Published on January 1, 2008
Slide1: Karst Hydrology – Basic Concepts Basic hydrological concepts, terms and definitions Aquifers Rock formations that store, transmit and yield economically significant amounts of water are aquifers Three types of aquifers: confined, unconfined and perched Aquifers also differentiated into 3 end member types due to nature of voids in which water stored and transmitted….. Slide2: Flow through pores and pipes What is the main issue about conventional groundwater hydrology when applied to karst? Some terms: Pressure head Hydrostatic Hydraulic head (h) Hydraulic potential (Φ) Since gravitational acceleration is constant near surface h and Φ are closely related Slide3: Specific discharge (u) is flow of water through tube, which is proportional to hydraulic head loss (Δh) between one end of tube and the other (Poiseuille’s Law): r = radius, μ = viscosity of water, l = length of tube Darcy found amount of water flowing through porous medium proportional to difference in total h, represented by hydraulic gradient (dh/dl) between inflow and outflow points This is Darcy’s law: Q = discharge, a = cross-sectional area, K = hydraulic conductivity K reflects properties of medium and fluid and permeability (k) is ability of medium to transmit fluid These two terms are related: ρ = mass density, μ = viscosity, g = acceleration of gravity Slide4: K has dimensions of velocity (L/T) expressed as m/s. k is L2 Expressed as darcy units, 1 darcy = 10-8 cm2. Darcy’s Law assumes laminar flow. What is it and how does this compare to turbulent flow? Karst enhancement of porosity Karst’s porosity changes with time. How? What is the difference between porosity and effective porosity? Pore size will influence water flow in an unconfined aquifer, and in karst system with interconnected voids of 1-103 mm, will yield all water freely. Slide5: Homogeneous and isotropic aquifers Well sorted sand and gravel aquifers have constant porosity and k, K independent of position within formation (homogeneous) Heterogeneous are those where K varies within formation How do isotropic and anisotropic aquifers differ? Karst aquifers become heterogeneous and anisotropic with time. Darcy’s Law only applied at regional scale. Conceptualize karst aquifer as rock pierced by vertical capillary tubes, below diagram shows how tube diameter and % porosity affect K. Slide6: Transmissivity and storage Ease of flow through aquifer varies according to direction. How? K is not constant for large distances, and vertical K decreases with depth. Why? Transmissivity (T) is aquifer’s ability to transmit water, dependent on? Specific discharge from aquifer is proportional to hydraulic gradient, so decrease hydraulic head, decrease outflow. What is storage capacity for an aquifer? Unconfined aquifer its called specific yield (Sy), confined? Storativity (S) in confined aquifer is product of….. Sy varies with vertical position in rock because effective porosity also varies vertically. Slide7: Flow nets Aquifers 3-D phenomena, must consider variations in hydraulic potential throughout aquifer. Flow net made up of: equipotential surfaces horizontal plane vertical plane streamline Mesh of equipotentials and streamlines are the flow net. How does water flow within net? Flow nets in vertical plane parallel to hydraulic gradient of water table flow to converge near valley floor or at coast What happens if conduit traverses a saturated zone? Slide8: Fresh water/salt water interface Near coast, water table declines towards sea level. Inland fresh water overlies salt water. Depth below sea level of interface (Zs) related to…. Ghyben-Herzberg principle states: So if density of fresh water is 1.0, density of salt water is 1.025, under hydrostatic equilibrium, depth of interface is 40x height of water table above sea level Important consequence of this is….. Under hydrodynamic conditions interface is deeper… Slide9: Interface is a zone and not a abrupt discontinuity, and much of fresh water escapes through sea bed, suggesting…. Applicability of Darcy’s Law to Karst Can karst be treated as porous medium in Darcian sense? Alternative is to treat aquifer as interconnected conduit system in porous matrix, focus on input/output, i.e. the spring hydrograph Assuming hydrograph is realistic representation of network Slide10: Another problem with Darcy’s Law is issue of laminar flow…. Use Reynold’s Number (Re) to different between turbulent and laminar which can be used to determine upper limit of Darcy’s law: Found that Darcy’s Law holds if Re between 1-10. Even if conduits increase in diameter, if velocity low, get laminar Under laminar flow, discharge of pipe using Poiseuille’s Law shows discharge is directly related to? Also use Hagen-Poiseuille equation: If flow turbulent, calculate discharge using Darcy-Weisbach equation: Where f is friction factor. In turbulent pipe, wall friction increases to a quadratic dependence of shear stress () on mean water velocity (v) – Darcy-Weisbach friction law: Slide11: Rearrange equation to find friction factor. Relative roughness (Rf) on flow boundary (walls of pipe) described by ratio of pipe radius (r) to length (e) representing size of features contributing to roughness. Relation between the two can be seen in below diagram: Relation between f and discharge is that f decreases with increased discharge until it obtains constant value. In simple conduit study, f related to hydraulic radius of passage and scallop size of walls.