Question

An aquifer has three different formations. Formation A has a thickness of 8.0 m and hydraulic conductivity of 25.0 m/d. Formation B has a thickness of 2.0 m and a conductivity of 142 m/d. Formation C has a thickness of 34 m and a conductivity of 40 m/d. Assume that each formation is isotropic and homogeneous. Compute both the overall horizontal and vertical conductivities.

Answer 1

The horizontal conductivity is 41.9 m/d.

The vertical conductivity is 37.2 m/d.

Step-by-step explanation:

Given that,

Thickness of A = 8.0 m

Conductivity = 25.0 m/d

Thickness of B = 2.0 m

Conductivity = 142 m/d

Thickness of C = 34 m

Conductivity = 40 m/d

We need to calculate the horizontal conductivity

Using formula of horizontal conductivity

`K_(H)=(H_(A)K_(A)+H_(A)K_(A)+H_(A)K_(A))/(H_(A)+H_(B)+H_(C))`

Put the value into the formula

`K_(H)=(8.0*25+2,0*142+34*40)/(8.0+2.0+34)`

`K_(H)=41.9\ m/d`

We need to calculate the vertical conductivity

Using formula of vertical conductivity

`K_(V)=(H_(A)+H_(B)+H_(C))/((H_(A))/(K_(A))+(H_(B))/(K_(B))+(H_(C))/(K_(C)))`

Put the value into the formula

`K_(V)=(8.0+2.0+34)/((8.0)/(25)+(2.0)/(142)+(34)/(40))`

`K_(V)=37.2\ m/d`

Hence, The horizontal conductivity is 41.9 m/d.

The vertical conductivity is 37.2 m/d.