Achievability using CSTRs

Consider the reaction studied in Illustration 10.1. Autothermal operation is to be achieved using a CSTR with an effective volume of1000 gal followed by a PFR of undetermined volume. Pure species A enters at a rate of 40.0 gal/hr and at a temperature of 20 °C. The overall fraction conversion is to be 0.97. This flow rate and conversion level will suffice to meet the annual production requirement of 2 million lb of B. Both the CSTR and the PFR are to be operated adiabatically. What PFR volume will be required, and what will be the temperature of the effluent stream ... 

This section contains several models whose spatiotemporal behavior we analyze later. Nontrivial dynamical behavior requires nonequilibrium conditions. Such conditions can only be sustained in open systems. Experimental studies of nonequilibrium chemical reactions typically use so-called continuous-flow stirred tank reactors (CSTRs). As the name implies, a CSTR consists of a vessel into which fresh reactants are pumped at a constant rate and material is removed at the same rate to maintain a constant volume. The reactor is stirred to achieve a spatially homogeneous system. Most chemical models account for the flow in a simplified way, using the so-called pool chemical assumption. This idealization assumes that the concentrations of the reactants do not change. Strict time independence of the reactant concentrations cannot be achieved in practice, but the pool chemical assumption is a convenient modeling tool. It captures the essential fact that the system is open and maintained at a fixed distance from equilibrium. We will discuss one model that uses CSTR equations. All other models rely on the pool chemical assumption. We will denote pool chemicals using capital letters from the start of the alphabet. A, B, etc. Species whose concentration is allowed to vary are denoted by capital letters... 

SIDE NOTE Achievability using the CSTR l j condition... 

The AR is composed of mixing lines and manifolds of PFR trajectories. The final approach to the extreme points of the AR boundary is achieved using PFR solution trajectories—if a desired operating point resides on the AR boundary, a PFR must be incorporated into the reactor structure in order to reach it, and thus PFRs are often the best terminating reactor to use in practice (for any kinetics and feed point). Only combinations of PFRs, CSTRs, and DSRs are required to form the AR. This result is true for all dimensions. Distinct expressions may be derived to compute critical a policies for the DSR profile and critical CSTR residence times. These expressions are intricate and complex in nature, which are ultimately based on the lack of controllability in a critical reactor. This idea is important in understanding the nature of the AR and how to achieve points on the true AR boundary. 

Continuous-Flow Stirred-Tank Reactor. In a continuous-flow stirred-tank reactor (CSTR), reactants and products are continuously added and withdrawn. In practice, mechanical or hydrauHc agitation is required to achieve uniform composition and temperature, a choice strongly influenced by process considerations, ie, multiple specialty product requirements and mechanical seal pressure limitations. The CSTR is the idealized opposite of the weU-stirred batch and tubular plug-flow reactors. Analysis of selected combinations of these reactor types can be useful in quantitatively evaluating more complex gas-, Hquid-, and soHd-flow behaviors. 

In previous studies, the main tool for process improvement was the tubular reactor. This small version of an industrial reactor tube had to be operated at less severe conditions than the industrial-size reactor. Even then, isothermal conditions could never be achieved and kinetic interpretation was ambiguous. Obviously, better tools and techniques were needed for every part of the project. In particular, a better experimental reactor had to be developed that could produce more precise results at well defined conditions. By that time many home-built recycle reactors (RRs), spinning basket reactors and other laboratory continuous stirred tank reactors (CSTRs) were in use and the subject of publications. Most of these served the original author and his reaction well but few could generate the mass velocities used in actual production units. 

One of the most promising ways of dealing with conversion oscillations is the use of a small-particle latex seed in a feed stream so that particle nucleation does not occur in the CSTRs. Berens (3) used a seed produced in another reactor to achieve stable operation of a continuous PVC reactor. Gonzalez used a continuous tubular pre-reactor to generate the seed for a CSTR producing PMMA latex. 

Thus, a single CSTR requires 144.6 times the volume of a single PFR, and the inefficiency of using a CSTR to achieve high conversions is dramatically illustrated. The volume disadvantage drops fairly quickly when CSTRs are put in series, but the economic disadvantage remains great. Cost consequences are explored in Problems 4.19 and 4.20. 

Example 4.12 used N stirred tanks in series to achieve a 1000-fold reduction in the concentration of a reactant that decomposes by first-order kinetics. Show how much worse the CSTRs would be if the 1000-fold reduction had to be achieved by dimerization i.e., by a second order of the single reactant type. The reaction is irreversible and density is constant. 

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

Figure 14.2 shows the numerical solution. Except for a continuous input of ten rabbits and one lynx per unit time, the parameter values and initial conditions are the same as used for Figure 2.6. The batch reactor has been converted to a CSTR. The oscillations in the CSTR are smaller and have a higher frequency than those in the batch reactor, but a steady state is not achieved.

Use the F(t) curve for two identical CSTR s in series and the segregated flow model to predict the conversion achieved for a first-order reaction with k = 0.4 ksec-1. The space time for an individual reactor is 0.9 ksec. Check your results using an analysis for two CSTR s in series. 

For the reaction in problem 14-13, determine the minimum reactor volume required for a two-stage CSTR used to achieve 65% conversion of A. What is the volume of each tank ... 

A performance comparison between a BR and a CSTR may be made in terms of the size of vessel required in each case to achieve the same rate of production for the same fractional conversion, with the BR operating isothermally at the same temperature as that in the CSTR. Since both batch reactors and CSTRs are most commonly used for constant-density systems, we restrict attention to this case, and to a reaction represented by... 

The operating parameter for the CSTR reactor is the liquid flow rate Q, which sets the residence time of the liquid through the ratio Q/VL and finally the conversion. From a production viewpoint, the (residence) time required to achieve a given conversion of S (or outlet concentration of S) is obtained by solving the set of Eqs. (33) and (34). The characteristics of the reactor kLa and VL must be known. In general, whereas VL is easily determined in a batch reactor, it is not in a CSTR. Rather, VL=fiLVR will be used, which requires knowledge of the liquid hold-up L. Correlations provide kLo (see below) and L characteristics for the different reactor types [3]. 

The conversion achieved in most reactors lies between that which would be expected from a PFR or CSTR of the same size. The tanks-in-series model can be used to predict this level of conversion once tracer test data have been recorded and processed. The following extimple illustrates typical calculations. 

CSTRs in series. The latter is often normalised by dividing by the volume of an ideal PFR required to perform the same duty. Different charts are required for each reaction rate expression. Figure 12 refers specifically to first-order kinetics, but other charts are available in, for instance refs. 17, 18 and 26. Figure 12 re-emphasises many of the points we have made already. In particular, the performance of the N CSTRs in series tends to that of a PFR of the same total volume as N becomes large and the PFR volume required to achieve a certain conversion for a first-order reaction is always smaller than the total volume of any array of CSTRs which perform the same duty. Charts in the form of Fig. 12 are particularly useful when performing approximate design calculations. 

Selective tertiary-huimoX (tBA) dehydration to isobutylene has been demonstrated using a pressurized reactive distillation unit under mild conditions, wherein the reactive distillation section includes a bed of formed solid acid catalyst. Quantitative tBA conversion levels (>99%) have been achieved at significantly lower temperatures (50-120°C) than are normally necessary using vapor-phase, fixed-bed, reactors (ca. 300°C) or CSTR configurations. Substantially anhydrous isobutylene is thereby separated from the aqueous co-product, as a light distillation fraction. Even when employing crude tBA feedstocks, the isobutylene product is recovered in ca. 94% purity and 95 mole% selectivity. 

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