Modeling of heat recovery steam generator performance

~

Pergamon MODELING

Applied Thermal Engineering Vol. 17, No. 5, pp. 427-446, 1997 © 1997 Elsevier Science Ltd All rights reserved. Printed in Great Britain P I h S1359-4311(96)00052-X 1359-4311/97 $17.00 + 0.00

OF HEAT RECOVERY STEAM PERFORMANCE

GENERATOR

A. Ong'iro,* V. I. Ugursal,*t A. M. A1 Taweel:~ and J. D. Walker§ *Department of Mechanical Engineering, Technical University of Nova Scotia, P.O. Box 1000, Halifax, Nova Scotia, Canada B3J 2X4; +Department of Chemical Engineering, Technical University of Nova Scotia, P.O. Box 1000, Halifax, Nova Scotia, Canada B3J 2X4; and §Gas Turbine Heat Recovery Engineering, Deltak Unit of Jason, Inc., Minneapolis, USA (Received 31 August 1996) A b s t r a e ~ T h e performance of the heat recovery steam generator (HRSG) strongly affects the overall performance of a combined-cycle power plant. An accurate simulation of the performance of the HRSG is therefore necessary to analyze the effects of various design and operating parameters on the performance of combined-cycle power plants. Unfortunately, there are many sources of uncertainty and operational variance which prevent the accurate prediction of the HRSG performance. Furthermore, the prediction of heat-exchanger performance is based on assumptions about flow patterns. Empirical correction for departures from these assumptions is not possible in cases where the benefits of new geometrical configurations are to be explored. A numerical method was developed to predict the performance of the HRSG in a fashion that accounts, as much as possible, for the design and operation constraints, while keeping computational complexity manageable. The method is intended for use in performance-simulation models of advanced power cycles, since its accuracy is acceptable without requiring large computational resources. The method was used to simulate the pressure, temperature, steam quality and heat-flux distributions in a commercially available HRSG (operating under full- and part-load conditions). The predicted results were found to compare well with measurements obtained on full-scale units. © 1997 Elsevier Science Ltd. All rights reserved. Keywords

HRSG. thermal-hydraulic analysis, numerical model.

NOMENCLATURE Afi. i

Ai. i Ao, i

BD

co Cpg

d

dro d, do Endo

f F

f,, L,f.f= G, Gsc h hi. i hm h, hw (Tw, Pw)i. hw (Tw, pw)ou,

Kfo Km.~ rhw, rh,

total area (finned and unfinned) on the water side of the ith grid (SI units) heat-transfer surface area on the water side of the ith grid (rmd~.~ AzJ (SI units) heat-transfer surface area on the gas side of the ith grid (SI units) percent blow-down coefficient of contraction ( = 0.586 for the limit as area ratio tends to zero) constant pressure specific heat capacity of hot gases (SI units) tube (clean) diameter (S1 units) fouled tube diameter (SI units) tube inside diameter (SI units) tube outside diameter (SI units) Euler number based on do ( = Ap/pu~n) Maning friction factor single-phase flow friction factor tube-side resistance to momentum flux (SI units) resistance to momentum flux in the x-, y- and z-directions, respectively (SI units) mass-velocity-based on internal tube cross-sectional area (SI units) constant in the source term enthalpy of shell-side fluid (Sl units) water-side heat-transfer coefficient of the ith grid (SI units) enthalpy of metal (S| units) gas-side heat-transfer coefficient of the ith grid (SI units) enthalpy of tube-side fluid (SI units) specific enthalpy of saturated steam at steam operating pressure (Sl units) specific enthalpy of feed water at inlet to HRSG (SI units) specific enthalpy of steam at outlet from HRSG (SI units) fouling thermal conductivity ( = 10 W/m K) metal thermal conductivity of the ith grid (SI units) mass flow rates of steam and combustion gases respectively (SI units)

"l'Author to whom correspondence should be addressed. 427

428

A. Ong'iro et al.

Nc8 n

convective boiling number number of tubes enclosed within the grid neighboring control volume faces Nusselt number (SI units) pressure of shell-side fluid (SI units) guessed pressure (SI units) pressure of tube-side fluid (SI units) the maximum of q and r resistance due to fouling on water side of the ith grid (SI units) tube-side fouling resistance (SI units) resistance due to fouling on steam side of the ith grid (SI units) Reynolds number based on tube-side diameter Reynolds number based on do source term (SI units) longitudinal pitch (SI units) transverse pitch (SI units) time (SI units) temperature of combustion gases at inlet to HRSG (SI units) pinch temperature (a value of 15°C was used) saturation temperature of water at steam operating pressure (SI units) mean bulk temperature of shell-side fluid (SI units) mean bulk temperature of tube-side fluid (SI units) metal temperature (SI units) turbulence intensity (SI units) velocity component of shell-side fluid in the x-direction (SI units) velocity components based on guessed pressure field p* (SI units) total heat-transfer coefficient between tube side and tube wall (SI units) total heat-transfer coefficient between shell side and tube wall (SI units) overall heat-transfer coefficient based on the outside area of the ith grid (SI units) velocity of the tube-side fluid (SI units) velocity component of shell-side fluid in the y-direction (SI units) velocity component of shell-side fluid in the z-direction (SI units) mass dryness fraction

nb Nu P p* P, IIq, r[I Rfi. i

Rfo Rfo, /

Re~ Re,lo S S~ S~ t

Tg. in Tpinch

T.., Tshell Twall

Tu U U ~, U ~ W ~

U, Uo Uo.i Ut V W X

Greek letters

Apo Ap~ Ap, At Az Az~ qi. i, rio. /1 P pr P~ P~ p~ pO

porosity (ratio of volume occupied by fluid to the total enclosed volume) two-phase pressure loss at tube exit to header (SI units) two-phase pressure loss at tube inlet from header (SI units) tube-side pressure loss (SI units) time interval (SI units) length of tube section (SI unit) axial length of the ith grid (measured in the normal direction) (SI units) water-side and gas-side surface effectiveness of the ith grid respectively fluid viscosity (SI units) density of shell-side fluid (SI units) density of saturated liquid (SI units) density of saturated vapor (SI units) density of tube-side fluid (SI units) density at time (t + At) (SI units) density at time t (SI units) water-side and gas-side fin efficiencies (functions of fin geometries) of the ith grid respectively

INTRODUCTION H e a t r e c o v e r y s t e a m g e n e r a t o r ( H R S G ) p e r f o r m a n c e h a s a large i m p a c t o n the overall p e r f o r m a n c e o f a c o m b i n e d - c y c l e p o w e r p l a n t . A n a c c u r a t e s i m u l a t i o n o f the p e r f o r m a n c e o f the H R S G is t h e r e f o r e n e c e s s a r y to a n a l y z e the effects o f n u m e r o u s p o s s i b l e o p e r a t i n g c o n d i t i o n s o n the c o m b i n e d - c y c l e p o w e r p l a n t p e r f o r m a n c e . S o m e o f the factors w h i c h i n f l u e n c e the p e r f o r m a n c e o f an H R S G include: • the gas a n d w a t e r flow rates, t e m p e r a t u r e s , p r e s s u r e s a n d gas c o m p o s i t i o n s w h i c h v a r y w i t h fuel type; • w a t e r a n d air t e m p e r a t u r e c h a n g e s d u e to d i u r n a l a n d s e a s o n a l t e m p e r a t u r e c h a n g e s ; • f o u l i n g o f the h e a t - t r a n s f e r surfaces w h i c h v a r y w i t h t i m e a n d lead to significant c h a n g e s in h e a t - t r a n s f e r rate a n d p r e s s u r e loss; • the g e o m e t r y o f the H R S G ; a n d • f l u c t u a t i n g c o n d i t i o n s at the gas t u r b i n e e x h a u s t , e.g. gas velocity a n d t e m p e r a t u r e .

429

Modeling heat recovery steam generator performance

Water tubes

/'/

/

.

/,

///

/,, / i '

Z Fig. 1. Schematic drawing of a section of the HRSG showing the coordinate system.

In addition, there are many sources of uncertainty and operational variance which prevent exact performance prediction. These include: • the uncertainties in the prediction of physical properties of the process fluids [1]; • the design methods, including the basic heat-transfer and pressure-drop correlations, which have substantial error ranges [2]; • the effects of barriers, such as baffles, on heat-transfer and pressure-drop characteristics; and • the effects of changes in thermodynamic and transport properties of the process fluids across the HRSG. Prediction of heat-exchanger performance can be based on assumptions about flow patterns. Departures from these assumptions can be accommodated using empirically derived degradation

y,v ,T

- " ~ X~ U

i'-

/

Z,W

(Sx). _ _ W

L, **

o w

t

II/ II

/w'

-I-

I~

Ax

e

~l

~I

E

"- 4

~ I

w

(Sx),+

I

t

S

/:',

I/ i!

I--

(Sz)s _ _ (SZ)n ' - ~ S

-I-

I.,

Az

(Sy)b

_.

b

T

o

I

o

B

I~

Av

_1 (8y)t

t I

:1

/7 g S

B

Fig. 2. Typical three-dimensional discretization control volume labeling convention.

=l "

T

430

A. Ong'iro et

al.

:%.--

x

-~,.

Fig. 3. Staggered grid control volume for velocitydiscretization (only x-direction velocitycomponents are shown). correction formulae. This practice is adequate for interpolation between common types of heat exchangers with only slight variations in geometry, but it will not work in cases where the benefits of a new geometrical configuration are to be explored [3]. In an attempt to account as much as possible for the above-mentioned factors, while keeping computational complexity manageable, we have developed a numerical method to predict the performance of HRSGs. The method is intended for use in performance simulation models of advanced power cycles since its accuracy is acceptable and it does not require large computational resources or computation time.

H P superheated steam

Fromdeaemtor

-I ~ I-liP I ~ l l e r ~

II

LP saturated

Boiler feed t pump

steam

i

! i" '1

Turbine (]as

Exhaust (TEG)

, t,j To deacrator Fig. 4. Schematicdrawing of the HRSG layout.

Condensate

pump

TEGto stack

M o d e l i n g heat recovery steam g e n e r a t o r p e r f o r m a n c e liP Steam

From lip

To HP

To HP

~om

To HP

Steam

Steam

Steam

BLR

Steam drum

A

eontrul zone

431

To Dearatof

Condensate/ ld,,da~-up

RII

/

A

/

'

/

/ From lip mud drum lIP

HP

lip

Superheater

Superheater

#1

#2

Boiler #1 and #2

Each panel is 2 rows deep Each panel is 32 sections wide Total tubes per panel =64

4 mud drum ItP Economizer

LP Boiler

Feed water heater

Each boiler is 32 sections wide LP boiler is 13 rows deep l i p Boiler #1 is 4 rows deep HP Boiler #2 is 9 rows deep

Fig. 5. Schematic d r a w i n g of the H R S G section s h o w i n g the c o o r d i n a t e system.

The proposed method involves the calculation of velocity and temperature fields by the discretization and solution of conservation equations (continuity, momentum and energy) derived for an H R S G of particular geometry and duty. The method permits the evaluation of the effects of variation in fluid properties, flow rates of gas and water, tube arrangement, and barriers such as baffles. It also provides information on the pressure and temperature distribution within the HRSG, as well as the rate of heat transfer. The H R S G is subdivided into control volumes such that the thermodynamic and transport properties can be calculated based on the local temperatures and pressures. A continuum approach is used which allows the use of coarse grids (low computation time) without loss of accuracy. In predicting pressure and temperature distributions, this approach also allows the use of empirical one-dimensional heat-transfer and pressure-drop correlations for single and two-phase tube-side flow and single-phase cross flow on a local basis, without the assumption of a uniform three-dimensional velocity field [4]. To demonstrate the applicability and predictive capability of the proposed method for power plant HRSGs, the method is used to simulate the pressure, temperature, steam quality and heat-flux distributions in a commercially available H R S G under full- and part-load conditions. The predicted results are compared with experimental measurements to validate the method. Results from a case-study simulation are then presented to demonstrate the capabilities of the method.

NUMERICAL METHOD The governing conservation equations with reference to the Cartesian coordinates shown in Fig. 1 can be written for the shell-side and tube-side fluids and metal as follows. Shell-side flow Continuity equations. ~(pflu) a(p[3u) d(pflv______~)+ a(pflw) _ 0 ~-------i---+ ~x + ~y Oz "

(la)

432

A. Ong'iro et al.

M o m e n t u m equations. Since the terms representing viscous action are negligible in densely filled spaces in HRSGs [5, 6], the momentum equations in the x-, y- and z-directions are: O(pflu) + t?(pfluu) + __t?(PflVU) + O(pflwu) dt dx Oy Oz

L u _ __OP Ox '

(lb)

~(p#v) ~(p#uv) + t?(pflwv) _ _~(p#vv) _ O----i-- + ~ + #y Oz

, f,.v _ - -#P

(lc)

Oy

O(pflw) + O(pfluw) + O(pflvw) + O(pflww) _ Ot t?---------~ t?y t?z

f:w -

#P -~z "

(ld)

T~ho,).

(le)

Energy equation. ) + _t3(pflvh ) + O(pflwh ) - U o ( T ~ . a(pflh) + _O(pfluh _ _ ~t ~x t?y Oz

Tube-side flow

The tube side obeys similar equations. However, since the fluid flows only in one direction inside the tubes, the mass velocity in each tube is constant, and only one convective term is present. The conservation equations are simplified to those shown below (assuming tube-side flow is parallel to the x-axis). Continuity equation. 0(G,)

#(G0

?---7- - +

f--

= 0.

(2a)

#x

--~---I

Hot gases from

,

lip f-

guperheated-

:

;

.xh.e,t

I

'

i

*

i

I

i

i

I.

.

y

I

f

in, . . .

I l~Oille, r IF,& I ,

~

/

. . . .

q

i ]~.,ed w a t e r

~from deaerator

Y 9

Flue gases to Stack - - ~

~

Water to deaerator

'

LP

_ ~

F

saturated

HP ,ul~rheatea

steanl

s~anl

LP

Fig. 6. ASPEN PLUS flowsheetfor the HRSG layout.


433

Table 1. Temperature profile at 100% load Water-side profile CC) Predicted

Gas-side profile CC)

Actual

% Error

Predicted

Actual

% Error

Superheater #1 Inlet Exit

332 400 ~

334 40(r

- 0.6 --

471' 455

47P 456

-- 0.2

257 332

256 334

+ 0.4 - 0.6

455 441

456 438

- 0.2 + 0.6

255 256

257 257

- 0.8 - 0.4

441 273

438 275

+ 0.6 - 0.7

138 ~ 255

138 ~ 257

-- 0.8

273 233

275 231

- 0.7 + 0.9

ll8 135

121 137

- 2.5 -- 1.6

233 144

231 146

+ 0.9 + 1.4

53 ~ 118

53 ~ 121

-- 2.5

144 113

146 108

+ 1.4 + 4.6


H P boiler #1 and #2 Inlet Exit

HP economizer Inlet Exit

LP boiler Inlet Exit

Feed water heater Inlet Exit

~Design input parameters.

Momentum equation. O(Gt) O(Gtu,) _ at + Ox

0t7, O---x"

(2b)

- U~(Tw~H- Tube).

(2C)

fxut-

Energy equation.

~(p,h,) 8t

+

O(Gtht) dx

Metal Energy equation. For the metal tube, no velocity terms and continuity and momentum equations are necessary. Thus, the energy equation for metal is: ~(hm) ~

Jl- Ui(Twal I -

Ttube) -I- U o ( T w a l l -

Tshell) =

0.

(3)

The resistance to momentum flux terms, f,, f. and f., for shell-side fluid are evaluated using

empirical equations for pressure loss in tube banks, and f , for the tube-side fluid is evaluated using empirical equations for pressure loss for single- and two-phase flow inside tubes. The shell-side Table 2. Temperature profile at 80% load Water-side profile CC) Predicted

Actual

Gas-side profile (°C) % Error

Predicted

Actual

% Error


332 394

331 390

+ 0.6 + 1.0

445 429

442 431

-- 0.5 -- 0.5

254 332

256 331

-- 0.4 + 0.6

429 412

431 411

-- 0.5 + 0.2

237 254

239 256

-- 0.8 -- 0.4

412 264

411 267

+ 0.2 -- 1.1

137 ~ 237

137" 239

--- 0.8

264 224

267 227

-- 1.1 -- 1.3

117 138

123 135

-- 4.5 + 2.2

224 144

227 143

-- 1.3 + 0.6

53" I 17

53 ~ 123

--- 4.5

144 112

143 106

+ 0.6 + 5.7


H P boiler #1 and #2 Inlet Exit

H P economizer Inlet Exit

LP boiler Inlet Exit

Feed water heater Inlet Exit

"Design input parameters.

A . O n g ' i r o et al.

434

Table 3. Pressure drop across H R S G components at 100% load Water-side profile (psi) Predicted

Actual

4.3 4.3 0.12 -0.12 1.6 0.15 4.9

3.0 3.0 0.0 -0.0 1.0 0.0 3.0

Superheater #1 Superheater #2 HP boiler #1 SCR HP boiler #2 H P economizer LP boiler Feed water heater

Gas-side profile (in H~O) % Error + 43 + 43 --+ 60 + 30

Predicted

Actual

0.41 0.41 0.81 5.3 1.62 1.22 1.64 0.48

0.3 0.3 1.1 5.0 2.0 0.8 2.2 0.9

% Error + 37 + 37 - 37 + 6 - 19 + 53 + 25 -- 47

overall heat-transfer coefficient term Uo is composed of the convective heat-transfer coefficient over tube banks, the effect of fouling due to turbine exhaust gas, and metal resistance. The tube-side overall heat-transfer coefficient term Uo. i is composed of a single-phase and two-phase (boiling) convective heat-transfer coefficient inside tubes, the effect of tube-side fouling due to impurities from water, and metal resistance. As explained before, one-dimensional empirical correlations can be used to evaluate the pressure-loss and heat-transfer coefficients. The empirical correlations used here to predict the pressure drops and heat-transfer coefficients are presented in Appendix A. D I S C R E T I Z A T I O N AND T H E S O L U T I O N OF T H E C O N S E R V A T I O N E Q U A T I O N S Since numerical methods work with a limited set of numbers, the H R S G space is divided into a finite number of continuous and non-overlapping control volumes in Cartesian coordinates by three sets of planes of fixed x-, y- and z-coordinates as shown in Fig. 1. Because the dimensions of the control volumes are large compared to the tube diameters, a typical control volume will enclose many tubes. Since each control volume can only be associated with one value of each dependent variable such as shell-side temperature, shell-side velocity, tube-side temperature, metal temperature, etc., average values of the dependent variables are needed. These average values are determined by iteration such that when they are substituted in the discretization equations (given below), they will give a reasonable representation of flux of mass, momentum and energy. The differential equations for each of the conserved quantities have similar structures and if the dependent variable is represented by ~b, the general equation in the tensor form is: c~

+

~x,

= t3-~j(F _ _ ) + S .

(4)

Figure 2 shows a single control volume and introduces the letter notation which indicates (in subscript) which control volume or face the dependent variables belong to. The central point is denoted by P, and the central points of the neighboring control volumes on the "east", "west", "north", "south", " t o p " and " b o t t o m " sides are denoted by E, W, N, S, T and B. The six faces of the control volume are given the symbols e, w, n, s, t and b respectively. Integrating the differential equation over such a typical control volume using a piecewise linear function for the differentials and a stepwise function for the source term, the conservation equations can be expressed in discretized form as [4]: apq~p =

CtE~bE "1-

aw~bwo+ aN~bN+ asq~s + aT~T + aBq~B+ b ,

(5a)

Table 4. Pressure drop across H R S G components at 80% load Water-side profile (psi) Predicted

Superheater #1 Superheater #2 HP boiler #1 SCR H P boiler #2 HP economizer LP boiler Feed water heater

2.7 1.4 0.07 -0.07 1.3 0.05 2.4

Actual 2.0 1.0 0.0 -0.0 1.0 0.0 2.0

Gas-side profile (in H:O) % Error + 35 + 40 ---+ 30 -+ 20

Predicted

Actual

0.27 0.27 0.6 3.9 1.2 0.9 2.2 0.35

0.2 0.2 0.8 3.6 1.5 0.6 1.7 0.7

% Error + 35 + 35 - 25 + 8 - 20 + 50 + 30 - 50


435

10.0r~

9.0-

0.042

0.042 - -

0.040

0.040 - -

8.1)-

0.036

0.036-

0.030

0.030-

7.0o

6.05.00.020 - -

0.020

4.03.0

0.012 -

0.012

0.008

110

0.008

115

210

2'.5

Width (m), y-axis Fig. 7. Vapor quality distribution in HP boiler #1. a n d the s o u r c e t e r m is expressed as: S = Gsc +

Sp~p,

(5b)

where:

a, = D , A ( I P e , I) +

10.0-I /

,~

, •i = e , n , t

II - Fe, 0ll for ~.I = W, S, B

~

~

(5c)

~

4.0-

:" 0.0

0.5

1.0

1.5

2.0

2.5

Width (m), y-axis Fig. 8. Gas exit temperature distribution from HP boiler #1 (°C).

A. Ong'iro et al.

436

i

ii

0.5

0.0

1.0

1.5

2.0

2.5

Width (In), y-axis

Fig. 9. Heat-flux distribution in HP boiler #1 (kW/m2).

at = D,A(IPe,I) +

a° -

lift, 011 for ~ / = w, s, b =W,S,B

(5d) (5e)

p°AxAyAz

At b

= GscAxAyAz

+

o o apq~p

ap = aE + aw + aN + as + a.r + aB - - S p A x A y A z

F~ = ( f l p u ) j A x j A x k

Pe,=

and D~ =

~

F~AxjAxk J'i = e, w, s, n, t, b (6x)g for ) i~j ~ k

for i = e , w , n , s , t , b .

(5f) (5g)

(Sh) (5i)

Using the power law to fit the flux (q~) which results in rapid convergence [4], the function A ( I P e i l ) becomes: A ( l e e , I) :

II0, (1 - O.11Pe,I)~ll for i = e, w, n, s, t, b .

(59

The temperature, pressure and velocity boundary conditions are introduced by their values at the inlet to the HRSG. The wall temperatures are extracted from an energy balance involving heat loss through the HRSG wall-lagging to ambient air by natural convection and radiation; the rate of heat loss from the wall is estimated from charts of heat loss for commercial steam generators [7]. The treatment of fluid in-flow and out-flow temperatures, velocity and pressure boundary conditions is performed according to Patankar [4]. In the solution of the momentum equations, a staggered grid is used for velocity components as shown in Fig. 3. This grid arrangement allows calculation of the convective flux across a control volume face without the need for interpolation of relevant velocity components, and therefore prevents wavy or oscillating pressure fields that are arithmetically possible with a coincident scalar and velocity grid system [4]. The technique known as SIMPLE (semi-implicit pressure linked equations) which manipulates the "primitive" variables, i.e. velocities and pressures [8], was used in this study. Essentially, a guessed pressure field p* is used in the momentum equations to solve for velocity components u*, v* and w*. The discretization equations used are:


437

aeu* = ~a,bu.~ + b + (p* - p ~ ) A y A z

(6a)

atv,* = ~a.bv.*b + b + (p* - p ~ ) A x A z

(6b)

a.w* = ~a,bW.*b + b + (p* -- p * ) A x A y .

(6c)

A correction for guessed pressure, p ' = p p*, is next required; p ' is defined as the pressure correction term, and u ' = u - u*, v ' = v - v*, and w ' = w - w* are defined analogously. The pressure correction equation is determined f r o m the continuity equation:

aepp' = aEpE" + awPw' + aNpN' + asPs' + a-rpT' + aBpB' + b ,

(6d)

where:

a t = (flP)' (AxjAxk)2 for { I = E , W , N , S , T , B i = e, w, n, s, t, b i~j~k

(6e)

and: ap = aE + aw + aN + as + aT + aB

b =

(6f)

(flpO _ flpp)AxAyAz + [(flpU*)w - (flpU*)e]AyAz + [(flpw*)~- (flpW*)n]AXAy At + [(flpV*)b -- ( f l p v * ) J A x A z .

!

.=,

",3

-0.0

0.5

1.0

1.5

2.0

2.5

Width (m), y-axis Fig. 10. Water temperature distribution in HP economizer row #1 (°C).

(6g)

438

A. Ong'iro et al.

"~

8.

g

6.

5.

3.0-0.0

(.,"

/ I"

I

I

I

0.5

1.0

1.5

2.0

Width (m), y-axis Fig. 11. Gas exit temperature distribution from HP economizer row #1 (°C). The mass flow rate of steam is estimated by performing an energy balance over the whole H R S G , and the heat loss through the casing is assumed to be 0.5 % of the available energy from combustion g a s e s - - a typical value for H R S G [7]:

0.98(rh~cp~[T~. m - T~.¢(pw)- Tpm~,]) rhw = hw(Tw,Pw)o.t -- hw(T,., Pw)~nd- BD[hw(T~at, Pw) - hw(T,,,, Pw)~n] '

(7)

To determine the initial boundary conditions, the shell-side gas conditions at the inlet to the H R S G are set equal to the gas turbine exhaust conditions. The tube-side outlet and inlet conditions are set equal to the steam turbine throttle conditions and H R S G feed water conditions respectively. The shell-side outlet pressure is set equal to atmospheric pressure and the shell-side outlet temperature is set to 30°C above the acid point of the combustion gases at atmospheric pressure. Initially, tube-side pressure loss is set to zero and the tube-side temperature is assumed to vary linearly in the economizer from the feed water inlet temperature to the saturation temperature. In the evaporator, the tube-side temperature is assumed to be fixed at the saturation temperature, and a linear variation of steam temperature is assumed in the superheater. The tube-side water quality varies from saturated liquid at the economizer outlet, to saturated vapor at the evaporator outlet. The shell-side temperature is assumed to vary in a piece-wise linear fashion from gas inlet temperature to pinch-point temperature [the pinch-point is assumed to be at the outlet of the high-pressure (HP) economizer]. The metal temperature is assumed to be equal to the mean temperature of shell-side and tube-side fluids. The thermodynamic and transport properties of the fluids are all initially evaluated at the mean bulk temperatures of the shell-side and tube-side fluids. For the shell side, the control volume frictional pressure-loss components in the source term of the discretized m o m e n t u m equations are evaluated from cross-flow pressure-loss correlations


439

(equation (A5) in Appendix A) while those for the tube side are evaluated from equation (A1) for subcooled liquid and superheated steam, and equation (A2) for forced convection boiling. The application of the SIMPLE technique can be summarized as follows. 1. Guess the pressure field p*. 2. Calculate the values of u*, v* and w* by solving the momentum equations 6(a)-(c). 3. Solve equation 6(d) for p'. 4. Determine p by adding p' to p* with an under-relaxation factor of 0.5. 5. Solve equations 5(a)-(j) for conserved quantities represented by q~ in equation (4) to determine enthalpy (temperature) and other scalar quantities like tube-side vapor quality, metal temperature, etc. 6. Update the thermodynamic and transport properties and recalculate the heat-transfer coefficients and frictional pressure-loss factor as outlined in the previous paragraph. 7. Use the calculated value of p as p* and repeat the procedure until convergence is reached. 8. If the desired HRSG performance is not achieved, an adjustment is made to the mass flow rate and thermodynamic conditions of the feed water at various points in the HRSG, and steps 1-7 are repeated until a satisfactory performance is achieved. In part-load operation, the mass flow rate of feed water is found by iteratively carrying out steps 1-7, with extra constraints imposed by both gas turbine and steam turbine part-load controls.

COMPUTER

MODEL

The HRSG is sized to handle the thermal load imposed by the gas turbine exhaust. The design was based on an HRSG configuration with a single reheater, supplying both high-pressure and low-pressure steam. The part-load performance calculations account for the variation of the overall heat-transfer coefficient with mass flow rates of gas and water, and changes of conditions at both

v

,.o

",3

-0.0

0.5

1.0

1.5

2.0

2.5

Width (m), y-axis Fig. 12. Heat-flux distribution in HP economizer row #1 (kW/m-').

440

A. Ong'iro et

al.

10.0-

"~

~

8.0-

6 . 0 -

?

i

Et 4.0

\

\

8

2.0

0.o

-0.0

t 0.5

1.0

!:J 1.5

2.0

2.5

Width (m), y-axis Fig. 13. Water temperature distribution in the feed water heater (°C). the gas turbine exhaust and water inlet. To accommodate geometrical irregularities such as expansions, contractions and bends, etc. in the computer model, an indexing system is used whereby the grid points are designated by zero if they lie outside the boundaries of the H R S G and by one if they are within the boundaries. This way it is possible to model H R S G s of irregular geometry.

r#j

Ii It

0.04

-0.0

~

0.5

~

1.0

1.5

2.0

'

,---x

2.5

Width (m), y-axis Fig. 14. Gas exit temperature distribution from feed water heater (°C).

Modeling heat recoverysteam generator performance

441

t~

g

-0.0

0.5

' 1.0

1..'$

2.0

I 2.5

W i d t h (m), y - a x i s Fig. 15. Heat-flux distribution in the feed water heater (kW/m2).

V A L I D A T I O N OF T H E M O D E L The H R S G model was incorporated in the ASPEN PLUS Shell and merged with a gas turbine model [9] to study the model performance. An H R S G consisting of two superheaters, two high-pressure (HP) boilers, one economizer, one low-pressure (LP) boiler with integral deaerator and one LP feed water heater was used to validate the model. The schematic and the configuration of the H R S G are shown in Figs 4 and 5, with the corresponding ASPEN PLUS flow diagram shown in Fig. 6. The actual performance data for the H R S G were obtained from D E L T A K [10]. Using a 75 MHz 486 personal computer, the simulation took about 140 s of computation time. A comparison of the actual and predicted temperature profiles in the H R S G and the pressure drop across the various sections of the H R S G are presented in Tables 1-4 for 100 and 80% loads. The temperature profile is predicted reasonably well to within 5% error, indicating that the model can be used with confidence. The pressure-drop predictions, however, have significant error as can be seen from Table 3 and 4. The large magnitude of the error can be attributed to uncertainties inherent in the pressure-drop correlations used (as discussed in Appendix A), and also due to the difficulty in predicting pressure drops around irregular geometries involved in an HRSG. The actual pressure drop of the H P and LP boilers are reported as zero because the circulation loop generates its own driving force which compensates for the pressure drop accompanying the two-phase flow within the circulation loop. However, considering the small effect of air- and water-side pressure drops on energy performance of an HRSG, the magnitude of error is not critical for the intended applications of the model. SIMULATION RESULTS FROM ACASE STUDY To demonstrate the capabilities of the model, it was used to predict local temperature, quality, pressure drop and heat-flux distributions around various H R S G components based on the

442

A. Ong'iro et al.

Yz

0.0

0.5

1.0 1.5 2.0 Width (m), y-axis

2.5

Fig. 16. Steam temperature distribution in superheater #1 (°C).

computer, the simulation took about 180 s. The results of the simulations are presented in Figs 7 - 18. These results could not be validated against actual performance data due to unavailability of data at the required level of detail, but they do exhibit reasonable trends expected from heat exchanger analysis. Figure 7 shows that the vapor quality increases uniformly to 0.05

v'~)l.0

015

1'.0 1'.5 210 Width (m), y-axis

2'.5

Fig. 17. Gas exit temperature distribution from superheater #1 (°C).


443

8.

",3

~)i0

015

110 115 210 Width (m), y-axis

2'.5

Fig. 18. Heat-flux distribution in the superheater (kW/m2).

(circulation ratio of approximately 20) within the HP boiler tubes, leading to a symmetrical gas exit temperature from the HP boiler as shown in Fig. 8, and a heat-flux distribution shown in Fig. 9. The heat flux is higher at the center and the gas temperature is coolest at the wall due to both the heat loss from the walls and the variation in the tube-side, two-phase convective heat-transfer coefficient. Figure 10 shows the water temperature distribution in one of the panels of the HP economizer. The resulting pattern is due to the four-pass tube arrangement on the water side. The gas exit temperature distribution shown in Fig. 11 closely follows the water temperature distribution, with higher gas outlet temperatures in regions of high water temperature due to a decreased available temperature differential between gas and water. The variation of heat flux shown in Fig. 12 also follows the same pattern. Figure 13 shows the water temperature distribution in one of the rows of the LP feed water heater. The resulting pattern is due to the four-pass tube arrangement on the water side. The gas exit temperature distribution shown in Fig. 14 closely follows the water temperature distribution, with a higher gas outlet temperature in regions of high water temperature due to decreased available temperature differential between gas and water. The variation of the heat flux shown in Fig. 15 also follows the same pattern. Figure 16 shows the water temperature distribution in one of the panels of the HP superheater. The resulting pattern is due to the two-pass tube arrangement on the water side. The gas exit temperature distribution, shown in Fig. 17, closely follows the water temperature distribution with a higher gas outlet temperature in regions of high water temperature due to the decreased available temperature differential between gas and water. The variation of heat flux shown in Fig. 18 also follows the same pattern. As should be expected, the distribution of heat flux in the HP boiler, economizer, feed water heater and superheater (shown in Figs 9, 12, 15 and 18) indicate that the heat flux accompanying evaporation in the HP boiler is much higher than in either the superheater or the feed water heater. The variation of heat flux across the feed water heater and the superheater can be attributed to the change in the local approach temperatures as the water/vapor temperature decreases along the tube length. The heat-flux variation in the HP boiler can be attributed to effects of forced convection suppression on nucleate boiling heat transfer, change in flow regimes, vapor blanketing and other phenomena associated with two-phase flow. ATE 17/5--B

444

A. Ong'iro et al.

As can be seen from this example analysis, the model can be used for a n u m b e r of purposes: • to predict the thermal a n d hydraulic p e r f o r m a n c e of H R S G s at full- a n d part-loads; • to evaluate the impact o f changes in design a n d operating c o n d i t i o n s (such as geometry, a d d i t i o n / r e m o v a l / c o n f i g u r a t i o n of modules, gas t u r b i n e exhaust temperature, composition, flow rate, etc.) o n performance; • to identify potential operating p r o b l e m s (such as cold-end acid corrosion, steaming in the economizer, p i n c h - p o i n t t e m p e r a t u r e violation, etc.); a n d • to define limits of safe operation. The results of such analyses can be used in p r e p a r i n g capital a n d operating cost projections a n d in t h e r m o - e c o n o m i c o p t i m i z a t i o n studies.

CONCLUSION A comprehensive c o m p u t e r s i m u l a t i o n of a n H R S G was developed. It features pressure-drop a n d temperature-profile predictions. Special a t t e n t i o n was paid to the i n p u t t i n g o f relevant b o u n d a r y conditions. The model is suitable to be used in p e r f o r m a n c e s i m u l a t i o n models of a d v a n c e d power cycles since its predictions are accurate a n d it does n o t require large c o m p u t a t i o n a l resources a n d time. The model was integrated with a gas t u r b i n e model in the A S P E N P L U S Shell, a n d it was validated using actual H R S G p e r f o r m a n c e data. U s i n g a sample case study, it was d e m o n s t r a t e d that useful i n f o r m a t i o n o n the local v a r i a t i o n of water- a n d gas-side t h e r m o d y n a m i c c o n d i t i o n s can also be predicted from the model. Acknowledgements--The authors gratefully acknowledge the financial support provided by the Natural Sciences and

Engineering Research Council of Canada (Operating Grant OGPOO41739), Canadian Commonwealth Scholarship and Fellowship Plan, and Deltak Unit of Jason, Inc.

REFERENCES I. S. G. Hauser, D. K. Kreid and B. M. Johnson, Investigation of combined heat and mass from a wet heat exchanger: II experimental results. A S M E - J S M E Thermal Engineering Joint Conference, Honolulu, HI, pp. 525-535, March (1983). 2. A. J. Chapman, Fundamentals of Heat Transfer. McMillan Publishing Co., New York (1984). 3. S. V. Patankar and D. B. Spalding, Computer analysis of the three dimensional flow and heat transfer in a steam generator. Forschung lng. -Wes. 44, 47-52 (1978). 4. S. V. Patankar, Numerical Heat TransJer and Fluid Flow. McGraw-Hill Book Co., New York (1980). 5. S. V. Patankar and D. B. Spalding, Simultaneous Predictions of Flow Pattern and Radiation for Three Dimensional Flames, Heat Exchangers (Edited by N. M. Afgan and J. M. Beer), pp. 73-94. Hemisphere, New York (1974). 6. R. R. Dils and P. S. Follansbee, Heat transfer coefficientsaround cylinders in cross flow from combustor exhaust gases. J. Engng Power, 497-507 (1977). 7. Babcock and Wilcox, Steam: Its Generation and Use. Babcock and Wilcox Co., New York (1992). 8. S. V. Patankar and D. B. Spalding, A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. Int. J. Heat Mass Transfer 15, 1787 (1972). 9. A. Ong'iro, V. I. Ugursal, A. M. AI Taweel and G. La Jeunesse, Using ASPEN PLUS Shell to simulate the performance of gas turbines. In Proceedings of the A S M E 1994 Engineering Systems Design and Analysis Conference, London, pp. 57~54, 4-7 July (1994). 10. DELTAK, HRSG Performance Data. DELTAK, Minneapolis, MN (1994). 11. S. W. Churchill, Comprehensive correlating equation for heat, mass and momentum transfer in a fully developed flow in smooth tubes. Ind. Eng. Chem. Fundam. 16(11), 109-116 (1977). 12. S. Kekac, The effect of temperature dependent fluid properties on convectiveheat transfer. In Handbook of Single Phase Convective Heat Transfer (Edited by S. Kekac, R. Shah and Wing Aung), Chapter 18. John Wiley and Sons, New York (1987). 13. J. R. Thorn, Prediction of pressure drop during forced circulation boiling of water. Int. J. Heat Mass Transfer 7, 709-724 (1964). 14. J. G. Collier, Convective Boiling and Condensation. McGraw-Hill Book Co., New York (1972). 15. A. A. Zukauskas, Convectiveheat transfer in cross flow. In Handbook of Single Phase Convective Heat Transfer (Edited by S. Kekac, R. Shah and Wing Aung), Chapter 6. John Wiley and Sons, New York (1987). 16. E. S. Gaddis and V. Gnielinski, Equations for heat and mass transfer in turbulent pipe and channel flow. International Chemical Engineering 25(1), 1-15 (1985). 17. V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow. International Chemical Engineering 16(2), 359-368 (1976). 18. V. V. Klimenko, A generalized correlation for two phase forced flow heat transfer. Int. J. Heat Mass Transfer 31, 541-552 (1988).


445

19. V. V. Klimenko, A generalized correlation for two phase forced flow heat transfer--second assessment. Int. J. Heat Mass Transfer 31, 2073-2087 (1988). 20. W. J. Marner and J. W. Suitor, A Survey of Gas Side Fouling in Industrial Heat Transfer Equipment, JPL Publication 83-74. Jet Propulsion Laboratory, Institute of Technology, Pasadena, CA (1984).

APPENDIX CORRELATIONS

TO PREDICT

HEAT-TRANSFER

A COEFFICIENTS

AND FRICTION

FACTORS

Pressure-drop correlations The tube-side single-phase (liquid water or dry steam) pressure drop is predicted using a correlation [11] which predicts the friction factor in laminar, transition and turbulent flow regimes. The correlation (equation (A1)) is in good agreement with well-established correlations for laminar flow and the Colebrook equation for turbulent flow, and is in fair agreement with experimental data [12].

~c =

,

[

[(8/Re~),o + (Rej/36,500)2o],'2 + 2.21 log~

(A1)

The tube-side, two-phase (boiling water) pressure drop in a horizontal tube is made up of two components--the pressure drop resulting from the increase in momentum of the mixture as it flows through the tube and vaporizes (acceleration), and the pressure drop due to friction drag. A correlation based on slip flow theory [13] is used to predict the total tube-side pressure drop (acceleration and friction):

2

]

Ap~ = G ( r r t + + r3 pr 1_ (r2 + 2)d "

(A2)

The evaluation of parameters r~, r2 and r3 is presented by Thorn [13]. The pressure drops at the exit from the tubes to the header, and at the inlet to the tubes from the header, are evaluated using the limits of two-phase pressure-drop correlations [14] for sudden expansion and contraction as the area ratios tend to zero respectively:

o2r! po=2p LC

,]-'[,

+

(A3)

Ap,=

(A4)

The pressure loss in cross-flow over the tube bundle is due to a combination of friction and pressure drag. The pressure loss consequently is a function of tube-bundle configuration, number of tube rows, type of tube fins and physical properties of the fluid. This can be expressed in non-dimensional form by:

St

Si

The functional relationship between the pressure drop and relevant variables for the different scenarios are in most cases determined experimentally[15]. The correlation for in-line and staggered tube bundles developed by Gaddis and Gnielinski [16] is used here due to its accuracy and convenience in incorporating it into a computer code, as it does not require the use of charts or tables. The correlation was developed by regression of about 2500 pressure measurements, and fits 90% of the data to 25% accuracy.

Heat-transfer correlations The tube-side, single-phase (liquid water or dry steam) convective heat-transfer coefficient is predicted by the following correlations for laminar, transition and turbulent regimes. Laminar region--Sieder and Tate correlation [2].

Nu~ = O.027ReO.SprL.3(\ la#..,,)o,,.

(A6a)

Transition region--Churchill correlation [11]. f3.657 for constant wall temperature

Nut. j = [4.364 for constant wall flux. Nut. ~ = Nuo +

O.079(,f/2)'2Re Pr (1 + Pr4/5)5'6

(A7)

(A8)

446

A. Ong'iro et al.

Nuo =

f4.8 for constant wall temperature 6.3 for constant wall flux.

Fully developed turbulent flow--Gnielinski correlation [17]. 12%. [12]

(A9)

The correlation agrees with experimental data to within

(F/2)(Red -- 1000)Pr NUd = 1 + 12.7(F/2)t2(Pr 2:3- 1)

(AI0)

F = (1.58 Iog~Red -- 3.28) z,

(AI 1)

for 2300 < Red < 5 x 106 and 0.5 < Pr < 2000• The prediction of the tube-side, two-phase (boiling water) convective heat-transfer coefficient with a high degree of accuracy is important, as the process involves high heat fluxes even at low wall-liquid temperature differences. However, this is difficult due to the dependence of the two-phase flow on different factors such as heat flux, pressure, condition and thermal properties of the liquid and wall material, non-adiabatic flow patterns, nucleate boiling suppression by forced convection, etc. [18]. A generalized correlation for two-phase, forced convection flow heat transfer [19] which is based on extensive experimental data for 21 different fluids, and which has an uncertainty of 1 4 0 is used here. SNUd b with NcB< 1.6 × 104 Nua. TP = ~ NUd. c with NcB> 1.6 X 104.

(AI2)

The evaluation of the two-phase Nusselt n u m b e r (NUd. w), convective boiling number (NcB), Nusselt number for nucleate boiling (NUd, B) and Nusselt n u m b e r for forced convection vaporization (NUd.c) is presented by Klimenko [19]. Heat transfer from tubes in cross-flow is predominantly determined by stream velocity, turbulence level, physical properties of the fluid, thermal load, heat-flux direction, and the geometry of the body. This can be expressed in non-dimensional form by: Nu=

Re, Pr, Tu,

I~

/~.,'

k

k~.li'

cp

Cp.~.'

P~ll

'

The functional relationship between the Nusselt n u m b e r and the relevant variables for the different scenarios are generally determined experimentally [15]. In this study, the average heat-transfer coefficient is needed, and therefore correlations from ref. [15] are used. These correlations are based on an extensive experimental study of bundles with both smooth tubes and finned tubes, and have an uncertainty of 15%. Fouling on the shell and tube sides

Fouling is the deposition of an insulating layer of material onto a heat-transfer surface. Accurate prediction of fouling is important in heat-exchanger performance evaluation as it leads to over-surfacing of the heat exchanger to compensate for a reduction in heat transfer due to fouling, over-specifying of p u m p s and fans to compensate for over-surfacing, and an increased pressure drop arising from a reduced flow area. In this study, the fouling resistances given in ref. [20] are used. A fouling resistance of 0.000176 m 2 K / W (Rro,o) is used for the shell side due to gas turbine exhaust, whereas a fouling resistance of 0.000352 m s K / W is used for the tube side due to treated makeup water. The estimation of the tube-side pressure drop due to fouling is based on the fouled tube diameter calculated using the correlation by Marner and Suitor [20]: dfo = a [ e x p ( -

2kfoRfo. .

)1

(AI4)

Overall heat-transfer coefficient The shell-side overall heat-transfer coefficient term Uo, o is composed of a convective heat-transfer coefficient over tube banks, the effect of fouling due to turbine exhaust gas, and metal resistance. The tube-side overall heat-transfer coefficient term Uo. ~is composed of single-phase or two-phase (boiling) convective heat-transfer coefficient inside tubes, the effect of tube-side fouling due to impurities from water, and metal resistance. The overall heat-transfer coefficient term based on the inside-tube cross-sectional area Uo is given by:

1 Uo -

1

qo.~ho + R r o . , +

ao. ,log~(Ao. ,/A~. ,) 2rckm ~(Az~)

.4o.,.

+ , 4 , . R, i +

q,., = 1 -- ~A, ~(1 -- g,. ,) and no., = 1 - ~Afo

Ao .i

(1 - go. i).

(AI5) (A16)