Isothermal reactors pressure drop

If the reactor operates isothermally and if the pressure drop is sufficiently low, we have achieved closure. Equations (3.11) and (3.13) together allow a marching-ahead solution. The more common case requires additional equations to calculate pressure and temperature. An ODE is added to calculate pressure P z), and Chapter 5 adds an ODE to calculate temperature T z). 

Example 3.2 Consider the reaction 2A B. Derive an analytical expression for the fraction unreacted in a gas-phase, isothermal, piston flow reactor of length L. The pressure drop in the reactor is negligible. 

The same result is obtained when the fluid is compressible, as may be seen by substituting Sr = Si = S into Equations (3.40) and (3.41). Thus, using geometric similarity to scale isothermal, laminar flows gives constant pressure drop provided the flow remains laminar upon scaleup. The large and small reactors will have the same inlet pressure if they are operated at the same outlet pressure. The inventory and volume both scale as S. 

Consider the reaction B — 2A in the gas phase. Use a numerical solution to determine the length of an isothermal, piston flow reactor that achieves 50% conversion of B. The pressure drop in the reactor is negligible. The reactor cross section is constant. There are no inerts. The feed is pure B and the gases are ideal. Assume bin = F and =0, Ui = 1, and k = n some system of units. 

Consider the gas-phase decomposition A B -b C in an isothermal tubular reactor. The tube i.d. is 1 in. There is no packing. The pressure drop is 1 psi with the outlet at atmospheric pressure. The gas flow rate is O.OSSCF/s. The molecular weights of B and C are 48 and 52, respectively. The entering gas contains 50% A and 50% inerts by volume. The operating temperature is 700°C. The cracking reaction is first order with a rate constant of 0.93 s . How long is the tube and what... 

Nerve gas is to be thermally decomposed by oxidation using a large excess of air in a 5-cm i.d. tubular reactor that is approximately isothermal at 620°C. The entering concentration of nerve gas is 1% by volume. The outlet concentration must be less than 1 part in lO by volume. The observed half-life for the reaction is 0.2 s. How long should the tube be for an inlet velocity of 2m/s What will be the pressure drop given an atmospheric discharge ... 

In the case of non-isothermal situations with significant pressure drop through the reactor, the term... 

Illustrations 8.3 and 8.4 indicate the application of the above analysis to isothermal tubular reactors with negligible pressure drop. 

If one desires to design a pilot scale tubular reactor to operate isothermally at 500 °C, what length of 6-in. pipe will be required to convert 90% of the raw feedstock to methyl acrylate The feedstock enters at 5 atm at a flow rate of 500 lb/hr. Ideal gas behavior may be assumed. A 6-in. pipe has an area of 0.0388 ft2 available for flow. Pressure drop across the reactor may be neglected. 

The dehydrogenation of ethane (A) to ethene (B) is conducted in a 0.5-m3 PFR. The reaction is first-order with respect to A, with a rate constant of 15.2 min-1 at 725°C. The feed contains pure ethane at 725°C, 400 kPa, and a flow rate of 1. 0 kmol min-1. Compare the conversion predicted if isothermal, isobaric conditions are assumed with that if the pressure drop is accounted for with isothermal flow. The diameter of the reactor tube is 0.076 m, and the viscosity of the gas is 2.5 X 10-5 Pa s. 

The E-Z Solve software can be used to integrate equations 15.2-4 and 15.2-11 numerically, while simultaneously updating q, u, p, Re, and / at each step (file exl5-8.msp). The predicted conversion for isothermal, nonisobaric conditions is 0.247 the calculated pressure drop is 114 kPa. If the pressure drop is ignored (i.e., P = 400 kPa throughout the reactor), the resulting conversion is 0.274. Thus, for this case, it is important that the pressure drop be accounted for. 

Reactor model for a first-order reaction To illustrate the effect of pressure drop, consider an isothermal two-phase fixed-bed operation (gas-solid system). In terms of a reactant, the intrinsic reaction rate is... 

Significant amounts of CH4 and C2H2 are also formed but will be ignored for the purposes of this example. The ethane is diluted with steam and passed through a tubular furnace. Steam is used for reasons very similar to those in the case of ethylbenzene pyrolysis (Section 1.3.2., Example 1.1) in particular it reduces the amounts of undesired byproducts. The economic optimum proportion of steam is, however, rather less than in the case of ethylbenzene. We will suppose that the reaction is to be carried out in an isothermal tubular reactor which will be maintained at 900°C. Ethane will be supplied to the reactor at a rate of 20 tonne/h it will be diluted with steam in the ratio 0.3 mole steam 1 mole ethane. The required fractional conversion of ethane is 0.6 (the conversion per pass is relatively low to reduce byproduct formation unconverted ethane is separated and recycled). The operating pressure is 1.4 bar total, and will be assumed constant, i.e. the pressure drop through the reactor will be neglected. 

Mehta (34) has carried out a reactor network optimization study to find improved designs for the production of acrylonitrile in a collaboration between UMIST and one of its industrial partners. Most industrial installations employ fluidized-bed reactors (BP/Sohio process) with a well-mixed reaction zone. Previous process improvements have mainly resulted from better catalysts, which have produced an increase in yield from 58% to around 80%. The reaction model employed in the optimization study is taken from Ref. 81 and considers seven reactions and eight components. Air, pure oxygen, and propylene are available as raw material streams. The optimization study assumes negligible pressure drop along the reaction sections, isothermal and isobaric operation, and negligible mass gas-solid transfer effects. 

To relate the reaction rate or conversion, pressure drop, and temperature variation over a catalyst bed with the operating variables of a reactor, flow rate, catalyst amount etc., so-called mass-, heat- and impulse balances are used in catalytic reaction engineering [4, 8]. This chapter assumes, however, that the catalyst bed is isothermal and the pressure drop over the bed is negligible. This leaves only mass balances for each reactant or product to be considered. For a component i this can be written for part of a catalyst bed or the whole bed as... 

The length of the bed should be at least 5 to 10 times larger than the particle diameter. However, the catalyst bed should also not be too long, as one might face problems with pressure drop and the limited length of the isothermal zone of the furnaces, which adjusts the temperature of the reactors. 

Selection of the laboratory reactor requires considerable attention. There is no such thing as a universal laboratory reactor. Nor should the laboratory reactor necessarily be a reduced replica of the envisioned industrial reactor. Figure 1 illustrates this point for ammonia synthesis. The industrial reactor (5) makes effective use of the heat of reaction, considering the non-isothermal behavior of the reaction. The reactor internals allow heat to exchange between reactants and products. The radial flow of reactants and products through the various catalyst beds minimizes the pressure drop. In the laboratory, intrinsic catalyst characterization is done with an isothermally operated plug flow microreactor (6). 

Champagnie et al. [1992] adopted the aforementioned model to describe the performance of an isothermal shell-and-tube membrane reactor for ethane dehydrogenation in a co-current flow mode. Using Equation (10-8la) to represent the reaction kinetics and assuming no reactions and pressure drops on both the tube and shell sides, they were... 

The reactions are elementary and take place in the gas phase. The reaction is to be carried out isothermally and as a first approximating pressure drop will be neglected. The feed consists of hydrogen gas, carbon monoxide, j carbon dioxide, and steam. The total molar flow rate is 300 mo /s. The entering pressure may be varied between 1 atm and 160 atm and the entering temperature between 300 K and 400 K. Tubular (PFR) reactor volumes between 0.1 m and 2 m are available for use. 

For the case of isothermal operafion with no pressure drop, we were able to obtain an analytical solution, given by equation B, which gives the reactor volume necessary to achieve a conversion X for a gas-phase reaction carried out isothermaliy in a PFR, However, in the majority of situations, analytical solutions to the ordinary differential equations appearing in (he combine step are not possible. Consequently, we include POLYMATH, or some other ODE solver such as MATLAB, in our menu in that it makes obtaining solutions to the differential equations much more palatable, ... 

Pressure drop in isothermal reactors a. Variable density with c 7 0 ... 

The differences between the TBR and the MR originate from the differences in catalyst geometry, which affect catalyst load, internal and external mass transfer resistance, contact areas, as well as pressure drop. These effects have been analyzed by Edvinsson and Cybulski [ 14,26] via computer simulations based on relatively simple mathematical models of the MR and TBR. They considered catalytic consecutive hydrogenation reactions carried out in a plug-flow reactor with cocurrent downflow of both phases, operated isothermally in a pseudo-steady state all fluctuations were modeled by a corresponding time average ... 

Membrane-enclosed packed-bed reactor. Plug-flow regime at both membrane sides. Isothermal system. No axial or radial diffusion. Mass transfer rate constant all over the membrane. Negligible pressure drop at the catalyst side. 

This chapter focuses attention on reactors that are operated isothermally. We begin by studying a liquid-phase batch reactor to determine the specific reaction rate constant needed for the design of a CSTR. After illustrating the design of a CSTR from batch reaction rate data, we cany out the design of a tubular reactor for a gas-phase pyrolysis reaction. This is followed by a discussion of pressure drop in packed-bed reactors, equilibrium conversion, and finally, the principles of unsteady operation and semibatch reactors. 

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