Analysis of optimal application for exhaust gas in thermal oxidizers with case studies

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1 Analysis o optimal appliation or exhaust gas in thermal oxidizers with ase studies Naser Hamedi 1,*, Arzhang Abadi 2, Ramin Imani Jajarmi 3 1,3 Linköping University, Linköping, Sweden 2 Urmia University, Urmia, Iran * Corresponding author. Tel: +46 (0) , nasha244@student.liu.se Abstrat: There is potential or optimizing thermal oxidizer plants to inrease industrial energy eiieny results in environmental and eonomi dimension o sustainability. In the present work, geneti algorithm is implemented or three thermal oxidizer ases in three dierent petrohemial plants to optimize the uel ost or the three Heat Reovery Steam Generators (HRSG s) whih are going to be used or the reovery o the heat rom the outlet o the thermal oxidizer units. Generally, thermal oxidizers are used in petrohemial plants to burn waste gases in the plant to redue the environmental impat o the o-gases o plant and normally the waste heat are released to the atmosphere via a stak. The optimization results have been ompared or three ases. Five deision variables have been seleted and the objetive untion was optimized. By inreasing the uel prie, the values o thermo-eonomial deision variables tend to those thermodynamially optimal designs. Keywords: Heat Reovery Steam Generator (HRSG), thermo-eonomis, Optimization, Thermal Oxidizer, Geneti Algorithm, Low Density Polyethylene (LDPE) Plant. Nomenlatures p Cost per exergy unit.. $. MJ 1 Cost o uel per energy unit $. MJ 1 Cost low rate.. $. se 1 Speii heat at onstant Pressure KJ. Kg 1. K 1 CRF Capital reovery ator Enthalpy.. KJ. Kg 1 LHV Lower heating value KJ. Kg 1 m Mass low rate. Kg. s 1 r Compressor pressure ratio T Temperature...K Z Capital ost o a omponent $ Z Capital ost rate $. se 1 P Pressure loss η a Compressor isentropi eiieny η Combustion hamber irst law eiieny γ Speii heat ratio φ Maintenane ator EA Evolutionary algorithm GA Geneti algorithm P,/Pr, pressure ratio o ompressor r ih η to W Inlet humidity perent Thermal eiieny o thermal oxidizer Work.KW Subsripts a Air ompressor a Air Combustion hamber ev Evaporator e Eonomizer Fuel F Fuel or a omponent g Combustion gasses j Stream k Component s Steam P Produt o a omponent Pinh Pinh point 1. Introdution One o the important ways to redue the eets o environmental impats o industrial plants is inreasing energy eiieny o the plants. Developing tehniques or designing eiient and ost-eetive energy systems is one o the oremost hallenges o energy engineering ae. In a world with inite natural resoures and inreasing energy demand by developing ountries, it beomes inreasingly important to understand the mehanisms whih degrade energy and resoures and to develop systemati approahes or improving the design o 1574

2 energy systems and reduing the impat on t he environment. The seond law o thermodynamis ombined with eonomis represents a very powerul tool or the systemati study and optimization o energy systems. This ombination orms the basis o the relatively new ield o thermo-eonomis. Ethylene is the main eed o LDPE (Low density polyethylene) plant to produe LDPE produt(s) in high pressure. By using a ompressor system, exess ethylene in dierent units o the plant, some traed gases like Methane and Propane, small quantity o water and air are ored to a multi hannel ombustion hamber o thermal oxidizer unit to burn and diminish the onentration o pollutant, as onsequenes o imposed environmental limitations that exist or the petrohemial o-gases. Ater burning the o-gases in the ombustion hamber, the onsiderable medium quality waste gas is released to atmosphere via vent stak. In pratise, in most o the petrohemial plants the thermal oxidizer units work ontinuously as a matter o exess amount o ethylene and other mentioned substanes. For a medium LDPE plant, maximum volume o gases reahes kg/h with onstant steady state pressure. This low produes an average thermal alori value o KJ/kg with average 300 C lue gas. The struture o a ommon thermal oxidizer is illustrated in igure 1. The installation onsists o two ompressor systems, multi hannel ombustion hambers, uel supply and burner systems. In urrent models or the environmental ondition the ollowing are onsidered (T = K and P = bar). The operating uel or the total plant is natural gas (taken as methane) with a lower heating value (LHV) equal to kj/kg. Fig. 1. Shemati sketh o thermal oxidizer with HRSG In the urrent researh, a part o waste heat energy system (thermal oxidizer) in LDPE (Low Density Polyethylene) plant is optimized aording to some deision variables. The hot gases rom the ombustion hamber are onduted to a HRSG (Heat Reovery Steam Generator) to be utilized or produing steam and hot water. This steam and/or hot water an be used in dierent ways in this plant (LDPE Plant) or other adjaent industrial plants. Moreover, in this investigation three dierent thermal oxidizers units were studied and data obtained are analysed or researh validation. The models used in this paper are realisti but inomplete 1575

3 rom an engineering point o view sine the objet o this study is to present distint models o thermoeonomi optimization. Thereore, it would be unreasonable to use an exessively ompliated mathematial model to desribe the perormane o the plant. 2. Methodology For modelling the system three ategories o equations have been onsidered, the equations whih desribe the behaviour o the system (physial model), the equations or alulating the apital osts o the omponents (eonomi model) and the equations whih has been used to alulate the thermodynami properties (thermodynami model) [1,2]. The deision variables seleted or the optimization are the ompressor pressure ratio P,/Pr, the isentropi eiienies o the ompressor (η ), inlet humidity perent (r ih ), the temperature o the ombustion gas at the HRSG inlet (T 2 ) and thermal eiieny o thermal oxidizer (η to ). The ollowing models are ormulated as a untion o these deision variables. To simpliy these models without loss o methodologial generality, the ollowing assumptions are made: (1) The air and the ombustion gases behave as ideal gases with onstant speii heats. (2) For ombustion alulations, the uel is taken to be methane CH4 (3) All omponents, exept the ombustion hamber, are adiabati. (4) Reasonable values are hosen or the pressure loss o the air and gas lows in the ombustion hamber and reuperate boiler. Our optimization program that is based on evolutionary algorithm has good onvergene and better results due to using three input ategory data rom three dierent petrohemial plants. As we know the optimization proedure is so ruial in engineering ields, espeially mehanial engineering. Among the various tehniques evolutionary algorithms (EAs) are o the greatest importane beause o their onvergene rate. Among EA algorithms, the Geneti Algorithm is the best option due to its less time onsuming or iteration time as well as satisying the several onstraints. Besides, at the end o this study the inluene o alteration in the demanded steam on the design parameters has been also studied. In this paper, ater thermodynami modelling o the system and ormation o the objetive untion, a ogeneration unit with thermal harateristis o well known problem [1,3,4,5] are simulated, optimized, and its results are ompared to the results o other ases; in order to ensure the validity o our physial modelling and optimization proedure. Subsequently, parameters o problem are modiied to math the onditions and requirements o the present work Thermodynami modeling o thermal oxidizer with HRSG Having known the values o deision variables (r, η, η to, T2 and r ih ) or a set o ixed demands o proess steam, the values o temperature and pressure in all lines o system was omputed. Consequently, the value o uel mass low rate m, whih should be expressed in terms o deision variables, is determined. The relations o thermodynami modelling are as ollows: Air ompressor 1 Tout = Tin 1 + η AC r γ a 1 γ a 1, (1) W = m ( T T ) (2) a a. p, a out in 1576

4 Combustion hamber m h + m LHV = m h + (1 ) m a 1 g 2 η LHV (3) P2 P 1 = (1 ) (4) P Heat reovery steam generator m s ( h5 h4 ) = m g ( h2 h3 ) (5) m h h ) = m ( h h ) (6) s ( 5 4a g 2 3a 2.2. Objetive untion The objetive untion is deined as the sum o two parts; the operational ost rate, whih is related to the uel expense, the rate o apital ost whih stands or the apital investment and maintenane expenses. Thereore, the objetive untion represents total ost rate o the plant in terms o dollar per unit o time. Obj Fun. m LHV + Z = k. (7) Sine the amounts o ultimate produts (proess steam) are ixed, the objetive untion is to be minimized so that the values o optimal design parameters would be obtained. For alulating the rate o operating ost equation, we have:. = m LHV (8) In whih = $/MJ is the regional ost o uel per unit o energy,m is the uel mass low rate, and LHV = kj/kg is the lower heating value o Methane. For expressing the purhase ost o equipment in terms o design parameters, several method have been suggested [2, 7-11]. In this paper, we used the ost untions mentioned in re [2]. However, some modiiations were made to tailor these results to the regional onditions in Iran and taking into aount the inlammation rate. For onverting the apital investment into ost per time unit: Z k = Z. CRF. ϕ k ( N 3600) (9) Where, Z k is the purhase ost o omponent in dollar, CRF (18%) is the apital reovery ator, N is the annual number o the operation hours o the unit (7500 hr), and φ (1.06) is the maintenane ator. 1577

5 2.3. Optimization Proedure Minimizing the objetive untion Eq.7 is a nonlinear optimization problem. In order to ahieve easible design parameters some physial onstraints should be onsidered seriously. The list o these onstraints and their reasons are brieed in table 1. Moreover, the ollowing inequality onstraints should be satisied in heat exhangers (air pre-heater and heat reovery steam generator). T 2 > T 1, T 2 > T 5, T 3a > T 5 + T pinh, min (10) In the present work a geneti algorithm ode is developed in Matlab Sotware Programming. Table1. The list o onstraints Constraints Reason T K Material limitation r 16 Commerial availability η a 0.9 Commerial availability η to 0.96 Commerial availability T3 400 K To avoid ormation o suluri aid in exhaust gases T4 a = T5 15 K To avoid evaporation o water in HRSG eonomizer 2.4. Evolutionary algorithm (Geneti Algorithm) Suh algorithms simulate an evolutionary proess where the goal is to evolve solutions by means o ross over, mutation, and seletion based on their quality (itness) with respet to the optimization problem at hand. Evolutionary algorithms (EAs) are highly relevant or industrial appliations, beause they are apable o handling problems with non-linear onstraints, multiple objetives and dynami omponents properties that requently appear in real-world problems. Moreover the input and output values or Geneti Algorithm method used in this study are shown in tables 2, 3. Table 2. Geneti algorithm input Tuning Parameters Value Population size 500 Maximum number o generation 1000 PC( Probability o Crossover) % 70 Pm ( Probability o mutation ) % 1 Number o rossover 2 Seletion in proess Tournament Tournament size 2 3. Disussion and result The numerial values o the optimum design parameters o the thermal oxidizer with HRSG are listed in table 3. Moreover, the onstraints o the problem are listed in table 1. These 1578

6 will in results results are ompared with other ase s results. Figure 2 depits the hanges in the objetive untion versus generation in the developed geneti algorithm ode. Table 3. The omparison o simulation and optimization numerial output or three mentioned ases. Deision variable Optimum design Optimum design Optimum design rr η C η to T 2 (K) r ih (K) Objetive Funtion ($/s) ($/s) ($/s) Objetive Funtion ($/s) Generation Fig. 2. Variation o Objetive Funtion o the system with Generation (CE=.003$/MJ). Study o the variation o the optimal deision variables versus uel unit ost reveals that by inreasing the uel ost optimal deision variables generally shit to thermodynamially more eiient design. As it an be learly seen the values o deision variables rrpr, ηrar,r Rand HRSG inlet temperature (TR2R) inrease with inreasing uel unit ost. It is worthy to mention that while inreasing ombustion inlet temperature (TR1R) redues the exergy destrution in ombustion hamber and heat exhangers (HRSG), due to the exhaust gases onstraint (TR3 R> 400K); it dereases with inreasing the uel unit ost. It should be noted that or eah TR2R there exists a T R1R whih the best thermodynamial eiieny may be ahieved. Moreover, an inrease in HRSG inlet temperature redues the exergy destrution in ombustion hamber; and sine inreasing TR2R in higher exhaust temperature o exhaust gases, the onstraint TR3 R> 400K does not ause any limitation or rising TR2R. Due the at that any inrease in TR2R dramatially aets the HRSG investment ost, igures 3-5 show the inluene o the unit ost o uel on the values o some the optimal deision variables. Figure 5 shows that when the uel prie inreased the ombustion hamber uel mass low rate derease or minimizing the objetive untion. Due to unertainty o apital investment data, it is imperative to study the results o apital expense variation on the optimal values o deision variables. 1579

7 T1(K) Fig. 3. The eets o uel unit ost on the optimal value o ombustion hamber inlet temperature, T1 Fig. 4. The eets o uel unit ost on the optimal value o Fuel Mass Flow Rate, m Fig. 5. The eets o uel unit ost on the optimal value o Objetive Funtion ($/s) 4. Conlusion The determined optimum design parameters or thermal oxidizer with HRSG apparently show a trade-o between thermodynamially and eonomially optimal designs. For example, rom thermodynami point o view, the deision variable η should be seleted as high as possible while this leads to an inrease in apital ost. It should be noted that any hange in the numerial values o a deision variable not only aets the perormane o the related equipment but also all the perormane o other equipments as well. It an be dedued rom the igures 3-5 that by inreasing the uel prie the values o deision variable in thermo-eonomially optimal design tend to those o thermodynamially optimal design. Using heat reovery, thermal oxidizers ause more energy eiieny and derease the level o green house gases aordingly. In spite o the at that utilizing these types o tehnologies 1580

8 ategorized as an end-o-pipe solution, nevertheless aording to the three pillars o sustainability it ontribute to both environmental dimension and eonomi dimension o sustainability. Reerenes [1] Valero, A., Lozano, Miguel A., Serra, L., Tsatsaronis, G., Pisa, J., Frangopoulos, C., and Von Spakovsky, M. R., 1994, CGAM Problem: Deinition and Conventional Solutions, Energy-The International Journal, 19, pp [2] Bejan, A., Tsatsaronis, G., Moran, M., 1996, Thermal design & optimization, John Wiley & Sons In. [3] Ghaarizadeh, A., 2006, Investigation on E volutionary Algorithms Emphasizing Mass Extintion, B.S thesis, Shiraz University o Tehnology, Shiraz, Iran. [4] Frangopouls, C. A., 1994, Appliation o the Thermoeonmi Funtional Approah to the CGAM problem, Energy-The International Journal, 19, pp [5] Tsatsaronis, G., and Pisa, J., 1994, Exergoeonomi Evaluation and Optimization o Energy Systems- Appliation to the CGAM Problem, Energy-The International Journal, 19, pp [6] Valero, A., Lozano, M.A., Serra, L., Torres, C., 1994, Appliation o the Exergeti Cost Theory to the CGAM problem, Energy -The International Journal, 19, pp [7] Spakovsky, M.R., 1994, Appliation o Engineering Funtional Approah to The Analysis and Optimization o the CGAM problem, Energy- The International Journal, 19, [8] Moran, M.J., 1989, A vailability Analysis: A Guide to Eiient Energy Use, ASME Press, New York. [9] Horlok, J.H., 1987, Cogeneration-Combined Heat and Power (CHP), Thermodynamis and Eonomis, pergamon press. [10] Kotas, T.J., 1995, T he exergy method o thermal plant analysis, Krieger Pub. Co., Florida. [11] Szargut, J., Morris, D.R., Steward, F.R., 1988, Exergy analysis o thermal, hemial, and metallurgial proesses, Hemisphere Pub. Co., New York. 1581