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To calculate the pressure drop in a given reactor, the following equation may be deduced: = + | |. This arrangement of the Ergun equation makes clear its close relationship to the simpler Kozeny-Carman equation, which describes laminar flow of fluids across packed beds via the first term on the right hand side.
The Ergun equation can be used to predict the pressure drop along the length of a packed bed given the fluid velocity, the packing size, and the viscosity and density of the fluid. The Ergun equation, while reliable for systems on the surface of the earth, is unreliable for predicting the behavior of systems in microgravity.
The Kozeny–Carman equation (or Carman–Kozeny equation or 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 creeping flow, i.e. in the slowest limit of laminar ...
A typical plug flow reactor could be a tube packed with some solid material (frequently a catalyst). Typically these types of reactors are called packed bed reactors or PBR's. Sometimes the tube will be a tube in a shell and tube heat exchanger. When a plug flow model can not be applied, the dispersion model is usually employed. [2] [3]
Kozeny published a textbook, “Hydraulics”, in 1953, a book which became a standard in the field. He was best known for his contribution to the Kozeny-Carman equation. Used to calculate the flow of a liquid through a packed bed of solids, the equation was first proposed by Kozeny in 1927 and later modified by Philip Carman. [6]
The Archimedes number is applied often in the engineering of packed beds, which are very common in the chemical processing industry. [3] A packed bed reactor, which is similar to the ideal plug flow reactor model, involves packing a tubular reactor with a solid catalyst, then passing incompressible or compressible fluids through the solid bed. [3]
The same equation applies in chromatography processes as for the packed bed processes, namely: = In packed column chromatography, the HETP may also be calculated with the Van Deemter equation. In capillary column chromatography HETP is given by the Golay equation.
The choice of equation depends on the system involved: the first is successful in correlating the data for various types of packed and fluidized beds, the second Reynolds number suits for the liquid-phase data, while the third was found successful in correlating the fluidized bed data, being first introduced for liquid fluidized bed system. [26]