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

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1 Raid Start-U of the Steam Boiler Cosiderig the Allowable Rate of Temerature Chages Ja TALER Piotr HARCHUT Deartmet of Power Egieerig, Cracow Uiversity of Techology Cracow, Polad Dawid TALER Deartmet of Power Istallatios, Academy of Sciece ad Techology Cracow, Polad ad Tomasz SOBOTA Magdalea JAREMKIEWICZ Deartmet of Power Egieerig, Cracow Uiversity of Techology Cracow, Polad ABSTRACT I this aer the roblem of the dyamics of boiler evaorator was reseted. A exressio for the heat flow rate from the furace to the evaorator, as a fuctio of chage of the ressure i the boiler drum was derived from the coservatio equatios of mass ad eergy. First, the allowable rate of the steam temerature chage i the boiler drum was determied with resect to the total stresses o the edge of the drum dow comer itersectio usig the TRD-31 boiler regulatios. Later, after solvig the differetial equatio, the temerature ad ressure chages i the boiler drum as fuctios of time, have bee determied. Kowig the ressure chages i the boiler drum, the heat flow rate, which shall be delivered to the boiler evaorator was determied. O the basis of the calculatios of the combustio chamber, the chages of the fuel flow, assurig the ressure chages i the boiler evaorator most comarable to the assumed oes, were determied. The fuel cosumtio was also determied durig the start u of the boiler for the case of the maximum allowable chage of the temerature of the medium. The results secified i this aer ca be used for desigig boilers ad for the automatio of the boiler start u rocesses. Keywords: Start u automatio, Dyamics of boiler, Thermal stresses. Nomeclature c m secific heat of the metal, J/(kg K) h w water ethaly, J/kg h secific ethaly of the fluid at the saturatio temerature, J/kg h secific ethaly of the steam at the saturatio temerature, J/kg m m mass of the metal, kg blowdow water mass flow rate, kg/s od saturated steam mass flow rate, kg/s w water mass flow rate, kg/s 1 2 water ressure at the start of the heatig rocess, Pa steam ressure at the ed of the heatig rocess, Pa saturated steam ressure, Pa Q & k heat flow rate from the furace to the boiler evaorator, W Q & ev heat flow rate, W t time, s T m metal temerature, K T saturatio temerature, K 1. INTRODUCTION The develomet of the wid turbie egieerig, which ca be characterised by large variatios i the amout of delivered electricity over time, geerated ew roblems regardig the regulatio of the ower egieerig system [1]. At high ad low wid seeds, the eergy roductio falls raidly, what meas that the covetioal heat or combied gas-steam blocks have to be activated very quickly. Steam boilers i blocks have to be desiged i a way, which will allow for a start u of the block withi several doze miutes. The mai comoets limitig the quick start-u of steam boilers are thick walled structural elemets, i which thermal stresses ca occur durig the start u cycle. Figure 1. Heatig rate of the ressure boiler elemet as a ressure fuctio, determied i accordace to the TRD-31 regulatios

2 To be able to esure the aroriate lifetime ad safety of the blocks adated for a raid start u, a accurate aalysis of the flow-heat rocesses, together with the stregth aalysis is required. The start u ad the shut dow rocesses shall be coducted i a way, which will esure that the stresses at the locatios of stress cocetratio do ot exceed the allowable values Germa boiler regulatios, TRD 31 [2] ad the Euroea Stadard, EN [3] allow to determie 2 allowable rates for heatig the ressure elemet: v T1 at the ressure 1 at the begiig of the start u rocess, v T2 at the ressure 2 at the ed of the start u rocess. Heatig rates for itermediate ressures shall be determied usig the method of liear iterolatio (Fig. 1). To be able to heat the boiler evaorator at the maximum allowable rate, heat flow rate Q & k should be delivered to the evaorator i the boiler combustio chamber (Fig. 2). The value of Q & k is a fuctio of may arameters, but for the boiler of a secific costructio, it deeds maily o the rate of chages of the saturatio ressure d /dt ad the mass of the saturated steam mass flow rate. T (t), the ressure chages (t) ca be determied, e.g. from fuctio (2). The ressure chages rate d /dt ad the saturatio temerature chages rate dt /dt i a fuctio of time are determied o the basis of the assumed ru v T ( ) (Fig. 1). I this aer, the dyamics of the boiler evaorator of the OP- 21M boiler will be aalysed. OP-21M is a ulverized coal fired boiler with atural circulatio. The T (t) ad (t) chages, determied for 1 = bar, v T1 = 2 K/mi ad 2 = 18.7 bar, v T2 = 5 K/mi are reseted i Fig. 2. After determiig the T (t) ad dt /dt time chages, it is ossible to determie the rate of ressure chages d /dt usig the followig formula: d d dt = (4) dt dt dt where the derivative d /dt for the saturated steam ca be determied by the differetiatio of formula (2). 2. PRESSURE AND TEMPERATURE CHANGES IN THE EVAPORATOR DURING THE BOILER HEATING PROCESS I accordace to the TRD 31 regulatios (Fig. 1), the chages of the heatig rate v T = dt /dt i the ressure fuctio are iterolated usig a straight lie. dt ν ν ν ν = + dt 2 T1 1 T 2 T 2 T ( T ) (1) The water saturatio ressure (T ) from Eq. (1) ca be exressed i the followig way i the temerature fuctio: = ex( T ) (2) Where ressure is exressed i bars, ad temerature T is exressed i C. Eq. (1) has bee itegrated usig the Ruge-Kutty method of the 4-th order, at the followig iitial coditio: T ( ) t T = (3) = 1 Figure 3. Rates of the ressure d /dt ad temerature dt /dt chages, durig the evaorator heatig rocess The ressure d /dt chages rate ca also be calculated usig a aroximate formula: ( + ) ( ) d t t t t = dt 2 t where: t is the time ste. For the calculatios, it ca be assumed for examle, that t = 1 s. Temerature dt /dt ad ressure d /dt chagig rates are reseted i Fig. 3. (5) 3. MASS AND ENERGY BALANCE FOR THE BOILER EVAPORATOR Figure 2. Temerature ad saturatio ressure chages i the boiler evaorator durig the heatig rocess After determiig, by solvig the iitial coditio (1-3), the flow of the saturatio temerature i a fuctio of time, that is Modellig of the trasiet state effects, occurrig i the boiler evaorator is usually doe while assumig that it is a object havig a cocetrated mass ad heat caacity [4-9]. The start oit for the determiatio of the heat flow rate Q & k, which assures that the evaorator is heated at the desired rate v T (t), are the mass ad eergy balace equatios for the evaorator (Fig. 4): d ( V ' ρ ' + V " ρ ") = w od (6) dτ d ( V ' ρ ' u + V " ρ " u + mmcmtm ) = whw h odhod + Q & k (7) dτ After trasformig Eqs. (6) ad (7) we obtai:

3 ( ) h h h h Q& ρ ρ ρ ρ = k od ( h h ) h w w m ρ ρ ρ ρ + & + ρ ρ (8) dh ρ ( h h ) d ρ + V ρ d ρ ρ d dh ρ ( h h ) dρ dt d + V ρ 1 m + + mcm d ρ ρ d d dt Figure 4. Diagram of the boiler evaorator Formula (8) allows to determie the heat flow rate Q & k, which should be delivered to the evaorator from the combustio chamber i order to esure the assumed rate of the ressure chage d /dt. Chages of the dρ /d ad dρ /d fuctios ad the dh /d ad dh /d fuctios, aearig i formula (8) are reseted i Fig. 5 ad Fig. 6. Figure 5. Chages of the dρ /d ad dρ /d derivatives, as a fuctio of ressure The accuracy of i determiig those fuctios is very imortat. The best way is to determie those fuctios through aalytical differetiatio of the ρ () ad ρ () fuctios, obtaied earlier usig the least square methods o the basis of the roerty tables. 4. HEAT FLOW RATE ABSORBED IN COMBUSTION CHAMBER From the coducted calculatios, we ca see that the heat flow rate Q & k delivered to the evaorator ca be lowered sigificatly by reducig steam mass flow rate delivered from the boiler drum. The miimum steam mass flow rate, which shall be roduced i the boiler durig the start u rocess ca be determied from the coditio, statig that the maximum allowable temeratures for the articular stages of the heater shall ot be exceeded. The furace oil mass flow rate, delivered to the burers durig the boiler start u rocess, which is ecessary to assure the heat flow rate Q & k, shall be determied o the basis of the calculatios of the boiler combustio chamber. The heat flow rate Q & k, kom absorbed by the walls of the boiler combustio chamber, exressed i W, ca be calculated from the followig formula: where: W d ow, ow Q& W c T c T (9) T ow Tow Ts k, kom = d + ow, ow ow s, s s fuel mass flow rate, kg/s, fuel calorific value, J/kg, air mass flow rate, kg/s, c average secific heat of air, at costat ressure ad T ow s T s c, s T s at temerature from to T ow [ C], J/(kg K), temerature of air delivered to the combustio chamber, C, flue gas mass flow rate, kg/s, average secific heat of flue gas, at costat ressure ad at temerature from to T s [ C], J/(kg K), flue gas temerature at the exit of the combustio chamber, C. The temerature of flue gases at the exit of the combustio chamber, T s is calculated from the equatio: Tad T s = a M + 1 Bo (1) where: Bo is the Boltzma umber, determied by the formula: m c Bo = & (11) σ ψ s, s 3 Ak Tad ad c, s is the average secific heat of flue gases i J/(kg K), at Figure 6. Chages of the dh /d ad dh /d derivatives, as a fuctio of ressure temerature ragig from T s to T ad

c Tad 273. 15 = c. (12), s, s T s 273.15 Other symbols i Eqs.

4 c Tad = c. (12), s, s T s Other symbols i Eqs. (1) ad (11) mea: a emissivity of the combustio chamber, M arameter characterisig the elevatio at which the flame temerature i the combustio chamber is maximum, A k area of the waterwalls of the boiler combustio chamber, m 2, T ad theoretical (adiabatic) combustio temerature, o C, σ Stefa-Boltzma costat, σ = W/(m 2 K 4 ), ψ waterwall thermal effectiveess defied as the ratio of the heat flux absorbed by the combustio chamber wall to the icidet heat flux. The calculatio of the heat flow rate Q & k, kom absorbed by the walls of the combustio chamber of the OP-21M boiler, have bee calculated, usig Eq. (9). I the fuctio of the fuel mass flow rate ad the excess air umber λ; the calorific value of the oil was assumed to be W d = 416 kj/kg. The results of the calculatios are reseted i Fig. 7. determiig from Eq. (8) the heat flow rate Q& k ( t), the oliear algebraic equatio ( ) Q& ( t) = Q&, λ (13) k k, kom is solved. The fuel mass flow rate, at the assumed value of the excess air umber λ, is determied from Eq. (13). The mass of the oil fuel used for the boiler start u rocess from time t = to t = t k ca be calculated usig the formula: t k m = m & dt. (14) The itegral (14) was calculated umerically, usig the traezoidal rule for itegratio. 5. CALCULATION RESULTS The calculatios have bee coducted for the evaorator of the OP-21M boiler, for the ressure chage rate d /dt reseted i Fig. 3. The temerature of the feed water T w durig the evaorator heatig rocess is at a give momet, lower by 1 K tha the saturatio temerature T. The temerature of the feed water T w, the saturatio temerature T ad the ressure i the evaorator are reseted i Fig. 8. Figure 7. Heat flow rate Q & k, kom, i kw, delivered to the evaorator of the OP-21M boiler, as a fuctio of the fuel mass flow rate i kg/s ad the excess air umber λ It was rove, that the icrease of the excess air umber λ at the assumed fuel mass flow rate leads to the reductio of the heat flux, delivered from flue gases i the combustio chamber to the evaorator. This is due to the fact, that the temerature of the flue gases i the combustio chamber T l was decreased sigificatly, what i tur, led to a sigificat decrease of the heat flow rate Q & k, kom, as the heat flux is roortioal to temerature differece betwee the flame temerature ad the temerature of the chamber walls raised to the fourth ower,. 4 4 that is ( Tl Tsc ) Whe λ icreases, Q & k, kom is reduced, ad the heat flux absorbed by the steam suerheaters icreases. Icreasig the fuel mass flow rate at the assumed excess air umber λ, leads to the icrease of the heat flow rate Q & k, kom absorbed by the walls of the combustio chamber. Next, the fuel mass flow rate delivered to the boiler durig the start-u (heatig) rocess was determied. After Figure 8. Temerature of the feed water T w, saturatio temerature T ad ressure i the evaorator, durig the boiler start u The calculatios have bee erformed for the followig data: =.51 kg/s, = 17.1 kg/s, = kg/s, m m = ods w 1719 kg, c m = 511 J/(kg K), V = 43.6 m 3 ad V = 15.9 m 3. The results of the Q & k calculatios for various saturated steam mass flow rates are reseted i Fig. 9a ad Fig. 9b. After aalysig the results show i Fig. 9a we ca see, that if the steam mass flow rate from the evaorator is zero, the the heat flow rate Q & k trasferred to the evaorator icreases. I this case, all heat absorbed from the combustio chamber is maily used for heatig water cotaied i the boiler evaorator. This is due to the icrease of the secific heat of water c w, which icreases with the ressure raise, for examle at the ressure = 1 MPa water secific heat is c w = 445 J/(kg K) while at the ressure = 1 MPa secific heat is c w = 6127 J/(kg K). Moreover, at the ed of the start u rocess a large icrease of the rate of temerature chages i the

5 evaorator occurs (Fig. 3), what requires icreased heat flow rate Q & k to be trasferred to the evaorator. For larger steam flow rates the heat flow rate Q & k, which should be delivered from the combustio chamber to the evaorator, icreases sigificatly, because there is a large ower cosumtio for water evaoratio (Fig. 9). However, for the evaorator caacities greater tha kg/h (Fig. 9b) the reductio of the heat flow rate Q & k occurs durig the ed hase of the heatig rocess, desite the icrease of the rate of evaorator heatig (Fig. 3). a) a) b) b) Figure 1. Fuel mass flow rate i kg/s, durig the start u of the OP-21M boiler for various mass flow rates of steam i t/h (i 1 3 kg/h) geerated i the boiler evaorator This is due to decreasig the water evaoratio heat, r = h h whe the ressure i the evaorator icreases. For examle at the ressure = 1 MPa, water evaoratio heat is r = J/(kg K) while at the ressure = 1 MPa, the evaoratio heat is reduced to r = J/(kg K). a) Figure 9. Heat flow rate Q & k trasferred to the evaorator of the boiler i the combustio chamber for various steam mass flow rates i t/h (i 1 3 kg/h) Fuel mass flow rate durig the start u of the OP-21M boiler obtaied from Eq. (13) for the excess air umber λ = 1.1 are show i Figs. 1a ad 1b. The calculatios are carried out for various steam flow rates geerated i the evaorator. The results of the calculatios of the fuel cosumtio m corresodig to the fuel mass flow rates show i Fig. 1, are reseted i Fig. 11.

6 b) [3] Euroea Stadard, EN , Water-tube boilers ad auxiliary istallatios Part 3: Desig ad calculatio for ressure arts, CEN Euroea Committee for Stadarizatio, rue de Stassart 36, B-15 Brussels, 25. July 21. [4] P. Profos, Die Regelug vo Damfalage, Berli: Sriger, [5] M.A. Styrykovich, K.J. Katkovskaia, E.P. Sierov, Steam Boilers, Moscow, Goseergoizdat, 1959 (i Russia). [6] E.P. Sierov, B.P. Korolkov, Dyamics of Steam Boilers, Secod Editio, Moscow, Eergia, 1981 (i Russia). Figure 11. Fuel cosumtio m, i kg, durig the start u of the OP-21M boiler, for various steam mass flow rates i t/h (i 1 3 kg/h) roduced i the boiler evaorator From the aalysis of the results reseted i Fig. 11, we ca see, that the fuel cosumtio deeds maily o the steam mass flow rate geerated i the boiler evaorator. Durig the start u rocess, lastig 8 s, the fuel cosumtio varies from m = 338 kg, at the steam mass flow rate = kg/h, to m = 2727 kg, at the steam mass flow = kg/h. Due to the high rice of the oil fuel, the boiler start u rocess should be coducted at the miimum steam mass flow rate, esurig the aroriate coolig of the suerheater tubes. 6. CONCLUSIONS The model of the dyamics of the boiler evaorator, reseted i this aer, ca be used for the determiatio of the heat flow rate, trasferred from the flue gases i the combustio chamber to the boiler evaorator, which is required to warm u the boiler evaorator at the assumed rate of medium temerature chage. The fuel mass flow rate which esures the rescribed rates of the medium temerature chages i the evaorator is determied from the combustio chamber calculatios. Fuel cosumtio durig the boiler start u rocess, ecessary for heatig the boiler evaorator from the iitial to the desig temerature has bee determied. The heatig of the boiler drum is coducted at the maximum allowable rate with resect to the stresses, caused by ressure ad thermal load, which occur at the boiler drum-dowcomer juctio. I order to limit the cosumtio of the exesive oil durig the boiler start u, the rocess should be coducted at the miimum steam mass flow rate esurig the aroriate coolig of the suerheaters. The excess air umber should be ket at the miimum value. The results of the aalysis coducted i the aer ca be used to formulate the otimum rocedure for the boiler start u rocess. 7. REFERENCES: [1] Staff Reort, Dealig with cyclig: TRD 31 ad the Euro Norm comared, Moder Power Systems, Vol 27, No. 5, 27, [2] TRD 31, Zyliderschale uter ierem Überdruck, Techische Regel für Damfkessel (TRD), Köl Berli: Heymas Beuth, 21.

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