硫酸鉀鋁批次結晶槽和長晶動力式模擬與最適化操作

Abstract

本篇研究分為兩個部分，藉由不同操作條件下進行批次結晶實驗。利用實驗數據建立硫酸鉀鋁的動力模型。此外，利用電腦最適化模擬最佳降溫曲線達到目標函數的需求。 去過飽和度實驗可以決定成長動力式的參數。藉由在不同過飽和度和溫度下的操作條件中回歸出成長係數(〖 k〗_g)和活化能數值(E_a)，進而得到完整動力式G=(T,S)=〖 k〗_g e^((-E_a)/RT)×S^g。在批次降溫結晶實驗中，操作不同降溫速率和起始過飽和度，得到不同粒徑分佈的產物，粒徑測量的儀器使用(LS230)雷射式散射分析儀，藉由體積粒徑分佈圖得到成核動力式和成長動力式。此外，電腦模擬部分本篇使用成長速率機率分佈曲線進一步優化模擬的體積粒徑分佈圖，並且與固定成長速率模型做比較。 本篇最適化模擬使用疊代方法，利用Matlab模擬最佳降溫曲線求得目標函數μ_(3.n)/μ_3 (最小成核體積比率)。

In this work batch crystallization experiments of potassium aluminum sulfate was performed with manipulating various operation valuables. Experimental results are used to determine the kinetic parameters of nucleation rate and growth rate. The second part of this work is computer program simulation to optimize temperature trajectories operating batch cooling experiment with specific objective function. The purpose of the desupersaturation experiment is to determine the kinetic parameters of growth rate equation. Data are collected under different conditions, degree of supersaturation and temperature and fit to the model form G=(T,S)=〖 k〗_g e^((-E_a)/RT)×S^g. There are two experimental variables in this simulation: temperature (T), supersaturation (S). We can determine the pre-experimental factor (〖 k〗_g), activation factor (E_a) and g opponent for potassium aluminum sulfate by regression. In batch cooling crystallization, the results show that we achieve different crystal size distribution by manipulating the cooling rate and the initial degree of supersaturation. The study also include the crystal size distribution(CSD) and volume size distribution(VSD) result of the crystal products measured by Laser Diffraction Particle Size Analyzer(Coulter LS230). In this study we investigate the growth rate, and nucleation based on the CSD results. Furthermore, we analyze the CSD and VSD with the growth rate dispersion model. The dispersion model show that the effect of growth rate dispersion on the crystal size distribution may be significant. In this study, the result show the CSD and VSD comparison between constant growth rate model and Gamma distribution type of growth rate dispersion model. The method of optimizations are the method of iteration. This work use Matlab program to construct the optimization problem which is to find the minimum μ_(3.n)/μ_3 (minimize the nucleation mass) which is the objective function in this work.