A brine solution is used to determine the absolute permeability of a core sample. The sample measures 4 cm in length and has a cross-sectional area of 3 cm². With a viscosity of 1.0 cP, brine flows at a constant rate of 0.5 cm³/s under a pressure differential of 2.0 atm. Calculate the absolute permeability of the sample.

To calculate the absolute permeability of a core sample using a brine solution, we can apply Darcy's Law, which is commonly used to describe fluid flow through a porous medium. The equation is:

Q = (k * A * ΔP) / (μ * L)

where: - Q is the flow rate - k is the permeability of the core sample - A is the cross-sectional area of the core sample - ΔP is the pressure differential - μ is the viscosity of the fluid - L is the length of the core sample

First, we need to make sure all our measurements are in consistent units. In this case, we will use the SI unit system. We have:

- Q = 0.5 cm³/s = 0.5 × 10⁻⁶ m³/s (since 1 cm³ = 10⁻⁶ m³) - A = 3 cm² = 3 × 10⁻⁴ m² (since 1 cm² = 10⁻⁴ m²) - μ = 1.0 cP = 1.0 × 10⁻³ Pa·s (since 1 cP = 1 × 10⁻³ Pa·s) - ΔP = 2.0 atm = 2.0 × 101325 Pa (since 1 atm = 101325 Pa) - L = 4 cm = 0.04 m

Now we can rearrange the Darcy's Law to solve for permeability k:

k = (Q * μ * L) / (A * ΔP)

Plugging in the numbers:

k = (0.5 × 10⁻⁶ m³/s * 1.0 × 10⁻³ Pa·s * 0.04 m) / (3 × 10⁻⁴ m² * 2.0 * 101325 Pa)

k = (0.5 × 10⁻⁶ * 1.0 × 10⁻³ * 0.04) / (3 × 10⁻⁴ * 2.0 * 101325)

k = (2 × 10⁻¹⁰) / (6.0795 × 10⁻²)

k ≈ 3.29 × 10⁻⁹ m²

Absolute permeability is often expressed in Darcies or millidarcies (mD) in the field of petrophysics. 1 Darcy ≈ 9.869233 × 10⁻¹³ m². To convert the permeability in m² to mD:

k = 3.29 × 10⁻⁹ m² / 9.869233 × 10⁻¹³ m²/mD = 333.33 mD

Therefore, the absolute permeability of the core sample is approximately 333.33 millidarcies (mD).