3.1. Hydraulic conductivity

Hydraulic Conductivity could be described as the relative ease with which a fluids (groundwater) flows through a medium (in this case a geological formation or rock) which is quite different from intrinsic permeability in that though it describes the water-transmitting property of the medium it is however not influenced by the temperature, pressure or the fluid passing through the geological formation. Hydraulic conductivity of a soil or rock or geological formation depends on a variety of physical factors amongst which includes porosity, particle size and distribution, arrangement of particles and other factors.

Mathematically hydraulic conductivity could be defined by the formula below:

$$K = k \frac{\rho \text{g}}{\mu} \tag{1}$$

where K is the hydraulic conductivity (cm/s or m/s), k is the intrinsic permeability, r is the density of fluid, μ is the dynamic viscosity of fluid.

Note: seconds (s) could be converted to days by time conversions.

Generally, for unconsolidated porous media, hydraulic conductivity varies with particle size as such clayey materials exhibits low values of hydraulic conductivity as compared to sands and gravels that exhibits high values of hydraulic conductivity (150 m/day for coarse gravels, 45 m/day for coarse sand and 0.08 m/day for clay). This is so because the small particle size arrangements (fine grained) in geological formations contained mainly of clayey materials though porous is not permeable enough to allow groundwater flow within it however in sands and gravels (medium to coarse grained) we have medium to coarse arrangement of particle sizes which results to a porous and permeable geological formations or rocks that allows a higher ease of groundwater flow. It is however essential to point out that we could have geological formations or rock that exhibit medium values of hydraulic conductivity, this is in the case where you have a geological formation made up of moderate amounts of clayey material and sandy materials. It should also be noted that variations in hydraulic conductivity values of geological formations or rocks is dependent on factors such as weathering, fracturing, solution channels and depth of burial.

#### 3.2. Porosity

boundary of groundwater within the unconfined aquifer is the water table, the groundwater in an unconfined aquifer is more vulnerable to contamination from surface pollution as compared to that in confined aquifers this been so due to easy groundwater infiltration by land pollutants. Fluctuation in the level of groundwater varies and depends on the stored up groundwater in the space of the aquifer which in turn affects the rise or fall of water levels in wells that derive their source from aquifers. Unconfined aquifers have a storative value greater than 0.01. "Perched aquifers" (Figure 3) are special cases of unconfined aquifers occurring in situation where groundwater bodies are separated from their main groundwater source by relatively impermeable rock layers of small areal extents and zones of aeration above the main body of groundwater The quantity of water found available in this type of aquifer is usually

Figure 3. Schematic cross-section of aquifer types (source: coloradogeologicalsurvey.org>wateratlas).

Petro-physical properties of aquifers are properties that help in the defining and characterizing

Hydraulic Conductivity could be described as the relative ease with which a fluids (groundwater) flows through a medium (in this case a geological formation or rock) which is quite different from intrinsic permeability in that though it describes the water-transmitting property of the medium it is however not influenced by the temperature, pressure or the fluid passing through the geological formation. Hydraulic conductivity of a soil or rock or geological formation depends on a variety of physical factors amongst which includes porosity,

particle size and distribution, arrangement of particles and other factors.

Mathematically hydraulic conductivity could be defined by the formula below:

minute and available for short periods of time.

3. Petro-physical properties of aquifers

aquifers. Some of the properties considered are:

3.1. Hydraulic conductivity

14 Aquifers - Matrix and Fluids

Porosity of a geological formation or rock or soil could be described as the measure of the contained voids or interstices expressed as a ratio of the volume of voids to the total volume. It could also be defined as the volume of pores within a rock or soil sample divided by the total volume of the rock matrix (pores and solid materials contained with the rock). When a rock is emplaced by either cooling from an igneous melt or induration from loose sediment or soil formation from weathering of rock materials, it possess an inherent porosity known as primary porosity which reduces with time by actions of cementation or compaction. However, when joints, fissures, fractures or solution cavities formed within rocks after the must have been emplaced it is referred to as secondary porosity. Therefore, total porosity is the sum of primary and secondary porosities.

If all the pores found contained in a rock are not connected, then only a certain fraction of the pores would allow for water movement. The fraction that allows for water movement is known as the effective porosity example of which includes pumice, glassy volcanic rock (solidified froth) probably would float in water because its total porosity is high and it contains much entrained gas.

Porosity of a rock is determined to a large extent by the packing arrangement of particle sizes and the uniformity of its grain-size distribution. As such a cubic packing (Figure 4A) would give a porosity of 47.65%, the greatest and most ideal a rock with uniform spherical grains can achieve as the centers of eight such grains from vertices of a cube. However, if the packing

Figure 4. (A) Cubic packing (B) Rhombohedral packing.

arrangement of the rock where to change to be that of a rhombohedral (Figure 4B) then, its porosity would reduce to 25.85% as the centers of the eight adjacent spheres form the vertices of rhombus.

Mathematically porosity (n) is given by the formula below:

$$\text{Porosity } (n) = \frac{Vp}{Vt} \tag{2}$$

4. Aquifer characterization – electrical techniques

been considered are electrical conductivity or dielectric constant.

collection is function of the purpose of the investigation.

4.1. Electrical resistivity

permission.

In geophysical investigations using electrical techniques, two primary properties of interest

Electrical techniques make involves profiling and sounding mode of data collection which both involves the use of direct currents or low frequency altering currents passing through the subsurface. While profiling use of the terms profiling involves the inferring of subsurface measurements based on lateral changes in electrical properties over constant subsurface, Sounding infers subsurface measurements of single location as a function of changes in petrophysical properties as function of depth (Figure 5). The use of either of the two modes for data

Electrical resistivity (ER) is more frequently been used as compared to other electrical techniques in groundwater investigations of which includes the characterization of aquifers. Electrical Resistivity (ER) involves the introduction of time – varying direct current (DC) or very low frequency (<1 Hz) current into the ground between two current electrodes to generate potential differences as measured at the surface with units of Ohm-meters (Ω-m). A deviation from the norm in the pattern of potential differences expected from homogeneous proffer the necessary information on the form and electrical properties of subsurface inhomogeneities.

A typical Electrical Resistivity (ER) investigation made up of a 2 – electrode system would include 2 – current electrodes and 2 – potential electrodes. As current is been injected into the ground, corresponding potential differences (ΔV) is measured. This measurement coupled with known current (I) and a geometric factor (K) that is a function of the particular electrode

<sup>r</sup> <sup>¼</sup> <sup>Δ</sup><sup>V</sup>

The expression in Eq. (4) for a homogeneous ground is also the same applied for heterogeneous ground; however the general term "apparent resistivity (ra)" is substituted for resistivity (r) in

Figure 5. Schematic geological section and associated resistivity and velocity contrasts at interfaces (from Burger [2]. With

<sup>I</sup> <sup>K</sup> (4)

Aquifer, Classification and Characterization http://dx.doi.org/10.5772/intechopen.72692 17

configuration, can be used to calculate resistivity (r) following Ohm's law:

where Vp is the pores of rock or soil sample, Vt is the total volume of pores and solid material.

#### 3.3. Transmissivity

Transmissivity (T) more simply could be defined as the property of aquifer to transmit water. It could also be defined as the amount of water that can be transmitted horizontally through an aquifer unit by full saturated thickness of the aquifer under a hydraulic gradient of 1 or as the rate at which water of prevailing kinematic viscosity is transmitted through a unit width of aquifer under a unit gradient.

It could be mathematically defined as:

$$T = Kb \ (m^2/day) \tag{3}$$

where T is the transmissivity, K is the hydraulic conductivity, b is the saturated thickness of the aquifer.

Aquifers are characterized by petro-physical properties such as hydraulic conductivity (alternatively called permeability), transmissivity (product of hydraulic conductivity and aquifer thickness) and diffusivity (ratio of transmissivity and storage coefficient). These properties could be examined using geophysical techniques such as Electrical Resistivity, Seismic techniques.
