Formula & Calculator
Hydraulic Conductivity from Intrinsic Permeability
Converts a rock or soil's intrinsic (fluid-independent) permeability into hydraulic conductivity, which depends on the specific fluid properties.
Interpretation
K = (k × ρ × g) / μ. Hydraulic conductivity K relates to intrinsic permeability k, fluid density ρ, viscosity μ, and gravity g. Used to compare water and other fluids.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| K | Hydraulic conductivity | m/s |
| k | Intrinsic permeability | m2 |
| ρ | Fluid density | kg/m3 |
| g | Gravitational acceleration | m/s2 |
| μ | Fluid dynamic viscosity | Pa*s |
What it means
Hydraulic conductivity K is a measure of a porous medium’s ability to transmit a fluid. It depends on both the medium (intrinsic permeability k) and the fluid properties (density ρ and dynamic viscosity μ). This relation allows conversion between permeability (in m²) and hydraulic conductivity (in m/s). It is important in hydrogeology for comparing conductivities for different fluids (e.g., water, oil, air). Understanding this helps in determining how fast water moves through soils and rocks, and is essential for groundwater modelling and for petroleum engineering.
Worked example
Hydraulic Conductivity from Permeability – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| k (m²) | 1.0e-12 |
| ρ (kg/m³) | 1000 |
| μ (Pa·s) | 1.0e-3 |
| Parameter | Value |
|---|---|
| k | 1.0e-14 |
| ρ | 1000 |
| μ | 1.0e-3 |
Common mistakes
- Hydraulic conductivity from intrinsic permeability: K = (k·ρ·g)/μ.
- k: Intrinsic permeability – in m² (darcy units can be converted).
- ρ: Fluid density (kg/m³).
- g: Gravitational acceleration (9.81 m/s²).
- μ: Dynamic viscosity (Pa·s) – temperature‑dependent.
- Units: K in m/s – ensure all SI units.
Applications
Hydraulic conductivity from intrinsic permeability, K = (k·ρ·g)/μ, relates the macroscopic hydraulic conductivity (K) to the intrinsic permeability (k) of the porous medium, fluid density (ρ), fluid viscosity (μ), and gravitational acceleration (g). This allows the conversion of permeability measurements from core samples to hydraulic conductivity for groundwater flow calculations. Hydrogeologists use it to characterise aquifers, to scale laboratory measurements to field conditions, and to predict flow in different fluids (e.g., oil vs. water). By understanding this relationship, professionals can estimate K for various geological materials and fluid conditions. This formula is fundamental for multiphase flow modelling and for interpreting hydraulic tests.
- Conversion of permeability data for groundwater models
- Characterisation of aquifer properties from core samples
- Petroleum reservoir evaluation (oil‑water flow)
- Geothermal energy and fluid flow modelling
- Soil science and vadose zone hydrology
Frequently Asked Questions
K = (k · ρ · g) / μ, where k is intrinsic permeability (m²), ρ is fluid density, g is gravity, and μ is dynamic viscosity. This formula converts a medium‑specific property (k) into a fluid‑dependent property (K).
Intrinsic permeability has units of m² (or darcies). 1 darcy ≈ 9.87×10⁻¹³ m². It is a measure of the ease with which a fluid flows through a porous medium.
Because the fluid’s density and viscosity affect how easily it moves. For example, water (low viscosity) flows more easily than oil (high viscosity) through the same medium, so K for water is higher.
Sand: 10⁻¹¹ – 10⁻¹³ m² (1–100 darcies). Gravel: 10⁻¹⁰ – 10⁻⁹ m². Clay: 10⁻¹⁷ – 10⁻¹⁵ m² (nanodarcies).
Temperature changes viscosity and density. For water, viscosity decreases with temperature, so K increases (by about 2% per °C). This must be considered in field measurements.
In common usage, 'permeability' often refers to intrinsic permeability (k). However, hydraulic conductivity (K) is more commonly used in groundwater hydrology.
Using a permeameter – a flow of fluid (usually water or air) is passed through a core sample under controlled pressure, and the flow rate is measured. Then k is derived from Darcy’s law.
Since K = (k·ρ·g)/μ, increasing density (e.g., saltwater vs freshwater) increases K for the same k, but density differences are small compared to viscosity differences.
T = K·b, where b is the aquifer thickness. Thus, T is the product of k, ρ, g, μ, and b.
It assumes laminar flow and a homogeneous medium. It does not account for chemical interactions, swelling clays, or fracture flow.