Chapter One

Chapter One

Introduction

Chapter One Introduction 1.1 General Groundwater constitutes an important component of many water resources such as water supply for domestic, agriculture, and industry. However, shallow groundwater level often represents a problematic state. It leads to soil salinity and alkalization and hence, to less or non productive state of land, in addition to its effect on buildings and constructions, because it can weaken soil stability and reduce bearing capacity. The present research deals with a problem of shallow groundwater level in the ancient Babylon city in which groundwater is considered as a source of problem rather than a water resource. The Babylon city is suffering from high groundwater level, which interferes with and hampers the process of archeological investigation and surveys. Another problem raised by groundwater is the increase in soil salinity and growth of weeds on the discovering surface. Therefore solving such problem is very critical, and special and very urgent measures must be taken to protect Babylon city from this disaster. The Babylon city is located about 90 km to the south of the capital Baghdad and about 10 km to the north of Hilla city. The Babylon city lies between longitude 44˚24́ 40˝ - 44˚27́ E and latitudes 32˚31́ 10˝- 32˚ 33́ N, Fig. (1.1). It is bounded from the west by Shatt Al-Hilla river, (a branch of the Euphrates river), and from the east by Babylon canal, while from north and south by two artificial lakes. The study area is about 5.5 km2.

1

Chapter One

Introduction

Ba b

ylo n

Hilla

32o33’20”

Artificial Mountain

Road Main

Sh att AlHil la

el an C

Babylon Wall

el hann ist C Tour

Riv er

on yl ab B

lake 1

lake 3

lake 2

32o31’15” o

44o27’

44 24’40”

Fig. (1.1) Location of the study area - Babylon city

1.2 Aim of the study Present work aims to study the possibility of lowering the water table level in Babylon city to a depth lower than the oldest archeological horizon, which was expected to be at a depth 14- 16 meters below present ground surface (General Directorate of Geological Survey and Mineral Investigation, GDGSMI, 1989). 2

Chapter One

Introduction

Groundwater now covers all of the old Babylonian remnants and prevents all excavation work of archeologists. Therefore dewatering is necessary for solving such problem. The suitable system of dewatering for the study area should be select.

1.3 Scope of the study The scope of this study is summarized as fallows: 1) Previous works and studies on Babylon city are presented and discussed in chapter two. 2) The hydrogeological aspects in the study area, including; historical background, geology, hydrology, aquifer characteristics, climate and chemical analysis, are expressed in chapter three. 3) The principles of various dewatering systems with their advantages and disadvantages are discussed in order to select a suitable system for the study area. These are presented in chapter four. 4) The formulation of both numerical and analytical models to evaluate the hydraulic head distribution as a function of space and time is covered in chapter five. 5) The design of the well field of the selected dewatering system is presented in chapter six. 6) The application of the mathematical models to the case study and analysis of the obtained results as well as to the comparison between the numerical and analytical simulations are viewed in chapter seven. 7) The main conclusions of the study and recommendations for future works and studies are outlined in chapter eight.

3

Chapter Two

Previous Works and Studies in the Ancient Babylon City

Chapter Two Previous Works and Studies in the Ancient Babylon City 2.1 General Several previous works and studies have suggested several solutions to the groundwater problem regarding the ancient Babylon city. Among these are a study carried out by the General Directorate of Geological Survey and Mineral Investigation (GDGSMI) during 1979, and the study performed by AL-Furat Center of Studies and Design of Irrigation Projects (FCSDIP) during 1989. As well as several sub soil investigations in various locations in the city to evaluate the soil properties. This chapter deals with the presentation and discussion of these studies.

2.2 The study of the (GDGSMI) The first work on the ancient Babylon city was that performed by the General Directorate of Geological Survey and Mineral Investigation (GDGSMI) during 1979. It was done according to a request made by the State Organization for Antiques to study the possibility of lowering the ground water level, since groundwater covers most of the old Babylonian remnants and used to obstruct the work of the archeologist to discover the old city. A preliminary study was made by the specialists of the (GDGSMI) to obtain information about the surface geology, lithology and the hydrogeological conditions of the area, as well as the geophysical methods were applied to study the water bearing horizon, because any previous data concerning the geology and the hydrogeology of the area was not available. The geological 4

Chapter Two


survey was carried out using (97) auger holes with a distance (50-200m) between each two holes. The depths of these holes ranged from 1.5 to 3 m. A water level contour map was constructed from the measured water level in all auger holes, bore holes, pits, and in the depression where the groundwater appears on the surface, Fig. (2.1).

32o33’20”

Artificial Mountain

l-H illa

Road Main

Sh att A

t le vu Ri

Babylon Wall

el hann ist C Tour

Riv er

n lo by Ba

lake 1

lake 3

lake 2

32o31’15” o

44o27’

44 24’40”

Fig. (2.1) Groundwater contour map (after GDGSMI,1979) The hydraulic parameters of the aquifer were determined from pumping test analysis. Two groups of pumping wells were drilled to a depth of 20m. The first group consists of one pumping well with three pizometers which were drilled in the central part of the old Babylon city. The second group consists of one pumping well with four piezometers; they were drilled near 5

Chapter Two


Shatt Al -Hilla River. Average values of the transmissivity and specific yield for the first group were found to be (350 m2/d) and (7.9*10-2), respectively and for the second group were to be (266m2/d) and (5*10-2), respectively. A multiple pumping test was carried out in three bore holes in order to evaluate the groundwater resources and to calculate the amount and influence of drawdown during multiple pumping. The process of pumping was carried out for only one day because of the continuous shutdown of electricity. The pumping was at rate of (9 l/s). The drawdown was calculated using the hydrodynamic method by applying the following ForchHaimer equation:

st = H − H 2 −

R R R 1 (Q1 ln 1 + Q2 ln 2 + − − − − Qn ln n ) r1 πK r2 rn

------------------ (2.1)

Where st : Total drawdown at cretin point ,p in the area ,(L). 3

Q : Rate of discharge at the pumping well ,(L /T) . K : Hydraulic conductivity of the aquifer, (L/T) . R : Radius of influence of the pumped well, (L). r : Distance between point p and the pumped well, (L) . H : Total head of the aquifer,(L) .

The total drawdown was found to be(5.72 m) near the bore holes and decreased gradually as we more away further from the wells until the effect of pumping reaches the recharge boundaries (i.e Shatt AL-Hilla river) where the drawdown will be equaled to zero. The (GDGSMI) had concluded from

this study that Shatt AL-Hilla river 6

participates

in

rising

the

Chapter Two

groundwater


level

about (4-5m), so they recommended to study the

possibility of changing the river course.

2.3 The study of (FCSDIP) AL-Furat Center of Studies and Design of Irrigation Projects (FCSDIP) conducted a study, during 1989 to evaluate the problem and to suggest a suitable well field design to Babylon city. The study consisted of an expression of the hydrogeological conditions in Babylon city, which was based on the previous work of the (GDGSMI), in addition of drilling several bore holes at different depths and sites. The hydraulic properties of the penetrated aquifer were calculated from the pumping test analysis ,and found to be varying between the strip parallel to Shatt AL-Hilla river, and the area behind it (i.e. the central part of the study area). The transmissivity and specific yield of Shatt AL-Hilla river strip were found to be (350m2/d) and (0.075), respectively. The area behind the river was found to have a transmissivity

of

(150m2/d)

and

a

specific

yield

about

(0.005).

The water balance equations were used to evaluate the amount of groundwater resources, which was found to be (280 l/s) including the static and dynamic resources. This amount of groundwater was suggested to be withdrawn by 30 bore holes (penetrated to a 25m depth), 14 of which have a pumping rate equal to (12 l/s), and the other 16 bore holes have a pumping rate equal to (7 l/s). The wells were assumed to be located on a ring surrounding Babylon city, Fig. (2.2). The total drawdown was calculated using the hydrodynamic equation, eq. (2.1). Maximum drawdown was found to be (6m) at the center of Babylon city and decreased toward the recharge boundaries, Fig. (2.3). 7

Chapter Two


3000

Riv la

Artificial Mountain

l-H il att A Sh

el hann ist C

Babylon Wall

Ro Main ad

2000

t le vu Ri

2500

Tour

er

n lo by Ba

lake 1

lake 3

1500

1000

500

Well

lake 2

500

1000

1500

2000

2500

3000

3500

Fig. (2.2) Locations of suggested wells (after FCSDIP, 1989)

3000

2500

2000

1500

1000

500

500

1000

1500

2000

2500

3000

3500

Fig. (2.3) Designed drawdown in old Babylon city (after FCSDIP, 1989)

8

Chapter Two


An alternative design for the vertical drainage was presented in the same study of (FCSDIP), including a well field design consists of (22) wells distributed on the perimeter of the area, Fig. (2.4).

3000

la

Artificial Mountain

l-H il att A Sh

et

el hann ist C

Babylon Wall

Road Main

2000

ul iv R

2500

Tour

Riv er

n lo by Ba

lake 1

lake 3

1500

1000

500

Well

lake 2

500

1000

1500

2000

2500

3000

3500

Fig. (2.4) Locations of the suggested wells

Maximum discharge rate of the pumping wells was estimated to be (15 l/s). Drawdown contours map was produced using the following equation, (Hantush, 1964) h = h1 − (h1 − h2 ) 2

2

2

x ----------------------------------------------------------- (2.2) L

where h : Hydraulic head at the desired point ,(L) h1and h2 : Hydraulic heads at the boundaries ,(L) . 9

Chapter Two


x : Distance along the flow path, (L). L : Length of the flow path , (L) . The produced drawdown contours are shown in figure (2.5). It is seen that maximum drawdown imposed in the city center is (5 m). 3000

2500

2000

1500

1000

500

500

1000

1500

2000

2500

3000

3500

Fig. (2.5) Designed drawdown in the old Babylon city (after FCSDIP, an alterative design, 1989)

2.4 Subsoil investigations The National Center for Construction Laboratories (NCCL) carried out several subsoil investigations in Babylon city, among them a sub soil investigation in the site of the Babylonian ancient theater during 1989 .Three boreholes were drilled at various locations in the theater site to depths 6, 9 and 13.5m . The investigation showed that the soil under ground surface consists of silty clay to a depth of about 4m below ground surface underlain 10

Chapter Two


by a fine sand bed. The maximum water table level was found to be at a depth of 2m from the ground surface. Others investigations were carried out in various sites of the city. The last investigation was carried out during1995, in which the water table level was found to be at a depth of 1.6m.

2.5 Discussion of the previous studies Considering all the data collected from the work done during previous studies, several points have been raised, particularly those connected with results and the concluded solutions of the previous studies. These points could be summarized as fallows: 1-The study of (GDGSMI) concluded that Shatt Al Hilla river course is the main source of recharge in old Babylon city, so the study came out with suggestion of changing the course of the river, which is very difficult and costly to execute, in addition to that it will raise environmental and social problems. 2- The well fields designed by both studies of ((GDGSMI) and (FCSDIP)) aimed to lower the water table within a range of (6-7 m) as a maximum dewatering level, as this level will help in the excavation of the second old Babylon city only keeping the first oldest city (below this level) buried to depth of about 17m below the ground surface according to the State Organization of Antiques. Therefore both studies would help to solve the problem only partially and not completely. In addition to that direct pumping from the upper aquifer will lead fast lowering of ground water level, which may result in causing subsidence in the area and that in term will obstruct the excavation efforts.

11

Chapter Two


3-The analysis of the vertical drainage in Babylon city in both ((GDGSMI) and (FCSDIP)) studies were analytical solutions only. A more reliable approach to analyze and solve the dewatering problems would be the numerical models. The use of numerical models (a finite elements or finite difference model) can accommodate any variation in the hydraulic parameters of the area. Also the numerical models would handle the unsteady state more accurate. 4-The analysis throughout these studies do not consider the net vertical recharge (infiltrations from ground surface). Although, the amount of net vertical recharge is limited, but it should be considered in the analysis, because cumulative values of these amounts would affect the water table level.

12

Chapter Three

Geological and Hydrological Aspects of Old Babylon City

Chapter Three Geological and Hydrological Aspects of Old Babylon City 3.1 Historical background Babylon , which is an Akkadian word means "the gate of God(s)" was the capital of the land of Babylonia , the ancient empire that existed in the Near East in southern Mesopotamia between the Tigris and the Euphrates rivers , (Encyclopedia Britannica ,2002) .Babylonia was a long , narrow country bordered on the north by Assyria , on the east by Elam , on the south and west by the Arabian desert , and on the southeast by the Arab Gulf , Fig (3.1) .

Fig.(3.1) Ancient Mesopotamia map (after Encyclopedia Britannica,2002)

13

Chapter Three


The first records indicate that Babylon was established as a city around the 23rd century BC. Before this it was a provincial capital ruled by the kings of the city of Ur. The Bible reveals much about Babylonians all the way back from the time of Hammurapi (about 2000 BC) to the fall of Babylon (about 500 BC). Hammurapi emerged as the ruler of Babylonia. He expanded the borders of the Empire and organized its laws in to a written system, also known as the code of Hammurapi. Around 626 BC, Babylonian was ruled by Nabopolassar. Under his leadership, Babylonia became the dominant imperial power in the Near East and thus entered into her "golden age”. In 605 BC, Nebuchadnezzar ΙΙ, the son of Nabopolasser, became ruler and reigned for 44 years. Under him the Babylonian Empire reached its greatest strength. He built Babylon into one of the leading cities of the world. The famous hanging gardens of Babylon were known to the Greeks as one of the Seven Wonders of the World .Throughout the long period of Babylonia history, the Babylonians achieved a high level of civilization that made an impact on the whole known world. Sumerian culture was it basis, which later Babylonians regarded as traditional. Traditionally the history of Babylonia has been broken down into three major periods: 1- The old Babylonian period (2000 – 1595 BC ) . 2- The middle Babylonian period (1595 – 1000 BC ) . 3- The new Babylonian period (1000 – 539 BC ) . Layout of the Babylon city with its external and internal walls, gates temples, etc, can be seen in Figure (3.2).

14

Chapter Three


Fig. (3.2) Layout of Babylon city (after Encyclopedia Britannica, 2002) Throughout the Old Testament there are references to the Babylonians, their people, culture, religion, military power, irrigation and drainage systems, etc. As irrigation was so vital to the Empire, a whole network of canals was formed and special officials appointed to supervise them. They made sure the canals were clear of rushes and water weed, the course ways dredged of silt, and the tank consolidated against floods. Water ran along a strengthened conduit of hardened earth, (The Plumber.com, 1995). Concerning the drainage, the terraces contained an extremely advanced system of internal drainage, which ensured that all moisture was led off into large sewers of baked brick. The sewers were roofed slightly ogival or pointed vaulting. They consisted of a series of slanting courses each resting on the one below compensating for the lack of wood or scaffolding in the design.

15

Chapter Three


3.2 Geology of the study area The study area is covered by flood plain and Aeolian sediments of Quaternary age, (DGGSMI, 1989). Lithologically, the sediments are represented by gravels, sands, and prevalently silt. The thickness of Quaternary sediments reaches about (20-25m). The first meter of these sediments generally shows homogeneity and consist mainly of silty clay and sand of local artificial channels. The western part of the area consist mainly of flood plain sediments of Shatt Al-Hilla river, Fig. (3.3a). The second meter of sediments below ground surface proved some differences between the deposition outside the outer wall and inside it, Fig.(3.3b). The area outside the wall composed of sandy deposits up to 1.5 m while the area within the wall composed mainly of silty clay. This means that the outer wall had acted as an embankment and protected the inner area from the floods. Mineralogically, the sand and silt fraction consist of quartz, feldspar, carbonate minerals (calcite, dolomite), chert and a variety of heavy minerals. The clay fraction is characterized by a suite of clay minerals including montmorillonite, chlorite, kaolinite and illite. Both the carbonate fraction and the clay minerals seem to be of detrital origin (Banat and Al – Rawi, 1986). Pre-Quaternary sediments had been found at a depth 25m below the ground surface, these sediments are mainly formed of sands and silty clays.

16

Chapter Three


32o33’20”

l by Ba

lake 1

Artificial Mountain

AlHil la

Riv e

Road

Sh att

l ne Ca

r

on

Main

el hann ist C Tour

Babylon Wall

lake 3

Sand Archiolegic Sites Silty clay Clay Silty Clay to Clayey Silty

lake 2

32o31’15” 44o24’40” o

44o27’

(a) First meter

’

32 33 20”

Riv e

Artificial Mountain

att AlHil la

Main Road

Sh

l ne Ca

Babylon Wall

el hann ist C Tour

r

n lo by Ba

lake 1

lake 3

Sand Archiolegic Sites Silty clay Clay Silty Clay to Clayey Silty

lake 2

32o31’15” o

44 24’40”

(b) Second meter

44o27’

Fig. (3.3) Geological map for the first and second meters of the sediment.

17

Chapter Three


3.3 Hydrology of the study area Hydrologic setting of the study area based on previous work carried out by (FCSDIP, 1989), included constructing groundwater flow pattern, Fig.(3.4).The figure clearly shows that the groundwater is highly affected by the Shatt Al-Hilla river. The flow directed from the river toward Babylon old city. So the main source for groundwater can be considered as surface water derived from Shatt AL-Hilla River. The depth of groundwater varies from less than 1

lake

n ca

AlHil la

n lo by Ba

Riv e

r

meter near the river course to 4 meter in the central parts of old Babylon city .

t Cha

ial ific Art ntain u mo (2)

nnel

et

Artificial mountain (1)

Sh att

l

is Tour

Stre

Babylon wall

lake

Stream lines - - - - Equipotential lines

Fig. (3.4) Groundwater flow pattern in the study area. The upper few meters of the study area consists of silty clay overlay fine sand layer to a depth of 24 m, which is considered as the first unconfined aquifer. From 24-26 m brown clay layer which acts as a semi impermeable

18

Chapter Three


layer. From 26-45 m medium sand and it can be considered as a second aquifer or as a part of the first aquifer, Fig. (2.6).

3.4 Climatic conditions The study area is characterized by a sub-humid to semi- arid climate with two well defined seasons, hot - dry summer and cold – wet winter. Recorded meteorological data of Hilla meteorological station have been used to evaluate the climate logical characteristics of the study area. Table (3.1) shows the monthly average meteorological elements at Hilla station. These elements are temperature, sunshine, relative humidity, wind, rainfall and evaporation. The average annual temperature is 23.08ºC. The maximum monthly average temperature is 34.64ºC in July, while the minimum is 10.1ºC in January. The fluctuation between day and night temperatures are appreciable in winter as well as in summer. The maximum sunshine duration occurs in June with a monthly average of 11.99 hr/day. The minimum monthly average is 6.28 hr/day in December, owing to the short days of that time of the year and the cloudiness of the rainy season. Average value of relative humidity varies from 31.2% in July to 73.07% in December, with annual average value reaches to 49.6%. Rainfall begins in October and ends in May after which becomes scarce. The maximum monthly average rainfall is 24.17mm occurring in January, the minimum is 5.03 during October, with an annual rainfall average of 110.72mm. The maximum and minimum monthly averages of evaporation are 363.73mm (in July) and 49.68mm (in January), respectively. Generally, high annual evaporation rates characterize the climate of the study area. So it is quit clear that the evaporation is many times higher than the rainfall, which means that there is no important groundwater recharge from rainfall within the study area.

19

Chapter Three


Most groundwater recharge from precipitation commonly occurs during spring months when evaporation is small and soil moisture is maintained at or above field capacity. During summer, evaporation and soil moisture requirements are so great and very effective in reducing groundwater runoff. So, groundwater stage is much less in July than in January. Table (3.1) Monthly average meteorological elements at Hilla station for the period (1976-1996). Relative

Wind

Humidity

Speed

%

m/sec

6.41

73

12.6

7.29

Mar.

16.8

Apr.

Mean

Sunshine

Temp.ºC

hr.

Jan.

10.1

Feb.

Month

Rainfall Evaporation mm

mm

1.45

24.17

49.68

63.47

1.92

19.03

72.99

7.92

56.14

2.35

20.09

131.37

22.97

8.8

47.53

2.06

12.77

190.87

May

28.73

9.49

37.69

2.24

1.26

278.49

Jun.

32.46

11.99

31.88

2.63

Nil

339.54

Jul.

34.64

11.96

31.2

3.01

Nil

363.73

Aug.

33.8

11.46

33.73

2.35

Nil

324.55

Sep.

31.09

10.13

37.79

1.68

Nil

243.18

Oct.

25

8.52

48.29

1.39

5.03

159.86

Nov.

16.97

7.29

61.57

1.39

15.16

82.17

Dec.

11.81

6.28

73.07

1.51

13.21

51.28

Annual

23.08

107.54

49.6

1.99

110.72

2287.71

20

Chapter Three


3.5 Characteristics of the aquifer system The study of the aquifer system characteristics based on data collected during field work of pumping test carried out by (FCSDIP) during 1989. Five sites were chosen to carryout the pumping test, Fig. (3.5). At each site one pumped well with two observation wells were drilled in order to observe hydraulic gradient during pumping. 32o33’20” w5

Riv er

Artificial Mountain

Road Main

Sh att AlHil la

Babylon Wall

w1

el an C

w2

l anne st Ch Touri

w3

on yl ab B

lake 1

lake 3

w4

w well lake 2

32o31’15” 44o24’40”

44o27’

Fig. (3.5) Locations of pumping test wells Obtaining the hydraulic characteristics of the upper layer both Chow's method ( Chow,1964 ) and Theis recovery method ( Kursman , 1994 ) were applied to evaluate the transmissivity ( T ) and specific yield (Sy) . Both methods gave close values which led to consider their average. Required data and detailed computations of both methods are illustrated in appendix (A1). Results are shown in Table (3.2).

21

Chapter Three


Table (3.2) Hydraulic characteristics of the upper aquifer. Transmissivity ( m2 /day) Recovery method

Average

Specific Yield

Site No.

Chow method

1

160

0.003

2

250

0.065

3

260

250

255

0.021

4

360

352

356

0.035

Variation in transmissivity values across the area in the upper aquifer showed that at the middle, the lowest value of transmissivity was observed, while the south eastern side was found to be the most prolific site in the study area. Such variation was to be achieved due to anisotropy of the upper aquifer. The storativities over the area are high, indicating unconfined condition except at the central part was semi unconfined. Analyzing the hydraulic characteristics of the lower semi confined aquifer; Hantush inflection point (Hantush, 1964) was applied. Values of tranismissivity (T) and storage coefficient(S) in addition to values of leakage factor (B) and hydraulic resistance (C) of the semi pervious layer were obtained and given as: Transmissivity, Storage coefficient, Leakage factor, Hydraulic resistance,

T = 424 m2 / day. S = 2.1×10-3. B = 230 m. C = 302 days.

Value of transmissivity using Recovery method was found to be 415 m2/day, again average value of 420 m2 /day was considered. Require data and detailed computations of both methods are illustrated in Appendix (A2).

22

Chapter Three


3.6 Quality of groundwater Water samples were taken and chemically analyzed for both upper and lower aquifers by (FCSDIP, 1989) to examine the water suitability for agriculture, domestic and drinking purposes. Locations of the samples are shown in Fig. (3.5), and the results of the analysis are given in Table (3.3). The analysis showed that cations (Na+, Ca+2, Mg+2) and anions (CL- . SO4- , HCO3-) are considered a dominant ions in the water samples According to Food and Agriculture Organization (FAO, 1985), and World Health Organization (WHO, 1983) limitations for agricultural and drinking uses, respectively, the groundwater in the study area is suitable for both agricultural and dinking (if it doesn't contain bacteria). The groundwater may be classified as very hard according to Todd (1980). Also it is relatively basic since its average pH is (7.97). Previous chemical investigations of Shatt Al-Hilla river water. and groundwater in Babylon city had indicated that both waters have similar chemical analysis results which may draw to a conclusions that Shatt Al- Hilla river water could be a main source to the groundwater. Table (3.3) Chemical analysis of the water samples. Site No.

Depth (m)

Cations (ppm) +

Na

+2

Ca

Anions (ppm) +2

Mg

Cl

-

-

SO4 HCO3

T.H* -

T.D.S** PH

S.A.R***

(ppm)

1

23

598 160

205

852 960 537

1243

3289

7.5

7.3

2

26

55 40

27

64

244

473

489

8.5

1.84

3

36

253 56

83

212 500

305

481

1409

7.9

5

302 85

105

376 501

362

732

1729

7.97

4.7

Average

43

*Total Hardness. **Total Dissolved Solids. ***Sodium Adsorption Ratio.

23

Chapter Four

Dewatering Systems

Chapter Four Dewatering Systems 4.1 Introduction A dewatering system is to be designed in order to get the optimum quantity of water economically from a given geological formation .The choice of dewatering system depends upon topography, geological condition of the underlying strata , Depth of groundwater table, climate and the quantity of water required, (Raghunath, 1982). Generally, groundwater dewatering can be accomplished in several ways. The methods which are being current wide use are: 1) Vertical drainage system. 2) Horizontal drainage system. 3) Well point system. 4) Open drain. To make a proper selection, adequate information on the above methods should be prepared including principles, advantages and disadvantages of each method.

4.2 Vertical drainage system The principle of vertical drainage is pumping water from the aquifer by network of wells. This system is suitable for the large area with deep strata, which may be more permeable than that near the surface. There are two classes of wells used for drainage purposes, the water table or gravity well is located in an unconfined aquifer and removes water directly from the water bearing large. It may be either, shallow or deep well, Fig. (4.1a).

24

Chapter Four

Dewatering Systems

The other class is the artesian well that taps an aquifer containing water under pressure, Fig. (4.1b).

Ground surface water table

static surface Piezometric surface Impermeable layer

Impermeable layer

Impermeable layer

(b) An artesian well

(a) A gravity well

Fig.(4.1) Vertical drainage system The aquifer is confined or semi confined when less permeable layer lying above it, (Luthin, 1978). The permeability of the soil layers which are to be drained are of paramount importance in the success of the used of drainage well. The drainage water must be able to percolate down to the aquifer being pumped. The water table must be continuous from the shallow soil layers down to the pumped aquifer, and the permeability of the intervening layers must not present a barrier to the water movement. Some of the most successful drainage wells have been located in deep sandy soil having a relatively high permeability. Others have been located in fractured lava rock that underlies a permeable soil .In both cases the surface water table is responsive to the pumping that takes place from the aquifer. The aquifer should be of sufficient area to insure that adequate drainage will be achieved. Most of the area to be drained should be underlain by the aquifer. Vertical drainage has certain advantages, these are, (Raghunath, 1982): 1- Do not require much space. 25

Chapter Four

Dewatering Systems

2- Can be constructed quickly. 3- Fairly sustained yield of water can be obtained even in year of scanty rainfall. 4- Economical when deep seated aquifers are encountered. 5- Flowing artesian wells can sometimes be struck. 6- Generally good quality of water is tapped, which can be used for Irrigation. The drainage water then has an economic value.

The system, also has certain disadvantages, these are: 1- Requires costly and complicated drilling equipment and machinery. 2- Requires skilled workers and great care to drill and complete the well. 3- Installation of costly turbine or submersible pumps is required, as well

as

high annual operation and maintenance costs, and a proper collection system to transport and dispose the pumped groundwater. 4- Possibility of missing the fractures, fissures and joints in hard rock areas resulting in many dry holes. 5- May result differential soil settlements, causing additional structural

and

environmental damage.

4.3 Horizontal drainage system Subsurface horizontal drains have been successfully used in draining large areas such as from lands and irrigated fields. It is buried out of sight, Fig.(4.2) and a wide variety of material is used include clay pipes in short sections, concrete pipe in various lengths, blankets of gravel laid in the soil, fibrous wood materials such as willow branches buried in the soil, covered stone drains, plastic pipe, and other materials which can be covered in the soil and which will remain intact for long periods of time, (Luthin,1978).

26

Chapter Four

Dewatering Systems

Ground surface water table

Preliminary trench Proposed excavation Perforated horizantal drain

Fig. (4.2) Horizontal drainage system The basic purpose of these drains is to collect the water that flow out of the soil and to carry this water into an outlet channel or conveyance structure. There are two principal types of outlets, gravity outlet and pump outlets. A gravity outlet is one in which the water flows out of the drainage system by gravity in to a natural stream channel , an open ditch drain, a lake, a down well, or some other facility that disposes of the water. Pumps are used where the main drains are not sufficiently deep or where it is necessary to discharge the water from land below sea level into the sea. The topography of the land as well as permeability of the soil dictates the choice of an out let. The use of gravity out let presupposes that the elevation of the out let is adequate to collect the water that flows through the drain. A variety of materials have been placed around subsurface drains for the purpose of filtering fine sand and silt from the inflowing water. Manholes are placed in the drain lines for the purpose of inspecting the operation of the line and trapping the silt that may be in the drainage water. In addition, a manhole provides for ready access to the line if repairs must be made to the line or if the line requires cleaning. 27

Chapter Four

Dewatering Systems

A sedimentation basin can be incorporated into an inspection manhole. The usual practice is to have both the inlet and outlet pipe enter into the basin at level grade. If this is done there will be less neglect of the maintains of the structure (Luthin, 1978). The important advantages of the horizontal drains are (Raghunath, 1982): 1 - Not interfering with the forming operation .The land can be farmed right over the drain and there is no less area due to the drainage system 2 - Require less maintains. However, it is a fallacy to think that they don’t require any maintains. 3 - Low in cost of construction. Disadvantages of the system are: 1 - Deep seated aquifers cannot be economically tapped. 2 - Difficulty of finding out whether or not it is operating satisfactorily. 3 - Require must space for construction.

4.4 Well point system Well point system are groups of closely spaced wells, usually connected to a header pipe or manifold and pumped by suction lift ,(Johnson, 1972). Well point system may be used for water supply or for dewatering. For a water supply system, it is important to space the individual wells so that their areas of influence overlap only slightly. In contrast, the areas of influence in a dewatering system must overlap extensively in order to lower the water table over the desired area. Well points in a dewatering system are usually spaced from 0.65 to 1.6 m depending upon the permeability of the saturated layer, the depth of which the water table must be lowered and the depth to which the well points can be installed Fig. (4.3).

28

Chapter Four

Dewatering Systems W

W

W

W

Legend P

P pump& motor W Well point

W

W

W P W

W

W W

W

W

W

P

W

(a) Single stage

W (b) Double stage

(c) Multi stage

Fig.(4.3) General forms of well point system (after Johnson,1972) When the well point has been sunk to the required depth, the well has to be developed so as to yield sand-free water to its maximum capacity, forming a natural gravel pack around the well point. The yields are of the order of (1.5– 4.17 l/s), (Raghunath, 1982). Advantages of the well point system can be expressed as: 1- Small diameter wells are employed, which may considered as economically benefit. 2- Supply large quantities of water economically where conditions are favorable (in case of water supply system). 3- Only several hours of pumping are required to fully develop the draw down in the saturated layer around each well point.

Disadvantages (or limitation) of the system are: 1- The water table must be within few meters of ground surface to permit pumping from the wells by suction lift (usually driven in shallow coastal aquifers). 2- Required good suction characteristics pump.

29

Chapter Four

Dewatering Systems

3- The presence of tight layers of silt or clay at various depths in the saturated soil complicates the design of the well point system since they prevent vertical drainage of the sand lying above them.

4.5 Open drain Open drains are widely used for surface and sub surface drainage. They are used as individual field drains and main drains, (U.S Army corps of engineer, 2001). The most efficient channel is the one that will have the maximum capacity for a given slope and cross-sectional area. The most efficient cross section is the one with the smallest wetted perimeter. For earth channels, Trapezoidal cross sections are used. Half hexagon has the smallest perimeter and has the must efficient cross section, Fig.(4.4).

Berm

Free board

Spoil

Water surface

1 1.5

Design depth

Design width

Fig. (4.4) General form of an open drain (after Luthin, 1978) The permanence of one open drain depends upon the stability of the side slope of the drain. The characteristics of the soil have a great deal of influence upon this stability. Sandy materials which possess little cohesiveness are relatively unstable .Although, there are various methods for

30

Chapter Four

Dewatering Systems

stabilizing the side slopes such as tamping the sides of the ditch with bucket of the drag line, or rolling the sides of the ditch with weighted rollers. Scouring and deposition in the open drain depend upon the soil material and the slope. A flattening of the slope will cause deposition, whereas an increase in the slope may cause accelerated scouring or erosion. The use of setting basins or law check dam is recommended in conjunction with the open drain .The silt is concentrated is the setting basin or check dam and can be removed easily. Erosion can be prevented by placing rock jetting in the ditch to deflect the water away from the bank which is being cut. Advantages of the open drain are: 1 - Low initial cost. 2 - Easy to construct . 3 - Ability to carry large quantities of water. On the contrary, there are some disadvantages that are outlined below: 1- Interfere with farming operation. 2- Require continuance maintenance to be kept operating. 3- Difficulty of keeping them operating in unstable soil conditions 4- Cost of land removed from cultivation. 5- Growth of weeds in the ditch can seriously reduce the capacity of the ditch to carry water. The above detailed discussions and presentations of the various dewatering systems led to conclude that the vertical drainage system is considered the only system suitable for the study area. Pumping should be performing by the deep wells in order to provide a slow dewatering rate and hence, to avoiding any settlement that may take place.

31

Chapter five

Groundwater Flow Modeling

Chapter five Groundwater Flow Modeling 5.1 General In groundwater flow problems, the mathematical model usually consists of a set of partial differential equations that are known to govern the flow. The equations are subjected to certain assumptions in order to describe the physical processes acting in the aquifer since the field situation is too complex to be simulated exactly. Only a simplified subset of the general equations can be solved by analytical models that describe idealized situations which are limited in application (when the medium is homogeneous and isotropic) .To deal with more realistic situations, it is usually necessary to solve the mathematical model numerically. In this chapter two models were considered; one is numerical and the other is analytical .The numerical model uses the finite difference technique based on the continuity hypothesis and Darcy's law. The analytical model is theoretically based on the Hantush analysis of interfering drainage wells in a leaky confined aquifer (Hantush, 1964) with the Superposition and Image principles.

5.2 Numerical model by finite difference technique 5.2.1 Review of finite difference simulation Use of the numerical techniques started to increase all over the world since the late sixties and early seventies. Avery well introduction and extensive list of references are given by Remson et al (1971). Finite difference technique was first introduced by Richardson in 1910. Application of this model was done by Prickett and Lonnquist (1971), they simulated one, two and there dimensional non steady flow of

32

Chapter five


groundwater in unconfined, non leaky and leaky aquifers. The model was based upon a modified alternating direction implicit method. Trescott et al, (1976) introduced leakage from a confining layer and evapotranspiration as a linear function of depth. The solving techniques used in the model are, strongly implicit method, Iterative alternating direction implicit method, and Line successive over relaxation method. McWhorter and Sunada, (1977) analyzed the areal distribution of heads in confined and unconfined aquifers by developing two dimensional model using Fully implicit central difference procedure. Gauss elimination technique was used in the solution. Rushton and Tomlison, (1977) investigated the maximum acceptable mesh spacing for finite difference models of groundwater problems. Recommendations are given for the design of a mesh; their validity is tested in the solution of two field problems. Rushton and Redshow, (1979) demonstrated the use of analog and digital computer methods in the solution of two and three dimensional flows in both steady and unsteady states with listing of computer programs. Boonstra and DeRidder, (1981) presented a model that facilitates the use of regular or irregular nodal networks iteration or Gauss Seidel technique in solving two dimensional finite difference equations in confined, unconfined and semi confined aquifers. McDonald and Harbaugh, (1984) developed a three dimensional finite difference groundwater flow model .The model is modified in several later versions titled as MODFLOW computer code. The first version of MODFLOW was used by Rasheedudine et al,(1988). He constructed a quasi three dimensional flow model for a multi aquifer system in eastern Saudi Arabia to determine the hydraulic properties of the system and to evaluate the consequences of various development alternatives .The later versions were used by many modelers. 33

Chapter five


The department of defense provided a Groundwater Modeling System,(1998) provided in software named as GMS, supported several types of numerical codes . The most important code which can be used in the present research is a graphical interface to the groundwater MODFLOW, which can perform both steady and transient analysis and has a wide variety of boundary conditions and input options. The model developed by the United States Geological Survey, (1998) .The model was used by many modelers. Abdulla et al, (2000) applied MODFLOW to simulate water level change in the complex multi aquifers system of the Azraq basin, Jordan. While Robert et al, (2000) developed a three dimensional finite difference ground water flow model for the Upper and Middle Trinty aquifer in the Hill country area, Texas to help estimate groundwater availability and water levels in response to pumping and potential future droughts.

5.2.2 Theory of finite difference technique Finite difference equations can be derived in two ways; i.e., from the physical stand point involving Darcy's law and the principle of conservation of mass, or by a conventional mathematical treatments, substituting the finite difference approximations for the derivatives of governing equation . Both derivational routes lead to the same result, (Domenco and Schwartz, 1998). A general form of the governing equation for the aquifer is: ∂⎛ ∂h ⎞ ∂ ⎛ ∂h ⎞ ∂ ⎛ ∂h ⎞ ∂h ⎜ k x h ⎟ + ⎜⎜ k y h ⎟⎟ + ⎜ k z h ⎟ − W = Sc ∂y ⎠ ∂z ⎝ ∂z ⎠ ∂t ∂x ⎝ ∂x ⎠ ∂y ⎝

------------ (5.1)

Where; x, y , z : Cartesian coordinates, (L) along the hydraulic conductivity axes kx, ky, kz ,(L/T) . h : Head of groundwater pressure, (L).

34

Chapter five


W: Flux per unit volume, it represents quantities discharged (or recharged)

to (or from) the aquifer, (L3/T) . Sc : Specific storage for the porous medium (dimensionless). t : Time (T) . Sc, k x , k y and k z can be function of space, while W and h are functions of

space and time . Finite difference method replaces the partial differential equation of flow, Eq. (5.1), by a set of difference equations in discredited space and time. The solution of the equations requires starting from an initial piezometric head distribution at time (t0) on the discrete nodes of the modeled region, then heads are computed at those nodes for later discrete time intervals t1, t2, t3,….. in a time step ∆t. The groundwater models can be classified in terms of spatial dimensions as two dimensional areal, two dimensional profile, quasi three dimensional, and full three dimensional. Two dimensional areal and quasi three dimensional models assume the aquifer view point, while two dimensional profile and full three dimensional models use the flow system view point, (Anderson and Woessner, 1992) .

5.2.3 Quasi Three Dimensional Finite Difference Flow Model (QTDFDM) A quasi three dimensional model simulates a sequence of aquifers with intervening confining layers. Confining layers are not explicitly represented, nor heads in the confining beds are calculated. The effect of a confining bed is simulated by means of a leakage term (Li,j) representing vertical flow between two aquifers,(Anderson and Woessner, 1992). Ignoring horizontal flow in the confining beds causes less than a 5 percent

35

Chapter five


difference in heads in modeled layers when the contrast in hydraulic conductivity between the aquifer and the confining beds is at least two orders of magnitudes, (Neuman and Witherspoon, 1969). When there is less than two orders of magnitude difference between the hydraulic conductivity of the confining beds and the aquifers, a full three dimensional model may be preferred. Using this approach, the system of the three layers is divided into a rectangular grid, which represented by a number of rectangular nodal cells. The dimensions of each cell can be varied. The variable grid minimizes the number of nodes in a simulation. However, care must be taken to change cell sizes gradually that the dimensions of adjacent cells in a given direction should not differ by more than a factor of 1.5, (Patrick, 1992). The grid cells are indicated by two subscript (i) and (j) with reference to Y and X directions, respectively. The grid extends in vertical direction over the entire depth of the system, Fig. (5.1).

Unconfined aquifer (upper layer)

i, j, k

Semi pervious layer Semi confined aquifer (lower layer)

i, j, k+1

Impermeable bed

Fig. (5.1) Discretization of the aquifer system by the (QTDFDM)

36

Chapter five


Since the system under consideration consists of two aquifers, derivation was made for each aquifer as a part of single typical cell, assuming that the confining bed represented by a function of leakance.

5.2.3.1 Simulation of the upper unconfined aquifer The upper layer of the model system is considered to be unconfined aquifer, which supplies leakage to the confined aquifer. To obtain appropriate equations for this case the partial derivatives of the flow equation is replaced by differences. The nodal equations is once again found by applying continuity and Darcy's law to every cell over a time interval of length ∆t, assuming that flow will occur only between the cell and its four direct neighbor cells. The resulting system of equations allows computing piezometer heads at the nodes at the end of a time interval (t, t+∆t) provided the heads are known in the beginning of that time interval. Consider the water balance of the cell over a time interval, Fig. (5.2).

37

Chapter five

Groundwater Flow Modeling QSFi,j QNet

Q12 i,j

i,j

Q13 i,j

Q11 i,j

Q14 i,j ∆yi-1,j

Qleak i,j ∆ y i,j

∆yi+1,j

∆xi,j+1

j

∆xi,j ∆xi,j-1

i

Fig. (5.2) Water balances around one nodal cell in the upper aquifer. As shown in the figure (5.2), there are: four in (out) flows from (to) the neighbor cells (Q11,Q12,Q13 and Q14), possibly a discharge from (to) the surface (QNet), leakage from (to) the surface water bodies (QSF), and (Qleak) which assumed to be outflow to the confining bed. It can be assumed sign of flows enter the cell are positive and vice versa. According to the principle of continuity, inflow minus outflows over the time interval (t, t+∆t) must be balanced against the quantity of water stored in the cell, so the continuity equation can be written as, (Kinzelbach, 1991): ⎡Q11i , j (t + ∆t ) + Q12i , j (t + ∆t ) + Q13i , j (t + ∆t )Q14i , j (t + ∆t ) + ⎤ ∆t ⎢ ⎥ ⎥⎦ ⎢⎣Q Net i , j (t + ∆t ) + QSFi , j (t + ∆t ) − Qleak i , j (t + ∆t ) = (H 1i , j (t + ∆t ) − H 1i , j (t ))S i , j ∆xi , j ∆y i , j

38

------------- (5.2)

Chapter five


Where; H 1i, j (t ) and H 1i , j (t + ∆t ) : Hydraulic heads of the upper aquifer at time (t),

and (t+∆t), respectively of a nodal cell (i,j),(L). Si , j : Specific yield of the upper aquifer at a nodal cell (i,j),(unitless).

∆xi , j and ∆yi , j : x and y dimensions, respectively of a nodal cell (i,j),(L).

Summation

QNet :

of discharge rates (pumping, evaporation and

evapotranspiration) and recharge rates (precipitation). It is assumed to be independent of the hydraulic head of the whole system. Pumping is assumed to be from the lower aquifer in the study area, so QNet is represented the net infiltration rate of the precipitation only or ---------------------------- (5.3a)

QNeti , j = Qpi , j

Where: 3

Qpi , j : Net rain water percolation rate at a nodal cell (i,j),(L /T) .

The amount of leakage between the upper aquifer and the lower aquifer through the middle layer, Qleak(i,j) can be expressed according to Darcy,s law as (Hantush, 1964) : QLeaki , j = Li , j (H 1i , j − H 2i , j )∆xi , j ∆yi , j

------------------------------ (5.3b)

Where; Li , j : Leakage factor, the transpose of hydraulic resistance of the middle

layer at nodal cell (i,j) (T-1) . and Li , j =

ki′, j bi′, j

ki′, j : Vertical permeability of the middle layer at nodal cell (i,j), (L/T) .

bi′, j : Thickness of the middle layer at nodal cell (i,j),( L) .

39

Chapter five H 1i , j and


H 2i , j : Hydraulic heads of the upper and lower aquifers,

respectively at a nodal cell (i,j), (L) . Leakage from a surface water body (river, lake, or reservoir), QSF (i,j) can be simulated using head dependent conditions as fallows: QSFi , j = Lsi , j (hsi , j − H 1i , j )∆xi , j ∆yi , j

---------------------------- (5.3c)

where; -1

Lsi , j : Leakage factor of surface water body bed at a nodal cell (i,j),(T ) .

and Lsi , j =

ksi , j bsi , j

ksi , j : Vertical permeability of surface water body at a nodal cell (i,j),(L/T). bsi , j : Thickness of surface water body at a nodal cell (i,j), (L) . hsi , j : : Water level of surface water body at a nodal cell (i,j),( L) .

Substituting Eqs. (5.3a- 5.3c) into Eq. (5.2), and dividing both sides by ∆t, Eq. (4.2) becomes (at a time level (t+ ∆t)) : Q11i , j (t + ∆t ) + Q12i , j (t + ∆t ) + Q13i , j (t + ∆t ) + Q14i , j (t + ∆t ) + Qpi , j +

Ls i , j (hsi , j (t + ∆t ) − H 1i , j (t + ∆t ))∆xi , j ∆y i , j − Li , j (H 1i , j (t + ∆t ) − H 3i , j (t + ∆t ))∆xi , j ∆y i , j

=

H 1i , j (t + ∆t ) − H 1i , j (t ) ∆t

S i , j ∆xi , j ∆y i , j

--------- (5.4)

Using Darcy's law following can be obtained: ⎡ H 1i −1, j − H 1i , j ⎤ Q11i , j = k1 * D1 ∗ ⎢ ⎥ ∆xi , j ⎢⎣ 0.5(∆yi −1, j + ∆yi , j )⎥⎦

--------- (5.5a)

⎡ H 1i , j +1 − H 1i , j ⎤ Q12i , j = k2 * D2 * ⎢ ⎥ ∆yi , j ⎣⎢ 0.5(∆xi , j +1 + ∆xi , j )⎦⎥

---------- (5.5b)

⎡ H 1i +1, j − H 1i , j ⎤ Q13i , j = k3 * D3 * ⎢ ⎥ ∆xi , j ⎣⎢ 0.5(∆yi +1, j + ∆yi , j )⎦⎥

---------- (5.5c)

⎡ H 1i , j −1 H 1i , j ⎤ Q14i , j = k4 * D4 * ⎢ ⎥ ∆yi , j ⎢⎣ 0.5(∆xi , j −1 + ∆xi , j )⎥⎦

------------ (5.5d)

40

Chapter five


Where; k1 , k2 , k3 and k4 : Harmonic average(a superior to the arithmetic average)

values of the upper aquifer hydraulic conductivity between a node (i,j) and its four direct nodes (i-1,j), (i,j+1), (i+1,j) and (i,j-1), respectively(L/T). D1 , D2 , D3 and D4 : Geometric average values of saturated thickness between

a node (i,j) and its four direct nodes (i-1,j), (i,j+1), (i+1,j),(i,j1), respectively (L).

Using harmonic average values of k rather than local once belonging to that in a realistic regional model, grid size may be anything from some ten meters to some hundred meters. The harmonic average reflects the fact that two values arranged in series are equivalent to two parallel resistances. Therefore, they are added harmonically as: k1 = 2(ki −1, j * ki , j )/ (ki −1, j + ki , j )

----------------------- (5.6a)

k 2 = 2(ki , j +1 * ki , j )/ (ki , j +1 + ki , j )

----------------------- (5.6b)

k3 = 2(ki +1, j * ki , j )/ (ki +1, j + ki , j )

------------------------ (5.6c)

k 4 = 2(ki , j −1 * ki , j )/ (ki , j −1 + ki , j )

------------------------ (5.6d)

Consequently, the geometric averages of saturated thickness can be formulated as: D1 =

(H 1

− Bi −1, j )(H 1i , j − Bi , j )

----------------------- (5.7a)

D2 =

(H1

− Bi , j +1 )(H 1i , j − Bi , j )

----------------------- (5.7b)

D3 =

(H 1

− Bi +1, j )(H 1i , j − Bi , j )

----------------------- (5.7c)

D4 =

(H 1

− Bi , j −1 )(H 1i , j − Bi , j )

----------------------- (5.7d)

i −1, j

i , j +1

i +1, j

i , j −1

41

Chapter five


Replacing values of transmissivity (T) by the hydraulic conductivity times saturated thickness (k*D) can be written as: T11 = k1 * D1

------------------- (5.8a)

T12 = k2 * D2

------------------- (5.8b)

T 13 = k3 * D3

------------------- (5.8c)

T14 = k4 * D4

------------------- (5.8d)

Substituting

Eqs.(5.6a-5.6d)

and

(5.7a-5.7d)

in

the

above

considerations shows that:

[

] (H 1

[

T 11 = 2(ki −1, j * ki , j )/ (ki −1, j + ki , j )

− Bi −1, j )(H 1i , j − Bi , j )

--------------- (5.9a)

] (H 1

− Bi , j +1 )(H 1i , j − Bi , j )

--------------- (5.9b)

[

] (H 1

− Bi +1, j )(H 1i , j − Bi , j )

-------------- (5.9c)

[

] (H 1

− Bi , j −1 )(H 1i , j − Bi , j )

-------------- (5.9d)

i −1, j

T 12 = 2(ki , j +1 * ki , j )/ (ki , j +1 + ki , j )

T 13 = 2(ki +1, j * ki , j )/ (ki +1, j + ki , j )

T 14 = 2(ki , j −1 * ki , j )/ (ki , j −1 + ki , j )

i , j +1

i +1, j

i , j −1

Substituting Esq.(5.9a- 5.9d) into Eqs.(5.5a- 5.5d) following can be obtained : ⎡ H 1i − 1, j − H 1i , j ⎤ Q 1 i , j = T 11 ⎢ ⎥ ∆ xi, j ⎣⎢ 0 . 5 (∆ y i − 1 , j + ∆ y i , j )⎦⎥

------------ (5.10a)

⎡ H 1i , j +1 − H 1i , j ⎤ Q 2i , j = T 12 ⎢ ⎥ ∆yi , j ⎢⎣ 0.5(∆xi , j +1 + ∆xi , j )⎥⎦

------------ (5.10b)

⎡ H 1i +1, j − H 1i , j ⎤ Q3i , j = T 13 ⎢ ⎥ ∆xi , j ⎣⎢ 0.5(∆yi +1, j + ∆yi , j )⎦⎥

------------- (5.10c)

⎡ H 1i , j −1 − H 1i , j ⎤ Q 4 i , j = T 14 ⎢ ⎥ ∆y i , j ⎢⎣ 0.5(∆xi , j −1 + ∆x i , j )⎥⎦

------------ (5.10d)

Finally substituting Eqs. (5.10a- 5.10d) in to Eq. (5.4) gives:

42

Chapter five


⎡ H 1i −1, j − H 1i , j ⎤ ⎡ H 1i , j +1 − H 1i , j ⎤ ⎡ H 1i +1, j − H 1i , j ⎤ T 11 ⎢ ⎥ ∆ x i , j + T 12 ⎢ ⎥ ∆y i , j + T 13 ⎢ ⎥ ∆x i , j ⎣⎢ 0.5(∆y i −1, j + ∆y i , j )⎦⎥ ⎣⎢ 0.5(∆xi , j +1 + ∆xi , j )⎦⎥ ⎣⎢ 0.5(∆y i +1, j + ∆y i , j )⎦⎥ ⎡ H 1i , j −1 − H 1i , j ⎤ + T 14 ⎢ ⎥ ∆y i , j + Qp i , j (t + ∆t ) + Ls i , j hs i , j (t + ∆t ) − H 1i , j (t + ∆t ) ∆xi , j ∆y i , j ⎣⎢ 0.5(∆xi , j −1 + ∆xi , j )⎦⎥

[

[

]

− Li , j H 1i , j (t + ∆t ) − H 2 i , j (t + ∆t ) ∆xi , j ∆y i , j =

]

H 1i , j (t + ∆t ) − H 1i , j (t ) ∆t

S i , j ∆xi , j ∆y i , j ----- (5.11)

Dividing both sides of Eq. (5.11) by ∆xi , j ∆yi , j and rearranging, it can be formed as: T 12 (t + ∆t ) T 13 (t + ∆t )

H 1i , j +1 (t + ∆t ) − H 1i , j (t + ∆t ) 0.5(∆xi , j +1 + ∆xi , j )∆xi , j

H 1i +1, j (t + ∆t ) − H 1i , j (t + ∆t )

Qpi , j (t + ∆t ) ∆xi , j ∆y i , j =

0.5(∆y i +1, j + ∆y i , j )∆y i , j

− T 14 (t + ∆t ) − T 11 (t + ∆t )

[

H 1i , j (t + ∆t ) − H 1i , j −1 (t + ∆t ) 0.5(∆xi , j −1 + ∆xi , j )

+

0.5(∆y i −1, j + ∆y i , j )∆y i , j

+

H 1i , j (t + ∆t ) − H 1i −1, j (t + ∆t )

]

+ Ls i , j hsi , j (t + ∆t ) − H 1i , j (t + ∆t ) − Li , j (H 1i , j (t + ∆t ) − H 2 i , j (t + ∆t ))

H 1i , j (t + ∆t ) − H 1i , j (t ) ∆t

-------------- (5.12)

Si, j

The last equation may be described as a quasi three dimensional finite difference flow equation in discredited form for the upper aquifer of the system.

5.3.2.2 Simulation of the lower semi confined aquifer Considering the lower leaky confined aquifer portion of a typical cell in figure (5.3) there are four in (out) flows, (Q21i,j, Q22i,j, Q23i,j, Q24i,j) from (to) the four neighboring cells in horizontal plane, while in vertical direction there are two flows (Qleaki,j and QWi,j) on the upper face only since the aquifer sets on impermeable bed. The flow QWi,j represents discharge rate from the aquifer by discharging wells. Using water balance principle in the portion over the time interval (t,t+∆t) gives: 43

Chapter five

Groundwater Flow Modeling QW i,j

Q22 i,j

Qleak i,j

Q23 i,j

Q21 i,j

Q24 i,j ∆yi-1,j

∆ y i,j

∆yi+1,j

∆xi,j+1 ∆xi,j

j

∆xi,j-1

i

Fig.(5.3) Water balance around one nodal cell in the lower aquifer . ⎡Q21i, j (t + ∆t ) + Q2 2i, j (t + ∆t ) + Q23i, j (t + ∆t ) +⎤ ∆t ⎢ ⎥ = H 2i, j (t + ∆t ) − H 2i, j (t ) Sci, j ∆xi, j ∆yi, j ⎣⎢Q2 4i, j (t + ∆t ) + Qleaki, j (t + ∆t ) − QWi, j (t + ∆t )⎦⎥ -------- (5.13)

[

]

Using Darcy’s law, the four lateral flows can be obtained as follows: Q 21i , j = T 21 Q 22i , j = T 22 Q 23 i , j = T 2 3 Q 24i , j = T 24

H 2i −1, j − H 2i , j

0.5(∆yi −1, j + ∆yi , j )

∆xi , j

------------------------ (5.14a)

∆yi , j

----------------------- (5.14b)

∆xi , j

---------------------- (5.14c)

∆yi , j

----------------------- (5.14d)

H 2i , j +1 − H 2i , j

0.5(∆xi , j +1 + ∆xi , j )

H 2i +1, j − H 2i , j

0.5(∆yi +1, j + ∆yi , j )

H 2i , j −1 − H 2i , j

0.5(∆xi , j −1 + ∆xi , j )

44

Chapter five


where; T21, T22, T23 and T24 are harmonic average values of lower leaky aquifer transmissivity between a node (i,j) and its four direct nodes (i-1,j), (i,j+1), (i+1,j) and (i,j-1), respectively (L2/T) . Values of transmissivity T21, T22, T23 and T24 can be determined harmonically as: T 21 = 2(T 2i −1, j * T 2i , j )/ (T 2i −1, j + T 2i , j )

-------------------- (5.15a)

T 2 2 = 2(T 2i , j +1 * T 2i , j )/ (T 2i , j +1 + T 2i , j )

-------------------- (5.15b)

T 23 = 2(T 2i +1, j * T 2i , j )/ (T 2i +1, j + T 2i , j )

--------------------- (5.15c)

T 2 4 = 2(T 2i , j −1 * T 2i , j )/ (T 2i , j −1 + T 2i , j )

--------------------- (5.15d)

Substituting Eqs. (5.14a- 5.14d) and Eq (5.3b) in to Eq. (5.13), dividing its both sides by (∆t*∆xi,j*∆yi,j), and rearranging it, the following equation obtained T 22 T 23

H 2i , j +1 (t + ∆t ) − H 2i , j (t + ∆t ) 0.5(∆xi , j +1 + ∆xi , j )∆xi , j

− T 24

0.5(∆yi +1, j + ∆yi , j )∆yi , j

− T 21

H 2i +1, j (t + ∆t ) − H 2i , j (t + ∆t )

Li , j (H 1i , j (t + ∆t ) − H 2i , j (t + ∆t )) −

H 2i , j (t + ∆t ) − H 2i , j −1 (t + ∆t ) 0.5(∆xi , j −1 + ∆xi , j )

+

0.5(∆yi −1, j + ∆yi , j )∆yi , j

+

H 2i , j (t + ∆t ) − H 2i −1, j (t + ∆t )

QWi , j ∆xi , j ∆yi , j

=

H 2i , j (t + ∆t ) − H 2i , j (t ) ∆t

--------- (5.16) This equation is a quasi three dimensional flow equation in finite difference form for the lower leaky confined aquifer of the system.

45

Chapter five


5.2.4 Solving system of finite difference equations Procedures for solving systems of algebraic equations, Eqs. (5.12 and 5.16) can be broadly cauterized as direct and iterative . Direct approaches involve rearranging the system of equations to a form that can easily be solved. The iterative approaches involve making some initial guess at the unknowns and refining these guesses through a series of repeated calculations until an accurate solution is obtained, (McDonald and Harbough, 1988). Direct or iterative approaches contained several solutions. The extremely fast and robust method is the Strongly Implicit Iterative Procedure (SIP), therefore this method is used in solving systems of linear equations. This procedure involves solving the unknowns for the entire grid simultaneously. In order to have, as far as possible, common algorithmic way of treating nodal equations. The grid is designed to form a rectangle of NX cells in X- direction and NY cells in Y– direction. Accordingly, there are (NX* NY) node contained by the grid and hence, (NX*NY) of Eq. (5.12) of the upper layer, and (NX*NY) of Eq. (5.16) of the leaky aquifer are found (Kinzelbac, 1992). The solution of (SIP) is desired, here, to be applied to the unconfined and the leaky aquifer simultaneously because their variables are dependent on each others. Equation (5.12) can be approximated by the following form:

[ ] [ ] [H1 (t + ∆t ) − H1 (t + ∆t )] − D [H1 (t + ∆t ) − H1 (t + ∆t )] +

Ai , j H 1i , j +1 (t + ∆t ) − H 1i , j (t + ∆t ) − Bi , j H 1i , j (t + ∆t ) − H 1i , j −1 (t + ∆t ) + Ci , j

i +1, j

Qpi , j (t + ∆t ) ∆xi , j ∆y i , j =

Si, j ∆t

i, j

i, j

i, j

⎛ H 1i , j (t + ∆t ) − ⎞ ⎟ + Ls i , j (hsi , j (t + ∆t ) − H 1i , j (t + ∆t )) − Li , j ⎜ ⎜ H 2 (t + ∆t ) ⎟ i, j ⎝ ⎠

[H1 (t + ∆t ) − H1 (t )] i, j

i −1, j

-------- (5.17)

i, j

46

Chapter five


In which, Ai , j =

T 12 (t + ∆t ) 0.5(∆xi , j +1 + ∆xi , j )∆xi , j

Bi , j =

T 14 (t + ∆t ) 0.5(∆xi , j −1 + ∆xi , j )∆xi , j

Ci , j =

T 13 (t + ∆t ) 0.5(∆yi +1, j + ∆yi , j )∆yi , j

Di , j =

T 11 (t + ∆t ) 0.5(∆yi −1, j + ∆yi , j )∆yi , j

Omitting each subscript not including a (+1) or (-1), and placed the unknown terms on the left hand side, equation (5.17) may be rearranged and expressed as, (Trescott, 1976): ------------------- (5.18)

DH 1i −1 + BH 1 j −1 + EH 1 + AH 1 j +1 + CH 1i +1 = b

in which; S ⎞ ⎛ E = −⎜ D + B + A + C + Ls − L + LH 2 + ⎟ ∆t ⎠ ⎝

and, b =

S Qp − Lshs H 1(t ) − ∆t ∆x∆y

Equation (5.18) can be expressed in matrix form as:

{a}{H1} = {b}

-------------------- (5.19)

Where {a}is the coefficient matrix, {H } is the vector of known head values, and {b} is a vector of constant terms. Equation (5.16) can be approximated by the same way as explained in approximation of Eq. (5.12), and the following form can be obtained:

[ ] [ ] C ′ [H 2 (t + ∆t ) − H 2 (t + ∆t )] − D′ [H 2 (t + ∆t ) − H 2 (t + ∆t )] + QW Sc [H 2 (t + ∆t )] − H 2 (t ) = L [H 1 (t + ∆t ) − H 2 (t + ∆t )] − ∆x ∆y ∆t Ai′, j H 2i , j +1 (t + ∆t ) − H 2i , j (t + ∆t ) − Bi′, j H 2i , j (t + ∆t ) − H 2i , j −1 (t + ∆t ) + i, j

i +1, j

i, j

i, j

i, j

i, j

i, j

i −1, j

i, j

i, j

i, j

i, j

i, j

i, j

In which;

47

i, j

--- (5.20)

Chapter five Ai′, j =

T 22 0.5(∆xi , j +1 + ∆xi , j )∆xi , j

Bi′, j =

T 24 0.5(∆xi , j −1 + ∆xi , j )∆xi , j

Ci′, j =

T 23 0.5(∆yi +1, j + ∆yi , j )∆yi , j

Di′, j =

T 21 0.5(∆yi −1, j + ∆yi , j )∆yi , j


Then; D′H 2i −1 + B′H 2 j −1 + E ′H 2 + A′H 2 j +1 + C ′H 2i +1 = b'

----------------- (5.21)

Where; Sc ⎞ ⎛ E ′ = −⎜ D′ + B′ + A′ + C ′ + L − LH 1 + ⎟ ∆t ⎠ ⎝

and; b′ =

Sc QW H 2(t ) + ∆t ∆x∆y

Also Eq.(5.21) can be expressed in matrix form as:

{a′}{H 2} = {b′}

--------------------------- (5.22)

Set of (Nx *Ny) equations forms of Eqs. (5.19 and 5.22) may be predicted for upper and lower aquifers , respectively , and their solution can be obtained through a simplified form of the Gaussian elimination approach.

5.2.5 Boundary conditions Correct selection of boundary conditions is a critical step in model design. Boundaries of groundwater flow systems may be physical or hydraulic boundaries. Physical boundaries are formed by the physical presence of an impermeable body of rock or a large body of surface water. Other boundaries form as a result of hydrologic conditions are hydraulic boundaries, that include groundwater divides and streamlines. All hydraulic 48

Chapter five


boundaries, including those that coincide with physical features, are transitory features that may shift location or disappear altogether if hydrologic conditions change. Hydrogeology boundaries are represented by the following three types of mathematical conditions, (Anderson and Woessner, 1992).

1-Specified head boundaries (Dirichlet Conditions) For which head is given. They are simulated by setting the head at the relevant boundary nodes equal to know head values .In two dimensional areal and quasi three dimensional models, specified head boundary nodes represent fully penetrating surface water bodies of the vertically overaged head in the aquifer at hydraulic boundaries .In profile three dimensional models, specified head node may represent the water table or water bodies surface. It is important to recognize that a special head boundary represents on inexhaustible supply of water. The groundwater system may pall water from the boundary or may discharge water in to the boundary without changing the heads. According to Andrson and Woessner, (1992), Jorgensen (1989) found that simulation rivers as specified head conditions led to large errors in the calculated heads around the stream and consequently in flow rates between the stream and the aquifer.

2-Specified flow boundaries (Neuman Conditions ) For which the derivative of heads (flux) across the boundary is given. They are used to describe fluxes to surface water bodies, springs flow, under flow, and seepage to or from bedrock underlying the modeled system. In finite difference models, specified flow boundaries are simulated by using injection or pumping wells to inject or extract water at a specified

49

Chapter five


rate. Inflows are treated as volumes of water uniformly distributed over the face of the cell. This kind of boundaries can be encountered, also the case of no flow or zero flux boundary, which represented impermeable bedrock a ground water divide, or streamline. No flow boundaries are simulated in finite difference grid by assigning zeros to the transmissivities (or hydraulic conductivities) in the inactive cells just outside the boundary. In this way the boundary is set at the edge of the first active block. In the modeled system fixed flux to the upper unconfined aquifer from precipitation (QPi,,j), or the wells flow from leaky aquifer ( QWi,j ) can simulated using specified flow boundary.

3- Head dependent flow boundaries (Couch or mixed boundaries conditions) For which flux across the boundary is calculated given a boundary head value. In finite difference models fluxes are calculated for cell. Leakage to or from a river, lake, or reservoir (Lsi,j ) and through confining bed ( Li.j ) in the leaky confined aquifer, can be simulated using head dependent conditions .

5.2.6 Initial conditions An initial conditions describes the distribution of a contaminant within the domain when simulation begins (time=0). In many simulations, the important results are not the computed head but the changes in head caused by a stress such as pumping wells .If initial conditions are specified so that transient flow is occurring in the system at the start of the simulation, it should be recognized that water levels will change during the simulation, not only in response to the new pumping stress, but also due to

50

Chapter five


the initial conditions. To start from steady state conditions in which flow is occurring, the model can be used to compute the initial head by leaving out the new stress (e.g. wells) and setting all storage terms to zero, (Trescott et al, 1976). Two types of steady state solutions can be used as initial conditions, (Anderson and Woessner, 1992), Fig. (5.4): 1. Static steady state conditions, head is constant throughout the problem domain and there in no flow of water in the system. This type solution is used for drawdown simulation in response to pumping, where relative heads as measured by drawdown are of interest, rather than absolute values of head. 2. Dynamic average steady state conditions, head varies spatially and flow into the system equal flow out of the system. The dynamic average steady state is the initial conditions used most frequently.

h(X1)

h(X1)

Time

X1

a-Static steady state

h(X1)

h(X1)

X1

a-Static steady state

Time

Time b-Dynamic average steady state X1

Fig.(5.4) Steady state conditions

51

X1

b-Dynamic average steady

Chapter five


5.2.7 Computer modeling of groundwater flow The use of digital computers in ground water resource evaluation has grown rapidly with in the past few years. Computers are now widely available that allow solution of large sets of simultaneous equations that are involved in studying case and effect relationships in heterogeneous aquifer systems with a wide variety of boundary conditions. The digital computer can deal with problems of much greater complexity than in practical with electric analog or analytical methods. However, digital computers will not case analytical methods or electric analog simulators to become obsolete, used in conjunction with other tools available to the hydrologist, digital computers can greatly improve the analysis of ground water problems, (Prickett and Lonnquist, 1971). Discussion of the digital techniques includes the necessary mathematical background, documented program listings, and field applications. Selecting the appropriate program for modeling job involves matching modeling needs with the capabilities and controls of available programs. There are numerous programmers for use in groundwater modeling. The modeler one is provided by the Department of Defense, Groundwater Modeling System (GMS), which provides a comprehensive graphical

environment

for

numerical

modeling,

tools

for

site

characterization, model conceptualization mesh and grid generation, and geostatistics. Several types of numerical codes are supported by GMS. GMS package has been used in the present study because: 1. It has numerical features necessary to model the study area. 2. It is well documented and widely used. 3. It is available through the public domain. A graphical interface to the groundwater model MODFLOW is provided in GMS. MODFLOW is a qusi three dimensional, cell centered, finite difference, saturated flow model, which can perform both steady state 52

Chapter five


and transient analysis and has a wide variety of boundary conditions and input option. GMS supports MODFLOW as a pre – and post– processor. The input data for MODFLOW are generated by GMS and saved to a set of files. These files then read by MODFLOW when MODFLOW is executed. The output from MODFLOW is then imported to GMS for post – processing. MODFLOW views a quasi three dimensional system as sequence of layers. The horizontal grid is generated in the usable way by specifying grid dimensions in the X and Y directions. As with all finite difference grids, the horizontal grid must be the same for each layer, (Anderson and Woessner, 1992). The approach of modeling the aquifer included two major steps : 1. Developing a steady state model. 2. Developing the transient mode. A future, third major step is assembling the data sets and running the model for predictive runs. At first the steady state model is developed because steady

state models are often much easier to calibrate than

transient models and results of the steady state model can easily be used as a starting point in the transient model, (Robert, et al, 2000) .

5.3 Analytical solution The analytical solution of subsurface drainage systems has frequently been developed by assuming the soil to be homogeneous and isotropic. Another assumption was considered in the analytical solution, that the wells are spaced at distances smaller than their radius of influence they affect each others drawdown and discharge rate, and the areas of influence can over lap which leads to greater draw downs.

53

Chapter five


The drawdown at any point in area near several pumping wells is equal to the sum of the individual well draw downs at that point. At a given location, total draw down, St. is: -------------- (5.23)

St = S1 + S 2 + S3 + .......... + S n

where; S1, S2,S3,............, Sn

are the drawdown at that location resulting from the

discharge of wells 1, 2, 3…….,n, respectively(L) . Since pumping in the well field of this research is designed to be from the leaky aquifer, so principles of leaky aquifer are considered to estimated total drawdown at any point over the area. Using Hantush-Jacob formula, the unsteady draw down equation at any point, P in well field can be written as: S p j ,t =

Q 4πT

n

⎛ ri 2 S ri ⎞

∑W ⎜⎜ 4Tt , B ⎟⎟ i =1

⎝

------------------ (5.24)

⎠

in which; ri =

(xi − x0 )2 + ( yi − y0 )2

Where; S p ,t : Total draw down at point p during the time t since pumping start (L). 3

Q : Constant discharge rate from each individual well (L /T).

ri : Distance from the point p to ith well (L).

(xi , yi ) : Location of ith well. (x0 , y0 ) : Locations of point p, which draw down simulation wanted to be carriedout Other parameters are previously defined. When there is no interaction among the responses produce by the different boundary conditions, principle of Superposition is used Eq. (5.24). Further more, effect of recharge boundary can be considered by

54

Chapter five


applying Image theory when any of the wells is located near this boundary or the line parallel to the boundary. Applying Image theory, the flow conditions can be modeled mathematically by imagining an equal well placed symmetrically about the image plane which is the plane of the boundary itself. The Image theory, Eq (4.24) can be rewritten as: S p j ,t =

Q 4πT

⎛ `ri 2 S `ri ⎞ ⎛ ri 2 S ri ⎞ ⎟ ⎜⎜ ⎜ , , ⎟⎟ W − W ∑ ⎜ 4Tt B ⎟ i =1 ⎠ ⎝ 4Tt B ⎠ ⎝ n

-------------- (5.25)

in which; `ri =

(`xi − x 0 )2 + (`yi − y 0 )2

Where;

(`xi , `yi ) : Coordinates of the center of ith Image well. Solving Eqs. (5.24) and (5.25) to obtain values of draw down at any point (pj) and any time (t) can be done with the aid of a computer program.

55

Chapter Six

Design of Well Field for the Babylon Site

Chapter Six Design of Well Field for the Babylon Site 6.1 Introduction Well field is defined as a group of wells operating in a given area. The overriding objectives in well field design are, the attainment of the highest yield possible with minimum drawdown in pumping wells, minimizing environmental effects, minimizing siltation and reasonable short and long term costs, ( U. S Army corps of engineer, 1999 ), Good well field design aims to ensure an optimum combination of performance and long service life at reasonable cost. The design should address the followings: 1- Design of production wells(size of the well and the screen, selection a suitable pump, well efficiency, and the optimum discharge of the well ) 2- Required number of wells and their distributions 3- Economic considerations of drainage by pumped wells.

6.2 Design of production wells A production well has to be designed to get the optimum quantity of water economically from a given aquifer, keeping in mind the future conditions and variations of various parameters during the projects life. The most important parameter among them is the anticipated drawdown under future conditions. Well design involves the following: 1- Selection of the diameter of the well and that of the casing. 2- The depth of well. 3- Design of well screen (including length, location of the screen, percentage open area, and gravel pack design). 56

Chapter Six


4- Allowable discharge of the production well. 5- Selection of a suitable pump sets for production well.

6.2.1 Well casing diameter Size of the well casing should be properly chosen since it significantly affects the cost of well construction. It must be large enough to accommodate the pump that is expected to be required for the head and discharge (yield) with proper clearance (of at least 5 cm around the maximum diameter of the bowel assembly), as suggested by Raghunath (1982) for installation and efficient operation. The yield of the well, Q at steady state flow conditions (constant draw down) is proportional to the diameter of the well (2 rw) and the radius of influence, (R) as: Q∝

1 ⎛R⎞ log⎜⎜ ⎟⎟ ⎝ rw ⎠

The required well casing diameter for various rates were suggested by Johnson, (Johnson, 1972) and presented in Table (6.1). According to the pumping test carried out by ( FCSDI P , 1989 ) , the discharge of the well in the study area ranges between ( 10 - 20 l/s ) , therefore a 250 mm well casing diameter will be appropriate .

57

Chapter Six

Design of Well Field for the Babylon Site Table (6. 1) Recommended well diameters Nominal size of

Size of well casing

Anticipated well yield

pump below

Minimum

Optimum

( l/s )

(mm)

( mm )

( mm)

< 6.5

100

125

150

6.5

125

150

200

10-24.5

150

200

250

23.5-36.5

200

250

300

36.5-50

250

300

350

50-75

300

350

400

75-100

350

400

500

6.2. 2 Depth of well The expected depth of well and the number of aquifers it has to penetrate is usually determined from the log of a test hole of other near by wells to the same aquifer, or during drilling of a production well in addition to the hydrogelogical information obtained by reinvestigations. The well is usually drilled up to the bottom of the aquifers so that the full aquifer thickness is available, permitting greater well yield. In the study area, the drilled wells were ensured fully penetrate the semi confined aquifer, because the upper aquifer is composed of very fine sand underling the Babylonian remnants, so it is not recommended to pump from this aquifer, to ensure not to wash out fine sand from underneath the remnants which might cause a collapse of sand and silt materials. According to the (GDGSMI ,1979), the total depth from the ground surface to the bottom of the semi confined aquifer is approximately 45m, Fig.(2.6) ,so this measure is assumed to be the depth of production wells.

58

Chapter Six


6.2.3 Design of Well Screen The length of the screen, it's location, percentage of open area, size and shape of the slots, and selection of screen material are to be considered in any production well casing and screen design. The optimum length of the well screen is chosen in relation to the aquifer thickness, available drawdown, and stratification of the aquifer, (Johnson, 1972). In homogeneous artesian aquifer about 70 to 80 percent of the aquifer thickness should be screened, assuming that the pumping water level is not expected to be below the top of the aquifer. In case the aquifer is less than 7.5 m thick, the screening of 70 percent is satisfactory. If it is between 7.5 and 15 m thick, 75 percent of the thickness should be screened and when it is more than 15 m thick, 80 percent of the thickness should be screened. Screen lengths corresponding to these rules make it possible to obtain about 90 percent or more of the maximum specific capacity that could be obtained by screening the entiner aquifer, (Johnson, 1972). Accordingly, for the study area the length of the screen discharge for the second aquifer would be 16 m. Theory and experience have shown that the screen should best be positioned at equal distance from top and bottom of the aquifer, in order to prevent accumulation of sediment at the bottom of the well which will partially block the slot openings and then reduce its efficiency. Artificial gravel pack should be use to provide highly permeable envelope of granular material around the well screen in an annular space that is expressly provided for this purpose. Since the second aquifer comprises of coarse sand and gravel, so naturally packing was not possible, therefore artificial pack was assumed to be use, with a thickness of 75 mm, in order to create a proper environmental envelope around the screen rather than to rely on a random distribution of natural materials.

59

Chapter Six


Gravel pack should be clean rounded grains that are smooth and uniform, having a size of 4 mm, as recommended by Raghunath (1982). According to Johnson (1972), the open area of artificially developed well should match the porosity attained in the development process, which may be at range of 15 to 20 percent. A 15 percent open area is suggested in the present study. Walton, (1972) suggested that the rate of entrance velocity to the well should not exceed 3 to 6 m/s in order to ensure a long life service of the production well. Assuming rate of well discharge in study area equals to 20 l/s, with 16 m screen length, 15 percent open area for the screen and 25 cm well diameter, entrance velocity will be (1.06 cm /sec) which is permissible . The best type of opening is the V – shaped slot that widens towards the inside of the screen, i.e. opening beveled inside. Regarding the choice of screen material, stainless, steel has excellent strength and is highly resistance to most corrosive conditions, (Raghunath, 1982).

6.2.4 Allowable discharge of the production well The maximum allowable discharge from a well or well field should not exceed any value after a steady state has been reached, since excessive lowering of water level may cause hydraulic problems such as soil settlement. Such problem should be avoided by considering the specific capacity of the field and selecting a suitable discharge. For a semi confined aquifer, the specific capacity ⎛⎜

Q ⎞ ⎟ at ⎝ Siw ⎠

unsteady state condition can be determined using the equation of Raghunath, (1982):

60

Chapter Six Q = Siw

Design of Well Field for the Babylon Site 1

---------------- (6.1)

⎛r S r ⎞ 1 W ⎜⎜ w , w ⎟⎟ + C w Q 4πT ⎝ Π Tt B ⎠ 2

In which Cw : is the well loss coefficient (T2/L5), it can be determine by experiment with the step – drawdown test . Other symbols are previously defined. Equation (6.1) shows that the specific capacity of a well is not constant but decreases as pumping rate, Q increase, and prolonged pumping time, t until a steady state is reached. For steady state conditions, Eq. (6.1) could be written as: Q = Siw

1 1 ⎛r ⎞ Kο ⎜ w ⎟ + C wQ 2πT ⎝B⎠

--------------- (6.2)

where; Kο : second kind modified Bessel functions of the zero order .

Other symbols are previously defined. Value of the well loss coefficient, Cw : in the present research was determined using data of step-drawdown test carried out by (FCSDIP), which found to be (0.043 day2/m5). Detailed computations of this test are illustrated in Appendix B. Using Eq. (6.2) and it's known parameters for the Babylon city, the allowable discharge rate for the required drawdown was found to be 1500 m3/ day (or ≈17 l/s).

6.2.5 Selection of a suitable pump sets for production wells Results of recommended yield will help in the selection of a suitable pumping set to be installed on the well and the data has to be furnished to select the pump.

61

Chapter Six


Selection of a proper pumping set is important to ensure continued satisfactory yields from a well. Factors to be considered are (Raghunath, 1982) 1- Finished inside diameter and total depth of the well. 2- Yield from well, the desired pumping rate and hours of pumping per day. 3- The lowest pumping level. 4- The total head on the pump. 5- The power required. Characteristics curves of the pump, Fig. (6.1) enable the selection of a pump which best suits the well. The pump characteristics i.e. discharge and head will gave the efficiency and the break horse power for the pump.

Fig.(6.1) Pump characteristics curves (after pump manual ,1998)

62

Chapter Six


Before a pump can be intelligently selected for any installation, it is necessary that accurate information be available with regard to a required capacity, location and operating condition, and total head. When these data are at hand, and only then a selection of type, class and size can be mode. Total head must always be determined as accurately as possible so as to be sure of the needed capacity and to calculate required power input. Total head is expressed by the formula, (Johnson, 1972): Ht=he + hf +hv

------------------------ (6.3)

Where; Ht: Total dynamic head (L) , Fig.(6.2) . he: Total vertical lift, form pumping level in the well to point of delivery of the water (L) . hf : Total of friction losses , expressed as head (L ) . hv : Velocity head ( L ) .

Static water level

he

Water level when pumping

Submergence head

hs

Fig.(6.2) Total head in the pumped well 63

Chapter Six


In the center of Babylon city, the static water level was found to be at a depth of 4 m below ground level. The required drawdown is 16m. The water is assumed to be lifted to 0.3 m above ground level, thus the total vertical lift, he was found to be 21.3 m. Velocity head, hv, is usually small and is, therefore neglected. Friction losses, hf was found to be 0.027 m by using convenient tabulation of friction losses in pipes and fitting (Johnson, 1972). According to these calculations, the total head, Ht was found to be approximately 22 m. Experts of water well drilling advice from experience to use a submersible pump (SP). Using pump characteristic curves, Fig. (6.2) with estimated discharge (17 l/s), and desired head (22 m), the efficiency of the pump was found to be 70 percent. Thus the brake horse power, B.h.P was found to be, approximately 5.5 kw .The selected pump is, therefore (SP 75-3).

64

Chapter Six


Fig. (6.3) showed a representation designed well section in the study area Discharge

about 0.3m

Concrete

about 3.0m

S.W. L Pump O=4"~10cm

Well pipe O=8.75"~25cm

about 20.0m

Well casing O=16"~40cm Well wall O=20"~50cm Cemetation middle layer k'=0.0066m/day (silty clay)

about 2.0m

Gravel pack thickness=6"~15cm

16.0m about 20.0m

Impermeable

. Fig.(6.3) Designed well section

6.3 Required number of wells and their distribution The spacing and wells arrangement depends on many factors, among them are: 1- Radius of influence of each well. 2- The minimum depth to which the water table should be lowered. 3- The characteristics of the aquifer and the source of water being drained The number of required wells can be calculated using the hydrologic budget or water balance equation. Water balance can be simulated for each aquifer by the terms of recharge and discharge rates. Table (6.2) shows the simulated water balance in the study area. Presumably the main 65

Chapter Six


contribution of water, particularly to the upper aquifer, comes from Shatt Al-Hilla river and some from precipitation. Based on Darcy's law, the infiltration rate of a stream is a direct function of permeability and head. Recharge from stream flow is directly proportional to the permeability of the stream bed and to the difference between water levels in the aquifer and the surface of the stream as,(Walton , 1970) , as given by the equation : Qs =

ks ∆HAs bs

---------------------------- (6.4)

Where; 3

Qs : Infiltration rate of the stream (L /T) . ks : Permeability of the stream bed (L/T) . bs : Thickness of the stream bed (L) .

∆H : Difference between water level in the aquifer and stream

surface (L) . 2

As : Area of the stream bed (L ).

The permeability of Shatt AL-Hilla river bed was calculated as an average value of the upper layer permeability which was found to be (0.45 m/day), while the average river bed thickness was assumed to be (0.4 m). The difference between groundwater level and the river surface was about (0.3 m) .The area influenced by the seepage was approximately (15725 m2). Therefore the river seepage along the study area was found to be (5307 m3/day). Only a small fraction of the annual precipitation percolates down ward to the water table. A large proportion of precipitation runs over land to streams or is discharged by the process of evapotranspiration before it reaches aquifers. Therefore, 50percent of the annual precipitation was assumed to be infiltrated to the upper aquifer. The annual precipitation, as illustrated previously is (110mm), so the rate of recharge from precipitation over the study area is (460 m3/day). 66

Chapter Six


Under ground flow during dewatering was calculated according to Darcyś law: Q = T ×i× L

---------------------------------------- (6.5)

In which, i represents the hydraulic gradient, and L is the length of the area perpendicular to flow. Equation (6.5) was used to estimate the under ground flow (boundary inflow) for both upper and lower aquifers. Average values of T, i and L for upper aquifer were found to be 250m2/d, 0.02 and 3000m, respectively, so the boundary inflow to the upper aquifer was 15000 m3/d. Values of T , i and L for the lower aquifer were found to be 420m2/d, 0.008 and 3000 m, respectively, again the boundary inflow to the lower aquifer was found to be 10080 m3/d. Loss of groundwater from storage within the study area is : Q=

S y × H ×W × l t

----------------------------------------- (6.6)

Where Sy : Drainable porosity (dimensionless) . H : Depth of the saturated layer (L) . W : Width of the study area (L) . l : Length of the study area (L) . t : Time required to dispose the static groundwater component (T). The required depth of lowering is 16m. The drainable porosity was fond to be 0.1 for the upper aquifer and 0.07 for the lower aquifer. Therefore, the loss of ground water from storage (during a year of pumping) was estimated to be 21173 m3/day and 14821 m3/day from the upper aquifer and lower aquifer, respectively. Since the estimated discharge of each well was fond to be (17 l/s) therefore forty five wells were recommended to dewater the study area according to Table (6.2).

67

Chapter Six


Table (6.2) Summary of the water budget simulation. Aquifer

Recharge

Discharge

(m3/day)

(m3/day)

Upper aquifer: Seepage from Shatt Al- Hilla

5307

Precipitation

460

Boundary inflow

15000

Loss of groundwater from storage

21173

Leakage to the lower aquifer

41940

(through the semi pervious layer) Lower aquifer: Leakage from the upper aquifer

41940

Boundary inflow

10080

Loss of groundwater from storage

14821

pumpage

66841

Wells may be arranged in various geometric patterns. To ensure adequate drawdown over the entire area, some over lapping of well regions of influences is necessary. Most of suggested wells in the study area were assumed to be located on the line parallel to Shatt Al-Hilla River in order to prevent the flow from the river .This line may be considered as barrier boundary. Others were assumed to be distributed around the study area, Fig. (6.4)

68

Chapter Six


32o33’20” 3000

b Ba

lake 1

o yl

Artificial Mountain

l-H il att A

et

Road

Sh

ul

Main

2000

iv R

la Riv er

n

Babylon Wall

el hann ist C Tour

2500

lake 3

1500

1000

500

3500

2500

2000

44 24’40”

1500

1000

500

o

3000

Suggested wells

lake 2

32o31’15”

44o27’

Fig.(6.4) Locations of suggested wells

5.4 Economic consideration of drainage wells The cost analysis of pumping wells include initial construction costs, operation and maintenance costs, the power installation, and the cost of connecting pipeline between the wells, all of which may be expressed as an annual cost per unit length of intervening distance . Excluding the constant cost of lifting the water against the head developed in each well when it is operating alone, the yearly cost of operating a well field may be considered as an average cost valve over a year as expressed by Hantush (1964) N

t0

n =1

0

C = C ′mδ + C ′′∑ Qn ∫ S n dt

------------------------------ (6.7)

Where; C: total yearly cost of operation as affected by well interferences.

69

Chapter Six


C': capitalized cost per unit length of pipe line for maintenance, depreciation, original cost of pipe line, etc., C″: cost to raise a unit volume of water a unit height, consisting largely of power charges, but also properly including some additional charges on the equipments Sn: total drawdown in the nth well caused by pumping all the other wells (L) mδ: length of connecting pipelines between wells and the power installation (L) N: number of wells in operation. Qn: discharge of nth well (L3/T) . t0: period of continuous pumping (T). m: distance between any two wells (L). S: constant when multiplied by m gives the length of connecting pipelines. All parameters of Eq. (6.7) should be prepared in order to estimate the yearly operation cost, which should be added to the yearly construction, power installation, and connecting pipe lines costs, in order to estimate the total cost.

70

Application of The Models and The Results

Chapter Seven

Chapter Seven

Application of the Models and The Results 7.1 General Applications of both numerical and analytical models are considered in this chapter. All input data that are possibly needed and the output of both models with their comparison are discussed. Modeling approach includes two major steps, steady state and unsteady state simulations. Priority was given to the steady state simulation, for its easiness to calibrate, on one hand and to apply its result in the unsteady state simulation on the other hand.

7. 2 Numerical model application The model domain was divided into (75) rows and (100) columns, making a total (7500) cells in each layer and covering an area of approximately (5.5 km2). All the cells have uniform lateral dimensions of (40 m) along rows (∆X) by (32 m) along columns (∆Y), Fig. (7.1). This cell size was chosen to be small enough to reflect the density of input data and the desired output detail and large enough for the model to be manageable. Cell thickness depended on the elevation of the contact between the layers.

71


Chapter Seven

K

J

I

Y

Z X

Fig. (7.1) Grid design for study area

7.2.1 Model boundaries and initial conditions Using the map of the ground water flow pattern, Fig. (3.4), the boundary conditions of the upper aquifer were identified. The western end of the studied area is bounded by Shatt Al- Hilla River, therefore it was considered as head dependent boundary allowing inflow to the model region as a proportional to head difference between the water surface in the river and the water table. The northwestern, southwestern and southeastern parts of the basin bounded by the artificial lakes. These parts were identified as constant head cells. Constant

72

Chapter Seven


head cells were defined, also in the eastern part of the model area since this part is bounded by Babylon canal and flow comes from this side. Other parts of the upper aquifer simulated as specified head boundaries (hydraulic boundaries) by setting the head at these boundary nodes equal to known head values, Fig. (7.2a). Concerning lower aquifer, the western boundary was defined as constant head boundary, while other sides were assumed to be the same as the upper aquifer, Fig. (7.2b). It should be maintained that the numerical model in the study area was considered upper and lower limits for the system. The upper limit is the water table in the unconfined aquifer and the lower limit is the impervious layer, which is the bottom of the leaky aquifer. All nodes out side the boundary of the modeled region are assigned fixed head nodes (inactive cells). The internal cells were considered variable head cells. The initial condition in the steady state is the head distribution within the model area at initial time (t = 0). The head distribution of the lower aquifer was assumed to be the same as for the upper aquifer, which means that the water table and the piezometric level coincide. The initial heads were considered as the initial condition for the steady state calibration.

73


Chapter Seven

+

(a)

Head dependent Constant head Specified head Veriable head

(b) Fig (7.2) Boundary assignments for (a) upper layer (b) lower layer

74

Chapter Seven


7.2.2 Input parameters Several input parameters were necessary to be provided as initial values to be used for simulation of steady and unsteady state flow conditions. Hydraulic properties of the aquifer systems were estimated using pumping tests analysis and lithology of the aquifer system, as were mentioned in chapter two. For the upper unconfined aquifer the initial estimates of the average permeability values were within the range of (2.5-17.5m/day), Fig.(7.3a), and the specific yield for this aquifer was found to be ranged between (0.01–0.07 ), Fig.(7. 3b). Transmissivity and storage coefficient of the lower aquifer were given the same values for all nodes because the data points were not enough in the study area. These values are 420 m2 /day and 0.00021, respectively. To simulate the effects of vertical flow from the upper aquifer to the lower aquifer through the confining zone, initial estimates of leakance values were used in the model. These values were found by dividing the vertical permeability value of (0.019 m/day) for the middle layer (found from the pumping test analysis) by the thickness of the middle layer at each node, Fig. (7.4). Top and bottom elevations for each layer were defined from the isopach map. The top level of the upper aquifer was assumed to coincide on water table (initial head) level, while the bottom level was assigned to be at the middle of the aquitard, Fig. (7.5). The top level of the lower aquifer was assumed to begin from the bottom of the upper aquifer.

75

Chapter Seven


(a)

(b) Fig.(7.3) Hydraulic properties of the upper aquifer, (a) hydraulic conductivity (m/day) and (b) specific yield 76

Chapter Seven


Fig (7.4) Thickness of the middle layer (m)

Fig. (7.5) Bottom elevation contour map for upper layer (a.s.l.) (m) 77

Chapter Seven


Recharge to the upper aquifer from precipitation was estimated to be as a net infiltration rate of (0.15 mm/day), which was considered to be constant rate in each grid block. The required and the estimated parameters were entered in Microsoft Excel connected with MODFLOW software by the scatter point moduls, which is used to interpolate the groups of three dimensional scatter point of data . Each of the scatter point set is defined by a set of X Y Z coordinates. Each data set represents a set of values which can be interpolated to a grid.

7.2.3 Steady state calibration Model calibration can be performed to steady state or transient data sets. Most calibrations are performed under steady state conditions but may also involve a second calibration to a transient data set. The most common type of transient calibration begins the simulation from the calibrated steady state solution, (Anderson and Woessner, 1992). A trial and error procedure of the calibration was used in the present study. All parameter values were initially assigned to each node in the grid. During calibration, parameter values were adjusted in sequential model runs to match simulated heads to the calibration targets. The data chosen for the calibration were the water table level during spring, 1989, Fig. (3.4). Hydraulic conductivity values of the unconfined aquifer and vertical leakance of the aquitard were used as an initial guess for the calibration process. Agreement between observed and simulated water levels was obtained after several iterations. This agreement is clearly shown in Fig. (7.6).

78


Chapter Seven

_________ Observation head _ _ _ _ _ _ Computed head

Fig.(7.6)Computed and observed heads Root mean square error (RMSE) was estimated to summarize the calibration performance using the following equation, (Rasheeduddin, et al, 1989):

∑∑ (h r

RMSE =

c

i =1 j =1

s i, j

− hi0, j

)

2

--------------------------------- (7.1)

rc

Where; hi0, j : Simulated head at row i, column j (L). his, j : Observed head at row i, column j (L). r

and c : Number of rows and columns, respectively.

rc : Number of cells within the modeled region.

Root mean square errors(RMSE) of twelve randomly selected cells are given in Table (7.1). The Table apparently shows that calibration stage led to significant improvement in parameter distribution. Value of (RMSE) was found 79


Chapter Seven

to be (4.62 cm). This RMSE is about 6 percent of the total hydraulic head drop across the modeled area, which is acceptable since the 10 percent is usually required for model calibration. So, it can say that the model successfully simulates steady state where close agreement was obtained between the observed and simulated heads. The results of the calibrated model indicate that the average permeability of the upper aquifer ranges between (2.5 - 9.5 m/day) and the leakance of the middle layer was found to be ranged between 0.008-0.01day-1, Fig.(7.7). Calibrated steady state head distributions were used as starting heads to simulate the unsteady state condition. Table (7.1) Summarization of Root Mean Square Error. Simulated head (hº)

Cell I

(m)

J

Observed head(hs)

(hs-hº)2

(m)

15

9

28

27.8

0.04

25

4

28

28.15

0.0225

35

6

28

28.25

0.04

10

19

27.5

27.3

0.04

25

12

27.5

27.4

0.01

40

22

27.5

27.3

0.04

10

27

27

26.9

0.01

20

21

27

26.85

0.0225

40

35

27

26.8

0.04

10

38

26.5

26.35

0.0225

20

27

26.5

26.4

0.01

35

45

26.5

26.3

0.04

80


Chapter Seven

(a)

(b) Fig.(7.7) Calibrated parameters of the aquifer systems (a) average permeability of the upper aquifer (m/day) (b) leakage coefficient of middle layer (day-1) 81

Chapter Seven


7.2.4 Unsteady state simulation Unsteady flow occurs during pumping. Therefore the dimensions of time and change in ground water storage must be incorporated. A system of 45 wells is assumed to be installed, Fig. (6.5), each well is suggested to be discharged at a constant rate of (17 l/s). Shatt Al-Hilla River which is distributed in each grid block .This rate will increase as increasing the difference between the river and aquifer heads because of declining the water table in the aquifer due to pumping. Storage coefficient of the lower aquifer may change as the ground water head falls below the confining layer, which means that the aquifer condition will change from confined to unconfined state. This situation could be included in a numerical model by modifying the storage coefficient using effective storage coefficient. When water table falls further, part of the lower aquifer can be dewatered, thus unconfined storage coefficient or specific yield of the aquifer may be used, since the specific yield is defined as a measure of water released by drainage response to decline of water table, while the storage coefficient is a measure of water released from aquifer compression and by expansion of water. In this research the specific yield of the lower aquifer was assumed to be (0.07). The accuracy of the results usually decreases with the simulation period. In the present work, the model has not been verified with observed aquifer response to production. Therefore, simulation results over a period longer than a year will have a lower accuracy in comparison with short periods. The simulation period was divided into fourteen non uniform time steps .The length of the first time step was (10.14) days, which increases in geometric fashion by a multiplication factor of (1.2) within each stress period.

82


Chapter Seven

For pumps maintenance, and other operating facilities, it is suggested to operate the wells at a rate of 75 percent of their efficiency, while keeping total discharge constant. Distribution of the wells was selected after several iterations of changing in order to get the optimum drawdown. It was found that most of wells were located near the recharge boundaries, Fig. (7.8).

Y

Z X

Fig. (7.8) Calibrated locations of the design wells Results of simulation yielded two contour maps for drawdown, one for each of the penetrated strata .More than one operation periods were considered in the simulations Figs.(7.9-7.11). The solutions predicted quasi steady water levels in the center of Babylon city at about 11 and 10 m (a.s.l.) for both upper and lower aquifers, respectively after 300 days since pumping started. Hydraulic characteristics of the aquifers were individually changed in order to examine the effect of each parameter on the unsteady state solution. Specific yield values of the upper aquifer were changed by increasing, or decreasing of 50 percent of their estimated values, resulted in slightly higher, or lower hydraulic heads in the aquifer system, Figs.(7.12&7.13). The same 83

Chapter Seven


situation was found by changing the storage coefficient for the lower aquifer by 50 percent, Figs.(7.14&7.15) The effect of vertical leakance change is shown in Figs.(7.16&7.17). When 50 percent increase, or decrease of the vertical leakance will lead to increase or decrease flow between the overlying and underlying aquifers. An increase, or decrease 25 percent in the transmissivity of the lower aquifer has resulted in higher, or lower hydraulic heads in the aquifer system, Figs.(7.18&7.19). Increasing the transmissivity will increase the ability of the aquifer to transport the flow easily, so the drawdown will decrease, and vice versa. The above conditions led to conclude that the changes in vertical leakance of the aquitared and transmissivity of the lower aquifer caused greatest changes in hydraulic heads of the aquifer system. In order to examine the effect of the Shatt Al-Hilla River, it was replaced by a no flow boundary in the model. A result of this case is represented in Fig.(7.20).When dewatering system operated with cutting off the river seepage it will give the required drawdown (14-16m) in the center of the Babylon city after 180 days only, which indicate that the river may be considered as a main source to the system. It should be mentioned that the model predicts declines in ambient water levels in the aquifer due to pumping, and the particular water levels decline in an individual well presumably to be more.

7.3 Analytical application The parameters involved in the computations of the total drawdown at any point are: 1 - Number of the wells and their locations. 2 - Time at which the drawdown is being calculated.

84

Chapter Seven


3- Hydraulic characteristics of the aquifer. A simple computer program has been developed for the simulation of the equation (5.24) according to the input data. Output including drawdown values at required point was transferred to the well known Software Surfer to draw the contour lines of drawdown. A flow chart of the program and a trial sheet of the computations can be seen in Appendix (B1&B2), respectively. Image well theory, eq. (5.25) was used for wells in the vicinity of the recharge boundaries, while Superposition theory was used for other locations. The analytical model was executed at different pumping periods. Comparison between the numerical and analytical applications for the 10 days pumping can be seen in figure (7.21). This figure indicate that the results of both models approach each other during early stages of pumping only, while clear difference between them was found during later periods .This is believed to be attributed to the effect of the time interval, since the analytical analysis deals with the total time (t) in the simulation process, while the numerical model deals with a time increments (∆t) at each stress period. Such effect causes to decrease the accuracy of the analytical model.

85

Chapter Eight

Conclusions and Recommendations

Chapter Eight Conclusions and Recommendations 8.1Conclusions From the information collected during this study, and from the analysis of results, the following conclusions are drawn: 1- The problem to be tackled in this research is not an ordinary one because it deals with an old berried remnant of Babylon city. Therefore, the phenomenon of slow drainage observed in an unconfined aquifer is suggested as results of the vertical leakage to the lower semi confined aquifer, which should be achieved by pumping with constant rate in order to avoid any collapse that may take place at some parts in the area of study, which might happen if the upper aquifer is to be pumped directly. 2- The ground water level in Babylon city can be lowered to the required levels to coincide with the base of the remnants by means of forty drainage wells located on a ring separating from the study area and continue to be parallel to Shatt Al-Hilla River. 3- The numerical solution indicates that water level at the middle of the study area i.e at Babylon city can be lowered to about 16 m from its present level after the steady state condition is reached within a period of 300 days. 4- The model designed was found to be the most practical solution from the hydrogeological and hydraulically point of view. 5- The comparison of results of proposed numerical solution with the analytical solution showed reasonable agreements between the two models during the early time of pumping. Some local discrepancy will arise due to the time interval effects. The 86

Chapter Eight


numerical analysis deals with time increments (∆t) at each stress period, while the analytical analysis is deal with total time (t) at each step. That's will decrease the accuracy of analytical model. 6- Although no current experimental data or field data are used, the predictions are believed to be in accordance with previous study carried out by (FCSDIP, 1989).

8.2 Recommendations The following recommendation are suggested:-

8.2.1 Future works 1- Developing the predictive datasets by digging several pumping test wells with observation wells for both upper and lower aquifers. The test wells must be distributed all over the study area. 2- The amount of recharge from Shatt Al- Hilla River could influence future water level declines near the river. River seepage losses could be decreased by digging a well point system along the right side of Shatt Al-Hilla River within the study area, or designing an open drain along the river bordering the study area (about 1800 m). 3- Since the pumped water is suitable for irrigation according to ground water quality test, so it is recommended to benefit the water by farmers in the area. 4- During operation of the dewatering system water level measurements must be carried out in all producing wells in order to avoid the over pumping rate.

87

Chapter Eight


8.2.2 Future Studies 1- A future study may be required to evaluate the effect of new open drain parallel to Shatt Al-Hilla River to intercept ground water comes in to the old city . 2- It may be worth while at tempting an optimization and economic studies of operation policy after steady state is reached. 3- It is recommended to study the proper settlement which may be caused by dewatering of Babylon city. 4- It is recommended to study the possibility of reducing the conductivity of the upper aquifer by pumping a reasonable material e.g. mud or asphelat in order to avoid filling the voids by water.

88

References

References 1. Abdulla, F. A., AL-Khatib, M.A. and AL-Ghazzawi, Z.D., 2000, "Developmen for the Azraq Basin, Jordan”, Environmental geology 40(1-2). 2. Al-Furat Center for Studies and Designs of Irrigation Projects (FCSDIP), 1989, "Lowering of groundwater level in Babylon city", Un published Report , Baghdad, Iraq . 3. Anderson, M.P. and Woessner, W.W., 1992,"Applied groundwater modeling simulation of flow and vertical transport", Academic press, Inc. San Diego, 246 P. 4. Banat, K.M. and Y.T.Al- Rawi, 1986, "Hydrochemestry, clay minerals and carbonates of the Euphrates river", Iraqi J. Sci., Vol.27, pp. 347-362. 5. Boonstra, J .and De Ridder, N.A., 1981," Numerical modeling of groundwater basins”, International Institute for Land Reclamation and Improvement (IILRI), publication 29, Wageningen, Nether lands. 6. Bouwer, H., 1978, "Groundwater hydrology" , McGrow Hill Inc., New York , 480 p . 7. Christopher, J.N. and Matthew, J.T., 2002, ''Representation of

8. 9.

10. 11.

12. 13.

14.

15.

multiaquifer wells in MODFLOW'', S. S. Papadopoulos and Associates, Inc. Domenico, P.A. and Schwartz, F.W., 1998, '' Physical and chemical hydrogeology'', John Wiley and Sons , Inc , New York , 506P. Dunlap,L.E.Lindgren,R.J. and Saur,C.G.,1985, ''Geohydrology and model analysis of stream aquifer system along the Arkansas river in Kearny and Finney countries, south western Kansas", U.S. Geological survey water supply paper 2253-52P . Encyclopedia Britannica, 2002, "Babylon , History of Babylonia" General Directorate of Geological Survey and Mineral investigation, (GDGMI), 1979, "The possibility of lowering under groundwater in Babylon'', Technical report , Baghdad . Haddad, H.R., 1980, "Protect Babylon from groundwater", Technical report, Baghdad. Hailog, L. and Jiao, J.J., 2002, “Analytical solutions of tidal groundwater flow in coastal two aquifers system", Advances in water resources, 25, PP417. 426. Hantush, M.S., 1964, ''Hydraulics of wells'', in Advances in Hydrosience. Chow, V.T. (ed), Vol.1. 1964, Academic Press, Inc., New York and London, pp: 281-432. Hongbin, Z ., 1999, "Analytical and numerical modeling of a 89

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double well capture zone'', Mathematical Geology, Vol .31,No.2. Irrigation Directorate at Hilla city, IDH, 1999, ''Study of high groundwater level in Hilla city'', unpublished report (in Arabic). Johson Division, 1972, ''Groundwater and wells.'', Universal Oil Products Co. Kinzelbach, W.,1989, ''Groundwater modeling: an Introduction with sample program in Basic'', Development in Water science, EI-Sevier Science publishing Co., Inc, New York, 333p. Kiraly, L., 1988, ''Large scale three dimensional groundwater flow modeling in highly heterogeneous geologic medium'', in Groundwater flow and quality modeling Custadio, E., Gurgui, A., and Ferreira, J.P. (eds). D. Reidel Publishing Co., The Netherlands, pp.761. 775. Kruseman, G.P., and De Ridder, N.A., 1974, ''Analysis and evaluation of pumping test data'', International Institute for Land Reclamation and Improvement, The Nether lands, 20gp. Luthin, J. N, 1978 , ''Drainage engineering " M.M. Hand, 1976, ''Improvement of soil condition for old Babylon city'', Technical report, Baghdad. McDonald, M.G. and Harbough, A.W., 1984, ''A modular three dimensional Finite Difference groundwater flow model'', U.S.Geol. Survey, Scientific Publication Co., Washington, D.C., (quoted by Mayer and Miller, 1988). Mohammed, A.G., 1983, ''Water table rise due to infiltration from canals'', J. of Hydrology, 70pp 337-352. Murray, R. Spiegel, 1968, ''Mathematical hand book of formulas and tables'', Schaum's out line series McGraw–Hill Book Company, New York. National Center for Construction Laboratories (NCCL). 1987, ''Sub soil investigation in the site of the Babylon ancient Theater'', Baghdad, un published report. Neuman, S.P., 1975, ''Analysis of pumping test data from anisotropic unconfined aquifers considering delayed gravity response'', Water Resources Research, Vol .11, No.2. Onyejekwa, O., Karama, A. and Kuwornoo, D., 1999, ''A modified boundary integral solution of recharging and dewatering of an confined homogeneous aquifer'', ISSN0378 – 4738,Water SA,Vol.25 No.1, pp9 – 13. Powers, J.P, 1981, "Construction Dewatering: A Guide to theory and practice", John Wiely and sons, Inc., New York, 484p. Pricket, T.A., and Lonnquist C.G, 1971, ''Selected digital computer techniques for groundwater resource evaluation'', Bulletin No.55, Illinois State Water Survey, Urbana, 62p . 90

References 31. Raghunath, H.M., 1982, ''Groundwater'', Witey eastern limited, New Dalhi, 459p. 32. Rasheeduddin, M., Yazicigil, H., and Al-Layal, R.I., 1989, ''Numerical modeling of multiaquifer system in Eastern of Saudi Arabia'', J.of Hydrology, Vol. 107, No. 1, 193-222. 33. Remson, I., Rosenberger, G.M., and Molz, F.J., 1971, ''Numerical methods in subsurface hydrology'', John Wiley and Sons Inc., New York, 389p. 34. Robert, E.M., Ali ,H.C, Roberto ,A. and Shao ,C.W., 2000, ''A numerical groundwater flow model of the Upper and Middle Trinity aquifer, Hill Country area'', Open file report 00-02,Texas Water Development Board . 35. Rushton, K.R. and Miles, J.C., 1983, ''A Coupled surface water and groundwater catchments model.'', J. of Hydrology, 62, pp159 - 177. 36. Rushton, K.R. and Redshow, S.C., 1979, "Seepage and groundwater flow", John Wily and sons, 339 p. 37. Rushton, K.R. and Tomlinson, L.M.1977, ''Permissible mesh spacing in aquifer problems solved by Finite Differences.'', J .of Hydrology 37, pp 63-76. 38. Sharma, H.C., Kapoor, P.N. and Chauhan, H.S., 2000, ''Transient ditch drainage of two–layered soil'', J. of Irrigation and Drainage Engineering, Jan. and Feb., pp14–20. 39. Trescott, P.C., Pinde, G.F., and Larson, S.P., 1976, ''Finite Difference model for aquifer simulation in two dimensions with results of numerical experiments'', U.S. Geol. Survey Techniques of Water Resources Investigations, Book 7, Chapter C1. 40. U.S .Department of Agriculture, Soil Conservation Service, 1978, ''Groundwater ‘‘, SCS National Engineering Hand Book. 41. U.S Army corps of engineer, 1999, ''Engineering and design groundwater hydrology'', Washington, DC 20314–1000 EM 1110-21421. 42. Wang, P.P. and Zheng, C., 1998, ''An efficient approach for successively perturbed groundwater models'', Advances in Water Resources, 21, pp 499-508. 43. WHO, 1983, ''International standards for drinking water'', World Health Organization. 4th edition Geneva, Switzerland, 36 p.

91

Appendix ( A ) Details of Aquifers Characteristics Calculations A.1) Calculations of upper aquifer characteristics 1) Chow method -----------------------

Chow method was applied to analyze the pumping tests data for the upper aquifer from the four wells. Drawdown data were plotted semi logarithmically versus time ,Fig .(A1.1) . Point (A) was chosen arbitrarily and a tangent to the curve was drawn . On the s-axis the draw down value for point A , (sA) was read ,and on the t-axis the time value ( t A ) was also read ,as well as

the slope of the tangent line , i.e. the draw down

difference per log cycle of time ,(∆sA). Values of sA , t A ,and ∆sA for each well can found in Fig.(A1.1).Values of the function F( u )are listed in Table(A1.1) . Knowing the values of F( u ),the corresponding values of W( u A ) and ( u A )were found using Chows nomogram (Kursman ,1994) and listed in columns (3)and (4) in Table (A1.1),respectively . The distance from observation well to pumping well, r and pumping rate ,Q for each well are listed in columns (5) and (6) , respectively . Transmissivity ,T and specific yield ,Sy for each site were determined using the following equation : T=

Q W (u A ) 4πs A

-----------------------(A1.1)

4u AT tA r2

-----------------------(A1.2)

and Sy=

Results of T and

Sy ,are listed in columns (7)and (8)of Table

(A1.1),respectively .

1-6

Table (A1.1) Analysis of data from pumping with the Chow method ,for the upper unconfined aquifer . r

Q

T

Site No.

F( u )

W( u A )

uA

1

1.34

2.8

0.06

15

432

77

2

1.46

3

0.05

34.5

86.4

362

3

1.85

4

0.01

16.5

260

223

4

3.1

6

0.002

22

475.2

326

(m)

Sy

(m3/day) (m2/day)

2) Recovery method ---------------------------Theis

recovery method was used to calculate the transmissivity

values for only two sites . The residual drawdown (s´)during the recovery period is given by the equation ,(Krusman,1994) : s' =

2.3Q t log 2πT t'

-----------------------(A1.3)

where s ' : Residual drawdown in m .

Q: Rate of recharge =rate of discharge in m3/day t : time in days since pumping started . t´: time in days since pumping stopped . For each site, s ' was plotted versus (

t ) on single logarithmic paper t'

t t'

(( ) on logarithmic scale) and a straight line was fitted through the plotted points, Fig.(A1.2). The slope of the line is equal to (2.3Q/4t) ; so that for ∆ s' ( the residual drawdown s' per log cycle of transmissivity becomes : T=

2.3Q 4π∆s'

-----------------------(A1.4) 2-6

t t'

( )), the

Values of Q , ∆ s ' , and computed T are listed in Table (A1.2 ) . No comparable value of Sy can be determined by this method . Table (A1.2) Analysis of data from pumping with the Recovery method for the upper unconfined aquifer. Q

∆ s'

T

(m3/day)

(m/m)

(m2/day)

3

260

0.2

243

4

475.2

0.3

348

Site No.

A.2) Calculation of leaky aquifer characteristics 1) Hantush inflection point method . -------------------------------------------Hantush inflection point method was used to calculate T, S, C and L from transient pumping test data which utilizes the halfway point or inflection point Pi on a curve relating s to log t ,Fig.(A2.1). The inflection point is defined as the point where the drawdown ,si is one half the final or equilibrium drawdown ,sf . The equation for si is : si =

1 Q ⎛r⎞ sf = k° ⎜ ⎟ 2 4πT ⎝ L ⎠

-----------------------(A2.1)

Furthermore , the u value at the inflection point .ui was found to be equal to r/2L so that ui =

r 2S r = 4Tti 2 L

-----------------------(A2.2)

where ti is the value of time read at the inflection point from the time axis .The slop of the curve at the inflection point, ∆si is given by 3-6

∆si =

2.3Q − r / L e 2πT

-----------------------(A2.3)

Finally ,the ratio between si and ∆si was derived as : 2 .3

si = e r / L k ° (r / L) ∆s i

-----------------------(A2.4)

Values of the function ( e r / L k° (r / L)

for different values of (r/L) are

given in special Table applied by Hantush,(1956) . The hydraulic resistance of semi pervious layer, C is : C=

L2 T

-----------------------(A2.5)

From the pumping test for only one site located in the north of Babylon city ,the drawdown data from the piezometer at (19.1m) distance from the pumping well were plotted versus t on single logarithmic paper , Fig.(A2.1). Using estimated values of si , ti and ∆si in the Eq.(A2.4) gives , ( e r / L k° (r / L) =3.382).

Therefore

(r/L=0.044),and( k ° (r / L) =3.241).

it Since

was (r=19.1m)

found so,(L=434

that m).

Substitution of these numerical values in to Eq.(A2.1) , Eq.(A2.2) and Eq.(A2.5) yield (T=394 m2/day ) , (S=2.07*10-3) and ( C =302 days),respectively . According to Hantush ,(1964) the radius of influence of a pumping well ,Re at steady state can be approximated by the following formula : Re=1.12 L

----------------------(A2.6)

Thus Re was found to be approximately (500m).

2) Recovery method --------------------------Residual drawdown s' was plotted versus t/t' for the pumping well site No. 5 and a straight line was fitted through the plotted point ,Fig. (A2.2).

4-6

The slope of the line , ∆ s' was found to be ( transmissivity value was found to be 408 m2/day.

5-6

). Using Eq.(A1.4),

APPENDIX B1

Flow-chart of the program used for the analytical simulation Read Q , T , S , t , L , scale

Read io , jo , i , j , iَ , jَ

2

r=√ r َ= √

2

-i ) + ( jo-j ) * scale

o

2

2

- iَ ) + ( jo- jَ ) * scale

o

2

U= r S / 4πt , r/L 2

Uَ= rَ S / 4πt , rَ/L

Look up table W(U,r/L) , Wَ(Uَ,rَ/L)

n

s = (Q/4πT) ∑ ( W-Wَ ) m= 1

6-6