The closer the reaction is to first order, the closer the predicted extremes of response. The more peaked the residence time distribution, the closer the extremes, and the smaller the extent of reaction, the closer the extremes. [Pg.214]

For reaction other than first order, the reaction probability depends on the time that a molecule has been in the reactor and on the concentration of other molecules encountered during that time. The residence time distribution does not allow a unique estimate of the extent of reaction, but some limits can be found. [Pg.564]

In the CRE literature, the residence time distribution (RTD) has been shown to be a powerful tool for handling isothermal first-order reactions in arbitrary reactor geometries. (See Nauman and Buffham (1983) for a detailed introduction to RTD theory.) The basic ideas behind RTD theory can be most easily understood in a Lagrangian framework. The residence time of a fluid element is defined to be its age a as it leaves the reactor. Thus, in a PFR, the RTD function E(a) has the simple form of a delta function [Pg.27]

Figure 4. Transient responses to slug (left) and step (right) inputs of reactant for first order reaction and selected kr values. The flow has the same residence time distribution as two perfectly mixed vessels in sequence. For slug input, c0 = m /V. |

ILLUSTRATION 11.4 COMPARISON OF CONVERSION LEVELS ATTAINED IN TWO DIFFERENT REACTOR COMBINATIONS HAVING THE SAME RESIDENCE TIME DISTRIBUTION CURVE—FIRST-ORDER REACTION [Pg.410]

A further important conclusion is that for a given C-curve or residence time distribution obtained from tracer studies, a unique value of the conversion in a chemical reaction is not necessarily obtainable unless the reaction is first order. Tracer measurements can certainly tell us about departures from good macromixing. However, tracer measurements cannot give any further information about the extent of micromixing because the tracer stimulus-response is a first-order (linear) process as is a first-order reaction. [Pg.77]

For isothermal, first-order chemical reactions, the mole balances form a system of linear equations. A non-ideal reactor can then be modeled as a collection of Lagrangian fluid elements moving independently through the system. When parameterized by the amount of time it has spent in the system (i.e., its residence time), each fluid element behaves as abatch reactor. The species concentrations for such a system can be completely characterized by the inlet concentrations, the chemical rate constants, and the residence time distribution (RTD) of the reactor. The latter can be found from simple tracer experiments carried out under identical flow conditions. A brief overview of RTD theory is given below. [Pg.3]

A system of N continuous stirred-tank reactors is used to carry out a first-order isothermal reaction. A simulated pulse tracer experiment can be made on the reactor system, and the results can be used to evaluate the steady state conversion from the residence time distribution function (E-curve). A comparison can be made between reactor performance and that calculated from the simulated tracer data. [Pg.273]

We observe that it is the uniformity of the dense phase and the linearity on the bubble side that allows us the freedom to use any residence time distribution. The reaction term, which we made first order for simplicity, can be nonlinear. A discussion of various generalizations is given in [310]. [Pg.43]

This program is designed to simulate the resulting residence time distributions based on a cascade of 1 to N tanks-in-series. Also, simulations with nth-order reaction can be run and the steady-state conversion obtained. A pulse input disturbance of tracer is programmed here, as in example CSTRPULSE, to obtain the residence time distribution E curve and from this the conversion for first order reaction. [Pg.333]

The black box is closed again. This section assumes that the system is isothermal and homogeneous and that its residence time distribution is known. Reaction yields can be predicted exactly for first-order reactions. For other reactions, [Pg.561]

Consider the system to possess a specific RTD, E(f), and that the reactor is fed with a homogeneous, perfectly mixed feed stream. If a first-order reaction takes place within this reactor the system will be described by linear equations. In this case, the reaction kinetics and the system residence time distribution totally define the conversion of reactant which would be achieved in that system. In other words, any reactor system possessing that particular RTD under consideration would give the same feed conversion [Pg.241]

Exercise 7.9.6, Investigate the model in which the feed is split into fractions X and (I — X) and sent to parallel reactors whose volumes are in the ratio / (1 — p). Find the residence time distribution, and the mean and variance of residence times. For a first order reaction A —> B, show that the ratio of the concentration of A in the product stream for this system to its concentration from a single tank of the same mean residence time 0 is [Pg.222]

Since the dimensionless time for a first-order reaction is the product of the reaction time t and a first-order rate constant k, there is no reason why k(x)t should not be interpreted as k(x)t(x), that is, the reaction time may be distributed over the index space as well as the rate constant. Alternatively, with two indices k might be distributed over one and t over the other as k x)t(y). We can thus consider a continuum of reactions in a reactor with specified residence time distribution and this is entirely equivalent to the single reaction with the apparent kinetics of the continuum under the segregation hypothesis of residence time distribution theory, a topic that is in the elementary texts. Three indices would be required to distribute the reaction time with a doubly-distributed continuous mixture. [Pg.191]

Now that a combination of the tabulated data and exponential tail allows a complete description of the residence time distribution, we are in a position to evaluate the moments of this RTD, i.e. the moments of the system being tested [see Appendix 1, eqn. (A.5)] The RTD data are used directly in Example 4 (p. 244) to predict the conversion which this reactor would achieve under specific conditions when a first-order reaction is occurring. Alternatively, in Sect. 5.5, the system moments are used to evaluate parameters in a flexible flow-mixing transfer function which is then used to describe the system under test. This model is shown to give the same prediction of reactor conversion for the specified conditions chosen. [Pg.236]

Thus, for known kinetics and a specified residence time distribution, we can predict the fractional conversion of reactant which the system of Fig. 9 would achieve. Recall, however, that this performance is also expected from any other system with the same E(t) no matter what detailed mixing process gave rise to that RTD. Equation (34) therefore applies to all reactor systems when first-order reactions take place therein. In the following example, we apply this equation to the design of the ideal CSTR and PFR reactors discussed in Chap. 2. The predicted conversion is, of course, identical to that which would be derived from conventional mass balance equations. [Pg.243]

Given [/( )] f°r any reactor, you automatically have an expression for the fraction unreacted for a first-order reaction with rate constant k. Alternatively, given aout(k), you also know the Laplace transform of the differential distribution of residence time (e.g., /f [/(/)] = exp(—t/t) for a PFR). This fact resolves what was long a mystery in chemical engineering science. What is f(t) for an open system governed by the axial dispersion model Chapter 9 shows that the conversion in an open system is identical to that of a closed system. Thus, the residence time distributions must be the same. It cannot be directly measured in an open system because time spent outside the system boundaries does not count as residence but does affect the tracer measurements. [Pg.563]

Another approach to evaluate the performance of a trickle-bed reactor (particularly a pilot-scale reactor) is to incorporate the RTD with intrinsic kinetics. Since the liquid holdup, catalyst wetting, or the degree of axial dispersion can all be obtained from the RTD, this approach is not exclusive of the ones described above. For a first-order reaction, if the residence-time distribution E(t) and the degree of conversion are known, they can both be related by an expression [Pg.112]

Tanks-in-series reactor configurations provide a means of approaching the conversion of a tubular reactor. In modelling, they are employed for describing axial mixing in non-ideal tubular reactors. Residence time distributions, as measured by tracers, can be used to characterise reactors, to establish models and to calculate conversions for first-order reactions. [Pg.405]

© 2019 chempedia.info