Superstructure Optimization of Multiple Cyclone Arrangements Using Mixed Integer Nonlinear Programming by Muhamad Fariz Failaka A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Applied Science in Chemical Engineering Waterloo, Ontario, Canada, 2015 (cid:13)c Muhamad Fariz Failaka 2015 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract The gas-solid cyclone has been remarkably widely used among all types of industrial gas-cleaning devices. Many studies have been conducted and reported excessive experi- mental, theoretical, and computational research aimed at understanding and predicting the performance of cyclones. However, the majority of these works have only focused on the development of single cyclones. In the meantime, the use of multiple cyclones can be considered as one solution to the demands of obtaining the best pollution control strategies to achieve a minimum level of pollution reduction. This has motivated the development of effective formulation for the cyclone arrangement problem. In this work a new opti- mization model of multiple cyclone arrangement is presented. The key idea is to present the capability of General Algebraic Modeling System (GAMS) software in obtaining the optimal number and dimensions of the cyclone, and the best cyclone arrangement for a certain condition with respect to the minimum total cost, including the operating cost and the capital cost. The proposed model of nonlinear programming (NLP) and mixed integer nonlinear programming (MINLP) has been successfully applied to different case studies. The NLP model is applied to an NPK (Nitrogen, Phosphorus, and Potassium) fertilizer plant to find the optimal number and dimensions of the 1D3D, 2D2D, and 1D2D cyclones arranged either in parallel or series. In another case study with the total flow rate of 165 m3/s of a stream to be processed in a paper mill, the best cyclone arrangement of parallel-series for three different combinations of the 1D3D and 2D2D cyclone is obtained through the use of MINLP modeling. The results show that different types of cyclones, applied in NPK fertilizer plant, result in different optimal numbers of cyclones. Each type of cyclone (i.e., 1D3D, 2D2D, and 1D2D) has an alternative that can be arranged either in parallel or in series configuration. Furthermore, different values used for the upper bound of D and N in the proposed MINLP model, result in a different cyclone arrangement of parallel-series selected as the optimal solution. The cyclone of 2D2D+2D2D arranged in parallel-series is found to be more economical and efficient compared to other arrangements. iii Acknowledgements First and foremost, I would like to express my sincere gratitude to my supervisor Pro- fessor Ali Elkamel for his great continuous encouragement, and valuable guidance during my entire Master program. I am extremely thankful and indebted to him for all the valu- able knowledge which has been greatly enrich my work. I would also like to thank Dr. Sabah Abdul-Wahab, for her assistance during my early days in Master studies. I would like to thank my co-supervisor Dr. Chandra Mouli R. Madhuranthakam for his guidance to my work. I would like to extend my thanks to the readers of my thesis, Professor Aiping Yu and Professor Ting Tsui. I would like to thank PT Pupuk Kaltim, for giving me the trust and also providing me with the opportunity to undertake Master study at the University of Waterloo. I would also like to extend my gratitude to Professor Renanto Handogo, Professor Ali Altway, and Professor Mahfud. I hope I have made all of you proud. I would like to thank my colleagues, Abdul Halim Abdul Razik, Saad Alsobhi, Hussein Ordoui, Lena Ahmadi, and Hariharan Krithivasan for the helpful discussions, and to all my friends in Waterloo for making my time becomes a very enjoyable experience. I would like to thank all the Indonesian families in the Region of Waterloo, Great Toronto Area (GTA), and surroundings for always making me feel like home. Last but not least, it is my privilege to express my deepest gratitude to my parents who have always been there for me. Finally, I would like to thank my beloved family, especially to my wife for constant encouragement throughout my research period. Thank you for being my editor and proof- reader. But most of all, thank you for being my best friend. I owe you everything. Living and studying in Waterloo, Canada is a once-in-a-lifetime opportunity and has probably become a moment that will always be remembered throughout a lifetime. iv Dedicated to my parents, and my beloved family v Table of Contents List of Tables ix List of Figures xi Nomenclature xiii 1 Introduction 1 1.1 Research capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Overview on cyclones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Literature Review 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Mathematical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Estimation of the cut-size diameter . . . . . . . . . . . . . . . . . . 10 2.2.2 Estimation of the pressure drop . . . . . . . . . . . . . . . . . . . . 12 2.3 Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 vi 2.4 Computational fluid dynamics (CFD) simulations . . . . . . . . . . . . . . 16 2.5 Mathematical programming models . . . . . . . . . . . . . . . . . . . . . . 16 2.5.1 Nonlinear Programming (NLP) models . . . . . . . . . . . . . . . . 17 2.5.2 Mixed Integer Nonlinear Programming (MINLP) models . . . . . . 19 3 Nonlinear programming optimization of series and parallel cyclone ar- rangement of NPK fertilizer plants 22 3.1 Overview of process of actual NPK granulation fertilizer plant . . . . . . . 23 3.2 Objective of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 The equations employed in the modeling . . . . . . . . . . . . . . . . . . . 26 3.3.1 Equation for the cut-size diameter . . . . . . . . . . . . . . . . . . . 26 3.3.2 Equation for the pressure drop . . . . . . . . . . . . . . . . . . . . . 30 3.3.3 Equation for the cost per unit of cyclone . . . . . . . . . . . . . . . 30 3.4 Mathematical models of parallel cyclone arrangement . . . . . . . . . . . . 31 3.5 Mathematical models of series cyclone arrangement . . . . . . . . . . . . . 33 3.6 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.7 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4 Mixed Integer Nonlinear Programming Optimization of Multiple Cy- clone Arrangement 50 4.1 Overview of proposed model . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.3 MINLP formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 vii 4.3.1 Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5 Conclusions and Recommendations 84 5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Appendices 88 A Copyright Release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 B MATLAB code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 References 91 viii List of Tables 1.1 Cyclone configuration ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1 Specification of input feed to the cyclone . . . . . . . . . . . . . . . . . . . 39 3.2 Optimization results from GAMS code for 1D3D cyclones in parallel . . . . 41 3.3 Optimization results from GAMS code for 2D2D cyclones in parallel . . . . 42 3.4 Optimization results from GAMS code for 1D2D cyclones in parallel . . . . 43 3.5 Comparison of predicted cyclone diameters and pressure drops for 1D3D, 2D2D and 1D2D cyclones in parallel arrangement . . . . . . . . . . . . . . 45 3.6 Optimal solution of 1D3D cyclone series arrangement . . . . . . . . . . . . 47 3.7 Optimal solution of 2D2D cyclone series arrangement . . . . . . . . . . . . 47 3.8 Optimal solution of 1D2D cyclone series arrangement . . . . . . . . . . . . 48 4.1 Composition of each level . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.2 Cyclone configuration ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.3 Specification of input feed to the cyclone system . . . . . . . . . . . . . . . 55 4.4 Bounds on decision variables, a . . . . . . . . . . . . . . . . . . . . . . . 69 i 4.5 Optimization result for DU = 0.3 m and NU = 500 . . . . . . . . . . . . . 70 p p 4.6 Optimization result for DU = 0.4 - 0.6, 0.8, 2.3 m and NU = 300 . . . . . 70 p p ix 4.7 Optimization result for DU = 0.7 m and NU = 100 . . . . . . . . . . . . . 70 p p 4.8 Optimization result for DU = 0.8, 1.0 - 1.1, 1.3 m and NU = 200 . . . . . 70 p p 4.9 Optimization result for DU = 0.9 m and NU = 400 . . . . . . . . . . . . . 71 p p 4.10 Optimization result for DU = 1.2, 1.5, 1.6, 1.8, 2.1, 2.2 m and NU = 250 . 71 p p 4.11 Optimization result for DU = 1.9, 2.0, 2.4 m and NU = 350 . . . . . . . . 71 p p 4.12 Optimization result for DU = 1.7 m and NU = 450 . . . . . . . . . . . . . 71 p p 4.13 Optimization result for DU = 1.3 - 1.5, 1.6 - 2.0, 2.2 - 2.5 m and NU = 30 72 p p 4.14 Optimization result for DU = 2.1 - 2.2, 2.4 - 2.5 m and NU = 40 . . . . . 72 p p 4.15 Optimization result using the decision variables N and η . . . . . . . . . 81 ov 4.16 Complete results for level 3 as the best arrangement and η = 80 % - 90 % 81 ovt 4.17 Comparison of the optimal solution of decision variables . . . . . . . . . . 82 x