臺灣博碩士論文加值系統

在蒸餾分離系統中，最小能量需求與最小迴流比之計算是一項重要的設計參數；相同地，最小理想板數決定了最低成本需求，利用精確的商用模擬軟體計算時，若給于正確的估計值則對於收斂問題可以獲得有效的解答。然而這些估算方法對於複合蒸餾塔(多重進料、多重出料、共沸蒸餾、反應蒸餾及受質傳限制蒸餾塔)的設計並不全然有用，那些傳統具啟發性的簡易設計方法，會因為無法正確計算非關鍵成分分布預估值，而得到錯誤的設計結果，或者僅能應用在特別的分離系統(如直接分離、間接分離、高純度分離系統) 。本研究的目的在發展一種具通用性以幾何為基礎之簡易設計方法，來計算蒸餾塔之最小迴流比與最小理想板數，此方法可以應用在各種型態的蒸餾分離系統，它包含整個設計問題的公式化，如何利用合適的數值演算法來尋找可靠有效的全域收斂解。本論文提出了對非莫耳守恆的反應蒸餾系統的數學模型，利用邊界值法開發成一般幾何捷徑設計方法的最適化問題，此外，根據Maxwell-Stefan質傳模式，我們也探討質傳作用對蒸餾系統設計的影響。各種情況的應用分析如多重進料、多重產物、受質傳限制蒸餾、反應蒸餾塔，利用諸多範例的說明可以證明，所提出的簡易設計方法可應用在蒸餾分離系統的概念設計上。

The minimum energy or minimum reflux ratio calculation is an important design parameter to distillation separation system. Similarly, determination of minimum number of plates gives a minimum estimate of the capital expenditure required. The rigorous commercial simulator could provide efficient solutions under good estimate for convergence problems. Such estimates may not be readily available for complex columns (multi-feed and multi-draw, azeotropic, reactive, mass-transfer limited distillations). The conventional heuristic shortcut design methods, which had been proposed either have not correct estimate to non-key component distribution caused erroneous results or restrict to specific separation (e.g. direct split, indirect split, sharp split). The objective of this work is to develop a general geometric based shortcut method for estimating the minimum reflux ratio and minimum number of stage that can be used for any columns. It includes the formulation of the problem, finding a suitable numerical algorithm that is efficient and guarantees global convergence. We have proposed the mathematical model to molar un-conservative reactive distillation system are developed a general geometric shortcut design method by formulating the boundary value method into an optimization problem. Furthermore, the influences of mass transfer effects to the design of distillation system are explored based on the Maxwell-Stefan mass transfer approach. Application analysis in various situations such as multi-feed and multi-product, mass transfer limited, and reactive columns will also be carried out. Many examples are implemented to show the ability and capability of the proposed shortcut design methods in conceptual design of distillation separation systems.

Contents

Chapter 1 Introduction 1
1.1 Brief Literature Survey 1
1.2 Objective, Scope and Organization 6
Chapter 2 Conventional Geometric Shortcut Design Methods 8
2.1 Binary Systems 8
2.1.1 McCabe and Thiele Diagram 8
2.1.2 Total Reflux 9
2.1.3 Condition of Feed Pinch and Minimum Reflux 10
2.2 Constant Relative Volatility Method for Multicomponents Systems 12
2.2.1 Fenske Equation 12
2.2.2 Underwood Equation 12
2.3 Conventional Geometric Shortcut Design Methods 13
2.3.1 Residue Curve Map 13
2.3.2 Boundary Value Method 19
2.3.3 Zero Volume Criterion 21
2.3.4 Minimum Angle Criterion 26
2.3.5 Eigenvalue Criterion 26
2.3.6 Rectification Body Method 27
2.4 Summary 29
Chapter 3 Solutions of Shortcut Design Problem for Multi-components Multi-feed Columns 31
3.1Conventional Multi-feed Columns Design Methods and Non-key Components Estimation 31
3.2 Theory 36
3.2.1 Basic CMO Model 37
3.2.2 Diverging Analysis 38
3.2.3 Minimum Reflux Ratio 39
3.2.4 Total Reflux 40
3.2.5 Finding Column Profiles and Reflux 40
3.2.6 Simulated Annealing Algorithm 41
3.3 Silmulation Results and Discussions 41
3.3.1 Single Feed Column 42
3.3.2 Double Feed Column 46
3.3.3 Multi-components Double Feed Column 49
3.3.4 Full Column Design Examples 50
3.4 Short Conclusions 53
Chapter 4 Solutions of Shortcut Design Problem for Reactive Distillation Systems 54
4.1 Literature Survey 54
4.2 Theory 66
4.2.1 Model of RDC 66
4.2.2 Feasible Column Design 70
4.2.3 Minimum Reflux Ratio 70
4.2.4 Minimum Number of Stages 71
4.3 Silmulation Results and Discussions 71
4.3.1 Solutions of Infinite Column Stages and Reflux Ratio 73
4.3.2 Solutions of Fixed Column Stages and Reflux Ratio 75
4.4 Short Conclusions 76
Chapter 5 Mass Transfer Effects on Minimum Reflux Ratio 78
5.1 Introduction 78
5.2 Distillation Curve with Mass Transfer 79
5.3 Effects of Mass Transfer on Different Pinch Scenarios 82
5.4 Nonideal Systems with Boundary Crossing 94
5.5 Mass Transfer Effects on Column Stages 99
5.6 Short Conclusions 101
Chapter 6 Conclusions 102
Notation 104
References 109


Figures

Figure 2-1：A standard McCabe-Thiele Diagram for a binary distillation system 9
Figure 2-2：Minimum number of stages at total reflux 10
Figure 2-3：Condition of "feed pinch" and minimum reflux 11
Figure 2-4：Condition of "tangent pinch" 11
Figure 2-5：A simple batch distillation still 15
Figure 2-6：Residual curve maps of an ideal ternary hydrocarbon mixture 16
Figure 2-7：RCM for acetone-chloroform-benzene at 1 atm 16
Figure 2-8：Operation leaves of feasible column products 18
Figure 2-9：Rectification and stripping curves at different reflux ratios 20
Figure 2-10：Classifications of direct and indirect split for ternary system 21
Figure 2-11：Collinearity condition of end pinch and saddle pinch for a sharp split 22
Figure 2-12：Collinearity condition of ZVC 23
Figure 2-13：Column profiles of non-sharp separation for ideal system 25
Figure 2-14：Geometric approximation of the manifold of plate-to-plate profiles at minimum reflux through rectification bodies 29
Figure 3-1：Different pinch scenarios 35
Figure 3-2：Example of bifurcation when starting point of a section is an end point 39
Figure 3-3：Column profiles of infeasible design in Case I 44
Figure 3-4：Column profiles of infeasible design in Case VI 45
Figure 3-5：Case VII-- rectification pinch for a two-feed column 47
Figure 3-6：Case VIII-- stripping pinch for a two-feed column 48
Figure 3-7：Case IX-- middle pinch for a two-feed column 48
Figure 3-8：Column profiles with infinite column stages for a two-feed column 51
Figure 3-9：Column profiles with infinite reflux ratio for a two-feed column 51
Figure 3-10：Column profiles with fixed column stages for a two-feed column 52
Figure 3-11：Column profiles with fixed reflux ratio for a two-feed column 52
Figure 4-1：RCM and column profiles at different reflux ratio for quaternary ideal system of RDC 64
Figure 4-2：Scheme of a double-feed, two-product RDC 67
Figure 4-3：Configuration of hypothetical ternary RDC 73
Figure 4-4：Column profiles of RDC at infinite column stages (Da=0.1, Keq=5,ε=90%, SPLK =99, SPHK =0.001) 74
Figure 4-5：Column profiles of RDC at infinite reflux ratio (Da=0.1, Keq=5,ε=90%, SPLK =99, SPHK =0.001) 74
Figure 4-6：Column profiles of RDC at finite column stages (Da=0.1, Keq=5,ε=90%, SPLK =99, SPHK =0.001, NT=15) 75
Figure 4-7：Column profiles of RDC at finite reflux ratio (Da=0.1, Keq=5,ε=90%, SPLK =99, SPHK =0.001, R=4.44) 76
Figure 5-1：Effect of mass transfer on pinch point locations (z=[0.3, 0.3, 0.4], R=1.465, SPLK=999, SPHK=0.001, SPNK=10-12) 84
Figure 5-2：Distillation curves and eigenvalues profiles for stripping end pinch(z=[0.3, 0.3, 0.4], R=1.465, SPLK=999, SPHK=0.001, SPNK=10-12, Noyref=19) 85
Figure 5-3：Effect of non-key split on stripping pinch (z=[0.3, 0.3, 0.4], SPLK=999, SPHK=0.001) 86
Figure 5-4：Effect of mass transfer effect on pinch point location to rectification pinch (z=[0.3, 0.3, 0.4], SPLK=999, SPHK=0.001) 88
Figure 5-5：Distillation curves and eigenvalues profiles for rectification end pinch (z=[0.3, 0.3, 0.4], SPLK=999, SPHK=0.001) 89
Figure 5-6：Effect of non-key distribution to indirect split (z=[0.3, 0.3, 0.4], SPLK=999, SPHK=0.001) 90
Figure 5-7：Infeasible design with mass transfer effect to different reflux ratios (z=[0.3, 0.3, 0.4], SPLK=999, SPHK=0.001) 90
Figure 5-8：Effect of mass transfer effect on minimum reflux for a feed pinch system (z=[0.3, 0.3, 0.4], SPLK=999, SPHK=0.001, SPNK=0.6, R=0.21) 92
Figure 5-9：Distillation curves and eigenvalues profiles for feed pinch (z=[0.3, 0.3, 0.4], SPLK=999, SPHK=0.001) 93
Figure 5-10：True minimum reflux ratio with large mass transfer effect on middle non-key split (z=[0.3, 0.3, 0.4], SPLK=999, SPHK=0.001) 94
Figure 5-11：Two columns separation flow sheet of non-ideal system 96
Figure 5-12：Location of products and distillation boundary of nonideal system 96
Figure 5-13：Effect of mass transfer on boundary crossing for a nonideal system in column 1 (z=[0.11, 0.214, 0.676], SPLK=99, SPHK=0.01, SPNK=10-12, R=10.04) 97
Figure 5-14：Effect of mass transfer on minimum reflux for a nonideal system in column 2 (SPLK=99, SPHK=0.01, R=8.17) 98
Figure 5-15：Effect of sharp non-key split leads an infeasible design to column2 98
Figure 5-16：Mass transfer effect on minimum number of stages to indirect split 100
Figure 5-17：Mass transfer effect on minimum number of stages to direct split 100


Tables

Table 3-1：Results of sharp separation to single-feed column (α1=2, α2=1.1,α3=1), q=1, z=(0.3, 0.3, 0.4), SPLK = 999, SPHK = 0.001 43
Table 3-2：Results of sharp separation to single-feed column (α1=2, α2=1.9,α3=1), q=1, z=(0.3, 0.3, 0.4), SPLK = 999, SPHK = 0.001 45
Table 3-3：Results of different pinch situations to double-feed column 47
Table 3-4：Results of sharp separation to multi-components double-feed column, z1=(0.4, 0.3, 0.2, 0.1), q1=1, z2=(0.1, 0.2, 0.3, 0.4), q2=1, SPLK = 999, SPHK = 0.001 49

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