**5.2.3 Coupling and adjustments**

Once the process and controls models are ready, they have to be coupled and tested according next steps:


### **5.3 Process modelling**

### **5.3.1 Systems considered to be simulated**

The systems that finally were simulated have all the information the instructor needs to train an operator and they may be controlled from the control screens, from the process itself, trough remote functions in the simulator, or from the DCS.

The systems included in the simulator are presented in Table 3. The simulator resulted with 13 process and 21 control models.

The combustor model includes the combustor blade path temperatures with 32 display values, the exhaust temperatures with 16 displays, the disc cavity temperatures with 8 displays, and emissions.

### **5.3.2 Models development**

224 Efficiency, Performance and Robustness of Gas Turbines

• Some equipments are not included in the DCS and the diagram or description of the local controls was sought. When the information was not available, the control

• A generic graphics library was integrated to create the analog and logic diagrams into

• The diagrams were transcribed into the VisSim program using the generic modules.

• VisSim generates ANSI C code. Some adjustments to the code have to be done with a program developed by the IIE to translate the code to C#, which can run in the simulator environment. This application generates the variables definitions that are loaded into the simulator database (global variables, remote functions, malfunctions, etc.). The control models are kept in graphic form to facilitate the updates and future

Once the process and controls models are ready, they have to be coupled and tested

• Local tests are performed and necessary adjustments on the models are made, *i.e.* in the *MAS* the model is run alone (with its control) and changes in some input variables are

• Coupling of the MSS and their controls are performed. All models are coupled into the *MAS*. In this case, the first model incorporated was the turbine, combustor and compressor model with its associated control. Then the fuel gas, then generator and electrical grid. Finally the models of the auxiliary systems, each with its control. The coupling order is an important factor and was done considering the best sequence to avoid as much as possible mathematical problems. An algorithm proposed and used previously in a simulator is to consider an execution sequence trying to minimise the retarded information (variables). To prove the successful integration of each model

• Final acceptance tests are achieved by the final user according their own procedures.

The systems that finally were simulated have all the information the instructor needs to train an operator and they may be controlled from the control screens, from the process

The systems included in the simulator are presented in Table 3. The simulator resulted with

The combustor model includes the combustor blade path temperatures with 32 display values, the exhaust temperatures with 16 displays, the disc cavity temperatures with 8

made in order to evaluate the general response of the model.

added, operation actions on the models were done. • Fabric global test are made with the needed adjustments.

itself, trough remote functions in the simulator, or from the DCS.

**5.3.1 Systems considered to be simulated** 

Each SAMA control diagram was drawn into a single VisSim drawing.

diagrams were proposed and accorded with the client.

the VisSim environment.

**5.2.3 Coupling and adjustments** 

adjustments.

according next steps:

**5.3 Process modelling** 

displays, and emissions.

13 process and 21 control models.

For the modelling, fundamental conservation principles were used considering a lumped parameters approach and widely available and accepted empirical relations. The lumped parameters approach simplifies the modelling of the behaviour of spatially distributed real systems into a topology consisting of few discrete entities that represent the behaviour of the distributed system (under certain assumptions). From a Mathematical point of view, the simplification reduces the state space of the system to a finite number, and the partial differential equations of the continuous (infinite-dimensional) time and space model of the physical system into ordinary differential equations with a finite number of parameters.


Table 3. List of process and control models

Figure 8 shows the flow information of MSS. For each MSS, the independent variables (inlets) are associated with the actions of the operators like open or close a valve, trip a

Models for Training on a Gas Turbine Power Plant 227

substances. The independent variables are pressure and temperature. The validity range is for low pressure to 80 bars. Twenty components were considered: nitrogen, oxygen, methane, ethane, propane, n-butane, i-butane, n-pentane, n-hexane, n-heptane, n-octane, nnonane, n-decane, carbon dioxide, carbon monoxide, hydrogen sulphide, sulphur dioxide,

The transport properties (viscosity, heat capacity, thermal expansion, and thermal conductivity) are calculated for liquid, steam and air with polynomial functions up to fourth

This model simulates any hydraulic or gas network in order to know the values of the flows and the pressures along the system. The general approach to represent the network is considering that a hydraulic network is formed by accessories (fittings), nodes (junctions and splitters) and lines (or pipes). Accessories are those devices in lines that drop or increment the pressure and/or enthalpy of the fluid, like valves, pumps, filters, piping, turbines, heat exchangers and other fittings. A line links two nodes. A node may be internal or external. An external node is a point in the network where the pressure is known at any time, these nodes are sources or sinks of flow (inertial or capacitive nodes). An internal node

The model is derived from the continuity equation on each of the nodes, considering all the

Also, the momentum equation may be applied on each accessory on the flow direction *x*,

*v P v = - - - + g <sup>v</sup> t xx x* τ

Considering that the temporal and space acceleration terms are not significant, that the forces acting on the fluid are instantly balanced, a model may be stated integrating the

> Δ =− Δ + Δ *P L* τ ρ

The viscous stress tensor term may be estimated with empirical expressions for any

( ) 2 ' *w k Ap P g z* ζ= Δ+ Δ

Here, the flow resistance is function of the valve aperture *Ap* and a constant *k´* that depends on the valve itself (size, type, etc.). The exponent *ζ* represents the behaviour of a valve to simulate the relation between the aperture and the flow area. The aperture applies only for valves or may represent a variable resistance factor to the flow, for example when a filter is getting dirty. For fittings with constant resistance the term *Apζ* does not exist. For a pump

 ρ

accessory. For example, for a valve, the flowrate pressure drop (*ΔP*) relationship is:

ρ

∂ ∂∂ ∂

*x x x*

density, *v* velocity, *g* the gravity acceleration and

ρ

(or a compressor), this relationship may be expressed as:

Σ −Σ *w w = 0 i o* (1)

viscous stress tensor:

*g z* (3)

(4)

τ

*x x*

∂ ∂∂ ∂ (2)

ρρ

nitrogen monoxide, nitrogen dioxide, and water.

**Flows and Pressures Networks** 

is a junction or split of two or more lines.

inlet (*i*) and output (*o*) flowrates (*w*):

equation along a stream:

degree.

being ρ

pump manually, etc., with the control signals, with the integration methods and with the information from other models.

A process model consists typically in the solution of the basic principles equations according the diagram shown in Figure 9. In this section the models related with the gas turbine, compressors and combustor are commented.

Fig. 8. Information flow of a model.

Fig. 9. Structure execution of a model.

### **Thermodynamic and physical properties**

These properties are calculated as water (liquid and steam) and hydrocarbon mixtures thermodynamic properties and transport properties for water, steam and air.

For the water the thermodynamic properties were adjusted as a function of pressure (*P*) and enthalpy (*h*). The data source was the steam tables by Arnold (1967). The functions were adjusted by least square method. The application range of the functions is between 0.1 *psia* and 4520 *psia* for pressure, and -10 *0C* and 720 *0C* (equivalent to 0.18 *BTU/lb* and 1635 *BTU/lb* of enthalpy). The functions also calculate *dTP/dP* (being *TP* any thermodynamic property) for the saturation region and *∂TP/∂P* and *∂TP/∂h* for the subcooled liquid and superheated steam.

The hydrocarbon properties were applied for the gas fuel, air, and combustion products. Calculations are based in seven cubic state and corresponding state equations to predict the equilibrium liquid-steam and properties for pure fluids and mixtures containing non polar substances. The independent variables are pressure and temperature. The validity range is for low pressure to 80 bars. Twenty components were considered: nitrogen, oxygen, methane, ethane, propane, n-butane, i-butane, n-pentane, n-hexane, n-heptane, n-octane, nnonane, n-decane, carbon dioxide, carbon monoxide, hydrogen sulphide, sulphur dioxide, nitrogen monoxide, nitrogen dioxide, and water.

The transport properties (viscosity, heat capacity, thermal expansion, and thermal conductivity) are calculated for liquid, steam and air with polynomial functions up to fourth degree.

### **Flows and Pressures Networks**

226 Efficiency, Performance and Robustness of Gas Turbines

pump manually, etc., with the control signals, with the integration methods and with the

A process model consists typically in the solution of the basic principles equations according the diagram shown in Figure 9. In this section the models related with the gas turbine,

> Models Process Model Control Model

Other Process and Control Models

Heat and mass transfer coefficients

through the network Capacitive nodes Other calculations

Console Control Screens

Instructor

Integration Methods

Energy balances

State Variables Derivatives

These properties are calculated as water (liquid and steam) and hydrocarbon mixtures

For the water the thermodynamic properties were adjusted as a function of pressure (*P*) and enthalpy (*h*). The data source was the steam tables by Arnold (1967). The functions were adjusted by least square method. The application range of the functions is between 0.1 *psia* and 4520 *psia* for pressure, and -10 *0C* and 720 *0C* (equivalent to 0.18 *BTU/lb* and 1635 *BTU/lb* of enthalpy). The functions also calculate *dTP/dP* (being *TP* any thermodynamic property) for the saturation region and *∂TP/∂P* and *∂TP/∂h* for the subcooled liquid and superheated

The hydrocarbon properties were applied for the gas fuel, air, and combustion products. Calculations are based in seven cubic state and corresponding state equations to predict the equilibrium liquid-steam and properties for pure fluids and mixtures containing non polar

thermodynamic properties and transport properties for water, steam and air.

information from other models.

Fig. 8. Information flow of a model.

Flows and pressures network (continuity and momentum equations)

Fig. 9. Structure execution of a model.

steam.

**Thermodynamic and physical properties** 

Thermodynamic and physical properties

compressors and combustor are commented.

This model simulates any hydraulic or gas network in order to know the values of the flows and the pressures along the system. The general approach to represent the network is considering that a hydraulic network is formed by accessories (fittings), nodes (junctions and splitters) and lines (or pipes). Accessories are those devices in lines that drop or increment the pressure and/or enthalpy of the fluid, like valves, pumps, filters, piping, turbines, heat exchangers and other fittings. A line links two nodes. A node may be internal or external. An external node is a point in the network where the pressure is known at any time, these nodes are sources or sinks of flow (inertial or capacitive nodes). An internal node is a junction or split of two or more lines.

The model is derived from the continuity equation on each of the nodes, considering all the inlet (*i*) and output (*o*) flowrates (*w*):

$$
\Sigma \varpi v\_i - \Sigma \varpi v\_o = 0 \tag{1}
$$

 Also, the momentum equation may be applied on each accessory on the flow direction *x*, being ρ density, *v* velocity, *g* the gravity acceleration and τviscous stress tensor:

$$
\rho \frac{\partial \upsilon}{\partial t} = \mathbf{\cdot} \frac{\partial P}{\partial \mathbf{x}} \mathbf{\cdot} \frac{\partial \mathbf{\sigma}\_{xx}}{\partial \mathbf{x}} \mathbf{\cdot} \rho\_{\upsilon \upsilon} \frac{\partial \upsilon\_{\upsilon}}{\partial \mathbf{x}} + \rho \ g\_{\upsilon} \tag{2}
$$

Considering that the temporal and space acceleration terms are not significant, that the forces acting on the fluid are instantly balanced, a model may be stated integrating the equation along a stream:

$$
\Delta P = -L\,\Delta \tau + \rho \,\varrho \,\Delta z \tag{3}
$$

The viscous stress tensor term may be estimated with empirical expressions for any accessory. For example, for a valve, the flowrate pressure drop (*ΔP*) relationship is:

$$w^2 = \stackrel{\circ}{k'} \stackrel{}{\rho}Ap^{\zeta'} \left(\Delta P + \rho \, g \, \Delta z\right) \tag{4}$$

Here, the flow resistance is function of the valve aperture *Ap* and a constant *k´* that depends on the valve itself (size, type, etc.). The exponent *ζ* represents the behaviour of a valve to simulate the relation between the aperture and the flow area. The aperture applies only for valves or may represent a variable resistance factor to the flow, for example when a filter is getting dirty. For fittings with constant resistance the term *Apζ* does not exist. For a pump (or a compressor), this relationship may be expressed as:

Models for Training on a Gas Turbine Power Plant 229

B

The exit properties for each turbine and compressor stage are calculated in a similar way, as an isoentropic expansion (or compression) and corrected with its efficiency. For example, the properties at the compressor's exhaust are calculated as an isentropic stage by a numerical Newton-Raphson method (i.e. the isoenthalpic exhaust temperature *To\** is

0 5 10 15 20 25 30 35

Flowrate *w*

where *c* is the gas composition. Then, the leaving enthalpy is corrected with the efficiency of

\* ( ) *o i o i h h h h* η

For the turbine it was considered that the work is produced instead of consumed. All other exhaust properties are computed with the real enthalpy and pressure. The efficiency *η* is a

An energy balance on the flows and pressures network is made in the nodes where a temperature or enthalpy is required to be displayed or when a mixture of flowrates is made. In this case, the state variables are the enthalpy *h*, and the composition of all the components

*wh wh i i o atm dh q*

In this equation, *m* is the mass of the node, and *qatm* the heat lost to the atmosphere. The subindex *i* represent the inlet conditions of the different flowstreams converging to the

*dt m*

\* \* \* ( ) ( , ,) ( , ,) 0 *o iii oo o fT sT Pc s T P c* =− = (9)

<sup>−</sup> = + (10)

C

− − <sup>=</sup> (11)

where *η* is the efficiency.

Pressure Drop

*Δ*

*P*

the compressor:

Fig. 10. Flowrate versus pressure drop linearization.

0

50

100

150

200

A

250

calculated at the exhaust pressure *Po* with the entropy inlet *si*):

function of the flow through the compressor and turbine.

*cj* is necessary in order to determinate all the variables of the node:

$$
\Delta P = \stackrel{\circ}{k\_1} w^2 + \stackrel{\circ}{k\_2} w \, \alpha \theta + \stackrel{\circ}{k\_3} \, \alpha^2 - \rho \, \text{g} \, \Delta z \tag{5}
$$

where *ω* is the pump speed and where *k´i* are constants that fit the pump behaviour.

If it is considered that in a given moment the aperture, density, and speed are constant, both equations (4) and (5) may be written as:

$$
\Delta w^2 = k\_a \, \Delta P + k\_b \,\tag{6}
$$

Applying equation (1) on each node and equation (6) on each accessory a set of equations is obtained to be solved simultaneously. A more efficient way to get a solution is achieved if equation (6) is linearised. To exemplify, equation (6) is selected for the case of a pump with arbitrary numerical values (same result may be obtained for any other accessory). Figure 10 presents the quadratic curve of flowrate *w* on the *x* axis and *ΔP* on the *y* axis (dotted line). In the curve two straight lines may be defined as AB and BC and represent an approximation of the curve. The error is lower if more straight lines were "fitted" to the curve. In this case two straight lines are used to simplify the explanation, but the model allows for any number of them.

For a given flow *w*, the pressure drop may be approximated by the correspondent straight line (between two limit flows of this line). If there are two or more accessories connected in series and/or two or more lines in parallel are present, an equivalent equation may be stated:

$$w = \mathbb{C}\,\Delta P + D\,\tag{7}$$

Substituting equation (7) on (1), for each flow stream, a linear equations system is obtained where pressures are the unknowns. The order of the equations system matrix is equal to the number of internal nodes of the network. Flows are calculated by equation (7) once the pressures were obtained.

The topology of a network may change, for instance, if a stream is "eliminated" or "augmented" for the network because a valve is opened and/or closed or pumps are turned on or off. The full topology is that theoretical presented if all streams allow flow through them. During a session of dynamic simulation a system may change its topology depending on the operator's actions. This means that the order of matrix associated to the equations that represent the system changes. To obtain a numerical solution of the model is convenient to count with a procedure that guarantees a solution in any case, *i.e*. avoiding the singularity problem. An algorithm was developed to detect the active topology in order to construct and solve only the equations related to the particular topology each integration time. The solution method is reported by Mendoza-Alegría *et al*. (2004). Figure 2 represents the flows and pressures network for the compressor and turbines.

#### **Energy balances on internal nodes**

Valves are considered isoenthalpic. The heat gained by the fluid due the pumping *Δhpump* when goes through a turned on pump is:

$$
\Delta \text{h}\_{p\text{comp}} = \left(\frac{\eta \Delta P}{\rho}\right) \tag{8}
$$

where *η* is the efficiency.

228 Efficiency, Performance and Robustness of Gas Turbines

'2 ' '2 Δ= + + − Δ *P kw kw k gz* 12 3 ω

If it is considered that in a given moment the aperture, density, and speed are constant, both

Applying equation (1) on each node and equation (6) on each accessory a set of equations is obtained to be solved simultaneously. A more efficient way to get a solution is achieved if equation (6) is linearised. To exemplify, equation (6) is selected for the case of a pump with arbitrary numerical values (same result may be obtained for any other accessory). Figure 10 presents the quadratic curve of flowrate *w* on the *x* axis and *ΔP* on the *y* axis (dotted line). In the curve two straight lines may be defined as AB and BC and represent an approximation of the curve. The error is lower if more straight lines were "fitted" to the curve. In this case two straight lines are used to simplify the explanation, but the model allows for any number

For a given flow *w*, the pressure drop may be approximated by the correspondent straight line (between two limit flows of this line). If there are two or more accessories connected in series

Substituting equation (7) on (1), for each flow stream, a linear equations system is obtained where pressures are the unknowns. The order of the equations system matrix is equal to the number of internal nodes of the network. Flows are calculated by equation (7) once the

The topology of a network may change, for instance, if a stream is "eliminated" or "augmented" for the network because a valve is opened and/or closed or pumps are turned on or off. The full topology is that theoretical presented if all streams allow flow through them. During a session of dynamic simulation a system may change its topology depending on the operator's actions. This means that the order of matrix associated to the equations that represent the system changes. To obtain a numerical solution of the model is convenient to count with a procedure that guarantees a solution in any case, *i.e*. avoiding the singularity problem. An algorithm was developed to detect the active topology in order to construct and solve only the equations related to the particular topology each integration time. The solution method is reported by Mendoza-Alegría *et al*. (2004). Figure 2 represents the flows

Valves are considered isoenthalpic. The heat gained by the fluid due the pumping *Δhpump*

<sup>Δ</sup> Δ =

ρ

*pump <sup>P</sup> <sup>h</sup>* η

and/or two or more lines in parallel are present, an equivalent equation may be stated:

where *ω* is the pump speed and where *k´i* are constants that fit the pump behaviour.

equations (4) and (5) may be written as:

of them.

pressures were obtained.

and pressures network for the compressor and turbines.

**Energy balances on internal nodes** 

when goes through a turned on pump is:

 ωρ

<sup>2</sup> *w k Pk* = Δ+ *a b* (6)

*wCP D* = Δ+ (7)

(8)

(5)

Fig. 10. Flowrate versus pressure drop linearization.

The exit properties for each turbine and compressor stage are calculated in a similar way, as an isoentropic expansion (or compression) and corrected with its efficiency. For example, the properties at the compressor's exhaust are calculated as an isentropic stage by a numerical Newton-Raphson method (i.e. the isoenthalpic exhaust temperature *To\** is calculated at the exhaust pressure *Po* with the entropy inlet *si*):

$$f(T\_o^\*) = s\_i(T\_{"{\prime}"}P\_{"{\prime}"}c) - s\_o^\*(T\_{"{\prime}"}^\*P\_{"{\prime}"}c) = 0\tag{9}$$

where *c* is the gas composition. Then, the leaving enthalpy is corrected with the efficiency of the compressor:

$$h\_o = \frac{\left(h\_o^\* - h\_i\right)}{\eta} + h\_i \tag{10}$$

For the turbine it was considered that the work is produced instead of consumed. All other exhaust properties are computed with the real enthalpy and pressure. The efficiency *η* is a function of the flow through the compressor and turbine.

An energy balance on the flows and pressures network is made in the nodes where a temperature or enthalpy is required to be displayed or when a mixture of flowrates is made. In this case, the state variables are the enthalpy *h*, and the composition of all the components *cj* is necessary in order to determinate all the variables of the node:

$$\frac{d\mathbf{h}}{dt} = \frac{\sum w\_i \, h\_i - w\_o \, h \, -q\_{atm}}{m} \tag{11}$$

In this equation, *m* is the mass of the node, and *qatm* the heat lost to the atmosphere. The subindex *i* represent the inlet conditions of the different flowstreams converging to the

Models for Training on a Gas Turbine Power Plant 231

The kinetics is not taken into account, but this approach considering these original two efficiencies, allows simulate the behaviour of the combustor. For this particular application of the combustor model, a linear function was defined for each efficiency, and for each reaction, based on the excess of oxygen (a thumb rule, but any equation could be

As an example the equations to obtain the stoichiometric coefficients related with the

If excess of oxygen 200% 0.1 0.0 If excess of oxygen 100% 0.0 0.1

1,1 ; 1,2 xcess of oxygen <=50% *a a* = = 0.0 0.0

The reactive stoichiometric coefficients *n* are known variables except for the oxygen. Thus,

1,1 1,1 1,18 1,19

Similar equations may be stated for the oxidation reaction of each component and all the coefficients may be calculated. With the coefficient *m*, the concentration of the product is obtained. This formulation may be applied in a generic way for any quantity and any

An iterative process may be followed to find the flame temperature as a function of the amount of all the present species considering: the heat of combustion, calculated from the component's formation enthalpies; reactive and product sensitive heat; and heat losses by

To develop the combustor model, it was conceptualised according Figure 11. Basically, the

Compressor Turbine

Reaction products Flame Temperature

Reaction Capacitive

node

Combustor exit components Combustor pressure and temperature

Combustor

0.5 2 – –

1,2 1,18 1,19

= +

*m nm m n mm*

( )

1,1 ; 1,2 1,1 ; 1,2 (15)

(16)

*a a a a*

>= = = = ==

1,1 1,1 1,18 1,19 2 1,2 1,18 1,19 1,2

= ++

*Nn mm m O m mm*

: n 0.5 ; 0.0

1,19 1,1 1,1 1,18 1,2 1,1

*m n m n*

division considered a mixing node, the reaction and the capacitive node.

= = =

2a 2a

0.5 1

=+ =

nitrogen (and the oxygen in the nitrogen reaction) are:

: 2 2

Here, a linear interpolation is used between the boundaries.

If e

for the nitrogen oxidation:

number of reactants.

radiation and convection.

Fuel gas

Fig. 11. Conceptual model of the combustor.

Gas and air

defined).

node. With the enthalpy and pressure it is possible to verify if the node works as a single or a two phase.

All the mass balances are automatically accomplished by the flows and pressures network solution, however, the concentration of the gas components must be considered through the network. The concentration of each species *j* is calculated as the fraction of the mass *mj* divided by the total mass *m* in a node. The mass of each component is calculated by integrating next equation:

$$\frac{dm\_j}{dt} = \sum w\_i \mathbf{c\_{i,j}} - \sum w\_o \mathbf{c\_j} \tag{12}$$

### **Combustor**

To calculate the flame temperature, the oxidation equations for each one of the 20 potential components were stated. Some of the reactions for the combustion process are:

2*n*1,1 *N*2 + 4*n*1,2 *O*2 0*m*1,1 *N*2 + 0*m*1,2 *O*2 + 0*m*1,18 *N*O + 4*m*1,19 *N*O2  *n*2,1 *O*2 *m*2,2 *O*<sup>2</sup>  *n*3,1 *H*2*S* + 1.5*n*3,2 *O*2 0*m*3,2 *O*2 + 0*m*3,3 *H*2*S* + 1*m*3,16 *H*2*O* + *m*3,20 *SO*<sup>2</sup>  *n*4,1 *CO*2 *m*4,4 *CO*<sup>2</sup>  *n*5,1 *CH*4 + 2*n*5,2 *O*2 *m*5,4 *CO*2 + 2*m*5,16 *H*2*O* + 0*m*5,2 *O*2 + 0*m*5,5 *CH4* + 0*m*5,17 *CO* • • • 10*n*15,1 *C*10*H*22 + 155 *n*15,2 *O*2 *m*15,4 *CO*2 + *m*15,16 *H*2*O* + 0*m*15,2 *O*2 + 0*m*15,15 *C*10*H*<sup>22</sup> + 0*m*15,17 *CO* 2*n*16,1 *H*2*O* 2*m*16,16 *H*2*O n*17,1 *CO* + 0.5*n*17,2 *O*2 *m*17,4 *CO*2 + 0*m*17,17 *CO* + 0*m*17,2 *O*<sup>2</sup>  *n*18,1 *NO* + 0.5*n*18,2 *O*2 *m*18,19 *NO*2 + 0*m*18,18 *NO* + 0*m*18,2 *O*<sup>2</sup>  *n*19,1 *NO*2 *m*19,19 *NO*2  *n*20,1 *SO*2 *m*20,20*SO*<sup>2</sup> (13)

The excess of oxygen may be calculated from the flowrates of the reactive components. The total combustion efficiency for each reaction *i* αi,1 is defined as the fraction of the theoretically amount of oxygen that is consumed for a total combustion: is 1 if a complete combustion reaction is hold, for example production of *CO2* and 0 if none of the products of a reaction is completely oxidised. The partial combustion efficiency αi,2 is defined as the fraction of the theoretically amount of oxygen that consumed for a partial combustion (is 1 if partial oxidised products are generated, for example production of *CO* and 0 if none of the products of a reaction is partially oxidised). The efficiencies are normally not constant and any function could be adjusted but considering that, to avoid imbalance problems, the restriction

$$
\alpha\_{i,1\*} \ a\_{i,2} \le 1 \tag{14}
$$

must be satisfied at any moment.

node. With the enthalpy and pressure it is possible to verify if the node works as a single or

All the mass balances are automatically accomplished by the flows and pressures network solution, however, the concentration of the gas components must be considered through the network. The concentration of each species *j* is calculated as the fraction of the mass *mj* divided by the total mass *m* in a node. The mass of each component is calculated by

,

To calculate the flame temperature, the oxidation equations for each one of the 20 potential

*i i j o j*

*dt* = − (12)

(13)

*wc wc*

*j*

components were stated. Some of the reactions for the combustion process are:

2*n*1,1 *N*2 + 4*n*1,2 *O*2 0*m*1,1 *N*2 + 0*m*1,2 *O*2 + 0*m*1,18 *N*O + 4*m*1,19 *N*O2

 *n*3,1 *H*2*S* + 1.5*n*3,2 *O*2 0*m*3,2 *O*2 + 0*m*3,3 *H*2*S* + 1*m*3,16 *H*2*O* + *m*3,20 *SO*<sup>2</sup>

 *n*5,1 *CH*4 + 2*n*5,2 *O*2 *m*5,4 *CO*2 + 2*m*5,16 *H*2*O* + 0*m*5,2 *O*2 + 0*m*5,5 *CH4*

10*n*15,1 *C*10*H*22 + 155 *n*15,2 *O*2 *m*15,4 *CO*2 + *m*15,16 *H*2*O* + 0*m*15,2 *O*2 + 0*m*15,15 *C*10*H*<sup>22</sup> + 0*m*15,17 *CO*

The excess of oxygen may be calculated from the flowrates of the reactive components. The

theoretically amount of oxygen that is consumed for a total combustion: is 1 if a complete combustion reaction is hold, for example production of *CO2* and 0 if none of the products of

fraction of the theoretically amount of oxygen that consumed for a partial combustion (is 1 if partial oxidised products are generated, for example production of *CO* and 0 if none of the products of a reaction is partially oxidised). The efficiencies are normally not constant and any function could be adjusted but considering that, to avoid imbalance problems, the

> α*i*,1 + α

α

i,1 is defined as the fraction of the

α

*<sup>i</sup>*,2 ≤ 1 (14)

i,2 is defined as the

+ 0*m*5,17 *CO*

 *n*17,1 *CO* + 0.5*n*17,2 *O*2 *m*17,4 *CO*2 + 0*m*17,17 *CO* + 0*m*17,2 *O*<sup>2</sup>  *n*18,1 *NO* + 0.5*n*18,2 *O*2 *m*18,19 *NO*2 + 0*m*18,18 *NO* + 0*m*18,2 *O*<sup>2</sup>

a reaction is completely oxidised. The partial combustion efficiency

*dm*

a two phase.

**Combustor** 

• • •

restriction

must be satisfied at any moment.

integrating next equation:

 *n*2,1 *O*2 *m*2,2 *O*<sup>2</sup>

 *n*4,1 *CO*2 *m*4,4 *CO*<sup>2</sup>

2*n*16,1 *H*2*O* 2*m*16,16 *H*2*O*

 *n*19,1 *NO*2 *m*19,19 *NO*2  *n*20,1 *SO*2 *m*20,20*SO*<sup>2</sup>

total combustion efficiency for each reaction *i*

The kinetics is not taken into account, but this approach considering these original two efficiencies, allows simulate the behaviour of the combustor. For this particular application of the combustor model, a linear function was defined for each efficiency, and for each reaction, based on the excess of oxygen (a thumb rule, but any equation could be defined).

As an example the equations to obtain the stoichiometric coefficients related with the nitrogen (and the oxygen in the nitrogen reaction) are:

$$\begin{aligned} \text{N}: \ 2n\_{1,1} &= 2m\_{1,1} + m\_{1,18} + m\_{1,19} \\ O\_2: \ \mathbf{n}\_{1,2} &= 0.5m\_{1,18} + m\_{1,19}, \newline m\_{1,2} &= 0.0 \\ \text{If excess of oxygen} &= 200\% & a\_{1,1} &= 0.1, a\_{1,2} &= 0.0 \\ \text{If excess of oxygen} &= 100\% & a\_{1,1} &= 0.0, a\_{1,2} &= 0.1 \\ \text{If excess of oxygen} &= 50\% & a\_{1,1} &= 0.0, a\_{1,2} &= 0.0 \\ \end{aligned} \tag{15}$$

Here, a linear interpolation is used between the boundaries.

The reactive stoichiometric coefficients *n* are known variables except for the oxygen. Thus, for the nitrogen oxidation:

$$\begin{aligned} m\_{1,19} &= 2 \mathbf{a}\_{1,1} n\_{1,1} \\ m\_{1,18} &= 2 \mathbf{a}\_{1,2} n\_{1,1} \\ m\_{1,1} &= 0.5 \left( \begin{array}{c} 2n\_{1,1} \ -m\_{1,18} \ -m\_{1,19} \end{array} \right) \\ m\_{1,2} &= 0.5 m\_{1,18} \ + 1 m\_{1,19} \end{aligned} \tag{16}$$

Similar equations may be stated for the oxidation reaction of each component and all the coefficients may be calculated. With the coefficient *m*, the concentration of the product is obtained. This formulation may be applied in a generic way for any quantity and any number of reactants.

An iterative process may be followed to find the flame temperature as a function of the amount of all the present species considering: the heat of combustion, calculated from the component's formation enthalpies; reactive and product sensitive heat; and heat losses by radiation and convection.

To develop the combustor model, it was conceptualised according Figure 11. Basically, the division considered a mixing node, the reaction and the capacitive node.

Fig. 11. Conceptual model of the combustor.

Models for Training on a Gas Turbine Power Plant 233

Phenomena occurring in other equipments and systems like heat exchangers, electrical motors, generator, electrical network, tanks, etc., are used for other MSS but their

The simulator testing was made with 16 detailed operation procedures elaborated by the costumer specialised personnel, namely the "Acceptance Simulator Test Procedures". The tests included all the normal operation range, from cold start conditions to full load, including the response under malfunctions and abnormal operation. In all cases the

From the real plant an automatic start up procedure was documented (with a total of 302 variables obtained from the DCS). The tests presented here are the results of an automatic start-up followed by two malfunctions. During these transients no actions of the operator

Although they are not any more mentioned in this work, must be noted that all the expected alarms were presented in the precise time. Results include variables concerning the gas turbine power plant in general. The idea is demonstrate that the gas turbine model is capable to reproduce the real plant behaviour in all cases and that its response is adequate for training purposes. In all cases, plant data were available during the first 2780 s where the

**ID Description** 

120 – 830 00:02:00 - 00:13:50 2 Combustor ignition is triggered and turbine

2790 – 2970 00:46:30 - 00:49:30 4 The plant is kept producing nominal load.

3000 – 3500 00:50:00 - 00:58:20 6 Simulator runs without external changes,

3680 – 4200 01:01:20 - 01:10:00 8 Simulator runs without external changes,

2970 – 3000 00:49:30 - 00:50:00 5 Progress malfunction of low efficiency in the

*kPa*).

830 – 2790 00:13:50 - 00:46:30 3 Initiates the electricity production up to nominal load (150 *MW*).

Simulation is initiated and plant stays in steady state for 5 s, then turbine is turned on in automatic mode and turbine roll-up initiates.

combustor up to its final value (50% of severity).

Progress malfunction of pressure loss in the delivery line of gas fuel up to its final value (4082

reaches its nominal speed (3600 *rpm*).

controls try to stabilise plant.

controls try to stabilise plant.

were allowed. In Table 4 a list of the events and the time they happen is presented.

**Event** 

formulations are not explained here.

response satisfied the ANSI/ISA norm.

**Time Period (***hh:mm:ss***)** 

0 – 120 00:00:00 - 00:02:00 1

3500 – 3680 00:58:20 - 01:01:20 7

Table 4. Description of the programmed events for the test.

**6. Tests and results** 

simulator results fit well.

**Time Period (***s***)** 

The mixing node just takes the air and fuel flowrates and concentrations to have single flowrate considering a perfect and instantaneous mixing. The reaction considers equations 13 to 16 to calculate the flame temperature, the flowrate and concentration of the products that enters into the combustor capacitive node, that has a volume and a concentration of the different species. Equation (12) applies for the mass of each component. The energy balance is done calculating the internal energy *u* in the node. The derivative of the internal energy is evaluated as:

$$\frac{du}{dt} = \frac{\Sigma w\_i h\_i - \Sigma w\_o h - u \frac{dm}{dt} - q\_c}{m} \tag{17}$$

The derivative of the total mass is the sum of the derivatives of each species as equation (12).

Here, the internal energy and density are known, this later by dividing the total mass and the volume of the node. The gas thermodynamic properties are a function of pressure and temperature, so all the properties are calculated with a double Newton-Raphson iterative method to have a solution. When two phases are present, some extra calculations are made to known the liquid and vapour volumes, but this is not treated here.

The combustor heat *qc* is calculated as the sum of radiant and convective phenomena using appropriate correlations. The heat is absorbed by the combustor metal that is cooled with air flow in the rotor air cooler (see Figure 2). This heat is divided to be absorbed by different parts of the metal, like the blade paths presented in Figure 5. In each part, the modelling of the temperature may be represented by Figure 12.

Fig. 12. Conceptual model of the combustor.

The temperature of the metal may be calculated by integration of next equation:

$$\frac{dT\_m}{dt} = \frac{q\_c - q\_a - q\_{atm}}{\mathcal{C}p\_m \ m\_m} \tag{18}$$

The metal heat capacity *Cpm* is calculated with a polynomial function of temperature. Note that the term *qatm* would not exist, depending on the particular position of each modelled metal. The exit air conditions changes due the absorbed heat. For these effects, Equation (11) is used.

Phenomena occurring in other equipments and systems like heat exchangers, electrical motors, generator, electrical network, tanks, etc., are used for other MSS but their formulations are not explained here.
