Isothermal reactors 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... 

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... 

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. 

Compute the transient behavior of the dispersed plug-flow reactor for the isothermal, liquid-phase, second-order reaction... 

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. 

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. 

Figure 7-5 shows the dependence of the isothermal conversion on the Damkoehler number for reactions of the first and second order performed in a batch reactor. If the expected conversion is equal to 90%, then the first order reaction will be four times faster than the second order reaction. 

The case of a steady- or unsteady-state reactor with a non-linear reaction rate is more complicated. For example, with a second-order reaction and isothermal conditions ... 

Clearly, for this second order reaction, the RTD assumption of complete segregation of the fluid elements in the reactor with complete micro-mixing within each individual fluid element affects the conversion of A. This is true for any non-linear reaction rate expression and / or non-isothermal conditions. 

Equation 5-247 is a polynomial, and the roots (C ) are determined using a numerical method such as the Newton-Raphson as illustrated in Appendix D. For second order kinetics, the positive sign (-r) of the quadratic Equation 5-245 is chosen. Otherwise, the other root would give a negative concentration, which is physically impossible. This would also be the case for the nth order kinetics in an isothermal reactor. Therefore, for the nth order reaction in an isothermal CFSTR, there is only one physically significant root (0 < C < C g) for a given residence time f. 

These investigators report that the second-order rate constant for reaction B is equal to 1.15 x 10 3 m3/mole-ksec at 20 °C. Determine the volume of plug flow reactor that would be necessary to achieve 40% conversion of the input butadiene assuming isothermal operating conditions and a liquid feed rate of 0.500 m3/ksec. The feed composition is as follows. 

Notice that in the region of fast chemical reaction, the effectiveness factor becomes inversely proportional to the modulus h2. Since h2 is proportional to the square root of the external surface concentration, these two fundamental relations require that for second-order kinetics, the fraction of the catalyst surface that is effective will increase as one moves downstream in an isothermal packed bed reactor. 

The Diels-Alder liquid-phase reaction between 1,4-benzoquinone (A, C6H4O2) and cy-clopentadiene (B, C5H6) to form the adduct CnHm02 is second-order with a rate constant kx = 9.92 X 10 6 m3 mol 1 s 1 at 25°C (Wassermann, 1936). Calculate the size (m3) of a batch reactor required to produce adduct at the rate of 125 mol h 1, if cAo = cBo = 100 mol m 3, the reactants are 90% converted at the end of each batch (cycle), the reactor operates isothermally at 25°C, and the reactor down-time (for discharging, cleaning, charging)... 

Calculate the ratio of the volumes of a CSTR and a PFR ( Vst pf) required to achieve, for a given feed rate in each reactor, a fractional conversion (/A) of (i) 0.5 and (ii) 0.99 for the reactant A, if the liquid-phase reaction A - products is (a) first-order, and (b) second-order with respect to A. What conclusions can be drawn Assume the PFR operates isothermally at the same T as that in the CSTR. 

At present conversion is 2/3 for our elementary second-order liquid reaction 2A 2R when operating in an isothermal plug flow reactor with a recycle ratio of unity. What will be the conversion if the recycle stream is shut off ... 

The reaction is second order and is performed in an isothermal constant pressure batch reactor. Determine the conversion with time... 

There are two reactors of equal volume available for your use one a CSTR, the other a PFR, The reaction is second order (-r kCX = A Clo(l - X -). irreversible, and is carried out isothermally. 

This is the conversion that will be achieved in a batch reactor for a first-order reaction when the catalyst decay law is second-order. The purpose of this example was to demonstrate the algorithm for isothermal catalytic reactor design for a decaying catalyst. 

P14-11b a second-order irreversible reaction takes place in a nonideal, yet isothermal CSTR. The volume of the reactor is 1000 dm, and the flow rate of the reactant stream is 1 dm /s. At the temperature in the reactor, k = 0.005 dm /mol-s. The concentration of A in the feedstream is 10 mol/dm. The RTD is obtained from a tracer test on this reaetor at the desired feed rate and reaction temperature. From the given RTD ... 

Figure 6.7 Operating curves of isothermal-isobaric batch reactor with second-order gaseous reaction A products for different values of A.

The rate of each reaction is second order (first order with respect to each reactant), and the reaction rate constants at 460°C are k = 0.5 L moP s, k = 0.25, 3/ 1 = 0.10. A gas mixture consisting of 60% propylene and 40% oxygen is charged into a 4-L isothermal reactor operated at 460°C. The initial pressure is 1.2 atm. 

Consider the following isothermal parallel reactions in a constant-volume batch reactor with the reaction order of 1 for the first reaction and order n for the second reaction ... 

Isothermal reactor. This example concerns an elementary, exothermic, second-order reversible liquid-phase reaction in a tubular reactor with a parabolic velocity distribution. Only the mole, rate law, and stoichiometry balance in the tubular reactor are required in ihi.s FEMLAB chemical engineering module. 

Estimate the mass of catalyst required in an isothermal fixed-bed reactor for the second-order, heterogeneous reaction. 

Figure 7.26 Molar flow of A versus reactor volume for second-order, isothermal reaction in a fixed-bed reactor. 

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