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NPA NPE A 2000-06-30 SolDescPrepared: Checked: Approved: Language Page:

Theo Gbelbecker Michael Layes Hans-Kaspar Scherrer en 1/26Valid for: Derived from: Replaces: Classify No.: Data set:

Standard 1AHL 105 891 PhysCalcLib.doc

We reserve all rights in this document and in the information contained therein. Reproduction, use or disclosure to thirdparties without express authori ty is st rictly forbidden. ABB Power Automation Ltd (CH) 2000

1AHQ 490010 Rev. -- / 96-09-27 / KWGQ (KW 200 600 P3)

Physical Calculations Library

Users Manual

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We reserve all rights in this document and in the information contained therein. Reproduction, use or disclosureto third parties without express authority is strictly forbidden. ABB Power Automation Ltd (CH) 2000

1AHQ 490010 Rev. -- / 96-09-27 / KWGQ (KW 200 600 P4)

Contents1. Modules of the Physical Calculations Library................................................................................................3

2. Module Descriptions...................................................................................................................................42.1. Calculation : Drum Level of Water, TC DRM_LVL..................................................................................4

2.1.1. Attributes......................................................................................................................................4

2.1.2. Function .......................................................................................................................................4

2.1.3. Interface.......................................................................................................................................52.1.4. Application....................................................................................................................................5

2.1.5. Example: Drum Level....................................................................................................................62.2. Calculation : Volume Flow for Gas, TC GAS_FLW.................................................................................7

2.2.1. Attributes......................................................................................................................................7

2.2.2. Function .......................................................................................................................................72.2.3. Interface.......................................................................................................................................82.2.4. Application....................................................................................................................................9

2.2.5. ApplicExample 1 : Mass Flow ........................................................................................................92.2.6. ApplicExample 2 : Volume Flow SI.................................................................................................92.2.7. Example 1: Fuel Gas Flow........................................................................................................... 10

2.2.8. Example 2: Nitrogen Gas Flow.....................................................................................................102.3. Calculation : Steam Enthalpy, TC ST_ENTH ....................................................................................... 11

2.3.1. Attributes....................................................................................................................................112.3.2. Function ..................................................................................................................................... 112.3.3. Interface..................................................................................................................................... 11

2.4. Calculation : Mass Flow for Steam, TC STM_FLW ...............................................................................12

2.4.1. Attributes....................................................................................................................................122.4.2. Function ..................................................................................................................................... 122.4.3. Calculation for steam................................................................................................................... 13

2.4.4. Calculation for saturated steam.................................................................................................... 132.4.5. Interface..................................................................................................................................... 142.4.6. Application.................................................................................................................................. 14

2.4.7. Example 1: Superheated Steam Flow........................................................................................... 152.4.8. Example 2: Saturated Steam Flow ............................................................................................... 15

2.5. Calculation : Saturated Steam Temperature, TC STM_T...................................................................... 16

2.5.1. Attributes....................................................................................................................................162.5.2. Function ..................................................................................................................................... 162.5.3. Interface..................................................................................................................................... 16

2.6. Calculation : Saturated Steam Temperature, TC STM_T6 .................................................................... 172.6.1. Attributes....................................................................................................................................172.6.2. Function..................................................................................................................................... 17

2.6.3. Interface..................................................................................................................................... 172.7. Calculation : Mass Flow for Water, TC WTR_FLW ...............................................................................18

2.7.1. Attributes....................................................................................................................................18

2.7.2. Function ..................................................................................................................................... 182.7.3. Calculation for feedwater............................................................................................................. 192.7.4. Calculation for saturated water.....................................................................................................19

2.7.5. Interface..................................................................................................................................... 20

2.7.6. Application.................................................................................................................................. 202.7.7. Example: Water Flow.................................................................................................................. 21

2.8. Calculation : Valve Physics for Compressible Fluid, TC VLV_GAS........................................................ 222.8.1. Attributes....................................................................................................................................222.8.2. Function ..................................................................................................................................... 22

2.8.3. Interface..................................................................................................................................... 232.8.4. Application.................................................................................................................................. 242.8.5. ApplicExample : ValveStroke(Flow_REF) ..................................................................................... 25

2.8.6. ApplicExample : ValveFlow(Strk_ACT)......................................................................................... 253. Revision Page.......................................................................................................................................... 26

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1. Modules of the Physical Calculations Library

DRuM_LeVeL Drum Level of Water

GAS_FLoW Volume Flow for Gas

STeam_ENTHalpy Steam Enthalpy

STeaM_FLoW Mass Flow for Steam

STeaM_Temp Saturated Steam Temperature

STeaM_Temp6 Saturated Steam Temperature

WaTeR_FLoW Mass Flow for Water

GAS_VaLVe Valve Physics for Compressible Fluid

Module Description applicable Status/lastMod

DRM_LVL Drum Level of Water AC450 AC160 00-03-28

GAS_FLW Volume Flow for Gas AC450 AC160 00-06-30

ST_ENTH Steam Enthalpy AC450 AC160 99-01-10

STM_FLW Mass Flow for Steam AC450 - 00-03-28

STM_T Saturated Steam Temperature AC450 - 00-03-28

STM_T6 Saturated Steam Temperature AC160 00-03-28

WTR_FLW Mass Flow for Water AC450 AC160 00-03-28

GAS_VLV Valve Physics for Compressible Fluid AC450 AC160 Draft

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2. Module Descriptions

2.1. Calculation : Drum Level of Water, TC DRM_LVL

This function is based on CHAAP GIAM TN 00004

2.1.1. Attributes

RequiredSolution Designation DRM_LVL

Solution Title Drum Level of Water

System Type Advant Power, AC450 / AC160

Owner CHPAU/NPA

Status Approved

Last Modification 00-03-28

Information Only

Processes CCPPProjects Standard

Solution Layers Incl Control

2.1.2. Function

The function calculates the drum level using the differential pressure between two measuring points on the drum.The drum pressure is required to calculate the densities of water and steam.

The results are valid between 1 barA and 210 barA. The maximum error generally is less than 1.5 %. For lowpressures (< 3 barA) and high level indications the maximum error is less than 4 %.

The calculation is based on the fact that the drum contains saturated water and steam.

o = water density in water leg [kg/m] o=f(pdrum,Twetleg)

W = water density in drum [kg/m] W=f(pdrum)

ST = steam density in drum [kg/m] ST=f(pdrum)

p = delta pressure [Pa] -

DP = delta pressure [bar] Pin DPLtd = tap distance [m] Pin TAP_DISTLa = actual level [m] -

L = actual level for indication [m] Pin LLmax = upper indication limit [m] Pin L_MAX = TAP_DIST L_0

Lmin = lower indication limit [m] Pin L_MIN = L_0

p calculation :

p

Level Indication Drum Water Leg

Lmax

0 mm

Lmin

LaLtd

W

ST O

L

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p = o * g * L td - [W * g * La + ST * g*( L td - La )]

therefore

La = [(o - ST) * Ltd - (p/g)] / [W - ST]

scaled to one and linearised to the upper and lower indication limit

L = Ltd * [(o - ST) - (DP * 105

/ (g * Ltd))] / (W - ST) + Lmin

2.1.3. Interface

Terminal Description Location I/O Unit DtaTpe DefltVal Usage

Inputs

DP Differential pressure 1 I bar RDP_ERR Differential pressure disturbed 2 I - BP Drum pressure 10 I bar R

P_ERR Drum pressure disturbed 11 I - BP_EQIV Equivalent pressure value if P_ERR = 1 12 I bar R 100 bar DP_MAX Maximum value of differential pressure 21 I bar R 0.1 bar

TRX_RIS Characteristic of differential pressure transmitter,0 = falling 1 = rising ( -> application)

22 I - B 0

P_ABS Type of drum pressure transmitter 1 = absolute 23 I - B 0

T_WETLEG Temperature of reference water leg 24 I Cel R 50 CelTAP_DIST Tapping point distance 39 I m R 1 mL_0 Distance to zero of level output 40 I m R 0.5 m

L_BACK Equivalent level value if DP_ERR = 1 41 I m R 0 m

OutputsL Level from L_MIN up to L_MAX 50 O m R

L_ERR Error from differential pressure 51 O - BL_DIST Error from pressure transmitter 52 O - BH_LIM Upper limit of level range reached 53 O - B

L_LIM Lower limit of level range reached 54 O - BL_MAX Maximum value of level range 61 O m RL_MIN Minimum value of level range 62 O m R

2.1.4. Application

Note: The function contains no signal filtering.

The following equation is assumed : DP_MAX / bar= TAP_DIST / m * 9.81/100

A falling transmitter characteristic means that the value zero at pin DP results in the highest possible level, and vice

versa a rising transmitter characteristic means the value Dpmax at pin DP results in the highest possible level.

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2.1.5. Example: Drum Level

TAP_DIST = 2.006 m = top tap bottom tap, means vertical distance of tapping points

L_0 = 1.104 m level above bottom tap for zero indication

P_EQIV = 6 barG e. g. normal operating pressure or any reasonable value,

same unit as pressure transmitter

DP_MAX = 0.197 bar = TAP_DIST * 9.81 /100, measuring range of differential pressure transmitter

TRX_RIS = 0 falling - means with 4 mA = 0.1968 barand 20mA = 0.0 bar

P_ABS = 0 gauge drum pressure transmitter

T_WETLEG = 40 Cel expected approximate temperature of reference water leg

L_BACK = 1.1 m level indication in case of disturbed differential pressure transmitter

902 mm

0 mm-101 mm

-1104 mm

top tap

normal operating levelcenter line of drum

bottom tap

level indication

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1AHQ 490010 Rev. -- / 96-09-27 / KWGQ (KW 200 600 P4)

RHOZETA

DPCvA)TW,PW,DP(FVOL

=

2.2. Calculation : Volume Flow for Gas, TC GAS_FLWThis function is based on

2.2.1. Attributes

RequiredSolution Designation GAS_FLW

Solution Title Volume Flow for Gas


Owner CHPAU/NPA

Status Draft


Information Only

Processes CCPP

Projects Standard


2.2.2. Function

The function calculates the volume flow of gas using the differential pressure over an orifice. For Equations andFormulae see ISO 5167, DIN 1952, or VDI/VDE 2040. Pressure and temperature of the gas are required to

calculate its density. Pressure and temperature are measured after the orifice. All calculations are based on thetheory of ideal gases.

The results are valid with an acceptable deviation from its measured value. Typical errors are less than 1 %.

The volume flow is calculated by the following formula :

with

RHO = (M_N * PW * Cd) / (R * tw) where tw / K = TW / Cel + T0

FVOL = volume flow [m3/h] Cv = 1 609 969

DP = differential pressure [bar] Cd = 100 000PW = pressure after orifice [barG/A] R = 8 314.51 J/kmol/KTW = temperature after orifice [Cel] T0 = 273.15 [K]

A = area of orifice [m2]

ZETA = orifice coefficient [1]

M_N = molecular weight nominal [g/mol]

At an additional output the density is get :

RHO(PW, TW) = RHO

RHO = density [kg/m] calculated depending from the values of PW and TW

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The molecular weight resp. the orifice coefficient may be built as follows :

M_N = RHOnom * (R * (TWnom + T0) / (PWnom * Cd)) < ideal gas >resp.

ZETA = (A * Cv / FVOLmaxN)2 * DPmaxN / RHOnom < ideal gas >

RHOnom = density at the nominal conditions PWnom and TWnomFVOLmaxN = value of volume flow at the conditions DPmaxN and RHOnom [ or alternatively

FVOLnom = value of volume flow at nominal conditions DPnom and RHOnom ]

2.2.3. Interface


InputsDP Differential pressure 1 I bar RDP_ERR Differential pressure disturbed 2 I - BPW Gas pressure after orifice 10 I bar RPW_ERR Gas pressure disturbed 11 I - BPW_N Nominal pressure

1, value if P_ERR = 1 12 I bar R 10 bar

TW Gas temperature after orifice 20 I Cel RTW_ERR Gas temperature disturbed 21 I - BTW_N Nominal temperature

1, value if T_ERR = 1 22 I Cel R 100 Cel

DP_MAX Maximum value of differential pressure 23 I bar RA Area of orifice 26 I m2 R 0.02 m2ZETA Orifice coefficient 27 I - R 5M_N Molecular weight of gas at nominal conditions 28 I g/mol R 28 g/molRAD_DP Differential pressure transmitter makes

square rooting ( -> application)29 I - B 0

P_ABS Type of pressure transmitter 1 = absolute 0 = gauge 30 I - B 0F_ZERO Indication limit for flow ( -> application) 40 I m3/h R 0 m3/hF_BACK Equivalent flow, value if DP_ERR = 1 41 I m3/h R 0 m3/h

OutputsFVOL Volume flow 50 O m3/h RF_ERR Error from differential pressure 51 O - BF_DIST Error from pressure or temperature transmitter 52 O - BRHO Density of gas 60 O kg/m3 RD_3600 Denominator for mass flow calculation 61 O - R (3600 s)

SymbolP0 Ambient pressure, active only if P_ABS = 0 - S bar R 1 bar

1

Nominal value corresponds to equivalent value

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2.2.4. Application


From a square rooting DP transmitter the true real value is assumed at pin DP in unit bar1/2

, e. g. for a given DP

01.5 bar the resulting value range is 01.2247 .

Output value of FVOL is set to zero if falling below the value 0.5 * F_ZERO and reanimated above the value

F_ZERO (hysteresis = 0.5 * F_ZERO).

2.2.5. ApplicExample 1 : Mass Flow

F / kg/s = FVOL / m3/h * RHO / kg/m3 / D_3600

F = mass flow [kg/s]D_3600= 3 600 [s]

Note: Use PC element DIV-MR(2,1)

2.2.6. ApplicExample 2 : Volume Flow SI

FVOLSI/ kg/s = FVOL / m3/h / D_3600

FVOLSI = volume flow [m3/s]

D_3600= 3 600 [s]

Note: Use PC element DIV(R)

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2.2.7. Example 1: Fuel Gas Flow

Name plate data of flow nozzle DPnom = Pnom = Tnom = FVOLnom = RHOnom =

0.184 5 bar 15.2 barG 300 Cel 363 000 m3/h 10.200 3 kg/m

3

DPmaxN = A = - FVOLmaxN = DP_MAX =

0.35 bar 2.0 m

2

500 000 m

3

/h 1.2 bar

Taking the values above you get the values for molecular weight M_N resp. for orifice coefficient ZETA,

thusM_N = RHOnom * (R * (TWnom + T0) / (PWnom * Cd)) =

29.981 118 g/mol R = 8 314.51, T0 = 273.15, Cd = 100 000

ZETA = (A * Cv / FVOLmaxN)2

* DPmaxN / RHOnom = Cv = 1 609 969

1.423

PW_N = 15.2 barG same unit as pressure transmitter

TW_N = 300 Cel

DP_MAX = 1.2 bar from measuring range of the differential pressure transmitter

RAD_DP = 0 differential pressure transmitter does not square root

P_ABS = 0 gauge pressure transmitter F_ZERO = 10 000 m

3/h output FVOL is not zero if FVOL > F_ZERO or zero if FVOL < 0.5 * F_ZERO

F_BACK = 500 m3/h indication in case of disturbed differential pressure transmitter

Aopt = 1.999 988 m2

see note below

< P0 > = 1.013 25 bar medium ambient pressure

Note: With Aopt an better value for the volume flow is get, i. e. volume flow changes to 500 000.000 m3/h exactly.

error_typical < 0.32 % ( e.g. err_max < 0.05 %at DP = 0.003 172 bar, PWmax = 20 barG, TWmax = 400 Cel,PWmin = 5 barG, and Twmin = 100 Cel ) .

2.2.8. Example 2: Nitrogen Gas Flow

Name plate data of flow nozzle DPnom = Pnom = Tnom = FVOLnom = RHOnom =

0.030 25 bar 3.94 barA 15 Cel 1 100 m3/h 4.626 8 kg/m

3

DPmaxN = A = - FVOLmaxN = DP_MAX =0.1 bar 0.02 m

22 000 m

3/h 0.22 bar

Taking the values above you get the values for molecular weight M_N resp. for orifice coefficient ZETA,

thusM_N = RHOnom * (R * (TWnom + T0) / (PWnom * Cd)) =

28.134 5 g/mol [ 28.087 g/mol if 2.94 barG ] R = 8 314.51, T0 = 273.15, Cd = 100 000

ZETA = (A * Cv / FVOLmaxN)2

* DPmaxN / RHOnom = Cv = 1 609 969

5.602

PW_N = 3.94 barA same unit as pressure transmitter

TW_N = 15 Cel

DP_MAX = 0.22 bar from measuring range of the differential pressure transmitter


P_ABS = 1 absolute pressure transmitter

F_ZERO = 200 m3/h output FVOL is not zero if FVOL > F_ZERO or zero if FVOL < 0.5 * F_ZERO

F_BACK = 10 m3/h indication in case of disturbed differential pressure transmitter

Aopt = 0.020 033 3 m2

see note below

[ < P0 > = 1.006 675 bar medium ambient pressure - usefull only if PW is gauge ]

Note: With Aopt an better value for the volume flow is get, i. e. volume flow changes to 2 000.000 m3/h exactly.

error_typical < 0.24 % ( e.g. err_max < 0.34 %at DP = 0.209 991 bar, PWmin = 1 barG (!), TWmax = 35 Cel,PWmax = 5 barG (!), and TWmin = 5 Cel ) .

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2.3. Calculation : Steam Enthalpy, TC ST_ENTHThis function is based on KWGA TN 1 99004

2.3.1. Attributes

RequiredSolution Designation ST_ENTH

Solution Title Steam Enthalpy


Owner CHPAU/NPA

Status Approved


Information Only

Processes CCPP

Projects Standard


2.3.2. Function

Many functions in the water/steam cycle are based on an enthalpy calculation. Inputs are temperature and absolute

pressure. This module calculates an approximation of the steam table values based on polynomials.

The results are valid between 1 barA and 200 barA, resp. 100 Cel and 600 Cel and all enthalpies higher than2950 kJ/kg. The maximum error in this range is less than 10 kJ/kg.

ENTH = f(TEMP, PRESS)

2.3.3. Interface


InputsTEMP Temperature 2 I Cel RPRESS Pressure 3 I barA R

OutputsENTH Enthalpy 10 O kJ/kg R

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2.4. Calculation : Mass Flow for Steam, TC STM_FLWThis function is based on CHAAP GIAM TN 00004

2.4.1. Attributes

RequiredSolution Designation STM_FLW

Solution Title Mass Flow for Steam

System Type Advant Power, AC450

Owner CHPAU/NPA

Status Approved


Information Only

Processes CCPP

Projects Standard


2.4.2. Function

The function calculates the mass flow of steam using the differential pressure over an orifice according DIN 1952.

Pressure and temperature of the medium are required to calculate the density of the steam.

The results are valid between 1 barA and 400 barA, resp. between 0 Cel and 700 Cel. The maximum error is lessthan 1 % in the range 1 barA and 310 barA, resp. between 0 Cel and 620 Cel excluding values too close to the

critical state of steam.

For all temperatures below the saturation temperature T_SAT is used in the calculation.

The mass flow is calculated by the following formula :

m?= ORI * SQRT(2 * DP * )and

RHO = (P, T)

m? = mass flow [kg/s] Pin FDP = differential pressure [bar] Pin DP

= density [kg/m] internal calculated depending from P and T

ORI = orifice parameter [m2] Pin ORI

The orifice parameter may be built as follows :

ORI = Fnom / SQRT(2 * DPnom * RHOnom)or

ORI = * * (d * /4) * 316.228

= flow coefficient [1] Fnom = flow at nominal conditions

= expansion coefficient [1] DPnom = differential pressure at nominal conditionsd = diameter orifice [m] RHOnom = density nominal at the conditions Pnom and Tnom

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2.4.3. Calculation for steam

The calculation of the steam density is based on special functions. The diagram below only shows the principleranges of the density.

2.4.4. Calculation for saturated steam

For the calculation of saturated steam only the differential pressure across an orifice and the steam pressure arenecessary.

0

20

50

80

110

1

40

1

90

22

0

26

0

300

340

380

420

460

500

540

580

620

660

0 bar

30 bar

90 bar

150 bar

0.0

200.0

400.0

600.0

800.0

1000.0

DENSITY [kg/m3]

TEMPERATURE [C]

PRESSURE [barg]

DENSITY OF WATER/STEAM AS FUNCTION OF PRESSURE AND TEMPERATUR

Steam

Density of Steam as Function of Pressure and Temperature

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2.4.5. Interface


Inputs

DP Differential pressure 1 I bar RDP_ERR Differential pressure disturbed 2 I - BP Medium pressure 10 I bar R

P_ERR Medium pressure disturbed 11 I - BP_EQIV Equivalent pressure value if P_ERR = 1 12 I bar R 100 bar

T Medium temperature 20 I Cel RT_ERR Medium temperature disturbed 21 I - BT_EQIV Equivalent temperature value if T_ERR = 1 22 I Cel R 500 CelDP_MAX Maximum value of differential pressure 25 I bar R

ORI Orifice parameter defined at nominal conditions 26 I m2 RRAD_DP Differential pressure transmitter makes


P_ABS Type of pressure transmitter 1 = absolute 29 I - B 0F_ZERO Indication limit for flow ( -> application) 40 I kg/s R 0 kg/sF_BACK Equivalent flow value if DP_ERR = 1 41 I kg/s R 0 kg/s

OutputsF Flow 50 O kg/s R

F_ERR Error from differential pressure 51 O - BF_DIST Error from pressure or temperature transmitter 52 O - BRHO Density of medium 60 O kg/m3 RSAT_LIN Temperature is given by the internal

calculated Tsat(P)61 O - B

2.4.6. Application


From a square rooting DP transmitter the true real value is assumed at pin DP in unit bar1/2

, e. g. for a given DP

01.5 bar the resulting value range is 01.2247 .

Output values are set to zero if falling below the value 0.5 * F_ZERO and reanimated above the value F_ZERO

(hysteresis = 0.5 * F_ZERO).

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2.4.7. Example 1: Superheated Steam Flow

DPnom Pnom Tnom FnomName plate data of flow nozzle

0.381 bar 6.9 barG 326.1 Cel 13.77 kg/s

You get out of steam table RHOnom(Pnom, Tnom) = 2.904 kg/m

3

Thus

ORI = Fnom / SQRT(2 * DPnom * RHOnom)9.257 m

2

P_EQIV = 7 barG or any reasonable value, same unit as pressure transmitter

T_EQIV = 326 Cel or any reasonable value

DP_MAX = 0.5 bar is measuring range of differential pressure transmitter


P_ABS = 0 gauge pressure transmitter

F_ZERO = 1 kg/s output F is not zero if F > F_ZERO or zero if F < 0.5 * F_ZERO

F_BACK = 0 kg/s indication in case of disturbed differential pressure transmitter

2.4.8. Example 2: Saturated Steam Flow

DPnom Pnom Tnom FnomName plate data of flow nozzle0.27 bar 6.1 barA sat 12.54 kg/s

You get out of steam table RHOnom(Pnom, Tsat (Pnom)) = 3.218 kg/m3

thus

ORI = Fnom / SQRT(2 * DPnom * RHOnom)9.513 m

2


T = 7 Cel below saturation at all operating conditions




P_ABS = 1 absolute pressure transmitter

F_ZERO = 1.5 kg/s output F is not zero if F > F_ZERO or zero if F < 0.5 * F_ZERO

F_BACK = F feedbacked from output F means last undisturbed value of

differential pressure transmitter is frozen in case of

disturbed differential pressure transmitter

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2.5. Calculation : Saturated Steam Temperature, TC STM_TThis function is based on CHAAP GIAM TN 00004

2.5.1. Attributes

RequiredSolution Designation STM_T

Solution Title Saturated Steam Temperature


Owner CHPAU/NPA

Status Approved


Information Only

Processes CCPP

Projects Standard


2.5.2. Function

Many functions in the water/steam cycle are based on a saturation temperature calculation. This module calculates

an approximation of the saturated steam temperature. The variable of the function is an absolute pressure.

The results are valid between 0.01 barA and 220 barA. The maximum error in this range is less than 2.2 K.

The maximum error is less than 0.6 K between 0.08 barA and 170 barA.

T_SAT = f(P + P_AMB)

2.5.3. Interface


InputsP Pressure 1 I bar RP_AMB Ambient pressure 2 I barA R 1.013 barA

OutputsT_SAT Saturation temperature 3 O Cel R

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2.6. Calculation : Saturated Steam Temperature, TC STM_T6This function is based on CHAAP GIAM TN 00004

2.6.1. Attributes

RequiredSolution Designation STM_T6

Solution Title Saturated Steam Temperature


Owner CHPAU/NPA

Status Approved


Information Only

Processes CCPP

Projects Standard


2.6.2. Function

Many functions in the water/steam cycle are based on a saturation temperature calculation. This module calculates

an approximation of the saturated steam temperature. The variable of the function is an absolute pressure.

The results are valid between 0.1 barA and 221.5 barA. The maximum error in this range is less than 0.3 K.

T_SAT = f(P + P_AMB)

2.6.3. Interface


InputsP Pressure 1 I bar RP_AMB Ambient pressure 2 I barA R 1.013 barA

OutputsT_SAT Saturation temperature 3 O Cel R

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2.7. Calculation : Mass Flow for Water, TC WTR_FLWThis function is based on CHAAP GIAM TN 00004

2.7.1. Attributes

RequiredSolution Designation WTR_FLW

Solution Title Mass Flow for Water


Owner CHPAU/NPA

Status Approved


Information Only

Processes CCPP

Projects Standard


2.7.2. Function

The function calculates the mass flow of water using the differential pressure over an orifice according DIN 1952.

Pressure and temperature of the medium are required to calculate the density of the water.

The results are valid between 0.1 barA and 370 barA, resp. between 0 Cel and 310 Cel. The maximum error is lessthan 1 % in the range 0.1 barA and 310 barA, resp. between 10 Cel and 300 Cel.

For all temperatures above the saturation temperature T_SAT is used in the calculation.

The mass flow is calculated by the following formula :

m?= ORI * SQRT(2 * DP * )and

RHO = (P, T)

m? = mass flow [kg/s] Pin F

DP = differential pressure [bar] Pin DP

= density [kg/m] internal calculated depending from P and T

ORI = orifice parameter [m2] Pin ORI

The orifice parameter may be built as follows :

ORI = Fnom / SQRT(2 * DPnom * RHOnom)or

ORI = * * (d * /4) * 316.228

= flow coefficient [1] Fnom = flow at nominal conditions

= expansion coefficient [1] DPnom = differential pressure at nominal conditions

d = diameter orifice [m] RHOnom = density nominal at the conditions Pnom and Tnom

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2.7.3. Calculation for feedwater

The calculation of the feedwater density is based on special functions. The diagram below only shows the principleranges of the density.

2.7.4. Calculation for saturated water

For the calculation of saturated water only the differential pressure across an orifice and the water pressure arenecessary.

0

20

50

80

110

140

190

220

260

300

340

3

80

420

46

0

500

540

580

620

660 0 bar

30 bar

90 bar

150 bar

0.0

200.0

400.0

600.0

800.0

1000.0

DENSITY [kg/m3]

TEMPERATURE [C]

PRESSURE [barg]

DENSITY OF WATER/STEAM AS FUNCTION OF PRESSURE AND TEMPERATUR

Feedwater

Density of Water as Function of Pressure and Temperature

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2.7.5. Interface


Inputs

DP Differential pressure 1 I bar RDP_ERR Differential pressure disturbed 2 I - BP Medium pressure 10 I bar R

P_ERR Medium pressure disturbed 11 I - BP_EQIV Equivalent pressure value if P_ERR = 1 12 I bar R 100 bar

T Medium temperature 20 I Cel RT_ERR Medium temperature disturbed 21 I - BT_EQIV Equivalent temperature value if T_ERR = 1 22 I Cel R 100 CelDP_MAX Maximum value of differential pressure 25 I bar R

ORI Orifice parameter defined at nominal conditions 26 I m2 RRAD_DP Differential pressure transmitter makes


P_ABS Type of pressure transmitter 1 = absolute 29 I - B 0F_ZERO Indication limit for flow ( -> application) 40 I kg/s R 0 kg/sF_BACK Equivalent flow value if DP_ERR = 1 41 I kg/s R 0 kg/s

OutputsF Flow 50 O kg/s R

F_ERRError from differential pressure 51 O - BF_DIST Error from pressure or temperature transmitter 52 O - B

RHO Density of medium 60 O kg/m3 RSAT_LIN Temperature is given by the internal

calculated Tsat(P)61 O - B

2.7.6. Application


From a square rooting DP transmitter the true real value is assumed at pin DP in unit bar

1/2

, e. g. for a given DP01.5 bar the resulting value range is 01.2247 .

Output values are set to zero if falling below the value 0.5 * F_ZERO and reanimated above the value F_ZERO

(hysteresis = 0.5 * F_ZERO).

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2.7.7. Example: Water Flow

DPnom Pnom Tnom FnomName plate data of flow nozzle

0.7119 bar 11.5 barG 48.9 Cel 90.42 kg/s

You get out of steam table RHOnom(Pnom, Tnom) = 989.02 kg/m3

thusORI = Fnom / SQRT(2 * DPnom * RHOnom)2.41 m

2





P_ABS = 0 gauge pressure transmitter

F_ZERO = 5 kg/s output F is not zero if F > F_ZERO or zero if F < 0.5 * F_ZERO

F_BACK = 0 kg/s indication in case of disturbed differential pressure transmitter

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1AHQ 490010 Rev. -- / 96-09-27 / KWGQ (KW 200 600 P4)

xM

tZ

xPHI1

1

P

vlvC)T,P,DP(VLV

=

2.8. Calculation : Valve Physics for Compressible Fluid, TC VLV_GASThis function is based on KWGA TN HTCT 427 814

2.8.1. Attributes

RequiredSolution Designation VLV_GAS

Solution Title Valve Physics for Compressible Fluid


Owner CHPAU/NPA

Status Draft

Last Modification 00-05-2.

Information Only

Processes CCPP

Projects Standard


2.8.2. Function

This function calculates the characteristic values for the following tasks :

Mass Flow depending from valve stroke, differential pressure, as well as pressure and temperature beforevalve.

Valve Stroke depending from flow reference , differential pressure, as well as pressure and temperature beforevalve.

The function calculates the valve factor using the differential pressure across the valve, the pressure before the

valve and the temperature before the valve (European Standard 60 534). Based on the valve factor both values, i.e. valve stroke and mass flow can be built.

The solutions can be found in chapter application below.

The output values are calculated by the following formulas :

with

x(DP,P) = MIN(DP / P, DPP_C) == DPP_Land

t(T) / K = T / Cel + T0

andPHI = 1 / (3 * DPP_C)

and

DPP_C = XT * GAM_GAS / gam_air

VLV = valve factor [m3/kg/3600]

DP = differential pressure [bar]P = pressure [barA]T = temperature [Cel] T0 = 273.15

Z = real gas factor [1] CVLV = 32.826 2 (J/kmol/K)0.5

XT = critical normalised pressure drop [1]

GAM_GAS = specific heat ratio of medium [1] gam_air = 1.4 (specific heat ratio of air)M = molecular weight [g/mol]

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DPP(DP,P) = DP / P

DPP_L(DP,P) = MIN(DPP, DPP_C)

DPP = normalized pressure drop [1]DPP_L = limited DPP [1]

CHOCKED := DPP > DPP_C

CHOCKED = sonic flow

To get the mass flow resp. valve stroke see the formulas in chapter application below.

2.8.3. Interface


InputsDP Differential pressure across valve 1 I bar RP Pressure before valve 2 I barA RT Temperature before valve 3 I Cel RXT Critical normalized pressure drop 4 I - R 0.804GAM_GAS Specific heat ratio of the medium 5 I - R 1.306

Z Real gas factor of the medium 6 I - R 0.03055M Molecular weight of the medium 7 I g/mol R 18.5 g/mol

OutputsVLV Valve factor 11 O m3/kg/3600 RDPP Normalized pressure drop 12 O - RDPP_L Limited DPP 13 O - RCHOCKED Chocked flow DPP > DPP_L 21 O - B

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2.8.4. Application

The mass flow is calculated by using the valve factor, the non-linear valve characteristic, and the actual valve

stroke.

m?(y,DP,P,T) = f(y) / VLV(DP,P,T) { * KV_CORR }

m? = mass flow calculated [kg/s] KV_CORR = 1.0 (valve flow capacity)f(y) = valve characteristic [m3/h] KV_CORR may be a function of DPP_L

y = valve stroke actual [%]

The valve stroke is calculated by using the valve factor, the inverted non-linear valve characteristic, and the actualflow reference.

y(m?ref,DP,P,T) = y(F)with

F = m?ref* VLV(DP,P,T) { / KV_CORR }

y = valve stroke calculated [%] KV_CORR see above

y(F) = inverted valve characteristic [%]

m?ref = flow reference [kg/s]

C_VLV = 3 600 / 10 000 * SQRT( R)with

R= 8 314.51 J/kmol/K

The critical normalized pressure drop XT is a function of the valve geometry. For a given valve design it should

not be used to calibrate the medium mass flow calculation.The real gas factor Z, the gas molecular weight M, and the gas specific heat ratio GAM_GAS are all mediumspecific inputs and must be set accordingly. Both the real gas factor and the gas molecular weight are standard

outputs of the medium composition analysis.

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2.8.5. ApplicExample : ValveStroke(Flow_REF)

2.8.6. ApplicExample : ValveFlow(Strk_ACT)

Note:

MEAS4 means opt. valve flow capacity KV_CORRSTRK_X means corr. volume flow points of valve characteristic

STRK_Y means corr. valve position points of valve characteristic

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3. Revision Page

Rev. Page (p.)Chapt. (c.)

Description DateDept. - Name

A c. 2.2 Addition of TC GAS_FLW 00-06-30, ly

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