Minimum residence time

The minimum residence time as determined by Stokes Law terminal settling velocity is ... 

Average residence time related to minimum residence time is ... 

ASpGr = Difference in specific gravity of the particle and the surrounding fluid tyvg = Average residence time based on liquid flow rate and vessel volume, min tmjp = Minimum residence time to allow particles to settle based on Stokes Law, min u = Relative velocity between particle and main body of fluid, ft/sec... 

Elucidation of degradation kinetics for the reactive extrusion of polypropylene is constrained by the lack of kinetic data at times less than the minimum residence time in the extruder. The objectives of this work were to develop an experimental technique which could provide samples for short reaction times and to further develop a previously published kinetic model. Two experimental methods were examined the classical "ampoule technique" used for polymerization kinetics and a new method based upon reaction in a static mixer attached to a single screw extruder. The "ampoule technique was found to have too many practical limitations. The "static mixer method" also has some difficult aspects but did provide samples at a reaction time of 18.6 s and is potentially capable of supplying samples at lower times with high reproducibility. Kinetic model improvements were implemented to remove an artificial high molecular weight tail which appeared at high initiator concentrations and to reduce step size sensitivity. 

Recently a kinetic model was developed to describe the reactions occurring in the extruder (1). However, thorough testing and further development of this model was limited mainly because only samples of feed and extrudate could be obtained (2.31. Reacted samples with reaction times less than the minimum residence time of the extruder were not available. This minimum time was approximately 2.8 min. All reactions were generally completed within that time. Thus,this work had two primary objectives ... 

GP 11] ]R 19] Using the above visual inspection technique, the minimum residence time can be estimated. Flow was increased and so the residence time decreased, until the whole reactor was glowing. This corresponds to a residence time as low as approximately 50 ps (0.1 slpm hydrogen, 0.14 slpm oxygen, 0.45 slpm nitrogen) [9]. 

The parameter for variable batch time is defined by constraint (2.9). This gives the amount of time required to process a unit amount of a batch corresponding to a particular effective state in a corresponding unit operation. Constraint (2.10) denotes the minimum processing time for the effective state in the corresponding unit operation. This is, in essence, the minimum residence time of a batch within a unit operation. In constraints (2.10) and (2.11), v (j n is the percentage variation in processing time based on operational experience. 

Design the optimal temperature sequence with respect to time per reactor length to obtain (a) a given fraction conversion, (b) a maximum rate of reaction, or (c) the minimum residence time. 

Post heater. Located immediately downstream of the candle filters, a post heater heats the offgas to a temperature of 1,000 to 1,100°F to destroy any agent that might exist in the gaseous effluent. The post heater is designed to provide a minimum residence time of 3 seconds at temperature. 

The settler. In this unit, gravitational settling frequently occurs and, in addition, coalescence of droplets must take place. Baffles are fitted at the inlet in order to aid distribution. The rates of sedimentation and coalescence increase with drop size, and therefore excessive agitation resulting in the formation of very small drops should be avoided. The height of the dispersion band ZB is influenced by the throughput since a minimum residence time is required for coalescence to occur. This height Zb is related to the dispersed and continuous phase superficial velocities, //,/ and uc by ... 

Vazquez and Calvelo (1983b) presented a model for the prediction of the minimum residence time in a fluidized bed freezer which can then be equated to the required freezing time. The model is defined in terms of a longitudinal dispersion coefficient D, which is a measure of the degree of solids mixing within the bed in the direction of flow (and has the dimensions of a diffusivity, and hence units of m s ), a dimensionless time T... 

Figure 5-18 Illustration of isothermal trajectories for an exothermic reversible reaction. At the lowest temperature the rate is low but the eqmlibiium conversion is high, while at the highest temperature the initial rate is high but the equilibrium conversion is low. From the 1/r versus X plot at these temperatures, it is evident that T should decrease as X increases to require a minimum residence time,...

Iliis minimum value of V(7 - 1) conesponds to the lower value of X, i.e. 0. However, since the model solution, eq. (4.141), is asymptotic to the X - axis, the lower X to be used is 0.01. Iliis dimensionless exit concentration can be viewed as the first appearance concentration. This restriction provides the maximum allowable relative flow rate or the minimum residence time in order to have the first appearance of the solute for 7 > 0. For La = 0.1, [7V(r 7)] = -1.2311 (eq. (4.141)). 

A minimum residence time of 10 to 30 minutes should be provided to assure that surges do not upset the system and to provide for some coalescence. As discussed previously, potential benefits of providing more residence time probably will not be cost efficient beyond this point. Skimmers with large residence times require baffles to attempt to distribute flow and eliminate short-circuiting. Tracer studies have shown dial skniimei tanks, even those with carefully designed spreaders and baffles, exhibit poor flow behavior and short-circuiting This is probably due to density and temper-atuie differences, deposition of solids, corrosion of spreaders. etc... 

The minimum value of 2 in our experiments was 221 and the minimum residence time studies was I minute. These values yield A= 1/221 and F(X) 0.0045. Thus, after the vessel volume has been swept once by bubbles, only 0.457 of the contents appears in the effluent. 

Beda (B3), 1961 Minimum residence time in agreement with Brauer s (B14) effective surface velocity results up to Nbm = 400. Distribution function agrees with theory in presence of surfactants. Theoretical treatment of film flow of liquid permeating through porous wall, with heat transfer. 

TABLE 14-8 Recommended Minimum Residence Time in the Downcomer... 

However, checks should be made that flow is fully turbulent at both scales and that the drop size remains within the inertial subrange of turbulence [Eq. (46)]. As a minimum, residence time should be maintained, i.e.,... 

Another method to increase the number of polymer particles produced in the first stage reactor with initiator and emulsifier concentrations fixed is to employ a plug flow type reactor such as a tubular reactor for the first stage. The minimum residence time of a plug flow reactor 6 necessary to produce the same number of polymer particles as in E batch reactor is tc. Thus, from Eq.(31) We have ... 

The mean residence time rm of gas can be related to the geometric configuration of the cyclone and the inlet flow rate. It is reasonable to take rm as the average of the minimum residence time rmi and the maximum residence time rm2, where rmi is the average time required for the gas to descend from the midlevel of the entrance to the exit at the bottom of the cyclone. Thus, we have... 

L Length of the settling chamber 1ml Minimum residence time... 

In this case, because perfect back mixing exists, the internal and external RTD functions are identical. This can be easily verified from Table 7.1, recalling that the minimum residence time in this case is zero. This is generally not the case in laminar flow systems where, in principle, the RTD functions can be calculated from the velocity profiles. It should be noted that in complex systems, a precise description of the path the fluid follows between subsystems is also needed to calculate the RTD. 

While the minimum residence time is significant for dispersive mixing, the residence time distribution in the extruder influences distributive mixing as a measure for longitudinal mixing performance [20]. The average residence time depends only on screw pitch and screw speed in partially-filled screw sections, and only on throughput in fully-filled screw sections. 

The minimum residence times in compounding twin screw extruders for an average production run range from 5-15 seconds. 

Maximum skin temperature m Tube length (m) Pressure drop (10 Pa) Average heat flux (kJ/h.m Minimum residence time (s)... 

Minimum flow rate is determined by suspension heat susceptibility. Available mechanical energy is high and 5 to 7 H. P. per gallon is available from the power train. High flow rates or minimum residence time make power consumption reasonable. 

Ethane enters the pyrolysis section, which comprises a series of cracking furnaces. The ethane is heated as quickly as possible to the cracking temperature and maintained at this temperature for the minimum residence time. In order to lower the hydrocarbon partial pressure and mitigate coke forming in the pyrolysis tubes, steam is added to the ethane prior to entering the pyrolysis section (not shown). 

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