Question

A fuel gas containing 95 mole% methane and the balance ethane is burned completely with 25% excess air. The stack gas leaves the furnace at 900°C and is cooled to 450°C in a waste-heat boiler, a heat exchanger in which heat lost by cooling gases is used to produce steam from liquid water for heating, power generation, or process applications.

(a) Taking as a basis of calculation 100 mol of the fuel gas fed to the furnace, calculate the amount of heat (kJ) that must be transferred from the gas in the waste heat boiler to accomplish the indicated cooling.

(b) How much saturated steam at 50 bar can be produced from boiler feed water at 40°C for the same basis of calculation? (Assume all the heat transferred from the gas goes into the steam production.)

(c) At what rate (kmol/s) must fuel gas be burned to produce 1280 kg steam per hour (an amount required elsewhere in the plant) in the waste heat boiler? What is the volumetric flow rate (m3/s) of the gas leaving the boiler?

Answer 1

Date: Page : steam CHy 458 95Y, Сис -0.05 57. stack gas gooc Combuster gas > Boiler 450°C Air 257. excess water a) Chemical reactions in the combuster are taking as follows: CHy + 202 CO₂ + 2H₂O С, И. + 200 + 340 Basis 100 mol of fuel gas entering the combuster. Step i Calculate Theoritical onygen required: & Theoritical Orggen is the required for complete combustion moles of onggen CHy feed 0.95 x 100 95 moles Igo moles 2x 95 = O₂ regeared for EHy theontius food Ce feed 0,00 x 100 = Or res for the 5 moles 17.5 moles Zx 5 = 2

Date Page & Total o repe a the Theoritical a moles 130t 17.5 2075 It means 207.5 moles of ę is required for complete combustion of the fuel. actual Step 2: Calculate excet oxygen required: Oz aut excess o O₂ act Og the * 100 On the 700 a act 207.5 207.5 =) - step 3: het O act 259.4 moles Calculate moles of Air required air composes of 79% (by mole) N₂ 21% (by mole) O2 Airry 100 21 0₂ 100 21 259.4 > 1235 moles moles of Ar ra 201 2) N = 79 259.4 X 21 - Also, 79 21 N2 O2 * N2, in = 975.7 mol

Date: Page: Step 4: Calculate moles of co & H₂O formed moly of co, formed from reach" 0 moles of CH4 consumed 95 moly moles of con formed from react @ 2x moles of G H consumed moles 2x 5 = 10 Total moles of conformed = 95+10= 105 moles Similarly, Total mols of the formed (from react oko) 2x gst 3x5 205 mols - Steps: Calculate composition of stack gas : O₂ act Othe O in stack gas O out 259.4-207.5 51,9 moly Since, N₂ does not take part in the combustion react Nein Nout 975-7 mols

Date : Page: Step 6: obtain the enthalpy table : determine especific enthalpies from table B.8 A T = 450°C be used to linear interpolation can estimate specific enthalpies. het Ti In 500°C 400°C Treg 450°c using the equ Hrey + HT HI Hi ) ( Top-T.) T- Ti here Hoy & Enthalpy (in kJ/md) at 450°C at HIE 500°C 400°C at & He, Specific Enthalpy table is obtained as: Hout (kJ/mol ) 18.85 Substance con tho O N moles 105 205 51.9 975.7 Hin (kJ/mol ) 42.94 33.32 28.89 27.19 15.12 13.38 12.685

Date : Page: Using Energy balance equ for open system Ф ДИ E hout Hout E hin Hin here, no work is done, W is ignored 7 Ehout Hout 18.85 KJ mol (105 mot con ( 205 mol the 15.12 kJ mol 51.9 not a 13.38 KT mol + (9 975.7 mol N₂ x 12.695 kJ 18159.78 KJ Shin Hin (los mol con x 42.94 kJ mol 205 not hox 33.32 KJ Trol } 51.9 mol a x 28.89 kJ ) + mos 975.7 mol N₂ x 27.19 hoy 39367.97 KI

Date Page kJ 39367.97 KJ - ΔΗ 18159.78 = -21208.19 KJ 21208.19 KJ the amount of heat that must be transferred from the gas сь) from table 85 At 40°C the enthalpy of lie water, hy a 167.5 kJ/kg from table B.6, enthalpy of steam, hy? 2794.2 KJ/kg SH 3 Hg the hg- he 2794.2 167.5 2626.7 KI lug 9 η ΔΗ. 21208.19 = 8.074 x 2626.7 Kg (0) Required steam production rate per sec. 1280 Kg 60x60 s 1280 kg steam h kg steam 0.3555 sec

Date : Page: Since, 100 moles of fuel is taken as basis Son 0.3555 mol fuel stean Kg R. 100 8.07 kg Steam I knol 1000 mol 0.0044 kmol fuel gas S 0.0044 kmol of fuel gas must be s burned to produce 1280 kg steam in the waste cheat boiler. per hour