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Hydrogeologic Principles 1

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Empirical law developed in 1856 for flow through porous media for saturated and unsaturated flow The flow of a fluid in a porous medium is equal to the product of a constant multiplied by the gradient of the force driving the fluid through the system divided by the porosity of the medium. where K = hydraulic conductivity (L/T), and dh/dl = fluid gradient. Q = -KiA where Q = flow rate (L 3 /T), i = fluid gradient (dh/dl) (L/L), and A = cross-sectional area (L 2 ). 2

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k = specific or intrinsic permeability (L 2 ); = mass density of the fluid (M/L 3 ); = dynamic viscosity (M/L/T); and g = acceleration due to gravity (L/T 2 ). Typical intrinsic permeability in a landfill k v = to m 2 ; k h = m 2 At very high flow rates, the flow regime changes from laminar to turbulent conditions, and Darcy’s law becomes invalid. The upper limit is defined by Reynold’s number: where q = specific discharge and d = length (mean pore dimension, or mean grain diameter). K = d 2 kgkg R e = = Inertial forces qd Viscous forces 3

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Laboratory measurement method q (rate of flow) = K h/l A Distilled water is generally used. Due to a decrease in permeability with distilled water when compared with those where pore fluid is used as the permeant, 0.1 N CaSO 4 solution should be used to properly simulate leachate or other waste liquids. l Soil Drainage h Influent liquid 4

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Field measurement methods Slug tests: instantaneous displacement of a known volume of water and recording the response with respect to time at the tested well - rising head (volume extracted) and falling head (volume added) Slug tests Injection tests and pumping tests: addition or removal of water, respectively, for an extended period of time (1 hr to several days) and recording of response (water level measurement) with respect to time at the tested well and at monitoring wells Alternative methods K (m/sec) = 0.01 d Hazen method where d 10 = effective soil particle size (mm) (10% of the particles in a sample are of smaller size). 5

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The rate of flow of water into soil through the bottom of a sealed, cased borehole is measured in each of two stages, normally with a standpipe in the falling head procedure. The standpipe can be refilled as necessary. In Stage 1, the bottom of the borehole is flush with the bottom of the casing for maximum effect of K v. The test is continued until the flow rate becomes quasi-steady. For Stage 2, the borehole is extended below the bottom of the casing for maximum effect of K h.This stage of the test is also continued until the flow rate becomes quasi-steady. The direct results of the test are apparent hydraulic conductivities K 1 and K 2. The actual hydraulic conductivities K v and K h can be calculated from these values. edu/~wang1/Fieldlist.html 6

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Determined through measurements of hydraulic head at different locations in the subsurface Saturated zone: measured using single and nested standpipe piezometers or pressure transducers Unsaturated zone: measured with hydraulic tensiometers Elevation difference of the water table, h Separation distance, l PiezometerGround surface i = hlhl 7

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For measuring pressure inside a vessel or pipe in which liquid is there, a tube may be attached to the walls of the container (or pipe) in which the liquid resides so liquid can rise in the tube. By determining the height to which liquid rises and using the relation P 1 = ρgh, gauge pressure of the liquid can be determined. Such a device is known as piezometer. To avoid capillary effects, a piezometer's tube should be about 1/2 inch or greater. It is important that the opening of the device to be tangential to any fluid motion, otherwise an erroneous reading will result. 8

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Measure the pressure head of the liquid 9

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10 1.Driver mechanism consisting of solid steel driver rod (C) and steel outer casing with flange (A) hammered into sediment to suitable depth using a cap fitting (B) 2.Driver rod (C) removed with the steel outer casing retained 3.Minipiezometer inserted into the outer steel casing 4.Outer steel casing removed with minipiezometer held in position and sediment was manually tamped around the minipiezometer. Bentonite clay can also be used to seal the annulus between minipiezometer and hole above the inlet. 5.Stilling well fitted and secured using a star picket

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11 Unconfined aquifer installation Confined aquifer installation Nested installation

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Between two fluids in contact with each other, or a fluid in contact with a solid, there is a free interfacial energy created by the difference between the forces that attract the molecules toward the interior of each phase and those that attract them to the contact surface. As these forces increase, fluids such as pore water are retained in the porous medium above the elevation of the water table. h1h1 d1d1 d2d2 h2h2 d 1 > d 2 12 h 1 < h 2

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Space that is occupied by fluids n = = Volume of the voidsV v Total unit volumeV T 13 Clay0.45~0.55 Sand0.35~0.4 Gravel0.3~0.4 Sand and gravel0.2~0.35 Peat0.85~0.9 Municipal waste0.3~0.4

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There exist nonconnected, dead-end pores through which advective migration cannot occur. Advective flow velocity (effective) That proportion of the total pore space in a rock which is capable of releasing its contained water. Clay, for example, may have a total porosity of 50% or more, but little if any of the water contained in these pores may be released, because of the retentive forces (e.g. surface tension) that hold it within the rock.pore space Clay In unsaturated flow through low-permeability soil (clay with porosity of 0.4~0.7), n e 0 15

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In the unsaturated zone, the pore spaces are partially filled with water and partially filled with air. The volumetric moisture content, For saturate flow, = n and for unsaturated flow, < n. Degree of saturation in the unsaturated zone , then, hydraulic conductivity Hydraulic conductivity (municipal refuse) 1 to 1 cm/sec (typical 1 cm/sec) = = Volume of waterV w Total volume of pore spaceV v 16

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Soil typeK, cm/sec Capillary head, cm 17 Gravel GP GW Sand SP SW 5 ⅹ Clay CL CH 3 ⅹ ~400 Refuse as placed Shredded refuse ~ Silt

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Retardation: due to interaction of chemicals with the solid phase of the porous medium where d = bulk density of the porous medium (g/m 3 ); and K d = Freundlich sorption coefficient. K d varies from zero to 10 3 L/kg; > 10 L/kg - immobile Ex. q = 1.6 m/sec; d = 1.6 g/m 3 ; n = 0.4; K d Sr +2 = 10 L/kg. R and v c ? R = /0.4 10 = 41; v = q/n = 1.6 /0.4 = 4.0 m/sec; v c = 4.0 /41 = 9.8 m/sec = = R = 1 + K d vAverage velocity of groundwater d v c Average velocity of a chemical n 18

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Advection: due to the bulk motion of the GW Dispersion: due to spreading out of the solute, molecular diffusion and mechanical mixing D l = l v + D * D * = D’ where l = dispersivity (L); D * = apparent or effective diffusion coefficient (L 2 /T); = tortuosity factor (0.01 to 0.5); and D’ = diffusion coefficient in free solution (L 2 /T). 19

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Initial conditions:C(0,t) = C 0 at t ≥ 0 C(z,0) = 0 at z ≥ 0 Boundary condition:C( ,t) = 0 at t ≥ 0 Governing Equation Solution Solution when v* 0 20

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