Constant volume reactor operation

The same consecutive reactions considered in Prob. 6.18 are now carried out in two perfectly mixed continuous reactors. Flow rates and densities are constant. The volumes of the two tanks (P) are the same and constant. The reactors operate at the same constant temperature. 

Polymerization reactions require stringent operating conditions for continuous production of quality resins. In this paper the chain-growth polymerization of styrene initiated with n-butyllithium in the presence of a solvent is described. A perfectly mixed isothermal, constant volume reactor is employed. Coupled kinetic relationships descriptive of the initiator, monomer, polystyryl anion and polymer mass concentration are simulated. Trommsdorff effects (1) are incorporated. Controlled variables include number average molecular weight and production rate of total polymer. Manipulated variables are flow rate, input monomer concentration, and input initiator concentration. The... 

If w e consider the constant-volume reactor with incompressible fluid (a = 0,Cv = Cp), Equation 6.16 reduces to Equation 6.15 as it should because Equation 6.15 is valid for any reactor operation with an incompressible fluid. We also notice that, in the constant-pressure case, the same energy balance applies for any fluid mixture (ideal gas, incompressible fluid, etc.), and that this balance is the same as the balance for an incompressible fluid in a constant-volume reactor. Although the same final balances are obtained for these two cases, the physical situations they describe are completely different. 

An initial charge of A (methylnaphthalene) is taken in the reactor at a concentration of [A]i, B (hydrogen peroxide solution) at a concentration of [fiJo is added, and the products are withdrawn, both continuously, at the same rate. This mode of operation is continued for a certain length of time corresponding to a fraction /sB of the total time, after which the flow of B is stopped, and the reaction is continued in the batch mode for the remaining fraction of time (1 -/sb)- This may be regarded as constant volume, semibatch operation. 

Industrial reactors operate in the steady state with the volume, concentration, and temperature of the reaction mixture being constant... 

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 feed is charged all at once to a batch reactor, and the products are removed together, with the mass in the system being held constant during the reaction step. Such reactors usually operate at nearly constant volume. The reason for this is that most batch reactors are liquid-phase reactors, and liquid densities tend to be insensitive to composition. The ideal batch reactor considered so far is perfectly mixed, isothermal, and operates at constant density. We now relax the assumption of constant density but retain the other simplifying assumptions of perfect mixing and isothermal operation. 

Consider the gas-phase decomposition A B -b C in an isothermal tubular reactor. The tube i.d. is 1 in. There is no packing. The pressure drop is 1 psi with the outlet at atmospheric pressure. The gas flow rate is O.OSSCF/s. The molecular weights of B and C are 48 and 52, respectively. The entering gas contains 50% A and 50% inerts by volume. The operating temperature is 700°C. The cracking reaction is first order with a rate constant of 0.93 s . How long is the tube and what... 

The reactor operates at constant volume, constant density, constant flow rate, and isothermally. The only difference between the two products is the addition of component C to the feed when Product II is made. 

Consider the reaction used as the basis for Illustrations 10.1 to 10.3. Determine the volume required to produce 2 million lb of B annually in a plug flow reactor operating under the conditions described below. The reactor is to be operated 7000 hr annually with 97% conversion of the A fed to the reactor. The feed enters at 163 C. The internal pipe diameter is 4 in. and the piping is arranged so that the effective reactor volume can be immersed in a heat sink maintained at a constant temperature of 160 °C. The overall heat transfer coefficient based on the... 

Pure phosphine is to be admitted to a constant volume batch reactor and allowed to undergo decomposition according to the above reaction. If pure phosphine enters at 672 °C and the initial pressure is 1 atm, determine the times necessary to decompose 20% of the original phosphine for both isothermal and adiabatic operation. 

Choice of type of reactor to be used and certain features relating to its mode of operation (e g., a BR operated at constant volume) these establish the numerical interpretation of the rate from the appropriate material balance equation (Chapter 2). 

For a constant-volume batch reactor operated at constant T and pH, an exact solution can be obtained numerically (but not analytically) from the two-step mechanism in Section 10.2.1 for the concentrations of the four species S, E, ES, and P as functions of time t, without the assumptions of fast and slow steps. An approximate analytical solution, in the form of a rate law, can be obtained, applicable to this and other reactor types, by use of the stationary-state hypothesis (SSH). We consider these in turn. 

Determine the time required for 80% conversion of 7.5 mol A in a 15-L constant-volume batch reactor operating isothermally at 300 K. The reaction is first-order with respect to A, with kA = 0.05 min-1 at 300 K. 

A liquid-phase reaction, A products, was studied in a constant-volume isothermal batch reactor. The reaction rate expression is (-rA) = kAcA, and k = 0.030 min 1. The reaction time, t, may be varied, but the down-time, td, is fixed at 30 min for each cycle. If the reactor operates 24 hours per day, what is the ratio of reaction time to down-time that maximizes production for a given reactor volume and initial concentration of A What is the fractional conversion of A at the optimum ... 

A continuous flow stirred reactor operates off the decomposition of gaseous ethylene oxide fuel. If the fuel injection temperature is 300 K, the volume of the reactor is 1500 cm3, and the operating pressure is 20 atm, calculate the maximum rate of heat evolution possible in the reactor. Assume that the ethylene oxide follows homogeneous first-order reaction kinetics and that values of the reaction rate constant k are... 

Example 15.13. The irreversible chemical reaction A B takes place in two perfectly mixed reactors connected in series as shown in Fig. 15.3. The reaction rate is proportional to the concentration of reactant. Let Xj be the concentration of reactant A in the first tank and X2 the concentration in the second tank. The concentration of reactant in the feed is Xg. The feed flow rate is F. Both Xo and F can be manipulated. Assume the specific reaction rates ki and >n Mch tank are constant (isothermal operation). Assume constant volumes Vi and 1. ... 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

This chapter deals with the design of reactors which do not conform to these ideal models its attention is restricted to constant volume, single phase, isothermal reactors which are operated in the steady state. It is not intended to be a state of the art review of non-ideal reactor design methods, but rather an introduction to basic ideas and techniques frequently, the reader will be referred to more extended or specific coverage of the material being considered. 

The experimental batch reactor is usually operated isothermally and at constant volume because it is easy to interpret the results of such runs. This reactor is a relatively simple device adaptable to small-scale laboratory set-ups, and it needs but little auxiliary equipment or instrumentation. Thus, it is used whenever possible for obtaining homogeneous kinetic data. This chapter deals with the batch reactor. 

Batch reactors are usually operated at constant volume because it is easy to construct a constant-volume closed container (as long as the pressure does not increase enough to burst the vessel). However, in flow reactors the density fiequently changes as the reaction proceeds, even though the reactor volume is constant, and we need to be able to handle this situation. 

It is obvious that if the gas-phase constitutes only one pure compound A, the use of eq. (3.365) is not sound, because it leads to zero values of the derivative and it seems that the equation is not needed. The latter is true only when the conversion of A is too low and so Qg can be considered practically constant. For systems of variable volume, eq. (3.360) or the equation derived in the previous example can be applied instead. The equation derived in the previous example specifically shows that it is the change of volume (flow rate) of the gas phase that affects the reactor operation and not the concentration change, since the concentration of A is constant throughout the reactor. Of course, the change of flow rate is due to the change in moles (xA is variable). 

We should also distinguish operating assumptions, which may be different even when the same materials are involved. For instance, if we were interested in finding out what goes on during the filling of the reactor, we would need both equations. However, if the reactor were operated at constant volume, only one would be needed. 

The continuously operated stirred tank reactor is fed with reactants at the same time as the products are removed by an overflow or a level control system (Figure 8.1). This ensures a constant volume and, consequently with a constant volume flow rate of the feed, a constant space hme. We further assume the reactor contents... 

The operation of an LC-Finer is best described by means of a process flow schematic (Figure 2). The LC-Finer reactor maintains the catalyst (typically American Cyanamid 1442B cobalt molybdenum 1/32 inch extrudate or Shell 324 nickel molybdenum 1/32 inch extrudate) in constant motion, suspended by the recirculation of copious volumes of liquid. This recirculation results in a 35-50% bed expansion and the reactor operates at a uniform temperature with essentially no pressure drop. In a commercial unit there is a recycle of hydrogen rich gas along with a distillate liquid stream which is combined with the fresh SRC. The PDU differs from the commercial unit design in that there is no recycle gas or liquid streams. The bed expansion is maintained with an external recirculation loop. It should be noted that the PDU fractionator separates the liquid product into a light oil (L.O.) and a heavy oil (H.O.). The combination of these two oil streams is designated as total liquid product (TLP). 

Note that we have said nothing about the size of the reactor vessel. If the reactor operates isothermally, the composition profiles shown in Figures 4.18 and 4.19 are independent of reactor size. Of course, attaining a constant-temperature trajectory becomes more difficult as the vessel size increases because of the reduction in area-to-volume ratio. 

Time is still an important variable for continuous systems, but it is modified to relate to the steady-state conditions that exist in the reactor. This time variable is referred to as space time. Space time is the reactor volume divided by the inlet volumetric flow rate. In other words, it is the time required to process one reactor volume of feed material. Since concentration versus real time remains constant during the course of a CSTR reaction, rate-data acquisition requires dividing the difference in concentration from the inlet to the outlet by the space time for the particular reactor operating conditions. 

An endothermic reaction A — R is performed in three-stage, continuous flow stirred tank reactors (CFSTRs). An overall conversion of 95% of A is required, and the desired production rate is 0.95 x 10 3 kmol/sec of R. All three reactors, which must be of equal volume, are operated at 50°C. The reaction is first order, and the value of the rate constant at 50°C is 4 x 10-3 sec-1. The concentration of A in the feed is 1 kmol/m3 and the feed is available at 75°C. The contents of all three reactors are heated by steam condensing at 100°C inside the coils. The overall heat transfer coefficient for the heat-exchange system is 1,500 J/m2 sec °C, and the heat of reaction is +1.5 x 108 J/kmol of A reacted. 

Briggs and Haldane [8] proposed a general mathematical description of enzymatic kinetic reaction. Their model is based on the assumption that after a short initial startup period, the concentration of the enzyme-substrate complex is in a pseudo-steady state (PSS). For a constant volume batch reactor operated at constant temperature T, and pH, the rate expressions and material balances on S, E, ES, and P are... 

An ideal batch reactor is a perfectly stirred tank of constant volume with no mass transfer from or to the outside. There is a single residence time, which is simply the duration of the reaction. Generally, a batch reactor is operated isothermally and therefore the reaction temperature may be considered as an independent variable. 

For a reactor operating with constant output, the criterion for optimal performance is for the cooling medium to have the highest possible temperature in the heat removal system. For a working example of the nonadiabatic reactor, there are 4631 cylindrical tubes with inner diameters of 7 mm packed with a catalyst and surrounded by a constantly boiling liquid at 703 K. Sulfur dioxide and air are fed into the reactor at a total pressure PT, in volume fractions of > s,, 2 =0.11 and >v,2 =0.10. The empirical expression oftakes into account diffusion and reaction kinetics, and we have... 

We have a first-order homogeneous reaction, taking place in an ideal stirred tank reactor. The volume of the reactor is 20 X 10 3 m3. The reaction takes place in the liquid phase. The concentration of the reactant in the feed flow is 3.1 kmol/m3 and the volumetric flow rate of the feed is 58 X 10 m3/s. The density and specific heat of the reaction mixture are constant at 1000 kg/m3 and 4.184kJ/(kg K). The reactor operates at adiabatic conditions. If the feed flow is at 298 K, investigate the possibility of multiple solutions for conversion at various temperatures in the product stream. The heat of reaction and the rate of reaction are... 

We carried out a decomposition reaction in the experimental device shown in Fig. 3.75. The reaction is endothermic and takes place in a permanently perfectly mixed (PM) reactor. As shown in Fig. 3.75, reactant A is fed at the reactor input in a liquid flow at constant concentration value. The heat necessary for the endothermic decomposition is supplied by an oil bath, which is electrically heated in order to maintain a constant temperature (t ). The reactor operates at constant volume because input and output flows are similar. 

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