Today's post will demonstrate how the equilibrium curve is used to explore the staged adiabatic bed option for a reactor. It appears that methane reforming is more commonly carried out in tubular reactors within the radiant section of a furnace, but let's explore the adiabatic option.
Set the goal
I have set 80% conversion of methane as the goal. This value was made arbitrarily after looking at some articles about industrial performance of fired tube reformers.
Assume a number of stages
I have assumed that there will be three stages. The inter-stage heaters will be tubular bundles within the radiant section of the furnace with the reactor(s) outside the furnace. To keep the cost down and minimize the piping complexity we need to minimize the number of stages.
Set the conversion change for each bed
I've assumed that the total conversion will be divided equally among the three beds. This should result in approximately equal inter-stage heat requirements and catalyst bed sizes.
Compute the equilibrium temperatures at bed outlets
The equilibrium methane conversion function, X0(T), is obtained from the neq(T) solve block result in the previous post. The X0(T) function was used to make the equilibrium conversion curve.
With a known conversion, x, previously set,we find the equilibrium temperature using a root operation:
Compute the inlet temperatures for each bed
With the outlet conversion and temperatures known for each stage, we can compute the bed inlet temperatures from the heat balance.
The inlet temperature can be found using QF in another root operation.
The root function finds the value of tin that makes QF zero (i.e. adiabatic). We know tout for the current bed and the inlet mole vector, nin, from the outlet value of the previous bed (or the feed for the first bed).
Add the temperature approach
The above sequence of operations will result in a vector of stage temperatures and conversions that assume the outlet reaches equilibrium. Since that is not practical (it would require a lot of catalyst), we add an approach temperature to the stage temperatures. I have used a 25 K approach temperature.
The main result is that the highest feed temperature is about 1200 K (1700 F). That temperature may challenge the furnace technology which possibly leads to the use of fired tube reactors being more common. Also, the catalyst may not be able to handle this temperature. Otherwise, the furnace for this option should be similar to the fired tube option because the overall heat load is the same. The inter-stage coils may even be more compact resulting in a reduced furnace size.
The reactor design
The adiabatic reactor is easier to load with catalyst the the large number of fired tubes. Each stage might be separately placed around the vertical furnace. Or, it might be possible to combine beds into one vessel with partitions.
Fired tube vs. staged adiabatic
If I were to make the full comparison of these options, I would begin by finding the maximum allowable catalyst temperature. That might eliminate the adiabatic option. If the adiabatic option is not eliminated , I would set the reactor outlet temperatures for the two options to a common value. This will yield common conversions so that the recycle and product separation for the options will be the same. That should leave just the furnace and reactors capital cost as the main difference.
Sizing of the adiabatic reactors requires knowledge of the required weight hourly space velocity (whsv) for each bed. This information can be obtained in a laboratory without a full kinetic study. The fired tube option doesn't require a kinetic model or whsv. The reaction is normally heat transfer limited for this option, so the number and size of tubes are determined by the total heat load and the heat flux capability of the furnace.
With reactor size and heat loads determined, I would then enlist the assistance of a furnace manufacturer and engineering design firm to get cost comparisons. The furnace for the tubular option will be almost "off the shelf" so the costs will be well known. The adiabatic option may not be standard so there needs to be enough detail in the cost estimate to get a valid comparison.
Back to reality...
The comparison described above has probably been done countless times and the fired tube option has won every time it would appear. However, this example of staged adiabatic analysis may prove useful for other reaction systems.
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