Residence time distribution in laminar flow systems. I. Hydrodynamic conception in study of distribution functions

1972 ◽  
Vol 37 (2) ◽  
pp. 412-428 ◽  
Author(s):  
O. Wein ◽  
J. Ulbrecht
Keyword(s):  
Laminar Flow ◽  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Distribution Functions ◽  
Flow Systems

Rate of advancement of reactions in turbulent flows

1964 ◽  
Vol 17 (8) ◽  
pp. 821 ◽  
Author(s):  
RCL Bosworth ◽  
CM Groden
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Residence Times ◽  
Cylindrical Reactor ◽  
The Times ◽  
Very High

When a reacting substance or mixture is caused to flow in a cylindrical reactor, all portions of the stream will not flow at the same rate and will exhibit different residence times and, accordingly, are subject to different extents of degrees of reaction. The average degrees of reaction following the residence time distribution proper to laminar flow are given in the earlier publication1 and this paper extends the treatment to that of turbulent flow. In the earlier treatment of laminar flow the ratio of average extent of reaction with non-interacting streams to that of complete intermingling, or the C/Cm, is plotted against the ratio of the times of flow with those of reaction (S). The C/Cm versus S curves are all above unity and increase with increasing S, with the exception of very high orders of chemical reaction for which values of C/Cm are all unity. In the case of turbulent flow the values of C/Cm are more nearly unity at all values of S.

The residence time distribution of laminar flow in curved tubes

1964 ◽  
Vol 19 (1) ◽  
pp. 77-79 ◽  
Author(s):  
E. van Andel ◽  
H. Kramers ◽  
A. de Voogd
Keyword(s):  
Laminar Flow ◽  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution

scholarly journals Derivation of a Multiparameter Gamma Model for Analyzing the Residence-Time Distribution Function for Nonideal Flow Systems as an Alternative to the Advection-Dispersion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Irucka Embry ◽  
Victor Roland ◽  
Oluropo Agbaje ◽  
Valetta Watson ◽  
Marquan Martin ◽  
...  
Keyword(s):  
Dispersion Equation ◽  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Flow Reactor ◽  
Plug Flow ◽  
Absolute Deviation ◽  
Suitable Alternative ◽  
Advection Dispersion ◽  
Flow Systems

A new residence-time distribution (RTD) function has been developed and applied to quantitative dye studies as an alternative to the traditional advection-dispersion equation (AdDE). The new method is based on a jointly combined four-parameter gamma probability density function (PDF). The gamma residence-time distribution (RTD) function and its first and second moments are derived from the individual two-parameter gamma distributions of randomly distributed variables, tracer travel distance, and linear velocity, which are based on their relationship with time. The gamma RTD function was used on a steady-state, nonideal system modeled as a plug-flow reactor (PFR) in the laboratory to validate the effectiveness of the model. The normalized forms of the gamma RTD and the advection-dispersion equation RTD were compared with the normalized tracer RTD. The normalized gamma RTD had a lower mean-absolute deviation (MAD) (0.16) than the normalized form of the advection-dispersion equation (0.26) when compared to the normalized tracer RTD. The gamma RTD function is tied back to the actual physical site due to its randomly distributed variables. The results validate using the gamma RTD as a suitable alternative to the advection-dispersion equation for quantitative tracer studies of non-ideal flow systems.

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