Steam Flow Compensation for Distributed Control Systems

Steam Flow Compensation for Distributed Control Systems

Steam Flow Compensation Equations for Distributed Control Systems By Tom Carter Principal Control Systems Engineer, Descon Engineering March 1, 2001

Summary Temperature and Pressure compensation of steam flow corrects for two factors: 1) changes in Specific Volume (or density) of the steam and 2) thermal expansion of the metal flow nozzle or orifice plate. The Steam Flow Compensation Factor for Specific Volume is a function of both Temperature and Pressure. The specific volume factor is calculated from "Steam Tables". A polynomial equation can be used in place of a table to calculate this Flow Compensation. The Thermal-expansion correction factor is a function of temperature only and is easily calculated. These two factors, along with the Meter Factor are multiplied with the square root of the measured differential pressure to yield a Temperature and Pressure compensated Steam Flow. The smaller the range of Temperature and Pressure, the smaller the error in the Specific Volume Factor calculated from a polynomial equation compared to an actual table of values. The uncompensated flow would result in errors up to 18.5% over the same range of P and T. The traditional compensation factor used is the ratio of square root of T and design P versus design T and P. The traditional yields an error of 1.3 %. An error of less than 0.3% can be achieved for an operating range from 860 DegF to 1100 DegF and 1500 Psia to 2000 Psia using the polynomial described: an improvement in accuracy by over 1%. The polynomial equation is proportional to Pressure and inverse square root of Temperature. A polynomial proportional to Pressure and Temp (i.e. no square root used) gives similar results with slightly higher errors over narrow range of T and P. The coefficients of these polynomial equations can be calculated in an EXCEL spreadsheet using simple slope and intercept functions. Boiler Main Steam Flow and Turbine Steam Flow for the Hunters’ Point Power Plant are used as examples.

Introduction Steam flow is traditionally expressed as a mass flow, usually in thousands of pounds per hour (KPPH or KLB/Hr). The density of steam changes with Temperature and Pressure of the steam in a very non-linear function. This results in very large mass flow errors (18 % and more ) when using differential Pressure flow devices such as orifice plates, flow nozzles and venturis without temperature and pressure compensation. Steam Tables list the specific volume (cubic feet / lb) for various values of Temperature and Pressure. The specific volume, based on temperature and pressure of the steam, can be used to correct (or compensate) the measured flow for actual conditions. Temperature and Pressure compensation of Steam Flow uses the square root of the design specific volume divided by the square root of actual specific volume of steam. The compensation Factor for Specific Volume (F

) is calculated as:

sv

http://www.desconengineering.com/WhitePapers/SteamFlow/Steam_Flow_Compensation.htm(1 of 12)1/14/2009 12:23:08 PM


Equation 1.0 Design conditions are the hypothetical values of temperature and upstream pressure of Steam when calculating the Flow Coefficients of the flow meter (e.g. orifice, venturi, flow nozzle). The design conditions are usually supplied by the meter manufacturer, along with the meter factor. Otherwise, a meter factor must be calculated using complex series of equations and tables from textbooks, for example Flow Measurement Engineering Handbook by R. W. Miller (1983). Actual conditions are the real-time upstream pressure and temperature of the steam as measured by the monitoring and control system. In most monitoring and control systems, the temperature and pressure Compensated Steam Flow is calculated as:

Equation 2.0 Where: q

is Steam Flow in KLbs/Hr (i.e. the compensated steam flow),

M

F

SV

F

a

F

is the Specific Volume Compensation Factor (based on Temperature and Pressure)

is the Thermal Expansion Correction Factor (based on Temperature)

M

is the meter factor (typically equal to maximum flow divided by the square root of max differential pressure),

and h

w

is the measured differential pressure across the flow meter (typically in inches H 2O).

Specific Volume Flow Compensation Factor (F

) Tables

SV

The most accurate means to calculate or derive the Specific Volume Compensation Factor (F

SV

) is to use a ‘look-up’ table of flow

compensation coefficients based on Temperature and Pressure of the Steam. This is essentially a three dimensional chart : (F

SV

fxn(T,P). A simple chart can be constructed by using the Steam Tables to look up specific volume at various temp and pressures. Then calculating the square root of the ratio of design specific volume / actual specific volume for T and P.


)=


Flow correction Factors (F

SV

)

for Design P=1830psig (1844.7psia) and 1000 DegF Design Specific Vol = 0.431289 (cu-ft / lb) Hunters’ Point P.P. Main Steam Flow Press (Psia)

1000

1100

1200

1300

1400

1500

1600

1700

1750

1800

1850

1900

2000

Temp DegF 650

0.8747 0.9271 0.9792 1.0316 1.0843 1.1382 1.1937 1.2514 1.2813 1.3121 1.3439 1.3769 1.4480

700

0.8422 0.8903 0.9376 0.9844 1.0308 1.0773 1.1238 1.1709 1.1946 1.2185 1.2426 1.2672 1.3169

750

0.8152 0.8603 0.9043 0.9475 0.9901 1.0321 1.0739 1.1153 1.1362 1.1570 1.1776 1.1984 1.2404

800

0.7919 0.8347 0.8763 0.9169 0.9566 0.9957 1.0342 1.0723 1.0912 1.1101 1.1289 1.1476 1.1851

860

0.7674 0.8081 0.8474 0.8857 0.9230 0.9595 0.9953 1.0305 1.0478 1.0652 1.0824 1.0994 1.1335

900

0.7528 0.7923 0.8304 0.8673 0.9034 0.9385 0.9728 1.0065 1.0233 1.0398 1.0562 1.0724 1.1047

960

0.7328 0.7708 0.8073 0.8426 0.8770 0.9105 0.9431 0.9751 0.9908 1.0064 1.0219 1.0372 1.0675

1000 0.7206 0.7577 0.7933 0.8277 0.8612 0.8937 0.9254 0.9564 0.9716 0.9867 1.0016 1.0164 1.0456 1060 0.7037 0.7395 0.7740 0.8073 0.8395 0.8708 0.9012 0.9309 0.9455 0.9600 0.9742 0.9885 1.0164 1100 0.6932 0.7283 0.7621 0.7946 0.8265 0.8567 0.8865 0.9155 0.9297 0.9438 0.9577 0.9715 0.9986 1160 0.6784 0.7126 0.7455 0.7770 0.8076 0.8373 0.8357 0.8625 0.9078 0.9215 0.9349 0.9482 0.9743 Table 1.0 – Steam Flow Spec. Vol. Compensation Factors- Main Steam Flow – Hunters’ Point P.P: based on Steam Tables by Keenan, Keyes, Hill and Moore (1969)

Table Note – The Bailey Flow nozzle specification Sheet dated 2/14/58 listed the design specific volume as .4306 cu. Ft./lb. Maximum capacity of 1,400,000 lb/hr and max Meter Differential as 331 inches of water. Some DCS provide steam tables or some other method to implement a table that can be used to calculate a flow compensation coefficient for actual T and P. But for many Control systems, there is not an easy way to implement tables. For example, most DCS (Distributed Control System) do not provide "two-input" table functions or "x-y-z" table functions required to do Temperature and Pressure based Flow coefficients.

Traditional Spec. Vol. Compensation Factors (F ) error > 1% SV If steam tables or x-y-z table functions are not available in the Control System, the traditional solution is to assume steam is an ideal gas and use the ideal gas law to compensate for T an P effects on density. The smaller the assumed operating range, the more accurate the approximation. The traditional compensation Factor for Specific Volume (F

) is calculated as:

sv

Equation 2.1



The traditional yields an error of 1.3 % for an operating range from 860 DegF to 1100 DegF and 1500 Psia to 2000. Error of over 3% for larger ranges of T and P.

% Error Traditional Gas Density Compensation F

SV

Hunters’ Point P.P.Boiler Main Steam Flow – 5.5% error for Design P=1830psig (1844.7psia) and 1000 DegF Design Specific Vol. = 0.431289 (cu-ft / lb.) Press Psia

1000

1100

1200

1300

1400

1500

1600

1700

1750

1800

1850

1900

2000

Temp DegF 650

4.40

3.31

2.16

0.93

-0.35

-1.73

-3.23

-4.85

-5.71

-6.62

-7.57

-8.58

-10.81

700

4.49

3.67

2.82

1.93

1.01

0.04

-0.95

-2.00

-2.55

-3.10

-3.68

-4.27

-5.49

750

4.29

3.64

2.99

2.30

1.60

0.89

0.14

-0.61

-1.01

-1.41

-1.81

-2.21

-3.07

800

3.95

3.43

2.91

2.36

1.82

1.25

0.68

0.09

-0.21

-0.51

-0.82

-1.12

-1.77

860

3.45

3.05

2.63

2.21

1.78

1.35

0.90

0.45

0.23

0.00

-0.24

-0.46

-0.94

900

3.09

2.74

2.38

2.02

1.65

1.28

0.91

0.53

0.33

0.14

-0.06

-0.25

-0.65

960

2.54

2.25

1.97

1.68

1.38

1.09

0.79

0.48

0.33

0.17

0.02

-0.14

-0.44

1000

2.17

1.92

1.67

1.42

1.16

0.90

0.64

0.37

0.25

0.11

-0.02

-0.15

-0.42

1060

1.63

1.42

1.22

1.00

0.80

0.58

0.37

0.16

0.05

-0.06

-0.16

-0.28

-0.50

1100

1.27

1.09

0.91

0.73

0.49

0.36

0.17

-0.02

-0.11

-0.21

-0.30

-0.39

-0.58

1160

0.76

0.61

0.46

0.31

0.15

-0.01

3.47

3.34

-0.39

-0.47

-0.55

-0.62

-0.78

Table 2.1 - %error traditional gas T and P compensation eqn 2.1 – Boiler Main Steam Flow Specific Volume coefficient

Polynomial Equation to calculate Spec. Vol. Compensation Factors (F ) SV If steam tables or x-y-z table functions are not available in the Control System, the solution is to use a polynomial equation that can replicate parts of the table. The smaller the assumed operating range, the more accurate the approximation The polynomial equation with the best fit is proportional to Pressure and the inverse of the square root of Temperature. This is consistent with the engineering mass flow equations for vapor. Polynomial proportional to Pressure and the square root of Temperature or simply to Pressure and Temperature can also be used in cases where the control system does not allow inverse or square root calculations. The difference in the three methods is the range of acceptable error. All three methods are approximations to the actual table result in error as actual T and P deviate from design. For example, a maximum error of 0.3% can be achieved over and operating range from 860 DegF to 1100 DegF and 1500 Psia to 2000 Psia using a polynomial proportional to Pressure and inverse square root of Temperature . The uncompensated flow would result in errors up to 18.5% over the same range of P and T.

Equation 3.0 – Spec. Vol. Flow Compensation Factor polynomial Where,

mSLOPES is the slope of m T1 through mTn (i.e. slope of slopes). http://www.desconengineering.com/WhitePapers/SteamFlow/Steam_Flow_Compensation.htm(4 of 12)1/14/2009 12:23:08 PM


bSLOPES is the intercept of m T1 through mTn (i.e. intercept of slopes). mINTERCEPTS is the slope of b T1 through bTn (i.e. slope of intercepts). bINTERCEPTS is the intercept of b T1 through b Tn (i.e. intercept of intercepts). mT1 is the slope of F

SV

or F

SV 1

SV

SV n

SV

for constant Temperature ( F

SV

SV 1

SV

SV n

= fxn(,P) at Constant Tn)


= fxn(,P) at Constant T1)


= fxn(,P) at Constant Tn)

SV

= mT1 (P) + b T1

bTn is the intercept of F or F

SV

= mT1 (P) + b Tn

bT1 is the intercept of F or F

= fxn(,P) at Constant T1)

= mT1 (P) + b T1

mTn is the slope of F or F


SV

= mT1 (P) + b Tn

The method is four steps.

1. First generate a linear curve fit on several rows in a table of Flow Coefficients. This generates a series of linear equations of Fsv versus Pressure. F = mT1 (P) + bT1 SV 1 2. Second, enter the slopes and intercepts in a table versus the inverse of square root of temperature: mT1 , mT2 , mT3 ,… mTn , and bT1 , bT2, bT3 ,… bTn

3. Third, generate a curve fit of the Slopes versus inverse Square Root of Temperature, this yields a slope and an intercept: mSLOPES and bSLOPES 4. Fourth generate a curve fit of the Intercepts versus inverse Square Root of Temperature, this yields a slope and an intercept : mINTERCEPTS and bINTERCEPTS Developing an acceptable accuracy is by trying different ranges of Temp and Pressure. Sometimes a curve fit over a smaller range of T and P results better fits at the fringes.



Hunters’ Point Boiler Main Steam Flow spec. vol. Compensation F equation SV Using Spec. Vol. Flow Compensation Coefficients in Table 1.0 and equation 3.0 over various ranges of temperature and pressure we get different curves that fit the best over a narrow range.

Note – The Bailey Flow nozzle specification Sheet dated 2/14/58 listed the design specific volume as .4306 cu. Ft./lb. Maximum capacity of 1,400,000 lb/hr and max Meter Differential as 331 inches of water. More modern version of the Steam Table described Design Specific Vol = 0.431289 (cu-ft / lb) for Design P=1830psig (1844.7psia) and Design T=1000 DegF) source: Steam Tables by Keenan, Keyes, Hill and Moore (1969) Equation 3.1 was derived by the steps outlined above for F

SV

over a range of 1500 psia to 2000 psia and 860 DegF to 1060DegF

for the Hunters’ Point Power Plant Boiler Main Steam Flow.

Equation 3.1 – Spec. Vol. Flow Compensation Factor polynomial for Spec. Vol., Boiler Main Steam Flow, 0.3% accuracy, narrow range 850 DegF to 1100 DegF and 1500 Psia to 2000. Equation 3.2 was derived by the steps outlined above For F

SV

over a range of 1500 psia to 2000 psia and 700 DegF to 1160DegF.

Equation 3.2 – Spec. Vol. Flow Compensation Factor polynomial Spec. Vol., Main Boiler Steam Flow, 1.0% accuracy, wide range, 700 DegF to 1100 DegF and 1100 Psia to 2000. The following tables 3.1 and 3.2 show the %error the polynomial equation yields versus the actual table of specific volume compensation coefficients found in table 1.

% Error Polynomial Equation 3.1 versus actual F

SV

Hunters’ Point P.P.Boiler Main Steam Flow – narrow range - High Accuracy - 0.3% error for Design P=1830psig (1844.7psia) and 1000 DegF Design Specific Vol = 0.431289 (cu-ft / lb) Press (Psia)

1000

1100

1200

1300

1400

1500

1600

1700

1750

1800

1850

1900

2000

650

0.32

-0.68

-1.56

-2.37

-3.13

-3.92

-4.76

-5.71

-6.22

-6.78

-7.37

-8.02

-9.55

700

1.19

0.31

-0.40

-0.98

-1.48

-1.95

-2.37

-2.81

-3.03

-3.25

-3.50

-3.75

-4.29

750

1.75

0.91

0.28

-0.21

-0.59

-0.89

-1.15

-1.36

-1.46

-1.56

-1.65

-1.74

-1.95

800

2.16

1.31

0.70

0.24

-0.08

-0.31

-0.48

-0.58

-0.62

-0.66

-0.69

-0.70

-0.74

860

2.51

1.64

1.01

0.55

0.24

0.04

-0.08

-0.14

-0.14

-0.14

-0.13

-0.10

-0.05

900

2.69

1.79

1.13

0.67

0.34

0.14

0.03

-0.01

-0.01

0.00

0.03

0.07

0.16

Temp DegF



960

2.93

1.96

1.26

0.76

0.41

0.19

0.07

0.02

0.03

0.04

0.07

0.12

0.24

1000

3.07

2.06

1.31

0.78

0.40

0.16

0.02

-0.03

-0.02

-0.01

0.02

0.07

0.19

1060

3.27

2.18

1.37

0.77

0.36

0.08

-0.09

-0.17

-0.18

-0.17

-0.15

-0.12

-0.02

1100

3.39

2.25

1.39

0.76

0.26

0.00

-0.20

-0.30

-0.32

-0.32

-0.31

-0.28

-0.18

1160

3.57

2.35

1.42

0.73

0.22

-0.14

3.24

3.13

-0.55

-0.58

-0.58

-0.57

-0.50

Table 3.1 - %error in polynomial eqn 3.1 – Boiler Main Steam Flow coefficient – narrow range


SV

Hunters’ Point P.P. Boiler Main Steam Flow – Wide Range -1% error for Design P=1830psig (1844.7psia) and 1000 DegF Design Specific Vol. = 0.431289 (cu-ft / lb) Press (Psia)

1000

1100

1200

1300

1400

1500

1600

1700

1750

1800

1850

1900

2000

650

0.35

-0.27

-0.80

-1.30

-1.78

-2.32

-2.93

-3.67

-4.09

-4.56

-5.08

-5.65

-7.05

700

1.00

0.49

0.11

-0.17

-0.40

-0.62

-0.81

-1.04

-1.17

-1.30

-1.45

-1.62

-1.99

750

1.37

0.88

0.55

0.35

0.22

0.16

0.12

0.12

0.10

0.10

0.10

0.10

0.05

800

1.58

1.06

0.74

0.55

0.47

0.46

0.50

0.59

0.64

0.69

0.75

0.82

0.93

860

1.71

1.14

0.77

0.56

0.48

0.48

0.55

0.67

0.76

0.84

0.93

1.04

1.24

900

1.76

1.13

0.73

0.49

0.38

0.37

0.44

0.57

0.65

0.74

0.84

0.95

1.19

960

1.79

1.08

0.60

0.31

0.15

0.11

0.15

0.26

0.33

0.42

0.52

0.63

0.88

1000

1.80

1.02

0.49

0.16

-0.05

-0.12

-0.11

-0.02

0.06

0.13

0.23

0.34

0.58

1060

1.81

0.93

0.32

-0.11

-0.36

-0.50

-0.53

-0.48

-0.43

-0.37

-0.29

-0.21

0.01

1100

1.81

0.86

0.18

-0.29

-0.64

-0.77

-0.84

-0.82

-0.78

-0.73

-0.67

-0.59

-0.40

1160

1.81

0.76

-0.01

-0.56

-0.94

-1.18

2.27

2.27

-1.34

-1.32

-1.27

-1.21

-1.06

Temp DegF

Table 3.2 - %error in polynomial eqn 3.2 – Boiler Main Steam Flow coefficient – wide range

Hunters’ Point Turbine Steam Flow F equation SV Using Flow Compensation Coefficients in Table 1.0 and equation 3.0 over various ranges of temperature and pressure we get different curves that fit the best over a narrow range.

Note – The Bailey Flow nozzle specification Sheet dated 1/14/58 listed the design specific volume as .4383 cu. Ft./lb. Maximum capacity of 1,200,000 lb/hr and max Meter Differential as 331 inches of water. More modern version of the Steam Table described



Design Specific Vol. = 0.439149 (cu-ft / lb) for Design P=1800psig (1814.7psia) and Design T=1000 DegF) source: Steam Tables by Keenan, Keyes, Hill and Moore (1969) Equation 4.1 was derived by the steps outlined above for F

SV

over a range of 1500 psia to 2000 psia and 860 DegF to 1060DegF

for the Hunters’ Point Power Plant Turbine Steam Flow.

Equation 4.1 – Flow Compensation Factor polynomial Spec. Vol., Turbine Steam Flow, 0.3% accuracy, narrow range 850 DegF to 1100 DegF and 1500 Psia to 2000. Equation 4.2 was derived by the steps outlined above for F

SV

over a range of 1500 psia to 2000 psia and 700 DegF to 1160DegF.

Equation 4.2 – Flow Compensation Factor polynomial Spec. Vol., Turbine Steam Flow, 1.0% accuracy, wide range, 700 DegF to 1100 DegF and 1100 Psia to 2000. The following tables 4.1 and 4.2 show the %error the polynomial equation yields versus the actual table of steam flow compensation coefficients found in table 1.


SV

Hunters’ Point P.P. Turbine Steam Flow – narrow range - High Accuracy - 0.3% error for Design P=1830psig (1814.7psia) and 1000 DegF Design Specific Vol. = 0.439149 (cu-ft / lb) Press (Psia)

1000

1100

1200

1300

1400

1500

1600

1700

1750

1800

1850

1900

2000

650

0.32

-0.68

-1.56

-2.37

-3.13

-3.92

-4.76

-5.71

-6.22

-6.78

-7.37

-8.02

-9.55

700

1.19

0.31

-0.40

-0.98

-1.48

-1.95

-2.37

-2.81

-3.03

-3.25

-3.50

-3.75

-4.29

750

1.75

0.91

0.28

-0.21

-0.59

-0.89

-1.15

-1.36

-1.46

-1.56

-1.65

-1.74

-1.95

800

2.16

1.31

0.70

0.24

-0.08

-0.31

-0.48

-0.58

-0.62

-0.66

-0.69

-0.70

-0.74

860

2.51

1.64

1.01

0.55

0.24

0.04

-0.08

-0.14

-0.14

-0.14

-0.13

-0.10

-0.05

900

2.69

1.79

1.13

0.67

0.34

0.14

0.03

-0.01

-0.01

0.00

0.03

0.07

0.16

960

2.93

1.96

1.26

0.76

0.41

0.19

0.07

0.02

0.03

0.04

0.07

0.12

0.24

1000

3.07

2.06

1.31

0.78

0.40

0.16

0.02

-0.03

-0.02

-0.01

0.02

0.07

0.19

1060

3.27

2.18

1.37

0.77

0.36

0.08

-0.09

-0.17

-0.18

-0.17

-0.15

-0.12

-0.02

1100

3.39

2.25

1.39

0.76

0.26

0.00

-0.20

-0.30

-0.32

-0.32

-0.31

-0.28

-0.18

1160

3.57

2.35

1.42

0.73

0.22

-0.14

3.24

3.13

-0.55

-0.58

-0.58

-0.57

-0.50

Temp DegF

Table 4.1 - %error in polynomial eqn 4.1 – Turbine Steam Flow coefficient – narrow range




SV

Hunters’ Point P.P. Turbine Steam Flow – Wide Range -1.25% error for Design P=1800psig (1814.7psia) and 1000 DegF Design Specific Vol. = 0.4391486 (cu-ft / lb) Press (Psia)

1000

1100

1200

1300

1400

1500

1600

1700

1750

1800

1850

1900

2000

650

0.35

-0.27

-0.80

-1.30

-1.78

-2.32

-2.93

-3.67

-4.09

-4.56

-5.08

-5.65

-7.05

700

1.00

0.49

0.11

-0.17

-0.40

-0.62

-0.81

-1.04

-1.17

-1.30

-1.45

-1.62

-1.99

750

1.37

0.88

0.55

0.35

0.22

0.16

0.12

0.12

0.10

0.10

0.10

0.10

0.05

800

1.58

1.06

0.74

0.55

0.47

0.46

0.50

0.59

0.64

0.69

0.75

0.82

0.93

860

1.71

1.14

0.77

0.56

0.48

0.48

0.55

0.67

0.76

0.84

0.93

1.04

1.24

900

1.76

1.13

0.73

0.49

0.38

0.37

0.44

0.57

0.65

0.74

0.84

0.95

1.19

960

1.79

1.08

0.60

0.31

0.15

0.11

0.15

0.26

0.33

0.42

0.52

0.63

0.88

1000

1.80

1.02

0.49

0.16

-0.05

-0.12

-0.11

-0.02

0.06

0.13

0.23

0.34

0.58

1060

1.81

0.93

0.32

-0.11

-0.36

-0.50

-0.53

-0.48

-0.43

-0.37

-0.29

-0.21

0.01

1100

1.81

0.86

0.18

-0.29

-0.64

-0.77

-0.84

-0.82

-0.78

-0.73

-0.67

-0.59

-0.40

1160

1.81

0.76

-0.01

-0.56

-0.94

-1.18

2.27

2.27

-1.34

-1.32

-1.27

-1.21

-1.06

Temp DegF

Table 4.2 - %error in polynomial eqn 4.2 – Turbine Steam Flow coefficient – wide range

Thermal Expansion Factor The material of the primary element (e.g. flow nozzle, venturi, orifice) and the pipe expands or contracts with temperature. The bore and pipe diameters are measured at room temperature, but will be larger or smaller at other temperatures. The thermal correction factor corrects for these effects. When the thermal-expansion coefficients of the primary element and pipe material are approximately the same, which is usually the case, and is assumed here, the Thermal Correction factor is:

Equation 5.0 – Design Thermal Expansion Flow Coefficient Factor in Meter Factor Where α

PE

is the coefficient of linear expansion for the primary element. F a can also be looked up graphically in texts, for example

ASME Fluid Meters (1971) or Flow Measurement Engineering Handbook by R. W. Miller (1983). http://www.desconengineering.com/WhitePapers/SteamFlow/Steam_Flow_Compensation.htm(9 of 12)1/14/2009 12:23:08 PM


The Ratio of F aDESIGN to FaACTUAL is the Compensation Factor F a

Equation 5.1 – Thermal Expansion Flow Correction Factor

Thermal-expansion Flow Correction Factor (F a ), Hunters Point Boiler and Turbine For 5% chrome moly,

α

PE

=7.37353E-06

(from Figure 9.5, Flow Measurement Engineering Handbook by R. W. Miller (1983). Using Equation 5.1, and the design Temperature of 1000 Degf, the equation for Thermal Expansion Steam Flow Correction Factor is

Equation 5.2 – Thermal Expansion Flow Correction Factor, Design Temp = 1000 DegF, 5% Chrome Moly Table 5.1 shows the range of Correction Factors over the operating range for Hunters Point Power Plant Boiler Main Steam Flow and Turbine Steam Flow meters. Without this compensation, the error introduced over the operating range is 0.51% maximum. Table 5.1 Thermal Expansion Flow Correction Factor, Hunters’ Point P.P. Boiler and Turbine Steam Flow, Design Temp = 1000 DegF, 5% Chrome Moly Temp (Deg F) Fa

650

700

1000

1060

1100

1160

0.994909

0.995636

1

1.000873

1.001455

1.002328

Boiler Main Steam Flow Equation – Hunters Point The temperature and pressure Compensated Steam Flow is calculated as: http://www.desconengineering.com/WhitePapers/SteamFlow/Steam_Flow_Compensation.htm(10 of 12)1/14/2009 12:23:08 PM


Equation 2.0 The meter Factor (Fm) is calculated from equation 6.1. For Boiler Main Steam Flow, the Bailey Flow nozzle specification Sheet dated 2/14/58 listed the design Temperature of 1000 DegF and design Pressure of 1830 psig. Maximum capacity of 1,400,000 lb/hr and max Meter Differential as 331 inches of water.

= 76950.96 Equation 6.1 – Meter Factor, Boiler Main Steam Flow The temperature and pressure Compensated Steam Flow is calculated as:

Equation 6.2 – Boiler Main Steam Flow Assuming the wider operating range is desired (1% error acceptable), the Specific Volume Correction Factor equation 3.2 is used:

Equation 3.2 – Spec. Vol. Flow Compensation Factor polynomial Spec. Vol., Main Boiler Steam Flow, 1.0% accuracy, wide range, 700 DegF to 1100 DegF and 1100 Psia to 2000. The equation for Thermal Expansion Steam Flow Correction Factor is Equation 5.1.

Equation 5.2 – Thermal Expansion Flow Correction Factor, Design Temp = 1000 DegF, 5% Chrome Moly

Turbine Steam Flow Equation – Hunters Point The temperature and pressure Compensated Steam Flow is calculated as:



Equation 2.0 The meter Factor (Fm) is calculated from equation 6.1. For Turbine Steam Flow, the Bailey Flow nozzle specification Sheet dated 1/14/58 listed the design Temperature of 1000 Degf and design pressure of 1800 psig. Maximum capacity of 1,200,000 lb/hr and max Meter Differential as 331 inches of water.

= 65957.97 Equation 7.1 – Meter Factor, Turbine Steam Flow The temperature and pressure Compensated Steam Flow is calculated as:

Equation 7.2 – Turbine Steam Flow Assuming the wider operating range is desired (1% error acceptable), the Specific Volume Correction Factor equation 3.2 is used:

Equation 4.2 – Flow Compensation Factor polynomial Spec. Vol., Turbine Steam Flow, 1.0% accuracy, wide range, 700 DegF to 1100 DegF and 1100 Psia to 2000. The equation for Thermal Expansion Steam Flow Correction Factor is Equation 5.1.


Steam Flow Compensation for Distributed Control Systems

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