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Tracer balance

Consider a series of well-stirred reactors each having the same volume, where the total volume is VR. Let Cl5 C2. . . Cm. . . Cn be the concentrations leaving the successive stages of the CSTR. The unsteady state tracer balance on the mth stage is... [Pg.713]

We perform a tracer balance on each reactor to obtain Cj(f)... [Pg.949]

Tracer balance Accumulation = -output. If perfectly mixed, = C... [Pg.481]

Taking an unsteady-state tracer balance around the reactor. [Pg.207]

Taking the unsteady-state tracer balance in the /th CSTR, we get... [Pg.211]

Consider a tubular reaction vessel (Figure 3.61) of length L and cross-sectional area A. q is the volumetric flow rate of the fluid flowing through the vessel, u = q/A is the mean velocity of the fluid. Q = L/u is the mean residence time of the fluid. Tracer test is conducted on the vessel by injecting the tracer material into the fluid at inlet. C(Z, 0) is the concentration of the tracer in the fluid at a distance Z from the inlet and at the time 0 after the time of injection of tracer. Taking an unsteady-state tracer balance around the vessel section of thickness AZ at a distance Z from the inlet, we get... [Pg.220]

The reaction vessel is subjected to a tracer test to obtain the RTD F(0) or E(0), which is further used for the estimation of model parameters. Assume that a step test is conducted and Cq is the feed tracer concentration, C(0) is the effluent tracer concentration and C (0) is the tracer concentration in the active volume. Tracer concentration in the bypass stream is the same as the feed concenfrafion Cq. Taking an unsteady-sfafe tracer balance around the active volume, we get... [Pg.238]

The tracer balance will be checked using Eqn. (10-2). Thisbalancemustbe satisfied ifthe data are... [Pg.390]

If the source fingerprints, for each of n sources are known and the number of sources is less than or equal to the number of measured species (n < m), an estimate for the solution to the system of equations (3) can be obtained. If m > n, then the set of equations is overdetermined, and least-squares or linear programming techniques are used to solve for L. This is the basis of the chemical mass balance (CMB) method (20,21). If each source emits a particular species unique to it, then a very simple tracer technique can be used (5). Examples of commonly used tracers are lead and bromine from mobile sources, nickel from fuel oil, and sodium from sea salt. The condition that each source have a unique tracer species is not often met in practice. [Pg.379]

Relatively uncomphcated transparent tank studies with tracer fluids or particles can give a similar feel for the overall flow pattern. It is important that a careful balance be made between the time and expense of calculating these flow patterns with computational flirid dynamics compared to their apphcabihty to an actual industrial process. The future of computational fluid dynamics appears very encouraging and a reasonable amount of time and effort put forth in this regard can yield immediate results as well as potential (or future process evaluation. [Pg.1642]

For operation with an inert tracer, the material balances are conveniently handled as Laplace transforms. For a stirred tank, the differential equation... [Pg.2075]

The unsteady material balances of tracer tests are represented by linear differential equations with constant coefficients that relate an input function Cj t) to a response function of the form... [Pg.2082]

Kinds oi Inputs Since a tracer material balance is represented by a linear differential equation, the response to anv one kind of input is derivable from some other known input, either analytically or numerically. Although in practice some arbitrary variation of input concentration with time may be employed, five mathematically simple input signals supply most needs. Impulse and step are defined in the Glossaiy (Table 23-3). Square pulse is changed at time a, kept constant for an interval, then reduced to the original value. Ramp is changed at a constant rate for a period of interest. A sinusoid is a signal that varies sinusoidally with time. Sinusoidal concentrations are not easy to achieve, but such variations of flow rate and temperature are treated in the vast literature of automatic control and may have potential in tracer studies. [Pg.2083]

A material balance on the tracer in the third reactor where C2 enters and C3 leaves gives... [Pg.716]

The tracer is injected into the duct at a constant rate and mixed with the flowing air. The concentration of the air-tracer mixture is measured further downstream. Assuming perfect mixing and that the air entering the test section has a zero concentration, the air volume flow rate can be calculated based on the mass balance of the tracer... [Pg.1166]

In gridpoint models, transport processes such as speed and direction of wind and ocean currents, and turbulent diffusivities (see Section 4.8.1) normally have to be prescribed. Information on these physical quantities may come from observations or from other (dynamic) models, which calculate the flow patterns from basic hydrodynamic equations. Tracer transport models, in which the transport processes are prescribed in this way, are often referred to as off-line models. An on-line model, on the other hand, is one where the tracers have been incorporated directly into a d3mamic model such that the tracer concentrations and the motions are calculated simultaneously. A major advantage of an on-line model is that feedbacks of the tracer on the energy balance can be described... [Pg.75]

The only respect in which the hot atom chemistry of organometallic compounds has so far been applied to other fields of study is in the area of isotope enrichment. Much of this has been done for isolation of radioactive nuclides from other radioactive species for the purpose of nuclear chemical study, or for the preparation of high specific activity radioactive tracers. Some examples of these applications have been given in Table II. The most serious difficulty with preparation of carrier-free tracers by this method is that of radiolysis of the target compound, which can be severe under conditions suited to commercial isotope production, so that the radiolysis products dilute the enriched isotopes. A balance can be struck in some cases, however, between high yield and high specific activity (19, 7J),... [Pg.247]

Total mass balance 15, 29, 131 Total reflux 588, 615 Tracer 162... [Pg.700]

The response of the axial dispersion model to step or pulse tracer inputs can be determined by writing a material balance over a short tubular segment and then solving the resultant differential equations. A transient material balance on a cylindrical element of length AZ gives... [Pg.397]

It should be noted that an overall material balance requires that all the tracer pass the monitoring station. [Pg.399]

Equations 11.1.33 and 11.1.39 provide the basis for several methods of estimating dispersion parameters. Tracer experiments are used in the absence of chemical reactions to determine the dispersion parameter )L this value is then employed in a material balance for a reactive component to predict the reactor effluent composition. We will now indicate some methods that can be used to estimate the dispersion parameter from tracer measurements. [Pg.401]

In Section 11.1.3.1 we considered the longitudinal dispersion model for flow in tubular reactors and indicated how one may employ tracer measurements to determine the magnitude of the dispersion parameter used in the model. In this section we will consider the problem of determining the conversion that will be attained when the model reactor operates at steady state. We will proceed by writing a material balance on a reactant species A using a tubular reactor. The mass balance over a reactor element of length AZ becomes ... [Pg.412]

Since both Xj and X] are independent of z, the relationship between X3 and X j can be approximated by material balance of the coarse particles injected into the bed to serve as the tracer. [Pg.304]

Consider a small volume of fluid q a entering the vessel virtually instantaneously over the time interval dt at a particular time (t = 0). Thus q 0 = qdt, such that q V and dt t. We note that only the small amount q 0 enters at t = 0. This means that at any subsequent time t, in the exit stream, only fluid that originates from q is of age f to t + dt all other elements of fluid leaving the vessel in this interval are either older or younger than this. In an actual experiment to measure E(t), q g could be a small pulse of tracer material, distinguishable in some manner from the main fluid. In any case, for convenience, we refer to q 0 as tracer, and to obtain E(t), we keep track of tracer by a material balance as it leaves the vessel. Note that the process is unsteady-state with respect to q 0 (which enters only once), even though the flow at rate q (which is maintained) is in steady state. [Pg.325]

If we let cf be the amount of tracer left in the vessel at time t, then the concentration (volume fraction) of tracer in the vessel is q /V. A material balance for the tracer around the vessel at time t is... [Pg.325]


See other pages where Tracer balance is mentioned: [Pg.349]    [Pg.3077]    [Pg.829]    [Pg.895]    [Pg.966]    [Pg.981]    [Pg.726]    [Pg.283]    [Pg.520]    [Pg.195]    [Pg.349]    [Pg.3077]    [Pg.829]    [Pg.895]    [Pg.966]    [Pg.981]    [Pg.726]    [Pg.283]    [Pg.520]    [Pg.195]    [Pg.47]    [Pg.269]    [Pg.181]    [Pg.57]    [Pg.979]    [Pg.352]    [Pg.565]    [Pg.593]    [Pg.597]    [Pg.56]    [Pg.234]    [Pg.403]    [Pg.68]    [Pg.368]   
See also in sourсe #XX -- [ Pg.881 ]

See also in sourсe #XX -- [ Pg.389 ]




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