Backmixed flow reactor

A stirred-tank flow reactor may be single-stage or multistage. As an ideal backmix flow reactor, it is referred to as a CSTR or multistage CSTR this is treated in Chapter 14. Nonideal flow effects are discussed in Chapter 20. 

Fig. 15.1. Types of electrochemical reactor (a) Batch reactor (b) Plug flow reactor (c) Backmix flow reactor.

Backmix flow reactor or continuously stirred tank reactor. The conversion rate is lower than for plug-flow reactors because the reagent is immediately diluted on being introduced into the reactor. Many flow reactors, e.g. tubular reactors, and especially in the turbulent regime are in this class. 

Plug-flow and backmix flow reactors can be used as single-pass, with recirculation or in cascade, leading to many possible configurations, but always with the aim of optimizing product yield in space and time. 

Mixing of product and feed (backmixing) in laboratory continuous flow reactors can only be avoided at very high length-to-diameter (aspect) ratios. This was observed by Bodenstein and Wohlgast (1908). Besides noticing this, the authors also derived the mathematical expression for reaction rate for the case of complete mixing. 

These boundary conditions are really quite marvelous. Equation (9.16) predicts a discontinuity in concentration at the inlet to the reactor so that ain a Q+) if D >0. This may seem counterintuitive until the behavior of a CSTR is recalled. At the inlet to a CSTR, the concentration goes immediately from to The axial dispersion model behaves as a CSTR in the limit as T) — 00. It behaves as a piston flow reactor, which has no inlet discontinuity, when D = 0. For intermediate values of D, an inlet discontinuity in concentrations exists but is intermediate in size. The concentration n(O-l-) results from backmixing between entering material and material downstream in the reactor. For a reactant, a(O-l-) [Pg.332]

Continuous-flow stirred tank reactor (CSTR), based on backmix flow,... 

Ideal flow is introduced in Chapter 2 in connection with the investigation of kinetics in certain types of ideal reactor models, and in Chapter 11 in connection with chemical reactors as a contrast to nonideal flow. As its name implies, ideal flow is a model of flow which, in one of its various forms, may be closely approached, but is not actually achieved. In Chapter 2, three forms are described backmix flow (BMF), plug flow (PF), and laminar flow (LF). 

The PFR model is frequently used for a reactor in which the reacting system (gas or liquid) flows at relatively high velocity (high Re, to approach PF) through an otherwise empty vessel or one that may be packed with solid particles. There is no device, such as a stirrer, to promote backmixing. The reactor may be used in large-scale operation... 

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. 

This recycle ratio can be made to vary from zero to infinity. Reflection suggests that as the recycle ratio is raised the behavior shifts from plug flow R = 0) to mixed flow (R = oo). Thus, recycling provides a means for obtaining various degrees of backmixing with a plug flow reactor. Let us develop the performance equation for the recycle reactor. 

Aiba (A3), Fox and Gex (F8), Kramers, Baars and Knoll (K15), Metzner and Taylor (MIO), Norwood and Metzner (N3), Van de Vusse (V5) and Wood et al. (W12) have studied flow patterns and mixing times. In addition, Brothman et al. (B22), Gutoff (G9), Sinclair (S16) and Weber (W3) analyzed flow in a stirred tank in terms of the recycle flow model of Fig. 23F. This model corresponds to the draft-tube reactor, and with sufficiently large recycle rate the performance prediction of this model approximates backmix flow. 

Aris (A13), Cholette and Blanchet (CIS), Cholette et al. (C17), and Trambouze and Piret (T12) have discussed using combinations of backmix and plug-flow reactors. 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid-phase is important in order to decide if we have to use a plug- or backmixed-flow model. The liquid-phase can be considered well mixed if (Ramachandran and Chaudhari, 1980)... 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid phase is important in order to decide if we have to use a plug- or backmixed-flow model. For the specified Reynolds number, the Peclet number for the liquid phase using the Stiegel-Shah correlation (eq. (3.422)) is 0.15, much lower than in the trickle bed, which was expected as the backmixing in the liquid phase in packed bubble bed reactors is relatively high. The liquid phase can be considered to be well mixed if (Ramachandran, and Chaudhari, 1980) (eq. (3.423))... 

The same general conclusions apply since backmixing of products with reactants should be avoided, a tubular plug-flow reactor or a batch reactor is preferred. However, there is one respect in which a series reaction involving a second reactant B does differ from simple series reaction with one reactant, even when the orders are the same. This is in the stoichiometry of the reaction the reaction cannot proceed completely to the product Q, even in infinite time, if less than two moles... 

Y. Lu, J. A. Biesenberger, and D. B. Todd, A Backmix Drag-flow Reactor, SPE. ANTEC, Tech. Papers, 51, 27-29 (1993) also Y. Lu, J. A. Biesenberger, and D. B. Todd, Continuous Polymerization in a back-mixed Drag Flow reactor, SPE. ANTEC Tech. Papers, 52, 113-115 (1994). 

Equation 5-354 determines the value of the recycle ratio for a given conversion, the residence time, and the rate constant in a plug flow reactor. Alternatively, an increase in R will lower the conversion since it produces backmixing in the reactor as it mixes with the feed entrance in the plug flow reactor. As R it yields... 

Davis et al. [9] have performed studies on the batch hydration of ethylene oxide. Their work determined the value of the product distribution constant K. This value is used in Equation 5-378 to determine the expected performance in a plug flow reactor. This value is also used in Equation 5-394 to illustrate the poor performance that would be obtained with complete backmixing. 

A tubular reactor will likely deviate from plug flow in most practical cases, e.g., due to backmixing in the direction of flow, reactor internals, etc. A way of simulating axial backmixing is to represent the reactor volume as a series of n stirred tanks in series. The steady-state solution for a single ideal CSTR may be extended to find the effluent concentration after two ideal CSTRs and then to n ideal stages as... 

Tubular Reactor with Dispersion An alternative approach to describe deviation from ideal plug flow due to backmixing is to include a term that allows for axial dispersion De in the plug flow reactor equations. The reactor mass balance equation now becomes... 

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