Steady state conditions reactors

Figure 13.13. Influence of pH on the rate of dissolution of carbonates in the system CaC03-MgC03. These experiments were carried out with a fluidized-bed reactor with carbonate species controlled by the steady-state condition reactor in open systems with controlled CO2. (Adapted from Chou et al., 1989.)...

The flow reactor is typically the one used in large-scale industrial processes. Reactants are continuously fed into the reactor at a constant rate, and products appear at the outlet, also at a constant rate. Such reactors are said to operate under steady state conditions, implying that both the rates of reaction and concentrations become independent of time (unless the rate of reaction oscillates around its steady state value). 

Assuming that this process runs under steady state conditions, as for an industrial flow reactor with a constant inflow of reactants and a constant outflow of products, the concentration of the intermediate will be constant, as expressed in the steady-state assumption ... 

In eqs. 1 and 2, ry M and rco2 denote the molar hourly production of each species per gram of catalyst while pt denotes the catalyst s bulk density (grams catalyst per reactor liter). Each of the catalysts from the Pd-Au-KOAc catalyst series was tested and evaluated under steady-state conditions in the fixed bed reactor under process conditions typical of vinyl acptata synthesis and the VAM STY and VAM SEL results are included as Table 1. 

Flow reactors are fed continuously at one location with streams of reactants already at the required temperature and pressure. The reaction mixture flows out continuously from the end of the reaction zone. Flow reactors are operated under steady-state conditions, i.e. concentrations, temperature, and pressure at a point of the reaction zone are constant. To be precise, they fluctuate with the quality of raw materials and the accuracy of controllers maintaining flows, temperatures, and pressure. 

Cross-flow reactors are fed continuously with streams of components of the reaction mixture whereby some components are introduced at the inlet, while others are introduced at other locations. The reaction mixture flows out continuously from the end of the reaction zone. A cascade of CSTRs with additional feeds to individual reactors represents a cross-flow reactor system. Cross-flow reactors are also operated at steady-state conditions ... 

Although continuous stirred-tank reactors (Fig. 3.12) normally operate at steady-state conditions, a derivation of the full dynamic equation for the system, is necessary to cover the instances of plant start up, shut down and the application of reactor control. 

Under steady-state conditions, variations with respect to time are eliminated and the steady-state model can now be formulated in terms of the one remaining independent variable, length or distance. In many cases, the model equations now result as simultaneous first-order differential equations, for which solution is straightforward. Simulation examples of this type are the steady-state tubular reactor models TUBE and TUBED, TUBTANK, ANHYD, BENZHYD and NITRO. 

The coupling of the component and energy balance equations in the modelling of non-isothermal tubular reactors can often lead to numerical difficulties, especially in solutions of steady-state behaviour. In these cases, a dynamic digital simulation approach can often be advantageous as a method of determining the steady-state variations in concentration and temperature, with respect to reactor length. The full form of the dynamic model equations are used in this approach, and these are solved up to the final steady-state condition, at which condition... 

At steady-state conditions, the mass balance design equations for the ideal tubular reactor apply. These equations may be expressed as... 

In continuous processes the reactants are fed to the reactor and the products withdrawn continuously the reactor operates under steady-state conditions. Continuous production will normally give lower production costs than batch production, but lacks the flexibility of batch production. Continuous reactors will usually be selected for large-scale production. Processes that do not fit the definition of batch or continuous are often referred to as... 

Two fixed-bed reactors can be used in parallel, one reacting and the other regenerating. However, there are many disadvantages in carrying out this type of reaction in a packed bed. The operation is not under steady state conditions, and this can present control problems. Eventually, the bed must be taken off line to replace the solid. Fluidized beds (to be discussed later) are usually preferred for gas-solid noncatalytic reactions. 

Analysis of CSTR Cascades under Nonsteady-State Conditions. In Section 8.3.1.4 the equations relevant to the analysis of the transient behavior of an individual CSTR were developed and discussed. It is relatively simple to extend the most general of these relations to the case of multiple CSTR s in series. For example, equations 8.3.15 to 8.3.21 may all be applied to any individual reactor in the cascade of stirred tank reactors, and these relations may be used to analyze the cascade in stepwise fashion. The difference in the analysis for the cascade, however, arises from the fact that more of the terms in the basic relations are likely to be time variant when applied to reactors beyond the first. For example, even though the feed to the first reactor may be time invariant during a period of nonsteady-state behavior in the cascade, the feed to the second reactor will vary with time as the first reactor strives to reach its steady-state condition. Similar considerations apply further downstream. However, since there is no effect of variations downstream on the performance of upstream CSTR s, one may start at the reactor where the disturbance is introduced and work downstream from that point. In our generalized notation, equation 8.3.20 becomes... 

TO test the reactor and analysis system, pulses of methanol, singly, and completely deuterated methanol were led over the commercial Pe (MoO.) VtoO, catalyst and the two separate phases, m this way, we can check-3if a kinetic isotope takes place on the separate phases, and the measurements can be extended to a larger temperature range more readily than under steady state conditions. The pulses contained about 12% methanol in argon and 10% oxygen. 

The interest in the dynamic operation of heterogeneous catalytic systems is experiencing a renaissance. Attention to this area has been motivated by several factors the availability of experimental techniques for monitoring species concentrations both in the gas phase and at the catalyst surface with a temporal resolution and sensitivity not previously possible, the development of efficient numerical methods for predicting the dynamics of complex reaction systems, and the recognition that in selected instances operation of a catalytic reactor under dynamic conditions can yield a better performance than operation under steady-state conditions. 

A solution of concentration C0 is pumped at a velocity u through a catalyst bed in which the dispersion, coefficient is D and the rate equation is r = 0.001(C-Ce) where Ce is constant. For a boundary condition, note that C will remain constant as distance z = > a>. Find the reactor lengths z that will reduce the displacement of concentration from the equilibrium value by 50% under steady state conditions when (a) D = 0,2 and u=0.05 (b) D - 0.2 and u = 0 (c) D = 0 and u = 0.05. 

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