GO WITH THE FLOW

I can go with the flow
(I can go)

("Go With The Flow," by Queens of the Stone Age, 2003)

WHAT HAPPENS WHEN HOT FLUIDS GO WITH THE FLOW?

PTOA Readers and Students recently learned that Convective Heat Transfer occurs when the heat contained in a fluid flows into the surroundings.

PTOA Readers and Students also recently determined how much convective heat transferred from a hot cup of coffee into the surrounding air ...

as well as how much heat the body of poor Fred the Stick Man transferred into the water that he drowned in.

Both of the above examples involved transferring heat into a vast heat sink.

The temperature of the surroundings did not change because the mass of the cooler area was much greater and easily absorbed all the heat that was transferred.

What happens when flowing thermal energy is not easily absorbed into a vast heat sink?

In the process industries, hot fluids flow through pipes; the thermal energy contained in the hot fluids cannot easily escape into the ambient atmosphere or surroundings.

And yet the Universe demands that the thermal energy contained in the hot fluids that flow through pipes must be shared with colder environments.

Therefore, since the thermal energy contained in a flowing fluid must be transferred ...

and the heat cannot be absorbed into a heat sink

...the temperature of a nearby material or fluid is going to be noticeably increased!

NEED TO TWEAK

The fascinating photo below captures a turbulent fluid flowing through a glass pipe.

The glass pipe clearly shows turbulent flow through a pipe. The fluid is flowing from the left to right.

PTOA Readers and Students should notice that the captured fluid that is forced to flow through a pipe is not flowing in distinct waves.

Therefore the definition of Heat Transfer via Convection must be tweaked a bit from:

Heat Transfer via Convection is thermal energy (aka: heat) transferred from waves of flowing fluids.

to the definition that accommodates flowing through pipes:

Heat Transfer via Convection is thermal energy (aka heat) that is transferred from the fluids that flow through pipes and will result in noticeably changed process temperatures.

THE EXPRESSION FOR CONVECTIVE HEAT TRANSFER APPLIES TO FLOW THROUGH PIPES, TOO.

Even though the definition of Heat Transfer via Convection has been tweaked, the mathematical expression that defines the amount of convective heat transfer is the same for fluids that flow through pipes and those fluids that lose their heat to vast heat sinks.

The heat contained in a fluid that flows through a pipe is likewise determined by the multiplied magnitude of these three things:

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

m = the mass of the hot fluid, typically measured in kilograms or pounds.

ΔT = the Temperature Differential between a hot temperature and a colder temperature, typically measured in degrees Celsius/Centigrade or degrees Fahrenheit.

THE CONVECTION HEAT TRANSFER RATE
IS MORE USEFUL IN PROCESS INDUSTRIES.

PTOA Readers and Students that have been reading the PTOA Segments in the intended sequence expertly understand the flow patterns through Shell and Tube Heat Exchangers like the one shown in the SHECO animated graphic to the right.

Unlike a shell and tube heat exchanger, the mass of fluid contained in a coffee cup or a human body is a known quantity because no more fluid can enter or flow out of the cup or the human body.

PTOA Readers and Students have already used the below expression to determine the magnitude of the convective heat (q, expressed in Joules or BTUs) that was transferred from the hot cup of coffee and poor Fred's body.

However, the above expression is not as useful for a piece of equipment ... like a shell and tube heat exchanger ... that has fluids constantly entering and exiting the equipment, all the while changing temperature.

Also, the mass of fluid flowing through a heat exchanger can vary as the Control Board Operator adjusts process stream flow controllers to increase or decrease a portion of flow around or through a HEx.

For a shell and tube heat exchanger, the rate of convected heat transferred (q/t, in Joules/hr or BTU/hr) is a more valuable piece of information regarding keeping process temperatures on target.

To determine the rate of convected heat transfer, the expression for Heat Transfer via Convection is tweaked a little by dividing both sides of the expression by time, t, as shown below.

The adjustment results in defining Convection Heat Transfer Rate (q/t) and mass flow rate (m/t).

q/t (in Joules/hr or BTU/hr ) =

C_p * m/t * (Delta T)

"Mass per unit of time,"... m/t ... is called a "mass flow rate."

Examples of typical units that describe mass flow rate are "pounds per hour" or "kilograms per hour" or "metric tons per hour."

UNDERSTANDING WHAT CONVECTION HEAT RATE MEANS

In PTOA Segment 32, PTOA Readers and Students determined the service duty of shell and tube heat exchangers shown in the schematic of a Desalter Preheater Exchanger Train.

As usual ... by taking a few things for granted ...

the Convection Heat Transfer Rate for the crude oil as it flows through Exchanger 1 (E1) can be quantified (meaning, given a real world number that everybody can understand).

Here's how:

The below statement is a fact inferred from the graphic:

The diagram shows that the crude enters E1 at 45 °C (113 °F) and exits E1 at 85 °C (185 °F).

The list of statements below are to be taken for granted; they are called "assumptions."

PTOA Readers and Students will learn the basis of the assumptions in future PTOA Segments. Until then, rest assured that your life will be complete if you just accept the following to be factual:

1. The crude oil has a specific heat capacity, C_p, of .46 BTU/(lb-deg F)

2. Several things need to be assumed to be able to calculate the crude mass flow rate, m/t.

a. Assume that the density of the crude is 7.21 lbs/gallon. (Crude is lighter than water, and the density of water is 8.34 lbs/gallon).

b. Assume the volumetric flowrate of the crude oil from tankage is 100,000 Barrels per day.(That's a good flow rate for a mid-sized fuels refinery).

Ergo, the mass flow rate, m/t, can be determined by factor-labelling:

100,000 ~~Barrels~~/1 ~~Day~~ * 1 ~~Day~~/24 hours * 42 ~~gallons~~/1 ~~Barrel~~ * 7.21 lbs/1 ~~gallon~~ =

m/t = 100,000/1 * 1/24 * 42/1 * 7.21/1 = 1,261,750 lbs/hr

Voila!

Taking things for granted has made it possible to calculate the Convection Heat Transfer Rate of the thermal energy picked up by the crude as it flows through E1:

q/t (BTU/hr) =

C_p * m/t * (Delta T)

0.46 BTU/(lb-deg F) * 1,261,750 lb/hr * (185 - 113) °F=

q/t = 41,789,160 BTU/hr

Shazam!

The flowing hot Top Pumparound fluid transfers 41.7 MMBTU* into 100,000 barrels of crude that flows through E1 each hour and and in the process raises the temperature of the crude by 72 °F.

(*MM = 1000*1000 = 1 million)

Wow!

That is too big of a number to imagine in the real world!

So here's a real world comparison to help our imaginations:

The BTU Calculator featured in PTOA Segment 59 informed PTOA Readers and Students that a single very well-insulated 1,000-square-foot home in Boston needs around 24,000 BTU/hr to heat in winter.

Ergo, the heat transferred into the crude that flows through E1 in one hour is sufficient to heat that Boston house 1,741 hours = 72 days = 2.4 months .... so like most of one entire winter!

TAKE HOME MESSAGES: The Convection Heat contained in fluids that flow through pipes is not exposed to the ambient environment and is thus not absorbed by a heat sink; the thermal energy of flowing process streams typically ends up being transferred into cooler process streams.

Since all process industry fluids must flow through pipes, each pipe in a processing facility contains flowing thermal energy.

Heat Transfer via Convection is thermal energy (aka heat) that is transferred from fluids that flow through pipes and will result in noticeably changed process temperatures.

The Rate of Convection Heat Transfer (q/t, in BTU/hr of J/hr) is more relevant to temperature-changing process industry equipment because the equipment has process fluids constantly entering and exiting; meaning there is not a confined mass of fluid in the equipment as there would be in a coffee cup or human body or other container.

The Mass Flow Rate (m/t, in pounds per hour or kilograms/hr or metric ton/hr) is one of the three factors that quantifies a Convection Heat Transfer Rate.

The other two factors that determine the magnitude of Convection Heat Transfer Rate are:

The specific heat of the fluid [Cp, in BTU/(pound-deg F) or J/(kg-deg C)]
Delta T (in °F or °C).

Otherwise stated, the Convection Heat Transfer Rate is expressed:

q/t (BTU/hr) = Cp * m/t * (Delta T)

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