6.23 Equation of State Prediction of Carbon Dioxide Properties

8/2/2019 6.23 Equation of State Prediction of Carbon Dioxide Properties

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KCP-GNS-FAS-DRP-0001

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Project Title: Kingsnorth Carbon Capture & Storage Project Page 1 of 70

Document Title: Equation of State Prediction of Carbon Dioxide Properties

Kingsnorth CCS Demonstration ProjectThe information contained in this document (the Information) is provided in good faith. E.ON UK plc, its subcontractors, subsidiaries, affiliates, employees, advisers, and the Department of Energy and Climate Change (DECC) make no representation or warrantyas to the accuracy, reliability or completeness of the Information and neither E.ON UK plc nor any of its subcontractors, subsidiaries, affiliates, employees, advisers or DECCshall have any liability whatsoever for any direct or indirect loss howsoever arising from the use of the Information by any party.

Equation of State Prediction of Carbon Dioxide Properties

Table of Contents

1 Executive Summary 52 Abbreviations and Glossary 92.1 Abbreviations 92.2 Glossary of Terms 93 Thermodynamic Behaviour of Pure Carbon Dioxide 103.1 Phases of Carbon Dioxide 103.2 Overview of CO2 Basic Properties 114 Basic Data for CO2 Mixtures 15

4.1 Introduction 154.2 Commercial Software Packages 165 Property Calculation Methods 185.1 Corresponding States Correlations 185.2 Equations of State 185.3 Special Methods 215.4 Thermodynamic Property Methods 225.5 Transport Properties 236 Selection of Method to Determine CO2 Property Data 256.1 Selected Equations of State for Equilibrium Properties 256.2 Selected Correlations for Transport Properties 256.3 Likely Errors 256.4 Comparison of Calculation Methods for Pure CO2 28

6.5 Mollier and Phase Diagrams 337 References 358 Appendix 1 CO2 Properties as Functions of Reduced Properties 369 Appendix 2 Multiflash Files 4110 Appendix 3 Binary Interaction Parameters for Span and Wagner EoS within Multiflash 4511 Appendix 4 Comparison of Multiflash Results for CO2 Mixtures 4612 Appendix 5 Thermal Conductivity and Viscosity Correlation and Uncertainty 4813 Appendix 6 Flow Diagram to Determine Recommended Calculation Method 5014 Appendix 7 Property Tables 51


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Table of Figures

Figure 1-1 Flow Diagram to Determine Recommended Calculation Method for Pure CO 2 and HighConcentration CO 2 Mixtures ...................................................................................................... 7 Figure 3-1 CO 2 Phase envelope ................................................................................................ 9 Figure 3-2 Density vs. Temperature in the Critical Region (reproduced from Ref 3) .............. 10 Figure 3-3 CO 2 Density vs. Temperature ................................................................................ 11 Figure 3-4 CO 2 Cp vs. Reduced Density and Temperature (reproduced from Ref 3) ............. 12 Figure 3-5 CO 2 Cv vs. Reduced Density and Temperature (reproduced from Ref 3) ............. 13 Figure 6-1 Percentage error in Span-Wagner EoS vs. Temperature and Pressure ............... 26 Figure 6-2 Comparison of 100% CO 2 and 95% CO 2 Phase Diagrams ................................... 27 Figure 6-3 Reference Conditions for Property Tables ............................................................. 28 Figure 6-4 CO 2 Pressure-Enthalpy Diagram ........................................................................... 32 Figure 6-5 CO 2 Pressure-Temperature Diagram..................................................................... 33 Figure 8-1 CO 2 Thermal Conductivity vs. Reduced Density and Temperature ....................... 35 Figure 8-2 CO 2 Expansion Coefficient vs. Reduced Density and Temperature...................... 36 Figure 8-3 CO 2 Heat of Vapourisation vs. Temperature ......................................................... 37 Figure 8-4 CO 2 Compressibility vs. Reduced Density and Temperature ................................ 38 Figure 8-5 Velocity of Sound vs. Reduced Density and Temperature .................................... 39 Figure 12-1 Vesovic et al Correlation for CO 2 Thermal Conductivity ...................................... 47 Figure 12-2 Vesovic et al correlation for CO 2 Viscosity ........................................................... 48 Figure 14-1 Key to Fluid Phase on Property Tables ............................................................... 50

Table of Tables

Table 1-1 Span Wagner Error vs. Experimental Data ............................................................... 5 Table 4-1 Important factors in basic data method selection ................................................... 14 Table 4-2 Equations of State Available in Software Packages for CO 2 Simulation ................. 16 Table 6-1 Span Wagner Error vs. Experimental Data ............................................................. 25 Table 6-2 CO 2 Density Calculated by Span Wagner EoS (kg/m) .......................................... 29 Table 6-3 CO 2 Density Calculated by Peng Robinson EoS (kg/m and vs. SW) ................. 30 Table 6-4 CO 2 Density Calculated by Soave Redlich-Kwong EoS (kg/m and vs. SW) ...... 31 Table 11-1 Dew Point Calculation at 0C ................................................................................ 45 Table 11-2 Dew Point Calculation at 10C .............................................................................. 45 Table 11-3 Dew Point Calculation at 20C .............................................................................. 46 Table 11-4 Dew Point Calculation at 30C .............................................................................. 46 Table 14-1 CO 2 Density Calculated by Span Wagner EoS (kg/m) ........................................ 51 Table 14-2 CO 2 Cv Calculated by Span Wagner EoS (kJ/kgK) .............................................. 51 Table 14-3 CO 2 Cp Calculated by Span Wagner EoS (kJ/kgK) .............................................. 52 Table 14-4 CO 2 Enthalpy Calculated by Span Wagner EoS (kJ/kg) ....................................... 52 Table 14-5 CO 2 Entropy Calculated by Span Wagner EoS (kJ/kg) ........................................ 53 Table 14-6 CO 2 Speed of Sound Calculated by Span Wagner EoS (m/s) .............................. 53 Table 14-7 CO 2 Compressibility Calculated by Span Wagner EoS (-) .................................... 54 Table 14-8 CO 2 Viscosity Calculated by Span Wagner EoS (cP) ........................................... 54 Table 14-9 CO 2 Density Calculated by Peng Robinson EoS (kg/m and vs. SW) ............... 55 Table 14-10 CO 2 Cv Calculated by Peng Robinson EoS (kJ/kgK and vs. SW)................... 56 Table 14-11 CO 2 Cp Calculated by Peng Robinson EoS (kJ/kgK and vs. SW) .................. 57 Table 14-12 CO 2 Enthalpy Calculated by Peng Robinson EoS (kJ/kg and vs. SW) ........... 58 Table 14-13 CO 2 Entropy Calculated by Peng Robinson EoS (kJ/kg and vs. SW) ............. 59 Table 14-14 CO 2 Speed of Sound Calculated by Peng Robinson EoS (m/s and vs. SW) .. 60 Table 14-15 CO 2 Compressibility Calculated by Peng Robinson EoS (N/A, vs. SW) ......... 61 Table 14-16 CO 2 Viscosity Calculated by Peng Robinson EoS (cP and vs. SW) ............... 62 Table 14-17 CO 2 Density Calculated by Soave Redlich-Kwong EoS (kg/m and vs. SW) .. 63 Table 14-18 CO 2 Cv Calculated by Soave Redlich-Kwong EoS (kJ/kgK and vs. SW) ........ 64 Table 14-19 CO 2 Cp Calculated by Soave Redlich-Kwong EoS (kJ/kgK and vs. SW) ....... 65


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Table 14-20 CO 2 Enthalpy Calculated by Soave Redlich-Kwong EoS (kJ/kg and vs. SW) 66 Table 14-21 CO 2 Entropy Calculated by Soave Redlich-Kwong EoS (kJ/kg and vs. SW) .. 67 Table 14-22 CO 2 Speed of Sound Calculated by Soave Redlich-Kwong EoS (m/s and vs. SW) 68 Table 14-23 CO 2 Compressibility Calculated by Soave Redlich-Kwong EoS (N/A and vs. SW) 69 Table 14-24 CO 2 Viscosity Calculated by Soave Redlich-Kwong EoS (cP and vs. SW) .... 70

Table of Holds

HOLD Description1 Removed2 Literature search for better description on shortcut methods such as COSTALD

for density.3 Correlation for surface tension used within Multiflash.4 Evaluation of the program Promax for CO 2 modelling using the Span and Wagner

equation.5 Removed


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1 Executive Summary

E-on propose to build a new state of the art, coal fired power plant at Kingsnorth, which is on the Isle ofGrain. The CO 2 produced by this plant is intended to be captured and stored in the depleted Hewettreservoir, which is approximately 40 km East of Bacton, and approximately 270 km from Kingsnorth.Pre-FEED studies are currently underway to evaluate the potential to use these facilities as part of aCarbon Capture and Storage (CCS) project.

The broad concept has been selected: CO 2 will be captured from the flue gas at the proposed E-on coalfired power plant located at Kingsnorth. The CO 2 will then be purified, compressed and dried at a newonshore plant at Kingsnorth before being transported in a new pipeline to a new offshore platform, whichis located at the Hewett reservoir.

This Technical Note is intended to serve as a reference guide for physical properties used in the designand operation of carbon dioxide facilities. Reliable estimation of phase behaviour and physicalproperties of mixtures is essential for the analysis and simulation of the processing, compression andtransportation of CO 2 for carbon capture and storage (CCS). The data, models and methods required forthis purpose are collectively known as basic data. Various methods are available for estimation of anygiven property. These basic data methods may be different in the thermodynamic path followed tocalculate the property, selected models or databanks, or in all of these.

The transient multiphase flow simulator OLGA (SPT Group versions 5.3.2 and higher) will be the mainsimulation tool to be used for flow assurance studies for the Kingsnorth Carbon Capture and storageproject. A single component module must be used within OLGA for pure or nearly pure CO 2 to get astable solution when working close or crossing the vapour pressure line. The equation of state modelused within OLGA for the CO 2 single component module is the Span and Wagner Equation. The SpanWagner equation is a generalised corresponding states EOS that supersedes the earlier equationsprovided in the IUPAC tables for Carbon Dioxide (Ref. 8), and is now generally recognised by industryas the most accurate representation of the available experimental PVT data for CO 2 and its mixtures. Asummary of the likely errors associated with the prediction of various parameters is shown in Table 1-1overleaf.


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Table 1-1 Span Wagner Error vs. Experimental DataProperty Nomenclature Likely error vs.

experimental dataFluid density +/- 0.03% to 0.05%Speed of sound w +/- 0.03% to 1%Isobaric heat capacity c p +/- 0.15% to 1.5%Triple point temperature T t +/- 0.003KTriple point pressure p t +/- 0.00010 MPaTriple point saturated liquiddensity ' t +/- 0.18 kg/mTriple point saturated vapourdensity '' t +/- 0.0034 kg/m

Critical temperature T c +/- 0.015 KCritical pressure p c +/- 0.0030 MPaCritical density c +/- 0.6 kg/mMelting pressure

pm

p m /p m:+/- 1.5% for Tt


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method for calculating a given parameter. Reference is made to a limited list of proprietary computerprograms. Other programs with the same or similar functionality are available and may be used with theapproval of the project manager. However, if other programs are used it is strongly recommended thatthe results are compared against values generated using the recommended methods in order to quantifythe likely error. It is not recommended to use any other method than the Span and Wagner equation forPVT predictions in the near critical region (unless the results are only to be used for preliminary scopingstudies), since significant deviation is likely from experimental values.


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KCP-GNS-FAS-DRP-0001_02-ktKKDoc1--Equation of State Prediction ofCarbon Dioxide Properties

Printed on: 18-Jan-2011

Figure 1-1 Flow Diagram to Determine Recommended Calculation Method for Pure CO 2 and High Concentration CO 2 Mixtures


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KCP-GNS-FAS-DRP-0001_02-ktKKDoc1--Equation of State Prediction ofCarbon Dioxide Properties

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2 Abbreviations and Glossary

2.1 Abbreviations

BIP Binary Interaction ParameterCCS Carbon Capture and StorageCPA Cubic Plus Association equation of stateDEG Di-Ethylene GlycolEoS Equation of StateIUPAC International Union of Pure and Applied Chemistry

LNG Liquefied Natural GasMEG Mono-Ethylene GlycolMW Molecular WeightNGL Natural Gas LiquidsPR Peng-Robinson equation of statePVT Pressure, Volume and TemperatureSG Specific GravitySRK Soave-Redlich-Kwong equation of stateTBP True Boiling PointTEG Tri-Ethylene GlycolVLE Vapour Liquid EquilibriaVLLE Vapour Liquid Liquid Equilibria

2.2 Glossary of Terms

Basic Data Comprises all elements (data as well as programs) that are required to describeand predict the phase behaviour and physical properties of chemical mixtures at any specificcondition.

Binary interaction coefficient/parameter (BIP) A constant that accounts for the deviationfrom ideality for two component mixtures. These are specific to one equation of state as theyare calculated by regression of measured data.Equation of state An equation that describes the relationship between pressure,temperature, and molar volume for any homogenous fluid at equilibrium.

Fugacity - Translated literally it means escaping tendency and is an indication of the ability ofa component to move between phases. At equilibrium, the fugacities of all phases are equal.For ideal gases where intermolecular interaction is, by definition, negligible, the fugacity andpartial pressure of a component are identical.

Ideal Gas - An ideal gas is one where the volume occupied by the molecules is infinitesimalwhen compared to the total volume occupied by the gas and the intermolecular forces ofattraction approaches zero.

Principle of corresponding states - All gases when compared at the same reducedtemperature and pressure have approximately the same compressibility factor and all deviatefrom ideality to the same degree.


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Kingsnorth CCS Demonstration ProjectThe information contained in this document (the Information) is provided in good faith. E.ON UK plc, its subcontractors, subsidiaries, affiliates, employees, advisers, and the Department of Energy and Climate Change (DECC) make norepresentation or warranty as to the accuracy, reliability or completeness of the Information and neither E.ON UK plc nor any of its subcontractors,subsidiaries, affiliates, employees, advisers or DECC shall have any liability whatsoever for any direct or indirect loss howsoever arising from the use of theInformation by any party.

3 Thermodynamic Behaviour of Pure Carbon Dioxide

3.1 Phases of Carbon Dioxide

A phase diagram for carbon dioxide is shown in Figure 3-1 below (Ref 34) .

Figure 3-1 CO 2 Phase envelope

The carbon dioxide diagram has three distinct phases: liquid, vapour and solid. The triplepoint (-56.5 C, 5.18 bara) is defined as the temperature and pressure at which three phasescan coexist in equilibrium. Above the critical point (73.7 bara, 31.0 C) liquid and gas cannotexist in separate phases; this is termed the supercritical region. In this region, the fluid hasproperties indeterminable from liquid and vapour phase and is o ften referred to as densephase. The dense phase has a viscosity similar to a gas but a density similar to a liquid.

Liquid carbon dioxide forms only at pressures above 5.1 bar; at lower pressures CO 2 sublimes directly from the solid to the vapour phase.


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3.2 Overview of CO 2 Basic Properties

3.2.1 The Critical Region

Investigation of the properties of CO 2 has historically been influenced by the location of thecritical region. The critical temperature of 31 C allows the possibility that, during processingand transportation of CO 2, it may exist as either liquid, gas or a dense phase fluid and passthrough the critical region. There is a large range of experimental data in the critical regionwith good agreement and thus CO 2 has been used to test almost every model for thedescription of the critical region.

As all properties of the two phases are identical at the critical point, many properties therefore

change abruptly in the critical region, often by several orders of magnitude. This isdemonstrated below for several key properties of carbon dioxide.

3.2.2 Density as Function of Temperature and Pressure

The critical state of a fluid is defined as the pressure and temperature at which the density ofthe liquid and gas phases become identical. In the region near the critical point the density ofvapour starts to converge towards that of a liquid.

A common method of identifying the critical state is by identifying the density of the liquid andvapour phases at a given temperature and calculating the average of the two phase densities.The critical point is thus at the intersection of the average line with the extrapolated liquid /

vapour density line, as shown in Figure 3-2.

Temperature

Figure 3-2 Density vs. Temperature in the Critical Region (reproduced from Ref 3)

For a pure substance the critical temperature and pressure are the highest at which liquid and

vapour phases can coexist. This is clearly indicated by isobars of carbon dioxide in Figure3-1 and Figure 3-3 below.

D e n s

i t y


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Figure 3-3 CO 2 Density vs. Temperature

For a given pressure slightly above the critical pressure the density increases significantly asthe temperature is changed such that very small differences in temperature can result insignificant changes in fluid density. Similarly for a given temperature marginally above thecritical point a very small increase in pressure can result in a significant increase in fluiddensity.

The near critical region is defined here approximately as: 0.95 < Tr, Pr < 1.05

Where,Tr = T / T c T = actual temperature (K)Tc = critical temperature (K)P r = P / P c P = actual pressure (abs)P c = critical pressure (abs)

The critical temperature and pressure of CO 2 are 73.7 bar and 31.1 C respectively. CO 2 willtherefore begin to display near-critical behaviour at temperatures between:16C < T < 46.2C


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70 bara < P < 77.4 bara

3.2.3 Other Properties near Critical Pressure and Temperature

The isobaric and isochoric heat capacity of CO 2 are shown below (Ref 3) as a function ofpressure and temperature. The pressure and temperature are expressed in terms of thereduced properties T/T c and / c, as defined above. Similar plots for thermal conductivity,heat of vapourisation and compressibility are shown in Appendix 1.

As a liquid approaches the critical point, the latent heat of vapourisation approaches zero,heat capacity increases sharply and vapourisation equilibrium ratios become unity.Accordingly the performance of the process equipment in the onshore plant and fluid

behaviour in the offshore pipeline will be affected if they are operated near the critical point.

Figure 3-4 CO 2 Cp vs. Reduced Density and Temperature (reproduced from Ref 3)


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Figure 3-5 CO 2 Cv vs. Reduced Density and Temperature (reproduced from Ref 3)


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4 Basic Data for CO 2 Mixtures

4.1 Introduction

As noted earlier, reliable estimation of phase behaviour and physical properties of mixtures isessential for the analysis and simulation of CCS processes. Various methods are available forestimation of any given property. These basic data methods may be different in thethermodynamic path followed to calculate the property, selected models or databanks, or inall of these. Making an appropriate choice for a specific problem is important. Various factors,listed in Table 4-1, may affect the choice of basic data method.

Table 4-1 Important factors in basic data method selectionFactors Example

available/preferred simulation program PRO/II Aspen Plus, HYSYS,Multiflash, Prosim, PVTsim etc.

type of system pure component, binary or multi-component mixture

kind of physical property thermodynamic, transport,surface

nature of the substance(s) non-polar, polar, associatingfluidselectrolytes, polymers, solids

conditions of the system or process sub- or supercritical temperaturelow or high pressuredilute or concentrated mixtureexpected phase behaviour

required accuracy screening or design purposeimportance of missingparameters

availability of experimental data fit or estimate missingparameters

computational speed simple or complex model

Usually it is necessary to compute pure component properties as well as mixture propertiesusing one of the simulation programs. For most pure component property computations, the

choice of models/correlations is fairly straightforward, because of the availability of purecomponent databanks containing specific correlations for the required properties. For thecomputation of mixture properties however, few such data banks exist, and the choice of theappropriate model is complicated by the fact that all models have limitations in terms of thefactors listed in Table 4-1.

The main tools for process simulations are the commercial packages PRO/II, Aspen Plus,HYSYS, Promax, Multiflash, PVTsim, Pipesim, Olga and Eclipse. These are equipped with alarge number of standard basic data methods.


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4.2 Commercial Software Packages

The following software packages are commonly used in industry to obtain basic data:

Baker & Jardine PIPESIM: This is a steady state multi-phase pipeline network simulationpackage which includes descriptions of well performance and simple processing facilities.

CMG GEM: GEM (Generalised Equation of State Model Compositional Reservoir Simulator)is a full equation of state compositional reservoir simulator.

CMG STARS: STARS (Steam, Thermal and Advanced Processes Reservoir Simulator) is anumerical solution reservoir simulator designed for modelling three-phase, multi-componentfluids.

Halliburton WELLCAT: This is a casing design software package which can be used forwellbore analysis and integrated casing and tubing design.

Hyprotech Programs: HYSYS is a fully integrated steady-state and dynamic processflowsheeting program. It exists in several flavors such as: HYSYS.Process, HYSYS.Plant-,HYSYS.Plant, and HYSYS.Refinery. DISTIL is primarily a physical properties package whichcan be used for conceptual process design (process synthesis).

Infochem Multiflash: Multiflash is a software package which performs multiphase equilibriumcalculations. Specialised applications such as solids formation, hydrate formation andinhibition, wax thermodynamics and deposition may be performed to a higher degree ofaccuracy than that achieved using general flowsheeting software.

NIST REFRPOP: National Institute of Science and Technology Reference Properties is aprogram using equations for the thermodynamic and transport properties to calculate thestate points of the fluid or mixture (Ref 10) . For carbon dioxide the Span Wagner equation ofstate is utilised.

Promax (by Bryan Research and Engineering) - Glycol BTEX systems: Promax is a general-purpose flowsheeter similar to HYSYS and PRO/II and can be used for hydrocarbonprocessing simulation. Promax has been recommended for simulation of glycol systems(MEG, DEG, TEG) as all of the GPA data on hydrocarbon/glycol solubility has been used totune the equation of state. Its ability to predict aromatic absorption into glycol better thansome competitor's programs has been proven in service. The Span and Wagner equation isavailable for the prediction of CO

2properties. Promax will be evaluated in the next edition of

this report (HOLD).

Petroleum Experts Prosper is a well performance, design and optimisation program formodelling well configurations. It may be used in conjunction with MBAL and GAP to modelassociated reservoirs and pipeline systems respectively.

Scandpower OLGA (v5.3.2 or higher): This is a transient simulator for multiphase pipelinesand networks, which includes descriptions of well performance and simple process facilities.Can simulate three phases (gas, oil, water), and has special feature for slugtracking ofgas/liquid slugs. A single component module has recently been added to allow simulation ofpure CO 2. The Span and Wagner equation is used for the thermodynamics prediction of theCO 2 properties.


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Schlumberger Eclipse: This is the benchmark reservoir simulation tool in the upstream oiland gas industry. Black oil and compositional models are available for predicting the dynamicbehaviour of a variety of reservoir types.

The equations of state (or calculation method if not a full EoS model) available for pure CO2and CO2 mixtures within the software packages likely to be utilised within this project aresummarised in Table 4-2.

Table 4-2 Equations of State Available in Software Packages for CO 2 SimulationSoftware Package Equation of State NotesEclipse N/A Black Oil Methodology

GEM / STARS PR (1)SRK (2)

Both 1976 and 1978 versions of PR available fora constant. Original and G&D a constants available for SRK.

HYSYS PRSRK

Multiflash Span WagnerCSMAPRRKSRK

The CO2 high accuracy model uses SW forequilibrium properties for pure CO2 andcorresponding states approach to determine theproperties of mixtures.

Olga Span Wagner CO 2 can currently only be modelled as a purecomponent within Olga i.e. cannot model CO 2 mixtures.

Promax Span WagnerPRSRK

Span Wagner may only be utilised for pure CO2streams; mixtures should be modelled using PRor SRK

Prosper PRSRK


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5 Property Calculation Methods

5.1 Corresponding States Correlations

The principle of corresponding states is based on Van der Waals theorem that all fluids, whencompared at the same reduced temperature and reduced pressure, have approximately thesame compressibility factor and all deviate from ideal gas behaviour to approximately thesame degree.

Material constants that vary for each type of material are eliminated, in a recast reduced formof a constitutive equation. The reduced variables are defined in terms of critical variables, i.e.

reduced pressure P r and reduced temperature T r, as defined above (P/P c and T/T c respectively).

The most prominent example is the van der Waals equation of state, the reduced form ofwhich applies to all gases/fluids.

The Span Wagner Equation of State is a form of corresponding states correlation, in thatphysical properties may be calculated as a function of reduced temperature and pressure.

5.2 Equations of State

5.2.1 Introduction

One of the first equations of state (EoS) that could quantitatively represent phase behaviour,at least for non-polar mixtures, was the still popular SRK equation of state proposed by Soavein 1972. More developed forms have been published since then, such as PR (1976) andvolume translation term variants such as Peneloux. Various equation of state options areavailable in simulation programs.

An equation of state requires pure-component properties and parameters. For application tomixtures it uses mixing rules for the EoS-parameters. These mixing rules contain one or morebinary interaction parameters (BIPs) that account for the effects of mixing dissimilarcompounds. The BIPs are used to tune the model predictions to experimental mixture data.For accurate mixture property predictions, optimised values for the BIPs of, at least, theimportant component pairs must be available in the database.

Both the SRK and the PR equation of state are very suitable for the calculation of the vapour-liquid equilibrium properties of dry oil and gas mixtures. One of the weaknesses of these EoS,the inaccurate liquid density prediction, can be overcome by making use of a separate liquiddensity method. Another disadvantage is that liquid-liquid equilibrium calculations cannot beperformed accurately, due to simplicity of the mixing rules.


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5.2.2 Soave Redlich-Kwong (SRK)

DescriptionThe temperature coefficients of the a parameter have been regressed from vapour pressuredata for methane to decane and many simple compounds such as CO 2. The b -parameter istaken constant. Binary interaction parameters are available to account for non-polar andweakly polar interactions.

ValidityThe prediction of liquid density is very poor (but see key points below). The mixing rule issimple, and therefore it cannot be used for polar compounds.

Application

Light, C 1-C10 , hydrocarbons. Simple water handling capability. Not for polar components or forheavy components above C 20 . May be used for CO 2 mixtures for a wide range of operatingconditions, though it is not applicable in the near-critical region.

Key PointsRobust and well proven. Ideal for use in basic flowsheeting problems.

Liquid densities should be calculated using a different method; this is defaulted to an APImethod in PRO/II and a API/Rackett method in Aspen Plus. The latter methods are, however,less accurate for liquid-like supercritical fluids. COSTALD is recommended for liquid densitiesof light hydrocarbons 1. HYSYS uses the COSTALD method as a default for all propertysystems for mixtures/streams with a pseudo-critical temperature below unity; for highertemperatures, the equation of state chosen is used.

5.2.3 Peng Robinson (PR)

DescriptionAnother modification of the van der Waals equation aimed at improving liquid densityprediction. The accuracy for CO 2 prediction has not yet been tested, but will be reported inthe next version of this technical note.

ValiditySame as SRK but prediction of liquid density is better than the SRK derivatives, none the lessit is still poor for heavier hydrocarbons (>C 3). Pressure range is extended (up to 1000 bar).

May be used for CO 2 mixtures for a wide range of operating conditions, though it is notapplicable in the near-critical region.

ApplicationAs SRK.

Key PointsRobust and well proven. Ideal for simple heat and mass balances, but liquid density shouldalways be calculated by a different method (as per SRK above). HYSYS was designed withthe PR equation of state in mind with special treatment for systems containing H 2, He, N 2,CO 2, H 2S, methanol, EG and TEG.

1 Although it is assumed that no hydrocarbons are carried over from the capture plant there will be small quantities oflight hydrocarbons remaining in the reservoir


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5.2.4 CPA (Cubic Plus Association)

DescriptionAn equation of state covering associating (hydrogen bonding) substances. To the basic cubicform, terms are added which explicitly account for hydrogen bonding type (association)interactions. For non-associating substances, the equation defaults to standard SRK; forthese components, pure component parameters are obtained as for SRK. For associatingcomponents, such as water, the parameters include association constants, and theparameters have to be determined simultaneously.

ValidityThis equation should be used for specific applications, where the standard models are knownto be inadequate. For example, the predictions for the partitioning of methanol over aqueous

and hydrocarbon phase, which is needed to predict the amount of methanol required for gashydrate inhibition, are more reliable than those obtained with other models. The availability ofparameters, especially for associating components, should always be checked.

ApplicationGas hydrate inhibition by methanol. Specific chemical systems.

5.2.5 Span Wagner

DescriptionEmpirical equation of state in the form of a fundamental equation explicit in the Helmholtz free

energy, developed specifically to cover the fluid region of carbon dioxide above the triplepoint.

ValidityThis equation is valid for equilibrium thermodynamic properties of carbon dioxide in the fluidregion up to temperatures of 1100 K (827 C) and pressures up to 800 MPa (8000 bar). TheEoS was developed with special interest focussed on the behaviour of thermal properties inthe critical region and extrapolation behaviour of empirical equations of state. It is thereforeable to represent thermal properties and speed of sound in the immediate vicinity of thecritical point.

ApplicationCarbon dioxide systems. Although developed for pure carbon dioxide, the EoS can be used

for CO 2 mixtures, with appropriate binary interaction coefficients.Key PointsThis equation is now generally regarded as the preferred method for equilibriumthermodynamic properties of CO 2 and its mixtures and supersedes the earlier equationssupplied for the IUPAC tables of CO 2 (Ref. 8).

5.2.6 Missing / Upgrading Binary Parameters

When dealing with properties of mixtures composed of dissimilar compounds, the contributionof BIPs is often crucial to quantitative model predictions. In such cases, their presence shouldalways be checked.


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In principle, BIPs are required for pairs of components that differ in size, shape and especiallyin polarity. The more dissimilar the components, the more non-ideal the mixing process andthe more important their BIP. BIPs for pairs of trace components are relatively unimportant.For missing or inadequate BIPs of important binaries, a similar binary can possibly beselected in the short term in advance of experimental data.

More reliable model predictions are obtained when the missing or incorrect BIPs areregressed from experimental data. Preferably, binary parameters should be based on datacovering the temperature, pressure and composition range relevant to the problem at hand.Here some problems may be encountered as model parameters often depend on the type ofdata, e.g., VLE or LLE data. Therefore, different parameter sets may sometimes be neededfor different process units.

When important BIP's are missing or suspect, basic data specialists should be contacted foradvice.

5.3 Special Methods

5.3.1 Introduction

Various methods customised to specific applications are available in stand-alone programs.These methods are generally more accurate but limited to the particular application range.For example, for water, a multi-term equation of state fitted to data from the Steam-Tables isavailable for the calculation of all thermodynamic properties along with special correlations fortransport properties. Similarly, natural gas custody transfers require a highly accurate EoS forthe calculation of compressibility factors.

Besides special models and special correlations (black oil correlations), there are standardmethods equipped with a special parameter package optimized to a specific process orprocess-unit.

5.3.2 Alcohol (Hydrate Mitigation)

Methanol and glycol are commonly used as hydrate inhibitors in the upstream oil and gasindustry. Modelling of alcohol partitioning between liquid, vapour and aqueous phases is

therefore required for hydrate inhibition calculations. This can be performed in a variety ofsoftware packages with varying degrees of accuracy. Note that the equation of state selectedmay greatly influence the partitioning results due to the polarity of such alcohols. Multiflashsoftware is proven in service for alcohol partitioning between hydrocarbon phases in the oiland gas industry.

It is assumed that methanol would be utilised if hydrate inhibition were required, as it is morevolatile than glycol and thus more suited to transportation in the vapour phase.

5.3.3 Solids

In phase behaviour calculations on oil, gas and chemical systems, a solid phase maysometimes be encountered.


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Carbon dioxide may exist as a solid at low temperatures. This has implications for theoperation of the conditioning, compression and transportation processes, as low temperaturesmay potentially be encountered when equipment or pipelines are depressurised. Thetemperature and pressure of solid CO 2 formation can generally be predicted in most commonthermodynamic packages, however modelling of the vapour / solid equilibrium is restricted tomore specialised packages such as Multiflash.

It should be noted that any solid CO 2 formed is likely to be pure CO 2. This means that thevapour phase could be rich in incompressible gas, which is likely to increase the deviationfrom pure CO 2 properties and behaviour.

Gas hydrate and ice utilities are available in most modern thermodynamic packages. Thesecalculate the temperature and pressure of gas hydrate formation, however the approach ofthese programs is not as rigorous as some other more specialised, packages such asMultiflash.

5.4 Thermodynamic Property Methods

5.4.1 COSTALD Liquid Density

The corresponding states liquid density methods are used for "LNG like" mixtures withexcellent accuracy. The COSTALD method uses two parameters to modify the individual purecomponent densities; one based on the acentric factor and one on experimental density data.It also corrects for high pressures using the Tait correlation. The method is valid for lighthydrocarbons between C 1-C8 only, as it was developed with data for light C 1-C5 hydrocarbonsand thus should not be used outside this range. There are no limits on pressure but thereduced temperature should be between 0.25 and 1.0.

This application is best suited for use with equations of state that cannot predict liquiddensities in light hydrocarbon systems. The applicability to CO 2 and its mixtures will beincluded in future revisions of this technical note.

5.4.2 Equilibrium Properties

Using an equation of state a variety of properties of a mixture can be derived which are ofinterest to many CCS applications. The equation of state presented by Span and Wagner(Ref 2) can be used for the following equilibrium properties of carbon dioxide mixtures:

Phase equilibriaVapour pressureDensityCritical PointTriple PointEnthalpyEntropyJoule-Thomson coefficientIsobaric and isochoric heat capacityThermal expansion coefficientSurface tensionSpeed of soundPhase transitions

o Fusiono Vapour / liquid


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5.5 Transport Properties

The thermodynamic properties of fluids often determine the feasibility of a proposed processdesign, while the transport properties of the fluids determine the type and size of theequipment and the timescale of the operations. The trend to minimize costs through processintegration and energy minimization has increased the need for reliable estimates of transportproperties.

Two types of methods for the transport properties of mixtures are available: i) model-basedpredictions and ii) correlations primarily developed for oils or condensates, based on bulk fluidproperties. The first class of methods is discussed in this technical note while the secondclass of methods is often used in reservoir simulation programs that run in non-compositional(black oil) modes.

Corresponding states correlations may be used for the following transport properties:

ViscosityDiffusionThermal conductivity

Vesovic et al (Ref 6) present representative equations for the viscosity and thermalconductivity of carbon dioxide; these are utilised within Multiflash. The correlations are shownas a function of temperature and pressure in Appendix 5.

5.5.1 Liquid and Vapour Viscosity

The term viscosity in this document stands for dynamic (absolute) viscosity, while thekinematic viscosity is simply obtained as the ratio of dynamic viscosity and density.

Accurate prediction of viscosity of a mixture is rather difficult to achieve. Only for well-behaved mixtures (e.g. hydrocarbon) errors within 10 % may be expected. Nearly all themethods rely on critical data developed from equations of state, and so the choice of thesedirectly affects the accuracy of the results. This is particularly true for CO 2 mixtures withprocess solvents such as amines or glycols. If accurate viscosity data is required for designpurposes, it should be measured in a laboratory at the relevant conditions.

The high accuracy CO 2 model within Multiflash utilises the correlation of Fenghou et al (Ref11) to estimate the liquid and vapour viscosity of CO 2.

5.5.2 Diffusivity Methods

In Aspen Plus and PRO/II, the diffusion coefficient of a component in a liquid mixture can becalculated with the Wilke-Chang method which uses liquid viscosity, molar volume, andmolecular weight as input.

5.5.3 Surface Tension


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Surface tension data are used in calculations of heat transfer, distillation column flooding andloading, and the wetting of packing materials. Surface tensions of liquid mixtures areconsidered here only. For interfacial tension data of liquid-liquid systems special correlationsshould be used or measurements should be carried out.

Multiflash utilises the Macleod-Sugden surface tension method (Ref 9) to predict surfacetension for pure components based on parachors stored in the Multiflash databank. Theliquid and vapour molar densities and liquid and vapour mole fractions calculated from theSpan Wagner correlations are also utilised. The surface tension for liquid mixtures isobtained by applying a mixing rule to the pure component saturated liquid surface tensions.

5.5.4 Thermal Conductivity

The thermal conductivity formulation used in the CO 2 high accuracy model within Multiflash isthat of Scalabrin et al (Ref 12).


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6 Selection of Method to Determine CO 2 Property Data

6.1 Selected Equations of State for Equilibrium Properties

6.1.1 Flow Assurance

The Span Wagner equation of state will be used to model the equilibrium thermodynamicproperties of carbon dioxide throughout the flow assurance studies, unless specificallyindicated otherwise. The circumstances in which it is envisaged that a correlation other thanSpan Wagner will be used are illustrated in Appendix 6.

6.1.2 Process Plant

The Span Wagner equation of state was designed for pure CO 2 and thus may only be usedwith very high purity CO 2 streams. It is therefore not applicable to the CCS plant, which willcontain a mixture of process gases, for which there a number of reliable proven equations ofstates, such as Peng Robinson. MHI (Mitsubishi Heavy Industries) modelling will also beutilised, which is based on experimental data from previous pilot and commercial plants.

6.1.3 Equipment Design

It is presumed that most vendors will have proprietary programs to model properties orbehaviour that are particularly important for the equipment being designed; e.g. water content

for compressor design. While equations of state (Span-Wagner, PR, SRK) can modelgeneral properties of water-saturated CO 2 sufficiently for the purposes of basic equipmentsizing, it is recommended that vendor packages are used to model water drop-out and otherpertinent properties specific to the equipment design.

6.2 Selected Correlations for Transport Properties

The correlations of Vesovic et al, Fenghou et al and Scalabrin et al (Ref 6, 11 an d12respectively) will be used within Multiflash to model the thermal conductivity and viscosity ofcarbon dioxide. The Macleod-Sugden method will be used to model the surface tension(HOLD).

6.3 Likely Errors

The Span Wagner EoS will be used to model the equilibrium thermodynamic properties ofcarbon dioxide throughout the flow assurance studies, unless specifically indicated otherwise.The likely errors (vs. experimental data) for pure carbon dioxide systems are defined below.

The likely error vs. experimental data for carbon dioxide mixtures is more difficult to quantify,as there is limited experimental data on CO 2 systems with a similar composition to thatexpected for the CO 2 stream from Kingsnorth Power Station.


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6.3.1 Experiments

The likely errors in the Span Wagner equation of state for pure CO 2 compared to the availableexperimental data are shown in Table 6-1.

Table 6-1 Span Wagner Error vs. Experimental DataProperty Nomenclature Likely error vs.

experimental dataFluid density +/- 0.03% to 0.05%Speed of sound w +/- 0.03% to 1%Isobaric heat capacity c p +/- 0.15% to 1.5%Triple point temperature T t +/- 0.003KTriple point pressure p t +/- 0.00010 MPaTriple point saturated liquiddensity ' t +/- 0.18 kg/mTriple point saturated vapourdensity '' t +/- 0.0034 kg/mCritical temperature T c +/- 0.015 KCritical pressure p c +/- 0.0030 MPaCritical density c +/- 0.6 kg/mMelting pressure

pm

p m /p m:+/- 1.5% for Tt


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0

10

20

30

40

50

60

70

80

90

-70 -50 -30 -10 10 30 50

P r e s s u r

e (

b a r a

)

Temperature (deg C)

Carbon Dioxide Phase Diagram(Multiflash 100% and 95% Compositions)

Dewpoint 95%

Bubblepoint 95%

Pure CO2

Figure 6-2 Comparison of 100% CO 2 and 95% CO 2 Phase Diagrams

Note that the phase envelope feature did not work for the 95% composition; instead the dewpoints and bubble points were calculated individually and used to create bubble and dewlines.

A table of results is shown in Appendix 4.

6.4 Comparison of Calculation Methods for Pure CO 2

The following physical properties of pure CO 2 were calculated at a range of temperatures andpressures using all the methods which will be utilised in this project:

DensitySpecific heat capacity (constant pressure)Specific heat capacity (constant volume)EnthalpyEntropySpeed of SoundCompressibility FactorViscosity

These were used to generate property tables, which could be compared for differentequations of state. The reference pressures and temperatures used are illustrated in Figure6-3.


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Figure 6-3 Reference Conditions for Property Tables

The property tables are provided in full in Appendix 7 Property Tables. Data has beenprovided for commonly available equations of state data for proprietary packages will beadded once this is made available (HOLD). Property tables for density (as calculated bySpan Wagner, Peng Robinson and Soave Redlich-Kwong) are shown below as an example.Note that the liquid viscosity correlation selected for PR and SRK was Lohrenz-Bray-Clark,which is a reduced density model.

key:liquidvapoursupercritical

Figure 6-4 Key to Fluid Phase on Property Tables


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Table 6-2 CO 2 Density Calculated by Span Wagner EoS (kg/m)Temperature

( C)Pressure (bara)

1.01 30 40 50 60 70 74 80 100 150-20 2.13 1036.33 1040.67 1044.85 1048.88 1052.77 1054.29 1056.53 1063.72 1080.030 1.97 77.34 932.11 940.52 948.20 955.31 958.02 961.94 974.05 999.53

10 1.90 71.01 108.41 868.63 881.78 893.11 897.25 903.13 920.46 954.1820 1.83 66.16 97.49 140.65 782.65 808.60 816.82 827.71 856.31 903.9630 1.77 62.21 89.76 124.02 171.44 266.56 647.42 701.72 771.50 846.9831 1.77 61.85 89.10 122.74 168.55 252.22 565.95 679.73 761.01 840.8132 1.76 61.50 88.45 121.51 165.87 241.66 314.99 652.12 749.98 834.5333 1.75 61.16 87.81 120.33 163.36 233.22 288.25 613.68 738.34 828.1535 1.74 60.49 86.59 118.08 158.79 220.08 259.77 419.09 712.81 815.06

40 1.71 58.89 83.76 113.05 149.26 198.02 224.07 277.90 628.61 780.2350 1.66 56.03 78.86 104.85 135.21 172.02 189.32 219.18 384.33 699.7560 1.61 53.52 74.73 98.30 124.91 155.53 169.21 191.62 289.95 604.0980 1.52 49.29 68.03 88.23 110.14 134.06 144.27 160.34 221.60 427.15

100 1.44 45.82 62.75 80.65 99.63 119.80 128.23 141.28 188.56 332.35120 1.36 42.89 58.41 74.61 91.54 109.24 116.54 127.74 167.31 280.36


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Table 6-3 CO 2 Density Calculated by Peng Robinson EoS (kg/m and vs. SW)Temperature

( C)Pressure (bara)

1.01 30 40 50 60 70 74 80 100 150

-20 2.13 1033.23 1039.74 1045.94 1051.86 1057.52 1059.72 1062.95 1073.18 1095.80

0.0% -0.3% -0.1% 0.1% 0.3% 0.5% 0.5% 0.6% 0.9% 1.5%

0 1.97 77.88 900.04 913.17 925.04 935.90 940.01 945.93 964.00 1000.95

0.0% 0.7% -3.4% -2.9% -2.4% -2.0% -1.9% -1.7% -1.0% 0.1%

10 1.90 71.85 109.66 817.39 837.78 855.16 861.48 870.40 896.41 945.73

0.0% 1.2% 1.2% -5.9% -5.0% -4.2% -4.0% -3.6% -2.6% -0.9%

20 1.83 67.04 99.14 143.12 706.08 744.71 756.86 772.92 814.90 883.89

0.0% 1.3% 1.7% 1.8% -9.8% -7.9% -7.3% -6.6% -4.8% -2.2%

30 1.77 63.06 91.37 126.69 175.43 269.79 551.08 617.82 709.99 814.080.0% 1.4% 1.8% 2.2% 2.3% 1.2% -14.9% -12.0% -8.0% -3.9%

31 1.77 62.70 90.69 125.39 172.54 256.52 470.36 593.02 697.49 806.61

0.0% 1.4% 1.8% 2.2% 2.4% 1.7% -16.9% -12.8% -8.3% -4.1%

32 1.76 62.34 90.03 124.14 169.84 246.44 316.46 563.51 684.50 799.04

0.0% 1.4% 1.8% 2.2% 2.4% 2.0% 0.5% -13.6% -8.7% -4.3%

33 1.76 61.99 89.38 122.93 167.31 238.23 291.96 526.03 670.96 791.37

0.0% 1.4% 1.8% 2.2% 2.4% 2.1% 1.3% -14.3% -9.1% -4.4%

35 1.74 61.30 88.13 120.63 162.65 225.23 264.77 400.25 642.07 775.75

0.0% 1.4% 1.8% 2.2% 2.4% 2.3% 1.9% -4.5% -9.9% -4.8%

40 1.72 59.67 85.22 115.45 152.87 202.94 229.32 282.27 556.57 734.960.0% 1.3% 1.7% 2.1% 2.4% 2.5% 2.3% 1.6% -11.5% -5.8%

50 1.66 56.74 80.16 106.93 138.26 176.10 193.75 223.87 372.26 646.58

0.0% 1.3% 1.6% 2.0% 2.3% 2.4% 2.3% 2.1% -3.1% -7.6%

60 1.61 54.15 75.86 100.10 127.48 158.90 172.85 195.55 290.57 554.32

0.0% 1.2% 1.5% 1.8% 2.1% 2.2% 2.2% 2.1% 0.2% -8.2%

80 1.52 49.78 68.90 89.56 111.98 136.39 146.76 163.03 223.84 406.91

0.0% 1.0% 1.3% 1.5% 1.7% 1.7% 1.7% 1.7% 1.0% -4.7%

100 1.44 46.20 63.40 81.62 100.95 121.44 129.97 143.15 190.31 325.110.0% 0.8% 1.0% 1.2% 1.3% 1.4% 1.4% 1.3% 0.9% -2.2%

1201.36 43.18 58.90 75.32 92.48 110.39 117.76 129.04 168.54 276.960.0% 0.7% 0.8% 1.0% 1.0% 1.1% 1.0% 1.0% 0.7% -1.2%


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Table 6-4 CO 2 Density Calculated by Soave Redlich-Kwong EoS (kg/m and vs. SW)Temperature

( C)Pressure (bara)

1.01 30 40 50 60 70 74 80 100 150

-20 2.13 932.91 939.61 945.97 952.03 957.82 960.06 963.36 973.78 996.75

0.0% -10.0% -9.7% -9.5% -9.2% -9.0% -8.9% -8.8% -8.5% -7.7%

0 1.97 76.34 811.33 824.38 836.12 846.83 850.87 856.70 874.42 910.60

0.0% -1.3% -13.0% -12.3% -11.8% -11.4% -11.2% -10.9% -10.2% -8.9%

101.90 70.53 106.70 737.66 757.51 774.32 780.41 789.00 813.96 861.25

-0.01% -0.67% -1.58%-

15.08%-

14.09%-

13.30% -13.02%-

12.64% -11.57% -9.74%

201.8 65.9 96.7 138.3 639.3 676.1 687.6 702.7 742.0 806.6

0.00% -0.39% -0.79% -1.68%

-

18.31%

-

16.38% -15.82%

-

15.11% -13.35% -10.77%

30 1.77 62.04 89.31 122.90 168.58 255.21 506.65 567.10 650.51 745.56

0.0% -0.3% -0.5% -0.9% -1.7% -4.3% -21.7% -19.2% -15.7% -12.0%

31 1.77 61.69 88.66 121.68 165.91 243.29 435.97 545.64 639.69 739.05

0.0% -0.3% -0.5% -0.9% -1.6% -3.5% -23.0% -19.7% -15.9% -12.1%

32 1.76 61.35 88.03 120.50 163.41 234.18 298.24 520.20 628.46 732.47

0.0% -0.3% -0.5% -0.8% -1.5% -3.1% -5.3% -20.2% -16.2% -12.2%

33 1.75 61.01 87.41 119.36 161.06 226.72 276.05 488.12 616.78 725.81

0.0% -0.2% -0.5% -0.8% -1.4% -2.8% -4.2% -20.5% -16.5% -12.4%

35 1.74 60.34 86.22 117.19 156.74 214.86 251.32 378.73 591.90 712.26

0.0% -0.2% -0.4% -0.8% -1.3% -2.4% -3.3% -9.6% -17.0% -12.6%

40 1.71 58.76 83.43 112.30 147.63 194.39 218.87 267.98 518.37 676.94

0.0% -0.2% -0.4% -0.7% -1.1% -1.8% -2.3% -3.6% -17.5% -13.2%

50 1.66 55.92 78.57 104.23 133.95 169.53 186.04 214.13 352.95 600.46

0.0% -0.2% -0.4% -0.6% -0.9% -1.4% -1.7% -2.3% -8.2% -14.2%

60 1.61 53.41 74.45 97.72 123.80 153.49 166.61 187.89 276.70 519.68

0.0% -0.2% -0.4% -0.6% -0.9% -1.3% -1.5% -2.0% -4.6% -14.0%

80 1.52 49.16 67.74 87.67 109.13 132.35 142.18 157.55 214.69 385.86

0.0% -0.3% -0.4% -0.6% -0.9% -1.3% -1.4% -1.7% -3.1% -9.7%

100 1.44 45.66 62.43 80.06 98.64 118.23 126.36 138.87 183.44 309.890.0% -0.3% -0.5% -0.7% -1.0% -1.3% -1.5% -1.7% -2.7% -6.8%

120 1.36 42.72 58.07 74.01 90.56 107.74 114.80 125.56 163.05 265.100.0% -0.4% -0.6% -0.8% -1.1% -1.4% -1.5% -1.7% -2.5% -5.4%


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6.5 Mollier and Phase Diagrams

The ChemicaLogic Mollier and phase diagrams for pure CO 2 (Ref 1) are recommended asgeneral methods for both pure CO 2 and the 99.94% mixture of CO 2. The diagrams areavailable in the form of excel spreadsheets which allow process information (such as thethermodynamic path through a unit operation) to be superimposed on top of the diagram.The diagrams should be used with care for the lower concentration CO 2 mixture. The Mollierand phase diagrams are shown in Figure 6-5 and Figure 6-6 respectively.

M e

l t i n g

L i n e

- 4 0

- 4 0 o C

t = 0 o

C

0 2 0

4 0

4 0

6 0

6 0

8 0

8 0

1 0 0

1 0 0

1 2 0

1 2 0

1 4 0

1 4 0

1 6 0

1 6 0

1 8 0

1 8 0

2 0 0

2 0 0

2 2 0

2 2 0

2 4 0 o C

2 6 0

2 8 0

Trip le Point (5.18 bar, -56.558 oC)

S u

b l i m a

t i o n

L i n e

r = 150

r = 100

r = 75

r = 50

r = 35

r = 10

r = 25

r =15

r = 8

r = 6

1

10

100

1,000

-500 -400 -300 -200 -100 0 100 200

P r e s s u r e ,

B a r

Enthalpy, kJ/kg

Carbon Dioxide: Pressure - Enthalpy Diagram

Drawn with CO 2Tab TMA Spreadsheet Add-in for the Thermodynamic andTransport Properties of Carbon Dioxide

Copyright 1999ChemicaLogic Corporation

www.chemicalogic.com

Figure 6-5 CO 2 Pressure-Enthalpy Diagram


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Figure 6-6 CO 2 Pressure-Temperature Diagram


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7 References

1. CO 2 Phase Diagram and CO 2 Enthalpy Diagram, ChemicaLogic Corp, Genesisreference J71018A_CRRPDC_IN_091

2. A New Equation of State for Carbon Dioxide Covering the Fluid Region from theTriple-Point Temperature to 1100K at Pressures up to 800 MPa, Span and Wagner,1996

3. Phase Equilibrium in Chemical Engineering, S. M. Wallas, Butterworth, 1985

4. Liquids and Liquid Mixtures, Rowlinson & Swinton, Butterworth, 1982

5. Chemical Engineering at Supercritical Conditions, M.E.

6. Transport Properties of Carbon Dioxide, Vesovic et al, 1989.

7. Basis of Design for Studies Phase 1A, J71584-GEN-0001 Rev 01, April 2010

8. S Angus et al, International Thermodynamic Tables of the Fluid state Carbon dioxide,IUPAC, Pergamon Press, 1976

9. Relation Between Surface Tension and Density, D. B. Macleod, Trans. Faraday Soc. ,19, 38-41, 1923

10. Lemmon, E.W., Huber, M.L., McLinden, M.O. NIST Standard Reference Database23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version8.0, National Institute of Standards and Technology, Standard Reference DataProgram, Gaithersburg, 2007.

11. The Viscosity of Carbon Dioxide, A. Fenghou, W.A. Wakeham and V. Vesovic, J.Phys. Chem. Ref. Data., Vol. 27, 31 (1998)

12. A Reference Multiparameter Thermal Conductivity Equation for Carbon Dioxide withan Optimized Functional Form, G. Scalabrin, P. Marchi, F. Finezzo and R. Span, J.Phys. Chem. Ref. Data., Vol. 35, 1549 (2006).


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8 Appendix 1 CO 2 Properties as Functions of Reduced Properties

A variety of equilibrium properties of carbon dioxide are shown below as a function of reduceddensity and reduced pressure, reproduced from Ref 3.

Figure 8-1 CO 2 Thermal Conductivity vs. Reduced Density and Temperature


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Figure 8-2 CO 2 Expansion Coefficient vs. Reduced Density and Temperature


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Figure 8-3 CO 2 Heat of Vapourisation vs. Temperature


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Figure 8-4 CO 2 Compressibility vs. Reduced Density and Temperature


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Figure 8-5 Velocity of Sound vs. Reduced Density and Temperature


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9 Appendix 2 Multiflash Files

The Multiflash fluid files to be utilised for the 100%, 99.94% and 95% CO 2 compositions areincluded below. These incorporate the

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6.23 Equation of State Prediction of Carbon Dioxide Properties

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