# Finding the amount of sulfur dioxide

## Homework Statement

A coal-fired steam power plant operates on the ideal Rankine cycle. Feedwater from the
condenser at P1= 10 kPa is pumped to the boiler at P2= P3 = 20 MPa, where it is superheated and exits the boiler at T3 = 550 °C.
The moisture content in the turbine is not to exceed 12% (i.e. steam quality is to be
maintained above x = 0.88 throughout the turbine). Up to two reheat stages can be added to
the steam cycle to satisfy this requirement.
If needed, one stage can be added to reheat the steam to T5 = 525 °C at P4 = P5 = 10 MPa. If
more reheating is required, a second stage can be added to reheat the steam to T7= 500 °C at
P6= P7 = 2.5 MPa.

(a). How many reheat stages are required for this power plant (no reheat, single reheat, or
(b). What is the thermal efficiency ηth of the power cycle?
(c). Determine the annual emission of sulfur dioxide, mSO2, in metric tons, from this power
plant, if the net generating capacity of the plant is 600 MW, and the boiler is 88%
efficient in transferring combustion heat into the feedwater superheat and steam reheat
stages. The boiler burns, to completion, Power River Basin coal that has a heating value
of 22,800 kJ/kg and contains 0.46 wt% sulfur.
Assume that all of the sulfur content of the coal is emitted as SO2 in the combustion flue gas, and that the coal-burning plant has a capacity factor of 0.85; i.e. the boiler is operational for 85% of the hours in one calendar year. (1 metric ton = 1000 kg)

## Homework Equations

Energy balance equations.

## The Attempt at a Solution

I completed the first 2 parts of the problem and I found out that one reheating stage is enough to active a steam quality more than 88.2%. I also calculated the thermal efficiency of 38/6% of this power plant.
My question is about part 3. How can I approach?

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Borek
Mentor
Mass of coal used per year -> mass of sulfur -> mass of SO2.

Shouldn't I have the heating value of coal in order to find the amount of coal?

Borek
Mentor
Have you read the question you posted, or have you just copy pasted it?

I absolutely read the question (I didn't post the last reply). I calculated the annual power generated in power plant. Is the mass of sulfur going to be 0.46% of the mass of the coal because it says "and contains 0.46 wt% sulfur" ?

Thank you

Borek
Mentor
Sorry, I didn't realize it wasn't you answering, my mistake.

About sulfur: yes, that would be my way of understanding the information given.

Thanks for the reply. Here is what I did:
600MW*365*24*3600 = 18.9216*10^12 kJ/year
18.9216*10^12 kJ/year *(capacity factor "0.85") = 16.0834*10^12 kJ/year <==actual output
Amount of coal = (16.0834 *10^12 kJ/year)/22800 kJ/kg = 7.0541*10^8 kg/year (coal)
Boiler's efficiency=88% => (7.0541*10^8 kg/year)/0.88 = 8.016*10^8 kg/year (coal)
amount of sulfur= 0.46*3.687*10^8 kg/year
----------------
Does it look good?

Thanks

I came from ScienceForums, when i saw your question there i googled it because it looked like a textbook question, and stumbled upon this site, so.... i'll just paste the same reply i posted there (after becoming a new member at PhysicsForums):

I don't think the value of quality you found is correct...
stage 5 is defined by T = 525 C and P = 10 MPa this gives h = 3437.7 and s = 6.6777
Then when this is extracted through the turbine we have that at stage 6: P = 10 kPa and s = 6.6777 (which is the same entropy as stage 5)
if you look at 10 kPa: s_f = 0.6493 s_g = 8.1502 and so s = 6.6777 gives you a quality of 80.35% not 88% (so this means in this question you need another reheat)

Given 600MW and the time the plant is functional in one year find the heat transferred to the steam
Then find the heat of combustion of coal
then find the mass of coal given the heating value
then use the wt% of sulfur to find the mass of sulfur

Borek
Mentor
Sulfur is not sulfur dioxide yet. Other than that I am not going to comment.

that is correct
moles of sulfur = moles of sulfur dioxide
then you use the molar masses to get mass of SO2