Final answer:
To calculate the permeability of the core plug, use Darcy's law and the given values for diameter, length, velocity, and pressure difference. Substitute the values into the formula and solve for k.
Step-by-step explanation:
To calculate the permeability of the core plug, we can use Darcy's law, which states that the flow rate of a fluid through a porous medium is proportional to the pressure difference across the medium and inversely proportional to the viscosity of the fluid. The formula for Darcy's law is Q = kAΔP/η, where Q is the flow rate, k is the permeability, A is the cross-sectional area, ΔP is the pressure difference, and η is the viscosity.
In this case, we are given the diameter of the core plug (5.410^m), the length of the plug (0.28m), the velocity of the water (0.001 m/s), and the pressure difference (1.010^Pa). We can calculate the cross-sectional area using the formula A = πr², where r is half the diameter. Substituting these values into Darcy's law, we can solve for k, which will give us the permeability.
Let's calculate:
- Calculate the radius of the plug: r = (diameter/2) = (5.410^m/2) = 2.705^m
- Calculate the cross-sectional area: A = πr² = π(2.705^m)² = 22.99 m²
- Convert the pressure difference from Pa to N/m2: ΔP = 1.010^Pa = 1.010^N/m2
- Substitute the values into Darcy's law and solve for k: Q = (k * 22.99 m² * 0.001 m/s)/(1.010^N/m2)
- Rearrange the equation to solve for k: k = (Q * η)/(A * ΔP)
By substituting the given values into the equation and calculating, we can determine the value of k, which represents the permeability of the core plug in meters.