Dynamic simulation of a circulating fluidized bed boiler system Part I: Description of the dynamic system and transient behavior of sub-models

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1 Journal of Mechanical Science and Technology 30 (12) (2016) 5781~ DOI /s Dynamic simulation of a circulating fluidized bed boiler system Part I: Description of the dynamic system and transient behavior of sub-models Seongil Kim 1, Sangmin Choi 1,* and Jongin Yang 1,2 1 Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea 2 Department of Mechanical Engineering, Texas A&M University, College Station, TX , USA (Manuscript Received April 19, 2016; Revised July 25, 2016; Accepted August 18, 2016) Abstract Dynamic performance simulation of a CFB boiler in a commercial-scale power plant is reported. The boiler system was modeled by a finite number of heat exchanger units, which are sub-grouped into the gas-solid circulation loop, the water-steam circulation loop, and the inter-connected heat exchangers blocks of the boiler. This dynamic model is an extension from the previously reported performance simulation model, which was designed to simulate static performance of the same power plant, where heat and mass for each of the heat exchanger units were balanced for the inter-connected heat exchanger network among the fuel combustion system and the water-steam system. Dynamic performance simulation was achieved by calculating the incremental difference from the previous time step, and progressing for the next time step. Additional discretization of the heat exchanger blocks was necessary to accommodate the dynamic response of the water evaporation and natural circulation as well as the transient response of the metal temperature of the heat exchanger elements. Presentation of the simulation modeling is organized into two parts; system configuration of the model plant and the general approach of the simulation are presented along with the transient behavior of the sub-models in Part I. Dynamic sub-models were integrated in terms of the mass flow and the heat transfer for simulating the CFB boiler system. Dynamic simulation for the open loop response was performed to check the integrated system of the water-steam loop and the solid-gas loop of the total boiler system. Simulation of the total boiler system which includes the closed-loop control system blocks is presented in the following Part II. Keywords: Dynamic simulation; CFB boiler; Naturally circulating boiler; Power plant control Introduction * Corresponding author. Tel.: , Fax.: address: smchoi@kaist.ac.kr Recommended by Associate Editor Tong Seop Kim KSME & Springer 2016 Circulating fluidized bed (CFB) boilers have become widely available due to their advantages of fuel flexibility and low pollutant emission. Recent progress is noticeable in the larger scale applications, especially in the electric power generation. Typical unit size of the boilers can accommodate power generation capacity of a few hundred MW [1]. General configuration of a CFB boiler in a power plant is shown in Fig. 1. The diagram shows a coal-fired power plant with a naturally circulating drum type boiler which supplies steam to the turbine. Here, two circulation systems are shown: the solid-gas circulation loop in the circulating fluidized bed furnace and the return parts, and the water-steam circulation loop in the boiler drum and evaporator. Boiler performance is an integral representation of the heat and mass transfer among the interconnected heat exchangers which ultimately transfer heat from the fuel to the steam. Mass and energy flow rate as well as the property values at each nodal point of the heat exchangers are dynamically changing. Performance prediction and simulation are now indispensable not only in the design process but also throughout the operation of the boiler and the entire power plants. Static thermal balance calculations are extensively performed at various load conditions as a part of the preliminary design evaluation process. Furnace and heat exchangers must be designed in such a way that the mass and energy flow must be balanced. Steam produced from the boiler would be supplied to the turbine at the specified pressure and temperature, at the specified flow rate to produce the required power output. Modern boilers are fully equipped with control systems to achieve these objectives. This complex system of heat exchangers along with associated control systems is running, and transient response of the behavior needs to be predicted. Dynamic performance simulation is designed to achieve this objective. Performance simulation of CFB boilers has been the topic of interest. Many studies considered the steady-state of the boiler but only a few reported the modeling of transient state of the boilers [2]. However, boilers experience transient states by the external environment changes such as the load variation or the changes in operating conditions during the operation.

2 5782 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~5792 Operators and designers have to properly handle the situations out of the design operation range and to understand the dynamic behavior of each component. Also, the CFB boiler system means a combination of the general boiler system and a circulating fluidized bed furnace. A large amount of the solid inventory and the solid circulation rate in the CFB loop determine the heat transfer rate to the water-steam side and the temperature of the gas-solid, which affects the performance. Because the water-steam circulation loop and the solid-gas circulation loop have to interact with each other in the furnace, modeling is required in association with the gas-solid side and the water-steam side. In this model, these considerations are highlighted in this paper. As to the dynamic performance prediction of CFB boilers, several attempts to develop dynamic models were reported [2-6]. However, these dynamic models focused on dynamic behavior of the circulating gas-solid flow of the furnace, but not on the evaporation side of the boiler. Also, these furnace side models were designed to describe dynamic performance of lab scale and/or pilot sized boilers where the heat transfer and the water evaporation were not major concerns. The model of Yang and Gou [2] was a dynamic model which considered the gas-solid side and the water-steam side for the large scale CFB boiler, which was not intended to simulate detailed dynamic behavior of the drum loop and the interaction with the gassolid circulation and the water-steam circulation in the furnace. Applying the commercial program in the water-steam side model showed limitation on the water-steam side prediction, and description of the controller and the load data processing for operation simulation were not specifically described [2]. The purpose of this study was to develop a physics-based dynamic model which considers the solid-gas side, the watersteam side and the wall side of the total boiler system. Dynamic performance of the total boiler system was to be predicted and the operation of a real plant to be simulated. This dynamic model was developed by extending the static model proposed by Kim [7, 8], in which the entire CFB boiler is functionally divided into a finite number of heat exchanger blocks. 2. The boiler plant and the models for simulation 2.1 The boiler Fig. 1. Diagram of the solid-gas circulation loop and the water-steam circulation loop in a CFB boiler (mass and energy flow rate as well a property values are dynamically changing). The boiler system selected for the dynamic simulation was a 340 MWe class utility power plant, currently operating, whose static performance simulation was reported previously [8]. At the maximum heat duty of 800 MW, the flow rate of the main steam is 1024 t/h at 541 C, 17.1 MPa. Design coal is subbituminous with 20.5 MJ/kg of higher heating value and the fuel supply is 48 kg/s. Excess air ratio is 1.19, and bed Fig. 2. Schematic diagram and dynamic sub-models of a 300 MWe-class CFB boiler system (1, 2, 2, 2, 6, 7, 8, 9, 10 blocks are linearly discretized, and each of the 2, 3, 4, 5 blocks is treated as a lumped block).

3 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~ material is sand with 2700 kg / m of density and 274 µm in average diameter, while the average diameter of coal is 513 µm. The boiler configuration is conceptually represented as a schematic in Fig. 2. The furnace is conceptually divided by the lower and the upper furnace. Fuel and air supplied into the furnace are circulating along with the bed material in a solidgas circulation loop, which consists of the furnace, the cyclone, the stand pipe and the loop seal. Gas separated from the cyclone is flowing through a series of back pass heat exchangers, which include reheater, superheater and economizer tube banks, before exiting through the flue gas treatment system, and eventually the stack. Steam evaporated and separated in the steam drum is further superheated, and then supplied to the steam turbine. Steam exiting from the high pressure turbine is reheated and then resupplied back to the lower pressure turbine. Boiler heat exchangers are allocated among the water wall riser tubes, and additional heat transfer surfaces such as the wing wall and the division wall are installed in the furnace. The water wall and loop-seal in the furnace are used as the evaporator, and the wing wall and the division wall installed in the furnace are used as the evaporator and the superheater. The cyclone wall is also used as the additional superheater surface. Convective heat exchangers in the back pass are used as the reheater, the superheater and the economizer. The boiler as represented by a set of heat exchanger blocks is identical to the one previously reported [8]. These boiler components are divided by the major submodels: the solid-gas circulation loop, the water-steam circulation and the heat exchanger train for the modeling. The solid-gas circulation loop includes the lower furnace (1) and the upper furnace (2), the cyclone (3), the stand pipe (4) and, the loop seal (5). The water-steam circulation loop model includes the drum (2 ) and the downcomer -riser loop (2 ). The heat exchanger train includes serial heat exchangers (6, 7, 8, 9, 10) in the back pass and the wing wall (2 ) for the absorption of required heat in the furnace. The number of each component follows the numbering rule of the previous study [8]. Inside the solid-gas circulation loop sub-model, the bubbling fluidized bed model with a solid-rare bubble phase and a solid-laden emulsion phase were applied in the lower furnace (1) and the core-annulus model was applied in the upper furnace (2) to calculate the solid volume fraction, according to the axial and the radial direction of the furnace. Meanwhile, each of the return parts (3, 4, 5) was considered as a lumped system, for simplicity of calculation. For the watersteam circulation loop model, the zero-dimension lumped system was applied in the drum and the downcomer -riser loop (2, 2 ) was represented as a one-dimensional system to calculate the interaction with the solid-gas side in the furnace. Also, the heat exchanger train represents a number of the gas to water-steam heat exchangers, each of which is idealized as a one-dimensional system with respect to the direction of the water-steam flow. 1, 2, 2, 2, 6, 7, 8, 9, 10 blocks are linearly discretized, and each of the 2, 3, 4, 5 blocks is treated as a lumped block. 2.2 The simulation models The static model, where boiler plant was divided into a series of heat exchanger blocks such as the furnace, the return part and the heat exchangers of the convection pass, was previously reported [8]. These heat exchanger blocks were used for the steady state zero-dimensional balance of mass and energy, while the solid circulation and the flue gas flow interact with the water-steam flow. Water evaporation through the evaporating riser and natural circulation hydrodynamics were not necessary in the overall heat transfer budgeting for the static performance simulation. To predict the dynamic performance of the boiler system, the static model of the previous study was improved in this study. The water-steam circulation loop model was added to consider the interaction with the solid-gas flow and the watersteam circulation by adopting the drum loop model [9, 10]. To accommodate the water-steam circulation, extensive discretization of the heat exchangers in the furnace was necessary. The solid-gas flow in the furnace was also further discretized to model the progress of solid fuel combustion and heat transfer to the various elements of the heat exchangers in the furnace. Water-steam side of the heat exchangers was also finely discretized to represent the local wall temperatures of the heat exchanger elements. Therefore, the one dimensional and the unsteady state of the governing equation were applied in this model. Also, the description of the coal combustion needed to be improved in this dynamic model by using the combustion rate of the upper furnace and the lower furnace. While in the previous study, the particle size was simply represented as an average value, the size distribution was considered to calculate the solid flow according to the particle size by allowing a finite division of particle size groups in this model. Also, an empirical equation of the solid circulation rate was derived from the operation data and used in the previous model, but the solid circulation rate was substituted by an extended correlation equation to account the particle size distribution in this model. In the previous model, evaporation in the furnace was handled as a simple block, while the natural circulation loop model was applied to predict the interaction between the solidgas flow and the water-steam flow in this model. 2.3 Discretization of heat exchanger model The basic concept of mass and heat flow in a spatially discretized heat exchangers system is shown in Fig. 3. A representative i-th cell is in itself a heat exchanger in which heat from the hot gas-solid side is transferred to the water-steam side. Material flow in the water-steam side is relatively easily defined, but material flow in the gas-solid side needs to consider the solid particle flow and the gas flow and also the combustion reaction of fuel. The diagrammatic representation

4 5784 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~5792 Fig. 3. The basic concept of heat and mass flow in a system of spatially discretized serial heat exchangers. in the Fig. 3 summarizes the representative material flows of gas, solid, and water-steam, and heat transfer from the gassolid to the tube wall and from the tube wall to the watersteam, and heat of reaction in the gas-solid side. The material state at the i-th cell must be described, which includes temperature, composition of the material components. The i-th cell heat exchanger is obviously interconnected upstream to the i-1-th and downstream to the i+1-th cell. 2.4 Marching approach for dynamic calculation The heat and mass flow of each cell in each sub-model must be balanced. The process of the iterative calculation of the sub-model balance to calculate the converged the dependent variables in each cell of each side is summarized in Fig. 4. First, the transport phenomena of each sub-model are evaluated. In the solid-gas circulation loop sub-model, the hydrodynamics for determining the bubble-emulsion construction and the core-annulus zone [11-14], the solid behavior for determining the solid circulation rate of each particle size group [15-20] and the particle size distribution, the coal combustion reaction for determining the generated each gas species and the rate of char consumption [21-24] are calculated. In the water-steam circulation loop sub-model, the drum level and the discharged steam mass flow rate are calculated [9, 10]. The used transport phenomena modules for CFB boiler modeling are listed in Table 1, which shows the reference sources for the modules used in the mathematical models. As the calculation of the transport phenomena is completed, the mass flow rates ( Mɺ gs, M ɺ ws ) for each cell are calculated by the mass balance. The momentum equation is also solved to calculate the pressure and the velocity in the water-steam side. For the calculation of the energy balance, the heat transfer coefficients ( h gs, h ws ) are calculated by the corresponding correlation equation [25, 26] from each cell, and the heat transfer rates ( Qɺ gs w, Qɺ w ws ) are calculated by the equation of (, Qɺ gs w = hgs A( Tgs Tw) Qɺ w ws = hws A( Tw Tws) ) for each cell. Finally, the temperatures ( T gs, T w T ws for each cell are calculated by the energy equation. The calculation is iterated until the mass and the temperature values for all discretized cells are converged. As the heat and mass balance are converged, the converged dependent values are reported. Once the static performance is simulated by checking the heat and mass balance of the heat exchanger blocks, which Fig. 4. Procedure for dynamic calculation. can be numerically executed by iteration and convergence check, the dynamic calculation can proceed by time marching for the next time step. Procedure for the dynamic calculation is schematically shown in Fig. 4. When a disturbance suddenly occurs in the steady state system, the input conditions such as the mass flow rate of the each side and the heat input are changed. With the changed input condition, the sub-model balance is called to calculate the values at the next time step. For calculating the dependent variables of the next time step, the generalized transport equation is as follows: ( ) φ( ) φ t+ t = t + S φ, (1) where φ is the dependent variables, which is the mole flow rate for each species ( nɺ k ), mass flow rate of the particle bed material, the char and the water-steam ( mɺ p, mɺ c, mɺ ws ), the temperature of the gas-solid side and the enthalpy of the water-steam side ( Tgs, h ws ) in this model. And S φ is the source term of each dependent variable (φ ) due to the change of input condition. When the dependent variables are converged, S φ (source term for the particular variable) is reevaluated. Finally, the new values at the next time step are determined by Eq. (1). These calculation processes are iterated in the next time step, as shown in Fig Transport equation The transport equations for calculating a new state according to the change of input condition are as follows. Heat transfer, along with flow of various fluids and combustion, needs to be described for each case of application in each heat exchanger. This model is composed of a set of sub-models based on numerical method, and these sub-models solve the corresponding transport equations. The unsteady term is considered to predict the transient response of each component in the transport equation. Because the gas-solid flow of the furnace, the water-steam flow of the riser tube and each heat exchanger are modeled in a longitudinal direction, the transport equations are defined in each cell, which would produce necessary information in the cell. In the gas-solid side, mass reactions

5 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~ produce components of material: The volatile, carbon dioxide, carbon monoxide, oxygen, sulfur dioxide, nitrogen and water vapor. Conservation of mass for each material species should consider mass: ( ) ( ) nɺ t+ t = nɺ t + S, (2) k, j, i k, j, i n and the source term for the nɺ k is given as: S = nɺ nɺ + Jɺ + nɺ, (3) n k, j, i 1 k, j, i k, j, i k, j, i t+ t where nɺ k is the mole flow rate of the component k ( O2, CO2, H2O, CH2O, CO, N2 ), J ɺ k is the gas mass transfer between the core-zone and the annulus-zone and ɺ n is the generated gas from the reaction. The subscripts i, j, k represent the cell number, the zone number and the gas species, respectively. As shown in Eq. (3), the in-out gas flow, the gas mass transfer between the core zone and the annulus zone, and the gas reaction are considered in the transport equation of the gas side at the time step. The applied theories of the gas mass transfer and the gas reaction are presented in Table 1. In the solid side, the mass balances of the fuel and the bed material such as the sand are considered in this study. The char mass balance is for the fuel side: ( ) ( ) mɺ t+ t = mɺ t + S, (4) c, i c, i c and the source term for the c c, i 1 c, i c, i t+ t mɺ c is given as: S = m ɺ mɺ mɺ, (5) where mɺ c is the char mass flow and ɺ mc is the rate of char consumption. The rate of char consumption is determined by the char combustion [24], and subscript c represents char. The solid circulation rate and the amount of solid in each cell have to be correctly calculated for the performance prediction. Because the particle in the furnace has each different size, the transport equation of the solid side needs to be evaluated in each particle size group. Therefore, the mass balance of the solid side is for each particle size: ( ) ( ) mɺ t+ t = mɺ t + S, (6) p, j, i p, j, i m and the source term for the ( ) ( ) mɺ p is given as: S = mɺ mɺ + Jɺ, (7) m p, j, i in p, j, i out p, j, i t + t where mɺ p is the solid mass flow for each size group and J ɺ p is the solid mass transfer between the core-zone and the annulus-zone. The subscript p represents the particle size group, respectively. As shown in Eq. (7), the in-out solid flow, the Table 1. Reference sources for the transport phenomena modules. Phenomena group Water steam circulation loop model Hydrodynamics of fluidized bed Solid side behavior Coal combustion reaction Heat transfer coefficients Property of water-steam Transport phenomena modules Mass and heat balance of drum and downcomer-riser solid mass transfer between the core-zone and the annuluszone are considered in the transport equation at the corresponding time step. The solid circulation rate is an important variable. In this study, the modified correlation equation of Redemann [20] according to the particle size is used. The solid circulation rate is determined by the particle size, the particle density and the gas velocity. In this study, the particle size of the bed material is divided into 7 size group. Because there are the gas side and the solid side in the furnace of the CFB boiler, two phases should be considered together in the energy equation. Therefore, the energy balance equation at each cell is: ( mɺ scps + mɺ gcpg) T, ( ) t t, j, i j i t+ t + = ( mɺ scps + mɺ gcpg) Tj, i( t) + ST t, j, i Drum level Discharged steam flow rate Turbulent fluidization regime Reference Astrom and Bell [9], Kim and Choi [10] Davidson and Harrison [11] Thickness of annulus Werther and Wein [12] Solid volume fraction (axial) Kunii and Levenspiel [13] Solid volume fraction (radial) Rhodes [14] Fragmentation Bellgardt [15] Attrition Terminal velocity Merrick and Highley [16] Haider and Levenspiel [17] Minimum fluidized velocity Grace [18] Solid-gas mass transfer Hua [19] Solid circulation rate Redemann [20] Devolatilization Arrhenius model [21] Volatile combustion CO combustion Jones and Lindstedt [22] Van der Vaart [23] Char combustion Smith [24] Furnace Cyclone, loop-seal Heat exchanger tube bank Cluster renewal model [25] Fitting data from operation data Tube bank heat transfer [26] - IAPWS-IF97 [27], (8)

6 5786 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~5792 and the source term is given as: {( mɺ scpst) + ( mɺ ) j, i gcpgt j, i} ( ɺ ) ( ɺ ) in ST = { mscpst + m j, i gcpgt j, i} + Qɺ + Qɺ + Qɺ Qɺ out Js, j, i Jg, j, i r, j, i gs w, i t+ t, (9) where cps, c pg is the heat capacity of the solid and the gas, Q ɺ Js is the heat transfer by the solid mass transfer, Q ɺ Jg is the heat transfer by the gas mass transfer, Q ɺ r is the reaction heat and Qɺ gs w, i the heat transfer to tube wall. And subscripts i, j represent the cell number and zone number, respectively. The in-out heat flow of the gas and solid, the heat transfer by the mass transfer between the core zone and the annulus zone, the heat reaction and the heat transfer to wall side are considered in the energy balance equation at a time step. Also, the applied theories of the reaction heat and the heat transfer to the wall side are presented in Table 1. In the water-steam side, the mass, momentum and energy equation are numerically solved. The governing equation and the applied solution method are identical with APROS program [28], and the water-steam properties of IAPWS are used [27]. Also, in the wall side, the energy balance equation is applied at each cell. 2.6 Numerical solution The implicit method and the upwind scheme are applied to solve the unsteady 1-d governing equation, and the staggered grid is applied in the water-steam equation. The calculation domain for the main furnace is divided into m 2 array control volumes to calculate the properties according to axial (m divisions) and radial direction (2 divisions) of the furnace. The calculation domain of the heat exchanger is divided into m 1 array control volumes because the water-steam side model can neglect the changes of dependent variables according to the radial direction. The grid tests and time step tests have been executed to determine the proper values, considering the calculation simplicity and the accuracy. In this model, the calculation domain of the furnace was, respectively, divided into 10 2, array of control volumes in the lower bed and in the upper bed. Calculation domain of the heat exchanger was divided into Also, the calculation domain of the downcomer - riser was divided into 20 1 after the grid test. For the dynamic calculation of each dynamic sub-model, the 0.5 time step was selected after time step test in each dynamic model. 3. Step response of dynamic sub-models under open loop (a) (b) (c) Fig. 5. Input data and dependent variables in each of the sub-models: (a) Solid-gas circulation loop; (b) water-steam circulation loop; (c) heat exchanger train. Since the static simulation results of the boiler performance were presented in the previous study [8], the purpose of this chapter is to check the transient response of the model following the step change of input conditions. The response of the dynamic sub-models, namely the solid-gas circulation loop sub-model, the water-steam circulation loop sub-model, and the heat exchanger train sub-model, as explained in the previous chapter, are to be checked independently under open loop condition. Each of the models was independently calculated, and the dynamic results were calculated and checked for validation. For the solid-gas circulation loop sub-model and the heat exchanger train sub-model, the dynamic system response following the step change of the input conditions was calculated and compared in terms of the time constant for the respective system of the globally simplified thermal mass as described in the Appendix A. Dynamic response of the watersteam circulation loop was checked against the results calculated following the Astrom model [9]. Fig. 5 summarizes the input data and dependent variables for each of the sub-models. In the solid-gas circulation loop sub-model, the fuel supply and the air flow were identified as input conditions, and the solid circulation rate, the flue gas flow, the gas-solid temperature and the flue gas composition were calculated as the dependent variables. When the input conditions change, the time response of these dependent variables can be calculated. Variables such as the drum pressure, the circulation flow rate, the steam quality (mass fraction of the steam to the total mass of the mixture), the water level and the enthalpy of the water-steam in the riser tube were calculated as dependent variables following the step change of the mass flow of the steam and the step change of the heat input to the riser tube in the water-steam circulation loop model. Also, in the heat exchanger train sub-model when the input conditions such as the water-steam flow and the heat input change, the temperature of the water-steam could be calculated. Fig. 6 shows the temperature response of the CFB loop when fuel feed rate suddenly increases by 5 % at 0 s. The furnace and the cyclone temperature are values at the exit. As shown in Fig. 6, when the fuel feed rate increases, the bed temperature increases due to the heat reaction. In the beginning, the furnace temperature was kept at 892 C. As the fuel flow rate increases from 47 kg/s to 50 kg/s as a step change, the heat of reaction increases as well. As a result, the furnace

7 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~ Fig. 6. The transient response of the solid-gas temperature at the furnace exit and cyclone exit in the solid-gas circulation loop, following the step change of the fuel supply. temperature reaches a final value of 933 C. This trend is exponential, and it takes about 305 seconds for the temperature to reach the 63.2 % of the final value. This figure matches the time constant from the Appendix A in an acceptable manner. Also, the temperature change of the cyclone is larger than that of the furnace due to the heat capacity difference. These results show the importance of the dynamics of the solid-gas side due to massive storage of mass and energy of the solid in the CFB boiler system, while the dynamics of the water-steam is only important in the other boiler system. Fig. 7 shows the temperature response of the heat exchangers when the heat input rate increases. Because the dynamic calculations of the heat exchangers show similarities except the corresponding properties, results for the primary economizer and the primary superheater are selected here for comparison. When the heat input rate increases, the wall temperature and the water-steam temperature increase. As the heat input increases by the step change of +10 % at 0 s, the watersteam temperature reaches a final value of 265 C from 263 C and 386 C from 385 C, respectively. Time to reach 63 % of the final value is 160, 35 seconds, respectively. Because the heat capacity of water is larger than that of steam, the time to reach the steady-state of the primary economizer takes longer. The simulation results of the heat exchanger show comparable agreement with the time constants in Table A.1. As shown in Table A.1, the time constant of the water steam circulation loop is about 400 sec. This value is larger than the time constant of other components due to the large thermal inertia of the water system, so the water steam circulation loop dominates the dynamic behavior of the CFB boiler system. However, the water-steam circulation loop model of a naturally circulating drum-type boiler is an unstable system and includes controllers, so it is difficult to predict the time constant, directly. Therefore, the model prediction of the current boiler system is compared against the dynamic response of the previous studies, such as Astrom [9] and Kim [10]. The configuration as well as the size of the plant is unique in each of the application, but the error was small and the overall results show good agreement [10]. Dynamic response of the Fig. 7. The transient response of the heat exchanger temperature following the step change of the heat input: (a) Temperature at the economizer 1 outlet; (b) temperature at the superheater 1 outlet. drum loop of a 340 MWe CFB boiler has to be calculated to validate the application of the approach. Fig. 8 shows the response of the drum loop following the step change of the heat input to the riser tube. Although it is unavailable to validate the response results directly against the measured data, the extended application of the Astrom model to a significantly large scale boiler can be validated through quantitative discussion of the results. As shown in Fig. 8, the drum pressure, the quality at the riser exit and the water level increase and the water-steam circulation rate decreases according to the increase of the heat input to the riser tube. Characteristic response patterns as well as the quantitative gradients match the experience in a typical power plant, although the scale and configuration of the drum loop are noticeably different. The drum loop model of Astrom is chosen to be applied in the simulated CFB boiler in this study. 4. Step response of total boiler system under open loop (Integration of sub-models) To simulate the dynamic behavior of the CFB boiler system, dynamic sub-models, which are introduced in previous chapters, are integrated according to the mass flow and the heat transfer as described in the boiler system of the power plant. The integrated dynamic model is named as the open loop

8 5788 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~5792 Fig. 9. Input-output structure and the heat transfer of the process in the CFB boiler system. Fig. 8. Water-Steam circulation loop dynamic behavior, following the step-up of the heat input. model of the CFB boiler system, in the current study. In the flue gas side, the solid circulation loop and the convective heat exchangers in the back pass are connected according to the flow direction of the solid-gas side. Fig. 9 shows the input-output structure and the heat transfer of the process in the CFB boiler system. As shown in Fig. 9, the input conditions of the solid-gas side are the coal, air and the solid system, and the outputs are the flue gas flow rate, temperature and the oxygen concentration. The input conditions of the water-steam side are the feed water and the reheat steam, and the outputs are the mass flow rate, the temperature and the pressure of the steam to the turbine. The heat transfers are connected with each side according to the heat transfer surface arrangement. In the integrated model, the heat transfer rate of each dynamic sub-model is determined by the heat transfer coefficient and the temperature difference of the connected dynamic sub-models. QECO, QSH, Q RH are the heat transfer from the flue gas to the water-steam in the economizer, superheater and reheater of the back pass. Q CYC is the cyclone heat transfer, and Q SH, wing is the heat transfer of the wing wall in the furnace. Q EVA is the evaporator heat transfer from the solid-gas flow to the water-steam circulation in the furnace. Especially, this evaporator heat transfer dominates the performance and the dynamic of the CFB boiler system. This open loop model can simulate the dynamics of flow condition, temperature and the heat transfer with the disturbance such as the coal, air and feed water condition, and these dynamic results can show and save along the time and space. As a case of the calculation of the open loop model, Fig. 10 shows the transient response of the total boiler system, when the fuel supply suddenly increased by 5 kg/s (from 48 to 53 kg/s) at time = 0 sec, while the air flow was maintained at the constant values. The feedwater inlet condition is 274kg/s, 232 C and 18.1 MPa, and the reheat inlet condition is 181 kg/s, 303 C and 2.9 MPa. As shown in Fig. 10(b), the temperature of the solid-gas in the furnace increases from 898 to 934 C at 418 sec, as a result of the heat balance in the heat reaction and the heat transfer to the water-steam side, and temperature drops slowly (unnoticeable in the figure) due to the continuous change of the properties of the water-steam circulation loop. Hence, the clear steady values of the temperature are not presented in the open loop model. Concentration of oxygen at the exit of the economizer decreases, Fig. 10(c), from 3.3 to 1.5 % at 430 sec, because of the increased fuel supply under the constant air flow. Response time to reach a steady state of oxygen concentration in response of increased fuel supply is around 430 sec. Drum pressure, however, increases monotonically, as a result of heat transfer to the riser-tube, and increased steam flow rate following the increased drum pressure. Dynamic response of the water level shows an opposite trend, as was simulated by Alatiqi [29]. At the beginning, the water level rises because the net flow between the inflow to drum at the riser exit and the outflow to the downcomer is larger than the discharged steam mass flow due to the increase of the heat transfer to the riser tube; after then, the water level lowers, because of steam discharge from the drum. As shown in Figs. 10(d) and (e), drum pressure, water level and steam flowrate increase or decrease monotonically under the open loop. Therefore, these variables have to be controlled for stable operation [29]. Drum temperature increases from 358 to 376 C due to the change in drum pressure, and temperatures of superheater and economizer slightly increase indicating the noticeably large heat capacity of the

9 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~ Fig. 10. Dynamic response of the boiler system under open loop following the step change of the fuel supply: (a) Fuel supply and air flow: Input condition; (b) solid-gas temperature; (c) O 2 concentration; (d) drum pressure and water level; (e) steam and feedwater flow; (f) water-steam temperature. water-steam side. Dynamic sub-models of the fuel-gas flow, the water-steam flow, and the inter-connected heat exchanger of the plant system need to be checked carefully for the interconnectivity of the boiler system under open loop condition. Acknowledgment This model was based on the Master s Thesis of Kim and Yang, improved by Seong-il Kim. Authors would like to acknowledge the support from KAIST through Brain Korea 21 program. Nomenclature Alphabets 2 A : Heat transfer area [ m ] C : Specific heat [kj/kg- ] H : Heat capacity [kj/ ] J : Mass transfer rate [kg/s] M : Mass [kg] Qgs w : Heat transfer from gas-solid side to wall side Q Js : Heat transfer by solid mass transfer Q Jg : Heat transfer by gas mass transfer Q r : Heat reaction by combustion Qw ws : Heat transfer from wall side to water-steam side S : Source term in char mass balance [kg/s] c S m : Source term in solid mass balance [kg/s] S n : Source term in gas mass balance [kmol/s] S T : Source term in energy balance [kw] T : Temperature ( ) X : Tolerance (-) 2 h : Heat transfer coefficient [kw/ m ] m : Mass (kg) n : Gas mole (kmol) t : Time (sec) x : Differential length (m) Greeks ε : Solid volume fraction ρ : Density (kg/m 3 ) τ : Time constant (sec) φ : Dependent variable Subscripts c : Char d : Drum e : Exit g : Gas phase gs : Gas-solid i : Cell number (1-n) j : 1-core zone, bubble zone, 0-annulus zone, emulsion

10 5790 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~5792 zone k : Gas species (O2, CO2, H2O, CH 2O, CO, N 2) p : Particle size class (6 size groups) r : Reaction s : Solid phase t : Time w : Wall ws : Water-steam References [1] J. Pan, G. Wu and D. Yang, Thermal-hydraulic calculation and analysis on water wall system of 600MW supercritical CFB boiler, Applied Thermal Engineering, 82 (2015) [2] C. Yang and X. Gou, Dynamic modeling and simulation of a 410 t/h Pyroflow CFB boiler, Computers and Chemical Engineering, 31 (2006) [3] J. R. Muir, C. Brereton, J. R. Grace and C. J. Lim, Dynamic modeling for simulation and control of a circulating fluidized-bed combustor, AIChE J.. 43 (1997) [4] C. K. Park and P. Basu, A model for prediction of transient response to the change of fuel feed rate to a circulating fluidized bed boiler furnace, Chemical Engineering Science, 52 (1997) [5] V. Weiss, J. Scholer and F. N. Fett, Mathematical modeling of coal combustion in a circulating fluidized bed reactor, Proceedings of the Second International Conference on Circulating Fluidized Beds, Compiègne, France (1988) [6] E. Ikonen and U. Kortela, Dynamic model for a bubbling fluidized bed coal combustor, Control Eng. Practice, 2 (1994) [7] T. H. Kim, S. M. Choi and J. S. Hyun, Perofmance prediction of a circulating fluidized bed boiler by heat exchangers block simulation at varying load condition, J. Power and Energy, 228 (2014) [8] T. H. Kim, S. M. Choi and J. S. Kim, Performance prediction of a large scale circulating fluidized bed boiler by heat exchangers block simulation, J. Power and Energy, 229 (2015) [9] K. J. Astrom and R. D. Bell, Drum-boiler dynamics, Automatica, 36 (2000) [10] H. L. Kim and S. M. Choi, A model on water level dynamics in natural circulation drum-type boilers, International Communications in Heat and Mass Transfer, 32 (2005) [11] J. F. Davidson and D. Harrison, Fluidized particles, Cambridge University Press, Cambridge, England (1963). [12] J. Werther and J. Wein, Expansion behavior of gas fluidized beds in the turbulent regime, AIChE J., 301 (1994) [13] D. Kunii and O. Levenspiel, Fluidization engineering. Butterworth-Heinemann, Stoneham USA (1991). [14] M. J. Rhodes, X. S. Wang, H. Cheng and T. Hirama, Similar profiles of solids flux in circulating fluidized bed risers, Chemical Engineering Science, 47 (1992) [15] F. Bellgardt, F. Hembach, M. Schossler and J. Werther, Modeling of large scale atmospheric fluidized bed combustors, Proceedings of the 9th International Conference on Fluidized bed combustion, Boston, USA (1987) [16] D. Merrick and J. Highley, Particle size reduction and elutriation in a fluidized bed process, AIChE J., 70 (2001) [17] A. Haider and O. Levenspiel, Drag coefficient and terminal velocity of spherical and nonspherical particles, Powder Technol., 58 (1989) [18] J. R. Grace, Fluidized-bed hydrodynamics, Handbook of multiphase systems, Hetsroni G. (Ed.), 8 (1982) [19] Y. Hua, G. Flamant, J. Lu and D. Gauthier, Modeling of axial and radial solid segregation in a CFB boiler, Chemical Engineering, 43 (2003) [20] K. Redemann, E. U. Hartge and J. Werther, Ash management in circulating fluidized bed combustors, Fuel, 87 (2008) [21] J. Tomeczek, Coal combustion, Krieger Publishing Company, Florida, USA (1994). [22] W. P. Jones and R. P. Lindstedt, Global reaction schemes for hydrocarbon combustion, Combustion and Flame, 73 (1988) [23] D. R. Vaart, The chemistry of premixed hydrocarbon/air combustion in a fluidized bed, Combustion and Flame, 71 (1988) [24] I. W. Smith, The combustion rates of coal chars; A Review, Nineteenth Symposium (Int.) on Combustion.19, Haifa, Israel (1982) [25] A. Dutta and P. Basu, An improved cluster-renewal model for estimation of heat transfer coefficient on the water-walls of commercial circulating fluidized bed boiler, J. Heat Transfer, 126 (2004) [26] F. P. Incropera, Fundamentals of heat and mass transfer, Wiley, New York, USA (2008). [27] J. Cooper, Revised release on the IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam, IAPWS 1997, Erlangen, Germany (1997). [28] APROS: advanced process simulation software, apros.fi/en/. [29] I. M. Alatiqi and A. M. Meziou, Simulation and parameter scheduling operation of waste heat steam-boilers, Computers chem. Engng., 16 (1992) [30] C. Maffezzoni, Boiler-turbine dynamics in power-plant control, Control Engineering Practice, 5 (1997) [31] P. Basu, Combustion and gasification in fluidized beds, Taylor & Francis, Boca Raton, USA (2006). Appendix A. Globally simplified lumped thermal mass system The dynamic system of the current study is represented by adopting a simplified lumped thermal mass system. As shown in Fig. A.1(a), the simplified lumped thermal mass system of

11 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~ the solid gas circulation loop considers the heat inflow, the heat out flow, the heat of reaction and the heat transfer to the water-steam side. As shown in Fig. A.1(b) is the heat exchanger system of the water-steam side which considers the heat inflow, the heat outflow, the heat transfer from the solidgas side and the wall inertia. In the steam heat exchanger, the fundamental time constant M wcw+ M wscws of the energy storage ( τ ES = ) like the Eq. mɺ c ws ws (A.3) was introduced by Maffezzoni, and the fundamental M time constant of mass storage ( τ MS = ) was also introduced. m ɺ In general, the mass storage can be ignored due to τ >> τ [30]. Time constant can be derived from the energy ES MS equation in a globally simplified thermal mass system. Major assumptions include the following: the temperature is uniform in the thermal system and the output temperature is the same as the temperature of the system. In the solid-gas circulation loop, the heat transfer is assumed as a constant value for the calculation of the time constant, and if the change of input condition such as the fuel supply is small, the change rate of the chemical reaction as the function of the temperature can be neglected. In the water-steam side of the heat exchanger system, the heat transfer to the wall side is the disturbance for the dynamic calculation, and there is no the heat reaction. Therefore, based on the above assumptions, the heat outflow, which is the result of the energy balance, dominates the simplified lumped thermal mass system in each lumped thermal system. The energy balance Eq. (A.1) of the thermal system can be presented as Eq. (A.2) of each model accepting the above assumptions. Thus the time constant can be mathematically obtained as Eq. (A.3); the time constant is calculated by dividing the stored energy (unit: kj) by output (unit: kj/s) in each component. The coefficients of Eq. (A.3) of each thermal system are summarized in Fig. A.1. ( MC) Qin Qout Qreaction Qtransfer. system dt = + (A.1) dt By assuming that Q= constant, the equation becomes dt MC Q mc T, system out dt where Q= Q Q Q ( ) = ( ɺ ) in reaction transfer (for system of Fig. A (b); Q = 0 ). reaction Solving the differential equation, ( MC) ( ) T T t = exp, where τ = T T τ mc ɺ o system out (A.2). (A.3) Table A.1. Reference sources for the transport phenomena modules. Independent dynamic sub-system Solid circulation loop Mass [ton] Out mass flow rate [kg/s] Gas-solid side Time constant [sec] 130 (Solid+gas) 370 kg/s 300 Superheater 0.12 (gas) 370 kg/s 0.2 Evaporatordrum Primary superheater Primary economizer Tube wall Watersteam Water-steam side kg/s kg/s kg/s 240 Fig. A.1. Globally simplified lumped thermal system: (a) Solid-gas circulation loop; (b) heat exchanger system. Table A.1 represents the time constants calculated by Eqs. (A.1)-(A.3) in each dynamic sub-system for the current case of the boiler. As shown in Table A.1, the time constants of the CFB loop, the drum loop and the economizer of water-steam side, which have a large thermal mass in material, are relatively larger than the ones for the sub-system. Therefore, these components would have significant impact on the dynamic behavior of the boiler. However, although it is difficult to compare the time constants of the water-steam circulation loop due to the required controller and the complexity, the time constants of the water-steam circulation loop show that the water-steam circulation loop dominates the dynamic behavior of the boiler system. In addition, because the time constant of the heat exchangers in the gas side is very small, these components can be modeled as the steady state.

12 5792 S. Kim et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5781~5792 Seong-il Kim received his M.S. from KAIST in Mr. Kim is currently a Ph.D. candidate at the Department of Mechanical Engineering at KAIST in Daejeon, Korea. His research interests includes dynamic simulation of CFB boiler system. Sangmin Choi is a Professor in Department of Mechanical Engineering at Korea Advanced Institute of Science and Technology (KAIST), since His research interests include power generation systems, iron-making process, and solid fuel combustion.