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Smokestack Diameter and Induced Draft Fans 4

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cokeguy

Electrical
Jan 29, 2006
117
We temporarily replaced a damaged 56" diameter, 100 ft tall fiberglass smokestack of a scrubber with a smokestack from an unused scrubber, with same height but a 42.5" diameter. My question is, how can I calculate the extra load on the induced draft fan caused by the smaller diameter smokestack? We have an ongoing debate here at the plant about whether the smaller smokestack is the cause of the ID fan´s VFD-driven 250 HP motor running at its upper limits, or else that we could have a undetected problem (air leakage) somewhere else at the scrubber or furnace. Previous operating conditions don´t help much because of different process conditions.

We already ordered a replacement smokestack, original dimensions, but we won´t have it for at least a couple of months, and the scrubber will undergo a major change in a few days which will probably overload the ID fan´s motor and force us to take it out of operation. If we sit still hoping for the new smokestack to correct the problem and it turns out not to be a significant factor, it will mean more downtime, hurries, etc... so if anybody can guide me or comment on a similar situation I woul appreciate it a lot. As general process data, fan is operating at about 1000 RPM, I don´t have the exact volume of air being moved by the fan but it is basically the flue gas of a furnace after passing the scrubber, so it means about 10,000 CFMs of combustion air plus fuel plus water vapor, pressure differential between fan´s inlet and outlet is typically about 10"H2O, fan motor is 250 HP, VFD driven, typically runnig close to full load amps and 60 Hz.

Thanks for your help, comments and suggestions.
 
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I think you will need to get a better handle on the actual cfms at the fan.

If we assume a 75% efficient fan + damper ass'y, the relation between fan shaft HP and DP and cfm is :

HP,shaft = cfm * DP / eff / 6356.

I get a cfm of 119,175 if a 0.75 eff is used and a 10" wc DP is used. This works out to a very high stack gas velocity and would completely explain the amping out of the fan.
 
davefitz has zeroed in on your problem. Can you change your process conditions at all? Can you flood the scrubber with more water (liquid) and bring down the stack gas temperature in order to lower the specific volume of the gas?

Check your duct work etc for leaks upstream of the ID fan. Any significant leakage that the fan/stack has to handle is really hurting you right now with the reduced diameter stack.

rmw
 
Thank you both for your help, I tried to gather a bit more process data, and here´s what I found out: supposedly the flue gas flowrate should be around 37,000 cfm, and corresponding stack gas velocities should be around 65 fps for the smaller stack and 37 fps for the original stack. Therefore, either actual fan efficiency is much lower than 75% (more like 25%) or actual flowrate is much higher than the theoretical 37,000 cfms, due to leakage or something else.

We measured gage pressure levels at the fan´s intake and discharge, and it turns out that we have about -6"H2O and 6"H2O respectively, for a total DP of 12"H2O. Taking these numbers into account, what reduction (if any) in discharge pressure and therefore total DP could we expect when we install the bigger smokestack?

We are still in the process of trying to detect leaks, but haven´t found anything yet.
 
It looks like with the inlet pressure of -6 in H2O ther may be a lot of air inleakage- there may be a tear in teh flue casing or in the scrubber section. You can check leakage rates by checking the O2 concentration at the (a) boiler outlet( b) air heater outlet (c) scrubber outelt flange (d) ID fan inlet flange. The difference between these O2 readings are indicative of the amount of air inleakge occurring.

After you find the main culprit, you can perform a smoke test during a cold outage to find the exact location of the tears.

The stack itself will only have about a 2 velocity head pressure drop ( inlet =0.5 vh, vertical stack section 0.5 vh, outlet discharge 1.0 vh), assuming there are no internal blockages .

vh(in H2O) = (1560/sv) *{cfm/A/1E5}^2
sv = spec volume, ft3/lbm

If you know the stack inlet temperature , you can estimate the stack spec volume, then back calulate what the apparent cfm is based on the monitored pressure drop ( ie, put a static pressure tap at the inlet to the stack, located in a zone taht is relatively dead ( ie zero gas velocity).

Now that I think of it, don't bother with the calculation- just measure the stack DP with a pressure tap at the base of the stack.
 
The fan practically discharges into the base of the stack, so the discharge pressure is pretty much equal to the stack base pressure, 6 in H2O as of this moment. There are no internal blockages in the stacks. Now, how could we estimate (ballpark figure) the outlet pressure and thus the total DP we´ll have after changing the stack?

ALdo, am I correct in assuming that, theoretically, if we were able to increase the stack´s diameter as much as we wanted, we could reach a point where outlet pressure would be zero, inlet would still be -6" H2O and fan power would be half of what we have right now? Forgive my questions, but I´m pretty much illiterate when it comes to fans, smokestacks, etc... Thanks again for your help.

p.s. with regards to one of rmw´s suggestions, we can´t put more water into the scrubber to lower the outlet temp, it is actually pretty low (I guess) right now at about 60-70 degC.
 
If teh inlet pressure is +6" H20 with a 42.5" dia stack, then it will drop down to + 2" H2O with a 56" dia stack. In this particular case, the pressure drop will vary by the 4th power of the diameter.

The current 250 HP at the fan will drop to 167 HP at the same gas flow, if the stack dia is increased to 56".
 
Thanks davefitz, you just made my day with that answer, precisely what I was looking for...although originally I didn´t like the idea of ordering a new smokestack, you have just confirmed to me that the corporate guy who "commanded" us to replace the stack was correct; what bothered me at the time (and still does) was that he never told us why it was necessary, his only reasoning was "... you have to change it because the original was 56 inches wide, and that´s it..." but never justified it technically.

Now, could you just give me an idea on how you came up with that 2" H2O discharge pressure value? what specific law or formula applies in this case, when you mention that pressure drop varies by the 4th power of the diameter?

Again, thanks a lot...
 
The frictional pressure drop varies by the square of the velocity , for the case where the total pressure drop is less than 5% of teh absolute pressure. The absolute pressure is 14.7 psia, and the total pressure drop is about 2-6 in H20 ( about 0.0722 psid - 0.2167 psid), so we meet the incompressible estimate of less than 5% pressure drop.

The velocity varies by the square of the diameter, so we end up with the 4th power.

If the stack was much longer, then the pressure drop would vary by the 5th power ( fL/d factor). If the total pressure drop was more than 5% of teh absolute pressure, then we would need to corect for compressibility effects, usually using the Fanno relations.
 
Firstly davefitz's estimate of flow is much closer to the mark than 37,000cfm. It should be around 100,000cfm at 12"wg. There are several reasons for this conclusion: 1. Given the power the fan must be sized to handle this larger volume. 2. With a flow of 37000cfm the stack resistance could not approach 6"wc even with the smaller stack.

The stack losses will be pricipally made up of the discharge velocity head loss and the entry bend loss. The actual tube friction losses will be quite small. However the 4th power relationship still holds good. Guessing the gas density, the velocity pressure loss at discharge will be around 4" at 100000cfm making a total of 6" quite likely. If everything is proportional this will indeed be reduced to 2"wc with the larger stack. This is still rather high but believable as a design figure. The higher flow rate is also substantiated by the typical velocity at discharge of the 56" stack. Suggest that you recheck that the figure of 37000cfm - maybe this is at NTP conditions or units are not cfm.

 
We have yet to verify actual flowrate, and plan on doing it ASAP, however we did check inlet and outlet pressures and they turned out to be -6"H2O and 2"H2O respectively, not the -6"H2O and 6"H2O figure I quoted earlier. It turns out that the guy making the measurements was doing it with the probe pointing upstream against the flow, so the 6"H2O value I reported was more or less the dynamic pressure, not the static pressure.

Now with this info in hand, does it mean that after changing the stack we can still expect a 2/3 reduction in outlet pressure to about 0.66 "H2O, but inlet pressure will still be -6"H2O and thus power will be reduced not by 33% but only by about 17%?

Also, I found a reference to the Darcy-Weisbach equation where loss is proportional to velocity squared over diameter (v*v/D), which I assume is what davefitz is referring to, but what about the velocity head loss fredt mentions, could somebody point me to the formula or theory describing this effect?

Also, fredt mentions an entry bend loss, but I am assuming that this loss will be the same for both stacks, because the fan discharges the flow horizontally into a cylindrical chamber, about 12 feet wide and 20 feet high (and totally empty), and on top of the cylinder we have a cone-shaped reduction connecting the cylinder and the stack, no bends. The outlet pressure I mention is actually measured within this chamber, before entering the stack. I did try to measure pressure inmediately at the fan´s discharge, and it gives me about 3"H2O (about 6"H2O with the L-shaped probe pointing upstream against flow). I don´t know if this measurement technique is adequate, but it is pretty much the only way I can think of. Thanks everybody for your help.
 
I believe you need to look at the fan curve from the OEM and the System curve which should have been furnished with the installation which will show you the exact conditions you are working with.
The smaller stack addes pressure drop to the system curve causing the use of more HP to meet the same process conditions.
You may increase the RPM's of the fan or the motor HP to solve your problem. Evaluate these alternatives as they may be less expensive than a new stack.
 
We have the fan curves and the original system curve, but the equipment has gone through a lot of changes so original system curve is practically useless..

What we are looking for is a rough estimate of the expected power reduction with the yet-to-arrive smokestack, and whether it will have a significant effect or not on our current situation where the ID fan´s VFD is on its high limit. The fan can supposedly go much faster, but that would mean a 300HP or more VFD motor combination ($$$). I´m a little out of my league here, have been studying fan and fluid theory quite a bit lately (researching into suggestions and theory from fredt and davefitz posts) but I still do not have a good grasp on the situation. Thanks again in advance for any complementary info or insight.
 
The new reading of +2" wc at the stack base would drop to +0.67 in wc if teh larger stack was provided. The fan power would only drop a little, as it will be proportional to the fan pressure drop, 6.67 in wc vs 8 in wc.

A better solution is to find out what the current cfm really is , and if it indicates massive air inleakage, then fix the air leaks. You can use the original fan performance curves, even though the duct system has been modified. If both the fan curves and the simple HP calculation both point toward too mauc air flow, then you need to get out the duct tape (!)and fix it.
 
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