examination of this method was not made.
Cooling Tower
A cooling tower is a device used to dissipate excess heat from a thermal discharge. A water spray directed to the packing (or fill, which is the material which forms the heat transfer surface within the tower
94 and over which the water is distributed in its passage down) increases the contact surface between the water and the atmospheric air. This air is drawn into the cooling tower by mechanical means (as in the case of the mechanical draft tower) or by the density gradient between the outside air and that within the tower, and by the aerodynamic lift produced by air passing over the chimney (as in the case of the natural draft tower).
The cooling tower is the most efficient device used to reduce the temperature of thermal discharges. The tower requires less land and also provides better temperature control of the exit water than does the cooling pond.
The natural draft tower has an advantage over the mechanical draft tower in that it has low maintenance and operation costs.
A disadvantage is the higher initial capital cost. Due to the fact that the natural draft tower depends on natural wind flow, this type of tower is usually built high and with broad sides facing the wind.
Careful design is necessary to ensure that the natural draft tower is stable in high wind. Furthermore, due to the large height of this structure, there is a need for additional pumping of the thermal discharge. Comparing the
total
cost of the natural and the mechanical towers indicates that these two types are comparable. However, the natural draft tower is unsuited for regions of high humidity and high air temperature. Therefore, the natural draft tower will not be presented in this paper.
95
Theory of Heat Transfer in
Counterflow
Evaporative Cooling
Counterflow is defined as the air flow direction, opposite to the water flow direction. In evaporative cooling, the amount of air involved in the cooling process is known. Air and water parameters are correlated with each other by the heat and mass balance equation.
Air is moved opposite of flowing water in evaporative cooling.
The heat flux from the water surface can be expressed as (Berman,
1961):
(1)
= Q
0 p T 1

(Q  dQ)C p
T
2
(3.28)
Heat is dissipated from the water surface by contact, expended by evaporation, and carried off by vapor. Therefore, equation
(3.28) can be rearranged as: d(I) = K(T s
 T) + rB
1
(P  P) + dQC a s a
P
T
2
(3
.29)
Comparing the right side of equation
(3.28) and
(3.29):
Q
I
C
P dT = K(T s
 T a
) + rB'(P s
 P a
)
(
3.
3
0
)
Ignoring the small reduction in water flow, at steady state, the heat dissipation from the water equals the heat absorbed by air.
Assuming the specific heat of water equals unity, then equation
(3.30) can be written as:
(3.31)
QdT = GdH
According to the theory of mass conservation, under steadystate
96 conditions the rate of mass leaving water by evaporation is equal to the rate of increase of humidity: dQ = Gd41
(3.32)
Heat transfer mechanisms are illustrated in Figs.
3.13 and
3.14.
Figure
3.13 illustrates the heat transfer process in the upper portion of an evaporative cooler when the water temperature is higher than the drybulb temperature. The humidity and temperature gradient decreases toward the air interface, resulting in a reasonable amount of heat loss accounted for by both latent and sensible heat loss.
On the other hand, when the water temperature is higher than wetbulb and lower than drybulb temperatures, the water continues to cool.
The temperature gradient increases toward the film, producing a flow of heat from the bulk air to the water. In contrast, the humidity gradient increases toward the water interface, causing massflow latent heat from the water to bulk air. The sum of total heat from or to the interface causes evaporation. This process is illustrated in Fig.
3.14.
Theory of Heat Transfer in Cooling Towers
The general concept of the cooling tower theory was first derived by Merkel
(1925).
The use of the theory was described by Baker and
Shryock (1961).
The heat and mass transfer theory of cooling towers is welldeveloped and can be found in numerous publications. It has been used for cooling tower designs and evaluating cooling tower performance:
e
0
97
C.)
e
Co
49
••
n
•
nn
.monsoo
••••
n
••• 11
n
=11.
N
\4
,
, n
4o
a)
0
9 8
99
= Qdt = K(T  T') + rfP(P s

P s ')
(3.33)
Consider a droplet of water falling through the tower within the volume surrounded by air flowing past an interfacial film (Fig.
3.15).
It has been shown by Lichtenstein
(1943) that, for a given unit area (a) of a cooling tower having a volume dv, with an active surface area per unit volume, the total heat flow from the water to the film interface is written as:
4 =
K
L adv(T s
 T')
(3.34)
Heat losses from the interface to the bulk air as sensible heat are expressed as: dcp s
= K(T
1

Ta )
= K
G adv(T' 
Ta )
(3.35) and the latent heat (heat of evaporation), assuming constant r: rdQ = W(P s

P a )
= rK'adv(W'  W)
(3.36)
The enthalpy of moist air is the sum of the enthalpy of dry air and water vapor:
H
= H a
+ WH v
(3.36a)
= C a
T a
+ W(r + C v
T a
)
(3.
36 b)
100 q(Kg/h0
T s
W dW
H + dH if
Differential
I
Volume dV
T s
—
dT s
H W
G(tKg/hr)
A
/
A
/
/
/
/
/
/
/
T < i.T1
CI /
/
/
/
/
\
\
\
\
\
\
\
\
\
\
\
\
Sensible Heat
14
5
2 K e adV (T' T a
)
W <
tW"
/
/
I
I
H< ;H'
\
Bulk
\
\
%
N
n
•n
..,
Bulk Air  ... .........."
,
/
/
/
/
\
1
1
I
1
/ g
Mass dC12 K l adV (
Interfacial Film
—W )
Fig.
3.15
Water
Droplet
for
Heat
and
MassTransfer Simulation.

From
Baker and
Shryock (1961).
101 and dH = C a dT a
+
WC v dT a
+ dW(r +
CvTa)
(3.36c)
The specific heat of humid air is defined as:
C m
=
C a
+
WC v
Substituting equations
(3.36c) and
(3.37) into
(3.31):
(3.37)
QdT =
GC m dT a
+ (r + C v
T a
1GdW (3.37a)
The first term of the right side of equation
(3.37a) represents sensible heat, whereas the second term represents latent heat.
Therefore:
K
G adv(T
1

Ta )
=
GC m dT
(3.38)
From equation
(3.31) and
(3.36) the mass transfer becomes:
Wadv(W'  W) = GdW
(3.39)
It has been found by Lewis (as reported by
Baker and
Shryock,
1961) that the rate of heat transfer by evaporation is analogous to heat losses coefficient for sensible heat, which both processes depend on temperature differences between the film surrounding immediately the water droplets and bulk air flow over the surface. This relationship is expressed as:
102
K
G
KIC m
= 1.0
Therefore:
O s
= K'
G
C m dVa(T' 
T a )
( 3 .4 o ) and
QdT = K
G adv[C p
(T'  T a
)
+ [r + C v
(T T a )](W'  W)
(3.41)
The enthalpies of humid and saturated air are written as:
H
=
C m
T a
+ Wr
(3.41a)
H'
= C m
T' + W'r
(3.41b)
Subtracting equation
(3.41a) from
(3.41b) with results substituted in
(3.41) yields:
QdT = K'adv(H'  H) = C v T(W'  W)
(3.42)
The second term on the right side of the equation above is small and can be ignored. Therefore, equation
(3.42) becomes:
QdT = Kadv(H" 
H)
= GdH
(3.43)
103
Assuming that Lewis' relationship is applied, equation (3.42) can be solved by relating the air stream to the interfacial and substituting
K
G and
K' by the overall coefficients K
G
and
K, respectively. Therefore:
The relationship can be applied with a certain degree of accuracy.
Equation
(3.43) is applied to the local condition inside the tower. Therefore, to determine the overall conditions of the tower performance of an integration is required:
11
2 dH
(H'  H)
H
I
KaV
G
(3.44)
The enthalpy of both air and water in
(3.43) are dependent on water temperature. Therefore, equation
(3.43) can be integrated over inlet and outlet temperatures:
KaV
'
T
1
2 dT
(H'

H)
(3.45)
The two equations are convertible with each other and they conform to the description of the transfer unit. Referring to
(3.44), it can be rearranged as:
1 04
H
2
L = G/KAa
f dH/(1

1
1

H)
H
1
(3.46)
whereas:
H
2
f
dH/(H' 
H)
H
1 equals the number of transfer units
(NTU), L equals packing height, and
G/KAa equals the height of the transfer unit.
The number of transfer units is defined as the height of the packing required to achieve maximum heat transfer. The theoretical calculation of
NTU corresponding to a set of hypothetical conditions is called the required coefficient. The same calculation can be applied to a set of test conditions called the available coefficient of the tower.
The enthalpies' temperature relationships for counterflow towers is given in Fig.
3.16.
The water entering the top of the tower, with bulk water temperature
T 1 , surrounded by the interfacial film and having an enthalpy of
H' 1 , is represented by A. As the water moves down the tower, its temperature decreases to
T 2
and enthalpy H' 2 .
As the film follows, the saturated curve is represented by point B.
In contrast, the air flow to the tower from the bottom with wetbulb temperature
Twb
and enthalpy
H
I
is represented by point
B'.
As the air moves up the tower, the temperature and humidity increase. Consequently, the enthalpy H 2
is at point A'. The driving force at any point
In the heat transfer unit in the tower is the distance between the line
H
I
2
1
Air
G
T
2
Wafer Discharge Temperature °C
Fig. 3.16
The
Effect of
Temperature the the
Air at
Local and
Different Enthalpies between
Air Flowing through the
Tower and
Saturated Enthalpy
Water Temperature.  From Fraas and of
Ozistk (1965).
105
106
AB and
A'B'.
The
form
of
equation
(3.31) is dH = Q/G 3
.
1
.
which leads to a straight air operation line having a
Q/G slope.
It indicates that the enthalpy of moist air varies linearly with water temperatures since the derivation of log mean temperature differences depends on linear relationships between the enthalpy and the temperature of both mediums.
Solutions of Equations
(3.44) and
(3.45)
Knowing the mitai condition of air and water, the numerical integration of equations
(3.35) and
(3.36) is performed. This can be checked by subdividing the tower into a finite element of volume having an equal temperature drop. Equations
(3.44) and
(3.45) can be written as:
Acp
n
= C
p
QdT = KadV(H'  H)
m
(3.47) where
(H'  H)
m
is the mean driving force over an increment of volume.
Therefore:
1
KaV = QC AT
Ps
E
(H"  H)
m
(
3.
48)
The value of the integral can be defined as the area under the curve if
1/(H
1
 H)
m
is plotted versus the local water temperature as shown in
Fig.
3.17.
The resulting quantities represent the value of the tower characteristic
KaV/Q which is a
function
of the inlet and outlet wetbulb air temperature and inlet and outlet water temperature.
The quantity of heat transfer within the cooling tower is a function of packing geometry and the water distribution system. The value of a in equation
(3.43) is not easy to determine but commonly ranges
from
T
2 dT
Water Temperature
°C
Fig. 3.17 The
Approximation of
Tower Characteristic by the Relation
Water Temperature.

From between
1/(H"  H) and Local
Fraas and Ozisik
.
(1965).
1
0
7
108
7 to
19 m
2
/m
3
(Fraas and
Ozisik, 1965).
The tower characteristics can be evaluated by approximating the water enthalpy line in Fig.
3.16 by a straight line. Use of the log mean will underestimate the cooling tower characteristic. Therefore, the position of the straight line in
Fig.
3.18 can be corrected by
Sh (Fraas and
Ozisik, 1965):
Sh 
H" 1 + H"
2
+ 2H" m
4
KaV = [
T
1
 T
2
1
(ti
i")
(3.49) where H'
1
and
H'
2 are the saturated enthalpy evaluated at the inlet and outlet water temperatures, respectively, and
H' m
is evaluated at the mean temperature
(T 1 + T
2 )12.
In Fig.
3.18, an approximation of log mean of the driving force inside the cooling tower can be expressed as:
(Ii"
2

AH"
)
AH"
= m log e
[(AH"
2
 Sh)/(An  dh)]
(3.50)
Therefore, the tower characteristic can be defined as:
(3.51)
Lewe and
Cristie, as reported by
Fraas and
Ozisik (1965), tested some
60 packings suitable for use in cooling towers and found that, for a given fill geometry matrix, the tower characteristic
(KaV/Q) is directly proportional to the height of packing. This gives a straight line relationship in terms of the number of decks. Furthermore, the experimental
10
9
H"
Sh
A
AH
S h
HB
Equivalent
Straight Line
Relation for H"
n °.
B'
H
*H"
A'
T
2
Local Water Temperature
°C
Fig. 3.18 Method for
Approximating Enthalpy Line by Straight Line to
Simplify the Tower Characteristic Calculation.  From Fraas and Ozisik
(1965).
110 data showed that
KaV/Q varies with some power of the Q/G ratio which can be defined as:
KaV
= .07 + BN(
Q n
)
G
(3.52)
Equation
(3.52) gives the effect of fill geometry on tower performance. This effect varies from one fill to another regardless of inlet water temperature. Figure
3.19 shows the effect of a three fill geometry matrix on the tower characteristic.
Pressure Drops in Cooling Towers
The pressure drop through the tower is a function of fill geometry matrix, air flow rate, and water flow rate. These relationships were analyzed by
Fraas and
Ozisik (1965) and can be expressed as:
AP
= DG
e
2 (
9
6
7 x 1
0
5
Ya
)
CQ
G
2 f
9.67
eg (
5

10
Y a
)
j
—
,R
(3.53) where
R is the mean free fall which is defined as the mean vertical distance that water droplets fall between slats. It is a function of free flow area of the droplets and deck spacing.
The value of
G
eg
is equivalent to the air loading corresponding to the mass velocity of the air relative to falling water droplets. Therefore, it is a function of air flow and free flow average distance.
1.65
1.60
4010
1.55
0
—
Tr;
1.50
77)
1:45
1.40
3
0
135
1.30
1.25
40 50 60
Tower Intake Temperature
°C
Fig.
3.19
The
Effect of Hot
Water Discharge Temperature on
Tower
Characteristic for
Various Deck Fills.

From
Kelly and
Swenson
(1956).
111
112
Mechanical Draft Tower Costs
The cost of a cooling tower is affected by different factors, such as its location and specific function. Cost varies from country to country, city to city, as well as different sites within the city.
Therefore, there is no standard figure or formula to estimate cooling tower costs.
The cost of cooling towers includes three major divisions: initial cost, annual fixed costs, and operation costs. Since there are no taxes, insurance premiums, or other similar expenses in
Libya, annual fixed costs will not be represented in this study. Furthermore, the following cost analysis will partially depend on American methods of estimating cooling tower costs since available data of cooling tower costs in Libya do not exist.
There are two ways of expressing cost information:
$/Kw of power produced and S. Both depend on past data.
Kolfate (1968) estimated the cost of mechanical draft towers in nuclear power plants as
$61Kw.
The cost increases if a closed approach is desired.
He also estimated that the fan of a mechanical draft tower consumed
.8% of generating capacity.
Lockhart,
Whitesell, and
Catland (1955) correlated the data obtained by
Koulton for
32 mechanical draft towers. These data are presented in Figs.
3.20 and
3.21.
The data have to be adjusted since costs have doubled since
1955.
Of the total generating capacity,
0.46% is consumed by the fan and
0.85% of the total horsepower is used to operate the pump and fan.
Approach
=3.9°C
4.4°C
5.0°C
5.5°C
6.7°C
7.8°C
8.9°C
10.0°C
11.1 °C
10
Range AT
°C
14
Fig.
3.20
Cooling
Factor as a
Function
of
Temperature
Ranges and the
Approach. 
From Carey, Ganley,
and
Maulbetsch (1969).
113
20
24
Wet Bulb Temperature
°C
Fig.
3.21
The
Relationship between
WetBulb
Coefficient. the
WetBulb Temperature
and

From
Garey
et
al.
(1969).
114
The capital cost is a function of location, land cost, design, ambient conditions, tower installation, and other auxiliary costs. It can be expressed as:
1
15
COS
= 47.6 x QGM x K
1413
x KX(IK) (3.54)
Capital cost is directly proportional to the range and flow rate and inversely proportional to the approach.
Operation costs include: maintenance costs and horsepower cost.
Maintenance of cooling tower parts is essential to prevent any adverse effects on the heat transfer capacity of the tower which depends on air flow, water flow, and tower characteristics. Willa
(1964) lists the effects of poor maintenance.
The main system subject to change is the water distribution system. Poor spray patterns usually are a result of corrosion, clogging, algae, mud or oil accumulation which reduces the air flow rate, and increases the static pressure through the tower.
Damages in the support structure and packing produce undesirable water and air distribution which reduces the heat transfer coefficient.
Unfavorable performance sometimes occurs as a result of flow pulsation within the fan.
The power cost is a function of approach; it increases as the approach decreases. Therefore, the operation cost is inversely proportional to the approach.
116
Computation Procedure
The method of computation basically depends on trial and error procedures in which the temperature of the well water changes over various ranges. Knowing the inlet and outlet of the water and water flow rate, the heat load of the well water can be computed using equation
(3.28).
Then the enthalpy of inlet and outlet air is calculated from the ambient condition. Air flow rate is computed for specific enthalpy using equation
(3.31).
However, recognizing that the fan is a constant volume device, a slight change in air mass flow is a function of air density. Therefore, density of inlet air is computed for given ambient conditions. Air flow rate drive by the fan can be calculated when density of the air is known. Pack height is calculated using the analytical solution developed by
Techbycheff
(Smith and
Maulbetsch,
1971).
Knowing the deck height, the enthalpy of saturated air can be determined which allows the computation of the saturated temperature of outlet air. Next, the heat of evaporation is computed, thus permitting the calculation of evaporative losses from the cooling tower. Total horsepower needed to drive the fans can be calculated with knowledge of the air flow rate.
A Fortran computer program was developed to accomplish the computation.
It is listed in Appendix B.
The heat load of well water expressed by equation
(3.28) assumes specific unit heat and neglects evaporation loss which is small compared with total flow rate:
(Pp
= Q(TI ". T2)
(3.55)
117
Air flow rate is determined by equation
(3.28) as (Garey et al.,
1 9
69 ):
( ho
(H
2
 H
1
) 
G
(3.56)
Since the specific heat of the air is a function of temperature, the enthalpy of air can be expressed by a power series:
H(T) = a
0
+ a l
T + a
2
T
2
+ a
3
T
3
+ a 4 T
(
3.57) where a
0' a l' a
2' a
3' and a
4 are constants given by Smith and
Maulbetsch
(1971).
The enthalpy of inlet air is computed at a given wetbulb temperature of the exit air. Outlet enthalpy is evaluated at the mean temperature of the water.
The computation of specific humidity and partial vapor pressure employs the following basic thermodynamic relations.
Assuming water vapor obeys the law of ideal gas, the specific humidity can be expressed as:
P
.622 P v
B
P
(3.58) or
W
 p
.622 (RH x P v
B

(RH x P
") v
")
118
Therefore, partial vapor pressure can be determined as:
P — v W + .622 p
B
The saturated vapor pressure can be expressed in terms of temperature by power series using Richard's
(1971) approach:
P(T) =
[a
0
+ a
1
T + a
2
T 2 + a
3
T 3
a
4
T
4
+ a
5
T
5
j ,
(3.59)
Inlet air density can be expressed by Bayle and Charles' law of ideal gas
(Severns and Fellows,
1949): y
=
P a
/R a
T
= P a
/29.27(T + 273)
The size of cooling components are based on calculation of tower characteristic
KaV/Q. The method of calculation for this characteristic is
Techbysheff's approach which modified equation
(3.51) for an approximate value of the numerical integration of equation
(3.45) such that:
KaV
— T
1
 T
2
rD
4
R2
R
3
Ro
(3.60) where
R
1'
R
2'
R
3'
and
R
4
are the inverse difference between the saturation enthalpy and the actual enthalpy evaluated as
[T
2
+ .1(T
1
 T
2
)],
[
1
2
+ .4(T
1
 T
2
)], [T
1
 .4(T
1

1
2
)], and
[T
1
 .1(T
1

1
2
)] (kcal/kg), respectively.
The packing height of the tower necessary to give the above characteristic was calculated using equation
(3.52) where the number of decks
(N) can be expressed as:
119
N  packing height deck height
Therefore, equation
(3.52) can be written as:
PHT 
DHT (
KaV
.7)
Q
B ( i )
n
Q
(3
.6
1) when the values of
B and n are given by
Fraas and
Ozisik (1965) for each specific deck height.
Knowing the packing height, the pressure drops through the tower are computed using equation
(3.53).
Air loading (mass velocity) and the equivalent air mass flow rate were found by
Smith and
Maulbetsch (1971) as:
G e
= G/
6
1 where ,
5
1 is the ratio of the flow to the water loading. Equivalent air mass (flow rate) is then computed
(Smith and
Maulbetsch, 1971).
Thus, equation
(3.53) becomes: pp
= [(PHT/DHT) x
9.67 x 10
5
Bya
] x
[DG e
2
+ CQ f
G eq
2 kg/m
2
(363)
where D and
C are constants for a given pack height given by
Fraas and
Ozisik (1964).
Water loss in cooling towers is not only dependent on the total
120 heat load, but also on the ratio of convectional heat transfer and latent heat (evaporative) transfer. Water consumption predictions in mechanical draft towers have been based on a rough rule of thumb (kg/555.5 kcal).
This approach neglects the effect of sensible heat transfer and the atmospheric ambient conditions which can produce up to a
20% overestimation of evaporative loss. The amount of water lost in the form of droplets suspended in the exit air usually does not exceed
1
0/ of the total water consumption.
Leung and Moore
(1971) estimated the evaporation losses in cooling towers of a power plant using the heat and mass transfer approach where the cooling tower evaporation rate can be related to the air flow rate and inlet and outlet specific humidity of the air.
Therefore, in order to solve for evaporation loss, assuming a constant air flow rate mass ratio may reduce accuracy. Evaporation losses are estimated by knowing the latent heat or heat of evaporation, since the total heat dissipation is the sum of latent heat and sensible heat. Thus, latent heat can be estimated by: c e =
( r)
4) s where cp s
= •24(T a '  T d )G, and where
Ta 's are defined as the temperature of saturated outlet air and can be expressed by a power series:
121
T' =
[a
+ aH' + aH' a 0 la 2a
2
+ a
H'
3a
3
+ aH
4a
'
4
] (3.62) where a o , a l
, a
2
, a
3
, and a
4 are constants given by Smith and
Maulbetsch
(1971) and where
4)1,
H' = H(T ) + — wb
Knowing the latent heat, the evaporation rate is computed as: dQ = (I) e /H v
kg/hr where
H v is the heat of evaporation approximated by Linsley et al.
(1958):
H v
= 597.3  .56H(
T
1
+ T
2
2
 32.2) kcal/kg
(3.63)
Lockhart states capital cost as: cost
= 31.7 x
GM x KCW + KX(IK)]
(3.64) but Converses' costs are:
2*(31.7 x (Q
0
x K wb
+ KX(IK)]
The averages of both costs are expressed in equation
(3.54). The wetbulb coefficient,
K cw
, was defined by Lockhart as: b
.
.7 + exp(4.17  .0767 x T wb
)
122 produced in Fig.
3.20.
The cooling factor by Lockhart,
KX(IK), obtained from a curve fit of data, is produced in Fig.
3.21.
Knowing the outlet air density air flow rate, the driven air flow rate
(G f ) is computed by:
With driven air flow rate and pressure drop through the tower known, the horsepower required to drive the fan is then computed as:
FHP = (G f
x AP)/(4562 x .80) where fan efficiency is assumed as
0.8. There is no need for the water pump to raise water to the top of the tower so the only horsepower needed is for the fan. Assuming maintenance cost is
.1 of capital cost, operating cost can be computed as:
OPC = .1 x COS I
THP x .03
Therefore, the total cost is the sum of operating costs and capital costs.
Results and Discussion
The same criteria employed for the cooling pond were used for the mechanical draft tower. Results were computed at sea level elevation.
The highest elevation of the investigated area was
200 m above sea level which had a negligible effect on the results of computations. The computed evaporation rate expressed as the percentage of well flow rate
123 for summer design criteria of differing discharge temperatures and cooling demands is shown in Table
3.2.
One can see that the evaporation rate significantly changes over cooling demands, but slightly changes over intake temperatures. Variation in evaporation rate for discharge temperatures changes linearly over various ranges (AT) with a magnitude of
224.5 kg/1
°
C, as shown in Fig.
3.22. Evaporation rates for the tower and of the cooling pond display comparable form. However, the evaporation rate of the pond at any given design criteria in this study is always greater than the evaporation rate of the tower with similar design criteria. This is related to the fact that, unlike the tower, evaporation rate of the pond is affected by natural evaporation loss. In contrast to the cooling pond, the evaporation rate of the tower for a given heat load increases over intake temperatures. This is primarily because higher intake temperatures increase the enthalpy of air flowing through the tower, resulting in a higher saturated air capacity.
As illustrated in Fig.
3.23, a higher evaporation rate will occur when the highest wetbulb temperature is combined with the lowest relative humidity. Monthly changes in wetbulb temperatures and relative humidity are shown in Fig.
3.24. The figure clearly demonstrates that the highest evaporation rate occurs during summer months. When employing parameters of ambient wetbulb temperature and relative humidity, it is obvious that when the incoming air is at a high wetbulb temperature coupled with low relative humidity, the evaporation loss is high and sensible heat transfer is low.
In contrast, when the incoming air is at
Table
3.2
Tower Evaporation Rate in Terms of Well
Discharge Percentage for Summer Design
Conditions.
48.9
50.0
51.1
52.2
53.3
54.4
55.5
56.7
57.8
58.9
60.0
Well
Discharge
Temperature
( ° C) 16.7
2.64
2.64
2.64
2.65
2.65
2.64
2.62
2.62
2.62
2.63
2.63
2.79
2.79
2.80
2.80
2.81
2.81
2.82
2.82
2.82
2.82
2.82
17.8
Cooling Range
18.9
20.0
(%)
21.1
2.97
2.97
2.99
2.99
3.00
3.00
3.00
2.97
2.97
2.98
2.98
3.15
3.16
3.16
3.17
3.14
3.14
3.14
3.15
3.17
3.17
3.18
3.31
3.31
3.32
3.32
3.32
3.33
3.34
3.34
3.35
3.35
3.35
2.22
3.49
3.49
3.49
3.49
3.50
3.50
3.51
3.51
3.52
3.52
3.53
124
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,
Nov.
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Oct.
Sept.
Aug.
f
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July
2
June
May
Apr.
Mar.
Feb.
Jan.
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3.1
3.3
Evaporation
Rate
(% of Flow)
/
/ i
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1
I
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3.5
i
Fig.
3.23
Variation of
Evaporation
Rate over the
Year in
Percentage of
Flow Rate for Various Cooling Ranges (AT) at 57.8
°
C
Well
Discharge Temperature.
126
r
(%)
9nitoi3
8
1 o
O
D
2
127
1
o
0, ainolgadwai
128 a low wetbulb temperature coupled with high relative humidity, the evaporation loss is low and sensible heat transfer is high.
In Fig.
3.25, unlike the pond, the annual evaporation loss of the tower increases over intake temperatures of a given heat load. For any given discharge temperature and range, annual evaporation loss from the tower is smaller than the cooling pond. This is related to the fact that the cooling tower is not affected by the solar radiation. Therefore, there is no accounted evaporation occurring in the cooling towers under natural conditions. Although annual evaporation loss of the towers was computed for only
65% of the operating time, the total annual evaporation loss of the pond is higher than that of the tower regardless of seepage.
A family of curves in Fig.
3.26 approximates a linear relationship of the approach (the difference between the tower outlet water temperature and wetbulb temperature) on pack height. A low approach coupled with a low saturated air enthalpy difference requires greater contact time demanding higher packing construction.
Figure
3.27 shows the total cost of the cooling tower affected exponentially by well discharge temperatures for various ranges. This effect fluctuates from
$0.62 per
555.5
kcal at a
60
°
C well discharge temperature
 16.7
°
C range (AT) to
$0.17 per
252 kcal at a
48.88
°
C well discharge temperature
 22.2
°
C range, compared with the cooling pond's total cost of
$.20 per
250 kcal to
$.67 per
252 kcal for the same design criteria. Capital cost of the tower and of the cooling pond is similar with the exception of operating costs. Difference in operating costs is mainly due to the effect of the approach (difference between wetbulb
12
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13
2 temperature of inlet air and outlet water temperature) on horsepower required to operate the fan at any given design criteria. It is evident that, at a low wetbulb temperature and high well discharge temperature coupled with a low cooling range (AT), the difference between the saturated enthalpies leaving and entering the tower is high. Therefore, the air flow rate through the tower will be small. On the other hand, when the wetbulb temperature of incoming air is high and the mean water temperature throughout the tower is low, heat gained by air is at its minimum and air flow rate at its maximum. Subsequently, air flow rate throughout the tower decreases as mean water temperatures increase, causing lower pressure drops. This demonstrates that, at a low air flow rate, a reduced amount of horsepower is required, implying that the maximum amount of horsepower is necessary in summer months, compared with the remainder of the year. In contrast to operating cost, capital cost of the tower reaches its maximum in winter and minimum in summer.
Total cost of the cooling tower was computed for a
25year life which is assumed to be a well's lifetime. Calculation does not include pump cost. It assumes well pressure is sufficient to raise water to the top of the tower equivalent to the pressure computed for irrigation in
Chapter
2 of this research.
Conclusions and Recommendations
Conclusions
By comparing the results of the cooling tower and cooling pond, it is clear that the cooling tower would be the most water efficient
133 method. The higher evaporation in the pond due to the effect of solar heating is absent in the cooling tower system. If seepage is also considered, then pond water consumption could be as much as two or three times that of the cooling tower. Even though initial pond construction costs may be half of the tower's, there are other factors that must be taken into consideration in determining the optimum method of cooling thermal waters:
I. The Wadi's width is an average of only
0.5 km. The project area is
10 km long. This would mean that the cooling ponds would require about
1.5% of this valuable agricultural land.
2.
The soil profile is alluvial to
1 meter deep, underlain by marly limestone of low permeability. A pond without lining will be subject to lateral subsurface outflow. The resultant drainage problem in adjacent agricultural lands will increase overall operations cost.
3.
Lining the cooling with concrete will increase the cost of the pond to as much as
20 times the cost of the tower.
4.
The capital cost of power for tower operation will not be a major factor because the project has already constructed its own power station to supply the needs of the pumping and irrigation activities as well as for residential requirements.
The total cost and annual evaporation losses required for dissipating
1.9 x 10
10 kcalkg/year or for a discharge temperature of
57.77°C and a
20
° F cooling range for
70% of operation time by using the two
134 cooling methods is summarized in Table
3.3.
The evaporation rate of the two systems using similar average summer conditions is found in Table
3.4.
As it has been mentioned in the first part of this research, well discharge temperatures range from
5558
°
C.
If we assume that the tower reduces the temperature to
38
°
C, and that a further reduction in temperature to
30
°
C occurs due to heat dissipation in the irrigation system and in the soil surrounding the plants, the water that will arrive at the roots of the plant will be suitable for the plant species utilized in the project.
In conclusion, based on the assumptions made, the cooling pond may not be considered as a viable method. The results of this study indicate that, given the two alternatives, the cooling tower system is by far the most efficient and economically optimal method for treating thermal water for agricultural purposes.
Furthermore, with some modification, the results of this study can be used for designing the cooling system of power plant condenser discharged water.
Recommendations
This investigation presented two cooling system analyses. The comparison between the two systems was made only on the basis of simplification and general empirical solutions coupled with some assumptions.
The applier of this result should be aware of the variation in climate data during the months.
The empirical analysis used for cooling pond design in this investigation was developed mainly by Brady et al.
(1969) from a field
Table
3.3
Comparison between
the
Tower Cooling
Pond of
57.8
°
C
Discharge Temperature
and
20
°
C
Cooling
per
Well
Range.
Cooling Method
Cooling tower
Cooling
pond
Total
Cost
(s)
7085
2746
Capital
Cost
(s)
5346
2650
Area Annual
Required Evaporation
2
3
(m)
Cm)
80
4249
25,964.7
30,220
135
Table
3.4
Evaporation
Rate of
57.8
and
20
°
C Cooling
Range.
°
C Discharge Temperature
Evaporation
Rate
Cooling Method (%)
Cooling tower
Cooling
pond
3.17
3.57
Evaporation
Rate
(m/yr)
8.7
Natural
Evaporation
(m/yr)
1.7
13
6 study in South Central United States. The accuracy of the empirical formula for the study area should be verified by field measurements. The cooling tower study was based on a simplified thermodynamic analysis. It should be known that the author was not capable of gathering all the necessary field data for making the check on the sensitivity of the calculations.
Therefore, the following study is recommended to be undertaken:
1.
A field experiment should be conducted to study the feasibility of using spray pond or spray modules as other means for lowering the high well water temperature.
2.
A smallscale model of the cooling systems (pond and tower) should be constructed and the following investigation should be made: a.
Compare the mathematical models with the field data for the two cooling systems, pond and tower.
b.
Determine the effect of daily meteorological fluctuations on cooling pond performance.
c.
Correlation analysis should be run to compare the actual evaporation with the computed one.
d.
Determine the effect of climatological instability on cooling pond performance.
3.
Make an economic evaluation of the two systems. It is obvious that an adjustment to the economic cost should be made on the basis of Libyan data.
137
4.
An agricultural experiment should be made to determine the effect of various water temperatures on plant growth and on productivity in the project area.
APPENDIX
A
DEFINITION
OF
SYMBOLS
Symbol
A
C a
C m
C v
C
B f(W)
Water
surface
area.
Definition
Specific heat
of air.
Specific heat
of
humid
air.
Specific heat
of water.
Specific heat
of vapor.
Brunt's
coefficient.
Equilibrium temperature.
Wind function.
Fan
horsepower.
FHP
G
Air flow rate.
Enthalpy of
moist air
in a
bulk water
H'
temperature.
Enthalpy of
moist
air
at water
interface
H"
temperature.
H al
Enthalpy of
inlet
air.
H a2
Enthalpy of
outlet
air.
H
Heat
of
vaporization.
V
H
1
Enthalpy of
moist
air
entering
the
tower.
H
2
Enthalpy of
moist
air
leaving
the
tower.
138 kg/hr kcal/kg kcal/hr kcal/kg kcal/kg kcal/kg kcal/kg kcal/kg m2
Units kcal/kg kcal/kg kcal/kg kcal/kg kcal/kg
°C
W/m mm
Hg
Symbol
K'
Definition
Surface heat exchange coefficient.
Mass transfer coefficient between saturated air at water temperature and the air stream.
Sensible heat exchange coefficient between water surface and the main air stream.
Units
W/m
2
 C
P a
P s
P v
P
B
PHT
Q o
Q pp
Q
E
QG
QGM
Wetbulb temperature coefficient.
b
K
G
Overall heat transfer coefficient between the main water body and the atmosphere.
K
L
Unit conductance, heat transfer, water to interface.
KX(1K)
Cooling factor.
Number of decks.
Partial air pressure. dQ
Partial saturated vapor pressure.
Partial water vapor pressure
Barometric pressure.
Seepage flux from the pond.
Flow rate of water mm
Hg mm
Hg mm mm
Hg
Hg
Pack height.
Flow rate from the well.
Outflow flux from pond. kg/hr
Evaporation flux from water surface.
kg/hr kg/hr
Precipitation flux falling directly on the pond. kg/hr kg/hr
Evaporation flux. liter
139
W'
W"
W
1
W
2
Symbol
Definition
T n
T o
T s
T wb
T
1
T
2
T'
Interfacial film temperature.
7 r

Mean excess temperature.
T a
T d
T.
Q
I
Inflow flux from thermal source
Q
R r
Runoff flux to the pond.
Latent heat of the medium.
R a
,R v
Universal gas constant of dry air and vapor.
Medium temperature
Air temperature.
Dew point temperature.
Excess temperature at lake intake.
Natural water temperature.
Excess temperature at discharge point.
Water surface temperature.
Wetbulb temperature
Water thermal discharge temperature.
Outlet water temperature or evaporative cooler water discharge temperature.
V
Volume of pond water.
Wind velocity.
Specific humidity of the bulk air.
Specific humidity of airwater interface.
Saturated specific humidity.
Specific humidity of intake air.
Specific humidity of outlet air.
Units kg/hr kg/hr kcal/kg
140
°C m3 m/sec
°C
°C
°C
°C
°C
°C
°C
°C
°C
°C
°C
(Pn
(I)
(1) o
(I)
PP
4) s y
Y a
Y v
AP
6
A m a
(1)
.9
Symbol
(1)ab
(I) br
(1)c
(i) d e
Definition
Vapor pressure difference proportionally factored to temperature difference.
Water density.
Air density.
Vapor density.
Pressure drops.
Emissivity of water surface.
Wavelength.
StefanBoltzmann constant.
Longwave atmospheric radiation incident on pond surface.
Longwave reflected atmospheric radiation by pond surface.
Longwave radiation from the pond surface.
Energy lost or gained by convection from the water surface.
Heat flux by conduction.
Energy transfer from the water surface by evaporation.
Net absorbed heat.
Outflow energy flux.
Well heat rejection.
Energy flux by precipitation.
Solar radiation incident on pond surface.
.97
W/m
2
W/m
2
W/m
2
W/m
2
W/m
2
W/m
2
W/m
2
W/m
2 w/m2
W/m
2
W/m
2
Units
141 mm Hg/
°
C kg/m3 kg/m3 kg/m 3
g
'sb
4)
1
(I)
N
4)
Ft
Symbol
Definition
Sensible heat.
Reflected solar radiation by pond surface.
Inflow heat flux.
Net absorbed radiation on pond surface.
Energy flux from runoff to the pond.
142
Units kcal/ft
2
/hr
W/m
2
W/m
2
W/m
2
W/m
2
APPENDIX B
COMPUTER PROGRAM
143
•
•
•
•
THE
PROGRAME
IS IN ENGLISH UNITS
PROGRAME
POND
(INPOT,OUTPUT)
5
DIMENSION
MONTH(1(4),EMONTH( 14) , AIRT( 14) ,DEWT (14) ,EVAPR (14) ,X V
AP
(14) , HRAD (14) , WIND
(14) ,EQUALT (14) , AREA
(14) , TOTCOS (14) ,EXCOEF
$ (14) ,HRJ (14) , WSURFT (14)
REAL
INTT (14)
FLO:4=79.17264E5
*.8
READ GENERAL INFORMATION OF THE
AMBIANT CONDITION
DO
35 L=1,1
READ 100, (MONTH (I)
, AIRT (I) , DEWT (I)
, HRAD (I) , WIND (I)
,EQUALT
(I)
5,1=1,1
1
4)
100
F3RMAT (3 X,A2,2F5.1,F7.1,3X,2F5.1)
PRINT GENERAL INFORMATION OF THE
AMBIANT CONDITION
PRINT 200, (MONTH (I)
,AIRT (I) , DEWT (I) ,[(RAD (I) ,WIND (I)
, EQUALT (I)
$, 1=1,1
(4
)
•
200
13
FORMAT (15X,A5,5F10.2)
CALCULAT THE MONTHLY
EQUALIBRIUM
TEMP.
DO 15 I=1,14
WIN
DF=70+.07*WIND (I)
**2
AVET= (DEWT
(I)
+EQU ALT (I)
) /2.
201
15
•
26
BETA=.255—.0085*AVET+.000204*AVET**2
COEF=15.7+
(BETA+.
26) *WINDF
EQUALT1= (—COEF+SQRT (COEF**2—. 2*
(—HEAD (I)
+1801— (BETA*DEWT
(I)
$. 26*AIRT
(I)
)*WINDF) ) )/. 1
EQDIF=EQUALT
(I)
—EQUALT1
IF (EQDIF. GT. —.5. AND. EQDIF.LT..5) GO TO 201
EQUALT
(I)
=EQUALT1
GO TO 13
EQUALT
(I)
=EQUALT1
CONTINUE
DO
35 K=30,40,2
WELLT=K
HRJ (14) =FLOW*WELLT
LPAGE=2
DO 35 J=120,140,2
DIST=J
DO 30 1=1,14
APR°
ACH= DIST—WELLT—EQUALT
(I)
WINDF=70+.07*WIND
(I)
**2
WSURFT
(I) =HRJ (/) / (FLOW*ALOG ( (DIST—EQU
ALT (I)
)/APROACH)) +EQUALT
(I)
AVET=
(WSURFT (I)
+DEWT (I) ) /2
BETA=.255—.0085*AVET+.000204*AVET**2
EXCOEF (1) =15.7+. 05* (EQUALT
(I)
+WSURFT
(I)
) +
(BETA+. 26) *WINDF
CALCULÂT THE
REQUARED
AREA
AREA (I) =FLOW/EXCOEF
(I)
*ALOG ( (DIST—EQU
ALT (I) ) /APROACH)
CALCUAT
THE TOTAL COST WHICH EQUAL TO THE OPERATION COST +CAPTAL COS:
COST=AREA (/) *0.06
OPCOS=COST*. 002
TOTCOS
(I) =COST+ OPCOS
COMPUT THE MONTH OPERATION
TEMPRETUR
WSURFT (I)
,


DIST—WELLT/2.
AVET= (WSURFT
(I) +DEWT
(I) ) /2.
BETA=.255—.0085*AVET+.000204*AVET**2
EXCOEF
(I) =15.7+. 05* (EQUA
LT (I) +WSURFT
(I)
) + (BETA+.26)*WINDF
SURTDIF=DIST—NSURFT
(I)
IF (SUR
TDIF.LT.. 5)
GO TO
29 siSURFT1=EQUALT
(I)
+HRJ
(I) / (EXCOEF
(I) *AREA (I) )
I
44
30
40
55
36
31
34
HOUT=H1+DELHS
TOUT
=.99674408E1+.24015952E1*HOUT
3.10255304E3*HOUT
.22686654E1*HOUT
**3.14174090E6*HOUT
**4
QLAT =QREJ
AFLR
*.24*(TOUT
TDB(I))
HV=1040

.523*((71+12)/2.90)
XEVAP(I)=QLAT/HV
WEVAP(I)=XEVAP(I)/(FLOW) *100
FUDG=FLOW*7.48/(62.2*60)*2.0*CWB
CAPCOS(I)=3.*FUDG
CALCULÂT THE TOTAL HORSPOWR THAT REQUARED TOOPRAT THE FAN
ACFd=AFLR/(60.*DIN)
HPFAN=(ACFM*DELP*5.2)/(33000.*FANEF)
TOTHP(I)=HPFAN
OPCOS=TOTHP(I)*.75*
COS1AI=.01*OPCOS
720*12*25*.65*.03
TOTCOS(I)=OPCOS+COSMAI+CAPCOS(I)
CALCULÂT THE YEARLY EVAPORATION
E1ONTH(I)=WEVAP(I)*30 *24 *.65
CONTINUE
EYEAR=0
DO 40 1=1,12
EYEAR=EYEAR+EMONTH(I)
LPAGE=LPAGE+1
PRINT 55
FORMAT(1H1)
PRINT 31,T1,RA
FORMAT(//,15X,*THE dONTHLY OPERATION CONDITION AND*,
**ANDTHEMAXIMUMCONDENSER TEMP.OF*,F8.2,*ARE*,//,
S*EVAPORATION FOR A TEMPRETURE*,/,16X,*RISE OF*,F8.2,
$5X,*MOUTH APROACH PACK RIGHT EVAPORATION
HORS POWER*)
PRINT 51,(MONTH(I),APR(I),
STOTCOS(I),TOTHP(I),CAPCOS(I),I=1,14)
PHT(I),WEVAP (I),
51 FORMAT((36X,A5,6(5X,F10.2)))
PRINT1000,EYEAR
1000 FORMAT(///,14X,*THE TOTAL YEARLY EVAPORATION IS*,F15.5)
35
CONTINUE
END
FUNCTION H(T)
H=21.572142.93539227*T+.2865243E01*T**2.26605772E03*
$T**3+.12608996E05*T**4
RETURN
END
FUNCTION P(T)
P=.16818166E1+.14461089E2*T+.83460247 E5*T**2+.4987537
SE6*T**3.20658843E9*T**4+.22620224E10*T**5
RETURN
END
**2+
TOTCOS
145
•
C
THE PROGRAME IS IN ENGLISH UNITS
PROGRAM MECH.TOWER(OUTPUT,INPUT)
DIMENSIONEMONTH(14),TDB(14),TWB(14),RH(14),TWAT(14),WEVAP(14),
SPHT(14),APR(14),MONTH(14)
3,CAPCOS(14)
,XEVAP(14) ,TOTCOS(14),TOTHP(14)
FLOW=3.29511E5
FANEF=.8
100
90
•
•
XK=2.
DO 35 L=1,1
READ 100,(MOUTH(I),TDB(I),TWB(I),RH(I),I=1,14)
FORMAT(A2,3F5.2)
PRINT 90,(MONTH(I),TDB(I),TWB(I),RH(I),I=1,14)
FORMAT(16X,A5,5X,3F10.2)
CALCULAI THE DESIGNE CONDITIN(ENTHALPY,EVAPORATION PRESUR
DENSITY OF TUS INLET AIR,ETC
DO 35 K=30,40,2
15
•
RA=K
QRJ=FLOW*RA
LPGE=2.
DO 35 J=120,140,2
T1=J
T2=11RA
TAXT=(T1+T2)/2.
DO 30 1=1,14
RH(I)=RH(I)/100.
APH(I)=T2TWB(I)
QREJ=QRJ
H1=H(TWB(I))
H2=H(TAXT)
AFLR=NEJ/(H2H1)
WACT=RH(I)*(.622*P(TDB(I)))/(14.696(RH(I)*P(TDB(I))))
APSAT=(WACT*14.696)/(.622+WACT)
DIN =144.*(14.696APSAT )/(53135*(TDB(I)+460.))
CONTINUE
WART=FLOW/AFLR
T3=T2+.1*RA
T4=T2+.4*RA
T5=T1.4*RA
T6=T1.1*RA
CO1=WART*RA
RDH1=1./(H(T3)H1.1*C01)
RDH2=1./(H(T4)H1.4*C01)
0DH3=1./(H(T5)H1+.4*C01)
RDH4=1./(H(T6)H1+.1*C01)
CHAR=(RA/4.)*(RDH1+RDH2+RDH3+RDH4)
PACKING EIGHT FROM RAAS ANDOZISTKDECK NUMBER
DECKHT=2.
PHT(I)=DECKHT* (CHAR
WLOAD=2500
.07)/(.103*WART
PLANA=FLOW/2500
ALDG=AFLR/PLANA
ALDGE=ALDG+3500.
DELP
=((PHT(I)/DECKHT)*.0675/DIN
32+.1E12*2500*ALDGE
**2*2.62)
**(.54))
)*(0.4E8*ALDG
RANG=RA
CW8
=.7+EXP(4.17.0767*TWB(I))
CALCULTE THE EVAPORATION RAT WHICH EQUAL TOTAL HEAT 
SINSIBEL HEAT DEVIDED BY HEAT OF EVAPORATION
DELHS=QREJ/AFLR
**
146
204
29
•
291
DIFSURF=VISURFT
(I)
WSURFT1
IF (DI FSUR F.GT..5. AND. DI FSURF. LT..5) GO TO 204
WSURFT (I)
=wsuRFr1
GO TO 26
WSURFT (I) =WSURFT1
EXCEST=DISTEQUALT (I)
INTT
(I)
=DISTWELLT
HRJ (I) =FLOW* (DISTINTT (I)
IF
(HRJ
(I)
.
GT.
HRJ (14) ) HRJ
(I) =I1RJ (14)
X=EXP (EXCOEF (I) *ARE A (I) /FLOW)
ENTT1=EQUALT (I) +EXCEST*X
ENTTDIF=INTT
(I) ENTT 1
IF (ENTTDIF.GT..5.AND.ENTTDIF. LT..5)
GO TO 293
INTT (I) =ENTT 1
GO TO
291
CALCULÂT THE SURFACE TENRETUR
AND BETA ,AND THE HEAT REJECTION BY
THE LAKE IF THE SPRAY IS REQUARED
• 293 SPRAY=DISTW ELLT
IF (INTT
(I)
.LT.SPRAY)
GO TO 295
POND
HRJ=HRJ
(I) * (DISTINTT
(I)
) /WELLT
WSURFT
(I)
=EQUALT
(I) +PONDHRJ/ (EXCOEF
(I) *AREA (I))
•
AVET= (ASURFT
(I) +DEWT (I) ) /2
HET k=.255.0085*AVET+.000204*AVET**2
CALCULAT
THE HEAT OF EVAPORATION AND EVAPORATION RATE
295
30
HVAPOR=1041.25. 5629* (WSURFT (I)9C)
XVAP
(I) =BETA*
(WSURFT
(I) DEW T
(I) )*WINDF*AREA (I) / (HVAPOR)
EVAPR
(I) =XVAP (I) / (62.2*AREA
(I) )
EMONTH (I)=EVAPR
(I)
*720
CONTINUE
40
55
34
31
EYEAR=0
DO 40 1=1,12
EYEAR=EYEAR+EMONT H
(I)
LPAGE=LPAGE+1
IF (LPAGE. LT.2)
GO TO 34
PRINT 55
FORMAT (1H1)
LPAG E=0
PRINT 31,WELLT,
DIST
FORMAT (//,15
X,* THE MONTHLY OPERATION CONDITION AND
*,*
$THE
MONTHLY MAXIMUME
WELL TEMP.*,F8.2,
4
ARE*,//,
$*OPERATIOM
AT TEMPRETIUR*,/, 16X ,*RISOF*, F8.2,
$5X,*MONTH
WSURFCE
INTAK K
EQUALIBRIUN
HRJ*)
32
1001
35
DO 33 1=1,14
IF
(INTT
(I) .
LT. SPRAY) ICC=" "
IF
(INTT
(I)
.GT.SPRAY) ICC="+"
32, ICC,
MONTH ( I)
, WSURFT (I) ,INTT (1) , EXCOEF
(I) ,EQUALT
(I)
,
SEVAPR
(I)
,AREA
(I) , TOTCOS
(I)
FORMAT(
(34X,A1,A5,4 (5X,F5.1) ,5X,F10.5,5X,
F10.2,1210.2))
33
CONTINUE
PRINT 1001,EYEAR
FORMAT (///,14X,*THE
TOTAL YEARLY EVAPORATION IS*,F15.5)
CONTINUE
END
EVAP.
1
47
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Theis, C.
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Throne, R. F.
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1960. Forecasting heat losses in ponds and streams. Journal W. P. C. F., Vol.
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Willa, J. L.
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Zarazzer,
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1975.
Ground water quality in the central region of the
Libyan
Arab
Republic. General Water Authority, Tripoli.
I
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Thesis
Hydrology
1977
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