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7

# Heat Balance For A Steam Reformer Unit

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### #226 PingPong

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Posted 08 May 2018 - 04:27 PM

Calculated WABT is OK. Formulas for WABT can be found using google.

It is not clear to me though why you spent time on calculating WHSV and WABT as I don't see what you would use that for. Was that your supervisor's idea? And why WHSV instead of GHSV ?

I know from designs by reputable licensors that I saw through the years that HTS cat volume for SMR is roughly 0.5 liter per Nm3/h hydrogen product (based on a typical bulk density of 1200 kg/m3 that gives about 0.6 kg per Nm3/h). If you feel that it would sound better (more "scientific") I could calculate what typical GHSV an HTS in a licensed SMR uses.

If you have to justify that number you can either say that it comes from a personal communication with an experienced process design specialist or you can try to find typical HTS cat quantity data on the internet using google, which will be tough.

Note that you used more typicals in your design that I proposed based on my experiences with licensed designs.

If I remember well you set the reformer outlet pressure at 20 bar, so the WGSR inlet pressure will actually be something like 19.7 bar (there is some pressure drop over the WHB) and its outlet pressure say 19.4 bar.

For heat and mass balance WGS pressure is not relevant as WGS equilibrium is not affected by pressure (no change in total moles of gas) and for enthalpies it does not matter as we assumed ideal gas behavior, which is valid.

Impact of WGS pressure on kinetics is very small (only a few kg of cat), which is why I did not comment on it before when I saw you using 20 bar, as I did not want to fuss about details knowing you are pressed for time.

### #227 MurtazaHakim

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Posted 08 May 2018 - 09:30 PM

Calculation of WHSV and WABT was our own idea. We are unaware of the relevance these parameters hold in case of WGS reactor(s) in an SMR unit. However most of the catalytic reactors in a refinery or a petrochemical plant have these parameters monitored on a regular basis in order to ensure that the product(s) do not go off-spec. That is why we thought it would be important to calculate these parameters. Do these parameters have any important role to play in the WGS reactor(s) of an SMR unit ?

If you feel that it would sound better (more "scientific") I could calculate what typical GHSV an HTS in a licensed SMR uses.

For calculating the GHSV we need to know the flowrate of reactant gas into the reactor and the volume of reactor employed. Volume of the catalyst is known in m3. How do we calculate the reactor volume using the catalyst volume ? The reactant gas flowrate in kg.hr-1 must be converted into m3.hr-1 by the division of total reactant gas flowrate with the reactant gas density in kg.m-3 . Is this approach correct in calculating GHSV ? We calculated WHSV simply because of the fact that we had both the weight of the catalyst and the feed flowrate (in kg.hr-1) known to us.

Edited by MurtazaHakim, 08 May 2018 - 09:38 PM.

### #228 PingPong

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Posted 09 May 2018 - 05:50 AM

WABT is monitored during operation using the temperature measurements installed. But for the design of your WGSR in an SMR it is not relevant as we already use realistic in and outlet temperatures for the design.

For a catalytic reactor with gas feed it is more common to use GHSV than WHSV.

GHSV is volumetric flow (at standard conditions) divided by catalyst volume.

Different companies use slightly different values for standard T and p. T could be 0 or 15 or 25 oC and p could be 1 bar or 1 atm.

I will use here 0 oC and 1 bar so that the volumetric flowrate for GHSV is to be in Nm3/h.

From my historic data I estimate that licensers use a GHSV of roughly 4500 h-1 for FeCr catalyst and 5 year runlength.

When we use that number your HTS reactor needs 116 kmol/h * 22.4 Nm3/kmol / 4500/h = 0.58 m3.

Not much different from what you had before, but now calculation looks more scientific because a typical GHSV was used instead of a typical 0.5 liter per Nm3/h H2 product.

### #229 MurtazaHakim

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Posted 10 May 2018 - 04:09 AM

We expected the GHSV calculation to be the other way round, I mean calculating GHSV using catalyst volume and not finding reactor volume using typical GHSV value. Anyway the method employed seems more scientific as you said.

We have collected and read a few more research articles related to modeling of reformers. It seems that there are two types in kinetics namely intrinsic and apparent which are used for modeling the reformer tubes. The Langmuir-Hinshelwood Hougen-Watson model is preferred for modeling the reformer tubes in most of the cases. How do we begin the modeling of reformer tubes ? The collected research articles are attached herewith.

### #230 PingPong

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Posted 10 May 2018 - 07:31 AM

I don't see how one could do kinetic calculation for reformer catalyst quantity by hand, unless one has a huge amount of time.

Problem is that, unlike the WGSR, the reformer tubes are not operating adiabatic and moreover you will be dealing not only with reforming reaction but also WGS reaction simultaneously.

There is input of heat into the tubes from the burner flames. Splitting the reformer into say 20 slices and calculate cat quantity per slice is severely complicated by the unknown heat input per slice.

You would have to start assuming a certain heat input Qi for each slice i, calculate temperature Ti and cat quantity Xi in each slice, and then adjust each slices Qi according to its Xi (as the exposed tube area receiving Qi is proportional to Xi). And then recalculate Ti and Xi, and again Qi, and again Ti and Xi, et cetera, and hope that you will get a converged solution in time for your exam.

And even if you would get a result then you would hear from me that the real quantity of reformer cat that licensors use is much bigger.

The furnace of an industrial size SMR has catalyst filled tubes with a total length of up to 13 meters of which about 10 meters is facing the burner flames. The average heat flux depends on the design of the furnace but is roughly 90 kW/m2 for wall fired (like Haldor Topsoe), or roughly 75 kW/m2 for top or bottom fired with cocurrent flow of syngas and fluegas (like most other licensors). The highest and lowest heat flux in a wall fired furnace is close to the average because the burners provide a fairly even heat release over the height of the radiant box, but in the other types the heat flux at the inlet is much higher than average and at the outlet lower. Tube diameter is usually in range of 3 to 5 inch.

Your calculation showed an absorbed radiant duty of about 1290 kW so at an average flux of 75 kW/m2 that would require about 50 meters of exposed 4 inch tube.

Your little furnace would not have only a few tubes with a length of 13 meters each, but let's say 10 tubes with an exposed length of 5 meters each, a total length of 7 meters each, and a total catalyst volume of about 0.42 m3 (about 420 kg).

Now it is your challenge to come up with a kinetic calculation that will give a similar result within the time you have left.

EDIT: total amount of catalyst was wrong.

Recalculation now uses ten 4 inch tubes (instead of twelve 3 inch)

and a resulting total catalyst volume of 0.42 m3.

Edited by PingPong, 10 May 2018 - 03:40 PM.

### #231 MurtazaHakim

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Posted 10 May 2018 - 02:36 PM

Certainly there are differences in modeling the WGSR and the reformer. In case of reformer we have several parallel reactions taking place which are difficult to model whereas in case of WGSR we have only one reaction taking place. It is difficult to assume the amount of heat received by a particular slice since the heat flux is non-uniform. Furthermore it is even more difficult to find the composition of gas at the outlet of each slice using which we could find the amount of catalyst required in that slice. Simplifying the assumption by considering only the main reforming reaction neglecting the water gas shift reaction and the other reactions involving ethane,propane,butane would not work either, would it ?

The volume of one reformer tube with diameter 3 inch and exposed length 5 metres is calculated to be 0.0228018 m3. Then the number of tubes required to accommodate 4 m3 of catalyst is calculated as the ratio of the total catalyst volume to the volume of one reformer tube which is equal to 4 / 0.0228018 = 175.424 ~ 176 tubes which seems to be a huge number for such a small production rate.

The amount of catalyst is 4000 kg and it is to be filled in 12 tubes which implies each tube has to be filled with 4000/12 = 333.34 kg of catalyst. If there is no void fraction in the filled tubes then the catalyst must have the density of 333.34/0.0228018 = 14619.02 kg/mconsidering the fact that only the exposed length is filled with the catalyst.

Since our reformer is either top fired or bottom fired we cannot consider the tubes to have a uniform heat flux but for calculating the number of tubes let us simplify our assumption and consider the tubes to be having uniform heat flux of 75 kW/m2. The radiant coil duty is 1292 kW. The ratio of radiant coil duty to the heat flux is the total curved surface area of reformer tubes required which is equal to 1292/75 = 17.2267 m2. The number of tubes by this approach is calculated as the ratio of total curved surface area to the curved surface area of one reformer tube. The curved surface area of one tube having 3 inch diameter and 5 metre exposed length = 2 π r h = 2 π (0.0381) (5) = 1.196946 m2. The number of tubes = 17.2267/1.196946 = 14.39 approximately 15 tubes. The volume of 15 tubes is then equal to the total catalyst volume required and is calculated as 15*0.0228018 = 0.342027 m3 but the amount you mentioned is around 12 times greater than that.

The task of cutting the reformer tube into 20 slices and then calculating the amount of catalyst required would take weeks to complete and is not even sure to provide correct results. Is there any other approach for determining the amount of catalyst ? Could we use the heat flux approach of the preceding paragraph to calculate the number of tubes and the amount of catalyst ?

Edited by MurtazaHakim, 10 May 2018 - 02:41 PM.

### #232 PingPong

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Posted 10 May 2018 - 03:39 PM

You are right, something went wrong in original my calculation of catalyst quantity.

I have recalculated using now ten 4 inch tubes and changed the wrong number into 0,42 m3.

Note that the 75 kW/m2 that I used is indicated as the average heat flux. For calculating the exposed tube area it does therefor not matter that the heat flux is not uniform. It would matter when doing the kinetic calculations.

Note also that a 3 inch tube would have 89 mm OD and probably 67 mm ID.

A 4 inch tube has 114 mm OD and probably 87 mm ID.

Furthermore it is even more difficult to find the composition of gas at the outlet of each slice using which we could find the amount of catalyst required in that slice. Simplifying the assumption by considering only the main reforming reaction neglecting the water gas shift reaction and the other reactions involving ethane,propane,butane would not work either, would it ?
It is easy to find the composition at the outlet of each slice because that you would simply assume, like you did in the WGS reactor. The problem is that the heat input of each slice is unknown as each slice has a different height (as was the case in the WGS reactor), which you do not know in advance, so you must first assume every Qi, calculate every Xi, adjust every Qi, again calculate Xi, again adjust Qi, et cetera, et cetera, et cetera.

Doing that by hand would be terrible so you would have to write a computer program to do that.

It is up to you how you want to proceed. I don't know how little time you have left. Maybe sit down with your supervisor to decide?

### #233 MurtazaHakim

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Posted 13 May 2018 - 10:31 AM

The reformer tube has been divided into 20 slices where each slice facilitates 5% conversion. The following reactions have been considered while computing the composition of gases at the outlet of each slice:

1. CH4 + H2O <==> CO + 3H2

2. C2H6 + 2H2O <==> 2CO + 5H2

3. C3H8 + 3H2O <==> 3CO + 7H2

4. C4H10 + 4H2O <==> 4CO + 9H2

5. CO+ H2O <==> CO2 + H2

The amount of total CH4 converted is divided into 20 parts 5% of which is converted in each slice. Similarly C2,C3,C4 react completely and hence their initial flowrates are divided into 20 parts 5% of which is converted in every slice. The total amount of CO generated in each slice is obtained from the reactions (1)-(4) whereas the amount of CO consumed in reaction (5) is obtained by the amount of CO2 generated in that slice. The amount of CO flowing to the succeeding slice is then obtained by subtracting the total amount of CO generated in that slice by the amount of CO consumed for generating CO2 in that slice. The amount of CO2 at the reformer outlet is known and that amount is subtracted from the amount of CO2 initially present in the feed in order to obtain the amount of CO2 generated during the reactions and that generated amount of CO2 is divided into 20 parts in order to obtain the amount of CO2 generated in each slice (and hence the amount of CO consumed in each slice). The amount of steam reacted in each slice is obtained from the reactions (1)-(5) and this amount of reacted steam is subtracted from the initial amount of steam (61.47 kmol/hr) to obtain the amount of steam flowing to the next slice. Lastly the amount of H2 generated in each slice is obtained from reactions (1)-(5) and is added with the amount of H2 initially present in the feed (recycle H2).

We are unable to decipher as to why the mass of the products increases as we move from one slice to another which violates the law of mass conservation.

The outlet enthalpy at each slice is calculated by the addition of its inlet enthalpy and the reaction enthalpy. The reaction enthalpy in every slice is calculated using the inlet and outlet composition of that slice. For example, the inlet enthalpy of slice 1 is known (reformer inlet enthalpy at XOT),the outlet composition is computed using the conversion methodology mentioned in the preceding paragraph. The outlet and inlet compositions are then used to compute the reaction enthalpy. The reaction enthalpy added to the inlet enthalpy yields the outlet enthalpy. A spreadsheet is then used to determine the temperature at which the enthalpy of that composition matches the one obtained by the addition of the inlet enthalpy and the reaction enthalpy. The temperature obtained is thus the outlet temperature of that slice. We have not yet finished with the slices but as far as we have reached, it is observed that the delta T is decreasing as we move from one slice to the other. Is the adopted methodology correct ? We are attaching a few thumbnails. It would be quite difficult to decipher though how we have worked them out. Our method seems a bit skeptical because the temperature at the outlet of each slice exceeds its inlet temperature by around 35 degrees Celsius or so. If we continue at the same rate of temperature increment we would cross the reformer outlet temperature (850 ⁰C) before we reach the 20th slice which is not possible.

#### Attached Files

Edited by MurtazaHakim, 14 May 2018 - 04:08 AM.

### #234 PingPong

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Posted 14 May 2018 - 02:57 AM

3. C3H8 + 3H2O <==> 3CO + 5H2
That equation is not correct.

From your description I get the impression that you do not take into account the heat input from the burner flames.

Reforming is an endothermic reaction. If the reactor would operate adiabatically the temperature in each slice would drop, not increase. If you find a temperature increase without heat input then something is wrong. Maybe you applied the enthalpy or reaction in the wrong way in the enthalpy balance of each slice.

In reality the reactor is not adiabatic and heat is added, and as I tried to explain already more than once it is very time consuming to do this by hand because that heat input into each slice is proportional to the catalyst quantity in each slice, which you don't know. So it requires iteration by software (or trial-and-error by hand). Reread my remarks in previous posts about this.

### #235 MurtazaHakim

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Posted 14 May 2018 - 04:56 AM

You would have to start assuming a certain heat input Qfor each slice i, calculate temperature Ti and cat quantity Xi in each slice, and then adjust each slices Qaccording to its Xi (as the exposed tube area receiving Qi is proportional to Xi). And then recalculate Ti and Xi, and again Qi, and again Ti and Xi, et cetera,

If we assume a certain heat input to the 1st slice and add that heat input to the inlet enthalpy of the 1st slice (reformer inlet enthalpy at XOT) we get the outlet enthalpy of the 1st slice. The outlet temperature of 1st slice is then calculated from the composition at the outlet of 1st slice which I think should be assumed (as in case of WGSR). The catalyst quantity should then be calculated from the conversion in the first slice. Does it mean that the slices are not equally divided and the heat input and conversion varies from slice to slice like the 1st slice may have 8% conversion while the 2nd slice may have 6% conversion ?

If these calculations are time consuming by hand then we should move on to the equipment dimensioning because we do not know how to generate a computer program for calculating the catalyst quantity.

Edited by MurtazaHakim, 14 May 2018 - 05:18 AM.

### #236 PingPong

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Posted 14 May 2018 - 06:25 AM

If we assume a certain heat input to the 1st slice and add that heat input to the inlet enthalpy of the 1st slice (reformer inlet enthalpy at XOT) we get the outlet enthalpy of the 1st slice.
And also take enthalpy of reaction into account.

When you look at your calculated WGSR catalyst quantities you see that each slice has a different catalyst quantity.

When applying a similar method to the Reformer each slice will also have a different catalyst quantity. As the reactor is a cylinder its external area (exposed to the flame radiation) is proportional to its catalyst quantity, so each slice will have a different heat input. That's the problem: you don't know in advance that slice i will have Wi % of total catalyst quantity and therefor must also have Wi % of total heat input (1292 kW). Wi is not simply 5 % for each slice. That's why it becomes an iterative process to simultaneously find the correct cat quantity and heat input to each slice.

### #237 MurtazaHakim

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Posted 16 May 2018 - 05:11 AM

As it is evident that the calculation of catalyst quantity for the reformer cannot be carried out by hand in the time we have at our disposal, we have decided to proceed with the design of equipment(s) namely SD+WHB, WGSR effluent-BFW exchanger and PSA beds. We are unaware of any additional hardware (if any) which need to be designed. Which one of the above mentioned equipment(s) should we begin the design with and how ?

### #238 PingPong

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Posted 16 May 2018 - 06:49 AM

The PSA unit is a packaged unit designed and supplied by a specialized vendor, e.g. UOP.

I don't know how to determine the number of beds and size them for a certain recovery. You can of course google and see if you find something useful if you need to size them.

The WHB and SD are also designed and supplied by a specialized vendor, but you can fairly easy determine realistic sizes good enough for your project. The simplest to start with is probably the steam drum. It is a separator so you need to read about Souders-Brown if you did not already come across it.

And it has a water hold-up volume of a certain amount of minutes. Let's say 20 minutes between maximum and minimum water operating level.

In an SMR unit the SD is usually horizontal but in your little unit it could be better to use a vertical SD.

### #239 MurtazaHakim

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Posted 18 May 2018 - 04:36 AM

The Souders-Brown equation requires a parameter Ks for calculating the maximum allowable vapor velocity which is further used to obtain the minimum vessel diameter. We have obtained the liquid and gas phase densities from the steam table at 257 °C. The saturated liquid and vapour at 257 °C have densities 788.33 kg.m-3 and 22.5453 kg.m-3 respectively. What would be the typical value for Ks in case of SMR unit steam drum(s) ? The Souders-Brown equation is mainly used for sizing vapour-liquid separators and knock out drums. There must be differences in construction and internals of steam drums and these separators. There is a demister pad located at the top in case of vertical separators. Please elaborate on the constructional details of steam drum and its internals. Would it be appropriate to use Souders-Brown approach in our case ?

### #240 PingPong

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Posted 18 May 2018 - 05:12 AM

SB equation is used for many applications.

For a wire mesh demister in a horizontal or vertical separator a value of K = 0.35 ft/s (0.105 m/s) is often used.

http://www.koch-glit...ductCatalog.pdf

How the internal design of an SMR steam drum looks like will depend on the specialized vendor. Surely your examiners don't know so don't worry too much about details.

### #241 MurtazaHakim

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Posted 18 May 2018 - 06:22 AM

The calculations are as follows:

VGmax = Ks [(ρL - ρG / ρ)]0.5

VGmax = 0.105 [(788.33 - 22.5453)/22.5453]0.5

VGmax = 0.611948 m.s-1

The vessel diameter is then calculated using the following correlation

D = [(4.Q) /( π.VGmax )]0.5 ; Q is the volumetric steam flowrate in m3.s-1

D = [(4*0.027057)/( π*0.611948)]0.5

D = 0.23726 m

The volumetric flowrate of steam is calculated by multiplying the mass flowrate of steam with the specific volume of steam at 257 °C.

Q= (121.90197*18.015/3600)*0.044355 = 0.027057 m3.s-1

A diameter of 23.7 cm is calculated for the steam drum. What about the height of SD then ?

Edited by MurtazaHakim, 19 May 2018 - 02:54 AM.

### #242 MurtazaHakim

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Posted 21 May 2018 - 03:06 AM

The preceding message is edited and the revised diameter is calculated as 0.237 m. Calculation of SD height requires the volume of steam drum which is the total volume occupied by vapour+liquid.

121.90197 kmol/hr of HPS is 20% of 609.50985 kmol/hr which flows from the SD to the WHB. Now considering 5% CBD,the inlet to the SD should be 609.50985/0.95 = 641.5893 kmol/hr

For the first pass

SD inlet = 641.5983

SD outlet/WHB inlet = 609.50985

WHB outlet = 121.90197+ 487.60788         (all the figures are in kmol/hr)

The 121.90197 kmol/hr generated in the first pass is taken for superheat and the remaining 487.60788 kmol/hr recycled back to the SD for HPS generation. But that 487.60788 kmol/hr would again have fresh inlet BFW (at 242 °C) in the second pass added to it. Continuous cycle in such a manner would then result in increasing accumulation of recycled liquid in the SD. The recycling should be carried out in a way that ensures constant CBD and HPS flowrate from SD and WHB respectively. How would that be achieved ? Where is the outlet of generated HPS located (in SD or WHB) ?

### #243 PingPong

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Posted 21 May 2018 - 07:38 AM

0.237 mm diameter of free circular demister area is correct. However due to the fairly high pressure a correction factor is to be applied. My data (which I cannot publish) indicate that at 45 bar a correction factor of about 0.82 is to be used for the K factor.

http://www.oilgaspro...ator Sizing.htm

gives a formula for a pressure correction. In the absence of better public data you could use that reference in your report.

So that means that you need a free demister diameter of about 260 mm. The demister is installed between support rings with a width of say 1.5 inch, so the demister diameter, and the inside diameter of the cylinder in which the demister is placed, has to be at least 340 mm. That corresponds roughly with that of a 16 inch pipe.

So you could have a vertical drum with a diameter of say 1000 mm for the bottom part, a 16 inch pipe for the top part, and a cone in between.

The water recirculation has no impact on the size of the steam drum, it only affects the size of the related nozzles.

About 128 kmol/h of BFW is converted into about 122 kmol/h sat HPS and about 6 kmol/h CBD.

Water hold-up volume is to be based on the BFW flow.

Hold-up time is typically 10 - 20 minutes depending on how secure the BFW make-up flow is. Client may also have rules for hold-up of various vessels in the unit based on their experience/preference.

As this is a fairly small steam drum I suggested earlier 20 minutes, but you are free to pick your favorite number.

20 minutes hold-up between maximum and minimum water level is about 1 m3, which is a height of about 1300 mm in a 1000 mm diameter.

Edited by PingPong, 21 May 2018 - 07:52 AM.

### #244 breizh

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Posted 22 May 2018 - 05:15 AM

Hi ,

To support your work on design , please consider the document attached .

Probably good to take a look at GPSA .

Breizh

### #245 MurtazaHakim

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Posted Yesterday, 03:26 AM

The description of steam drum as per message #243 indicates that the vessel is funnel shaped with 16 inch pipe at the top and circular bottom with conical structure in between. The vessel geometry as per the book CHEMICAL ENGINEERING DESIGN by Towler,Sinnot is as shown in the thumbnail. Please provide a sketch if possible for the steam drum description of message #243.

The WHB is a shell and tube type heat exchanger where the reformed gas flows at the tube side and the BFW on the shell side. We must begin the design of WHB now. What parameters are expected to be determined in WHB design ? How should we begin with the design of waste heat boiler ?

### #246 PingPong

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Posted Yesterday, 09:19 AM

I will come back later on SD.

Design of WHB is like any other shell & tube exchanger.

You need to determine the heat transfer coefficients ho and hi on outside and inside of the tubes.

For that you first of all need the physical properties (density, specific heat, viscosity, thermal conductivity) of the fluids.

So I suggest you start determining those for the syngas which is not a pure gas but a mixture of several components. There are books like API Data Book and Properties of Gases and Liquids and Perry's Chemical Engineers' Handbook that may be of use, and several websites I expect.

Edited by PingPong, Yesterday, 09:29 AM.

### #247 PingPong

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Posted Today, 04:04 AM

There are many websites and books that give sketches with minimum distances, but unfortunately all somewhat different.

A few other examples from GPSA databook and Shell DEP:

Vertical separator - GPSA Databook.jpg   101.88KB   0 downloads

Vertical wiremesh demister - Shell DEP.jpg   121.01KB   0 downloads

What I meant in message #243 is the left one in:

Vertical Separators.jpg   185.74KB   0 downloads

But you can also use the one on the right with an internal 16 inch pipe in it to hold the demister although that will probably cost more as it requires more steel.