In this section, most of the concepts regarding the aquifer properties are discussed in qualitative terms (conceptual model), and the equations are used to support the concepts that are
introduced in this sections. Aquifers have properties such as: porosity (𝑛), thickness (𝑏), perme-
ability (𝑘), hydraulic conductivity (𝐾), discharge (𝑄), transmisivity (𝑇), hydraulic gradi-
ent (𝑑ℎ
𝑑𝑙), specific yield (𝑆𝑦), specific retention (𝑆𝑟), flow direction, and average linear veloc-
ity (𝑣𝑥). In aquifers, water is transmitted under the influence of gravity, viscosity, and hydraulic
gradient, which represents the loss of head over distance or potential energy over distance [Hiscock, 2005]. K defines the ability of a fluid to pass through a medium by accounting for both fluid properties (density, gravity, and viscosity) and solid properties (grain size, permeabil- ity) of the media [Fetter, 2001; Weight, 2008]. K is a function of porosity, and the arithmetic
difference in porosity results in exponential difference in K, which varies over 13 measured or- ders of magnitude, making it one of the most variable “constants” in geophysical nature accord- ing to a table provided by [Hiscock, 2005], which was derived from the data provided by [Back et al., 1989; Freeze and Cherry., 1979]. Effective porosity (𝑛𝑒) is the interconnectedness of the
available pores that allow for fluid movement. If K values are different for all directions (𝐾𝑥 ≠
𝐾𝑦 ≠ 𝐾𝑧), then the medium is anisotropic, and K becomes a tensor (Kij). On the other note, if the
K values are the same in all directions (𝐾𝑥 = 𝐾𝑦 = 𝐾𝑧), than the medium is isotropic [Hiscock, 2005].
Darcy [1856] found out that one-dimensional flow in a pipe filled with sand is propor- tional to the cross sectional area (A), the head loss along the pipe (dh), and inversely proportional to the flow length (l). Darcy’s work became the Darcy’s Law shown in Equation 3.1. Equation 3.2 shows the Equation 3.1 rewritten to account for the solid and fluid properties [Domenico and Schwartz., 1998].
𝑸 = −𝑲𝑨𝒅𝒉
𝒅𝒍
Equation 3.1: Darcy’s Law
𝑸 = −𝒌 ∗𝝆𝒈
𝝁 𝑨
𝒅𝒉 𝒅𝒍
Equation 3.2: Darcy’s Law rewritten
In areas where geology is predominantly crystalline rock (e.g., Piedmont in Georgia), groundwater access depends on fractures. Based on Snow’s Law, Equation 3.3 provides an ex-
pression for the hydraulic conductivity and permeability within fractures in which 𝜌𝑤is the den-
sity of water, 𝑔 is the acceleration of gravity, 𝑏 is aperture of a fracture, and 𝜇 is the viscocity of
1980]. According to the Cubic Law (Equation 3.4), to calculate the discharge (𝑄), Darcy’s Law is modified to include Snow’s Equation 3.3 [Domenico and Schwartz., 1998].
𝑲 =𝝆𝒘𝒈𝑵𝒃
𝟑
𝟏𝟐𝝁 𝒌 =
𝑵𝒃𝟑
𝟏𝟐
Equation 3.3: Hydraulic conductivity and permeability within fractures
𝑸 = [𝝆𝒈𝒃
𝟐
𝟏𝟐𝝁] ∗ 𝒃𝒘 ∗
𝒅𝒉 𝒅𝒍
Equation 3.4: The Cubic Law
Aquifers have two functions: storing and transmitting water. Aquifer’s ability to transmit water is measured by its transmissivity, which is a product of K and aquifer’s saturated thickness (b) (Equation 3.5) [Ingebritsen et al., 2006; Weight, 2008]. Transmissivity is “a measure of the amount of water that can be horizontally transmitted through a unit width by the full saturated thickness of the aquifer under a hydraulic gradient of 1” [Fetter, 2001]. Basically, aquifers with high T values will have high K values and the aquifers will be thicker, which result in a minimal effect from pumping water from the aquifer.
𝑻 = 𝑲𝒃 Equation 3.5: Transmissivity
Storage of an aquifer is the volume of the water that can be released per unit area and per
change in head, which is defined by its storage coefficient or storativity (𝑆) that has dimension-
less units (Equation 3.6). In order to calculate the storativity for unconfined and confined aqui-
fer, specific storage (Ss) needs to be determined, which was the focus of studies by [Cooper
[1966]; Jacob [1940]], but specific storage will not be discussed in this section because it is out- side the scope of this project. During pump/discharge, not all the water is released by aquifer, which means the volume of the pores is not equal to the volume of the water released, or specific
yield (𝑆𝑦). This happens because aquifers retain some water in the pores, and this is called spe-
cific retention (𝑆𝑟), which is going to be greater in aquifers that have more silt and clay particles.
On the other hand, aquifers with sand and gravel will have no (𝑆𝑟), which means the (𝑆𝑦) is
equal to the porosity (Equation 3.7) [Weight, 2008].
𝑺 = −𝒗𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒘𝒂𝒕𝒆𝒓 𝒓𝒆𝒍𝒆𝒂𝒔𝒆𝒅
−(𝑨𝒓𝒆𝒂 ∗ ∆𝒉)
Equation 3.6: Storage coefficient
𝒏 = 𝑺𝒚+ 𝑺𝒓 Equation 3.7: Porosity
Water retention in the pores is caused by adhesion and the attraction of water molecules to one another is cohesion, and this phenomenon is called capillarity [Meinzer, 1923b]. In the vadose zone (zone of aeration), the water that is contained is not subject to the hydrostatic forces; instead, the water is held in the pores by the molecular attraction i.e. electrostatic force (Equation 3.8) [Fetter, 2001; Meinzer, 1923a]. Adhesion represents the water attraction to the grain (i.e., mineral surface), and cohesion represents the characteristic of water, which is hydrophilic. Elec- trostatic force is greatest at a close distance; hence, force is inversely proportional to distance as shown in Equation 3.8 [Kaufman and Anderson, 2010]. This explains why clay and fine grained sediments have enormous surface retention. In Equation 3.8, q is charge, d represents the separa-
tion distance between the two charges, and 𝐾𝑐 is the Coulomb constant.
𝑭 = 𝑲𝒄(−𝒒) ∗ (+𝒒)
𝒅𝟐
Equation 3.8: Electrostatic Force
Hydraulic head (h) is one of the most important measures in groundwater geology. Hy- draulic head is akin to energy (potential energy) as it flows from high potential energy (high h) to low potential energy (low h). Head is equal to the sum of elevation (z) of water at a measuring
point and pressure head (Ψ) of water above that point (Equation 3.9) [Fetter, 2001]. Hydraulic
gradient (𝑑ℎ
𝑑𝑙) is determined by the difference of h over distance (Equation 3.10), and 𝑑ℎ
𝑑𝑙 is pro- portional to the average velocity (Equation 3.11) [Domenico and Schwartz., 1998; Fetter, 2001]. Total porosity is inversely proportional to the average velocity. Tortuosity (Equation 3.12) is a
dimensionless ratio measurement of a tortuous flow path 𝐿𝑒and a straight line distance between
the two measuring points 𝐿[Bear, 1988; Fetter, 1999; Mishra and Kuhlman, 2013; Weight,
2008]. This would mean that with lower porosity, the tortuosity is lower and vice versa. How- ever, according to [Mishra and Kuhlman, 2013] and studies conducted by [Boudreau, 1996; Herrick and Kennedy, 1994] tortuosity cannot be determined from the porosity because of the changing geometric profile. In a brief summary, this section on aquifer properties provided a very brief overview of basic concepts about the fluid mechanics for groundwater, and all the equations from this section will be expressed in the ontology by datatype properties. For addi- tional information and details on fluid mechanics see the following references [Aris, 1989; Bear, 1988; Fetter, 2001].
𝒉 = 𝚿 + 𝐳 Equation 3.9: Hydraulic head
𝒅𝒉
𝒅𝒍 =
𝒉𝟏− 𝒉𝟐
𝒅𝟏− 𝒅𝟐
Equation 3.10: Hydraulic gradient
𝒗𝒙 = 𝑲
𝒏𝒆
𝒅𝒉 𝒅𝒍
Equation 3.11: Average velocity
𝑻 =𝑳𝒆
𝑳