PREDICTING THE PRODUCTS OF CRUDE OIL DISTILLATION COLUMNS
A thesis submitted to the University of Manchester for the degree of Master of Philosophy in the Faculty of Engineering and Physical Sciences
2012
By Jing Liu School of Chemical Engineering and Analytical Science Contents
Abstract 15
Declaration 17
Copyright 18
Acknowledgements 19
1 Introduction 20
1.1 Features of crude oil distillation systems ...... 21
1.2 Heat integration in crude oil distillation systems ...... 23
1.3 Motivation and objectives of this work ...... 25
1.4 Overview of this thesis ...... 26
2 Literature Review 27
2.1 Introduction ...... 27
2.2 Shortcut distillation column model ...... 28
2 2.2.1 Total reflux condition (Fenske method) ...... 28
2.2.2 Minimum reflux condition (Underwood method) ...... 31
2.2.3 Finite reflux condition and theoretical stages ...... 34
2.2.4 Average relative volatility ...... 35
2.2.5 Extensions and applications of these shortcut methods ...... 36
2.3 Design of crude oil distillation columns ...... 37
2.3.1 Existing design and analysis of crude oil distillation systems . . . 38
2.3.2 Shortcut models for crude oil distillation columns ...... 40
2.4 Product characteristics for crude oil distillation columns ...... 43
2.4.1 Industry product specifications for crude oil distillation columns 43
2.4.2 Product specifications for shortcut models ...... 46
2.4.3 Existing methods for characterizing crude oil products in shortcut models ...... 47
2.5 Concluding remarks ...... 52
3 Shortcut Modelling of Crude Oil Distillation Columns 54
3.1 Introduction ...... 54
3.2 Further analysis on the limitations of the existing methods for connecting industry product specifications to those of shortcut models ...... 55
3.2.1 Effect of reflux ratio on predicting product compositions in shortcut models ...... 55
3.2.2 Algorithm analysis of the existing methods ...... 59
3 3.2.3 Summary and proposal ...... 62
3.3 Applying Fenske method to crude oil distillation columns ...... 62
3.3.1 Application of Fenske method in simple crude oil distillation columns ...... 64
3.3.2 Illustrative example: Applying Fenske method to a simple steam- stripped crude distillation column ...... 66
3.3.3 Application of the Fenske method in steam-stripped complex columns ...... 69
3.3.4 Illustrative example: Applying the Fenske method to a complex crude oil distillation column (geometric mean α)...... 72
3.3.5 Illustrative example: Applying the Fenske method to a decom- posed crude oil distillation column (feed α)...... 78
3.3.6 Application of the Fenske method in an atmospheric crude distillation column ...... 81
3.3.7 Illustrative example: Applying the Fenske method to an atmo- spheric distillation column ...... 81
3.4 Summary ...... 83
4 Systematic selection of Fenske parameters and applications 84
4.1 Methodology Statement ...... 84
4.2 Selecting Fenske parameters for simple distillation columns ...... 85
4.2.1 TBP curve reconstruction ...... 85
4.2.2 Systematic approach for selecting Fenske parameters of a simple column ...... 88
4 4.2.3 Illustrative example: Applying proposed approach to a simple distillation column ...... 93
4.3 Selecting Fenske parameters for a sequence of simple columns ...... 95
4.3.1 Systematic approach for selecting Fenske parameters of a se- quence simple columns ...... 95
4.3.2 Illustrative example: Applying proposed approach to a crude oil distillation column ...... 97
4.4 Applying proposed approach to optimize a specific product flow rate in a crude oil distillation column ...... 102
4.5 Applying the proposed approach to optimize the total product income for a crude oil distillation column ...... 107
4.6 Summary ...... 111
5 Case Studies 113
5.1 Case study 5.1: Profit improvement by maximizing the flow rate of the most valuable product of a crude oil distillation column ...... 113
5.1.1 Base case data ...... 114
5.1.2 Optimization approach and results ...... 116
5.2 Case study 5.2: Maximizing the total product income for an atmospheric distillation column ...... 118
5.3 Summary ...... 122
6 Conclusions and future work 124
6.1 Conclusions ...... 124
5 6.2 Future work ...... 126
References 128
A Data for illustrative example 3.3.5 133
B HYSYS-Matlab interface for vapour-liquid equilibrium calculation 135
6 List of Tables
2.1 Method for defining light and heavy components (Gadalla et al., 2003b) 47
3.1 Interpolation method for determining product compositions in the work of Suphanit (1999) ...... 56
3.2 True boiling point curve data of a crude oil (Watkins, 1979, p.129) . . . 66
3.3 Crude oil compositions in the form of pseudo-component (corresponding to Table 3.2) ...... 67
3.4 Crude oil feed conditions and product specifications ...... 67
3.5 Steam conditions ...... 68
3.6 Selections of key components and recoveries for the simple column in Figure 3.6 ...... 68
3.7 Simulation specifications for a decomposed crude oil distillation column (Figure 3.11b) ...... 72
3.8 Initial selection of key components for the decomposed columns . . . . . 75
3.9 New selection of key components and recoveries for the decomposed columns shown in Figure 3.11b (trial and error results) ...... 75
3.10 Pumparound specifications for the atmospheric distillation column . . . 82
7 3.11 Product property specifications for the atmospheric distillation column . 82
3.12 Selection of key components and recoveries for the atmospheric distilla- tion column shown in Figure 3.29a (trial and error results) ...... 82
3.13 Product property calculations for the atmospheric distillation column (Fenske results obtained from the specifications in Table 3.12) ...... 82
4.1 Crude oil TBP data (Watkins, 1979) ...... 87
4.2 Product specifications for applying the proposed approach to a simple distillation column ...... 94
4.3 Optimized Fenske parameters for the simple distillation column . . . . 94
4.4 Product specifications for applying the proposed approach to an atmo- spheric column ...... 97
4.5 Optimization results with comparison to product specifications . . . . . 99
4.6 Optimized Fenske parameters corresponding to the results in Table 4.5 . 99
4.7 Optimization results and specifications of Chen (2008, Chap. 3) . . . . . 101
4.8 Optimized key components and recoveries of Chen (2008, Chap. 3) (corresponding to results in Table 4.7) ...... 101
4.9 Crude oil cost and prices of the product streams obtained from an atmospheric distillation column (Chen, 2008, p. 145) ...... 103
5.1 Case Study: Crude oil TBP data (Watkins, 1979, p. 129) ...... 115
5.2 Case Study: Product properties of the base case ...... 115
5.3 Case Study: Unit prices of all the streams (Chen, 2008, p. 145) . . . . . 115
5.4 Product property results for maximizing the flow rate of heavy gas oil . 116
8 5.5 Optimized key components and recoveries corresponding to results shown in Table 5.4 ...... 117
5.6 Profit increase of a case study in the work of Chen (2008, p.184) . . . . 118
5.7 Case study: Product constraints for the product income optimization . . 119
5.8 Optimal product results of the product income maximization ...... 121
5.9 Key components and recoveries for the results shown in Table 5.8 . . . . 121
9 List of Figures
1.1 Schematic diagram of crude oil distillation systems ...... 21
1.2 Optimization framework for design of heat-integrated crude oil distilla- tion systems (Chen, 2008, p. 150) ...... 24
2.1 Pinch zone locations for binary and multi-component mixtures (adapted from Smith (2005, p. 167)) ...... 32
2.2 Decomposition of the atmospheric distillation column (Liebmann, 1996) 39
2.3 Modification of the FUG method to overcome the assumption of constant vapour flow rates (adapted from Suphanit (1999)) ...... 41
2.4 True boiling point curve of a crude oil ...... 44
2.5 Temperature relationships around the cut point between adjacent frations (Watkins, 1979, p. 22) ...... 45
2.6 TBP curves of a crude oil and its fractions for an atmospheric distillation column (Parkash, 2003, p. 4) ...... 46
2.7 Component distribution ratios for a fractionation column (Alattas et al., 2011) ...... 50
2.8 CDU representation for the product planning model using FI method (Alattas et al., 2011) ...... 51
10 3.1 Distribution ratio of components at various reflux conditions (King, 1980, page: 435) ...... 57
3.2 A complex column with one side-stripper and its decomposed configura- tion (adapted from Suphanit (1999, chap. 3)) ...... 58
3.3 Method of searching for key components and recoveries in Gadalla et al. (2003b) ...... 60
3.4 Method of searching for key components and recoveries in the work of Chen (2008) ...... 60
3.5 Evaluation of the Fenske method in crude oil distillation columns . . . . 63
3.6 Application of the Fenske method to a simple crude oil distillation column 64
3.7 Component recoveries in the simple crude column ...... 65
3.8 Top product composition of a single column ...... 69
3.9 Ture boiling curve of bottom product of a single column ...... 70
3.10 Decomposition method to a complex column ...... 71
3.11 Decomposition method to a crude distillation column ...... 73
3.12 Products components recoveries in a complex crude column ...... 74
3.13 Fenske calculation for a decomposed crude oil distillation column (using geometric mean α)...... 74
3.14 Mixed Top product composition for Fenske and Rigorous methods . . . 75
3.15 Heavy Naphtha product composition for Fenske and Rigorous methods . 76
3.16 LGO product composition for Fenske and Rigorous methods ...... 76
3.17 HGO product composition for Fenske and Rigorous methods ...... 76
11 3.18 Residue composition for Fenske and Rigorous methods ...... 77
3.19 True boiling curve of HN product for Fenske and Rigorous methods . . 77
3.20 True boiling curve of LGO product for Fenske and Rigorous methods . . 77
3.21 True boiling curve of HGO product for Fenske and Rigorous methods . 78
3.22 True boiling curve of Residue for Fenske and Rigorous methods . . . . . 78
3.23 Fenske calculation for a decomposed crude oil distillation column (using feed α)...... 79
3.24 Mixed Top product composition for Fenske (feed K-values) and Rigorous methods ...... 79
3.25 Heavy Naphtha product composition for Fenske (feed K-values) and Rigorous methods ...... 79
3.26 LGO product composition for Fenske (feed K-values) and Rigorous methods ...... 80
3.27 HGO product composition for Fenske (feed K-values) and Rigorous methods ...... 80
3.28 Residue composition for Fenske (feed K-values) and Rigorous methods . 80
3.29 Applying Fenske to an atmospheric distillation column ...... 81
4.1 A simple flow chart of the optimization approach ...... 85
4.2 Arranging pseudo-components for TBP reconstruction ...... 86
4.3 TBP curve reconstruction ...... 87
4.4 TBP curve generated by calculation in Matlab and HYSYS ...... 88
4.5 Search space for key components ...... 90
12 4.6 A contour plot of objective function for one simple column ...... 91
4.7 Optimization of recoveries for a pair of given key components ...... 92
4.8 An example for illustrating the selection method if multiple solutions of optimization exist in one column ...... 92
4.9 Overall mass balance on a simple distillation column ...... 94
4.10 Applying the proposed optimization model to a series of columns . . . 95
4.11 Generating K-values of the feed to column j + 1 by flash calculations . . 96
4.12 Contour plot of objective function for simple column 1 (RLK1-RHK1).. 98
4.13 Contour plot of objective function for simple column 2 (RLK2-RHK2).. 98
4.14 Contour plot of objective function for simple column 3 (RLK3-RHK3).. 98
4.15 Contour plot of objective function for simple column 4 (RLK4-RHK4).. 99
4.16 Effect of increasing the yield of heavy gas oil on product TBP charac- teristics ...... 104
4.17 Block diagram representing product yields of a series of simples columns 105
4.18 Gaussian Distribution for generating a new solution for a product flow rate ...... 108
4.19 Random Optimization for maximizing total product income ...... 110
4.20 A single run with 100 iterations for maximizing product income using the method illustrated in Figure 4.19 ...... 111
5.1 Case study 5.1: Atmospheric distillation column ...... 114
5.2 10 runs of optimization with 100 iterations for maximizing total product income ...... 119
13 5.3 Product income increase of each 50 iterations (1000 iterations in total) . 120
5.4 10 runs for optimizing the total income starting from an infeasible case . 122
A.1 True boiling curve of HN product for Fenske and Rigorous methods (feed K-value) ...... 133
A.2 True boiling curve of LGO product for Fenske and Rigorous methods (feed K-value) ...... 133
A.3 True boiling curve of HGO product for Fenske and Rigorous methods (feed K-value) ...... 134
A.4 True boiling curve of Residue for Fenske and Rigorous methods (feed K-value) ...... 134
14 Abstract
Crude oil distillation systems, consisting of crude oil distillation columns and the associated heat recovery systems, are highly energy intensive. Heat-integrated design of crude oil distillation systems can provide opportunities to find the energy-efficient design solutions. Shortcut distillation models, based on the Fenske-Underwood- Gilliland model, have been applied to model the crude oil distillation columns, taking advantage of their simplicity and robustness in convergence. However, product specifications in the petroleum industry, related to boiling properties (e.g. true boiling point temperatures) and flow rates, have to be translated to those required by shortcut models, namely the key components and their recoveries. However, the two kinds of product specifications are so different from each other that ’translating them’ is a very challenging task.
In this thesis, an optimization-based methodology for transforming the product specifications used in industry to those for shortcut modelling is developed. This method is based on the Fenske distillation model; it can automatically identify the most appropriate key components and the associated recoveries that characterize specified separations. The proposed method may be applied to simple columns and atmospheric distillation columns. Case studies demonstrate that the product results predicted by the method, in terms of boiling temperatures and flow rates, are in good agreement with those obtained from the rigorous simulations. Compared to the existing methods (e.g. method of Chen (2008)), the method is simpler, such as column design and energy balances are not required, and much more robust in convergence. Moreover, the method is applicable to the heat-integrated design of crude oil distillation systems, especially in the optimization framework involving shortcut column models, e.g. Suphanit (1999), Chen (2008).
The proposed method is applied in two optimization contexts: one optimizes a particular product flow rate in a crude oil distillation column; the other maximizes
15 the total product income of a crude oil distillation column for given product unit values. A stochastic method, Random Optimization, is applied in the maximization of total product income. True boiling temperature constraints are considered in these optimizations. Case studies illustrate the application of the two optimization methods, and the key components and recoveries associated with the optimal solutions can be easily identified.
16 Declaration
No portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.
17 Copyright
i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the “Copyright”) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the “Intellectual Property”) and any reproductions of copyright works in the thesis, for example graphs and tables (“Reproductions”), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the Uni- versity IP Policy (see http://www.campus.manchester.ac.uk/medialibrary/ policies/intellectual-property.pdf), in any relevant Thesis restriction dec- larations deposited in the University Library, The University Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations) and in The University’s policy on presentation of Theses
18 Acknowledgements
First and foremost, I would like to deeply express my gratitude to my supervisor, Dr. Megan Jobson, for her invaluable guidance and support throughout my postgraduate study. I would also greatly appreciate her cooperation during the stage of writing-up of this thesis. I would also sincerely thank to Prof. Robin Smith for his valuable research direction during this work.
I would also thank to Centre for Process Integration for giving me a great opportunity to study here. I am very thankful to all the staff members in this centre. Special thanks to Dr. Nan Zhang for his valuable suggestions of this research. My sincere gratitude to Steve Doyle for supporting me in the learning and using softwares. I also thank Li Sun for her support during my study.
A big thanks to all my friends in our centre. I thank to Lu for helping me to start this work. I also thank to Lluvia, Mona, Maria, Muneeb, Yannis, Michael, Shiwen, Luyi, Kok Siew, Ankur, Bostjan, Blessing for creating a delightful and friendly atmosphere.
My great thanks goes to my parents and brother for their unfailing supports and encouragements during my studies.
Finally, a special thanks to my husband Shaobo Hou for his endless support, love, understanding during my stay in the UK.
19 Chapter 1
Introduction
The crude oil distillation systems, including distillation columns and their heat recovery systems, is the first stage of processing in a petroleum refinery. It is a highly energy intensive process, consuming fuels at an equivalent of 1% to 2% of the crude oil processed (Liebmann, 1998). As the price of energy increases, considerable effort has been made to reduce the energy requirement of the crude oil distillation process. At the same time, increasing concerns about the environment resulted in stricter regulations on the emission of green house gases. Consequently, both economic and environmental issues are important factors in the design of crude oil distillation system.
Inside crude oil distillation systems, the distillation columns have strong interactions with the associated heat recovery systems. Compared to the conventional design approach of crude oil distillation systems, the heat-integrated design approach is more likely to find a better solution, from which the minimized energy consumption can be obtained (Suphanit, 1999). Less energy consumption also means less gas emissions, which is beneficial for the environment. The heat-integrated design approach is facilitated by shortcut column models and the pinch analysis method (Suphanit, 1999). In order to apply shortcut column models, product specifications in the refineries need to be translated into specifications required by shortcut column models. However, there are a number of limitations present in the existing translation methods. This thesis aims to extend the existing methods and overcome their limitations.
20 CHAPTER 1. INTRODUCTION 21
1.1 Features of crude oil distillation systems
The current configuration of crude oil distillation systems appeared more than 80 years ago (Miller and Osborne, 1938). Figure 1.1 shows a typical configuration of a crude oil distillation system. In most petroleum refineries, the crude oil distillation system includes two main columns: the atmospheric distillation unit column (ADU) and the vacuum distillation unit column (VDU), although some plants may also have a prefractionator before the ADU. These columns separate crude oil into different product fractions according to required boiling temperature ranges. The products of the crude oil distillation columns can be either final products or feedstock to downstream processes, such as Fluidized Catalytic Cracking units.
Off-Gas
Water
Light Naphatha
TPA A To Vacuum System
MPA
D Kerosene V BPA VLGO LGO U HGO Steam D VHGO HGO Desalter ADU Furnace ADU Steam U Crude ADU Residue VDU Furnace
VDU Steam VDU Residue
Figure 1.1: Schematic diagram of crude oil distillation systems where ADU and VDU: atmospheric and vacuum distillation columns; TPA, MPA and BPA: the top, middle, and bottom pump-arounds of ADU; LGO and HGO: light gas oil and heavy gas oil for the atmospheric distillation column; VLGO and VHGO: light gas oil and heavy gas oil for the vacuum distillation column.
Raw crude oil is first pumped into a heat exchanger network (HEN), where heat is transferred from hot process streams to the cold crude oil. The crude oil is then sent to a desalter, where salts are removed to avoid corrosion later. Thereafter, the crude oil passes through another HEN to recover more heat from high temperature products or intermediate streams, e.g. pump-arounds. In the furnace for atmospheric distillation column, the crude oil is finally heated up to 340-370◦C by hot exhaust of CHAPTER 1. INTRODUCTION 22 fuel combustion.
The partially vaporized crude oil is then fed to the lower part of the flash zone of the atmospheric distillation column, and flashed into vapour and liquid. The liquid is withdrawn from the bottom as ADU residue, and the vapour travels up the column to every product collecting stage. Side withdrawals are fed to side-strippers, which strip the lighter components and return them to the main tower. Three to four products can be collected from these strippers, e.g. heavy gas oil (HGO), light gas oil (LGO), kerosene, etc. At the very top, a partial condenser cools the vapour, producing light naphtha and Off-Gas which contains uncondensed gas and very light hydrocarbons. Off-Gas can serve as a fuel source for furnaces.
Unlike conventional distillation columns, live steam is injected into the bottom of the atmospheric distillation column, rather than applying reboilers. Liquid from the flash zone still contains some light components, the boiling temperatures of which are less than 350◦C. Introducing superheated live steam at the bottom of the column can vaporize the light components back into the rectifying section. The purpose of adding steam is to reduce the partial pressure in the column, increase the lighter product yields and decrease the processing flow rates of the vacuum distillation column.
In order to obtain products with the desired quality, in terms of boiling point temperature ranges, extra heat needs to be removed from the distillation column. Besides the top reflux, which is the same as in a simple distillation column, pump- around loops are placed along the atmospheric column. These pump-around loops withdraw a hot stream from a given stage, cool it down by heat recovery and return the colder stream one or more stages above the draw stage. The pump-arounds provide heat in the heat recovery systems. Some columns have pump-backs, the returning location of which is lower than the draw stage.
The residue from the atmospheric column is further heated from 350◦C to 400◦C in the VDU furnace, before fed to the vacuum column. A typical configuration of the vacuum column is shown in Figure 1.1. The vacuum distillation column operates under vacuum to avoid cracking and other heat sensitive reactions, allowing light hydrocarbons to be separated from the ADU residue. The vacuum condition is supplied by a series of ejectors at the top of the column. Typically, products from the vacuum column are: VDU gas, light vacuum gas oil (LVGO), heavy vacuum gas oil (HVGO) and VDU residue (with boiling points greater than 500◦C). CHAPTER 1. INTRODUCTION 23
The atmospheric column is the focus of this thesis, due to its importance in the whole crude oil distillation systems.
1.2 Heat integration in crude oil distillation systems
As discussed in Section 1.1, the crude oil distillation systems contain distillation columns and heat recovery systems (i.e. heat exchanger networks). Traditionally, the design of distillation columns and the design of heat recovery systems are carried out sequentially. However, this sequential design approach may miss energy-saving opportunities, and hence considerable research has been carried out on the heat- integrated design approach, which considers the design of distillation columns and their heat recovery systems simultaneously. Several researchers have addressed the importance of heat-integrated design of crude oil distillation systems. Researchers in the Centre for Process Integration at the University of Manchester have applied shortcut column models to develop a heat-integrated design methodology. The reason for using shortcut models is that they are simpler and more robust, compared to rigorous column models. These shortcut models are the focuses of this research.
Suphanit (1999) applied the column decomposition method of Liebmann (1996) and the pinch analysis method (Linnhoff, 1983), and proposed a heat-integrated design approach. This approach involves shortcut column models, heat recovery models and other practical constraints. The models and constraints are then incorporated into an optimization framework, allowing some design variables to be optimized in order to minimize the total annualized cost. This optimization framework was later extended and modified by Gadalla (2003), Rastogi (2006) and Chen (2008). The optimization framework for the heat-integrated design of crude oil distillation systems developed by Chen (2008) is shown in Figure 1.2.
In Figure 1.2, two main components of the optimization framework are the simulations of crude oil distillation columns and the heat exchanger networks (HEN). In order to optimize the design of crude oil distillation systems, the distillation column and the HEN have to be simulated first. For grassroots design, an initial feasible design is required; while for retrofit design, the existing units are simulated. After the simulations are established, they are then included in the optimization, which aims to minimize the total annualized cost or maximize profit. During the optimization, some column design parameters become adjustable variables, e.g. preheat crude feed temperature, pump-around flow rates; some configuration parameters of the HEN can also become CHAPTER 1. INTRODUCTION 24
Figure 1.2: Optimization framework for design of heat-integrated crude oil distillation systems (Chen, 2008, p. 150) adjustable variables, e.g. adding or deleting an exchanger, moving or re-sequencing an exchanger. The optimization also takes account of constraints such as product quality in terms of boiling points and flow rates and column hydraulic constraints. All the adjustable variables are then optimized within specified boundaries by a simulated annealing algorithm for the given objective. Finally, the optimal design for the crude oil distillation columns and HEN is obtained from the optimization results (Chen, 2008).
In the heat-integrated design of crude oil distillation systems, the crude oil distillation columns are simulated using shortcut distillation models, i.e. modified Fenske- Underwood-Gilliland method of Suphanit (1999). The reason for adopting shortcut column models is that they are simple and robust, and can also provide a good preliminary design for distillation columns. Moreover, applying shortcut column models can allow many important design variables to be optimized simultaneously, which may provide more opportunities to find better design solutions. However, rigorous column models may involve significant convergence problems when many variables are optimized at the same time. CHAPTER 1. INTRODUCTION 25
1.3 Motivation and objectives of this work
In petroleum refineries, the crude oils and their fractions are specified by boiling point properties, e.g. true boiling point curves, ASTM boiling curves. However, in the shortcut models, the product specifications are expressed in terms of key components and their recoveries. Whether the shortcut column models can calculate the required product relies on the selection of appropriate key components and their corresponding recoveries. If the key components and their recoveries are not appropriately specified, the product specifications (in terms of boiling temperature ranges and flow rates) may not be met. However, the separation may be feasible if more appropriate key components and recoveries are applied. Therefore, transforming the industry product specifications into those of shortcut models is very important. In this thesis, the method used for transforming industry product specifications to those of shortcut models, by finding the most appropriate key components and recoveries, is called a search method.
The search method proposed by Gadalla (2003) uses rigorous simulations to identify the appropriate key components and recoveries. This search method is only applicable to retrofit design, and requires trial and error by designers. Chen (2008) proposed a search method based on numerical optimization. The search method of Chen (2008) is able to automatically choose the most suitable key components and recoveries; however, it is very sensitive to the initial guesses and has significant convergence problems. In the method of Chen (2008), the search for appropriate key components and recoveries and the column design are carried out at the same time. Specifically, given some initial values of key component and recoveries, the minimum vapour mole overflow and the energy balances of the column are calculated using the shortcut models; if these design values are feasible, then the key components and recoveries are updated; otherwise, the search method terminates. Moreover, the product compositions used in the search method of Chen (2008) are obtained by interpolating the product compositions calculated by the Underwood method and those calculated by the Fenske method; then, a factor (R/Rmin) required by this interpolation is introduced to the search method and needs to be updated manually. If the appropriate key components and their recoveries cannot be found, the distillation columns will not be successfully simulated, causing no optimization framework to be carried out regardless how good it is. Therefore, developing a simple and robust search method is necessary.
The main objective of this work is to develop a method which can systematically identify the most appropriate key components and recoveries for the shortcut column models, given separation requirements of an atmospheric distillation column. This CHAPTER 1. INTRODUCTION 26 method should be easy to converge, and sufficiently accurate for predicting the product properties, in terms of boiling temperature ranges and flow rates.
Besides finding the appropriate key components and recoveries for a given specification, the proposed search method can also be used to adjust the product distributions of a crude oil distillation column for various reasons. One such reason is maximizing the flow rate of a particular product, given some quality constraints in terms of boiling temperature points. This approach can be used to increase the flow rate of the most valuable product and hence increase its income. More generally, the proposed search method can be used to maximize the total product income by finding the optimal combination of flow rate requirements for all products.
1.4 Overview of this thesis
Chapter 2 reviews the literature relating to shortcut distillation design models and previous research on applying these shortcut models to the design of crude oil distillation columns.
In Chapter 3, a shortcut method for predicting the product properties of a crude oil distillation column is proposed. Rigorous simulations are employed to provide candidate key components and recoveries, and used to evaluate the calculated product properties obtained from this shortcut method.
Chapter 4 presents an approach for systematically identifying the most suitable key components and recoveries for given product requirements. The approach is then applied to optimize the flow rate of a specific product and optimize the total product income while the quality specifications of all the products (in terms of boiling temperature ranges) are met.
Chapter 5 presents two case studies to demonstrate the applicability of the approach proposed in Chapter 4 and discusses their results.
Chapter 6 summarises the achievements of this research work, discusses the limitations of the work and recommends some future work. Chapter 2
Literature Review
2.1 Introduction
Design of crude oil distillation systems, which consist of distillation columns and heat recovery systems, is of great importance in refineries. The conventional design procedure is to design the distillation columns first and then design their heat recovery system (Watkins, 1979). Recently, increasing attention has been paid to heat-integrated design of crude oil distillation systems, which considers the columns and their heat recovery system simultaneously (Suphanit, 1999; Chen, 2008). This heat-integrated design usually involves using numerical optimizations to find the optimal design solution. However, it is very difficult for rigorous column models to handle a large number of optimization variables; and they also suffer from convergence problems. Consequently, researchers have developed shortcut column models, i.e. modified Fenske-Underwood-Gilliland model, which may be employed in design and retrofit optimization of crude oil distillation systems.
This chapter reviews various shortcut distillation column design methods, considering their application to both simple and complex columns; and then discusses the design of crude oil distillation columns using shortcut models. Finally, product specifications for shortcut models and in refineries are addressed. Some existing methods of transferring product specifications in industry to those used in shortcut models are also reviewed.
27 CHAPTER 2. LITERATURE REVIEW 28
2.2 Shortcut distillation column model
The shortcut distillation design model here refers to the F enske − Underwood − Gilliland or FUG model, which is an approximate method that has been widely used for preliminary design and optimization of simple distillation processes (Seader and Henley, 1998).
FUG model consists of the Fenske method which is based on total reflux condition and calculates the minimum number of stages (Nmin) for a given separation; the Underwood method, which is based on minimum reflux condition and calculates the minimum reflux ratio (Rmin); and the Gilliland empirical correlations, which can determine the actual number of stages required for a given separation. Nmin and Rmin are very important in the preliminary design of distillation columns. Although these methods can be applied readily by manual calculation, computer calculations are preferred, and the FUG model is included in most computer-aided process design programs (Seader and Henley, 1998, p. 492).
The FUG model relies on certain simplifying assumptions, such as constant relative volatilities and constant molar overflow along each column section (Khoury, 2005).
2.2.1 Total reflux condition (Fenske method)
The total reflux condition can be achieved by operating the column at finite feed and product output with a very high reflux rate or by operating it with no further input of feed and no withdrawal of products and maintaining the internal boil-up and reflux
(Seader and Henley, 1998). For a given separation, a minimum number of stages (Nmin) is required under the total reflux condition.
The column considered here is a conventional simple column, which has the following features: a single feed, an overhead product, a liquid bottom product, multi-stage column with one condenser at the top and one reboiler at the bottom. The method assumes that the column diameter, the condenser and the reboiler, are large enough to handle the internal reflux and boil-up required to achieve the total reflux condition (Khoury, 2005, chap. 12).
An important assumption of this method is related to the vapour-liquid equilibrium CHAPTER 2. LITERATURE REVIEW 29 coefficient or K-value, which refers to the ratio of mole fractions of a component i in vapour and liquid phases. The ratio can be written as:
Ki = yi/xi (2.1) where yi and xi are the compositions of component i in the vapour and liquid products respectively.
The relative volatility, defined by the ratio of K-values of any two components (i and j), is assumed to be constant throughout the whole column (Seader and Henley, 1998).
αi,j = Ki/Kj (2.2)
For a binary distillation, if vapour-liquid equilibrium data and operating lines are available, the minimum number of stages Nmin for a specified separation can be determined by the McCabe-Thiele (1925) graphical solution on a Y − X diagram. The
Nmin for a given separation in a binary distillation can also be calculated by equations discussed below.
Fenske (1932) developed a set of equations to calculate the minimum number of stages for a given separation.
For a binary separation, the Fenske equation is shown in Equation 2.3. A and B in this equation denote the two components. The ratios xA and xA are the molar xB d xB b composition ratios in the top and bottom products respectively.
x x A Nmin A = (αAB) (2.3) xB d xB b
For mixtures with more than two components or multi-component mixtures, two key components between which the cut or fractionation is made, was introduced by Lewis and his co-workers (Lewis and Wilde, 1928; Lewis and Smoley, 1930). The concept of key components was adopted in the work of Fenske (1932), which allows multi- component separations to be treated as separations of simple binary mixtures.
The Fenske equation for a multi-component mixture is shown in Equation 2.4.
x x LK Nmin LK = (αLK,HK ) (2.4) xHK d xHK b where LK and HK are the light and heavy key components for a multi-component CHAPTER 2. LITERATURE REVIEW 30
mixture. αLK,HK is the relative volatility between LK and HK. Equation 2.4 can also be written as: R 1 − R LK Nmin HK = (αLK,HK ) (2.5) 1 − RLK d RHK b where RLK and RHK are the recovery of the light key component in the top product and the recovery of the heavy key component in the bottom product, respectively.
Besides the two key components, no other components are involved in Equation 2.5. Therefore, once a pair of light and heavy key components is chosen and its recoveries are specified, the minimum number of stages (Nmin) for the desired separation can be determined. The distribution of all non-key components, in terms of recoveries in one product, can then be estimated by Equation 2.6 (Seader and Henley, 1998).
R 1 − R i Nmin HK = (αi,HK ) (2.6) 1 − Ri d RHK b
By defining key components and recoveries in the Fenske equations, the problem of determining Nmin for a given separation becomes relatively simple regardless of how many components are contained in the mixture. The compositions of all non-key components in each product can also be approximated.
The light and heavy key components can be either adjacent or non-adjacent in order of volatility (King, 1980; Seader and Henley, 1998, chap. 9). If only two adjacent components appear in both top product and bottom product, then the two adjacent components are chosen to be the light and heavy key components. If more than two components exist in both top and bottom products, then any two of these components can be chosen as key components, which means the light and heavy key components can be non-adjacent. The selection of key components and their corresponding recoveries are directly related to the approximations of other non-key components, as shown in Equation 2.6. Therefore, a suitable selection of a pair of key components is very important for predicting product compositions. However, the challenge of choosing the suitable pair increases with the bigger number of candidate key components.
The simplicity of the Fenske method is an advantage for predicting product composi- tions, especially for a mixture involving a large number of components, such as crude oil distillation or other separations in the petroleum industry. More will be discussed in Section 2.3. CHAPTER 2. LITERATURE REVIEW 31
2.2.2 Minimum reflux condition (Underwood method)
Total reflux is one extreme condition for distillation, and can be approximated by the Fenske method. The other extreme condition for a distillation column is the minimum reflux.
Under the minimum reflux condition, Underwood (1948) developed sets of equations to calculate the minimum vapour flow rate. The detailed discussion related to the minimum reflux condition and how the derivation of the Underwood equations can be found in many separation textbooks (King, 1980, chap. 9; Seader and Henley, 1998, chap. 9; Smith, 2005, chap. 9). In this section, only some important features of the Underwood method are addressed.
At the minimum reflux condition, an infinite number of stages for a given separation is required, and at least one zone of constant composition (pinch zone) of all the components exists in the column (King, 1980). In general, there will be one pinch zone in the rectifying column section and one pinch zone in the stripping column section (Smith, 2005). For a binary distillation at minimum reflux, the two pinch zones are usually adjacent to the feed stage, as shown in Figure 2.1a. For a multi-component distillation at minimum reflux, the pinch zones are located just above and below the feed stage if all components are distributing (exist in both top and bottom products), which is also shown in Figure 2.1a; if light non-key and heavy non-key components are not distributing (only exist in either top or bottom product), the pinch zones in the rectifying and stripping sections are away from the feed stage, which is shown in Figure 2.1b (Smith, 2005, p.167).
The Underwood method makes the following assumptions (Seader and Henley, 1998):
Constant vapour and liquid molar overflow in the rectifying section and in the stripping section of a column.
Constant relative volatility through the whole column.
The Underwood method first solves an equation which relates to feed composition xf,i, thermal condition of the feed q, and relative volatility αi in order to determine a factor φ, which lies numerically between the relative volatilities of the two key components. This factor φ is the root of the Underwood method. The minimum reflux ratio in each CHAPTER 2. LITERATURE REVIEW 32
Top Product Top Product
Vmin Feed Feed
V'min
Bottom Product Bottom Product (a) Binary system or multi-component (b) Multi-component system with LLK system with all components distributing and HHK components not distributing (LLK: lighter than light key component; HHK: heavier than heavy key compo- nent)
Figure 2.1: Pinch zone locations for binary and multi-component mixtures (adapted from Smith (2005, p. 167)) column section can then be calculated by applying the root to another equation. The Underwood method is described as below:
1. Find the root of the Underwood equations (φ) by trial and error.
R X αixf,i 1 − q = (2.7) α − φ i=1 i
where R is the number of the components in the mixture; αi is the relate volatility of component i. For binary distillation (R=2), there is only one root which exists between the relative volatilities of the two components:
α1 > φ > α2
For a multi-component mixture (R=n), multiple candidate roots exist between the specified light key and heavy key components (King, 1980). The further away the key components are from each other, in terms of volatility, the more roots can be found, as shown below:
αLK > φ1 > α(LK+1) > φ2 > ... > α(HK−1) > φm > αHK CHAPTER 2. LITERATURE REVIEW 33
where m denotes the number of the roots.
A root has to be chosen from all possible solutions (φ1, φ2, ..., φm) and applied to Equation 2.8 to calculate the minimum reflux of this separation.
2. The minimum reflux in the rectifying section (Vmin) is determined by
R X αidi V = (2.8) min α − φ i=1 i
where di is the flow rate of component i in the top product. 0 The minimum vapour flow rate in the stripping section (Vmin) can be calculated from Equation 2.9. 0 Vmin = Vmin − (1 − q)F (2.9)
3. After solving these equations, the minimum reflux ratio for the given separation can then be determined: V R = ( min ) − 1 (2.10) min D The minimum reflux ratio depends on which root is chosen.
For a binary distillation, the Underwood equations can be easily solved using the three steps listed above, since the components in the mixture are the light and heavy key components and there is only one root lying between the volatilities of key components.
For multi-component distillations with only two adjacent distributing components, the Underwood equations can still be solved as binary component calculations and achieve accurate results (Shiras, Hanson and Gibson, 1950).
For multi-component distillations with non-adjacent key components, the Underwood equations are difficult to solve, as multiple roots exist for Equation 2.7 but only one is required. The flow rates of all the components in the top product (di) are also required, but they are unknown and need to be estimated. The minimum vapour overflow can be approximated by applying the estimated di and one root φ to Equation 2.8. There is another rigorous way for solving the Underwood equations which assumes all the components lighter than the light key (LLK) and heavier than the heavy key (HHK) are recovered entirely in distillate or bottom products (Hanson and Newman, 1977; Treybal, 1979). The flow rates for these components are known from the feed. To estimate the unknown di for distributing components between the light and heavy key components, a method was suggested by Treybal (1979, p. 435-439) and King (1980, p. 420). The method is that Equation 2.8 can be written as many times as there are CHAPTER 2. LITERATURE REVIEW 34 the values of φ obtained from Equation 2.7 and be solved simultaneously. Then both the unknown di between the key components and the minimum reflux ratio can be calculated. An illustrative example of this method can be found in Treybal (1979, p. 436).
Even though the assumption that all the LLK and HHK are recovered completely in one product can provide estimated compositions for these components in the products, it does not correctly describe the actual distributions of these components. A non- key component may be away from the key components in the volatility and still be distributing (King, 1979, p. 420). In the case of crude oil distillation, the pseudo- components, generated by cutting the continuous temperature boiling curves, have similar volatilities to their adjacent components. Therefore, applying this assumption to crude oil distillation for estimating the product compositions can cause inaccuracy.
Other methods for estimating the flow rates of non-key components in distillate (di) can also be used, such as those from the Fenske calculation at total reflux (Hanson and Newman, 1977; King, 1980, p. 420; Smith, 2005).
2.2.3 Finite reflux condition and theoretical stages
To achieve a given separation specified by two key components, the actual reflux ratio R and the actual number of stages N have to be greater than their minimum values. The actual reflux ratio is generally estimated at some multiple of the minimum reflux ratio, which can be written as:
R = k(R/Rmin)Rmin (2.11)
The multiplier k(R/Rmin) is assumed to be constant and is usually determined by economic considerations. The optimal value for k(R/Rmin) in the work of Fair and Bolles (1968) is approximately 1.05. However, in practice, the values are chosen between 1.1 and 2.0 (Seader and Henley, 1998; King, 1980).
The actual number of stages for a given separation can be determined by empirical correlations, in the form of either graphical methods or empirical equations. The most successful and simplest empirical correlation method is the Gilliland graphical correlation (Seader and Henley, 1998), which shows the relationship between the two
N−Nmin R−Rmin terms ( N+1 ) and ( R+1 ). CHAPTER 2. LITERATURE REVIEW 35
Since Gilliland derived the original plot, several researchers developed numerical equations to represent it (Kister, 1992). The two most popular equations are developed by Eduljee (1975) and Molokanov et al. (1972), as shown in Equation 2.12 and Equation 2.13 respectively. The latter can be used when high accuracy is required (King, 1980).
Y = 0.75 − 0.75X0.5668 (2.12)
1 + 54.4X X − 1 Y = 1 − exp (2.13) 11 + 117.2X X0.5 Where N − N Y = min (2.14) N + 1 R − R X = min (2.15) R + 1 The feed location can then be determined by Kirkbride correlation (Kister, 1992):
" #0.206 N B x x 2 R = f,HK b,LK (2.16) NS D xf,LK xdH K
2.2.4 Average relative volatility
In the FUG model, the relative volatility (α) is an important parameter. As discussed in Section 2.2.1 and 2.2.2, both the Fenske and the Underwood methods assume constant relative volatility throughout the whole column. The relative volatilities may vary somewhat with composition and temperature inside a column, so it is necessary to use average values (King, 1980, p. 397). Several methods for approximating the average values of α for a column are summarized from Kister (1992, p. 106) and Smith (2005, p. 166), as shown in Equation 2.17 to Equation 2.21.
2 ln(αtop) ln(αbtm) αav = exp (2.17) ln(αtop) + ln(αbtm)
αav = (αtop + αbtm)/2 (2.18)
αav = αfeed−stage (2.19) √ αav = αtopαbtm (2.20) √ αav = 3 αtopαmidαbtm (2.21) where αav is the average relative volatility for a component; αtop, αbtm, αmid and
αfeed−stage are the relative volatilities of the component in the top, bottom, mid-column CHAPTER 2. LITERATURE REVIEW 36 and feed-stage of the column respectively.
The most commonly used approximation is Equation 2.20, for which the average α is computed as the geometric mean value (King, 1980, p. 397; Seader and Henley, 1998, p. 498; Kister, 1992). The feed-stage relative volatility, as shown in Equation 2.19, can also be approximated as geometric-mean value (King, 1980, p. 397).
Since some assumptions have been made in the FUG model, the results from this model, e.g. product compositions, will be less accurate than those obtained from more rigorous models, which involve material balance, equilibrium balance, summation balance and energy balance for each column stage (Smith, 2005, p.159). However, the FUG model is simple, robust and fast; it can also provide a good preliminary design for a conventional simple column. Consequently, a number of researchers have extended this model in order to accommodate different column configurations and operating conditions, which will be discussed in Section 2.2.5.
2.2.5 Extensions and applications of these shortcut methods
As discussed in Section 2.2.1 to Section 2.2.3, the shortcut distillation design methods have their advantages compared to more rigorous models, such as simplicity of calculation and robustness in convergence. However, the developments of these shortcut methods (e.g. the Fenske method and the Underwood method) were based on conventional simple distillation columns. In practice, distillation columns can have complex configurations, e.g. column with side-strippers or side-rectifiers, column with live steam instead of reboiler. Thus, extensions of the FUG model have been proposed to accommodate these complex column configurations.
Glinos and Malone (1985) presented a method to extend the Underwood equations to a complex distillation column with a side-stripper. The complex column was first decomposed into two simple columns, and then the minimum vapour flow rates of the two simple columns were calculated using the Underwood method. Fidkowski and Krolikowski (1987) also extended the Underwood method to complex columns with a side-stripper or a side-rectifier in order to calculate the overall reflux. As these methods are restricted to ternary mixtures, they cannot be applied to n-component mixtures.
Carlberg and Westerberg (1989) applied the Underwood method to a multi-component separation in several complex column configurations, e.g. multiple side-strippers and CHAPTER 2. LITERATURE REVIEW 37 side-rectifiers. The method decomposed the complex column into simple columns, and then assumed that the light and heavy key components for each simple column were adjacent. Therefore, only one Underwood root existed in each column, which made the Underwood calculation relatively easy (see Section 2.2.2). However, assuming adjacent key components restricts the application of this method to multi-component separations which may have non-adjacent key components, e.g. distillation in petroleum industries.
Suphanit (1999) developed a shortcut column design model for crude oil distillation columns, which involve multi-component separation, complex column configurations (see Section 1.1) and non-adjacent key components. This model overcame the Underwood limitation of constant molar overflow in column sections, and determined the number of stages in the stripping section by consecutive stage-by-stage calculations. However, it cannot be applied to retrofit column design and cannot automatically specify the appropriate key components for a required separation. Gadalla (2003) and Gadalla et al. (2003b) extended the model of Suphanit (1999) to retrofit column design, but the selections of key components for a given separation were still carried out manually. In the work of Chen (2008), a systematic method for selecting the appropriate key components and recoveries was proposed. However, the method is highly sensitive to initial guesses and has significant convergence problem; consequently, feasible solution of key components cannot be guaranteed. Without appropriate key components and recoveries, this modified FUG method of Chen (2008) cannot be used to carry out the column design. As the works of Suphanit (1999), Gadalla (2003) and Chen (2008) are highly relevant to the research in this thesis, more details of these works will be discussed in the following sections.
2.3 Design of crude oil distillation columns
The current configuration of crude oil distillation columns began more than 80 years ago (Miller and Osborne, 1938). Over the years, the costs of energy and capital cost have changed dramatically, from higher capital cost to higher energy cost. Consequently, the design of crude oil distillation systems began to change from the traditional approach to more energy-efficient design, e.g. heat-integrated design approach, which considers the crude oil distillation columns and their heat recovery systems simultaneously.
In this section, traditional design of crude oil distillation systems are reviewed first, followed by heat-integrated design which usually involves optimizations of distillation columns and their heat recovery systems. In the heat-integrated design of crude oil CHAPTER 2. LITERATURE REVIEW 38 distillation systems, simulations of the crude oil distillation columns are generally required, which can be accomplished using rigorous column models (e.g. Aspen Plus) or shortcut column models (e.g. FUG model). More discussions about the shortcut column models for design of heat-integrated crude oil distillation systems will be carried out in Section 2.3.2, due to their relevance to the work of this thesis.
2.3.1 Existing design and analysis of crude oil distillation systems
The conventional design of crude oil distillation column was pioneered by Packie (1941), as discussed by Watkins (1979), Bagajewicz and Ji (2001a). In the work of Packie (1941), empirical charts were used to express the relation among the 5-95 gaps and overlaps, reflux ratio, and the number of stages of column sections. The 5-95 gaps and overlaps (more details in Section 2.4) can be used as separation criteria for two adjacent crude oil fractions. However, these empirical charts were based on experience rather than rigorous calculation, therefore they can bring inaccuracy to the column design and fail to find the optimal design. Moreover, Packie (1941) designed the crude oil distillation column and heat recovery systems in a sequential manner, and no heat- integration was considered.
Nelson (1958, chap. 16) presented a design procedure for crude oil distillation columns, which also relied on empirical correlations. A similar design procedure was suggested by Watkins (1979). In the work of Nelson (1958) and Watkins (1979), empirical rules were presented for determining column features, e.g. the number of stages in each column section, column temperatures, pumparound duties, etc. Although the importance of heat exchanger network in the design of crude oil distillation systems was noted by Watkins (1979), simultaneous design of distillation columns and heat recovery systems was not considered.
Liebmann (1996) proposed an integrated approach for the design of heat-integrated crude oil distillation systems. In his work, the atmospheric column was simulated using the commercial simulation package, i.e. Aspen Plus; and the grand composite curves (Dhole and Linnhoff, 1993) were employed to assess the appropriate design of integrated crude oil distillation column. Liebmann (1996) decomposed the crude distillation column into a sequence of simple columns, as shown in Figure 2.2.
The major advantage of the approach presented by Liebmann (1996) is that the design of crude oil distillation column and its associated heat recovery system was CHAPTER 2. LITERATURE REVIEW 39
Off-Gas Off-Gas Water Water LN LN TPA TPA A HN
MPA HN MPA D LGO BPA BPA Steam U LGO Steam Crude HGO Crude HGO Steam Residue Steam Residue (a) Complex ADU configuration (b) Decomposed ADU configuration
Figure 2.2: Decomposition of the atmospheric distillation column (Liebmann, 1996) considered simultaneously. Moreover, the decomposition approach provided guidance for the development of shortcut models in the work of Suphanit (1999), Gadalla (2003), Rastogi (2006) and Chen (2008). However, the column design of Liebmann (1996) was performed by rigorous simulators, which can be difficult to converge.
A rigorous procedure for design of crude oil distillation systems was developed by Bagajewicz and his co-workers (Bagajewicz and Ji, 2001a; Bagajewicz and Soto, 2001b; Bagajewicz and Soto, 2003). The aim of the approach was to design energy-efficient crude oil distillation columns and the heat exchanger network. First, by using rigorous simulator, the method set energy target to find the optimal column condition, e.g. pump around duty, steam flow rates; then, a heat exchanger network was designed based on the previous optimal column design results. In this method, both the columns and the heat exchanger network have individually optimal design, however, it is not sure whether the columns and the heat recovery system together is optimal. Furthermore, an initial design of crude oil distillation system was required in the method, which was obtained from Watkins (1979).
In order to find the optimal design of crude oil distillation systems, in terms of minimum total cost or maximum profit, related optimizations were carried out by many researchers (Seo, Oh and Lee, 2000; Basak, Abhilash, Ganguly and Saraf, 2002; Inamdar, Gupta and Saraf, 2004; More, Bulasara, Uppaluri and Banjara, 2010). In these design optimizations, rigorous column models were applied, either by using rigorous simulation packages, e.g. Aspen Plus (More et al., 2010) or by building column models from rigorous equations, e.g. MESH equations (Basak et al., 2002). The column design and heat recovery systems were considered, however, no details about the CHAPTER 2. LITERATURE REVIEW 40 heat recovery systems were presented. Most optimizations were formulated as mixed- integer non-linear programming (MINLP) problems. However, these rigorous column models can significantly affect the convergences of the MINLP optimizations, as these rigorous models contain considerable information, e.g. flow rates and compositions of all streams, temperatures and pressures of all stages, products properties (More et al., 2010).
For design and optimization of crude oil distillation systems, instead of using rigorous column models, simpler column models can also be applied to represent the crude oil distillation column.
Liau, Yang and Tsai (2004) developed an optimization model using artificial neural network to represent the crude oil distillation column, in order to optimize the production of the column. This statistic model can help inexperienced operators find the optimal operating conditions for the crude oil distillation column. However, a large number of rigorous simulations are required to build and test this model, which means it can only be applied to existing systems. The black-box nature of neural network can also bring difficulties when further tuning of the model is needed.
Shortcut column models, i.e. modified FUG models, were applied to the design of crude oil distillation systems, which included column design and its heat recovery design (Suphanit, 1999; Gadalla, 2002; Rastogi, 2006; Chen, 2008). The detailed review of these models will be discussed in Section 2.3.2.
2.3.2 Shortcut models for crude oil distillation columns
Due to the complexity of the rigorous distillation models, it can be time-consuming or even impossible to obtain feasible design solutions for crude oil distillation systems. Therefore, it is worthwhile to develop shortcut models for crude oil distillation columns; these models are relatively simple, accurate enough for preliminary design, and robust in convergence. Shortcut models for design and retrofit of heat-integrated crude oil distillation systems (Suphanit, 1999; Gadalla, 2003; Rastogi, 2006; Chen, 2008) are reviewed.
Suphanit (1999) modified the FUG model and introduced a revised shortcut design model. This approach overcame some limitations of the FUG model, in particular, the assumptions of constant vapour fow rate and the estimation of the number of stages in CHAPTER 2. LITERATURE REVIEW 41 refluxed stripper. Using this shortcut model, Suphanit (1999) assessed different column configurations: columns with side-strippers or rectifiers or side-exchangers, Petlyuk column (Petlyuk, 1965), complex columns with live steam, and crude oil distillation columns. The decomposition concept presented in Liebmann (1996), was used in this model to divide the complex columns into simple ones, as shown in Figure 2.2 (Section 2.3.1). The major features of the modification are outlined below:
Enthalpy balance calculations were applied to relax the FUG assumption of constant molar overflow in each column section. First, the Underwood method was used to estimate the vapour flow rates at the top and bottom pinch zones, 0 Vmin,pinch and Vmin,pinch, as shown in Figure 2.3. Then, enthalpy balances were carried out around the top section to determine the minimum vapour flow rate
at the top of the column, Vmin,top and the minimum condenser duty. Finally the reboiler duty and the minimum vapour flow rate at the bottom of the column, 0 Vmin,bottom, were calculated from the overall and bottom enthalpy balances, respectively.
Top enthalpy balance
Top Product
Vmin, pinch
Feed Overall enthalpy balance V'min, pinch
Reboiler enthalpy balance
Bottom Product
Figure 2.3: Modification of the FUG method to overcome the assumption of constant vapour flow rates (adapted from Suphanit (1999))
The product compositions were approximated by interpolating between product compositions predicted by the Fenske and the Underwood methods.
To estimate the number of stages in a refluxed stripper at finite reflux, the CHAPTER 2. LITERATURE REVIEW 42
Gilliland correlation was only applied in the rectifying section. In the stripping section, consecutive flash calculations were carried out from the bottom stage to the feed stage.
The shortcut model of Suphanit (1999) can only be used in grassroots design. However, column retrofit is frequently of interest to make the best use of the existing equipments and achieve new processing objectives with minimum capital investment. Moreover, similar to the conventional FUG model (Section 2.2), this revised FUG model also requires key components and recoveries as specifications for each simple column. The suitable key components and recoveries in the work of Suphanit (1999) were selected by trial and error, which is inefficient when a large number of pseudo-components existed.
Gadalla (2003) extended the modified shortcut model of Suphanit (1999) to accom- modate retrofit design of simple distillation columns, complex columns, and crude oil distillation column. In the work of Gadalla (2003), the existing number of stages in each column section and the steam flow rates were fixed; then the flow rates, compositions and temperatures of all products were calculated. The calculation was repeated until the calculated number of stages of each column section corresponded to the existing values. Gadalla (2003) validated the simulation results of the extended shortcut model by comparison with the results of HYSYS simulations.
Gadalla et al. (2003b) also presented a method for transforming traditional product specifications of crude oil distillation columns into key components and recoveries for each simple column. Rigorous simulations and trial and error were required to identify the key components and their recoveries, causing this method can only be applied to existing columns.
Rastogi (2006) further extended the shortcut model of Suphanit (1999) and Gadalla (2003), by taking into account pressure drop in the atmospheric column. He also further developed the shortcut model for applications to the vacuum distillation column.
As discussed in Section 2.2, both the Fenske method and the Underwood method require specifications of key components and their corresponding recoveries. However, the conventional design specifications in refineries use product boiling properties, e.g. temperature boiling curves. In the works of Suphanit (1999), Gadalla (2003), Gadalla et al. (2003b) and Rastogi (2006), the transformation of specifications from refineries to specifications of shortcut models were carried out manually using trial and error. CHAPTER 2. LITERATURE REVIEW 43
Chen (2008) proposed a systematic approach for linking the specifications from industry and those of shortcut models. More information about the the products specifications from industry will be discussed in Section 2.4.1. The methods proposed by Chen (2008), Gadalla et al. (2003b) and other research related to transferring product specifications of refineries into those of shortcut models (Gilbert et al., 1966; Alattas et al., 2011) will be reviewed in Section 2.4.3.
2.4 Product characteristics for crude oil distillation columns
In this section, products quality specification in conventional CDU design and in shortcut design are discussed. Existing methods relating to the two kinds of specifications are also discussed.
2.4.1 Industry product specifications for crude oil distillation columns
Crude oil is an exceedingly complex mixture, consisting of countless hydrocarbon compounds ranging from methane, with only one carbon atom, to large compounds containing 300 and more carbon atoms, as well as sulfur, nitrogen and metals, etc (Jones and Pujado, 2006). A complete component-by-component analysis of crude oil is an impossible task; hence, a true boiling point distillation curve (TBP curve) is used to represent the composition of a crude oil (Watkins, 1979). TBP curves measure the volume percentage distilled against the corresponding temperature in a batch distillation, using a large number of stages and high reflux ratio (Parkash, 2003). TBP curves are normally only run on crude oils and not on petroleum products (Watkins, 1979; Parkash, 2003). A typical crude oil TBP curve and its required product fractions are shown in Figure 2.4.
Instead of TBP curves, ASTM curves (American Society for Testing Materials) can also be used to represent the qualities of crude fractions. ASTM curves are measured in a rapid batch distillation employing no stages or reflux between the stillpot and the condenser (Watkins, 1979).
Another laboratory distillation curve is the EFV curve (Equilibrium Flash Vaporiza- tion), which can be run at pressures above atmospheric or under vacuum, whereas the TBP and ASTM distillations can only be used at atmospheric pressure or under CHAPTER 2. LITERATURE REVIEW 44 vacuum (Parkash, 2003). The EFV curves are seldom used due to the inconvenience, cost or other issues (Watkins, 1979).
Even though these boiling curves are constructed under different distillation conditions, it is possible to translate one curve to another by conversion correlations (Riazi and Daubert, 1986; Jones and Pujado, 2006, chap. 1; Fahim, Sahhaf and Elkilani, 2010, chap. 3). Many commercial simulation packages have built-in facilities for performing the conversions, e.g. Aspen Plus, HYSYS.
TBP
Residue HGO
LGO Kerosene
Naphatha
OffGas
Volume percentage distilled
Figure 2.4: True boiling point curve of a crude oil
In addition to boiling curves, a number of bulk properties can also be used to further characterize crude oils and their fractions. These properties include API Gravity, Reid Vapour Pressure, Pour Point, Sulfur Content, End Point, Salt Content, Metal Content, etc (Nelson, 1958; Gary and Handwerk, 2001). Each fraction may emphasize one or more properties as its specifically important features. Similar to boiling curves, these bulk properties can be set in rigorous simulation packages, while specifying a refinery column.
Because of the complex composition, crude oil and petroleum fractions are usually characterized as a mixture of discrete pseudo-components (Nelson, 1958). Each pseudo- component corresponds to several or more unknown actual hydrocarbons, and is assigned an average boiling point on the TBP distillation curve (Fahim et al., 2010). This allows crude oil to be treated as a defined multi-component mixture, which can be used in the calculations of crude oil distillation column. CHAPTER 2. LITERATURE REVIEW 45
Separation criteria in the refining industry are quite different to those in conventional chemical processes. In refineries, three terms are used to describe the degree of separation between two adjacent fractions (Packie, 1941; Watkins, 1979), as shown in Figure 2.5.
Cut volume: the volumetric yield point between two fractions
Cut point: the temperature at which two fractions are intended to be separated (Jones and Pujado, 2006, chap. 1). Watkins (1979) gave the definition of this term as:
1/2(T100%L + T0%H )
where T100%L and T0%H stand for the temperature at which 100 volume percent of light fraction is distilled and the temperature at which 0 volume percent of heavy fraction is distilled.
T T100%L Heavy fraction T95%L
TBP cut temperature
(T5%H-T95%L) Gap
T5%H Light fraction TBP cut T0%H volume Volume percent distilled
Figure 2.5: Temperature relationships around the cut point between adjacent frations (Watkins, 1979, p. 22)
T emperature gap (or overlap): degree of separation between two adjacent fractions. Typically, the temperature gap is expressed as the difference between the 95 volume percent temperature of a light fraction and the 5 volume percent temperature of the adjacent heavier fraction. The temperature difference may be positive (gap) or negative (overlap). A gap indicates good separation while an overlap indicates poor separation (Jones and Pujado, 2006, p.117).
T 5 - T 95 gap (overlap) = (T 5%H − T 95%L) (2.22) CHAPTER 2. LITERATURE REVIEW 46
A crude oil and its fractions can be illustrated in Figure 2.6.
Figure 2.6: TBP curves of a crude oil and its fractions for an atmospheric distillation column (Parkash, 2003, p. 4)
Since product specifications in refineries are mainly dependent on cut point and temperature gaps, as shown in Figure 2.6, they can not be applied directly into shortcut models which require key components and recoveries, as discussed in Section 2.2. Therefore, methods for transferring the two kind of specifications are needed.
2.4.2 Product specifications for shortcut models
As discussed in Section 2.4.1, conventional design specifications of a refinery column is defined in terms of cut point and temperature gap, and product flow rates (Watkins, 1979). However, conventional shortcut distillation models (Section 2.2) require specifications of key components and recoveries to characterize the separation. Therefore, extended shortcut models (Suphanit, 1999; Gadalla, 2003; Rastogi, 2006; Chen, 2008) cannot be directly applied to refinery distillation processes.
In these shortcut models, crude oil is represented by a finite number of pseudo- components; the complex crude oil distillation column is decomposed into a series of simple columns (Liebmann, 1996). Each simple column requires light and heavy key components and their recoveries as specifications. The key components have to be chosen from the defined set of pseudo-components of the crude oil, which number is CHAPTER 2. LITERATURE REVIEW 47 usually more than 20 or even 30 (Fahim et al, 2010, chap. 3). However, it is not easy to choose the light and heavy key components in a multi-components mixtures (see Section 2.2). Furthermore, the product properties obtained from these shortcut models are in the form of pseudo-component compositions, rather than temperature boiling curves and cut points. A translation from pseudo-component composition to products temperature boiling curves is therefore required. The problem of identifying the suitable key components and recoveries of each simple column to generate the desired crude oil fractions, is therefore an important issue. Existing methods for choosing the key components and recoveries will be reviewed in Section 2.4.3
2.4.3 Existing methods for characterizing crude oil products in shortcut models
Gadalla et al. (2003b) proposed a method for selecting suitable key components and recoveries. The method is based on the material balance of a crude oil distillation column, and requires data from a rigorous simulation with a standard specifications, such as product flow rates or cut points. The main procedure is summarized below:
1. For a given crude oil, the cut points and temperature gaps of each pair of adjacent fractions were calculated using the required TBP curves of the crude oil and various products. For a given column configuration, a crude oil distillation column was simulated using the cut points and temperature gaps as product specifications. From the converged simulation results, the product compositions in terms of mole fraction of each pseudo-component were calculated.
2. The given column configuration was then decomposed into an equivalent sequence of simple columns (Liebmann, 1996). For each product, the recoveries of all pseudo-components with respect to the feed of the simple column were calculated.
3. The light and heavy components, which are the candidates of light and heavy key components, are identified using one of the methods in Table 2.1.
Table 2.1: Method for defining light and heavy components (Gadalla et al., 2003b)
Method1 Method2 Ki,n = yi,n/xi,n δ = xi,n − xi,n−1 Ki,n > 1 Light δ < 1 Light Ki,n < 1 Heavy δ > 1 Heavy Ki,n = 1 Ignore δ = 1 Ignore CHAPTER 2. LITERATURE REVIEW 48
where Ki,n denotes the equilibrium constant of component i on the draw stage
n, while yi,n and xi,n denote the corresponding compositions in the vapour and liquid phases respectively. n − 1 denotes the stage above the draw.
4. For each simple column, a pair of light and heavy key components are chosen from the light and heavy components respectively using one of the methods in Table 2.1. Given the two key components and their recoveries from the rigorous simulation, material balance calculation over each column was carried out by the shortcut model in Suphanit (1999), in order to predict product flow rates and compositions. The calculation procedure starts from an initial guess of LK, HK,
RLK and RHK , and then iteratively improved by trial and error until the product flow rates and compositions correspond to those in the rigorous model.
As illustrated above, this method requires a rigorous simulation, which means it can only be applied to retrofit design of existing crude oil distillation columns (Chen, 2008, chap. 3). Moreover, the identification of key components and recoveries is not carried out automatically; intervention and judgement from designers are required, e.g. defining potential key components by the methods described in Table 2.1.
Chen (2008) developed a new systematic approach for identifying key components and their recoveries. This method, supported by an optimization model, is applicable to both grassroots and retrofit design. The summary of the method is as follows:
1. For a given crude oil TBP curve and the desired product outputs, three TBP points and the product flow rate are used to specify a product. Only n − 1 products can be specified (n is the total number of products). The three TBP points are the temperatures at which 5%, 50% and 95% of an oil fraction is vaporized, which are referred to as T 5, T 50 and T 95. The reason for selecting these three TBP points is that T 5 and T 95 are linked to temperature gap (product specification in the refineries) and T 50 is used to control the middle point of a boiling curve and the shape of the curve (Chen, 2008, p. 60). In addition to the quality criteria, product quantity is also controlled by the bottom flow rate (B) or distillate flow rate (D).
2. Choose a set of LK, HK and their recoveries and apply them to shortcut models. The results from shortcut models in terms of pseudo-component composition are then translated to a TBP curve for each product. Specifically, three calculated
TBP points are compared, in the form of T 5%calc, T 50%calc and T 95%calc. The
flow rate Bcalc or Dcalc can also compared using the shortcut models. CHAPTER 2. LITERATURE REVIEW 49
3. An optimization model is then used to minimize the residual between the calculated values and the specified values. The objective function is defined as:
T F (X) = [f1(X), f2(X), f3(X), f4(X)] = 0 (2.23)
where
f1(X) = T 5%spec − T 5%calc
f2(X) = T 50%spec − T 50%calc
f3(X) = T 95%spec − T 95%calc
f4(X) = (Bspec − Bcalc) T X = [x1, x2, x3, x4]
and x1, x2, x3, x4 denote LK, HK, RLK , RHK respectively
From a given initialization of the four variables (LK, HK, RLK , RHK ), the Levenberg-Marquardt (LM) algorithm is used to iteratively update the values until the deviations between the calculated values and specified values are less than an acceptable tolerance. In the updating procedure carried out by the LM algorithm, the integer variables (LK, HK) are treated as continuous variables and then rounded up to the nearest integer values.
The method of Chen (2008) provides a systematic way of searching for appropriate key components and recoveries, without using data from rigorous simulations, as was required in the method of Gadalla et al. (2003b). However, failure to converge is a significant problem in this approach. Further discussion about the convergence problem will be discussed in Section 3.2.2.
Alattas et al. (2011) presented a fractionation index (FI) model for refinery planning optimization. In modern refineries, product planning is a vital part of their operation (Grossmann, 2005); therefore it is worthwhile to develop an accurate and effective optimization model. The FI model employs a shortcut calculation for predicting product yields and qualities, by applying the equation presented in Geddes (1958):
xi,top FI xo,top = (αi,o) (2.24) xi,btm xo,btm where xi,top, xi,btm denote the compositions of component i in the top and bottom products respectively; xo,top, xo,btm are the compositions of the reference component o in the top and bottom products respectively; αi,o is the relative volatility of component i with respect to the reference component o. CHAPTER 2. LITERATURE REVIEW 50
The fractionation index in this model, which was first proposed by Geddes (1958), is the slope of a straight line, as shown in Figure 2.7. In a multi-component mixture, if the reference component is defined and the relative volatilities of other components are calculated, the fractionation index can be used to predict the product distribution ratios (xi,top/xi,btm).
Log(xi, top /x i, btm )
4
3 Slope
2 1
-1 0 1 2 -1 Log i, o)(α -2 Slope -3
Figure 2.7: Component distribution ratios for a fractionation column (Alattas et al., 2011)
The approach for predicting product compositions using the fractionation index method is very similar to that of the Fenske method. The Fenske equation for estimating compositions of non-key components (Equation 2.6) can be re-arranged:
x x i,top Nmin HK,top = (αi,HK ) (2.25) xi,btm xHK,btm
From Equation 2.25 and Equation 2.24, it can be seen that they are very similar to each other, e.g. a reference component is required and an exponent is associated with relative volatility.
However, there are still some differences. Firstly, the physical insight of Nmin is the minimum number of stages for a given separation (Section 2.2.1); the fractionation index can have two values, which are related to the number of stages in the rectifying and stripping sections respectively (Geddes, 1958; King, 1980, p. 434). Secondly, Nmin is calculated by specifying two key components and recoveries; the fractionation index in the work of Geddes (1958) was derived from the Log(xi,top/xi,btm) Vs Log(αi,o) plot, and assumed fractionation index values were used in his following examples. CHAPTER 2. LITERATURE REVIEW 51
Gilbert et al. (1966) presented a method for introducing the fractionation index into crude oil distillation. He developed equations which can describe the relationship between the fractionation index and product distributions; he also derived equations for defining the reference components.
Alattas et al. (2011) applied the methods of Geddes (1958) and Gilbert et al. (1966) to a CDU product planning model. For the relative volatilities (α), Alattas et al. (2011) adopted the suggestion of Jakob (1971), which used the component equilibrium constant K as an approximation for the relative volatility α. To use the FI method, Alattas et al. (2011) modeled the complex crude oil distillation column as a series of simple fractionation units, as shown in Figure 2.8. Given the feed crude oil assay, feed condition, FI values, mass balance of these simple columns were carried out to predict product compositions. The objective function was to maximize one of the product flow rates. The cut temperatures associated with the maximized value of a flow rate can also be determined.
T4
T3
T2
Feed T1
Figure 2.8: CDU representation for the product planning model using FI method (Alattas et al., 2011)
The fractionation index model provided a shortcut method for calculating all the product flow rates or maximizing one product flow rates without the expense of detailed energy, equilibrium or momentum calculatiosn, as noted by Alattas et al. (2011). However, the values of the fractionation index are required in this model, and the fractionation index values used in Alattas et al. (2011) were generated from column test runs. If crude oil distillation column is not available, then obtaining the fractionation index values is not a straightforward process. Furthermore, only product flow rates were optimized in this model, and no detailed product boiling properties (e.g. TBP points) were considered. CHAPTER 2. LITERATURE REVIEW 52
2.5 Concluding remarks
In this chapter, various methods for design models of crude distillation columns were reviewed. Among these models, shortcut design methods for the crude oil distillation columns have attracted increasing attentions due to their simplicity and robustness in convergence. Even though the existing shortcut models (Suphanit, 1999; Gadalla, 2003; Rastogi, 2006; Chen, 2008) have demonstrated their advantages in the optimization of heat-integrated CDU systems, there are several drawbacks associated with these models.
The limitations of the existing approaches can be summarized as follows:
The compositions of product using these shortcut models are calculated by interpolating between the results from the Fenske method and the Underwood method. The Underwood calculation requires more effort to solve than the Fenske equations. If unsuitable key components and recoveries are given, the Underwood assumption that all the components lighter than the light key and heavier than the heavy key components are totally recovered in one product (Sections 2.2.2) can increase the inaccuracy of the product compositions.
Products specifications in refineries and in established shortcut models are very different from each other; therefore, a method for translating these two specifications is very important. The method of Gadalla et al (2003b) is applicable to retrofit design and requires analysis and judgements from designers. Furthermore, each iteration of this method is carried out by trial and error, which is potentially time-consuming.
Although the methodology of Chen (2008) addresses the problem in a systematic way, the resulting mixed-integer non-linear problem is difficult to solve. Appro-
priate initialization of key components and recoveries (LK, HK, RLK , RHK ) is extremely important. Treating the integer variables (LK, HK) as continuous variables and rounding up to the nearest integers can also create infeasible solutions.
The product planning model from Alattas et al. (2011) applied the fractionation index method to predict product qualities of a crude oil distillation column. Obtaining the fractionation indices is not straightforward for designers without experience or suitable laboratory equipments. Moreover, only the product flow CHAPTER 2. LITERATURE REVIEW 53
rates are considered in this model. The TBP points of the products are not considered.
Therefore, a new systematic approach to translate refinery products specification to shortcut models is needed. The method should be simple, sufficiently accurate, robust, and easy to incorporate to the overall crude distillation optimization framework (Chen, 2008). Chapter 3
Shortcut Modelling of Crude Oil Distillation Columns
3.1 Introduction
Crude oil distillation is a very important process in petroleum refineries. In order to design crude oil distillation columns and the heat recovery systems simultaneously, various shortcut distillation models have been developed, rather than using rigorous models. Even though the shortcut distillation models have advantages, in terms of simplicity and robustness in convergence, for the overall optimization (Rastogi, 2006; Chen, 2008), there are still some problems and limitations.
Product requirements in petroleum industries cannot be applied directly in the shortcut distillation models; therefore a systematic method to connect these two products specifications is needed. In this chapter, further analysis of the limitations in the existing methods (Gadalla et al. (2003b) and Chen (2008)) will be addressed. Next, a shortcut method is proposed to predict product property (e.g. boiling temperature points) and provide key components and recoveries. Evaluations of this method, in terms of accuracy, are carried out with the support of rigorous simulations. This shortcut method is applied to simple columns, complex columns and atmospheric column, and illustrated by some examples, in which the results are compared to those of rigorous simulations.
54 CHAPTER 3. SHORTCUT MODELLING 55
3.2 Further analysis on the limitations of the existing methods for connecting industry product specifica- tions to those of shortcut models
In the shortcut distillation models, some key points are worth discussing, because they can provide guidance for finding the limitations of the existing methods and provide opportunity to extend them.
3.2.1 Effect of reflux ratio on predicting product compositions in shortcut models
As discussed in Section 2.2, the FUG shortcut distillation models are based on the Fenske method and the Underwood method, which correspond to the minimum reflux condition and the total reflux condition respectively. For a given separation under actual reflux condition, the reflux ratio is bigger than the minimum reflux ratio, but smaller than the total reflux ratio (infinite reflux). In other words, the actual reflux is between the two extreme conditions.
Both the Fenske and the Underwood methods require specifications of light and heavy key components and their recoveries, in order to predict product compositions (Section 2.2.1 and Section 2.2.2). Given key components and recoveries, the product compositions can be determined using Fenske method (Equation 2.3 to Equation 2.6). For the Underwood method, only providing key components and their recoveries are not enough to predict product compositions; assumptions are needed. These assumptions are that the components lighter than the light key are entirely recovered in the top product and those heavier than the heavy key are entirely recovered in the bottom product. The compositions of the components between the two key components and the minimum reflux ratio are determined by simultaneously solving a number of equations. These equations are written in the form of Equation 2.8, with the unknown reflux ratio, multiple Underwood roots between the two key components, and unknown compositions of intermediate components between the two key components (see Section 2.2.2 for detailed information).
Since the actual operating condition in terms of reflux ratio is between the two extreme conditions, i.e. the Fenske and the Underwood methods, both methods can estimate the product compositions, Suphanit (1999) proposed a method to predict the actual CHAPTER 3. SHORTCUT MODELLING 56 component compositions by interpolating the results obtained from the two extreme conditions. The reflux ratio in the Fenske condition is infinite, but the reflux ratio in Underwood condition is a finite number. Therefore, a term R/(R + 1) was used in Suphanit (1999), as shown in Table 3.1.
Table 3.1: Interpolation method for determining product compositions in the work of Suphanit (1999)
Reflux Condition R/(R + 1) xi
Total Reflux (Fenske) R∞/(R∞ + 1) xi∞ Actual Reflux Ract/(Ract + 1) ?
Minimum Reflux (Underwood) Rmin/(Rmin + 1) ximin
where xi∞ and ximin are product compositions estimated from total reflux and minimum reflux conditions respectively; R∞, Ract and Rmin are the reflux ratios under Fenske, actual and Underwood conditions respectively.
As shown in Table 3.1, the values required by this interpolation method are: xi∞ , calculated from the Fenske method, the ximin and Rmin, calculated from Underwood method, and Ract, which can be approximated by assigning a multiple (kRact/Rmin ) to the minimum reflux ratio.
This interpolation method of Suphanit (1999) was adapted from Treybal (1979, p: 435-441), in order to estimate product compositions under actual reflux condition. However, Treybal (1979) proposed this interpolation method on the assumption that all the components lighter than light key are totally recovered in the top product and all the components heavier than heavy key are totally recovered in the bottom product; he only applied this interpolation to the components between the light and heavy key components. However, Suphanit (1999) applied this interpolation to predict compositions of all the components in crude oil distillation columns (detailed information is not documented in the thesis of Suphanit (1999) and is only available in the original code).
An interesting behavior observed by Stupin and Lockhart (1968), as shown in Figure
3.1, illustrates the product distribution ratios (xi,d/xi,b) at various reflux conditions. This observation was further explained in King (1980, page: 434-436), Seader and Henley (1998, p. 512-514).
In Figure 3.1, four curves describe the product distribution ratios at various reflux conditions. Curves 1 and 4 correspond to the total reflux and the minimum reflux CHAPTER 3. SHORTCUT MODELLING 57
Log(xi, d /xi, b ) 1 Total reflux 4 3 2 High reflux (~ 5 Rmin) 1 3 Low reflux (~ 1.1 Rmin) 4 Minimum reflux 2
Light key
Heavy key
Log(αi ) Figure 3.1: Distribution ratio of components at various reflux conditions (King, 1980, page: 435) respectively, and curves 2 and 3 to high reflux and low reflux respectively. As the reflux ratio decreases from the total reflux condition – position 1 in the Figure 3.1, the component distribution curve first moves away from the minimum reflux to position
2, where the reflux ratio is approximately 5 times Rmin. As the reflux ratio is further reduced, the distribution curve then moves back toward the total reflux condition. When the reflux ratio reduces further, the distribution curve moves to position 3, where the reflux ratio is very close to the minimum value (1.1 times Rmin). Tsubaki and Hiraiwa (1972) have also explored these trends and methods for analyzing them quantitatively.
It might be expected that a component distribution curve under actual reflux condition would lie between those at the minimum reflux and total reflux conditions. However, from these curves in Figure 3.1, the component distribution at finite reflux may actually lie outside the two limits; it is bounded only if the reflux ratio is very small (less than
1.1 Rmin). For this behavior, Stupin and Lockhart (1968) provide an explanation that CHAPTER 3. SHORTCUT MODELLING 58 is consistent with the Gilliland correlation. As the reflux ratio decreases from total reflux while maintaining the specified split of the two key components, the number of stages required increases slowly at first, but later rapidly towards the minimum reflux. Consistently, as the reflux is decreased from total reflux, the large loss of reflux cannot be adequately compensated by the increase of stages, which cause the inferior distribution of non-key components, as shown in curve 2 in Figure 3.1. Therefore, interpolating product compositions between those obtained from the total reflux and minimum reflux may not always predict values closer to the actual ones, especially when actual reflux ratio is high.
In the heat-integrated design of crude oil distillation columns (Suphanit, 1999; Gadalla, 2003; Rastogi, 2006; Chen, 2008), the crude oil distillation column is decomposed into a series of simple columns (Liebmann, 1996). If a complex distillation column, as shown in Figure 3.2a, is decomposed into two simple columns, shown in Figure 3.2b, a hypothetical condenser can be assumed at the top of the first column. This hypothetical condenser provides liquid reflux to the first column and net feed to the second column.
The value of kRact/Rmin is one of the degree of freedoms for a simple column; it is required to be defined in the beginning for column simulation and then set as variables in the following optimizations (Suphanit, 1999; Gadalla, 2003; Rastogi, 2006; Chen,
2008). In the work of Suphanit (1999), a range of 1.05 to 2 for kRact/Rmin was set as lower and upper bounds. In the examples and case studies of Chen (2008), most optimal value of kRact/Rmin was between 1.1 to 1.7.
Off-Gas Off-Gas
Water Water
Distillate Distillate
Hypothetical condenser
Side-stripper steam Feed
Feed Side-product Main Steam Side-stripper steam
Side-product Main Steam
Bottom product Bottom product (a) A complex column with one side-stripper (b) Decomposed configuration
Figure 3.2: A complex column with one side-stripper and its decomposed configuration (adapted from Suphanit (1999, chap. 3))
With bigger values of kRact/Rmin , the interpolation between the Fenske and the CHAPTER 3. SHORTCUT MODELLING 59
Underwood methods may not always be the most appropriate way to predict product compositions. King (1980, p. 436) suggested that the component distributions calculated for total reflux should be a good approximation to the actual distributions in the range of reflux ratios 1.15 to 1.25 times the minimum. Seader and Henley (1998, p. 514) also provided a suggestion that: at a reflux ratio 1.3 time the minimum, the non-key component distributions are close to those estimated by the Fenske method for total reflux conditions.
The Fenske method itself may also be a good way to estimate the component distributions for a crude oil distillation column; it is far simpler than the interpolation method proposed in Suphanit (1999). However, for a crude oil distillation in the decomposed configuration, no work has been done so far to predict component compositions using the Fenske method itself. Moreover, the observation of Stupin and Lockhart (1968) in Figure 3.1 is only a graphical presentation; it was not carried out on the specific distillation column, i.e. decomposed crude oil distillation column, and no further application of this observation has been reported. Therefore, validations of the Fenske method for predicting product compositions are needed, which will be carried out in Section 3.3.
The reason for trying to find a simple way to estimate product compositions is that current interpolation method limits the shortcut column design, particularly on transferring the product specifications in industry to those required in the shortcut model. The limitation will be summarized in Section 3.2.2.
3.2.2 Algorithm analysis of the existing methods
In Section 2.4, different product specifications in the shortcut models and in the petroleum industries have been discussed. The industry requirements of product quality, in terms of boiling points curve (e.g. TBP curve) and temperature gaps, need to be translated into the specifications of the shortcut models, in terms of light and heavy key components and the associated recoveries.
To search for suitable key components and recoveries, the ideal method should be: easy to control, less designer influence, fast and robust in convergence and accurate enough for predicting product qualities.
The search method of Gadalla et al. (2003b), shown in Figure 3.3, is based on CHAPTER 3. SHORTCUT MODELLING 60
R/Rmin (assumed); LK, HK, R , R LK HK (from rigorous simulation)
Trial and error
Check calculated product qualities
( x i, d x i, b B D) and TBP curves close enough to the specified values
Figure 3.3: Method of searching for key components and recoveries in Gadalla et al. (2003b) results from a rigorous simulation; hence, it provides a reasonable initial guess for key components and their recoveries. Also, by using the judgement and experience of the designers, the search range is reduced compared to randomly updating the values of key components and recoveries. However, this method can not be applied in the grassroots design, and requires trail and error to manually update the four variables
(LK, HK, RLK and RHK ).
Compared to the search method of Gadalla et al. (2003b), the search method in the work of Chen (2008) can be applied to both grassroots and retrofit design. Given industry specifications (T 5%, T 50%, T 95% and product flow rate), this method can systematically find the corresponding specifications (key components and recoveries) for the shortcut model. The search algorithm of Chen (2008) is shown in Figure 3.4.
R/Rmin, LK, HK, R LK , R HK (from initial guess)
1. Levenberg-Marquardt (LM) 1. Check T5, T50, T95 and B or D Algorithm to update LK, HK, 2. Check if the column design is feasible: RLK , R HK Stream temperatures, pressures; 2. Treat LK, HK, R LK , R HK as Condenser and reboiler duties; continuous variables; Pumparound temperatures, duties; Round up the new LK, HK Number of stages of each section; values to the nearest integers ...... 3. Manually update R/Rmin
Figure 3.4: Method of searching for key components and recoveries in the work of Chen (2008) CHAPTER 3. SHORTCUT MODELLING 61
The search method of Chen (2008) is a breakthrough in specifying key components and recoveries for shortcut models according to the industry products specifications. Unfortunately, it is very difficult to run this searching optimization.
Firstly, it is extremely difficult to define the initial guesses. Reasonable initial guesses are very important. This method is a mixed-integer nonlinear programming (MINLP) problem, which is very sensitive to initialization. Since the search space may not be continuous, it is highly possible for the program to terminate in an infeasible area if poor starting points are provided. Unfortunately, it is not straightforward to choose an appropriate pair of key components out of a number of pseudo-components and define suitable recoveries. Meanwhile, a
suitable multiplier – kRact/Rmin should be set for each column. Thus, for a given simple column, the number of initial values required is 5. Assuming a crude oil distillation column is decomposed into four simple columns, the total number of initialization values will be 20, in which any inappropriate value can lead the
optimization to a dead-end. Moreover, the value of kRact/Rmin need to be updated manually.
Secondly, in the approach of Chen (2008), the search process is also the design process of these simple columns. Hence, any infeasible design results can stop the search. Once a group of initial or updated values are given, not only is the estimation of product compositions carried out by the shortcut models, but also a full design of these simple columns, including predictions of stream temperatures, condenser and reboiler duties, pumparound duties, the number of stages of each column section, etc. If any calculation for the column design fails, the search algorithm terminates, and therefore, the key components and recoveries cannot be updated.
Finally, when the program reaches the step of updating the key component and recovery values, the Levenberg-Marquardt (LM) algorithm is used to complete this task. The MINLP problem is treated as an non-linear programming (NLP) problem, by the means of treating the key components as continuous variables and then rounding them up to the nearest integers. By doing this, it is possible to introduce the variables into infeasible search space, as there are constraints subjected to the optimization, e.g. boiling temperatures and flow rates.
Given the full analysis above, it is better to modify the existing search methods. The modified search method should not be highly sensitive to initializations, nor associated with many column design results, but can still provide good estimations for product CHAPTER 3. SHORTCUT MODELLING 62 qualities. That is the reason for proposing a simple shortcut method, Fenske method, to predict product compositions and identify key components and recoveries.
3.2.3 Summary and proposal
In Section 3.2.1 and Section 3.2.2, the product compositions obtained from various reflux ratios have been discussed, indicating that the Fenske method may be a suitable alternative method to estimate product compositions. The limitations and difficulties of the methods presented in Figure 3.3 and 3.4 support the need for simplifying these existing search method.
Therefore in this work, the Fenske method is applied in a crude oil distillation column, in order to estimate the product qualities, in terms of composition and temperature boiling points. The results calculated from Fenske method are evaluated by comparisons with those of rigorous simulations.
3.3 Applying Fenske method to crude oil distillation columns
The Fenske-Underwood-Gilliland method has been widely applied to the design of various distillation columns, including the design of simple and complex columns (Section 2.2). Several researchers (Suphanit, 1999; Gadalla, 2003; Rastogi, 2006; Chen, 2008) extended the FUG shortcut model, and then applied the extended models to design of heat-integrated crude oil distillation columns (Section 2.3.2). In these extended shortcut models, the separation criteria are specified by key components and recoveries rather than boiling point curves in petroleum industry (Section 2.4). The existing methods for transferring the product specifications of industry to those of shortcut models have limitations (e.g. highly sensitive to initial guess, kRact/Rmin required and updated manually, robustness influenced by feasible column design ). Therefore, a method, which is simple, robust and accurate enough for predicting product composition, is needed.
In the existing shortcut models, the estimation of product compositions is determined by interpolating between the results from Underwood and Fenske. However, this interpolation method may not always be the most appropriate method; Fenske method CHAPTER 3. SHORTCUT MODELLING 63 itself may also provide good estimations for the product composition, as discussed in Section 3.2.1. If Fenske is capable of calculating product compositions with certain acceptable tolerance, then it can be used to transferring the product specifications from industry to those required in the shortcut models, which are key components and recoveries.
However, as known from Section 2.2.1, the Fenske method, as a shortcut method, is applicable in conventional distillation columns which require a condenser at the top and a reboiler at the bottom. Yet, a crude distillation column is injected with live steam from the bottom rather than placing reboilers. Some side-strippers of the crude oil distillation columns are also using live steam. The reason for this configuration can be found in the feature of crude oil distillation systems in Section 1.1. Therefore, validation of Fenske method in steam-stripped crude oil distillation columns needs to be carried out first.
In this section, the Fenske method is firstly applied to a simple steam-stripped crude oil distillation column. Thereafter, it is applied to a series of simple columns, which represent a decomposed complex distillation column. The results from this shortcut method, in terms of product composition and boiling properties (true boiling curves), are compared to those predicted by rigorous simulations. The rigorous simulations are built in HYSYS using conventional column specifications, e.g. product and steam flow rates, reboiler duty.
The evaluation procedure of the Fenske method proposed in this work can be described in Figure 3.5.
D: Product distributions C: Fenske method from Fenske method
Compare
A: Rigorous B: simulation results LK, HK, R LK , R HK
Figure 3.5: Evaluation of the Fenske method in crude oil distillation columns
In Figure 3.5, rigorous simulation results (A) provide the source for the specifications of the Fenske method (LK, HK, RLK and RHK ). Then, the extracted key components CHAPTER 3. SHORTCUT MODELLING 64 and recoveries (B) are used to carry out the Fenske calculation (C). Next, the product results predicted by Fenske are compared with those in rigorous simulations.
In this section, the key components and recoveries for this shortcut method are generated by rigorous material balance. The systematic approach to choose appropriate key components and recoveries for a given separation will be presented in Chapter 4.
3.3.1 Application of Fenske method in simple crude oil distillation columns
For a simple crude oil distillation column, as shown in Figure 3.6a, there is one feed and three products: Off-Gas, Distillate and Residue. According to the decomposition approach of Liebmann (1996), this simple column corresponds to the bottom section of a crude oil distillation column, which is shown in Figure 3.6b.
Off-Gas Water LN Off-Gas Mixed-Top P Water d i 1 Distillate P2 ... HN di PLK Feed ... f i PHK LGO fi ... Feed Steam Pn HGO Steam Steam Residue Residue bi bi (a) A simple crude oil distillation column (b) Corresponding part in an atmospheric column
Figure 3.6: Application of the Fenske method to a simple crude oil distillation column where fi, di and bi are the mole fractions of pseudo-component in the feed, top and bottom products respectively; P1 to Pn are the pseudo-components; PLK and PHK represent the light and heavy key components.
Since the Fenske method was derived on the basis of one top product and one bottom product for a simple column, it cannot account for vapour and liquid products at the CHAPTER 3. SHORTCUT MODELLING 65 top of the column. Hence, a mixed top product is formed by combining the Off-Gas and the Distillate together, as shown in Figure 3.6a. The crude oil is ’cut’ into a number (n) of pseudo-components and then introduced to the column. Only hydrocarbons in the form of pseudo-components are considered in this thesis, as the previous work did (Suphanit, 1999; Gadalla, 2003; Rastogi, 2006; Chen, 2008).
The procedure is listed as below:
1. Rigorously simulate a simple crude oil distillation column. For a given crude oil, a simple distillation column is simulated by specifying product flow rates.
2. Calculate the recoveries of each pseudo-component in the mixed top product (Mixed-Top) and the bottom product (Residue), with respect to the crude oil feed. di bi Ri,d = ,Ri,b = (3.1) fi fi
where Ri,d and Ri,b are the recoveries of component i in the mixed top and bottom products
Two curves, representing the recoveries of all the components in the mixed top and bottom, are shown in Figure 3.7.
1.00 0.90 0.80
0.70 0.60 0.50 Ri,d
0.40 Recovery 0.30 Ri,b 0.20 0.10 0.00 0 5 10 15 20 25 Pseudo-component
Figure 3.7: Component recoveries in the simple crude column
From Figure 3.7, it can be seen that the end parts of both recovery curves appear to be flat, which indicates these components are totally recovered in one product. However, in the middle parts of the two recovery curves, components have non- negligible proportions in both products. Since the two key components should CHAPTER 3. SHORTCUT MODELLING 66
appear in both top and bottom products (Fenske, 1932), they should be located in these parts of the two curves.
3. Apply different pairs of key components and their corresponding recoveries to the Fenske equation (Equations 2.5 and 2.6) to determine the product compositions. As discussed in Section 2.2.4, the average relative volatilities are usually approximated by the geometric mean values from the top and bottom products. Therefore, geometric mean values are applied in this simple column.
4. Compare the calculated product results to those obtained from the rigorous model.
3.3.2 Illustrative example: Applying Fenske method to a simple steam-stripped crude distillation column
A simple steam-stripped crude oil distillation column, as shown in Figure 3.6, processes a crude oil into three products: Off-Gas, Distillate and Residue. The crude assay data is the same as the one used in the work of Suphanit (1999), the Tia Juana Light oil from Watkins (1979, p: 128-129). The true boiling points of this oil is listed in Table 3.2. Table 3.2: True boiling point curve data of a crude oil (Watkins, 1979, p.129)
% Distilled (Volume) TBP(◦C) 0 -3 5 63.5 10 101.7 30 221.8 50 336.9 70 462.9 90 680.4 95 787.2 100 894 Density 865.4 kg/m3
The crude oil is ’cut’ into 25 pseudo-components by HYSYS simulation software (vHYSYS 2006.5), from which the composition and flow rate of each component can be extracted. Later, these pseudo-components can be used in the Fenske calculation. The detailed compositions and flow rates of the 25 pseudo-components are shown in Table 3.3. CHAPTER 3. SHORTCUT MODELLING 67
Table 3.3: Crude oil compositions in the form of pseudo-component (corresponding to Table 3.2)
Component NBP xi,f fi No (◦C) (Mole fraction) (kmol/h) 1 9 0.0502 131.0629 2 36 0.0488 127.4277 3 61 0.0581 151.5974 4 87 0.0709 185.0241 5 111 0.0711 185.6084 6 136 0.0687 179.2449 7 162 0.0661 172.4852 8 187 0.0614 160.2055 9 212 0.0569 148.6483 10 237 0.0517 134.9129 11 263 0.0467 121.8539 12 288 0.0415 108.2346 13 313 0.0373 97.2869 14 339 0.0342 89.2142 15 364 0.0313 81.6637 16 389 0.0286 74.5765 17 414 0.0259 67.6652 18 447 0.0361 94.3710 19 493 0.0267 69.7825 20 538 0.0210 54.9362 21 584 0.0177 46.1598 22 625 0.0126 32.8241 23 684 0.0151 39.2967 24 772 0.0113 29.5907 25 855 0.0103 26.9965
In refineries, the crude oil is usually heated up to approximately 370◦C. Here, a value of 372.3◦C from an example in Chen (2008) is chosen in this work. The feed pressure is set at 3.0 bar, which is above the column pressure of 2.5 bar. Superheated steam, with a temperature of 260◦C and pressure of 4.5 bar, is injected to the bottom of the column. The detailed conditions for the crude oil and steam can be found in Table 3.4 and 3.5 respectively.
Table 3.4: Crude oil feed conditions and product specifications
Preheated Temperature (◦C) 372.3 Pressure (bar) 3.0 Flow rate (kmol/h) 2611 Distillate (kmol/h) 2035 Bottom (kmol/h) 571 CHAPTER 3. SHORTCUT MODELLING 68
Table 3.5: Steam conditions
Temperature (◦C) 260 Pressure (bar) 4.5 Flow rate (kmol/h) 138
The column is simulated by specifying product flow rates, which can be found in Table 3.4. Then the recovery of each pseudo-component in the top and bottom products is calculated, as is shown in Figure 3.7. Since both of the light and heavy key components are distributing components, the potential light and heavy key components should exist in the sloped part of the recovery curves. Four pairs of light and heavy key components along the slope are chosen in order to test the Fenske method. Other pairs of key components and recoveries can also be chosen to test the Fenske calculation for this case.
With the specifications of two key components and their recoveries, the Fenske method then predicts non-key component flow rates in each product. All four sets of results are compared with the rigorous values from HYSYS, as shown in Figures 3.8 and 3.9. Here, the calculated results of bottom product are presented using the TBP points, as it is the final product of a crude oil distillation column and typically specified by boiling properties.
Table 3.6: Selections of key components and recoveries for the simple column in Figure 3.6
Parameters Simple Columns Case (a) Case (b) Case (c) Case (d) Light key component 11 12 13 14 Heavy key component 17 17 16 15 Light key component recovery 0.9741 0.9372 0.8756 0.7842 Heavy key component recovery 0.9053 0.9053 0.5204 0.3433
In Figure 3.8, although the calculated flow rates of some components may be slightly underestimated (e.g. Figures 3.8a and 3.8b), or slightly overestimated, (e.g. Figures 3.8c and 3.8d), most of results of the Fenske method are in good agreement with those of HYSYS. Figure 3.9 shows the corresponding TBP curves of Residue, generated by using Fenske results and rigorous results. Among these four sets of results, the most appropriate prediction is calculated from the components 11-17 as light and heavy key components, however, manually selecting the combination of key components is not effective.
Two main reasons can be used explain these deviations. The first one is the limitation CHAPTER 3. SHORTCUT MODELLING 69
200 200
180 180 160 160 140 140 120 120 100 100 80 Fenske 80 Fenske 60 HYSYS 60 Hysys
40 40 Flowrate (kmol/h) Flowrate Flowrate (kmol/h) Flowrate 20 20 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Pseudo-component Pseudo-component
(a) 11-17 as LK-HK (b) 12-17 as LK-HK
200 200
180 180 160 160 140 140 120 120 100 100 80 Fenske 80 Fenske 60 HYSYS 60 HYSYS
40 40 Flowrate (kmol/h) Flowrate Flowrate (kmol/h) Flowrate 20 20 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Pseudo-component Pseudo-component
(c) 13-16 as LK-HK (d) 14-15 as LK-HK
Figure 3.8: Top product composition of a single column of the Fenske method, which is derived from total reflux condition; the other one is that the light key and heavy key components chosen here may not be the best combination. Therefore, an optimization model is needed in order to automatically specify the most appropriate key components and recoveries, which will be proposed in Chapter 4.
3.3.3 Application of the Fenske method in steam-stripped complex columns
Complex columns can be decomposed into thermally-coupled simple columns (Lieb- mann, 1996). In Figure 3.10a, a complex column with one side-stripper can be divided into two parts: the content included by the dashed line, which will form the second simple column, and the left part which will form the first simple column. Consequently, the number of stages of the complex column and its side-stripper are re-distributed into the new configuration, as shown in Figure 3.10b. In the main column of the complex configuration, the vapour and liquid flow rates under the stage of 16 (denoted by V and L), will be the feed and liquid withdrawal of the second column. Note that, the vapour feed to and liquid withdrawal of the second simple column are assumed at the CHAPTER 3. SHORTCUT MODELLING 70
1000 1000
900 900
C)
C) ° ° 800 800 700 700 600 600 500 500 HYSYS HYSYS 400 400 300 Fenske 300 Fenske
200 200 True boiling points ( boiling points True 100 ( points boiling True 100 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 % Mole distilled % Mole distilled
(a) 11-17 as LK-HK (b) 12-17 as LK-HK
1000 1000
900 900
C)
C) ° 800 ° 800 700 700 600 600 500 500 HYSYS HYSYS 400 400 300 Fenske 300 Fenske
200 200 True boiling points ( boiling points True 100 ( boiling points True 100 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 % Mole distilled % Mole distilled
(c) 13-16 as LK-HK (d) 14-15 as LK-HK
Figure 3.9: Ture boiling curve of bottom product of a single column same stage (Carlberg and Westerberg, 1989a; Suphanit, 1999, p. 36).
The net feed to the second column is the pseudo-components in the vapour from the first column subtracted by the ones in the liquid withdrawal. Thus, the recoveries of all the pseudo-components for the second column will be calculated with respect to the net feed, as shown in Equations 3.2 to 3.4:
fi,Net = fi,V − fi,L (3.2)
di,2 Ri,D2 = (3.3) fi,Net
bi,2 Ri,B2 = (3.4) fi,Net where Ri,D2 and Ri,B2 are the recoveries of component i in the second column with respect to the net feed fi,Net.
Before using the shortcut calculation to predict the product compositions, the average relative volatilities of all the pseudo-components should be calculated. As discussed in Section 2.2.4, several methods can be used to approximate the average relative CHAPTER 3. SHORTCUT MODELLING 71
Off-Gas
Water
1 Distillate
15 V' 16 L'
L V Feed 22 2 27 Main Steam Side steam
Side-product
Bottom product (a) Applying decomposition to a complex column with one side-stripper
Off-Gas
d i,2 (Mixed) Water Distillate 16 fi,V V f L 2 i,L L' V' Side steam 6 bi,2 Side-product Feed 5 Main steam bi,1 Bottom product (b) Corresponding decomposed configuration
Figure 3.10: Decomposition method to a complex column volatilities of the components in a column. The most widely used one is the geometric mean values from the top and bottom products, as shown in Equation 2.20. In order to calculated the geometric mean values of relative volatilities, the K-values of pseudo-components in the top and bottom product should be available. However, these K-values cannot be obtained, as product compositions have not been calculated. King (1980, p. 397) suggested the relative volatilites from the feed K-values can be approximated as the geometric-mean values (Equation 2.19). If the product compositions can be predicted with equal accuracy using K-values from the feed and the products (top and bottom), then the feed K-values can be applied in the shortcut CHAPTER 3. SHORTCUT MODELLING 72 calculations. Thus, the top product obtained from a calculated upstream column can provide both material feed and K-values for the calculation of its downstream column.
This decomposition and calculation procedure is applied to a crude oil distillation column. The relative volatilities from both geometric mean and the feed are applied in the shortcut calculations, which will be illustrated in Section 3.3.4 and Section 3.3.5, respectively.
3.3.4 Illustrative example: Applying the Fenske method to a complex crude oil distillation column (geometric mean α)
The crude oil assay, crude oil feed and steam conditions are the same as those in Section 3.3.2. A complex crude oil distillation column with three side-strippers and live steam is shown in Figure 3.11a; its equivalent decomposed configuration is shown in Figure 3.11b. Both configurations of this complex crude oil distillation column are simulated in HYSYS (v2006.5). The specifications for its decomposed configuration are shown in Table 3.7. Table 3.7: Simulation specifications for a decomposed crude oil distillation column (Figure 3.11b)
Column Specifications Column 1 Column 2 Column 3 Column 4 Feed preheat temp (◦C) 372.3 Operating pressure (bar) 2.5 2.5 2.5 2.5 Number of stages 11 7 9 10 Feed stage 5 2 4 4 Vaporisation mechanism Steam Steam Reboiler Reboiler Steam flow rate (kmol/h) 95.8 42.2 Reboiler duty (MW) 6.785 1.681 Bottom product (kmol/h) 571 291.6 512 396.7
The decomposed configuration in Figure 3.11b illustrates using four simple columns to rigorously simulate the complex crude oil distillation column, and it will be the reference simulation for the Fenske calculation. There are three liquid withdrawals going back to the upstream simple columns in Figure 3.11b, which means three recycle units are employed in the HYSYS simulation. Recycle streams can cause convergence problem in this simulation, therefore it is better to build up this model by adding one column at a time. The initial value for the recycle streams can be extracted from the complex column simulation in Figure 3.11a, which is relatively easy to simulate. CHAPTER 3. SHORTCUT MODELLING 73
Off-Gas
Water
LN
5 6
4 10 11
15 4 HN 16
2 LGO
Crude 22 Steam
27 HGO
Residue Steam (a) Complex configuration of a crude oil distillation column
Off-Gas
Water
6 LN
4 5 HN
Column 4 4 5 LGO Column 3
2 Steam 6 Crude HGO
5 Column 2
Steam Residue
Column 1 (b) Corresponding decomposed configuration of a crude oil distillation column
Figure 3.11: Decomposition method to a crude distillation column CHAPTER 3. SHORTCUT MODELLING 74
After the simulations are converged, the recoveries of all the pseudo-components in each product with respect to the crude feed is shown Figure 3.12. Based on the simulation results of the decomposed configuration, the recoveries of all the pseudo-components in each simple column with respect to its net feed can be calculated. For each simple column, both the K-values from the top and bottom products are extracted in order to calculate the geometric mean values of the relative volatilities. The initial selection of key components for each simple column is from the example in Gadalla (2003, page:72), as shown in Table 3.8.
1.2000
1.0000
0.8000 Top 0.6000 HN LGO 0.4000 Recovery HGO
0.2000 Residue
0.0000 0 5 10 15 20 25 30 -0.2000 Pseudo-component
Figure 3.12: Products components recoveries in a complex crude column
LN + Gas
NetFeed 3 Column 4
NetFeed 2
Column 3 HN
NetFeed 1 Column 2 LGO
Crude Column 1 HGO
Residue
Figure 3.13: Fenske calculation for a decomposed crude oil distillation column (using geometric mean α) where the dashed circles indicate the K-values from top and bottom products are used in this case
With the initial key components, the recoveries and the K-values obtained from the simulation of the decomposed simulation, the Fenske calculations are carried out sequentially, as shown in Figure 3.13. The calculated product results, in terms of component flow rates and true boiling curves, are compared with those from the rigorous CHAPTER 3. SHORTCUT MODELLING 75
Table 3.8: Initial selection of key components for the decomposed columns
Parameters Simple Columns Column 1 Column 2 Column 3 Column 4 LK 13 11 7 3 HK 16 14 9 6 simulation. Then, the selections of key components are iterated by trial and error. An appropriate result of key components and their recoveries is shown in Table 3.9.
Table 3.9: New selection of key components and recoveries for the decomposed columns shown in Figure 3.11b (trial and error results)
Parameters Simple Columns Column 1 Column 2 Column 3 Column 4 LK 11 11 7 4 HK 17 14 9 7 RLK 0.9596 0.9002 0.9754 0.9928 RHK 0.7770 0.9795 0.9167 0.5792
The component flow rates of each product, obtained from the Fenske calculations with the specifications in Table 3.9 are shown in Figures 3.14 to 3.18 and compared with those from rigorous simulation of Figure 3.11b.
200 180 160 140 120 100 80 MixedTop_Fenske
60 MixedTop_HYSYS Flowrate (kmol/h) Flowrate 40 20 0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.14: Mixed Top product composition for Fenske and Rigorous methods
As discussed in Section 2.4, the quality of a crude oil product is measured by boiling point curves, rather than in terms of product compositions. Thus, a more meaningful way to analyze the Fenske results is through the comparisons of product TBP curves, which are included in Figures 3.19 to 3.22. The product TBP curves related to the Fenske calculation are reconstructed by the facilities in HYSYS for given product compositions. HYSYS is not the only way to produce the TBP curves from product compositions. Another TBP reconstruction method will be developed in Section 4.2.1. CHAPTER 3. SHORTCUT MODELLING 76
200 180 160 140 120 HN_Fenske 100 80 HN_HYSYS
60 Flowrate (kmol/h) Flowrate 40 20 0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.15: Heavy Naphtha product composition for Fenske and Rigorous methods
200 180 160 140 120 100 80 LGO_Fenske
60 LGO_HYSYS Flowrate (kmol/h) Flowrate 40 20 0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.16: LGO product composition for Fenske and Rigorous methods
120
100
80
60 HGO_Fenske HGO_HYSYS
40 Flowrate ()kmol/h) Flowrate
20
0 0 10 20 30 Pseudo-component
Figure 3.17: HGO product composition for Fenske and Rigorous methods
From the comparisons of TBP curves in Figures 3.19 to 3.22, it can be seen that the curves of heavy naphtha (HN), light gas oil (LGO) and Residue are in good agreement with those from rigorous simulations. In Figure 3.21, the TBP curve of heavy gas oil (HGO) has a good match with the curve from rigorous simulation in the range of approximately 5% to 95% (mole) distilled; the end parts of the curve, which are less than 5% and greater than 95%, have bigger deviations than the range in between. The deviation of TBP curve of HGO corresponds to its product composition, which is shown CHAPTER 3. SHORTCUT MODELLING 77
120
100
80
60 Residue_Fenske
40 Residue_HYSYS Flowrate (kmol/h) Flowrate 20
0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.18: Residue composition for Fenske and Rigorous methods
250
C) 200 °
150 points ( points
100 HN_Fenske
Boiling HN_HYSYS
50 True True
0 0 20 40 60 80 100 120 % Mole distilled
Figure 3.19: True boiling curve of HN product for Fenske and Rigorous methods
350
300
C) ° 250
200
150 LGO_Fenske 100 LGO_HYSYS
True Boiling points ( points Boiling True 50
0 0 20 40 60 80 100 120 % Mole distilled
Figure 3.20: True boiling curve of LGO product for Fenske and Rigorous methods in Figure 3.17. The example in Gadalla (2003, p. 69-79) also showed that the biggest deviation between the product compositions obtained from the shortcut and rigorous models was associated with heavy gas oil. The difficulty of using shortcut models to predict HGO product may be caused by the complexity of the chemistry content in this product (Speight, 2002, p. 45; Riazi, 2005, p. 121).
As discussed in Section 3.3.2, two reasons can be used to explain the deviations observed in the Fenske results: one is the limitation of the Fenske method, and the other is related to the selection of key components and recoveries. CHAPTER 3. SHORTCUT MODELLING 78
500 450
C) 400 ° 350 300 250 200 HGO_Fenske 150 HGO_HYSYS
100 True Boiling points ( points Boiling True 50 0 0 20 40 60 80 100 120 % Mole distilled
Figure 3.21: True boiling curve of HGO product for Fenske and Rigorous methods
1000 900
C) 800 ° 700 600 500 400 Residue_Fenske 300 Residue_HYSYS
200 True Boiling points ( points Boiling True 100 0 0 20 40 60 80 100 120 % Mole distilled
Figure 3.22: True boiling curve of Residue for Fenske and Rigorous methods
3.3.5 Illustrative example: Applying the Fenske method to a decom- posed crude oil distillation column (feed α)
In the previous example, the calculation of product composition is based on the relative volatilities from the geometric mean values of the top and bottom products, which can be obtained from the K-values of the product streams. However, to get both top and bottom products K-values requires the product compositions to be known.
In this illustrative example, the Fenske calculations are carried out again to the decomposed complex column of Figure 3.11b. The only difference from the example in Section 3.3.4 is that feed K-values are applied rather that geometric mean values, as shown in Figure 3.23. The feed K-values for column 1 are from the preheated crude oil; the feed K-values for a downstream column is generated by flashing the top product calculated from its upstream column using Fenske method. Then, three sets of product compositions from the Fenske method with geometric-mean α values, denoted by Fenske1, the Fenske method with feed-stage α, denoted by Fenske2, and rigorous simulations, denoted by HYSYS are compared in Figures 3.24 to 3.28. CHAPTER 3. SHORTCUT MODELLING 79
LN + Gas
NetFeed 3 Column 4
NetFeed 2
Column 3 HN
NetFeed 1 Column 2 LGO
Crude Column 1 HGO
Residue
Figure 3.23: Fenske calculation for a decomposed crude oil distillation column (using feed α) where the dashed circles indicate the feed K-values are used in this case
200 180 160 140 120 100 MixedTop_Fenske1 80 MixedTop_HYSYS 60
Flowrate (kmol/h) Flowrate 40 MixedTop_Fenske2 20 0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.24: Mixed Top product composition for Fenske (feed K-values) and Rigorous methods
200 180 160 140 120 100 HN_Fenske1 80 HN_HYSYS 60
Flowrate (kmol/h) Flowrate 40 HN_Fenske2 20 0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.25: Heavy Naphtha product composition for Fenske (feed K-values) and Rigorous methods
From these results, it can be seen that the pseudo-component flow rates predicted by Fenske1 and Fenske2 are almost identical to each other, as long as the specifications of key components and recoveries keep the same. The TBP curves of Fenske1 and Fenske2 cannot be distinguished and are shown in Appendix A. This comparison indicates that: CHAPTER 3. SHORTCUT MODELLING 80
200 180 160 140 120 100 LGO_Fenske1 80 LGO_HYSYS 60
Flowrate (kmol/h) Flowrate 40 LGO_Fenske2 20 0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.26: LGO product composition for Fenske (feed K-values) and Rigorous methods
120
100
80
60 HGO_Fenske1
40 HGO_HYSYS
Flowrate (kmol/h) Flowrate HGO_Fenske2 20
0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.27: HGO product composition for Fenske (feed K-values) and Rigorous methods
120
100
80
60 Residue_Fenske1
40 Residue_HYSYS
Flowrate (kmol/h) Flowrate Residue_Fenske2 20
0 0 5 10 15 20 25 30 Pseudo-component
Figure 3.28: Residue composition for Fenske (feed K-values) and Rigorous methods applying Fenske method to a series of simple columns does not necessarily require K- values from the top and bottom products; the feed K-values can also be used. CHAPTER 3. SHORTCUT MODELLING 81
3.3.6 Application of the Fenske method in an atmospheric crude distillation column
In Sections 3.3.3 to 3.3.5, the Fenske method is applied to the decomposed complex columns. The product compositions calculated using the K-values from products and feed almost have equal values, which indicates the Fenske calculation can be carried out independently as long as the key components and recoveries are given.
If only mass balance is taken into account, an atmospheric distillation column, as shown in Figure 3.29a, can be represented by a series of blocks, as shown in Figure 3.29b, which is the Fenske representation. The specifications for the Fenske representation are the key components and recoveries for each block. An illustrative example about the atmospheric distillation column is shown in Section 3.3.7.
Off-Gas Water LN + Gas LN
Column 4 TPA A
MPA Column 3 HN D HN
BPA Column 2 LGO U LGO Crude Steam Crude Column 1 HGO HGO Residue Steam Residue (a) Atmospheric distillation column (b) Fenske representation of the atmospheric distillation column
Figure 3.29: Applying Fenske to an atmospheric distillation column
3.3.7 Illustrative example: Applying the Fenske method to an atmospheric distillation column
In this example, the Fenske method is applied to an atmospheric distillation column, as shown in Figure 3.29a. The pumparound duties of this column are shown in Table 3.10. Other specifications can be found in Table 3.7. The crude oil and feed conditions are the same as the examples in Section 3.3.2.
The product properties, in terms of three TBP points and flow rate, are generated by CHAPTER 3. SHORTCUT MODELLING 82
Table 3.10: Pumparound specifications for the atmospheric distillation column
Top Pumparound Mid Pumparound Btm Pumaround Duty (MW) 11.35 18.95 12.6 Temp Drop (◦C) -45.3 -38 -48
Table 3.11: Product property specifications for the atmospheric distillation column
T5 (◦C) T50 (◦C) T95 (◦C) Flow rate (kmol/h) Residue 320.51 481.75 810.06 571.00 HGO 236.71 335.11 407.69 291.60 LGO 176.50 238.78 307.82 512.00 HN 110.21 162.32 207.87 396.70
Table 3.12: Selection of key components and recoveries for the atmospheric distillation column shown in Figure 3.29a (trial and error results)
Parameters Simple Columns Column 1 Column 2 Column 3 Column 4 LK 11 10 7 5 HK 17 14 9 7 RLK 0.9596 0.9332 0.9418 0.8727 RHK 0.7748 0.9349 0.8445 0.9531
Table 3.13: Product property calculations for the atmospheric distillation column (Fenske results obtained from the specifications in Table 3.12)
T5 (◦C) T50 (◦C) T95 (◦C) Flow rate (kmol/h) Residue 313.82 479.46 809.30 570.00 HGO 246.67 329.51 415.58 314.08 LGO 176.74 235.91 303.21 481.43 HN 112.84 160.77 207.55 418.52 the Fenske calculations with the specification in Table 3.12. Compared with those from the rigorous simulation, as shown in Table 3.11, the maximum deviation for calculated TBP points is less than 10◦C, and the maximum deviation for the product flow rate is around 7%. The specifications associated with these results, in terms of key components and recoveries (Table 3.12), are identified by trial and error which may miss some better solutions. Therefore, a more efficient and systematic method is necessary for selecting the most suitable combinations of key components and their corresponding recoveries and predicting product qualities and quantities. CHAPTER 3. SHORTCUT MODELLING 83
3.4 Summary
In this chapter, discussion about the effects of reflux ratio on product distributions is carried out. Even though the interpolation method of Treybal (1979) is a good method for estimating the product compositions, it may not always be the most appropriate one. The Fenske method can also be a good alternative way to approximate the product compositions.
Trial and error was used in the work of Gadalla (2003) to obtain proper key components and recoveries, but it is not an efficient method and requires judgement and analysis from designers. The search method of Chen (2008) can systematically select the key components and recoveries. However, this method is highly sensitive to initial guesses; the search process and column design are carried out at the same time, therefore, any infeasible design generated by inappropriate initial guess or updated values will terminate the search algorithm; treating the MINLP problem as an NLP may lose some opportunities to find the optimum result.
The Fenske method focuses on component material balances and can provide a much simpler search path for key components and recoveries. However, the Fenske shortcut method itself has not been used to translate product specifications from industry to those specifications of shortcut models. Thus, evaluation of the Fenske method on predicting product compositions is required.
The evaluation of Fenske method is supported by rigorous simulations, which can provide candidate key components and recoveries. Different pairs of key components and recoveries are then selected and set as specifications for the Fenske model, which can then predict the product compositions. This method is applied to a simple steam- stripped column, decomposed complex distillation column and atmospheric distillation column. Both geometric mean and feed values of relative volatilities are applied in the Fenske calculations and their results show very good agreement with each other, therefore the feed relative volatilities can be used to approximate the geometric values. The product TBP curves are compared to those from rigorous simulations and show good agreements in the range of approximately 5% to 95% mole distilled.
So far, the evaluation of the Fenske method on crude oil distillation column is based on HYSYS simulations. In the next chapter, a systematic method, which is independent of rigorous models, will be proposed. Chapter 4
Systematic selection of Fenske parameters and applications
In Chapter 3, the evaluation of the Fenske method for predicting product qualities (composition and TBP curves) was carried out with the support of rigorous simulations. The Fenske parameters, i.e. the key components and their recoveries, were obtained from rigorous simulations. The product TBP curves, generated by using the results from the Fenske calculations, showed good agreement with those obtained from rigorous simulations between the range of approximately 5 % and 95 % mole distilled.
Chapter 3 shows that the selections of key components and recoveries are very important for predicting products qualities. In this chapter, a systematic method for selecting key components and recoveries is proposed.
4.1 Methodology Statement
As discussed in Section 2.4, in refineries, crude oils and their product fractions are commonly represented using various boiling point curves. One important boiling curve is the TBP curve, which is widely used in commercial process simulation software. For example, HYSYS requires a minimum of 5 distillation data points (or at least two bulk properties if the distillation points are not available) as assay data to characterize a petroleum oil; regardless of the assay data provided, an internal TBP curve is generated by HYSYSY using interpolation and extrapolation methods; this internal TBP curve
84 CHAPTER 4. SYSTEMATIC SELECTION 85 is then used to generate all the physical and critical properties (Aspen HYSYS User’s Guide, 2006; Aspen HYSYS Help, 2006). Given a TBP curve and a specific gravity, Aspen Plus estimates other bulk properties, such as molecular weight and critical properties (Aspen Plus Help, 2006). In this work, TBP curves are also used to represent the product qualities.
Separation requirements for the products of a crude oil distillation column are typically defined by cut points and the 5-95 temperature gap on boiling point curves (Watkins, 1979, p. 10). In this work, three true boiling point temperatures, T5%, T50% and T95%, are used to specify the quality of distillation product. The flow rate, either bottom flow rate (B) or top product flow rate (D) can be used to specify the quantity of a distillation product. These three temperatures and the flow rates of the products together specify the target product requirements. In this work, bottom product flow rates are applied, as the top product of a simple column is fed into the downstream column and is not a final product for a crude oil distillation column.
Rather than using trial and error to identify suitable key components and their recoveries, an optimization approach is proposed. The proposed approach utilizes the Fenske equations to systematically find the most appropriate key components and recoveries that can best achieve a given product requirement. An overview of this process is shown in Figure 4.1.
Product Specifications: Optimization: Optimized Fenske Boiling points (T5%, T50%, T95%) Change Fenske parameters parameters Product flow rates: B (or D) Minimize deviations
Figure 4.1: A simple flow chart of the optimization approach
4.2 Selecting Fenske parameters for simple distillation columns
4.2.1 TBP curve reconstruction
Although the composition of a crude oil is extremely complex, as discussed in Section 2.4, it can be characterized as a mixture of discrete pseudo-components with specific boiling point ranges, which can be determined by commercial simulation packages such as HYSYS, Aspen Plus, etc. Pseudo-components are employed in shortcut distillation CHAPTER 4. SYSTEMATIC SELECTION 86 models (Suphanit, 1999; Chen, 2008), from which the directly calculated product results are compositions of pseudo-components rather than boiling point temperatures. These shortcut column models include the Fenske method which will be used in the proposed optimization approach.
The relationship between pseudo-components and the TBP curve is described in detail using the concepts of mid-point percentage in Nelson (1958, p. 105-108), Khoury (2005, p. 52-54) and Fahim et al. (2010, p. 40-42). Each pseudo-component represents a small temerature range on a TBP curve (see Figures 4.2 and 4.3) and is defined by the average temperature of this range, which can be approximated by the mid-point of the normal boiling temperature of this range. The whole TBP curve is then represented by all these pseudo-components. The number of pseudo-components is decided by designers; the bigger the number is, the closer these pseudo-components can represent the TBP curve. However, too many pseudo-components can lead to excessive computation time. Therefore, a trade-off should be considered.
In an opposite way of cutting TBP curve into pseudo-components, a TBP curve can be reconstructed from compositions of pseudo-components using mid-points. The procedure is as follows:
According to the normal boiling point temperatures (NBP), the pseudo-components are arranged in ascending order using cumulative mole compositions, as shown in Figure 4.2.
TBP
NBP n Additional point
... Mid-point ...... NBP 2
NBP 1
x1 (x1 + x 2 ) ... 100% Cumulative Mole Percent Distilled
Figure 4.2: Arranging pseudo-components for TBP reconstruction
The mid-points of pseudo-components are marked; additional points are also CHAPTER 4. SYSTEMATIC SELECTION 87
marked to support the reconstruction of TBP curve. These additional points can be approximated by the mid-points of adjacent normal boiling temperatures of adjacent pseudo-components, such that the two triangles above and below the TBP curve are of the same area, as shown in Figure 4.3 (Nelson, 1958, p. 106).
Reconstruct the TBP curve by linear interpolating between these mid-points and linear extrapolating at both ends.
TBP Extrapolation
NBP n
......
NBP 2
NBP 1
Extrapolation x 1 (x 1 + x 2 ) ... 100% Cumulative Mole Percent Distilled
Figure 4.3: TBP curve reconstruction
In order to illustrate this TBP reconstruction method, a crude assay data, as shown in Table 4.1, is first input into HYSYS and cut into 25 pseudo-components. A TBP curve based on this assay data and the mole compositions of all the pseudo-components are obtained from HYSYS. Then, these pseudo-components’ mole compositions are applied to reconstruct a TBP curve using the proposed TBP reconstruction method.
Table 4.1: Crude oil TBP data (Watkins, 1979)
% Distilled (Volume) TBP(◦C) 0 -3 5 63.5 10 101.7 30 221.8 50 336.9 70 462.9 90 680.4 95 787.2 100 894 Density 865.4 kg/m3 CHAPTER 4. SYSTEMATIC SELECTION 88
Figure 4.4 shows the TBP curve reconstructed from the proposed method and compares it against the reference TBP curve generated by HYSYS. It can be seen that the reconstructed TBP curve matches well with the reference TBP curve. The only noticeable differences between the two curves is the first and last points, which denote the initial and end boiling points of this particular crude oil (0 % and 100% distilled).
It is difficult to measure the initial and end boiling points precisely in the laboratory, making it unsuitable for representing an oil quality (Aspen HYSYS User’s Guide, 2006). Moreover, the 0 % and 100% temperatures may represent infinite small quantity of material, so are not necessarily significant in process simulation and design. Therefore, crude oil fractions are usually defined by the 5-95 temperature gap rather than the 0-100 temperature gap (Watkins, 1979).
1000
900
800 CrudeTBP_Calc 700
CrudeTBP_HYSYS
600
C) ° 500
TBP ( TBP 400
300
200
100
0 0 0.2 0.4 0.6 0.8 1 Cumulative Mole Percent Distilled
Figure 4.4: TBP curve generated by calculation in Matlab and HYSYS
Given a reconstructed TBP curve, the temperature corresponding to any specific cumulative mole percent can be easily obtained from this curve. In this work, the proposed optimization model seeks to produce a TBP curve that best matches an industry specification for three product TBP temperatures (T5%, T50%, and T95%), as well as the flow rates.
4.2.2 Systematic approach for selecting Fenske parameters of a simple column
The proposed optimization method for predicting crude oil product properties (TBP points and flow rates) consists of three parts: input values, adjustable variables and output values. The input values refer to the product specifications from industry, which are the three TBP points (T5%, T50%, and T95%) and flow rate for each product. The CHAPTER 4. SYSTEMATIC SELECTION 89 adjustable variables refer to the Fenske parameters, which are the light and heavy key components and their recoveries. The output values refer to the calculated product properties, in terms of the three TBP points and flow rates. The objective function of the proposed optimization model minimizes the difference between the calculated values and the specified values by adjusting the Fenske parameters.
For a simple column, the objective function is defined as follows:
Minimize [(∆T 5)2 + (∆T 50)2 + (∆T 95)2 + (∆B)2] (4.1) Θ where
Θ = (LK, HK, RLK ,RHK )
∆T 5 = T 5%calc − T 5%spec
∆T 50 = T 50%calc − T 50%spec
∆T 95 = T 95%calc − T 95%spec
∆B = Bcalc − Bspec
LK and HK are light and heavy key components, which are integer variables; RLK and RHK are the corresponding recoveries of the two key components, and they are continuous variables with values between 0 to 1.
Note that, only one product flow rate can be specified in a simple column, as the other product flow rate is determined by mass balance. In this work, the bottom product mole flow rate, denoted by B, is chosen to be the specified value. T 5%spec, T 50%spec and T 95%spec denote the specified TBP points for the bottom product, while T 5%calc,
T 50%calc and T 95%calc denote the calculated temperatures for the bottom product.
For a simple column, the optimization method works by first finding the optimal recoveries for each possible pair of light and heavy key components, and then choosing the pair of key components with the smallest minimized difference. Firstly, for a given possible pair of light and heavy key components, as shown in in Figure 4.5, their recoveries are optimized using Conjugate Gradient Method, aiming to satisfy the objective function Equation 4.1. Then, the optimal recoveries and the minimum value of the objective function for this pair of key components can be obtained and recorded in one cell of the table in Figure 4.5. Next, the minimization is repeated with different pairs of light and heavy key components until all the cells in the table are CHAPTER 4. SYSTEMATIC SELECTION 90
filled. The smaller the minimized value of the objective function, the more appropriate the Fenske parameters. Finally, the key components and the associated recoveries with the smallest minimized value of the objective function are then selected as the optimal Fenske parameters.
LK
1 2 3 ... LK ... 24 25
1 2 3
..
HK Minimization
HK ..
... 24 25
Figure 4.5: Search space for key components
For a given pair of light and heavy key components, an example contour plot of the objective function is shown in Figure 4.6. The two axes are the recoveries of the two key components respectively. As can be seen from the two figures, the objective function for optimizing the recoveries of given key components is smooth and has only one minimum in the region where both recoveries are closed to unity. Similar contour plots can be obtained when different pair of key components are employed.
In order to reach to the optimum, an iterative method is needed for updating the recoveries. In this work, an effective iterative method, Conjugate Gradient method, is applied. This iterative method uses first order derivatives, requires relatively small number of iterations and has a faster convergence speed (Edgar, Himmelblau and Lasdon, 2001, chap. 6). Other iterative methods can also be used, e.g. Gradient descent method, which is slower than Conjugate Gradient method. Since the objective function Equation 4.1 is not a simple quadratic function and involves TBP reconstruction, it is difficult to accurately determine both first and second order derivatives, therefore second order derivative methods, e.g. Newton’s method, is not suitable for solving this minimization problem.
Using Conjugate Gradient method to continuously update recoveries, the minimization CHAPTER 4. SYSTEMATIC SELECTION 91
50
10 55
20 60
30 65
40 70
50 75
60 80
70 85 Recovery of light key component Recovery of light key component 80 90
90 95
100 10 20 30 40 50 60 70 80 90 100 50 55 60 65 70 75 80 85 90 95 Recovery of heavy key component Recovery of heavy key component (a) A whole contour plot (b) Optimal area of the contour plot
Figure 4.6: A contour plot of objective function for one simple column procedure for a pair of key component is illustrated in Figure 4.7. In Figure 4.7, only recoveries of the given light and heavy key component are optimized. The initial values of recoveries for the two key components are chosen from 0.5 to 1. Each pair of key components have its best recoveries.
In addition, the optimization approach is also subject to the following constraints:
The heavy key component in each column should be heavier than the correspond- ing light key component. Therefore, the integer value representing the light key should be smaller than the value representing the heavy key component in the optimization.
The lower bound of recovery values is set at 0.5. The intuition is that, given the definition of key components, a significant amount (i.e. more than 50%) of the light key component should be recovered in the top product, and similarly, a significant amount of the heavy key component should be recovered in the bottom product (Fenske, 1932). Because of this constraint, the contour plot in Figure 4.6 has blank triangle area, which is infeasible region for the objective function.
If multiple solutions exist for the simple column, i.e. two or more pairs of key components can achieve equally small minimized values of the objective function, then a heuristic method is used to select the most appropriate pair of key components and recoveries. This heuristic method is proposed according to the explanation of key components in Fenske (1932), and aims to avoid the solution, in CHAPTER 4. SYSTEMATIC SELECTION 92
A pair of LK HK
RLK RHK (set initial values from 0.5 - 1)
Fenske method (Equations 2.4 - 2.6) Conjugate Gradient Method TBP reconstruction (Section 4.2.1)
N Minimization Equation 4.1
Y
best R LK , best R HK
Figure 4.7: Optimization of recoveries for a pair of given key components
1.00
0.90 LK: 12 0.80 R (12): 0.9352 LK: 9 LK 0.70 min_value: R (9): 0.9891 LK 3.8270 0.60 min_value: 0.50 3.8337 LK:15 Ri,d 0.40 RLK(15): 0.6027
Recovery min_value: 0.30 Ri,b 3.9369 0.20 0.10 0.00 0 5 10 15 20 25 30 Pseudo-component
Figure 4.8: An example for illustrating the selection method if multiple solutions of optimization exist in one column where Ri,d and Ri,b are the recoveries of component i in the top and bottom products respectively; min value is the minimized value of the objective function.
which key component recovery in one product is approaching unity, and to avoid the solution, in which key component recovery in the top and bottom product has CHAPTER 4. SYSTEMATIC SELECTION 93
comparable values. Figure 4.8 shows a simple example for this proposed heuristic method. The data in Figure 4.8 is from an illustrative example in Section 4.2.3, which is a simple crude oil distillation column. In this example, three light key components with different recovery values have very similar minimized values of objective function. As shown in Figure 4.8, the difference between these minimized values is less than 0.5. Specifically, the recovery of component 9 in the top product is approaching to unity leading to nearly zero recovery in the bottom product; component 15 has non-negligible compositions in both the top and the bottom products. According to the explanations of key components (Fenske, 1932; Searder and Henley, 1998), neither of component 9 or 15 is appropriate for specifying a separation. It can also be seen that the lighter a light key component is, the higher the corresponding recovery becomes. Therefore the optimal light key component can be selected based on a compromise between choosing a heavier component (e.g component 15) and having a higher recovery (e.g. component 9), which is component 12 in the example given. Similarly, the optimal heavy key component can be selected based on a compromise between choosing a lighter component and having a higher recovery.
4.2.3 Illustrative example: Applying proposed approach to a simple distillation column
As discussed in the literature review (Section 2.3.1), a crude oil distillation column can be decomposed into an indirect sequence of thermally-coupled simple columns (Liebmann, 1996). The example illustrated in this section corresponds to the first column in such a sequence. Since only the mass balance is considered in the optimization method proposed in Section 4.2.2, the distillation column can be represented by Figure 4.9:
In this example, the crude oil is the one presented in Table 4.1, which is cut into 25 pseudo-components using HYSYS (v2006.5, Aspen Technology Inc.). The composition of each pseudo-component is then obtained from the Oil Manager in HYSYS. Only hydrocarbons are taken into account.
The product specifications (bottom products) for this column are shown in Table 4.2. The K-values of all the pseudo-components in the crude oil feed are extracted from HYSYS (Vapour liquid equilibrium was modelled using the Peng Robinson Equation CHAPTER 4. SYSTEMATIC SELECTION 94
Top product
Crude oil feed
Residue
Figure 4.9: Overall mass balance on a simple distillation column
Table 4.2: Product specifications for applying the proposed approach to a simple distillation column
T5 (◦C) 320.50 T50 (◦C) 481.70 T95 (◦C) 810.10 Flow rate (kmol/h) 571.00 of State). The feed condition is set as: temperature of 372◦C and pressure 3 bar. Using the proposed method in Section 4.2.2, the Fenske parameters in terms of key components and recoveries are optimized, and the product properties in terms of TBP points and flow rate are calculated. These results are shown in Table 4.3.
Table 4.3: Optimized Fenske parameters for the simple distillation column
Specification Calculation Fenske parameters Optimized values T5 (◦C) 320.50 320.55 LK 12 T50 (◦C) 481.70 479.39 HK 18 ◦ T95 ( C) 810.10 808.72 RLK 0.9339 Flow rate (kmol/h) 571.00 570.08 RHK 0.9324
The optimized results in Table 4.3 show very good agreements with the specified values, as the deviations of the TBP temperatures and flow rate are less than 3 ◦C and 1 kmol/h respectively. The optimal key components and recoveries for this column were automatically selected by the proposed optimization model, without the need for initial guesses.
The results in Table 4.3 indicate that the proposed model can provide good predictions for the first simple column in a decomposed column sequence. In the next section, the CHAPTER 4. SYSTEMATIC SELECTION 95 methodology is applied to a sequence of simple columns.
4.3 Selecting Fenske parameters for a sequence of simple columns
4.3.1 Systematic approach for selecting Fenske parameters of a sequence simple columns
In this work, the crude oil distillation column is decomposed into a series of simple columns. A decomposition with five products including Residue, HGO, LGO, HN and a mixed top product (LN and Gas) is shown in Figure 4.10. As discussed in Section 2.2.1, the Fenske method is applicable to a simple column with one feed, a top product and a bottom product, therefore the top product of the last column is a mixed top product containing both LN and Gas. Only material balance is taken into account in these columns. Note that the degrees of freedom for the product flow rate specifications are: number of total products − 1
LN + Gas
NetFeed3 Column 4
NetFeed2 Column 3 HN
NetFeed1 Column 2 LGO
Crude Column 1 HGO
Residue
Figure 4.10: Applying the proposed optimization model to a series of columns
The objective function for column j is to to minimize the difference between the calculated values and the specified values.
2 2 2 2 Minimize [(∆T 5j) + (∆T 50j) + (∆T 95j) + (∆Bj) ] (4.2) Θj CHAPTER 4. SYSTEMATIC SELECTION 96 where
Θj = (LKj,HKj, RLKj,RHKj)
∆T 5j = T 5%j,calc − T 5%j,spec
∆T 50j = T 50%j,calc − T 50%j,spec
∆T 95j = T 95%j,calc − T 95%j,spec
∆Bj = Bj,calc − Bj,spec j: number of the simple column in an indirect sequence
In this decomposition, the top product of each column is used as the feed to the next column. The first simple column is optimized to generate the most appropriate key components and recoveries, using the approach in Section 4.2.2. Then the final calculated top product of column 1 (flow rate and component mole fraction) provides feed for the second simple column, and then the second column can be optimized to obtain its best Fenske parameters. This procedure is repeated until the last simple column is optimized.
To calculate the relative volatilities of the first simple column, it is straightforward to obtain the K-values of all pseudo-components from the crude oil feed in HYSYS. However, the K-values for the following simple columns have to be calculated. In order to obtain these K-values, vapour-liquid equilibrium data for each feed stream (excluding the crude oil feed to the first column) are needed, which can be determined by stream flash calculations. In this work, the flash calculations, assuming saturated vapour of the feed streams, are supported by simulation software HYSYS. The procedure is illustrated in Figure 4.11. The detailed information of this link can be found in Appendix B.
Top product composition link of column j
Flash Calculation for K-values of feed to column j+1 (HYSYS)
Optimization for column j+1 link
Figure 4.11: Generating K-values of the feed to column j + 1 by flash calculations CHAPTER 4. SYSTEMATIC SELECTION 97
Besides the constraints that apply to a single column (see Section 4.2.2), other constraints should also be obeyed when applying the optimization model to a series of simple columns. The light and heavy key components in a downstream column (j + 1) should be lighter than those of an upstream column j. This is because the decomposition of the crude oil distillation column is in an indirect sequence, and a downstream column should contain a higher proportion of lighter components than those of the upstream column.
4.3.2 Illustrative example: Applying proposed approach to a crude oil distillation column
In order to apply the proposed approach to a crude oil distillation column, assay data of the crude oil and its required product fractions in terms of TBP points and flow rates should be provided first.
The product TBP points and flow rates used in this example are obtained from a rigorous simulation of a crude oil distillation column, whose operating conditions and specifications can be found in Section 3.3.7. The product TBP points are generated from facilities in HYSYS (i.e. Oil Manager), as shown in Table 4.4. Only four products, Residue, heavy gas oil (HGO), light gas oil (LGO), and heavy naphtha (HN) can be specified at the same time, as the fifth product (top distillate) is determined by mass balance with the given crude oil feed.
Table 4.4: Product specifications for applying the proposed approach to an atmospheric column
T5 (◦C) T50 (◦C) T95 (◦C) Flow rate (kmol/h) Residue 320.20 481.00 810.00 571.00 HGO 236.50 335.20 407.80 291.60 LGO 176.40 238.80 307.90 512.00 HN 110.00 162.30 207.90 396.70
Given the product specifications presented in Table 4.4, the method proposed in Section 4.3 systematically determines the most appropriate key components and recoveries (Fenske parameters), and calculates the corresponding product properties, which are shown in Table 4.5.
Using the key components from Table 4.5, the contour plots of the objective function CHAPTER 4. SYSTEMATIC SELECTION 98 for the four simple columns are visualised in Figures 4.12 to 4.15. These contour plots further demonstrate that the objective function of each column is smooth and has only one minimum, and thus the minimum can be guaranteed to be found by the proposed optimization method.
10
20
30
40
50
60
70
Recovery of light key component 80
90
100 10 20 30 40 50 60 70 80 90 100 Recovery of heavy key component
Figure 4.12: Contour plot of objective function for simple column 1 (RLK1-RHK1)
10
20
30
40
50
60
70
Recovery of light key component 80
90
100 10 20 30 40 50 60 70 80 90 100 Recovery of heavy key component
Figure 4.13: Contour plot of objective function for simple column 2 (RLK2-RHK2)
10
20
30
40
50
60
70
Recovery of light key component 80
90
100 10 20 30 40 50 60 70 80 90 100 Recovery of heavy key component
Figure 4.14: Contour plot of objective function for simple column 3 (RLK3-RHK3)
Table 4.5 compares the calculated product TBP temperatures and flow rates against CHAPTER 4. SYSTEMATIC SELECTION 99
10
20
30
40
50
60
70
Recovery of light key component 80
90
100 10 20 30 40 50 60 70 80 90 100 Recovery of heavy key component
Figure 4.15: Contour plot of objective function for simple column 4 (RLK4-RHK4)
Table 4.5: Optimization results with comparison to product specifications
T5 T50 T95 Flow rate (◦C) (◦C) (◦C) (kmol/h) Residue calc 320.55 479.39 808.72 570.08 Residue spec 320.50 481.70 810.10 571.00 Deviation 1 0.05 -2.31 -1.38 -0.92 HGO calc 237.31 329.78 415.63 291.68 HGO spec 236.70 335.10 407.70 291.60 Deviation 2 0.61 -5.32 7.93 0.08 LGO calc 175.60 237.74 314.08 512.17 LGO spec 176.50 238.80 307.80 512.00 Deviation 3 -0.9 -1.06 6.28 0.17 HN calc 110.29 161.48 210.40 396.76 HN spec 110.20 162.30 207.90 396.70 Deviation 4 0.09 -0.82 2.50 0.06
Table 4.6: Optimized Fenske parameters corresponding to the results in Table 4.5
Parameters Simple Columns Column 1 Column 2 Column 3 Column 4 LK 12 10 7 4 HK 18 14 10 7 RLK 0.9339 0.9217 0.9054 0.9684 RHK 0.9324 0.8602 0.9687 0.8971 the specified values in Table 4.4; Table 4.6 shows the key components and recoveries returned for each column by the proposed optimization approach. Most deviations of TBP temperatures are around 2◦C or less. The maximum deviation is 7.9◦C, which is associated with heavy gas oil. The calculated flow rates of all the four products show good agreement with the specified values, with deviations less than 1 kmol/h. CHAPTER 4. SYSTEMATIC SELECTION 100
As discussed in Section 3.2.2, there are some limitations in the existing search methods for identifying the suitable key components and recoveries, e.g. highly sensitive to the initialization; the search methods and column design are carried out at the same time, which causes significant convergence problems; product compositions are obtained by interpolating between the results from Underwood and Fenske methods, introducing multipliers kRact/Rmin to the search method which need to be updated manually. The proposed method in this work is developed to overcome these limitations.
The proposed method is based on the total reflux condition, and is more simpler than the previous approach. The features of the new method are summarized as follows:
Theres is no need to provide suitable initial guesses for key components and recoveries. Given product specifications, solutions for key components and recoveries can be easily found. In contrast, the convergence of the existing method (Chen, 2008) is highly sensitive to initialization.
There is no need to solve the complex Underwood equations and no need to carry out column design during the search process. From the author’s experience of using the previous method, most convergence failures are caused by enthalpy balances while designing a column. Therefore, in the proposed method, the suitable key components and recoveries are identified without involving detailed column design, e.g. enthalpy balances.
There is no need to assume the ratio of finite reflux to the minimum reflux
(R/Rmin) for each simple column. Previous works (Gadalla et al., 2003b; Chen,
2008) set initial R/Rmin values for simple columns, in order to carry out the interpolation to predict product compositions. If a convergence failure is caused
by unbalanced heat duty calculation of any simple column, the R/Rmin values have to been updated manually. The proposed method employs Fenske method itself rather than both Fenske and Underwood methods. Thus, no interpolation
is needed, and therefore the manually updated variables R/Rmin are not required any more.
Due to its simplicity and user friendly feature, the proposed method is much easier to converge and requires significantly less computation, compared to the existing automatic search method of Chen (2008). However, the accuracy should also be compared, in order to check whether the approximation of product properties (TBP temperatures and flow rates) have been compromised. CHAPTER 4. SYSTEMATIC SELECTION 101
Given the same crude oil data from Table 4.1, the product properties in terms of TBP temperatures and flow rates, and the corresponding key components and recoveries are obtained directly from the work of Chen (2008), as shown in Tables 4.7 and 4.8, respectively. The largest deviation in TBP temperature in Table 4.7 appears in heavy naphtha, which is 7.2◦C. Although the deviation of flow rate for each product is less than 4%, the method of Chen (2008) underestimates all the bottom product flow rates, which can lead to a difference of 22 kmol/h in the last top distillate product. The 22 kmol/h hydrocarbons should belong to heavier products (e.g. Residue, HGO), and therefore they are heavy hydrocarbons. With more heavy hydrocarbons than that specified, the boiling temperatures of the last top distillate can be much different than the specified values, and therefore the quality of this product can be compromised. Table 4.7: Optimization results and specifications of Chen (2008, Chap. 3)
T5 T50 T95 Flow rate (◦C) (◦C) (◦C) (kmol/h) Residue calc 322.70 483.10 809.50 563.40 Residue spec 320.20 483.30 809.80 571.00 Deviation 1 2.50 -0.20 -0.30 -7.60 HGO calc 237.80 336.50 410.50 284.50 HGO spec 240.80 334.60 405.50 291.60 Deviation 2 -3.00 1.90 5.00 -7.10 LGO calc 178.20 239.90 311.90 508.60 LGO spec 176.10 238.00 307.1 512.30 Deviation 3 2.10 1.90 4.80 -3.70 HN calc 103.80 166.10 210.70 393.20 HN spec 111.00 162.70 207.90 396.70 Deviation 4 -7.20 3.40 2.80 -3.50 Table 4.8: Optimized key components and recoveries of Chen (2008, Chap. 3) (corresponding to results in Table 4.7)
Parameters Simple Columns Column 1 Column 2 Column 3 Column 4 LK 11 10 7 3 HK 18 13 9 7 RLK 0.9740 0.8520 0.9000 0.9800 RHK 0.9650 0.5040 0.77007 0.9800
From Tables 4.5 and 4.7, it can be seen that the product TBP temperatures predicted by the proposed method and by Chen (2008) have similar degrees of accuracy, for which the maximum deviation is less than 8◦C. The proposed method is better for predicting flow rates than the method of Chen (2008), in terms of deviations from specifications.
Both methods can systematically determine the key components and recoveries for CHAPTER 4. SYSTEMATIC SELECTION 102 the corresponding shortcut distillation model, which are then used to estimate product properties. The proposed method can achieve similar predictions for product properties as the method of Chen (2008).
The key advantage of the proposed method is that significantly less computation is required. However, those advantages also present limitations of the new method:
Since the proposed method is based on the Fenske condition, no detailed column design is carried out. The minimum number of stages is calculated.
The proposed method does not take into account heat balances of the simple columns, and as such it cannot be directly applied to design of heat-integrated crude oil distillation columns. No information is related to the stream tempera- tures, duty of pumparound and condenser, etc. to allow heat-integration aspects to be considered.
The method can be incorporated into the optimization framework for design of heat- integrated crude oil distillation columns. For example, the proposed method can be used to replace the corresponding part in the framework for generating key components and recoveries in the model of Chen (see Section 1.2). This point will be discussed further in terms of future work (Chapter 6).
The proposed method is also useful for optimizing a specific product flow rate or maximizing the total product income given certain product quality constraints. These applications will be presented in Sections 4.4 and 4.5.
4.4 Applying proposed approach to optimize a specific product flow rate in a crude oil distillation column
In refineries, the crude oil distillation columns is used to separate the crude oil into different products, which are suitable for various downstream processing units or blended into end products. For instance, light naphtha can be directly blended into final product gasoline. Heavy naphtha (HN), however, requires catalytic reforming before it is blended into gasoline, so HN is an intermediate product. For those products which are blended into a final product, the prices of the final product may be used to indicate the values (or ”transfer price”) of the crude oil distillation product, as the cost of CHAPTER 4. SYSTEMATIC SELECTION 103 blending processes can be ignored (Chen, 2008, p. 144). The value of the intermediate products may be approximated by the value of the corresponding final product less by the downstream operating cost (Maples, 2000). For example, the unit price of the crude oil feed and the unit values for the distillation products are summarized in Table 4.9 (Chen, 2008).
Table 4.9: Crude oil cost and prices of the product streams obtained from an atmospheric distillation column (Chen, 2008, p. 145)
Stream End product Downstream process Cost/Value of streams ($/barrel) ($/kmol) LN Gasoline Blending 91.7 73.4 HN Gasoline Catalyst Reforming 71 92.7 LGO Jet fuel Hydrotreating 79.1 128.1 HGO Diesel Blending 84.6 215.7 Residue Residue fuel oil N/A 47.9 204.3 Crude oil 66.7 108.2
Table 4.9 shows that the values of different crude oil products are different, and the HGO product is the most valuable product in terms of molar flow. One of the objectives of the refining industry is to maximize product profit, which means the crude oil distillation process should produce more valuable products. Therefore, the product flow rates of a crude oil distillation column should be optimized.
In this section, a method is proposed to optimize a product flow rate in order to increase the product profit. This optimization method is based on the Fenske model presented in Sections 4.1 to 4.3, with the objective of maximizing the flow rate of the most valuable product.
As reviewed in Section 2.4.3, Alattas et al. (2011) proposed a product planning model to optimize the product yields of a crude oil distillation column. This model is based on mass balance calculations using the fractionation index (see Equation 2.24). However, no explicit method for defining the fractionation index is provided; therefore it is not possible to apply this method to other cases. Moreover, no constraints of temperature deviation are set when maximizing a product flow rate, so product qualities cannot be controlled.
In Sections 4.2 and 4.3, the objective is to minimize the deviation between the calculated values and specified values of product properties, in terms of three TBP temperatures and product flow rates. The most appropriate key components and recoveries can then be obtained from the optimization results. During this optimization, the TBP CHAPTER 4. SYSTEMATIC SELECTION 104 temperatures and flow rate specifications are fixed.
In the approach presented here, to identify opportunities to increase the product profit, the yields of all the crude oil products may change. Consequently, the TBP temperature profiles will be different to those in the reference case. As shown Figure 4.16, if the yield of the most valuable product, which is heavy gas oil here, is to be increased, the two limiting lines representing the mass balance for this product should move away from each other. At the same time, the product quality represented by TBP temperatures should be within an acceptable range.
TBP
LN HN LGO HGO Residue
Off-Gas
Volume percentage distilled
Figure 4.16: Effect of increasing the yield of heavy gas oil on product TBP characteristics
In the work presented in this section, the Fenske parameters (key components and recoveries) are varied to allow the product flow rates to be optimized, and the TBP temperatures are included as constraints. The distillation column model equations, the objective function and its constraints are described as follows.
For component i, the mass balance is
fi = bi + di (4.3) where fi, bi and di are the molar flow rate of component i in the feed, top and bottom products.
The Fenske equation for predicting non-key component distributions (Equation 2.6) CHAPTER 4. SYSTEMATIC SELECTION 105 can be rearranged as:
d 1 − R i Nmin HK = (αi,HK ) (4.4) bi RHK b
By substituting Equation 4.3 in Equation 4.4 gives
fi bi = (4.5) N 1−RHK 1 + (αi,HK ) min RHK b
The minimum number of stages for a given separation Nmin can be calculated by rewriting Equation 2.5, which is h i ln RLK / 1−RHK 1−RLK d RHK b Nmin = (4.6) ln(αLK,HK )
Applying Equations 4.5 and 4.6 to a sequence of simple columns, as shown in Figure 4.17, the bottom product flow rate of each column can be determined.
D4
Column 4
B4 Column 3
B3 Column 2
Crude B 2 Column 1
B1
Figure 4.17: Block diagram representing product yields of a series of simples columns
For component i in column j for a n-component separation, its flow rate in the bottom product is fi,j bi,j = (4.7) 1−RHK Nmin,j j 1 + (αi,HKj ) R HKj b CHAPTER 4. SYSTEMATIC SELECTION 106 where RLKj 1−RHKj ln 1−R / R LKj d HKj d Nmin,j = ln(αLKj ,HKj )
The objective function for maximizing the product flow rate of column j will be as follows. n X Maximize bi,j Θ i=1
subject to |T 5%j,opt − T 5%j,base| ≤ δj (4.8) |T 50%j,opt − T 50%j,base| ≤ δj
|T 95%j,opt − T 95%j,base| ≤ δj
Θ = (LKj,HKj,RLKj ,RHKj ) where T 5%j,base, T 50%j,base and T 95%j,base denote the TBP points for the bottom product of the column j in the base case; T 5%j,opt, T 50%j,opt and T 95%j,opt denote the
TBP points for the optimized bottom product of the column j; LKj, HKj, RLKj and
RHKj are the key components and recoveries of column j; LKj and HKj are integer variables, while RLKj and RHKj are continuous variables.
The objective can also be defined as minimizing one product flow rate with a given tolerance for temperature deviations. Since Fenske mass balance calculations for these simple columns are carried out sequentially, minimizing a product flow rate of an upstream column may facilitate increasing the product flow rate of its downstream column.
Then the net profit generated by product and crude oil feed can be written as
r n X X net profit = Pprod,j ∗ ( bi,j) − Ccrude ∗ Fcrude (4.9) j=1 i=1 where Pprod,j and Ccrude are the unit price of product j and the crude oil respectively; Pn i=1 bi,jand Fcrude are the flow rates of product j and crude oil feed; r is the number of the product of the crude oil distillation column.
The model for optimizing product flow rate is formulated as a mixed integer non-linear constrained programming problem (Edgar, Himmelblau and Lasdon, 2001) and coded in Matlab (v2009b). A case study is presented in Section 5.1 to demonstrate the model. CHAPTER 4. SYSTEMATIC SELECTION 107
4.5 Applying the proposed approach to optimize the total product income for a crude oil distillation column
The main purpose of an optimization-based design approach for a refinery is to identify an optimal design solution, which can generate more product profit or decrease the total cost of the process. In Section 4.4, if TBP tolerances are given, the maximum or minimum flow rates of one product can be calculated. Using the maximum flow rate of the most valuable product, the total product profit can be increased. However, the flow rates of all the products are optimized one-by-one from the upstream column to the downstream column. This sequential optimization method is not suitable for maximizing the total product income, as it is not designed to search for the best combination of product flow rates.
In this section, the objective is to maximize the total product profit with product quality constraints. As discussed in Section 4.4, the net product profit is written as
r n X X net profit = Pprod,j ∗ ( bi,j) − Ccrude ∗ Fcrude j=1 i=1
If the flow rate of the crude oil feed and its unit price are constant, then the cost of the crude oil (Ccrude ∗ Fcrude) is fixed. Therefore, maximizing the net product profit can Pr Pn be treated as maximizing the total product income ( j=1 Pprod,j ∗ ( i=1 bi,j)). All the calculations involve non-linear equations (Fenske equations), integer and continuous variables, and also the product qualities have to be controlled. Thus, the maximization of the total product income is an mixed-integer non-linear problem.
For non-linear problems, it is very difficult to determine the global optimum due to the non-convex feature in the objective function and constraints (Weise, 2009). Non-linear problems have also been shown to often contain multiple local optima (Esposito and Floudas, 2000). For this product income maximization, in addition to existence of multiple solutions, there are some special features: the variable values involved (flow rates of all the products) are determined by sequential Fenske calculations of simple columns, hence they are not independent of each other; TBP reconstruction and K- value HYSYS calculations are included in this optimization, causing the optimization to be more complicated. It is well known that deterministic optimization methods, such as those based on gradient descent, can be easily trapped in a local optimum.
Stochastic methods utilize random vectors to update the variables, and they are more CHAPTER 4. SYSTEMATIC SELECTION 108 suitable to find the global optimum than deterministic methods. Many stochastic methods have been proposed to search for the global solution, e.g. Simulated Annealing, Random Optimization, Genetic Algorithms, Particle Swarm Optimization, Hill Climbing (Weise, 2009).
In this work, the Random Optimization method is used to maximize the total product income due to its effectiveness and simplicity of implementation (White, 1971; Gentle, 2004). Random Optimization works by iteratively moving to better solutions in the search-space, which are sampled using a probability distribution surrounding the current position. The Random Optimization can be pure random search-based (blind random search) or creeping random search-based (localized random search) (White, 1971; Gentle, 2004). Pure random search, which applies uniform probability distribution, is not efficient in the optimization (White, 1971). Creeping random search, which applies normal probability distribution (Gaussian distribution), is more efficient when the optimal solution is not too far away from the base case. That is, the optimal value of a product flow rate should be located within a certain range according to the given TBP temperature constraints.
In this work, Normal Distribution or Gaussian Distribution is used. Some main features are:
Gaussian Distribution is shown in Figure 4.18. The current position (µ) in Figure 4.18 denotes one of the current product flow rates; all the independent product flow rates have their own Gaussian distributions. The flow rates of all the products are changed at the same time to form a new mass balance and thus new value of product income. If the product income obtained from the new solution is increased, then the current positions (the combination of all the product flow rates) is then replaced by the new positions. The process repeats until convergence.
0.4
0.3
0.2
0.1
-3σ -2σ -σ μ μ' σ 2σ 3σ Figure 4.18: Gaussian Distribution for generating a new solution for a product flow rate CHAPTER 4. SYSTEMATIC SELECTION 109
where µ is the mean and σ is the standard deviation of the Gaussian distribution; µ0 is the new solution.
As a stochastic optimization method, the optimum solution is not dependent on the initialization of the problem. It can also cope with discontinuity in the objective function (Edgar, 2001).
Although the Random Optimization method can avoid being trapped in local optima, it cannot guarantee to find the global optimum unless an infinite number of iterations are carried out, which is impossible in practice. Therefore, a trade- off between the computation time and the quality of solution has to be made by defining convergence criteria and optimization parameters appropriately.
The objective function and the constraints of the optimization for increasing product income are:
r n X X Maximize Pprod,j ∗ ( bi,j) Θ j=1 i=1
subject to T 5%j,opt ∈ (T 5%j,lower − T 5%j,upper) (4.10) T 50%j,opt ∈ (T 50%j,lower − T 50%j,upper)
T 95%j,opt ∈ (T 95%j,lower − T 95%j,upper)
Θ = (LKj,HKj,RLKj ,RHKj ); (j = 1, ..., r − 1) where T 5%j,opt, T 50%j,opt and T 95%j,opt denote the TBP points for the optimized bottom product of the column j; T 5%j,lower, T 50%j,lower and T 95%j,lower are the lower bound of the TBP points for bottom product j; T 5%j,upper, T 50%j,upper and
T 95%j,upper are the upper bound of the TBP points for bottom product j.
Although there are r products, only r − 1 products are specified, as the last one is determined by material balance when the feed is fixed. The optimization algorithm is illustrated in Figure 4.19. Using this method, a single run of this optimization with 100 iterations is shown in Figure 4.20.
As a stochastic method, the Random Optimization approach improves the product income using random moves, i.e. randomly updating the current values to new positions within certain probabilities (Gaussian Distribution). Therefore, the results from different runs are unlikely to be identical to each other. Thus, multiple runs are required in order to find better solutions. The more runs are used, the more chance a better solution can be found. However, a trade-off is needed between the computational CHAPTER 4. SYSTEMATIC SELECTION 110
Get initial solution
Generate a new solution using Gaussian Distribution
Fenske sequential calculations
Calculate new product income
Product income improved? Then move to new solution; otherwise, keep the old value
Convergence criteria
Final solution (flow rates, total income)
Figure 4.19: Random Optimization for maximizing total product income time consumed by multiple runs and the quality of the results, in terms of total product income and the flow rates for each product.
Suitable values for the standard deviation of Gaussian distribution, σ, have to be selected. If the σs are too small, then the range of variability for new positions are very small, which means more iterations will be required to achieve a certain product income. If the σs are too big, then infeasible solutions are likely to be generated, which is not effective for optimization. Therefore, appropriate σs should be chosen for the optimization.
This Random Optimization method for maximizing the product income is coded in CHAPTER 4. SYSTEMATIC SELECTION 111
x 105 3.475
3.47
3.465
3.46
3.455
3.45
3.445 Total product income ($/h) 3.44
3.435
3.43 0 20 40 60 80 100 120 Iteration times
Figure 4.20: A single run with 100 iterations for maximizing product income using the method illustrated in Figure 4.19
Matlab (v2009b) and will be demonstrated in Case Study 5.2.
4.6 Summary
The Fenske distillation design method is proposed for predicting product compositions and hence product qualities in terms of boiling points of a crude oil distillation column. Given the product specifications from a petroleum refinery, in terms of TBP points and flow rates, the new search method can systematically identify the most suitable key components and recoveries for the required separation.
The proposed method has advantages, compared to the existing search methods presented by Gadalla et al. (2003b) and Chen (2008). It rarely requires intervention by the designer, does not require converged column simulation results, and can be applied to both design and retrofit scenarios. More importantly, the proposed method does not require initial guesses for key components and recoveries; the solutions of appropriate key components and recoveries can be easily found; the factor kR/Rmin that requires manual updating is not needed. The method is applied to simple columns and atmospheric columns, and the product results are compared with the specifications. The maximum deviation of TBP points of this method is around 8 ◦C, the accuracy of which is similar to those obtained from Chen (2008); the product flow rates show better predictions than those of Chen (2008). CHAPTER 4. SYSTEMATIC SELECTION 112
There are also some limitations for this method, such as no energy balance and detailed column design are involved during the search. This limitation can be overcome by incorporating the results of this method as inputs to the design framework of Chen (2008).
The proposed model may be applied to optimize a particular product flow rate. TBP constraints, which are not included in the work of Alattas et al. (2011), are considered during the optimization. Based on the proposed method, an optimization approach is presented to maximize the total product income, taking into account product quality constraints. The Random Optimization algorithm is employed in this income maximization approach. The optimal key components and recoveries in these applications can be obtained automatically. Two case studies illustrating these applications are presented in Chapter 5. Chapter 5
Case Studies
In Chapter 4, a search method for systematically transforming industry product specifications to those of shortcut column models is proposed. The application of the proposed method will be illustrated in this chapter by two case studies, including optimizing a specific product flow rate and maximizing total product income.
Case study 5.1 applies the method presented in Section 4.4 to maximize or minimize a particular product flow rate. The flow rates of all the products are not optimized simultaneously. Product TBP temperatures are also considered during these optimiza- tions.
Case study 5.2 utilizes the Random Optimization proposed in Section 4.5 to maximize the total product income within certain constraints. In this case study, product flow rates are optimized simultaneously in order to maximize income. The key components and recoveries associated with the optimal solution are also generated.
5.1 Case study 5.1: Profit improvement by maximizing the flow rate of the most valuable product of a crude oil distillation column
In this case study, the approach proposed in Section 4.4 is applied to a series of simple columns for optimizing the a particular product flow rate. As discussed at the beginning
113 CHAPTER 5. CASE STUDIES 114 of Section 4.4, heavy gas oil (HGO) is the most valuable product. Thus, the objective of this optimization is to maximize the product flow rate of HGO. Consequently, the flow rates of the adjacent products for HGO, which are Residue and LGO, are reduced. The base case data of the existing crude oil distillation column are presented in Section 5.1.1.
5.1.1 Base case data
An existing atmospheric distillation column, presented in Figure 5.1a, processes 2611 kmol/h (100,000 bbl/day) of crude oil to produce five products: Residue, heavy gas oil (HGO), light gas oil (LGO), heavy naphtha (HN) and mixed-top product (light naphtha (LN) and Gas). This atmospheric distillation column can be represented by the block flow diagram shown in Figure 5.1b.
Off-Gas Water LN + Gas LN
Column 4 TPA A
MPA Column 3 HN D HN
BPA Column 2 LGO U LGO Crude Steam Crude Column 1 HGO HGO Residue Steam Residue (a) Atmospheric distillation column (b) Block flow diagram of the atmospheric distilla- tion column
Figure 5.1: Case study 5.1: Atmospheric distillation column
The true boiling point curve of the crude oil is in Table 5.1. The product specifications of this atmospheric distillation column are shown in Table 5.2, which is the base case for improving the product income by the approach presented in Section 4.4.
The product unit values and crude oil cost in this case study are shown in Table 5.3. Either the molar unit price or volumetric unit price can be applied to calculate the total product income. The material balances of all the simple columns are carried out by Fenske method, in which molar calculations are used. Therefore, it is straightforward to obtain the product income by using the molar unit prices in Table 5.3 and flow rates in Table 5.2. If the barrel price is applied, then the molar flow rates can be transformed CHAPTER 5. CASE STUDIES 115
Table 5.1: Case Study: Crude oil TBP data (Watkins, 1979, p. 129)
% Distilled (Volume) TBP(◦C) 0 -3 5 63.5 10 101.7 30 221.8 50 336.9 70 462.9 90 680.4 95 787.2 100 894 Density 865.4 kg/m3
Table 5.2: Case Study: Product properties of the base case
T5 (◦C) T50 (◦C) T95 (◦C) Flow rate (kmol/h) Residue 320.20 481.00 810.00 571.00 HGO 236.50 335.20 407.80 291.60 LGO 176.40 238.80 307.90 512.00 HN 110.00 162.30 207.90 396.70 to barrels using the molecular weight and density of each pseudo-component, which can be extracted from Oil Manager in HYSYS. In the case studies of this chapter, the molar price is used. The current total product income of the base case is 2967 MM$/y.
Table 5.3: Case Study: Unit prices of all the streams (Chen, 2008, p. 145)
Stream End product Downstream process Price/Values for streams ($/barrel) ($/kmol) LN Gasoline Blending 91.7 73.4 HN Gasoline Catalytic Reforming 71 92.7 LGO Jet fuel Hydrotreating 79.1 128.1 HGO Diesel Blending 84.6 215.7 Residue Residue fuel oil N/A 47.9 204.3 Crude oil 66.7 108.2
The cost of crude oil and unit prices of its products vary frequently, according to the market of petroleum industry. However, in this work, these values are treated as constant values in the optimizations for improving product income. Using different cost of crude oil and different prices of products will not affect the fundamental basis of the proposed optimization methods in Sections 4.4 and 4.5. CHAPTER 5. CASE STUDIES 116
5.1.2 Optimization approach and results
Given the base case presented in Section 5.1.1, the flow rate of HGO is maximized using the method proposed in Section 4.4. The maximum deviation of product TBP temperatures should not exceed 10 ◦C. A smaller deviation can be specified according to product quality requirements. Different deviations can be applied to different products according to the designer, however, these deviations should be specified within the maximum value.
The optimization starts from the first column and sequentially transfers the calculated top product to the downstream columns. In the first column, the Residue product flow rate is minimized for a given TBP deviation, in order to provide more feedstock for the second column, which will produce the most valuable product HGO. For the second column, the flow rate of HGO is maximized and the quality of HGO in terms of TBP temperatures are controlled within the tolerance of 10 ◦C. So far, the flow rate of the most valuable product, HGO, has achieved its maximum value for the given deviation, which results in less feedstock to its downstream column. As shown in Table 5.3, LGO is the third valuable product, so its flow rate is also maximized. No optimization is carried out in the last column. The optimization results are shown in Table 5.4, with comparison to the values from the base case. The corresponding key components and recoveries are shown in Table 5.5. Table 5.4: Product property results for maximizing the flow rate of heavy gas oil
T5 T50 T95 Flow rate (◦C) (◦C) (◦C) (kmol/h) Residue opt 318.20 483.00 810.39 558.35 Residue base 320.50 481.70 810.10 571.00 Deviation 1 -2.30 +1.30 +0.29 -12.65 (-2%) HGO opt 246.49 325.20 416.83 355.13 HGO base 236.70 335.10 407.70 291.60 Deviation 2 +9.79 -9.90 +9.13 +63.53 (+22%) LGO opt 186.05 235.46 297.90 432.91 LGO base 176.50 238.80 307.80 512.00 Deviation 3 +9.54 -3.34 -9.90 -79.09 (-15%) HN opt 109.97 163.22 200.14 396.27 HN base 110.20 162.30 207.90 396.70 Deviation 4 -0.23 +0.92 -7.76 -0.43 (-0.1%) MixedTop* opt 3.56 77.18 149.50 858.34 MixedTop* base 3.31 75.50 139.50 839.70 Deviation 5 + 0.25 +1.68 +10 +28.64 (+3%) * MixedTop: the top product of column 4, which contains LN and Gas. CHAPTER 5. CASE STUDIES 117
Table 5.5: Optimized key components and recoveries corresponding to results shown in Table 5.4
Parameters Simple Columns Column 1 Column 2 Column 3 Column 4 LK 13 8 8 5 HK 19 14 9 7 RLK 0.8802 0.9894 0.7539 0.8589 RHK 0.9828 0.9593 0.8627 0.8426
In Table 5.4, the flow rate of heavy gas oil increases by 64 kmol/h (+22%) compared to the base case value; the Residue and light gas oil are reduced by 13 kmol/h (-2%) and 79 kmol/h (-15%) respectively. According to the prices listed in Table 4.9 and net profit calculation method in Equation 4.9, the net profit increased by this new product distribution (flow rates of all the products) is approximately 5% (26 MM$/y), compared to that of the base case. The corresponding key components and recoveries for each simple column are also optimized, as shown in Table 5.5. These key components and recoveries can be used as the specifications for shortcut column models, in order to generate the optimized product distributions and TBP points shown in Table 5.4.
This optimization approach for increasing product flow rate is simple, requires no initialization, and it can quickly provide an optimal product flow rate for a specific product, with given temperature specifications and tolerances. The model can automatically select the most appropriate key components and recoveries for shortcut column models, i.e. the Fenske-Underwood-Gilliland model or its modified versions.
The limitation of this model is that only the mass balance is carried out. As no enthalpy calculations are carried out, this model cannot consider the effect of operating cost on total profit increase, especially utility costs. Heat-integrated design of crude oil distillation systems needs to be carried out using more detailed models, e.g. the shortcut model of Chen (2008) or using commercial simulation softwares, e.g. HYSYS, Aspen Plus. However, the case study for optimizing total profit in Chen (2008, p.184) shows that the increase of product income has a dominant effect in the total profit increase. The total operating cost saving, the additional exchanger investment, the product income and the total profit are extracted directly from the case study in Chen (2008, p.184) and listed in Table 5.6.
From Table 5.6, it can be seen that the total operating cost saving (1.03 MM$/y) is much smaller than the increase in product income (34.58 MM$/y). However, the product income increase is 34.09 MM$/y, which is a dominate contributor for the total CHAPTER 5. CASE STUDIES 118
Table 5.6: Profit increase of a case study in the work of Chen (2008, p.184)
Parameter Unit Value Total operating cost saving MM$/y 1.03 Additional heat exchanger investment MM$/y 0.54 Increase of product income MM$/y 34.09 Total profit increase MM$/y 34.58 profit increase, 34.58 MM$/y. The results in Table 5.6 provide indications: product income is more important than operating cost savings, in terms of contribution to the total profit increase. Therefore, although the proposed method in this work cannot calculate the operating costs, it is still very beneficial for identifying opportunities to increase the total profit of a crude oil distillation column.
The proposed optimization method applied in this section is capable of maximizing or minimizing a specific product flow rate, which is useful when a particular product is of interest. However, the optimizations of simple columns are carried out sequentially, e.g. minimization in the first column and then maximization in the second column. Therefore, the flow rates of all the products cannot be optimized at the same time. With this limitation, opportunities may be lost to find the best combination of all the product flow rates that can achieve the maximum product income. The Random Optimization method proposed in Section 4.5 aims to overcome this limitation; it will be illustrated in Section 5.2.
5.2 Case study 5.2: Maximizing the total product income for an atmospheric distillation column
In Section 4.3, industry product specifications are translated to appropriate key components and recoveries, which are required in shortcut column models. The key components and recoveries of a simple column are important degrees of freedom, which will affect the product properties in terms of flow rates and TBP temperatures. In this case study, the objective is to maximize the total product income with certain product constraints. From the base case in Table 5.2, 10◦C is set as the maximum deviation of the three TBP temperatures for each product specified; the deviation provides lower and upper bounds for product qualities, as shown in Table 5.7.
The flow rates of the four products are used as the initial values for the income CHAPTER 5. CASE STUDIES 119
Table 5.7: Case study: Product constraints for the product income optimization
Parameters Residue HGO LGO HN Bound Lower Upper Lower Upper Lower Upper Lower Upper T5 (◦C) 310.2 330.2 226.5 346.5 166.4 186.4 100.0 120.0 T50 (◦C) 471.0 491.0 325.2 345.2 228.8 248.8 152.3 172.3 T95 (◦C) 800.0 820.0 397.8 417.8 297.9 317.9 197.9 217.9 optimization. The Random Optimization algorithm presented in Section 4.5 is then applied to maximize the total product income. As discussed in Section 4.5, reasonable values for the standard deviation of Gaussian distribution σ need to be selected. Using trial and error, the value 15 (kmol/h)2 is selected as the standard variation of the Gaussian distribution σ2 for all the bottom products.
Starting from the base case in Table 5.2, 10 optimization runs are employed to search for the maximum product income. Figure 5.2 shows the results of 10 runs with 100 iterations each for improving the total product income. The total computation time required for the 10 optimization runs with 100 iterations each is approximately 50 minutes. In Figure 5.2, it is noted that this stochastic method, which utilizes Gaussian probability, gives rise to different optimization ’pathways’. Thus, the results of these runs are different.
5 x 10 3.48
3.475
3.47
3.465
3.46
3.455
3.45
Total product income ($/h) 3.445
3.44
3.435
3.43 0 10 20 30 40 50 60 70 80 90 100 110 Iteration times
Figure 5.2: 10 runs of optimization with 100 iterations for maximizing total product income CHAPTER 5. CASE STUDIES 120
As shown in Figure 5.2, the total product income of each run climbs up rapidly from iteration 0 (the base case) to iteration 50, leading the total product income increase to approximately 1% with respect to the base case. Compared to that in the first 50 iterations, the product income increases much more slowly in the last 50 iterations. By the end of the 100 iterations, the maximum increase of product income is 35.8 MM$/y (or 1%). Even though the rate of increase in product income is lower after 50 iterations, it can be noticed that product income of some runs still gradually improves, as shown in the Figure 5.2. Therefore, more iterations are needed.
35.00
30.00
25.00
increase increase
20.00
15.00
(MM$/y) income 10.00
5.00 Product 0.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Every 50 iterations
Figure 5.3: Product income increase of each 50 iterations (1000 iterations in total)
As the number of iterations increases, the improvement in product income become smaller and smaller. Figure 5.3 is an example of 1000 iterations, showing product income increase against each 50 iterations. It is noticeable that in the last 500 iterations (11-20 in the horizontal axis of Figure 5.3), the increase in product income is very small. In theory, the more iterations are used, the better the income will be. As discussed in Section 4.5, the global optimum of this stochastic optimization can be found when infinite iterations are provided. However, it is impossible to carry out infinite iterations in practice. A trade-off between the computation time and the quality of the result should be made.
For the case with 1000 iterations, the best income increase is 57.3 MM$/y (1.93% increase with respect to that of the base case). The associated product yields and TBP temperatures, and the corresponding key components and recoveries are shown in Tables 5.8 and 5.9.
As discussed in Section 4.5, one of the advantages of stochastic optimization is that it is not dependent on the initialization case, which is illustrated in Figure 5.4. Given CHAPTER 5. CASE STUDIES 121
Table 5.8: Optimal product results of the product income maximization
T5 T50 T95 Flow rate (◦C) (◦C) (◦C) (kmol/h) Residue opt 320.13 483.97 810.81 555.38 Residue base 320.50 481.70 810.10 571.00 Deviation 1 -0.37 +2.27 +0.71 -15.62 (-2.7%) HGO opt 237.34 325.30 417.37 354.00 HGO base 236.70 335.10 407.70 291.60 Deviation 2 +0.64 -9.80 +9.67 +62.40 (+20%) LGO opt 176.97 231.17 299.75 487.61 LGO base 176.50 238.80 307.80 512.00 Deviation 3 +0.47 -7.77 -8.05 -24.39 (-4.8%) HN opt 110.42 154.99 197.95 440.96 HN base 110.20 162.30 207.90 396.70 Deviation 4 +0.22 - 7.31 -9.95 +44.26 (+11%) MixedTop* opt 2.80 72.50 136.60 773.06 MixedTop* base 3.31 75.50 139.50 839.70 Deviation 5 +0.51 -3.00 -2.9 -66.64 (-8%) * MixedTop: the top product of column 4, which contains LN and Gas.
Table 5.9: Key components and recoveries for the results shown in Table 5.8
Parameters Simple Columns Column 1 Column 2 Column 3 Column 4 LK 12 10 7 5 HK 18 13 9 6 RLK 0.9366 0.8940 0.9133 0.7946 RHK 0.9100 0.7965 0.8908 0.8074 different initial values of product flow rates, the calculated TBP temperatures of products can violate the specified constraints (lower and upper bounds in Table 5.7). If the constraints are not satisfied, zero values are returned to the total product income, as shown in the first 10 iterations in Figure 5.4a. However, after the 10 iterations, the income of all the runs fall into a reasonable range, above 3.4 × 105 $/h. The optimizations continue for 100 iterations.
From Figure 5.4a, it is difficult to see the income increase after all the runs are in the feasible range. However, the income increase can be seen in Figure 5.4b, which shows the income are improved gradually. The results indicate that the income optimization are not sensitive to the initial values, which are the flow rates of the products. If inappropriate flow rates are given as initial values, the income optimization can still be carried out, as long as upper and lower TBP bounds are specified. The only difference between starting from feasible solution and infeasible solution is that the CHAPTER 5. CASE STUDIES 122
5 x 10 3.5
3
2.5
2
1.5
1
0.5 Total product income ($/h)
0 0 20 40 60 80 100 Iteration times (a) The whole figure of income optimization starting from initial income value of 0
(b) Part of figure (a) for indicating the income increase of the 10 runs
Figure 5.4: 10 runs for optimizing the total income starting from an infeasible case latter consumes more iterations for achieving the same income value.
5.3 Summary
This chapter presents two case studies to illustrate the application of the proposed method for automatically translating the industry product specifications to those of shortcut column models. CHAPTER 5. CASE STUDIES 123
Case study 5.1 shows that the Fenske model is readily applied to optimize a specific product flow rate. In this case study, the most valuable product, heavy gas oil, can be maximized within specified constraints, aiming to increase the product income. Consequently, the yields of the adjacent products of heavy gas oil, Residue and light gas oil, are reduced. The net product profit increases 26 MM$/y (approximately 5% to that of the base case). Compared to the method of Alattas et al. (2011), the method proposed here considers the quality of the product (TBP points) during optimization; also, there is no need of fractionation index values to carried out the mass balances; the key components and recoveries can be easily found.
In Case study 5.2 shows that the Fenske model is applicable to maximize the total product income. Using Random Optimization algorithm, the product income is maximized by varying the product flow rates and specifying lower and upper bonds for controlling the product quality. A trade-off exists between the computation time and quality of optimization results. The total product income, obtained from this case study with 1000 iterations, increases by 57.3 MM$/y (1.93% compared to base case). Key components and recoveries associated with this optimal solution can be automatically identified. Moreover, the optimization is not dependent on a good initialization. Chapter 6
Conclusions and future work
6.1 Conclusions
In this thesis, a methodology is presented for facilitating the design of heat-integrated crude oil distillation systems (i.e. crude oil distillation columns and the associated heat recovery systems). The approach applies short cut methods, so it is easy to use and robust in convergence. It is shown to be sufficiently accurate to predict products of crude oil distillation columns.
The Fenske method is proposed to approximate the desired products of a crude oil distillation column and to search for the most appropriate key components and recoveries, as it is much simpler and more robust than the Underwood method. However, the Fenske method is based on the total reflux condition, and the method itself has not been applied to a decomposed crude oil distillation column for translating the industry product specifications into key components and recoveries.
Therefore, an evaluation of the Fenske method needs to be carried out. This evaluation is supported by rigorous simulations for providing candidate key components and recoveries; then trial and error is applied to identify the best combination of light key and heavy key components with associated recoveries. Evaluation of the Fenske method is carried out for simple steam-stripped columns, steam-stripped complex columns and atmospheric distillation column.
Using the product compositions calculated by the Fenske method, product TBP
124 CHAPTER 6. CONCLUSIONS AND FUTURE WORK 125 temperature profiles are generated using simulation software. These TBP temperature profiles show good agreement with those obtained from rigorous column models in the range of approximately 5%-95% mole distilled. It is shown that the average relative volatilities, required for Fenske calculations of simple columns, can be approximated by the relative volatilities of the feeds.
The evaluation of the Fenske method shows that the Fenske method is capable of predicting product properties (e.g. TBP temperature profiles) with sufficient accuracy, as long as suitable key components and recoveries are given. Conversely, given the product property specifications, an optimization approach is developed to identify the most appropriate key components and recoveries.
The proposed optimization approach can automatically search for the most suitable key components and recoveries for given product requirements. Compared to existing methods (Gadalla, 2003b; Chen, 2008), the main features of this approach are summarized as: it is not dependent on the initialization, which is crucial in the existing methods; energy balances and the complex Underwood equations are not involved during the search; the factor R/Rmin, which has to be manually updated in an existing method, is avoided; the light key and heavy key components are treated as integer variables during the search, rather than treated as continuous variables and rounded up to the nearest integers. With these features, this approach is much simpler and more robust in convergence than the existing method of Chen (2008). The approach is applied to simple columns and complex crude oil distillation columns, and can easily identify the suitable key components and recoveries. The maximum deviations between the calculated and specified product properties, i.e. TBP temperature points and flow rates are 8◦C and 1 kmol/h, respectively.
The proposed optimization method can also be used to adjust the product flow rates for various objectives, and to generate the corresponding key components and recoveries that are useful for the shortcut models, e.g. short cut model of Chen (2008). Two applications are considered in this work. The first one is to optimize a particular product flow rate for a simple column, while the product qualities in terms of TBP temperatures are constrained. Either maximizing or minimizing product flow rate of a simple column can be set as the objective. The second application is to maximize the total product income, i.e. to find the optimal combination of flow rates of all the products. A stochastic method, Random Optimization, is used to carry out the income maximization. The case study shows the optimal increase for the total product income is 57.3 MM$/y (1.93% with respect to the base case). Key components and recoveries CHAPTER 6. CONCLUSIONS AND FUTURE WORK 126 of this optimal solution are also determined.
The proposed approach overcomes some limitations of the previous methods proposed by Chen (2008), especially with regard to convergence problems. With less computation time and robustness in the convergence, the approach can efficiently translate industry product specifications to those required in the shortcut column models. Column simulation using the shortcut column models plays a major part in the optimization framework of heat-integrated design of crude oil distillation systems, hence facilitating the column simulation can enhance the performance of the whole optimization framework.
The Fenske method, which itself has not been applied in the previous research to predict the crude oil distillation columns and provide key components and recoveries, is explored in this thesis. The simplicity of this method allows the ’transforming of product specifications’ to be carried out easily; the computation time is significantly reduced, compared to the existing methods. The solution, in terms of key components and their recoveries, can be guaranteed for given product separation requirements in industry. The key components and recoveries are very important design variables in shortcut column models, and they are also important degrees of freedoms in the heat-integrated optimization framework (Section 1.2). A significant improvement for identifying the most appropriate key components and recoveries may greatly enhance the heat-integrated design of crude oil distillation systems. Less effort required and much more robust in convergence indicates that more people, rather than a limited number of experienced engineers, can apply the method to transfer product specifications and then to smoothly carry out the simulation and optimization in the heat-integrated design framework.
6.2 Future work
Possible directions for future work include:
1. The approach for predicting products can be incorporated into the optimization framework of design of heat-integrated crude oil distillation systems. The approach only accounts for mass balances; neither column design nor energy balances are considered. Therefore, it needs to be incorporated into more rigorous softwares, e.g. the optimization framework of Chen (2008), and be CHAPTER 6. CONCLUSIONS AND FUTURE WORK 127
tested. To do this, the approach can be coded as a subroutine and embedded into the framework, instead of applying the existing search method of Chen (2008), in order to identify the most appropriate key components and recoveries. Alternatively, a modification of the existing search method can be carried out to replace the interpolation method for predicting products (Section 3.2.1) with Fenske method. The Fenske calculation and K-value flash calculation are already coded in the framework. However, the constraints presented in Section 4.1 may be required.
2. The accuracy of the proposed method may be further improved. For instance, the K-values applied in the proposed method are derived from the composition of the feed to each ’simple’ column. However, the live steam, injected into the crude oil distillation column, will affect the vapour-liquid equilibrium. Therefore, in the proposed shortcut calculations, if the K-values can take into account the effect of live steam, the product results obtained from the method may be more accurate than when only applying feed K-values. In this work, the TBP curve reconstruction applies linear interpolation and extrapolation. Other interpolation and extrapolation methods can also be applied to achieve more accurate TBP curves, in terms of deviation from the curves generated by rigorous models.
3. The crude oil used in this work is Tia Juana Light oil (Watkins, 1979, p: 128-129). Crude oil distillation columns process different feedstock, including light or heavy crude oils. Therefore, the proposed approach can be extended to be applied into different crude oils.
4. Although this approach is developed for crude oil distillation columns, it can also be applied to other petroleum distillation processes, where boiling properties are the product specifications, e.g. Fluidized Catalytic Cracking process, Delayed Coker downstream separations. References
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Data for illustrative example 3.3.5
250
C)
° 200
150 HN_Fenske 1 100 HN_HYSYS HN_Fenske 2
50 True boiling points ( boiling points True 0 0 20 40 60 80 100 120 % Mole distilled
Figure A.1: True boiling curve of HN product for Fenske and Rigorous methods (feed K-value)
350
300
C) ° 250
200 LGO_Fenske 1 150 LGO_HYSYS 100 LGO_Fenske 2
50 True boiling points ( True 0 0 20 40 60 80 100 120 % Mole distilled
Figure A.2: True boiling curve of LGO product for Fenske and Rigorous methods (feed K-value)
133 APPENDIX A. DATA FOR ILLUSTRATIVE EXAMPLE 3.3.5 134
500
450 C)
° 400 350 300 250 HGO_Fenske 1 200 HGO_HYSYS 150 HGO_Fenske 2 100
True boiling points ( points boiling True 50 0 0 20 40 60 80 100 120 % Mole distilled
Figure A.3: True boiling curve of HGO product for Fenske and Rigorous methods (feed K-value)
1000
900 C)
° 800 700 600 500 Residue_Fenske 1 400 Residue_HYSYS 300 Residue_Fenske 2 200
True boiling points ( points boiling True 100 0 0 20 40 60 80 100 120 % Mole distilled
Figure A.4: True boiling curve of Residue for Fenske and Rigorous methods (feed K-value) Appendix B
HYSYS-Matlab interface for vapour-liquid equilibrium calculation
Aspen HYSYS simulation can be accessed from external softwares using Automation method (HYSYS 2006.5 Customization Guide*). Automation requires the use of third party software to link to HYSYS in a client-server relationship. HYSYS is the server and the third party software is the client. Using this functionality, the complexity of a simulation can be hidden, and only the important parameters of the simulation is accessed. Some client softwares that can access HYSYS are Microsoft Visual Basic, C++, Matlab, etc.
In this work, a HYSYS-Matlab interface is required for a flash calculation in order to generate the K-values. The top product of an upstream column is sent to the flash calculation and then provide the feed K-values for the downstream columns. The procedure is as follows.
Open HYSYS with only one active file, and then specify the components and fluid property package (Peng-Robinson).
Create a material stream and a spreadsheet. The spreadsheet is used to receive data from Matlab and sent the calculated data back to Matlab.
135 APPENDIX B. HYSYS-MATLAB INTERFACE FOR VAPOUR-LIQUID EQUILIBRIUM CALCULATION136
The Matlab code for this interface is shown below.
%*******************Interface with HYSYS******************************
%Specify molar composition of the mixture XF = Xi D;
%Start the MATLAB−HYSYS commuication hy = actxserver('HYSYS.Application');
% Active the HYSYS document and flowsheet opened in HYSYS hyActive = hy.ActiveDocument; hFlowsheet = hyActive.Flowsheet;
% Connect to HYSYS solver hSolver = hyActive.Solver;
% Link to the material stream'DEW' hDEW = hFlowsheet.Streams.Item('DEW');
% Link to the spreadsheet'SPRDSHT' hSprd = hFlowsheet.Operations.Item('SPRDSHT');
%Link to cells A1 to A25 in'SPRDSHT' hCellA1 = hSprd.Cell('A1'); hCellA2 = hSprd.Cell('A2'); hCellA3 = hSprd.Cell('A3'); hCellA4 = hSprd.Cell('A4'); hCellA5 = hSprd.Cell('A5'); hCellA6 = hSprd.Cell('A6'); hCellA7 = hSprd.Cell('A7'); hCellA8 = hSprd.Cell('A8'); hCellA9 = hSprd.Cell('A9'); hCellA10 = hSprd.Cell('A10'); hCellA11 = hSprd.Cell('A11'); hCellA12 = hSprd.Cell('A12'); hCellA13 = hSprd.Cell('A13'); hCellA14 = hSprd.Cell('A14'); hCellA15 = hSprd.Cell('A15'); hCellA16 = hSprd.Cell('A16'); hCellA17 = hSprd.Cell('A17'); hCellA18 = hSprd.Cell('A18'); hCellA19 = hSprd.Cell('A19'); hCellA20 = hSprd.Cell('A20'); hCellA21 = hSprd.Cell('A21'); hCellA22 = hSprd.Cell('A22'); hCellA23 = hSprd.Cell('A23'); APPENDIX B. HYSYS-MATLAB INTERFACE FOR VAPOUR-LIQUID EQUILIBRIUM CALCULATION137
hCellA24 = hSprd.Cell('A24'); hCellA25 = hSprd.Cell('A25');
% Set the pressure of'STREAM' to be2.5 bar hDEW.Pressure.SetValue(2.5,'bar');
% Set the vapour fraction of'STREAM' as saturated vapour hDEW.VapourFraction.SetValue(1);
% Turn HYSYS Solver off hSolver.CanSolve = 0;
% Delete the currrent values in cells A1 to A25 hCellA1.Erase; hCellA2.Erase; hCellA3.Erase; hCellA4.Erase; hCellA5.Erase; hCellA6.Erase; hCellA7.Erase; hCellA8.Erase; hCellA9.Erase; hCellA10.Erase; hCellA11.Erase; hCellA12.Erase; hCellA13.Erase; hCellA14.Erase; hCellA15.Erase; hCellA16.Erase; hCellA17.Erase; hCellA18.Erase; hCellA19.Erase; hCellA20.Erase; hCellA21.Erase; hCellA22.Erase; hCellA23.Erase; hCellA24.Erase; hCellA25.Erase;
% Set the mole fraction of components as given byXF hCellA1.CellValue = XF(1); hCellA2.CellValue = XF(2); hCellA3.CellValue = XF(3); hCellA4.CellValue = XF(4); hCellA5.CellValue = XF(5); hCellA6.CellValue = XF(6); hCellA7.CellValue = XF(7); APPENDIX B. HYSYS-MATLAB INTERFACE FOR VAPOUR-LIQUID EQUILIBRIUM CALCULATION138
hCellA8.CellValue = XF(8); hCellA9.CellValue = XF(9); hCellA10.CellValue = XF(10); hCellA11.CellValue = XF(11); hCellA12.CellValue = XF(12); hCellA13.CellValue = XF(13); hCellA14.CellValue = XF(14); hCellA15.CellValue = XF(15); hCellA16.CellValue = XF(16); hCellA17.CellValue = XF(17); hCellA18.CellValue = XF(18); hCellA19.CellValue = XF(19); hCellA20.CellValue = XF(20); hCellA21.CellValue = XF(21); hCellA22.CellValue = XF(22); hCellA23.CellValue = XF(23); hCellA24.CellValue = XF(24); hCellA25.CellValue = XF(25);
% Turn HYSYS Solver on(HYSYS automatically determines phase equilibrium) hSolver.CanSolve = 1;
% Define hDplSTREAM to use for retrieving phase equilibrium data hDupl DEW = hDEW.DuplicateFluid;
% Get the composition of liquid phase in equilibrium with xf x = hDupl DEW.lightliquidPhase.MolarFractionsValue;
% Get theK −value of the liquid phase in equilibrium with XF. %K −value= yi/xi. In this case, feedXF is yi(vapour phase). Kvalues = XF./x';
%K −value from this dew point flash calculation is applied to the next column %******************End of Hysys calculation********************************
(* From http : //support.aspentech.com/P ublic/Documents/Engineering/Hyprotech /2006.5/AspenHY SY S2006 5 − Cust.pdf)