Procedure for Conducting Pumping Tests part (4)

Procedure for Conducting Pumping Tests part (4)

Water-level measurements:
The water levels in the well and the piezometers must be measured many times during a test, and with as much accuracy as possible. Because water levels are dropping fast during the first one or two hours of the test, the readings in this period should be made at brief intervals. As pumping continues, the intervals can be gradually lengthened. After the pump has been shut down, the water levels in the well and the piezometers will start to rise - rapidly in the first hour, but more slowly afterwards. These rises can be measured in what is known as a recovery test.

Duration of the pumping test:
The question of how many hours to pump the well in a pumping test is difficult to answer because the period of pumping depends on the type of aquifer and the degree of accuracy desired in establishing its hydraulic characteristics. At the beginning of the test, the cone of depression develops rapidly because the pumped water is initially derived from the aquifer storage immediately around the well.

Conversion of the data:
The water-level data collected before, during, and after the test should first be expressed in appropriate units. The measurement units of the International System are recommended, but there is no fixed rule for the units in which the field data and hydraulic characteristics should be expressed.
Transmissivity, for instance, can be expressed in m2/s or m2/d. Field data are often expressed in units other than those in which the final results are presented.
Time data, for instance, might be expressed in seconds during the first minutes of the test, minutes during the following hours, and actual time later on, while water-level data might be expressed in different units of length appropriate to the timing of the observations.
It will be clear that before the field data can be analyzed, they should first be converted: the time data into a single set of time units (e.g. minutes) and the drawdown data into a single set of length units (e.g. metres), or any other unit of length that is suitable.

Pump regime - General guidance:

For Confined aquifers:

Transmissivity is more important than storativity: observation wells are not always needed (although accuracy lost without them!).
For Unconfined aquifers: Storativity much larger, and has influence over transmissivity estimates: observation wells important as is larger test duration.
Care is needed if aquifer only partly screened.

Measurement intervals to be considered:
Water levels measurements for pumping well could be taken as the following :

Similarly, for observation wells, water level measurement can be taken as the following:

After the pump has been shut down, the water levels in the well will start to rise again. These rises can be measured in what is known as recovery test.
If the pumping rate was not constant throughout the pumping test, recovery-test data are more reliable than drawdown data because the water table recovers at a constant rate.
Measurements of recovery shall continue until the aquifer has recovered to within 95% of its pre-pumping water level.
Amongst the arrangements to be made for pumping test is a discharge rate control. This must be kept constant throughout the test and measured at least once every hour, and any necessary adjustments shall be made to keep it constant.

Basic Assumptions :
We need to make assumptions about the hydraulic conditions in the aquifer and about the pumping and observation wells. All geological formations are horizontal and of infinite horizontal extent.
The potentiometric surface of the aquifer is horizontal prior to the start of the pumping. The potentiometric surface of the aquifer is not changing with time prior to the start of the pumping.
All changes in the position of the potentiometric surface are due to the effect of the pumping well alone. The aquifer is homogeneous and isotropic. All flow is radial toward the well. Groundwater flow is horizontal. Darcy’s law is valid. Groundwater has a constant density and viscosity.

Proper discharge of the pumped water:
Proper discharge of the pumped water is important to ensure there is no damage due to erosion, flooding or sediment deposits in streams.
For land disposal, direct the water from the pumping well in a down-hill direction at a sufficient distance from the pumping well. This will prevent re-circulation of the pumped water into the well or aquifer and will preserve both the pumping water level and the integrity of the pumping test.

Collecting water samples for analysis:
A pumping test is a good time to collect water quality samples to assess the chemical, physical and bacterial properties of the water.

Water samples should be collected when conditions have stabilized.

Hydrofracturing :
If hydrofracturing (fracking) has been used to increase the productivity of the well, it may advisable to wait up to a week before conducting the pumping test.

Pumping Test Report:
The formal report for a pumping test should be submitted at the end of the work.

This report should contain the following:
• information on the well (i.e., the well construction report, type of well and a diagram showing the well’s location on the property, etc.);
• information on field procedures and personnel involved in the test,
• information on the hydrogeologic setting, including references to mapped aquifers.
• pumping test information including the date of the pumping test, all data on the pump type, depth of pump setting, pumping rates, method of flow measurement, observations made during the pumping test, duration of the test, available drawdown, specific capacity, method of water level measurements and water levels/times recorded during the pumping test and recovery period;
• analysis and assessment of the pumping test data including an assessment of the long-term sustainable yield and potential impacts to neighbouring wells and/or streams.

Borehole Performance Curves
Borehole performance curves are best plotted on a graph of water level against pumping rate.
Water levels are used (in metres below datum) instead of drawdowns so that seasonal variations can be plotted on the same graph if the borehole is tested again at a different time of year.

Multiple Production Wells:
For cases in which there are multiple production wells, all such wells must be monitored during the test. In addition, the test must be conducted in a way that will obtain information pertinent to the operational needs of the entire wellfield. If wells may have to be operated simultaneously in order to meet demand, the test must be designed to produce data representative of these conditions.

Limitations of pumping tests:

Analysing groundwater levels and pumping rates measured during pumping tests provide some indication of the behaviour or state of ‘health’ of the aquifer or groundwater system. These tests undoubtedly provide valuable information and help to understand the groundwater system. However, the decisions should be based on a wider understanding of the regional geology, hydrogeology and environment. View publication

END OF PART 4

Procedure for Conducting Pumping Tests part (3)

Procedure for Conducting Pumping Tests part (3)

The pump : -
The pump and power unit should be capable of operating continuously at a constant discharge for a period of at least a few days.
There are several factors to be considered when determining the type of pump to be used and the depth at which it should be set, including:
1) well diameter
2) desired pumping rate
3) total dynamic head including the pumping water level, the above ground head (if applicable) and all friction losses in the casing, pipes, fittings, etc.;
4) reliability of power source; and
5) horsepower requirements.

An even longer period may be required for unconfined or leaky aquifers, and especially for fractured aquifers. In such cases, pumping should continue for several days more. The capacity of the pump and the rate of discharge should be high enough to produce good measurable drawdowns in piezometers as far away as, say, 100 or 200 m from the well, depending on the aquifer conditions.

Discharging the pumped water:
The water delivered by the well should be prevented from returning to the aquifer of the same well. This can be done by conveying the water through a large-diameter pipe, say over
a distance of 100 or 200 m, and then discharging it into a canal or natural channel.

Piezometers:
Bore wells used to only measure the water levels nearer to the pumping wells are called as piezometers. The water levels measured in piezometers represent the average head of the nearby aquifer. Piezometers should be placed not too near the well, and not too far from it, also.

Depth of the piezometers:
The depth of the piezometers is at least as important as their distance from the well. In an isotropic and homogeneous aquifer, the piezometers should be placed at a depth that coincides with that of half the length of the well screen. For example, if the well is fully penetrating and its screen is between 10 and 20 m below the ground surface, the piezometers should be placed at a depth of about 15 m.

The type of aquifer:
When a confined aquifer is pumped, the loss of hydraulic head propagates rapidly because the release of water from storage is entirely due to the compressibility of the aquifer material and that of the water. The drawdown will be measurable at great distances from the well, say several hundred metres or more. In unconfined aquifers, the loss of head propagates slowly. Here, the release of water from storage is mostly due to the dewatering of the zone. A leaky aquifer occupies an intermediate position.

Transmissivity:
When the transmissivity of the aquifer is high, the cone of depression induced by pumping will be wide and flat . When the transmissivity is low, the cone will be steep and narrow. In the first case, piezometers can be placed farther from the well than they can in the second.


The duration of the test:
The duration of the pumping test depends on the purpose of the well, the type of aquifer and any potential boundary conditions.

Theoretically, in an extensive aquifer, as long as the flow to the well is unsteady, the cone of depression will continue to expand as pumping continues. Therefore, for tests of long duration, piezometers can be placed at greater distances from the well than for tests of short duration.

The discharge rate :
During the aquifer test, discharge should be measured accurately and frequently enough to verify that a constant discharge rate is being achieved. Waste of the discharge should be avoided.
If the discharge rate is high, the cone of depression will be wider and deeper than if the discharge rate is low. With a high discharge rate, therefore, the piezometers can be placed at greater distances from the well.

Control of the pumping rate:
Control of the pumping rate during the test is important. Because it allows for reliable drawdown data to be collected to determine the yield of the well and aquifer properties.
Controlling the pumping rate by adjusting the pump speed is generally not satisfactory.
It is better to use a gate valve to adjust the pumping rate to keep it constant.
The discharge pipe and the valve should be sized so that the valve will be from ½ to ¾ open when pumping at the desired rate.
The valve should be installed at a sufficient distance from the flow measurement device to avoid any impacts from turbulence.
Measuring the discharge of pumped water accurately is also important and common methods of measuring discharge include the use of an orifice plate and manometer.

Aquifers with stratification:
Homogeneous aquifers are rare in nature. Most of the aquifers are stratified to some extent. Stratification causes differences in horizontal and vertical hydraulic conductivity, so that the drawdown observed at a certain distance from the well may differ at different depths within the aquifer. As pumping continues, these differences in drawdown diminish. Moreover, the greater the distance from the well, the less effect stratification has upon the drawdowns.

Fractured rock :
Deciding on the number and location of piezometers in fractured rock poses a special problem, although the rock can be so densely fractured that its drawdown response to pumping resembles that of an unconsolidated homogeneous aquifer; if so, the number and location of the piezometers can be chosen in the same way as for such an aquifer.

The measurements to be taken:
The measurements to be taken during a pumping test are of two kinds:
- Measurements of the water levels in the well and the piezometers.
- Measurements of the discharge rate of the well.
Ideally, a pumping test should not start before the natural changes in hydraulic head in the aquifer are known

- both the long-term regional trends and the short-term local variations.

So, for some days prior to the test, the water levels in the well and the piezometers should be measured, say twice a day.


END OF PART 3

Procedure for Conducting Pumping Tests part (2)

Procedure for Conducting Pumping Tests part (2)

Planning Stage:
Designing and planning a pumping test is critical prior to testing. Lack of planning can result in delays, increased costs, technical difficulties and poor or unusable data.

Some things to consider in the pre-planning stage are:
1) time of year the pumping test should be done
2) natural variations in the groundwater levels that occur during the test
3) informing others who may be affected
4) depth of pump setting and type of pump
5) pumping duration
6) pumping rate
7) control and measurement of the pumping rate
8) frequency of measurements of the water levels
9) measuring water levels in neighbouring wells and/or streams
10) discharge of pumped water
11) collection of water samples for water quality analysis
special conditions to be aware of e.g., salt water intrusion in coastal aquifers

Materials required for conducting pumping tests:
For conducting pumping tests and analysing the data, the following items may be required:
1) generator
2) submersible pump
3) discharge pipe, connections
4) flow measurement device(s)
5) tape measure(s), steel tape(s) and carpenter's chalk
6) pressure transducer(s), cables, data logger(s)
7) electric water-level sounder(s) and batteries
8) watches/stopwatches
9) barometric sensor/ thermometer
10) pH and conductivity meters
11) sample bottles
12) toolkit, , wires
13) data collection forms, log book, permanent-ink pens
14) computer, calculator
15) graph paper (semilog, log) and/or computer software
16) references, standard operating procedures
17) manufacturer's operating manuals for equipment
18) maps (site, geologic and topographic), cross section(s).

Well-Inventory analysis:

Well-inventory is one basic step. Well inventories are also conducted as part of most of the environmental investigations.
Different types of wells are studied for recording their yielding capacities, main aquifers contributing to yield, etc. The nature and period of their use and sustainability are also recorded. The hydrostatic heads of the aquifers are monitored on a monthly basis through shallow dugwells (monitoring stations), piezometers, deep wells, etc, in the areas. Water samples are collected from selected wells and analysed to determine the variation of water quality over time and space.
Before conducting a pumping test the geological and hydrological information of the area should be collected.
1. The geological characteristics of the subsurface (i.e. all those lithological, stratigraphic, and structural features that may influence the flow of groundwater).
2. The type of aquifer and confining beds. 3.The thickness and lateral extent of the aquifer and confining beds.
4. The aquifer may be bounded laterally by barrier boundaries of impermeable material in the lithology (e.g. the bedrock sides of a buried valley, a fault, or simply lateral changes of the aquifer material);
Data on the groundwater-flow system: horizontal or vertical flow of groundwater, water table gradients, and regional trends in groundwater levels.

Details of any existing surrounding wells in the area.

Selecting the well for the pumping tests:
Well should be suitable for the test.

1) The hydrogeological conditions should not change over short distances and should be representative of the area under consideration, or at least a large part of it;
2) The site should not be near railways or motorways where passing trains or heavy traffic might produce measurable fluctuations in the hydraulic head of a confined aquifer;
3) The site should not be in the vicinity of existing discharging wells;
4) The pumped water should be discharged in a way that prevents its return to the aquifer.

The gradient of the water table or piezometric surface should be low;
Manpower and equipment must be able to reach the site early and easily.

New Exploratory and observations wells:
If there is no existing well in a region, bore wells are drilled for pumping test purpose. Sometimes, bore well drilled for drinking water supply purpose are tested to know the hydrological properties, by conducting pumping tests.

Well diameter:
Before conducting the pumping test the dimensions of the well should be measures.

Radius for circular wells. length and width for rectangular wells.
The depth also should be measured. if it is new well, during the drilling operations, samples of the geological formations that are pierced should be collected and described lithologically.


Records should be kept of these lithological descriptions, and the samples themselves should be stored for possible future reference.

Well screen: for bore wells, the casing pipe length should be measured.


END OF PART 2

Procedure for Conducting Pumping Tests part (1)

Procedure for Conducting Pumping Tests part (1)

What is a pumping test ?
A pumping test consists of pumping groundwater from a well, usually at a constant rate, and measuring water levels in the pumped well and any nearby wells (observation wells) or surface water bodies during and after pumping.

A pumping test is a practical, reliable method of estimating well performance, well yield, the zone of influence of the well and aquifer characteristics (i.e., the aquifer’s ability to store and transmit water, aquifer extent, presence of boundary conditions and possible hydraulic connection to surface water).

Aquifer test and aquifer performance test (APT) are alternate designations for a pumping test. In petroleum engineering, a pumping test is referred to as a drawdown test.

Purpose of conducting Aquifer Tests:
Hydrogeological studies include determination of aquifer parameters by conducting pumping tests on dug / bore / tube wells and analysis of pumping test data.

Basically, pumping tests are conducted for a wide variety of reasons, including the following:

1) To determine the reliable long-term yield (or ‘safe’ yield) of a borehole.
2) To assess the hydraulic performance of a borehole, usually in terms of its yield-drawdown characteristics. How much drawdown does it take to yield a certain amount of water?
3) To derive the hydraulic properties of the aquifer.
4) Pumping tests are the classic (and perhaps the only) way to derive in situ aquifer hydraulic properties, such as transmissivity and the storage coefficient, or to reveal the presence of any hydraulic boundaries.
5) To test the operation of the pumping and monitoring equipment,
6) To determine the effects of abstraction on neighbouring abstractions (sometimes referred to as derogation).
7) To determine the environmental impact of the abstraction.
8) To provide information on water quality. Is the water quality suitable for the intended use? Are there likely to be any problems such as drawing in saline or polluted water after extended periods of pumping?
9) To optimize operational pumping regimes.
10) To help determine the correct depth at which the permanent pump should be installed in the borehole.

Common types of pumping tests
The common types of pumping tests conducted include the following:

Constant-rate tests:
In this test it is necessary to maintain pumping at the control well at a constant rate. This is the most commonly used pumping test method for obtaining estimates of aquifer properties. These tests are carried out by pumping at a constant rate for a much longer period of time than the step test, and primarily designed to provide information on the hydraulic characteristics of the aquifer. Information on the aquifer storage coefficient can be deduced only if data are available from suitable observation boreholes.

Step-drawdown tests :
These tests proceed through a sequence of constant-rate steps at the control well to determine well performance characteristics such as well loss and well efficiency. Step tests are designed to establish the short-term relationship between yield and drawdown for the borehole being tested. It consists of pumping the borehole in a series of steps, each at a different discharge rate, usually with the rate increasing with each step. The final step should approach the estimated maximum yield of the borehole

Recovery tests :
These tests use water-level (residual drawdown) measurements after the termination of pumping. Although often interpreted separately, a recovery test is an integral part of any pumping test. Recovery test are carried out by monitoring the recovery of water levels on cessation of pumping at the end of a constant-rate test (and sometimes after a step test). It provides a useful check on the aquifer characteristics derived from the other tests but is valid only if a foot-valve is fitted to the rising main; otherwise water surges back into the borehole.

Preliminary studies:
When planning a pumping test, it is useful to gather together all the information that can be found about the aquifer and the borehole itself.

Basic geology:
Are the rocks crystalline basement, volcanic, consolidated sediments or unconsolidated sediments? Groundwater occurs in these rocks in different ways, and behaves in different ways.
Aquifer configuration:
Is the aquifer confined, unconfined or leaky?
Borehole construction:
How deep is the borehole, and of what diameter?
Has solid casing, screen or gravel pack been installed?
Installed equipment:
If a pump is already installed in the borehole, what are its type and capacity, and at what depth is the pump’s intake? Can the pumping rate be varied?
Historical or background water levels:
Information about the historical behaviour of the groundwater level is very useful.
Does the water level vary much from wet season to dry season?
In the period before the test takes place, is the water level already falling or rising or is it stable? What is the current water level?
Local knowledge:
Residents often have a surprisingly good understanding of how the groundwater in the area behaves. For example, how does the water level respond to rainfall?
Can borehole yields be maintained?
Is the water safe for drinking, and does the water quality change over time?


END OF PART 1

Aquifer Properties part (2)

Aquifer Properties part (2)

7-Hydraulic Conductivity

It refers to aquifer’s ability to transmit or conduct water. It is defined as volume rate of water of given kinematic viscosity moving through unit cross sectional area per unit hydraulic gradient (Equation-9). It is to be noted that the unit cross sectional area mentioned above is at right angle to the direction of groundwater flow.

K =Q/(A×(Δh/Δl))---------Equation-9

Where:

K is hydraulic conductivity

Q is the volume rate of the water

A is the cross sectional area

(Δℎ/Δ𝑙) is the hydraulic gradient

It can be observed from equation-9 that the unit of hydraulic conductivity is

m/day with dimension of LT-1

It is to be noted that hydraulic conductivity is a function of the porous media and

the fluid passing through it.

8- Intrinsic Permeability

Intrinsic permeability (k) is fundamental property of the aquifer, which

determines its ability to transmit any fluid through it. It is a function of media

only (equation-10).

k = C × d2--------Equation-10

Where:

C is a constant dependent on factors like distribution of grain size, sphericity

and roundness of grains, nature of their packing etc.

d is diameter of the grains.

The dimension of intrinsic permeability is L2 and the popularly used unit is”Darcy”, where 1 Darcy ≈ 10-8 cm2 (CGWB 1982).

The relationship between hydraulic conductivity and intrinsic permeability can

be understood with help of equation-11.

K =(k × ρ ×g)/μ -------Equation-11

Where:

K is hydraulic conductivity

k is intrinsic permeability

ρ is density

g is acceleration due to gravity

μ is kinematic viscosity

9-Transmissivity

It is yet another property, which refers to aquifer’s ability to transmit or conduct

water. It is defined as volume rate of water of given kinematic viscosity

conducted under influence of unit hydraulic gradient through unit saturated

width of the aquifer at right angle to the direction of groundwater flow (After

Theis 1935) (Equation-12).

T =Q/(w×(Δh/Δl)) -------Equation-12

Where:

T is Transmissivity

Q is the volume rate of the water

w is the saturated width of the aquifer

Δℎ/Δ𝑙 is the hydraulic gradient

It can be observed from equation-12 that the unit of transmissivity is m2/day with dimension of L2 T-1

As in case of hydraulic conductivity, transmissivity is also a function of the

porous media and the fluid passing through it.

10- Relationship between hydraulic conductivity and transmissivity

Let us examine how the two fundamental aquifer parameters concerned with

transmission of groundwater through aquifer are related by dividing equation-9

by equation-12 as shown below in equation-13:

(𝐾=𝑄/(𝐴×(Δℎ/Δ𝑙))) /(𝑇=𝑄/(𝑤×(Δℎ/Δ𝑙))) ---- Equation-13

Now the area A given at numerator in equation-13 is visualized with help of a

simple schematic saturated cross section of the aquifer at right angle to the

groundwater flow direction

A schematic saturated cross-section of the aquifer at right angle to the

groundwater flow direction. Here ‘w’ is saturated width while ‘b’ is saturated

thickness.

The area A in Fig is saturated width ‘w’ multiplied by saturated thickness ‘b’.

We substitute this in equation-13 and we get equation -14 as given below:

T = K × b -----Equation-14

Where:

T is Transmissivity

K is hydraulic conductivity

b is saturated thickness of the aquifer

Summary

           1.      An aquifer refers to a geological formation, which can store and transmit

groundwater in sufficient amount for economic utilization.

2.    On the basis of their geological settings and distinct hydrological regime, we

have mainly four types of aquifer: unconfined, confined, semi confined and

perched aquifer.

3.      Porosity of a formation is measure of void spaces in the formation. It is

expressed as ratio of the volume of voids to the total volume of the rock or

formation.

4.      Effective porosity of a formation is measured as a ratio of interconnected

pore space/voids available for fluid flow to the total volume of the rock or

formation.

5.      Specific yield of a rock or formation is measured as the ratio of volume of

water that after saturation is yielded/drained under influence of gravity to the

volume of the rock or formation.

6.      Specific retention of a rock or formation is measured as the ratio of volume

of water that after saturation is retained against the force of gravity to the

total volume of the rock or formation.

7.      Storage coefficient is a general term, which refers to volume of water either

taken in or released out by the aquifer per unit surface area per unit change in

hydraulic head.

8.      Specific storage is defined as the volume of water that an aquifer takes in or

releases per unit volume of the aquifer per unit decline in hydraulic head.

9.      Hydraulic conductivity is defined as volume rate of water of given kinematic

viscosity conducted under influence of unit hydraulic gradient through unit

cross sectional area at right angle to the direction of groundwater flow.

10.   Transmissivity is defined as volume rate of water of given kinematic

viscosity conducted under influence of unit hydraulic gradient through unitsaturated width of the aquifer at right angle to the direction of groundwater

flow.

End part 2

Aquifer Properties part (1)

Aquifer Properties part (1)

We know by now that an aquifer refers to a geological formation, which can store

and transmit groundwater in sufficient quantity, so that the water can be

economically utilized from the aquifer. Now in this section we will be discussing

about the properties of a formation, which makes it an aquifer.

1-Porosity

Porosity of a formation is measure of void spaces in the formation. It is

expressed as ratio of the volume of voids to the total volume of the rock or

formation (Equation-1). Generally, it is expressed as percentage. Thus:

                      n =(Vv/V) x 100 ----- Equation-1.

Where

n = porosity

vv = volume of voids

v = total volume of rock

A look at equation-1 reveals that porosity is ratio of two volumes and does not

have any unit, rather it is dimensionless.

An aquifer can have either primary or secondary porosity. The flow

chart in Fig.6 clearly shows that the primary porosity is formed during genesis of

the rock, while secondary porosity is formed after genesis of the rock. The

porosity of loose sand is the best example of primary porosity, while porosity

imparted to hard rock because of fracturing is an example of secondary porosity.

Primary porosity is a function of sorting, packing, shape and fabric of the grains,

while secondary porosity is a function of intensity of fracturing, degree of

solution of the hard rock etc. It must be mentioned explicitly that if all the grains

are spherical then in such case porosity is not a function of the diameter of the

sphere. Thus if you just magnify the grain size while sorting, packing etc. of the

grains remain same, and then the porosity remains same.

2-Effective porosity

Effective porosity of a formation refers to the fraction of porosity available for

fluid flow. It is measured as a ratio of interconnected pore space/voids available

for fluid flow to the total volume of the rock or formation (Equation-2).

Generally, it is expressed as percentage. Thus:

                            e =Vi/Vx 100 ----- Equation-2.

Where

e = effective porosity

vi = volume of interconnected pore space/voids

v = total volume of rock

A look at equation-2 reveals that effective porosity is ratio of two volumes and

does not have any unit, rather it is dimensionless.

3-Specific Yield

Specific yield of a rock or formation is measured as the ratio of volume of water

that after saturation is yielded/drained under influence of gravity to the volume

of the rock or formation (Meinzer 1923) (Equation-3).

                            Sy =Vw/V ----- Equation-3.

Where

Sy = Specific yield

Vw = Volume of water drained under influence of gravity

V = total volume of rock

A glance at equation-3 reveals that Specific yield is ratio of two volumes and

does not have any unit, rather it is dimensionless.

It is to be noted that specific yield is also an approximate estimate of the volume

of water required to saturate an aquifer by flow under influence of gravity.

4- Specific Retention

Specific retention of a rock or formation is measured as the ratio of volume of

water that after saturation is retained against the force of gravity to the total

volume of the rock or formation (Meinzer 1923) (Equation-4).

                              Sr =Vr/V ----- Equation-4.

Where

Sr = Specific retention

Vr = Volume of water retained against the force of gravity

V = total volume of rock

A look at equation-4 reveals that Specific retention is ratio of two volumes and

does not have any unit, rather it is dimensionless.

Here if we add specific yield and specific retention we get equation-5. In this

equation, it is clear that Vy: the volume of water yielded plus Vr: the volume of

water retained is a measure of total voids or pores in the formation. Hence, it is

clear that specific yield added with specific retention equal to porosity of the

formation.

          S𝑦 + S𝑟 =(V𝑦+V𝑟)/𝑉= n (porosity) ----- Equation-5

5- Storage Coefficient and Storativity

Storage coefficient helps in estimation of the storing capability of an aquifer.

Storage coefficient is a general term, which refers to volume of water either

taken in or released out by the aquifer per unit surface area per unit change in

hydraulic head (Equation-6).

                        Sc =Vw/(A×Δh)-----Equation-6

Where:

Sc refers to storage coefficient

Vw refers to the volume of water either taken in or released out by the aquifer

A refers to the surface area of the aquifer

Δh refers to change in hydraulic head

A glance at equation-6 reveals that Storage coefficient does not have any unit

and is dimensionless.

Storage coefficients for confined aquifer are also referred to as Storativity.

6-Specific Storage

Specific storage is defined as the volume of water that an aquifer takes in or

releases per unit volume of the aquifer per unit decline in hydraulic head

(Equation-7).

                         Ss =Vw/(V×Δh)----Equation-7

Where

Ss refers to specific storage

vw refers to the volume of water either taken in or released out by the aquifer

v refers to the volume of the aquifer

Δh refers to change in hydraulic head

A look at equation-6 reveals that it has unit of per meter and dimension of L-1

In case of confined aquifers, the relationship between Storativity and Specific

storage is given by equation-8 below:

                           S = Ss × b -------Equation-8

Where

S is storage coefficient

Ss is specific storage

b is the saturated thickness of the aquifer

End of part 1