Flow to Wells 6 Boundaries and Superposition Groundwater

Flow to Wells - 6 Boundaries and Superposition Groundwater Hydraulics Daene C. Mc. Kinney 1

Introduction • Wells pumping near boundaries – for an Impermeable Boundary – for a Constant Head Boundary • Multiple wells systems • Partially penetrating wells 2

Pumping a Well in a Confined Aquifer • Steady Flow y Well pumping Q r • Unsteady Flow (xw, yw)=(-a, 0) x – Theis – Jacob (u small) 3

Superposition (2 Wells pumping)

Superposition (2 Wells pumping) y Q Q x 5

Well Pumping in an Unconfined Aquifer Q Ground surface Pre-pumping Water level Pumping well y Observation well Well pumping Q r (xw, yw)=(-a, 0) h 0 h r x R Unconfined aquifer Q Bedrock 6

Flow to a Well Near a Stream (Constant Head Boundary) 7

Well Pumping in an Unconfined Aquifer Near a Stream y (Constant Head Boundary) x Real pumping well Image injection well 8

Example • A well of radius 0. 2 m produces 550 m 3/day from an unconfined aquifer with K = 10 m/day. The well is located 250 m from a river and the saturated thickness at the river is 30 m. What is the drawdown at the well? y x 9

Effect on Drawdown When Pumping Near a Stream y x 10

Flow to a Well Near an Impermeable Boundary 11

Image Well to Simulate Impermeable Boundary y x Real pumping well Image pumping well 12

Effect on Drawdown When Pumping Near an Impermeable Boundary y x 13

Pumping in a Confined Aquifer Near an Impermeable Boundary y x Steady Flow 14

Pumping in a Confined Aquifer Near an Impermeable Boundary y x Unsteady Flow Theis 15

Pumping in a Confined Aquifer Near an Impermeable Boundary y x Unsteady Flow Jacob 16

Example – Impermeable Boundary Find the drawdown in the observation well after 10 hours of pumping Q = 0. 03 m 3/s T = 6. 4 x 10 -3 m 2/s S = 3 x 10 -5 t = 36, 000 s u < 0. 01, use Jacob 17

Example – Impermeable Boundary Q = 0. 03 m 3/s T = 6. 4 x 10 -3 m 2/s S = 3 x 10 -5 t = 36, 000 s 18

Drawdown Near Impermeable Boundary 19

Superposition (n Wells pumping) 20

Example - Multiple Well System 200 m Find the steady-state pumping rate for each well so that the drawdown in each well will not exceed 2 m. T = 27. 8 x 10 -3 m 2/s rw = 0. 2 m b = 40 m R = 800 m sij = drawdown in well i due to pumping in well j 21

Example - Multiple Well System 22

Example - Multiple Well System So more drawdown at middle well for given Q 63. 36 > 59. 39 23

Partially Penetrating Wells 24

Partially Penetrating Wells 25

Partially Penetrating Wells rw = 0. 5 m b = 28 m R = 150 m Compare Q/s for each case 26

Partially Penetrating Wells 27

Partially Penetrating Wells 28

Partially Penetrating Wells 29

Summary • Wells pumping near boundaries – for an Impermeable Boundary – for a Constant Head Boundary • Multiple wells systems • Partially penetrating wells 30