Second-order reactions isothermal

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

The kinetic rate constant may be computed from the adiabatic temperature rise [38] or the isothermal heat release [37]. For a second order reaction ... 

Consider an isothermal, laminar flow reactor with a parabolic velocity profile. Suppose an elementary, second-order reaction of the form A -h B P with rate SR- = kab is occurring with kui 1=2. Assume aj = bi . Find Uoutlam for the following cases ... 

Determine the yield of a second-order reaction in an isothermal tubular reactor governed by the axial dispersion model with Pe = 16 and kt = 2. 

Determine the fractional Ailing rate QflulQ that will All an isothermal, constant-density, stirred tank reactor while simultaneously achieving the steady-state conversion corresponding to flow rate Q. Assume a second-order reaction with aj kt = 1 and t = 5 h at the intended steady state. 

Suppose Figure 20.2 gives the experimental Eft) for a reactor in which a liquid-phase, second-order reaction (A —> products) is taking place isothermally at steady-state. The... 

We shall see in Chapter 5 that knowledge of /a.bCV X, V b) suffices to close the chemical source term for the isothermal, second-order reaction... 

For complex chemical source terms, this expression generates new unclosed terms that are particularly difficult to model. Even for an isothermal, second-order reaction with... 

For non-linear chemical reactions, this term leads to new unclosed terms that are difficult to model. For example, even the isothermal second-order reaction, (3.142), where the joint dissipation chemical source term is given by... 

For an irreversible second-order reaction to which eqn. (13) applies, integration of the design equation, again assuming isothermal conditions, yields... 

A great deal of attention has been devoted to this topic because of the interesting and often solvable mathematical problems that it presents. Results of such calculations for isothermal zero-, first-, and second-order reactions in uniform cylindrical pores are summarized in Figure 17.6. The abscissa is a modified Thiele modulus whose basic definition is... 

According to Eqs. (18)-(20), a generalized isothermal model of reaction and diffusion in a catalyst slab with the second order reaction can be solved to obtain the solution series ... 

The accuracy of low-dimensional models derived using the L S method has been tested for isothermal tubular reactors for specific kinetics by comparing the solution of the full CDR equation [Eq. (117)] with that of the averaged models (Chakraborty and Balakotaiah, 2002a). For example, for the case of a single second order reaction, the two-mode model predicts the exit conversion to three decimal accuracy when for (j>2(— pDa) 1, and the maximum error is below 6% for 4>2 20, where 2(= pDd) is the local Damkohler number of the reaction. Such accuracy tests have also been performed for competitive-consecutive reaction schemes and the truncated two-mode models have been found to be very accurate within their region of convergence (discussed below). 

Example 4-11 Isothermal Semibatch Reactor with Second-Order Reaction... 

Fxanqde 4—11 Isothermal Semibatch Reactor with a Second-order Reaction Professional Reference Shelf... 

The use of the PDF is best illustrated by use of a simple example for a single irreversible second order reaction at isotherm conditions, defined by ... 

A second order reaction model gave a good fit to the polymerization reaction in both the catalyzed formulations. In the case of the extended system, this was also confirmed by isothermal measurements at 32°C (Figure 4). The slope of the plot of log reaction rate vs log fraction remaining was 2.1 before the discontinuity and 2 afterwards. This implies that second order kinetics are still followed after the discontinuity which occurs between 55 and 60% reacted. 

Determine the yield of a second order reaction, A -F B — prodnct with ai = bm in an isothermal tubular reactor governed by the axial dispersion model. Specifically, plot fraction unreacted versus aiJd for a variety of Pe. Be sure to show the limiting cases that correspond to a PER and a CSTR. 

The operation of a PFR is constrained by two limits previously discussed maximum allowable pressure drop limits the shortest space times available, while lack of turbulence at low feed rates limits the longest. Within these limits the second-order reaction under discussion here will produce the curve shown in Figure 2.1 if enough error-free points at different space times could be collected. However, the real isothermal PFR operates at steady state and there is a finite, and sometimes considerable, period of clock time required for conditions to settle down after a change in feed rate (i.e. space velocity or space time). 

This section analyses the second order reaction A + B P taking place in an isothermal CSTR-Separator-Recycle system. When the reactants are completely recycled, feasible operation is possible only if the ratio of reactants in the feed matches exactly the stoichiometry. For this reason, only one reactant feed may be on flow control (/a,o=1), while the feed flow rate of the second reactant (/b,o) must be used to control its inventory. Two possible control structures are discussed (Fig.13.22) flow control of the recycle stream of one reactant, or of the reactor effluent, respectively. 

Figure 13.23 Multiple steady states of two-reactants, second-order reaction in isothermal CSTR-Separator-Recycle system...

As our last plantwide control example, let us consider a process in which a second-order reaction A + B — C occurs. There are two fresh feed makeup streams. The process flowsheet consists of a single isothermal, perfectly mixed reactor followed by a separation section. One distillation column is used if there is only one recycle stream. Two are used if two recycle streams exist. 

A second-order reaction A + B C occurs in an isothermal CSTR. The reaction rate is proportional to the concentrations of each of the reactants, and Zb (mole fractions of components A and B). 

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