Permeability & Darcy's Law
Permeability measures a rock's ability to transmit fluids, governed by Darcy's Law.
A rock can be highly porous, like a sponge, but if those pores are completely sealed off from one another, no fluid will ever flow. The property that dictates connectivity and flow is permeability.
Defining Permeability
Permeability ($k$) is a property of the porous medium that measures the ease with which fluids can flow through its interconnected pore network. The standard unit is the darcy, though most reservoir rocks have permeabilities measured in millidarcies (md). A rock with high porosity does not necessarily have high permeability; a rock can be porous but impermeable if the pores are isolated.
In laboratory Darcy units, the proportionality constant is exactly 1. Darcy's Law is written linearly as $q = (k \cdot A \cdot \Delta p) / (\mu \cdot L)$, where $q$ is flow rate, $A$ is cross-sectional area, $\Delta p$ is pressure drop, $\mu$ is fluid viscosity, and $L$ is length. In field units, a conversion constant is required, but the fundamental relationship remains the same.
- Rearrange Darcy's Law to solve for $k$: $k = (q \cdot \mu \cdot L) / (A \cdot \Delta p)$.
- Substitute the given lab values: $k = (1.0 \cdot 1.0 \cdot 3.0) / (2.0 \cdot 2.0)$.
- Calculate the numerator: $1.0 \times 1.0 \times 3.0 = 3.0$.
- Calculate the denominator: $2.0 \times 2.0 = 4.0$.
- Divide to find $k$: $k = 3.0 / 4.0 = 0.75$ darcy.
- Convert to millidarcies: $0.75 \times 1000 = 750$ md.
Check your understanding
- Permeability quantifies the ability of a rock to transmit fluids through interconnected pores.
- In lab Darcy units, $k = (q \cdot \mu \cdot L) / (A \cdot \Delta p)$ with a constant of 1.
- A rock can have high porosity but zero effective permeability if pores are unconnected.