How do you calculate Steam turbine heat rate and efficiency???

How do you calculate the Turbine efficiency?

Turbine efficiency is the ratio of heat out put to the heat input

Here, heat input is heat content in inlet steam and out put is power generation.

Actually, total  power generation =Power generated on generator terminal / (Gear box efficiency X Alternator efficiency).

What is Turbine heat rate?

Turbine heat rate is the ratio of total heat required to generate unit power.

Turbine efficiency = 860 X 100 / Turbine heat rate

Thermal power plant turbine heat rate

= Steam flow (Main steam enthalpy-Feed water enthalpy) / Power generation

Co-generation Turbine heat rate:

=((Steam Flow x Steam Enthalpy +Makeup Water flow x Its Enthalpy+ RC Flow x RC Enthalpy)-(Process-1 steam flow x its Enthalpy + Process-2 steam flow x Its Enthalpy+ FW Flow x FW Enthalpy)) /Power Generation

Co-generation Turbine heat rate is also calculated as;

((Steam Flow x Steam Enthalpy)-(1St EXT Flow x Its Enthalpy + 2nd Ext flow x its Enthalpy + 3rd Ext flow x Its Enthalpy+ Exhaust Steam flow x its Enthalpy)) /Power Generation

Calculations:

A thermal power plant is generating 55 MW power at specific steam consumption 3.7 MT/MW and at pressure and temperature 110 kg/cm2 and 540 deg C respectively.Calculate the Turbine heat rate and  efficiency if its feed water inlet temperature at economizer is 215 deg C

Turbine inlet steam flow = 55 X 3.7 = 203.5 TPH

Enthalpy of inlet steam at rated pressure and temperatures = 821 kcal/kg

Enthalpy of feed water = 217 kcal/kg

Thermal power plant turbine heat rate= Steam flow (Main steam enthalpy-Feed water enthalpy) / Power generation

THR = 203.5 X (821-217) / 55

THR = 2234.8 kcal/kwh

Turbine efficiency = 860 X 100 / 2234.8

Turbine efficiency = 38.48%

A back pressure turbine is generating 7.5 MW load at specific steam consumption 7.5 MT/MW, calculate the turbine heat rate and efficiency if inlet steam pressure and temperatures are 64 kg/cm2 and 485 deg C and exhaust steam parameters are 4 kg/cm2 and 165 deg C

Inlet steam flow = 7.5 X 7.5 = 56.25 TPH

Enthalpy of inlet steam= 810 kcal/kg

Enthalpy of exhaust steam = 665 kcal/kg

Turbine heat rate = (Inlet steam flow X Enthalpy-Exhaust steam flow X Enthalpy) / Power generation

Turbine heat rate =(56.25 X 810-56.25 X 665) / 7.5

Turbine heat rate = 1087.5 kcal/kw

Turbine efficiency = 860 X 100/ Heat rate

= 860 X 100/1087.5

= 79%

The operation details of a 22 MW condensing cum extraction turbines are as below, calculate its heat rate & efficiency

 SL No Particular UOM Value 1 Turbine inlet steam pressure Kg/cm2 88 2 Turbine inlet steam temperature Deg C 515 3 Turbine inlet steam flow TPH 120 4 Process steam flow TPH 65 5 Process steam pressure Kg/cm2 2.0 6 Process steam temperature Deg C 140 7 Exhaust steam pressure Kg/cm2 -0.88 7a Exhaust steam flow TPH 55 8 Process return condensate flow TPH 58 9 Process condensate temperature Deg C 115 10 DM Make up water flow TPH 9 11 DM Make up water temperature Deg C 27 12 Feed water flow TPH 121 13 Feed water temperature Deg C 145

Solution:

Enthalpy of turbine inlet steam = 818 kcal/kg

Enthalpy of process steam =655 kcal/kg

Enthalpy of feed water= 147 kcal/kg

Enthalpy of return condensate=116 kcal/kg

Enthalpy of DM water = 25 kcal/kg

Enthalpy of exhaust steam in( liquid form) = 52 kcal/kg

Co-generation Turbine heat rate:

=((Steam Flow x Steam Enthalpy +Makeup Water flow x Its Enthalpy+ RC Flow x RC Enthalpy)-(Process-steam flow x its Enthalpy + FW Flow x FW Enthalpy)) /Power Generation

=((120 X 818 + 9 X 25 + 58 X 115)-(65 X 655 + 121 X 147)) / 22

=2031.5 kcal/kg

Turbine efficiency = 860 X 100 / 2031.5

= 42.33%

Same can be calculated by another formula

THR=((Steam Flow x Steam Enthalpy)-(EXT Flow x Its Enthalpy ++ Exhaust Steam flow x its Enthalpy)) /Power Generation

THR =(120 X 818 -65 X 655 - 55 X 52) / 22

THR =2396.5 kcal/kg

Turbine efficiency = 860 X 100 / 2396.5

= 35.88%

Read more>>>powerplant and calculations

How do you calculate power plant efficiency???

Efficiency of the power plant is calculated based on heat input and out put.

Power plant efficiency = Heat out put X 100 / Heat out put

In power plant, generally heat input is fuel, make up water and condensate return water from process.

Heat out put is power generation.

The formula for efficiency calculation is different for different plants.

Efficiency of the power plant is given as

Efficiency = 860 X 100 / Heat rate

1-For thermal power plants efficiency is calculated as;

Efficiency = 860 X Power generation / Heat input

Efficiency = 860 X PG X 100 / (Fuel consumption X Fuel GCV)

2-For co generation plants heat rate is calculated as;

Efficiency = 860 X Power generation X 100 / (Fuel consumption X GCV + Make up water X Make up water enthalpy + Return condensate water X Enthalpy-Process steam flow X Enthalpy)

3-Cogen plant Efficiency is also calculated as;

Efficiency = 860 X Boiler efficiency X 100 / Turbine heat rate

Calculation:

1.Calculate the efficiency of power plant having heat rate 3451 Kcal/kwh

Efficiency of the power plant = 860 X 100 / Heat rate

Efficiency of the power plant = 860 X 100 / 3451

Efficiency of the power plant = 24.92%

Read power plant O&M reference books

2.A 75 MW Thermal power plant consumes 1100 MT coal per day, calculate the plant efficiency, consider the GCV of coal 5000 Kcal/kg

Efficiency of the plant = 860 X 24 X 75 X 100 / (1100 X 5000)

Efficiency of the plant = 28.15%

3. A 29 MW thermal power plant is having Turbine of heat rate 2798 kcal/kwh, which consumes steam at the rate of 4.2 MT/MW from a boiler having efficiency 69%.Calculate the efficiency of power plant

Efficiency = 860 X Boiler efficiency X 100 / Turbine heat rate

Efficiency = 860 X 0.69 X 100 / 2798

Efficiency = 21.2%

4. A 30 MW biomass Co generation plant consumes 1750 MT fuel per day and supplies 2880 TPH steam to process at pressure 2 kg/cm2 & 135 deg C, in turn receives 90% return condensate at 119 deg C temperature.The make up water for this plant is 610 m3 at temperature 27 deg C.Calculate the efficiency of the plant, consider GCV of biomass fuel 2250 kcal/kg.

Efficiency of Co-gen plant  = 860 X Power generation X 100 / (Fuel consumption X GCV + Make up water X Make up water enthalpy + Return condensate water X Enthalpy-Process steam flow X Enthalpy)

Enthalpy of process steam at 2 kg/cm2 and 135 deg C is 652 kcal/kg

Enthalpy of return condensate water is 121 kcal/kg

Enthalpy of make up water at 27 deg C is 27.2 kcal/kg

Efficiency of Co-gen plant  = 860 X 30 X 24 X 100 / (1750 X 2250 + 610 X 27.2 + 2880 X 80% X 121 X 2880 X 652)

Efficiency of Co-gen plant  = 860 X 30 X 24 X 100 / (1750 X 2250 + 610 X 27.2 + 2880 X 80% X 121 - 2880 X 652)

Efficiency of Co-gen plant = 26.29%

5. A thermal power plant operating at 125 MW operating  at pressure 110 kg/cm2 and temperature 545 deg C.A AFBC boiler of efficiency 84% consumes 379 TPH Feed water at temperature 200 degC to generate 375 TPH steam.Calculate the efficiency of the thermal power plant.

We have, Turbine heat rate = (Inlet steam flow X Enthalpy-Feed water flow X Enthalpy) / Power generation

Turbine heat rate = 375 X 821-379 X 202) / 125

Turbine heat rate = 1850.5 kcal/kwh

Turbine efficiency = 860 X 100 / 1850.5

Turbine efficiency = 46.5%

Power plant efficiency = Turbine efficiency X Boiler efficiency = 46.5 X 0.84 =39.06%

For more calculations read Powerplant and calculations

How do you calculate the efficiency of pumps???

How do you calculate the efficiency of a pump?

Efficiency of the pump is the ratio of output power to the input power

Pump efficiency = Output power X 100 / Input power

Centrifugal pumps efficiency varies from 40% to 95% well.

Pump efficiency is equal to the power of the water/liquid produced by the pump divided by the pump’s shaft power input.

A pump’s output power is determined by how much water and how much pressure it delivers

On what factors pumps efficiency depends on?

Pumps efficiency depends on

• In put power
• Output power
• Type of liquid
• Fluid temperature
• Flow
• Suction & discharge head
• Losses & leakages
• Fluid viscosity
• Pump operating load
• Pumps internal frictions

What do you mean by volumetric efficiency of a pump?

It is the ratio of actual flow delivered by the pump to the theoretical flow

How do you calculate the Mechanical or hydraulic efficiency of the pump?

Mechanical/Hyd.efficiency = Pump output power X 100 / Pump input power or pump shaft power

Mechanical efficiency is also calculated as

= Theoretical torque required to drive the pump X 100 / Actual torque provided to drive the pump

Calculations:

A centrifugal pump delivers 0.2 m3/sec flow at total head 27 m, calculate its hydraulic power. Assume density of water 995 kg/m3

Pump hydraulic power = Pump flow in m3/sec X pump total head in meter X Fluid density in kg/m3 X 9.81 m/sec2 / 1000

Pump hydraulic power = 0.2 X 27 X 995 X 9.81 / 1000

Pump hydraulic power = 52.7 KW

A centrifugal pump of capacity 0.05 m3/sec flow has to lift the water from 3.5 m deep well & has to discharge the water at 45 meter height. Calculate the pump efficiency if its shaft power is 30 KW

Assume water density 998 kg/m3

Pump hydraulic power = Pump flow in m3/sec X pump total head in meter X Fluid density in kg/m3 X 9.81 m/sec2 / 1000

Total head = Discharge head + Suction lift

Total head H = 45 + 3.5 = 48.5 meter

Pump hydraulic power = 0.05 X 48.5 X 998 X 9.81 / 1000

Ph = 23.74 KW

Pump efficiency =Pump hydraulic power X 100 / Pump shaft power

Pump efficiency =23.74 X 100 / 30

Pump efficiency =79.13%

A centrifugal pump of delivering  0.65 m3/sec flow at 75 meter discharge head, pump has positive suction head around 2.7 meter from overhead tank.Pump efficiency is 59%, calculate the motor input power if efficiency power if efficiency of motor is 92.5%.

Assume water density 1000 kg/m3

Pump hydraulic power = Pump flow in m3/sec X pump total head in meter X Fluid density in kg/m3 X 9.81 m/sec2 / 1000

Total head H = 75 -2.7 = 72.3 meter

Pump hydraulic power = 0.65 X 72.3 X 1000 X 9.81 / 1000

Ph = 461 KW

Pump efficiency =Pump hydraulic power X 100 / Pump shaft power = Ph X 100 / Ps

59 =461 X 100 / Ps

Ps = 781.35 KW

Motor efficiency = Pump shaft power X 100 / Motor input power =Ps X 100 / Pm

92.5 = 781.35 X 100 / Pm

Pm = 844.7 KW

A centrifugal pump of efficiency 63% develops hydraulic power 27.5 KW, calculate the motor efficiency if motor input power is 45 KW

Pump shaft power, Ps = Pump hydraulic power Ph / Efficiency of pump

Ps = 27.5 / 0.63 =43.65 KW

Motor efficiency = Pump shaft power X 100 / Motor input power

Motor efficiency= 43.65 X 100 / 45

Motor efficiency = 97%

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How to calculate ESP efficiency??

On what factors ESP efficiency depends on?

ESP efficiency depends on following factors.

• Dust collection area of ESP
• Dust particles size
• Dust or flue gas volume
• Resistivity of dust particles present in flue gas

What do you mean by Corona Power ratio?

Corona power ratio is the ratio of power consumed in watts to the flue gas flow in cubic feet per minute.

Corona power ratio = Power consumed by ESP in watts / Flue gas flow in CFM

This tells us about the energy consumed in filtering one cubic foot of flue gas per minute. The corona power ratio affects the efficiency of an electrostatic precipitator. Higher the corona power ratio, higher is the efficiency of the electrostatic precipitator

What do you mean by specific collecting area (SCA) & how do you calculate it?

It is the ratio of total collecting surface area of the ESP to the flue gas flow rate

SCA = Total collection area in m2 / Gas flow rate in m3/sec

SCA = m2/m3/sec

What do you mean by Aspect ratio in ESP?

It is the ratio of length of ESP to its Height

It should be in the range of 0.5 to 2

Calculation:

Calculate the aspect ratio of an ESP of total length 12 meter having its collecting plates height 11 meter.

Aspect ratio (AR) = Length of ESP / Height of ESP

Aspect ratio (AR) = 12/11 =1.09.

What is the treatment time in ESP having flue gas flow rate 90 m3/sec at velocity 0.7 m/sec.ESP having total 4 nos of fields each of length 3.5 meter.

We have, total length of ESP = 3.5 X 4 = 14 meter

Velocity of flue gas in ESP = 0.7 m/sec

So, total Treatment time for flue gas = 14 / 0.7 =20 seconds

Read power plant O&M reference books

An ESP consumes 7 KW power for treating flue gas of 17 m3/sec, calculate its Corona power ratio.

Corona power ratio = Power consumed by ESP in watts / Flue gas flow in CFM

We have flue gas flow = 17 m3/sec = 599.9 X 60= 35994 CFM

CPR = 7000 / 35994 = 0.2

An ESP handles total flue gas at the rate of 61920 m3 /h., its specific collecting surface area is 131.9 m2/m3/sec, calculate the efficiency of ESP if ash particles migration velocity is 5.46 cm/sec.

Solution:

Given that,

Flue gas flow in ESP, Q = 61920 m3/hr / 3600 = 17.2 m3/sec

Total collecting area A= 131.9 X 17.2 =2268.68 m2

Migration velocity of dust particles, V = 5.46/100 = 0.0546 m/sec

Efficiency of ESP = 1–eˆ (-AV/Q) X 100

= 1– eˆ (-2268.68 X 0.0546/17.2) X 100

ηESP = 99.92%

Read more>>> for such calculations powerplant & Calculations

Also read ESP troubleshooting guide

How do you calculate the efficiency of Economiser in Boiler??

What is the Economiser in power plants?

It’s the heat exchanger used in Boilers to recover the heat from exhaust flue gases.

What are the functions of economisers in Boilers?

Functions of economisers:

It recovers the heat from flue gas leaving the boiler, there by reduces the losses

It helps in raising the feed water temperature, there by reduces the fuel consumption

It increases the Boiler efficiency

It lowers the power plant operation cost

What are the different types of economisers?

Types of economisers

Pressurized economisers

Non pressurized economisers

Steaming type

Non steaming pipe

What do you mean by steaming type economisers?

Economisers where only sensible heat is added to feed water

What do you mean by non-steaming type economisers?

Economisers where sensible heat and part of latent is added to feed water

Efficiency Calculations:

 ηEco. = (Economiser outlet feed water temperature Two-Economiser inlet feed water temperature Twi)  X 100 / (Economiser inlet flue gas temperature Tfi- Economiser inlet feed water temperature Twi)

Example:

Calculate the economiser effectiveness, whose feed water inlet & outlet temperatures are 160 Deg C & 240 Deg C respectively & flue gas inlet & outlet temperatures 390 deg C & 220 deg c respectively.

Solution:

Twi = 160 deg C

Two = 240 deg C

Tfi = 390 deg C

Tfo = 220 deg C

ηEco = (Two-Twi) X 100 / (Tfi-Twi)

ηEco = (240-160 ) X 100 / (390-160)

ηEco= 34%

In an non steaming economiser of efficiency 51%, feed water inlet and outlet temperatures are 105 deg c & 160 deg C respectively, calculate the flue gas temperature entering the economiser

Solution:

Twi = 105 deg C

Two = 160 deg C

Tfi = 370 deg C

Tfo = ? deg C

ηEco= 51%

ηEco = (Two-Twi) X 100 / (Tfi-Twi)

51= (160-105 ) X 100 / (Tfi-105)

Tfi X 51-105 X51 = 5500

Tfi = 212.8 deg C

A economiser inlet feed water & flue gas temperature are 125 deg C and 405 deg C respectively, calculate the feed water leaving the economiser, consider efficiency of economiser 43%

Solution:

Twi = 125 deg C

Two = ? deg C

Tfi = 405 deg C

ηEco= 43%

ηEco = (Two-Twi) X 100 / (Tfi-Twi)

43= (Two-125 ) X 100 / (405-125)

12040 = 100 X Two-12500

Two = 245.4 deg C

For more calculations related to power plant read Powerplant & Calculations

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