Hydrogeology (Lecture 7) Hydrogeological Properties
• proportional to the cross-sectional area, • proportional to the difference in hydraulic head, • inversely proportional to the travel distance. • Groundwater flow is directed from regions with high hydraulic head to regions with low hydraulic head.
For Darcys law for 1D ground water flow The volumetric flow rate or discharge is ___4 things___(?)
Dark blue = immobile water = subterranean water not participating in water movement Light blue = mobile water = subterranean water participating in water movement The volumetric share of voids which can be occupied by mobile water is termed effective porosity or flow-through porosity:
a) What is the dark blue color, explain! What is the light blue color, explain! b) How is this realted to effective porosity?
Water content realeted to a saturated clay ca 50%. 90% is not possible since there is not that much porosity.
Please estimate the water content for a fully saturated clay?
1. clay 2. silt 3. fine sand 4. gravel 5. coarse sand
Please sort the following sediments according to their effective porosity. Start with the smallest. fine sand clay coarse sand gravel silt
1. LEC: He wanted to calculate the difference between discharge and pressure levels. We measure the head difference (which is the result of the flow (flow of diffusion in this case)). • column with constant cross section (A = const.) • sand as filling material ("porous medium") • voids between sand grains completely filled with water (saturated conditions) • constant discharge through the column (Q = const.) • Purpose: to quantify the relationship between discharge, flow velocity, pressure difference, flow distance, and cross section column with water flow ( • (Q ≠ 0), arbitrarily oriented • measurement points ("standpipes" or "piezometers") for hydrostatic pressure head [blomma] = p/(ρ·g) and hydraulic head (piezometric head) h at distance L 2. A1 & A2 = Pressure head B2 = Elevation head C2 = Hydraulic head 3. Right to left Extra: We would like to know how is the pressure difference related to the sediments. Case 1 is sand case 2 is silt in the column, we put in waterpressure and we get different hydraulic heads. In silt this pressure needs to be higher, than in the sand. Silt therefore has lower hydraulic conductivity.
1. Förklara förutsättningarna för Darcys experiment med kolumnen med sand, och vad syftet var. 2. Vad är A1 & A2, B1 & B2 och C2? 3. What is the overall dircetion?
a) Transmissivity b) Hydraulic resistence c) Hydraulic conductivity d) Porosity
According to the flow direction in layered aquifers: If all layer thicknesses are identical and flow is parallel to layering, the largest discharge will pass through the layer with the highest ___a___and thus smallest___b___ . According to anisotropy of aquifers: Anisotropy of aquifers is usually associated with__c___ , other typical aquifer properties like for instance___d___ cannot depend on direction.
K = (4*Q*L)/(pi*d^2*(a1+L-a2)) = (4*250/36*10)/pi^(4)*(6+10-3)= 0,425cm/s = 4,25*10^-3m/s
Calculate the constant head
Hydraulic gradient = i = ∆h/L Första: 20+30=50 20+40=60 60-50=10 ∆h=10 L=50 10/50=0,2 På den sista: 10 + 124 = 134 10 + 17 +100 = 127 134-127 = 7 7/100 = 0,07
Calculate the flow direction and the hydraulic gradient for these 4 models.
a) No flow condition (no diffrence in head) b) from 2 to 1 c) from 2 to 1 d) from 2 to 1
Darcy's experiment allows the prediction of water movement within a column. For the following Darcy's experiments please indicate the direction of the flow within the column.
The porosity (precisely: total porosity) n of a porous medium is the relative amount of void space: n = Vv/Vt*100% n = is the porosity given in % v = volume of void space (cm^3 eller m^3) t = volume of the sample (cm^3 eller m^3)
Define porosity of a poreous medium, what is the equation for calculating porosity?
a) heterogeneity b) anisotropy
Effective hydraulic conductivity of layered aquifers depends on the orientation of the flow direction relative to the layering (parallel vs. perpendicular). On a larger scale, it may not be possible to identify or resolve inhomgeneities like thin layers, small lenses, shape and orientation of grains (see figure) etc. Nevertheless, hydraulic conductivity appears to be direction-dependent when groundwater flow is quantified at the larger scale. In these cases, small scale __a__ (e.g. due to layering) expresses itself as __b__ of hydraulic conductivity at the larger scale.
The measured hydraulic heads here are: (pressure head + elevation head = hydraulic head) h1 = [blomma]1 + z1 h2 = [blomma]2 + z2 here: h1 < h2 (alos seen in the figure) Thus, flow is from cross section 2 towards cross section 1. Differences of hydraulic head are independent from the position of the origin of the z-axis!
Explain what is happening here (flow direction)?
The difference n - ne is termed specific retention or field capacity. Specific retention is the volumetric share of water which is retained in the porous medium after drainage due to gravitation.
Explain what specific retention is?
L = flow distance A = flow through area h = hydraulic head diffrence K = hydraulic conductivity Q = discharge
Groundwater movement can be described by Darcys law: Q=−A⋅KΔhLQ=−A⋅KΔhL Please assign the following symbols to the individual measures of the equation.
porous media aquifer (gravel) = 77 m/d porous media aquifer (sand) = 0.6 m/d fractured bedrock aquifer = 700 m/d karstic aquifer = 5300 m/d
Groundwater moves in the underground with a specific velocity. Please assign to each of the following aquifer types a typical groundwater velocity. porous media aquifer (gravel) porous media aquifer (sand) fractured bedrock aquifer karstic aquifer with+ 5300 m/d 0.6 m/d 700 m/d 77 m/d
Hazen equation K = Cd10^2 C= constant between 100 and 150 to satisfy the equation (with K in [m/s]) C needs to have the unit (cm*s) Value for the constant à empirical • d10 = grain size for which 10% of grains are finer, also known as effective grain size • d60 = grain size for which 60% of grains finer • uniformity coefficient U=d60/d10; if U<5 then well sorted
How can you calculate hydraulic conductivityfrom grain size distribution? What is the equation
ΔVw'/Vw = relative change in water volume αw= compressibility of water [LT²/M] Δpw = hydrostatic pressure change [M/L/T²] ΔVw'/Vw = αw*Δpw (Increase / Decrease in hydrostatic pressure results in an inflow / outflow of water) ΔVw' = αw*Vw*Δpw = n*αw*VT*Δpw= n*αw*VT*pw*g*Δ[blomma] Δ[blomma] = change in pressure head [L] n = total porosity [-] VT = represents a change in volume of the porous medium as a whole.
How do you calculate Change in Water Volume Invoked by Δpw = ΔVw' (Δpw --> the water pressure)
Effective porosity ne: Interconnected pore space/bulk volume • Effective porosity is most commonly considered to represent the porosity of a rock or sediment available to contribute to fluid flow through the rock or sediment (thus: not a property relevant in unsaturated materials) • Excluded from fluid flow are: - Water in pores so small they do not allow the passage of a water molecule - Water bound to the surfaces of solids - Water in pores which are not connected to others
How do you calculate effective porosity? What is it?
i = ∆h/L
How do you calculate hydraulic gradient?
Confined aquifers: saturated thickness = aquifer thickness m. Transmissivities in a confined aquifer: Tx = Kx*b Ty = Ky*b with Kx and Ky are vertically averaged hydraulic conductivities [L/T] along the x - and y - coordinate For a horizontally isotropic confined aquifer we simply have T = K·b
How do you calculate transmissivity in confined aquifers?
Unconfined aquifers: saturated thickness = difference between hydraulic head h and the elevation head zbot of the aquifer bottom. Tx = Kx*(h-zbot) Ty = Ty*(h-zbot) If the aquifer bottom is horizontal, it is convenient to use this level as reference level (z = 0).
How do you calculate transmissivity in unconfined aquifers?
(hydrostatic) pressure head [blomma] = p/(p·g) p(pressure) = pgL (densitet * gravitations konstant * höjden(?) L = p/pg = pressure/densitet * gravitations konstant Why is this important? Pressure diffrence? - Yes There is a flow!
How do you calcultae pressure head.
250 litres 25% mobile porosity
How much water can appox be pumped out of a volyme of 1 cubicmeter?
Vv = 75 --> (75/200)*100= 37,5% Vv = 85 --> (85/200)*100= 42,5%
How much water can be filled in a 200 cm^3 cylinder filled with sediments? Vt = 200 cm^3 Vv = 75 Vv = 85
1 Clay (smallest) 2 Silt 3 silty sand 4 coarse sand 5 gravel (most)
Hydraulic conductivity is the volumetric flow rate through a unit corss section under a unit hydraulic gradient and depends on the properties of the fluid and the porous media. Please sort the following soiGravell textures from the smaller (1) to higher (5) hydraulic conductivity value
4. The grain diameter for which x% mass of the sieved material is smaller than this diameter.
In the following granulometric curve, the value for dx denotes: 1. The grain diameter for which x% volume of the sieved material is higher than this diameter. 2. The grain diameter for which x% mass of the sieved material is higher than this diameter. 3. The grain diameter for which x% volume of the sieved material is smaller than this diameter. 4. The grain diameter for which x% mass of the sieved material is smaller than this diameter.
Constant head permeameter CHP falling head permeameter FHP both B suitable for silt FHP The discharge varies with time FHP the hydraulic head is measured B suitable for fine sands B The amount of discharge is measured CHP suitable for coarse sand CHP duration of the experiment can be long (up to several hours)FHP
Permeameter are used to determine the hydraulic conductvity in the laboratory. There are two fundamental setups for permeameters. Please indicate in the follwing, which statements belong to those setups (or to both). suitable for silt The discharge varies with time the hydraulic head is measured suitable for fine sands The amount of discharge is measured suitable for coarse sand duration of the experiment can be long (up to several hours)
a) larger b) smaller c) increase
Please complete the following statements about porosity and sediment types. - Well sorted unconsolidated porous media exhibit __a___total porosities in comparison to poorly sorted ones. - Total porosity of consolidated porous media is usually __b__ than total porosity of unconsolidated porous media. - For unconsolidated porous media, total porosity tends to __c__ with decreasing grain size.
Storativity = Sy+bSs 0.17 + 195 m * 9 x 10-5 m-1 = 0.19
Please compute the Storativity for the follwong unconfined aquifer: aquifer thickness = 195 m hydraulic conductivity = 2.7 x 10-3 ms-1 total porosity = 0.21 specific yield = 0.17 specific storage = 9 x 10-5 m-1
197 m * 8.6 x 10-3 ms-1 = 1.69
Please compute the transmissivity for the following aquifer setup: aquifer thickness = 197 m hydraulic conductivity = 8.6 x 10-3 ms-1 total porosity = 0.14 specific yield = 0.11 specific storage = 6 m-1
Diameter of the soil particles
Porosity depends on some characteristics and parameters of the porous media within an underground structure. Please indicate for the following list, from which parameters porosity is independent (mark the most adequate): Diameter of the soil particles Arrangement of the soil particles Mixture of the different grain sizes Shape of the grains
Volumetric water content --> Ratio between volume of water and total volume Degree of saturation --> Ratio between volume of water and volume of voids Total porosity --> Ratio between volume of voids and total volume Bulk density --> Ratio between particle mass and total volume
Relate the following terms with its correspnding calculation: Volumetric water content Degree of saturation Total porosity Bulk density
a) Homogenious isotropic b) Homogenius, anisotropic c) Hetrogenius, isotropic d) Hetrogenious, anisotropic
Right the combinations of heterogeneity and anisotropy with respect to a vertical cross-section (coordinates x and z).
a) aquiclude b) aquitard c) aquifuge
Subterranean formations can be classified by the capability to store and/or transmit groundwater under natural conditions. According to this, choose the correct term in the following definitions: 1. An ___a__can store groundwater but cannot transmit it. 2. An __b__can store and transmit groundwater but to a much lesser extent than a adjacent groundwater reservoir. 3. An___c__ can neither store nor transmit groundwater
The grain size distribution. • The grain size distribution is therefore frequently determined in laboratory experiments in order to deduce important flow properties. • There are five major grain size classes (ordered by increasing diameter): clay, silt, sand, gravel, cobbles (or debris) • The classes for silt, sand and gravel are usually subdivided by "fine", "medium", and "coarse" (or "very fine", "fine", "medium" „coarse", and "very coarse"). • Different ranges for individual grain size classes have been defined by different authorities or regulators!
The ability of unconsolidated porous media to transmit water is highly dependent on one factor, which is?
-0.2
The figure shows the setup for the Darcy experiment. The direction of the x-axis is pointed from left to right (see figure). Please compute the hydraulic gradient. The following data are given: a = 0.80 m b = 0.21 m c = 0.49 m d = 0.15 m e = 1.80 m The computed hydraulic gradient is
- The degree of saturation equals volumetric water content over total porosity. - The water content exceeds the effective porosity in the capillary fringe - When volumetric water content equals total porosity, means that degree of saturation equals 1
The following sentences relate degree of saturation, volumetric water content and porosity in porous media. Please select which are true: - The degree of saturation equals volumetric water content over total porosity. - The water content exceeds the effective porosity in the capillary fringe. - When degree of saturation equals 1, means that there is no water within the voids. - When volumetric water content equals total porosity, means that degree of saturation equals 1. - The degree of saturation cannot exceed the total porosity in a defined volume.
Fine sand = -5 Clay = -9 Coarse gravel = -1
The hydraulic conductivity K describes groundwater flow in the subsurface. Please assign the following K-values with the respective sediment classes.
Hydraulic head: h(z) = (p(z)/pg) + z Pressure head: [blomma](z) = p(z)/pg Elevation head = z
The state of groundwater is characterized by heads. Please assign the correct formula to the different heads.
Solid phase - mineral grains - organic matter: remains of plants and animals that are undergoing decay Liquid phase - mainly water (if contaminated, others can be involved!) - containing dissolved solutes and gases Vapor phase - "air" but with different composition, e.g. much higher CO2, CH4
The unsaturated Zone is typically a three-phase system, which contains of:
Sandstone: Fractured porous medium: Genesis of fractures or cracks due to mechanical or thermal processes (stress / strain or cooling / warming) Gypsum: Karstified porous medium: Genesis of fractures or tubes (conduits) due to chemical processes (i.e. dissolution of rock by water)
These are consoludated porous mediums, can you give a more detailed name of the sandstone and the gypsum?
True
True or false? For unconsolidated porous media, total porosity tends to increase with decreasing grain size.
Storativity Hydraulic gradient
Various parameter describe hydrogeological properties. Please indicate in the following the dimensionless parameters. Specific storage Hydraulic conductivity Hydraulic head Hydrostatic head Storativity Hydraulic gradient
Most important ones • gravity • attractive forces between water molecules (cohesion) • attractive forces between water and solids (adhesion, see figure).
What are the most active forces for water movement in a porpous medium?
Effective vs. Total Porosity • Effective porosity cannot exceed total porosity, i.e. ne ≤ n • The difference n - ne is termed specific retention or field capacity. a) Effective porosity b) Total porosity
What does this graph illustrate? What is a and b?
The volume of water released from an aquifer per unit surface area of the aquifer and per unit change in head. Eq: For confined aquifers S = Ssb Storativity can be interpreted: • volume of water • released from an aquifer volume extending from the aquifer bottom up to the aquifer top • over a unit area • if the hydrostatic pressure is reduced by one unit. • Storativity is dimensionless. (like porosity) Def.of storativity: unchanged in principle but the considered aquifer volume now extends from the aquifer bottom up to the water table. For unconfined aquifers: Storativity values correspond to effective porosities / specific yield. • Explanation: free groundwater table --> Pressure changes lead to filling or emptying of voids. • This is fundamentally different from the storage properties of confined aquifers: all voids remain filled and storage properties depend on the compressibilities of water and the porous medium. The reference volume for defining storativity S is a cuboid (Rätblock) extending from the aquifer bottom to the aquifer top over a unit area (e.g. A= 1 m² and VT = A·m).
What is Storativity? What is the storativity for confined versus unconfined aquifers?
Permeameter = instrument to determine hydraulic conductivity; design based on Darcy's experiment. • Permeameters --> to determine hydraulic conductivities of soil samples in the laboratory. • Two types: • constant-head permeameter • falling-head permeameter
What is a Permeameter? There are two types, which are these?
A porous medium or a porous body is a solid containing voids (or holes). The subsurface can be regarded a porous medium. Voids may have very different shapes (interstitial between ball-like grains, planar crack-like fractures, cylindrically shaped tubes or conduits etc.). Voids may be connected to or disconnected from each other. Voids may contain fluids (mostly air and / or water). Size, shape and connectivity of voids are influential for the ability of the porous medium: - to store water - to transmit water
What is a Porous medium?
sediments consisting of fluvial deposits of sands and gravels
What is a Unconsolidated porous medium?
Q = volumetric flow rate [m3/s or l/s] q = flux[m/s]; Darcy flux or Darcy velocity "flow rate independent of an area"
What is a and what is b?
Frequently, people wish to represent the spatial distribution of hydraulic conductivity in a heterogeneous aquifer by an average value such that steady-state groundwater discharge remains the same as in the heterogeneous case. This average K value is termed effective hydraulic conductivity. Effective hydraulic conductivity: - for a fictitious homogeneous aquifer - with same discharge / same overall head difference (under steady-state conditions) - as a heterogeneous aquifer.
What is effective hydraulic conductivity?
Example: Transport of a salt-tracer by advection Jadv = advective mass flow [M/T Q = discharge [L^3/T] c = concentration [M/L^3]
What is this equation?
Relevant in confined systems and it is the compressiability of water and sediments. For a confined aquifer or aquitard, storativity is the vertically integrated specific storage value. Specific storage is the volume of water released from one unit volume of the aquifer under one unit decline in head. This is related to both the compressibility of the aquifer and the compressiility of the water itself. Therefore, if the aquitard is homogeneous Equation: Ss = 1: Ss = ΔVw/VT*Δ[blomma] 2: Ss = (n*αw+αpm)pw*g αpm = compressibility of the porousm medium pw = hydrostatic pressure Typical values for specific storage range from 10^-6 1/m (e.g. gravel) to 10^-2 1/m (e.g. clay). IMPORTANT: Due to their relatively large lateral extent, aquifers are mostly considered as spatially two- dimensional (2D) systems. --> Specific storage Ss is replaced by storativity or storage coefficient S The reference volume for defining specific storage Ss is a unit cube (e.g. VT = 1 m³)
What is specific storage?
Relevant in unconfined systems: Specific Yield (drainable Porosity) The specific yield is the ratio of the volume of water which will drain from a porous medium by gravity to the volume of the porous medium. Fine grained sediments can have high total porosity but very low specific yield (fig)!
What is specific yield?
storage properties are physical properties that characterize the capacity of an aquifer to release groundwater. These properties are storativity (S), specific storage (Ss) and specific yield (Sy).
What is storage properties in hydrogeology?
Continuity equation: Q = A·v = const. with v = flow velocity [L/T] Lec: Continuity: Mass conservation is important here. Area is higher but velocity is smaller In wiki: In fluid dynamics, the continuity equation states that the rate at which mass enters a system is equal to the rate at which mass leaves the system plus the accumulation of mass within the system.
What is the Continuity equation?
homogeneous: if its properties do not vary in space. heterogeneous: (inhomogeneous) if at least one of its properties varies in space. Consequence: K=K(x,y,z) for a heterogeneous aquifer. (Of course) groundwater flow is affected by aquifer heterogeneity. Impact of aquifer heterogeneity even more relevant with regard to the transport of solutes. For aquifers usually: heterogeneity or homogeneity related to hydraulic conductivity.
What is the diffrence of a homogeneous medium versus hetrogenus medium?
Flow parallel to layering: - Effective hydraulic conductivity equals the weighted arithmetic mean of layer conductivities. Flow perpendicular to layering: - Effective hydraulic conductivity equals the weighted harmonic mean of layer conductivities. - Weights are given by relative layer thicknesses. - harmonic mean of a set of positive numbers cannot exceed the arithmetic mean. - Usually: "harmonic mean < arithmetic mean". --> flow direction perpendicular to the layering is associated with a smaller effective hydraulic conductivity than the flow direction parallel to the layering.
What is the effective conductivity for flow parallel to layering versus Flow perpendicular to layering?
Intrinsic permeability (also called specific permeability or absolute permeability) of nonwoven fabric depends solely on the nonwoven fabric structure and represents the void capacity through which a fluid can flow. Relationship between material (e.g clay) and the permeability and hydraulic conductivity.
What is the intristic permeability?
A rock with zero porosity is impermeable. But: Rocks with a relatively high porosity can be (almost) impermeable as well (e.g if voids are not connected, tuff). For certain rock types, especially medium and coarse clastic sediments (sand, gravel, sandstone, conglomerate) a correlation between porosity and permeability exists. But in principal, hydraulic conductivity can not be expressed as a function of porosity.
What is the realtionship between hydraulic conductivity and Porosity?
The soil water saturation Sw is the volume of the contained water divided by the volume of the voids
What is the soil water saturation? What's the equation?
The volumetric water content of the soil is the volume of the contained water divided by the total volume of the soil.
What is the volumetric water content? What's the equation?
0.50 Water content: amount of water compared to the whole volume. 100% is therefore not possible.
What is the water content for fully saturated clay?
Example: Transport of a salt-tracer by diffusion JDiff = Diffusive mass flow [M/T] A = Area [L2] ∆c = Concentration difference [M/L3] D = Diffusion-Coefficient [L2/T] L = Distance [L]
What is this equation?
Hydraulic head equation (sum of pressure head and elevation head) What drives the water flow --> diffrence in hydraulic heads. h(z) hydraulic head [L] P(z)/p*g = pressure head (z = L) z = elevation head
What is this equation?
Darcy's Law Equation (discharge or voumetric flow rate) Q = discharge [L³/T] A = total cross-sectional area [L²] K = hydraulic conductivity [L/T] ∆h = hydraulic head difference [L] L = distance
What is this equation? Explain the variables.
consolidated rock with fractures
What is this?
Product of a vertically averaged conductivity with the saturated thickness (= distance from aquifer bottom to a level up to which all pores are filled with water) = transmissivity (T). Eq. T = Kb (K = conductivity b =thickness) Aquifers frequently treated as 2D systems (lateral extension >> than vertical extension) vertical variations in hydraulic conductivity are neglected rather, vertically averaged values are employed.
What is transmissivity and why should we consider it?
a) Loosed packed sediments b) dence packed sediments The process of sedimentation always leaves pore spaces, thus unconsolidated sediments always have pores. Maximum porosity: well sorted sediments without any compaction, and rearrangement of particles. Stresses like comapaction, shear forces, diagenesis, metamorphism vibration. Porosity are also affected by the influence of grain geometry which depends on depends on mineralogy: e.g. quartz, isotropic tends to form spherical grains. sheet silicates (mica) will form flat, band and chain silicates elongated grains certain minerals will never be round (calcite, [feldspar]). Sorting is also affceting porosity!! Total porosity depends on the grain size distribution which is a consequence of grains with diffren size.
What the diffrence between these two? And what is maximum porosity? There are factors that effects the porosity of sediments, what are these factors?
- Gravity (most important) - Ytspänning (cohesion) - Attractive forces between water and soild (adhesion) - Diffusion (?)
Which are the acting forces that defines how the water behaves?
- Pore (fracture) connectivity - Pore size & and pore size distribution - Pore orientation (since hydraulic conductivity is a tensor) - Pore geometry
Which factors affect the Hydraulic conductivity?
c) n = Volume of voids/Total volume
Which of the following ratios represents the correct formula for porosity (n): a) n = Volume of voids/Water volume b) n = Volume of solids/Volume of voids c) n = Volume of voids/Total volume d) n = Volume of voids/Volume of solids
Constant head permeameter K = QL/A(hin-hout) with Q= discharge [L³/T] L= length of sample [L] A= cross-sectional area of sample [L²] hin= hydraulic head at column inlet [L] hout = hydraulic head at column outlet [L] hout can be set equal to zero as only head differences are important. Explanation: Hydraulic heads at inflow and outflow of the Darcy column are constant in time. As a consequence, the discharge is not changing with time.
Which permemeter is this, how do you calculate hydraulic conductivity with this instrument? Explain!
with L = length of sample [L] dc= diameter of sample cylin-der [L] dt= tube diameter [L] t = time interval [T] hin(0) = initial hydraulic head at co-lumn inlet [L] hin(t)= final hydraulic head at co-lumn inlet [L] hout = hydraulic head at column outlet [L] Explanation: The hydraulic head at the outflow of the Darcy column is not changing, but the hydraulic head at the inflow is decreasing with time. As a result, the discharge also decreases with time. Larger experimental time periods are needed for the falling-head permeameter, in particular if hydraulic conductivity is low. On the other hand, no measurement of discharge or water volume is required.
Which permemeter is this, how do you calculate hydraulic conductivity with this instrument? Explain!
Clay (Clay however, can have a larger porosity as the particles are not spherical and can be arranged such that larger pore spaces are possible. Basically, the average grain size has no influence on the total porosity)
Which sediments has (usually) the larger porosity?
Two reasons for this: - Variability of hydraulic conductivity is much more pronounced; - Data about variability of storativity or porosity are scarce.
Why are storativity and porosity treated as spatially constant usually?
Ss: needed to establish equations of groundwater flow based on the physical/mechanical behavior of porous material (control volume); regard the flow process independent from aquifer geometry, just look at the properties of the material: --> general description of groundwater flow in porous media S: for practical reasons, Ss is not (really) measurable in the field (and difficult in the lab); an aquifer test (Topic 9 ) typically yields S
Why distinguish between Storativity/Specific storage?
a) if its properties are independent of direction b) at least one of its properties is dependent on direction Anisotropy of aquifers is associated with hydraulic conductivity. Other aquifer properties like storativity or porosity cannot depend on direction. • Groundwater flow is affected by anisotropy. However, in unconsolidated aquifers the impact of heterogeneity is usually more important.
a) A solid or a porous medium is isotropic if...? b) A solid or a porous medium is anisotropic if...?
Sw = Vw/Vv 0v = Vw/Vt
a) How do you calculate soil water saturation (Sw)? b) How do you calculate volumetric water content (0v)?
a) dx denotes the grain diameter for which x % (in mass or weight, not volume!) of the sieved material is smaller than this diameter. b) d10, d60 (and others) are of practical importance with regard to groundwater flow properties. The ratio of d60 and d10 is called coefficient of uniformity U, and is calculated: U = d60/d10 Based on these data, other parameters can be determined, for example hydraulic conductivity
a) What is dx symbolyzing? b) What is coefficient of uniformity? How and why do we calculate this?
a) q =Q/A b) va = q/ne ne = effective porosity (dimentionless) Interconnected pore space /bulk volume (diffrent values for diffren sediments). In its simplest and traditional form, effective porosity ne is ne = q/v were v = where v is the mean velocity of a conservative tracer were q = and q is the specific discharge, or Darcy velocity
a)How do you calculate specific discharge? b) Related to the question "How long need water to reach a point in the distance" we want to figure out the velocity of water molecules or particles (named average velocity Va). And what is effective porosity?
if a flow is parallel to the layering, whats the equation for the effective hydraulic conductivity?
byt sida! In the above equation, effective hydraulic conductivity K is obtained as the weighted harmonic average of layer conductivities Ki. Weights correspond to relative thicknesses mi/m • The largest term in the sum contributes most to the harmonic average . The above equation can therefore be approximated by K ≈ m/max(mi/Ki)