Perfectly Stirred Reactors

K. K. Boon, "A Flexible Mathematical Model for Analy2ing Industrial P. F. Furnaces," M.S. thesis. University of Newcasde, AustraUa, Sept. 1978. R. H. Essenhigh, "A New AppHcation of Perfectly Stirred Reactor (P.S.R.) Theory to Design of Combustion Chambers," TechnicalEeport FS67-1 (u), Peimsylvania State University, Dept, of Euel Science, University Park, Pa., Mar. 1967. 

Figure P8.38 shows a simplified block diagram of the process. The plant consists of a perfectly stirred reactor, a decanter, and a distillation column in series. There is recycle from the column reboiler to the reactor.

COSILAB Combustion Simulation Software is a set of commercial software tools for simulating a variety of laminar flames including unstrained, premixed freely propagating flames, unstrained, premixed burner-stabilized flames, strained premixed flames, strained diffusion flames, strained partially premixed flames cylindrical and spherical symmetrical flames. The code can simulate transient spherically expanding and converging flames, droplets and streams of droplets in flames, sprays, tubular flames, combustion and/or evaporation of single spherical drops of liquid fuel, reactions in plug flow and perfectly stirred reactors, and problems of reactive boundary layers, such as open or enclosed jet flames, or flames in a wall boundary layer. The codes were developed from RUN-1DL, described below, and are now maintained and distributed by SoftPredict. Refer to the website http //www.softpredict.com/cms/ softpredict-home.html for more information. 

Fig. 15.9 Steady-state solutions for the benzene mole fraction from the simulation of benzene oxidation near a turning point in a perfectly stirred reactor. Depending on the starting estimates, a number of spurious (nonphysical) solultions may be encountered. The true solution is indicated by the filled circles, while the shaded diamonds indicate (sometimes spurious) solutions that are computed through various continuation sequences.

The primary objective of this chapter is to develop low-dimensional representations of chemically reacting flow situations. Specifically these include batch reactors (corresponding to homogeneous mass-action kinetics), plug-flow reactors (PFR), perfectly stirred reactors (PSR), and one-dimensional flames. The derivations also serve to illustrate the approach that is taken to derive appropriate systems of equations for other low-dimensional circumstances or flow situations. 

Three ideal reactors—the batch reactor, the plug-flow reactor and the perfectly stirred reactor—are mathematical approximations to corresponding laboratory reactors that are used regularly to study chemical kinetics (Section 13.3.2). The batch reactor (or static reactor) is particularly useful to characterize explosion limits [241] and kinetic behavior at temperatures below 1000 K (e.g., [304,351]), while stirred reactors (e.g., [151,249,296, 367,397]) and flow reactors (e.g., [233,442]) have proved highly valuable in the study of chemical kinetics at higher temperatures. 

The perfectly stirred reactor (PSR) or continuously stirred tank reactor (CSTR) is an idealization that proves useful in describing laboratory experiments and can often be used in the modeling of practical situations. As illustrated in Fig. 16.4, gases enter the reactor with a mass-flow rate of m, a temperature of T, and a mass-fraction composition of Y . Once inside the reactor, the gases are presumed to mix instantaneously and perfectly with the gases already resident in the reactor. Thus the temperature and composition within the reactor are perfectly uniform. 

Deriving the conservation equations that describe the behavior of a perfectly stirred reactor begins with the fundamental concepts of the system and the control volume as discussed in Section 23. Here, however, since the system is zero-dimensional, the derivation proceeds most easily in integral form using the Reynolds transport theorem directly to relate system and control volume (Eq. 2.27). 

Fig. 16.5 The reactor formed in the head space above an oscillating piston may be modeled as a perfectly stirred reactor with a time-varying volume.

In Section 16.4 the perfectly stirred reactor problem is derived, without considering surface reaction at the channel walls. Reformulate the problem to include the possibility of elementary heterogeneous chemistry at the reactor walls. 

Assume that the combustion process occurs under well-mixed conditions. Use perfectly stirred reactor software together with the GRI-Mech mechanism (GRIM30. mec) to estimate the formation of NO in adiabatic combustion of CH4 with an excess-air ratio of 1.1... 

Simulate the process using a perfectly stirred reactor model. For the nominal processing conditions, plot the O-atom number density as a function of pressure for... 

Fig. 16.14 A perfectly stirred reactor that is used to develop relatively high levels of atomic oxygen.

Aurora, simulates zero-dimensional perfectly stirred reactor problems, including heterogeneous chemistry at the walls. 

Batch isothermal perfectly stirred reactor (the reaction mixture is at equilibrium with the heat transfer medium). 

PSR A FORTRAN Program for Modeling Well-Stirred Reactors. P. Glar-borg, R. J. Kee, J. F. Grcar, and J. A. Miller. Sandia National Laboratories, Livermore, CA, Sandia Report SAND86-8209,1986. PSR is a FORTRAN computer program (psr.f) that predicts the steady-state temperature and species composition in a perfectly stirred reactor. Input parameters include the reactor volume,... 

The two extremes of the state of mixedness arc represented by the plug flow reactor (PFR, no mixing) and by the perfectly stirred reactor (PSR, perfectly mixed). The reactant flow in the PFR is neither macro nor micro mixed, whereas in the PSR mixing occurs down to the molecular level, thus both macro and micro mixing take place (see Figure 6). A variety of real flows can be characterised by series, parallel or loop connections of PFR and PSR. Additionally there exist other models such as the dispersion model (dispersed plug flow) which allows to model mixing conditions between the two extremes of PFR and PSR. 

Fig. 6 Reactor dynamics of plug flow reactor (PFR), perfectly stirred reactor (PSR) and dispersed plug flow (dispersion model parameter value Bo = 8.8)...

The stability of the uniform stationary states in system (3,4) to small spatially uniform perturbations (SUPs) was studied in detail by the theory of perfectly stirred reactors (see reference 9). It will be recalled that the system... 

To describe patterns of combustion processes, ideal models are often introduced such as piston flow or a perfectly stirred reactor as well as an ideal stirred boiler. For describing the flameless oxidation the model of the loop reactor is appropriate. Figure 23.6 shows different combinations of loop reactors. Here the piston flow (k, = 0) and the well-stirred reactor (k, = °°) can be considered as limiting cases of loop reactors. 

---