Rapid Start-Up of the Steam Boiler Considering the Allowable Rate of Temperature Changes

In this paper the problem of the dynamics of boiler evaporator was presented. An expression for the heat flow rate from the furnace to the evaporator, as a function of change of the pressure in the boiler drum was derived from the co nservation equations of mass and energy. First, the allowable rat of the steam temperature change in the boiler drum was det ermined with respect to the total stresses on the edge of t he drum – down comer intersection using the TRD-301 boiler regulat ions. Later, after solving the differential equation, the temper atu e and pressure changes in the boiler drum as functions of time, have been determined. Knowing the pressure changes in th e boiler drum, the heat flow rate, which shall be delivered to the boiler evaporator was determined. On the basis of the calc ulations of the combustion chamber, the changes of the fuel flo w, assuring the pressure changes in the boiler evaporator most comparable to the assumed ones, were determined. The fuel con sumption was also determined during the start up of the boil er for the case of the maximum allowable change of the temperature of the medium. The results specified in this paper can be us d for designing boilers and for the automation of the boi ler start up processes.

Nomenclature c m -specific heat of the metal, J/(kg•K) h w -water enthalpy, J/kg h' -specific enthalpy of the fluid at the saturation temperature, J/kg h" -specific enthalpy of the steam at the saturation temperature, J/kg m m -mass of the metal, kg

INTRODUCTION
The development of the wind turbine engineering, which can be characterised by large variations in the amount of delivered electricity over time, generated new problems regarding the regulation of the power engineering system [1].At high and low wind speeds, the energy production falls rapidly, what means that the conventional heat or combined gas-steam blocks have to be activated very quickly.Steam boilers in blocks have to be designed in a way, which will allow for a start up of the block within several dozen minutes.The main components limiting the quick start-up of steam boilers are thick walled structural elements, in which thermal stresses can occur during the start up cycle.To be able to ensure the appropriate lifetime and safety of the blocks adapted for a rapid start up, an accurate analysis of the flow-heat processes, together with the strength analysis is required.The start up and the shut down processes shall be conducted in a way, which will ensure that the stresses at the locations of stress concentration do not exceed the allowable values German boiler regulations, TRD -301 [2] and the European Standard, EN-12952-3 [3] allow to determine 2 allowable rates for heating the pressure element: − v T1 at the pressure p 1 at the beginning of the start up process, − v T2 at the pressure p 2 at the end of the start up process.Heating rates for intermediate pressures shall be determined using the method of linear interpolation (Fig. 1).To be able to heat the boiler evaporator at the maximum allowable rate, heat flow rate k Q & should be delivered to the evaporator in the boiler combustion chamber (Fig. 2).The value of k Q & is a function of many parameters, but for the boiler of a specific construction, it depends mainly on the rate of changes of the saturation pressure dp n /dt and the mass of the saturated steam mass flow rate.

PRESSURE AND TEMPERATURE CHANGES IN THE EVAPORATOR DURING THE BOILER HEATING PROCESS
In accordance to the TRD 301 regulations (Fig. 1), the changes of the heating rate v T = dT n /dt in the pressure function are interpolated using a straight line.
The water saturation pressure p n (T n ) from Eq. ( 1) can be expressed in the following way in the temperature function: exp( 19.710662 4.2367548 ) Where pressure p n is expressed in bars, and temperature T n is expressed in °C.
Eq. ( 1) has been integrated using the Runge-Kutty method of the 4-th order, at the following initial condition: T n (t), the pressure changes p n (t) can be determined, e.g. from function (2).The pressure changes rate dp n /dt and the saturation temperature changes rate dT n /dt in a function of time are determined on the basis of the assumed run v T (p n ) (Fig. 1).In this paper, the dynamics of the boiler evaporator of the OP-210M boiler will be analysed.OP-210M is a pulverized coal fired boiler with natural circulation.The T n (t) and p n (t) changes, determined for p 1 = 0 bar, v T1 = 2 K/min and p 2 = 108.7 bar, v T2 = 5 K/min are presented in Fig. 2.
After determining the T n (t) and dT n /dt time changes, it is possible to determine the rate of pressure changes dp n /dt using the following formula: where the derivative dp n /dT n for the saturated steam can be determined by the differentiation of formula (2).The pressure dp n /dT n changes rate can also be calculated using an approximate formula: where: ∆t is the time step.
For the calculations, it can be assumed for example, that ∆t = 1 s.Temperature dT n /dt and pressure dp n /dt changing rates are presented in Fig. 3.

MASS AND ENERGY BALANCE FOR THE BOILER EVAPORATOR
Modelling of the transient state effects, occurring in the boiler evaporator is usually done while assuming that it is an object having a concentrated mass and heat capacity [4][5][6][7][8][9].The start point for the determination of the heat flow rate k Q & , which assures that the evaporator is heated at the desired rate v T (t), are the mass and energy balance equations for the evaporator (Fig. 4): ( ) After transforming Eqs. ( 6) and ( 7) we obtain: Formula (8) allows to determine the heat flow rate k Q & , which should be delivered to the evaporator from the combustion chamber in order to ensure the assumed rate of the pressure change dp n /dt.Changes of the dρ'/dp and dρ"/dp functions and the dh'/dp and dh"/dp functions, appearing in formula (8) are presented in Fig. 5 and Fig. 6.The accuracy of in determining those functions is very important.The best way is to determine those functions through analytical differentiation of the ρ'(p) and ρ"(p) functions, obtained earlier using the least square methods on the basis of the property tables.

HEAT FLOW RATE ABSORBED IN COMBUSTION CHAMBER
From the conducted calculations, we can that the heat flow rate is solved.The fuel mass flow rate, at the assumed value of the excess air number λ, is determined from Eq. ( 13).The mass of the oil fuel used for the boiler start up process from time t = 0 to t = t k can be calculated using the formula: The integral ( 14) was calculated numerically, using the trapezoidal rule for integration.

CALCULATION RESULTS
The calculations have been conducted for the evaporator of the OP-210M boiler, for the pressure change rate dp n /dt presented in Fig. 3.The temperature of the feed water T w during the evaporator heating process is at a given moment, lower by 10 K than the saturation temperature T n .The temperature of the feed water T w , the saturation temperature T n and the pressure in the evaporator p n are presented in Fig. 8. the heat flow rate k Q & transferred to the evaporator increases.In this case, all heat absorbed from the combustion chamber is mainly used for heating water contained in the boiler evaporator.This is due to the increase of the specific heat of water c w , which increases with the pressure raise, for example at the pressure p n = 1 MPa water specific heat is c w = 4405 J/(kg•K) while at the pressure p n = 10 MPa specific heat is c w = 6127 J/(kg•K).Moreover, at the end of the start up process a large increase of the rate of temperature changes in the evaporator occurs (Fig. 3), what requires increased heat flow rate k Q & to be transferred to the evaporator.
For larger steam flow rates p m & the heat flow rate k Q & , which should be delivered from the combustion chamber to the evaporator, increases significantly, because there is a large power consumption for water evaporation (Fig. 9).However, for the evaporator capacities greater than 90⋅10 3 kg/h (Fig. 9b) the reduction of the heat flow rate k Q & occurs during the end phase of the heating process, despite the increase of the rate of evaporator heating (Fig. 3).

CONCLUSIONS
The model of the dynamics of the boiler evaporator, presented in this paper, can be used for the determination of the heat flow rate, transferred from the flue gases in the combustion chamber to the boiler evaporator, which is required to warm up the boiler evaporator at the assumed rate of medium temperature change.
The fuel mass flow rate pal m & which ensures the prescribed rates of the medium temperature changes in the evaporator is determined from the combustion chamber calculations.Fuel consumption during the boiler start up process, necessary for heating the boiler evaporator from the initial to the design temperature has been determined.The heating of the boiler drum is conducted at the maximum allowable rate with respect to the stresses, caused by pressure and thermal load, which occur at the boiler drum-downcomer junction.In order to limit the consumption of the expensive oil during the boiler start up, the process should be conducted at the minimum steam mass flow rate ensuring the appropriate cooling of the superheaters.The excess air number should be kept at the minimum value.
The results of the analysis conducted in the paper can be used to formulate the optimum procedure for the boiler start up process.
od m & -blowdown water mass flow rate, kg/s p m & -saturated steam mass flow rate, kg/s w m & -water mass flow rate, kg/s p 1 -water pressure at the start of the heating process, Pa p 2 -steam pressure at the end of the heating process, Pa p n -saturated steam pressure, Pa k Q & -heat flow rate from the furnace to the boiler evaporator, W ev Q & -heat flow rate, W t -time, s T m -metal temperature, K T n -saturation temperature, K

Figure 1 .
Figure 1.Heating rate of the pressure boiler element as a pressure function, determined in accordance to the TRD-301 regulations

Figure 2 .
Figure 2. Temperature and saturation pressure changes in the boiler evaporator during the heating process After determining, by solving the initial condition (1-3), the flow of the saturation temperature in a function of time, that is

Figure 3 .
Figure 3.Rates of the pressure dp n /dt and temperature dT n /dt changes, during the evaporator heating process

Figure 4 .
Figure 4. Diagram of the boiler evaporator

Figure 5 .Figure 6 .
Figure 5. Changes of the dρ'/dp and dρ"/dp derivatives, as a function of pressure k Q & delivered to the evaporator can be lowered significantly by reducing steam mass flow rate p m & delivered from the boiler drum.The minimum steam mass flow rate p m & , which shall be produced in the boiler during the start up process can be determined from the condition, stating that the maximum allowable temperatures for the particular stages of the heater shall not be exceeded.The furnace oil mass flow rate pal m & , delivered to the burners during the boiler start up process, which is necessary to assure the heat flow rate k Q & , shall be determined on the basis of the calculations of the boiler combustion chamber.The heat flow rate , k kom Q & absorbed by the walls of the boiler combustion chamber, expressed in W, can be calculated from the following formula: heat of air, at constant pressure and at temperature from 0 to T pow [°C], J/(kg•K), T pow -temperature of air delivered to the combustion chamber, °C, sp m & -flue gas mass flow rate, kg/s, heat of flue gas, at constant pressure and at temperature from 0 to sp T′′ [°C], J/(kg•K), sp T′′ -flue gas temperature at the exit of the combustion chamber, °C.The temperature of flue gases at the exit of the combustion chamber, sp T ′′ is calculated from the equation: Bo is the Boltzmann number, determined by the formula: specific heat of flue gases in J/(kg•K), at temperature ranging from sp T ′′ to T ad Eqs.(10) and (11) mean: a p -emissivity of the combustion chamber, M -parameter characterising the elevation at which the flame temperature in the combustion chamber is maximum, A k -area of the waterwalls of the boiler combustion chamber, m 2 , T ad -theoretical (adiabatic) combustion temperature, o C, σ -Stefan-Boltzmann constant, σ = 5.67•10 −8 W/(m 2 K 4 ), ψ -waterwall thermal effectiveness defined as the ratio of the heat flux absorbed by the combustion chamber wall to the incident heat flux.The calculation of the heat flow rate , k kom Q & absorbed by the walls of the combustion chamber of the OP-210M boiler, have been calculated, using Eq.(9).In the function of the fuel mass flow rate pal m & and the excess air number λ; the calorific value of the oil was assumed to be W d = 41060 kJ/kg.The results of the calculations are presented in Fig. 7.

Figure 7 .
Figure 7. Heat flow rate , k kom Q & , in kW, delivered to the evaporator of the OP-210M boiler, as a function of the fuel mass flow rate pal m & in kg/s and the excess air number λ It was proven, that the increase of the excess air number λ at the assumed fuel mass flow rate pal m & leads to the reduction of the heat flux, delivered from flue gases in the combustion chamber to the evaporator.This is due to the fact, that the temperature of the flue gases in the combustion chamber T pl was decreased significantly, what in turn, led to a significant decrease of the heat flow rate , k kom Q & , as the heat flux is proportional to temperature difference between the flame temperature and the temperature of the chamber walls raised to the fourth power, that is ( ) 4 4 pl sc T T − .When λ increases, , k kom Q & is reduced, and the heat flux absorbed by the steam superheaters increases.Increasing the fuel mass flow rate pal m & at the assumed excess air number λ, leads to the increase of the heat flow rate , k kom Q & absorbed by the walls of the combustion chamber.Next, the fuel mass flow rate pal m & delivered to the boiler during the start-up (heating) process was determined.After

Figure 8 .
Figure 8. Temperature of the feed water T w , saturation temperature T n and pressure in the evaporator p n , during the boiler start up The calculations have been performed for the following data: ods m & = 0.51 kg/s, w m & = 17.1 kg/s, p m & = 16.57kg/s, m m = 171900 kg, c m = 511 J/(kg•K), V' = 43.6 m 3 and V" = 15.9 m 3 .The results of the k Q & calculations for various saturated steam mass flow rates are presented in Fig. 9a and Fig. 9b.After analysing the results shown in Fig. 9a we can see, that if the steam mass flow rate from the evaporator p m & is zero, then

Figure 9 .Figure 10 .Figure 11 .
Figure 9. Heat flow rate k Q & transferred to the evaporator of the boiler in the combustion chamber for various steam mass flow rates p m & in t/h (in 10 3 kg/h)