I neglected the pressure drop and assumed that the temperature of the coolant does not change down the length of the reactor

Design Of A Cumene Production Facility
#26
Posted 23 April 2019  02:00 AM
#27
Posted 23 April 2019  05:42 AM
It is not very clear to me what you are doing.
For example: I have no idea what "CT0 Feed Gas Total Concentration" means. Is a and A the same variable? What is Ta ? Et cetera.
I suggest you first make a complete list of all the variables that you are using/defining, including their units of measurements.
And make a drawing on which those variables are indicated.
Also list the reactor feed quantity, composition, temperature and pressure that you are using.
No info about the temperature of the medium Ta is given in the problem statement so do I just assume saturated water at the inlet pressure from the inlet pressure and use the heat of reaction given off to generate steam?Is Ta the temperature of the boiling water? It is up to you to choose that temperature so as to remove enough of the reaction heat so that the reactor outlet temperature does not get higher than you want. So you have to decide what reactor outlet temperature you want.
U*a=4/D*UI have no idea what that means.
I am not familiar with polymath but in any case I suggest you forget about differential equations and first do the calculations simply in a spreadsheet table.
Divide the total length Z of the reactor tube into say 100 parts. That gives you 100 lines in the table. Each line represents a small part of the reactor with length 0.01Z. Each part has a constant temperature and pressure, and a certain volume. The first part obviously has the reactor inlet temperature. In each part a certain amount reacts, a certain amount of heat is generated and a certain amount of heat is removed by heat transfer to the boiling water. Each part has a U , a wetted tube area and a temperature difference between process gas and boiling water. As a result each part has a temperature change, which sets the temperature of the next reactor part. After 100 parts you reached the reactor outlet with a certain temperature and conversion. If these are not what you like then you adjust inlet parameters like number of tubes, tube length, temperature of boiling water, reactor inlet temperature, et cetera.
You need to either assume a U for each part, or try to calculate it, that's for you to decide.
#28
Posted 23 April 2019  10:09 AM
The constraint on the reactor exit temperature is 400 degrees Celsius.
I don't find myself comfortable using excel. In polymath I can easily adjust the design parameters such as Number of tubes, Length of tube..
For the mole balance of each species should I just divide the initial condition which I computed by the number of tubes or do I just account for the number of tubes by multiplying the crosssectional area of one tube, A, by the number of tubes, N?
Reactor Inlet Temperature=623K
Also, the differential equation describing the reactor temperature down the reactor length, we are considering the change in temperature in a single tube which is the same for all other tubes so should the flowrate in flowrate*molar heat capacity term in the be the flowrate in a single tube?
Inlet Pressure=3075 kPa
I assumed saturated water at the inlet pressure from which the saturation temperature is deterined as=506K
Attached Files
#29
Posted 23 April 2019  11:21 AM
I don't have time to figure out all your formulas.
What is C_{To} which you now call "Initial Total Concentration" but initially was called "Feed Gas Total Concentration" ?
And what is meant by ΔH_{irx} ? The heat of reaction of component i ? What would that be ? Or do you mean the heat of formation of component i ?
It is not clear to me how you obtain the heat of reaction for both reactions. I don't see you calculate it using heats of formation. Or was it given somewhere in the task description?
For the mole balance of each species should I just divide the initial condition which I computed by the number of tubes or do I just account for the number of tubes by multiplying the crosssectional area of one tube, A, by the number of tubes, N?
What is meant by "initial condition" ? Does that mean the reactor inlet feed? Or what?
Assuming it is the reactor feed then it does not matter which option you choose as long as you use it consistently everywhere.
Also, the differential equation describing the reactor temperature down the reactor length, we are considering the change in temperature in a single tube which is the same for all other tubes so should the flowrate in flowrate*molar heat capacity term in the be the flowrate in a single tube?
That flowrate should be the flowrate through your selected definition of A.
Inlet Pressure=3075 kPa
I assumed saturated water at the inlet pressure from which the saturation temperature is determined as=506K
The pressure of the boiling water is not the same as the reactor inlet pressure. You choose the boiling water temperature (and consequently pressure) such that the reactor outlet temperature is to your satisfaction.
#30
Posted 23 April 2019  12:29 PM
ΔH1 and ΔH2 are the heats of reaction at temperature T for the following reactions
1) Propylene+Benzene>Cumene
2) Cumene+Propylene>DIPB
I found the heat of reaction under standard conditions from a similar project to mine and CT0 is the Concentration of the feed (Propane, Propylene and Benzene).
Edited by AAAIK, 23 April 2019  12:29 PM.
#31
Posted 23 April 2019  03:43 PM
I meant the ΔH_{irx} in the differential equation dF/dZ = ......................
It is there multiplied by ν_{ij}
I assume that i stands for component i, but where does j stand for? Reaction number?
Maybe you should check that equation again.
#32
Posted 23 April 2019  04:57 PM
do you mean the reactor temperature differential equation, istands for the reaction number and j stands for the component, heat is released with respect to.
ΣΔH_{irx*rij=}ΔH1(T)*(k1CPCB)+ΔH2(T)(k2CPCC)
ΔH1(T) Heat of reaction 1 per mol of propylene
ΔH2(T) Heat of reaction 2 per mol of propylene
k1CPCB and k2CPCC rate of disappearance of propylene in reactions 1 and 2.
Edited by AAAIK, 23 April 2019  05:10 PM.
#33
Posted 24 April 2019  07:52 AM
istands for the reaction number and j stands for the componentReally?
Then why not use F_{j} and Cp_{j} in the denominator, instead of F_{i} and Cp_{i} ?
You have to very clear and consistent in the use of variables, subscripts and superscripts otherwise outsiders (and your supervisor) will get confused.
#34
Posted 28 April 2019  02:15 AM
I ran polymath and by adjusting the tube length, diameter and length of tubes, I obtained the required conversion (92%) of Propylene. From these design parameter how can I compute the catalyst volume, weight of catalyst, and reactor volume, knowing that the tube diameter is larger than in tube sheet layouts, and assuming that tube crosssectional area is 1/3 of shell crosssectional area.
My attempt at this
The catalyst is packed equally in all tubes so
Number of tubes=Volume of Catalyst/Volume per tube
Volume of catalyst*Density of catalyst=Weight of Catalyst
The total Cross Sectional area of tubes=Volume of catalyst/Tube Length
Shell CrossSectional Area=3*Total cross sectional area of tubes
Shell Crosssectional area*Tube length=Reactor volume
In the problem statement I am given the porosity but I don't know how to account for it the above equations
#35
Posted 28 April 2019  03:21 AM
Hi ,
Check for Ergun equation .
Attached document can help.
good luck
Breizh
Attached Files
#36
Posted 28 April 2019  05:02 AM
From these design parameter how can I compute the catalyst volume, weight of catalyst, and reactor volumeTo do the calculations you must have assumed a number of tubes N, either to obtain F for one tube, or obtain A for N tubes.
So you can easily calculate the total catalyst volume in all the tubes.
Catalyst particle density is given as 1600 kg/m^{3} and void fraction ε is given as 0.5
so catalyst bulk density is 1600 * (1  ε) = 800 kg/m^{3}
and that is the density you should have used in your differential equation(s).
I suggest you also check the heat of reactions as they also seem wrong to me. Use heat of formations of products and reactants to calculate them.
I don't know where you got the formulas for the component Cp values, but make sure they are correct by checking them again literature data from another source.
Also make sure you used the correct value and units of measurement of R in rate equations.
#37
Posted 28 April 2019  06:51 AM
I recalculated the heat of reactions for reactions 1 and 2 and I checked the Cp expression they match the values from the literature. To make sure everything is right before I run the polymath code again , Should A the cross sectional area of a single tube be multiplied by the number of tubes. The initial conditions for the mole balance should be that of the flowrate entering all the tubes, yes? If I were to assume Isothermal operation, for A in the Differential equation describing the temperature variation of the coolant, should the diameter be that of the shell?
#38
Posted 28 April 2019  09:12 AM
Should A the cross sectional area of a single tube be multiplied by the number of tubes. The initial conditions for the mole balance should be that of the flowrate entering all the tubes, yes?When you work with the total flowrate for F to all tubes then you need to base A on the total number of tubes.
If I were to assume Isothermal operation, for A in the Differential equation describing the temperature variation of the coolant, should the diameter be that of the shell?I don't see why you would want to assume isothermal operation, because it is not.
But in any case the diameter of the shell is not relevant. It is about the catalyst weight in the tubes (affects reaction rate) and the surface area of the tubes (affects heat transfer). Size of shell is resultant after you determine number, diameter and length of the tubes and tube pitch.
#39
Posted 28 April 2019  11:56 AM
I assumed Isothermal operation because when I assumed adiabatic operation the temperature exceeded the limit set by the catalyst operating conditions.
For the coolant temperature variation how can I calculate the surface area of the tubes?
#40
Posted 28 April 2019  12:26 PM
If the reactor outlet temperature is too high then you should lower the boiling water temperature Ta
In addition you could also lower the reactor inlet temperature somewhat.
The surface area of the tubes is simply resulting from the length, diameter and number of the tubes, which you choose and adjust until you get the desired propylene conversion.
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