Chemical reactors stoichiometric model

To minimize these costs it is therefore necessary to maximize the conversion in the reactor and to avoid as far as possible inert substances in the reaction mixture. With irreversible reactions (e.g., partial oxidations) the trend is therefore towards a highly concentrated, approximately stoichiometric feed composition, which may occasionally be in the explosive range. The resulting problems are addressed in Sections 10.1.3.3 and 10.1.4.2) Since fixed-bed reactors constitute one of the most important classes of chemical reactors, much work has been devoted to their proper mathematical modeling as well as to the study of their stability, sensitivity and automatic control. The following standard text books and monographs can be recommended for further reference [1-4]. 

As the main responsible for the changes in the material balance, the chemical reactor must be modelled accurately from this point of view. Basic flowsheeting reactors are the plug flow reactor (PFR) and continuous stirred tank reactor (CSTR), as shown in Fig. 3.17. The ideal models are not sufficient to describe the complexity of industrial reactors. A practical alternative is the combination of ideal flow models with stoichiometric reactors, or with some user programming. In this way the flow reactors can take into account the influence of recycles on conversion, while the stoichiometric types can serve to describe realistically selectivity effects, namely the formation of impurities, important for separations. Some standard models are described below. 

The selection and design of a chemical reactor is covered in Chapter 8. As mentioned, in an early stage of process development a detailed stoichiometric description is sufficient. Kinetics is necessary only when the recycles have significant influence on products distribution and in consequence on separations. In this case, accurate modelling of the whole reaction system is required, which often is not a simple matter. 

Figure 15.2 shows the flow sheet of the FP-FC system. The fuel forthe system is an aqueous solution of methanol at the molar ratio of methanol to water of 1 2 for the standard case. The fuel is evaporated in the vaporizer (VAP) at 150°C. In the reformer, the vaporized methanol and water react at 250 °C to form a hydrogen-rich gas, which contains also some CO2 and CO. The steam reformer is modeled as a Gibbs reactor assuming chemical equilibrium between the species at the outlet of the reactor. At the reforming temperature of 250 °C, the equilibrium conversion of methanol is almost 100%. The selectivity of methanol to CO2 is about 97% and to CO about 3%. In the mixer (MIX), the hydrogen-rich gas from the reformer is mixed with a small quantity of air, which is needed for the oxidation of CO present in the product gas from the reformer. The selective CO oxidation takes place in the COS reactor at 150 °C. The COS reactor is modeled as a stoichiometric reactor where 50% of the supplied O2 from the air is used for complete oxidation of CO and the remaining 50% of O2 reacts with H2. 

Fig 13.5 Modeling predictions for reaction of a stoichiometric methane-air mixture in a batch reactor at constant temperature (1200 K) and pressure (1 atm) using a detailed chemical kinetic model [31]. 

The general equations for chemical reaction in a turbulent medium are easy to write if not to solve (2). In addition to those for velocities (U = U + uJ and concentrations (Cj = Cj + Cj), balance equations for q = A u, the segregation ( , and the dissipations e and eg can be written (3). Whatever the shape of the reactor under consideration (usually a tube or a stirred tank), the solution of these equations poses difficult problems of closure, as u S, 5 cj, cj, and also c cj, c Cj in the reaction terms have to be evaluated. The situation is even more complicated when the temperature and the density of the reacting mixture are also fluctuating. Partial solutions to this problem have been proposed. In the case of instantaneous reactions (t << Tg) the "e-quilibrium assumption" applies the mixed reactants are immediately converted and the apparent rate of reaction is simply that of the decrease of segregation, with Corrsin s time constant xs. For instance, with a stoichiometric proportion of reactants, the extent of reaction X is given by 1 - /T ( 2), a simple result which can also be found by application of the IEM model (see (33)). 

From a simulation viewpoint units SO, S6 and S7 may be considered blackboxes. On the contrary, SI to S5 are simulated by rigorous distillation columns, as sieve trays. In the steady state all the reactors can be described by a stoichiometric approach, but kinetic models are useful for Rl, R2 and R4 in dynamic simulation [7, 8]. As shown before, the reaction network should be formulated so as to use a minimum of representative chemical species, but respecting the atomic balance. This approach is necessary because yield reactors can misrepresent the process. 

When a detailed chemical description is not required, a limited set of a few stoichiometric equations can be included into the scheme just to describe the rate of heat evolution and change of total number of gas species in the system. Chemically oversimplified models of this kind are widely used, for instance, to describe heat-transfer and to optimize thermal regimes in reactors (see, e.g., Fukuhara and Igarashi, 2005 Kolios et al., 2001). A similar approach is used to describe the fuel combustion and corresponding dynamic phenomena in engines of different types simplified equations describing kinetic features are solved together with complex equations of heat- and mass-transfer and fluid dynamics (Frolov et al., 1997 Williams, 1997). 

Bourne and coworkers [21-23] have developed the mathematics and applied their model to predict the effects of stoichiometric ratio, startup of a semi-batch reactor, effect of volumetric feed ratio, batch vs. continuous operation, etc. They have also experimentally demonstrated the use of reaction systems with well-characterized kinetics to determine the level of micro-mixing. Thus chemical reactions can be considered as molecular probes to be used to study segregation. Other... 

The model consists of a set of partial differential equations for the fluid as well as for the solid catalyst phase with special parameters for the different mechanisms acting in the reactor, such as forced convection, dispersion, mass and heat transfer and the chemical conversion. In case of a complex reaction like the butene oxidation to maleic anhydride /3/ depicted in Figure 2 (with 18 identified reaction steps and even more reactants), the reaction rate term in the reactor model becomes very complex and the number of equations is increased since for any stoichiometrically independent reactant a separate mass balance in both phases is needed. Also an equation describing the pressure drop across the catalyst bed has to be added. 

Fig. 5.25 Normalised estimates of first-order contributions to the overall variance of predicted butane mole fraction at 750 K calculated using first-order local sensitivities (grey) and the global HDMR method (black). Both are derived from a model describing the oxidation of n-butane in a jet stirred reactor (residence time of 6 s, atmospheric pressure, stoichiometric mixtures containing 4 % (mol) -butane diluted in helium). EXGAS notation is used. Adapted with permission from Cord et al. (2012). Copyright (2012) American Chemical Society...

Aspen is capable of modeling chemical reactions. It can handle single and multiple reactions. Material balance can be done in the stoichiometric reactor, Rsto/c from Reactors in the model library. Click on Material Streams, and connect the inlet and product streams. Click on Components and choose the components involved. Peng-Robinson EOS is selected as the thermodynamic fluid package. Doubleclick on the conversion reaction block. Click on the Specification tab enter pressure as 1 atm and temperature as 25°C. Then click on the Reactions tab, click on New and enter the components involved in the reaction, stoichiometric coefficient, and fractional conversion as shown in Figure 3.13. Close the stoichiometric windows and then double click on the inlet stream, specify temperature, pressure, flow rate, and composition. Click Run and then generate the stream table as shown in Figure 3.14. 

---