Calculation of residence time

The calculation of time quantities half-life (r1/2) in a BR and a CSTR (constant density), problem 2-1 calculation of residence time t for variable density in a PFR (Example 2-3 and problem 2-5). 

If liquids are controlling, the residence time varies from 2.5 to 5 min, half full, depending on water content. With this vessel design parameter In mind, reference should be made to the expected production decline and produced water cut time profiles. A decision can then be made based on calculation of residence times If 75% or 50% unit trains should be designed For the problem illustrated, 2 x 73% units would be selected to permit flex iblllty (Table 4). 

Numerical Calculation of Residence Time and Dispersion Number. 

An important step forward in understanding elemental abundance in the ocean was the calculation of residence times for each element (Barth, 1952). Some elements, like Be and Al, have a residence time of the order of 102 years, while the value for Na is 108 years. Any large-scale change in the chemistry of the oceans would have had to influence the input and output of the main ions over at least millions or even billions of years. 

Pilot plant work is essential as a basis for full scale design. It may be directed to finding suitable velocities, temperatures and drying times, or it may employ more basic approaches. The data provided for Example 9.8, for instance, are of particle size distribution, partial pressure of water in the solution, and heat and mass transfer coefficients. These data are sufficient for the calculation of residence time when assumptions are made about terminal temperatures. 

Calculations of residence times can be useful in estimating how far from its source a species is likely to remain airborne before it is removed from the atmosphere. 

The effects of substrate location in the reactor and flow rate are discussed in the same section since these two variables are the ones that have the most influence on the residence time of the reactant molecules in the hot zone of the reactor upstream of the substrate. The calculation of residence time is as follows... 

T can be calculated from the geometry of the ceU and the drift velocity, but ion residence time in an ICR cell is a complex function of many variables. As Smith and Futrell 2 2) have shown experimentally, calculations of residence times are correct only for very low electron currents and trapping voltages. When dc electron currents approach 0.5 [i,A, or when the trapping voltage is equal to or greater than one-half of the drift voltage, the theoretically calculated residence time may be in error by more than 25%. These authors therefore determine the residence time experimentally from the lag time of a pulse sequence and measurements of TIC 200,262) ... 

Krokida et al. [28] proposed a model for the design of a rotary dryer, based on the estimation of the drying kinetics of the material that express data from laboratory experiments, and the calculation of residence time of the dryer from... 

Axial Dispersion and the Peclet Number Peclet numbers are measures or deviation from phig flow. They may be calculated from residence time distributions found by tracer tests. Their values in trickle beds are fA to Ve, those of flow of liquid alone at the same Reynolds numbers. A correlation by Michell and Furzer (Chem. Eng. /., 4, 53 [1972]) is... 

Calculate the residence time and volume of an MSMPR crystallizer required to produce 1000 kg/li of potash alum having a dominant crystal size of 600 pm using a slurry density of 250 kg crystals/m slurry. 

There is some debate about what controls the magnesium concentration in seawater. The main input is rivers. The main removal is by hydrothermal processes (the concentration of Mg in hot vent solutions is essentially zero). First, calculate the residence time of water in the ocean due to (1) river input and (2) hydro-thermal circulation. Second, calculate the residence time of magnesium in seawater with respect to these two processes. Third, draw a sketch to show this box model calculation schematically. You can assume that uncertainties in river input and hydrothermal circulation are 5% and 10%, respectively. What does this tell you about controls on the magnesium concentration Do these calculations support the input/removal balance proposed above Do any questions come to mind Volume of ocean = 1.4 x 10 L River input = 3.2 x lO L/yr Hydrothermal circulation = 1.0 x 10 L/yr Mg concentration in river water = 1.7 X 10 M Mg concentration in seawater = 0.053 M. 

Figure 5.31 Experimental results ( ) and calculated values ( ) for conversion of butyraldehyde as a function of residence time [10],...

The comparison is made by calculating the residence times required for a particular value of fraction conversion. This allows a comparison of the reactor volumes for a given flow rate. Levenspiel (1972) presents graphical plots similar to those generated by this program. 

Vessels in which chemical reactions are conducted in the plant or laboratory are of various shapes and internal arrangements. The distribution of residence times in them of various reacting molecules or aggregates, the RTD, is a key datum for determining the performance of a reactor, either the expected conversion or the range in which the conversion must fall. How the RTD is measured or calculated and applied is the subject of this chapter. The main application of interest here is to find how nearly a particular vessel approaches some standard ideal behavior, or what its efficiency is. 

In a well-stirred reservoir at steady-state, we can calculate the residence time of the element from... 

Broecker and Li (1970) and Broecker (1974) found that the 14C/12C ratio in the deep ocean was 84 percent of this ratio in the pre-bomb surface ocean. Assuming that surface carbon (dissolved and falling debris) is the only source of deep ocean carbon, calculate the residence time tc of this element in the deep-ocean. The 14C decay constant is 1.2 x 10 4a 1. 

From equation (7.2.19), we calculate the residence time of 14C in the deep ocean as... 

Calculate the ratio of residence times in CSTR and PFTR for the wth-order irreversible reaction... 

There is a link between the two calculations in terms of residence time, r, which is influenced by thermodynamic issues. 

Graessley and his co-workers have made calculations of the effects of branching in batch polymerizations, with particular reference to vinyl acetate polymerization, and have considered the influence of reactor type on the breadth of the MWD (89, 91, 95, 96). Use was made of the Bamford and Tompa (93) method of moments to obtain the ratio MJMn, and in some cases the MWD by the Laguerre function procedure. It was found (89,91) that narrower distributions are produced in batch (or the equivalent plug-flow) systems than in continuous systems with mixing, a result referrable to the wide distribution of residence times in the latter. 

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