And though the holes were rather small
They had to count them all.

("A Day in The Life," by Lennon-McCartney, 1967)

 

Grab a cup of java, this is a long one!

Using an example of a chiller, this PTOA Segment explains how conduction and convection heat transfer work together in a shell and tube heat exchanger. The information applies to all shell and tube heat exchangers (HExes), not just those using water for coolant.

This PTOA Segment also features the heat transfer problems that inhibit the efficiency of heat transfer in HExes.

 

CHILLERS IN COOLING WATER SYSTEMS 

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order learned in PTOA Segment 40 that cooling towers are part of cooling water systems.

A schematic of a cooling water system is shown at the right.

Warm water effluent from all the chillers in the processing facility flow into the hot water Return header and thence to the cooling tower where, once again, the water is chilled primarily by evaporation.

In the above schematic all the chillers are represented as a single shell and tube heat exchanger ...  because the drawing is just a simplified schematic of a cooling water system.

FYI, chillers are sometimes called "trim coolers."

"Imagine" the animated graphic to the left is a chiller; the cold water enters shell side cold and exits warmer (follow the flow of the red arrow).

Heat is transferred via convection and conduction from the warm process stream that flows through the tube bundle (follow the flow of the yellow arrow).

After transferring heat into the water, the process stream exits the channelhead at a cooler process temperature than it had when it entered the tube bundle.

 

HEx HEAT TRANSFER BEGINS WITH THE HOT PROCESS STREAM

Unlike a fired heater/boiler/reaction furnace there is no radiant heat transfer in a shell and tube heat exchanger.

The driving force ... the hot temperature that initiates all heat transfer in a HEx ...  is from the "bulk" or "average" temperature of the hot process stream.

This bulk temperature is not as easy to figure out as you would think; when that happens Your Mentor leaves it to the experts to figure out and graph!

The temperature differential between the hot and cold process streams constantly changes while both streams flow through the HEx.

PTOA Readers and Students already know that the hot process stream leaves the HEx at a cooler temperature and the cold process stream leaves the HEx at a warmer temperature.

The graphic above shows the temperature profile of the hot and cold streams as they flow through two different styles of shell and tube heat exchangers.

As expected, the temperature profile of the hot process fluid decreases (red line and arrow) while the temperature of the cold process fluid increases (blue line and arrow).

The graphic labelled "A" above shows the temperature profile for a counterflow shell and tube heat exchanger and "B" shows the temperature profile for a parallel flow heat exchanger.

The schematic to the right clarifies that  parallel flow means that both the hot and cold fluids flow in the same direction.

Counterflow means the hot and cold process fluids enter and exit the exchanger in opposite direction.

Judging by the greater temperature differential of the hot and cold streams as the enter a parallel flow style exchanger,the initial assumption might be that the parallel flow style exchanger is more efficient than counterflow style exchanger with respect to heat transfer.

However, the counterflow HEx design is more efficient because the exiting temperature of the cold process stream can be greater than the exiting temperature of the hot process stream; the Universe does not allow that efficiency to occur with a parallel flow architecture.

 

TUBE SIDE HEAT TRANSFER IN HExes

Convection Heat Transfer in HExes.

The PTOA Department of Redundancy Department believes that Convection Heat Transfer is harder to understand than Conduction Heat Transfer.

So, here we go again:

The hot, flowing process fluid has internal thermal energy, the energy of convection.

The rate of heat transfer from this hot process fluid is mathematically described by the below convection heat transfer expression PTOA Readers and Students learned in PTOA Segment 65 and are becoming more and more comfortable with.

This time note how Delta T has been tweaked for a shell and tube heat exchanger and the important role mass flow rate has regarding the internal energy of the flowing, hot  process stream. 

Convection Heat Transfer Rate (q/t) is mathematically expressed;

q/t (in Joules/hr or BTU/hr ) = C_p * m/t * (Delta T)

and

C_p = the specific heat of a mass of tube side process fluid,  typically measured in Joules/(kilogram-deg C) or BTU/(lb-deg F)

The specific heat of fluids varies greatly. A table of C_p can be found in this link:

http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html

m/t = mass of flowing tube side fluid per unit of time (aka "mass flow rate") typically measured in "pounds per hour" or "kilograms per hour" or "metric tons per hour."

Sometimes Board Operators intentionally reduce flow rate through exchangers by bypassing process flow around them.

When the Board Operator intentionally reduces the flow rate of the hot fluid through a tube bundle s/he reduces the convection heat energy in the fluid because the mass flow rate is likewise reduced.

The mass flow rate can also be significantly reduced by gunky buildup on the interior of the tubes as shown in the above picture of a gunky tubesheet. Gunky build up will stay put until the next turnaround.

ΔT = the Temperature Differential between the average temperature of the mass of process fluid flowing through a tube in the tube bundle and the temperature at the inside wall of that tube,expressed in Celsius/Centigrade or degrees Fahrenheit.

 

Conduction Heat Transfer in HExes

"Imagine" that the above photo shows a hot process stream flowing through one tube in a chiller's tube bundle.

The black area is water that is flowing through the shell side of a chiller.

The convection heat energy of the hot process fluid (quantified as stated in the above paragraphs) has established a hot temperature at the inside interior skin of the tube.

The driving force for conduction heat transfer is the Delta T between the hot temperature at the interior skin of the tube and the colder temperature of the water flowing on the exterior (shell side) of the tube.

PTOA Readers and Students learned in PTOA Segments 62 and 63 that the rate of conduction heat transfer(Q/t, in BTU/hr or J/hr)  through the tube is mathematically expressed:

Q/t = [k* A* (Delta T)] / d

and

k = Thermal Conductivity Factor and is expressed in
[Watt/(meters-°K)] = 0.5779 [ BTU / (foot hr °F)]

Tube bundles are often fabricated of copper because of its high thermal conductivity factor of 401 W/m-K.

Copper has the highest Conductivity Factor of all the materials listed in this link:Thermal Conductivity Table

A = the surface Area of the tube interior and exterior walls that are exposed to heat transfer. 

Increasing area for heat transfer is the reason that the entering hot process stream was separated to flow through several dozen if not hundreds of tubes.

As shown in the temperature profile graphics above, heat transfer is a-happening at every inch of length on the tube bundle and through each pass.

Delta T = (Hot Temp - Cold Temp) = (T_Hot - T_Cold) in °F or °C

As was stated above, the driving force for conduction heat transfer is the Delta T between the hot temperature at the interior skin of the tube and the colder temperature of the water flowing on the exterior (shell side) of the tube.

d = thickness of the tube, expressed in inches, maybe millimeters. 

The thickness of the tube (the inner diameter subtracted from the outer diameter) is determined during the designing of the tube bundle.

As shown in the photo to the left, the tubes can get clogged up with process stream gunk. As stated above, gunk in the tubes restricts mass flow rate which reduces the rate of convection heat transfer.

Gunk also impairs conduction heat transfer:

The gunk effectively adds to the thickness of the pipe diameter through which conduction heat is being transferred.

Furthermore, the conductivity factor "k" of gunk is always much less than that of clean metal. Prove it to yourself by looking up the thermal conductivity of materials listed on the above link.

 

 

SHELL SIDE HEAT TRANSFER IN HExes

Once again "imagine" that the photo above depicts a single tube in a tube bundle through which a hot process stream is flowing; the black area is the cooling water flowing on the shell side.

The exterior tube wall is now hot since the thermal energy in the flowing hot process stream has been conducted through the tube wall as described in way too much detail above.

Transferring heat from the hot exterior tube wall into the flowing water coolant follows all the rules of convection heat transfer featured above; the rate of convection heat transfer (q/t) can be determined from the heat capacity of water (C_p), the mass flow rate of water (m/t), and Delta T.

In this case the Delta T is created between the hot temperature of the exterior tube wall and the temperature of the flowing cool water.

Contaminants in the coolant shell side fluid most definitely can impair heat transfer into the water.

PTOA Readers and Students know that circulating cooling water contains a controlled amount of heebie jeebies.

The buildup of circulating biofilm slime and scale on the exterior tube surfaces will effectively increase the thickness, d, of the tube ... this time by adding gunk on the outside.

The "k" factors for both biofilm and mineral scale that circulates with cooling water are very low.

Recall that the chiller's tube bundle is more than likely made of copper which has a Thermal Conductivity Factor of 401 [Watt/(meters-°K)].

However, a very thin film of scale or biofilm can greatly decrease conductive heat transfer:

A calcium carbonate scale just 1.5 millimeters thick would decrease the thermal efficiency 12.5%!

And the thermal conductivity of biofilms is even worse! The k for biofilm is just 3 percent of k for calcium carbonate! A thin coating of biofilm would severely hinder the rate of conductive heat transfer.

At a minimum, the outcome of inhibited heat transfer would increase operating expenses for the processing plant by hundreds of thousands of dollars annually.

 

TAKE HOME MESSAGES:  The purpose of the shell and tube heat exchanger is to exchange heat between a hot fluid and a cold fluid.

Using the example of a chiller in a cooling water system, this PTOA Segment detailed how convection and conduction heat transfer work together in all shell and tube heat exchangers. The information applies to all shell and tube HExes, not just chillers.

Chillers are sometimes called "trim coolers."

Examples of convection and conduction heat transfer problems that are caused by interior and exterior tube fouling were illustrated.

Parallel and counterflow heat exchanger designs and temperature profiles were featured.

The counterflow HEx design is more efficient with respect to heat transfer because the exiting temperature of the cold fluid can exceed the exiting temperature of the hot fluid. 

 

©2015 PTOA Segment 00078
PTOA Heat Transfer Focus Study Area

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