Presentation on theme: "Yhd Soil and Groundwater Hydrology"— Presentation transcript:
1Yhd-12.3105 Soil and Groundwater Hydrology Steady-state flowTeemu KokkonenTelRoom: 272 (Tietotie 1 E)Water EngineeringDepartment of Civil and Environmental EngineeringAalto University School of Engineering
2Aquifer types Aquifer Confined aquifer Latin: aqua (water) + ferre (bear, carry)An underground bed or layer of permeable rock, sediment, or soil that yields waterConfined aquiferBetween two impermeable layersGroundwater is under pressure and will rise in a borehole above the confining layerUnconfined aquifer (phreatic aquifer)Groundwater table forms the upper boundary
4Some Terms Saturated zone (vadose zone) Pore space fully saturated with waterGroundwater level (water table)Is defined as the surface where the water pressure is equal to the atmospheric pressureIn groundwater studies the atmospheric pressure is typically used as the reference point and assigned with the value of zeroCapillary fringeSaturated (or almost saturated) layer just above the grounwater levelUnsaturated zoneBoth water and air are present in the pore space
6Equation for Groundwater Flow Steady state 1D Inflow per unit time Qi = 2 l s-1Inflow per unit time and unit area (influx) qi = 2 l s-1 / 0.4 m2 = 0.5 cm s-1When the water level in the container does not change it is in steady-stateThe influx and outflux must then be equal to each otherOutflow per unit time Qo = 2 l/sOutflow per unit time and unit area (outflux) qo = 0.5 cm s-1
7Equation for Groundwater Flow Steady state 1D Darcy’s lawConservation of momentumContinuity equationConservation of massIn steady state conditions the amount of stored water does not changeThe outgoing flux must equal the incoming flux
8Equation for Groundwater Flow Steady state 1D Conservation of massInserting Darcy’s law to describe the flux q yields:Under the assumption of homogeneity:Laplace equation in 1D
9Equation for Groundwater Flow Steady state 3D The groundwater equation just derived in one dimension is easy to generalise to three dimensionsAnalogous analysis to the previous slide yields for the homogeneous 3D case:
10Equation for Groundwater Flow Steady state 2D Typically thicknes of aquifers is relatively small compared to their areal extent, which justifies the assumption of essentially horizontal flow
11Exchange of Water: Sink or Source An aquifer can receive (source) or loose (sink) water in interaction with the world beyond its domainSource: recharge from precipitation, injection wellsSink: pumping wellsIn the groundwater equation added or removed water is described using a sink / source term
12Equation for Groundwater Flow Steady state 2D, Sink / Source qx(x) = 9 ? qx(x+Dx) = 6 ?qy(y) = 2 ? qy(y+Dy) = 5 ?Dx = 3 ? Dy = 2 ? b = 2 ?R = -1 ?Explain in your own words what water balance components the circled terms in the above equation represent. Use then the values given below to compute their values assuming that the derivatives are constant within the rectangular control volume. Give also units to the quantities listed below.
13Equation for Groundwater Flow Steady state 2D, Sink / Source
14Equation for Groundwater Flow Steady state 2D, Sink / Source How does the equation change if the aquifer is homogeneous?How does the equation change if the aquifer is isotropic?Defining transmissivity T to be the product of hydraulic conductivity K and the thickness of the water conducting layer b yields:
15Equation for Groundwater Flow Steady state 2D, Sink / Source Does R vary in space? When?Does T vary in space? When?
16Boundary Conditions Governing equation for groundwater flow Describes how the water flux depends on the gradient of the hydraulic head (Darcy’s law)Requires the mass to be conservedTo represent a particular aquifer boundary conditions need to be definedBoundary conditions describe how the studied aquifer interacts with the regions surrounding the aquifer
17Boundary Conditions Two main categories Constant head (fixed head, prescribed head)Dirichlet conditionWater bodies (lakes, rivers)Constant fluxNeumann conditionImpermeable boundary is a common special case (clay, rock, artificial liners...)
18Numerical Solution Steady-state 1D DxHomogeneous aquiferLet us derive a numerical approximation for the steady-state 1D groundwater flow equation.Step 1. How would you approximate the spatial derivative between nodes i and i+1?Step 2. How would you approximate the spatial derivative between nodes i-1 and i?Step 3. How would you approximate the 2nd spatial derivative around node i?
19Numerical Solution Steady-state 1D Geometric averageHeterogeneous aquiferDxLet us again derive a numerical approximation for the steady-state 1D groundwater flow equation.How to compute and ?
20Numerical Solution 2D Steady-state Flow, Sink/source Term j
21Boundary Conditions Numerical Solution Hydraulic head to be computed from the groundwater flow equation.Hydraulic head set to a fixed value representing the level of the lake.Hydraulic head value is ”mirrorred” across the no-flow boundary.Lake H = 10 mIIIClay (almost impermeable)HII = HIHydraulic gradient across this line becomes zero => no flow