Reactors reaction time constant

Reactor capacity per unit volume appears to depend on four resistances in series the gas-phase transfer resistance, two liquid-phase transfer resistances, and the kinetic resistance. The highest resistance limits the capacity of the reactor. The four resistances have the unit of time and each one individually represents the time constant of the particular process under study. For example, 1 lkjigl is the time constant for the transfer of A from the bulk of the gas through the gas film to the gas-liquid interface. The same holds for the three other resistances. For a first-order reaction in a batch reactor, for example, the concentration after a certain time is given by C/C0 = exp(-r/r), in which r = 1/ A is the reaction time constant. For processes in series the individual time constants can be added to find the overall time constant of the total process. 

From Eq. (2), the measured diffusivities may be used to determine the mean lifetime of the reactant and product molecules within the individual crystallites under the assumption that the molecular exchange is exclusively controlled by intracrystalline diffusion. These values, being of the order of 30 ms, are found to agree with the real intracrystalline mean lifetime directly determined by NMR tracer desorption studies (208], so that any influence of crystallite surface barriers may be excluded. From an analysis of the time dependence of the intracrystalline concentration of the reactant and product molecules, the intrinsic reaction time constant is found to be on the order of 10 s. This value is much larger than the intracrystalline mean lifetimes determined by PFG NMR, and thus any limiting influence of mass transfer for the considered reaction may be excluded. In agreement with this conclusion, the size of the applied crystallites was found to have no influence on the conversion rates in measurements with a flow reactor (208]. 

In other words, E is not a function of conversion or molar densities. The characteristic chemical reaction time constant is 25 min. The temperature is the same in each case. The following reactor configurations are employed. 

All reactors operate at the same temperature. The reactor types and configurations are described below. Notice that the total residence time for each configuration is 1 min, whereas the chemical reaction time constants are 1 minutes for the first reaction and 20 min for the second reaction. 

Consider a train of five CSTRs in series that have the same volume and operate at the same temperature. One first-order irreversible chemical reaction occurs in each CSTR where reactant A decomposes to products. Two mass-transfer-rate processes are operative in each reactor. The time constant for convective mass transfer across the inlet and outlet planes of each CSTR is designated by the residence time x = Vjq. The time constant for a first-order irreversible chemical reaction is given >y X = l/k. The ratio of these two time constants,... 

This expression for co is also appUcable for reversible chemical kinetics when the forward and backward reactions are both nth-order. In other words, it is acceptable to define the chemical reaction time constant for reversible reactions in terms of the kinetic rate constant for the forward step. The differential design equation given by (22-14) for one-dimensional convection and one chemical reaction in a plug-fiow tubular reactor reduces to... 

As expected, a shorter reactor is required to achieve the same final conversion when the characteristic chemical reaction time constant u> is smaller and the effectiveness factor E is larger. Since the integral in equation (22-27) that contains the dimensionless kinetic rate law reduces to a constant when the final conversion of... 

The effectiveness factor E is expressed in terms of the intrapellet Damkohler number, and the chemical reaction time constant co is the inverse of the best pseudo-first-order kinetic rate constant. The reactor design engineer employs an integral form of the design equation to predict the length of a packed catalytic tubular reactor Lpfr that will achieve a final conversion of CO specified by /final. The approximate analytical solution, vahd at high mass transfer Peclet numbers, is... 

At high-mass-transfer Peclet numbers, sketch the relation between average residence time divided by the chemical reaction time constant (i.e., r/co) for a packed catalytic tubular reactor versus the intrapeUet Damkohler number Aa, intrapeiiet for zeroth-, first-, and second-order irreversible chemical kinetics within spherical catalytic pellets. The characteristic length L in the definition of Aa, intrapeiiet is the sphere radius R. The overall objective is to achieve the same conversion in the exit stream for all three kinetic rate laws. Put all three curves on the same set of axes and identify quantitative values for the intrapeiiet Damkohler number on the horizontal axis. 

The decomposition of nitrous oxide (NjO) to nitrogen and oxygen is preformed in a 5.0 1 batch reactor at a constant temperature of 1,015 K, beginning with pure NjO at several initial pressures. The reactor pressure P(t) is monitored, and the times (tj/2) required to achieve 50% conversion of N2O are noted in Table 3-19. Use these results to verify that the N2O decomposition reaction is second order and determine the value of k at T = 1,015 K. 

The models presented correctly predict blend time and reaction product distribution. The reaction model correctly predicts the effects of scale, impeller speed, and feed location. This shows that such models can provide valuable tools for designing chemical reactors. Process problems may be avoided by using CFM early in the design stage. When designing an industrial chemical reactor it is recommended that the values of the model constants are determined on a laboratory scale. The reaction model constants can then be used to optimize the product conversion on the production scale varying agitator speed and feed position. 

In Fig. 28, the abscissa kt is the product of the reaction rate constant and the reactor residence time, which is proportional to the reciprocal of the space velocity. The parameter k co is the product of the CO inhibition parameter and inlet concentration. Since k is approximately 5 at 600°F these three curves represent c = 1, 2, and 4%. The conversion for a first-order kinetics is independent of the inlet concentration, but the conversion for the kinetics of Eq. (48) is highly dependent on inlet concentration. As the space velocity increases, kt decreases in a reciprocal manner and the conversion for a first-order reaction gradually declines. For the kinetics of Eq. (48), the conversion is 100% at low space velocities, and does not vary as the space velocity is increased until a threshold is reached with precipitous conversion decline. The conversion for the same kinetics in a stirred tank reactor is shown in Fig. 29. For the kinetics of Eq. (48), multiple solutions may be encountered when the inlet concentration is sufficiently high. Given two reactors of the same volume, and given the same kinetics and inlet concentrations, the conversions are compared in Fig. 30. The piston flow reactor has an advantage over the stirred tank... 

Example 4. Depolymerization under Pressure.62 PET resin was depolymerized at pressures which varied from 101 to 620 kPa and temperatures of 190—240° C in a stirred laboratory reactor having a bomb cylinder of2000 mL (Parr Instrument) for reaction times of 0.5, 1, 2, and 3 h and at various ratios of EG to PET. The rate of depolymerization was found to be directly proportional to the pressure, temperature, and EG—PET ratio. The depolymerization rate was proportional to the square of the EG concentration at constant temperature, which indicates that EG acts as both a catalyst and reactant in the chain scission process. 

The concept of a well-stirred segregated reactor which also has an exponential residence time distribution function was introduced by Dankwerts (16, 17) and was elaborated upon by Zweitering (18). In a totally segregated, stirred tank reactor, the feed stream is envisioned to enter the reactor in the form of macro-molecular capsules which do not exchange their contents with other capsules in the feed stream or in the reactor volume. The capsules act as batch reactors with reaction times equal to their residence time in the reactor. The reactor product is thus found by calculating the weighted sum of a series of batch reactor products with reaction times from zero to infinity. The weighting factor is determined by the residence time distribution function of the constant flow stirred tank reactor. 

The most important characteristic of an ideal batch reactor is that the contents are perfectly mixed. Corresponding to this assumption, the component balances are ordinary differential equations. The reactor operates at constant mass between filling and discharge steps that are assumed to be fast compared with reaction half-lives and the batch reaction times. Chapter 1 made the further assumption of constant mass density, so that the working volume of the reactor was constant, but Chapter 2 relaxes this assumption. 

The flow reactor is typically the one used in large-scale industrial processes. Reactants are continuously fed into the reactor at a constant rate, and products appear at the outlet, also at a constant rate. Such reactors are said to operate under steady state conditions, implying that both the rates of reaction and concentrations become independent of time (unless the rate of reaction oscillates around its steady state value). 

Viscosity evolution.—Figure 2 shows the evolution of the relative viscosity of the reaction medium during the reaction time for a reactor without membrane. Relative viscosity decreased because of the depolymerising activity of the enzyme. After 6 hours of reaction the viscosity became almost constant, which suggested that almost no molecules (polymers) were present in the reactor to contribute to the viscosity. 

The critical feed time t it depends on the location and number of feed pipes, stirrer type, and mixing intensity, and increases with increasing reactor volume. When a constant power-to-volume ratio is preserved, ta-u is proportional to and where D., is the stirrer diameter and Vr the reactor volume (Bourne and Hilber, 1990 Bourne and Thoma, 1991). The productivity of the reactor expressed as the amount of product formed per unit time becomes almost independent of reactor volume. The reason is that the reaction goes to completion in the zone nearby the stirrer tip. The size of this zone increases independently of the tank size it only depends on the velocity of the liquid being injected, the location of the nozzle, and the stirrer geometry and speed of rotation. Accordingly, for rapid reactions, the feed time will also be the reaction time. 

This equation has two parameters t, the mean residence time (z = V/F) with dimensions of time and k, the reaction rate constant with dimensions of reciprocal time, applying for a first-order reaction. The concentration of reactant A in the reactor cannot, under normal circumstances, exceed the inlet feed value, Cao and thus a new dimensionless concentration, Cai, can be defined as... 

The dynamic error existing between and Cr depends on the relative magnitudes of the respective time constants. For the reactor, assuming a first-order, constant volume reaction... 

The reaction time for complete cyanide oxidation is rapid in a reactor system with 10-30 min retention times being typical. The second-stage reaction is much slower than the first-stage reaction. The reaction is typically carried out in the pH range of 10-12 where the reaction rate is relatively constant. Temperature does not influence the reaction rate significantly. 

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