Evaporative Cooling Towers (part 4)

The amount of evaporated water in the surface portion dA can be expressed through the relationship:

dL = k_v (p_sat – p_v) dA, where k_v is the evaporation function index.

The following expression describes the amount of heat (Q_D) removed from water during evaporation:

dQ_D = r dL    (3), where r is the heat of vaporization.

In equilibrium conditions, there is a balance between the amount of heat loss due to fluid evaporation and to  the quantity of heat  (Q_c)  transferred to it by conduction: dQ_D = dQ_c 

which written in terms of temperature leads to the following expression:

r dL = G c_p dt

while in terms of heat exchange surface, we have:

r [k_v (p_sat – p_v)] dA = α (t_G,DB- t_L1) dA    (4)

Instead of  the p_sat and p_v pressure functions, it's possible to calculate water quantity (dL) as a function of water contained in air or specific humidity (x); this gives an immediate idea of the amount of water vapor that is transferred to the air.

If p_A and p_V represent the partial pressures due to the above-mentioned components, the total pressure of the air is p_T = p_A + p_V  (Dalton); since the steam is overheated and its behavior is very close to that of a perfect gas, it's possible to apply the law PV = RT; meaning that for the two components, after the appropriate steps, it's possible to describe water content in saturated air (x_sat) as x.

PMV = molecular weight of water vapor = 18

PMG = molecular weight of the dry air »29

It's thus possible to obtain the values of saturation and water vapor pressure, respectively.

The simplified expressions have been written taking into account that generally, and especially, in the temperature range where cooling towers operate, the values p_v and p_sat are small compared to the value of the total pressure, where the constant c is a function of the total pressure and of the molecular weights of the components.

All this allows rewriting equation (4), which after appropriate simplification becomes:

r [c k_v (x _sat - x)] = α (t_G,DB- t_L)

i.e., introducing the overall coefficient of mass transfer K = c (kV) in relation to the water content:

r (x _sat - x) = (α / K) (t_G,DB- t_L)    (5)

then,

((t_G,DB-t_G,DB1) c_p = (x₁ - x) r        (6)

If we consider a channel of infinite length, we must attend a full compensation between water and air to the complete saturation, i.e., for which continues to be valid equation (6), hence:

(t-θ_e) c’_p = (X’’_e - X) r    (7)

when the temperature (θ_e ) and the relative water content at saturation level (X’’_e) are at fixed values, i.e., values that are known and do not vary can be considered both the specific heat of air (c’_p). The evaporation heat (r): equation (7) shows that the relationship between temperature and water content in air is linear.

The temperature measured in air-saturated conditions, also called wet-bulb temperature or adiabatic saturation (t_WB), is the limit temperature of water cooling.

The above content wants to illustrate that the cooling water temperature for cooling towers cannot be lower than the wet-bulb temperature. Therefore, the greater the difference in temperature between cooling water and wet-bulb temperature (approach), determines a smaller cooling tower.

Evaporative Cooling Towers (part 3)

EVAPORATION OF FLUID INTO GAS

The following discussion is based on the following assumptions:

(1) Inside the water there is no heat exchange;

(2) The water that has decreased in volume, due to the evaporation effect, will be replenished with the same water that has evaporated to the surface.

In virtue of such assumptions, it's reasonable to assert that the water temperature doesn't undergo any variations along with the different layers of the water itself.

Conduction and convection 

The amount of heat that is transferred from air to water by conduction and convection can be expressed by the following law of conduction:

DQ_C = a (t_{G, DB}- t_L) dA or, in a fully equivalent manner, according to the definition of specific heat:

DQ_C = G c_p dt = G

The amount of evaporated water at the surface of contact between the two fluids, air, and water, depends on the speed of vapor diffusion, that was created from mixing vapor-air. This is located near the interface between the two fluids.

According to the law of partial pressure (Dalton's law):

In a volume containing a mixture of several different gases or vapors at a given temperature, the value of the total pressure is the sum of the pressures, where each of the gases or vapors in the mixture components would have exerted separately. If by itself, it would occupy the entire volume.

p_T = p_A + p_B + p_C + ...

In other words, each gas in a mixture contributes with its partial pressure to the total pressure, as if acting independently from all others.

For example, the evaporation of water in an environment containing air continues to take place until the vapor produced reaches the required amount to fill the available volume and thus arriving at saturation, at the specific temperature of the environment taken under consideration.

The produced vapor exerts pressure as any other gas; this pressure is called vapor pressure and its value depends only by the fluid temperature. For this reason, the total pressure reached in the container – by which the determined temperature was reached, assumed constant, vaporization stops - at that determined temperature it exceeds the value of the initial pressure by an amount equal to the saturated vapor pressure.

Working at normal atmospheric pressures, Dalton's law of partial pressures finds the exact experimental results.

The vapor tension or pressure of saturated vapor on the water surface has the same value of saturation pressure (p_sat) detectable at water temperature (t_L).

Evaporative Cooling Towers (part 2)

WATER-AIR TURBULENCE

Water cooling takes place according to three phenomena:

1. CONDUCTION: (disposal of sensible heat1).

The heat flows from a region with a higher temperature to a region with a lower temperature through one or more means that are in direct physical contact, in compliance with the laws of heat conduction (Fourier Transform). Energy is transmitted by direct contact between the molecules, and the potential that governs this phenomenon is the difference of temperature between the two different regions.

2. EVAPORATION: (disposal of latent heat2).

The change of state from liquid to vapor causes the absorption, from the side of the evaporated mass unit, of a quantity of heat called evaporation latent heat, which causes the cooling of the mass unit that remained in the liquid state.

The potential difference that governs this phenomenon is due to the difference of concentration levels, which for the gas phase it's expressed in terms of partial pressures assuming we're using assimilated gases to ideal gases.

    The loss of energy and, consequently, the obtained cooling, with the transfer of latent heat, is important:  to evaporate one kilogram of water there is a need to dispose of approximately 540 kcal or 2257 kJ (evaporization latent heat), i.e.,  100 liters of water gets cooled to about 6 ° C ..

3. IRRADIATION

Electromagnetic waves propagation, in absence of physical contact, make heat flow from a body that has a greater temperature to a body with a lower temperature. When the radiation emitted by a body meet another body, their energy remains absorbed near the surface.

Thermal exchange by irradiation becomes always more important as the temperature of a body increases, and in the case of temperatures close to the atmospheric ones, the irradiation can be neglected.

We can again highlight the concept that the evaporative towers are essentially based on the use of latent heat by mixing air stream with water flow, by which a small part evaporates by passing through the air current, taking away latent heat from the remaining water.

The heat removed from the water will be dispersed in the environment as water vapor that is contained in the outgoing air stream, so that it will be more humid and warmer with respect to the incoming air.

The water exiting the tower will be colder but in smaller quantities than the incoming water. This is the reason that the tower is replenished with make-up water in quantities (Wo) equal to that lost by evaporation and temperature qo.

Principles

1. Thermal balance (first principle of thermodynamics)

In the following set of equations, we are neglecting the effect of the barometric pressure; although in some cases, for example, plant installations that are 500 meters above sea level, the barometric pressure is important because it helps to vary pressures relative to air.

Cooling system thermal balance

1. Q + (Wo qo ).= L(i2 - i1)
2. Q = W( q2 - q1).+ Wo( q1 - q0).
3. W( q2 - q1).+ Wo( q1 ).= L(i2 – i1)

From the moment the amount of make-up water (Wo) is not thermally significant with respect to the total quantity of water W.

1Sensible heat is the one that transferred/subtracted to/from a body varies the temperature.

2Latent heat is the one that transferred/subtracted to/from a substance causes the physical state to vary.

The importance of water in the cooling tower industry - Water (part 6)

SYSTEMS THAT COOL WATER IN AN EVAPORATIVE WAY: WHERE THEY ARE USED

A hint is given by knowing how refrigerators function in terms of "transfer of energy-heat". Although this topic is very interesting, we will not linger on the quality of energy.

We only need to know that not all energy is equal. There is no difference between the physical and mathematical way.

In practice, from an economic point of view, it is very important to know how to take advantage of the energy that is available.

We must say that the waste heat (energy that cannot be used) from plants, unfortunately, can only be used in a few plants. This is because their natural use in "cascade" presupposes that the plant being served needs to use the same amount of energy at the same time, and this is what makes more difficult. Let us recall that it's very difficult to store energy in an economically way.

Now we will discuss refrigerators

Contrary to what is known, refrigerators "do not produce cold." Cold cannot be produced, or make!

Cold is something you “feel", it exists because “it lacks” heat; in other words, we do not produce cold but we remove heat, hence, we have cold.

Refrigerating machines do the following: remove heat, or better carries heat from one system component (called evaporator) to another component (called condenser).

For example, to learn how much heat a refrigerator carries, it's enough to know the power of the engine required to make the refrigerator function. In practice, usually, 1 kW is required to "carry" about 2,500-3,000 kCal / h.

The importance of water in the cooling tower industry - Water (part 3)

COOLING WATER

The concept of temperature and heat

Temperature is a physical quantity that expresses the thermal state of an object. It is closely correlated to the amount of heat contained in the object itself.

A hot body is characterized by the amount of energy stored as heat. The amount of heat depends on the body mass and its specific heat (heat retention capacity).

When we speak of cooling we always almost think of refrigerators or temperatures that are lower than those of the environment we live in; on the other hand, when we speak of heating we think of fireplaces, electric heaters, etc., that is, temperatures that are higher than then the environment we live in. Hence. "hot" and "cold" are physical states which we are accustomed to "feel" or "perceive”.

Temperature and heat measurements
The temperature measurement is the degree "°C" for Celsius or "K" for Kelvin (K = ° C + 273).
The energy-heat measurement is the "J" (Joule).

Heat is normally related to time Js = power = W.

How to cool water in an economical way

A refrigerating machine uses a fair amount of energy to activate the process to transfer the heat, from a place that has to be cooled, to another place.

In evaporative cooling, however, the heat is transferred to air according to a physical principle that exploits the characteristics of the air to absorb moisture. This is very advantageous.

We, therefore, have moisture = water; water, which in our case contains heat.

The drier the more it can absorb moisture – water – heat.

Hence, hot and dry air can cool the water even at a temperature lower than air itself.

The importance of choosing the cold water temperature according to the process plant to cool
As we have seen, the cold water temperature is not very important as the difference in temperature at the outlet and inlet water liquor used as heat transport.

Let's not forget that our task with cooling towers is to dispose of heat. However, some plants in order to work better require low temperatures.

Condensers or heat exchangers of any one type are correlated to the cold water temperatures.

The choice of the outlet water temperature of the tower is, hence, of fundamental importance.

A tower is a machine that uses air as a cooling element.

The degree of the temperature is important to size the tower and need to be very careful in choosing the temperature.
A slight degree over the wet bulb air temperature forces us to increase the size of the tower, sometimes even double it!

Considering that the wet bulb temperature is very high for a few hours a year, we would have doubled the size of a plant for a few hours a year: an unforgivable economical mistake!

Imagine the waste and design error.

We can emphasize the fact that the difference in temperature between cold water and air, at wet bulb temperature, is a very important design piece of data because it is closely correlated with the size of the tower.

The importance of water in the cooling tower industry - Water (part 4)

UP TO WHAT TEMPERATURE CAN WATER BE COOLED

The capacity of air to cool water, according to latent heat. Practical benefits.

The physical states are well known: solid, liquid, gaseous.

When an element goes from one physical state to another, it frees energy but, at the same time, it requires energy. That is:

• If a solid element changes from solid to liquid, it requires energy (e.g., a solid metal requires heat/energy to become liquid/molten);
• in the reverse proceedings, the molten metal cools down (losing energy-heat) and becomes solid.

Other examples: a liquid that is heated to the right temperature, e.g., in the case of water it's 100 ° C, it evaporates and passes to the gaseous state. This is called "evaporation temperature". This process required heat, hence, energy.

Let us take a closer look:

• We have employed heat-energy to heat up water to its evaporation temperature, which is 100 ° C.

By the definition of the unit of heat measurement, the amount of heat is determined in an exact way. In fact, 1 (one) calorie of energy is required to increase the temperature if 1 ° C in a liter of distilled water.
The increase in temperature, with respect to ambient temperature, is called "sensible heat". This is because it is perceived by one of our senses: touching.
If you put a finger in a pot of water that is heating up on top of a fire, we soon realize, or rather we feel, the increase in temperature. This is the sensible heat.

Let us now calculate how much sensible heat is required to bring a liter of normal tap water to the evaporation temperature. Normally, tap water comes out at a temperature of 15 ° C.

We mentioned that: 

• the water must reach a temperature of 100 ° C to evaporate;
• 1 calorie of energy is required to raise the temperature in a liter of water by 1 ° C. 

Hence, the 1 liter of tap water must be brought from 15 ° C to 100 ° C. The operation is simple arithmetic: 100 - 15 = 85 calories. So that the sensible heat of the water is 85 calories, and we have the same water at 100 ° C and, hence, in the evaporative state. If we continue to heat the water temperature will always remain at 100 ° C, but the water will evaporate until it is exhausted.

For the latter operation, 539 calories are required, which are called latent heat of vaporization. It's called latent because it's not detected since the water temperature will always be 100 ° C. 

This principle is also used in the kitchen to cook foods "in a water bath", that is, the food is cooked in a container immersed in another container containing water that is brought to the boiling point. With this method, the food will not exceed a cooking temperature of 100 ° C, with respect to fried foods or foods that are in direct contact with fire.

So we have seen that to evaporate one liter of tap water at 15 ° C, there is a need of 85 calories of heat sensitive and 539 calories of vaporization latent heat: a total of 624 Cal. This is a fixed datum.

To evaporate a liter of water it takes 624 calories.

Now let's try to do another experiment:

We have a liter of water and can make it evaporate with another stratagem. We will describe it in another paragraph, and it's not the pot on the stove. The new system will evaporate a liter of water by removing 539 calories, that is, the quantity of vaporization latent heat.

Remember, removing heat means cooling!

But let's see what is this thing that is well known since ancient times. First, we must use another element present in nature: air. 

The air, with the exception when it is raining, is not saturated with moisture. The air has the possibility to always absorb water up to its saturation. 

The air that we find in the environment, hence, has this important feature, which is to absorb water.

Absorb ...., hence, make evaporate.

By now the concept should be clear!

If we can "transfer" a liter of water to the air, we have transferred the 539 calories and the heat was removed with the new system (and not with the pot on the stove).

Air absorbs water, hence, latent heat from the water. This is the important phenomenon that we exploit to cool water in cooling towers. 

Relative humidity is the percentage of water vapor that the air holds under certain conditions, in relation to the amount of water vapor contained from saturated air in the same conditions.

Example:

If the relative humidity is 80% and the temperature is 20 ° C, since the saturated air contains 17.7 g / m3, the ambient air taken under consideration will contain 80% of the water, or better 0.8 x 17 7 = 14.6 grams of water per m3.

What happens if the cooling tower is not working properly and the plant is blocked? First thing: do not panic!

What happens if the cooling tower is not working properly and the plant is blocked?


First thing: do not panic! 

Many things could go wrong!  We might not even be aware of the many inconveniences that can occur to an industrial plant when the water cooling tower is not working properly.

Some of the causes are:

• malfunctioning of one or more components that make up the tower (breakage, wear, fluid hammer, high temperature)
• encrustation, algae, and clogging of the water or air side passages
• bad design

We shall focus on the last point, i.e., bad design.

Bad design is due to:

• thermal load assessment error
• water tower temperature outlet assessed with great accuracy
• wrong design assumption for the wet-bulb air temperature

What will happen in the various plants?

Usually, the tower used in industry serves:

• steelworks
• refineries
• plants for the production of chemical products
• others

For each different plant, the damage caused by a non-functioning tower can be calculated in terms of production lost.

In the next posts, we will analyze the risk and try to resolve bad accuracy in the design work with the help of our followers.

The importance of water in the cooling tower industry - Water (part 7)

Process plants that can be cooled with evaporation systems.
The importance of disposing quantity of energy.
Efficiency of the cooling system.

Image from previous post "NERI Calculator". Click on the above image to learn more about the calculator. 

From what has been written on this subject, the disposal of heat from evaporative cooling towers use something in particular, that is, disposing large amounts of heat from the water by means of the air: two natural elements.

Heat disposal has, therefore, a relatively low cost.

To name a few examples where towers are used:

(a) disposing heat from the various refrigeration groups and city building air conditioning condensers.

(b) in industries such as oil refineries, chemical plants,

(c) in industrial process plants for the production of food products,

(d) in thermoelectric power plants,

(e) in geothermal systems.

(f) …

Obviously each type of installation has different requirements for heat disposal (amount of cooled water). Temperatures and their range must be designed appropriately and carefully, and, most of all, the air thermal characteristic data to be considered for cooling tower design.

Air data has to include temperature, humidity and altitude related to the location of the tower. These three values (temperature, humidity, altitude) are very important.

If the data is not chosen correctly, this can lead to the wrong tower sizing, up to three or four times higher, or lower, than the actual needs of the system.

If the tower sizing is higher than the correct value, this will lead to waste of material and, hence, higher cost of the system. On the other hand, if faulty sizing will lead to equipment that is not adequate to the system, hence, useless!

→ See NERI Calculator ←

The importance of water in the cooling tower industry - Water (part 6)

SYSTEMS THAT COOL WATER IN AN EVAPORATIVE WAY: WHERE THEY ARE USED

A hint is given by knowing how refrigerators function in terms of "transfer of energy-heat". Although this topic is very interesting, we will not linger on the quality of energy.

We only need to know that not all energy is equal. There is no difference between the physical and mathematical way.

In practice, from an economic point of view, it is very important to know how to take advantage of the energy that is available.

We must say that the waste heat (energy that cannot be used) from plants, unfortunately, can only be used in few plants. This is because their natural use in "cascade" presupposes that the plant being served needs to use the same amount of energy at the same time, and this is what makes more difficult. Let us recall that it's very difficult to store energy in an economically way.

Now we will discuss about refrigerators

Contrary to what is known, refrigerators "do not produce cold." Cold cannot be produced, or make!

Cold is something you “feel", it exists because “it lacks” heat; in other words, we do not produce cold but we remove heat, hence, we have cold.

Refrigerating machines do the following: remove heat, or better carries heat from one system component (called evaporator) to another component (called condenser).

For example, to learn how much heat a refrigerator carries, it's enough to know the power of the engine required to make the refrigerator function. In practice, usually, 1 kW is required to "carry" about 2,500-3,000 kCal / h.

Evaporative Cooling Towers (part 4)

Evaporation

The amount of evaporated water in the surface portion dA can be expressed through the relationship:

dL = kv (psat – pv) dA

where kv is the evaporation function index.

 The following expression describes the amount of heat (QD) removed from water during evaporation:

dQD = r dL    (3)

where r is the heat of vaporization.

In equilibrium conditions, there is a balance between the amount of heat lost due to fluid evaporation and to  the quantity of heat  (Qc)  transferred to it by conduction:

dQD = dQc

which written in terms of temperature leads to the following expression:

r dL = G cp dt

while in terms of heat exchange surface, we have:

r [kv (psat – pv)] dA = α (tG,DB- tL1) dA    (4)

Instead of  the psat and pv pressure functions, it's possible to calculate water quantity (dL) as a function of water contained in air or specific humidity (x); this gives an immediate idea of the amount of water vapor that is transferred to the air.

If pA and pV represent the partial pressures due to the above mentioned components, the total pressure of the air is pT = pA + pV  (Dalton); since the steam is overheated and its behavior is very close to that of a perfect gas, it's possible to apply the law PV = RT; meaning that for the two components, after the appropriate steps, it's possible to describe water content in saturated air (xsat) as x.

PMV = molecular weight of water vapor = 18

PMG = molecular weight of the dry air »29

It's thus possible to obtain the values of saturation and water vapor pressure, respectively.

The simplified expressions have been written taking into account that generally, and especially, in the temperature range where cooling towers operate, the values pv and psat are small compared to the value of the total pressure, where the constant c is a function of the total pressure and of the molecular weights of the components.

All this allows to rewrite equation (4), which after appropriate simplification, becomes:

r [c kv (x sat - x)] = α (tG,DB- tL)

i.e., introducing the overall coefficient of mass transfer K = c (kV) in relation to the water content:

r (x sat - x) = (α / K) (tG,DB- tL)    (5)

then,

((tG,DB-tG,DB1) cp = (x1 - x) r        (6)

If we consider a channel of infinite length, we must attend a full compensation between water and air to the complete saturation, i.e., for which continues to be valid equation (6), hence:

(t-θe) c’p = (X’’e - X) r    (7)

when the temperature (θe ) and the relative water content at saturation level (X’’e) are at fixed values, i.e., values that are known and do not vary can be considered both the specific heat of air (c’p). The evaporation heat (r): equation (7) shows that the relationship between temperature and water content in air is linear.

The temperature measured in air saturated conditions, also called wet-bulb temperature or adiabatic saturation (tWB), is the limit temperature of water cooling.

The above content wants to illustrate that the cooling water temperature for cooling towers cannot be lower than the wet-bulb temperature. Therefore, the greater the difference of temperature between cooling water and wet-bulb temperature (approach), determines a smaller cooling tower.