# Solution to Exercise 5

5) A factory is disposing of hot waste water by injecting it into a 1000 m deep well that penetrates a confined aquifer. The sandstone aquifer contains water at 35 °C, a similar temperature as the waste water. A regulator wanted the company to model how far the contaminated water would travel in the aquifer over a 10-year period. Hydraulic conductivity values were sparse. They required the company to core part of the 50 m thick confined aquifer and determine a representative value of hydraulic conductivity. A portion of the core was placed in a constant head permeameter as illustrated in the accompanying figure.

5a) If an average of 34.0 ml/min was collected at the outlet, what is K in cm/s?

Hydraulic conductivity can be determined by rearranging Equation 15 of this book

where:

 Q = volumetric flow rate (L3/T) K = hydraulic conductivity, is the proportionality constant reflecting the ease with which water flows through a material (L/T) Δh = difference in hydraulic head between two measuring points as defined for Equation 14 (L) ΔL = length along the flow path between locations where hydraulic heads are measured (L) = gradient of hydraulic head (dimensionless) A = cross-sectional area of flow perpendicular to the direction of flow (L2)

Rearranging:

5b) If the laboratory experiment was completed using 15 °C water, what is the intrinsic permeability of the sandstone in cm2?

If the test was conducted at 15 °C, the intrinsic permeability, k, of the sandstone in cm2 can be calculated using Equation 31 of this book, using the relationships for the physical properties of water and temperature shown as Figure 28 of this book.

where

 k = intrinsic permeability (L2) ρ = fluid density (M/L3) g = gravitational constant (acceleration of gravity) (L/T2) μ = dynamic viscosity (M/LT)

rearranging:

5c) What is the hydraulic conductivity of the sandstone if the water temperature is 35 °C (in cm/s)?

If the water temperature in the sandstone is 35 °C, Equation 31 of this book can be used to calculate, K, of the sandstone at that temperature in cm/s, using the relationships for the physical properties of water and temperature shown as Figure 28 of this book.