Classical and alternative fuel mix optimization in cement production using mathematical programming

Fuel 90 (2011) 1277–1284

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Classical and alternative fuel mix optimization in cement production using mathematical programming Ioannis K. Kookos a,⇑, Yiannis Pontikes b, George N. Angelopoulos a, Gerasimos Lyberatos a a b

Department of Chemical Engineering, University of Patras, 26500 Rio, Greece Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, B-3001, Heverlee (Leuven), Belgium

a r t i c l e

i n f o

Article history: Received 21 May 2010 Received in revised form 2 December 2010 Accepted 19 December 2010 Available online 1 January 2011 Keywords: Cement production Alternative fuels Optimization

a b s t r a c t In this paper a systematic methodology is presented for the simultaneous optimal selection of raw materials, fossil fuels and alternative fuels in cement production. The aim is to offer a generic mathematical formulation that can be used as the basis for developing case specific mathematical formulations that can assist the strategic decision-making process. The mathematical model presented takes into consideration the essential elements of a cement plant operation. The final formulation is a mixed integer linear programming problem that aims at minimizing the overall operating cost. A realistic case study is presented which demonstrates the usefulness of the proposed mathematical programming methodology. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Cement has been the ultimate material for the construction industry and the basis for the development of society and for the welfare of the people. According to the European Cement Association, the representative organization for the cement industry in Europe, European Union produces about 270 Mt/y of cement [1], accounting for nearly 10% of world production, and consumes approximately an energy equivalent of 27 Mt of coal. Cement production is therefore an energy intensive process and results in significant greenhouse gases (GHG) emissions accounting, for instance, for nearly 5% of global anthropogenic, non-biogenic CO2 emissions [2]. The main strategies that can be followed in order to reduce energy consumption, and therefore reduce emissions, in the short and medium term are: replacing currently used raw materials by materials that are less energy intensive to produce or have smaller CO2 emissions or improving energy efficiency through process redesign or fossil fuel replacement. During the last 20 years specific energy consumption in European cement plants has been reduced by about 30%, and dust emissions have been reduced by 90% as the industry has invested heavily in process redesign and various emission abatement techniques [3]. As cement industry is able to use alternative materials and fuels to reinforce its competitiveness and at the same time ⇑ Corresponding author. Address: Department of Chemical Engineering, University of Patras, 26500 Rio, Patras, Greece. Tel.: +30 2610 969 567; fax: +30 2610 990 917. E-mail address: [email protected] (I.K. Kookos). 0016-2361/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2010.12.016

contribute to solutions to some of society’s waste problems there is a significant interest in exploring further this opportunity to improve its environmental footprint. Table 1 shows the most important alternative fuels used in European cement industry together with representative values for their net calorific value and amounts consumed in EU27 in 2004. Alternative fuels today substitute approximately 2.5 Mt of coal every year [1,3]. The use of alternative fuels in the cement industry has numerous environmental benefits such as [2]:    

reduces the use of non-renewable fossil fuels such as coal, contributes towards minimizing emissions, maximizes energy recovery from waste, maximizes the recovery of the non-combustible part of the waste and eliminates the need for disposal of slag or ash (as the inorganic part substitutes raw material in the cement).

The organic constituents of the most common alternative fuels are completely destroyed through complete pyrolysis and breakdown due to the high temperatures (>1450 °C), long residence time (8 s) and oxidizing conditions in a cement kiln. The inorganic constituents combine with the raw materials in the kiln and are incorporated in the cement. These unique characteristics of the cement plants have led many authors to identify cement plants as ‘‘scavengers’’ in large-scale industrial ecology projects where the aim is to achieve circular flow of energy and materials in industrial complexes mimicking the organization of natural ecosystems [4,5]. In this paper a systematic methodology is presented for the short and medium term scheduling of alternative fuels

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Nomenclature AC AR C CEF CTax FCI LSF m NCV s SR StO2 TED TSR UC VC Vfg X

annual capacity alumina ratio concentration carbon emission factor carbon tax fixed capital investment lime saturation factor mass of component per t of clinker produced net calorific value sensitivity measure silica ratio stoichiometric oxygen required for complete combustion thermal energy demand thermal substitution rate unit cost variable cost volume of flue gas produced per t of clinker produced binary variable in the optimization model

Greek letters u mass fraction x mass fraction

Table 1 Representative alternative fuels used in EU27 cement industry and representative net calorific value (adapted from [3]). Alternative fuel

NCV (MJ/kg)

Mt/y (2004)

Waste oil Textiles Used tires – tire derived fuel (TDF) Residue derived fuel (RDF) Industrial solvents Plastic – industrial and commercial waste Meat and bone meal Wood, paper, cardboard – industrial and commercial Sewage sludge (SS) Agricultural waste Industrial sludge Solid waste Oil and oily waste

35 35 30 25 25 20 20 17 15 15

0.51 0.01 0.81 0.74 0.66 0.46 1.28 0.30 0.26 0.07 0.25 0.45 0.51

consumption in cement industries. Certain cement plants, due to their location and environmental policies adopted, may have the opportunity to choose among different alternative fuels. It is therefore necessary to develop systematic tools to assist the strategic decision-making process as the selection of the most favorable mix of classical fossil fuels and alternative fuels is a multifaceted problem. A mixed integer linear programming (MILP) formulation of the mathematical problem involved is presented that accounts for the material balances, energy balances, quality and environmental constraints of a cement plant operation. The mathematical model can be used to decide on the most profitable selection of raw materials, fossil fuels and alternative fuels in order to minimize the cost and increase revenues from non-biogenic CO2 emission reduction while meeting all operational constraints. 2. Literature survey Kleppinger [6] offers an early but comprehensive discussion of the issues relative to the use of alternative (waste derived) fuels in cement manufacturing. A large number of early references rela-

Subscripts BG biogenic g gaseous component in flue gases i oxide j raw material k alkali L lower value l fuel NBG non-biogenic n heavy metal p clinker phase Superscripts Air air C cliner CB clinker composition as predicted by Bogue methodology F fuel fg flue gas R raw material U upper bound value V flue gas

tive to the faith of heavy metals are discussed and reviewed critically. Conesa et al. [7] present an analysis of the emission of different pollutants when replacing partially the fuel type used in a cement kiln by tire derived fuel and sewage sludge. Dioxins and furans, polycyclic aromatic hydrocarbons (PAHs) and other hydrocarbons, heavy metals, HCl and HF, CO, CO2, NOx and other parameters of the stack were analyzed, according to the standard methods of sampling and determination, through more than 1 year in six series: one blank (no sewage sludge) and five more with increasing amount of sludge and/or tires. The emission of PAHs and dioxins seems to increase with the amount of tires fed to the kiln, probably due to the feed point used. Karstensen [8] presents a comprehensive study of more than 2000 PCDD/PCDF (polychlorinated dibenzo-p-dioxins/polychlorinated dibenzofurans) cement kiln measurements, representing most production technologies and waste feeding scenarios. The data generally indicate that most modern cement kilns can meet an emission level of 0.1 ng I-TEQ/m3 and that proper and responsible use of organic hazardous and other wastes to replace parts of the fossil fuels is not an important factor influencing the formation of PCDD/PCDFs. Many earlier emission factors show a tendency of exaggerating the influence of the use of hazardous waste on the emissions of PCDD/PCDFs. Van Loo [9] evaluates around 2200 dioxin/furan stack emission measurements collected from various sources. It is demonstrated that most cement kilns can meet an emission level of 0.1 ng TEQ/Nm3 if primary measures are applied. Reducing the temperature to a level lower than 200 °C at the inlet of the air pollution control device is the key factor which has shown to limit dioxin formation and emissions at all types of cement kilns. Schuhmacher et al. [10] conducted a systematic and comprehensive study on the partial substitution (20%) of fossil fuels by sewage sludge in a Spanish cement plant. In order to establish the environmental impact for the surroundings the levels of polychlorinated dibenzo-p-dioxins and dibenzofurans and heavy metals were monitored in soil and vegetation samples collected near the cement plant. The temporal trends in the pollutant levels were studied by comparing the concentrations with those obtained

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in a previous survey in the same sampling sites. Very slight changes of the PCDD/F concentrations were registered in the period 2003–2006 but there was a notable heterogeneity in the evolution of metal levels, which varied according to each particular element. They conclude that the current levels of organic and inorganic pollutants are in the low part of the range in comparison with other zones impacted by cement plants and that no impact changes for the environment and the local population are detected. IPPC draft publication [3] on the best available techniques in the cement industries contains an extensive up-to-date database on potential emissions from cement plants utilizing alternative fuels including a large number of actual site measurements. Prisciandaro et al. [11] demonstrated the technical feasibility of using alternative fuels in the clinker production process using real plant data: shredded tires and waste oils were used as alternative fuels in clinker kilns of two different cement plants. Experimental data statistically analyzed show encouraging results, if less than 20% of a regular fuel is replaced with an alternative one. In particular, clinker characteristics were unmodified, and stack emissions (NOx, SO2 and CO mainly) were, in the case of tires, slightly incremented, but remain almost always below the limits. In the case of waste oils, emissions were even decreased. Some statistical tools were applied in the data analysis to understand the behavior of the parameters monitored during the process. Kaantee et al. [12] use commercial simulators to predict the behavior of cement plants under conditions of thermal substitution of fossil fuels by alternative fuels. The calculations performed show that the air demand is higher with the alternative fuels considered (meat and bone meal and sewage sludge) than for the reference case. Then the exhaust gas amounts are larger, which will affect the function of the pre-heating system as a whole. They also stress that it is of great importance to maintain the product quality at all times; therefore, the conditions (oxidizing/reducing, temperature) in the kiln system must be carefully controlled. Corti and Lombardi [13] present a Life Cycle Assessment (LCA) to compare different processes for the treatment of exhausted tires: combustion in a conventional waste-to-energy (WtE) process, substitution of conventional fuel in the cement production process and two different hypotheses of reuse as filling material based on a cryogenic pulverization process (CPP) or on a mechanical pulverization process (MPP). The analysis shows that the fuel substitution in cement production and the use in WtE processes are the most promising alternatives due to the reduction in fossil fuel consumption. Between these two alternatives, a better result is obtained with the fuel substitution in cement production. CPP and MPP for reuse as filling materials show worse results in terms of environmental impact with respect to the other alternatives, because of the high energy consumption related to the pulverization processes. Pipilikaki et al. [14] study the possibility of using TDF as alternative fuels in substitution of conventional (fossil) fuels. They identify several environmental advantages such as complete destruction of the organic compounds, cost effectiveness (the use of scrap tires reduces coal and iron consumption). Six percent of the total fuel used in a semi-industrial scale facility was TDF and the results were very promising as differences in the final product quality were observed only in cement setting time and water demand. Reijnders [5] and Hashimoto et al. [4] discuss the unique features of cement plants that have established them as important element in large-scale industrial ecology projects. They have characterized cement plants as ‘‘scavengers’’ in order to emphasize their ability to consume most industrial and municipal wastes. Hashimoto et al. [4] give extensive details of the on-going industrial ecology project in the coastal area near the city of Kawasaki, Japan, from which the potential of cement plants to act as facilita-

tors for achieving the cyclic structure of flows met in natural ecosystems is clearly demonstrated. The problem of selecting the best raw materials mix is discussed briefly in classical references such as Lea’s [15] and Taylor [16]. A more systematic treatment is presented by Xirokostas and Zoppas [17] where the selection of the raw materials is based on a nonlinear programming problem where the cost of raw materials is minimized and several operational constraints are satisfied. Carpio et al. [18] present an optimization based framework for the selection of both raw material and fuels that include one alternative fuel, namely TDF. The present work is based on these two papers and a general mathematical formulation is presented for selecting raw materials simultaneously with fuels involving any combination and number of fossil fuels and waste derived fuels. Detailed material and energy balances are derived for the kiln system including solid material balances as well as gaseous material balances. The selection of the best possible solution is based on an economic objective function that accounts for the cost of raw materials, fossil fuels, alternative fuels and emissions. The cost of alternative fuels includes the fixed cost necessary to build the infrastructure for handling the alternative fuels as well as the variable cost related to the handling of a new potential fuel. The overall mathematical model is a mixed integer linear problem (MILP) that can be solved very efficiently using currently available software and computer power. 3. Mathematical model In order to facilitate the presentation of the proposed mathematical model for the raw materials and fuel mix optimization the following indices and sets are defined: j 2 RawMaterials = {Limestone, Clay, Sand, Fly Ash, FeSource, . . .} l 2 Fuels = {Coal, PetCoke, TDF, . . .} = {FosilFuels} [ {AlternativeFuels} i 2 Oxides = {SiO2, Al2O3, Fe2O3, CaO, MgO} k 2 Alkalis = {K2O, Na2O} s 2 Sulfur = {SO3} n 2 HeavyMetals = {Hg, Tl, Cd, . . .} p 2 ClinkerPhases = {C3S, C2S, C3A, C4AF} g 2 FlueGases = {CO2, O2, N2} The mathematical model consists of the material balances that are expressed as equality constraints and product specification constraints that are expressed as inequality constraints. Equality constraints (1) and (2) express the material balances of the most important oxides and alkalis in the rotary kiln:  Mass of oxides in clinker

mCi ¼

X

xRi;j mRj þ

j2RawMaterials

X

xFi;‘ mF‘ ; 8i 2 Oxides

ð1Þ

xFk;‘ mF‘ ; 8k 2 Alkalis

ð2Þ

‘2Fuels

 Mass of alkalis in clinker

mCk ¼

X

j2RawMaterials

xRk;j mRj þ

X

‘2Fuels

The material balances are expressed using a basis of 1 t of clinker produced. mCi (mCk ) is the mass of oxide i (alkali k) in the clinker in kg i/t clinker. mRj (mF‘ ) is the mass of raw material j (fuel ‘) consumed to produce 1 t of clinker. xRi;j and xFi;‘ are the mass fractions of corresponding oxides in the raw materials and fuels. It is assumed that the fuel ash is fully incorporated in the clinker produced. As a result the mass fractions of the oxides in the fuel are calculated by multiplying the mass fraction of the oxides in the fuel ash and the mass fraction of the ash in the fuel.

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genic C in a certain alternative fuel is defined as uBG (see [20–22] and the references therein). In a similar way the material balance of the oxygen, nitrogen and total flue gas can be written as:  Oxygen material balance

Eq. (3) is the material balance of sulfur expressed as SO3:  Mass of sulfur in clinker

X

mCSO3 ¼

X

xRSO3 ;j mRj þ

j2RawMaterials

xFSO3 ;‘ mF‘  V fg C fgSO3

ð3Þ

‘2Fuels

Air mfg  O2 ¼ 0:232m

X

mF‘ StO2;‘

ð8Þ

‘2Fuels

xRSO3 ;j ðxFSO3 ;‘ Þ is the mass fraction of SO3 in raw material j (fuel ‘). The

mass fraction of the SO3 in a fuel is calculated by expressing the S in wt.% as SO3 (using the formula (80/32) (%S/100)). The last term in Eq. (3) accounts for the SO3 emissions from the flue-gas stream. 3 C fg SO3 is the concentration of SO3 in the flue gas (in kg SO3/Nm ) and Vfg is the volumetric flowrate of the flue gas (in Nm3/t clinker):

X

V fg ¼ 22:414

g2FlueGases

Air mfg N2 ¼ 0:768m

 Mass of heavy metals in clinker

¼

R R n;j mj

x

þ

j2RawMaterials

X

F F n;‘ m‘ ;

x

8n 2 HeavyMetals

ð5Þ

‘2Fuels

 Mass of clinker produced

mCi þ

i2Oxides

X

mCk þ mCSO3 þ

k2Alkalis

X

mCn ¼ 1000 kg

ð6Þ

n2HeavyMetals

Carbon dioxide is produced by the fuel combustion (C + O2 ? CO2) and by the calcination of CaCO3 (CaCO3 ? CaO + CO2) and can be divided to non-biogenic (NBG) CO2 and biogenic (BG) CO2:  Carbon dioxide material balance

mVCO2 ¼ mVCO2 ;NBG þ mVCO2 ;BG mVCO2 ;NBG ¼ mVCO2 ;BG ¼

44 56

X

xRCaO;j mRj þ

j2RawMaterials

X

/BG CEF ‘ mF‘

in

kg O2 kg fuel

ð9Þ

ð7aÞ X

ð1  /BG ÞCEF ‘ mF‘

ð7bÞ

‘2Fuels

ð7cÞ

‘2Fuels

where CEF is the carbon emission factor which is easily calculated from the ultimate analysis of the fuel based on the fact that 12 kg of C produce 44 kg of CO2. It is important to note that CO2 emissions are classified as biogenic, i.e. derived from biogenic, plant or animal sources excluding fossil carbon, and non-biogenic. When sustainable biogenic CO2 sources, such as biomass, are burned or aerobically decomposed the emissions are not counted when the greenhouse gases impacts are evaluated. The mass fraction of bio-

ð10Þ

 Total mass of flue gas (dry basis) fg fg mfg ¼ mfg O2 þ mN2 þ mCO2

ð11Þ

The O2 in flue gas is normally controlled at a level of 10%, i.e.  Oxygen in flue gas

mfg O2 ¼ 0:1

It is known that, apart from mercury, selenium and thallium, all heavy metals are almost perfectly (>99%) absorbed by clinker or cement kiln dust. In any case, the amount of heavy metals calculated by Eq. (5) is the maximum amount that can be incorporated into the clinker for the selected raw materials and fuel mix. A comprehensive discussion of the issue can be found in Kleppinger [6] and Achternbosch et al. [19]. Eq. (6) expresses the constraint that the amount of clinker produced must be equal to 1000 kg:

X

    32 %C 1 %O %S þ ; þ %H  100 12 4 8 32

ð4Þ

where is the mass of gaseous component g in the flue-gas stream (in kg/t clinker) and mwg the corresponding molecular weight. Eq. (5) is the material balance of the heavy metals, where it is assumed that clinker is a perfect sink for the bulk of the heavy metals added to the kiln system:

X

StO2 ¼

 Nitrogen material balance

mfg g mwg

mfg g

mCn

where mAir is the total air fed to the system (which is 23.2 wt.% O2) and StO2 is the stoichiometric oxygen required for complete combustion of the corresponding fuel, which can be calculated by [23]:

32 V fg 22:414

ð12Þ

The energy required for producing 1 t of clinker must be supplied from fuel combustion:  Specific heat consumption constraints

X

mF‘ NCV ‘ ¼ TED

ð13Þ

‘2Fuels

NCV is the net calorific value of the fuel (in kJ/kg fuel) and TED is the specific (per t of clinker) thermal energy demand which can vary between 5.3  106 and 7.1  106 kJ/t clinker for wet kiln systems and between 3.2  106 and 3.5  106 kJ/t clinker for dry kiln systems with 4/5-stage pre-heating. The use of waste derived fuels as a supplemental fuel is subjected to approvals and permits issued to a specific upper limit of total energy limit. This is normally called the thermal substitution rate (TSR) and is expressed as a percentage of the TED:

X ‘2AlternativeFuels

mF‘ NCV ‘ 6



 TSR  TED 100

ð14Þ

Chemical analysis of cement and clinker can be expressed in terms of oxide components but it is common practice in cement industry to use semi-theoretical indices which are [15,16]:  the alumina ratio (or modulus) AR = Al2O3/Fe2O3  the silica ratio (or modulus) SR = SiO2/(Al2O3 + Fe2O3)  lime saturation factor LSF = CaO/(2.8SiO2 + 1.1 Al2O3 + 0.65 Fe2O3). where chemical formulae denote weight percentages. For ordinary Portland cement (OPC) clinker SR is usually between 2.0 and 3.0 and AR between 1.0 and 4.0. AR is related to the ratio of aluminate to ferrite phases which has a significant impact on cement properties. SR indicates the proportions of the silicate phases in the clinker. LSF is usually between 0.88 and 0.98 but values up to 1.02 can be acceptable. LSF relates the ratio of alite to belite and indicates whether an unacceptable level of free lime can be present in clinker. The inequalities that follow express the permissible levels of the three indices introduced above:  Constraints on alumina ratio (AR)

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mCAl2 O3

ARL 6

6 ARU

mCFe2 O3

ð15Þ

where subscript L indicates a lower bound and superscript U an upper bound. Inequalities (15) can be expressed as



X



xRAl2 O3 ;j  ARU xRFe2 O3 ;j mRj

j2RawMaterials

X

þ

ðxFAl2 O3 ;‘  ARU xFFe2 O3 ;‘ ÞmF‘ 6 0

ð16Þ  Constraints on clinker composition in oxides and clinker potential phases

‘2Fuels

  xRAl2 O3 ;j þ ARL xRFe2 O3 ;j mRj

X

mCL;i 6 mCi 6 mC;U i ;

j2RawMaterials

X

þ

ðx

F Al2 O3 ;‘

F F Fe2 O3 ;‘ Þm‘

þ ARL x

60

ð17Þ

‘2Fuels

mCSiO2 mCAl2 O3

þ mCFe2 O3

6 SRU

ð18Þ

ðxRSiO2 ;j  SRU ðxRAl2 O3 ;j þ xRFe2 O3 ;j ÞÞmRj

j2RawMaterials

X

ðxFSiO2 ;‘  SRU ðxFAl2 O3 ;‘ þ xFFe2 O3 ;‘ ÞÞmF‘ 6 0

ð19Þ

‘2Fuels

X

ðxRSiO2 ;j þ SRL ðxRAl2 O3 ;j þ xRFe2 O3 ;j ÞÞmRj

j2RawMaterials

þ

X

ðxFSiO2 ;‘ þ SRL ðxFAl2 O3 ;‘ þ xFFe2 O3 ;‘ ÞÞmF‘ 6 0

ð20Þ

‘2Fuels

 Constraints on lime saturation factor (LSF)

LSF L 6

2:8mCSiO2

X

mCCaO 6 LSF U þ 1:2mCAl2 O3 þ 0:65mCFe2 O3

ð21Þ

U

ðxRCaO;j  LSF ð2:8xRSiO2 ;j þ 1:2xRAl2 O3 ;j þ 0:65xRFe2 O3 ;j ÞÞmRj

j2RawMaterials

þ

6

mCB p

6

8i 2 Oxides

mCB;U ; p

X

X

ðxFCaO;‘  LSF U ð2:8xFSiO2 ;‘ þ 1:2xFAl2 O3 ;‘ þ 0:65xFFe2 O3 ;‘ ÞÞmF‘ 6 0

‘2Fuels

ð22Þ

X

ðxRCaO;j þ LSF L ð2:8xRSiO2 ;j þ 1:2xRAl2 O3 ;j

j2RawMaterials

X

þ 0:65xRFe2 O3 ;j ÞÞmRj þ

ð26Þ

8p 2 ClinkerPhases

UC Rj mRj þ

j2RawMaterials

X þ

mCB L;p

ð27Þ

The objective function considered consists of three parts. The first part is the cost of raw materials and the cost of fuels (traditional fossil fuels and waste derived – alternative fuels):

 Constraints on silica ratio (SR)

SRL 6

It is important to note that the mCCaO must be corrected to account for the presence of free lime. In grey cement C3S varies between 40% and 80%, C2S between 10% and 50% and C3A between 0 and 15% and C4AF between 0 and 20% [3]. Typical concentrations are C3S: 65% w/w, C2S: 15% w/w, C3A: 10% w/w and C4AF: 10% w/w. Quality constraints are introduced as bound constraints in the oxide composition and/or potential phase composition:

ðxFCaO;‘ þ LSF L ð2:8xFSiO2 ;‘ þ 1:2xFAl2 O3 ;‘

X

UC F‘ mF‘

‘2Fuels

where UC is the cost per unit of raw material or fuel in €/kg dry material. It is important to note that each term has units of €/t clinker. The second part of the objective function is the annualized fixed capital investment cost and the variable cost associated with the use of a waste derived fuel as a fossil fuel substitute. The quality control, storage, handling, preparation and combustion of alternative fuels necessitate process modifications and auxiliary facilities construction which demand fixed capital investment that can be significant. In addition, variable costs associated with the handling of waste derived fuels, such as costs related to quality control, safety and emissions control, must be taken into consideration in order to evaluate process alternatives on a consistent basis:

X ‘2Fuels

!

e AC

FCIF‘ X F‘

þ

VC ‘ mF‘

where FCI is the fixed capital investment, e is a coefficient that transforms the fixed capital into annual basis (in €/y), AC is the annual capacity of the plant in t clinker/y and VC is the variable cost associated with the combustion of the corresponding alternative fuel (in €/kg fuel). X F‘ is a binary variable, i.e. it can obtain either the value 1 or the value 0, and is defined as:

X F‘ ¼ 1; if alternative fuel l is used as a fossil fuel substitute

‘2Fuels

þ 0:65xFFe2 O3 ;‘ ÞÞmF‘ 6 0

ð23Þ

An alternative approach, which is based on the work by Bogue [16], is to express the likely quantitative phase composition as a linear function of the oxides present in the clinker. The main assumption is that the compositions of the four major phases are C3S (alite, 3CaOSiO2), C2S (belite, 2CaOSiO2), C3A (tricalcium aluminate, 3CaOAl2O3) and C4AF (tetracalcium aluminoferrite, 4CaOAl2O3Fe2O3):  Potential phase in clinker as predicted by Bogue equations

mCB p ¼

X

Boguep;i mCi ;

8p 2 ClinkerPhases

X F‘ ¼ 0; otherwise If X F‘ ¼ 0 then the contribution of the annualized fixed capital investment cost becomes zero and the cost is calculated consistently. The third part of the objective function consists of the costs or savings arising from a potential increase or decrease in the nonbiogenic CO2 emissions. If the carbon value (or carbon tax) is CTAX (see Lund [24]) then the complete objective function is given by:  Objective function (in €/t clinker)

ð24Þ

where mCB p is the mass of phase p in the clinker as predicted by Bogue methodology. Boguep,i is given by:

Bogue ¼

C3 S C2 S C3 A C4 AF

2 SiO2 Al2 O3 Fe2 O3 CaO 3 7:6 6:72 1:43 4:07 6 8:6 5:07 1:08 3:07 7 4 0 2:65 1:69 0 5 0 0 3:043 0

X

Cost ¼

i2Oxides

j2RawMaterials

þ

X 

‘2Fuels

ð25Þ

UC Rj mRj þ

e AC

FC F‘ X F‘

X

! UC F‘ mF‘

‘2Fuels

 þ VC ‘ mF‘ þ C Tax dmCO2 ;NBG

ð28Þ

where

 fg dmCO2 ;NBG ¼ mfg CO2 ;NBG  mCO2 ;NBG

ð29Þ

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F mFL;‘ X F‘ 6 mF‘ 6 mF;U ‘ X‘ ;

X F‘ 2 f0; 1g;

8‘ 2 Fuels

ð30Þ

8‘ 2 Fuels

ð31Þ

 fg m CO2 ;NBG is the currently non-biogenic CO2 emitted in flue gas per t of clinker produced and mfg CO2 ;NBG is the non-biogenic CO2 emitted when using an optimal mix of alternative and fossil fuels. mF;U is ‘ the maximum amount of fuel ‘ that is available per t of clinker produced (it can be calculated by dividing the total amount of the fuel available by the plant capacity). mFL;‘ is the minimum amount of fuel ‘ that has to be consumed. This can be zero but normally, for strategic reasons, a minimum nonzero amount should be selected in order to support a sustainable market for the alternative fuel considered (and possibly reduce plant dependency on a restricted set of energy supply options). The complete mathematical model consists of the Eqs. (1)–(14) and (16), (17), (19), (20) and (22)–(31). This is an MILP optimization model that can be solved with classical branch and bound or Table 2 Representative chemical analysis of raw materials for the production of cement clinker. Component

SiO2 Al2O3 Fe2O3 CaO MgO K2O Na2O SO3 Cl LOI

Mass% dry material Limestone

Clay

Sand

Fly ash

Fe source

10.0 1.0 1.0 50.0 0.5 0.3 0.1 0.01 0.1 37.0

60.0 10.0 5.0 10.0 2.0 2.0 1.0 0.05 0.2 9.75

80.0 5.0 2.5 3.0 2.0 1.5 0.5 0.05 0.0 5.0

50.0 25.0 8.0 5.0 1.0 1.0 1.0 0.9 0.1 8.0

1.0 0.5 95.0 2.0 1.0 0.1 0.1 0.3 0.2 0.0

branch and cut algorithms [25] in commercially available solvers using, for instance, the GAMS interface [26]. 4. Case study In this section a case study is considered in order to demonstrate the usefulness of the proposed mathematical formulation in solving real world problems. A cement plant with a capacity of 2 Mt clinker/y is considered which produces OPC. The available raw materials and their characteristics are summarized in Table 2. In Table 3, the characteristics of six alternative, classical and waste derived, fuels are shown. Table 4 shows all other data necessary to define the case study including quality constraints and cost elements details. Data for the composition and thermal characterization of the alternative fuels were derived by [1–3,7,12,27–31]. Estimates of the fixed capital as well as operational costs associated with the use of alternative fuels are adapted by ALF-CEMIND [32]. Availability of the alternative fuels and unit prices are taken from the same report (adapted to 2010). It is assumed that if a waste derived fuel is selected for co-firing in the cement kiln then at least 20% of the available quantities must be used in the plant in order to support a sustainable market. The proposed formulation is applied and the GAMS interface to CPLEX MILP solver was used to solve the case study. Initially the optimum solution, without the opportunity of co-firing waste derived fuels, is established. The results are shown in Table 5 under the column of 0% thermal substitution rate. Then, a maximum thermal substitution rate of 10% is assumed and the optimization problem is solved again. The results are summarized in Table 5. Cost savings of around M€ 0.63 per annum are predicted. All available MBM and part of the RDF are used in this solution to achieve a TSR of 10%. Co-firing of SS and TDF is not advisable under the specific economic figures. It is important to note that the non-biogenic CO2 emissions are reduced by 27 kg of CO2 per t of clinker

Table 3 Representative chemical analysis of primary and alternative fuels. Component

Coal (CL)

Petroleum coke (PC)

RDF (RDF)

Sewage sludge (SS)

Tire derived fuel (TDF)

Meat and bone meal (MBM)

NCV (kJ/kg dry fuel) StO2 (kg O2/kg fuel) CEF (kg CO2/kg fuel)

30,000 2.32 2.75 0.00 100

33,000 2.67 3.30 0.00 90

26,000 2.16 2.20 0.50 50 30,000

16,000 1.59 1.58 0.50 40 30,000

32000 2.34 2.56 0.00 30 20,000

17,000 1.45 1.54 1.00 20 20,000

Ultimate analysis mass% dry material C 75.0 H 5.0 O 8.0 S 0.3 N 0.01 Ash 10.0

90.0 3.0 1.0 4.0 1.0 1.0

60.0 10.0 25.0 1.0 0.1 10.0

43.0 9.0 27.2 0.2 1.8 20.0

70.0 7.0 10.0 1.5 0.5 10.0

42.0 6.0 15.3 0.4 7.5 30.0

Ash analysis (mass%) SiO2 Al2O3 Fe2O3 CaO MgO K2O Na2O SO3 Cl NiO V2O5 ZnO (expressed as Zn) Cadmium Cd Lead Pb Thallium Tl Arsenic As Mercury Hg

40.0 10.0 7.0 1.0 3.0 0.5 0.5 2.0 0.1 15.0 20.0 0.0050 0.0001 0.0010 0.0080 0.0005 nd

40.0 25.0 2.0 20.0 2.5 1.0 1.0 2.0

40.0 15.0 5.0 20.0 2.5 1.0 1.0 1.0

22.0 10.0 1.5 11.0 1.5 1.0 1.0 15.0 0.4

0.5 0.0

0.0085 0.0001 0.0050 nd 0.0005 0.0002

0.0700 0.0005 0.0300 nd 0.0020 0.0015

35.0 (28.1) 0.0005 0.0050 0.00001 0.00001 nd

uDG Unit cost UC (€/t) Available amount t/y

52.5 30.0 10.0 3.0 1.0 1.5 0.5 1.5 0.1

0.0200 0.0010 0.0200 0.0004 0.0002 nd

20.0 0.5

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I.K. Kookos et al. / Fuel 90 (2011) 1277–1284 Table 4 Parameters of the mathematical model for the case study examined. Parameter

Symbol

Value

Units

Annual plant capacity Thermal energy demand Upper bound on alumina ratio Lower bound on alumina ratio Upper bound on silica ratio Lower bound on silica ratio Upper bound on lime saturation factor Lower bound on lime saturation factor Upper bound on the mass of silica in clinker

AC TED ARU ARL SRU SRL LSFU LSFL

2,000,000 3,500,000 2.7 1.0 2.5 1.5 1.02 0.85 240

t clinker/y kJ/t clinker – – – – – – kg/t clinker

Lower bound on the mass of silica in clinker

mCL;SiO2

220

kg/t clinker

Upper bound on the mass of alumina in clinker

mC;U Al2 O3

60

kg/t clinker

Lower bound on the mass of alumina in clinker

mCL;Al2 O3

50

kg/t clinker

Upper bound on the mass of ferric oxide in clinker

mC;U Fe2 O3

40

kg/t clinker

Lower bound on the mass of ferric oxide in clinker

mCL;Fe2 O3

30

kg/t clinker

Upper bound on the mass of calcium oxide in clinker

mC;U CaO

670

kg/t clinker

Lower bound on the mass of calcium oxide in clinker

mCL;CaO

630

kg/t clinker

Upper bound on the mass of C3S in clinker

mCB;U C3 S

600

kg/t clinker

Lower bound on the mass of C3S in clinker

mCB L;C 3 S

500

kg/t clinker

Upper bound on the mass of C2S in clinker

mCB;U C2 S

350

kg/t clinker

Lower bound on the mass of C2S in clinker

mCB L;C 2 S

100

kg/t clinker

Upper bound on the mass of C3A in clinker

mCB;U C3 A

150

kg/t clinker

Lower bound on the mass of C3A in clinker

mCB L;C 3 A

10

kg/t clinker

Upper bound on the mass of C4AF in clinker

mCB;U C 4 AF

150

kg/t clinker

Lower bound on the mass of C4AF in clinker

mCB L;C 4 AF

10

kg/t clinker

Carbon tax Fixed capital investment for using TDF Variable cost associated with the use of TDF Fixed capital investment for using RDF Variable cost associated with the use of RDF Fixed capital investment for using SS Variable cost associated with the use of SS Fixed capital investment for using MBM Variable cost associated with the use of MBM SO3 in flue gas (sulfur expressed as SO3)

CTAX eFCITDF VCTDF eFCIRDF VCRDF eFCISS VCSS eFCIMBM VCMBM

0.020 300,000 0.010 200,000 0.005 200,000 0.005 300,000 0.010 0.000030

€/kg CO2 €/y €/kg fuel €/y €/kg fuel €/y €/kg fuel €/y €/kg fuel kg SO3/Nm3

mC;U SiO2

C Vs

Table 5 Solution summary of the case study. TSR

%

0

10

15

20

32

mLimostone mClay mSand mFlyAsh mFeSource mCoal mPetCoke mRDF mSS mTDF mMBM mAIR Non-biogenic CO2 Biogenic CO2 Total CO2 dCO2 (non-biogenic) dCO2 (non-biogenic) dCO2 (non-biogenic) SR AR LSF

kg/t clinker

1285.614 0.000 0.000 178.723 5.464 32.710 76.324 0.000 0.000 0.000 0.000 2498.520 853.992 0.000 853.992 – – – 2.408 1.791 0.923

1284.093 0.776 0.000 178.545 5.622 29.439 68.692 6.923 0.000 0.000 10.000 2506.802 826.884 23.016 849.900 27.11 54.22 3.17 2.406 1.787 0.922

1284.132 1.070 0.000 177.964 5.660 27.804 64.875 13.654 0.000 0.000 10.000 2509.465 817.213 30.420 847.633 36.78 73.56 4.31 2.407 1.787 0.922

1284.340 0.928 0.000 178.382 5.647 26.128 61.059 8.077 0.000 10.000 10.000 2488.494 819.674 24.285 843.959 34.32 68.64 4.01 2.407 1.787 0.922

1284.092 0.856 0.000 176.435 5.693 22.243 51.900 15.000 15.000 10.000 10.000 2524.751 797.942 43.75 841.692 56.05 112.10 6.56 2.409 1.787 0.922

Total cost

M€/y

10.140

9.514

9.185

8.970

8.474

kt/y (%) (–)

produced. This number corresponds to CO2 emissions reduction by 54 kt CO2 per year. 10% reductions in non-renewable fossil fuels is achieved. Results for increasing TSR are also shown in Table 5.

Finally, the maximum thermal substitution rate, that is profitable to the organization, is estimated and the solution is also shown in Table 5. The maximum TSR is 32%. The cost savings are of the or-

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I.K. Kookos et al. / Fuel 90 (2011) 1277–1284

Table 6 Summary of approximate sensitivity analysis. Parameter

NCV CEF StO2 UC VC eFCI mF,U

References

Alternative fuel RDF

SS

TDF

MBM

22.201 +3.894 0 +8.850 +0.885 +1.180 8.684

13.666 +2.797 0 +7.080 +0.885 +1.180 3.021

18.220 +1.369 0 +3.540 +1.180 +1.770 7.530

9.680 0 0 +2.360 +1.180 +1.770 6.250

der of M€1.67 per annum while the reduction in the fossil fuel consumption is 17% and the non-biogenic CO2 emissions reduction 112 kt CO2 per year. In Table 6, a summary of an approximate sensitivity analysis is shown. The mathematical formulation includes discrete variables and as a result the sensitivity measures are only rough approximations. The sensitivity analysis was performed for the maximum TSR and is based on the calculation of the following sensitivity measures:

soi ¼

ðDCost=Costo Þ ðDhi =hNi Þ

ð32Þ

where h is any parameter of the formulation, superscript o denotes the optimal solution and superscript N the nominal value. D denotes the difference between the final and initial values. The values of the sensitivity coefficients so for the most important parameters of the mathematical model, that are related to the characteristics of the alternative fuels, are given in Table 6. It is important to observe that economics is very sensitive to the net calorific value (NCV) of the waste derived fuels and to the unit cost (UC) of the alternative fuels and maximum quantities available (mF,U). It is much less sensitive to the fixed capital cost (eFCI), to the variable cost (VC) assumed as well as to the carbon emission factor (CEF). It is therefore imperative that, in order to minimize the potential risks associated with the projects related to the co-firing of waste derived fuels and fossil fuels, that the thermal characteristics and available quantities of the available alternative fuels are carefully determined. 5. Conclusions In this work, a mathematical programming methodology is presented for the simultaneous selection of raw materials, fossil fuels and waste derived fuels to be fed in a cement production facility in order to improve process economics while meeting all quality and operational objectives. The proposed model can be used as the basis for building case specific mathematical formulations that incorporate additional constraints that are specific to any actual industrial installation. The proposed formulation is used in order to solve a particularly demanding case study where the selection among five alternative raw materials and 6 fuels is considered. The results show that the proposed novel methodology can be used to answer important and multifaceted questions arising in the cement industry which is characterized by fierce national and international competition and limited resources. Furthermore, it is shown that the economic and environmental benefits can be significant. Acknowledgement Dr. Yiannis Pontikes is thankful to the Research Foundation – Flanders for the post-doctoral fellowship.

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