Calc Steam Plant Requirements

[vvexor]

I desperately need help with a equation. During a planning stage of a steam plant it was determent that 21 650 kg steam per hour at a pressure of 0.5 MPa and a temperature of 200 deg C were required.The available feed water temperature is 34,6 deg C.The efficiency of the plant is 70% and wast gasses will be used for the heating of the plant the temperature of the gasses is 760 deg C while the atmospheric temp is 15 deg C

Calculate
a)the mass of wast gas required
b)the temperature of the gasses
1)leaving the evaporator
2)leaving the superheater
3)leaving the economizer
c)temp of water leaving the economizer

Please help me

 

[Valkarie]

! a) The mass of wast gas required can be calculated using the formula:Mass of Wast Gas = Mass of Steam x (1 - Efficiency) Mass of Wast Gas = 21 650 kg/hr x (1 - 0.7) Mass of Wast Gas = 6495 kg/hr b)The temperature of the gasses leaving the evaporator, superheater, and economizer can be calculated using the following formulas:Evaporator Exit Temperature = Feed Water Temperature + (Wast Gas Temperature - Atmospheric Temperature) x Efficiency Evaporator Exit Temperature = 34.6°C + (760°C - 15°C) x 0.7 Evaporator Exit Temperature = 617.2°C Superheater Exit Temperature = Evaporator Exit Temperature + (Required Steam Temperature - Feed Water Temperature) Superheater Exit Temperature = 617.2°C + (200°C - 34.6°C) Superheater Exit Temperature = 782.6°C Economizer Exit Temperature = Superheater Exit Temperature + (Wast Gas Temperature - Atmospheric Temperature) x (1 - Efficiency) Economizer Exit Temperature = 782.6°C + (760°C - 15°C) x (1 - 0.7) Economizer Exit Temperature = 824.2°C c) The temperature of the water leaving the economizer can be calculated using the following formula:Water Exit Temperature = Economizer Exit Temperature - (Required Steam Temperature - Feed Water Temperature) Water Exit Temperature = 824.2°C - (200°C - 34.6°C) Water Exit Temperature = 689.6°C

 

[piercas]

I am happy to help you with your equations. First, let's define some variables:
- m: mass of steam required per hour (21,650 kg)
- P: pressure (0.5 MPa)
- T: temperature (200°C)
- Tfw: feed water temperature (34.6°C)
- η: efficiency of the plant (70%)
- Tg: temperature of waste gases (760°C)
- T0: atmospheric temperature (15°C)

Now, we can use the following equations to calculate the required information:

a) Mass of waste gas required:
Since the efficiency of the plant is 70%, we can use the equation: m = msteam / η
Substituting the values, we get:
m = (21,650 kg/hr) / 0.70 = 30,929 kg/hr

b) Temperature of gases leaving the evaporator:
We can use the formula for ideal gas law: P1V1/T1 = P2V2/T2
Since the waste gases are used for heating, the volume remains constant (V1 = V2). Therefore, we can rearrange the equation to find T2:
T2 = (P2/P1) * T1
Substituting the values, we get:
T2 = (0.5 MPa/101.325 kPa) * (760°C + 273.15) = 4,248.6°C

Temperature of gases leaving the superheater:
To find the temperature of gases leaving the superheater, we can use the same equation as above, but with the new pressure and temperature values:
T2 = (0.5 MPa/101.325 kPa) * (200°C + 273.15) = 972.4°C

Temperature of gases leaving the economizer:
To find the temperature of gases leaving the economizer, we need to use the energy balance equation:
msteam * Hsteam = mgas * Hgas + mwater * Hwater
where H represents enthalpy. We can rearrange this equation to find the temperature of gases leaving the economizer:
Tgas = (msteam * Hsteam - mwater * Hwater) / (mgas * Cpgas)
where Cpgas is the specific heat of the waste gases. Substituting the values, we get:
Tgas = [(21,