1 The radices of the cylindrical rock core is 1cm, the length
is 5cm, and the viscosity of the oil is impa. 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

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.

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

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