Reactors backmix

Recycle reactors at that time were called Backmix Reactors. They were correctly considered the worst choice for the production of a reactive intermediate, yet the best for kinetic studies. The aim of the kinetic study for ethylene oxidation was to maximize the quality of the information, leaving the optimization of production units for a later stage in engineering studies. The recycle reactors could provide the most precise results at well defined conditions even if at somewhat low selectivity to the desired product. 

A CSTR is a deliberately backmixed reactor and, in principle, its effluent temperature and composition are the same as the reactor contents. With an ideal CSTR, the feed blends instantaneously with the uniform reactor contents. In actual practice, of course, we find that feed blending time may be protracted, and varying degrees of segregation, short circuiting and stagnation exist in the reactor contents. 

Gas phase olefin polymerizations are becoming important as manufacturing processes for high density polyethylene (HOPE) and polypropylene (PP). An understanding of the kinetics of these gas-powder polymerization reactions using a highly active TiCi s catalyst is vital to the careful operation of these processes. Well-proven models for both the hexane slurry process and the bulk process have been published. This article describes an extension of these models to gas phase polymerization in semibatch and continuous backmix reactors. 

The kinetic models for the gas phase polymerization of propylene in semibatch and continuous backmix reactors are based on the respective proven models for hexane slurry polymerization ( ). They are also very similar to the models for bulk polymerization. The primary difference between them lies in the substitution of the appropriate gas phase correlations and parameters for those pertaining to the liquid phase. 

Continuous Model "C0NGAS". This model predicts performance of an ideal continuous wellstirred polyreactor. The model system consists of a continuous backmix reactor in which the total powder volume is held constant. There are four inlet streams 1) Makeup of pure propylene, 2) Catalyst feed, 3) Hydrogen feed, and 4) Recycle. The single effluent powder stream is directed through a perfect separator that removes all solids and polymer and then the gases are recycled to the reactor. The makeup propylene is assumed to disperse perfectly in the well-mixed powder. 

For all likely operating conditions, (ie., for t < X), the appropriate values of the concentration and the polymerization rate constant are the values calculated at t = t ( 2). To prove this, the exit age distribution function for a backmix reactor was used to weight the functions for Cg and kj and the product was integrated over all exit ages (6). It is enlightening at this point to compare equation 18 with one that describes the yield attainable in a typical laboratory semibatch reactor at comparable conditions. ... 

The yield that can be attained by a semibatch process is generally higher because the semibatch run starts from scratch, with maximum values of both variables Cg (o) = Cg and k] (o) = k . However, the yield from a continuous run in which t equals the batch time is governed by the product of Cg (t) and kj (t), so > and k (t) = k °. Because neither of these conditions is likely to be fulfilled completely, a continuous polymerization in a backmix reactor will probably always fail to attain the Y attainable by a semibatch reactor at the same t. However, several backmix reactors in series will approach the behavior of a plug flow continuous reactor, which is equivalent to a semibatch reactor. 

Figure 6. Simulation of a continuous backmix reactor (propylene gas phase polymerization—kg° = 0,0249 cm/sec, X = 9.68 hr, 400 psia reactor gas composition—99% CsH6,1% inerts)...

Yields from a Continuous Backmix Reactor, Simulated with C0NGAS... 

The effects of diffusion and catalyst decay cause yields from a continuous backmix reactor to be 25 to 30% lower than from a semibatch reactor at the same residence time. This yield penalty can be reduced by staging backmix reactors in series. 

In principle, the same rules hold true when zeolitic alkylation catalysts are used. A detailed study of the influence of PO and OSV on the performance of zeolite H-BEA in a backmix reactor was reported by de Jong et al. (80). The authors developed a simple model of the kinetics, which predicted catalyst lifetimes as a function of P/O and OSV. Catalyst lifetime (which is equivalent to the catalyst productivity, the reciprocal of acid consumption) increased with increasing P/O ratio and decreasing OSV. Furthermore, the authors persuasively demonstrated the superiority of a backmix reactor over a plug flow reactor. Qualitatively similar results were obtained by Taylor and Sherwood (222) employing a USY zeolite catalyst in a backmix reactor. The authors stressed the detrimental effect of unreacted alkene on the catalyst lifetime and product quality. Feller et al. (89) tested LaX zeolites in a backmix reactor and found the catalyst productivity to be nearly independent of the OSV within the examined OSV range. At higher values of OSV, the catalyst life was shorter, but in this shorter time the same total amount of product was produced. The P/O ratio had only a moderate influence on the catalyst performance. 

The other ideal steady-state flow reactor is called the mixed reactor, the backmix reactor, the ideal stirred tank reactor, the C " (meaning C-star), CSTR, or the CFSTR (constant flow stirred tank reactor), and, as its names suggest, it is a reactor in which the contents are well stirred and uniform throughout. Thus, the exit stream from this reactor has the same composition as the fluid within the reactor. We refer to this type of flow as mixed flow, and the corresponding reactor the mixed flow reactor, or MFR. 

Stead et al. (S23) and Johnson and Edwards (J3) showed that homogeneity can be achieved in as short a time as 0.1 sec., with sufficient agitation in a laboratory sized stirred tank. The relation between this time and the intensity of agitation was studied by MacDonald and Piret (Ml). Eldridge and Piret (E5) then used kinetic experiments to show that a series of up to five laboratory-sized stirred tanks with sufficient agitation acted as perfect backmix reactors. 

For a series of equal-sized backmix reactors the exit age distribution function is... 

For a series of unequal-sized backmix reactors with mean residence times ti, t2,. .., ti,. .., h v/e have... 

In summary, for a backmix reactor, J is unity for perfect segregation and zero for perfect molecular mixing. 

Reaction rates are measured in either a plugflow or in a backmix reactor. 

The results show that the plant reactor falls between the plug flow and backmixing reactor lines. The distance between lines (2) and (3) in Figure 5-41 measures the degree of backmixing. There is considerable departure from the theoretical plug flow curve. This shows... 

A longitudinal tubular reactor in place of a high backmixing reactor results in substantial savings in processing costs because selectivity and productivity are increased. 

Figure 4.9 shows the results of a dynamic simulation we performed featuring the open-loop behavior of a backmixed reactor that satisfies the slope condition for steady-state stability but has dynamically unstable roots. Table 4.1 contains the reactor parameters and operating conditions used in the model, as listed by Vleeschhouwer et al. (1992). 

Series-of-stirred-tanks model The series-of-stirred-tanks model (often referred to as the cell model) is perhaps the simplest type of stagewise model for the backmix reactor. In this model, the reactor is represented by a series of perfectly mixed stages. The degree of backmixing is characterized by the number of stages the... 

The above solution is rigorous for a completely backmixed reactor and it becomes less accurate as the Peclet number increases. Similar solutions for other cases of slow reaction can be obtained in a straightforward manner. 

The opposite of the large diameter pipeline with little axial or radial mixing is the perfect backmixed reactor with instantaneous mixing and uniformity. For polystyrene reactors with several hours of residence time, complete mixing in 1-2 min is usually adequate to satisfy a practical definition of perfectly mixed. The probability of exit of any fluid element from this type of reactor is independent of when it entered. The residence time distribution is exponential and the molecular weight distribution in the case of no termination is Mw/Mn = 2.0, which will spread out to 2.3 when chain transfer controls. If product requirements necessitate a narrower residence time distribution, one can utilize several of these reactors in series. This becomes necessary to control the grafting distribution in rubber modified polystyrene. 

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