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Optimization of Cement Production and Hydration for Improved Performance, Energy Conservation, and Cost

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Title:
Optimization of Cement Production and Hydration for Improved Performance, Energy Conservation, and Cost
Creator:
Tao, Chengcheng
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (134 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering
Civil and Coastal Engineering
Committee Chair:
MASTERS,FORREST J
Committee Co-Chair:
FERRARO,CHRISTOPHER CHARLES
Committee Members:
GURLEY,KURTIS R
DEMPERE,LUISA AMELIA

Subjects

Subjects / Keywords:
cement -- kiln -- metaheuristic -- optimization -- vcctl
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Civil Engineering thesis, Ph.D.

Notes

Abstract:
This dissertation presents a new computational framework to optimize the chemistry of cements and thermal energy of cement rotary kiln to achieve user defined performance criteria for strength, materials cost, energy consumption, durability, and sustainability. Pareto optimization reveals the inherent tradeoff between modulus of elasticity, time of set, and kiln temperature and is applied to objectively rate cements in these contexts. A scalable approach built on particle swarm optimization of the NIST Virtual Cement and Concrete Testing Laboratory (VCCTL) is successfully demonstrated for about 150,000 combinations of cement phase distributions and water to cement ratios, using about 10% of the VCCTL runs required to fully enumerate the discretized solution space. VCCTL was also coupled with a virtual cement plant (VCP) to study the cement production lifestyle from the raw feed to the finished product. Clinker production process consumes most of the energy and all of the fuel used in cement industry, and the rotary kiln wastes the most heat in the plant. A one dimensional physical chemical model incorporating clinker chemistry and thermodynamics within a rotary cement kiln was developed to characterize the temperature profiles of freeboard gas, bulk bed, internal wall and shell of the cement kiln and clinker mass fractions under given kiln inlet conditions. Predictions are verified by comparing them with published experimental data. The clinker mass fractions at the kiln outlet are then imported into the VCCTL to simulate hydration and predict mechanical performance for hardened mortar and concrete. Metaheuristic optimization algorithms were paired with the kiln cement virtual model on the HiPerGator High Performance Computer (HPC) at the University of Florida. Insofar as VCCTL VCP accurately models cement hydration and the resultant mechanical and thermal properties, the proposed approach opens a new pathway to optimally proportion and blend raw materials (and eventually, waste byproducts) to reduce production costs, extend the life of a quarry, or reduce a plant carbon footprint. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2017.
Local:
Adviser: MASTERS,FORREST J.
Local:
Co-adviser: FERRARO,CHRISTOPHER CHARLES.
Statement of Responsibility:
by Chengcheng Tao.

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UFRGP
Rights Management:
Applicable rights reserved.
Classification:
LD1780 2017 ( lcc )

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OPTIMIZATION OF CEMENT PRODUCTION AND HYDRATION FOR IMPROVED PERFORMANCE, ENERGY CONSERVATION, AND COST By CHENGCHENG TAO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 201 7

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201 7 Chengcheng Tao

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To my family

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4 ACKNOWLEDGMENTS I would like to express my deepest gratitude and sincere appreciation to my advisor Prof. Forrest Masters for accepting me into Ph.D. program and providing me academic guidance for the last three years study at University of Florida. Without his support, this dissertation and research would not come to realization His expert knowledge and attitude on research and work are great inspiration to be. It is a great privilege to work with him. I also sincerely appreciate the help I received from Dr. Christopher Ferraro and his Ph.D. student Mr. Benjamin Watts My Ph.D. research is a collaborative project with them. Dr. Ferraro and Ben have always been very supportive for the last three years in regards of our research and experiment Without their support these achievements would not be possible I am grateful to my committee members: Prof. Kurtis Gurley from the Department of Civil and Coastal Engineering, and Dr. Luisa Amelia Dempere from the Depart ment of Materials Science and Engineering I would like to thank Prof. Anthony Straatman and Mr. Christopher M. Csernyei from University of Western Ontario for their help on the development of cement kiln model I also want to acknowledge the support of t his research by the Florida Department of Transportation (FDOT). I could not have asked for better labmates than Mr. Pedro Fernndez Cabn and Mr. Ryan C atarelli I want to thank them for many interesting conversation s on research and life It has been a great pleasure working with them in the same lab and office. In addition, I want to give my special thanks to my parents. They have been always supportive for my whole life. I would not be here today without their patience, encouragement a nd love.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 10 ABSTRACT ................................ ................................ ................................ ................................ ... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 16 1.1 Background ................................ ................................ ................................ ....................... 16 1.2 Organizati on of Dissertation ................................ ................................ ............................. 18 2 BACKGROUND ................................ ................................ ................................ .................... 21 2.1 Introduction ................................ ................................ ................................ ....................... 21 2.2 Cement P roduction ................................ ................................ ................................ ........... 21 2.3 Formulation of 1D Physical chemical Model of a Rotary Cement Kiln .......................... 24 2.3.1 Heat Transfer Equations ................................ ................................ ......................... 25 2.3.2 Clinker Formation ................................ ................................ ................................ .. 28 2.3.3 Heat Balance ................................ ................................ ................................ ........... 31 2.4 Cement Hydration Modeling ................................ ................................ ............................ 32 2.5 Optimization Techniques in Cement and Concrete ................................ .......................... 33 3 METAHEURISTIC ALGORITHMS APPLIED TO VIRTUAL CEMENT MODELING ... 46 3.1 Overview ................................ ................................ ................................ ........................... 46 3.2 Methodology ................................ ................................ ................................ ..................... 46 3.3 Cement Optimization based on Metaheuristic Algorithms ................................ .............. 4 9 3.3.1 Overview ................................ ................................ ................................ ................ 49 3.3.2 Pareto Front Generation Applying Particle Swarm Optimization .......................... 51 3.3.3 Pareto Front Generation Applying Genetic Algorithm ................................ .......... 53 3.4 Case Studies ................................ ................................ ................................ ...................... 54 3.4.1 Example 1: Single Objective Optimum for Modulus ................................ ............. 54 3.4.2 Example 2: Bi objective Pareto Front for Modulus and Time of Set ..................... 55 3.4.3 Example 3: Tri objective Optimization of Modulus, Time of Set and Heat Proxy ................................ ................................ ................................ ............................ 56 3.5 Remarks on Convergence ................................ ................................ ................................ 57 3.6 Potential for Objective Rating of Cement Q uality ................................ ........................... 59 3.6.1 Cement Scoring System ................................ ................................ ......................... 59

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6 3.6.2 Scoring System Applied to Example 3 ................................ ................................ ... 60 3.7 Implication ................................ ................................ ................................ ........................ 62 4 PHYSICAL CHEMICAL MODELING OF A ROTARY CEMENT KILN ......................... 85 4.1 Model Validation ................................ ................................ ................................ .............. 85 4. 1.1 Solution Methodology ................................ ................................ ............................ 85 4.1.2 Results and Discussion ................................ ................................ ........................... 87 4.2 Model Modification ................................ ................................ ................................ .......... 88 4.2.1 CO 2 Mass Fraction ................................ ................................ ................................ 88 4.2. 2 Raw Meal and Fuel Costs ................................ ................................ ....................... 88 5 OPTIMIZATION OF COUPLED VCP/VCCTL MODEL ................................ .................. 101 5.1 Coupling VCP and VCCTL Modeling ................................ ................................ ........... 101 5.1.1 Input Generation ................................ ................................ ................................ ... 101 5.1.2 Input Range Testing ................................ ................................ ............................. 104 5.1.3 Schematic of coupled VCP VCCTL model ................................ ......................... 104 5.1.4 Case Studies ................................ ................................ ................................ .......... 104 5.2 Optimization of VCP VCCTL Model ................................ ................................ ............ 105 5.2.1 Cost vs. Modulus ................................ ................................ ................................ .. 105 5.2.2 CO 2 Emissions vs. Modulus ................................ ................................ ................. 106 5.2.3 Cost vs. CO 2 Emissions vs. Modulus ................................ ................................ ... 106 6 CONCLUSIONS AND RECOMMENDATIONS ................................ ............................... 125 LIST OF REFERENCES ................................ ................................ ................................ ............. 126 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 134

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7 LIST OF TABLES Table page 2 1 Raw meal components and clinker phases ................................ ................................ ......... 37 2 2 Thermal information for clinker reaction (Darabi, 2007) ................................ .................. 38 2 3 Reaction rate, pre exponential factors and activation e nergies for clinker reactions ........ 39 2 4 Production rates for each component of reactions ................................ ............................. 40 3 1 Lower and upper bounds of VCCTL inputs ................................ ................................ ...... 64 3 2 Database column identifier. ................................ ................................ ............................... 65 3 3 Comparison of computational cost ................................ ................................ .................... 66 3 4 First 30 non dominated solutions for min min max case (w/c=0.25) ............................... 67 4 1 prediction ................................ ................................ ................................ ........................... 90 4 2 ................. 91 4 3 Unit price for raw material of cement plant ................................ ................................ ....... 92 5 1 Comparison of VCP raw meal mass fraction from different input generation approaches ................................ ................................ ................................ ........................ 108 5 2 Comparison of VCP clinker mass fraction from different input generation approaches ................................ ................................ ................................ ........................ 109 5 3 Expanded VCP material inp industrial kilns ................................ ................................ ................................ .................. 110 5 4 Comparison of VCP cases with different material input range ................................ ....... 111 5 5 Coupled VCP VCCTL results with 53,700 inputs ................................ .......................... 113

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8 LIST OF FIGURES Figure page 2 1 Schematic of rotary cement kiln with four regions ................................ ............................ 41 2 2 Cross section of rotary cement kiln ................................ ................................ ................... 42 2 3 Heat transfer among internal wall, freeboard gas and solid bed ................................ ........ 43 2 4 3D initial microstructure from VCCTL ................................ ................................ ............. 44 2 5 Algorithm of VCCTL ................................ ................................ ................................ ........ 45 3 1 Relationship between kiln temperature and C 3 S/C 2 S ................................ ........................ 68 3 2 Results of VCCTL simulations ................................ ................................ .......................... 69 3 3 Potential discrete combinations of cement and concrete ................................ ................... 70 3 4 Elastic modulus vs. iteration wi th PSO ................................ ................................ .............. 71 3 5 Distribution of cement phases for optimum with singe objective PSO ............................. 72 3 6 Pareto fronts of four different bi objective optimization scenarios without constraints compared with the data envelope ................................ ................................ ....................... 73 3 7 Comparison of PSO and GA of bi objective optimization. ................................ ............... 74 3 8 3D surface mesh of Pareto front from non dominated solution (red dots) for the Min (Time of set) Min (C 3 S/C 2 S) Max (E) case with different water cemen t ratios .......... 75 3 9 (a) 3D surface mesh of Pareto front from non dominated solution (red dots) for the Max Max Max case (b) 3D surface mesh of Pareto front from non dominated solution (red dots) for the Min Min Min case (c) 3D surface of Pareto fronts for the combined cases ................................ ................................ ................................ .................. 76 3 10 Consolidation ratio and Improvement ratio for population size = 300 .............................. 77 3 11 Convergence gener ation, number of simulations, number of optimal solutions vs. population size ................................ ................................ ................................ ................... 78 3 12 Process of deciding convex hull for evaluat ion cement data ................................ ............. 79 3 13 Marginal probability of non exceedance with regard to time of set and heat proxy for E 20 GPa cements ................................ ................................ ................................ ......... 80 3 14 Different w/c with single cement chemistry on the marginal probability of non exceedance curve ................................ ................................ ................................ ............... 81

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9 3 15 Effect of w/c on scores with regard to time of set under single chemistry ........................ 82 3 16 H ermite and Beta distribution fitting for reduced data ................................ ...................... 83 3 17 Joint score of cement ................................ ................................ ................................ ......... 84 4 1 ........................... 93 4 2 Species mass fractions along cement kiln without bed height adjustment compared with published data ................................ ................................ ................................ ............ 94 4 3 Species mass fractions along cement kiln with bed height adjustment compared with published data ................................ ................................ ................................ .................... 95 4 4 Temperature profiles in cement kiln from heat transfer. ................................ ................... 96 4 5 Mass fraction of CO 2 emissions from kiln model ................................ .............................. 97 4 6 Relationship between 7 day modulus (GPa) and cost of raw meal ($/Ton) under different gas peak temperature ................................ ................................ ........................... 98 4 7 Relationship between 7 day modulus (GPa) and cost of fuel ($/Ton) under different gas peak temperature ................................ ................................ ................................ .......... 99 4 8 Relationship between 7 day modulus(GPa) and total cost under different g as peak temperature ................................ ................................ ................................ ...................... 100 5 1 Distribution of inputs for VCP generated from fixed intervals ................................ ....... 116 5 2 Distribution of raw meals derived from fixed interval inputs of VCP ............................ 117 5 3 Distribution of input for VCP generated from uniformly distributed inputs ................... 118 5 4 Distribution of raw meals derived from uniformly distributed inputs of VCP ................ 119 5 5 Example of gas temperature input profile for VCP ................................ ......................... 120 5 6 Flow of coupled VCP VCCTL model ................................ ................................ ............. 121 5 7 Pareto fronts of four different bi objective optimization scenarios on E vs. cost of raw meal compared with the data envel ope ................................ ................................ ..... 122 5 8 Pareto fronts of four different bi objective optimization scenarios on E vs. CO 2 emissions from limestone compared wit h the data envelope ................................ ........... 123 5 9 Pareto fronts of tri objective optimization scenarios on E vs. CO2 emissions from limestone vs. cost ................................ ................................ ................................ ............. 124

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10 LIST OF ABBREVIATIONS A cgb Convection area internal gas to bulk bed (m) A cgw Convection area internal gas to internal wall (m) A cwb Conduction area internal wall to bed (m) A rgb Radiation area internal freeboard gas to bulk bed (m) A rgw Radiation area internal freeboard gas to internal wall (m) A rwb Radiation area internal wall to bulk bed (m) A s Area of bed segment (m) A sh Area of steel s hell (m) A i Initial mass fraction of Al 2 O 3 at inlet of the kiln A j Pre exponential factor for j th reaction (1/s) AR Alumina ratio C p b Specific heat of bulk bed (J/kg.K) C Tmax Maximum coating thickness (m) D e Hydraulic diameter of kiln (m) D Diameter of kiln (m) d n Normalized Pareto front distance E j Activation energy for j th reaction (J/mol) E 0 Minimum allowable modulus F i Initial mass fraction of Fe 2 O 3 at inlet of kiln f i Objective function h cgb Convection heat transfer coefficient freeboard gas to bed (W/m 2 .K) h cgw Convection heat transfer coefficient gas to internal wall (W/m 2 .K) h cwb Conduction heat transfer coefficient from wall to bed (W/m 2 .K)

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11 h csh Convective heat transfer coefficient from shell to air (W/m 2 .K) k a Thermal conductivity of air (W/m.K) k b Thermal conductivity of bulk bed (W/m.K) k g Thermal conductivity of fluid (W/m.K) k 1 Reaction rate CaC O 3 (1/s) k 2 Reaction rate C 2 S (1/s) k 3 Reaction rate C 3 S (1/s) k 4 Reaction rate C 3 A (1/s) k 5 Reaction rate C 4 AF (1/s) LSF Lime saturation factor P c Probability of non exceedance Q cgb Convection heat transfer freeboard gas to bulk bed (W/m) Q cgw Convection heat transfer freeboard gas to internal wall (W/m) Q cwb Conduction heat transfer in ternal wall to bulk bed (W/m) Q rgb Radiation heat transfer freeboard gas to bulk bed (W/m) Q rgw Radiation heat transfer freeboard gas to internal wall (W/m) Q rwb Radiation heat transfer internal wall to bulk bed (W/m) Heat gained by bulk bed due to heat transfer (W/m) q c Heat generated by chemical reactions (W/m 3 ) R g Universal gas constant (J/mol.K) R Internal radium of kiln (m) S comb Combining score S i Initial mass fraction of SiO 2 at inlet of the kiln

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12 SR Silica ratio T g Freeboard gas temperature (K) T b Bulk bed temperature (K) T w Internal wall temperature (K) T o Temperature of atmosphere (K) T sh Temperature of steel shell (K) Velocity of i th particle at k th generation v s Velocity of bulk bed (m/s) Position of i th particle at k th generation Y n Mass fraction of n th species b Bulk bed thermal diffusivity (m 2 /s) g Absorptivity of freeboard gas Angle of repose (rad) b Emissivity of bulk bed g Emissivity of freeboard gas sh Emissivity of steel shell w Emissivity of internal wall Angle of fill of the kiln (rad) g Dynamic viscosity of freeboard gas (s/m 2 ) Degree of solid fill Rotational speed of kiln (rad/s) g Density of freeboard gas (kg/m 3 ) s Density of solids (kg/m 3 )

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13 Stefan Boltzmann constant g Kinematic viscosity of freeboard gas (m 2 /s) H CaCO3 Heat of reaction CaCO 3 (J/kg) H C2S Heat of reaction C 2 S (J/kg) H C3S Heat of reaction C 3 S (J/kg) H C3A Heat of reaction C 3 A (J/kg) H C4AF Heat of reaction C 4 AF (J/kg)

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14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OPTIMIZATION OF CE MENT PRODUCTION AND HYDRATION FOR IMPROVED PERFORMANCE, ENERGY CONSERVATION, AND COST By Chengcheng Tao August 201 7 Chair: Forrest J. Masters Cochair: Christopher C. Ferraro Major: Civil Engineering This dissertation presents a new computational framework to optimize the chemistry of cements and thermal energy of cement rotary kiln to achieve user defined performance criteria for strength, materials cost, energy consumption, durability, and sustainability. Pareto optimization reveals the inherent tradeoff between modulus of elasticity, time of set, and kiln temperature and is applied to objectively rate cements in these contexts. A scalable approach built on particle swarm optimization of the NIST Virtual Cement and Concrete Testing Laboratory (VCC TL) is successfully demonstrated for ~150,000 combinations of cement phase distributions and water cement ratios, using ~10% of the VCCTL runs required to fully enumerate the discretized solution space. VCCTL wa s also coup led with a virtual cement plant (V CP) to study the cement production lifestyle from the raw feed to the finished product. Clinker production process c onsumes most of the energy and all of the fuel used in cement industry, and the rotary kiln wastes the most heat in the plant. A one dimensi onal physical chemical model incorporating clinker chemistry and thermodynami cs within a rotary cement kiln wa s developed to characterize the temperature profiles of freeboard gas, bulk bed, internal wall and shell of the cement kiln and

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15 clinker mass fract ions under given kiln inlet conditions. Predictions are verified by comparing them with published experimental data. The clinker mass fractions at the kiln outlet are then imported into the VCCTL to simulate hydration and predict mechanical performance for hardened mortar and concrete. Metaheuristic optimization algorithms were paired with the kiln cement virtual model on the HiPerGator High Performance Computer (HPC) at the University of Florida. Insofar as VCCTL/VCP accurately models cement hydration and the resultant mechanical and thermal properties, the proposed approach opens a new pathway to optimally proportion and blend raw materials (and eventually, waste byproducts) to reduce production costs, extend the life of a on footprint.

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16 CHAPTER 1 1 INTRODUCTION The computational framework presented in this dissertation applies multi objective metaheuristic optimization to virtual cement and virtual cement plant modeling. It is unique to connect metaheuristic algorithms with models of cement production and cement hydration. The optimization algorithms guide the search for optimal cements based on their performance, which would save more computational expense than blind search. It serves as a quantitative optimization tool to s tudy energy efficiency measures within cement plants that conserve energy, increase cement productivity, and decrease greenhouse gas emissions. It also provides guidance o n the design of raw material distribution and cement phases to optimize material cost and ensure competitive performance of the materials. 1.1 B ackground Portland cement concrete is widely used in the global construction industry (A tcin, 2000; Mindess & Young, 1981) because of its flexibility in civi l engineering applications and the widespread availability of its constituent materials; however there is a growing need to reduce the energy costs and environmental impact associated with cement production (Romeo, Catalina, Lisbona, Lara, & Martnez, 2011; Worrell, Kermeli, & Galitsky, 2013; Zhang et al., 2011) From an operational perspective, the goal is to increase energy efficiency without sacrificing productivity. Plants have incorporated efficiency measures during raw meal preparation, clinker production, and finish grinding among other areas (W orrell et al., 2013) For example, p rocess knowledge based systems (KBS) have been applied to the energy management and process control during clinker production e.g., the predictive control system described in Caddet (2000a). Also, switching from coal to natural gas as the fuel for the cement kiln has been shown

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17 to provide higher flame temperature, higher levels of clinker production (5 10%), lower fuel consumption, lower build ups and dust losses (Akhtar, Ervin, Raza, & Abbas, 2013) Due to the complexity of the reactions of cement hydration and scale of cement plant, full scale experimental testing for cement properties and energy cost within the production are costly and impractical. Therefore, there is an increasing need for the development of computational modeling for cement and cement plant Ferraris, Garboczi, Martys, & Stutzman, 2004; Garboczi, Bullard, & Bentz, 2004; Hain & Wriggers, 2008; Vallgrda & Redstrm, 2007) The current study applies the Virtual Cement and Concrete Testing Laboratory (VCCTL) which is available for commercial use from The National Institute of Stan dards and Technology (NIST) (Bullard, 2014) VCCTL incorporates microstructural modeling of Portland cement hydration and supports the predicti on of different properties of hydrated products. For computational modeling both in cement and cement plant, the number of control parameters is sufficiently large making it impossible to analyze all combinatorial cases. Thus, the problem of identifying o ptimal mixtures is not possible without introducing techniques that require a smaller sample space Some statistical methods have been used to conduct the optimization for high performance concrete and cement (Ahmad & Alghamdi, 2014; Lagergren, Snyder, & Simon, 1997; MJ Simon, 2003; M Simon, Snyder, & Frohnsdorff, 1999) ; however, these methods have some difficulties in solving large discrete problems with multi objective optimization problems due to computational limita tions. C ement plant models have also been investigated to simulate heat and chemistry in cement production (Barr, 1986; C. Csernyei & Straatman, 2016; Darabi, 2007; S. Q. Li, Ma, Wan, & Yao, 2005; Martins, Oliveira, & Franca, 2002; Mastorakos et al., 1999; K. Mujumdar &

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18 Ranade, 2006; Sadighi, Shirvani, & Ahmad, 2011; Spang, 1972) These models predicted the behavior cement plant with respect to heat transfer and clinker formation inside the cement rotary kiln considering given kiln conditions and raw material inputs. During the last two decades, metaheuristics techniques have bee n extensively applied to complicated optimization problems in different fields (Collins, Eglese, & Golden, 1988; Jaumard, OW, & Simeone, 1988; Nissen, 1993; Osman, 1995; Pirlot, 1992; Rayward Smith, Osman, Reeves, & Smith, 1996; Sharda, 1994; Stewar t, Liaw, & White, 1994; Vo, Martello, Osman, & Roucairol, 2012) The algorithms employ strategies that guide a subordinate heuristic method to find the near optimal solution efficiency by intelligently searching space with different strategies (Osman & Laporte, 1996) Among these metaheuristic methods, two important and widely used computational methods that deal with the engineering optimization proble ms are the particle swarm optimization (PSO) (Hu, Eberhart, & Shi, 2003; L. Li, Huang, & Liu, 2009; L. Li, Huang, Liu, & W u, 2007; Shi, 2001) and the genetic algorithm (GA) (Goldberg & Samtani, 1986; Rajeev & Krishnamoorthy, 1992; Wu & Chow, 1995) They are both pattern search techniques, which do not need to calculate the gradient s of objective functions to optimize using methods such as quasi Newton or gradient descent (Bonnans, Gilbert, Lemarchal, & Sagastizbal, 2006; Press, Teukolsky, Vetterling, & Flannery, 2007) This dissertation will show how metaheuristic algorithms are applied for discrete problems matching the discrete input data required by VCCTL. 1.2 Organization of Dissertation Chapter 2 provides a brief summary of the background of the Portland cement composition and hydration mechanics inside VCCTL and optimization methods applied on cement and concrete. This chapter also reviews the literature relevant to the development of computational model s for rotary cement kiln.

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19 Chapter 3 discusses the metaheuristic optimization algorithm s applied to Portland cement and evaluation of optimal solutions. Single objective and multi objective optimization cases with Pareto analysis are demonstrate d on Portlan d cements. Convergence is discussed to assist users replicating this approach. Finally, we demonstrate that tri objective optimization is a flexible and objective tool to rate cements and offer remarks on the potential of this approach to solve much large r combinatorial problems arising from the introduction of other variables such as cement fineness and aggregate proportions. Chapter 4 discusses the virtual cement plant (VCP) with a one dime nsional physical chemical model including clinker chemistry and he at transfer within a rotary cement kiln Formulations from previously developed c omputational fluid dynamics (CFD) modeling of temperature profiles and calcination of raw meal into cement clinkers that happened in solid bed of cement kilns are integrated t o form the model. Predictions of the model are verified by comparing them with published experiment data and Bogue calculation in Portland cement clinker ( Bogue, 1929 ) Chapter 5 discusses the coupling of VCP and VCCTL model by importing the ou t put of the cement kiln model into VCCTL and run ning the integrated VCP VCCTL model on HiPerGator High Performance Computer (HPC) at the University of Florida Metaheu ristic algorithms a re applied on the integrated model to optimize energy consumption, cem ent strength, CO 2 emission s and production cost. Pareto fronts are plotted to show the trade off solutions between energy, price and greenhouse gas emissions. Chapter 6 summarizes all the research reported in this dissertation on optimization of virtual cement and virtual cement plant and provides recommendations for blending raw materials to reduce production cost, increase sustainability and extend life of a quarry.

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20 Ch allenges and limitations are also present for future studies to continue the advanceme nt of the proposed methods

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21 CHAPTER 2 2 BACKGROUND 2.1 Introduction This Cha pter describes cement production modeling, cement hydration modeling and current optimization techniques in cement modeling. 2.2 Cement Production Portland cement is the most common type of cement used in construction worldwide because of its affordability and the widespread availability of its constituent materials (e.g., limestone and shale). (Mindess & Young, 1981; Watts, 2013) It is produced from the grinding of clinker, which is produced by the calcination of limestone and other raw minerals in a cement rotary kiln. Combining Portland cement with water causes a set of exothermic hydraulic chemical reactions that result in hardening and ultimately the curing of placed concrete. According to United States Geolo gical Survey (USGS), U.S. cement and clinker production in 2015 was 82.8 million tons and 75.8 million tons respectively U.S. ready mixed concrete production is 325 million tons (Worrell et al., 2013) The production of cement and concrete consumes a significant amount of energy. The associated energy assumption accounts for 20 40 % of the total cost (Chatziaras, Psomopoulos, & Themelis, 2016; Worrell et al., 2013) In 2008, the U.S. cement i ndustry spent $1.7 billion on energy alone with electricity and fuel cost ing $0.75 billion and $0.9 billion respectively Cement production contributes 4% of the global industrial carbon dioxide (CO 2 ) emission s Among the emission s 40% CO 2 comes from the consumption of fossil fuels, 50% comes from calcination/decomposition of limestone inside the cement kiln and 10% comes from transportation of raw mea l and electricity consumption (Benhelal, Zahedi, Shamsaei, & Bahadori, 2013) During the cement and concrete production, clinker production process inside the cement rotary kiln consumes more than 90% o f the total

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22 energy use and all of the fuel use. For the modern cement plan t coal and coke have become principal fuel which took the place of natural gas in 1970s (Worrell et al., 2013) Currently, industry is seeking different energy efficiency technologies to reduce these energy costs The challenge lies in r educ ing production costs and energy consumption without negatively affectin g product quality (Worrell et al., 2013) measure d the energy efficiency through multiple technologies including finer raw meal grin ding, multiple preheater stages, combustion improvement, lower lime saturation factor, cement kiln shell heat loss reduction, location optimization of cement factory for transportation cost reduction and high efficient f acility such roller mills, fans and motors which means there is ample room for energy efficiency improvement Among all of the energy efficient technologies in cement production fuel combustion improvement is most important because it costs most energy (>50%) and produces most emission s (>40%). There are two types of rotary cement kilns: wet and dry. Wet kilns are typical ly longer (200 m) than dry kilns (50 100 m) in order to consider evaporation of water (C. M. Csernyei, 2016) Dry typ e rotary kilns are more thermally efficient and common in industry (Worrell et al., 2013) There are four regions in a kiln: Preheat ing/Drying, Calcining / Decomposition, Burning/Clinkerizing, and Cooling (Peray & Waddell, 1986) Precalciners are typically utilized to dry ki lns to improve thermal efficiency, which allows for shorter kilns. In this dissertation, dry type rotary kilns are modeled. Prior research has produced mathematical models to simulate thermal energy within the cement kiln and clinker formation to characte rize the operation parameters, temperature profiles, clinker formation and energy consumption in the design. (Akhtar et al., 2013; Atmaca & traatman, 2016; C. M. Csernyei, 2016; K. S. Mujumdar,

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23 Ganesh, Kulkarni, & Ranade, 2007; Nrskov, 2012; Sadighi et al., 2011; Saidur, Hossain, Islam, Fayaz, & Mohammed, 2011; Spang, 1972; Stadler, Poland, & Gallestey, 2011) Due to the complexities of rotary kiln modeling, there is no single, universal model developed in research or commercial use. The oldest cement kiln model developed by (Spang, 1972) is a dynamic model that predicts the temperature file of freeboard gas, bulk bed and internal wall and the species compositions of each clinker pr oduct as they progress along the state solution inside the kiln. The formulations of wall temperature profiles and species mass fractions are function of time. Partial differential equat ions are built to calculate temperature and species mass fraction at different stage. For models applying a steady state solution, there exists two types of one dimensional models (K. Mujumdar & Ranade, 2006) The firs t type is a two point boundary value problem, where the inlet temperature profiles of freeboard gas and bulk bed are given (C. Csernyei & Straatman, 2016; S. Q. Li et a l., 2005; Martins et al., 2002; K. Mujumdar & Ranade, 2006; Sadighi et al., 2011; Spang, 1972) From the solution of a series of ordinary differential equations, the temperature profiles and species mass fraction al ong the kiln are solved numerically. The second type incorporates coupled the three dimensional CFD models of burner for freeboard gas profile and clinker chemistry due to the complexity of three dimensional nature of flow generated from a burner (Barr, 1 986; Darabi, 2007; Mastorakos et al., 1999; K. S. Mujumdar, Arora, & Ranade, 2006) In this study a steady state one dimensional kiln model is applied because of its flexibility of parameters and computational availability for solvers in MATLAB paired with high performance cluster. Mathematical f ormulations are built based on Sadighi, Mujumdar and

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24 work, which are covered in Section 2. 3 This one dimensional physical chemical kiln model is developed to simulate the behavior of virtual cement plant (VCP). VCP was then coupled with VCCTL a nd metaheuristic optimization tool for an integrated optimized computational model that predicts measures of performance and sustainability. 2.3 Formulation of 1D Physical chemical Model of a Rotary Cement Kiln A Rotary cement kiln is a large piece of equipment converting raw meal to cement clinkers. Figure 2 1 shows the schematic of rotary cement kiln (C. M. Csernyei, 2016) Raw meal enters at the higher end with a certain solid flow rate. Fuel (coal, natural gas or petroleum coke) enters at the lower end. There are four main processes i n the rotary kiln: Drying, calcining, burning and cooling (Peray & Waddell, 1986) First, the raw materials are preheated a nd dried to reduce moisture of the mixture for calcination. Then the limestone (CaCO 3 ) is calcined into calcium oxide (also known as free lime) and carbon dioxide (CO 2 ). After the calcination, a series of solid solid and solid liquid chemical reactions hap pens to form clinker. During this burning process, the temperature inside the kiln reach es its highest point Alite (C 3 S) and belite (C 2 S) are formed from fr ee lime. Coating also happens in this stage because of the presence of liquid. After burning proces s, the hot clinkers are transported into a cooler for fast cooling. After that, the clinkers are grinded with cement mill and added some additives (such as gypsum and limestone) based on the requirement of users to get final cement. Table 2 1 shows the name and chemical formula of raw meal and clinkers. In Portland cement production, r otary kilns are considered as the core for cement manufacturing plants. At the entry of the kiln, grinded and homogenized raw material comprised of limestone (CaCO 3 ), alumina (Al 2 O 3 ), iron (Fe 2 O 3 ), silica (SiO 2 ) and small amount of other minerals pass through a preheater for initial calcination. I nside the kiln, the formation

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25 of cement clinker occurs from a series of chemical reactions including limestone calcination/ decomposition and clinker formation. Clinker is then cooled at the exit of the kiln and grinded to fine powder for package. During t he entire cement production process, the production of clinker inside cement kiln consumes most thermal energy, which is about 90% of the total energy (Atmaca & Yumru 50 60% of the energy consumption is attributed to the combustion of fuel (Kabir, Abubakar, & El Nafaty, 201 0) Multiple 2D and 3D physical chemical model s exist in the literature, e.g., (Barr, 1986; Darabi, 2007; Mastorakos et al., 1999; K. S. Mujumdar et al., 2006) More recent research has focused on creating a simplified 1D model which is more computational ly efficient (C. Csernyei & Straatman, 2016; S. Q. Li et al., 2005; Martins et al., 2002; K. Mujumdar & Ranade, 2006; Sadighi et al., 2011; Spang, 1972) The current study applies the 1D kiln model described in (C. M. Csernyei, 2016; K. Mujumdar & Ranade, 2006) fr om University of Western Ontario. It couples the heat ba lance equation and clinker chem ical reaction rate equa tions to calculate the temperatu re of the different component s of the kiln and the mass fraction for each phase of clinker production at steady st ate. 2.3.1 Heat Transfer Equations For the kiln model, t hree types of heat transfer: radiation, convection and conduction happen inside and outside the kiln simultaneously. The interactive heat transfer happens between the gas phase and the solid phase, the gas phase between the wall, the solid and the wall, which is shown as cross section of the kiln in Figure 2 2 A group of heat equations including conduction from inter nal wall to solid bed, convection from freeboard gas to solid bed, convection from freeboard gas to internal wall, radiation from freeboard gas to solid bed, radiation from freeboard gas to internal wall and radiation from wall to solid have been developed to investigate the heat transfer. Figure 2 3

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26 shows the heat transfer between internal wall, freeboard gas and solid bed inside the cement rotary kiln. First, Equation (2 1 ) describes general energy balance of a steady state, steady flow model. (2 1 ) Equation s (2 2 ) to (2 9 ) show the formulation describing each heat transfer variables inside the kiln ba sed on the previous heat transfer knowledge and numerical models for rotary kiln (Hottel & Sarofim, 1965; S. Q. Li et al., 2005; Martins et al., 2002; K. Mujumdar & Ranade, 2006; K. S. Mujumdar et al., 2006; Tscheng & Watkinson, 1979) The conduction heat transfer happens whe n two objects are in contact. Inside the kiln, conduction happens between the solid and the internal wall from direct contact Q cwb is expressed as the conduction heat transfer between the internal wall and the solid bed. (2 2 ) (2 3 ) Where, A cwb is the conduction area between the internal wall and the solid bed, which is the product of solid bed arc length and kiln length. Convection and radiation areas are calculate d in similar ways. k b is the thermal conductivity of the solid bed. is the rotational speed of the kiln, R is the radius of the of the kiln. All of the parameters are listed at the beginning of this dissertation as List of Abbreviations The radiative heat transfer happens by the emission s of the elec tromagnetic radiation from the high temperature object. Inside the cement rotary kiln, both gas and the internal wall

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27 emit the radiation. Q rwb is expressed as the radiative heat transfer from the internal wall to solid bed (2 4 ) (2 5 ) Q rgb is the radiative heat transfer from the freeboard gas to solid bed. Q rgw is the radiative heat transfer from the freeboard gas to internal wall (2 6 ) (2 7 ) The convectio n heat transfer happens between the object and its environment which happens between the freeboard gas phase and the wall, and between the gas phase and the solid. Q cgb is the convective heat transfer from the freeboard gas to solid bed. Q cgw is the conve ctive heat transfer from the freeboard gas to internal wall. Calculation for h cgb and h cgw are discussed in (C. M. Csernyei, 2016) (2 8 ) (2 9 ) From Equation s (2 2) to (2 9), the total heat flux received by solid bed from internal heat tran sfer is calculated as Equation 2 10 (K. Mujumdar & Ranade, 2006) (2 10 )

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28 From the above equations, the heat transfer between different components is related to each other. The temperature of the wall, the gas phase and the solid phase could not be solved directly from the above equations. 2.3.2 Clinker Formation Cement clinker for m ation is a complex chemical process that numerous chemical reactions happen simultaneously. Each reaction requires a separate thermodynamic condition (Babushkin, Matveev, & Mchedlov Petros n, 1985) Typically, a series of five reactions has been applied to represent the complex chemical reactions inside cement kiln (Bogue, 1929) : CaCO 3 CaO + CO 2 (2 1 1 ) 2CaO +SiO 2 C 2 S (2 1 2) C 2 S + CaO C 3 S (2 1 3) 3CaO + Al 2 O 3 C 3 A (2 1 4) 4CaO + Al 2 O 3 + Fe 2 O 4 C 4 AF (2 1 5) where the primary mineral constituents consist of tricalcium silicate C 3 S (Alite), dicalcium silicate C 2 S (Belite), Tricalcium aluminate C 3 A and tetracalcium aluminoferrite C 4 AF. The main mineral in all of these compounds is calcium oxide CaO, which is acquired from the calcination and decomposition of limestone CaCO 3 Inside the kiln, the solid material flows to the burner end of the kiln through the 2 5 degree of inclination (shown in Figure 2 1 ). H eated freeboard gas flows from the burner end to the entry on the top of solid bed material. From the heat transfer between the hot freeboard gas, solid bed material and internal wall of th e kiln (shown in Figure 2 2 and Figure 2 3 ), a series of complex exothermic and endothermic chemical reactions happens inside the kiln for clinker formation. To simplify the process and make it convenient to analyze, only the major clinker formation chemical reactions (shown in Equation (2 1 1 ) to (2 1 5)) are considered.

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29 Table 2 2 taken from (Darabi, 2007) shows the five major chemical reactions occurring inside the cement kiln, which are used for clinker formation analysis in current model. Differ ent reactions happen at different temperature ranges, which are used to set starting and ending point for each reaction in the model. I n Table 2 2 positive sign indi cates the reaction is endothermic and negative sign indicates the reac tion is exothermic. Equation (2 16 ) from (C. M. Csernyei, 2016; Spang, 1972) gives the heat transfer from chemistry including heat absorbed from 1 st and 3 rd reactions and heat generated from 2 nd 4 th and 5 th reactions. (2 16) Where, A i F i and S i are the input mass fraction for Al 2 O 3 Fe 2 O 3 and SiO 2 is the heat of reaction. k is the reaction rate for j th reaction. Y is the mass fraction for the reactant or product participating in j th reaction. Based on Arrhenius is equation (Arrhenius, 1889) reaction constants for the five chemical reactions inside the kiln are cal culated f rom Equation (2 17 ). (2 17) Where A j is the pre exponential factor for j th reaction (1/s), E j is the activation energy for j th reaction (J/mol). R g is the universal gas constant, which is 8.314 (J/g.mol.K). Table 2 3 list the calculation of reaction rates and values for Aj and Ej, which are taken from (Darabi, 2007; Spang, 1972) Once reaction rates are calculated, the pr oduction rate of each component could be calculated based on the reactions the component participates in For example, CaO is the product of 1st reaction and reacta nt of 2 nd 5 th reaction. Therefore,

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30 production rate for CaO is Table 2 4 lists the reaction rate for all components in the five chemical reactions. Mass fraction of each species could be calculated from material balance equation (2 18) which is from plug flow reactor with constant axial velocity at steady state (Darabi, 2007) (2 18) where R n is the production rate for species n is the solid velocity (m/s) in the kiln. The production rates for the 10 components listed in Table 2 4 are subst ituted into Equation (2 18 ) and normalized with mass of CaO, shown as Equation (2 19) (2 27 ) (2 19) (2 20) (2 21 ) (2 22 ) (2 23 ) (2 24 ) (2 25 ) (2 26 ) (2 27 )

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31 After the equations for mass fraction of each component is done, the temperature of solid bed could be calculated based on the mass fractions and the total heat re ceived by solid bed w hic h is expressed as Equation (2 28 ) (2 2 8 ) The meanings of each variables are given in the List of Abbreviations The production rate for mass fraction of eac h component in the reactions is related to the temperature of so lid bed (Equation (2 16) (2 27 )). And heat received by solid bed is calculated from heat transfer (Equations (2 1) (2 10 )). The heat transfer items and clinker chemistry ite ms are coupled by Equation (2 2 8 ). By solving the ordinary differential equations (2 1 ) to (2 2 8 ), the temperature and the mass fractions of each species inside the kiln could be calculated simultaneously. More importantly, the above equations could be integrated with the metaheuristic method to optimize the factor as the user requests. 2.3.3 Heat Balance Equation (2 29 ) from (C. M. Csernyei, 2016) ) shows the heat balance relation among shell, refractory and coating satisfied for a kiln at steady state. The calculation for shell (C. M. Csernyei, 2016) which will not be explained in detail in t his section. (2 29 ) The heat balance equation is applied to check the accuracy temperature profiles using the Newton Raphson Method, which will be discussed in Chapter 4

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32 2.4 Cement Hydration Modeling The concrete research community has long sought to reduce its reliance on physical testing of Portland cements & Wriggers, 2008; Vallgrda & Redstrm, 2007) however advancem ents in computational modeling (Bentz, 1997; C. Haecker, Bentz, Feng, & Stutzman, 2003; Thomas et al., 2011) have yet to produce a widely accepted, purely numerical approach that performs as reliably and accurately as experimental methods (ASTM C109, ASTM C1702, ASTM C191) One of the longest standing efforts to create a numerical framework is the software known as the Virtual Cement and Concrete Testing Laboratory (VCCTL) which has been available for commercial use from the National Institute of Standards and Technology (NIST) for several years. The study model predicts the thermal, electrical, diffusional, and mechanical properties of cements and mortars from user specified phase distribution, particle size distribution, water/cement ratio (w/c), among other parameters (Bullard et al., 2004) Figure 2 4 and Figure 2 5 illustrates VCCTL model, which is a three stage process: 1. Volume and surface area fractions of the four major cement phases (alite, belite, aluminate and ferrite) are obtained from X ray powd er diffraction, scanning electron microscopy, and multispectral image analysis to create a 3D microstructure of unreacted paste Figure 2 4 that is comprised of Portla nd cement, fly ash, slag, limestone and other cementitious materials 2. Kinetics and thermodynamics of Portland cement hydration are simulated under specified curing conditions including adiabatic and isothermal heating, producing virtual models of the materi al that can be analyzed for multiple properties, including linear elastic modulus, compressive strength, and relative diffusion coefficient (Bentz, 1997) The rate of hydration and resulting products are governed largely by the relative concentrations of the four major consti tuents of Portland cement: alite (C 3 S), belite (C 2 S), aluminate (C 3 A), and ferrite

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33 (C 4 AF). The most reactive compounds are C 3 A and C 3 S. For strength development, although the calcium silicates provide most of the strength in the first 3 to 4 weeks both C 3 A and C 2 S contribute equally to ultimate strength. C 2 S hydrates in a similar way with C 3 S; however, C 2 S hydrates much slower since it is a less reactive compound. Consequently, the amount of heat liberated by the hydration of C 2 S is also lower than the amount of heat C 3 S liberates (Mamlouk & Zaniewski, 1999) Gypsum is introduced into the raw meal to slow the early rate of hydration of C 3 A. 3. Finite element analysis of the resultant virtual microstructure gives the elastic mod ulus (E) (Watts, 2013) In order to validate VCCTL model researchers have analyzed the sensitivity to various inputs for the model, checked errors related with the digital image approximation method (Garboczi & Bentz, 2001) and compared simulated results to plastic and hardened properties of CCRL reference cements (Bentz, Feng, & Stutzman, 2000; Bullard & Stutzman, 2006) Those validation results show VCCTL could simulate hydration and predict strength and other properties quite we ll. 2.5 Optimization Techniques in Cement and Concrete As discussed in previous sections, cement compounds play critical roles in the hydration process. C hanging the proportion of each constituent compound adjusting o t her factors such as particle size or fine ness can vastly change the mechanical and thermal properties of the hydration process, and ultimately the final product. Due to the various factors in cement production and hydration it is necessary and efficient to develop optimal computational models re flecting the effect of each factor and giving directions based on specific performance requirement s instead of conducting large amount s of physical testing.

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34 As the awareness of potential of cement and concrete to achieve higher performance grows, the probl em of designing cement and concrete to exploit the possibilities has become more complex. In the past few years, statistical design of experiments, such as the response surface approach (Ahmad & Alghamdi, 2014; Ghezal & Khayat, 2002; Lagergren et al., 1997; Muthukumar & Mohan, 2004; Patel, Hossain, Sheh ata, Bouzoubaa, & Lachemi, 2004; MJ Simon, 2003; M Simon et al., 1999; Sonebi & Bassuoni, 2013; Soudki, El Salakawy, & Elkum, 2001; Tan, Zaimoglu, Hinislioglu, & Altun, 2005; Xiaoyong & Wendi, 2011) were developed to optimize cement and concrete mixtures to meet a set of performance criteria at the same time with lease computational cost. Those performance criteria w ithin cement and concrete properties include time of set, modulus of elasticity, viscosity, creep and shrinkage, heat of hydration and durability. Considering that cement and concrete mixtures consist of several components, the optimization should be able to take into account several attributes at a time. However, statistical methods become inefficient due to the excessive number of trial batches for each simulation to find optimal solutions. Here we apply a metaheuristic optimization method, which is an it erative searching process that guides a subordinate heuristic by exploring and exploiting the search space intelligently with different learning strategies. O ptimal solutions are found efficiently with this technique. Those methods have had widespread succ ess and become influential methods in solving difficult combinational problems during the last several decades in engineering, mathematics, economics and social science (Collins et al., 1988; Jaumard et al., 1988; Nissen, 1993; Osman, 1995; Osman & Laporte, 1996; Pirlot, 1992; Rayward Smith et al., 1996; Stewart et al., 1994) Some of the most popular metaheuristic algorithms include genetic algorithms,

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35 particle swarm optimization, neutral networks, harmony search, simulated annealing, tabu search, etc (Osman & Laporte, 1996) Particle Swarm Optimization is a population based met aheuristic originally proposed by Kennedy and Eberhart in 1995 (Eberhart & Kennedy, 1995) This metaheuristic algorithm mimics swarm behavior in nature, e.g., the synchronized mov ement of flocking birds or schooling fish It is straightforward to implement and is suitable for a non differentiable and discreditable solution domain (Bonnans et al., 2006; Press et al., 2007) A PSO algorithm guides a swarm of particles as it moves through a search space from a random location to an objective location based on given objective functions. Another important search method is the genetic algorithm (GA), which is developed from principles of genetics and natural selection (Bremermann, 1958; Fraser, 1957) This method was developed by Joh n Holland at the University of Michigan for machine learning in 1975 (Holland, 1975) GA encodes the decision variables of a searching problem with series of strings. The strings c ontain information of genes in chromosomes (Burke & Kendall, 2005) GA analyzes coding information of the parameters. A key factor for this method is working with a population of designs that can mate and create offspring population designs. For this method to work, fitness is used to select the parent populations based on their objective function value, and the o ffspring population designs are created by crossing over the strings of the parent populations. Selection and crossover form an exploitation mechanism for seeking optimal designs. Furthermore, the m utation s are add ed to the string as an element of exploration. A multi objective optimization pro blem (MOOP) considers a set of objective functions. For most practical decision making problems, multiple objectives are considered at the same time to make decisions. A series of trade off optimal solutions instead of a single optimum, is

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36 obtained in such problems (Burke & Kendall, 2005) Those trade off optimal solutions are also called Pareto optimal solutions. For the current cement and concrete mo deling, multi objective optimizations are applied because several performance criteria of cement and concrete need to be considered at the same time. As introduced above, VCCTL require s a number of input variables to execute a complete virtual hydrated cem ent model for analyzing mechanical and material properties. The re are a large number of po tential combinations for inputs (~10 6 ). It takes one hour to run each combination on VCCTL with high performance computing cluster. Therefore, a b lind search for spec ified performance criteria is not practical. M etaheuristic techniques however, provide a reasonable direction for searching through a large feasible domain, which is efficient and suitable for the inputs and outputs from VCCTL. Both PSO and GA solve MOOPs to give a Pareto frontier, which consists of optimal solutions. Elitism strategy (Burke & Kendall, 2005) is applied to ke ep the best individual from the parents and offspring population. Also, the idea of non dominated sorting procedure can be applied to the PSO to solve the MOOP and increase the efficiency of optimization. In this dissertation, metaheuristic algorithms are applied based on VCCLT to solve MOOP in virtual cement.

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37 Table 2 1 Raw meal components and clinker phases Type Name Chemical Formula Raw meal Calcium carbonate CaCO 3 Silicon dioxide (Silica) SiO 2 Aluminium oxide (Shale) Al 2 O 3 F errate oxide Fe 2 O 3 Clinker phases Tricalcium silicate (Alite) C 3 S (3CaO.SiO 2 ) Dicalcium silicate (Belite) C 2 S (2CaO.SiO 2 ) Tricalcium aluminate C 3 A (3CaO.Al 2 O 3 ) Tetracalcium aluminoferrite C 4 AF (4CaO.Al 2 O 3 .Fe 2 O 3 )

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38 Table 2 2 Thermal information for clinker reaction (Darabi, 2007) No. Reaction Temperature Range (K) Enthalpy of Reaction (J/kg) 1 CaCO 3 CaO + CO 2 823 1233 +1.782e6 2 2CaO +SiO 2 C 2 S 873 1573 1.124e6 3 C 2 S + CaO C 3 S 1473 1553 +8.01e4 4 3CaO + Al 2 O 3 C 3 A 1473 1553 4.34e4 5 4CaO + Al 2 O 3 + Fe 2 O 4 C 4 AF 1473 1553 2.278e5 6 Clinker solid Clinker liquid >1553 +6.00e5

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39 Table 2 3 Reaction rate, pre exponential factors and activation energies for clinker reactions No. Reaction Constant Reaction Rate Pre exponential Factor ( A j ) (1/s) Activation Energy ( E j ) (J/mol) 1 k 1 4.55e31 7.81e5 2 k 2 4.11e5 1.93e5 3 k 3 1.33e5 2.56e5 4 k 4 8.33e6 1.94e5 5 k 5 8.33e8 1.85e5

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40 Table 2 4 Production rates for each component of reactions Component of Reactions Production Rate CaCO 3 CaO SiO 2 C 2 S C 3 S Al 2 O 3 C 3 A Fe 2 O 3 C 4 AF CO 2

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41 Figure 2 1 Schematic of rotary cement kiln with four regions (C. M. Csernyei, 2016)

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42 Figure 2 2 Cross section of rotary cement kiln (Noshirvani, Sh irvani, Askari Mamani, & Nourzadeh, 2013)

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43 Figure 2 3 Heat transfer (radiation, convection, conduction) among internal wall, freeboard gas and solid bed

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44 Figure 2 4 3D initial microstructure from VCCTL

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45 Figure 2 5 Algorithm of VCCTL

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46 CHAPTER 3 3 METAHEURISTIC ALGORITHMS APPLIED TO VIRTUAL CEMENT MODELING 3.1 Overview This chapter presents the application of metaheuristic algorithms on VCCTL to optimize chemistry and water cement ratio of cement and mortar This study adopts a forward looking view that this goal will be reached, turning to how its full investigative power can be app lied to characterize a broad range of cements and hydration conditions. It successfully demonstrates that a multi objective metaheuristic optimization technique can generate the Pareto surface for the modulus of elasticity, time of set and kiln temperature for approximately 150,000 unique cements that encompass the clear majority of North American cement compositions in ASTM C150 (Cement) Insofar as the hydration mod el is accurate, the benefit of applying large scale simulations to characterize the strength, durability and sustainability of an individual cement relative to a broad range of cement compositions is shown. This section describes the hydration study model in VCCTL the metaheuristic algorithm, and different case studies that demonstrate the utility of metaheuristic algorithms to find optimal solutions and P areto analysis on Portland cements. Convergence is discussed to assist users replicating this approac h. Finally, the study demonstrate s that tri objective Pareto analysis is a flexible and objective tool to rate cements and offer remarks on the potential of this approach to solve much large combinatorial problems arising from the introduction of other var iables such as cement fineness and aggregate proportions. 3.2 Methodology T he VCCTL algorithm was ported to the University of Florida HiPerGator High Performance Computer (HPC), operating up to 500 cores for nearly one month to complete 149,572 unique simulati ons based on the input bounds shown in Table 3 1 Cement phases and

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47 w/c were discretized into ten and 15 equally spaced intervals, respectively, with the constraint t hat the mass fractions for all phases must sum to unity. These data were archived and reused during algorithm development (thus preventing the need to rerun VCCTL) and for the case studies in Section 3 .3 that compare the Pareto Front technique to the fully enumerated solution space. Once a completed VCCTL simulation is done, a set of outputs for hydrated cement paste models is created from the hydration, transport and mechanical properties. Model data applied in this study were the (a) output seven day elas tic modulus (b) output time of set of the hydrated paste, and (c) a proxy for kiln temperature, the ratio of inputs alite (C 3 S) and belite (C 2 S). A brief introduction for the three outputs is as follows: (a ) S even day elastic modulus is calculated directly from the 3D image using a finite element method (Garboczi & Berryman, 2001) The elastic modulus of the cement paste is directly related to the stiffness of a concrete made with that paste and provides an indication of the relative stiffness for different cement compositions and water cement ratio s. The elastic modulus can also be used to calculate the compressive st rength of concrete, which is considered as an important design parameter in many applications; (b ) Time of set is the final setting time of the concrete (Mamlouk & Zaniewski, 1999) Setting refers to the stage changing from a pla stic to a solid state, also known as cement paste stiffening It is usually described in two levels: initial set and final set. Initial set happens when the cement paste starts to stiffen noticeably. Final set happens when the cement has hardened enough fo r load. To determine the setting time, measurements are taken through a penetration test; (c) A proxy for kiln temperature alite : belite was chosen based on the assumption that they form at higher and lower kiln temperatures which represent the embodied energy in cement production process due to the direct relationship

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48 between embodied energy and carbon content (Reddy & Jagadish, 2003; Reddy, Leuzinger, & Sreeram, 2014) A kiln model developed by (C. M. Csernyei, 2016) was combin ed with VCCTL to simulate virtual cement plant Input including gas temperature, raw meal composition was given to VCP to get clinker composition. Figure 3 1 shows the position relation between kiln gas temperature and alite to belite ratio. Thus alite:belite was chosen to represent kiln temperatures. Figure 3 2 plots values for ea ch cement, with marker color corresponding to the w/c (shown on the right). Seen as a whole, the results compare well with expected behavior. The range of E, time of set, and C 3 S/C 2 S are [11.1, 32.0] GPa, [3.2,17.4] hrs, and [1.2,3.9], respectively, which are acceptable ranges based on the bounds shown in Table 3 1 The model captures the effect of paste densifying as w/c decreases, which causes the modulus to increase (Neville, 1995) Further, the observed relation ship between E and w/c matches the experimental measurements described by (C. J. Haecker et al ., 2005) The modulus is also observed to increase proportionally with increasing C 3 S/C 2 S, which is consistent with past research (e.g., (Taylor, 1997) ) that has shown alite is the primary si licate phase contributing to early strength development in Portland cement. The model also captures the decrease in time of set associated with a lower w/c, which increases the rate of hydration (Odler, 1998) The setting of paste occurs as the growth of hydration solids bridges the spaces between suspended cement partic les (Chen & Odler, 1992) Higher water to cement ratios result in larger spaces between particles, generally increasing the time required for setting to occur (Garboczi & Bentz, 1995) as well as the sensitivity of setting time to differences in cement co mposition. Table 3 2 lists the structure of VCCTL data base for virtual cement. The database consisting of inputs and outputs of VCCTL for 149,572 different Po rtland cement compositions is sample data for metaheuristic optimization introduced in the following section s

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49 3.3 Cement Optimization based on Metaheuristic Algorithms 3.3.1 Overview Multiple objectives drive cement production (e.g., minimize kiln temperature whi le maximizing the modulus), thus a set of trade off optimal solutions must be obtained instead of a single optimum (Burke & Kendall, 2005) The solution is the so called Pareto front, which is an envelope curve on the plane f or two objectives and a surface in space f or three objectives. The optimal solution set on a Pareto front are the set of solutions not dominated by any me mber of the entire search space (Burke & Kendall, 2005) This is generally not the case for cements, however. For example, one composition may have a larger E than a second composition with a lower heat proxy than the first. All else being equal, neither cement dominates another in terms of quality without additional user input to differentiate the relative importance of each variable. Therefore, n on dominated solutions were selected by simultaneously comparin g three objectives (described in Section 3.3.2) to evaluate the fitness (optimality) of each cement. Another consideration in the analysis was the combinatorial explosion arising from studying larger variable sets. While the Pareto front can be calculated directly from enveloping VCCTL results for every unique combination of cement phase and w/c, it would generally be impractical for a problem larger than what this paper presents. Consider Figure 3 3 which depicts the number of computer simulations a s a function of the variable count. The current study (8 variables) required hundreds of cores on a HPC running nearly one month to complete. Adding one new variable (e.g., concrete fineness) would increase the run time by a factor of ten. Adding a second new variable would render the simulation impractical in most HPC infrastructures. The realization that computational expense would ultimately be a significant barrier to implementation motivated the application of the multi objective metaheuristic search algorithm

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50 described in the next section. The study will show that it is possible to study the Pareto front of Portland cement with a vastly reduced number of simulations than what is required to build a data driven Pareto front, thus hopefully creating ex tensibility to larger combinatorial problems that will follow this work. C ement and concrete optimization primarily applies statistical methods, (Ahmad & Alghamdi, 2014; Ghezal & Khayat, 2002; Lagergren et al., 1997; Muthukumar & Mohan, 2004; Patel et al., 2004; MJ Simon, 2003; M Simon et al., 1999; Sonebi & Bassuoni, 2013; Soudki et al., 2001; Tan et al., 2005; Xiaoyong & Wendi, 2011) In contrast, this study applies metaheuristic optimization, which has shown widespread success in solving difficult combinational problems in other fields (Collins et al., 1988; Jaumard et al., 1988; Nissen, 1993; Osman, 1995; Osman & Laporte, 1996; Pirlot, 1992; Rayward Smith et al., 1996; Stewart et al., 1994; Vo et al., 2012) Common methods include particle swarm optimization (PSO) (Eberhart & Kennedy, 1995 ; Hu et al., 2003; L. Li et al., 2009; L. Li et al., 2007; Shi, 2001) genetic algorithms (Goldberg & Samtani, 1986; Rajeev & Krishnamoor thy, 1992; Wu & Chow, 1995) harmony search (Geem, Kim, & Loganathan, 2001) si mulated annea ling (Aarts & Korst, 1988; Kirkpatrick, 1984) and TABU search (Glover & Laguna, 2013) This r esearch applies the PSO and Genetic Algorithm because they are st raightforward to implement and suitable for a non differentiable and discretizable solution domain (Bonnans et al., 2006; Press et al., 2007) Both methods are population based metaheuristic approaches, which maintain and improv e multiple candidate solutions by using population characteristics to guide the search. To conduct a metaheuristic search, good solutions need to be distinguished from bad solutions. In the current study solutions for each individual are evaluated from ob jectives such

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51 as seven day modulus, time of set, heat proxy of each virtual cement from simulation result in VCCTL. And t he elitism strategy (or elitist selection), known as the process to allow best individuals from current generation to next generation, is used by both search algorithms to guide the evolution of good solutions (Burke & Kendall, 2005) The population size which is defined by users, plays an important role in algorithms. It affects the performance of the algorithm: if too small, premature convergence will happen to give unacceptable solutions; if too large, a lot of computational cost will be wasted. The b asic ideas and procedures of PSO and GA are explained as follows (Burke & Kendall, 2005) 3.3.2 Pareto Front Generation Applying Particle Swarm Optimization The PSO algorithm developed by (Eberhart & Kennedy, 1995) mimics swarm behavior in nature, e.g., the synchronized movement of flocking birds or schooling fish (Parsopoulos & Vrahatis, 2002) Each particle (here the unique combination of phase chemistry and w/c) in the search space has a fitness value calculated from a user specified objective function. During each solution area in the search space (Grosan, Abraham, & Chis, 2006) The procedure is as follows: 1. Initialize the particle positions from the set: drawing from the uniform distribution of each design variable within the bounds shown in Table 3 1 where i is the particle number and k is the generation 2. Copy to which are the best positions of each particle up to the current generation 3. Calculate the corresponding objective functions , i.e ., E, tim e of set and C 3 S /C 2 S from VCCTL

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52 4. Randomly assign one of the non dominated positions in the swarm to For example, consider the tri objective case minimizing time of set and C 3 S/C 2 S and maximizing E. The variable is a non dominated position if and only if there is no in the generation with one of the three characteristics below for min f 1 min f 2 max f 3 case: and and and and (3 1) and and 5. If initialize the velocities to zero, 6. If update the velocities of each particle with (3 2) where c 1 and c 2 are the acceleration coefficients associate d with cognitive and social swarm effects, respectively; r 1 and r 2 are random values uniformly drawn from [0,1], and w is the inertia weight, which represents the influence of previous velocity (L. Li et al., 2007) Based on trial and error, we selected both c 1 and c 2 to equal 0.8 respectively, and w decrease linearly from 1.2 to 0.1 over 500 generatio ns 7. Update the new position of each particle i : ( 3 3) 8. Calculate the three objective functions for each particle of the current generation (Eq. 3 2), and update with the non dominated positions if it is better than 9. Update by randomly assigning one of the non dominated position s in the swarm 10. Store and update non dominated solution found from the cu rrent generation in an external archive (known as elitist selection ) 11. Repeat steps 6 10 until the algorithm converges ( Section 3.5 gives more detail)

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5 3 3.3.3 Pareto Front Generation Applying Genetic Algorithm Based on principles of genetics in evolution and natural selection Holland came up with Genetic Algorithm in 1975 ( Holland, 1992 ) In this algorithm, string s containing the information of the design variables are created which imitates DNA containin g gene information in nature Once the optimization problem for virtual cement is encoded in a c hromosomal manner and objectives are calculated to evaluate the fitness of the solution s GA starts to evolve a sol ution using the following steps: 1. Similar with PSO, initialize the population set by randomly generating from the uniform distributed search ing space of design variable with bounds shown in Table 3 1 2. Evaluate the fitness of each candidate solution by calculating and comparing the objectives with Equation 3 1 3. Select solutions with better fi tness based on Step 2 to assign more good solutions for next generation. T ournament selection, is used in current study ( Burke & Kendal l, 2005 ) 4. Conduct crossover by combining parts of the parent population to create offspring population 5. Randomly modify one or two points at the parent chromosomes during the crossover, which mimics the gene mutation to give more random ness in the nearing space to candidate solution 6. After steps 3 5, replace parent population by offspring population. Replacement: The offspring population created by selection, crossover and mutation replaces the original parental population. One of the most popular replacem ent techniques, Elitism ( Deb, Pratap, Agarwal, & Meyarivan, 2002 ) is applied for replacement in current study 7. Repeat steps 2 to 6 until algorithm converges

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54 3.4 Case Studies 3.4.1 Example 1: Single Objective Optimum for Modulus To verify whether the optimization method is appropriate to solve optimization problems based on VCCTL, a single objective optimization is conducted as the first case study Since the 7 day elastic modulus ( E) factor is directly related to the strength of cement, it is selected as the objective to be optimized to a user specified value. From the output database of VCCTL, the range of the 7 day elastic modulus is from 11.1 to 32 GPa which is consistent with literatu re (Odelson, Kerr, & Vichit Vadakan, 2007) To demonstrate this case, the 7 day elastic modulus is optimized to a target value E target of 15 GPa. Other target values could also be selected based on In this way, the single objective function of this problem is | E E target |, which should be minimized to get the optimal solution. For this single objective problem, the PSO algorithm is applied. The procedure was illustrated in Section 3.3.2. For this problem, the particle population size is set to 100, balancing between the number of generation required to converge and com putational cost. And t he optimization process is considered converged when the objective function is less than 1 0 6 Figure 3 4 shows the values of the objective funct ion for 100 iterations. The whole optimization process converges after about 40 iterations, where the 7 day elastic modulus is closest to E t arget The exact solution is also calculated and shown in Figure 3 4 which is the same value after PSO method converges. Furthermore, Figure 3 5 shows the distribution of each cement phase at the optimal solution calculated by PSO method. For this case it takes 3,8 00 times run in VCCTL to find the target modulus, which is the product of the particle swarm size (100) and the number of generation required for convergence (4 0) deducting repeated individuals during searching for each generation

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55 3.4.2 Example 2: Bi objective Pareto Front for Modulus and Time of Set Multiple objectives drive cement production, thus a set of trade off optimal solutions must be obtained instead of a single optimum (Burke & Kendall, 2005) Therefore, the proposed approach is framed as multi objective optimization problem (MOOP) that calculates the Pareto front, an envelope curve on the plane for a bi objective case or a surface in space for a tri objective case that encompasses all optimal solutions. The optimal solution set on Pareto front is defined as a set of solutions that are not dominated by any member of the entire search space (shown in Equation 3 1) The Pareto front is visualized by connecting all the non dominated solutions. The second case study calculates the Pareto front (and the inherent trade off) of E and time of set. Figure 3 6 shows the full simulation outputs, with the Pareto fronts superimposed for four cases: [1] min i mize ti me of set and min im ize E (Min Min); [2] min im ize time of set and ma x i mize E (Min Max); [3] max i mize time of set and min i mize E (Max Min); and [4] max i mize time of set and max i mize E (Max Max). The Pareto fronts obtained from the PSO were generated using 30% of the simulations required to fully enumerate the sample space. Further, the curves coincide for the majority of the data envelope, varying by less than one hour and 5 GPa on the horizontal and vertical scales, respectively, in the absolute worst case. This example, while simple, demonstrates the potential of the PSO g enerated Pareto front as a substitute for bulk analysis. A Genetic Algorithm wa s also verified to work for the bi objective optimization problem. The bi objective optimization results obtained from PSO and GA are compared. From Figure 3 7 the results from both methods have similar Pareto front curves and match very well. This proves that both the PSO and GA methods are appropriate to solve the bi objective optimization problem of the VCCTL. Also, the converging speed and computational time are also compared

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56 between these two methods with the same population size (1000). The comparison results are shown in Table 3 3 From Table 3 3 PSO and GA require a different number of generation s to converge to the optimal solution It takes about 200 generations to converge for the PSO method, while only about 30 generations for the GA method with a population size of 1000. On the other hand, it takes 80 times longer to execute the GA method than the PSO method In summary, for this case, GA converges in fewer generation s than PSO, but requires more time to execute. 3.4.3 Example 3: Tri objective Optimization of Modulus, Time of Set and Heat Proxy After both the optimization algorithms are verified for bi objective opti mization a more complicated problem is introduced to demonstrate the application of these methods. From the knowledge of cement materials, cement paste with less setting time will develop strength earlier. Thus, time of set of the cement needs to be minim ized. As mentioned earlier in Chapter 2, C 3 S is the most reactive compound among the cement constituents, whereas C 2 S reacts much more slowly. In this way, t he compounds are the most abundant within the Portland cement system with C 3 S (alite) which requires higher kiln temperatures to form, while the C 2 S phase forms at lower kiln temperatures. Thus, C 3 S/C 2 S should be minimized to ensure less energy is used to create the cement liberate less heat and less greenhouse gas emissions The 7 day elastic m odulus needs to be maximized to obtain more strength for cement paste. In the third example, objective functions for C 3 S/C 2 S, time of set, and 7 day E are optimized simultaneously to identify the Pareto fronts bounded by three cases: [1] min i mize C 3 S/C 2 S, minimize ti me of set, and maximize E (Min Min Max); [2] min i mize C 3 S/C 2 S min im ize ti me of set, and min im ize E (Min Min Min); and [3] maximize C 3 S/C 2 S, maximize ti me of set, and maximize E (Max Max Max). Figure 3 8 shows the Pareto fronts for different water to cement ratios when minimizing time of set, minimizing kiln temperature proxy, and maximizing 7 day elastic modulus.

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57 Separating the dataset by w/c enables visualization of the variation in the data due to different cement chemistri es. The changing slopes of the P areto surfaces as w/c increases show an increasing sensitivity of modulus and time of set to variations in cement variation. The possibl e range of moduli at a w/c of 0.53 is larger than that at a w/c of 0.25. C 3 S/C 2 S is not affected by water cement ratio because C 3 S, C 2 S and water cement ratio are all inputs of cement and independent from one another. The different Pareto fronts provide th e non dominated solutions for different water cement ratios which could be used as guidance for design. Taking the optimization results with a specified water cement ratio (0.25) as an example, there are 88 non dominated solutions found by the PSO algorith m. Table 3 4 lists the inputs and outputs of the first 30 non dominated solutions. These solutions provide useful guidance for cement designers. From all trade off optimal solutions, the selection of inpu ts for cement design is based on the requirements for cement paste performance. Figure 3 9 (a) and (b) show the two Pareto fronts (gray meshes) from non dominated sol utions (red markers) for Max Max Max and Min Min Min. Figure 3 9 (c) shows the two Pareto fronts for all water cement ratios. The color bar on the left shows the change with water cement ratio from 0.25 (red) to 0.53 (blue) for cement data and the color ba r on the right shows the change with modulus on the Pareto front surfaces. 3.5 Remarks on Convergence To minimize the computational expense, metaheuristic search algorithms can be terminated once the estimated value is close to the target value. Thus, investig ating the convergence properties of the multi objective evolutionary algorithms is necessary. In the past few years, efficient stopping criteria for MOOP algorithms have been explored (G. Li, Goel, & Stander, 2008; Mart, Garca, Berlanga, & Molina, 2007; Roudenko & Schoenauer, 2004; Tra utmann, Ligges, Mehnen, & Preuss, 2008) Convergence to the global Pareto front is

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58 considered to assess the performance of algorithm (Kaige, Murata, & Ishibuchi, 2003; Zitzler, Thiele, Laumanns, Fonseca, & Da Fonseca, 2003) In the cases where problems do not have an exact solution, a true Pareto front cannot be established. Therefore, a convergence test is applied based on the self improvement of the algorithm. Goel and Stand er (Goel & Stander, 2010) proposed a metric tracking of the change of the archive based on non domination criterion to generate the convergence curve for MOOP. As mentioned in Section 3.3 during t he process of updating non dominated solution, an external archive of non dominated solutions is maintained and updated for each generation. The solutions dominated in the old archive dominated by newly evolved solutions are removed. New solutions which ar e non dominated with respect to archive are added. They suggested two terms, the improvement ratio and consolidation ratio. The improvement ratio is the scaled number of dominated solutions representing the improvement in the solution set while the consoli dation ratio is the scaled number of non dominated solutions representing the proportion of potentially converged solutions. The algorithm is considered to converge when improvement ratio is close to zero and consolidation ratio close to one. This method w as applied to the Min Min Min case above to test the convergence for the PSO algorithm with different population sizes. Consolidation ratio and improvement ratio are calculated for each generation to create the convergence table. Figure 3 10 shows when population size equals 300, the consolidation ratio becomes 1 and improvement ratio becomes 0 at 600 th generation, which means the number of convergence generation fo r the algorithm is 600 when the population size is 300. The relations between population size with number of PSO simulations, number of convergence generation, number of non dominated solutions and percentage of PSO search with

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59 blind search are plotted i n Figure 3 11 The algorithms will not converge if the population size is less than 10. With increasing population size, the number of generations requ ired for convergence decreases and the number of optimal solutions increases. This trend means a larger population size results in faster convergence. Also, the minimum number of simulations with PSO is about 19,812 out of 149,572 VCCTL simulations, which means the computational cost is reduced by up to 90% by applying PSO compared with the blind search of VCCTL. Thus, the PSO algorithm drastically decreases the computational cost in the process of searching optimal solutions for cement. 3.6 Potential for Obje ctive Rating of Cement Quality The paper now shifts to how Pareto front analysis can be applied to quantify the performance of a single cement relative to other cements, with user specified constraints such as imposing a minimum allowable modulus or maximu m allowable time of set. Currently, a numerical rating system to objectively rate cement quality does not exist in practice. Similar to other civil engineering materials such as timber and steel (Standard) Portland cements are stratified into discrete classes based on physical testing results and intended service applications (Cement) A major lim itation of this approach in practice is the assumption that all cements of a given class are equivalent in performance. The integration of PSO with cement hydration modeling allows for performance based scoring on a continuous basis without physical testin g, and defines a framework for the practical implementation of performance based specifications that complement existing approaches. 3.6.1 Cement Scoring System The proposed scoring system is based on the probability of non exceedance of the data encompassed b y the Pareto fronts given a user 0 : ( 3 4 )

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60 where Pc is the joint probability of non exceedance within time of set (x) and C 3 S/C 2 S (y), and E0 is the minimum allowable modulus. In this case, the Min Min Min and Max Max Max Pareto fronts ( Figure 3 9 c ) give the boundary cases for all modeled cement s. These fronts are used as lowest score (0) and highest score (1) for the group of cement. The procedure is shown as follows: 1. Project cements with E E0 to the surface E = E0 (E0 = 20 GPa) 2. Unite two Pareto fronts (Min Min Min and Max Max Max) at E=E0 to create a conve x hull 3. Evaluate the marginal probability of non exceedance and with regard to for time of set and heat proxy for all cements 4. Since less time of set and less heat proxy get higher scores, the score for each cement is calculated with S = 1 P with regard to time of set and heat proxy 5. Calculate the joint cumulative probability of time of set and heat proxy, which is considered as score for cement with user specified constraint 3.6.2 Scoring System Applied to Example 3 Figure 3 13 demonstrates the scoring procedure with an example cement. Figure 3 13 (a) shows the p rojected convex hull from two Pareto Fronts in the time of set and heat proxy directions. Figure 3 13 (b) and Figure 3 13 (c) illustrate the assignment of probabilit y of non exceedance score using the cumulative distribution of time of set and heat proxy in Figure 3 13 (a). The probability of non exceedance of the specific cement (shown in black dot) with regard to time of set and heat proxy are and Thus, the score for that cement and

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61 The two scores shows the marginal non exceedance probability within time o f set and heat proxy. Figure 3 14 shows the probability of non exceedance curve with regard to time of set. Cements sharing single chemistry with fiv e different w/c are plotted with five dots in different colors on the curve. Figure 3 15 shows the effect of water cement ratio on cement scores. When the water to cement ratio increases from 0.24 to 0.26 (8.3% increase), score decreases from 0.33 to 0.18 (44.3% decrease). When the water to cement ratio increases from 0.24 to 0.28 (16.7% incr ease), score decreases from 0.33 to 0.067 (79.5% decrease). After the scoring system is demonstrated, the full data set of cements is fitted with Hermite (Yang, Gurley, & Prevat t, 2013) and Beta distribution for time of set and heat proxy directions. In order to score the cements with solutions from metaheuristic searching algorithm, the fitting model from the empirical data is demonstrated on randomly picked reduced data. Figure 3 16 shows the distribution fitting for 50% and 10% of the data set compared with empirical data. From Figure 3 16 Hermite and Beta distribution generated from empirical data fits the reduced data well. 10% of the dataset has the same distribution with empirical data. In this way, cements in s pace could be scored from the results found by PSO algorithm, which only takes at least 10% of full data set. And the score with fit distribution with existing models will be same as s core based on the full dataset Figure 3 17 shows the spectrum of joint score for all cement with user specified constraint For example, if cements with time of set less th an 7.43 hr and heat proxy less than 2.52 is evaluated, j oint score for those cements is:

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62 In the figure colorbar purple represents the lowest score and dark green represents the hi ghest score. This provides a visual map of the ideal cases based on the relative priority of the two scored parameters, where all cases satisfy the constraint E>20 GPa. 3.7 Implication This chapter presents the successful application of multi objective optimiz ation of cement modeling, applied to a cement database created from ~150,000 VCCTL simulations. Pareto fronts were explored for constrained bi objective or non constrained tri objective problems. Compared to full enumeration of the VCCTL parameter space, t he metaheuristic algorithm search decreases the cost by nearly 90%. This finding suggests that this approach may be promising for evaluating much larger input variable sets. The Portland cement industry is moving toward the implementation and use of perfo rmance specifications (Bickley, Hooton, & Hover, 2006) It is often the case that to ensure durability cement and concrete producers specify concrete mixtures to be stronger than required, even when overdesign is specified due to perc eived uncertainty regarding the ultimate performance of the material. To alleviate this, performance based design must address the needs of the industry, which include the assurance of strength, durability, economy, and sustainability Pareto front based s coring of virtual testing results allows for the rapid assessment of solutions through constraints on critical parameters, while providing relative performance values for secondary parameters of interest This e nables immediate visualization of possibiliti es, and rapid selection of ideal cases. Objective, performance based scoring has the potential to improve the economic performance of ordinary Portland cement (OPC) systems without the requirement of supplementary materials. Modern Type I/II Portland ceme nts are empirically optimized for fast construction and low cost (Shetty, 2005) Current cement compositions require supplementary

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63 materials to improve longevity and increase sustainability (Damtoft, Lukasik, Herfort, Sorrentino, & Gartner, 2008) Quantification of the tradeoffs between rapid strength development, cost of production, and long term durability for Portland cement could motivate changes to cement chemistry and lead to optimization of the production process.

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64 Table 3 1 Lower and upper bounds of VCCTL inputs Input Mass F raction Lower Bound Upper Bound Water to Cement Ratio (w/c) 0.20 0.53 Alite (C 3 S) 0.50 0.70 Belite (C 2 S) 0.15 0.37 Ferrite (C 4 AF) 0.05 0.20 Aluminate (C 3 A) 0.03 0.10 Gypsum 0.00 0.06 Anhydrite 0.00 0.04 Hemihydrate 0.00 0.04

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65 Table 3 2 Database column identifier Column Item Inputs 1 Water to Cement Ratio 2 Alite Mass Fraction 3 Belite Mass Fraction 4 Ferrite Mass Fraction 5 Aluminate Mass fraction 6 Gypsum Mass Fraction 7 Anhydrite Mass Fraction 8 Hemihydrate Mass Fraction Outputs 9 7 day Heat (kJ/kg) 10 Time of Set (hours) 11 Degree of hydration (%) 12 7 day Elastic Modulus (GPa)

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66 Table 3 3 Comparison of computational cost Optimization techniques Population size Number of iteration Time to run (sec) PSO 1000 200 10.9 GA 1000 30 814.9

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67 Table 3 4 First 30 non dominated solutions for min min max case (w/c=0.25) Inputs: Mass F raction Outputs: Mechanical and Hydration Properties Alite Belite Ferrite Aluminate Gypsum Anhydrite Hemihydrate 7 day Heat (kJ/kg) Time of Set (hours) Degree of hydration (%) 7 day Elasitc Modulus (GPa) 0.54 0.27 0.07 0.07 0.01 0.03 0.00 264 4.55 0.03 31.1 0.69 0.17 0.06 0.05 0.01 0.01 0.01 288 4.39 0.03 32.0 0.57 0.19 0.07 0.09 0.00 0.04 0.04 275 3.30 0.04 30.7 0.51 0.24 0.08 0.09 0.02 0.04 0.02 257 3.60 0.04 29.8 0.61 0.15 0.06 0.10 0.00 0.04 0.03 285 3.16 0.03 31.4 0.50 0.28 0.07 0.09 0.01 0.03 0.01 248 4.55 0.03 29.9 0.65 0.19 0.05 0.06 0.00 0.03 0.01 275 3.60 0.03 31.1 0.53 0.24 0.07 0.09 0.01 0.03 0.03 262 3.45 0.03 30.4 0.52 0.26 0.07 0.10 0.02 0.03 0.01 269 4.55 0.03 30.7 0.50 0.30 0.10 0.05 0.01 0.03 0.00 242 4.90 0.03 29.8 0.54 0.28 0.05 0.09 0.00 0.03 0.01 271 4.90 0.03 31.0 0.61 0.16 0.11 0.07 0.00 0.03 0.01 280 3.90 0.03 31.8 0.59 0.21 0.11 0.05 0.00 0.02 0.02 267 4.39 0.03 31.3 0.58 0.19 0.11 0.08 0.00 0.03 0.00 277 4.90 0.03 31.8 0.65 0.20 0.07 0.04 0.00 0.02 0.02 274 4.22 0.03 31.7 0.60 0.20 0.12 0.04 0.00 0.03 0.00 268 4.39 0.03 31.4 0.52 0.29 0.07 0.08 0.00 0.03 0.01 259 4.90 0.03 30.8 0.52 0.18 0.14 0.10 0.00 0.03 0.02 273 4.06 0.04 30.9 0.52 0.29 0.10 0.05 0.00 0.03 0.01 249 4.72 0.03 30.5 0.53 0.27 0.09 0.06 0.00 0.03 0.01 252 4.39 0.03 30.7 0.54 0.27 0.07 0.07 0.01 0.03 0.00 264 4.55 0.03 31.1 0.69 0.17 0.06 0.05 0.01 0.01 0.01 288 4.39 0.03 32.0 0.57 0.19 0.07 0.09 0.00 0.04 0.04 275 3.30 0.04 30.7 0.51 0.24 0.08 0.09 0.02 0.04 0.02 257 3.60 0.04 29.8 0.61 0.15 0.06 0.10 0.00 0.04 0.03 285 3.16 0.03 31.4 0.50 0.28 0.07 0.09 0.01 0.03 0.01 248 4.55 0.03 29.9 0.65 0.19 0.05 0.06 0.00 0.03 0.01 275 3.60 0.03 31.1 0.53 0.24 0.07 0.09 0.01 0.03 0.03 262 3.45 0.03 30.4 0.52 0.26 0.07 0.10 0.02 0.03 0.01 269 4.55 0.03 30.7 0.50 0.30 0.10 0.05 0.01 0.03 0.00 242 4.90 0.03 29.8

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68 Figure 3 1 Relationship between kiln temperature and C 3 S/C 2 S

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69 Figure 3 2 Results of VCCTL simulations

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70 Figure 3 3 Potential discrete combinations of cement and co ncrete

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71 Figure 3 4 Elastic modulus vs. i teration with PSO

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72 Figure 3 5 Distribution of cement phases for optimum with singe objective PSO

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73 Figure 3 6 Pareto fronts of four different bi objective optimization scenarios without constraints compared with the data envelope. Exploring the Pareto fronts with the PSO decreases the computational cost by more than 70%

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74 Figure 3 7 Comparison of PSO and GA of bi objective optimization

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75 Figure 3 8 3D surface mesh of Pareto front from non dominated solution (red dots) for the Min (Time of set) Min (C 3 S/C 2 S) Max (E) case with different water cement ratios. (a) w/c=0.25; (b) w/c=0.33; (c) w/c=0.43; (d) w/c=0.53

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76 Figure 3 9 (a) 3D surface mesh of Pareto front from non dominated solution (red dots) for the Max Max Max case (b) 3D surface mesh of Pareto front from non dominated solution (red dots) for the Min Min Min case, and (c) 3D surface of Pareto front s for the combined cases

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77 Figure 3 10 Consolidation ratio and Improvement ratio for population size = 300

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78 Figure 3 11 Convergence generation, number of simulations, number of optimal solutions vs. population size

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79 Figure 3 12 Process of deciding convex hull for evaluation cement data. (a) Finding convex hull for Min (Time of set) Min (C 3 S/C 2 S) Min (E) case; (b) Finding convex hull for Max (Time of set) Max ( C 3 S/C 2 S) Max (E) case; (c)(d) Combined convex hull. For cement data points close to Min (Time of set) Min (C 3 S/C 2 S) Min (E) Pareto Front have higher score and those close to Max (Time of set) Max (C 3 S/C 2 S) Max (E ) Pareto Front have lower score

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80 Figure 3 13 Marginal probability of non exceedance with regard to time of set and heat proxy for E 20 GPa cements. The score is defined as the 1 probability of non ex ceedance for the specified cement relative to all cement that meet the user specified constraints (h ere the modulus). Scores of zero and unity represent the worst and best possible outcomes

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81 Figure 3 14 Different w/c with single cement chemistry on the marginal prob ability of non exceedance curve

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82 Figure 3 15 Effect of w/c on scores with regard to time of set under single chemistry

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83 Figure 3 16 Hermite and Beta distribution fitting for reduced data

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84 Figure 3 17 Joint score of cement

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85 CHAPTER 4 4 PHYSICAL CHEMICAL MODELING OF A ROTARY CEMENT KILN As introduced in Chapter 2, numerical models (C. Csernyei & Straatman, 2016; Martins et al., 2002; Mastorako s et al., 1999; K. S. Mujumdar et al., 2006; Sadighi et al., 2011; Spang, 1972) exist to understand the behaviors of cement kilns, increase the cement production and decrease the energy consumption and greenhouse gas emissions To simulate reactions of the rotary kiln and optimize the process and outputs, i n this c hapter, a physical chemical one dimensional kiln model is developed based on knowledge of thermodynamics and clinker chemistry from existing models. MATLAB R2016a TM solver ODE15s is used to solve an ordinary partial differential equation system of the kiln model. The temperature profiles and clinker species mass fractions are validated with the existing industrial kiln model and Bogue calculation. Although measuring data from operation cement plants is available at times, it is subject to confidentiality a nd inherent limitations (C. M. Csernyei, 2016) The cement plant data such as clink er production, energy cost, CO 2 emission s is restricted to the precise operating paramet ers that occurred at that time. Also, the majority of these parameters can only be estimated within a certain degree of accuracy. Due to these reasons, research on the continued understanding of cement rotary kiln s is slow and heavily focused on computational modeling. 4.1 Model Validation 4.1.1 Solution Methodology According to previous kiln models developed during the last 50 years, knowledge inside the model is similar includi ng the thermodynamics and clinker chemistry. However, the approaches researchers used to solve the model are quite different. Some people developed their own code with numerical methods (usually the fourth order Runge Kutta method) to solve for

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86 the ODE/PDE s (C. Csernyei & Straatman, 2016; Martins et al., 2002; Spang, 1972) while others use d commercial software or open source numerical solves for their models (Darabi, 2007; Guirao, Iglesias, Pistono, & Vzquez; Mastorakos et al., 1999; K. Mujumdar & Ranade, 2006; Nrskov, 2012; Sadighi et al., 2011; Wang, Lu, Li, Li, & Hu, 2006) For the current st udy, the kiln model Equations (2 1) ( 2 29 ) are implanted into Matlab 2016 a TM and the solver ODE15s is applied to solve the ODE system because of its high computational efficiency and convenience in coupling with the op timization tool developed in Chapter 3. By testing different ODE solve r s including ODE45, ODE 23, ODE15s, ODE23s, ODE23t, ODE 23tb in Matlab2016, ODE15s is more stable and performs better than other solvers in solving stiff differential equations and dealing with singular matrix. The procedure to solve for the computational kiln model is as follows: 1. An assumed temperature profile for the bed, gas, and shell was generated by assuming what the temperatures may be throughout the kiln based on results from other researchers (C. M. Csernyei, 2016; K. Mujumdar & Ranade, 2006) linear profile for the gas temperature is generated in order to simplify the model. This profile was generated using the in let and outlet gas temperature, as well as an assumption for the temperature and location of the peak gas temperature based on data r eceived from the partner plant. The initial temperature profile was obtained by using a tool to dig itize the plot s from papers. This tool allows users to pick the axis of a graph and choose the points on the plot, then it generates a table of the x and y values (shown in Figure 4 1 ) 2. Internal heat transfer components were solved from Equation ( 2 1) to ( 2 10) exc luding the effects of clinker chemistry

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87 3. ODE system (2 16) (2 29 ) were solved for b ed temperature and species mass fractions through the use of Matlab 2016a ODE15s solver. T he bed temperature requirement for each chemical reaction shown in Table 2 2 is taken into consideration 4. Shell temp erature was solved using the heat balance Equation (2 29 ) by Newton Raphson method (Chapra & Canale, 1998) 5. A chec k was performed to see if the new temperature profiles of shell and solid bed were within residual of 0 .000001 of the previous profile 6. The new temperature profiles were passed back to the beginning of the model (step 2) and the process repeated again till convergence 4.1.2 Results and Discussion From the solution methodology in Section 4.3, the 1D physical chemical kiln model using (C. M. Csernyei, 2016) is solved after the iterative process es converge to a solution for solid bed temperature and shell temperature. Mas s fraction is plotted on the top of 3 S at the exit of the kiln. Red lines in Figure 4 2 show spec ies mass fraction along the axial length of cement k iln without adjusting bed height which generate 20% more C 3 shown with black lines Red lines in Figure 4 3 show the species mass fraction s along the cement kiln after adjusting the bed height from 0.75m to 0.58m. The mass fraction for each species matc hes Figure 4 4 shows the temperature profiles of solid bed, shell, internal wall and freeboa rd gas along the kiln, which Table 4 1 shows the comparison of inlet and outlet mass fraction of material compared to the results of Bogue calculation (Bogue, 1929) mass fraction at the outlet of t he kiln, the present (1.24% difference), while

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88 for the difference is Bogue assume s entire amount input constituent are converted into their species, which causes inherent error. the present model is verified with more published industrial data as well as some other res earcher prediction s (K. Mujumdar & Ranade, 2006) Table 4 2 shows the comparison between the prediction of present the prediction of present work matches with published plant data very well. 4.2 Model Modification 4.2.1 CO 2 Mass Fraction The virtual cement plant kiln model in Chapter 2 c alculated the mass fraction of each solid component. Similarly, mass fraction of CO 2 emissions from limestone decomposition could be calculated with Equation (4 1 ). ( 4 1 ) The mass fraction of CO 2 emissions from limestone decomposition is shown in blue dash line in Figure 4 5 4.2.2 Raw Meal and Fuel Costs First, the cost of raw material for cement plant was estimated and is provided in Table 4 3 which lists the unit price for cement raw material in the current market (sand and gravel only). ( https://www.statista.com/statistics/219381/sand a nd gravel prices in the us/ ). By incorporating the unit price into VCP model based on the mass fraction of raw meal, the relationship between 7 day modulus and raw meal cost was calculated (see Figure 4 6 ). Modulus is observed to increase with the cost of raw meal, which is due to the increase of limestone used as raw meal. From the linear regression fit for the data, a positive correlation

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89 between gas peak temperature and modulus is obtained. That is because higher peak temperature gives more alite, which plays an important role in cement strength development. After the material cost is calculated, energy cost, or cost of fuel is considered. From (Chatziaras et al., 2016) t he average energy required to produce one ton of cement is 3.3 GJ, which can be generated by 120 kg coal with a calorific value of 27.5 MJ/kg. Coal is the major fuel used for cement production (Worrell et al., 2013) The cost of coal is $2.07/GJ ( https://www.statista.com/statistics/244479/us consumer price estimates for coal energy/) Figure 4 7 shows the relationship between modulus and cost of fuel. Because of the linear relation between energy and temperature, the cost of fuel has a linear relationship with temperature. Figure 4 8 shows the relationship between modulus and total cost by combining material cost and fuel cost. Similar with Figure 4 6 modulus increases with total cost because of the positive correlation between modulus and both cost. From Figure 4 8 energy cost accounts about 30% of the total cost, which is verified by (Chatziaras et al., 2016)

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90 Table 4 1 prediction Raw Meal at inlet Mass Fraction Work Mass F raction of Present Work CaCO 3 0.3798 0.3798 CaO 0.3019 0.3019 SiO 2 0.1594 0.1594 Al 2 O 3 0.0246 0.0246 Fe 2 O 3 0.0396 0.0396 Inert + Other 0.0947 0.0947 Clinker at the O utlet Mass F raction Calculation Mass F raction from Work Mass Fr action of present work C 3 S 0.582 0.546 0.546 C 2 S 0.130 0.049 0.041 C 3 A 0.063 0.027 0.027 C 4 AF 0.075 0.068 0.068 CaO 0.000 0.034 0.033 Summation 0.85 0.724 0.715

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91 Table 4 2 Industrial kiln 1 (2006) Industrial kiln 2 (2006) Industrial kiln 3 (2006) Plant Data Mujumdar Prediction Present W ork Plant Data Mujumdar Prediction Present W ork Plant Data Mujumdar Prediction Present W ork Inlet Mass F raction CaCO 3 0.340 0.398 0.305 CaO 0.396 0.335 0.418 SiO 2 0.179 0.185 0.190 Al 2 O 3 0.0425 0.041 0.043 Fe 2 O 3 0.0425 0.041 0.043 Initial Temperature of S olid, K 1123 1250 1025 Outlet Mass F raction C 3 S 0.483 0.508 0.489 0.508 0.502 0.503 0.500 0.504 0.506 C 2 S 0.239 0.222 0.202 0.257 0.263 0.209 0.269 0.249 0.222 C 3 A 0.051 0.051 0.048 0.048 0.051 0.048 0.042 0.052 0.048 C 4 AF 0.143 0.149 0.116 0.151 0.148 0.109 0.142 0.147 0.118 Residual 1.82% 2.38% 2.08%

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92 Table 4 3 Unit price for raw material of cement plant Raw material Chemical Composition Unit Price ($ /Ton ) Limestone CaCO 3 +CaO 15 Sand and Gravel SiO 2 4.4 Clay Al 2 O 3 +Fe 2 O 3 4

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93 Figure 4 1

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94 Figure 4 2 Species mass fractions along cement kiln without bed height adjustment compared with published data

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95 Figure 4 3 Species mass fractions along cement kiln with bed height adjustment compared with published data

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96 Figure 4 4 Temperature profiles in cement kiln from heat transfer.

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97 Figure 4 5 Mass fraction of CO 2 emissions from kiln model

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98 Figure 4 6 Relationship between 7 day modulus (GPa) and cost of raw meal ($/Ton) under different gas peak temperature

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99 Figure 4 7 Relationship between 7 day modulus (GPa) and cost of fuel ($/Ton) under different gas peak temperature

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100 Figure 4 8 Relationship between 7 day modulus(GPa) and total cost under different gas peak temperature

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101 CHAPTER 5 5 OPTIMIZATION OF COUPLED VCP/VCCTL MODEL This chapter introduces a coupled model which utilizes the VCP in combination with the VCCTL to create a tool which models the production of Portland cement from the mine to the point of placement. The coupling of VCP and VCCTL was performed to provide a tool that couples cement production and hydration Portland cement. The model is a tool for the optimization of raw material input, fuel, energy emission s and cost for manufacture of Portland cement in addition to the optimization of the physical properties of the resultant concrete. 5.1 Coupling VCP and VCCTL M odel ing 5.1.1 Input Generation Chapter 4 introduce d 1D physical chemical cement kiln model, which is considered as virtual cement plant (VCP). In order to simulate the VCP, input files including the mass fraction of raw meal, peak gas temperature and the location where peak gas temperat ure occurs within the kiln are required. The chemical composition of the r aw meal at the inlet of cement kiln include s CaCO 3 CaO, SiO 2 Al 2 O 3 Fe 2 O 3. It is common to use lime saturation factor (LSF), silica ratio (SR) and alumina ratio (AR) in chemical analysis for cements, clinkers and phases instead of using oxide components directly. The relationship between LSF, SR, AR and raw meal is as follows (Taylor, 1997) : Lime saturation factor (LSF) = CaO/(2.8SiO 2 +1.2Al 2 O 3 +0.65Fe 2 O 3 ) (5 1) Silica ratio (SR) = SiO 2 /(Al 2 O 3 +Fe 2 O 3 ) (5 2) Alumina ratio (AR) = Al 2 O 3 /Fe 2 O 3 (5 3) LSF is a ratio of CaO to other three oxide components, which control the ratio of alite:belite produced within the cement kiln. The VCP model requires the mass fraction of raw

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102 meal, calculated from Equation s (5 1) (5 3) where the LSR, SR, AR, Fe 2 O 3 CaCO 3 / CaO are considered as input s which generate oxide components from the raw meal. According to Taylor, the typical range for each ratio for the production of portland cement is as follows: LSF [0.9, 1.05] SR [2.0, 3.0] AR [0.8, 2.0] Furthermore, the typical range of Fe 2 O 3 content [0.01,0.1] The CaCO 3 to CaO ratio is typically within a range of [40%,60% ] and is directly obtained from the decarbonation of the limestone through the kiln Ultimately the mass fraction of the components, (CaCO 3 CaO, SiO 2 Al 2 O 3 Fe 2 O 3 ) should be equal to 1 The inputs are generated utilizing two methods : a ) fixed intervals; b ) uniformly distributed random numbers based on the ranges from each input. Figure 5 1 and Figure 5 2 provide the distribution of 1956 inputs generated by fixed intervals where distribution s of raw meal derived from Equation (5 1) (5 3). The input was generated from 1 0 0 ,000 individual s amp les however, 1956 input s or 1.96% satisfy the constrain t (components equal to 1) Figure 5 3 and Figure 5 4 show the distribution of inputs generated by uniformly distributed random number s from available section s and distribution of raw meal T he number 200,000 individual samples were generated and only 1732 (0.87%) inputs satisfy the cons traint. The methodology used for the generation of different sample sizes (100,000 and 200,000) was done in an effort to acquire roughly the same number of inputs for each case (1956 and 1732). The fixed intervals (method a) did not provid e a uniform distribution as shown in figure 5 1; method b, the uniformly distributed random numbers were used to generate the inputs for the coupled model.

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103 T able 5 1 and Table 5 2 compare the VCP raw meal and clinker mass fraction with different input generation approaches. The results of the two approaches are sl ightly different which is to be expected since different methods to generate inputs were used and provides differences with in the raw mea l as well as cement clinker. Taylor reported that the maximum LSF for modern cements is 1.02 and the range for LSF (0 .90 1.05) was borne from the use of a range slightly above the maximum reported. However, the results obtained in Table 5 2 provide a low range of alite (18 48%) b ut is typically 40 70% by mass (Stutzman, 2004) Subsequent to the production of the low values for alite, the model was reproduced using the raw meal mass fractions from published industrial kiln data (C. M. Csernyei, 2016; K. Mujumdar & Ranade, 2006) and are applied to det ermine the range of inputs. After calculating LSF, AR, SR, Fe 2 O 3 and CaCO 3 /CaO from Equation (5 1) (5 3) using the mass fractions of raw meal at inlet of the four industrial kiln s (shown in Table 4 1 and Table 4 2 ) the ranges for material inputs is as follows : LSF [1.18, 1.36], SR [2.1, 2.5] AR [0.6, 1.0] Fe 2 O 3 [0.0396, 0.0430], CaCO 3 /CaO [42%, 56%]. Table 5 3 lists from industrial kilns. As introduced in Chapter 4, gas temperature profile is considered as input for the VCP model, which contains the peak gas temperature and location of the peak gas temperature. Figure 5 5 gives an example of gas temperature as input profile for VCP. The peak ga s temperature is about 2100K, which happened at the point 0.84 of normalized kiln length away from entry of the kiln. Based on other researcher s gas profiles (C. M. Csernyei, 2016; K. Mujumdar & Ranade, 2006) peak gas temperature range is chosen as [1976, 2176] K and the range of location of peak gas is chosen as [0.6, 0.9]

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104 5.1.2 Input Range Testing After the ranges for VCP inputs are established, cases with different range of material input are analyzed. Table 5 4 shows the VCP results with di fferent material input ranges. The results are shown with regards to alite and belite mass fractions at different g as peak temperature s From Table 5 4 clinker mass f does not cover enough searching space for the optimization tool. After expanding the input range by using information from industrial kiln s for VCP, alite space increases from [0.2, 0.45] to [0.2, 0.7] and belite space increase from [0.25, 0.38] to [0, 0.38] 5.1.3 Schematic of coupled VCP VCCTL model In the following sections, the expanded input s including 537 different kinds of chemistry, 10 different peak gas temperatures and 10 different locations of peak gas tempe rature are considered for coupled VCP/VCCTL model. 53,700 inputs were ported to VCP, after 20 hours running with Matlab2016a, 53,700 clinkers containing the information of mass fractions of virtual clinker phases and related temperature profiles we re created. T he clinker phase chemistry and fineness are passed to VCCTL and run on UF HPC for virtual cement initial microstructure reconstruction and hydration, as described in Chapter 2. Subsequent to 6 days of run time on the HPC, a series of output indicat ors with respect to the performance for each virtual cement including time of set, 7 day mortar modulus, 7 day morta r strength, 3 day heat are calculated 5.1.4 Case Studies Table 5 5 shows the results of coupled VCP VCCTL with 53 700 inputs. Based on the output of VCP, mass fractions of different c ement clinker phases are plotted versus different peak gas temperature and peak gas locations (also kno wn as flame location s ) For example, the first plot in Table 5 5 shows alite mass fraction of virtual cements with 537 raw meal

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105 combinations versus 10 peak gas temperatures. The results indicate that alite increase s with the peak gas temperature (or the hi ghest temperature of flame inside the kiln), belite decrease s with the peak gas temperature and CaO decrease s with the peak gas temperature. The sensitivity of clinker phases to temperature is increased when the flame is close to the exit of the kiln. Tha t means, if more alite is desired one could move the flame position closer to the kiln exit, which provides more of an influence than just increasing the peak gas temperature. Similarly, based on the output of coupled VCP VCCTL model, 7 day modulus and 3 day heat of hydration h as a similar trend with peak gas tempe rature and flame position which matches with the results from Figure 4 6 This case gives a meaningful g uidance for the design of a cement kiln Instead of increasing the maximum temperature of flame inside the kiln to create a cement with higher early strength a simple position change of the flame is more energy efficient and sustainable. 5.2 Optimization of VCP VCCTL M odel This section proposed an optimization tool for cement by applying PSO on coupled VCP VCCTL model to save material cost, energy consumption, and decrease CO 2 emission s 5.2.1 C ost vs. Modulus The production of cement typically involves two major costs: energy and material s The cost of e nergy is reported to represent a total of 2 0 40 % of the total cost (Chatziaras et al., 2016; Worrell et al., 2013) Multi objective PSO was integrated into the coupled VCP VCCTL model to create an integrated computational optimization VCP VCCTL tool for energy saving, cost saving and greenhouse gas emissions reduction without sacrificing cement productivity and performance. S imilar to Chapter 3, Pareto front s of four different bi objective scenarios are plotted in Figure 5 7 to show clear trade off between modulus and material cost

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106 In Figure 5 7 the Min (cost of raw meal) Max (E) Pareto front is what the cement industry wants. To preserve strength, the cost cannot be reduced too much from 24.7 to 24.1 $/Ton (2.43% savings). From the Min Max Pareto front, some moduli have to be sacrificed if less cost is required. Most of t he cement in Figure 5 7 is cheaper and weaker. 5.2.2 CO 2 Emission s v s. Modulus As introduced in Chapter 2, 50% of the total emission s comes from calcination/ decomposition of limestone inside the cement kiln which is a considerable amount of emission s Reduction of CO 2 emis sion s from limestone is taken in to consideration in this section. In order to reduce CO 2 emissions without sacrificing cement strength CO 2 emission s from limestone and 7 day modulus are considered as the objectives in PSO at the same time. Figure 5 8 shows the four Pareto fronts for different optimization scenari os on E vs. CO 2 emission s from limestone decomposition. In Figure 5 8 the Min(CO 2 emssion) Max(E) Pareto front is what the cement industry want s The point with 0.14 CO 2 emission s and 27.8 GPa is the optimal cement. When mass fraction of CO 2 emissions is more than 0.14, m ost of the cement give more emissions without sacrificing too much strength. More alite means more decomposition, which typically gives more strength. Th e results of this optimization suggest the coupled VCP/VCCTL model could be used as a tool to optimize for a design cement. 5.2.3 Cost vs. CO 2 Emission s vs. Modulus Figure 5 9 shows the Pareto front for Min(cost) Min(CO 2 emssions) Max(E), which is what the cement industry wants. From the Pareto front, producing cements with high modulus cost more money and release more CO 2 emissions. If the cost of raw meal is reduced from 12.4 $/ton to 11.4 $/ton (9% reduction) and the mass fraction of CO 2 emissions is reduced from 0.16 to 0.14 (15% reduction), modulus would be reduced from 26GPa to 22GPa (18% reduction). This info rmation could be used for make the decision based on the weight of strength, economy

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107 and sustainability. For example, if it is acceptable to sacrifice 18% strength for a cement company, both the sustainability and economic value would improve a lot.

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108 T able 5 1 Comparison of VCP raw meal mass fraction from different input generation approaches Lower B ound Upper B ound Mean Value Fixed Interval Uniformly Distributed Fixed Interval Uniformly Distributed Fixed Interval Uniformly Distributed CaCO 3 0.2645 0.2666 0.4288 0.4258 0.3440 0.3424 CaO 0.2645 0.2665 0.4288 0.4250 0.3440 0.3457 SiO 2 0.1997 0.2014 0.2447 0.2433 0.2211 0.2216 Al 2 O 3 0.0342 0.0337 0.0691 0.0740 0.0512 0.0512 Fe 2 O 3 0.0264 0.0247 0.0591 0.0599 0.0398 0.0394

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109 Table 5 2 Comparison of VCP clinker mass fraction from different input generation approaches From fixed interval inputs From random inputs Lower bound Upper bound Mean Value Lower bound Upper bound Mean Value C 3 S 0.1890 0.4822 0.2998 0.1953 0.4574 0.3028 C 2 S 0.2330 0.3972 0.3343 0.2445 0.3917 0.3360 C 3 A 0.0406 0.1268 0.0797 0.0412 0.1149 0.0725 C 4 AF 0.0691 0.1405 0.0989 0.0712 0.1360 0.1008

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110 Table 5 3 industrial kilns VCP Material Input Range of Industrial Kilns Gap Range between Taylor and Industrial Kilns Expanded Range LSF [0.9, 1.05] [1.18, 1.36] [1.05 ,1.18] [0.9,1.36] SR [2.0, 3.0] [2.1, 2.5] [2.1,2.5] [2.0,3.0] AR [0.8, 2.0] [0.6, 1.0] [0.6,1.0] [0.6,2.0] Fe 2 O 3 [0.01,0.1] [0.0396, 0.0430] [0.0396,0.0430] [0.01,0.1] CaCO 3 /CaO [40%, 60%] [42%, 56%] [42%,56%] [40%,60%]

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111 Table 5 4 Comparison of VCP cases with different material input range 543 Chemistry ( 537 + 4 Industrial Kiln Range ) 561 Chemistry (Industrial Kiln Range) 366 Chemistry ( Gap Range ) 537 Chemistry ( Expanded Range ) C 3 S vs. T g_peak C 3 S vs. T g_peak (Box Plot) C 2 S vs. T g_peak

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112 Table 5 4. Continued 543 Chemistry ( 537 + 4 Industrial Kiln Range ) 561 Chemistry (Industrial Kiln Range) 366 Chemistry ( Gap Range ) 537 Chemistry ( Expanded Range ) C 2 S vs. T g_peak (Box Plot)

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113 Table 5 5 Coupled VCP VCCTL results with 53,700 inputs L g_peak =0.6 L g_peak =0.7 L g_peak =0.8 L g_peak =0.9 C 3 S vs. T g_peak C 3 S vs. T g_peak (Box Plot) C 2 S vs. T g_peak C 2 S vs. T g_peak (Box Plot)

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114 Table 5 5. Continued L g_peak =0.6 L g_peak =0.7 L g_peak =0.8 L g_peak =0.9 CaO vs. T g_peak CaO vs. T g_peak (Box Plot) 7 day modulus vs. T g_peak 7 day modulus vs. T g_peak (box plot)

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115 Table 5 5. Continued L g_peak =0.6 L g_peak =0.7 L g_peak =0.8 L g_peak =0.9 3 day heat vs. T g_peak 3 day heat vs. T g_peak (box plot)

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116 Figure 5 1 Distribution of inputs for VCP generated from fixed intervals

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117 Figure 5 2 Distribution of raw meals derived from fixed interval inputs of VCP

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118 Figure 5 3 Distribution of input for VCP generated from uniformly distributed inputs

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119 Figure 5 4 Distribution of raw meals derived from uniformly distributed inputs of VCP

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120 Figure 5 5 Example of gas temperature input profile for VCP

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121 Figure 5 6 Flow of coupled VCP VCCTL model

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122 Figure 5 7 Pareto fronts of four different bi objective optimization scenarios on E vs. cost of raw meal c ompared with th e data envelope

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123 Figure 5 8 Pareto fronts of four different bi objective optimization scenarios on E vs. CO 2 emissions from limestone compared with the data envelope

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124 Figure 5 9 Pareto fronts of tr i objective optimization scenarios on E vs. CO2 emission s from limestone vs. cost

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125 CHAPTER 6 6 CONCLUSIONS AND RECOMMENDATIONS In summary, the completed research work to date focuses on the metaheuristic algorithms applied to virtual cement and cement plant modeling Single objective and multi objective optimizations with PSO and GA are applied to a set of sample cement data from VCCTL. A scoring system is created to evaluate cement base d on Pareto front optimization results. A 1D physical chemical cement rotary kiln model is simulated with Matlab2016a solver and integrated with VCCTL and multi objective metaheuristic algorithm on the HiperGator high performance computing cluster at Unive rsity of Florida. A computational framework simulating cement and cement pl ant intelligently based on user s requirement s and guiding the optimal designs is proposed The integrated model in this dissertation could p rovide a quantitative optimization tool for different energy efficiency measures addressed from cement plants and reduce energy, material consumption and greenhouse gas emissions without losing the performance of material. However, there is some limitatio ns of the computational framework including lack of criterion for detecting unrealistic virtual testing data. Currently, user defined range of input is given to VCP VCCTL model to conduct optimization. For the future work, thr eshold could be introduced int o the model to detect unrealistic cases. Another cha llenge of this model is it needs more experiment data from cement plant to validate the accuracy of the model. Also, the model could be less computationa l l y expensive with mor e efficient approaches within the coupling and the algorithm.

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126 LIST OF REFERENCES Aarts, E. H., & Korst, J. H. (1988). Simulated annealing. ISSUES, 1 16. Ahmad, S., & Alghamdi, S. A. (2014). A statistical approach to optimizing concrete mixture design. The Scient ific World Journal, 2014 A tcin, P. C. (2000). Cements of yesterday and today: concrete of tomorrow. Cement and Concrete research, 30 (9), 1349 1359. Akhtar, S. S., Ervin, E., Raza, S., & Abbas, T. (2013). From coal to natural gas: Its impact on kiln prod uction, Clinker quality and emissions. Paper presented at the Cement Industry Technical Conference (CIC), 2013 IEEE IAS/PCA. Arrhenius, S. (1889). ber die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Suren. Zeitschrift fr physikalisch e Chemie, 4 (1), 226 248. a rotary kiln in cement industry. Applied Thermal Engineering, 66 (1), 435 444. Babushkin, V. I., Matveev, G. M., & Mchedlov Petros n, O. P. ( 1985 ). Thermodynamics of silicates : Springer. Barr, P. V. (1986). Heat transfer processes in rotary kilns. University of British Columbia. Benhelal, E., Zahedi, G., Shamsaei, E., & Bahadori, A. (2013). Global strategies and potentials to curb CO 2 e missions in cement industry. Journal of cleaner production, 51 142 161. Bentz, D. P. (1997). Three Dimensional Computer Simulation of Portland Cement Hydration and Microstructure Development. Journal of the American Ceramic Society, 80 (1), 3 21. Bentz, D. P., Feng, X., & Stutzman, P. E. (2000). Analysis of CCRL proficiency cements 135 and 136 using CEMHYD3D : National Institute of Standards and Technology, Technology Administration, US Department of Commerce. Bickley, J. A., Hooton, R. D., & Hover, K. C. (2006). Performance specifications for durable concrete. Concrete international, 28 (09), 51 57. Computational modelling of concrete structures. Paper presented at the Proc. of the EURO C Con ference. Bogue, R. H. (1929). Calculation of the compounds in Portland cement. Industrial & Engineering Chemistry Analytical Edition, 1 (4), 192 197. Bonnans, J. F., Gilbert, J. C., Lemarchal, C., & Sagastizbal, C. A. (2006). Numerical optimization: theor etical and practical aspects : Springer Science & Business Media.

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134 BIOGRAPHICAL SKETCH Chengcheng Tao was born in Wuhu, Anhui Province, China. In June 2011, s he received her b achelor degree with highest honor in c ivil e ngineering from Shanghai Normal University, China. Then, s he received her master degree in civil engineering from Carnegie Mellon University in May, 2012 and master degree in mechanical engineering from Johns Hopkins University in August, 2014. Crystal plasticity based finite element modeling in poly crystalline ti 7al alloys In August 2014 she was accepted into the Ph D program in the Department of Civil and Coastal Engineering at the University of Florida with a focus on optimization in cement and concrete and cement plant modeling under the guid ance of Dr. Forrest Masters and Dr. Christopher Ferraro