Residence time distribution functions for stirred tanks in series

1970 ◽  
Vol 48 (6) ◽  
pp. 723-725 ◽  
Author(s):  
R. L. Stokes ◽  
E. B. Nauman
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Distribution Functions ◽  
Stirred Tanks ◽  
In Series

scholarly journals Explicit Residence Time Distribution of a Generalised Cascade of Continuous Stirred Tank Reactors for a Description of Short Recirculation Time (Bypassing)

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 615 ◽  
Author(s):  
Peter Toson ◽  
Pankaj Doshi ◽  
Dalibor Jajcevic
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Flow Reactor ◽  
Plug Flow ◽  
Stirred Tank ◽  
Stirred Tank Reactors ◽  
Delayed Impulse ◽  
In Series ◽  
Back Mixing

The tanks-in-series model (TIS) is a popular model to describe the residence time distribution (RTD) of non-ideal continuously stirred tank reactors (CSTRs) with limited back-mixing. In this work, the TIS model was generalised to a cascade of n CSTRs with non-integer non-negative n. The resulting model describes non-ideal back-mixing with n > 1. However, the most interesting feature of the n-CSTR model is the ability to describe short recirculation times (bypassing) with n < 1 without the need of complex reactor networks. The n-CSTR model is the only model that connects the three fundamental RTDs occurring in reactor modelling by variation of a single shape parameter n: The unit impulse at n→0, the exponential RTD of an ideal CSTR at n = 1, and the delayed impulse of an ideal plug flow reactor at n→∞. The n-CSTR model can be used as a stand-alone model or as part of a reactor network. The bypassing material fraction for the regime n < 1 was analysed. Finally, a Fourier analysis of the n-CSTR was performed to predict the ability of a unit operation to filter out upstream fluctuations and to model the response to upstream set point changes.

Characterising bioreactor mixing with residence time distribution (RTD) tests

1998 ◽  
Vol 37 (12) ◽  
pp. 43-47 ◽  
Author(s):  
Bob Newell ◽  
Jeff Bailey ◽  
Ashraful Islam ◽  
Lisa Hopkins ◽  
Paul Lant
Keyword(s):  
Residence Time ◽  
Nutrient Removal ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Dynamic Models ◽  
Biological Nutrient Removal ◽  
Hydraulic Characteristics ◽  
Stirred Tanks ◽  
Process Simulations ◽  
Real Plant

This paper presents a technique for configuring wastewater process simulations so that the hydraulic characteristics are similar to the real plant. Residence time distribution (RTD) tests are performed on two biological nutrient removal pilot plants. The RTD tests proved valuable for evaluating mixing effectiveness, volume utilisation and for determining an appropriate hydraulic topology for the dynamic models of the pilot plants. As a result of this work, simulation execution times became much faster due to a significant reduction in the number of effective stirred tanks required in the model. The work also identified short circuiting and dead zones in the pilot plants.

scholarly journals Experimental Study on the Solids Residence Time Distribution in Multiple Square-Based Spouted Beds

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4694
Author(s):  
Filippo Marchelli ◽  
Massimo Curti ◽  
Mattia Tognin ◽  
Giorgio Rovero ◽  
Cristina Moliner ◽  
...  
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Lateral Wall ◽  
Continuous Stirred Tank Reactor ◽  
Spouted Bed ◽  
Bed Height ◽  
Spouted Beds ◽  
Reactor Networks ◽  
In Series

The present work aims at investigating the residence time distribution (RTD) of a multiple spouted bed reactor, which will be applied for the pyrolysis and gasification of residual biomass. The unit is composed of square-based spouted beds, placed in series and at descending heights, and communicating with each other through an opening in the lateral wall. The gas is fed evenly in parallel. The experimental analysis is based on tracer experiments in cold-flow units, assessing the influence of the number of units and the bed height. The tests proved the good mixing properties of the spouted beds, which create a stable fluidization regime and do not feature dead zones. Each spouted bed can generally be well assimilated to an ideal continuous stirred tank reactor (CSTR). The RTD of the device seems adequate for the application, and also seems to be well tuneable through the selection of the bed height and number of units. Given the good similarity with ideal reactor networks, these represent a valid tool to estimate the final behavior in terms of RTD.

scholarly journals Spatial Variation of Longitudinal Dispersion in LECA-Based Vegetated Beds

2012 ◽  
Vol 326-328 ◽  
pp. 279-284
Author(s):  
António Albuquerque
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Loading Rate ◽  
Solid Material ◽  
Dead Volume ◽  
Nitrogen Compounds ◽  
In Series ◽  
Reactive Tracer ◽  
Tracer Experiments

The evaluation of the dispersion in vegetated beds may allow indentifying mechanisms that affect the transport and reaction of solutes, namely organic and nitrogen compounds. A set of non-reactive tracer experiments (slag injection) was performed in a vegetated bed (a mesocosm with a LECA-based substratum and colonized withPhragmites australis) used for the removal of organic and nitrogen pollutant loads. Loads of approximately 300 mg COD/L and 30 mg NH4-N/L and a hydraulic loading rate of 3.5 cm/d were used. The results showed a delay in all the residence time distribution (RTD) curves and a variation in the dimensionless residence time (μ(m,θ)) of the E(θ) curves, which means that the mass centre of the impulse was late relatively to the expected one. A strong dispersion and tracer retention (due to the presence of stagnated areas and internal recirculation) was observed, especially in the first 33 cm of the bed, which seems to have been related to the presence of complex clusters of roots, solid material, biofilm and LECA particles. An analytical solution of the Multiple-Tanks-in-Series (MTS) model well represents the RTD curves obtained in the tracer experiments. The detected dispersion and dead volume ratios (7% to 12%) did not affect the performance of the bed, which presented mean removal efficiencies of 85% and 60.4% for COD and NH4-N, respectively.

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