Kozeny–Carman equation
The Kozeny–Carman equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. It is named after Josef Kozeny and Philip C. Carman. The equation is only valid for creeping flow, i.e. in the slowest limit of laminar flow. The equation was derived by Kozeny and Carman from a starting point of modelling fluid flow in a packed bed as laminar fluid flow in a collection of curving passages/tubes crossing the packed bed and Poiseuille's law describing laminar fluid flow in straight, circular section pipes.
Equation
The equation is given as:where:
- is the pressure drop;
- is the total height of the bed;
- is the viscosity of the fluid;
- is the porosity of the bed ;
- is the sphericity of the particles in the packed bed ;
- is the diameter of the volume equivalent spherical particle;
- is the superficial or "empty-tower" velocity which is directly proportional to the average volumetric fluid flux in the channels, and porosity.
This equation is a particular case of Darcy's law, with a very specific permeability. Darcy's law states that "flow is proportional to the pressure gradient and inversely proportional to the fluid viscosity" and is given as:
Combining these equations gives the final Kozeny equation for absolute permeability:
where:
- is the absolute permeability.