Single-Feed Reactions

Reactions with a single reactant producing two products are easy to design and control because there is no need to balance the stoichiometry 

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Single irreversible reactions. An excess of one feed component can force another component toward complete conversion. As an... 

At a fixed temperature, a single, reversible reaction has no interior optimum with respect to reaction time. If the inlet product concentration is less than the equilibrium concentration, a very large flow reactor or a very long batch reaction is best since it will give a close approach to equilibrium. If the inlet product concentration is above the equilibrium concentration, no reaction is desired so the optimal time is zero. In contrast, there will always be an interior optimum with respect to reaction time at a fixed temperature when an intermediate product in a set of consecutive reactions is desired. (Ignore the trivial exception where the feed concentration of the desired product is already so high that any reaction would lower it.) For the normal case of bin i , a very small reactor forms no B and a very large reactor destroys whatever B is formed. Thus, there will be an interior optimum with respect to reaction time. 

The difference between complete segregation and maximum mixedness is largest when the reactor is a stirred tank and is zero when the reactor is a PFR. Even for the stirred tank case, it has been difficult to find experimental evidence of segregation for single-phase reactions. Real CSTRs approximate perfect mixing when observed on the time and distance scales appropriate to industrial reactions, provided that the feed is premixed. Even with unmixed... 

The input to each SCWO reactor will be an aqueous solution containing agent and energetics hydrolysates. Mixing these streams provides a single feed stream for the SCWO step and simplifies the overall process. In the reaction zone at the upper end of the reactor, oper-... 

The single feed composition investigated consisted of 133mmols/L of caprolactam-magnesium-bromide and 45 mmols/L of the difunctional isophthaloyl-bis-caprolactam. Note that 45 mmols/L of the difunctional isophthaloyl-bis-caprolactam contain 90 mmols/L of the active acyllactam group, which react with the monolunctional caprolactam-magnesium-bromide to initiate the polymerization reaction. 

Let us consider a shallow fluidized bed combustor with multiple coal feeders which are used to reduce the lateral concentration gradient of coal (11). For simplicity, let us assume that the bed can be divided into N similar cylinders of radius R, each with a single feed point in the center. The assumption allows us to use the symmetrical properties of a cylindrical coordinate system and thus greatly reduce the difficulty of computation. The model proposed is based on the two phase theory of fluidization. Both diffusion and reaction resistances in combustion are considered, and the particle size distribution of coal is taken into account also. The assumptions of the model are (a) The bed consists of two phases, namely, the bubble and emulsion phases. The voidage of emulsion phase remains constant and is equal to that at incipient fluidization, and the flow of gas through the bed in excess of minimum fluidization passes through the bed in the form of bubbles (12). (b) The emulsion phase is well mixed in the axial... 

Steady-state Flow Consider the simple case of a single feed stream and a single product stream, as shown in Fig. 3-1 a. The properties of these streams do not change with time. Hence the first and second terms in Eq. (3-1) are constants, equal to the mass-flow rate of limiting reactant multiplied by At. Suppose there is only one reaction occurring. If the mass-flow rate of reactant corresponding to zero conversion is F, and its conversion in the feed stream is Xp, then F(-l — Xp) At is the first term and, similarly, F(1 — x At is the sei nd. Since the reaction mixture in the vessel is at uniform temperature and composition, the rate of reaction is constant and should be evaluated at the temperature and composition of the product stream. If the rate of conversion of reactant is r, with the subscript e indicating exit or product conditions, the third term in Eq. (3-1) is x VAt. There can be no accumulation of mass of reactant in the reactor at steady-state conditions, so the fourth term is zero. Then Eq. (3-1) can be written... 

In this chapter, we describe an algorithm for predicting feasible splits for continuous single-feed RD that is not limited by the number of reactions or components. The method described here uses minimal information to determine the feasibility of reactive columns phase equilibrium between the components in the mixture, a reaction rate model, and feed state specification. This is based on a bifurcation analysis of the fixed points for a co-current flash cascade model. Unstable nodes ( light species ) and stable nodes ( heavy species ) in the flash cascade model are candidate distillate and bottom products, respectively, from a RD column. Therefore, we focus our attention on those splits that are equivalent to the direct and indirect sharp splits in non-RD. One of the products in these sharp splits will be a pure component, an azeotrope, or a kinetic pinch point the other product will be in material balance with the first. 

In contrast to other esterifications, a significant extent of reaction can be reached even without a catalyst though the reaction equilibrium constant is approximately one. A compilation of the major physical property data can be found elsewhere [25, 87]. Fig. 10.2 shows the residue curve map in transformed coordinates as introduced by Doherty and coworkers [108] at a pressure of 1.013 bar. Due to a single maximum azeotrope, there are two distillation regions. The concentration profile in a single feed, two product lab-scale column with 45 bubble cap trays is also displayed in Fig. 10.2. The column is fed with a stoichiometric feed of formic acid and methanol and operated at a reflux ratio of 5. Water and the desired methyl formate are recovered at purities of about 97 % molar concentration in the bottoms and at the top, respectively. 

The design equations for a single-feed distillation column using these variables have been formulated by Barbosa and Doherty (1988a,b,c) (see also Rev, 1994). The procedure has been extended to multiple reactions by several authors (see, e.g., Ung and Doherty, 1994a,b,c, and Kolah et al., 1996). The appearance of multiple steady states in the solution of the DCR equations has also been considered (Huan et al., 1995) in methyl-/ert-butyl ether production. 

I Reaction and Feed Specification All of the examples described in this chapter possess equivalent versions involving residence time as well. If it is desired to retain the same components as before, and also include residence time in the state vector, then the resulting AR must be of one dimension higher than that originally posed— two-dimensional problems in concentration space are thus three-dimensional problems if residence time is considered as well. With this in mind, consider now the single autocatalytic reaction involving components A and B... 

We find that all six vertices in 8j and 8j belong to 8 j. All three stoichiometric subspaces are shown in Figure 8.5. Note that 8(ot is a convex polytope that resides in a three-dimensional space, whereas 8[ and 82 alone are both two-dimensional subspaces, indicating that the AR from a single feed Cfi or is two-dimensional—they both exist as planes in c -Cb-Cc space. Thus, for multiple feeds, the dimension of the AR could exceed the number of independent reactions, as mixing between different stoichiometric subspaces is possible. 

Copolymers can be obtained from a single feed (e.g., ethylene) by concurrent tandem catalysis, using two catalysts. The first makes ethylene oligomers, while the second copolymerizes the oligomers with ethylene to give linear, low-density polyethylene (LLDPE). This is illustrated in Scheme 5.8. While the need for mutual chemical compatibility limits possible catalyst combinations in solution, dispersed supported catalysts may be unable to interact as long as they remain immobilized, and may therefore tolerate each other better. However, it is necessary to match the catalytic activity of the two catalysts (via the catalyst ratio, as well as the reaction conditions) so that both contribute significantly to the overall reaction. 

In single phase reactions carried out in one pass, as a neutralization would be, accurate control of the ratio of the reactants is of paramount importance. Excess of any reactant is not only wasted, but may cause undesirable side reactions, Including corrosion. If an end-point analyzer, such as pH, is available, it must be used for feedback trim of the reactant ratio. iManually set ratio control of the feed streams is ordinarily not accurate enough, particularly if the composition of one stream is variable. 

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