Hydraulic Conductivity Calculator

Background.

Groundwater moves through sand, gravel and fractured rock at a pace set by two quite different things: how open the pore network is, and how easily the water itself flows. Hydrogeologists keep the two apart. Intrinsic permeability, k, belongs to the soil or rock alone. It depends on the size, shape and connectedness of the pores and has the units of an area. Hydraulic conductivity, K, is the coefficient Darcy's law actually uses, and it describes one particular fluid moving through that medium, in metres per second.

Turning one into the other means bringing in the fluid: K = kρg/μ, where ρ is the fluid's density, g the acceleration due to gravity and μ its dynamic viscosity. Density and gravity together supply the weight that drives the flow; viscosity is the internal friction that holds it back.

The conversion earns its keep whenever the fluid changes. Petroleum engineers quote permeability in darcies, a unit close to 10⁻¹² m², because the same reservoir may hold oil, gas and brine. Hydrogeologists dealing with cold groundwater, warm geothermal water or a dense saline plume need a K for that water, not for the water used in a laboratory test. Water's viscosity alone is about 30% higher at 10 °C than at 20 °C, and K falls in proportion.

The page evaluates that single equation in SI units with no material or temperature lookup: you supply all four values, and each must be positive. It converts a property at one fluid state. Anisotropy, flow through partly dry soil, flow along fractures, the way measured K changes with the scale of a test, and the choice of test method all lie outside it.

What is hydraulic conductivity calculator?

Hydraulic conductivity measures how readily a fluid passes through a porous material under a hydraulic gradient. In Darcy's law, q = −K × dh/dl, it is the flow per unit cross-sectional area produced by a unit gradient, one metre of head lost per metre travelled, which is why it carries the units of a velocity. Unlike intrinsic permeability it depends on the fluid as well as the medium: the same sand conducts cold water less readily than warm water, and a viscous oil far less readily still.

How to use this calculator.

1. 01Enter the intrinsic permeability in square metres. To convert from darcies multiply by 9.869233 × 10⁻¹³, and from millidarcies by 9.869233 × 10⁻¹⁶.
2. 02Enter the fluid's density in kg/m³ at the temperature and salinity you are modelling. Fresh water near room temperature is about 998 kg/m³, and seawater is denser, around 1,025 kg/m³.
3. 03Leave gravity at the standard 9.80665 m/s² for ordinary problems. Change it only for a case such as a geotechnical centrifuge model, where the effective acceleration is a multiple of g.
4. 04Enter dynamic viscosity in Pa·s, not kinematic viscosity in m²/s or centistokes. Water is about 0.001 Pa·s near 20 °C and about 0.0013 Pa·s at 10 °C.
5. 05Read K in metres per second; multiply by 86,400 for metres per day, the unit many field reports use.

The formula.

K = k × ρ × g ÷ μ. Here k (m²) is the intrinsic permeability of the medium; ρ (kg/m³) times g (m/s²) is the fluid's specific weight, the weight of a cubic metre that pushes flow down a head gradient; and μ (Pa·s) is the dynamic viscosity, the fluid's resistance to shearing. The units cancel to a velocity: m² × kg/m³ × m/s² ÷ kg/(m·s) = m/s. The relationship is linear in every term, so doubling the permeability doubles K and doubling the viscosity halves it. Across natural materials k ranges over many orders of magnitude, so it dominates any comparison between soils; for one material, temperature matters most, mainly through viscosity. The default 9.80665 m/s² is the standard acceleration of gravity, a defined value.

A worked example.

Frequently asked questions.

References& sources.

1. [1]USGS Techniques of Water-Resources Investigations, Book 3, Chapter B1, Aquifer-Test Design.
2. [2]Freeze and Cherry, Groundwater (1979), chapter 2 (OPEN TEXT).
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.