The Heating Furnaces Operating Parameters Optimization Issue ...

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ScienceDirect Procedia Engineering 152 (2016) 366 – 371

International Conference on Oil and Gas Engineering, OGE-2016

The heating furnaces operating parameters optimization issue Paramonov A.M.a* a

Omsk State Technical University, 11, Mira Pr., Omsk 64405, Russian Federation

Abstract The ways of thermal efficiency and economy improving of flaming metal heating are considered. The expanded technical and economic optimization problem of furnace units having metal heating chamber operation is solved. The method and optimization algorithm analytically considering the correlation of thermal, design, operating parameters and discounted costs for the furnace unit were developed. The obtained optimization functionality provides the achievement of furnace units appropriate thermal indices at minimum discounted costs. The results of the carried out research prove the expediency of proposed solutions, make it possible to decide on the most profitable parameters of the heating furnaces thermal conditions. © 2016 2016Published The Authors. Published Elsevier Ltd.access article under the CC BY-NC-ND license © by Elsevier Ltd. by This is an open (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Omsk State Technical University. Peer-review under responsibility of the Omsk State Technical University Keywords: optimization; a heating furnace; heat exchange; temperature; fuel; efficiency; recovery

1. Introduction The heating furnaces having chamber temperature conditions are used to heat the metal for metal forming and thermal treatment in forging and heat-treatment shops. According to cost the metal heating makes up a significant proportion of forging and thermal manufacture output production costs (up to 35 %). One of the ways to improve the thermal and economical efficiency is the temperature and thermal conditions optimization. The series of papers [1-6] is devoted to this issue investigation. The ways to improve the efficiency of fuel use and to reduce the specific fuel consumption as well as economic efficiency and airheaters application optimal conditions are examined in the above-mentioned papers. The heating furnaces optimization problem has not yet been solved without taking into account the correlated parameters and factors, their influence on the thermal conditions and furnaces design.

* Corresponding author. Tel.: +7-961-882-9029. E-mail address: [email protected]

1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Omsk State Technical University

doi:10.1016/j.proeng.2016.07.716

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This study presents the solving of expanded technical and economic optimization problem of heating furnaces having metal heating chamber operation. The method and optimization algorithm analytically correlating thermal, design, operating parameters and discounted costs for the furnace unit were developed. The obtained optimization functionality provides the achievement of furnace units appropriate thermal indices at minimum discounted costs taking into consideration the actual operation conditions changing depending on the furnace design, capacity and cost, on the recuperator design and cost, on the cost and kind of the fuel, on the maximum capacity utilization period and other factors. The comparative cost-effectiveness analysis of the furnace unit capital investments at minimum discounted costs is accepted as the optimality criterion. 2. The study subject (Model, Process, Device, Synthesis, Experimental procedure, etc.) The study subject is the heating furnace. In order to get the appropriate furnace working method, it is necessary to define objectively its best temperature required for the body heating technology and capacity providing, and to choose the structural design requiring least costs. The furnace capacity is defined by the heat-exchange conditions and by the working space temperature tw in particular. The furnace working space exit gases temperature t g influences both tw and metal heating time. The increase of tg results in the rising of tw, in heat transfer enhancement and furnace specific capacity increasing. If the furnace capacity is set, the heat transfer enhancement results in furnace size reduction and provides construction and operation cost savings. But simultaneously the heat loss grows which effects the furnace operating economy. However, owing to the wide application of recuperators for air heating by means of exit gases heat recovery it is possible and economically feasible to have higher temperature of exit gases. Meanwhile, it is appropriate to obtain the maximum possible and reasonable heat recovery rate. Consequently, furnace working space exit gases temperature and heat recovery rate (r) determine the furnace, recuperator, fuel and draft equipment costs to a large extent. 3. Methods Therefore, the adequate choice of the furnace working space exit gases temperature as well as of their heat recovery rate gives the significant effect. The more complete heating furnaces optimization problem solution is attained only if each value of the furnace opt working space exit gases optimal temperature tg corresponds to their heat optimal recovery rate Ropt. This is achieved by solving the system of equations obtained according to the necessary optimality conditions (1) and expressions for the furnace unit discounted costs (2, 3) and recuperator and fuel total costs (4):

w Cf ­ w E f .u. Cm  Cp w Sr  Cn w Vf .w. °wt w t w tg w tg ° g g ® ° w E r C w Cf  C w Sr 0. m p °¯ w p wp wp E f .u.

(Ef +Edep +Eair )  R i If .u.

Ef .u.

Af Cf

Er

Af Cf

 ArSr  Af .w.Vf .w.

 ArSr

0; (1)

(2) (3) (4)

Ef

A f Cf

(5)

Af

Cf .q. h

(6)

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E dep.

R dep. If .u.

(7)

E air

Ce.p. h (N d.u. Vf .w.  'N d.u.Sr )

(8)

Ar

Ir R  'Nd.u.[Kr Cd.u.R

 Ce.p.h]

(9)

If .w. R  N d.u.[Cd.u. R

 Ce.p. h]

(10)

A f .w.



If .u.

I r Sr

R

R i  R dep.

If .w. Vf .w.  Cd.u. (N d.u. Vf .w.  K r 'N d.u.Sr )

(11) (12)

where Ef.u., Er are the total discounted expenditures for the furnace unit, recuperator and fuel, correspondingly; Ef, Edep, and Eair are the annual expenditures for the fuel, allowance for depreciation, air supply for the fuel burning and exhaust gases extraction expenditures; Ri is the investments discount rate; If.u. is the capital investments for the furnace unit; Cf and Af. are the consumption and annual cost of the fuel; Cf.q. is the fuel quantity unit cost; h is the furnace annual operating hours; Sr is the recuperator heating surface; Ar and Ir are the annual cost and capital investments for the 1 m2 recuperator heating surface construction; If.w. and Af.w. are the capital investments and annual cost of 1 m3 furnace working space; Vf.w. is the furnace working space volume; Nd.u. is the draft units capacity accounting for 1 m3 furnace working space without recuperator; ΔN d.u. is the capacity required for 1 m2 recuperator heating surface maintenance (for gas and air resistances overcoming); Cd.u. and Ce.p. are the draft units and electrical power cost; Kr is the reserve coefficient; Rdep is the allowance for depreciation rate. First of all, the heat optimal recovery rate of the exit gases is defined from the second system equation (1) for any possible temperature value at the exit from the furnace working space. Subsequently, the exit gases optimal temperature tgopt is defined from the first system equation (1) by substituting the calculated value Ropt. for the specific one. In this case the reasonable fuel consumption, efficient costs for recuperator, the most acceptable furnace working space size are determined, as well as the furnace operation ideal characteristic values achievement is provided. The estimated equations for determining tgopt were obtained on the basis of the developed metal heating mathematical model. The model includes heat-transfer and heat balance equations, furnace lining temperature field, boundary conditions for heated metal and lining surfaces. The furnace working space volume, recuperator heating surface, fuel consumption in the first system equation (1) were expressed as the functions of the exit gases temperature, while in the second equation - as the fuctions of their heat recovery rate. For this purpose, the peculiarities of heat exchange mode in the furnace working space; the correlation of heat-exchange processes between gases, metal, lining; the influence of workpieces layout at the furnace sole on the metal heating were taken into account. The adequacy of mathematical models and derived dependences was estimated by the comparison of parameters obtained if using various computing methods. Considering that the problem solution accuracy is defined by the relative error, the models and dependences adequacy is admitted as reasonable. In deriving the computing formulas, the following assumptions were adopted: the furnace capacity is specified and constant; the metal heating is carried out at the constant furnace temperature; the furnaces with radiation heat transfer dominating are studied. After differentiation the explicit system equations (1) expression for the thermally "thin" bodies heating takes the following form:

A.M. Paramonov / Procedia Engineering 152 (2016) 366 – 371

­ d1t g2  d 2 t g  f DK air DM ˜   С °Ct р 2 kH 't (1  T )C gc ( E1  Mtg ) 2 (U c  W ct g ) 2 ° ( E1  Mtg ) ° ª§ 4( B1t g  N )[(B1t g  N )  Tm B1t g  N ] · qB1 ° ¸˜ «¨1   ˜ C n 2 4 ° 2 4 ¨ ¸ ( )   B t N Т 2 [( ) ]    B t N B t N T « 1 g m 1 g 1 g m ® ¹ ¬© ° º ( B1t g  N  Tm )(Т f .m.  Т i.m. ) B1t g  N  Ti.m. ° » 0,  °˜ ln (13) ( )( ) B t N Т B t N T B t N T       »¼ 1 . . 1 . . 1 . . g f m g f m g i m ° ° ¯ ap 2  bp  d 0. for the thermally "massive" bodies heating:

­ d1t g2  d 2t g  f DKair qcB1 DM C  С ˜  Cn ˜ ° t р 2 2 2 c c c H T E  Mt k  C E  Mt U  W t ( ) (1 ) ( ) ( ) B t  N 2 1 1 ' g t g g g ° 1 г ° 2 4 8 B1t g  N  Ti.m. ° 10 [( B1t g  N )  Т m ]  4( B1t g  N )[( B1t g  N )  Tm B1t g  N ] °­ ˜ ˜ ˜  ln ® 2 4 2 ° C B t  N  Т [( ) ] B t  N  Т 1 gm g m 1 g f .m. ° ®¯ ° 8 ½ º Т f .m.  Т i .m. ° ª 10 ( B1t g  N  Tm ) S ° « »   ˜ ¾ 0, ° C [( B t  N ) 2  Т 4 ] (k  2)O B t N T B t N T ( )( )     « » 1 g m 1 gm 1 g f . m . 1 g i . m . ° ° ¬ ¼ ¿ ° (14) ¯ ap 2  bp  d 0. Where D, M, E1, d1, d2, f, U`, W`, B1, q, a, b, d, q` are the values defined from the corresponding expressions. At defining tgopt and Ropt it seems possible to find the most cost-efficient temperatures of air heating inside recuperator t’’air opt and flue gases outside recuperator t’’g . The reliability of the equations obtained through the fulfillment of necessary optimality conditions (1) was examined for the validity. For this purpose the extremum existence studies in the tested stationary point were conducted. The fulfillment of the objective function positive definiteness condition was verified by taking second derivatives of the first system equation (1) after the furnace working space exit gases temperature and the second equation after the gases heat recovery. Multiple computations of the quantities w 2 Er wp2 и w 2 Eп wtg2 at the furnace working space exit gas optimal temperature different values and of the most cost-efficient heat recovery rate showed they are constantly positive in the cases analyzed. Consequently, the necessary and sufficient conditions of extremum existence of two variables E(tg, p) function are fulfilled simultaneously. The conditions reliability examination (1) was performed by the objective function examination at debugging calculations by means of every search step result printing as well. Thermotechnical, consumable and design parameters of the furnace unit cannot take random values but are subject to variation only within the physically and technically feasible states of energy carriers and constructions as well as within the technically permissible initial and operating states of the materials. Therefore, the developed algorithm is valid taking into account a number of limitations. The consideration of limitations not only influences the selected parameters optimal values but also considerably alters the procedure itself and the method for parameters determining. These include the following limitations: by the furnace working space exit flue gases temperature, by the recuperator air heating temperature and others. The limitations identify some region in the variables space tg, t”air called the acceptable region. Thermotechnical, consumable and design parameters in the

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process of optimization can take the values being within or on the boundary of the acceptable region. The clear determination of the parameters variation acceptable region is included into their mathematical definition and it is absolutely necessary condition under the furnace units optimization problem formulation. The calculation can give the optimal parameters values exceeding the limit ones. In such cases it is necessary to take not optimal but technically permissible values on the assumption of the furnace equipment development estimation at a given period of time and metal heating quality assurance. 4. Results and discussion The studies of basic data and cost indexes changing impact on the furnace working space exit gases optimal temperature value and air heating optimal temperature one in recuperator were carried out. This made it possible to establish: 1) the relations of furnace operation parameters (the temperature of its working space, air heating, exit gases etc.) and their influence on the furnace unit performance indicators; 2) the influence of the external and internal factors (the cost and kind of the fuel, the furnace and recuperator cost, the installed capacity utilization period and others) on the parameters correlation and performance indicators; 3) the additional costs value estimation resulting from the divergence of real parameters from their optimal values; 4) the influence of the basic data (the heating power, the furnace capacity, the metal heating final temperature and others) on the optimal parameters values change. The analysis of the obtained results showed the following. The variation of the heated thermally thin workpieces effective thickness, of the heating power from 12600 to 29300 kJ/m3 has a little impact on the optimal parameters value (within the range of 0.5 - 2 %). The increase of the furnace capacity G, the metal heating final temperature tf.m. results in the increase of furnace working space exit gases optimal temperature t g.opt (up to 19 %), of the optimal heat recovery rate Ropt, of the air heating inside recuperator optimal temperature tair//opt (up to 38 %), the decrease of exit gases temperature outside recuperator tg// (up to 12 %) (Fig. 1): 1 – tg opt = f (G); 2 – Ropt = f (G); 3 – tair// opt = f(G); 4 – tg// = f (G); 5 – tg opt = f(tf.m.); 6 – Popt = f(tмк); 7 – tair//opt = f(tf.m.); 8 – tg// = f(tf.m.). For the purpose of proving the obtained results, the furnace units reconstruction having the capacity of 1200 and 600 kgph designed for steel workpieces heating up to 1473 K was carried out. Every furnace unit included a chamber heating furnace, a recuperator, loading and unloading mechanism of workpieces from the furnace, draft equipment, a thermal control board. The air used for the fuel combustion was heated in recuperators up to 533 K. In the process of reconstructed furnace units designing, the optimal parameters calculated by the developed algorithm were accepted as basic data. The optimal technical and economic parameters values amounted to tgopt = 1603 – 1638 K, the air heating optimal temperature did to t’’air opt = 773 – 805 K. The temperature in furnaces was raised as a result of furnace working space exit gases temperature increasing by 60-85 K and of the air heating temperature in recuperators by 250-270 K. This made it possible to intensify the metal heating, to improve the furnace units thermal effectiveness and operating economy significantly. By means of the furnaces specific capacity increasing the furnace sole area was reduced to 1.78 – 1.83 time, the specific fuel consumption decreased by 36-40 %, the exit gases heat recovery rate increased 1.83 – 1.95 time, the iron loss was reduced to 34 – 38 %, the coefficient of thermal efficiency increased 10.5 – 11.4 % and amounted to 33.2 – 33.7 %.

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a

b

Fig. 1. The dependences tq opt , Popt, tair//opt, tq//: a – on the furnace capacity; b – on the metal heating final temperature.

5. Conclusion The study results showed the expediency of furnace units application having optimal technical and economic parameters of thermal conditions. The developed method and algorithm of optimization are recommended for practical use in designing new furnace units and modernizing existing ones. References [1] Ian Cz.X. Szargut, Ioachim Koziot, Majza Eugeniusz, Analiza mozliwosci zmniejszenia zuzycia paliwa w piecach grzejnych, Gosp. paliw. i energy. 1986, 34, №4, рp. 9-13. [2] M. Coombs, M. Strumpf, D. Kotchic, R. Vogt, C. Dobos, A high-temperature flue gas heat recovey system, Gas Warme International. 1983, №7,8, pp. 292-296. [3] K.H. Kohnken, Energy Conservation-vital in todays comparative international to increase thermal efficiency, Industrial Heating. 1983. №7, pp.17-18. [4] A. Gaba, Consideratif priving alegerea variantei optime de recuperare a caldurii fizice a gaselos arse evacuafe din cuptoarele de incalzire, Cerc. met. 1984, 25, pp. 77-86. [5] Niklas Grip, Carl-Erik Grip, Leif Nilsson,Wavelet study of dynarmic variations in steel and ironmaking rest gases. Potential effect on external use. Appl. Energy. 20013. 112, pp.1032-1040. [6] Ju.A. Vasilev, M.V. Simonova, A.A. Golova, Optimizacija rekuperativnogo ispolzovanija teploty othodjashhih gazov promyshlennyh pechej, Izvestija vuzov. Energetika 1986, №2, pp. 77-83. (In Russian)

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