# 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 (L^{3}/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 (L^{2}) |

Rearranging:

*5b) If the laboratory experiment was completed using 15 °C water, what is the intrinsic permeability of the sandstone in cm ^{2}?*

If the test was conducted at 15 °C, the intrinsic permeability, *k*, of the sandstone in cm^{2} 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 (L^{2}) |

ρ |
= | fluid density (M/L^{3}) |

g |
= | gravitational constant (acceleration of gravity) (L/T^{2}) |

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.