A horizontal pipe 10 cm in diameter and 3000 cm long is filled with a sand of 20 % porosity. The permeability of the sand is estimated to be 250 md. The sand is saturated with an oil of viscosity 0.65 cp, and the same oil is injected into the sand pipe. You are asked to calculate

a. What is the Darcy velocity in the sand pipe under a 100-psi pressure differential?

b. What is the flow rate through the sand pipe under a 100-psi pressure differential?

c. Calculate the oil contained in the pipe and the time needed to displace it at the rate of 0.055 cm3/sec using another fluid which has the same properties with oil but it is cheaper so that it is profitable to replace with oil.

d. If there is an immobile water saturation of 30% in the sand (i.e. water does not flow only oil flows) what will be the flow rate to oil under a pressure differential of 120 psi (assume permeability is reduced to 200 md due to presence of immobile water)