Residence time definition

Reference electrode, 1104, 1108, 1113 potential, 819, 874 Refractive index, determination with ellipsometry, 1148. 1151 Reflection coefficient, 1151 Residence time, definition, 1310 Reversal techniques, determination of intermediate radicals, 1416 Reversible adsorption of organic molecules, 969, 970... 

Figure 4,4 Residence time definitions. Residence time tn given by For vapor disentrainment = (V2+V3)/(P+R) for a and c...

Guidelines for sump residence time are scarce in the published literature. Those given by Wheeler (420) for chimney trays are the only detailed list available (Table 4.1). Wheeler (420) did not state the residence time definition on which his guidelines are based. The author believes that their application with the above definition is reasonable for chimney trays, bottom sumps, and side-draw drums. Caution is needed when these guidelines are applied, particularly when the main consideration is to buffer upsets. 

Two different definitions are used for downcomer residence time (371). The "apparent residence time is the ratio of the downcomer volume to the clear liquid flow in the downcomer. The downcomer volume is based on the tray spacing times the average downcomer cross section. The true residence time is the ratio of froth volume in the downcomer to the frothy liquid flow in the downcomer. The true residence time can alternatively be expressed as the ratio of the clear liquid volume in the downcomer to the clear liquid flow. Different literature sources use different definitions the definition adopted here is that of the apparent downcomer residence time. The author found this definition easier to apply, and to give a better correlation with the guidelines below [which were based on apparent residence times (49,86)]. Further, the author found that applying the true residence time definition as outlined by some early sources (371) can lead to oversized downcomers. 

Operating condition Basis for residence time definition Recommended residence ... 

Equation (4-51) is the basic design equation for what is popularly called a continuously stirred tank reactor (CSTR). The derivation assumes equality of volumetric flow rate of feed and effluent as in the case of the PFR, the residence-time definition must be changed if this is not so. In most applications of the CSTR, however, reactions in the liquid phase are involved and volume changes with reaction are not important. 

Nonreacdive substances that can be used in small concentrations and that can easily be detected by analysis are the most useful tracers. When making a test, tracer is injected at the inlet of the vessel along with the normal charge of process or carrier fluid, according to some definite time sequence. The progress of both the inlet and outlet concentrations with time is noted. Those data are converted to a residence time distribution (RTD) that tells how much time each fracdion of the charge spends in the vessel. 

The definition of turnover time is total burden within a reservoir divided by the flux out of that reservoir - in symbols, t = M/S (see Chapter 4). A typical value for the flux of non-seasalt sulfate (nss-SOl"") to the ocean surface via rain is 0.11 g S/m per year (Galloway, 1985). Using this value, we may consider the residence time of nss-S04 itself and of total non-seasalt sulfur over the world oceans. Appropriate vertical column burdens (derived from the data review of Toon et ai, 1987) are 460 fxg S/m for nss-801 and 1700 jig S/m for the sum of DMS, SO2, and nss-S04. These numbers yield residence times of about 1.5 days for nss-S04 and 5.6 days for total non-seasalt sulfur. We might infer that the oxidation process is frequently... 

Material flowing at a position less than r has a residence time less than t because the velocity will be higher closer to the centerline. Thus, F(r) = F t) gives the fraction of material leaving the reactor with a residence time less that t where Equation (15.31) relates to r to t. F i) satisfies the definition. Equation (15.3), of a cumulative distribution function. Integrate Equation (15.30) to get F r). Then solve Equation (15.31) for r and substitute the result to replace r with t. When the velocity profile is parabolic, the equations become... 

To quantify Rp in terms of a fundamental, model for the particle residence time the definition in terms of average velocites is used. 

The precise definition of residence times for various stages of reactions by introducing reactants in a spatially confined manner in micro flow devices allows new ways... 

GL 18] ]R 6a]]P 17/Using the same experimental conditions and catalysts with the same geometric surface area, the performance of micro-channel processing was compared with that of a fixed-bed reactor composed of short wires [17]. The conversion was 89% in the case of the fixed bed the micro channels gave a 58% yield. One possible explanation for this is phase separation, i.e. that some micro channels were filled with liquids only, and some with gas. This is unlikely to occur in a fixed bed. Another explanation is the difference in residence time between the two types of reactors, as the fixed bed had voids three times larger than the micro channel volume. It could not definitively be decided which of these explanations is correct. 

In the case of a one-compartment open model with single-dose intravenous administration, the mean residence time is simply the inverse of the elimination transfer constant kp, since according to the above definition we obtain ... 

Figure 5. A schematic representation of superposed steady-state reservoirs of constant volumes Vi (fractional crystallization is omitted in this schema). At steady-state, Vi/xi=V2/x2=..., where x is the residence time. This is analogous to the law of radioactive equilibrium between nuclides 1 and 2 Ni/Ti=N2/T2=...A further interest of this simple model is to show that residence times by definition depend on the volume of the reservoirs.

Vocabulary of Terms Used in Reactor Design. There are several terms that will be used extensively throughout the remainder of this text that deserve definition or comment. The concepts involved include steady-state and transient operation, heterogeneous and homogeneous reaction systems, adiabatic and isothermal operation, mean residence time, contacting and holding time, and space time and space velocity. Each of these concepts will be discussed in turn. 

This is also the fraction of the stream leaving vessel 2 that is of age between t and t + dt, since only the amount nUo entered at t = 0. But this fraction is also E(t)dt, from the definition of E(t). Thus, with V/q = t, the mean residence time for fluid in the two tanks (of total volume V), from (E),... 

This involves obtaining the mean-residence time, 0, and the variance, (t, of the distribution represented by equation 19.4-14. Since, in general, these are related to the first and second moments, respectively, of the distribution, it is convenient to connect the determination of moments in the time domain to that in the Laplace domain. By definition of a Laplace transform,... 

The holdup is calculated from the definition of mean residence time of solid particles ... 

In the statistical theory of fluid mixing presented in Chapter 3, well macromixed corresponds to the condition that the scalar means () are independent of position, and well micromixed corresponds to the condition that the scalar variances are null. An equivalent definition can be developed from the residence time distribution discussed below. 

The site of assembly of the Lp(a) particle, by covalent linkage of apo-B100 to apo(a), is not definitively established. White et al. (W12) proved in baboon hepatocytes that inside the cell two types of apo(a) existed, of which only the larger form was recovered from the culture medium. The lower-molecular-weight form proved to be a precursor with a prolonged residence time in the endoplasmatic reticulum. Density gradient ultracentrifugation and immunoblot analysis showed that the majority of apo(a) was secreted into the medium in a... 

Accordingly, isotopic equilibration for Cr and Se species is expected to be much slower than for the aqueous Fe(III)-Fe(II) couple, which reaches equilibrium within minutes in laboratory experiments (Beard and Johnson 2004). Additionally, Cr(III) and Se(0) are highly insoluble and their residence times in solution are small, which further decreases the likelihood of isotopic equilibration. In the synthesis below, isotopic fractionations are assumed to be kinetically controlled unless otherwise stated. However, definitive assessments of this assumption have not been done, and future studies may find that equilibrium fractionation is attained for some reactions or rmder certain conditions. 

In this model, Fe isotope exchange is envisioned to most likely occur between soluble Fe(III) and Fe(II) components, such as Fe(III)-LFe(in) and Fe(II)-Lpe(n) (Beard et al. 2003a), although only the Fe(II)aq component is measured. If this model is valid, a critical issue is whether isotopic equilibrium may be attained between these soluble pools of Fe, despite the changing reservoir sizes and fluxes that occur through Equations (5)-(8). As noted in the previous chapter (Chapter 1OA Beard and Johnson 2004), attainment of isotopic equilibrium will depend upon the elemental residence time in an Fe pool relative to the time required for isotopic exchange. We can define the residence time for Fe(III)-L, for example, using standard definitions, as ... 

Skeggs innovative step, the introduction of air bubbles into the flowing stream, attempted to minimize the time taken for a steady-state condition to be reached in the detector. The definitive description of dispersion in segmented streams (Snyder [37]) showed a complex relationship between internal diameter, liquid flow rate, segmentation frequency, residence time in the flow system, viscosity of the hquid and surface tension. 

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