Flow in Aquifers 1 Confined Aquifer Flow Groundwater

Flow in Aquifers – 1 Confined Aquifer Flow Groundwater Hydraulics Daene C. Mc. Kinney 1

Summary • Confined Aquifer Flow – Continuity Equation – Steady Horizontal Flow – Transmissivity 2

Horizontal Flow Approximation • Previously used CV approach to develop continuity equation for flow in porous media. • Now we want to focus on groundwater flow in aquifers (confined and leaky to begin). • Flow in aquifers is essentially horizontal. • Instead of considering flow as three-dimensional, with • we may treat the problem in terms of an average head, • Where the average is taken along a vertical line extending from the bottom to the top of the aquifer 3

Aquifer Transmissivity • Transmissivity (T) – Discharge through entire thickness of an aquifer per unit width per unit head gradient Hydraulic gradient = 1 m/m ri et it om n te Po – Volume of water released from (or added to) storage in the aquifer per unit horizontal area per unit decline (or rise) of the average (over the vertical) piezometric head in the aquifer b B ing n nfi Transmissivity, T, volume of water flowing an area 1 m x b under hydraulic gradient of 1 m/m ce fa ed Co • Storativity (S) ur c. S 1 m 1 m Co ne nfi qu d. A r ife 1 m Conductivity, K, volume of water flowing an area 1 m x 1 m under hydraulic gradient of 1 m/m 4

Flow in a Confined Aquifer Darcy’s law Ground surface Head in confined aquifer Confining Layer b qx Confined aquifer K h b Bedrock 5

Continuity Equation in a Confined Aquifer • 6

Flow in a Leaky Aquifer Ground surface Water table in unconfined aquifer Head in confined aquifer h 0 Leaky Confining Layer K’ b b’ Leakage from above qx Confined aquifer K h b Bedrock Datum, z = 0 7

Flow in a Leaky Aquifer • 8

Continuity Equation in a Confined Aquifer • Homogeneous aquifer (K = constant) • Steady flow • No leakage • One-dimensional flow 9

Well in a Leaky Aquifer • Dirac delta function 10

Notation • Gradient operator – Rectangular coordinates – Cylindrical coordinates • Divergence – Rectangular coordinates – Cylindrical coordinates • Laplacian – Rectangular coordinates – Cylindrical coordinates 11

Groundwater Notation 12

1 -D Steady Flow in a Confined Aquifer • Find the head in a homogeneous, confined aquifer with steady flow from left to right Governing equation Simplifications: steady, 1 -D flow, T = Constant, No leakage Ground surface Confining Layer Head in the aquifer Confined aquifer h. A z y x Bedrock Qx K h. B b L 13

Steady Flow in a Confined Aquifer • Ground surface Confining Layer Confined aquifer h. A=100 m z y x Bedrock Qx K=2 -m/d b h. B=80 m L=1000 m 14

Summary • Confined Aquifer Flow – Continuity Equation – Steady Horizontal Flow – Transmissivity 15