Operation isothermal

A more important case is the adiabatic reactor. As mentioned before, it is difficult in practice to achieve isothermal operation because most reactions have a significant heat effect. In adiabatic operation heat transfer to the reactor wall can be neglected, and the temperature change is only in the longitudinal direction. global rate wiU,.vary Jnw the ed FeSn of concentration and temperature c This case is considered in Sec. 13-4. 

In Chap. 4 the plug-flow model was used as a basis for designing homogeneous tubular ow reactors. The equation employed to calculate the conversion in the effluent stream was either Eq. (3-13) or Eq. (4-5). The same equations and the same calculational procedure may be used for fixed-bed catalytic reactors, provided that plug-flow behavior is a vahd assumption. AH that is necessary is to replace the homogeneous rate of reaction in those equations with the global rate for the catalytic reaction. 

A section of a fixed-bed catalytic reactor is shown in Fig. 13-4. Consider a small volume element of radius r, width Ar, and height Ar, through which reaction mixture flows isothermally. Suppose that radial and longitudinal diffusion can be expressed by Pick s law, with and Dj as effective diffusivities, based on the total (void and nonvoid) area perpendicular to the direction of diffusion. We want to write a mass balance for a reactant over the volume element. With radial and longitudinal diffusion and longitudinal convection taken into account, the input term is 

The volume of the element, which is 2-Kr Ar Az, contains both solid catalyst pellets and surrounding fluid. The concentration in the fluid phase is constant within the element, and the global rate is known (from Chap. 12) in terms of this bulk-fluid concentration. The axial velocity- of the reacting 

Xp = global rate per unit mass of catalyst pp = density of catalyst in the bed u = superficial velocity in the axial direction 

For a liquid-phase reaction, or gas-phase reaction at constant temperature and pressure with no change in the total number of moles, the density of the system may be considered to remain constant. In this circumstance, the system volume (V) also remains constant, and the equations for reaction time (12.3-2) and production rate (12.3-6) may then be expressed in terms of concentration, with cA = nAlV  

Determine the time required for 80% conversion of 7.5 mol A in a 15-L constant-volume batch reactor operating isothermally at 300 K. The reaction is first-order with respect to A, with kA = 0.05 min-1 at 300 K. 

Note that for a first-order reaction, t is independent of cAo 

A liquid-phase reaction between cyclopentadiene (A) and benzoquinone (B) is conducted in an isothermal batch reactor, producing an adduct (C). The reaction is first-order with respect to each reactant, with kA = 9.92 X 10-3 L mol-1 s-1 at 25°C. Determine the reactor volume required to produce 175 mol C h-1, if fA = 0.90, cAo = cBo = 0.15 mol L-1, and the down-time td between batches is 30 min. The reaction is A + B - C. 

This example illustrates the use of the design equations to determine the volume of a batch reactor (VO for a specified rate of production Pr(C), and fractional conversion (/A) in each batch. The time for reaction (0 in each batch in equation 12.3-22 is initially unknown, and must first be determined from equation 12.3-21. 

Since the reaction involves only liquids, it will be assumed that the density remains constant throughout. 

For an isothermal first-order reaction, the design equation may be integrated to give 

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In both of these pieces of apparatus, isothermal operation and optimum membrane area are obtained. Good temperature control is essential not only to provide a value for T in the equations, but also because the capillary attached to a larger reservoir behaves like a thermometer, with the column height varying with temperature fluctuations. The contact area must be maximized to speed up an otherwise slow equilibration process. Various practical strategies for presetting the osmometer to an approximate n value have been developed, and these also accelerate the equilibration process. 

When an atom or molecule receives sufficient thermal energy to escape from a Hquid surface, it carries with it the heat of vaporization at the temperature at which evaporation took place. Condensation (return to the Hquid state accompanied by the release of the latent heat of vaporization) occurs upon contact with any surface that is at a temperature below the evaporation temperature. Condensation occurs preferentially at all poiats that are at temperatures below that of the evaporator, and the temperatures of the condenser areas iacrease until they approach the evaporator temperature. There is a tendency for isothermal operation and a high effective thermal conductance. The steam-heating system for a building is an example of this widely employed process. 

In many appHcations, especially in the chemical and semiconductor fields, the closest possible approach to isothermal operation may be desired. Under these conditions, the effects of vapor velocity must be considered if the velocity of the vapor exceeds about Mach 0.1, when a noticeable temperature differential shows itself in the heat pipe. If near isothermal operation is desired, designers restrict the vapor velocity to lower levels. 

Stea.m-Ra.ising Converter. There are a variety of tubular steam-raising converters (Fig. 7d) available, which feature radial or axial flow, with the catalyst on either shell or tube side. The near-isothermal operation of this reactor type is the most thermodynamically efficient of the types used, requiring the least catalyst volume. Lower catalyst peak temperatures also result in reduced by-product formation and longer catalyst life. 

Separation of Norma/ and Isoparaffins. The recovery of normal paraffins from mixed refinery streams was one of the first commercial appHcations of molecular sieves. Using Type 5A molecular sieve, the / -paraffins can be adsorbed and the branched and cycHc hydrocarbons rejected. During the adsorption step, the effluent contains isoparaffins. During the desorption step, the / -paraffins are recovered. Isothermal operation is typical. 

Continuous-flow stirred-tank reactors ia series are simpler and easier to design for isothermal operation than are tubular reactors. Reactions with narrow operating temperature ranges or those requiring close control of reactant concentrations for optimum selectivity benefit from series arrangements. 

When heat-exchange surface is being provided in the design of an absorber, the isothermal design procedure can be rendered valid by virtue of the exchanger design specifications. With ample surface area and a close approach, isotherm operation can be guaranteed. 

FIG. 23-17 Multiple steady states of CSTRs, stable and unstable, adiabatic except the last item, (a) First-order reaction, A and C stable, B unstable, A is no good for a reactor, the dashed line is of a reversible reaction, (h) One, two, or three steady states depending on the combination Cj, Ty). (c) The reactions A B C, with five steady states, points 1, 3, and 5 stable, (d) Isothermal operation with the rate equation = 0 /(1 -I- C y = (C o Cy/t. 

In the desorption step, ammonia is passed downflow through the bed which has completed the adsorption cycle. The ammonia is heated to approximately the same temperature as that of the feed in the adsorption step in order to maintain a nominally isothermal operation. The first portion of the desorbate, although rich in n-paraffms, contains impurities and is recycled to the second bed which is simultaneously operating on the adsorption cycle. The remaining product is condensed and separated from ammonia. The product is freed of dissolved ammonia by distillation. 

Equation 5-16 is the time required to aehieve a eonversion Xa for either isothermal or non-isothermal operation. Equation 5-16 ean also be expressed in terms of eoneentration at eonstant fluid density as... 

The axial dispersion plug flow model is used to determine the performanee of a reaetor with non-ideal flow. Consider a steady state reaeting speeies A, under isothermal operation for a system at eonstant density Equation 8-121 reduees to a seeond order differential equation ... 

The column is enclosed in a thermostatically controlled oven so that its temperature is held constant to within 0.5 °C, thus ensuring reproducible conditions. The operating temperature may range from ambient to over 400 °C and for isothermal operation is kept constant during the separation process. 

The above consequences of isothermal operation may be largely avoided by using the technique of programmed-temperature gas chromatography (PTGC) in which the temperature of the whole column is raised during the sample analysis. 

Assume isothermal operation, and that no work done by the system. Then the fust law simplifies to ... 

The catalyst in an isothermal tube-wall reactor (experiment TWR-6 in Ref. 2) deactivated much more slowly than did the catalyst in the best test (experiment HGR-14) in an adiabatic HGR reactor (0.009 vs. 0.0291 %/mscf/lb), and it also produced much more methane (177 vs. 32 mscf/lb catalyst). This indicates that adiabatic operation of a metha-nation catalyst between 300° and 400°C is not as efficient as isothermal operation at higher temperature ( 400°C). 

The use of even the very simple models for isothermal operation described in Section IV,B requires a substantial amount of information regarding the elementary iate processes occurring in a gas-liquid-particle operation, as discussed in Section IV,A. While a considerable amount of information of this kind is available in the chemical engineering literature, it is widely scattered. It will be attempted in this section to present a comprehensive review of this information in order to facilitate its use. It is hoped that this review will be of value not only to those chemical engineers directly interested in the practical applications of gas-liquid-particle operations, but also, by pointing to the several areas characterized by very limited information, to those interested in research in this field. 

The most comprehensive simulation of a free radical polymerization process in a CSTR is that of Konopnicki and Kuester (15). For a mechanism which includes transfer to both monomer and solvent as well as termination by combination and disproportionation they examined the influence of non-isothermal operation, viscosity effects as well as induced sinuoidal and square-wave forcing functions on initiator feed and jacket temperature on the MWD of the polymer produced. 

The feed is charged all at once to a batch reactor, and the products are removed together, with the mass in the system being held constant during the reaction step. Such reactors usually operate at nearly constant volume. The reason for this is that most batch reactors are liquid-phase reactors, and liquid densities tend to be insensitive to composition. The ideal batch reactor considered so far is perfectly mixed, isothermal, and operates at constant density. We now relax the assumption of constant density but retain the other simplifying assumptions of perfect mixing and isothermal operation. 

The molar ratio of steam to ethylbenzene at the inlet is 9 1. The bed is 1 m in length and the void fraction is 0.5. The inlet pressure is set at 1 atm and the outlet pressure is adjusted to give a superficial velocity of 9 m/s at the tube inlet. (The real design problem would specify the downstream pressure and the mass flow rate.) The particle Reynolds number is 100 based on the inlet conditions 4 x 10 Pa s). Find the conversion, pressure, and velocity at the tube outlet, assuming isothermal operation. 

This chapter assumes isothermal operation. The scaleup methods presented here treat relatively simple issues such as pressure drop and in-process inventory. The methods of this chapter are usually adequate if the heat of reaction is negligible or if the pilot unit operates adiabatically. Although included in the examples that follow, laminar flow, even isothermal laminar flow, presents special scaleup problems that are treated in more detail in Chapter 8. The problem of controlling a reaction exotherm upon scaleup is discussed in Chapter 5... 

As a general rule, scaled-down reactors will more closely approach isothermal operation but will less closely approach ideal piston flow when the large reactor is turbulent. Large scaledowns will lead to laminar flow. If the large system is laminar, the scaled-down version will be laminar as well and will more closely approach piston flow due to greater radial diffusion. 

Suppose an inert material is transpired into a tubular reactor in an attempt to achieve isothermal operation. Suppose the transpiration rate q is independent of and that qL = Qtrms- Assume all fluid densities to be constant and equal. Find the fraction unreacted for a first-order reaction. Express your final answer as a function of the two dimensionless parameters, QtranslQin and kVIQm where k is the rate constant and... 

Example 4.13 Determine the outlet concentration from a loop reactor as a function of Qi and q for the case where the reactor element is a PFR and the reaction is first order. Assume constant density and isothermal operation. 

Suppose that catalyst pellets in the shape of right-circular cylinders have a measured effectiveness factor of r] when used in a packed-bed reactor for a first-order reaction. In an effort to increase catalyst activity, it is proposed to use a pellet with a central hole of radius i /, < Rp. Determine the best value for RhjRp based on an effective diffusivity model similar to Equation (10.33). Assume isothermal operation ignore any diffusion limitations in the central hole, and assume that the ends of the cylinder are sealed to diffusion. You may assume that k, Rp, and eff are known. 

Comparison of isothermal and nonisothermal policies revealed some interesting features of the polymer system. When M , values determine the isothermal policy, a nonisothermal operation reduces the minimum time compared to isothermal operation (by about 15%). However, when dead-end polymerization influences isothermal operation, a nonisothermal operation does not offer significant improvement. 

Fig. 1 shows the thermal decomposition curves of HDPE mixed with Al-MCM-41, with respect to time, at isothermal operating temperatures. Lag periods were formed at the initial stage of decomposition, possibly due to the heat transfer effect, which could delay the decomposition of a sample until the latter reaches the operating temperatures. As the reaction ten erature increased, the reaction time became noticeably shorter. The shortening of the reaction time was clearly observed when the reaction occurred at the reaction teirperatures between 420 and 460 °C. The HDPE on Al-MCM-41-P decomposed faster than that on blank and that on A1-MCM-41-D, as shown in Fig. 1(b). 

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