Residence time distribution nature

In this chapter, we consider nonideal flow, as distinct from ideal flow (Chapter 13), of which BMF, PF, and LF are examples. By its nature, nonideal flow cannot be described exactly, but the statistical methods introduced in Chapter 13, particularly for residence time distribution (RTD), provide useful approximations both to characterize the flow and ultimately to help assess the performance of a reactor. We focus on the former here, and defer the latter to Chapter 20. However, even at this stage, it is important to realize that ignorance of the details of nonideal flow and inability to predict accurately its effect on reactor performance are major reasons for having to do physical scale-up (bench —> pilot plant - semi-works -> commercial scale) in the design of a new reactor. This is in contrast to most other types of process equipment. 

Any process takes a certain amount of time and the length of the residence time often dictates the occasions when particular equipment or technology can be used. On the other hand, in almost all chemical unit processes the driving forces vary from time to time, and therefore time has the nature of non-equivalence, i.e., an equal time interval yields different, even greatly different, results for the early and later stages of a process. The result mentioned here means the processing amount accomplished, such as the increments of reaction conversion, absorption efficiency, moisture removal etc. Normally, these parameters vary as parabolic curves with time. Because of the nature of the non-equivalence of time, in addition to the mean residence time, the residence time distribution (RTD) affects the performance of equipment, and thus receives common attention. 

In nature, residence time distribution is an important behavior of particle crowds because of its complexity, it will be subject of focus in this chapter. 

An impinging stream contactor usually contains several flow spaces of different natures, which exhibit not only different flow characteristics but also different contributions to the residence time distribution. 

According to the nature of residence time distribution, the following relationship should hold ... 

There are various ways to classify mathematical models (5). First, according to the nature of the process, they can be classified as deterministic or stochastic. The former refers to a process in which each variable or parameter acquires a certain specific value or sets of values according to the operating conditions. In the latter, an element of uncertainty enters we cannot specify a certain value to a variable, but only a most probable one. Transport-based models are deterministic residence time distribution models in well-stirred tanks are stochastic. 

In all the just-mentioned examples, quantitative prediction and design require the detailed knowledge of the residence time distribution functions. Moreover, in normal operation, the time needed to purge a system, or to switch materials, is also determined by the nature of this function. Therefore the calculation and measurement of RTD functions in processing equipment have an important role in design and operation. 

Example 7.7 Residence Time Distribution in a CST Stochastic Derivation10 A better insight into the nature of RTD functions can be obtained by deriving the RTD in CST... 

The asymptotic mean size is 59A reached at 0.5 m, assuming that the reactor is an ideal plug flow reactor where all the particles are the same size. To further this anal3 is, we can add dispersion into this reactor analysis and correct for the nonideal nature of this reactor. The dispersion analysis allows the prediction of the geometric standard deviation of the partice size distribution due to variations in the residence time distribution. 

The single-bed reactor is the simplest catalysis reactor. It is completely filled with catalyst and is mainly used for thermally neutral and autothermal gas reactions. Owing to its design, the pressure drop is high, and the residence-time distribution has a major influence on the selectivity and conversion of the reaction. Of particular importance is the maintenance of temperature limits, both axially and radially, as heat removal is naturally poor. An advantage is the ease of catalyst regeneration. 

For the flowing solids phase, a complication in interpretation of the residence time distribution is caused by the nature of the solids holdup. The dynamic holdup is usually assumed to be the operating holdup, and static holdup is often treated as a dead part of flowing solids. However, if there is an exchange between static and dynamic holdup, this affects the residence time distribution of flowing solids, and consequently, the contactor performance. 

The final disposal of nuclear waste is a major question in the environmental debate. One scenario for waste disposal is burying waste in bedrock. Radiotracers have been used to determine bedrock properties by the residence time distributions between boreholes. Another source giving information on how nuclear waste would behave in the bedrock is to study natural analogies, e.g., uranium deposits. 

The batch emulsion polymerization is commonly used in the laboratory to study the reaction mechanisms, to develop new latex products and to obtain kinetic data for the process development and the reactor scale-up. Most of the commercial latex products are manufactured by semibatch or continuous reaction systems due to the very exothermic nature of the free radical polymerization and the rather limited heat transfer capacity in large-scale reactors. One major difference among the above reported polymerization processes is the residence time distribution of the growing particles within the reactor. The broadness of the residence time distribution in decreasing order is continuous>semibatch>batch. As a consequence, the broadness of the resultant particle size distribution in decreasing order is continuous>semibatch>batch, and the rate of polymerization generally follows the trend batch>semibatch>continuous. Furthermore, the versatile semibatch and continuous emulsion polymerization processes offer the operational flexibility to produce latex products with controlled polymer composition and particle morphology. This may have an important influence on the application properties of latex products [270]. 

A factor in addition to the RTD and temperature distribution that affects the molecular weight distribution (MWD) is the nature of the chemical reaciion. If the period during which the molecule is growing is short compared with the residence time in the reactor, the MWD in a batch reactor is broader than in a CSTR. This situation holds for many free radical and ionic polymerization processes where the reaction intermediates are very short hved. In cases where the growth period is the same as the residence time in the reactor, the MWD is narrower in batch than in CSTR. Polymerizations that have no termination step—for instance, polycondensations—are of this type. This topic is treated by Denbigh (J. Applied Chem., 1, 227 [1951]). 

The deposition velocities depend on the size distribution of the particulate matter, on the frequency of occurrence and intensity of precipitation, the chemical composition of the particles, the wind speed, nature of the surface, etc. Typical values of and dj for particles below about 1 average residence time in the atmosphere for such particles is a few days. 

Due to its chemical inertness, vaporizable nature (enthalpy of vaporization = 59.15 kJ/mol), and low water solubility (at 20°C, 2 x 10 6 g/g), elemental mercury vapor has over one year of residence time, long-range transport, and global distribution in the atmosphere [3-8]. 

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