# Making sense of temperature sensing

Jan. 6, 2006
Readers provide solutions to a thermowell problem in this month's Process Puzzler.
 THIS MONTH'S PUZZLER Why did a thermowell in a recirculation pipeline near the discharge of a pump indicate a change in temperature sooner than a thermowell inserted via a top nozzle about half way down into a well mixed vessel?

Velocity is important
Even in a well mixed vessel, the average bulk velocity tends to be less than 1 fps whereas in a pipeline it is often more than 5 fps. The higher velocity makes the heat transfer coefficient larger which reduces the primary thermowell thermal lag for convective heat transfer from the process to the thermowell. The higher velocity also helps reduce the formation of coatings that can act as an insulating barrier. Additionally, the shorter thermowell length in the pipeline reduces the secondary thermal lag associated with the heat capacity of the thermowell mass.

If the thermowell is close to the recirculation pump discharge, the additional transportation delay is 1 or 2 seconds, which is usually less than the reduction in thermowell thermal lags from the higher velocity and cleaner and smaller metal mass. For a ramp in the vessel temperature, the trend in the indicated temperature is behind the true temperature by the summation of the thermowell time lags and the transportation time delay.

Greg McMillan, Consultant
Austin, Texas

Poor mixing?
This can be explained in the following ways: 1) the thermowell in the tank may not be in contact with the liquid or the contact is such that the liquid in not representative of the mix; it may be sitting in the tank vortex; 2) the tank may not have baffles, thus mixing is not at optimum; 3) two different temperature liquids are being blended but do not have sufficient residence time in the tank to be homogeneous; 4) the liquid at the discharge of the tank has gone through two very turbulent zones; these include a vortex and the mixing of liquids in the propeller.

Mixing has produced a temperature that is different from the probe in the tank by blending of the two different temperature liquids. It is possible that the final equilibrated temperature of the tank is different from the temperature read by the thermometer at the discharge of the pump.

Girish Malhotra, President
EPCOT International, Pepper Pike, Ohio

There could be a number of causes.

1. The sensor used in the recirculation line has a faster response than the one in the vessel. This could be due to using a grounded thermocouple versus a non-grounded one or the transmitter of the sensor in the recirculation line has a lower damping value than the one in the vessel.

2. The sensor in the vessel could be coated with sediments that slow down its response time. I’ve seen this happen before. Though the vessel may be well-mixed, the flow rate in the recirculation line could be fast enough that sediments can’t stick to the thermowell.

3. The meaning of well-mixed can be different from one person to another. Though a rapidly swirling surface may look like it’s being well-mixed, if the swirl is toward the center and the vessel discharge is also in the center, it could be that some of the contents are being discharged before the vessel is properly mixed. As with any troubleshooting analysis, the accuracy of the diagnosis depends on the facts obtained.

Eric Marcelo, I/E supervisor
Nestle Philippines., Inc., Philippines

Pipe thermowell has more mass
The thermowell in the recirculation line responds faster to temperature than the thermowell installed in the top of the vessel. This is because the recirculation line thermowell (8 in. insertion length, typically) has less mass than the thermowell (5 ft insertion length minimum) installed at the top of the vessel (Figure 1). An energy balance around the thermowell yields the following differential equation:

dT  =  Qdt        mCp

Where: T is temperature, t is time, Q is heat transferred per unit time into or out of the thermowell, m is mass of the thermowell, Cp is heat capacity of the thermowell. From the equation, it is clear that as the mass increases, then dT/dt or the response goes to zero.  A smaller thermowell has less “thermal inertia” and will respond faster than a larger thermowell.

Robert Frey, P.E., Technical Associate
Eastman Chemical-Jefferson Site, West Elizabeth, Pa.

Check the mass of the thermowells
Making use of the following assumptions: the thermowells are made of the same material, that "well mixed" means that skin effects can be ignored, the source of temperature change is not the pump or a second flow in the suction side of the pump, the source of the temperature increase is the inlet to the vessel and that it is not so close to the suction of the pump so that the vessel is short circuited, that the source of temperature change is not environmental (radiation to / from piping or vessel walls), the two thermowells actually see the same temperature fluid,that the vessel is full of liquid, the two temperature measuring elements and transmitters have the same (or nearly the same) response time and they are in good contact with the interior of the well.

Then the difference in response time of the two thermowells is due to the difference in mass of the two thermowells. A thermowell that is inserted into a pipe would have a much smaller mass than a thermowell half the length of a vessel (even for a relatively small vessel).  Since the rate of temperature rise is directly proportional to mass, for the same heat input, the temperature would rise faster for a smaller mass.  Therefore the pipe thermowell, having the smaller mass, would increase in temperature faster than the vessel thermowell, having the larger mass.  This is the reason that the tip of the thermowell should be as thin as possible and one of the reasons that we use tapered thermowells; we are trying to keep the mass at the sensing point as small as possible as well as limit conduction via the thermowell itself to an area with a different temperature, or with a larger heat transfer rate.

Patrick Richards, Sr. Instrumentation Designer
Irving Oil Refinery, Saint John, NB

 MARCH'S PUZZLER A 30-tray sieve vacuum distillation column has a habit of developing a foaming problem. The turn-down ratio of the column is non-existent. The pressure drop across the lower trays is much higher than design. It has a poor temperature profile. The condenser shows an off-spec. (high) concentration of the lowest boiling constituent. What can be done to reduce foaming and improve the column performance?Send us your comments, suggestions or solutions for this question by May 30. We’ll include as many of them as possible in the July 2005 issue. Send visuals, too — a sketch is fine. E-mail us at [email protected] or mail to ProcessPuzzler, Chemical Processing, 555 W. Pierce Rd., Suite 301, Itasca, IL 60143. Fax: (630) 467-1120. Please include your name, title, location and company affiliation in the response.And, of course, if you have a process problem you’d like to pose to our readers, send it along and we’ll be pleased to consider it for publication.

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