Batch reactor down-time

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)... 

There are two important types of ideal, continuous-flow reactors the piston flow reactor or PFR, and the continuous-flow stirred tank reactor or CSTR. They behave very diflerently with respect to conversion and selectivity. The piston flow reactor behaves exactly like a batch reactor. It is usually visualized as a long tube as illustrated in Figure 1.3. Suppose a small clump of material enters the reactor at time t = 0 and flows from the inlet to the outlet. We suppose that there is no mixing between this particular clump and other clumps that entered at different times. The clump stays together and ages and reacts as it flows down the tube. After it has been in the piston flow reactor for t seconds, the clump will have the same composition as if it had been in a batch reactor for t seconds. The composition of a batch reactor varies with time. The composition of a small clump flowing through a piston flow reactor varies with time in the same way. It also varies with position down the tube. The relationship between time and position is... 

The emphasis in this chapter is on the generalization of piston flow to situations other than constant velocity down the tube. Real reactors can closely approximate piston flow reactors, yet they show many complications compared with the constant-density and constant-cross-section case considered in Chapter 1. Gas-phase tubular reactors may have appreciable density differences between the inlet and outlet. The mass density and thus the velocity down the tube can vary at constant pressure if there is a change in the number of moles upon reaction, but the pressure drop due to skin friction usually causes a larger change in the density and velocity of the gas. Reactors are sometimes designed to have variable cross sections, and this too will change the density and velocity. Despite these complications, piston flow reactors remain closely akin to batch reactors. There is a one-to-one correspondence between time in a batch and position in a tube, but the relationship is no longer as simple as z = ut. 

In a batch reactor, the relative monomer concentrations will change with time because the two monomers react at different rates. For polymerizations with a short chain life, the change in monomer concentration results in a copolymer composition distribution where polymer molecules formed early in the batch will have a different composition from molecules formed late in the batch. For living polymers, the drift in monomer composition causes a corresponding change down the growing chain. This phenomenon can be used advantageously to produce tapered block copolymers. 

For transesterification/esterfication, continuous reactors may be more attractive than batch reactors. This is particularly true if a distillation-column reactor can be adopted, as it tends to use a much lower ratio of reactants to drive the reaction to the desired degree of conversion, entailing lower energy lost. Even when metal alcoholates are used these can be recycled, eliminating problems faced in batch plants. Relative process costs may well approach 50% of those in batch plants. Higher purity, less plant down time, better process control, and improved yield are other attractive features of continuous plants (Braithwate, 1995). 

To produce 100 000 tonnes of nonanal per year (25% down time, 100% conversion of substrate, 80% selectivity to nonanal) requires a production rate from the reactors of 19 tonne h 1, so that each batch must be 6.3 tonnes. Assuming a 1 1 ratio by volume of fluorous solventdiquid substrate and a 75 % loading, each reactor must have a volume of 20 m3. If the distillation column were fully integrated into the system it would be required to handle 19 tonnes aldehyde h 1. An increase in selectivity to the linear product, which could be achieved using careful ligand design would reduce the reactor size by up to 25%. 

Suppose reaction 12.3-1 is carried out in a batch reactor of volume V on a continual basis. To determine the rate of production, we must take into account the time of reaction (t in equation 12.3-2) and the down-time (td) between batches. The total time per batch, or cycle time, is... 

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 ... 

The hydrolysis of methyl acetate (A) in dilute aqueous solution to form methanol (B) and acetic acid (C) is to take place in a batch reactor operating isothermally. The reaction is reversible, pseudo-first-order with respect to acetate in the forward direction (kf = 1.82 X 10-4 s-1), and first-order with respect to each product species in the reverse direction (kr = 4.49 X10-4 L mol-1 S l). The feed contains only A in water, at a concentration of 0.050 mol L-1. Determine the size of the reactor required, if the rate of product formation is to be 100 mol h-1 on a continuing basis, the down-time per batch is 30 min, and the optimal fractional conversion (i.e., that which maximizes production) is obtained in each cycle. 

Operation is adiabatic and conversion is to be 95%. Find the volumes of (a) a tubular flow reactor (b) a CSTR (c) a batch reactor when the down time is 1 hr per batch and the daily charge is 3(1440) cuft/day. 

Investigate an isothermal, batch reactor (Set batch=l und isothermal=l) with an irreversible first-order (k1 k2). For this purpose set REST to a very high value, say le20. Determine the necessary reaction time to achieve a fraction conversion, XA, of 90, 95 und 99%. Determine also the cycle time and the productivity. For this assume the down-time between batches is 30 min (1800 s). Perform this for two different temperatures between 300K and 320K. 

The initial charge to the reactor is 950 kg and 90% of this is converted in an isothermal batch time of 3.20 h. If the shut-down time between... 

First of all, before we compare flow reactors, let us mention the batch reactor briefly. The batch reactor has the advantage of small instrumentation cost and flexibility of operation (may be shut down easily and quickly). It has the disadvantage of high labor and handling cost, often considerable shutdown time to empty, clean out, and refill, and poorer quality control of the product. Hence we may generalize to state that the batch reactor is well suited to produce small amounts of material and to produce many different products from one piece of equipment. On the other hand, for the chemical treatment of materials in large amounts the continuous process is nearly always found to be more economical. 

The PFTR was in fact assumed to be in a steady state in which no parameters vary with time (but they obviously vary with position), whereas the batch reactor is assumed to be spatially uniform and vary only with time. In the argument we switched to a moving coordinate system in which we traveled down the reactor with the fluid velocity , and in that case we follow the change in reactant molecules undergoing reaction as they move down the tube. This is identical to the situation in a batch reactor ... 

Next consider the response of a PFTR with steady flow to a pulse injected at f = 0. Wc could obtain this by solving the transient PFTR equation written earher in this chapter, but we can see the solution simply by following the pulse down the reactor. (This is identical to the transformation we made in transforrning the batch reactor equations to the PFTR equations.) The S(0) pulse moves without broadening because we assumed perfect plug flow, so at position z the pulse passes at time z/u and the pulse exits the reactor at time T = L/u. Thus for a perfect PFTR the RTD is given by... 

When operating continuously at steady state each particle in a bed is subject to constant conditions but the concentration of reagents changes with the position in the column. When substrate is converted to product in a single pass the pattern of conversion down the bed resembles that seen when the same reaction is followed with respect to time in a batch reactor. This stems from the fact that distance travelled through the column is equivalent to processing with an equal concentration of biocatalyst in the batch reactor for the period of the column contact time. 

Inputs = Outputs + Sinks + Accumulations The sink term of a material balance is Vrra and the accumulation term is the time derivative of the content of reactant in the vessel, or d(VrCa)/dt, where both Vr and Ca depend on time. An unsteady condition in the sense used in this section always has an accumulation term. This sense of unsteadiness excludes the batch reactor where the conditions do change with time but are taken account of by the sink term. Startup and shut down periods of batch reactors, however, are classified as unsteady. 

Thus 1 m3 of reactor volume produces 1.26 kmol of ethyl acetate (molecular weight 88) in a total batch time of 6720 s, i.e. in 4920 s reaction time and 1800 shut-down time. This is an average production rate of ... 

Flo. 1.10. Maximum production rate in a batch reactor with a shut-down time ts... 

The SSE is an important and practical LCFR. We discussed the flow fields in SSEs in Section 6.3 and showed that the helical shape of the screw channel induces a cross-channel velocity profile that leads to a rather narrow residence time distribution (RTD) with crosschannel mixing such that a small axial increment that moves down-channel can be viewed as a reasonably mixed differential batch reactor. In addition, this configuration provides self-wiping between barrel and screw flight surfaces, which reduces material holdback to an acceptable minimum, thus rendering it an almost ideal TFR. 

The parameters for PFRs include space time, concentration, volumetric flow rate, and volume. This reactor follows an integral reaction expression identical to the batch reactor except that space time has been substituted for reaction time. In the plug flow reactor, concentration can be envisioned as having a profile down the reactor. Conversion and concentration can be directly related to the reactor length, which in turn corresponds to reactor volume. 

Start up of a jacketed batch reactor requires control of the heat-up and cool-down rates. This involves determining and setting the jacket heat transfer fluid temperatures. An alternative is to make a trial heat-up and incorporate the results into a time-dependent heat transfer equation ... 

Water used in the experiments was doubly distilled and passed through an ion exchange unit. The conductivity was approximately 1 x 10"6 S/m. Simulated HLLW consisted of 21 metal nitrates in an aqueous 1.6 M nitric acid solution as shown in Table 1 and was supplied by EBARA Co. (Tokyo, Japan). Concentrations were verified by AA for Na and Cs with 1000 1 dilution and by ICP for the other elements with 100 1 dilution. Total metal ion concentration was 98,393 ppm. The experimental apparatus consisted of nominal 9.2 cm3 batch reactors (O.D. 12.7 mm, I.D. 8.5 mm) constructed of 316 stainless steel with an internal K-type thermocouple for temperature measurement. Heating of each reactor was accomplished with a 50%NaNO2 + 50% KNO 2 salt bath that was stirred to insure uniform temperature. Temperature in the bath did not vary more than 1 K. The reactors were loaded with the simulated HLLW waste at atmospheric conditions according to an approximate calculated pressure. Each reactor was then immersed in the salt bath for 2 min -24 hours. After a predetermined time, the reactor was removed from the bath and quenched in a 293 K water bath. The reactor was opened and the contents were passed through a 0.1 pm nitro-ceflulose filter while diluting with water. Analysis of the liquid was performed with methods in Table 1. Analysis of filtered solids were carried out with X-ray diffraction with a CuK a beam and Ni filter. Reaction time was defined as the time that the sample spent at the desired temperature. Typical cumulative heat-up and cool-down time was on the order of one minute. Results of this work are reported in terms of recoveries as defined by ... 

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