Kozeny-Carman equation
Encyclopedia
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 is given as:
where
is the pressure drop, 
is the total height of the bed, 
is the superficial or "empty-tower" velocity
,
is the viscosity
of the fluid,
is the porosity
of the bed,
is the sphericity of the particles in the packed bed, and 
is the diameter of the related spherical particle.
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
.
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
to calculate the pressure drop
Pressure drop
Pressure drop is a term used to describe the decrease in pressure from one point in a pipe or tube to another point downstream. "Pressure drop" is the result of frictional forces on the fluid as it flows through the tube. The frictional forces are caused by a resistance to flow. The main...
of a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
flowing through a packed bed
Packed bed
In chemical processing, a packed bed is a hollow tube, pipe, or other vessel that is filled with a packing material. The packing can be randomly filled with small objects like Raschig rings or else it can be a specifically designed structured packing...
of solids. It is named after Josef Kozeny
Josef Kozeny
Josef Kozeny was an Austrian physicist . Today he is mainly remembered for Kozeny–Carman equation of a fluid flowing through a packed bed of solids.-Further reading:...
and Philip C. Carman. The equation is only valid for laminar flow
Laminar flow
Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents...
.
The equation is given as:
where
is the pressure drop, is the total height of the bed, is the superficial or "empty-tower" velocitySuperficial velocity
Superficial velocity , in engineering of multiphase flows and flows in porous media, is an hypothetical fluid velocity calculated as if the given phase or fluid were the only one flowing or present in a given cross sectional area. Other phases, particles, the skeleton of the porous medium, etc...
,
is the viscosityViscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
of the fluid,
is the porosityPorosity
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...
of the bed,
is the sphericity of the particles in the packed bed, and is the diameter of the related spherical particle.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
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
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
Darcy's law
Darcy's law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments on the flow of water through beds of sand...
.
History
The equation was first proposed by Kozeny (1927) and latter modified by Carman (1937, 1956).See also
- Fractionating columnFractionating columnA fractionating column or fractionation column is an essential item used in the distillation of liquid mixtures so as to separate the mixture into its component parts, or fractions, based on the differences in their volatilities...
- Random close packRandom close packRandom close packing is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained when they are packed randomly. For example, when a solid container is filled with grain, shaking the container will reduce the volume taken up by the objects, thus allowing...
- Raschig ringRaschig ringRaschig rings are pieces of tube used in large numbers as a packed bed within columns for distillations and other chemical engineering processes. They are usually ceramic or metal and provide a large surface area within the volume of the column for interaction between liquid and gas or vapour...
- Ergun equation