Condensation Heat Transfer Calculations

In the case of condensing economizers with horizontal plain or finned tubes, water vapor condenses outside while the cooling medium flows inside the tubes. Since the heat transfer coefficients on both inside and outside the tubes are of the same order, calculations for U must consider both the condensing and the tube-side coefficients.

Miscellaneous Boiler Calculations 313

Sensible heat Latent heat

5000 t 4000 Kilowat

Temperature, °C

FIGURE 6.2

Amount of energy recovered from natural gas products of combustion.

The condensing heat transfer coefficient h c in kcal/m 2 h°C is given by the following equation [1]:

where k l is thermal conductivity of liquid, kcal/m h °C ρ l is the density of liquid, kg/m 3 Δ

H is the latent heat of condensing vapor, kcal/kg µ l is the viscosity of liquid, kg/m h

d is the tube OD, m Δ T is the saturation temperature – tube wall temperature, °C

g = 9.8 × 3600 2 m/h 2

Properties of the vapor may be estimated at the film temperature, which may be taken as the average of vapor and tube wall temperature. With a tube bundle, the presence of

neighboring tubes adds to the complexity of the calculation of h c . If condensate does not drain properly, it reduces h c as the thickness of the water film increases. When these drop- lets strike the tubes below, splashing occurs, causing turbulence and stripping of the condensate; the heat transfer coefficient could be higher but difficult to predict. Staggered arrangement of tubes is recommended to enhance the condensation process, which is also impacted by the number of rows along the gas flow direction. Kern proposed a correction for the average condensing heat transfer coefficient h cm considering the number of rows

deep N d as follows:

h −0 167 . cm = hN c d (6.2)

314 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

Example 6.2

In a condensing economizer, 100,000 kg/h of flue gas from natural gas combustion with analysis as given earlier is cooled from the water dew point temperature of 57°C to 45°C by 250,000 kg/h of condensate at 20°C. Plain tubes are used. Determine the size of the exchanger; plain tube size = 50.8 × 44 mm. There are 30 tubes/row of length 3 m long. S T = 80, S L = 70 mm, with 30 streams in staggered arrangement. Fouling factor of 0.0002

m 2 h °C/kcal is used on gas and water sides.

Solution

One may perform detailed calculations for condensation at 45°C and estimate the sensible and latent heat energy transferred to the water both as discussed earlier; however, using Figure 6.2, one can see that the total sensible and latent heat duty is 3,976 kW = 3,419,000 kcal/h (3,542 kW latent heat and 434 kW sensible heat); the temperature rise of water = 3,419,000/250,000 = 13.6°C. The exit water temperature = 33.6°C. The average film temperature is taken as 40°C (average of gas and water temperatures). Log-mean temperature difference (LMTD) = 24°C. The difference between saturation temperature and tube wall may be taken as 20°C.

Let us first estimate the condensing heat transfer coefficient h c . From Table F.13, one may determine the property of saturated water. At 40°C (104°F),

k l = 0.3656 Btu/ft h °F = 0.545 kcal/m h °C; ρ l = 61.9 lb/ft 3 = 990 kg/m 3 ; ΔH = 1035 Btu/ lb = 575 kcal/kg; µ l = 1.586 lb/ft h = 2.36 kg/m h; d = 0.0508 m; ΔT = 20°C

Substituting, h c = 0.725[0.545 3 × 990 2 × 575 × 9.8 × 3600 2 /(2.36 × 0.0508 × 20)] 0.25 = 6044 kcal/m 2 h °C (1233 Btu/ft 2 h °F). We may have to correct this for a number of rows

deep. Assume the number of rows deep is 24 and correct it later if necessary. Correction

factor = 24 − 0.167 = 0.588 and corrected h c = 0.588×6044 = 3554 kcal/m 2 h °C.

The tube-side convective heat transfer coefficient h i at an average water temperature of 27°C is estimated as follows (from Table B.3). C = 250 − 0.0063 × 27 × 27 + 4.023 × 27 =

354. Hence, h i = 0.0278 × (10,000/3,600) 0.8 × 354/.044 1.8 = 5,326 W/m 2 K (4,580 kcal/m 2 h °C).

The gas-side convective heat transfer coefficient may be estimated as follows using the methods discussed in Appendix C. At the gas film temperature of 40°C, gas properties are C p = 0.2642 kcal/kg°C; µ = 0.066 kg/m h; and k = 0.0235 kcal/m h °C. Nonluminous coefficient is too small and neglected.

S T /d = 80/50.8 = 1.57, S L /d = 1.38. From Table C.2 by interpolation, B = 0.48, N = 0.565. Gas mass velocity G = 100,000/[30 × (0.080 − 0.050.8) × 30 × 3] = 38,051 kg/m 2 h. Reynolds number Re = G d/µ = 38,051 × 0.0508/0.066 = 29,288

Nu = . 0 48 29288 × . 0 565 = 160 = h o × . 0 0508 0 0235 / . or h o = 75 kcal/m h C 2 ° (n eeglect the effect of varying gas flow)

Weighted outside coefficient is estimated as follows = 3976/[(3542/3554) + (434/75)] =

586 kcal/m 2 h °C. [The condensation duty divided by its heat transfer coefficient and the

sensible heat duty divided by its coefficient are added, and the reciprocal gives an estimated weighted heat transfer coefficient as the condensation and sensible heat transfer occur in parallel.]

The overall U o = 1/586 + 0.0002 + 0.0508 × ln(50.8/44)/2/37 + 0.0002 × 50.8/44 + (50.8/44) × (1/4632) = 0.001706 + 0.0002 + 0.000098 + 0.00023 + 0.000249 = 0.002483 or U o = 402 kcal/

m 2 h °C Required surface S = 3976 × 860/24/402 = 354 m 2 = 3.14 × 0.0508 × 30 × 3 × N or

number of rows deep = 25. The correction for this is 0.584 versus 0.588. LMTD is 24°C.

Miscellaneous Boiler Calculations 315

Revised calculations are not necessary as the difference is marginal. Hence, one may use, say, 26 rows deep considering some margin; also an even number of rows brings the headers on the same side! The disadvantage of using plain tubes is obvious. It requires a large number of rows deep. One may use a smaller transverse pitch and improve the convective coefficient and see the effect on gas pressure drop. That is left as an exercise to the reader. The purpose of this exercise is to show the sizing proce- dure for a condensing economizer. Since condensation process is complex, field data from similar projects will help fine-tune or correct the U values.

Condensation Heat Transfer Calculations