Kozeny–Carman equation
The Kozeny–Carman equation (or Carman–Kozeny 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 laminar flow. The equation was derived by Kozeny and Carman (see ) from a starting point of (a) modelling fluid flow in a packed bed as laminar fluid flow in a collection of curving passages/tubes crossing the packed bed and (b) Poiseuille's law describing laminar fluid flow in straight, circular section pipes.
The equation is given as:
where:
This equation holds for flow through packed beds with particle Reynolds numbers up to approximately 1.0, after which point frequent shifting of flow channels in the bed causes considerable kinetic energy losses.
This equation can be expressed as "flow is proportional to the pressure drop and inversely proportional to the fluid viscosity", which is known as Darcy's law.
Combining these equations gives the final Kozeny equation for absolute (single phase) permeability
The combined proportionality and unity factor has typically average value of 0.8E6 /1.0135 from measuring many naturally occurring core plug samples, ranging from high to low clay content, but it may reach a value of 3.2E6 /1.0135 for clean sand. The denominator is included explicitly to remind us that permeability is defined using [atm] as pressure unit while reservoir engineering calculations and reservoir simulations typically use [bar] as pressure unit.
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