10  Design of Reactors

Chapter 5 described four types of reaction engineering tasks: response, optimization, design, and parameter estimation. Chapters 6 through 9 showed how to generate and solve models for ideal BSTRs, SBSTRs, CSTRs, and PFRs, and illustrated using them to complete response and optimization tasks. This chapter presents a brief introduction to design tasks involving those four ideal reactor types.

10.1 Design Tasks

Reactor design is an advanced aspect of reaction engineering. Chemical reactors are virtually always one part of a larger process. At the largest scale, reactive process design starts with a decision to build a process from scratch. The decision to do this would be informed by some number of preliminary analyses of the market for the products from the process, the economic potential of the process, the technical feasibility of the process, etc. Full reactive process design will involve a team comprising members with expertise in finance, planning, procurement, law, construction, chemistry, engineering, safety, etc. The members with engineering expertise would include a reaction engineer among other engineering specializations such as process design, separations, control, heating and cooling, etc.

In response, optimization, and parameter estimation tasks, the reactor type is known or at least has been proposed at the time the task is assigned. While this could also be true in the simplest design tasks, more generally reactor design tasks require the reaction engineer to determine what type of reactor to use. Among other things, reactor design includes choosing the type of reactor to use, specifying its volume, heat transfer area, reactant feed rate and composition, operating protocol (including start-up and shutdown for continuous reactors), and identifying potential hazards and procedures for avoiding them.

This chapter offers a very basic introduction to reactor design. Its intent is to make the reader aware that most reactor design assignments are open-ended and do not have a single “correct” answer like those considered in previous chapters. Unlike those assignments, reactor design assignments can provide opportunities for a reaction engineer to be very creative and not simply follow some “cookie-cutter” approach to completing assignments. They can lead to discovery of innovative ways to operate reactors and the invention of new kinds of reactors.

Of course, doing so requires deeper thinking. Simply analyzing a reactor requires a relatively shallow level of understanding of reactor performance and a relatively low level of thinking. That is, if one learns how to generate and simplify the reactor design equations for a given system along with some important definitions, modeling the reactor is straightforward. Interpreting the results from modeling a reactor involves a deeper level of understanding and a higher level of thinking. At that level, physical explanations for observed phenomena are sought and developed, as in the discussion of reactor modeling results. It can be argued that reactor design requires an even deeper level of understanding of reactor performance and an eveh higher level of thinking. During reactor design the reaction engineer isn’t trying to explain an observed reactor response. Rather, the engineer needs to predict how to cause a desired reactor response by altering the reactor, what goes into it, and how it is operated. When a reaction engineer lacks an appropriate level of understanding or has not learned to think at an appropriate level, their design strategy can devolve to the point of trial and error which is at best inefficient and at worst, ineffective.

10.2 Design Principles and Objectives

Design assignments can vary in scale from design of a single reactor to design of an entire process. There are principles that should guide the design no matter the scale. Among the more important principles, the process should be safe to operate, it should comply with all governmental regulations, it should not have unfavorable or unjust environmental and societal impacts, and it should be profitable.

Some of the economic factors that must be evaluated as part of the process design are capital costs (one time expenses to purchase the necessary equipment, etc.), operating costs (including labor, utilities, feedstock costs, waste disposal, etc.), maintenance costs, licensing costs (e. g. royalties for use of patented technology), income the process will generate and the return on investment. Business and legal activities include choosing the site for the process, securing necessary permits, licensing any necessary technology, identifying all regulatory restrictions that apply to the process, purchasing the equipment as specified by the design engineers, and others. The engineering team lays out the piping and processing equipment and designs the individual components, making sure that they are all properly and efficiently integrated. Specific tasks that a reaction engineer would be involved in include selecting the type of reactor(s) to be used, sizing the reactor(s) and specifying operational prameters (heating and cooling, feed temperature and composition, etc.), specifying turn-around tasks and timing for non-continuous processes, and developing procedures for start-up, operation, shut-down, and various possible emergencies.

Participation in a full reactive process design of the kind just described requires much deeper knowledge of reaction engineering and much more reaction engineering experience than most readers of this book are likely to possess. Preliminary design involves a more limited scope. A preliminary reactor design might be one of the factors that go into the decision to build the full process. This chapter considers preliminary design that only includes the reactor.

10.3 Reactor Selection

Reactor design tasks begin with either an unspecified reactor (e. g. for a new process) or an underspecified reactor (e. g. to modify an existing process). The assignment identifies the chemical to be produced, but not the reactor to be used for doing so. When the reactor type is not specified, that is the first decision a design engineer needs to make. This involves two primary decisions. First, is the process going to operate continuously or in a batch-wise manner? Then, which type of reactor should be used?

10.3.1 Batch vs. Continuous

Most of the criteria used when choosing between a continuous process and a non-continuous process have been alluded to in previous chapters. The most important criterion, perhaps, is the anticipated amount of the product to be produced anually. If the product is a commodity that is going to be produced and sold in large volumes, a continuous process is most likely preferred. The profit margin on commodity chemicals is often small, and production costs need to be minimized because they cannot be passed on to the consumer easily. The additional labor and logistics of a non-continuous process lead to a larger production cost per pound of product compared to a continuous process.

When a small annual production is anticipated, but the profit margin is large, a non-continuous process may be preferred. A non-continuous process allows production of value-added products on demand. This can reduce the costs associated with storing the products during seasons of low demand while allowing for ramping up production when demand is greater.

Another important factor is the number of different reactor operating conditions required to produce the product. If the “recipe” for making the product involves multiple reactive steps at different temperatures and of different durations, a non-continuous process will likely be preferred. For example if the reactive processing requires holding at one temperature for some period of time, then adding a reagent and holding at a different temperature for a different amount of time, a non-continuous process would probably be preferred. It is simply easier to follow this kind of recipe using a non-continuous process.

Similarly, if the reaction must be run at conditions where the reaction rate is very low, a non-continuous process may be the better choice. For processes where the rate is much faster, where additional reagents do not need to be metered into the process, and where multiple reaction temperatures are not required, a continuous process can be advantageous.

Flexibility is another consideration when deciding between a continuous and a non-continuous process. A non-continuous process may be more suitable if the same reactor will be used to produce different products at different times. That is, it may be more challenging to use the same feed and product piping to conduct one chemical processes part of the time and a different reaction at other times in a continuous reactor system. Generally continuous processes are best when they can be started up and allowed to operate at steady state for extended periods of time.

In the final analysis, though, none of these criteria are definitive. Ultimately the choice between using a non-continuous process or a continuous process comes down to safety and economics.

10.3.2 BSTRs vs. SBSTRs

If the process will be non-continuous, the next question boils down to deciding between a BSTR or an SBSTR. Chapter 7 identified three situations where an SBSTR can offer a clear advantage over a BSTR: fast, highly exothermic reactions, reactions where the selectivity is strongly affected by the relative amounts of the reactants, and reversible reactions where a product can be selectivity removed. If one of these situations pertains, the choice to use an SBSTR is obvious.

When the choice between a BSTR and an SBSTR isn’t clear, the engineer might initially select a BSTR and begin the design process. The operation of a BSTR is slightly less detailed than an SBSTR because it isn’t necessary to meter the flow going into the reactor. Using a BSTR simplifies operation slightly and perhaps reduces labor costs compared to an SBSTR. As the design calculations proceed, the engineer may find that an SBSTR would be more appropriate, in which case the use of a BSTR can be abandoned, and replaced with design of an SBSTR. If the engineer had initially selected an SBSTR and successfully completed a preliminary design for it, they wouldn’t know whether a BSTR could accomplish the same task more easily or economically.

10.3.3 CSTRs vs. PFRs

If the process will be continuous, the next question is whether to use a CSTR or a PFR. In some instances this choice is an easy one, but under other circumstances it is not clear at all. The most significant differences between the two reactor types are how the temperature and composition vary during the reaction time and whether the reacting fluid needs to be agitated. In continuous reactors, the reaction time is the length of time that the reacting fluid spends in the reactor.

The ease of agitating the reacting fluid can be a determining factor. For example, when solid catalyst particles are required, achieving the perfect mixing required in a CSTR may be impractical or impossible. In contrast, packed-bed PFRs are very common.

When agitation isn’t an issue, the choice between a CSTR and a PFR is easiest when only one reaction is taking place, and the reactor is isothermal (or nearly so). For typical reaction kinetics a high rate is favored by large reactant concentrations and, if the reaction is reversible, by small product concentrations. In an isothermal CSTR the concentrations are the outlet values and they do not vary during the reaction time. The reactant concentrations are smaller than in the feed, the product concentrations are larger than in the feed, and the reaction rate does not change during the reaction time.

In an isothermal PFR the concentrations change monotonically during the reaction time. The reactant concentrations start at their feed values and decrease steadily to their outlet values during the reaction time. The product concentrations start at their feed values and increase steadily to their outlet values. Based on those variations the rate of a typical reaction decreases steadily during the reaction time in a PFR.

Comparing equal feeds at equal conversions, the rate will be constant during the reaction time in a CSTR. When comparing at equal conversions, the outlet composition from a PFR will equal the CSTR composition. Therefore rate in a PFR will become equal to the CSTR rate at the end of the reaction time. Except at the very end of the reaction time, the rate in the PFR will be greater than the rate in the CSTR, so a PFR volume smaller than the CSTR volume is needed to reach the same final conversion.

Comparing equal feeds at equal space times means the reaction times for the reactors are the same, but the conversions differ. Again, the CSTR rate will be constant during the reaction time. Because the initial rate in the PFR is higher, the PFR will reach the same conversion as the CSTR in less reaction time than the CSTR. the PFR fluid will continue to react for the remainder of the reaction time, so its final conversion will be greater than the CSTR conversion.

Thus the choice between a CSTR and a PFR for a single, isothermal reaction is quite straightforward, but few commercial reactors operate isothermally. When the reactors are adiabatic, the composition effects are the same as in isothermal reactors, but temperature effects must also be considered. In a CSTR, the temperature does not change during the reaction time. The temperature and composition in the CSTR are constant and equal to their outlet values.

The temperature will change during the reaction time in a PFR, and the effect of that change can either reinforce the effect of composition change or it can oppose it. If the reaction is endothermic, the temperature decreases steadily during the reaction time. Taken alone, this change decreases the rate and so it reinforces the effect of decreasing reactant concentration. If the reaction is exothermic, the temperature increases during the reaction time. Taken alone, this increases the rate, so for an exothermic reaction the effect of changing temperature during the reaction time opposes the effect of composition. This results in three possible rate behaviors in an adiabatic PFR with an exothermic reaction.

  • The rate increases steadily during the reaction time as would happen if the temperature effect was stronger than the composition effect over the reactor’s entire conversion range.
  • The rate increases, passes through a maximum, and then decreases during the reaction time as would happen if the temperature effect predominated at early reaction times and the concentration effect predominated at later reaction times.
  • The rate decreases steadily during the reaction time as would happen if the concentration effect was stronger than the temperature effect over the reactor’s entire conversion range. (As noted above, this rate behavior also occurs when the reaction is endothermic.)

Comparing equal feeds at equil conversions as above, the rate will not change during the reaction time in a CSTR, and because the conversions are equal, the rate in a PFR will become equal to the CSTR rate at the end of the PFR reaction time. If the rate in the PFR increases steadily during the reaction time (first rate behavior above) the required PFR volume will be larger than the CSTR. This is because the rate only become equal to the CSTR rate at the very end of the reaction time; prior to that the PFR rate is lower than the CSTR rate so the required volume is larger. Conversely, if the rate in the PFR decreases steadily (third rate behavior above) the required PFR volume will be smaller than the CSTR. If the PFR rate increases, passes through a maximum, and then decreases during the reaction time, the required PFR volume could be smaller or larger than the CSTR volume.

Comparing equal feeds at equil space times for a single reaction in adiabatic reactors, the rate again will not change during the reaction time in the CSTR. The reaction time in the PFR will equal the reaction time in the CSTR. If the PFR rate increases steadily during the reaction time, the conversion will be smaller in the PFR than in the CSTR. If the PFR rate decreases steadily during the reaction time, the conversion will be larger in the PFR than in the CSTR. Not surprisingly, if the PFR rate increases, passes through a maximum, and then decreases during the reaction time, the conversion in the PFR could be either larger or smaller than that in the CSTR.

Some reactors are neither isothermal nor adiabatic, and in these cases the variation of the rate during the reaction time will differ from the rate behaviors described above. When more than one reaction is taking place the selectivity may be just as important as the reaction rate. The effects of temperature and composition upon the selectivity may be different from their effects upon the rate. This can lead to trade-offs between conversion and selectivity.

In summary, for a single reaction in an isothermal reactor the choice between a CSTR and a PFR is straightforward. For single reactions in adiabatic reactors it is straighforward if the reaction is endothermic. When the reaction is exothermic it won’t be known which of the three rate behaviors applies without performing at least a few preliminary calculations.

Furthermore, all of the preceding qualitative analysis assumed typical kinetics. For atypical kinetics (autocatalytic reactions, reactant-inhibitie reactions, etc.) a similar analysis can be used. As was found for typical kinetics, in some cases the choice between a CSTR and a PFR will be straightforward while in others it won’t.

In the simplest of situations it may be possible to make a choice between a CSTR and a PFR on the basis of a qualitative analysis. In many other situations preliminary modeling of both reactor types may be needed to inform the choice of which reactor type to use.

10.4 Design Strategy

Having chosen the first reactor type to assess, a model for it can be generated. However, many of the quantities appearing in that model will be unspecified, and the design engineer will need to choose the “best” values for them. As the design of the entire process evolves, values for many of these quantities will be determined by process economics, and the need for integration with other components in the overall process. The discussion here focuses on preliminary design where a full economic analysis is not possible or available and where other components of the process are not finalized.

One strategy for preliminary design involves identifying a key metric to be optimized. Ultimately the process economics will serve this purpose, but many different factors affect the overall process economics. During preliminary design one unspecified reactor model quantity can be chosen as the key metric. This key metric should be one that impacts process economics significantly. The preliminary design calculations then seek to find values for all other unspecified quantities in the reactor model that optimize the key metric.

An important aspect of the preliminary design is to identify as many constraints on the unspecified quantities as possible. Constraints are limits on the allowed values of the unspecified quantities. They can be physical limitations, such as maintaining the temperature below some critical value where phase transition occurs or undesired reactions occur. Safety can impose constraints, such as avoiding a design that is parametrically sensitive. If the desired annual production rate or something equivalent is known, that imposes another constraint.

Once a key metric is chosen and the constraints are identified, the reactor model is used to optimize the key metric with respect to the unspecified quantities, subject to the constraints. Dedicated computer functions for maximizing or minimizing the key metric with respect to multiple optimization parameters and subject to multiple constraints are available in many software packages and can be used to accomplish this. After it is optimized, the sensitivity of the key metric to each unspecified quantity can be assessed. This may offer opportunities for the reaction engineer to be creative by altering the reactor design or operation to reduce such sensitivity and allow further optimization.

10.4.1 Reactor Properties as Economic Indicators

One of the primary goals of process design is to arrive at a fully specified reactor that will yield greatest rate of financial profit while satisfying any specifications included in the design assignment and all constraints. At the preliminary design stage there are still too many unknowns for that sort of financial analysis. Instead, a reactor parameter, input, or output that strongly affects profit can be used as the key metric to assess and compare reactors.

For example, the capital and operating costs for a reactor often scale with its volume. In that case, one of the goals of the preliminary design would be to minimize the reactor volume while satisfying the specifications in the design assignment. Similarly, the use of steam or another medium for heating and the use of chilled water or another coolant have associated costs, and the amount of each heat exchange fluid used can serve as a cost indicator. The selling price of the product may depend upon its purity, and production of hazardous wastes can add to operating costs. In both of these cases, conversion and selectivity may be important metrics that are related to process profit. Any reactor design assignment is likely to have several metrics that are related to the economics of the reactor process. Typically the engineer will choose a key metric that is expected to have the greatest effect upon the economics of the process.

10.4.2 Design Constraints

The engineer may not have complete freedom when specifying the missing reactor model parameters. Other considerations may constrain their freedom. For example, there may be temperature limits on various process streams. These might include a maximum allowed reaction temperature (to prevent undesired reactions, phase changes in the reactor, or catalyst deactivation), a maximum outlet temperature on chilled water, or a maximum final temperature for a batch process. Safety can also impose other constraints such as a maximum temperature and/or pressure that feed and product piping can withstand, composition limits to avoid danger of explosion, etc. If anything is being discharged to the atmosphere or waterways, regulations may restrict composition.

The design specifications often set the annual production rate or equivalently, the total volume to be processed and the total time during which that must happen. For a non-continuous process, this establishes a relationship between the volume per batch (i. e. the reactor volume) and the total time per batch. Specifically, both the volume per batch and the time per batch are related to the number of batches, Equation 10.1.

\[ N_{batches} = \frac{V_{total}}{V_{batch}} = \frac{t_{total}}{t_{batch}} \tag{10.1}\]

If the design assignment specifies the net production rate, but does not fix either the volume per batch or the time per batch, then the design engineer can specify one or the other. If the reaction engineer specifies the volume per batch, the time per batch is constrained as shown in Equation 10.2, and if the engineer specifies the time per batch, the volume per batch is constrained as shonw in Equation 10.3. Equations 10.1, 10.2, and 10.3 are written in terms of the volume being processed, but any measure of the amount to be processed could be used. A specified annual production rate will establish similar relationships between volume, space time, and conversion in continuous processes.

\[ N_{batches} = \frac{V_{total}}{V_{batch}} \qquad \Rightarrow \qquad t_{batch} \le \frac{t_{total}}{N_{batches}} \tag{10.2}\]

\[ N_{batches} = \frac{t_{total}}{t_{batch}} \qquad \Rightarrow \qquad V_{batch} \ge \frac{V_{total}}{N_{batches}} \tag{10.3}\]

10.4.3 Comparing Fully Specified Reactors

In the simplest design assignments, optimization of the key metric may be all that is needed.Alternatively, it may happen that when the key metric is minimized, one or more of the other economically important metrics has a large and unfavorable value. In design assignments, a trade-off between the economically important metrics is often observed. That is, as one important metric is optimized, another important metric changes in an unfavorable way.

Sometime in this situation, the engineer might decide to analyze the same fully specified reactor system multiple times, maximizing a different key metric each time. This can provide useful insight into the magnitude of the coupling between the important metrics. Based on the results and guided by insight, knowledge, and intuition, the engineer might elect to specify the missing reactor model parameters in a totally different way, or even to examine a different reactor type.

Ultimately the engineer selects one of the fully specified reactors as the one that is most preferred. A few other fully specified reactors may be designated as alternatives, pointing out the trade-offs between the economically important reactor metrics. The quantity or quantities chosen as key metrics, the other quantities identified as economically important metrics, and the different ways the engineer specifies the missing reactor model parameters leading up to the selection of the preferred and alternative reactor systems can be referred to as that engineer’s design strategy.

10.5 Learning Objectives and Examples

Upon completion of this chapter, readers should

  • know the definition or defining equation for key metric, constraint, and design strategy
  • understand
    • that reactor design is often one component of an overall process design
    • that process design often involves a large team with a variety of expertise
    • that reactor design tasks are open-ended and do not have a single “correct” solution
    • that economics, safety, regulatory compliance, and process operability are important design considerations
  • be able to perform a preliminary reactor design

Readers who have assimilated the knowledge and skills from Chapters 5 through 9 are capable of reactor analysis. This chapter emphasizes design strategy, not analysis. More specifically, the focus is on choosing the reactor type, identifying a key reactor metric and other economically important metrics, and specifying the missing reactor model parameters.

For this reason, the examples provided here do not include any calculations. Instead, they focus on the engineer’s thought processes and the resulting design strategy the engineer develops. The engineer may revise or expand their design strategy as they proceed through the analyses. The examples describe one engineer’s thinking and design strategy. A different engineer might think differently and develop a different design strategy. Assuming they are competent, both engineers will arrive at a preliminary design that satisfies the design specifications, but their preliminary designs may be different from each other.

As such, it is important for readers to recognize that these examples are not a “cook book” for what one should be thinking while developing a design strategy, but rather an example of what one engineer might be thinking as they develop theirs. Since the engineer’s thinking is the essence of these examples, “Click Here to See What an Expert Might be Thinking at this Point” callouts are not used.

10.5.1 Preliminary Reactor Design for an Autocatalytic Reaction

Background: Based on a preliminary marketing study, a chemical company is considering producing 30,000 gal of reagent Z per year. The market analysis is based on a purity of 99% or greater. The proposed process would produce Z three times per year with each production period lasting four-weeks. The reactor would be used for other purposes the rest of the time. Chilled water at 18 °C is available as is saturated steam at 50 psi. Storage tanks will be used to hold the 99% pure product between the time it is produced and the time it is sold.

Z can be produced from reagent A which is available in essentially pure form at ambient temperature (20 °C). The irreversible, exothermic, autocatalytic reaction, \(A + Z \rightarrow 2Z\), is first order in A and in Z. In the absence of Z, the rate is very small. When both A and Z are present, the rate is measurable at 20 °C. The reaction is moderately exothermic. Reagents A and Z are liquids and form an ideal solution. The product, Z, has the lower boiling point, 96 °C. A rate expression and all necessary thermochemical data are available.

Assignment: Perform a preliminary design of a reactor that can be used as described above.

10.5.1.1 Design Strategy

As the engineer who was given this assignment, here’s what I’m thinking:

  • Because the annual production is small and does not require year-round operation, a batch process is preferred.
  • I could use either a BSTR or an SBSTR.
    • The reaction is exothermic, so if the temperature cannot be safely controlled, I will have to use an SBSTR.
    • I’ll start my analysis assuming the reactor operates as a BSTR.
  • I’ll use one week as the basis for my calculations.
    • 30,000 gal must be processed over 12 weeks or 2500 gal per week.
  • I’ll assume that capital and operating costs scale with the reactor volume, in which case I’ll want to minimize the volume of the reactor.
    • The resulting volume will impose an upper limit constraint on the processing time, Equation 10.2.
  • I want the rate to be as large as possible at all times.
  • Having some Z present initially is essential for an acceptable rate.
    • This suggests that during turnaround the reactor should not be emptied completely.
  • The reaction is exothermic; the temperature will rise continually if no cooling is provided.
    • I’ll assume that some cooling will be necessary, but I’d like to use as little cooling water as possible to reduce operating costs.
    • Since the reaction rate is “measurable” at ambient conditions, I’ll assume no heating is necessary.
  • The conversion must be at least 99%.
  • To provide a margin of safety and keep the product from boiling (at 96 °C), I’ll specify a maximum temperature of 90 °C.
  • The product that is left in the reactor during turnaround will be hot and the A that is added to it will be at 20 °C (ambient temperature)
    • The initial temperature will depend upon the relative amounts of A and Z.
  • For cooling I’ll assume the reactor is jacketed and that the jacket volume and heat transfer area are geometrically related to the volume.
    • I’ll assume that I can determine that relationship along with the heat transfer coefficient from stirred tank vendor literature.
  • If the temperature cannot be controlled below 90 °C, I’ll switch to using an SBSTR.

A reactor model can be developed as follows:

  1. Assume the reactor is a jacketed BSTR with a volume, \(V\).
    1. Use stirred tank manufacturer’s literature to estimate the jacket volume, heat transfer area and heat transfer coefficient.
    2. Assume that chilled water flows into the jacket at 18 °C with a flow rate of \(\dot{m}_{ex}\).
  2. At the end of processing \(X\)% of the reactor contents are removed and transferred to storage.
    1. the turnaround time needed for this can be estimated.
  3. To start a batch, a sufficient amount of pure A at 20 °C to fill the reactor is added instantaneously.
    1. Assuming perfect mixing, the initial temperature and molar amounts of A and Z can be calculated.
  4. The processing ends when the conversion of A reaches 99%.

Based upon my thinking above, here is my design strategy.

Using the reactor design equations for this system, the reactor volume can be minimized with respect to \(\dot{m}_{ex}\) and \(X\) subject to the constraints that the temperature is below 90 °C at all times and that the processing time satisfies Equation 10.2.

The reactor volume is the key metric to be minimized. The coolant flow rate is also an economically important metric that should be as small as possible.

It may not prove possible to meet the design specifications and satisfy the constraints using my initial specifications for the missing reactor model parameters. Whether or not it is possible, the following modifications of the system should be analyzed.

  • During turnaround, partially cool the fluid that is not removed from the reactor prior to adding the fresh feed and starting the next batch.
  • Drain the jacket during turnaround and initially operate the reactor adiabatically, starting the coolant flow when the temperature reaches \(T_1\), with \(T_1\) as an additional optimization parameter.
  • Operate as an SBSTR, adding the fresh feed at a steady rate, \(V_{in}\), with \(V_{in}\) as an additional optimization parameter.

The minimized volumes for each system should be compared and the one with the smallest \(V\) should be reported as the preferred design. If any of the other designs have a volume close to the volume of the preferred design, but with a coolant usage much smaller than the preferred design, they should be reported as alternative designs.

10.5.1.2 Discussion

This was a very simple example, and many details were not included in the design strategy. One thing to note is that by minimizing with respect to the coolant flow rate, the possibliity that no cooling is necessary is included. In that case the optimim coolant flow rate would be essentially zero.

The total volume to be processed per week in this example is 2500 gal. It is important to recognize that the minimized volume, \(V\) that is found using the design equations is the total reactor volume. However, at the start of the process \(X\%\) of that volume was not fresh feed. Also, the time per batch is the processing time plus the turnaround time. As a result, the constraint on the processing time is given by equation (1).

\[ t_{batch} \le \frac{t_{total}}{N_{batches}} \]

\[ N_{batches} = \frac{2500\text{ gal}}{\left(1 - \frac{X}{100}\right)V} \]

\[ t_{turnaround} + t_{processing} \le \frac{1\text{ week}}{2500\text{ gal}}\left(1 - \frac{X}{100}\right)V \]

\[ t_{processing} \le \frac{1\text{ week}}{2500\text{ gal}}\left(1 - \frac{X}{100}\right)V - t_{turnaround} \tag{1} \]

There are a lot of “what-if’s” associated this assignment. For example, what if, with no cooling, the heat of reaction only caused the temperature to rise to 50 °C? In that case, it might be beneficial to use heat to raise the initial temperature. That would lead to a higher rate, and consequently a smaller reactor. (Of course the costs associated with the heating would need to be offset by the lower capital and operating costs due to a smaller volume.) A good design engineer is constantly asking and answering these what-if’s as one means of refining and improving their design strategy.

10.5.2 Preliminary Design for an Exothermic Autocatalytic Reaction

Background: A chemical company is considering construction of a new plant to produce 15 million pounds of reagent Z per year. This will be the first time the company will produce Z. It is produced from reagent A in an irreversible, autocatalytic, exothermic reaction, equation (1). The rate expression is shown in equation (2) where the rate coefficient \(k_2\) is much, much smaller than \(k_1\). Kinetics and thermodynamic data are available for the system. The product, Z, must be at least 95% pure, and the reacting fluid temperature cannot exceed 115 °C. A small steam generator and a chilled water plant will be built to support the process.

\[ A \rightarrow Z \tag{1} \]

\[ r_1 = k_1C_AC_Z + k_2C_A \tag{2} \]

Assignment: Perform a preliminary design for the reactor to be used in the new plant.

10.5.2.1 Design Strategy

The annual production is large, so the process will be continuous. There isn’t an existing plant that I can use for reference, so I’ll need to decide whether to use a CSTR or a PFR. Some qualitative reasoning may help me make that choice.

If I use a CSTR, it will operate at the final conditions where the temperature will be as high as allowed and the composition will consist of 95% Z and 5% A. Both of these factors favor a high rate, and consequently a small volume. (The reaction is auto-catalytic, so the rate remians high despite a lower reactant concentration and higher product concentration.)

If I use a PFR, the composition near the inlet will be almost all A and the temperature will be low. This will lead to a very low rate near the inlet, a lower average rate, and consequently a large reactor. Based on this reasoning, it seems clear that a CSTR should be used.

I’d like the reactor to be as small as possible which means I’d like the rate to be as large as possible. I can’t exceed 115 °C, so to provide a margin of safety, I’ll set the outlet temperature to be 95 °C. For the rate to be as large as possible, and knowing the conversion must equal 95%, that fixes the outlet composition and temperature.

I’ll assume two weeks of down time per year, which fixes the outlet flow rate of Z at 1.5 x 106 lb per 50 weeks. I can convert that to a molar outlet flow rate, then, knowing the conversion, I can calculate the inlet molar flow rate of A. Then, knowing the rate and the inlet flow rates, I can calculate the reactor volume.

I’m not sure whether the heat of reaction is sufficiently high to operate adiabatically. I might need to add heat or I might need to remove it so that the outlet temperature is 95 °C. I’ll need to calculate the necessary heat transfer area and exchange fluid temperature. I’ll assume that steam and cooling water will be available at the same temperatures as in other plants the company operations for the purposes of this preliminary design. If the design proceeds to a larger scale, the design of the steam and chilled water plants will need to be integrated into the reactor design.

Since the reactor volume is essentially fixed by the specified production rate, the costs that scale with the reactor volume are also fixed. I expect that the steam and/or chilled water will be the next most significant contributors to the operating costs. If I need cooling, I can minimize the amount of coolant used by adjusting the heat transfer area.

Even if I don’t need steam for steady-state operation, I will likely want to supply heat during process start-up. I’ll need to devise a start-up procedure and calculate its heat exchange requirements. If the steady-state process also requires steam, I’ll need to design the reactor for the more demanding of the two operating modes. I’ll assume that any steam used will be saturated, and adjust the heat transfer area to minimize the steam flow rate. I’ll assume that only 85% of the steam condenses to provide a margin of error.

10.5.2.2 Discussion

In this assignment, the choice between a CSTR and a PFR was quite easy. The kinetics were such that high product concentration favors a high rate, and the reaction was exothermic, so adiabatic operation would give a high temperature, which also favors a high rate. The choice of a CSTR could be made on the basis of a qualitative analysis without requiring any computational analysis of a PFR.

In Example 10.5.1, the reactor volume was used as the key metric affecting the operating costs for the process. Here the reactor volume was effectively established by the specified production rate, product purity, and maximum temperature. Thus, the coolant and steam flow rates could be used as the key metrics affecting operating costs. Further, if both cooling (during steady-state operation) and heating (during start-up) were required, they could both be minimized because they would not be used simultaneously. The cooling could be minimized for steady-state operation and the heating for start-up.

10.5.3 Preliminary Design of a Continuous Reactor for an Endothermic Reaction

Background: Z is the monomer used to produce a commodity polymer. Typically Z is produced from A via the endothermic, irreversible dehydrogenation reaction (1). The gas-phase dehydrogenation reaction is second order in A. A company wants to build a process to produce 10,000 tons of Z per year. The feed A will be avialable at 200 °C and 10 atm. The reactor must operate at 98% conversion, and its temperature must be kept below 800 °C.

\[ A \rightarrow Z + H_2 \tag{1} \]

Assignment: Perform a preliminary design of a reactor for use in this process.

10.5.3.1 Design Strategy

The amount of Z to be produced per year is very large, so I’ll design a continuous reactor. It is likely that I’ll need to heat the reactor whichever type I choose. If I choose a CSTR, it will operate at the outlet composition where the concentration of A will be very small, leading to a low rate of reaction, and therefore requiring a large reactor. Additionally, because the reacting fluid is a gas, it might be challenging to design the agitation so that mixing is perfect. So, it seems clear that I need to use a PFR.

Having chosen the reactor, most of the operational details are fixed. The conversion and outlet flow rates are set by the given process specifications, and knowing the conversion, I can calculate the feed flow rate. I want the reactor to be as small as possible because I expect operating costs to scale with the reactor volume. I could simply design the reactor to operate close to the maximum allowed temperature, leaving an appropriate margin of error.

However, I don’t really know whether it is necessary to operate right at the limit. The rate may be sufficiently large at lower temperatures. Clearly there will be a trade-off between reactor volume and heating demand where using less heat will result in a larger volume. I also don’t know what the heat exchange fluid is going to be. It might be saturated steam, but depending upon the temperature, a molten salt might be preferred.

For the purposes of this preliminary design, I’ll assume that the temperature of the heat exchange fluid will be constant, and I’ll create a graph showing the reactor volume as a function of the heat exchange fluid temperature. That may prove helpful for choosing what to use as a heat exchange fluid as the design moves forward. That is, for a given volume it will show the necessary exchange fluid temperature, and that can be used to estimate the associated costs for various heat exchange fluids.

10.5.3.2 Discussion

In this example, the choice of the type of reactor to use was unequivocal. The remaining available specifications were insufficient to go too far with the preliminary design. In situations like this it can be useful to explore the trade-offs between different operating parameters instead of choosing a key metric and minimizing it. In this way, preliminary choices can be made to more fully specify the nature of the system, after which a preliminary optimization can be performed.

For this system, the engineer would really need more details about the metals to be used for the reactor (what temperatures can it withstand, at what temperature might hydrogen embrittlement become an issue) and its compatibility with different heat exchange fluids. A very preliminary calculation of reactor volume versus heat exchange temperature like the one described above can inform decisions about the metallurgy, heat transfer medium, etc. Then a slightly improved preliminary design can be undertaken.

10.5.4 Preliminary Design of a Reactor for an Exothermic Reaction

Background: The liquid-phase, exothermic reactions of A and B, equations (1) and (2), are exothermic, irreversible, first order in A and first order in B. D is the desired product because its value is significantly greater than U. The activation energy for reaction (1) is smaller than the activation energy for reaction (2) while their pre-exponential factors are comparable. The kinetics and thermodynamics of the reactions are well-documented.

\[ A + B \rightarrow D + Z \tag{1} \]

\[ A + B \rightarrow U + Z \tag{2} \]

Assignment: For a proposed process to manufacture D, separate streams of A and B will be available at 30 °C where they will react at a modest rate when combined. The adiabatic temperature rise for the reactions at these feed conditions is approximately 60 °C. Chilled water will also be available at 25 °C. Perform a preliminary design of a continuous reactor for the conversion of A and B.

10.5.4.1 Design Strategy

The assignment doesn’t specify a production rate, so I’ll choose a feed rate as a basis in my analysis. There are two important performance metrics in this system, the reactor volume and the yield of D. Based upon the information given in the assignment, the reactor could operate adiabatically, but it might be preferrable to cool it because lower temperature will favor the production of D (because the activation energy is smaller).

The choice of reactor is not clear-cut. If a CSTR is used, it will operate at higher temperature and lower reactant concentrations. Those factors have opposing effects upon the reaction rates, and by extension the reactor volume. If a PFR is used, the temperature at the inlet will be smaller, and the concentrations of the reactants will be larger. As the fluid progresses through the reactor, the temperature will rise, tending to increase the rate, while the reactant concentrations will decrease, tending to decrease the rate. Depending upon the conversion, it is possible that the average rate in the PFR will be close to the rate in the CSTR, and consequently, their volumes will be comparable. Because the temperature will vary in the PFR, it also isn’t clear which reactor will offer the better selectivity.

Given those uncertainties, it would not be prudent to choose the reactor type without performing any analysis. Instead, I will evaluate both reactor types and, if possible, choose the preferred reactor based upon a comparison of their performance. For either reactor type, I’m also not sure which of the performance metrics is most important, the reactor volume or the yield of D. That is, it might result that when the reactor volume is minimized, the yield of D is very small, or vice versa.

In light of the uncertainties described above, my design strategy for each of the two reactors will be as follows:

  1. Choose a range of reactor volumes.
    1. for each volume, maximize the yield of D with respect to the coolant flow rate and heat transfer area.
    2. plot the maximum yield of D as a function of the reactor volume.
  2. Choose a range of values of the yield of D.
    1. for each yield of D, minimize the reactor volume with respect to the coolant flow rate and heat transfer area.
    2. plot the minimum reactor volume as a function of the yield of D.

This will generate four graphs, two for the CSTR and two for the PFR. These graphs should make any trade-offs between reactor volume and yield apparent, and they may also show that one of the two reactor types is clearly superior. In any case, these graphs should be useful for refining the the design specifications.

10.5.4.2 Discussion

In this assignment it wasn’t possible to select the reactor type on the basis of a qualitative analysis. This is often the case, especially if the reactor is being heated or cooled. It is better to do at least an initial computational analysis of both reactors and use the results to inform future design decisions.

10.6 Symbols Used in Chapter 10

Symbol Meaning
\(t_{batch}\) Total time (processing plus turnaround) per batch.
\(t_{total}\) Total time available for processing the total volume of feed.
\(N_{batches}\) Number of batches.
\(V_{batch}\) Volume of feed to be processsed per batch.
\(V_{total}\) Total volume of feed to be processsed.