Temperature-time trajectories

In many large-scale reactors, such as those used for hydrotreating, and reaction systems where deactivation by poisoning occurs, the catalyst decay is relatively slow. In these continuous-flow systems, constant conversion is usually necessary in order that subsequent processing steps (e.g., separation) are not upset. One w to maintain a constant conversion with a decaying catalyst in a packed or fluidized bed is to increase the reaction rate by steadily increasing the feed temperature to the reactor. (See Figme 10-26.) 

We will neglect any variations in concentration so that the product of the activity, a, and specific reaction rate, k, is constant, and equal to the specific reaction rate, kp at time t = 0 and temperature Tq, i.e., 

Equation (10-119) tells us how the temperature of the catalytic reactor should be increased with time in order for the reaction rate to remain unchanged with time. 

For a first-order decay, Krishnaswamy and Kittrell s expression [Equation (10-119)] for the temperature-time trajectory reduces to 

---

If, for example, the reactor temperature is disturbed from 2/3, the high temperature steady state, to y4 that is not a steady-state temperature, then the static diagram helps us to determine the direction of temperature change towards a steady state of the system as follows. At y4 the heat generation exceeds the heat removal since G(y4) > R(y4) from the graph. Therefore, the temperature will increase. A quantitative analysis of the temperature-time trajectory can of course only be determined from a dynamic model of the system. 

Figure E7-2.2 Comparison for temperature-time trajectory for ethylene.

Adapted from the problem by Ronald Willey, Seminar on a Nitroanaline Reactor Rupture. Prepared for SAGHE, Center for Chemical Process Safety, American Institute of Chemical Engineers, New York (1994). The values of and UA were estimated in the plant data of the temperature-time trajectory in the article by G. C. Vincent, Loss Prevention, Vol. 5. p. 46-52, AIChE, New York NY. 

Plot the temperature-time trajectory up to a period of 120 min after the reactants were mixed and brought up to 175°C. Showthat the following three conditions had to have been present for the explosion to occur (1) increased ONCB charge, (2) reactor stopped for 10 min, and (3) relief system failure. 

Return of the cooling occurs at 55 min. The values at the end of the period of adiabatic operation (T = 468 K, X = 0.04.23) become the initial conditions for the period of operation with heat exchange. The cooling is turned on at its maximum capacity, Q = UA(29S — T),at 55 min. Table E9-2.1 gives the POLYMATH program to determine the temperature-time trajectory. 

The complete temperature-time trajectory is shown in Figure E9-2.2. One notes the long plateau after the cooling is turned back on. Using the values of Qg and 2, at 55 min and substituting into Equation (E9-2.S), we find that... 

Slow decay - Temperature-Time Trajectories (10.7.2) Moderate decay -Moving-Bed Reactors (10.7.3)... 

Gra uaUj raisi The goal is to find how the temperature should be increased with time (i.e., the e temper ure c temperature-time trajectory) to maintain constant conversion. Substituting for... 

Figure 10-27 Temperature-time trajectories for deactivating hydrocracking catalyst, runs 3 and 4. [Reprinted with permission from S. Knshnaswamy and S. R. Kittrell, Ind. Eng. Chern. Process Des. Dev., 18,399 (1979)..Copyright 1979 American Chemical Society.]...

For slow catalyst decay the idea of a temperature-time trajectory is to increase the temperature in such a way that the rate of reaction remains constant. 

Suppose that E- = 25 kcal/mol and Ej = 10 kcal/mol. What would the temperature-time trajectory look like for a CSTR What if Ep = 10 kcal/mol andE = 25 kcal/mol ... 

Model the reactor as a fluidized-bed CSTR. The following temperature-time trajectory was implemented to offset the decay. 

Batch reactors operated adiabatically are often used to determine the reaction orders, activation energies, and specific reaction rates of exothermic reactions by monitoring the temperature-time trajectories for different initial conditions. In the steps that follow, we will derive the temperature-cons crsion relationship for adiabatic operation. 

Again, this temperature is called the onset temperature. A typical thermal history of data collected by the ARSST is shown in Figure 9-2 in terms of the temperature-time trajectory. 

The self-heating rate. 7s. can be easily found by differentiating the temperature-time trajectory, or 7s can be deieimined directly from the output instrumentation and software associated with the ARSST. 

Acetic anhydride is placed in the ARSST to form a 6.7 molar solution of ai anhydride and a 20,1 M solution of water. The sample volume is 10 ml. The ele cal heating is started, and the temperature and its derivative, fs. are recorded function of time by the ARSST system and computer. Analyze the data to fine heat of reaction Affni, the activation energy E. and the frequency factor A, and to compare theoretical and experimental temperature-time trajectories. 

Figure E9-5.2 Temperature-time trajectory for CSTR startup.

Explain the observed temperature-time trajectory. To make your analysis simpler, you may assume that the only reaction taking place is... 

What would the temperature-time trajectory look like for a CSTR ... 

WC. and . 1 and. 2. Each set of parameters had a Temperature time trajectory and a tempcratureconcentration phase plane. These are the four graphs. 

---