Frequently Asked Questions (FAQs)

Chapter 4

In solving problems for this class, is there ever a case where you need more steps than the mole balance, rate law, stoichiometry, and combining? (When do you deviate from this algorithm?)
We will always use this basic algorithm and then just add to these steps to it, e.g. the energy balance. We will not deviate from these first four steps.
What specifically causes a CSTR in series to have a higher conversion than a CSTR in parallel?
The CSTR is always operating a the lowest concentration, the exit concentration. When say two CSTRs are in series, the first operates at a higher concentration, therefore the rate is greater, therefore the conversion is greater. The second reactor in series builds on the conversion in the first reactor. The conversion in the parallel scheme is the same as the conversion to the first reactor to the series scheme. See Figure p.50 and Example 4-2.
When are reactors in parallel used since it seems as though reactors in series would always achieve higher conversion?
The PBRs in parallel are ued when there would otherwise be a large pressure drop in one long reactor or identically several PBRs connected in series.
Is it possible to have a pressure drop for a liquid phase reaction, as is possible for a gas phase reaction?
You can have a pressure drop in liquid phase systems, but it does not affect the reaction rate because liquids are virtually incompressible and therefore the concentration does not change with pressure.
Since two equal CSTR in series give a higher conversion than two in parallel, are reactors in parallel ever used to increase conversion?
Not for a CSTR, only a PFR/PBR when there is a significant pressure drop.
The Damköhler (Da) number
1. What is the Damköhler number?
  See p.138 of text.
2. How is the Damköhler (Da) number defined for a reaction
  (A + B C) when the reaction is first order in A, first order in B, but second order overall?
  Just substitute the rate law evaluated entrance to the reactor, -r_A0, [e.g. -r_Ao=kC_AoC_Bo] into the definition . See p.138.
3. Is Da always indicative of certain conversion?
  Yes, for irreversible reactions.
4. How does defining an extra variable, the Damk›hler number, save us time and confusion, as opposed to solving without it? When should it be used?
  It serves as rule of thumb. When Da < 0.1 then X < 10% and when Da >10 then X >90%. See margin note p.138 of Ch.4.
Why do they use a batch reactor to determine k if they are going to be using CSTR in actual industrial process?
Batch experiments are most always easier to take the necessary data to determine k.
In what cases would you use the order of magnitude reaction times other than to check k values that you calculate?
When you are short on time and want to get quick engineering estimates.
At some of the polymer plants and refineries I've visited, a huge problem is fouling of the reactors. The plant workers would sometimes have to go into the reactors to break through the solids/sludge that adhere to the reactor walls. I imagine this solid build up leads to a drastic volume decrease. So, how do we take into account the change of volume and it's detrimental effect to conversion?
Good point. It would change the volume; however, catalyst decay by fouling is usually more important. See Ch.10.
Is rinsing the reactor with water after a batch ample cleaning, or are chemical cleans necessary in between batches?
It depends, if there are no side reactions, a chemical clean is probably not necessary. Also the larger the reactor the greater the cleaning time.
Please clarify the method for deriving the rate law expressed with partial pressures.
When studying catalytic reactions the rate law is developed in terms of partial pressure,
e.g. .
To rewrite the rate law just use ideal gas law to relate to concentrations C_A and C_B

and then write concentration in terms of conversion.
Writing partial pressures in terms of conversion
How accurate is the perfect mixing assumption in dealing with CSTRs? It seems kind of far fetched that the entire CSTR is at the same concentration as the exit.
True but these are ideal CSTRs, and non ideal reactors and the perfect mixing assumption is discussed and modeled in Ch.13. Once we understand ideal reactors (perfectly mixed), we can easily model non-ideal reactors.
In a PFR or CSTR reactor, wouldn't the reaction still be taking place in the pipe that the products leave through? Why does the reactor just magically stop occurring when the contents leave the reactor? Is there a good way to model a CSTR that is not perfectly mixed?
It does continue to react to some extent. It depends on the temperature in the pipe! However, these are ideal reactors. Different models for Non-ideal reactors are discussed in Chapters 13 and 14, but we must understand ideal reactors first.
Can you compare space time for a flow reactor to the time spent in a batch reactor for the purposes of measuring conversion?
Sometimes. See Lecture 6 on the CD-ROM.
We understand that for a CSTR, the conversion X increases as residence time increases. We were unsure as to what the relationship is for a PFR?
The same is true for a PFR If you increase and you increase X.
Is the CSTR conversion equation always the same no matter the order of reaction?
No! This equation is only for first order.
Is the assumption that there are no radial gradients a good one for most tubular reactors? When is it not valid?
It is quite a good assumption for turbulent flow. It is not valid for Laminar flow - see Ch.13 p.831.
When trying to determine the optimal catalyst size for the internal diffusion limited case, do we always use the relation or are there any other relations that can be used?
You can only use this relationship in the internal diffusion limited regime shown in Figure 12-5, p.750. For a first order reaction with
(12-35)
or lumping all the constants not involving particle size into a parameter, we have "a" Then . Thus then k₂ = k₁ for Pb. 4-23 one must use all of Figure 12-5. It can be shown that Figure 12-5 can be represented as
When accounting for pressure drop in a membrane reactor, does the same method as we would use with a PFR apply?
Yes,
Do we only use the form of the PBR design equation for membrane reactors (IMRCF)?
NO!! The mole balance is
The relationship between reactor volume and catalyst weight is
Substituting for W
Then
In the text it states that for developing the design equation for a PBR when X << 1 you can use the relationship

Neglecting X

For what values of X is this valid?
Is there a transition regime for the engineering analysis we performed, if so, what is the relations?
Yes, in the transition region one must use full equations for
For what particle size (if any) does the porosity change (or void) to make a calculation difference?
It changes with packing of catalyst, but usually very little for the PBR and catalysts commonly used.
Why can't you write the membrane equations in terms of conversion X?
Because you can't relate the concentration of the product diffusing out, C_B, and X.
In the chapter we are given total cycle times excluding reaction for a batch polymerization. Is there a similar standard for a PBR when the catalyst must be removed and are there similar standards for flow systems that experience coking on the walls and need cleaning eventually.
The onstream time for flow systems is much much greater than the down time for cleaning and repair.
Would there ever by a case in which a membrane reactor would be used for the reverse? I.e. if H₂, for example, was used as a reactant in a reaction, would one ever want to run concentrated H₂ along the sides of the reactor and let it diffuse into the reaction zone?
Yes, especially when O₂ is one of the reactants.
In a membrane reactor, how can one quantify the equilibrium point on the graph of F vs. V?
In this region (i.e. after the knee) the reaction is in equilibrium and the rate of removal of B is what limits the overall rate of reaction.
How can you assume that a semi-batch system has constant density? (p.199).
Most liquids do not change density during the course of the reaction.
On page 199, why does and not not like in all of the other examples? Is it just for C_D?
In Case I, it was for a batch system, thus no flow, and that is why there is no vot term. If it was a semi-batch system plus immediate evaporation:
When is the compressibility factor in the ideal gas law not equal to one? Will w ever encounter this?
You are only interested in the ratio Z/Z_o being the same, we don't care if Z doesn't equal one.
On page 157 equation 4-30, I am having trouble understanding the concept that when epsilon is negative, change in P will be less (i.e. higher pressure) than for epsilon=0.
If epsilon is greather than 1, density is greater than if epsilon=0 because
A larger density results in a smaller change in pressure.