The function of a cooling system is to remove heat from
processes or equipment. Heat removed from one medium is transferred
to another medium, or process fluid. Most often, the cooling medium
is water. However, the heat transfer concepts and calculations discussed
in this chapter can also be applied to other fluids.
Efficient removal of heat is an economic requirement in the design
and operation of a cooling system. The driving force for the transfer
of heat is the difference in temperature between the two media. In most
cooling systems, this is in the range of 10200 degrees F. The heat
flux is generally low and in the range of 5,000 to 15,000 Btu/ft^{2}/hr.
For exceptional cases such as the indirect cooling of molten metal,
the heat flux can be as high as 3,000,000 Btu/ft^{2}/hr.
The transfer of heat from process fluids or equipment results in a
rise in temperature, or even a change of state, in the cooling water.
Many of the properties of water, along with the behavior of the contaminants
it contains, are affected by temperature. The tendency of a system to
corrode, scale, or support microbiological growth is also affected by
water temperature. These effects, and the control of conditions that
foster them, are addressed in subsequent chapters.
TYPES OF SYSTEMS
Water heated in the heat exchange process can be handled in one of two ways.
The water can be discharged at the increased temperature into a receiving body
(oncethrough cooling system), or it can be cooled and reused (recirculating
cooling system).
There are two distinct types of systems for water cooling and reuse: open and
closed recirculating systems. In an open recirculating system, cooling is
achieved through evaporation of a fraction of the water. Evaporation results in
a loss of pure water from the system and a concentration of the remaining
dissolved solids. Water must be removed, or blown down, in order to control this
concentration, and fresh water must then be added to replenish the system.
A closed recirculating system is actually a cooling system within a cooling
system. The water containing the heat transferred from the process is cooled for
reuse by means of an exchange with another fluid. Water losses from this type of
system are usually small.
Each of the three types of cooling systemsoncethrough, open recirculating,
and closed recirculatingis described in detail in later chapters. The specific
approach to designing an appropriate treatment program for each system is also
contained in those chapters.
HEAT TRANSFER ECONOMICS
In the design of a heat transfer system, the capital cost of building
the system must be weighed against the ongoing cost of operation and
maintenance. Frequently, higher capital costs (more exchange surface,
exotic metallurgy, more efficient tower fill, etc.) result in lower
operating and maintenance costs, while lower capital costs may result
in higher operating costs (pump and fan horsepower, required maintenance,
etc.). One important operating cost that must be considered is the chemical
treatment required to prevent process or waterside corrosion, deposits
and scale, and microbiological fouling. These problems can adversely
affect heat transfer and can lead to equipment failure (see Figure 231).
Heat Transfer
The following is an overview of the complex considerations involved in the
design of a heat exchanger. Many texts are available to provide more detail.
In a heat transfer system, heat is exchanged as two fluids of unequal
temperature approach equilibrium. A higher temperature differential results in a
more rapid heat transfer.
However, temperature is only one of many factors involved in exchanger design
for a dynamic system. Other considerations include the area over which heat
transfer occurs, the characteristics of the fluids involved, fluid velocities,
and the characteristics of the exchanger metallurgy.
Process heat duty, process temperatures, and available cooling water supply
temperature are usually specified in the initial stages of design. The size of
the exchanger(s) is calculated according to important parameters such as process
and water flow velocity, type of shell, layout of tubes, baffles, metallurgy,
and fouling tendency of the fluids.
Factors in the design of a heat exchanger are related by the heat transfer
equation:
Q = UA DTm
where
Q = rate of heat transfer (Btu/hr)
U = heat transfer coefficient (Btu/hr/ft^{2}F)
A = heat transfer surface area (ft^{2})
DTm = log mean temperature difference
between fluids (degrees F)
The rate of heat transfer, Q, is determined from the equation:
Q = WC DT + WDH
where
W = flow rate of fluid (lb/hr)
C = specific heat of fluid (Btu/lb/degrees F)
D T = temperature change of the fluid
(degrees F)
D H = latent heat of vaporization (Btu/lb)
If the fluid does not change state, the equation becomes Q = WC DT.
The heat transfer coefficient, U, represents the thermal conductance of
the heat exchanger. The higher the value of U, the more easily heat is
transferred from one fluid to the other. Thermal conductance is the
reciprocal of resistance, R, to heat flow.
The total resistance to heat flow is the sum of several individual
resistances. This is shown in Figure
232 and mathematically expressed below.
Rt = r1 + r2 + r3 + r4
+ r5
where
Rt = total heat flow resistance
r1 = heat flow resistance of the processside film
r2 = heat flow resistance of the processside fouling (if any)
r3= heat flow resistance of the exchanger tube wall
r4 = heat flow resistance of the waterside fouling (if any)
r5 = heat flow resistance of the waterside film
The heat flow resistance of the processside film and the cooling
water film depends on equipment geometry, flow velocity, viscosity,
specific heat, and thermal conductivity. The effect of velocity on heat
transfer for water in a tube is shown in Figure 233.
Heat flow resistance due to fouling varies tremendously depending on
the characteristics of the fouling layer, the fluid, and the contaminants
in the fluid that created the fouling layer. A minor amount of fouling is
generally accommodated in the exchanger design. However, if fouling is not
kept to a minimum, the resistance to heat transfer will increase, and the
U coefficient will decrease to the point at which the exchanger cannot
adequately control the process temperatures. Even if this point is not
reached, the transfer process is less efficient and potentially wasteful.
The resistance of the tube to heat transfer depends on the material of
construction only and does not change with time. Tube walls thinned
by erosion or corrosion may have less resistance, but this is not a
significant change.
The log mean temperature difference (DTm) is a mathematical expression
addressing the temperature differential between the two fluids at each
point along the heat exchanger. For true countercurrent or cocurrent
flow:
When there is no change in state of the fluids, a countercurrent flow
exchanger is more efficient for heat transfer than a cocurrent flow exchanger.
Therefore, most coolers operate with a countercurrent or a variation of
countercurrent flow. Calculated DTm formulas may be corrected for exchanger configurations that are not truly countercurrent.
MONITORING Heat transfer equations are useful in monitoring the condition of heat
transfer equipment or the efficacy of the treatment programs. The resistance of
the tube is constant; system geometry does not change. If flow velocities are
held constant on both the process side and the cooling water side, film
resistance will also be held constant. Variations in measured values of the U
coefficient can be used to estimate the amount of fouling taking place. If the U
coefficient does not change, there is no fouling taking place on the limiting
side. As the exchanger fouls, the U coefficient decreases. Therefore, a
comparison of U values during operation can provide useful information about the
need for cleaning and can be utilized to monitor the effectiveness of treatment
programs.
The use of a cleanliness factor or a fouling factor can also be helpful in
comparing the condition of the heat exchanger, during service, to design
conditions. The cleanliness factor (Cf) is a percentage obtained as
follows:
The resistance due to fouling, or fouling factor (R_{f}), is a
relationship between the initial overall heat transfer coefficient (U_{i})
and the overall heat transfer coefficient during service (U_{f})
expressed as follows:
Heat exchangers are commonly designed for fouling factors of 0.001
to 0.002, depending on the expected conditions of the process fluid
and the cooling water.

Table of Contents 

(Chapter 22 ColdEnd Deposition And
Corrosion Control) 
(Chapter 24 Corrosion
ControlCooling Systems) 
