Answer:
0.995 Darcys
Question:
The radius of the cylindrical rock core is 1cm, the length is 5cm and the viscosity of the oil is 1mpa.s. The Pressure difference between the two ends of the rock core is 0.2 atmospheric pressure and we get 15 cm3 oil from the outlet in 2 minutes. Please find permeability of the rock Core.
Step-by-step explanation:
The viscosity of the oil in the initial question cannot be ascertain because there is an error in the value given. Let's consider the question above to enable us determine the permeability of the rock core.
From the question we are asked to find the permeability constant.
Given:
Radius = 1cm
Length = 5cm
viscosity of the oil (μ) = 1mpa.s = 1×10^-3pa.s
1pascal seconds = 1000centipoise
10^-3pa.s = 1cp
Viscosity of oil = μ = 1cp
Pressure difference between the two ends of the rock core (∆P) = 2atm
Volume of oil = 15 cm^3
time = 2min = 2×60s = 120s
Volumetric flow rate (Q) = volume/time
= 15/120
Q = 0.125cm^3/s
From Darcy equation:
Q = (k×A×∆P) / (μ ×L)
k = constant of permeability
A = area = πr^2
A = π × (1)^2 = 3.14×1
A = 3.14cm^2
0.125 = (k×3.14×2)/(1×5)
0.125×1×5 = k×3.14×2
k = (0.125×1×5)/(3.14×2)
k = (6.25×1)/6.28
k = 0.995 Darcys
permeability of the rock core = 0.995 Darcys