Steam Generator Modeling Using Thermofluid Matlab-Simulink Library

Steam Generator Modeling Using Thermofluid Matlab-Simulink Library

F. Betchine A. Lamamra

Automatic laboratory of Setif Automatic laboratory of Setif LAS – Algeria – LAS – Algeria –

Abstract

The modeling of process engineering systems is still an open field because of its complexity. These processes have a highly non-linear behavior mainly due to the mutual interaction of several phenomena of various kinds and the combination of technological components that implement the laws from different disciplines (mechanical, thermal , chemical). Even if these types of processes are present in a many industries with risk (nuclear, chemical, etc…), which require for their knowledge and control models more precise and usable.

The aim of this work is to create a model in Matlab-Simulink, of the steam generator situated at Lille 1 University, such a process occurred in many risky process, is characterized by multidomain energy.

Key words– Modeling, Matlab-Simulink, Steam Generator, Condenser, boiler, expansion.

1. Introduction

   The steam generation process is widely used in process engineering. Furthermore, such phenomena occur in many risky processes such as nuclear and chemical, it is why their modeling is needed.

   Because of the complexity of the thermodynamic phenomena which govern the dynamic behavior of thermal power plants, the modeling problem is still with a great interest.

2. Process description

   Let us consider the supervision of the pilot process schematically shown on fig 1. The test plant designed to be a scale-model of part of a power station is a complex non linear system. This installation is mainly constituted of four subsystems: a receiver with the feedwater supply system, a boiler heated by a 60 KW resistor,

   a steam flow system and a complex condenser coupled with a heat exchanger.

   The feed water flow is pressurized via the feed pump which is controlled by a relay to maintain a constant water level inside the steam generator. The heat power is determined based on the available accumulator pressure P7. The expansion of the generated steam is realized by three valves in parallel connection. V5 is a controlled valve, which allows passing around the steam flow to the condenser. V6 is automatically controlled to maintain proper pressure to the condenser. In an industrial plant, the steam flows to turbine for generating power, but at the test stand, the steam is condensed and stored in a receiver tank and returned to the steam generator [5],[6].

   Fig 1. Schematic of the pilot process

   1. The feedwater system

      It consists of a pump, a pipe and a tank receiver (Fig 2):

      PP

      is the difference between the output pressure

      PP and the input pressure PT of the pump:

      P 105 (P P ) (5)

      P P T

      KD (zv1 )

      is the flow nonlinear characteristic of the

      Fig 2. Feedwater system

      The tank is initially full of water at ambient temperature, and therefore under-saturated: the pressure and temperature are independent. The pressure at the bottom of the tank depends only on the volume or mass:

      pipe identified experimentally and depending on valve V1 position ZV1. b1 is a Boolean variable based on the reference (LB_ref) and the actual (LB) water level inside the boiler. It depends also on the dead zone , of the "on-off" controller.

   2. The boiler

   P .g.N

   .g. VT

   T .g mT g.mT

   (1)

   The boiler belongs to the class of saturated fluid

   T

   T

   T T T

   AT AT T AT

   accumulator, as it is shown in fig 3:

   Where

   PT , T , g, NT ,VT , AT ,mT refer to the pressure,

   density of water, gravity, and water level in the tank, the volume of water, the tank section and the mass of water.

   The input and output Enthalpy flows of the storage tank are expressed as a function of temperature Tin, the specific enthalpy HAL, the input and output

   • Fig 3. The boiler

   mass flow min , and mout :

   The energy conservation equation is given by (6):

   Hin min cpTin

   (2)

   d HB

   (6)

   • H AL

     (3)

     dt H B QTH H AL EW H VD

     H out mout

     mAL

     HB is the total enthalpy in the boiler

     The mass flow refueled by the pump m AL is

     determined as the intersection between the pump

     We assume that the fluid in the boiler exits as a saturated, homogeneous mixture of vapor and

     • liquid at uniform pressure PB, the mixture is

   and the pipe characteristics ( mPA and m AL ) which are given by the following equations [3],[6]:

   characterized by the steam quality X (dryness fraction) in the boiler

   The pressure PB and the steam quality X in the

   P

   P

   mp

   AL

   8,33*1010 P 9,722 *104

   (4)

   boiler, are determined solving the mixture equation:

   mp

   (P P )105

   AL

   P B

   KD (zv1 )

   h HB h (P ).X h (P ).(1 X )

   B m v B l B

   B

   (7)

   B

   B

   is the water density equal to 1000 kg/m3.

   v VB v (P ).X v (P ).(1 X )

   AL B m v B l B

   Where hl and hv represent water and steam

   The flow of under-saturated liquid through the three parallel valves is given as follows:

   saturation specific enthalpy,

   vl and vv

   specific

   volumes. All are thermodynamic functions of

   pressure [3]:

   2

   2

   hv 0.74P 17.21P 2680

   l

   l

   h 0.0243P4 0.8487P3 11.9P2 99.97P 347

   m1 Kv1 (zv1 ).

   m2 Kv 2 (zv 2 ).

   (P P ) PC

   T

   T

   B C

   B C

   B

   T

   T

   B C

   B C

   (P P ) PC

   B

   P

   (8)

   v

   v

   v 5.3*105 P5 0.00207P4 0.0032P3

   mB KvB (zvB ).

   (PB PC ) C

   TB

   0.2498P2 1.03P 2.166

   Kv1 (zv1 )

   , Kv2 (zv2 )

   and

   KvB (zvB ) , Are the pressure

   l

   l

   v 3.59*107 P3 1.2456*105 P2 1.03*103

   drop coefficients in the corresponding valve, these coefficients are nonlinear functions of the position

   The temperature

   TB is determined then by the

   z of the flap valve.

   following thermodynamic relationship

   TB f PB :

   2.4. The condenser

   T 0.4594P2 12.72P 99.003

   B B B

   2.3. Steam expansion

   The steam expansion system is shown in fig 4:

   Fig 4. The steam expansion system

   The expansion of generated steam is realized by three valves in parallel connection. VM1 is a manually controlled valve, simulating that corresponds in an industrial plant to pass around the steam flow to a condenser. VM2 is automatically controlled to maintain proper pressure to the condenser. The bypass valve VMB, normally closed allows simulating a leakage pressure in the system.

   In an industrial plant, the steam flows to turbine for generating power, but at the test stand, the steam is condensed and stored in a receiver tank for returning to the boiler.

   The condenser of the steam generator is one of the most complex components; Figure represents a schematic diagram of this component. Its role is to transform the dry steam coming from the steam expansion system to liquid.

   Fig 5. Condenser schemaic

   The steam coming from the expansion system to the condenser is condensed over the vertical tubes through which the cooling water flows. The tubes are split into three parts: at the input to the condenser in touch with the steam, within the condensate and then again in contact with the steam at the output from the condenser. There the water outflow )condensate) is controlled by three valves, in order to keep its level constant.

   Steam phase

   The mass of saturated steam coming from the boiler is given by:

   Mcv v *Vcv

   (9)

   The specific enthalpy of the steam in the condenser is obtained from thermodynamic tables

   Vcv : Volume of steam ( m3 ).

   h 3*107 T 5 2.0766*104 T 4 7.0061*102 T 3

   cv cv cv cv

   8.9607 *T 2 1.18506*103 T 2.5202*106

   : Mass density of steam Kg .

   cv cv

   v m3

   (15)

   Liquid phase

   M ec M ct dt

   (10)

   v

   v *V

   v0

   The condensate flow is:

   T cv

   *

   * g *e3 * * d * n

   M ec : Entering steam flow Kg .

   M ct l

   l v x t t

   3* l

   (16)

   S : Mass density of the liquid ( Kg ).

   M ct : Condensate flow Kg .

   S

   3

   3

   v0 : Initial mass density of steam Kg .

   l m3

   v : Mass density of the steam ( Kg ).

   m3

   m l : Dynamic viscosity of the liquid ( Kg

   ).

   m.s

   The volume of steam in the condenser Vcv is :

   dt : Tubes' diameter (m).

   Vcv

   V Sc

   • Ncond

     (11)

     nt : Number of tubes.

     V : Total volume of the condenser ( m3 ).

     Sc : Horizontal section of the condenser ( m2 ).

     ex : The height of the condensing film it is extracted from a Nusselt type formula:

     4* *l N *T T * 1/ 4

     ex

     l

     cond

     cv vt l

     Ncond : Level of liquid in the condenser ( m ).

     (17)

     g * l *

     l v

   • Lv 0.68*ctv * Tcv Tvt

     Ncond

     Ml

     l * Sc

     (12)

     l :Thermal conductibility of the condensate

     Where Ml is the liquid mass:

     (W m. c).

     M

     * dt M

     (13)

     l M ct

     M vd l 0

     Tvt

     : Temperature entering steam (°C).

     v

     T

     : Partial derivative of saturated steam density

     ctv : Specific heat of the metal tube in vapor

     is evaluated from saturated steam tables[5]:

     section ( J ).

     v 4.59*1011T 4 1.59159 *109 T 3

     Kg. c

     T cv cv L

     v

     v

     8.0471*107 T 2 1.1346 *105 T

     (14)

     : Latent condensation heat ( J ).

     Kg

     cv cv

     1.90366 *104

     L 3.4 *1011T 4 4.421*1011T 3

     Depending on whether the flow is laminar or

     v cv cv

     1.545403*106 T 2 2.21406 *103T

     (18)

     turbulent.

     cv

     249716 *106

     The pressure of the liquid is:

     cv

3. Modeling hypotheses

   The steam generator is modeled by considering the following hypotheses [1], [5]:

   P N

   • g * l P

   (19)

   • The water and the steam in the boiler are supposed

     cl cond

     105 cv

     to be in thermodynamic equilibrium, due to their homogenization;

     The flow of outlet liquid

     P P

   • The boiler mixture is under an uniform pressure; where the effect of the superficial pressures of the steam bubbles is neglected.

     K

     K

     M vd M ct bi * c * cl ls

     dv

     (20)

   • The variables are localized on the real system.

   • The steam generator is not correctly insulated,

     Specific enthalpy of outlet liquid (J/kg) is given by:

     where the heat losses are by conduction towards external environment.

     h c *T

     (21)

   • The fluid in the feeding circuit is considered

   vd l cl

   cl : Specific heat of the liquid ( J Kg. c).

   incompressible because the water is taken at the ambient temperature.

4. process model

   Tcl : Temperature of outlet liquid (°C).

   Mixture equation [2] [3]:

   hcv hv Pcv * X hl Pcv *(1 X )

   1

   (22)

   v P

   * X v P *(1 X )

   v

   v cv

   l cv

   2.5. The discharge valves

   The level of the condensate is controlled by means of three onoff valves placed in parallel between the condenser and the tank. These valves keep the condensate level LC within 0.5 l of a given set point.

   It is considered that the inertia of the valves is negligible. They have the same coefficient drop pressure KDC.

   The flow of each branch is determined by

   Bernoulli's law because the liquid is assumed incompressible:

   Fig 6. Process model

5. Simulation Results

3

m bi .KDC

i1

Psc

• PB

(23)

Or:

3

m bi .KDC

i1

Psc PB

(24)

Fig 7.a. boiler pressure

Fig 7.b. water level in the boiler

Fig 8.a. Condenser pressure

Fig 8.b. condensate temperature

The global Matlab-Simulink model Fig 6 of the process is validated through comparison between the model outputs (simulation results) and those of the Bondgraph model [1], [4].

The simulation results for the pressure and water level inside the boiler are given in Fig. 7.a and Fig. 7.b.

Simulation results for the pressure, outlet coolant temperature of the condenser are given in Fig 8.a and Fig 8.b.

As can be seen from Fig. 7.a, the level in the boiler continues to drop (because of the generated steam flowing into the condenser). After a long time , when the level falls below the lower threshold specified by a setpoint, the pumps are switched on to fill the boiler up to the upper threshold specified by the aforementioned setpoint.

It can be seen from Fig. 7.b that the stored condensate initially heats up due to mixing with the high temperature just condensed liquid phase flowing from the U-tubes. The heat transfer from stored condensate to submerged tubes increases with increase in condensate level. Consequently, the stored condensate temperature attends a dynamic steady state.

Conclusion

The Matlab-Simulink model of the steam generator has been developed. The global behavioral model is then simulated and the results are compared to the Bond graph model simulation results and Matlab – simulink library realization (that had been compared to experiments observation) . The steam generator model shows acceptable coherence with the process behavior.

REFERENCES

1. Arun K. Samantaray, Belkacem Ould Bouamama, Model- based Process Supervision A Bond Graph Approach, Springer, 2008.

2. B. Ould Bouamama, J. U. Thoma et J.P. Cassar, Bond graph modelisation of steam condensers. IEEE-SMC, IMACS Multiconference, pp. 2490-2494, Vol. 3, Olando USA, October 16-17, 1997.

3. B. Ould Bouamama R. Litwak and M. Staroswiecki, "Detection And Isolation Of Process Faults In An Industrial Boiler", 3rd IFAC Workshop, on-line-Fault detection and supervision in the chemical process industries, vol.2, Solaize, France, 4-5 june 1998.

4. B. Ould Bouamama, K. Medjaher, A.K. Samantary et M. Staroswiecki, "Supervision of an industrial steam generator. Part I: Bond graph modelling", Control Engineering Practice journal, Vol. 14, pp. 7183, 2006.

5. F. Busson, A. Aïtouche, B. Ould Bouamama, M. Staroswiecki, "Sensor Failures Detection in Steam Condensers", 3rd IFAC Workshop, on-line-Fault detection and supervision in the chemical process industries, vol.2, IFP, Solaize , France, 4-5 june 1998.

6. R. Litwak, B. Ould Bouamama Et M. Staroswiecki, &quotModélisation et surveillance dun générateur de vapeur", Journal Européen des Systèmes Automatisés (JESA), vol 33, n° (5-6), pp. 611 650, 1999.