Interpretación de resultados

Several forms of deposits can occur in cooling systems including scale formation, biological fouling, and general fouling. Deposition of such materials may result in plugging, loss of cooling, and underdeposit corrosion.

Scale formation is characterized by the formation of insoluble inorganic compounds. This occurs by the precipitation of slightly soluble ions such as calcium, magnesium, or zinc together with carbonate, sulfate, phosphate, hydroxide, or silicate.

Scale formation is different from fouling. Fouling can be either general or microbiological in nature. General fouling is caused by the settling of any suspended matter such as iron oxides, silt, mud, oil, and other debris. Microbiological fouling results from the growth of algae, bacteria, or fungi.

Effect of Scale on Heat Transfer

In a heat exchanger, thermal energy is usually transferred by conduction from a process fluid across a metal barrier to the cooling water. In conduction, heat is transferred through or between stationary media such as metals, water, or air. It results from short range interactions of molecules and/or electrons. In the metals, electrons contribute to this process. In gases and liquids, energy is also conducted by molecular collisions. The heat transferred (Q) across a flat plate by conduction is described by the following equation:

Where

Q = heat transferred, Btu/hr

K = thermal conductivity, Btu/hr °F A = cross sectional area, ft2

t2-t1 = temperature difference across the plate, °F

L = thickness of the plate, ft.

From this equation, it follows that thin plates made from materials with high thermal conductivities, e.g., metals, are the best conductors of heat. Scales and fouling deposits have lower thermal conductivities than metals and effectively increase the thickness and lower the thermal conductivity of the barrier.

Saudi Aramco DeskTop Standards 32

The basic equation for a steadily operated exchanger follows, in which U is the overall heat transfer coefficient and the dT and dt values are the terminal temperature differences for the process and watersides. In this simple case we are assuming constant U, constant mass flowrates, no changes in phase, constant specific heats, and negligible heat loss.

Q = U A dTm

where

Q = Heat transfer rate, Btu/hr

U = Heat transfer coefficient Btu/hr ft2 °F

A = Heat transfer surface area, ft2

dTm = Log mean temperature difference, °F

where

dT = T2 - t1, dt = T1 - t2

t1 = Inlet water temperature, °F

t2 = Outlet water temperature, °F

T1 = Inlet process temperature, °F

T2 = Outlet process temperature, °F

The rate of heat transfer from the process to the cooling water is proportional to the mass flow rate of the material, its heat capacity, and the temperature change the material undergoes. Since we are neglecting heat losses:

Q = Mw Cpw (t2-t1) = Mp Cpp (T1-T2)

where:

Mw, Mp = mass flow rates for water and process, lb/hr

Heat capacity is an intrinsic property of a material. Tables of heat capacity data can be found in chemical handbooks. The heat capacity of pure water is 1.00 Btu/lb °F, by definition.

When an exchanger is designed, a design heat transfer coefficient, UD, can be calculated.

After being put in service, an actual heat transfer coefficient (UA) can be calculated using

these equations. The fouling factor (Rf) is the difference between the reciprocals of the

actual and designed coefficients.

The fouling factor is the resistance to heat flow caused by fouling. Plotting the fouling factor over time is a useful way to monitor the amount of fouling occurring in an

exchanger. If the factor increases, the system is becoming fouled. A general rule of thumb for fouling factors is that when they are on the order of 0.001 to 0.002 hr ft2 °F/Btu, the

system is clean. If the factor is greater than 0.005, the system is fouled. Scales Formed in Cooling Water and Their Prevention

As water evaporates in an open-evaporative system, the inorganic salts naturally present in the water and those added for corrosion control increase in concentration. Consequently, the tendency for many of these ions to precipitate from solution increases, resulting in scale formation.

The rate of scale formation depends on temperature, alkalinity or acidity of the water, the velocity of the water, and other factors as well as the concentration of the scale-forming ions. Calcium carbonate, calcium sulfate, calcium phosphate, and magnesium silicate are the scales most likely to form in open-evaporative systems.

Calcium Carbonate Scale

Calcium carbonate is the most common scale found in cooling water systems. It forms when the calcium hardness and bicarbonate alkalinity, naturally present in water, are concentrated and/or are subjected to increased pH and temperature.

Ca+2 + CO

3-2 ——> CaCO3 (solid)

In 1936, Langelier published a formula for calculating the tendency of water to either deposit or to dissolve the calcite form of calcium carbonate. The formula expresses the effect of pH, calcium, total alkalinity, dissolved solids, and temperature on the solubility of calcium carbonate for water from pH 6.5 to 9.5. The equation is:

Saudi Aramco DeskTop Standards 34

where pHs is the pH value at which water with a given calcium content and alkalinity is in

equilibrium with calcite. The terms pK2 and pKs are the negative logarithms of the second

dissociation constant for carbonic acid and the calcite solubility product constant. The last two terms are the negative logarithms of the molar and equivalent concentrations of calcium and titratable alkalinity. The Langelier Saturation Index (LSI) is a qualitative index of the tendency of calcium carbonate to deposit or dissolve, expressed as the following equation:

LSI = pH - pHs

A simple formula for calculating LSI is given in Figure 21. A positive LSI indicates a tendency to deposit calcite. A negative LSI indicates an undersaturation condition exists; therefore, solid calcite will dissolve. If LSI = 0, the water is in equilibrium with respect to calcium carbonate saturation.