Discretization approach

학위논문(박사)--서울대학교 대학원 :공과대학 화학생물공학부(에너지환경 화학융합기술전공),2019. 8. 이원보.In recent years, many researchers in chemical engineering have made great efforts to develop mathematical models on the theoretical side that are consistent with experimental results. Despite these efforts, however, establishing models for a system with complex phenomena such as multiphase flow or stirred reactors is still considered to be a challenge. In the meantime, an increase in computational efficiency and stability in various numerical methods has allowed us to correctly solve and analyze the system based on the fundamental equations. This leads to the need for a mathematical model to accurately predict the behavior of systems in which there is interdependence among the internal elements. A methodology for building a model based on equations that represent fundamental phenomena can lower technical barriers in system analysis. In this thesis, we propose three mathematical models validated from laboratory or pilot-scale experiments. First, an apparatus for vaporizing liquid natural gas is surrounded with a frost layer formed on the surface during operation, and performance of the apparatus is gradually deteriorated due to the adiabatic effect. Because the system uses ambient air as a heat sink, it is necessary to consider the phase transition and mass transfer of water vapor, and natural gas in the air in order to understand the fluctuation of system characteristics. The model predicts the experimental data of a pilot-scale vaporizer within a mean absolute error of 5.5 %. In addition, we suggest the robust design methodology and optimal design which is able to maintain the efficiency under the weather conditions for a year. Two or more data analysis techniques including discrete waveform transformation and k-means clustering are used to extract features that can represent time series data. Under the settings, the performance in the optimized desgin is improved by 22.92 percentage points compared to that in the conventional system. In the second system, the continuous tubular crystallization reactor has advantages in terms of production capacity and scale-up compared with the conventional batch reactor. However, the tubular system requires a well-designed control system to maintain its stability and durability, and thus; there is a great deal of demand for the mathematical model of this system. We were able to estimate crystal size distribution by considering the population balance model simultaneously with several heat exchanger models. The model constructed based on the first principle reaction scheme successfully predicted the results from the full-factorial experiment. The experiments were conducted with LAM (L-asparagine monohydrate) solution. In the prediction, the average crystal length and standard deviation were within 20% of the results of an experiment where the crystals were not iteratively dissolved in the liquid but maintained a low-level supersaturation. Furthermore, to confirm the controllability of the crystal size distribution in the system, we replaced the LAM solution with HEWL (Hen-egg white lysozyme) solution. Finally, we propose a multi-compartment model to predict the behavior of a high-pressure autoclave reactor for polymer production. In order to simulate a complex polymer synthesis mechanism, the rotation effect of impellers in the reactor on polymerization and the influence caused by polymerization heat were sequentially evaluated. As a result, This model turned out to be able to predict the physical properties of the polymers produced in an industrial-scale reactor within 7% accuracy. In this thesis, all three systems are distributed parameter systems which can be expressed as partial differential equations for time and space. To construct a high order model, the system was interpreted based on discretization approach under minimal assumptions. This methodology can be applied not only to the systems suggested in this thesis but also to those consisting of interpdependent variables. I hope that this thesis provides guidance for further researches of chemical engineering in nearby future.최근에 몇 년에 걸쳐서 많은 연구자들이 이론을 기반으로 실험 결과와 일치하는 수학 모델을 개발하고자 많은 노력을 기울여 왔다. 하지만 이런 노력에도 불구하고 다상 흐름 혹은 교반 반응기와 같은 복잡한 현상을 내포한 시스템을 위한 모델을 수립하는 것은 여전히 화학 공학 분야에서 쉽지 않은 일로 여겨진다. 이 와중에 다양한 수치적 방법에서의 계산 효율의 증가와 안정성의 향상은 기본방정식에 기초한 시스템을 정확하게 해결하고 분석할 수 있게 해주었다. 이로 인하여 내부 요소들 간의 상호 의존성이 존재하는 시스템의 거동을 정확하게 예측하기 위한 수학적 모델의 필요성이 부각되었다. 기본 현상들을 표현할 수 있는 방정식들을 기반으로 모델을 구축하기 위한 방법론은 시스템 해석에 있어서 기술적 장벽을 낮출 수 있다. 이 학위 논문에서 우리는 실험실 또는 파일럿 규모의 실험으로부터 입증된 세 가지 수학적 모델을 제안한다. 첫 번째로, 공기를 사용하여 액상의 천연가스를 기화시키는 장치는 운전 도중에 기화기 표면에 서리 층이 형성되고 그로 인한 단열 효과로 장비의 성능이 서서히 저하된다. 시스템은 주변 공기를 열 흡수원으로 사용하기 때문에 시스템 특성의 변동을 파악하기 위해서는 공기 중 수증기 및 천연 가스의 상전이 및 전달 현상을 동시에 고려하여야 한다. 제시된 수학적 모델에 의해 예측한 결과는 파일럿 규모 기화기로부터 얻은 실험 데이터와 5.5% 평균 절대 오차를 보였다. 이에 더하여, 앞에서 제시한 기화기 모델을 이용하여 1년 동안의 기상 조건에서 운전 효율을 유지하면서 지속 운전이 가능한 기화기의 설계 방법과 결과를 제안하였다. 이산 파형 변환과 k-평균 군집화를 포함하는 두 가지 이상의 데이터 분석 기법을 사용하여 시계열 데이터를 대표할 수 있는 특징을 추출한다. 추출된 특징 아래에서 최적화된 디자인은 기존 제시된 안에 비해 22.92% 만큼 향상된 성능을 보여주었다. 두 번째 시스템은 신 제약 기술 공정인 연속 관형 결정화 반응기는 기존에 널리 쓰이던 회분식 반응기에 비하여 생산 속도 및 스케일 업 측면에서 장점이 많다. 하지만 제어기술이 기반이 되어야한다는 점에 있어서 그 도입이 늦어졌고 이에 따라 자연스럽게 개발된 모델 또한 전무하다. 우리는 이 장치에서 결정 크기 분포를 추산하기 위한 인구 균형 모델을 열 교환 모델과 동시에 고려하여 결정 크기 분포를 추산할 수 있었다. 제 1원리 결정 반응식을 기반으로 구축된 모델은 완전 요인 배치법을 기반으로 실험된 데이터를 성공적으로 예측하였다. 결정이 액상에 용해되지 않으면서 낮은 수준의 과포화 상태를 유지한 실험에 대해서는 평균 결정 길이와 표준편차가 실험 결과와 20% 이내의 오차를 보였다. 앞에서 모델의 검증에 사용된 데이터가 LAM (L-아스파라긴 일 수화물)용액으로부터 얻어진 것이었다면 이후에는 HEWL (달걀 흰자 리소자임)를 사용하여 제품의 결정 크기 분포의 조절 가능성을 보였다. 마지막으로 폴리머 생산을 위한 고압 오토클레이브 반응기의 거동을 예측하기 위한 다중 구획 모델을 제안하였다. 복잡한 고분자 합성 메커니즘을 모사하기 위하여 반응기 내 임펠러의 회전이 중합에 미치는 효과와 중합 열로 인한 영향력을 순차적으로 평가하였다. 제안된 모델은 3D 구조를 가진 산업화된 반응기에서 생산된 두 가지 고분자의 물성을 7%이내 정확도로 예측할 수 있다. 본 학위논문에서는 다루는 시스템은 모두 분포 정수계 시스템으로 시간과 공간에 대하여 편미분방정식으로 표현할 수 있다. 고차 모델을 구축하기 위해 이산화 접근법을 기반으로 최소한의 가정 하에 시스템을 해석하였다. 이는 논문에 제시한 시스템 뿐만 아니라 시공간에서 예측 어려운 분포를 가지는 변수를 가진 모든 시스템에 대하여 적용이 가능하다. 이 논문이 앞으로 화학 공학 분야의 시스템을 해석하는 데 있어서 더 발전된 연구를 위한 지침서가 되기를 희망한다.Abstract i Contents iv List of Figures viii List of Tables xii Chapter 1 1 Introduction 1 1.1 Research motivation 1 1.2 Research objective 3 1.3 Outline of the thesis 4 1.4 Associated publications 9 Chapter 2 10 Distributed parameter system 10 2.1 Introduction 10 2.2 Modeling methods 11 2.3 Conclusion 16 Chapter 3 17 Modeling and design of pilot-scale ambient air vaporizer 17 3.1 Introduction 17 3.2 Modeling and analysis of frost growth in pilot-scale ambient air vaporizer 24 3.2.1 Ambient air vaporizer 24 3.2.2 Experimental measurement 27 3.2.3 Numerical model of the vaporizer 31 3.2.4 Result and discussion 43 3.3 Robust design of ambient air vaporizer based on time-series clustering 58 3.3.1 Background 58 3.3.2 Trend of time-series weather conditions 61 3.3.3 Optimization of AAV structures under time-series weather conditions 63 3.3.4 Results and discussion 76 3.4 Conclusion 93 3.4.1 Modeling and analysis of AAV system 93 3.4.2 Robust design of AAV system 95 Chapter 4 97 Tunable protein crystal size distribution via continuous crystallization 97 4.1 Introduction 97 4.2 Mathematical modeling and experimental verification of fully automated continuous slug-flow crystallizer 101 4.2.1 Experimental methods and equipment setup 101 4.2.2 Mathematical model of crystallizer 109 4.2.3 Results and discussion 118 4.3 Continuous crystallization of a protein: hen egg white lysozyme (HEWL) 132 4.3.1 Introduction 132 4.3.2 Experimental method 135 4.3.3 Results and discussion 145 4.4 Conclusion 164 4.4.1 Mathematical model of continuous crystallizer 164 4.4.2 Tunable continuous protein crystallization process 165 Chapter 5 167 Multi-compartment model of high-pressure autoclave reactor for polymer production: combined CFD mixing model and kinetics of polymerization 167 5.1 Introduction 167 5.2 Method 170 5.2.1 EVA autoclave reactor 170 5.2.2 Multi-compartment model of the autoclave reactor 173 5.2.3 CFD simulation of mixing effects in the autoclave reactor 175 5.2.4 Region-based dividing algorithm 178 5.2.5 Polymerization kinetic model 182 5.3 Results and discussion 191 5.4 Conclusion 203 5.5 Appendix 205 Chapter 6 210 Concluding Remarks 210 6.1 Summary of contributions 210 6.2 Future work 211 Appendix 214 Acknowledgment and collaboration declaration 214 Supplementary materials 217 Reference 227 Abstract in Korean (국문초록) 249Docto

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