Reactor Selection: Plug Flow or Continuously Stirred Tank?

Use this graphical technique to choose a reactor configuration based on optimizing residence time.

The use of gas-phase continuously stirred tank reactors (CSTRs) for chemical reactions today appears to be confined mainly to the laboratory, while the predominant reactor type in industrial usage is a plug flow reactor (PFR) or a modified PFR such as an inert porous membrane reactor (IMR). Under certain circumstances, the use of a CSTR in industry can be justified, specifically in terms of the required residence time In some instances, a PFR and a CSTR in series will require a shorter total residence time than a single PFR.

A previous article (1) presented a graphical method for assessing the performance characteristics of a PFR. This article extends that technique to derive the performance of a CSTR for the same feed and operating conditions, and to determine which reactor type is the best choice, in terms of residence time, for a particular reaction.

Prepare the graphical representation

Obtaining the information required to choose between a CSTR and a PFR involves the following seven steps.

The effective rate constant, k^sub i^, and the reaction rate, r^sub i^, for each species at the reactor's mass- and heat-transfer conditions are known. The reaction is such that at equilibrium, all of species A has been consumed, as has species C.

Plot the yield of C as a function of the concentration of A, as shown in Figure 1. The scale of the y-axis in this figure is arbitrary, as is the shape of the profile for the general case.

2. Vary the initial concentration of A. Repeat step 1 for different initial molar values of A to get the plot in Figure 2.

3. Identify the concentration locus for species C and A in a CSTR. In Figure 2, draw tangents from the feed concentration of A corresponding to unity molar concentration, [1,0], to each of the other profiles, to create Figure 3. The points where the tangents touch the profiles define the concentration locus for a CSTR with a molar feed concentration of unity for species A and operating under the same flowrate, temperature and pressure conditions as in the PFR.

The concentration locus for the family of CSTRs is A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T. The derivation of this locus is based on the fact that it lies upon those boundary regions of a PFR profile where the rate vector lies on the tangent from the feed point to each PFR profile in the two-dimensional space. A and C (2, 3).

For a PFR, this is equivalent to dividing the conversion by the reaction-path-averaged reaction rate, which is aptly named the average rate.

6. Plot the residence times. Plot the CSTR and PFR residence times as functions of species A and of species C concentrations.

7. Plot the residence time ratios. For a specific concentration of species A, plot the ratio of the corresponding PFR residence time to that of the corresponding CSTR residence time. This is the residence time ratio (RTR). Repeat for values of species C.

Where the RTR is greater than unity, the CSTR residence time for a specific concentration of species i is less than that for the equivalent PFR. Where the RTR is less than unity, the PFR residence time for a specific concentration of species i is less than that for the equivalent CSTR.

Practical application of this technique

Previous papers (4, 5) on the oxidative dehydrogenation (ODH) of n-butane, butene and butadiene in an IMR reported that the yield of the desired hydrocarbon was enhanced by maintaining the partial pressure of oxygen at a low constant value. The oxygen partial pressure was judged to be an important operating parameter.

The graphical technique described in this article was applied to the same reaction system to determine the CSTR concentration locus for the ODH of butene to butadiene, to calculate the respective reactor residence times, and to derive and analyze the resulting RTR profiles.

The reaction network for the ODH of butene was postulated (6, 7) as depicted in Figure 4. The reactor configuration, which employed a V/MgO catalyst, is shown in Figure 5.

Figure 6 presents the CSTR locus for the ODH of butene to butadiene for an initial (and constant) oxygen partial pressure of 65 kPa. The maximum butadiene yield in a CSTR is approximately 0.26 moles, which corresponds to 0.44 moles of butene. For the IMR. the maximum butadiene yield is 0.38 at a butene concentration of 0.29.

The residence times for butene in a CSTR and IMR are shown in Figure 7. At butene concentrations greater than 0.07. residence times in an IMR are less than those for a CSTR. At a butene concentration of 0.07, the curves cross, and below this value the residence times for an IMR are greater than those for a CSTR.

The significance of the point of intersection is that it defines the operational parameters (in terms of butene) at which it becomes advantageous to switch from a CSTR to an IMR (and vice versa) from the perspective of residence time.

Figure 8 shows the respective residence times for a CSTR and an IMR in terms of moles of butadiene. For all butadiene concentrations, IMR residence times are less than those for a CSTR. This means that it always will be more advantageous to deploy an IMR, with a residence time less than 9 s, for any desired yield of butadiene.

Butadiene yields greater than 0.26 cannot be obtained from a CSTR operating at a constant oxygen partial pressure of 65 kPa.

Figure 9 illustrates the ratio of IMR and CSTR residence times as a function of butene concentration (which were derived from Figure 7). The horizontal line demarcates the CSTR and IMR regions. The CSTR region is that area within which a CSTR requires a shorter residence time than does an IMR for the same selectivity. Similarly, in the IMR region, an IMR requires less residence time than a CSTR.

Figure 9 indicates that for butene concentrations greater than 0.07, an IMR reactor has a smaller residence time than a CSTR. Once the butene concentration falls below 0.07, a CSTR requires a shorter residence time than an IMR.

Figure 10 shows the ratio of IMR and CSTR residence times as a function of butadiene concentration. All values of the RTR are less than unity. That is, an IMR has a smaller residence time than a CSTR as the butadiene concentration increases from zero to its maximum of 0.26. This condition holds as the butadiene concentration wanes (through its oxidation to carbon monoxide, carbon dioxide and water).

However, this is not necessarily always the case. There may be instances involving different reactants over another catalyst where the RTR for one of the products transverses a value of unity and, in so doing, demarcates PFR and IMR (PFR) regions.

[Reference]

Literature Cited

1. Milne, D., et al., "Graphically Assess a Reactor's Characteristics," Chem. Eng. Progress, 102 (3), pp. 46-52 (Mar. 2006).

2. Classer, D., et al.. "Reactor and Process Synthesis." Computers ami Chemical Engineering. 21 (Supplement) pp. 5775-5783 (1997).

3. Classer, D., et al., "A Geometric Approach to Steady Row Reactors: The Attainable Region and Optimisation in Concentration Space." InJ. Eng. Chem. Res., 26, pp. 1803-1810. (1987).

4. Milne, D., et al., "Application of the Attainable Region Concept to the Oxidative Dehydrogenation of 1-Butene in Inert Porous Membrane Reactors." Ind. Eng. Chem. Res., 43, pp. 1827-1831 (2004).

5. Milne, D., et al., "The Oxidative Dehydrogenation of nButane in a Fixed Bed Reactor and in an Inert Porous Membrane Reactor - Maximizing the Production of Butenes and Butadiene." accepted for publication in Industrial and Engineering Chemistry Research.

6. T�llez, C., et al., "Kinetic Study of the Oxidative Dehydrogenation of Butane on V/MgO Catalysts," J. Catal., 183, pp. 210-221 (1999).

7. T�llez, C. et al., "Simulation of an IMR for the Oxidative Dehydrogenation of Butane." Chem. Eng. Sci., 54, pp. 2917-2925 (1999).

[Author Affiliation]

DAVID MILNE

DAVID CLASSER

DIANE HILDEBRANDT

BRENDON HAUSBERGER

CENTRE OF MATERIAL AND PROCESS SYNTHESIS, UNIV. OF THE WITWATERSRAND, JOHANNESBURG

[Author Affiliation]

DAVID MILNE is currently conducting chemical engineering research and working toward a PhD degree at the Univ. of the Witwatersrand, Centre of Material and Process Synthesis (COMPS, School of Process and Materials Engineering, Univ. of the Witwatersrand, Private Bag 3, WITS 2050, South Africa; Phone: +27 (11) 394 7683; Cell: +27 (82) 903 3632; E-mail: admilne@mweb.co.za). He holds a bachelor's and a master's degree in chemical engineering from Univ. College Dublin. He emigrated to South Africa in 1969, and for the last 30 years has been active in project management affairs there. He is a Fellow of the Cost Engineering Association of Southern Africa, a member of the Project Management Institute of South Africa, and a registered professional engineer. He retired in 1998.

DIANE HILDEBRANDT is the Unilever Professor of Reactor Engineering and Director for the Centre of Materials and Process Synthesis at the Univ. of the Witwatersrand (Phone: +27 (11) 717 7557; Cell: +27 (83) 395 2921; E-mail: diane.hildebrandt@comps.wits.ac.za). She is also a part-time professor of process integration at the Univ. of Twente, The Netherlands. She has received numerous awards, and was the first engineer to be awarded the Meiring Naude Medal from the Royal Society of South Africa and the first academic to be awarded the Bill Neale-May Gold Medal by The South African Institute of Chemical Engineers (SAIChE) in 2000. She earned her BSc, MSc and PhD in chemical engineering from the Univ. of the Witwatersrand.

DAVID CLASSER is a professor of chemical engineering and Director for the Centre of Materials and Process Synthesis at the Univ. of the Witwatersrand (Tel: +27 (11) 717 7557; Cell: +27 (83) 395 2925; E-mail: david.glasser@comps.wits.ac.za). He is an Ai-rated scientist of the National Research Foundation of South Africa. He was the first academic to be awarded the Bill Neale-May Gold Medal by the South African Institution of Chemical Engineers (SAIChE) in 2000 and the first recipient of the Harry Oppenheimer Memorial Fellowship and Gold Medal in 2002. He has published over 100 papers and has given many invited talks all over the world. He holds a BSc in chemical engineering fromthe Univ. of Cape Town and PhD from Imperial College of Science and Technology (London).

BRENDON HAUSBERGER is the research manager at the Centre of Materials and Process Synthesis at the Univ. of the Witwatersrand (Tel: +27 (11) 717 7563; Cell: +27 (82) 903 5540; E-mail : brendon.hausberger@comps.wits.ac.za). He earned his PhD in the field of process synthesis in 2001, and completed postdoctoral studies at Carnegie Mellon Univ. He has over 13 publications in the field and has presented more that 40 papers in the area at various conferences.