Time constant isothermal operation

One irreversible chemical reaction occurs in a constant-volume batch reactor. The reaction is exothermic and a digital controller removes thermal energy at an appropriate rate to maintain constant temperature throughout the course of the reaction. Sketch the time dependence of the rate of thermal energy removal, d 2/t< f)removai vs. time, for isothermal operation when the rate law is described by ... 

Example 14.1 Consider a first-order reaction occurring in a CSTR where the inlet concentration of reactant has been held constant at uq for f < 0. At time f = 0, the inlet concentration is changed to Up Find the outlet response for t > 0 assuming isothermal, constant-volume, constant-density operation. 

The design q>roblem can be approached at various levels of sophistication using different mathematical models of the packed bed. In cases of industrial interest, it is not possible to obtain closed form analytical solutions for any but the simplest of models under isothermal operating conditions. However, numerical procedures can be employed to predict effluent compositions on the basis of the various models. In the subsections that follow, we shall consider first the fundamental equations that must be obeyed by all packed bed reactors under various energy transfer constraints, and then discuss some of the simplest models of reactor behavior. These discussions are limited to pseudo steady-state operating conditions (i.e., the catalyst activity is presumed to be essentially constant for times that are long compared to the fluid residence time in the reactor). 

Some aspects of reactor behavior are developed in Chapter 5, particularly concentration-time profiles in a BR in connection with the determination of values of and k2 from experimental data. It is shown (see Figure 5.4) that the concentration of the intermediate, cB, goes through a maximum, whereas cA and cc continuously decrease and increase, respectively. We extend the treatment here to other considerations and other types of ideal reactors. For simplicity, we assume constant density and isothermal operation. The former means that the results for a BR and a PFR are equivalent. For flow reactors, we further assume steady-state operation. 

From heat balance, the heat removal by jacket along time such that reactor operates in constant temperature X2 (isothermic operation) can be computed. Thus, from heat balance, the heat removal to induce steady-state in reactor temperature is as follows... 

Equation 5-16 is the time required to achieve a conversion XA for either isothermal or non-isothermal operation. Equation 5-16 can also be expressed in terms of concentration at constant fluid density as... 

External mass transfer limitations, which cause a decrease in both the reaction rate and selectivity, have to be avoided. As in the batch reactor, there is a simple experimental test in order to verify the absence of these transport limitations in isothermal operations. The mass transfer coefficient increases with the fluid velocity in the catalyst bed. Therefore, when the flow rate and amount of catalyst are simultaneously changed while keeping their ratio constant (which is proportional to the contact time), identical conversion values should be found for flow rate high enough to avoid external mass transfer limitations.[15]... 

Fluid mechanics and mixing operations in various types of equipment, agglomeration as well as disintegration and mechanical separation processes, just to mention a few, are described by parameters, the dimensions of which only consist of three base dimensions Mass, Length and Time. An isothermal process is assumed The physical properties of the material system under consideration are related to a constant process temperature. The process relationships obtained in this way are therefore valid for any constant, random process temperature to which the numerical values of the physical properties are related. This holds true as long as there is no departure from the scope of the validity of the respective process characteristic verified by the tests. 

The PTGC technique involves increasing the column temperature at a preset rate during the elution process. This rate may be constant throughout the run, or periods of isothermal operation may be automatically programmed at set times between temperature increases. Generally, the electronically controlled ovens are designed to increase temperature at rates from 0.5-30°C per minute. The initial temperature should be chosen to minimize the retention time for the least retained solute, while the final temperature must be sufficient to elute the least volatile compound in a reasonable time. The instrument then automatically resets the temperature to the initial value in preparation for the next sample. 

It is possible to express Eq. (3-10) for isothermal operation in simpler forms when assumptions such as constant density are permissible. These will be considered in Chap. 4. The constant-density form of Eq. (3-10) was used in Chap. 2 to calculate rate constants from measured conversions or concentrations as a function of time (see, for example. Sec. 2-7). It is important to recall that we could determine the rate equation for the chemical step from a form of Eq. (3-10) because the reactor is assumed to be an ideal stirred-tank type, with no physical resistances involved. 

The isothermal batch polymerization in Example 2.8 converted 80% of the monomer in 2 h. You want to do the same thing in a meso-pilot plant using a capillary tube. (If the tube diameter is small enough, assumptions of piston flow and isothermal operation may be reasonable even for laminar flow. Criteria are given in Chapters 8 and 16.) The tube has an ID of 0.0015 m and it is 1 m long. The monomer density is 900 kg m and the polymer density is 1040 kg m . The pseudo-flrst-order rate constant is 0.8047 h and the residence time needed to achieve 80% conversion is t = 2 h. What flow rate should be used ... 

Fig. 10. The fraction of oil vapor formed which is degraded due to overcracking as function of oil vapor residence time. Data for isothermal operation at 482°C (Wilkins et al., 1981). The calculations were carried out with a first-order reaction rate constant for oil degradation, kt = 3 x 103exp(—8700/7 ) [s-,l...

In the case of isothermal operation one component with or without solvent is charged initially. The reactor contents are then heated up to the desired temperature. At this point the feed of the second reactant, separately premixed and preheated, is started with a constant rate. The jacket temperature is adjusted in proportion to the heat production rate with the help of controls. The maximum driving temperature difference occurs within the first half of the feed time. 

Besides the flow, one shonld consider the mass and heat transfer limitations. In reactors without bed, one may calculate the heat and mass exchange and determine the conditions for an adiabatic or isothermal operation, since the temperatnre profile in the reactor is known. For uniform velocities, the heat transfer depends on the heat capacities if they are constant, the temperature profile is uniform. Otherwise, there are considerable deviations and consequently large temperatnre variations. In catalytic reactors, there is also the influence of conductive heat of the particles. The temperature affects substantially the rate constant and conseqnently the reaction rate. At the same time, mass transfer limitation may be present dne to convection and diffnsion inside the pores of the particles, which depend on the flnid flow and the diffnsive properties of molecules. Mass transfer limitation affects significantly the rate constant and consequently the reaction rate causing different residence times of the molecnles. 

In thermal characterization, a controlled amount of heat is applied to a sample and its effect measured and recorded. In isothermal operations, the effect is recorded as a function of time at constant temperature. In a programmed temperature operation, the temperature is changed in a predetermined fashion, e.g., at a certain rate, and the effect is recorded as a function of temperature. General texts on thermal characterization inciude Wendlandt [85], Daniels [86], and Turi [87]. 

For an isothermal operation and a first-order reaction with respect to reactant A rj = kcA) and constant volume, rearrangement of Eqs. (4.10.19) and (4.10.25) yields the residence time and Da number, respectively, needed to reach a certain conversion in a CSTR and a PFR ... 

For non-isothermal operation of a CSTR, the term non-isothermal only refers to the difference between the reaction temperature and the inlet temperature. For steady-state operation, the reaction temperature is constant at any time but higher (lower) than the feed temperature for an exothermic (endothermic) reaction. Thus, the heat and mass balances have to be examined simultaneously. The steady-state mass balance for an ideal CSTR, Eq. (4.10.17), for a first-order reaction with reactant A is given in terms of conversion and residence time as ... 

A stream of groundwater flowing at a rate of 700 gal/min and containing 100 ppm of trichloroethylene (TCE) is to be stripped with air to reduce the TCE concentration to 5 ppb (drinking water quality). The tower is to be packed with 2-in polypropylene slotted rings and is to operate at 30 percent of flooding defined at constant liquid rate L, at a gas flow rate four times the minimum. Determine the tower diameter and height. Assume isothermal operation at 50°F and 1 atm. The density of the liquid stream is 62.4 Ib/ft that of the gas stream is 0.0778 Ib/ft. ... 

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