Hydraulic Permeability – Definition, Calculations, & Applications

Stebin
Samuel

Hydraulic permeability is a unit of measure that describes the mobility and ease by which fluids are able to navigate. It is notated by the letter k in scientific and engineering equations and applications. Hydraulic permeability plays a vital role in filter design and fluid behavior across membranes. This article discusses what hydraulic permeability is, how to calculate it, and the different applications in industry.

What is Hydraulic Permeability?

Hydraulic permeability refers to the mobility and ease by which a fluid is able to move through different mediums and across different membranes. The measurement relates specifically to filtration. Hydraulic permeability does not refer to the fluid, rather the medium and its ability to be permeable. Additionally, hydraulic permeability is useful in categorizing different types of soils, membranes, and other engineering materials. Generally speaking, hydraulic permeability has been identified to be independent of porous medium or membrane hole sizing and more dependent on permeability as a unit.

The units by which permeability is quantified are known as Darcy and are represented by the symbol k or K.

GC8CTV5 Permeability (Earthcache) in North Carolina, United States created  by McCaching
Courtesy: GeoCaching

Darcy’s Equation and Permeability

Darcy’s equation identifies flow rate as it relates to the hydraulic permeability of a fluid. The equation results from experimental results from water flow through a sand filter and a pilot apparatus. The conclusions were direct proportionality of flow rate and cross-sectional area. Darcy’s equation is as follows:

    \[ q = \frac{-k\Delta p}{\mu} \]

Useful in soil mechanics and other various engineering applications, Darcy’s equation helps to identify adequate soil conditions when it comes to geotechnical engineering applications. The determining factors when calculating flow rate are the medium’s granular textures, sizing and pore orientations, and their distribution. These calculations become useful in soil and subsoil studies that are crucial in the pre-construction phases of a project.

Originally, Darcy’s equation derives the formula for hydraulic permeability as a characteristic of the medium. Rearranging the previous equation yields the following equation that quantifies permeability, typically in units Darcy. The unit Darcy sees wide use in petroleum engineering and is a unit of length by length.

    \[ k = \frac{-q\mu}{\Delta p} \]

Calculating Hydraulic Permeability

The following is a sample calculation that calculates the hydraulic permeability of a medium. Representative quantities and units are as follows.

  • Flow rate = 2000 cc of air at 1 atm in 400 sec
  • Downstream pressure = 1 atm
  • Viscosity of air at test temperature = 0.02 cP
  • Core cross sectional area = 3 cm2
  • Core length = 5 cm
  • Upstream Pressure = 1.75 atm

    \[ P= \frac{P1 + P2}{2} = \frac{1.75 + 1}{2} = 1.375 atm \]

    \[ P1V1 = P2V2 = PV = 1*2000 \rightarrow V = 1454.5 cc \]

    \[  Q = V/t = 1454.5/200 = 3.64 cc/sec \]

    \[ k = \frac{Q\mu L}{A\Delta P}=\frac{3.65*.02*5}{3*.75}=.17 darcy \]

Hydraulic Permeability Applications

Permeability plays a significant role in a vast array of many different industries and applications. Among the main applications for hydraulic permeability are geoenvironmental engineering, soil physics, and construction material as it relates to permeability.

Construction Applications

Geoenvironmental engineering is a subsection of civil engineering that studies the permeability across several types of earthen material and engineering their behaviors as it relates to construction. As geoenvironmental engineering is crucial in the pre-construction stages of a project’s lifecycle, the discipline exists to run site investigations, surveys, and general studies of a plot of land before construction may start at a location.

A crucial aspect of site investigation includes studying and sampling soil. Hydraulic permeability’s relevance applies to studying the subsurface in question. Soil and rock properties identify limitations and design considerations that should be met. Geoenvironmental engineering investigations are a requirement by law to be performed and permitted before actual construction begins.

Soil Applications

Depending on the application of construction, permeability among different types of soils and rocks found at a site is a main consideration in the field of geotechnical engineering. Using materials like gravel, sand, silt, and clay are common sediments analyzed in subsurface studies. Each material has its own hydraulic permeability that allows engineers to identify how the sub-surface interacts based on its given composition.

Once soil conditions are studied, they offer insight as to whether or not the soil offers sufficient support for structures. Studying the permeability and composition of a subsurface provides foundational insight into the structural and foundational design of any concrete substructure. Additionally, through the study of soil permeability and composition, contractors are able to reconcile discrepancies with their original build plan should there be any major considerations. Projects may altogether be stopped due to inadequate soil conditions as identified by soil permeability studies and how it relates to the ability of the subsurface to support the intended construction.

Petroleum Applications

When determining reservoir estimation methods, hydraulic permeability and pressure relationships play a huge role. Manipulating capillary pressure relationships allows engineers to estimate the capacity of a reservoir. Relating the capillary pressure, permeability, and chemistry of the fluid in question allows engineers to assume reservoir capacity and the rate at which it may flow.