Appendix F: Properties of Gases

In boiler performance estimation, one of the important calculations is the determination of thermal and transport properties of a flue gas mixture such as products of combustion of fuel oil or natural gas or any waste gas stream. The specific heat, viscosity, and thermal

conductivity data for individual gas such as CO 2 ,H 2 O, N 2 ,O 2 , and SO 2 are available in literature (see Tables F.1 through F.3); mixture properties have to be evaluated in order to determine the tube-side or outside heat transfer coefficient.

For a gaseous mixture, the following equations may be used: µ m =∑ yµ i i √ MW/ y i ∑ i √ MW i (F.1)

. k 33

m =∑ y k MWi / y MW ii ( ) ∑ . 0 33 i ( ) (F.2)

C pm =∑ yC i pi ( MW / y MW i ) ∑ i ( i ) (F.3)

where µ m ,k m ,C pm are the viscosity, thermal conductivity, and specific heat of the mixture, respectively y i is the volume fraction of the particular constituent MW is the molecular weight of that constituent

Example F.1

Turbine exhaust gases contain % volume of CO 2 = 3, H 2 O = 7, N 2 = 75, O 2 = 15. Determine the C pm ,k m ,µ m at 300°C. Table F.4 gives the data for the individual gases.

Solution

C pm = (0.2521 × 0.03 × 44 + 0.4795 × 0.07 × 18 + 0.2569 × 0.75 × 28 + 0.2395 × 0.15 × 32)/ (0.03 × 44 + 0.07 × 18 + 0.75 × 28 + 0.15 × 32) = 0.2636 kcal/kg °C = 1.103 KJ/ kg K = 0.2636 Btu/lb °F.

µ m = (0.0941 × 0.03 × √44 + 0.0734 × 0.07 × √18 + 0.1017 × 0.75 × √28 + 0.1204 × 0.15 × √32)/(0.03 × √44 + 0.07 × √18 + 0.75 × √28 + 0.15 × √32) = 0.1028 kg/m h = 2.86 × 10 −5 Pa s = 0.0689 lb/ft h

k m = [0.0328 × 0.03 × (44) 0.33 + 0.0375 × 0.07 × (18) 0.33 + 0.0365 × 0.75 × (28) 0.33 + 0.0397 × 0.15 × (32) 0.33 ]/[0.03 × (44) 0.33 + 0.07 × (18) 0.33 + 0.75 × (28) 0.33 + 0.15 × (32) 0.33 ] = 0.0369 kcal/m h °C = 0.0429 W/m K [0.02478 Btu/ft h °F]

Enthalpy calculation is often required while doing heat balances (Tables F.1 through F.3 and F.5 through F.9). Tables F.10 and F.11 shows the enthalpy of a few common gases with

a reference of 15°C.

448 Appendix F: Properties of Gases

TABLE F.1

Specific Heats for Various Gases, kcal/kg °C

Temp., °C 100 200

0.3005 0.3056 0.3098 H 2 O

0.2786 0.2831 0.2873 Note: Multiply by 4.187 to convert to kJ/kg K and by 1 to obtain C p in Btu/lb °F.

TABLE F.2

Viscosity of Gases, kg/m h

Temp., °C 100 200

0.1517 0.1611 0.1699 H 2 O

0.1587 0.1677 0.1762 Note: Multiply by 0.0002778 to convert to Pa s (kg/m s) or divide by 1.489 to obtain lb/fth.

TABLE F.3

Thermal Conductivity of Gases, kcal/m h °C

Temp., °C 100 200

0.0615 0.0662 0.0706 H 2 O

0.0588 0.0629 0.0670 Note: Divide by 0.86 to convert to W/m K or divide by 1.489 to obtain Btu/ft h °F.

Appendix F: Properties of Gases 449

TABLE F.4

Gas Properties at 300°C

Note: C p in kcal/kg °C, µ in kg/m h, k in kcal/m h °C.

TABLE F.5

Analysis of Important Flue Gases

Gas Temp., °C Press. bara

5 200–1000 1 12 10 72 6 Trace Trace 6 300–1450

Notes: (1) Raw sulfur gases, (2) SO 3 gases after converter, (3) reformed gas in hydrogen plant, (4) gas turbine exhaust, (5) MSW incinerator exhaust, (6) sulfur condenser effluent, (7) preheater gas in cement plants, (8) incineration of plastics, (9) flue gas from natural gas combustion, (10) flue gas from fuel oil combustion (sulfur neglected).

TABLE F.6

Specific Heat of Some Common Flue Gases, kcal/kg °C

Temp, °C 100 200

0.2640 0.2681 0.2717 Notes: Multiply by 4.187 to convert to kJ/kg K and by 1 to obtain C p in Btu/lb °F.

Gas 1: Flue gases from combustion of natural gas—% volume CO 2 = 8.29, H 2 O = 18.17, N 2 = 71.08, O 2 = 2.46. Gas 2: Flue gases from combustion of fuel oil—% volume CO 2 = 11.57, H 2 O = 12.29, N 2 = 73.63, O 2 = 2.51.

Gas 3: Gas turbine exhaust—% volume CO 2 = 3, H 2 O = 7, N 2 = 75, O 2 = 15.

Gas 4: Reformed gas in hydrogen plant—% volume CO 2 = 6, CO = 8, H 2 O = 37, N 2 = 0.5, CH 4 = 5.5, H 2 = 43.

Gas 5: Sulfur combustion—% volume SO 2 = 10, N 2 = 80, O 2 = 10.

450 Appendix F: Properties of Gases

TABLE F.7

Viscosity of Flue Gases, kg/m h

Temp, °C 100 200

0.1543 0.1633 0.1717 Note: Multiply by 0.0002778 to convert to Pa s (kg/m s) or divide by 1.489 to obtain lb/ft h.

TABLE F.8

Thermal Conductivity of Flue Gases, kcal/m h °C

Temp., °C 100 200

0.0554 0.0594 0.0633 Note: Divide by 0.86 to convert to W/m K or divide by 1.489 to obtain Btu/ft h °F.

TABLE F.9

F g Factor for Various Gases = k 0.67 C p 0.33 /μ 0.32

Temp., °C 100

Gas A 0.1295

Note: Gas A: GT exhaust. % volume CO 2 = 3, H 2 O = 7, N 2 = 75, O 2 = 15;

Gas B: Fired GT exhaust. % volume CO 2 = 4.28, H 2 O = 9.51, N 2 = 74.0, O 2 = 12.17.

Example F.2

Analysis of a flue gas is as follows: % volume CO 2 = 8, H 2 O = 18, N 2 = 71.5, O 2 = 2.5.

Determine the energy recovered when 100,000 kg/h of this flue gas is cooled from 500°C to 100°C. First let us convert the % volume analysis to % weight basis.

Molecular weight MW = 0.08 × 44 + 0.18 × 18 + 0.715 × 28 + 0.025 × 32 = 27.58 % weight CO 2 = 8 × 44/27.58 = 12.76 % weight H 2 O = 18 × 18/27.58 = 11.74 % weight N 2 = 71.5 × 28/27.58 = 72.59 % weight O 2 = 2.5 × 32/27.58 = 2.9

Enthalpy of gas at 100°C = 0.1276 × 18 + 0.1174 × 37.7 + 0.7259 × 20.9 + 0.029 × 18.7 =

22.43 kcal/kg Enthalpy at 500°C = 0.1276 × 118.2 + 0.1174 × 231 + 0.7259 × 124.5 + 0.029 × 113.8 = 135.87 kcal/kg

Energy recoverable = 100,000 × (135.87 − 22.42) = 11.34 MM kcal/h = 13.19 MW (45 MM Btu/h) (Tables F.10 and F.11)

Appendix F: Properties of Gases 451

TABLE F.10

Enthalpy of Products of Combustion, kcal/kg

Temperature, °C

Nat. Gas

Fuel Oil

Note: Natural gas is Gas 1 and fuel oil refers to Gas 2 as

shown in Table F.6. Multiply enthalpy given by 4.187 to obtain in kJ/kg and by 1.8 to obtain in Btu/lb.

TABLE F.11

Enthalpy of Some Common Gases, kcal/kg

Temp., °C 100

205.4 235.9 267 H 2 O

Note: Multiply by 1.8 to obtain enthalpy in Btu/lb and by 4.187 to obtain enthalpy in kJ/kg.

Appendix F: Properties of Gases