Stirred-tank reactor steady-state design

Consider the schematic representation of a continuous flow stirred tank reactor shown in Figure 8.5. The starting point for the development of the fundamental design equation is again a generalized material balance on a reactant species. For the steady-state case the accumulation term in equation 8.0.1 is zero. Furthermore, since conditions are uniform throughout the reactor volume, the material balance may be... 

Steady-State Absorption Column Design 471 Oxidation of O-Xylene to Phthalic Anhydride 324 Continuous Stirred Tank Reactor Model of Activated 577... 

The equations that have been developed for design using these pseudo constants are based on steady-state mass balances of the biomass and the waste components around both the reactor of the system and the device used to separate and recycle microorganisms. Thus, the equations that can be derived will be dependent upon the characteristics of the reactor and the separator. It is impossible here to present equations for all the different types of systems. As an illustration, the equations for a common system (a complete mix - stirred tank reactor with recycle) are presented below. 

In Table I the high-vacuum (HV) range means a pressure of 10 to 10 Torr entries designated by Torr mean pressures between 0.1 and 10 Torr flow refers to an unspecified steady-state flow pattern. It is apparent from Table I that there is a great diversity in the different oscillation conditions and catalytic systems. The pressures under which oscillations have been observed vary from 10 Torr for the CO/NO reaction on Pt(lOO) 141, 142) to atmospheric pressure for a large number of systems. The reactors used in these studies include ultrahigh-vacuum (UHV) systems, continuous stirred tank reactors (CSTRs), flow reactors, and reactors designed as infrared (IR) cells, calorimeters, and ellipsometric systems. 

The classical problem of steady-state multiplicity in a continuous stirred tank reactor (CSTR) was brought to popular attention in 1953 in the theoretical article by Van Heerden. " Large amounts of experimental work which measured these steady states were performed by the group of Schmitz beginning in 1970. Schmitz also wrote two excellent reviews on multiplicity, stability, and sensitivity of steady states in chemical reactors and the application of bifurcation theory to determine the presence of steady-state multiplicity in chemical reactors.Even these reviews are not inclusive and it is our intention in this subsection to only provide a background to the novice in reactor design. 

Design of a Steady-State Stirred-Tank Reactor... 

To illustrate the design/control trade-off more quantitatively, let us consider a simple chemical engineering system a series of continuous stirred-tank reactors (CSTRs) with jacket cooling. This type of reactor system is widely used in industry. The reactions and the reactors are quite simple, but they provide some important into evaluating the tradc-offs between steady-state design id eontroL In this section we consider the sin pfe po ibie reai ih reaction A... 

Multiple steady-state behavior is a classic chemical engineering phenomenon in the analysis of nonisothermal continuous-stirred tank reactors. Inlet temperatures and flow rates of the reactive and cooling fluids represent key design parameters that determine the number of operating points allowed when coupled heat and mass transfer are addressed, and the chemical reaction is exothermic. One steady-state operating point is most common in CSTRs, and two steady states occur most infrequently. Three stationary states are also possible, and their analysis is most interesting because two of them are stable whereas the other operating point is unstable. 

The simplest flow-sheet for the reaction Aj o Aj is the RD column sequence with an external recycling loop shown in Fig. 5.1. The system as a whole is fed with pure Aj. According to the assumed relative volatility of the two components a > 1, the reaction product A2 is enriched in the column distillate product whereas the bottom product contains non-converted reactant Aj, which is recycled back to the reactor (continuous stirred tank reactor, CSTR, or plug flow tube reactor, PFTR). The process has two important operational variables the recycling ratio cp = B/F, that is the ratio of recycling flow B to feed flow rate F, and the reflux ratio of the distillation column R = L/D. At steady-state conditions, D = F since the total number of moles is assumed to be constant for the reaction Aj A2. As principal design variables, the Damkohler number. 

There is one significant difference between batch and continuous stirred tanks. The heat balance for a CSTR depends on the inlet temperature, and Tm can be adjusted to achieve a desired steady state. As discussed in Section 5.3.1, this is a very scaleable approach to reactor design. 

Nonisothermal stirred tanks are governed by an enthalpy balance that contains the heat of reaction as a significant term. If the heat of reaction is unimportant so that a desired Tout can be imposed on the system regardless of the extent of reaction, then the reactor dynamics can be analyzed by the methods of the previous section. This section focuses on situations where Equation 14.3 must be considered as part of the design. Even for these situations, it is usually possible to control a steady-state CSTR at a desired temperature. If temperature control can be achieved rapidly, then isothermal design techniques again become applicable. Rapid means on a time scale that is fast compared to reaction times and composition changes. 

Different types of continuous reactor systems will be described in this chapter. Particular emphasis will be placed on configurations fliat contain one or more stirred tanks. The influence of reactor system design and opmtional variables on product characteristics will be reviewed for some systems. The utility of steady-state CSTRs for fundamental kinetic studies will be illustrated with several... 

The limiting cases of continuous reactors considered in most reactor design textbooks are the perfectly mixed stirred tank and the plug-flow tube. These reactors can differ significantly in the amount of mixing and, therefore, the residence time distribution. The plug-flow tube (PFT) is assumed to be without any axial mixing. Hence, at steady state, the residence time distribution of the material in the effluent stream is represented by the Dirac function as shown by Equation (8.1) ... 

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