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Estimating Petroleum Exergy Production andConsumption Using a Simulated Annealing ApproachYavuz Ozcelik a & Arif Hepbasli ba Chemical Engineering Department, Faculty of Engineering , Ege University , Bornova, Izmir,Turkeyb Department of Mechanical Engineering, Faculty of Engineering , Ege University , Bornova,Izmir, TurkeyPublished online: 22 Sep 2006.

To cite this article: Yavuz Ozcelik & Arif Hepbasli (2006) Estimating Petroleum Exergy Production and ConsumptionUsing a Simulated Annealing Approach, Energy Sources, Part B: Economics, Planning, and Policy, 1:3, 255-265, DOI:10.1080/00908310600718809

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Energy Sources, Part B, 1:255–265, 2006Copyright © Taylor & Francis Group, LLCISSN: 1556-7249 print/1556-7257 onlineDOI: 10.1080/00908310600718809

Estimating Petroleum Exergy Productionand Consumption Using a Simulated

Annealing Approach

YAVUZ OZCELIK

Chemical Engineering DepartmentFaculty of EngineeringEge UniversityBornova, Izmir, Turkey

ARIF HEPBASLI

Department of Mechanical EngineeringFaculty of EngineeringEge UniversityBornova, Izmir, Turkey

This study deals with the development of the petroleum exergy production and con-sumption relations in order to better analyze exergy values and predict the futureprojections using the simulated annealing (SA) approach, which is a powerful tech-nique used to solve many optimization problems. The exergy estimation is performedbased on the indicators of gross domestic product (GDP) and the percentage of vehicleownership figures in Turkey, which is given as an illustrative example. The so-calledSA exergy production and consumption (SAPEX) model is developed, while the ex-ergy values obtained using the SAPEX model are also compared with those using thegenetic algorithm (GA) approach. It is determined that the SAPEX model developedpredicts the exergy values better than the GA model. It may be concluded that themodels proposed here can be used as an alternative solution and estimation tech-nique to available estimation techniques in predicting the future energy and exergyutilization values of countries. This study is also expected to give a new direction toengineers, scientists, and policy makers in implementing energy planning studies andin dictating the energy strategies as a potential tool.

Keywords energy demand, energy modeling, energy planning, exergy, exergy mod-eling, future projections, genetic algorithm, simulated annealing approach, Turkey

Energy modeling is a subject of widespread current interest among engineers and sci-entists concerned with problems of energy production and consumption. Modeling insome areas of application is now capable of making useful contributions to planning and

Address correspondence to Assoc. Prof. Dr. Arif Hepbasli, Mechanical Engineering Depart-ment, Faculty of Engineering, Ege University, 35100 Bornova, Izmir, Turkey. E-mail: arif.hepbasli@ege.edu.tr

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256 Y. Ozcelik and A. Hepbasli

policy formulation. In this regard, energy planning is not possible without a reasonableknowledge of past and present energy consumption and likely future demands (Dincerand Dost, 1996; 1997).

Exergy is a useful concept since it is a link between the physical and engineeringworld and the surrounding environment, and expresses the true efficiency of engineeringsystems, which makes it a useful concept to find improvements. Therefore, it is usedin the design of engineering systems as well as sectoral energy and exergy utilization(Dincer, 2002).

In recent years, various powerful techniques have been widely used to solve manyoptimization problems of engineering systems. Among these, genetic algorithm (GA) andsimulated annealing algorithm (SAA) are noteworthy in terms of their limited applicationsto the energy and exergy estimations.

GAs were first proposed by John Holland (1975) and further developed for engi-neering applications by Goldberg (1989). They manipulate concepts derived from biologyand are philosophically based on Darwin’s theory of survival of the fittest.

The SAA is a powerful, random search technique. Its main principle was initiallypresented in Metropolis et al. (1953) and received its name from the physical processcalled annealing, which brings a solid to a state of minimum energy. In other words, SAAis a stochastic method based on stochastic generation of solution vectors and employssimilarities between the physical processes of annealing and the optimization problems.Moreover, SAA was proposed by Kirkpatrick et al. (1983) as a general-purpose optimiza-tion technique, suitable for solving many complex combinatorial problems (Terzi et al.,2004).

GAs have been used by a few investigators to predict energy and exergy utilizationvalues (Haldenbilen and Ceylan, 2005; Ceylan et al., 2005; Ozturk et al., 2004, 2006).Although SAAs have been successfully applied to a wide range of engineering problems(Dolan et al., 1989; Athier et al., 1997; Xambre et al., 2003; Mantawy et al., 2003), noone study on the application of SAAs to estimating the future projections of energy andexergy uses has appeared in the literature to the best of the authors’ knowledge.

In this study, the SA approaches are applied to the prediction of the petroleum exergyproduction and consumption values in order to better analyze exergy use and to makefuture projections based on SA notion. In this regard, Turkey is selected as an applicationcountry and the three various forms of the SAPEX model are developed and validatedwith the actual data. The results of the SAPEX model are also compared to those of GAmodels proposed by Ozturk et al. (2004).

Model Development

The objective function, F , selected in this study is to minimize total sum of squared error(SSE) between observed and estimated values of exergy consumption and production, andtakes the following form:

Min F =n∑

i=1

(EobservedEestimated)2 (1)

where Eobs and Eest are the observed and estimated exergy consumption or exergyproduction, respectively, and n is the number of observations. The three forms of the

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Estimating Petroleum Utilization Values Using SAA 257

models [1] were used to estimate exergy consumption in the following way (Ozturket al., 2004):

Y = w1 + w2X1 + w3X2 (2)

Y = w1 + w2Xw31 + w4X

w52 (3)

Y = w1 + w2Xw31 + w4X

w52 + w6X1X2 (4)

where Y is the estimated exergy consumption in PJ, X1 is the gross domestic product(GDP) in 109$, and X2 is the percentage of vehicle ownership per person.

The proposed time series model for exergy production is in the following form(Ozturk et al., 2004):

Y = w1X + w2X2 + w3 exp(w4 + w5X) + w6X

w7 (5)

where Y is the estimated exergy production in PJ, and X is the time series such that1990 = 1, 1991 = 2 . . . , 2000 = 11.

The Method, Application and Comparison of the Models Developed

In this study, the method of SA was used to estimate the parameters of the models, whilethe results of the SA models developed were compared with the GA results to indicatethe validity and the accuracy of the models proposed.

Simulated Annealing

The Physical Process of Annealing. The aim of the process is to find the atomic con-figuration that minimizes internal energy. For a given configuration, a random move iscarried out by randomly picking a molecule and moving it in a random direction fora random distance. The new configuration is then accepted or rejected according to anacceptance criterion, based on the Boltzman function given by

p = e�EkbT (6)

where �E is the change in the energy of the configurations, kB is the Boltzman constantand T is the temperature of the system. The acceptance of a new configuration dependson �E and T , which is reduced to reach a lower energy state. The low temperature isnot a sufficient condition to find ground states of matter. The cooling process shouldbe accomplished slowly, otherwise the resulting crystal will have many defects or thesubstance may form a glass with no crystalline order.

Optimization by Simulated Annealing

In the simulated annealing, the value of the objective function is analogous to the energyof the system and the aim is to minimize the value of the objective function where thevalues of the continuous and discrete variables represent a particular configuration of thesystem. The behavior of the system, subject to such a neighborhood move, is determinedfrom the value of the two successive values of the objective function. The basic steps of

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258 Y. Ozcelik and A. Hepbasli

Figure 1. Basic steps of the algorithm.

the algorithm are illustrated in Figure 1, while they are briefly explained in the followingsubsections.

Determination of the Initial Value of Pseudo Temperature. The value of the initial tem-perature for a physical process depends on the properties of the system and can beestimated experimentally. Analogously, the initial value of the temperature for an opti-mization problem is estimated by the observation of the behavior of the problem using aspecified time, determined experimentally. The alternative schemes are available to esti-mate the initial temperature. The schemes of Aarst and Van Laarhoven (1985), and Aarstand Korst (1989) were used in this work. In this approach, any temperature value thatsatisfies the following equality is selected as the initial temperature:

0.95 = m1 + m2e�f +Ti

m1 + m2(7)

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Estimating Petroleum Utilization Values Using SAA 259

where m1 and m2 are the number of successful and unsuccessful moves, respectively,and �f + is the average increase in the objective function value for m2 moves. The totalnumber of moves to determine an initial temperature is proposed as 100 × N . N is thenumber of variables.

Acceptance Criteria. A nonequilibrium metropolis algorithm proposed by Margaridaet al. (1996) is used to accept or reject the generated points. The algorithm acceptsall downhill moves and accepts uphill moves with a probability p, which depends ontemperature and the change of the objective function values evaluated in successive iter-ations, as given below:

�F ≤ 0 p = 1

�F > 0 p = e�FT

(8)

when a downhill move occurs in the objective function, cooling is applied.

Annealing Schedule. The schedule of Aarst and Van Laarhoven (1985) is used in thereduction of annealing temperature, as given below:

T k+1 = T k

1 + T k ln(1 + δ)

3σ(T k)

(9)

where σ(T k) is the standard deviation of the objective function at T k , and δ is the speedparameter lying on the range of 0–1 (the value of δ was taken as 0.01).

Termination Criteria for Constant Temperature Step and Cooling Step. The constantnumber of moves or nonequilibrium comes together when the constant number of movingapproach can be used for the constant temperature step. In this approach, if the newfunction value is lower than the previous one, the temperature is reduced without reachingequilibrium; otherwise, the approach of constant number of moves is applied. To terminatethe overall procedure, the following relation was used.

dF(T )

dT

T

F(T )≤ ε (10)

Application and Scenarios

The GDP, the petroleum exergy production and consumption values and numbers ofvehicles are collected from Ozturk et al. (2004). The petroleum exergy production, con-sumption and their corresponding parameters between 1990 and 2000 are illustrated inTable 1.

Petroleum Exergy Modeling

Petroleum Exergy Consumption. The optimal or near-optimal parameter values calculatedusing GA given by Ozturk et al. (2004) and SA approach developed for the three models

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260 Y. Ozcelik and A. Hepbasli

Table 1Turkey’s petroleum exergy production and consumption values and

socio-economic indicators between 1990 and 2000

Years

Petroleum exergyproduction

(PJ)

Petroleum exergyconsumption

(PJ)GDP

(109$)

Vehicleownership

(%)

1990 161.5 986.3 15.24 5.281991 193.4 960.8 15.24 5.751992 186.0 1028.1 16.08 6.421993 169.1 1174.8 18.2 7.351994 160.2 1123.6 13.11 7.761995 152.8 1213.1 17.2 8.071996 152.1 1286.3 18.47 8.451997 150.2 1267.7 19.44 9.071998 140.1 1261.0 20.6 9.601999 127.7 1522.5 18.77 9.982000 119.4 1462.8 20.15 10.59

Source: Ozturk et al. (2004).

are given by the following relations:

Y = 337.65 + 13.67X1 + 77.77X2 (GAPEX) (11a)

Y = 299.54 + 13.44123X1 + 83.7824X2 (SAPEX) (11b)

Y = 825.42 + 0.128X2.3271 + 0.709X2.835

2 (GAPEX) (12a)

Y = 798.3874 + 0.0002X3.87141 + 7.1576X1.9045

2 (SAPEX) (12b)

Y = 636.55 + 3.975X1.4081 + 9.479X1.832

1 − 0.686X1X2 (GAPEX) (13a)

Y = 860.797 − 7.192X1.2491 + 6.94621.723

2 + 2.406X1X2 (SAPEX) (13b)

where X1 and X2 correspond to GDP and percentage of vehicle ownership, respectively.

Table 2The minimum objective function values

calculated by the algorithm of SA and GA

Model GAPEX SAPEX

Linear 2877.142 1454.37Exponential 44015.32 34131.8Quadratic 37288.7 32295.2

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Estimating Petroleum Utilization Values Using SAA 261

Table 3Estimated GDP and vehicle ownership

GDP Vehicle ownershipYears (109$) (%)

2000 20.15 10.592005 24.64 12.502010 29.72 14.222015 35.72 15.722016 37.04 15.992017 38.39 16.262018 39.78 16.522019 41.20 16.782020 42.67 17.03

Source: Ozturk et al. (2004).

The application of the three forms of the models for GA and SA results and thecorresponding minimum objective function values are given in Table 2. As can be seenfrom this table, the minimum objective function value on linear model is the lowestcompared to the others, and SAPEX gives lower minimum objective function valuescompared with the GAPEX approach proposed by Ozturk et al. (2004) for all the modelsbetween 1990 and 2000.

In order to make the future projections for the total exergy consumption of Turkey,the estimated values of the GDP/year and Turkey’s vehicle ownership must also be takeninto account. The estimated values of GDP and vehicle ownership are given in Table 3(Ozturk et al., 2004).

If the projections of Turkey’s Ministry of Energy and Natural Resources (MENR) arecompared with the results of the proposed models, both the exponential and mixed modelsare acceptable with lower average percentage error values of 2.2 and 2.3, respectively,as shown in Table 4.

While both of the exponential and mixed models are alternative appropriate modelsin SAPEX approach, the mixed model is only preferable for the GAPEX approach. Thefuture projections of GAPEX, SAPEX and MENR are illustrated in Figure 2.

Table 4The exergy consumption projections for the years between 2000 and 2020

MENR GAPEX SAPEX GAPEX SAPEXYear (PJ) (exponential) (exponential) (mixed) (mixed)

2005 1675.47 1959.8 1725.9 1756.3 1724.22010 1940.35 2483.8 2022.5 2045.1 2027.52015 2400.67 3099.4 2363.6 2336.6 2375.12020 2796.69 3814.2 2791 2629.9 2771.4Average error (%) 27.6 2.2 4.7 2.3

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262 Y. Ozcelik and A. Hepbasli

Figure 2. The future projection of MENR, SAPEX and GAPEX.

Figure 3. Fitted time series model for petroleum exergy production.

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Estimating Petroleum Utilization Values Using SAA 263

Figure 4. The projections of GAPEXTS, SAPEXTS and MENR.

Petroleum Exergy Production. In order to estimate petroleum exergy production, themodel is used on the basis of time series approach. The reason for this is that thepetroleum exergy production is not dependent on the socio-economic indicators anddepends only on its own natural resources. Therefore, time series (TS) expression is usedfor estimating the petroleum exergy production. The application of the model resulted inthe following optimal-or-near optimal parameter values in GAPEX and SAPEX for thetotal energy production:

Y = −10.92X + 0.165X2 + 4.13 exp(9.32 + 3.09X)

− 38.97X−20.53 (GAPEX)(14a)

Y = 1.655 − 3.30X + 0.084X2 + 5.56 exp(3.624 − 0.03X)

− 38,897X−13.4289 (SAPEX).(14b)

The objective function values of GAPEX and SAPEX between 1990 and 2000 arefound to be 184.1 and 183.17 with the averaged percentage errors of 2.356% and 2.353%,respectively.

The estimated GAPEXTS and SAPEXTS results and observed exergy productionvalues are shown in Figure 4. The averaged errors of GAPEXTS and SAPEXTS com-pared with the projection of MENR projections are obtained to be 88.2% and 74.3%,respectively. The projections of GAPEXTS, SAPEXTS and MENR are also illustrated inFigure 4. It is evident from this figure that GAPEXTS and SAPEXTS estimate the exergyproduction higher than the MENR projections. The reason for this is that the sharp fluc-tuations on the measured exergy production between 1990 and 2000, and the fluctuationson the MENR estimations between 2000 and 2020. Although SAPEXTS estimate the ex-ergy production higher than the MENR projections, it may be used as a better alternativemodel to estimate petroleum exergy production of Turkey compared with GAPEXTS.

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Conclusions

Use of SAAs has been growing exponentially since Kirkpatrick et al. proposed themin 1983 as a general-purpose optimization technique, and a number of studies havebeen performed by many scientists, researchers and engineers since that time. In thisstudy, the petroleum exergy production and consumption values were estimated by usingSAA based on GDP and the percentage of vehicle ownership figures in Turkey. Theparameters of the SAPEX model developed were obtained using the observed data. TheSAPEX was validated for the period of 1990–2000 with observed and estimated data.The various forms of the modeling approach were performed, while the results obtainedwere compared to the MENR projections and the results of the GAPEX models. Thefollowing main conclusions may be drawn from the results of the present study:

1. The SAA can be used as an alternative solution algorithm to estimate the futurepetroleum exergy values of Turkey.

2. This study estimated petroleum exergy production and consumption values inTurkey using SAA approach. The results were compared with the MENR projec-tions. However, an estimation of exergy values can also be investigated withfuzzy logic, neural networks or other methods. The results of the differentmethods could be compared with the SA method to see the performance ofmethods.

3. The results of the present study are also expected to give a new direction toengineers, scientists, and policy makers in implementing energy planning studiesas a potential tool.

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