CHAPTER 3 MODELLING AND SIMULATION

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1 58 CHAPTER 3 MODELLING AND SIMULATION 3.1 NEED FOR SIMULATION Simulation is the use of modeling to represent (but not replicate ) a system or process at an appropriate level of detail, and thereby help the User to experiment in a perfectly safe and sufficiently realistic environment. They can easily process many complex, inter-dependent decisions and so quickly provide the likely consequences of a given scenario. Significant insight and greater understanding of the problem can be gained from the very process of model design in addition to the execution of Scenarios and the analysis of outcomes. One of the primary advantages of simulators is that they are able to provide users with practical feedback when designing real world systems. It helps to determine the correctness and efficiency of a design before the system is actually constructed. Consequently, the merits of alternative designs are explored without actually physically building the systems. By investigating the effects of specific design decisions during the design phase rather than the construction phase, the overall cost of building the system diminishes significantly. 3.2 POWER PLANT SIMULATION The software used for modeling is EBSILON Professional EBSILON is the abbreviation for "Energy balance and simulation of the load response of power generating or process controlling network structures" and

2 59 is suitable for nearly all stationary thermodynamic model request coming out of energy cycles or plant schemes. It is a mass and energy balance calculation program for thermodynamic cycles. The software can be used to simulate the performance of a combined cycle power plant in design and off design conditions, which is adequate for analyzing its performance under several loading conditions. The simulation is applicable for design, evaluation and optimisation of different types power plants and other thermodynamic processes. During the design process, it helps in identifying an optimal cycle and also evaluating various options and alternate configurations. It can be also be used during plant operations to evaluate losses and suggest possible plant improvements. It is built from first principles of physics and conserves the energy and mass balance of all power plant processes. It can therefore be used for simulating plant conditions at different loads to a high degree of fidelity. 3.3 CAPABILITIES OF SIMULATION Ebsilon permits the balancing of components, individually or in groups, as well as subsystems integrated in bigger systems, without taking into account whether these components or systems form a closed or an open cycle. The model structure of Ebsilon is based on: standard components, which are used for modeling common power plants, programmable components for modeling complex power plants processes with user defined behaviour. The data basis of Ebsilon is made up of APWS-IF97 or the IFC67 steam table and specific heat (Cp) polinomial for air/fuel gas. Ebsilon is a

3 60 variable program system, by means of which all occurring power plant circuits can be balanced using a closed solution based on a sequential solution method. 3.4 SOFTWARE The Ebsilon Professional is a mass and energy balance cycle calculation program that is highly integrated with common operating environments and applications. It is suitable for nearly all, stationary thermodynamic modelling requirements for evaluating thermodynamic cycles or plant schemes. It uses the well-known mathematical kernel of Ebsilon, which can solve the non-linear mass and energy balance equations of the plant. The mathematical kernel of Ebsilon has excellent convergence and stability properties allowing complex problems to be solved quickly. Data analysis and the generation of process models are supported by a powerful graphical user interface. All the components are represented both mathematically and graphically, allowing plant models to be built component by component and in one-to-one correspondence with the actual plant. The validation of measured values of the plant allows a reliable and consistent process representation. 3.5 MODELLING FEATURES The software is built with a powerful graphic editor, which allows the models to be built using single components, group of components, sub systems or complete systems. It also allows that components or systems can be in open or closed circuit. This makes it possible to simplify certain areas, and focus on those areas that are the interest of the modeler, which then can be modeled in much greater details.

4 61 Figure 3.1 Modeling of a simple cycle in Ebsilon The Figure 3.1 shows a simple cycle built in an Ebsilon graphic editor. This contains the modules that represent the components of the power plant. After defining the appropriate operating and design values (according to specification from manufacturer (Figure 3.2) for all components, the model is ready for calculations. The results of the calculations are stored as reference values. If the calculations do not run successfully, then the Ebsilon provides an option for error analysis component wise or system wise. It is also possible to compute the behavior and performance of each component under different operating conditions. Ebsilon provides different modes of calculations, viz., Design mode and Off-design mode. Normally, Design mode is used for the construction of new cycles and in this mode appropriate values for all components are defined by the designer according to specifications from

5 62 manufacturer. The calculation results of the Design mode are then stored as reference values for the Off-design mode calculations. Figure 3.2 Specification values input for components The Off-design mode is used for a cycle already completed and calculated in the Design mode. It may be used to calculate different variations (different set of input data) of plant operations. After successful calculations, the model computes the efficiencies and Heat rates of the system in both design and in different operating conditions as shown in Figure 3.3.

6 63 Figure 3.3 Simulation ready model for a gas turbine The performance of the components, e.g., Heaters, Turbines, etc., can be shown in Q-T or H-S diagram, drawn automatically from the operating behavior of the components in the specified conditions. Also Ebsilon provides a convergence diagram for the evaluation of the performance of the unit. 3.6 COMPONENT AND OTHER LIBRARIES In the Ebsilon, the modelling is done by using a component library, which consists of 95 components as e.g. turbines, heat-exchangers, boiler, pumps, generators, gas-turbines, combustion chambers, tanks, gasifier, FBC, fuel cell, cooling towers dryer, filters, separators, fans, etc. The cycle is first modeled topologically by using the component toolbox and the inserted components are then parameterized. All components are equipped with sets of default values. The sets are taken from a library, which can be modified and enlarged by the user. From this library, both total and parts of cycles can be selected. A gas turbine library is also available.

7 64 For media properties, different property libraries and tables are available. Fuels (bituminous coal, lignite, gas, oil, hydrogen, biomass etc.) can be used from such a library. Flue gases can be selected with any composition or a selected from default composition. 3.7 BUILDING A MODEL The entire plant is first mapped by the Ebsilon Software to establish the consistency of plant data and compare it with the design parameters of the plant. The outcome of this exercise gives a complete mapping of the target plant into Ebsilon which allows Ebsilon to simulate various plant conditions. This allows the identification of problems where there are mismatches of the design data with the plant. Through its powerful validation routines, Ebsilon also can pinpoint wrong instrumentation data. The plant personnel provide the data used for the mapping of the Power Plant. The Power Plant is mapped based on data inputs and validates the data input set by a number of trial runs. This approach is interactive since initial power plant data set provided will usually not be consistent due to hidden or known instrumentation errors as well as inaccurate equipment and fuel specifications. 3.8 GAS TURBINE LIBRARY Through an individual model component the gas turbine performance characteristics can be integrated with a detailed plant model, and in-depth thermodynamic analysis can be performed benefiting from the features of EBSILON Professional, such as individual equipment characteristics in design and off-design mode

8 65 full record of all gas, water/steam and electrical flows of the plant flexibility in equipment arrangement, plant configuration and mix of technologies a powerful, fast and reliable equation-based solver open architecture to include user-defined models for new technology or vendor data Data is continuously updated from gas turbine vendors to grow the Gas Turbine Library (Figure 3.4) to become a valuable and living source for gas turbine performance information, so that engineers around the globe can make use of reliable and first-hand data to analyze and improve combined cycle plants. Figure 3.4 Data library for PG9351(9FA) combined cycle

9 STRUCTURE AND SOLUTION OF EQUATION SYSTEM A power cycle consists on n connecting pipes between the individual components. The simulation is complete, when, based on the physical laws, to every pipe i values of the following base variables can be associated p : pressure h : specific enthalpy m : mass flow The dependent variables, like temperature T or power Q can be calculated from the base variables through A property state function T = T(p,h) An algebraic correlation Q = m h for Therefore it is necessary to solve a (non-linear) system of equations N = n 3 unknowns (n pipes with 3 base variables each) The mathematical relation between the N equations is formulated in the individual components. These relations are based on the physical laws of conservation of mass, energy and momentum. For a typical heat exchanger which will be used in the model, the system of equations is created as follows. The Figure 3.5 represents a heat exchanger as a component in the simulation software.

10 67 Figure 3.5 Heat Exchanger component The ingoing pipes are: Pipe i1 (primary flow) Pipe i3 (secondary flow) The outgoing pipes are : Pipe i2 (primary flow) Pipe i4 (secondary flow) The following balances are valid for the base variables: Pressure (the pressure drop DP12 can be configured inside the component) p(i1)-p(i2) = DP12 (3.1) p(i3)- p(i4) = DP34 (3.2) Enthalpy (from conservation of energy and heat-transfer) m(i2) h(i2) - m(i1)h(i1) = ktm (3.3) m(i3)h(i3) - m(i4) h(i4) = ktm (3.4)

11 68 Mass flow (from conservation of mass) m(i1) - m(i2) = 0 (3.5) m(i4) - m(i3) = 0 (3.6) Through these balance equations the outlet variables are correlated with ingoing variables. For a cycle, consisting of several components, a non-linear system of equations is created, which correlates the base variables x i (pressure, specific enthalpy and mass-flow) of different pipes. f 1 (x 1, x 2, x 3.. x 1 ) = 0 (3.7) f 2 (x 1, x 2, x 3.. x 1 ) = 0 f x (x 1, x 2, x 3.. x 1 ) = 0 The system of equation is non-linear, because of variable coefficients (for example m is present also in enthalpy equations) and variable right hand sides (for example the mean logarithmic temperature difference Tm depends on p and h of all connecting pipes of a heat exchanger). solved iteratively. Because of the non-linearity the system of equation can only be

12 69 In vector formulation the system of Equation (3.7) can be written as F(x) = 0 (3.8) x is the vector containing the values of all base variables x i (i=1,,n) and F denotes the vector of all functions f i In the neighbourhood of the sought solution vector x any function f i can be developed into a Taylor series ( + ) = () + + ( ) (3.9) The matrix of the partial derivatives, which occur in the summation, is the Jacobian matrix J of the partial derivatives of F with the matrix elements J i given by = (3.10) can be written as In vector formulation therefore the Taylor series expansion (3.9) ( + ) = () + + ( ) (3.11) Neglecting the terms with quadratic deviations and taking into account only the linear deviations and assuming ( + ) =0 (3.12) For 0, the following linear system of equation is obtained =0 (3.13)

13 70 The partial derivatives of the Jacobian matrix (10) are substituted by numerical derivative ( finite differences ). Therefore the system of Equations (3.13) is linear. The system of Equations (3.13) is only sparsely populated. Direct methods (like Gaussian elimination) cannot take advantage of the sparse population because computing time depends on the square of the rank of the matrix. Therefore an iterative method (Gauss Seidal) is used, because the computing time depends only linearly on the rank of the matrix. generated. With the found values for a new approximation for x is x k+1 = x k + (3.14) The values x k+1 together with x k are again substituted in (3.13) and the method is continued in an outer iterative loop (k = 0,.k max ) until a certain precision is reached. A relaxation factor can accelerate the rate of convergence. x k+1 =x k (3.15) The method converges faster if the starting values x o (i.e. of the 0 th iteration step) are close to the sought solution vector x THERMODYNAMICS OF COMPONENTS Steam Turbine A steam turbine converts the enthalpy difference of the steam between inlet and outlet of a turbine into mechanical work. Every steam turbine can be separated into different sections, according to the number of

14 71 extractions (Figure 3.6). The balances for mass, energy and pressure are then valid for each single section. Figure 3.6 Section of a steam turbine and fluid properties used in the balance equations Mass balance: = 0 (3.16) Energy balance: (3.17) Pressure: (3.18) used: For the calculation of the outlet enthalpy h 2 the following relation is ( ) (3.19) denotes the isentropic efficiency. The off-design performance of the isentropic efficiency is stored as a characteristic line and depends on other variables, for example = (, p,) Enthalpy losses due to exhaust losses or due to wet steam can be taken into account. The relation between inlet and outlet pressure in off-design is described by the law of ellipses of Stodola.

15 72 = (3.20) With a given outlet pressure p 2 (for example condenser pressure), given mass flow, specific volume at inlet V 1 and the nominal values (denoted by subscript N ) the inlet pressure p 2 can be calculated for any load condition (off-design) Gas Turbine For the gas turbine the same physical laws like for the steam turbine are valid. Compared to the steam turbine no wet-steam conditions have to be taken into account and therefore the equation of state for ideal gases can be used Heat Exchanger Heat is transferred form the secondary side (pipe with index 3) to the primary side (pipe with index 1) as shown in Figure 3.7. The balances for mass, energy and pressure for an ideal heat-exchanger without losses are given according to the diagram Figure 3.7 Fluid properties used in the balance equations for heat exchanger

16 73 Mass: = 0 (3.21) = 0 (3.22) Enthalpy: = (3.23) = (3.24) Pressure: (3.25) (3.26) For the heat transferred the following relation is used = (3.27) which is valid for parallel flow as well as for counter-flow heatexchangers. In this formula k denotes the heat-transfer coefficient, A the heattransfer area and m T the mean logarithmic temperature difference. The mean logarithmic temperature difference is calculated as: = ( ) (3.28) Parallel flow heat-exchangers: =, = (3.29) Counter flow heat-exchangers: =, = (3.30) The off-design performance for the heat-transfer is described by a characteristic line for the heat-transfer coefficient k and the nominal value ( ) :

17 74 = ( /, / () (3.31) The off-design behavior of the pressure drop is calculated as : = (3.32) where p denotes the nominal pressure drop. The relations given are in principal valid for all types of heatexchangers, also for condensing heat-exchangers and desuperheaters Condenser For a condenser (where the primary side is given by the pipes 1 2) the same equations like for a heat-exchanger without condensation are valid. One additional equation describes that the secondary fluid leaving the condenser is in the saturated liquid state: ( ) (3.33) From this additional equation it follows that 1 and 2 can be calculated from the energy balance if 3, 4, enthalpy h 3 and pressure p 3 of the steam entering the condenser are known. If an auxiliary condensate flow 5 & with specific enthalpy h 5 into the condenser exists, it is additionally taken into account in the balances for mass and energy Pump and Compressor Pumps and compressors are described again by the mass and energy balance as shown in Figure 3.8. The medium (liquid or gaseous) is brought from a low pressure level to a higher pressure level.

18 75 Figure 3.8 Fluid properties used in the balance equations for pump and compressor Mass balance: = 0 (3.34) Energy balance: = 0 (3.35) Pressure: (3.36)