以三種反應剖面與不同曲線擬合方式探討主導動力學曲線模型之普適性

A Study on the Universality of the Master Kinetics Curve Model: Using Three Types of Reaction Profiles and Different Curve Fitting Methods

陳玟卉(Wen-Hui Chen)

指導教授 ： 鄧茂華

國立臺灣大學/理學院/地質科學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201804290

摘要

主導動力學曲線(Master Kinetics Curve, MKC)模型是以一般化學反應速率方程式為基礎推導的動力學模型，其具有使用方便、預測準確、應用範圍廣三個主要優點。前人研究中已將此模型成功應用在熱分解反應、相變反應、燒結反應與油母質生油反應，說明主導動力學曲線模型有可能是一種具普適性之動力學模型。所有化學反應皆可以原始資料反應剖面曲線型態分為三型，S型、減速型與加速型。然而，上述已成功應用之反應的反應剖面曲線型態皆為S型，其他曲線型態則尚未有系統的測試其主導動力學曲線模型之適用性與限制。故本研究以水鎂石熱分解反應探討減速型原始資料反應剖面的模型適用性，擬合數據包含熱重分析實驗數據、熱膨脹分析實驗數據、理論合成數據與文獻數據。主導動力學曲線模型分析結果顯示，除了熱膨脹分析實驗數據外，此模型可用於減速型反應，並得到擬合良好之S型預測曲線與視活化能，其視活化能分別為117.5 kJ/mol、135.0 kJ/mol、153.2 kJ/mol、147.0 kJ/mol。在熱膨脹實驗中，坯體長度變化綜合了坯體熱膨脹與熱分解反應造成之收縮，而總收縮量卻只有1.6%，使熱膨脹的影響無法被忽略，也造成主導動力學曲線之擬合不佳。加速型原始資料反應剖面方面則以焦碳氧化反應文獻數據與power-law理論合成數據進行分析討論，兩種數據皆可以得到擬合良好之主導動力學曲線，而且其曲線型態為指數型。綜合減速型與加速型反應剖面的結果顯示，主導動力學曲線模型適用性與原始資料反應剖面之曲線型態無關，且其應用限制只與一般化學反應速率方程式相關。只要反應為單步驟反應或為有速率決定步驟之多步驟反應，即可以利用主導動力學曲線模型進行動力學分析。另外，主導動力學曲線模型並未限制擬合曲線之型態，故本研究嘗試以五種不同曲線擬合方程式討論S型與指數型主導動力學曲線的擬合情況，擬合結果顯示本研究目前使用的S型曲線擬合方程式為最佳擬合方式，其擬合結果佳且適用於各種曲線型態。由於三種不同反應剖面之原始資料包含所有反應機制之反應，故本研究顯示主導動力學曲線模型為具有普適性之動力學模型且拓展了模型的應用範圍。

關鍵字

反應動力學 ； 主導動力學曲線模型 ； 反應剖面 ； 曲線擬合 ； 水鎂石熱分解反應

並列摘要

The Master Kinetics Curve (MKC) model is developed from a general reaction rate equation. The MKC model has three advantages easy to use, accurate predictions and wide applications. In previous studies, researchers had already applied the model to thermal decomposition, phase transformation, sintering reaction, and kerogen-to-oil conversion to show the possibility of the MKC model serving as a universal kinetic model. However, the reaction profile of the reaction mentioned above is S-shaped. Reactions with different reaction profiles (i.e. accelerating-type and decelerating-type) have not yet been tested.
In this study, the thermogravimetric analysis data, dilatometric analysis data, theoretical synthetic data, and literature data on brucite thermal decomposition have been applied to the MKC model to explore whether the reactions in which the reaction profile is the decelerating-type, can be applied to the MKC model. The results show that the MKC model can be used to analyze and predict the decomposition reaction of brucite except for the dilatometric analysis data. The apparent activation energies of the thermogravimetric analysis data, dilatometric analysis data, theoretical synthetic data, and literature data were 135.0 kJ/mol, 153.2 kJ/mol, 147.0 kJ/mol, respectively. In the dilatometric experiment, the length change of green compact combines the shrinkage caused by the thermal decomposition and thermal expansion of the green compact. Since the shrinkage of the thermal decomposition reaction is only 1.6%, the effect of thermal expansion cannot be ignored. This situation caused the bad fitting of the MKC, because the MKC model cannot use single MKC to describe the reaction process with multiple reactions combined. To explore whether the reactions in which the reaction profile is accelerating-type can be applied to the MKC, theoretical synthetic data and literature data on coke oxidation reaction have been applied to the MKC model. The MKC results show that good fitting prediction curves and apparent activation energies can be obtained. The applicability of the MKC model is independent of the reaction profile. The application limits of the MKC model are only related to the general chemical reaction rate equation. If the reaction is a one-step or multi-step reaction with a rate-determining step, the kinetic study can be conducted using the MKC model.
The MKC model does not limit the curve fitting method. Therefore, this study uses five different curve fitting equations to discuss the fittings of the S-type and accelerating-type MKCs. The fitting results show that the S-type fitting equation, which is currently used in this study, is the best fitting method. The S-type fitting equation has great fitting goodness and is suitable for various curves. This study proves that reactions with three types of reaction profiles can be applied to the MKC model, which indicates that reactions with all reaction models can be applied. Therefore, the MKCmodel is a universal kinetic model.

並列關鍵字

reaction kinetics ； Master Kinetics Curve (MKC) model ； reaction profile ； curve fitting ； thermal decomposition of brucite

參考文獻

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