Showing posts with label Efficiency & performance. Show all posts
Showing posts with label Efficiency & performance. Show all posts

### 100 + formulae for power plant calculations

A-Boiler

1-Boiler efficiency direct method

Boiler efficiency = (Mass of steam flow X Steam enthalpy-Feed water flow at economizer inlet X Enthalpy-Attemperator water flow X Enthalpy) / (GCV of fuel X Fuel consumption)

2-Boiler efficiency by indirect method

Boiler efficiency = 100-Various losses

3-Theoretical air requirement for combustion

Theoretical air Thair = ((11.6 X C% + (34.8 X (H2-O2/8)) + (4.35 X %S))/100

Where C = % of carbon in fuel

H2 = % of Hydrogen present in fuel

S = % of sulphur present in fuel

4-Excess air requirement for combustion

%EA = O2% / (21-O2%)

Where O2 = % of oxygen present in flue gas

5-Mass of actual air supplied

AAS = (1 + EA / 100) X Theoretical air

6-Mass of flue gas

Mfg = Mass of Air + 1

6-Mass of dry flue gas

Mfg = Mass of Co2 in flue gas + Mass of Nitrogen in fuel + Mass of Nitrogen in combustion air + Mass of oxygen in flue gas + Mass of So2 in flue gas

Mfg =(Carbon % in fuel X Molecular weight of CO2 / Mol.weight of Carbon) + N2 in fuel + (Mass of actual air supplied X % of N2 in air i.e 77/100) + ((Mass of actual air – Mass of theoretical air) X 23/100) + S2 in fuel X Mol.weight of SO2 / Mol.weight of sulphur)

7-% of heat loss in dry flue gas

Heat loss = Mfg X Cp X (Tf-Ta) X 100 / GCV of fuel

Where,

Mfg = Mass of flue gas

Cp = Specific heat of flue gas in kacl/kg

Tf = Temperature of flue gas

Ta = Ambient air temperature

9-% of heat loss due to moisture in fuel

Heat loss = M X (584 + Cp X (Tf-Ta))  X 100 /  GCV of fuel

Where,

M = Moisture in fuel

Cp = Specific heat of flue gas in kcal/kg

10-% of heat loss due to moisture in air

Heat loss = AAS X humidity X Cp X (Tf-Ta) X 100/ (GCV of fuel)

Where,

AAS = Actual air supplied for combustion

Cp = Specific heat of flue gas in kcal/kg

Tf = Temperature of flue gas

Ta = Ambient air temperature

11-% of Boiler water blow down

Blow down % = (Feed water TDS X % of makeup water) X 100 / (Maximum permissible TDS in Boiler water –Feed water TDS)

12-Steam velocity in line

Velocity of steam in pipe line,V = Steam flow in m3/sec / Area of pipe line (A)

Steam flow in m3/sec = (Steam flow in kg/hr / Density of steam X 3600)

Area of pipe, A = Pi X D2 / 4

Where D is pipe internal diameter

13-Condensate flash steam calculation

Flash steam % = (H1-H2) X 100 / Hfg)

Where, H1 = Sensible heat at high pressure condensate in kcal/kg

H2 = Sensible heat of steam at low pressure in kcal/kg

Hfg = Latent heat of flash steam

14-Calculation of amount of heat required to raise the water temperature

Heat required in kcal=Mw X Cp X (T2-T1)

Where, Mw = Mass of water

Cp = Specific heat of water in kcal/kg (1 kcal/kg)

T1 = Initial temperature of water in deg C

T2 = Final temperature of water in deg C

15-Calculation of heat required to raise air temperature

Heat required in kcal=Mair X Cp X (T2-T1)

Where, Mw = Mass of water

Cp = Specific heat of flue gas in kcal/kg (0.24 kcal/kg)

T1 = Initial temperature of air in deg C

T2 = Final temperature of air in deg C

16-Surface heat loss calculation

S = (10 + (Ts-Ta) / 20) X (Ts-Ta) X A

S = Surface heat loss in kcal/hr m2

Ts= Hot surface temperature in deg C

Ta = Ambient air temperature in deg C

17-Dryness fraction of steam

X = Mass of dry steam / (Mass of dry steam + Mass of water suspension in mixture)

18-Heat content in wet steam

h = hf + xhfg

h= Heat content in saturated steam

x = Dryness factor of steam

Hfg =Enthalpy of evaporation

19-Heat content in dry saturated steam

h = hf + hfg

h= Heat content in saturated steam

Hfg =Enthalpy of evaporation

20-Heat content in superheated  steam

h = hf + hfg + Cps (Tsup - Ts)

h= Heat content in super heated steam

hfg =Enthalpy of evaporation

Cps = Specific heat of super heated steam

Tsup= Superheated steam temperature in deg C

Ts = Saturated temperature of steam in deg C

21-Calculation of Equivalent evaporation

Me = Ms X (h-hf) / hfg

Ms = Mass of steam

h = Steam enthalpy

hf= Feed water enthalpy

22-Factor of evaporation

Fe = (h-hf) / 539

23-Ash (Total) generation calculation

Ash generation in TPH = Fuel consumption per hour X % of ash in fuel / 100

24-Fly ash generation calculation

Fly ash generation in TPH = Fuel consumption per hour X % of ash in fuel X 80% / 100

25-Bottom  ash generation calculation

Bottom ash generation in TPH = Fuel consumption per hour X % of ash in fuel X 20% / 100

26-Calculation of ash generation in ESP

Ash generation in ESP in TPH = Fuel consumption per hour X % of ash in fuel X 80% X 80% / 100

27-Boiler safety valve blow down calculation

Blow down % = (Set pressure - Re seat pressure) X 100 / Set pressure

28-Calculation of attemperator water flow

Attemperator water flow  in TPH= Steam flow in TPH X (h1-h2) / (h2-h3)

h1 = Enthalpy of steam before desuper heating in kcal/kg

29-Economiser efficiency calculation

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

30-APH efficiency calculation

APH air side efficiency

ηAPHa = (Air outlet temp-Air inlet temp)) X 100 / (Flue gas inlet temperature -Air inlet temperature)

APH gas side efficiency

ηAPHg = (Flue gas inlet temp.-Flue gas outlet temp) X 100 / (Flue gas inlet temperature -Air inlet temperature )

31-Calculation of steam cost

Steam cost per ton = Steam enthalpy  in kcal/kg X Fuel price per ton/ (Boiler efficiency % X GCV of fuel used in kcal/kg)

32-Travelling grate Boiler heating surface calculation

Boiler heating surface (Appx) = Boiler capacity in kg/hr / 18

33-AFBC Boiler heating surface calculation

Boiler heating surface (Appx) = Boiler capacity in kg/hr / 22

34-Travelling grate slop fired Boiler heating surface calculation

Boiler heating surface (Appx) = Boiler capacity in kg/hr / 12

35-AFBC  slop fired Boiler (Low pressure up to 10 kg/cm2 WP) heating surface calculation

Boiler heating surface (Appx) = Boiler capacity in kg/hr / 8.2

36-Calculation of draught produced in Chimney

Hw = 353 X H (1/Ta – 1/Tg (Ma+ 1)/Ma)

H = Chimney height in meters

Ta = Atmospheric temperature in K

Tg = Flue gas temperature in K

Ma = Mass of air & Mass of flue gas = Ma+1

Also given as;

P = 176.5 X H / Ta

Hw = Chimney height in meters

Ta = Absolute atmospheric temperature in Kelvin

Hw = Draught in mmwc

37-Calculation of mass of flue gas flowing through chimney

Mg (kg/sec)= Density of gas (kg/m3) X Area of Chimney (m2) X Velocity of flue gas in Chimney (m/sec)

B-Turbine and Auxiliaries

1-Turbine heat rate calculation

a-Heat rate of Thermal power plant Turbine in kcal/kw =

Steam flow X (Steam enthalpy in kcal/kg-Feed water enthalpy in kcal/kg) / Power generation

b-Heat rate of Co-gen plant Turbine in kcal/kg =

Inlet steam flow X Enthalpy-(Sum of extraction steam flow X Their enthalpy + Exhaust steam X Enthalpy) / Power generation

i.e THR = ((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

Or

THR=((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

2-Turbine efficiency calculation

Efficiency = 860 X 100 /  Turbine heat rate

3-Steam condenser efficiency calculation

Condenser efficiency =Difference in cooling water inlet & outlet temperatures X 100/(Vacuum temperature-condenser Inlet temperature of cooling water)

Condenser efficiency = (T2 - T1) X 100/(T3 - T1)

T2: Condenser outlet cooling water temperature,

T1: Condenser inlet cooling water temperature,

T3: Temperature corresponding to the vacuum or absolute pressure in the condenser.

4-Vacuum efficiency calculation

Vacuum efficiency = (Actual vacuum in condenser X 100)/Max. Obtainable vacuum.

I.e

Vacuum efficiency in % =Actual vacuum X 100 / (Atmospheric pressure or barometric pressure-Absolute pressure)

5-Cooling tower range

Range = Cooling tower outlet water temperature-Cooling tower inlet water temperature

6-Cooling tower approach

Approach = Cooling tower outlet cold water temperature - Wet bulb temperature

7-Cooling efficiency calculation

Efficiency = Range X 100 / (Range + Approach)

8-Heat rejected or heat load of cooling towers

Heat load =Mass of circulating water X Specific heat of water Cp X Range

9-Cooling tower evaporation loss calculation

Evaporation loss in m3/hr = 0.00085 X 1.8 X Water circulation rate  m3/hr X Range

Evaporation loss in % = Evaporation loss X 100 / Water circulation rate  m3/hr

10-Cooling tower blow down loss calculation

Blow down loss in % = Evaporation loss X 100 / (COC-1)

Where COC: Cycles of concentration

Its generally calculated as;

COC = Conductivity in circulation water / Conductivity in makeup water

OR

COC = Chloride in circulation water / Chloride in makeup water

11-Calculation of mass of cooling water required to condenser steam in surface condensers

Mw = (Ms X (hfg X dryness fraction(x) + Cpw (T3 - Tc)))/(Cpw X (T2 - T1))

Mw = Mass of cooling water required in TPH

Ms = Mass of exhaust steam to condenser in TPH

Hfg = Enthalpy of evaporation at exhaust pressure in kcal/kg

Cpw = Specific heat of cooling water in kcal/kg

T3= Temperature at exhaust pressure in deg C

Tc= Temperature of condensate in deg C

T1=Cooling water temperature entering condenser in deg C

T2 = Cooling water temperature leaving condenser in deg C

12-Steam turbine wheel chamber pressure calculation (Appx)

Turbine wheel chamber pressure (kg/cm2 ) = (Turbine inlet pressure (kg/cm2 ) X Turbine operating load (MW) X 0.6) / Turbine rated capacity (MW).

13-Calculation of power generation in steam Turbine

Power generation in MW= Turbine inlet steam flow  in TPH X (Inlet steam enthalpy in kcal/kg- Exhaust steam enthalpy in kcal/kg) / 860

14-Power generation calculation in multi stage Turbines

Power generation in MW= Steam flow from 1st stage X (Inlet steam enthalpy in kcal/kg- 1st stage extraction steam enthalpy in kcal/kg) + Steam flow from 2nd  stage X (Inlet steam enthalpy in kcal/kg- 2nd  stage extraction steam enthalpy in kcal/kg) + Exhaust steam flow to condenser X (Inlet steam enthalpy in kcal/kg- Exhaust  steam enthalpy in kcal/kg) / 860

15-Calculation of work done per kg of steam in Turbine

Work done/kg of steam = Inlet steam enthalpy in kcal/kg-Exhaust steam enthalpy in kcal/kg

16-Calculation of steam required per per KWH

Steam required per KWH = 860 / (Work done per kg of steam)

Or

Steam required per KWH =860/(Inlet steam enthalpy in kcal/kg-Exhaust steam enthalpy in kcal/kg)

17-Thermal power plant efficiency calculation

Efficiency = 860 X Power generation / Heat input

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

18-Co gen-plant efficiency calculation

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)

19-HP heater steam consumption calculation

Steam flow in TPH = FW flow in TPH X (HP heater outlet FW temperature-HP heater inlet FW temperature) /(Steam enthalpy in kcal/kg-HP heater outlet condensate water enthalpy in kcal/kg)

Where, FW =  Feed water

20-Deaerator steam consumption

Mass of steam in TPH = (Deaeraor outlet Feed water flow in TPH X Enthalpy –CEP flow X Enthalpy-Makeup water X Enthalpy) / (Enthalpy of steam-Enthalpy of deaerator outlet water)

Note: Enthalpy in kcal/kg

Feed water, CEP water & Make up water flow in TPH

C-Pumps fans and air compressors

1-Centrifugal pumps hydraulic power consumption

Hydraulic power in Kwh = Flow (M3/sec) X Total head (m) X Fluid density (kg/m3) X g (m/s2) / 1000

2-Pump shaft power calculation

Pumps shaft power Ps = Hydraulic power / Pump efficiency

3-Pump electrical power calculation

Electrical power = Pump shaft power / Motor efficiency

4-Pump affinity laws

a-Q1/Q2 = N1/N2

Q1 & Q2 are pump flow at different RPM

N1 & N2 are pump speed

b-H1 / H2 = (N1)2 / (N2)2

Where H1 & H2 are pump head at different RPM

N1 & N2 are pump speed

c-P1 / P2 = (N1)3 / (N2)3

P1 & P2 are pump flow at different RPM

N1 & N2 are pump speed

5-Relation between head,flow ,power and impeller diameter

Q = D (Flow is directly proportional to impeller diameter)

H = D2 (Head is directly proportional to square root of impeller diameter)

P =D3 (Power is directly proportional to impeller diameter)

6-Relation between NPSHR, flow and speed

NPSHR = N2 (NPSHR is directly proportional to square root of speed)

That is as the flow and speed increase, pump need more NPSH

7-Fans volumetric flow calculation

Flow (m3/sec) = Velocity of fluid (m/sec) X Area of duct (m2)

8-Fans Mechanical efficiency calculation

Mechanical efficiency % = Flow (m3/sec) X Total pressure (mmwc) X 100 / (102 X power input to fan shift in KW)

9-Fans Technical efficiency calculation

Static efficiency % = Flow (m3/sec) X Static pressure (mmwc) X 100 / (102 X power input to fan shift in KW)

11-Fans affinity laws

a-Q1/Q2 = N1/N2

Q1 & Q2 are fans flow in m3/sec at different RPM

N1 & N2 are fans speed

b-SP1 / SP2 = (N1)2 / (N2)2

Where SP1 & SP2 are static pressure in mmwc of fan at different RPM

N1 & N2 are pump speed

c-P1 / P2 = (N1)3 / (N2)3

P1 & P2 are flow flow at different RPM

N1 & N2 are pump speed

11-Isothermal power of reciprocating compressors

P = P1 X Q X loge r/36.7

Where, P = Isothermal power

Q = Free air delivered by compressor in m3/hr

R = P2/P1

P1 & P2 are absolute inlet & deliver pressure respectively

10-Isothermal efficiency of reciprocating compressors

Isothermal efficiency = Isothermal power X 100 / Actual measured input power

11-Isothermal efficiency of reciprocating compressors

Isothermal efficiency = Free air delivered (m3/min) X 1007 / Compressor displacement (m3/min)

12-Compressor displacement = 3.142 X D2 X L X S X n X N

Where, D = Cylinder bore in meter

L = Cylinder stroke in meter

S = Compressor speed in rpm

n= 1 for single acting & 2 for double acting cylinders

N=No.of cylinders

13-Compressed air leakage calculation

% of leakage = T X 100 /  (T+t)

Or air leakage in m3/min = T X Compressor capacity (m3/min) / (T+t)

14-Calculation of intermediate pressure of reciprocating air compressors

P2 =SQRT ( P1 X P3)

Where P1,P2 & P3 are suction pressure, intermediate pressure and discharge absolute pressure respectively

D-Fuel handling

1-Minimum length of belt conveyor take up

Total belt length X 1.5%

2-Conveyor belt speed calculation

Belt speed (m/sec) = 3.142 X D X N / 60

Where, D= Head pulley diameter in meter

N = Head pulley speed in RPM

Head pulley speed = Moto RPM / Gear box reduction ratio

3-Conveyor start up tension calculation

T (N/mm)= P X 3.2 / (V X W)

Where,P = Power consumption of conveyor

V = Belt speed in m/sec

W = Belt width in mm

4-Tensile strength of belt

Initial tension of the belt X 5.4 / Belt splicing efficiency

E-Mechanical Maintenance

1-V pulley speed calculation

N1/N2 = D2/D1

N1 & N2 are speed in RPM of drive and non drive end pulleys

D1 & D2 are diameter (inch or mm) of drive and non drive end pulleys

2-Gear box output speed calculation

Gear box out put shaft speed = Motor RPM / Reduction ratio

3-Speed of pulley calculation

Pulley speed (m/sec) = 3.142 X D X N / 60

Where, D = Diameter of pulley in meter

N = Pulley rotary speed in RPM

4-V belt length calculation

L =∏ (R1+R2) + 2C + (R2+R1)2/C

Where, R1 & R2 are radius of DE & NDE pulleys

5-C is centre distance between two pulleys

6-Torque developed on a shaft

T = P X 60 / (2 X ∏ X N)

Where, P = Power consumption, N is speed of the shaft

7-Calculation of hub diameter of a shaft

Hub diameter = 2 X Shaft diameter

8-Bearing lubrication quantity calculation

Bearing lubrication quantity in grams = Bearing OD (D) X Width (B) X 0.05

9-Safe working load of steel wire rope of size D (inches)

SWL = 8D2

Safe working load of chain block = 80 X 0.4 X D2

Where 80 is the grade of chain block steel material

D is the link diameter in mm

12-Safe working load of Nylon lifting rope of  diameter D in mm

Safe working load of chain block = D2

13-Calculation of weight of steel plate

Weight in kg = Plate length (m) X width (M) X Thickness (m) X density of steel (kg/m3)

14-Calculation of weight of round steel plate

Weight in kg = (∏D2/4) X plate thickness in meter

D is diameter of plate in meter

15-Calculation of weight of hollow cylinder

Weight in kg = (∏R22X h- ∏R21X h) X steel density in kg/m3

Where, R1 & R2 are outer radius & inner radius of tank in meter

H is height of tank in meter

F-Electrical and Instrumentation

1-Single phase power consumption calculation

P = VI Cos θ

Where,Cos θ P is power consumption in Watts, V&I are Voltage in volts and current in Amps receptively

Cos θ is power factor

2-Three  phase power consumption calculation

P = 3VI Cos θ

3-Apparent power = V X I (Voltage X Current)

4-Real power = 3VI Cos θ

5-Reactive power of 3-phase power =3VI Sin θ

Reactive power of single-phase power =VI Sin θ

6-Resistance of a conductor

R = ƍ X L/A

R = Resistance in Ohm-meter or Ohm-cm

L & A are Length and area of conductor measured in meter & m2

7-Voltage, current and resistance relation

Voltage = Current X Resistance, i.e. V = IR

8-Resistance of a conductor at temperature t °C is given by

Rt = R0 (1 + α t) Where α is temperature coefficient at t °C.

8-Electrical Power calculation

Power= Work done watt-sec./Time in second

P = VI X t/t i.e. VI Watts

P = I2R… Watts

9-Power factor calculation

Power factor (cosՓ) = Active power (KW) / Apparent power (KVA)

10-Synchronous speed calculation

Synchronous speed/RPM = (120 X frequency)/No. of poles.

11-Absolute Pressure = Gauge Pressure + Atmospheric Pressure

12-Relation between flow and differential pressure (DP). Flow (Q) = √(DP

Q1/Q2 = (√∆P1/∆P2)

13-Compensated flow calculation

Compensated flow= Raw value from flow meter X Sqrt ((Absolute Design temperature/Absolute Operating temperature) X (Absolute operating pressure/Absolute design pressure))

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