CA2253658C - Method and system for simulating the behavior of an industrial plant - Google Patents
Method and system for simulating the behavior of an industrial plant Download PDFInfo
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- CA2253658C CA2253658C CA002253658A CA2253658A CA2253658C CA 2253658 C CA2253658 C CA 2253658C CA 002253658 A CA002253658 A CA 002253658A CA 2253658 A CA2253658 A CA 2253658A CA 2253658 C CA2253658 C CA 2253658C
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B17/00—Systems involving the use of models or simulators of said systems
- G05B17/02—Systems involving the use of models or simulators of said systems electric
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F22—STEAM GENERATION
- F22B—METHODS OF STEAM GENERATION; STEAM BOILERS
- F22B35/00—Control systems for steam boilers
- F22B35/004—Control systems for steam generators of nuclear power plants
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F22—STEAM GENERATION
- F22B—METHODS OF STEAM GENERATION; STEAM BOILERS
- F22B35/00—Control systems for steam boilers
- F22B35/18—Applications of computers to steam boiler control
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06G5/00—Devices in which the computing operation is performed by means of fluid-pressure elements
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Abstract
In a particularly reliable and flexible process for simulating the behaviour of a technical installation in which a medium existing in a plurality of phases (W, D) circulates in a partial region, according to the invention a heat flow (Q fg) and a mass flow (M fg) between two phases (W, D) are detected by means of a linear combination of differences from derivations of the entropy (S f, S g) of the phase concerned (W, D) according to the internal energy (U) or the mass (m m, m g) of the phase concerned. The linear coefficients (L ij) of an equation system derived from the linear combinations form a symmetrical matrix. As an application of irreversible thermodynamics to the simulation process there arise on the one hand representations for the mass and heat flows (M fg, Q fg) as a function of "forces" and on the other relations between the flows (M fg, Q fg) based on the Onsager relation.
Description
Description Method and system for simulating the behavior of an industrial plant The invention relates to a method for simulating the behavior of an industrial plant in which a medium present in a number of phases circulates in a section. It furthermore relates to a simulation system for carrying out this method.
In the planning of a nuclear plant or for an approval procedure for such a plant, a very precise knowledge of the plant behavior also in the case of accident or fault situations is essential. For an analysis of the plant behavior which is required for this purpose, a simulation method with specification of selectable situations can reveal scenarios.
Such a simulation method is also important when used in simulators with the aid of which, for example, the power station personnel are trained.
For simulating the behavior of the ~~primary circulation's section of a pressurized water reactor in which a water-steam mixture present in the "liquid" and "gaseous" phases irculates as a cooling medium in some cases, the section in which the medium circulates is organized in a number of part-volumes.
Thermal equilibrium exists in each part-volume for each phase, in the sense that there is no local dependency for the parameters of state which describe each phase. For the simulation, a mass equation and an energy equation are customarily formulated for each phase. These equations contain mass and heat flows. The simulation of the development phase as a function of time is performed separately for each part-volume, the convective mass and heat exchange with neighboring part-volumes being taken into account by means of momentum equations.
AMENDED SHEET
In the simulation method disclosed in the publicaticn by ' Ruan and H. austregeliso "an integral Modeling Technique for High-Speed and Detailed Simulation of L'r~lR Thermo-Hydraulic Processes", Proc. Int. Topical Meeting on Nuclear Thermal Hydraulics, 1993, Grenoble, France, pages 599-0'07, a number of these part-volumes are combined in each case to give so-called "malvo volumes" in order thus to pernit a simulation Kith a comparatively small number of low-order differential equations.
The mass and heat flows are usually divided into interfacial mass and heat transfer and into a wall heat transfer.
An approach using the following equation can be adopted for the interfacial mass and/or heat transfer, i.e. (or due to) condensation or evaporation:
_ H~f CTS - Tf ~ Hag CT~a~ - Tg ) 1 ) Mfg- hg*-hf*
hg * Hrf CTs~ - Tf ~ hf * H~s CTSa~ - Tg Qjg- hg*-hf* 2) -z-Mfg describes the mass flow of the liquid phase into the gaseous phase, whereas Qfg represents the corresponding heat flow. Tf and Tg are the temperatures of the liquid and gaseous phase, respectively, and Tsar describes the saturation temperature. In the usual method, the constants hg* and hf*
depend on the transfer direction. In the case of evaporation, hg* is an enthalpy of saturation of the steam and hf* the enthalpy of the liquid (supercooled in this state). In the case of condensation, on the other hand, hf* is the enthalpy of saturation of the liquid and hg* is the enthalpy of the steam (superheated in this state). The interfacial heat and mass transfer can thus be simulated by two selectably coefficients Hif and Hig. These depend on the thermal hydraulic state in the part-volume considered.
The magnitude of the wall heat transfer can be simulated for a part-volume using three components. The distribution of the heat flow from the environment to the respective phases, the -2a-establishment of a heat flow between the phases and the assignment of an enthalpy flow to this mass flow are taken into account in the energy equations.
The quantification of the coefficients Hif and Hig is necessary for carrying out such a simulation method. However, the coefficients are subject to physical boundary conditions.
Thus, in the simulation of a case where the temperature of the liquid phase Tf is above the saturation temperature Tsat. or in the case of a very high steam content, the coefficient Hif must be set to a very high value. In the case of a very low steam content or if the temperature of the gaseous phase Tg is below the saturation temperature Tsat, on the other hand, the coefficient Hig must be set to a very high value. The range of the values for the coefficients hif and hig can vary by about six powers of ten. This can lead to numerical instabilities when the simulation calculations are performed. In the simulation method, these can lead to a failure of the simulation, so that such a simulation method would be only of limited reliability.
It is therefore the object of the invention to provide a particularly reliable and flexible method and a system for simulating the behavior of an industrial plant. The method should be physically correct and mathematically stable in all ranges of values.
This object is achieved, according to the invention, by a simulation method for an industrial plant of the abovementioned type if a heat flow and a mass flow between two phases are each determined on the basis of a linear combination of differences between derivatives of the entropy of the respective phase with respect to extensive thermodynamic quantities, such as the internal energy and the mass, respectively, of the respective phase, the linear coefficients of a system of equations which is formed from the linear combinations forming a symmetrical matrix.
The invention is based on the consideration that a particularly reliable and numerically stable simulation of the plant behavior, deviating from the approach according to the equations 1), 2), should be based on physical principles.
Since the system to be simulated is in thermal non-equilibrium, the laws of irreversible thermodynamics are particularly suitable for this purpose. Irreversible thermodynamics described the approach of a system to a thermal equilibrium state with the aid of flows, each of which can be represented as a linear combination of forces. The forces generating the mass and heat flows in turn can be represented as the difference between the derivatives of the entropies of two phases with respect to the internal energy or as the difference between the derivatives of the entropies of two phases with respect to the mass. The linear coefficients of the linear combinations should furthermore fulfill the Onsager relations, so that an essential law of irreversible thermodynamics is applied in the simulation method.
For a simulation of the plant behavior which is also reliable in the case of a section of high complexity, the section is advantageously divided into a number of part-volumes, the heat flow and the mass flow being determined for each part-volume by the methods described.
In addition, the matrix formed from the linear coefficients is advantageously positively defined. Thus, an increase in the entropy of the simulated industrial plant as a function of time is achieved in a particularly simple manner.
In order reliably to take into account a heat transfer to a wall of the section in the simulation, a heat flow between this phase and the wall as the environment is advantageously determined for each phase on the basis of a further linear combination, each linear combination containing a difference between derivatives of the entropy of the respective phase and of the entropy of the environment with respect to the internal energy as a linear coefficient.
Advantageously, the differences between the derivatives of the entropies of two phases or the environment with respect to the internal energy are approximated by a difference between the temperatures of the respective phases and the wall. The stated section of the industrial plant is expediently the primary circulation or the secondary circulation of a nuclear power station.
The advantages achieved by the invention consist in particular in the fact that the simulation method is particularly reliable owing to the use of irreversible thermodynamics. The coefficients of the linear combination have a particularly small range of values. Thus, it is ensured that even extreme physical situations, such as, for example, a superheated liquid or supercooled steam, are reliably described. The simulation method is thus numerically particularly stable. In particular, the interactions between the mass and heat flows are taken into account in a physically correct manner. The application of irreversible thermodynamics to the simulation method results on the one hand in representations as a function of "forces" for the mass and heat flows and, on the other hand, in relationships between the flows on the basis of the Onsager relation.
An embodiment of the invention is described in more detail below with reference to a drawing. In the drawing:
Figure 1 schematically shows a simulation system, and Figure 2 schematically shows the primary circulation of a pressurized water reactor and Figure 3 shows a part-volume of the primary circulation, in section.
Identical parts are provided with the same reference symbol in all figures.
The simulation system 1 according to Figure 1 comprises a computer unit 2. A number of circuit or construction diagrams 8 deposited in a database 6 can be read into the computer unit 2 via a dataline 4.
A section of an industrial plant can be completely described on the basis of each of the circuit or construction diagrams 8. The circuit and construction diagram 8 shown in Figure 2 completely describes, for example, the primary circulation 9 of a pressurized water reactor. Two steam generators 14 are connected to a reactor pressure tank 10 of the pressurized water reactor via a coolant system 12. Moreover two coolant pumps 16 and a pressure-maintaining dome 18 are connected in the coolant system 12.
For a planning or approval procedure for~a such a pressurized water reactor, an exact knowledge of its system behavior, in particular in fictitious fault or accident situations, is essential. For this purpose, the plant behavior is simulated on simulation system 1 by calculating the behavior of a specifiable section in a specifiable situation on the basis of the circuit or construction diagram 8 describing said section.
For such a calculation, a section to be simulated is first selected, and its circuit or construction diagram 8 is read into the computer system 2 from the database 6.
In the embodiment, the fictitious fault to be simulated is -as indicated in Figure 2 - a hypothetical fault involving coolant loss, which develops as a result of a leak 22 occurring in the coolant system 12. That section of the pressurized water reactor which is to be simulated is therefore its primary circulation 9 in which the medium transported is a water-steam mixture W, D which is present as water W in the liquid phase and as steam D in the gaseous phase.
In the case of the fault to be simulated involving coolant loss, coolant emerges from the primary circulation 9 as a result of the leak 22. This results in a pressure drop, which in turn causes evaporation in all regions of the primary circulation 9. Owing to the nuclear after-heat of the reactor core, the evaporation is further increased. In the further course of the simulated fault, supercooled water W is fed into the primary circulation 9, resulting in condensation.
For simulating its behavior, that primary circulation 9 of the pressurized water reactor which is selected as the section in the embodiment is first divided into a number of part-volumes 20, one of which is shown in Figure 4. The starting conditions and boundary conditions for the fictitious fault to be simulated, i.e. the characteristics for the leak 22 in the embodiment, are then specified.
For each part-volume 20, the behavior of the water W present in it and of the steam D present in it is then determined in the simulation. First - as indicated in Figure 4 by the arrows Dmg, Dmf - the direct mass transfer of the two phases W, D
with the respective neighboring part-volumes 20 with which the part-volume 20 considered is undergoing convective mass transfer is taken into account.
A mass transfer and a heat transfer between the two phases w, D and a heat transfer between each phase W, D and an environment of the part-volume 20 are determined on the basis of irreversible thermodynamics. The environment of the part-volume 20 is represented by its wall 26. Thus, in the simulation of the behavior of the phases W, D in the part-volume 20, the following quantities are taken into account in addition to the heat transfer and mass transfer terms Dmg, Dmf associated with its neighboring part-volumes 20: the heat flow Qwf from the wall 26 into the water W, the heat flow Qwg from the wall 26 into the steam D, the heat flow Qgf from the water W into the steam D and the mass flow Mgf from the water W into the steam D. Negative heat and mass flows mean that heat or mass is transported in the opposite direction.
The heat or mass flows QWf, QWg, Qgf, Mgf are each represented on the basis of a linear combination of differences between derivatives of the entropy Sf, Sg, SW of the respective phase W, D or of the wall 26 with respect to thermal variables of state. At the same pressure in the two phases, thermal variables of state are the internal energy U and also the mass mf, mg of a phase W,D.
According to the laws of thermodynamics, the derivative of the entropy with respect to the internal energy U gives the reciprocal temperature. Thus, the following is obtained for a -g_ difference between derivatives of the entropies Sf, Sg of the respective phases W, D with respect to their internal energies Uf and Ug, respectively:
aS f _ asg -_ 1 - 1 3 ) av av Tf Tg Tf is the temperature of the liquid phase W and Tg is the temperature of the gaseous phase D.
Furthermore, according to the laws of thermodynamics, the derivative of the entropy Sf, Sg of a phase W, D with respect to the mass mf and mg, respectively, is given by its chemical potential:
as.f _ asg _ am am T f Tg 4 ) To determine the heat and mass flows Mgf, Qqf, Qwf, QWg, the linear combinations of the respective derivatives are formed according to:
M~. -L" - +L,z - +L13 - +L14 =
T T T T T T 8 H' T 8 T 8 I x' Q~. -L,2- + T T + T T + T
_ L22 - L23 - L24 T T r g r r g . 5) Qwr -L~ - + - + - +
= 3 L23 L33 L34 T T T T T T
.r g r g r Qwg -L14 , + - + T - +
= - L24 L34 T L44 T ~ T T I
I g f a The matrix formed from the linear coefficients Lid of this system 5) of equations is symmetrical. This takes into account the Onsager relations (Onsager's reciprocity relationship, Onsager's symmetry relationship). In addition, the linear coefficients Lid are chosen so that the matrix is positively defined. The entropy change of the part-volume 20, which change is described by the system 5) of equations, is thus always positive.
For particularly simple processing, the difference between the derivatives of the entropies Sf, Sg can be approximated by:
1 1 _ 1 Tr Tg Tsar g T f 6 ) After a reduction of the reciprocal temperatures to higher terms, the common denominator was approximated by the assumption that both the temperature Tf of the water W and the temperature Tg of the steam D were approximately equal to a saturation temperature Tsat~
With pressure equivalence in the two phases W, D and at the same assumption as above, the difference between the derivatives of the entropies with respect to the masses can furthermore be approximated by:
~r _ ~.r _ hs,sat ~ - T ~ hg.sot ~ _ T ~ ~ ) T T T 2 sar .~ T 2 sar g j g snr eat where, hf,sac and hg, sat are the saturation enthalpies of the respective phases W and D.
The heat and mass flows Mgf, Qgf, S2Wf, Qwg are determined on the basis of the system 5) of equations and are taken into account in the balancing equations for the part-volume 20. On this basis, the balancing equation for each part-volume 20 and for each time step are solved.
Owing to the use of irreversible thermodynamics, this simulation method is mathematically particularly stable and hence particularly reliable.
In the planning of a nuclear plant or for an approval procedure for such a plant, a very precise knowledge of the plant behavior also in the case of accident or fault situations is essential. For an analysis of the plant behavior which is required for this purpose, a simulation method with specification of selectable situations can reveal scenarios.
Such a simulation method is also important when used in simulators with the aid of which, for example, the power station personnel are trained.
For simulating the behavior of the ~~primary circulation's section of a pressurized water reactor in which a water-steam mixture present in the "liquid" and "gaseous" phases irculates as a cooling medium in some cases, the section in which the medium circulates is organized in a number of part-volumes.
Thermal equilibrium exists in each part-volume for each phase, in the sense that there is no local dependency for the parameters of state which describe each phase. For the simulation, a mass equation and an energy equation are customarily formulated for each phase. These equations contain mass and heat flows. The simulation of the development phase as a function of time is performed separately for each part-volume, the convective mass and heat exchange with neighboring part-volumes being taken into account by means of momentum equations.
AMENDED SHEET
In the simulation method disclosed in the publicaticn by ' Ruan and H. austregeliso "an integral Modeling Technique for High-Speed and Detailed Simulation of L'r~lR Thermo-Hydraulic Processes", Proc. Int. Topical Meeting on Nuclear Thermal Hydraulics, 1993, Grenoble, France, pages 599-0'07, a number of these part-volumes are combined in each case to give so-called "malvo volumes" in order thus to pernit a simulation Kith a comparatively small number of low-order differential equations.
The mass and heat flows are usually divided into interfacial mass and heat transfer and into a wall heat transfer.
An approach using the following equation can be adopted for the interfacial mass and/or heat transfer, i.e. (or due to) condensation or evaporation:
_ H~f CTS - Tf ~ Hag CT~a~ - Tg ) 1 ) Mfg- hg*-hf*
hg * Hrf CTs~ - Tf ~ hf * H~s CTSa~ - Tg Qjg- hg*-hf* 2) -z-Mfg describes the mass flow of the liquid phase into the gaseous phase, whereas Qfg represents the corresponding heat flow. Tf and Tg are the temperatures of the liquid and gaseous phase, respectively, and Tsar describes the saturation temperature. In the usual method, the constants hg* and hf*
depend on the transfer direction. In the case of evaporation, hg* is an enthalpy of saturation of the steam and hf* the enthalpy of the liquid (supercooled in this state). In the case of condensation, on the other hand, hf* is the enthalpy of saturation of the liquid and hg* is the enthalpy of the steam (superheated in this state). The interfacial heat and mass transfer can thus be simulated by two selectably coefficients Hif and Hig. These depend on the thermal hydraulic state in the part-volume considered.
The magnitude of the wall heat transfer can be simulated for a part-volume using three components. The distribution of the heat flow from the environment to the respective phases, the -2a-establishment of a heat flow between the phases and the assignment of an enthalpy flow to this mass flow are taken into account in the energy equations.
The quantification of the coefficients Hif and Hig is necessary for carrying out such a simulation method. However, the coefficients are subject to physical boundary conditions.
Thus, in the simulation of a case where the temperature of the liquid phase Tf is above the saturation temperature Tsat. or in the case of a very high steam content, the coefficient Hif must be set to a very high value. In the case of a very low steam content or if the temperature of the gaseous phase Tg is below the saturation temperature Tsat, on the other hand, the coefficient Hig must be set to a very high value. The range of the values for the coefficients hif and hig can vary by about six powers of ten. This can lead to numerical instabilities when the simulation calculations are performed. In the simulation method, these can lead to a failure of the simulation, so that such a simulation method would be only of limited reliability.
It is therefore the object of the invention to provide a particularly reliable and flexible method and a system for simulating the behavior of an industrial plant. The method should be physically correct and mathematically stable in all ranges of values.
This object is achieved, according to the invention, by a simulation method for an industrial plant of the abovementioned type if a heat flow and a mass flow between two phases are each determined on the basis of a linear combination of differences between derivatives of the entropy of the respective phase with respect to extensive thermodynamic quantities, such as the internal energy and the mass, respectively, of the respective phase, the linear coefficients of a system of equations which is formed from the linear combinations forming a symmetrical matrix.
The invention is based on the consideration that a particularly reliable and numerically stable simulation of the plant behavior, deviating from the approach according to the equations 1), 2), should be based on physical principles.
Since the system to be simulated is in thermal non-equilibrium, the laws of irreversible thermodynamics are particularly suitable for this purpose. Irreversible thermodynamics described the approach of a system to a thermal equilibrium state with the aid of flows, each of which can be represented as a linear combination of forces. The forces generating the mass and heat flows in turn can be represented as the difference between the derivatives of the entropies of two phases with respect to the internal energy or as the difference between the derivatives of the entropies of two phases with respect to the mass. The linear coefficients of the linear combinations should furthermore fulfill the Onsager relations, so that an essential law of irreversible thermodynamics is applied in the simulation method.
For a simulation of the plant behavior which is also reliable in the case of a section of high complexity, the section is advantageously divided into a number of part-volumes, the heat flow and the mass flow being determined for each part-volume by the methods described.
In addition, the matrix formed from the linear coefficients is advantageously positively defined. Thus, an increase in the entropy of the simulated industrial plant as a function of time is achieved in a particularly simple manner.
In order reliably to take into account a heat transfer to a wall of the section in the simulation, a heat flow between this phase and the wall as the environment is advantageously determined for each phase on the basis of a further linear combination, each linear combination containing a difference between derivatives of the entropy of the respective phase and of the entropy of the environment with respect to the internal energy as a linear coefficient.
Advantageously, the differences between the derivatives of the entropies of two phases or the environment with respect to the internal energy are approximated by a difference between the temperatures of the respective phases and the wall. The stated section of the industrial plant is expediently the primary circulation or the secondary circulation of a nuclear power station.
The advantages achieved by the invention consist in particular in the fact that the simulation method is particularly reliable owing to the use of irreversible thermodynamics. The coefficients of the linear combination have a particularly small range of values. Thus, it is ensured that even extreme physical situations, such as, for example, a superheated liquid or supercooled steam, are reliably described. The simulation method is thus numerically particularly stable. In particular, the interactions between the mass and heat flows are taken into account in a physically correct manner. The application of irreversible thermodynamics to the simulation method results on the one hand in representations as a function of "forces" for the mass and heat flows and, on the other hand, in relationships between the flows on the basis of the Onsager relation.
An embodiment of the invention is described in more detail below with reference to a drawing. In the drawing:
Figure 1 schematically shows a simulation system, and Figure 2 schematically shows the primary circulation of a pressurized water reactor and Figure 3 shows a part-volume of the primary circulation, in section.
Identical parts are provided with the same reference symbol in all figures.
The simulation system 1 according to Figure 1 comprises a computer unit 2. A number of circuit or construction diagrams 8 deposited in a database 6 can be read into the computer unit 2 via a dataline 4.
A section of an industrial plant can be completely described on the basis of each of the circuit or construction diagrams 8. The circuit and construction diagram 8 shown in Figure 2 completely describes, for example, the primary circulation 9 of a pressurized water reactor. Two steam generators 14 are connected to a reactor pressure tank 10 of the pressurized water reactor via a coolant system 12. Moreover two coolant pumps 16 and a pressure-maintaining dome 18 are connected in the coolant system 12.
For a planning or approval procedure for~a such a pressurized water reactor, an exact knowledge of its system behavior, in particular in fictitious fault or accident situations, is essential. For this purpose, the plant behavior is simulated on simulation system 1 by calculating the behavior of a specifiable section in a specifiable situation on the basis of the circuit or construction diagram 8 describing said section.
For such a calculation, a section to be simulated is first selected, and its circuit or construction diagram 8 is read into the computer system 2 from the database 6.
In the embodiment, the fictitious fault to be simulated is -as indicated in Figure 2 - a hypothetical fault involving coolant loss, which develops as a result of a leak 22 occurring in the coolant system 12. That section of the pressurized water reactor which is to be simulated is therefore its primary circulation 9 in which the medium transported is a water-steam mixture W, D which is present as water W in the liquid phase and as steam D in the gaseous phase.
In the case of the fault to be simulated involving coolant loss, coolant emerges from the primary circulation 9 as a result of the leak 22. This results in a pressure drop, which in turn causes evaporation in all regions of the primary circulation 9. Owing to the nuclear after-heat of the reactor core, the evaporation is further increased. In the further course of the simulated fault, supercooled water W is fed into the primary circulation 9, resulting in condensation.
For simulating its behavior, that primary circulation 9 of the pressurized water reactor which is selected as the section in the embodiment is first divided into a number of part-volumes 20, one of which is shown in Figure 4. The starting conditions and boundary conditions for the fictitious fault to be simulated, i.e. the characteristics for the leak 22 in the embodiment, are then specified.
For each part-volume 20, the behavior of the water W present in it and of the steam D present in it is then determined in the simulation. First - as indicated in Figure 4 by the arrows Dmg, Dmf - the direct mass transfer of the two phases W, D
with the respective neighboring part-volumes 20 with which the part-volume 20 considered is undergoing convective mass transfer is taken into account.
A mass transfer and a heat transfer between the two phases w, D and a heat transfer between each phase W, D and an environment of the part-volume 20 are determined on the basis of irreversible thermodynamics. The environment of the part-volume 20 is represented by its wall 26. Thus, in the simulation of the behavior of the phases W, D in the part-volume 20, the following quantities are taken into account in addition to the heat transfer and mass transfer terms Dmg, Dmf associated with its neighboring part-volumes 20: the heat flow Qwf from the wall 26 into the water W, the heat flow Qwg from the wall 26 into the steam D, the heat flow Qgf from the water W into the steam D and the mass flow Mgf from the water W into the steam D. Negative heat and mass flows mean that heat or mass is transported in the opposite direction.
The heat or mass flows QWf, QWg, Qgf, Mgf are each represented on the basis of a linear combination of differences between derivatives of the entropy Sf, Sg, SW of the respective phase W, D or of the wall 26 with respect to thermal variables of state. At the same pressure in the two phases, thermal variables of state are the internal energy U and also the mass mf, mg of a phase W,D.
According to the laws of thermodynamics, the derivative of the entropy with respect to the internal energy U gives the reciprocal temperature. Thus, the following is obtained for a -g_ difference between derivatives of the entropies Sf, Sg of the respective phases W, D with respect to their internal energies Uf and Ug, respectively:
aS f _ asg -_ 1 - 1 3 ) av av Tf Tg Tf is the temperature of the liquid phase W and Tg is the temperature of the gaseous phase D.
Furthermore, according to the laws of thermodynamics, the derivative of the entropy Sf, Sg of a phase W, D with respect to the mass mf and mg, respectively, is given by its chemical potential:
as.f _ asg _ am am T f Tg 4 ) To determine the heat and mass flows Mgf, Qqf, Qwf, QWg, the linear combinations of the respective derivatives are formed according to:
M~. -L" - +L,z - +L13 - +L14 =
T T T T T T 8 H' T 8 T 8 I x' Q~. -L,2- + T T + T T + T
_ L22 - L23 - L24 T T r g r r g . 5) Qwr -L~ - + - + - +
= 3 L23 L33 L34 T T T T T T
.r g r g r Qwg -L14 , + - + T - +
= - L24 L34 T L44 T ~ T T I
I g f a The matrix formed from the linear coefficients Lid of this system 5) of equations is symmetrical. This takes into account the Onsager relations (Onsager's reciprocity relationship, Onsager's symmetry relationship). In addition, the linear coefficients Lid are chosen so that the matrix is positively defined. The entropy change of the part-volume 20, which change is described by the system 5) of equations, is thus always positive.
For particularly simple processing, the difference between the derivatives of the entropies Sf, Sg can be approximated by:
1 1 _ 1 Tr Tg Tsar g T f 6 ) After a reduction of the reciprocal temperatures to higher terms, the common denominator was approximated by the assumption that both the temperature Tf of the water W and the temperature Tg of the steam D were approximately equal to a saturation temperature Tsat~
With pressure equivalence in the two phases W, D and at the same assumption as above, the difference between the derivatives of the entropies with respect to the masses can furthermore be approximated by:
~r _ ~.r _ hs,sat ~ - T ~ hg.sot ~ _ T ~ ~ ) T T T 2 sar .~ T 2 sar g j g snr eat where, hf,sac and hg, sat are the saturation enthalpies of the respective phases W and D.
The heat and mass flows Mgf, Qgf, S2Wf, Qwg are determined on the basis of the system 5) of equations and are taken into account in the balancing equations for the part-volume 20. On this basis, the balancing equation for each part-volume 20 and for each time step are solved.
Owing to the use of irreversible thermodynamics, this simulation method is mathematically particularly stable and hence particularly reliable.
Claims (8)
1. A method for simulating the behavior of an industrial plant in which a medium present in a number of phases (W, D) circulates in a section, in which method a heat flow (Qfg) and a mass flow (Mfg) between two phases (W, D) are each determined on the basis of a linear combination of differences between derivatives of the entropy (S f, S g) of the respective-phase (W, D) with respect to the internal energy (U) and with respect to the mass (mf, mg), respectively, of the respective phase (W, D), the linear coefficients (Lij) of a system of equations which is formed from the linear combinations forming a symmetrical matrix.
2. The method as claimed in claim 1, in which the section is divided into a number of part-volumes (20), the heat flow (Qfg) and the mass flow (Mfg) between two phases (W, D) being determined separately for each part-volume (20).
3. The method as claimed in claim 1 or 2, in which the matrix formed from the linear coefficients (Lij) is positively defined.
4. The method as claimed in any of claims 1 to 3, in which, for each phase (W, D), a heat flow (Qwf, Qwg) between this phase (W, D) and a wall (26) as the environment is determined in each case on the basis of a further linear combination, each linear combination comprising a difference between derivatives of the entropy (Sf, Sg) of the respective phase (W, D) and of the entropy (Sw) of the environment with respect to the internal energy (U).
5. The method as claimed in any of claims 1 to 4, in which the differences between the derivatives of the entropy (Sf, Sg) of two phases (W, D) or of the environment with respect to the internal energy (U) are approximated by a difference between the temperatures (Tf, Tg, Tw) of the respective phases (W, D) and of the wall (26).
6. The method as claimed in any of claims 1 to 5, in which the section of the industrial plant is the primary circulation (9) of a nuclear power station.
7. The method as claimed in any of claims 1 to 5, in which the section of the industrial plant is the secondary circulation of a nuclear power station.
8. A simulation system (1) for carrying out the method as claimed in any of claims 1 to 7, in which a number of circuit or construction diagrams (8) deposited in a database (6) can be read into a computer unit (2), which, on the basis of the circuit or construction diagrams (8), determines a heat flow (Qfg) and a mass flow (Mfg) between two phases (W, D) of a medium present in a number of phases (W, D), in each case on the basis of a linear combination of differences between derivatives of the entropy (Sf, Sg) of the respective phase (W, D) with respect to the internal energy (U) and with respect to the mass (mf, mg) of the respective phase (W, D), the linear coefficients (Lij) of a system of equations which is formed from the linear combinations forming a symmetrical matrix.
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DE19618745A DE19618745C2 (en) | 1996-05-09 | 1996-05-09 | Process and system for simulating the behavior of a technical system |
| DE19618745.1 | 1996-05-09 | ||
| PCT/EP1997/002077 WO1997043725A1 (en) | 1996-05-09 | 1997-04-23 | Process and system for simulating the behaviour of a technical installation |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2253658A1 CA2253658A1 (en) | 1997-11-20 |
| CA2253658C true CA2253658C (en) | 2004-05-11 |
Family
ID=7793877
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002253658A Expired - Fee Related CA2253658C (en) | 1996-05-09 | 1997-04-23 | Method and system for simulating the behavior of an industrial plant |
Country Status (8)
| Country | Link |
|---|---|
| EP (1) | EP0897564B1 (en) |
| JP (1) | JP2000512741A (en) |
| AR (1) | AR007034A1 (en) |
| CA (1) | CA2253658C (en) |
| DE (2) | DE19618745C2 (en) |
| ES (1) | ES2140978T3 (en) |
| TW (1) | TW350017B (en) |
| WO (1) | WO1997043725A1 (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102009033605B4 (en) | 2009-07-17 | 2011-03-31 | Siemens Aktiengesellschaft | Method for simulating an operation of a technical system based on state variables |
| CN104239724B (en) * | 2014-09-19 | 2017-04-12 | 国家电网公司 | Online monitoring and assessment method for heat exchange efficiency of water-cooling system of converter valve |
| CN110887027B (en) * | 2019-11-19 | 2021-12-03 | 中广核工程有限公司 | Vertical steam generator thermal performance evaluation system and method |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| AU2683192A (en) * | 1991-09-17 | 1993-04-27 | General Physics International Engineering & Simulation, Inc. | Real time analysis of power plant thermohydraulic phenomenon |
-
1996
- 1996-05-09 DE DE19618745A patent/DE19618745C2/en not_active Expired - Lifetime
-
1997
- 1997-04-23 CA CA002253658A patent/CA2253658C/en not_active Expired - Fee Related
- 1997-04-23 EP EP97921727A patent/EP0897564B1/en not_active Expired - Lifetime
- 1997-04-23 JP JP09540427A patent/JP2000512741A/en active Pending
- 1997-04-23 ES ES97921727T patent/ES2140978T3/en not_active Expired - Lifetime
- 1997-04-23 WO PCT/EP1997/002077 patent/WO1997043725A1/en active IP Right Grant
- 1997-04-23 DE DE59700764T patent/DE59700764D1/en not_active Expired - Lifetime
- 1997-05-06 TW TW086106007A patent/TW350017B/en not_active IP Right Cessation
- 1997-05-07 AR ARP970101894A patent/AR007034A1/en active IP Right Grant
Also Published As
| Publication number | Publication date |
|---|---|
| AR007034A1 (en) | 1999-10-13 |
| EP0897564B1 (en) | 1999-11-24 |
| CA2253658A1 (en) | 1997-11-20 |
| DE19618745A1 (en) | 1997-12-04 |
| WO1997043725A1 (en) | 1997-11-20 |
| ES2140978T3 (en) | 2000-03-01 |
| DE59700764D1 (en) | 1999-12-30 |
| TW350017B (en) | 1999-01-11 |
| JP2000512741A (en) | 2000-09-26 |
| DE19618745C2 (en) | 1998-04-09 |
| EP0897564A1 (en) | 1999-02-24 |
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