Measurement and Advanced Thermodynamic Modelling for Accurate Predictions in Liquefied Natural Gas Distillation Columns

Transcription

1 Measurement and Advanced Thermodynamic Modelling for Accurate Predictions in Liquefied Natural Gas Distillation Columns by Jerry Yuning Guo A thesis submitted for the requirements for the degree of Doctor of Philosophy University of Western Australia School of Mechanical and Chemical Engineering 2015

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3 SUMMARY As one of the major methods to transport and store natural gas, liquefied natural gas (LNG) production technology is widely utilised and its role in the international natural gas market has been continuously increasing. It is well known that natural gas liquefaction is a very complex and high cost process. To make LNG an even more economically viable option over a range of production scales, it is important to further reduce the cost of liquefaction. Currently, commercial process simulators containing with well-established EOS are being used to optimise the design and operation of LNG plants. They are needed to make reliable predictions of fluid properties at process conditions, so as to reduce the over-design required to compensate for uncertainties, and ultimately reduce the cost and improve the efficiency of natural gas processing. The core element of a process simulator is the equation of state (EOS). The EOS currently incorporated in process simulators have been developed via regression to the available Vapour Liquid Equilibrium (VLE) data for the key binary mixtures at conditions relevant to LNG scrub columns. This means that the reliability of an EOS is highly dependent on the quality of those VLE data. However, the quality of the available VLE data in the literature can be shown to be somewhat lacking even for these relatively simply mixtures due to the difficulties in measuring such data at the desired conditions. As a result, significant discrepancies have been identified between the measured data and the predictions made using an EOS, as well as between the predictions made by different EOS. In this study, an apparatus designed for the measurement of reliable VLE data at conditions representative of the scrub column operation in the LNG process has been modified, improved and calibrated. The capacity, robustness and accuracy of the improved apparatus in measuring VLE data have been examined and verified. It has been demonstrated that the improved apparatus is able to measure quality VLE data for binary and multi-component i

4 mixtures of light hydrocarbons over a large range of pressures and temperatures relevant to natural gas liquefaction. This apparatus was used to obtain VLE data for the four principal methane binary mixtures and two multi-component mixtures. The measured datasets have been compared with the available literature data, as well as with values calculated via widely used EOS. The comparisons have demonstrated the accuracy and reliability of the new VLE data obtained in this study. These new data have demonstrated (i) which of the literature data contain significant errors or uncertainties and which are reliable, and (ii) quantitative measures of the primary deficiencies of the EOS used to describe these systems in process simulations. With the VLE data obtained by this study, as well as the literature data identified as highquality, this study has also explored one approach to improving EOS predictions at scrub column conditions through the implementation of a crossover Peng-Robinson EOS. Two versions of this crossover models were implemented in two different software packages, which differed in their method of performing flash calculations (Gibbs Energy Minimisation and the numerical calculation of partial fugacities). A recent attempt to implement a crossover Peng-Robinson EOS described in the literature, which simply estimated critical shifts for mixtures using a mole fraction average of the pure component critical shifts, was found to perform significantly worse than the classical Peng-Robinson EOS for most of the binary systems considered. By introducing one or two binary parameters to allow the critical temperature and volume shifts of the mixture to be adjusted, it was possible to substantially improve the accuracy of phase compositions for binary mixtures calculated in the near critical region. Importantly, these critical shift binary parameter values determined by forcing agreement between the crossover EOS and near-critical VLE data for binary mixtures substantially improved predictions for the near-critical VLE of the multi-component mixtures. Several further improvements, however, will need to be made if such a crossover model is to be utilised more widely and in particular in process simulations of the LNG scrub column. These include: (i) improving the form of the crossover switching function to avoid the degradation of VLE predictions outside the critical region when the critical shift parameters are adjusted, and (ii) significantly reducing the time required to complete a VLE calculation, potentially by finding a more efficient means of identifying the largest root of the parametric crossover switching function. ii

5 CONTENTS SUMMARY... i ACKNOWLEDGEMENT... v CHAPTER 1 INTRODUCTION Brief Introduction of Liquefied Natural Gas Natural Gas Liquefaction Process Optimal Design of Liquefaction Process Process Simulators Research Objective Thesis Layout CHAPTER 2 EQUATION OF STATE FOR LNG SCRUB COLUMN SIMULATIONS EOS Basics and Common Cubic EOSs Crossover Cubic EOS Non-cubic EOS Non-cubic van der Waals EOS Statistical Associating Fluid Theory Multi-parameter Equations of State CHAPTER 3 VLE MEASUREMENTS: LITERATURE DATA & EXPERIMENTAL METHODS Experimental Systems for VLE Measurement Synthetic Method Analytical Method Non Sampling Analytical Method Sampling Literature Data Review Available literature data on light binary mixtures Analyses of the literature principal binary mixtures CHAPTER 4 EXPERIMENTAL APPARATUS ITS MODIFICATION, IMPROVEMENT AND CALIBRATION Cryogenic VLE Apparatus Improvements to the VLE Apparatus Improvements to Thermal Stability Improvement to Measurement Sensors Improvement to Sampling Valve Configuration Improvement to the temperature control Mixture Preparation Preparation of Mixtures iii

6 4.3.2 Sample preparation Experiment Calibration GC Response Calibration In-situ Calibration of Temperature Sensors Pressure Calibration Measurement Pathways Measurement Methodology Uncertainty Minimization CHAPTER 5 EXPERIMENTAL RESULTS Quality VLE data for the Principal Methane Binaries VLE data for CH 4 + C 2 H VLE data for CH 4 + C 3 H VLE data for CH 4 + ic 4 H VLE data for CH 4 + nc 4 H Quality VLE data for Multicomponent Mixtures VLE data for CH 4 + C 2 H 6 + C 3 H 8 + ic 4 H VLE data for CH 4 + C 2 H 6 + C 3 H 8 + nc 4 H CHAPTER 6 ADVANCED CROSSOVER EOS Crossover PR EOS Development of the Crossover PR EOS Simulation Models Mathematica Model Gibbs Energy Minimisation VBA Model Partial Fugacity Flash Algorithm Modelling Result Pure Fluids Binary Mixtures Assessment of critical shift parameters Multicomponent Mixtures Overall Assessment of the Crossover PR EOS Model CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS VLE Apparatus Improvement Quality VLE Data for Binary and Multicomponent Mixtures Implementation and Improvement of a Crossover PR EOS Recommended Future work REFERENCES iv

7 ACKNOWLEDGEMENT I would like to express my sincere gratitude to my supervisor Winthrop Professor Dr Eric May for supervising my study and ensuring the financial supports. This thesis would not be possible without his continuing guidance and encouragement. I would like also to thank my co-supervisors Professor Ken Marsh and Dr Mohamed Kandil. Their support and guidance have been invaluable in every stage of my study. My gratitude is extended to Chevron Australia Limited for providing the Scholarship for this study. My gratitude is also extended to the Australia-China Petroleum Association, and the Graduate Research School of University of Western Australia for awarding me supplementary scholarships to aid in my studies. I am also grateful to Professor Thomas Hughes and Professor Brendan Graham. Their ongoing support and encouragement have inspired me to succeed in my study. I also wish to thank my fellow students Beau Ryan, Corey Baker, Kamil Szajnkienig and Sean McCallum, as well as Parisa Askaran and Andrea Porras. Their dedication and friendship all ensured the success of this research project. My friends were also instrumental in helping me finishing my studies. My heart-felt thanks especially go to Carol Mao, Jeremy Wong, Lana Tian, Saifuddin Essajee and Zhen Xu. Their encouragement and companionship during those long nights in the laboratory, and those days when things didn t go well, provided me with very valuable supports. Finally I would like to take this chance to express my deepest gratitude to my father Jingnan Guo and my mother Yi Yuan. Their endless love, continuing support, tremendous amount of encouragement and patience made it all possible for me to complete the Ph.D. v

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9 CHAPTER 1 INTRODUCTION 1.1 Brief Introduction of Liquefied Natural Gas Natural gas is currently one of humanity s primary fuel sources. The abundance of reserves available to be developed and produced at relatively low cost, as well as its relatively low greenhouse gas emissions, means the utilisation of natural gas has been gradually increasing. Over the past half century, natural gas has gained market share on an almost continuous basis, growing from some 15.6 % of world energy consumption in 1965 to around 24 % in 2011 (Moniz et al., 2011). It has recently been forecast by the United States Department of Energy that the likely growth in the world s annual demand for natural gas is 1.6 % per year, from 104 trillion cubic feet (TCF) in 2006 to a projected 153 TCF in In comparison, oil consumption is only projected to grow at the rate of 0.9 % per annum (Energy- Information-Administration, 2009). The utilisation of natural gas, however, can be limited by the difficulty in its transportation from the production site to the marketplace. Natural gas is transported to its end users using two major methods extensive pipeline networks and the shipment of liquefied natural gas (LNG). A recent study indicated that about 70 % of natural gas was transported through pipeline networks, while 30 % through shipments of LNG (Wang and Marongiu-Porcu, 2008). Due to the high capital and operating cost of LNG facilities, transporting gas at high pressure in a pipeline is an obvious choice for short to medium distances. However, the associated cost using the pipeline increases significantly with the transporting distances getting longer. In such circumstance, the use of LNG for the gas transportation will become a more economically competitive method. According to a Gastech report (Durr et al., 2005), as a general rule of thumb, pipeline versus LNG transport economics break even at approximately 3200 km onshore and 1600 km for offshore. This indicates that, for Australia to participate in this international trade, LNG is the only economically viable transportation method 1

10 The recent improvements in LNG technology and the increasing economy of scale have significantly reduced the capital cost of LNG facilities per megajoule produced over the last decade (Durr et al., 2005). For instance, the liquefaction cost had been reduced by as much as 40 to 50 % from 1993 to The LNG transportation vessels had also increased in size from 125,000 m 3 to 145,000 m 3, while the ship building costs had decreased from more than US$300 million to less than US$170 million during the same period (Hiroki, 2003). As a result, the overall cost associated with LNG has continuously decreased, making this option more and more commercially viable. LNG is made by cooling natural gas to around C at atmospheric pressure. Under these conditions, natural gas is a liquid with an energy density 600 times that of its gas form at standard temperature and pressure. The transportation of the liquefied natural gas over long distances is normally conducted through specialized ocean-going LNG tankers. The use of LNG has significantly increased the global natural gas trade. For instance, world natural gas trade only doubled over the 15 years between 1993 and 2008, with LNG trade increased by 270 % in the same period (Moniz et al., 2011). As the world s 18 th largest producer of natural gas, Australia is the 7th largest exporter of LNG (Austrade, 2010). The recent development of the Carnarvon Basin containing 1.75 trillion cubic metres of known natural gas reserves, together with the future exploration and development of additional reserves in the Browse Basin and Timor Sea, will bring even more natural gas for possible export in the future (Energy-Information-Administration, 2009). It can be expected that Australia will significantly increase its LNG production and its share in the world s LNG trade in the near future. 1.2 Natural Gas Liquefaction Process Unrefined natural gas extracted from gas fields consists of methane, ethane, propane and small quantities of heavier hydrocarbons. Typically, with variations due to geological conditions, nitrogen, carbon dioxide, water, sulphur compounds and mercury are also present in natural gas. The typical composition quantities of natural gas from the two Gorgon Project fields in Western Australia s Carnarvon Basin are illustrated in Table

11 Table 1.1: Typical composition of natural gas as percentage by volume (Chevron, 2013). Component Gorgon Jansz CO % 0.28 % N % 2.35 % Hydrocarbons Methane Ethane Propane Butane Pentane and heavier Total 83+ % 97.4 % Natural gas liquefication is a complex process, which can be shown by a flow chart in Figure 1.1. To liquefy natural gas, the gas must first be controlled to the designed operating pressure of the plant. Through a slug catcher system, any solid particulates and condensates are removed. The gas then undergoes acid gas (CO 2 and H 2 S) removal in an acid gas removal unit (AGRU). By utilising an amine-based process, carbon dioxide (CO 2 ) and hydrogen sulfide (H 2 S) can be selectively removed. For cryogenic gas processing, CO 2 must be controlled down to 90 mg/m 3 to avoid freezing and blockage in the heat exchangers. H 2 S must be regulated to below 5 mg/m 3 and total sulfur content must be limited to 30 mg/m 3 to prevent corrosion and satisfy the international market specifications for export. Water is removed down to less than 1ppmv by dehydration using molecular sieve beds. Furthermore, if the natural gas contains any mercury then a mercury removal facility is essential to prevent corrosion and/or embrittlement of the aluminium heat exchanger in the cryogenic process (Coyle et al., 2007). The treated natural gas that then enters the low temperature section of the plant still containing a number of non-methane components including the light hydrocarbons ethane, propane and butanes, as well as heavier benzene-based hydrocarbon compounds such as toluene and xylenes (Coyle et al., 2007). The heavier hydrocarbons can be a source of problem in LNG production, potentially freezing out in the cryogenic heat exchangers. These components must be separated from the lighter hydrocarbons using a LNG scrub column a cryogenic distillation column to a sufficiently low concentration prior to further processing (Laskowski et al., 2008). A typical scrub column operates at an approximate pressure of 5000 kpa, with a bottom reboiler unit operating at between 0 and 50 o C, and a 3

12 top condenser unit at about -40 o C (Laskowski et al., 2008). The thermal gradient causes the treated natural gas components to separate via the formation of vapour and liquid phases at equilibrium with each other at several stages (trays) within the column: the lighter hydrocarbons remain in the vapour phase and the heavier hydrocarbons condense. This controls the heating value of the LNG by stripping the heavier hydrocarbons from the top product stream and prevents freezing problems during liquefaction. The stripped heavier hydrocarbons can be recovered as valuable liquefied petroleum gas products.. The lean mixture, predominantly methane, is then liquefied at the main heat exchanger (MCHE). Currently the most predominant liquefaction processes are mixed refrigerant systems such as the Propane-mixed refrigrant (C3MR) system, which accounts for over 60% of the installations (Ballout and Price, 2008). However, alternative systems such as cascade and multi-loop are also increasingly deployed (Shah et al., 2014). For the C3MR system, the gas and the mixed refrigrant, which typically consists of methane, ethane, propane and nitrogen (Ballout and Price, 2008), are first pre-cooled by a propane cycle, where compressed propane is vapourized to provide cooling. The pre-cooled natural gas then enters the tube circuit of the MCHE, while the mixed refrigerant vapourizes and flows downward on the shell side of the MCHE, proving the refrigeration for liquefaction of natural gas at -161 o C under atmospheric pressure (Pillarella et al., 2007). The bottom product of the scrub column is processed separately with a fractionation train, which allows the heavier hydrocarbons to be separated into various saleable products including liquefied petroleum gas (LPG) for producing additional revenue. The ethane and propane from the fractionation train can also be used to make-up the refrigerant inventory, which is particularly important in remote plant locations. Furthermore, the stored lighter hydrocarbons can also be blended into certain LNG cargoes to improve and satisfy the various heating value requirements of customers (Chevron, 2013). 4

13 Dehydration Mercury Removal Heavies Removal Liquefaction Acid Gas AGRU Water Storage Ethane Dethaniser Nitrogen Stripper Gas LPG Recycle Offshore Slug Catcher Cond Condensation Stablisation Propane Depropaniser LNG Storage Nitrogen Rejection Unit Nitrogen MEG MEG Regeneration Water / MEG Storage Debutaniser Water BOG Water Treatment Condensate Condensate Storage Fuel Gas Service Demin Water, Discharge or Reuse Figure 1.1: LNG Process Flow Diagram (Woodside, 2011). The scrub column is a crucial operation within an LNG processing train, which is also one of the most difficult unit operations in an LNG plant to simulate accurately (Laskowski et al., 2008). It has been found that the optimised scrub column could better recover the heavy hydrocarbons in the natural gas. This would in turn better prevent the freezing out in the MCHE, while increase the cost effectiveness of LNG process by additional liquid petroleum gas (LPG) products from the bottom stream, which may also be used as make-up for the mixed refrigerant used in the MCHE (Laskowski et al., 2008). To optimise the LNG scrub column, the thermodynamics of the multi-component phase equilibrium occuring on each tray is required to be accurately predicted. Achieving this is the focus of this study. 1.3 Optimal Design of Liquefaction Process Although the technology for liquefication of natural gas was first implemented in 1912 (Ballout and Price, 2008), LNG processing has remained capital intensive and involved high operating costs. Any improvement to the design of the liquefication process would significantly improve the competitiveness of LNG projects and benefit natural gas exporters like Australia. 5

14 In 2008, typical LNG project costs were approximately US$0.50 per thousand standard cubic feet (MSCF) in the production of natural gas, US$2.50 per MSCF in liquefication, US$0.75 per MSCF in transportation and US$0.25 in regasification (Kelkar, 2008). Clearly, liquefication (which here includes the gas treatment and pre-processing) is the most costly part of an LNG project and any improvement in its efficiency, e.g. through the optimisation of the liquefaction process design, could significantly reduce cost and improve the competitiveness of LNG production. Reliable measurement and accurate prediction of the properties of the reservoir fluid are vital for the optimisation of the design of the liquefaction process. Since the first set of binary vapour-liquid-equilibria (VLE) for components of natural gas was measured in 1934 (Sage et al., 1934, Katz, 1990), the prediction of natural gas product compositions in processes such as cryogenic distillation has become possible through a series of flash calculations (Katz, 1990). The accuracy of such predicitons has been significantly improved with the refinement of empirical cubic equations of state (EOS) such as the Peng-Robinson EOS and the use of interaction parameters to describe VLE more precisely. Such predictions are widely applicable to, and used in, the design of oil and gas processes (Katz, 1990). However, the simulation of the LNG scrub column is still in relative terms a very complicated problem, which requires simultaneous flash calculations for each of the different stages in the column. The introduction of commercial process simulators, incorporated with well-adopted EOS, has been central to the ability of engineers to a cost effectively simulate LNG processes (Laskowski et al., 2008, May, 2009). 1.4 Process Simulators Process simulators such as Aspen HYSYS (AspenTech, 2011), PRO/II (Invensys, 2013) and VMGSim (VMG, 2013) have been widely used in the LNG industry, with some of them been used for more than two decades. They have been proven valuable tools in designing, verifying and optimising new process plants. The employment of process simulators is crucial to the success of new LNG projects, which can significantly reduce the time and cost for feasibility studies, while increase the accuracy of cost estimation and ensure the stringent design goals are met (Aspen Technology, 2011). In addition, process simulators are also quite often used to model and optimise existing plants. It has been demonstrated that by the use of process simulators, operators are able to identify how to improve output and revenue, pin point and fix problems, and improve energy efficiency within the plant with minimal cost (Brown et al., 2005). 6

15 However, it has been found that the predictions of the LNG process simulators are often not very reliable. Significant discrepancies are frequently reported between the predicted values from the simulators and the actual measured on-site data, which are especially evident surrounding the scrub columns and flash vessels (Laskowski et al., 2008). Furthermore, significant discrepancies were also found in the sensitivity of scrub column simulation in Aspen HYSYS when different EOS was chosen (Laskowski et al., 2008). Currently, the Peng-Robinson (PR) EOS and Soave-Redlich-Kwong (SRK) EOS are the two EOS recommended for the simulation of LNG scrub columns, as indicated by the manual of HYSYS (AspenTech, 2011). However, when a typical scrub column was modelled using first the SRK EOS and then the PR EOS, as shown in Figure 1.2, significant and measureable shifts in the predicted compositions of the liquid and vapour phase products were found (Laskowski et al., 2008), as shown in Figure 1.3. Figure 1.2: Process Flow Diagram of a simple simulation of LNG scrub column modelled using AspenTech HYSYS (AspenTech, 2011) (Laskowski et al., 2008). 7

16 Figure 1.3: Relative percentage changes between the vapour and liquid product compositions caused by changing from the SRK to PR EOS in the simulation basis (Laskowski et al., 2008). It is noted that the discrepancies are not only caused by the EOS (PR or SKR), but also by the adopted mixing rules and binary interaction parameters. The discrepancies shown in Figure 1.3 is the comparison between those using the default PR EOS (with its default mixing rules and binary interaction parameters) and those using the default PR SKR (with its different associated default mixing rules and binary interaction parameters). Figure 1.3 shows the relative shift in the predicted mole fraction for each component of the two product streams simulated using the two different but nominally equivalent EOS. The predicted liquid compositions of methane and ethane vary by 5 % and 3.5 %, respectively. Figure 1.3 also shows that LPG components (propane and the butanes) in the vapour phase are very sensitive to the selection of the EOS, with 8 % more of the butanes predicted to be carried over to the vapour stream when the PR EOS is selected. Such differences between the predictions made by two near equivalent EOS represent a substantial uncertainty in the process simulation. Industry requires and applies significant over design of the physical plant to overcome these uncertainties, which ultimately increases both capital and operation cost. A central factor that governs this uncertainty lies with the accuracy of the EOS used in the process simulator. However, the accuracy of the EOS has been limited at least by the 8

17 following two factors. Firstly there are theoretical limitations to all cubic EOS in the dense fluid region. Secondly as these EOS are anchored to available VLE data for key binary mixtures measured over a wide range of process conditions, there are limited high quality data available at the operating condition of the scrub column, where the low temperature coupled with near critical pressure conditions made measurements very difficult (Chu et al., 1976). Take the VLE measurement of methane-alkane binaries with alkanes heavier than propane as an example: it is very difficult to measure the dew point phase compositions at low temperatures, where the heavy alkane vapour phase concentration becomes very small. The difficulties in the measurement of VLE for multicomponent mixtures are even larger, even though such multi-component mixture data measured at scrub column conditions would represent an excellent test of EOS predictions. The cost benefit of better accuracy in process simulation is obvious. It has been noted by Whiting (1996) that the amount of overdesign may be reduced considerably with increased simulator precision. In his example, to achieve an 80 % design confidence for the performance of a distillation column, the original design parameters required 25 stages in the tower. When the simulation precision was improved with better parameters as a result of quality experimental data, only 21 stages were required to achieve the same level of design confidence. It has also been demonstrated by Aspen Technology (Dhole et al., 2012) in one of their case studies that, for a close-boiling distillation column, a 5 % uncertainty in the VLE data contributed to 50 % more stages in the column design, which doubled the column s capital cost estimate from $18 million to $36 million. Clearly with better VLE data and EOS predictions, there is a great potential that the cost associated with LNG production can be significantly reduced. 1.5 Research Objective The major goal of this study is to measure high quality VLE data through a modified and improved VLE apparatus, and to anchor these data to improve the predictions of EOS that are readily deployed within process simulators. The contribution of this study will ultimately help improve the reliability of process simulation, and thereby help reduce the need for overdesigning of LNG processes. This study has been designed to achieve a number of objectives as follows: 9

18 1. Modify and commission an apparatus capable of conducting accurate VLE measurements in binary and multi-component mixtures of light hydrocarbons at pressures up to 9 MPa and over the temperature range (150 to 250) K with small, wellquantified uncertainties. 2. Measure reliable and accurate VLE data for binary and multi-component mixtures including methane + n-alkane binary and methane-dominant multicomponent mixtures at conditions relevant to LNG scrub columns. The measurements should clarify the quality of existing literature data and enable the deficiencies in VLE predictions specific to EOS to be identified unambiguously (as opposed to EOS deficiencies due to the quality of the available literature data). 3. Develop improved EOS predictions at scrub column conditions by using the measured and selected literature data to improve the interaction parameters in conventional cubic PR EOS, to explore alternative mixing rules as well as advanced crossover EOS. 1.6 Thesis Layout The research background and research objectives are discussed in this introduction chapter. Chapter 2 presents a literature review of EOS models including the background and development of cubic EOS, the sophisticated multi-parameter GERG 2008 (Kunz et al., 2007) and SAFT EOS (Huang and Radosz, 1990), as well as the crossover concepts (Kiselev, 1998) that have been developed for improving predictions in the critical region. Chapter 3 presents a review of the literature, which summarises the availability and reliability of data to which existing EOS are anchored. This chapter also examines the various methodologies of VLE data collection, and critically reviews the suitability of each experimental method. Chapter 4 describes the modifications made to the VLE apparatus and the development of the measurement method during the course of this study. The achieved improvements in both temperature control and calibration are presented. The increase in measurement accuracy due to improved methods is also discussed. 10

19 Chapter 5 presents the measurements and compares them with available literature data and the calculated values from existing EOS. Deficiencies in cubic EOS predictions observed in the near critical region of the mixtures are illustrated and discussed. In Chapter 6, an implementation of the crossover EOS is presented with the goal of addressing the divergence of classical cubic EOS from the data in the near critical region of the mixtures. The results indicate that, with the optimally tuned critical parameters, significant improvements are achievable. The great potential of the crossover EOS and future endeavours required to make the crossover EOS practicably implementable are also discussed. Conclusions made from this study, as well as suggestions for future research, are presented in Chapter 7. 11

20 CHAPTER 2 EQUATION OF STATE FOR LNG SCRUB COLUMN SIMULATIONS The accuracy of an LNG scrub column model is highly dependent on the EOS embedded in process simulators. Since the development of the van der Waals EOS, many different variations of EOS with both empirical and theoretical bases have been developed. This chapter looks at the development of equations of state and critically assesses some of the current EOS that can be used for the prediction of natural gas fluid properties within a scrub column. 2.1 EOS Basics and Common Cubic EOS Equations of state are thermodynamic models relating the pressure, temperature, volume and compositions of fluids. The simplest EOS is the ideal gas EOS (IGEOS), which combines Charles law, Boyle s law, and Gay-Lusac s law (Assael et al., 1996) into a single mathematical relation, as given by: nrt P, (2.1) V where P is the pressure of the gas, V is the volume of the gas, n is the amount of substance of gas (number of moles), T is the temperature of the gas in kelvins and R is the universal gas constant. Equation (2.1) can also be rearranged to give an expression for the molar volume of an ideal gas V m, where V m =V/n. As the IGEOS does not take into account the volume occupied by molecules themselves and the existence of attractive intermolecular forces, it is 12

21 limited to the prediction of the properties of gases at low pressures and high temperatures, and it fails to predict the coexistence of vapour and liquid phases. The most significant improvement to the IGEOS was achieved in 1873 by van der Waals (Van der Waals, 1873). In his work, the molecular volumes were accounted for by a repulsion pressure P R, where the molar volume (V m ) of the IGEOS is reduced by a term b accounting for the volume occupied by molecules. An attraction pressure, P A, was also introduced to account for intermolecular attraction forces that correct the pressure (P) by the term a/v m2. As the result of van der Waals modification, the EOS became P V a m RT V b 2, (2.2) where parameters a and b are pressure and volume corrections for different fluid species, respectively. The van der Waals EOS was the first equation to be cubic in the molar volume, and as a result the first to provide a qualitative description of the vapour and liquid phases and phase transitions (Konynenburg and Scott, 1980). However, the quantitative accuracy of van der Waals EOS is still insufficient for critical properties and phase equilibria calculations. For example, the critical compressibility factor of all fluids predicted by Eq. (2.2) is 0.375, whereas actual values for different hydrocarbons vary from 0.24 to A large number of studies have been conducted to modify and improve the performance of cubic EOS based on the original proposed by van der Waals to enable more accurate quantitative predictions of the fluid s thermodynamic properties. The first important modification of the van der Waals EOS was the Redlich-Kwong (RK) EOS (Redlich and Kwong, 1949). In this modification, a temperature-dependent attractive term was introduced, for the equation to take the form: m RT a P V b V ( V b ) T m m m 0.5. (2.3) The RK EOS improved the predicted critical compressibility factor (Z C ) with Z C = for all fluids. The significant improvement of the RK EOS over the van der Waals EOS comes from a better description of the attractive term. In its application to mixtures (discussed below), Deiters and Schneider (1976) and Baker and Luks (1980) successfully applied the RK EOS to high pressure phase equilibria of binary mixtures. Abbott (1979) noted that the RK EOS performs relatively well for the simple fluids, of which the molecules are largely spherical. However, for fluids with asymmetric molecules, or a non-zero acentric factor, the 13

22 performance of the RK EOS was found to be lacking (Abbott, 1979). The acentric factor is a recognised measure of the shape (or asymmetry) of molecules. For fluids comprised of spherical molecules, such as the noble gases, this factor is almost zero. Consequently, further effort was concentrated on improving the RK EOS. The two most commonly used EOS in modern process simulators are the results of these further modification efforts. They are the Soave s modification to the RK EOS (SRK) (1972) and the EOS by Peng and Robinson (PR) (1976). The SRK EOS was developed by replacing the temperature dependent attraction term (a/t 0.5 ) in the RK EOS with a more general temperature dependence (a ), to give RT a P, (2.4) V b V ( V b ) m m m where: a = ( R2 T c2 P c ) {1 + m [1 ( T 0.5 T c) ]} m = ω 0.176ω 2 b = R2 T c and ω is the acentric factor. In contrast to the RK EOS, Soave s modification provides a better fit to experimental data, by forcing the EOS to reproduce the vapour pressure at reduced temperature T r = 0.7 (Anderko, 2000). This modification improved the accuracy of vapour-liquid equilibria and critical properties predicted with the SRK EOS for 95 binary systems containing hydrocarbons, hydrogen, nitrogen, hydrogen sulphide, carbon monoxide and carbon dioxide (Elliott and Daubert, 1985, Elliott and Daubert, 1987). The PR EOS, on the other hand, is a slight modification of the SRK EOS, which aims to improve the accuracy of the model s predictions of liquid density and critical compressibility factor. Recognising that the critical compressibility factor of SRK EOS of was overestimated, the PR EOS contains a different volume dependence with the following form: P c 2 RT a P V b V ( V b ) b ( V b ) m m m m. (2.5) 14

23 The PR EOS in Eq. (2.5) slightly improves the prediction of the liquid volumes relative to the SRK EOS and gives a critical compressibility factor T C = However, for these properties, the predictions of all cubic equations with just the two parameters a and b such as the vdw, RK, SRK and PR EOS are still poor. Their primary advantage is their ability to describe efficiently the vapour liquid equilibrium of hydrocarbon multicomponent mixtures essentially as accurately as any other model. For their application to mixtures, the attractive and co-volume parameters of both the SRK and PR EOS are typically obtained from mixing rules containing the parameters for the pure fluids within the mixture: n n a xi x j (1 kij ) ( ai i )( a j j ), and (2.6) i 1 j 1 b x i b i, (2.7) i where k ij are binary interaction parameters (BIP), which are adjustable parameter used in the regression of the EOS to experimental VLE data for binary (n=2) systems. As demonstrated by Peng and Robinson (1976), the use of this interaction parameter is needed to improve VLE predictions. The examination of PR EOS for the prediction of phase behaviour and volumetric behaviour of single component, binary, ternary and multicomponent systems concluded that the PR EOS performed as well as, or even better than, the SRK EOS, especially for liquid density prediction (Peng and Robinson, 1976, Robinson et al., 1985). Han et al. (1988) further reported that the PR EOS was superior for the prediction of VLE in mixtures containing hydrogen and nitrogen. A review by Anderko (2000) suggested that the PR EOS predicted better liquid volumes for medium-size hydrocarbons, and other compounds with intermediate values for the acentric factor. However the SRK EOS performed better for compounds with small acentric factors. The investigation of many comparative studies made by Danesh (1998) concluded that the SRK EOS and PR EOS generally provided similar predictions for natural gas components, and neither could be singled out as a superior EOS when predicting all properties at all conditions. Although the SRK and PR equations are simple cubic EOS models, they are both able to predict VLE behaviour for multicomponent mixtures of light hydrocarbons as well as any other models, and are considered effective tools for the modelling of LNG processes (Assael 15

24 et al., 1996). As the roots of cubic equations can be found essentially without iteration, minimal computer resources are required to produce rapidly phase equilibrium predictions for multicomponent mixtures. This is the main reason why the PR and SRK EOSs are the most commonly used in process simulators (Assael et al., 1996, Mushrif and Phoenix, 2008). A lot of effort has been focused on the improvement of both the SRK and PR EOS (Assael et al., 1996). Many attempts to improve these cubic EOS have been made by introducing additional parameters. Schmidt and Wenzel (1980) designed a three parameter EOS that interpolated between the PR and SRK EOSs to predict liquid volumes more reliably for fluids within a certain range of acentric factors. Fuller (1976) and Patel and Teja (1982), on the other hand, both introduced an additional parameter to the SRK and PR EOS respectively, which provided the flexibility to adjust the compressibility factor. Attempts to increase the flexibility of the cubic EOS further by introducing even more parameters were also made in several other studies, however the results only led to small, incremental improvements (Anderko, 2000). Introducing a volume translation correction into cubic EOS was the focus of other attempts to improve liquid density predictions (Peneloux et al., 1982, Soave et al., 1999). In this improvement, a simple empirical correction was introduced by replacing the molar volume V m in the cubic EOS with a translated molar volume, given as: V V c( T), (2.8) ' m m where c(t) is a temperature dependent correction, which can be adjusted so that the translated molar volume agrees with measurements of the fluid s saturated liquid density. Peneloux et al. (1982) showed that, except in the vicinity of the critical point, this approach provided a consistent method of improving the prediction of liquid volumes. Two parameter cubic EOS implicitly contain the assumption that the critical compressibility factor is equal for all substances, which leads to inherent limitations of their prediction capabilities for accurate VLE and density predictions in the critical region (Ji and Lempe, 1997). In addition, like all classical EOS with analytic derivatives, cubic equations cannot describe the non-analytic behaviour of real fluids in the vicinity of their critical point. The poor performance of cubic EOS extends over a relatively wide near-critical region, due to the simplicity of their functional form. Other more sophisticated (but still classical) EOS can give better descriptions of fluid behaviour much closer to the critical points (Lafitte et al., 2013). 16

25 2.2 Crossover Cubic EOS One reason why typical cubic EOS, such as the PR and SRK EOS, fail to describe the actual behaviour of fluids in the critical region is that they are derived from a classical theory of the critical point, and attempt to describe it using the mean-field approximation, which neglects complex intermolecular interactions such as local density fluctuations (Anisimov and Sengers, 2000). When the critical point is approached, the intensity of these fluctuations diverges, and several of the fluid s properties exhibit a singularity at the critical point (Kiselev et al., 2000). The renormalisation group theory (RNG) has been developed to deal with these fluctuations, where scaling laws are applied to the thermodynamic potential of the system asymptotically close to the critical point (Anisimov and Sengers, 2000). The asymptotic scaling laws only work for an extremely small range of temperature and densities around the critical point. However, it was observed that the predictions of classical EOS began to diverge from the observed behaviour over a larger temperature and density range (Kiselev and Sengers, 1993) than described by the RNG theory. One approach to addressing this problem is to use a parametric model like that first developed by Nicoll and Albright (1985), which was later implemented and examined by Albright et al. (1987) and Chen et al. (1990). In this parametric model, a crossover expression incorporates the transition between the singular behaviour near the critical point with the classical, non-asymptotic behaviour of the fluid far from the critical point. This approach is the basis of so-called crossover EOS. Using this concept, Kiselev (1998) described an approach that integrated the scaling laws into an analytical EOS. In this approach, the classical Helmholtz free energy is first written in its dimensionless form as A T, V V A T, V A T, V P0 T 0 T, (2.9) RT V where the classical critical properties P 0c, T 0c and V 0c are determined from the following conditions: 0C P P PV V V RT 2 0c 0c 0, 0, 2 T 0c T 0c 0c Z 0c. (2.10) Here T T / T0 C 1 is the dimensionless deviation of temperature from the classical critical temperature, A T, V is the near-critical contribution of the classical Helmholtz energy, 17

26 and 0 T is an analytical function of temperature. The term P T 0 in Eq. (2.9) is the dimensionless pressure at the critical isochor V as V, which is determined by Kiselev (1998) 0C To implement the crossover EOS, P T PV RT. (2.11) 0 0 C / T and V are renormalized near the true critical point of the fluid by introducing a dimensionless temperature shift term and a volume shift term η. These two parameters constitute the essential elements of the crossover EOS, and are determined by 22 1 c Y Y, and (2.12) cy Y. (2.13) In these equations, T / T C 1and V / V C 1are the dimensionless temperature and volume deviations from the fluid s true (experimental) critical parameters, respectively. Similarly, c TC / T0 C 1 and c VC / V0 C 1 represent the shifts of the real critical properties from the classical critical properties determined by Eq. (2.9). The other terms, γ=1.24, β=0.325, α=2-γ-2β= and Δ 1 =0.51 are the best estimates of the critical exponents from the non-classical theory (Sengers and Sengers, 1986, Anisimov et al., 1992). The crossover function Y in Eqs. (2.12) and (2.13) is used to switch between the classical EOS and the RNG theory. It is defined in the parametric form of Y q 2 2 q q, R( q) 1 R( q) 1 q. (2.14) 1 2 Here q is the normalized distance to the critical point, which is obtained by solving the following non-linear equation (Kiselev, 1998) d1 d1 q blm Y( q) Gi Gi, (2.15) 18

27 where parameters Gi, b LM, d1 and d2 are all system dependent variables needed to apply the crossover approach to a given fluid. The value of the crossover functions Y q effectively approaches zero, when the normalized distance gets close to the critical point. However, in the region far from the critical point, the crossover function approaches unity. In such situation, Y 1, T and V, and the crossover EOS reduces to the original classical EOS. The dimensionless Helmholtz energy can be finally determined by substituting the renormalization A T, V with A, in Eq. (2.9). By differentiation with respect to volume, the crossover expression comes to its final form of the pressure equation as P A RT V A V V V 0C T 0C C T 0 P T. (2.16) Kiselev (1998) first applied this approach to the three-parameter cubic developed by Patel- Teja (PT) (1982), and stated that this empirical approach was also applicable to all classical EOS. He compared the performance of the crossover PT EOS and the original PT EOS with the experimental data of pure CO 2, water and refrigerant R32 and R125 in both single and 2-phase regions. The results demonstrated a much better representation by the crossover PT EOS for the thermodynamic properties of the pure fluids, especially in the critical region and for vapour-liquid equilibrium, than achieved with the original PT EOS. Kiselev and Friend (1999) extended the crossover PT EOS to mixtures by utilising a traditional mixing rule, in which the dimensionless Helmholtz energy took the form of,,,,,, A T V x A x V P T x T x, (2.17) 0 0 while the van der Waals mixing rules were used for the classical EOS parameters, a and b, simple linear mixing rules were used for the critical parameters G i (x), v 1 (x), a 20 (x) and a 21 (x), as below: 1 i Gi x x () i () i i, v1( x) xiv1, a20( x) xia20 and Gi i i 19 i a ( x) x a. (2.18) () i 21 i 21 i For the shifts from the pseudo critical temperature and volume to their real critical counterparts (1999): and c, the following mixing rules were proposed by Kiselev and Friend c

28 , and (2.19), x x x x c i c i i j ij i i j. (2.20), x x x x c i c i i j ij i i j The two mixing coefficients ij and in Eqs. (2.19) and (2.20) were treated as adjustable ij parameters, which, analogous to the classical binary interaction parameters, are intended to allow improvement of the predicted critical shifts for mixtures from that obtained from the shifts for the constituent pure fluids. From the comparison of their cubic crossover PT EOS with experimental data for mixtures, Kiselev and Friend (1999) found that the mixing coefficients of Eq. (2.20) for mixtures methane + ethane and CO + ethane are ij statistically insignificant and can be set zero. It was then concluded that was the only ij mixing coefficient requiring adjustment to improve the description of mixtures by the crossover EOS. Kiselev and Friend (1999) concluded that together with the classical adjustable BIP, the cubic crossover EOS can be tuned over a wide range of temperatures and pressures. Kiselev and Friend (1999) stated that the implementation of the scaling law near the critical point for mixtures is applied to the pseudo critical temperature of the mixture, rather than the true critical temperature, due to its formulation. Therefore the calculated singularities would strictly be inside the 2-phase region and not observable, which would not allow the reproduction of the observed asymptotic behavior of the mixture near its true critical point. This is not a major problem in practice, as the correct asymptotic behaviour can be provided by incorporating the universal scaling functions in the critical part of the Helmholtz free energy. Kiselev and Friend (1999) demonstrated that good agreement between the calculated value and experimental data were achieved for both methane + ethane and carbon dioxide + methane binary mixtures, when extending the crossover PT EOS to mixtures. However, it is important to note that the EOS used by Kiselev and Friend (1999) was a three parameter cubic, in which the additional degree of freedom allowed the pure fluid pseudo critical volumes to be matched directly with the true critical volume. When applied to mixtures, the additional flexibility of this model allowed it to perform well over an extended region. While Kiselev (1998) and Kiselev and Friend (1999) presented a general analysis of how the cross over approach may be applied to any cubic EOS, including 2 parameter versions, Feyzi et al. (2010) presented a specific implementation for the most commonly used PR EOS, that also included a new crossover function. Feyzi s study indicated that the conventional forms of crossover function do not reduce to unity at temperatures far from the critical point. To 20

29 overcome this problem, a new form of the crossover function was introduced to ensure the reproduction of the conventional PR EOS behaviour in the regions outside the critical, as below: 2 1 q' 12.2T Y q ', q ' qexp 12.2 q' 1 T. (2.21) c Here q is the normalized distance to the critical point. The introduction of the term q is the modification of q. Comparison of the conventional crossover functions Y q and the improved crossover function Y q ' was made by Feyzi, as shown in Figure 2.1. It can be seen that while both Y q ' and Y q give similar results in the region near the critical point ( 1) approaches unity outside the critical region, while Y q does not. T, Y q ' r Figure 2.1: Crossover function against reduced temperature (Feyzi, 2010). However, while the stated objective of the work by Feyzi et al. was to use the PR EOS, their implementation of it included the introduction of additional fluid-specific parameters including an adjustable (pseudo-)critical compressibility factor. This extended parameterisation means that the classical model is no longer the simple two-parameter cubic 21

30 EOS, but rather something quite similar to the three-parameter cubic EOS discussed by Kiselev (1998). In addition, the pure fluid crossover parameters specific to this implementation of the PR EOS were adjusted to match experimental saturation densities and vapour pressures measured in the vicinity of the true critical point. Given the additional tuning and parameterisation, it is difficult to assess the significance for of the improved description presented for the pure fluids. Feyzi et al. (2010) also applied their crossover PR (CPR) EOS algorithm to mixtures and presented results for the prediction of mixture VLE. While the two graphical comparisons of measured and calculated P-x,y envelopes for methane + butane at 211 K and 255 K (Figure 12 and Figure 13 in Feyzi et al. (2010)) suggest improved mixture predictions by their CPR EOS, the average absolute deviations presented in Table 5 of the same paper for five binary mixtures actually indicate no general improvement. Potentially, this was because they did not attempt to tune any of the parameters describing binary interactions in the CPR EOS, including ij or ij. Accordingly, one objective of the research presented in this thesis was to test whether a CPR EOS model could be constructed to describe the quality experimental data obtained by this study for binary mixtures (by tuning) and, if so, whether such a model could predict the data obtained for multicomponent mixtures in the vicinity of their critical points. 2.3 Non-cubic EOS Many efforts have also been made to improve the predictions of fluid phase behaviour by using EOS other than the cubic equations commonly used in process simulators. These efforts range from adjustments of the repulsive term of the van der Waals EOS, the development of perturbation theory based EOS for associating fluids, and extended multiparameter models. Several examples of these models are introduced below for the purpose of providing an overview of the progress that has been made along these lines. These more complicated, sophisticated models have not been actively used in this research because for the system of primary interest VLE of mixtures of simple hydrocarbon molecules - the cubic EOS give just as good results (Muller and Gubbins, 2000). The focus on the development of these non-cubic models has been the accurate description of a wide range of properties and fluid mixtures, which cannot be described adequately by cubic EOS, and it is therefore relevant to provide a brief summary of their attributes here. 22

31 2.3.1 Non-cubic van der Waals EOS Most of efforts to improve upon the original van der Waals EOS aimed to keep the model in its cubic form, and generally limited the modifications to the attractive interaction term of the EOS. There have, however, been other attempts to modify the van der Waals EOS which focussed on modifying the repulsive interaction term in the EOS, with the primary purpose of improved liquid phase descriptions and generally at the expense of the cubic polynomial in volume. Many accurate representations of the repulsive interaction of hard spheres have been developed and incorporated into EOS (Mulero et al., 2001). The Guggenheim EOS (1965) and the Carnahan and Starling EOS (1969) are two of the most commonly used models developed by modifying the repulsive terms of the van der Waals EOS. Both the Carnahan and Starling EOS and Guggenheim EOS model the intermolecular interactions of fluids by combining an accurate hard-sphere repulsion term with simple van der Waals dispersion interactions. Deiters and Schneider (1976) reported a further example of an equation of state, based on the Carnahan-Starling hard-sphere term plus an improved attractive term. A feature of Deiters s equation of state is that the Carnahan-Starling term is adjusted to more accurately reflect the repulsion of real fluids and the attractive term is obtained from an approximate formulation of square -well fluid interactions. The Guggenheim EOS has been widely used to predict the critical properties of a diverse range of binary mixtures. Despite the diversity of the systems studied, more accurate results have been consistently reported for the vapour-liquid critical locus with this modified EOS (Wei, 1998). The Carnahan and Starling EOS, on the other hand, has demonstrated improved prediction of real hydrocarbon densities, pressures and saturation fugacities when further combining the attractive term from the Redlich-Kwong EOS with a more accurate model of repulsion behaviour (Carnahan and Starling, 1972) Statistical Associating Fluid Theory Molecular modelling is another major approach, in which a system s description starts from a model for the potential energy of interaction for the molecules. The model is solved using methods based on statistical mechanics, and aims to expand the accurate prediction of thermodynamic properties to associating species such as water and alcohol (Checoni and Ravagnani, 2013), and highly non-spherical molecules (Muller and Gubbins, 2000). These molecular bases provide the equation with a reliable predictive and extrapolative power. The SAFT EOS (from the Statistical Associating Fluid Theory) is one of the most popular 23

32 versions of this approach. Originally developed by Chapman et al. (1988, 1990), the version of this EOS which demonstrated its applicability for real engineering problems was developed by Huang and Radosz (1990), in which the equation was parameterized for several fluids and mixtures. The SAFT EOS is based on the first-order perturbation theory of Wertheim (1987). The essence of this theory is to replace the existing hard sphere model with a reference monomer fluid model that incorporating both chain length and association, so that the Helmholtz energy is given by a sum of expressions to account not only for the effects of repulsion and dispersion forces, but also for association and/or solvation. The SAFT EOS is presented as a sum of three Helmholtz energy terms as below: where A Res is the total residual Helmholtz energy; and Res Seg Chain Assoc A A A A, (2.22) Seg HS Disp A A A (2.23) is the residual Helmholtz energy for non-associated spherical segments consisting of a hard sphere term A HS, calculated by Carnahan and Starling (1969) and a dispersion term A Disp calculated using a power series that was initially fitted by Alder et al. (1972); A Chain is the residual Helmholtz energy increment due to bonding derived from associating fluid theory, where the association bonds are replaced by covalent, chain-forming bonds; and A Assoc is the residual Helmholtz energy due to association (Huang and Radosz, 1990). Huang and Radosz (1990) investigated the application of SAFT by correlating the vapourliquid-equilibria of over 100 real fluids. Their results demonstrated that SAFT EOS could be applied successfully to systems with molecules that were small, large, polydisperse and associating over a wide density range. The application of the SAFT EOS was further extended to 60 mixtures and results indicated further extensions to other hydrocarbon molecules was possible based on molecular structure and molar mass alone (Huang and Radosz, 1991). There have subsequently been many different embodiments of the general SAFT approach in the more recent studies, which are mainly differentiated by the interaction potential used to model the reference monomer fluid (Lafitte et al., 2013). More recent developments include the SAFT-VR EOS (Gil-Villegas et al., 1997), the PC-SAFT EOS (Gross and Sadowski, 2001) and the soft-saft EOS (Blas and Vega, 1997, Blas and Vega, 1998, Pàmies 24

33 and Vega, 2001, Lafitte et al., 2013). Most of these modifications replaced the original hard sphere reference monomer fluid and an attractive perturbation term by an attractive and repulsive interaction unique term. Significant improvements were achieved by these modified models in comparison with the original model. For instance, the SAFT-VR model broadened the scope of the original SAFT EOS (Gil-Villegas et al., 1997), and the PC-SAFT was found to improve the SAFT dispersion term (Gross and Sadowski, 2001). The success of SAFT is illustrated by the number of related publications produced over the past two decades, and it is gradually becoming a standard equation for engineering purposes (Müller and Gubbins, 2001, Economou, 2001, Yan et al., 2011). In spite of the huge potential of broader and practical applications, there are some limitations with the SAFT approach. One of these limitations is the difficulty associated with the transferability of the developed codes for different applications (Vega et al., 2005). Due to the inherent difficulty of its theory and the complexity of the EOS behind it, the development of different codes by different research groups have been focused on different applications (Muller and Gubbins, 2000). As such, without a general code and a wide database of molecular parameters for more compounds and their mixtures, the use of SAFT EOS in a process simulator still represents a difficult task (Vega et al., 2005). Although continuous efforts have been made to develop a generalised, user-friendly, multi-optional, and modular code covering a wide database of compounds and mixtures, there is still some way to go before the SAFT is truly ready for a generic process simulator (Vega et al., 2005) Multi-parameter Equations of State Although over the past several decades, there have been significant improvements to theorybased EOS and their predictions of thermodynamic properties for both pure fluids and mixtures, more accurate EOS are still often required for both engineering applications and scientific data needs (Jacobsen et al., 2000). The development of sophisticated multiparameter EOS has aimed to meet these requirements. These multi-parameter EOS drastically improve the prediction of fluid thermodynamic properties (Jacobsen et al., 2000) in comparison with more general models, to the point where available data are represented within their experimental uncertainty. Although first developed for reference-quality descriptions of pure fluids, these multi-parameter EOS have also been applied successfully to mixtures, by utilising a multi-fluid approach, where the EOS for individual components are implemented along with further correlations accounting for residual mixture behaviours (Kunz and Wagner, 2012). 25

34 The first applications of multi-parameter EOS to mixtures were developed independently by Tillner-Roth (1993) (Tillner-Roth and Yokozeki, 1997) for mixed refrigerants and Lemmon (1996) for natural gas mixtures containing both polar and non-polar species. Currently, the most developed and utilised version of multi-parameter EOS for mixtures is the GERG 2004 EOS, which was developed by the Groupe European de Recherche Gaziere (GERG) (Kunz et al., 2007), and was recently further updated to the GERG 2008 EOS (Kunz and Wagner, 2012). The GERG 2008 EOS is explicit in Helmholtz free energy as a function of density, temperature and composition. It was developed to make accurate predictions for 21 natural gas components with a normal temperature range of (90 to 450) K and pressures up to 35 MPa (Kunz and Wagner, 2012). Central to the basis of these multicomponent EOSs is the availability of quality experimental data, which can be selected and used in the model s development. The GERG 2008 EOS was based on more than 125,000 experimental data from 650 different sources, which included a large number of binary and multicomponent experimental data of natural gas and LNG mixtures. Kunz and Wagner (2012) claimed that due to the large amount of reliable data, the relative uncertainty of density predicted by GERG 2008 EOS was less than 0.1 %, while that of VLE composition was less than 3 %. However, Kunz and Wagner (2012) also noted the accuracy of the GERG 2008 EOS was mostly restricted by the limited or poor experimental data. One of the deficiencies of the GERG 2008 EOS was the lack of quality data for hydrocarbon binary mixtures containing n-butane, isobutane and other heavier hydrocarbon components. Kunz and Wagner (2012) concluded that the GERG 2008 EOS could be further improved if improved VLE, density and measurements of these binaries became available, especially for predictions of richer natural gas properties (Kunz and Wagner, 2012). In this study, the GERG 2008 EOS was used in the designing of the VLE measurements and its predictions were compared with the data measured in this study. The acquired quality data from this study in turn has the potential to improve the correlations and accuracy for future versions of the GERG 2008 EOS. 26

35 CHAPTER 3 VLE MEASUREMENTS: LITERATURE DATA & EXPERIMENTAL METHODS 3.1 Experimental Systems for VLE Measurement The accuracy of the VLE predictions made with an EOS is limited fundamentally by the availability of quality VLE data. Though it has been found that it is both difficult and expensive to measure and obtain high quality VLE data, it can be more costly if imprecise data or poor estimates are used when quality data is not available (Fonseca et al., 2011). To account for the large variation of mixture properties and a wide range of temperatures and pressures, many different experimental methods are required for the measurement of all required VLE data (Richon and De Loos, 2005). An apparatus that can be used for collecting VLE data relevant to the process conditions of an LNG scrub column needs to be robust and capable of gathering reliable VLE data at low temperatures and high pressures. A typical VLE apparatus consists of an equilibrium cell, within which the different phases of the mixture come into equilibrium. The cell is temperature controlled and temperature and pressure monitored. The time required to reach equilibrium is usually decreased by either the recirculation of one of both phases by pumping, rocking the autoclave or by agitation using an internal stirrer (Dohrn et al., 2010). However, the design of the cell can vary significantly with dimensions from 0.5 cm 3 (Bahramifar et al., 2003) to 9000 cm 3 (Gozalpour et al., 2003), from stainless cells to sapphire visual cells, and with phase compositions measured by different analytical methods or known synthetically. To successfully design a VLE apparatus that is able to collect the quality VLE data representative of LNG process conditions, it is important to conduct a comprehensive review into VLE experimental techniques, and understand the cell design and its optimisation. 27

36 High pressure is a relative term for phase equilibria measurements. They are generally considered as high pressure, as long as one of the measurement points is greater than 1 MPa (Dohrn and Brunner, 1995). High pressure phase equilibria experimental methods and data have been continuously investigated and reviewed by several authors, such as Hicks (1978), Knapp et al. (1981) and Fornari et al. (1990). More recently, a prominent research group based in Germany studied every 4 to 5 years the techniques and data development from 1988 to 2008 (Dohrn and Brunner, 1995), (Christov and Dohrn, 2002), (Dohrn et al., 2010), and (Fonseca et al., 2011). Very comprehensive reviews were also conducted in parallel by other authors such as Richon and De Loos (2005). The experimental approaches to VLE measurements can be classified in several ways based on their methodologies. They are generally first grouped into one of two categories - analytical and synthetic methods - with further sub classifications (Fonseca et al., 2011) Synthetic Method The synthetic method utilises the fact that the composition of a synthesized mixture being studied is known and remains constant. It aims to determine the temperature and pressure where a phase transition occurs for that mixture. With this method, no sampling is necessary and temperature and/or pressure are usually varied for a homogeneous single phase mixture until the beginning of a second phase is observed (Dohrn et al., 2010). A visual observation cell is often employed to identify the occurrence of this phase transition, not only for just simple VLE, but for more complicated systems such as solid-liquidequilibria, multiphase equilibria and gas hydrate formation. Optical techniques such as laser scattering (de Sousa and Rebelo, 2000) and Raman spectroscopy (Jager and Sloan, 2001) are often used to improve the detection of phase transitions. Non-visual cells can also be used to detect phase changes by monitoring other physical properties that change in a suitable manner upon a phase transition. This can simply be the change in the value of P/ T observed for an isochoric pathway that crosses either the dew or bubble point curve, except at the cricondentherm (Rowlinson John et al., 1986, Atilhan et al., 2011). Alternatively, the measurement could aim to detect discontinuities in thermophysical properties that can be measured with greater sensitivity. For instance, abrupt changes due to phase transition will induce a slope discontinuity of dielectric properties and sudden changes in acoustic properties. By monitoring these properties, experimental 28

37 methods such as microwave re-entrant resonator (May et al., 2001) and speed of sound techniques (Takagi et al., 2003) can be used to detect vapour-liquid phase transitions. The synthetic method is often considered to be quicker and easier than the analytical method, as no sampling is involved. However it yields less information for a multicomponent system than an analytical method. Furthermore, it is more suitable for gathering phase transition data than the VLE data required for the simulation of scrub columns (Dohrn et al., 2010) Analytical Method Non Sampling The analytical method refers to experiments in which the composition of one or both phases at equilibrium is determined using an analytical measurement. The non-sampling analytical method does so without attempting to first acquire a representative sample of that phase. Rather, it utilizes physicochemical methods of analysis to probe the composition(s) of the phases inside the equilibrium cell under pressure (Dohrn et al., 2010). One of the main non-sampling analytical methods is Raman spectroscopy, as used for example by Andersen et al (2001) and Zhu et al. (2007). This method allows for the measurement of composition by monitoring the amplitude of carbon-hydrogen (C-H) band frequency shifts characteristic of individual species within the mixture. The ratios of the Raman absorption bands for each component can be related to the ratios of the component amounts present if the absorption response to each component is adequately calibrated. Though this method effectively eliminates the need for sampling, it has been found to be difficult in practice, due to its requirement of substantial calibration. Furthermore, this method can be challenging to use for hydrocarbon systems, due to the limited ability to distinguish between the respective C-H frequencies of different hydrocarbon compounds (Zhu et al., 2007). The gravimetric method is another major non-sampling analytic method. This method measures the mass of a condensed phase in phase equilibrium with a fluid phase. By knowing additional information like phase densities, phase compositions can be determined (Dohrn et al., 2010). To accurately measure fluid phase density, Kleinrahm and Wagner (1986) developed a dual sinker magnetic suspension balance, where magnetic coupling transmitted the suspension force without contact from the pressure cell to a microbalance. May et al. (2001) demonstrated that this apparatus was capable of obtaining densities of hydrocarbon components to within 0.03% accuracy. However, the gravimetric method alone is not sufficient to obtain multicomponent VLE data required for this study, as it requires an assumption that the mixture contains only two components. For multicomponent 29

38 measurements, additional information would be required to obtain the phase compositions due to the increased degrees of freedom Analytical Method Sampling The sampling analytical method involves taking a representative portion from a mixture for analysis, usually with a gas chromatograph (GC) (Dvoskin, 2004). This is a well-established method that has been commonly used for obtaining VLE data representative of the natural gas liquefaction process (Dohrn et al., 2010). In general, after the sample is injected into the cell, equilibrium is eventually achieved by mixing at constant temperature. After mixing, sufficient time without agitation is allowed to ensure that samples taken are homogeneous. Often, pressure is monitored to provide an indication of the system achieving equilibrium. For example, Fredenslund et al. (1973) used a change in pressure of 0.05% in less than half an hour as an indication of equilibrium. Of course, the observed rate of pressure change with time is sensitive to the total vapour volume in the cell, with a larger volume reducing the pressure change caused by a given mass flux. The process of sampling from an equilibrium cell poses the greatest challenge to this analytical method of VLE measurement (Peper and Dohrn, 2012). This is because when a sample is taken from the cell, there is always a drop in pressure. This pressure drop will disturb the equilibrium within the cell, which leads to measurement error and uncertainties. Often there is also a change in temperature between the equilibrium cell and the analytical instrumentation, which can also give rise to inadvertent changes in the composition of the sample while it is en route to the GC. Up to now, quite a large amount of VLE data has been gathered with the sampling analytical method. However, the review of the available data indicates that there is a large amount of scatter within this literature data, as discussed in Section 2.4. This large scatter is attributed to the challenges with this technique during the process of achieving temperature and composition equilibrium, in particularly during the process of taking samples (Peper and Dohrn, 2012). Therefore, methods to minimise the equilibrium disturbance should be adopted if reliable VLE data are to be obtained. One solution to minimize the pressure drop during sampling is the use of a large equilibrium cell, which reduces the sample to volume ratio and leads to a smaller sampling disturbance. Gozalpour et al. (2003) used a 9000 cm 3 cell compared to the average cell size of 278 cm 3 (Peper and Dohrn, 2012). A sampling system was developed to measure VLE data for gas 30

39 condensates at elevated temperatures ( to K) and pressure ( MPa). The measurement results indicated that both internal consistency and reliability of measurement were significantly improved (Gozalpour et al., 2003). However, it has been recognised that such an experimental setup incurs a much higher cost in terms of apparatus, laboratory space and materials required. In addition, the large-volume equilibrium cells require more time and effort for temperature control and equilibration (Peper and Dohrn, 2012), as well as, potentially, long times for liquid drainage. Furthermore, as the materials investigated for LNG are all highly flammable, such large quantities of sample volume in a laboratory presents a greater safety hazard, particularly for combustible materials and gases under pressure. For these reasons, the vast majority of studies using the sampling analytical method have limited their equilibrium cells to volumes between 100 and 500 cm 3 (Peper and Dohrn, 2012). Control of the pressure of the equilibrium cell during sampling is another approach to reduce the effect of the disturbance. This is normally achieved by utilizing a variable volume cell where the pressure is controlled by reducing the system volume when samples are withdrawn (Price and Kobayashi, 1959, Wang and McKetta, 1964), or by injecting a pure component (Wichterle and Kobayashi, 1972a). Mercury has been utilised in many high pressure VLE measurements because it provides a convenient means of controlling cell pressure as samples are withdrawn or the system is manipulated. However, due to its toxicity, it has been found that an acceptable level of mercury is hard to achieve in any laboratory (Kendall, 1966). As a result of its hazards to operators, as well as the potential exposure to environment, the use of mercury in VLE measurements has largely been phased out. As an alternative, syringe pumps are now more commonly utilised to both inject samples and maintain pressure. Latest models of these syringe pumps, like the Quizix pumps used by both the University of Calgary (Nourozieh et al., 2013) and Imperial College London (Al Ghafri et al., 2013), have been reported to provide an accuracy of charging or discharging the fluid within cm 3. In the particular system of Kariznovi et al. (2011), the ability to control the fliud volume allowed the pressure control within the VLE cell to be within 5 kpa. The injection of pure components to compensate for the pressure drop up on sampling was well discussed by Wichterle & Kobayashi (1972a). Quite large amounts of VLE data were collected by using this method in 1970s. For example, in the VLE measurements of the methane + propane mixture at low pressure, when a sample was taken, methane was added into the cell to compensate for the loss of pressure by a proportioning pump. To account 31

40 for the change in total composition when methane was added and ensure the system remained well mixed prior to any further sample, the equilibrium cell needed to be continuously recirculated to return to equilibrium. However, this method was found to be very complicated and time consuming, due to the potential partial condensation and vaporization from the recirculation line, the temperature differential between the cell and methane supply, the time it took to reach equilibrium and the care required to ensure the sample taken was not corrupted by the addition of pure methane. The disturbance to the equilibrium cell can also be reduced if the amount of sample being taken is smaller. It has been shown by Peper and Dohrn (2012) that the equilibrium is not affected greatly by drawing only a small sample from the equilibrium cell. This approach generally involves using specialised sampling valves and, in some instances, using multiple capillaries at different heights inside the cell to sample different phases in the VLE cell. There are some challenges, however, that must be addressed when taking small samples through the capillaries. One potential difficulty is that differential vaporization and scattering may occur, especially for mixtures containing light and heavy components, due to the pressure drop along the capillary. Furthermore, the temperature change associated with the Joule-Thompson effect may cause solid formation in the transfer line (Peper and Dohrn, 2012). Baba-Ahmed et al. (1999) described a solution to avoid the problems caused by differential vaporisation. The pressure drop along the capillary is avoided by employing a valve with a micro-stem that ends with a nose which enters inside the capillary. This reduces the crosssectional area at the end of the capillary and is the feature that determines the critical mass flow rate out of the cell, ensuring that most of the pressure drop occurs close to the chromatographic circuit. Another major improvement to this approach to the analytical method was first made by Laugier and Richon (1986) and further improved by Guilbot et al. (2000). They developed rapid on-line sampler valves (ROLSI TM sampler) to enable fast and repetitive sampling; two of such valves were used to allow acquisition of samples from two different phases. This significantly improved and made VLE measurements more reliable as demonstrated by the successful measurement of VLE in the oxygen-argon and argon-nitrogen systems at conditions between (95 to 123) K and up to 2.8 MPa (Baba-Ahmed et al., 1999). A similar apparatus was utilised in this work for the purpose of measuring reliable VLE data representative of LNG process conditions in the scrub column. Its development and 32

41 construction commenced in 2007 and adopted the small sampling analytical method by incorporating the ROLSI TM sampler valves based on those used by Baba-Ahmed et al. (1999). The apparatus design evolved over several years, with a primary focus being improved temperature control and operational reliability. Its use was first reported by Kandil et al. (2010) who used it for a limited set of methane + isobutane measurements. A second version was then used to measure VLE for methane + pentane and methane + hexane (Kandil et al., 2011). While the data produced by the first and second generations of the apparatus were adequate, the limited temperature control and monitoring meant that the uncertainties of the phase compositions were similar to those already in the literature, as shown in Section 3.2. As part of this thesis, a third generation of this apparatus was constructed with substantially improved temperature control, which was able to produce reference quality VLE data for the primary methane binaries and multicomponent mixtures of light hydrocarbons. 3.2 Literature Data Review Due to the importance of quality VLE data to the accuracy of EOS utilised in process simulators for modelling the LNG process, constant efforts have been made for obtaining the quality VLE data in the past several decades. The available VLE data on light hydrocarbon binary mixtures obtained from various studies and their comparisons are presented below Available literature data on light binary mixtures A detailed analysis was conducted on the available literature data on ten light hydrocarbon binary mixtures, namely methane + ethane, methane + propane, methane + isobutane, methane + n-butane, ethane + propane, ethane + isobutane, ethane + n-butane, propane + isobutane, propane + n-butane, and isobutane + n-butane. The reviewed VLE literature (p, T, x) and (p, T, x, y) data were extracted from the thermodynamics database, ThermoData Engine (TDE), developed by the Thermodynamics Research Center at the National Institute of Standards and Technology (NIST) (Frenkel et al., 2011). The data for ten binary mixtures that can be formed from methane, ethane, propane, isobutane and normal butane were extracted from TDE. The sources of these data were checked with the GERG monograph (Kunz et al., 2007) and shown to be essentially the same. Given the predominance of methane in LNG processing, the five methane + alkane sets are generally considered the principal binary interactions, and the cross binaries (those 33

42 not containing methane) are regarded as secondary. The literature data were analysed by comparing them against predictions made using the default PR EOS implemented in Aspen HYSYS (AspenTech, 2011), which is a widely-used process engineering simulation tool. Information summarising the available literature data for these ten principal and secondary binary mixtures, such as the total number of data points and the temperature ranges, is given in Table 3.1. The composition deviation is the averaged root-mean-squared (RMS) deviation between the measured data set and the predictions made by HYSYS PR EOS. Since the deviation of the vapour phase is generally smaller, the RMS deviation reported is only for the liquid phase, as defined: RMS= 1 n (x n i,pr-x i,lit ) 2 i=1, (3.1) where the x i,pr is the predicted liquid mole fraction for the first component of the binary mixture, and x i,lit is the liquid mole fraction from literature data. components would have the same deviation. Table 3.1: Summary of Literature Binary Data Comparison. For binaries, both Binary Temperature Range No. of Data points Liquid Composition RMS Deviation methane + ethane (110 to 280) K methane + propane (130 to 344) K methane + isobutane (110 to 378) K methane + n-butane (138 to 411) K ethane + propane (127 to 369) K ethane + isobutane (203 to 394) K ethane + n-butane (260 to 394) K propane + isobutane (237 to 320) K propane + n-butane (237 to 363) K isobutane + n-butane (273 to 406) K

43 As shown in Table 3.1, there are significant literature data available for some binary mixtures, but not for others such as ethane + n-butane and isobutane + n-butane. The averaged RMS deviations between the measured data and those calculated by the HYSYS PR EOS for the datasets also vary significantly from one mixture to another. For instance, a large number of data points are available for the most well studied binary mixture methane + ethane (CH 4 + C 2 H 6 ). The small RMS deviation of in liquid mole fraction for this binary mixture suggests that HYSYS model is sufficient in its prediction for such binary mixture because the experimental uncertainties associated with analytical techniques are in the order of Table 3.1 also shows not only the lack of literature data, but also the larger deviations over the predicted values for other principal and secondary binary mixtures, such as ethane + n- butane at temperature (260 to 394K), where there are only 85 available data points, and an average RMS deviation is as high as in liquid ethane mole fraction Analyses of the literature principal binary mixtures The conventional and convenient way of presenting VLE data for binary mixtures and comparing them with EOS predictions is through a (p, x, y) plot. At a fixed temperature, a binary mixture at VLE only has one degree of freedom and, hence, specifying the mixture s pressure, p, sets the composition of the liquid and vapor phases. Thus (p, x, y) plots generally show isothermal phase envelopes comprising of a bubble point curve (p, x) and a dew point curve (p, y): the value of the abscissa corresponds either to the liquid phase composition (x) or the vapor phase composition (y), depending on which of these curves is being considered. Generally, however, the deviations of EOS predictions from measured VLE data for the mixtures of interest are much larger for the liquid phase than for the vapor phase. Specifically, the deviations between EOS predictions and vapor measurements were generally comparable to the experimental uncertainty (about ±0.002 to ±0.005 in the measured mole fractions for high-quality VLE measurements), whereas the liquid phase deviations were generally larger by an order of magnitude or more. Accordingly, comparisons in this review will focus almost exclusively on the liquid phase. The vapor phase comparisons are shown only to illustrate that tuning an EOS to liquid-phase data has not affected significantly its vapor phase predictions. The use of (p, x) plots to conduct a detailed assessment of the quality of measured VLE data and/or EOS performance is still limited by the large scale of the pressure axis, which is required to represent the normally wide range of bubble-point conditions. To solve this problem, the deviation plots showing the difference between the measured data and the 35

44 compositions predicted by the EOS at the specified temperature and pressure are used for the analyses of this study. In these plots, deviations are plotted against EOS predictions as the horizontal axis. The advantages of using the deviation plots for analyses can be demonstrated in Figure 3.1, where the literature data for the binary of methane + ethane are compared with the EOS predictions. In Figure 3.1(a), several measured data sets for methane + ethane at 250 K and 270 K are plotted in (p, x) plots, together with the corresponding predictions of the default PR EOS implemented in HYSYS (AspenTech, 2011). It can be shown in Figure 3.1(a) that while the (p, x) plot is able to indicate a reasonable agreement between the measurements and the model predictions, it is difficult to assess, for example, the consistency of the different data sets or whether the agreement of the model with the data is better at one temperature than another. These limitations can be readily overcome with the deviation plots, as shown in Figure 3.1(b). By showing the deviations of the measured (methane) liquid mole fraction, x measured, from the EOS prediction, x calc, the different data sets at both temperatures are generally consistent and clearly seen to be within a reasonable estimate of their uncertainties. Figure 3.2(b) also clearly shows that the EOS deviates systematically from the data with increasing methane liquid mole fraction, x 1, and that the slope of this systematic deviation is larger at 270 K than at 250 K. The literature VLE data for the principal binary systems containing methane are reviewed and compared with the default HYSYS PR EOS predictions. Results of these analyses and comparisons are presented in the following sections. These systems contain the information about the dominant binary interactions occurring in natural gas and LNG and, thus, are the most important for scrub column simulations. 36

45 (a) (b) Figure 3.1: (a) (p, x) plots of the measured and predicted (curves) bubble-points for the CH 4 + C 2 H 6 binary system for isotherms at 250 and 270 K, and (b) plots of the deviations of the same sets of data from the corresponding predictions. 37

46 The literature data for CH 4 + C 2 H 6 binary mixtures The comparison between the measured and predicted liquid composition for the CH 4 + C 2 H 6 binary is presented in Figure 3.2, using both a (p, x) plot (a) and a deviation plot (b). The (p, x) plots in Figure 3.2(a) display the selected isotherm datasets representative of the temperature at scrub column conditions, which include those from Wichterle and Kobayashi (1972b), Wei et al. (1995), Janisch et al. (2007), Davalos et al. (1976), Gupta et al. (1980) and Raabe et al. (2001). The deviation plots in Figure 3.2(b) contain more available literature measurements from Wichterle et al. (1971) (1972a) (1972b), Wilson (1975), and Miller (1977). The RMS deviation for the data in Figure 3.2(b) is liquid methane mole fraction and the distribution of the deviations does not exhibit any clear trend with composition. These results suggest that the default HYSYS PR EOS with a BIP for CH 4 + C 2 H 6, (default) k = is adequate over this range of conditions. Potentially some improvement could be achieved by (1) filtering out the 1972 data of Wichterle and Kobayashi (1972a) (1972b), which exhibit significantly more scatter than the other data sets, and then (2) allowing k 12 to become temperature dependent, as suggested by the trends apparent in Figure 3.2(b). However, given that the RMS deviation is already comparable with typical experimental uncertainty, it is difficult to justify the need for improving upon the default HYSYS PR EOS description of the CH 4 + C 2 H 6 binary system. (a) 38

47 (b) Figure 3.2: (a) Selected measured and predicted (curves) bubble-points for CH 4 + C 2 H 6 binary mixture, and (b) deviations of measured over calculated values as a function of CH 4 mole fraction (x 1 ) The literature data for CH 4 + C 3 H 8 binary mixtures Much larger deviations between measured and calculated liquid mole fractions were observed for the other binary mixtures. Figure 3.3 shows a comparison of measured and predicted liquid compositions for the CH 4 + C 3 H 8 binary. The (p, x) plots in Figure 3.3(a) display the selected isothermal data sets of Wichterle (1972c), Kalra and Robinson (1975), Webster and Kidnay (2001), Benham and Katz (1957), Price et al. (1959), Reamer et al. (1969) and Wiese et al. (1970b). The deviation plots in Figure 3.3(b) contain all 429 literature data measured between 130 K and 344 K, which also include the measurements from Akers et al. (1954), Joffe (1976), Raimondi (1980) and Webster et al. (2001). The RMS deviation for the data in Figure 3.3(b) is mole fraction and the distribution of the deviations exhibits a positive divergence of the data from the EOS with increasing liquid methane mole fraction. This divergence is even apparent for some of the isotherms in the (p, x) plot shown in Figure 3.3(a). For example, at 230 K the experimental pressures as the critical point is approached are noticeably lower than those predicted with the default HYSYS PR EOS: conversely at a given pressure the measured methane liquid mole fraction is increasingly larger than the calculated value. A great amount of scatter in literature data is also observed in Figure 3.3(b) (Wichterle et al., (1970), (1972c) and, (1990), Weise et al., (1970a) and (1970b), Joffe, (1976)). 39

48 (a) (b) Figure 3.3: (a) Selected measured and predicted (curves) bubble-points for CH 4 + C 3 H 8, and (b) deviations of measured CH 4 liquid mole fractions (x measured) from the calculated values as a function of CH 4 mole fraction (x 1 ). 40

49 The literature data for CH 4 + ic 4 H 10 binary mixtures The comparison between the measured and predicted liquid composition for the CH 4 + ic 4 H 10 binary is presented in Figure 3.4. The (p, x) plots in Figure 3.4(a) display the single source of Barsuk et al. (1970), whose measurements range from (198 to 378) K: these are the only literature VLE data for this binary system at conditions relevant to LNG scrub columns. The deviation plots in Figure 3.4(b) contain 145 literature data measured between 110 K and 378 K, which also include the only other two literature VLE data sets available for this system. They are of limited relevance having been measured only either at high temperatures (311 to 377) K (Olds et al., 1942), or very low temperatures (110 to 140) K (Haynes, 1983). The RMS deviation for all the data in Figure 3.4(b) is mole fraction and the distribution of the deviations exhibits a positive divergence of the data from the EOS with increasing liquid methane mole fraction. This divergence, which is again apparent on the (p, x) plots shown in Figure 3.4(a), does indicate a possible temperature dependence. However, the scatter in the measured data and the lack of data sources make it difficult to assess critically any temperature dependent structure in the data. It is apparent that the HYSYS default PR EOS and BIP for CH 4 -ic 4 H 10, (default) k 1,iC4 = provide a reasonable compromise in describing the literature VLE data for this system using the standard approach. It is also clear though that this situation could be improved significantly through the use of a temperature dependent mixing rule for better accounting for the near-critical divergence of the EOS from the data. Given the current reliance on a single low quality data-source, the acquisition of new, high quality VLE data for the CH 4 + ic 4 H 10 system at conditions relevant to LNG scrub columns would be of significant value. 41

50 (a) (b) Figure 3.4: (a) Measured and predicted (curves) bubble-points for CH 4 + ic 4 H 10 mixture, and (b) deviations of measured CH 4 mole fractions (x measured ) over calculated values (x calc ) as a function of CH 4 mole fraction (x 1 ). 42

51 The literature CH 4 + n-c 4 H 10 binary mixtures Figure 3.5 shows a comparison of measured and predicted liquid compositions for the CH 4 + nc 4 H 10 binary. The (p, x) plots in Figure 3.5(a) display the selected isothermal datasets of Roberts et al. (1962), Wang et al. (1964), Kahre (1974) and Elliot et al (1974). The deviation plots in Figure 3.5(b) contain all available 416 literature data measured between 138 K and 411 K and further include the measurements of Nederbragt (1938), Sage et al. (1940), Rigas et al. (1958) and Raimondi (1980). The RMS deviation for all the data in Figure 3.5(b) is mole fraction, which has the worst performance of all four primary methane binaries and reflects the fact that this system suffers the most from the two key afflictions identified in this review: poor quality experimental VLE data and the near-critical divergence of the EOS from the measurements. The isothermal data shown in Figure 3.5(a) are a small subset of those in Figure 3.5(b); they were selected because they illustrate clearly both key problems and, importantly, occur at temperatures near those used in LNG scrub columns. At 244 K there is a very large discrepancy between the data of Roberts et al. (1962) and Wang and McKetta (1964), as well as those of Elliot et al. (1974). The HYSYS default PR EOS, with (default) k 1,nC4 = , appears to be tuned to the latter data set at lower pressures but transitions to the former data sets as the critical point is approached. p/kpa x 1 Roberts et al. (1962) 211K Wang et al (1964) 211K Kahre (1974) 211K Elliot et al (1974) 211K Roberts et al (1962) 244K Wang et al (1964) 244K Elliot et al (1974) 244K Roberts et al (1962) 278K Wang et al (1964) 278K Elliot et al (1974) 278K (a) 43

52 x measured -x calc x 1 (b) Nederbragt (1938) K Sage et al (1940) K Rigas et al (1958) 311K Roberts et al (1962) K Wang et al (1964) K Elliot et al (1974) K Kahre (1974) K Raimondi (1980) K Figure 3.5: (a) Measured and predicted (curves) bubble-points for CH 4 + n-c 4 H 10 mixture and (b) deviations of measured CH 4 mole fractions (x measured ) over the calculated values (x calc ) as a function of CH 4 mole fraction (x 1 ). It is abundantly clear from Figure 3.5 that the reliability of VLE predictions for the CH 4 + nc 4 H 10 system could be greatly improved through the use of a model capable of better accounting for the near-critical divergence of the EOS and the acquisition of new, high quality VLE at conditions relevant to LNG scrub columns. Large scatter in literature data in secondary binaries was reported, however, no apparent trend suggesting the same near-critical divergence and possible composition dependence as seen for the principal binaries was observed. This indicates that the default HYSYS PR EOS can describe the available VLE data for these cross binary systems reasonably well. New high-quality VLE data of the secondary binaries would improve the situation for some of the systems of LNG process simulators. However, the resulting benefit would not be as significant as that from new high-quality VLE data for the principal binaries, due to the fact that methane is the predominant species in natural gas. In summary, there are significant deficiencies in current literature data available at conditions representative of LNG scrub columns for the principal methane binaries. As discussed above, CH 4 + ic 4 H 10 has only one dataset within the temperature range of interest, therefore the EOS models based on this dataset are limited by the large scatter within this dataset. 44

53 Although there are several literature datasets for CH 4 + n-c 4 H 10, the large variations amongst the datasets indicate large uncertainties for EOS based on these datasets. Clearly, the accuracies of the EOS models can be improved if these data deficiency problems are addressed. 45

54 CHAPTER 4 EXPERIMENTAL APPARATUS ITS MODIFICATION, IMPROVEMENT AND CALIBRATION 4.1 Cryogenic VLE Apparatus The cryogenic VLE apparatus that was constructed in 2008 employs a sampling analytical method and adopts the same design concept of the VLE measurement system described by Baba-Ahmed et al. (1999). The core element of the Cryogenic VLE apparatus is the equilibrium cell (EC). A schematic and the photo of this EC in its original configuration are shown in Figure 4.1. Figure 4.1: Photo of the Cryogenic VLE apparatus in its original form. 46

55 The body of the cell was machined from a single grade 316 stainless steel billet and served as the pressure vessel, with a maximum operating pressure of up to 30 MPa. Its internal diameter was 3 cm and the internal volume was 60 cm 3. The outer surface of the cell was plated with 1 mm thick copper, which improved the heat transfer needed for achieving temperature uniformity. The temperature control of the cell was achieved by a foil type heating element and a 100 Ω platinum resistance thermometer (PRT). The foil heater (not shown in the photograph in Figure 4.1) was wrapped and glued to the outer surface of the cell using high thermal conductivity epoxy suitable for cryogenic operations, while the PRT was glued directly underneath the heating foil to complete the temperature control (TC) circuit. Wells were bored in the top (lid) and the bottom of the EC to house two calibrated 100 Ω PRTs (T1) and (T2) used for monitoring the temperature gradient of the cell. These two PRTs were supplied by Lakeshore Cryotronics, and were calibrated to ITS-90 by the supplier over the temperature range from (60 to 330) K with a claimed uncertainty of ±0.02 K. Shown in Figure 4.2 is the schematic diagram of the UWA VLE cell (Kandil et al., 2010). To obtain the temperatures in the region of LNG processes, the cell was placed inside a cryogenic Dewar (CRY) equipped with an automatic liquid nitrogen pump (LNP) that was equipped with a level control sensor that controlled the liquid nitrogen level inside the Dewar, and the required cooling was achieved through liquid nitrogen boil off. Attached to the bottom of the cell were two cryogenically compatible variable speed motors. The lower motor M1 was used to drive a fan that stirred the liquid nitrogen boil-off vapour inside the Dewar to both accelerate the cooling rates and provide some temperature uniformity of the air bath surrounding the cell. The second motor M2 was used to mix the liquid to achieve thermal equilibrium inside the EC. The motor rotated a magnet which in turn drove a Teflon-coated magnetic bar located inside the cell at its base. A Mylar film was placed between the Teflon-coated magnetic bar and the cell bottom inner surface to prevent any wear from the spinning magnet bottom (Teflon and Mylar are registered trademarks of E.I. du Pont de Nemours & Co.). To minimize any dead volume associated with the fill valve, the lid of the cell was machined carefully to fit a custom, cryogenically compatible fill valve V1, with a nonrotating stem that was flush with the inner surface of the cell lid when closed. 47

56 Figure 4.2: Schematic diagram of the VLE experiment (Kandil et al., 2010). The pressure inside the EC was measured by a Kulite model CT-190 pressure transducer P1. This transducer was housed in the lid to minimize dead volume, and utilised a strain-gauge on a silicon diaphragm that is suitable for operation at temperatures from (77 to 393) K. The relative standard uncertainty of the Kulite transducer s calibration was given as ±0.5 % for the pressure range from (1 to 14) MPa. It was calibrated in situ by comparison with a reference quartz-crystal Paroscientific Digiquartz series 1000 pressure transducer P2, with a full scale of 14 MPa and a relative uncertainty of 0.01 % full scale as specified by the manufacturer (Paroscientic, 2014). The liquid and vapour samples were collected from the EC by the two capillaries mounted in the cell lid, respectively. These capillary tubes were made from Monel 400 with internal diameters of less than cm. One of the capillaries VV used for sampling the vapour phase had a total length of 13 cm and extended 1.5 cm below the bottom of the cell lid. The other capillary VL used for sampling the liquid phase had a total length of 20 cm and extended nearly to the bottom of the cell. The other end of each capillary sampling tube was located inside a specialized ROLSI TM electromagnetic solenoid valve supplied by Transvalor. As shown in Figure 4.1, the two red 48

57 ROLSI TM electromagnetic sampling valves are mounted on the top side of a steel plate approximately 5 cm above the top of the VLE cell lid. These two valves had no direct contact with the nitrogen boil-off vapour. Resistive heating wires and a 100 Ω PRTs were attached to each of the external surfaces of the capillaries TL and TV, and the temperature controlled by a proportional-integral (PI) temperature control loop. This was to address the potential condensation or even solidification of samples within the capillaries and sample lines during the sampling process (Kandil et al., 2010). A temperature control system with heating elements was also used to maintain the ROLSI TM sampling valves at a temperature above 273 K. The transfer lines were also maintained above the temperature of the boiling point of the least volatile component of the mixture using a temperature control system. These measures were essential for obtaining representative samples of the equilibrium phases in the VLE cell. A carrier gas line was connected to each of the ROLSI TM sampling valves, where helium continuously flowed through the valves and into their respective gas chromatography (GC) columns. The ROLSI TM sampling valves were control by a control box (VSC) allowing for an opening time resolution of 0.01 s. When the ROLSI TM sampling valves were actuated, the samples from both vapour and liquid phases in the cell were swept with the carrier gas helium to their respective columns. To compensate for the different pressures inside the EC, the amount of sample withdrawn by opening the valves could be adjusted by varying the opening time using the VSC. A Varian model 3800 GC was used for analysis. The GC was equipped with two capillary columns, two flame ionization detectors (FID) and a thermal conductivity detector (TCD). From the transfer lines, the vapour and liquid phases were each connected to a 25 m long capillary PoraPLOT Q packed column (Agilent, 2014), where the different components were separated. The column used for the vapour phase was connected to the sample side of the TCD detector, whereas the column used for the liquid-phase sample was connected to the reference side of the TCD. Once passing through the TCD, the liquid and vapour compositions were determined using the respective FIDs FID L for liquid sample and FID V for vapour sample. Since all the binaries investigated in this study were combustible, only the FIDs were used. The TCD allowed for the detection of non-combustible components in future works. Despite the features of the initial design, problems with the operation of this apparatus were identified that often affected its robustness and accuracy. The major problems identified 49

58 with the original apparatus included pressure drops in the ROLSI TM sampling valve and transfer lines; blockages in the sampling capillaries; a large temperature gradient with the cell; ice built-up near the electrical connectors; and calibration shifts. Rectifying these problems was one of the first major tasks of this research project. 4.2 Improvements to the VLE Apparatus Figure 4.3 shows a schematic of the modified experimental setup of the Cryogenic VLE apparatus implemented for this work. The sections of the apparatus that were modified and improved are highlighted in red, and will be discussed in detail below. Vent Carrier Gas + Sample VSC RV1 TS3 DAQ DAQ and & Sampling Control Control RV2 TS2 FID V FID L TS1 TRC VL VV TRS M2 P2 Gas Chromatograph TCu T2 TC LC TL P1 TV VC vapour V1 Filter Carrier Gas Helium T1 liquid Stirrer Motor TCuB Copper Can Radiation Shield Exhaust Liquid Nitrogen Pump Liquid N 2 Stainless steel can Sample Cylinder Vacuum Pump Cryogenic dewar Figure 4.3: Schematic diagram of the improved VLE experiment. 50

59 4.2.1 Improvements to Thermal Stability The major modification to the apparatus is the introduction of multiple thermal stages to eliminate direct contact of the cooling agent with the cell, the capillaries and the ROLSI TM valves. These modifications have addressed the problems caused by liquid nitrogen boil off vapour, and also improved the thermal stability of the system. Figure 4.3 shows that the cell and the ROLSI TM valve assemblies are now completely sealed inside a copper can. To operate the fill valve V1, a stepper motor M2 (Phytron UHVC-80) was also sealed inside the copper can to provide its drive. The stirrer that was used to mix the liquid nitrogen vapour to ensure constant boil off was discarded. Instead, a helium line is used to fill the copper can at atmospheric pressure to provide good heat transfer between the can and the cell. The copper can is placed inside an aluminium radiation shield, which is completely surrounded by a stainless-steel can to prevent the direct contact of the shield with the boil-off nitrogen vapour. A line also supplies helium to the space between the stainless-steel can and the aluminium shield to allow for good heat transfer during cooling and heating. The space is evacuated during an experiment to improve thermal stability by reducing heat transfer into the radiation shield and copper can. The stainless-steel can is placed in a much larger cryogenic Dewar, where a metallic lid stops moisture from the air condensing into the Dewar. Cooling is still provided by the automatic liquid nitrogen dosing pump. All electrical signals between the sealed cans are transmitted through electrical feed-throughs capable of operating at cryogenic temperatures and near vacuum conditions. As a result of these modifications, the thermal stability of the system was significantly improved and the problems associated with the nitrogen boil-off were avoided. Another advantage of this improvement was the reduction of the power to maintain the temperature control especially on the equilibrium cell, which resulted in reduced gradients in the cell and improved reliability of the data collected Improvement to Measurement Sensors Reliable temperature, pressure and composition measurements are essential to the reliability and accuracy of the VLE data. A considerable effort to improve the reliability of the VLE measurements was focused on improving the measurement sensors. Broken PRTs in the apparatus were discovered multiple times during the system s initial operation. Accordingly, the system was equipped with a new batch of DIN Class-A PRTs, which came from the supplier with a specified uncertainty of ±( T)/K, 51

60 where T was the temperature deviation from 273 K. These sensors were then calibrated using a Lakeshore PT-102 as a reference thermometer, where the reference sensor was calibrated externally to ITS-90 with an uncertainty of ±0.01 K. The performance of reference thermometer was checked at liquid nitrogen temperature and the ice point of water to ensure its reliability. The measured resistances of each PRT were converted to temperatures using a quadratic function, the parameters of which were determined by correlating the resistance from each PRT to the corresponding temperature from the reference thermometer. All PRTs were calibrated over the temperature range (245 to 323) K in a liquid bath, and at 77 K using liquid nitrogen. The estimated uncertainty of any PRT used in the VLE apparatus was less than ±0.1 K. The three PRTs (T1, T2 and TC) used for the control and monitoring of the EC had calibration uncertainties of ±0.02 K. Additional accuracy of the temperature measurement was achieved by rewiring all of the PRTs and modifying those with the 2-wire configuration to 4-wire configuration. The advantages of a 4-wire configuration for PRTs over a 2-wire one are well documented in the literature (Wilson, 2013). After installing the new sensors into the VLE cell, no significant drift in temperature was observed Improvement to Sampling Valve Configuration Another modification was the addition of two rotating valves RV1 and RV2 for improved sampling. These two valves were introduced in the transfer line between the ROLSI TM sampler valve and the FID detectors. RV1 allowed for the complete purge of the sample and the transfer lines, so the capillaries could be flushed entirely before a representative sample was sent to the FID detectors. RV2 enabled the sampling of both phases with both FID detectors. This improvement significantly reduced the uncertainty of the detector response, resulting in more accurate composition measurements Improvement to the temperature control To improve the temperature control, the automatic liquid nitrogen dosing pump was reconfigured to be temperature controlled to 2 K lower than the cell set temperature, via a temperature sensor that monitored the temperature at the bottom of the stainless steel can. With this modification, the dosing rate was adjusted according to the desired temperature, which ensured that only just sufficient liquid nitrogen is pumped in to meet the cooling 52

61 requirements for temperature control. This modification reduces the power required from the heaters used for temperature control. The outside of the copper can was also wrapped with a foil-type heating element with power output up to 150 W, which controlled the copper can to a temperature of 2 K below the cell temperature. This process is monitored by the control PRT T Cu and the reference sensor T CuB. This improvement allowed the temperature gradient inside the copper can to be monitored, leading to the improvement to the thermal stability of the EC. The temperature control of the capillary tubes (VC and LC) leading to the ROLSI TM valves was also improved by replacing the resistive wire heaters wrapped around the capillaries with Peltier modules mounted on copper plates containing grooves machined to match the capillary circumference. The temperatures of the capillaries were controlled by the PRTs (TV and TL) mounted on the copper plates. Due to the larger surface contact of the copper plate, the new heaters transferred heat more uniformly to the capillaries. As a result of this modification, the chances of hot spots and damage to the capillaries were reduced. The temperatures of the ROLSI TM valves VV and VL were controlled using heating elements and a control PRT (TRC). An additional sensing PRT (TRS) is introduced to monitor the temperature gradient. To prevent condensation, all sections of the sample transfer lines between the ROLSI TM valves and the outside of the Cryogenic Dewar are now individually temperature controlled using resistive wire heaters. Their temperatures are monitored using three calibrated PRTs as shown in Figure 4.3: TS1 monitors the temperature inside the copper can, TS2 between the copper can and the stainless-steel can, and TS3 between the stainless steel can and the lid of the Dewar. This system gives a better temperature control of the ROLSI TM valves and transfer lines, compared to that of the previous generation VLE apparatus. Ultimately, it has reduced the possibility of condensation and blockage in the sample transfer lines. 4.3 Mixture Preparation To make VLE measurements, it was necessary to prepare the binary and multicomponent mixtures. The compositions of the mixtures were first determined by considering the phase envelopes generated by the GERG 2008 EOS (Kunz and Wagner, 2012). These mixtures were then prepared using a special high pressure mixing system. 53

62 4.3.1 Preparation of Mixtures The mixtures were prepared gravimetrically. One of the main considerations in preparing a mixture gravimetrically is that the composition of the mixture has to be maintained when it is transferred into the VLE cell from the cylinder it was prepared in. This means that the mixture must be single phase at room temperatures, say 20 o C. The GERG EOS was first used to design the experiment, where a series of phase envelopes on a range of compositions were generated within the 2-phase region. The mixtures were then selected with the highest permissible concentration of heavy components, in order to maximise signal-to-noise during VLE measurements, while ensuring they remained single phase at room temperature. Shown in Figure 4.4 is an example of how the binary mixture of CH 4 + n-c 4 H 10 was chosen, where the mole fraction of this binary was designed with 93.5 % CH 4 and 6.5 % n-c 4 H 10. Figure 4.4 shows that the phase envelope predicted by the GERG EOS for this binary has a cricondentherm of less than 286 K, as shown in the red line. This indicates that this mixture will be single phase at room temperature. Figure 4.4: Calculation for CH 4 (1) + n-c 4 H 10 (2) at x 1 =

63 Once the composition of the mixture was determined, the amount of mixture required to ensure a sufficient amount of liquid phase formed in the cell could also be determined. In this example, 3 isochoric experiments were considered using the GERG EOS with the proposed composition. An initial pressure was specified at room temperature. By assuming the cell remained at constant overall density along the near isochoric pathway, the pressure at each sequential temperature was determined. The liquid level for each temperature was then determined. The masses of each component added to give the required mole fraction were then calculated such as to ensure that the liquid level was above the end of the liquid capillary at all conditions Sample preparation Once the composition and pressure were determined, the mixtures were then prepared using a specialized mixing manifold. A schematic of this manifold and a photo of it are shown in Figure 4.5 (Szajnkienig, 2009). Figure 4.5(a) shows that the pressure of the gas is controlled by two regulators. Both vent (V4) and a vacuum pump are used to flush and evacuate the mixing system and the sampling vessel. A high pressure gauge is used to accurately measure the pressure of the regulated gas, while the low pressure gauge determines the status of the evacuation. (a) 55

64 (b) Figure 4.5: Schematic of High Pressure Mixing Manifold (a) and its photo (b). As shown in Figure 4.5(b), a 300 cm 3 cylinder with a mass of about 1000 g was attached to the mixing manifold and a ball bearing was placed inside the cylinder to enable mixing. The cylinder was initially flushed with high pressure methane and evacuated with the entire mixing manifold by venting through V4 as shown in Figure 4.5(a). This was completed twice before both the bottle and the manifold were evacuated using the vacuum pump. The evacuated bottle was then disconnected and weighed before reconnected to the mixing manifold. When each of the components was added into the cylinder, it was then charged into the entire manifold and then vented through V4, and then the manifold was again evacuated. This step was repeated twice to purge any residual gases from the system. To load the correct mass of each component into the cylinder, the pressure was regulated to a value (i) above the pressure in the cylinder and (ii) that corresponded with density that would allow a sufficient mass of that component to reside in the vapour space of the cylinder. To fill the cylinder with the required mass of a fluid that was condensable at room temperature the cylinder was cooled in a liquid nitrogen bath to allow for enough material to condense into the cylinder. The components were added to the cylinder in the order of increasing vapour pressure. Using an electronic balance with a resolution of g and a full scale of 1100 g, the 56