Consider the radial flow problem shown in the top and side views below, where the shaded

area represents a damaged zone due to the drilling operations. Permeability of this damaged

zone is lower than the permeability of the formation. Assume there are three horizontal layers

of equal heights $($thickness$),$ and the permeability of the undamaged formation is $45$ mD in

layer $1,25mD$ in layer $2,$ and $30$ mD in layer $3.$ Further, assume that the radius of damage is

$2\mathrm{.}2$ ft and the permeability of the damaged zone is $1\mathrm{.}5$ mD in all the three layers. Radius of the

wellbore is $0\mathrm{.}6$ ft $,$ and radius of the reservoir is $450$ ft $.$

a$)$ What is the average permeability in each horizontal layer?

b$)$ What is the average permeability of the whole system?

$($Top View$)$