pvts im method doc

Method Documentation

PVTsim 20

PVTsim Method Documentation Contents 2

Contents

Introduction 7Introduction ............................................................................................................................... 7

Pure Component Database 8Pure Component Database.........................................................................................................8

Component Classes .....................................................................................................8Component Properties ............................................................................................... 10User Defined Components ........................................................................................ 12Missing Properties.....................................................................................................12

Composition Handling 14Composition Handling............................................................................................................. 14

Types of fluid analyses .............................................................................................. 14Handling of pure components heavier than C6 .......................................................... 15Fluid handling operations .......................................................................................... 16Mixing ....................................................................................................................... 16Weaving .................................................................................................................... 16Recombination........................................................................................................... 16Characterization to the same pseudo-components..................................................... 16

QC of Fluid 18QC of Fluid .............................................................................................................................. 18

Bottomhole samples ..................................................................................................18STO Oil Density (bottomhole) .................................................................................. 19GOR (bottomhole).....................................................................................................20Critical Point/Fluid Type (bottomhole) .....................................................................20C7+ Molar Distribution (bottomhole) .........................................................................20Plus Component Amount (bottomhole).....................................................................20Plus Molecular Weight (bottomhole) ........................................................................20Plus Component Density (bottomhole) .....................................................................21Bottomhole Sample Saturation Pressure (bottomhole).............................................. 21Bottomhole Flowing Pressure (bottomhole).............................................................. 21Sample Cylinder Shutting/Opening Pressures (bottomhole) .....................................21Test Separator GOR (bottomhole)............................................................................. 21Test Separator Oil Density (bottomhole)...................................................................22OBM Contamination (bottomhole) ........................................................................... 22Separator Samples .....................................................................................................22STO Oil Density (separator)...................................................................................... 23Separator GOR (separator) ........................................................................................ 23Separator Conditions (separator) ............................................................................... 23Saturation Temperature Separator Gas (separator).................................................... 24Saturation Pressure Separator Oil (separator)............................................................ 24K-Factor Plot (separator)........................................................................................... 24Mass Balance Closure Plot (separator)......................................................................24Hoffmann Plot (separator) ......................................................................................... 25C7+ Molar Distribution (separator) ............................................................................ 25Plus Component Amount (separator) ........................................................................25

PVTsim Method Documentation ContentsIntroduction 3

Plus Molecular Weight (separator)............................................................................ 26Plus Fluid Density (separator) ................................................................................... 26Critical Point/Fluid Type (separator).........................................................................26References ................................................................................................................. 27

Flash Algorithms 27Flash Algorithms ..................................................................................................................... 27

Flash Options............................................................................................................. 28Flash Algorithms .......................................................................................................28K-factor Flash............................................................................................................ 31Other Flash Specifications......................................................................................... 32Phase Identification ...................................................................................................33Components Handled by Flash Options ....................................................................33References ................................................................................................................. 34

Phase Envelope and Saturation Point Calculation 36Phase Envelope and Saturation Point Calculation ...................................................................36

No aqueous components............................................................................................ 36Mixtures with Aqueous Components ........................................................................37Components handled by Phase Envelope Algorithm ................................................ 37References ................................................................................................................. 38

Equations of State 39Equations of State .................................................................................................................... 39

SRK Equation............................................................................................................ 39SRK with Volume Correction ................................................................................... 41PR/PR78 Equation.....................................................................................................42PR/PR78 with Volume Correction ............................................................................ 43Classical Mixing Rules.............................................................................................. 43Temperature Dependent Binary Interaction Parameters............................................ 44The Huron and Vidal Mixing Rule............................................................................ 44Phase Equilibrium Relations ..................................................................................... 45References ................................................................................................................. 46

Characterization of Heavy Hydrocarbons 48Characterization of Heavy Hydrocarbons................................................................................ 48

Classes of Components.............................................................................................. 48Properties of C7+-Fractions ........................................................................................ 49Extrapolation of the Plus Fraction ............................................................................. 50Estimation of PNA Distribution ................................................................................ 50Grouping (Lumping) of Pseudo-components ............................................................ 51Delumping ................................................................................................................. 53Characterization of Multiple Compositions to the Same Pseudo-Components .........54References ................................................................................................................. 55

Thermal and Volumetric Properties 56Thermal and Volumetric Properties......................................................................................... 56

Density ...................................................................................................................... 56Enthalpy .................................................................................................................... 56Internal Energy ..........................................................................................................58Entropy ...................................................................................................................... 58Heat Capacity ............................................................................................................ 59Joule-Thomson Coefficient ....................................................................................... 59Velocity of sound ......................................................................................................59References ................................................................................................................. 59

PVTsim Method Documentation Contents 4

Transport Properties 60Transport Properties................................................................................................................. 60

Viscosity.................................................................................................................... 60Thermal Conductivity................................................................................................ 68Gas/oil Interfacial Tension ........................................................................................ 73References ................................................................................................................. 73

PVT Experiments 75PVT Experiments..................................................................................................................... 75

Constant Mass Expansion.......................................................................................... 75Differential Depletion................................................................................................ 76Constant Volume Depletion ...................................................................................... 76Separator Experiments............................................................................................... 76Viscosity Experiment ................................................................................................ 77Swelling Experiment .................................................................................................77Multiple Contact Experiment .................................................................................... 77Slim Tube Experiment............................................................................................... 78References ................................................................................................................. 81

Compositional Variation due to Gravity 82Compositional Variation due to Gravity.................................................................................. 82Isothermal Reservoir................................................................................................................ 82Reservoirs with a Temperature Gradient ................................................................................. 83

Prediction of Gas/Oil Contacts .................................................................................. 85References ................................................................................................................. 85

Regression to Experimental Data 86Regression to Experimental Data............................................................................................. 86

Experimental data......................................................................................................86Object Functions and Weight Factors........................................................................87Regression for Plus Compositions............................................................................. 87Regression for already characterized compositions................................................... 89Regression on fluids characterized to the same pseudo-components ........................ 90Regression Algorithm................................................................................................ 90References ................................................................................................................. 90

Minimum Miscibility Pressure Calculations 91Minimum Miscibility Pressure Calculations............................................................................ 91

References ................................................................................................................. 92

Unit Operations 93Unit Operations........................................................................................................................ 93

Compressor................................................................................................................ 93Expander.................................................................................................................... 96Cooler ........................................................................................................................ 96Heater ........................................................................................................................ 96Pump.......................................................................................................................... 96Valve ......................................................................................................................... 96Separator.................................................................................................................... 97References ................................................................................................................. 97

Modeling of Hydrate Formation 98Hydrate Formation................................................................................................................... 98

Types of Hydrates .....................................................................................................98Hydrate Model........................................................................................................... 99

PVTsim Method Documentation ContentsIntroduction 5

Hydrate P/T Flash Calculations............................................................................... 101Calculation of Component Fugacities.................................................................................... 102

Fluid Phases............................................................................................................. 102Hydrate Phases ........................................................................................................102Ice ............................................................................................................................ 103References ............................................................................................................... 103

Modeling of Wax Formation 105Modeling of Wax Formation .................................................................................................105

Vapor-Liquid-Wax Phase Equilibria .......................................................................105Extended C7+ Characterization ................................................................................ 106Viscosity of Oil-Wax Suspensions ..........................................................................108Wax Inhibitors .........................................................................................................108References ............................................................................................................... 108

Asphaltenes 109Asphaltenes............................................................................................................................ 109

Cubic Equation of State........................................................................................... 109PC-SAFT model ......................................................................................................110PC-SAFT C7+ characterization procedure.............................................................. 112Properties of P, N and A C7 components................................................................. 113References ............................................................................................................... 114

H2S Simulations 115H2S Simulations..................................................................................................................... 115

References ............................................................................................................... 116

Water Phase Properties 117Water Phase Properties ..........................................................................................................117

Properties of Pure Water ......................................................................................... 117Properties of Aqueous Mixture................................................................................ 125H2O.......................................................................................................................... 127Methanol.................................................................................................................. 127Ethanol .................................................................................................................... 127MEG ........................................................................................................................ 127DEG......................................................................................................................... 128TEG ......................................................................................................................... 128Salt Solubility in Pure Water ................................................................................... 129Salt Solubility Salt-Inhibitor-Water Systems .......................................................... 132Viscosity of water-oil Emulsions ............................................................................ 133References ............................................................................................................... 134

Modeling of Scale Formation 135Modeling of Scale Formation ................................................................................................ 135

Thermodynamic equilibria ...................................................................................... 136Amounts of CO2 and H2S in water ..........................................................................139Activity coefficients of the ions............................................................................... 139Calculation procedure.............................................................................................. 145References ............................................................................................................... 146

Wax Deposition Module 147Modeling of wax deposition ..................................................................................................147

Discretization of the Pipeline into Sections............................................................. 147Energy balance ........................................................................................................147Overall heat transfer coefficient .............................................................................. 148Inside film heat transfer coefficient.........................................................................149

PVTsim Method Documentation 6

Outside Film Heat Transfer Coefficient ..................................................................150Pressure drop models............................................................................................... 150Single-phase flow ....................................................................................................151Two-phase flow.......................................................................................................151Mukherjee and Brill pressure drop model ............................................................... 151Handling of an aqueous phase in the model ............................................................ 153Wax deposition........................................................................................................154Boost pressure .........................................................................................................155Porosity.................................................................................................................... 155Boundary conditions................................................................................................ 155Mass Sources........................................................................................................... 155References ............................................................................................................... 155

Clean for Mud 157Clean for Mud........................................................................................................................ 157

Cleaning Procedure .................................................................................................157Cleaning with Regression to PVT Data...................................................................158References ............................................................................................................... 158

Black Oil Correlations 159Black Oil Correlations ........................................................................................................... 159

Bubble-point Pressure ............................................................................................. 159Saturated Gas/Oil Ratio ........................................................................................... 161Oil Formation Volume Factor ................................................................................. 162Dead-Oil Viscosity ..................................................................................................165Saturated Oil Viscosity............................................................................................ 166Gas Formation Volume Factor ................................................................................ 168Gas Viscosity........................................................................................................... 169Nomenclature ..........................................................................................................171References ............................................................................................................... 172

Allocation 173Allocation .............................................................................................................................. 173

References ............................................................................................................... 175

PVTsim Method Documentation Introduction 7

Introduction

Introduction

When installing PVTsim the Method Documentation describing the calculation procedures used in PVTsim. iscopied to the installation directory as a PDF document (PVTdoc.pdf). The Methid Documentation may further beaccessed from the menu in PVTsim. The menu also gives access to a Users Manual, which duringinstallation is copied to the PVTsim installation directory as the PDF document PVThelp.pdf.

PVTsim Method Documentation Pure Component Database 8

Pure Component Database

Pure Component Database

The Pure Component Database contains approximately 100 different pure components and pseudo-componentsdivided into 6 different component classes

Component Classes

PVTsim distinguishes between the component classes

Water

Hydrate inhibitors

Salts

Other inorganic

Organic defined

Pseudo-components

The program is delivered with a pure component database consisting of the following components:

Short Name Systematic Name Formula Name

WaterH2O Water H2O

Hydrate inhibitorsMeOH Methanol CH4OEtOH Ethanol C2H6OPG Propylene-glycol C6H8O2DPGME Di-propylene-glycol-methylether C7H16O3MEG Mono-ethylene-glycol C2H6O2PGME Propylene-glycol-methylether C7H10O2DPG Di-propylene-glycol C6H14O3DEG Di-ethylene-glycol C4H10O3TEG Tri-ethylene-glycol C6H14O4


Glycerol Glycerol C3H8O3

SaltsNaCl Sodium chloride NaClKCl Potassium chloride KClNaBr Sodium bromide NaBrCaCl2 Calcium chloride (anhydrous) CaCl2HCOONa Sodium formate (anhydrous) HCOONaHCOOK Potassium formate (anhydrous) HCOOKKBr Potassium bromide KBrHCOOCs Caesium formate (anhydrous) HCOOCsCaBr2 Calcium bromide (anhydrous) CaBr2ZnBr2 Zinc bromide ZnBr2

Other inorganicHe Helium-4 He(4)H2 Hydrogen H2N2 Nitrogen N2Ar Argon ArO2 Oxygen O2CO2 Carbon dioxide CO2H2S Hydrogen sulfide H2S

Organic definedC1 Methane CH4C2 Ethane C2H6C3 Propane C3H8c-C3 Cyclo-propane C3H6iC4 Iso-butane C4H10nC4 Normal-butane C4H102,2-dim-C3 2,2-Dimethyl-propane C5H12c-C4 Cyclo-propane C4H8iC5 2-methyl-butane C5H12nC5 Normal-pentane C5H12c-C5 Cyclo-pentane C5H82,2-dim-C4 2,2-Dimethyl-butane C6H142,3-dim-C4 2,3-Dimethyl-butane C6H142-m-C5 2-Methyl-pentane C6H143-m-C5 3-Methyl-pentane C6H14nC6 Normal-hexane C6H14C6 Hexane --------m-c-C5 Methyl-cyclo-pentane C6H12Benzene Benzene C6H6Napht Naphthalene C10H8c-C6 Cyclo-hexane C6H12223-tm-C4 2,2,3-Trimethyl-butane C7H163,3-dim-C5 3,3-Dimethyl-butane C7H162-m-C6 2-Methyl-hexane C7H16c13-dm-cC5 Cis-1,3-Dimethyl-cyclo-pentane C7H14t13-dm-cC5 Trans-1,3-Dimethyl-cyclo-pentane C7H143-m-C6 3-Methyl-hexane C7H16t12-dm-cC5 Trans-1,2-Dimethyl-cyclo-pentane C7H14nC7 Normal-heptane C7H16m-c-C6 Methyl-cyclo-hexane C7H14et-c-C5 Ethyl-cyclo-pentane C7H14113-tr-cC5 1,1,3-Trimethyl-cyclo-pentane C8H16Toluene Toluene C7H82-m-C7 2-Methyl-heptane C8H18c-C7 Cyclo-heptane C7H143-m-C7 3-Methyl-heptane C8H18


11-dm-cC6 1,1-Dimethyl-cyclo-hexane C8H16c13-dm-cC6 Cis-1,3-Dimethyl-cyclo-hexane C8H16t12-dm-cC6 Trans-1,2-Dimethyl-cyclo-hexane C8H16nC8 Normal-octane C8H18c12-dm-cC6 Cis-1,2-Dimethyl-cyclo-hexane C8H16Et-cC6 Ethyl-cyclo-hexane C8H16et-Benzene Ethyl-Benzene C8H10p-Xylene Para-xylene C8H10m-Xylene Meta-xylene C8H102-m-C8 2-Methyl-octane C9H20o-Xylene Ortho-xylene C8H101m-3e-cC6 1-Methyl-3-Ethyl-cyclo-hexane C9H181m-4e-cC6 1-Methyl-4-Ethyl-cyclo-hexane C9H18c-C8 Cyclo-octane C8H164-m-C8 4-Methyl-octane C9H20nC9 Normal-nonane C9H20Mesitylene 1,3,5-Tri-methyl-Benzene C9H12Ps-Cumene 1,2,4-Tri-methyl-Benzene C9H12nC10 Normal-decane C10H22Hemellitol 1,2,3-Tri-methyl-Benzene C9H12nC11 Normal-undecane C11H24nC12 Normal-dodecane C12H26nC13 Normal-tridecane C13H281-m-Napht 1-methyl-Naphthalene C11H10nC14 Normal-tetradecane C14H30nC15 Normal-pentadecane C15H32nC16 Normal-hexadecane C16H34nC17 Normal-heptadecane C17H36nC18 Normal-octadecane C18H38nC19 Normal-nonadecane C19H40nC20 Normal-eicosane C20H42nC21 Normal-C21 C21H44 nCn Normal-Cn CnH2n+2 nC40 Normal-C40 C40H82

The database furthermore contains carbon number fractions from a C7 to C100. Each fraction Cn consists of allcomponents with a boiling point in the interval from that of nCn-1 + 0.5C/0.9F to that of nCn + 0.5C/0.9F.

Finally the database contains the components CHCmp_1 to CHCmp_6, which are dummy pseudo-components andonly accessible when working with characterized fluids. The only properties given in the database are the molecularweight, a and b. The molecular weight will usually have to be modified by the user. All other componentproperties must be entered manually.

Component Properties

For each component the database holds the component properties

Name (short, systematic, and formula)

Molecular weight

Liquid density at atmospheric conditions (not needed for gaseous components)


Critical temperature (Tc)

Critical pressure (Pc)

Acentric factor ( )

Normal boiling point (Tb)

Weight average molecular weight (equal to molecular weight unless for pseudo-components)

Critical volume (Vc)

Vapor pressure model (classical or Mathias-Copeman)

Mathias-Copeman coefficients (only available for some components)

Temperature independent and temperature dependent term of the volume shift (or Peneloux) parameter for theSRK or PR equations

Ideal gas absolute enthalpy at 273.15 K/0C/32F (Href)

Coefficients in ideal gas heat capacity (Cp) polynomial

Melting point temperature (Tf)

Melting point depression (Tf)

Enthalpy of melting (Hf)

PNA distribution (only for pseudo-components)

Wax fraction (only for n-paraffins and pseudo-components)

Asphaltene fraction (only for pseudo-components)

Parachor

Hydrate formation indicator (None, I, II, H and combinations)

Hydrate Langmuir constants

Number of ions in aqueous solution (only for salts)

Number of crystal water molecules per salt molecule (only for salts)

Pc of wax forming fractions (only for n-paraffins and pseudo-components)

a and b in the SRK and PR equations

The component properties needed to calculate various physical properties and transport properties will usually beestablished as a part of the fluid characterization. It is however also possible to input new components withoutentering all component properties and it is possible to input compositions in characterized form.

Tc, Pc, , a, b and molecular weight are required input for all components to perform simulations. What othercomponent properties are needed depend on the simulation to be performed and may be seen from the below table.

Physical or transport property Component properties neededVolume Peneloux parameter*1)

Density Peneloux parameter*1)

Z factor Peneloux parameter*1)

Enthalpy (H) Ideal gas CP coefficients, Peneloux parameter*1)Entropy (S) Ideal gas CP coefficients, Peneloux parameter*1)

Heat capacity (CP) Ideal gas CP coefficientsHeat capacity (CV) Ideal gas CP coefficients, Peneloux parameter*1)

Kappa (CP/ CV) Ideal gas CP coefficients, Peneloux parameter*1)

Joule-Thomson coefficient Ideal gas CP coefficients, Peneloux parameter*1)

Velocity of sound Peneloux parameter*1)

Viscosity Weight average molecular weight*2), Vc*3)


Thermal conductivitySurface tension Parachor, Peneloux parameter*1)

*1) Only if an equation of state with Peneloux volume correction is used.*2) Only if corresponding states viscosity model selected.*3) Only if LBC viscosity model selected.

User Defined Components

User defined components may be added to the database. It is recommended to enter as many component propertiesfor new components as possible. The following properties must always be entered

Component type

Name

Critical temperature (Tc)

Critical pressure (Pc)

Acentric factor ()

a and bMolecular weight (M)

For pseudo-components it is highly recommended also to enter the liquid density.

Missing Properties

PVTsim has a option for estimating missing component properties for a fluid composition entered incharacterized form. The number of missing properties estimated depends on the properties entered manually. It isassumed that Tc, Pc, , a, b, and molecular weight have all been entered. Below is shown what other propertiesare needed to estimate a given missing property and a reference is given to the section in the Method Documentationwhere the property correlation is described.

Property Component propertiesneeded for estimation

Section where described

Liquid density T independent term of Penelouxparameter

SRK with Volume Correction. PRwith Volume Correction.

Normal boiling point None Extrapolation of Plus Fraction.Weight average molecular weight Assumed equal to number average

molecular weight-

Critical volume None Lohrenz-Bray-Clark (LBC) part ofViscosity section.

Vapor pressure model Not estimated -Mathias-Copeman coefficients Not estimated -T-independent term of SRK or PRPeneloux parameter

for defined components. Liquiddensity for pseudo-components

SRK with Volume Correction or PRwith Volume Correction

T-dependent term of SRK or PRPeneloux parameter

Not estimated for definedcomponents. Liquid density for

SRK with Volume Correction or PRwith Volume Correction


pseudo-componentsMelting point depression(Tf)

Only for pseudo-components.Viscosity data for anuninhibited/inhibited fluid.

Ideal gas absolute enthalpy at 273.15K/0C/32F (Href)

Molecular weight Compositional variation due togravity

Ideal gas Cp coefficients Not estimated for definedcomponents. Liquid density forpseudo-components

Enthalpy

Melting temperature (Tf) Irrelevant for defined components.None for pseudo-components

Extended C7+ Characterization

Enthalpy of melting (Hf) Irrelevant for defined components.None for pseudo-components


PNA distribution Irrelevant for defined components.Liquid density for pseudo-components

Estimation of PNA Distribution

Wax fraction Irrelevant for defined components.None for pseudo-components.


Asphaltene fraction Irrelevant for defined components.Liquid density for pseudo-components

Asphaltenes

Parachor Not estimated for definedcomponents. Liquid density forpseudo-components

Gas/Oil interfacial tension.

Hydrate former or not Not estimated -Hydrate Langmuir constants Not estimated -Number of ions in aqueous solution(only for salts)

Not estimated -

Number of crystal water moleculesper salt molecule (only for salts)

Not estimated -

Pc of wax forming fraction Irrelevant for defined components.Liquid density for pseudo-components


PVTsim Method Documentation Composition Handling 14

Composition Handling

Composition Handling

PVTsim distinguishes between the fluid types

Compositions with Plus fraction

Compositions with No-Plus fraction

Characterized compositions

Compositions with Plus fraction are compositions as reported by PVT laboratories where the last component is aplus fraction residue. A C20+ fraction for example contains the carbon number fractions from C20 and heavier. Forthis type of composition the required input is mole%s of all components and molecular weights and densities of theC7+ components (carbon number fractions). It is possible to enter the mole%s to a higher carbon number thanmolecular weights and densities. If the mole%s are given to C20 and the molecular weights and densities to C10, theprogram will interpret the molecular weight and density entered for C10 as properties of the whole C10+ fraction.

Compositions with No-Plus fraction require the same input as compositions with a plus fraction. In this case theheaviest component is not a residue but an actual component or a boiling point cut. Gas mixtures with only amarginal content of C7+ components are to be usually classified as No-Plus fraction compositions.

Simulations can only be made on characterized compositions. These are usually generated from a Plus fraction orNo-Plus fraction type of composition. They may alternatively be entered manually.

Types of fluid analyses

A reservoir fluid may either be sampled as a bottom hole sample or as a separator sample. Bottom hole samples aretaken in the bottom of the well and are usually single-phase at sampling conditions and therefore representative forthe reservoir fluid. A separator sample consists of two samples, a separator gas and a separator oil from a well headseparator.

In the laboratoy the samples are flashed to standard conditions before making any analyses. Flashing the oil resultsin a gas and a liquid sample that are analyzed separately. The gas will always be analyzed by a gas chromatographic(GC) analysis. Two alternative types of fluid analyses are used for the liquid. These are a gas chromatographic (GC)


analysis and a true boiling point (TBP) analysis. None of these analyses will identify all the chemical speciescontained in the fluid but will separate the C7+ fraction into boiling point cuts.

GC analysis

Also oil compositions are often analyzed by GC. It is relatively cheap, very fast, and requires only small samplevolumes. A GC analysis suffers from the problem that heavy ends may be lost in the analysis, especially heavyaromatics (asphaltenes). The main problem with a GC analysis is however that no information is retained onmolecular weight (M) and density of the cuts above C9. Instead standard molecular weights and densities areassigned to the heavier fractions. This may results in large uncertainties on the molecular weight and density of theplus fractions. Because the component quantities measured in a GC analysis are on weight basis, this uncertaintyalso transfers to an uncertainty on the mole% of the plus fraction.

A GC composition may for example consist of mole%s given to C30+ while molecular weight and density are onlygiven to C7+. In this case one may enter the mole%'s to C30 together with the M and density of the total C7+ fraction,leaving the M and density fields blank for C8-C30. With this input the program will estimate the molecular weightsand densities of the fractions C7-C30 while honoring the reported composition and matching the input C7+ molecularweight and density. One may as an alternative input the composition (the mole%s) lumped back to C7+, which willoften provide equally accurate simulation results as with the detailed GC composition.

TBP Distillation

A TBP distillation requires a larger sample volume, typically 50 200 cc and is more time consuming than a GCanalysis. The method separates the components heavier than C6 into fractions bracketed by the boiling points of thenormal alkanes. For instance, the C7 fraction refers to all species with a boiling point between that of nC6 +0.5C/0.9F and that of nC7 + 0.5C/0.9F, regardless of how many carbon atoms these components contain. Eachof the fractions distilled off is weighed and the molecular weight and density are determined experimentally. Thedensity and molecular weight in combination provide valuable information to the characterization procedure. Theresidue from the distillation is also analyzed for amount, M and density.

Whenever possible, it is recommended that input for PVTsim is generated based on a TBP analysis. The accuracy ofthe characterization procedure relies on good values for densities and molecular weights of the C7+ fractions.Parameters such as the Peneloux volume shift for the heavier pseudo-components are estimated based on the inputdensities, and consequently the quality of the input directly affects the density predictions of the equation of state(EOS) model.

Handling of pure components heavier than C6

When the compositional input is based on a GC analysis, there will often be defined components (pure chemicalspecies) reported, which in the TBP-terminology would belong to a boiling point cut. Such components may beentered alongside with the boiling point fraction, which then represents the remaining unresolved species within thatboiling point interval. Before the entered composition is taken through the characterization procedure, the purespecies are lumped into their respective boiling point fraction and the properties of that fraction adjustedaccordingly. After the characterization, the pure species and the remaining fraction (pseudo-component) are splitagain and the properties adjusted accordingly.


Fluid handling operations

Quite often there is a need to mix two or more fluids and continue simulations with the mixed composition. PVTsimsupports a Mixing, a Weaving and a Recombination option for combining two or more fluid compositions.

Mixing

PVTsim may be used to mix 2 to 50 fluid compositions. A mixing will not necessarily retain the pseudo-componentsof the individual compositions. Averaging the properties of the pseudo-components in the individual compositionsgenerates new pseudo-components. Mixing may be performed on all types of compositions. For fluids characterizedin PVTsim, mixing is done at the level where the fluid has been characterized but not yet lumped. The mixed not yetlumped fluid is afterwards lumped to the specified number of components.

Weaving

Weaving will maintain the pseudo-components of the individual compositions and can only be performed for alreadycharacterized compositions. In a weaved fluid all pseudo-components from all the original fluids are maintained inthe resulting weaved fluid. This may lead to several components having the same name, and it is therefore advisableto tag the component names before weaving in order to avoid confusion later on. The weaving option is useful totrack specific components in a process simulation or for allocation studies.

Recombination

Recombination is a mixing on volumetric basis performed for a given P and T (usually separator conditions).Recombination can only be performed for two compositions, an oil and a gas composition. The recombination optionis often used to combine a separator gas phase and a separator oil phase to get the feed to the separator. When thetwo fluids are recombined, the GOR and liquid density at separator conditions must be input. Alternatively thesaturation point of the recombined fluid can be entered along with the liquid density. When the GOR is specified, theprogram determines the number of moles corresponding to the input volumes and mixes the two fluids based on thismolar ratio. When the saturation pressure is specified, the amount of gas tobe added to the oil to yield this saturationpressure is determined in an iterative manner.

Characterization to the same pseudo-components

The goal of characterizing fluids to the same pseudo-components is to obtain a number of fluids, which are allrepresented by the same component set. Numerically this is done in a similar fashion as the mixing operation withthe only difference that the same pseudos logic keeps track of the molar amount of each pseudo-componentcontained in each individual fluid.

The characterization to the same pseudo-components option is useful for a number of tasks. In compositionalpipeline simulations where different streams are mixed during the calculations or in compositional reservoirsimulations where zones with different PVT behavior are considered, mixing is straightforward when all fluids havethe same pseudo-components. It is furthermore possible to do regression in combination with the characterization tothe same pseudos, in which case one may put special emphasis on fluids for which PVT data sets are available.


Characterization to same pseudo-components is described in more detail in the section on Characterization of HeavyHydrocarbons.

PVTsim Method Documentation QC of Fluid 18

QC of Fluid

QC of FluidHigh quality PVT simulation results on petroleum reservoir fluids are heavily dependent on representative andaccurate fluid compositions. The characterization procedure in PVTsim (Pedersen et al. (1992) and Krejbjerg andPedersen (2006)) generally provides PVT simulations results within experimental accuracy based on reliable fluidcompositions measured to C10+ or C20+. When a bad correspondence is seen with experimental PVT data, the reasoncould be an inaccurate reservoir fluid composition.

The PVTsim QC module is designed to analyze reservoir fluid compositions for any inconsistencies betweencompositional analyses, sampling data and basic PVT data.

Reservoir fluid samples can either be

Bottomhole samples.

Separator samples.

The approach to QC evaluation is dependent on the sample type. All conducted QC evaluations must pass for thesample to pass the overall QC evaluation.

Bottomhole samples

The following input is mandatory to conduct a QC on a bottomhole sample. The information should be readilyavailable in a PVT report

Molar composition of bottomhole sample. The composition must be a Plus composition

Reservoir Pressure

Reservoir Temperature

STO Oil Density (Single Stage Flash)

GOR (Single Stage Flash)

Reservoir Fluid Type (Oil must be chosen if the STO API Gravity is above 25 API and Heavy Oil must be chosen ifthe STO API Gravity is below 25 API)

The following additional, optional information can be entered when available from the PVT report


Bottomhole Sample Saturation Pressure

Bottomhole Flowing Pressure

Sample Cylinder Shutting Pressure

Sample Cylinder Opening Pressure

Test Separator Information

o Separator Pressureo Separator Temperatureo Oil Densityo GOR

The total QC evaluation scheme for a bottomhole sample is

No. QC Evaluation Mandatory Optional

1 STO Oil Density (Single Stage Flash) X

2 GOR (Single Stage Flash) X

3 Critical Point/Fluid Type X

4 Logarithmic Mole Fraction vs. Carbon Number X

5 Plus Component Amount X

6 Plus Component Molecular Weight X

7 Plus Component Density X

8 Reservoir Pressure vs. Bottomhole Sample Saturation Pressure X

9 Bottomhole Flowing Pressure vs. Bottomhole Sample SaturationPressure

X

10 Sample Cylinder Shutting Pressure vs. Sample Cylinder OpeningPressure

X

11 Oil Density (Test Separator) X

12 GOR (Test Separator) X

13 Possible OBM Contamination X

In the following the QC evaluations are described in terms of

Simulation method

Accepted deviation between measured and simulated results

Possible key sources in case of failure are listed in the QC report with suggestions on how to correct the sample topass the QC.

STO Oil Density (bottomhole)

The bottomhole composition is flashed to at standard conditions (typically 1.01 bara/15C or 14.7 psia/59F), andthe density of the flashed liquid compared with the input STO Oil density.

The fluid fails the QC test if the deviation exceeds 3%.

The QC evaluation will also fail if a single-phase gas is detected at standard conditions.


GOR (bottomhole)

The GOR from a single stage flash of the bottomhole composition at standard conditions is compared with the inputGOR.

The fluid fails the QC test if the deviation exceeds 10%. The same applies if a single phase is detected at standardconditions.

Critical Point/Fluid Type (bottomhole)

The following should apply

Critical temperature less than reservoir temperature -> Fluid Type: Gas or gas condensate.

Critical temperature higher than reservoir temperature -> Fluid Type: Oil or heavy oil.

A mismatch between the reported and simulated fluid type should only be observed for near critical fluids (typicallyheavy gas condensates or volatile oils), i.e. fluids for which the reservoir temperature and the critical temperature arevery close. In this case only a small change in the fluid description (e.g. a different lumping) may cause the fluidtype to shift.

The test is only performed on fluids with one and only one simulated critical point.

C7+ Molar Distribution (bottomhole)

For most reservoir fluids the logarithm of the mole fraction of C7+ fractions (except the plus component) versuscarbon number will follow an almost straight line (Pedersen et al., 1992). With a fluid composition to for exampleC20+ an almost straight line is to be expected for logarithm of the mole%s of C7-C19 versus carbon number.

A best fit should have a coefficient R2 above 0.80 for the fluid pass the test. Before the test is performed, defined C7+components as for example benzene and toluene are added to the appropriate carbon number fraction.

For heavy oils, the carbon number, at which the logarithmic decay starts, is dependent on the STO API Gravity ofthe heavy oil. Based on the findings by Krejbjerg and Pedersen (2006), the following equation can be derived

918.22API5492.0CN B

where CNB is the carbon number where the logarithmic decay begins for heavy oils, and API is the API gravitymeasured for the heavy oil. The fluid analysis must be to at least CNB + 4.

Plus Component Amount (bottomhole)

By extrapolation of the best-fit line generated in the C7+ Molar Distribution analysis, an estimate can be provided ofthe molar amount contained in the plus fraction (C20+ molar amount if compositional analysis ends at C20+).

The extrapolation is continued to C80 (C200 for heavy oil). The simulated plus fluid molar amount found by thisextrapolation should agree with the reported plus molar amount within 100% for the fluid to pass the test.

Plus Molecular Weight (bottomhole)

An extrapolation of the best-fit line generated in the C7+ Molar Distribution analysis enables the reported plusmolecular weight to be checked. The plus molecular weight can be calculated from

maxC

Cii

i

maxC

Cii

z

MzM


where C+ is plus fraction carbon number. Cmax is C80 (C200 if the fluid is a heavy oil). The molecular weights of thecarbon number fractions contained in the plus fraction are found from

M = 14 CN 4

where CN is carbon number.

A deviation of more than 25% from the reported plus molecular weight will make the QC test fail.

Plus Component Density (bottomhole)

An extrapolation of the best-fit line generated in the C7+ Molar Distribution analysis enables the reported plusdensity weight to be checked. The plus density is calculated from

maxC

Ci i

ii

maxC

Ciii

Mz

Mz

where C+ is plus fraction carbon number and CMax is either C80 (C200 for heavy oils). The densities of the carbonnumber fractions contained in the plus fraction are found from

NCNlnDC

where CN is carbon number and the constants C and D are found from a best-fit line for through density versusln(carbon number) for the carbon number fractions except the plus fraction. A best fit should have a coefficient R2above 0.85 for the fluid pass the test.

The fluid fails the plus component density check if the simulated plus density deviates by more than 5% from theplus density input for the fluid.

The test is not performed unless C7+ densities are given to at least C20+.

Bottomhole Sample Saturation Pressure (bottomhole)

If the fluid sample is representative for the fluid in the reservoir, the Bottomhole Sample Saturation Pressure must belower than the Reservoir Pressure. If this is not the case, the sample has most likely been obtained at conditions withtwo phases present. It is therefore most likely not representative and the test will fail.

The test is not performed if the Bottomhole Sample Saturation Pressure is not given as input.

Bottomhole Flowing Pressure (bottomhole)

The Bottomhole Flowing Pressure must be higher than the Bottomhole Sample Saturation Pressure. If this is not thecase, then there will be free gas flowing in the vicinity of the wellbore, and it is highly likely that the samplecollected has lost lighter hydrocarbon components and therefore is not representative. Even though the reservoirpressure may be above the saturation pressure, a high drawdown pressure may cause the flowing bottomholepressure to drop below the saturation pressure.

The test is performed if both Bottomhole Flowing Pressure and Bottomhole Sample Saturation Pressure are input.

Sample Cylinder Shutting/Opening Pressures (bottomhole)

The Sample Cylinder Shutting Pressure must be higher than the Sample Cylinder Opening Pressure. The oppositewould suggest that the sample in the laboratory is heated to a temperature above reservoir temperature before thesample cylinder is opened. That is obviously not the case. Something else has gone wrong and the test will fail.

The test is performed if both Sample Cylinder Shutting Pressure and Sample Cylinder Opening Pressure are input

Test Separator GOR (bottomhole)


If data at test separator conditions is available, the QC of a bottomhole sample can be extended with a test ofseparator GOR. The simulated GOR is found as GOR at standard conditions divided by the Bo of the oil at separatorconditions.

A deviation of more than 10% from the input separator GOR will make the test fail.

The evaluation will fail if a single-phase gas is detected at separator conditions.

Test Separator Oil Density (bottomhole)

If data at test separator conditions is available, the QC of a bottomhole sample may be combined with a separatortest QC.

If the separator oil density has been input, the sampled fluid composition is flashed to separator conditions and thesimulated separator oil density compared with that input. The test will fail if the deviation exceeds 4%.

The evaluation will fail if a single-phase gas is detected at separator conditions.

OBM Contamination (bottomhole)

For most (clean) reservoir fluids the logarithm of the mole fraction of C7+ fractions (except plus component) versuscarbon number will follow an almost straight line (Pedersen et al. (1992)). With a fluid composition to for exampleC20+ an almost straight line is to be expected for logarithm of the mole%s of C7-C19 versus carbon number.

The evaluation is conducted by a calculation of the best-fit straight line through the logarithm of the mole fraction ofC7+ fractions (except plus component) versus carbon number. Before the test is performed, the defined componentsheavier than C6 are added to the appropriate carbon number fraction.

An analysis to at least C20+ is required for gas condensates and oils, whereas a composition to C30+ is required forheavy oils.

If the analysis shows signs of OBM, it is recommended to obtain a composition of the mud and perform a Clean ForMud calculation in PVTsim.

Separator SamplesA separator sample is taken from a separator operating at elevated P and T. The separator oil is in the PVTlaboratory flashed to standard (typically 1.01 bara/15C or 14.7 psia/59F) in a single stage.

The following input is mandatory if a QC evaluation is to be conducted for a separator sample. The informationshould be readily available in a PVT report.

Molar composition of separator gas and oil. The oil must be a Plus composition and the gas either a plus ora No Plus composition

Molar composition of recombined fluid PVT report.

Separator Pressure

Separator Temperature

STO Oil Density

Separator GOR

Reservoir Fluid Type (Oil must be chosen if the STO API Gravity is above 25 API and Heavy Oil must be chosen ifthe STO API Gravity is below 25 API)

The following additional information can optionally be entered


Reservoir Temperature

The total QC evaluation scheme for a separator sample is

No. QC Evaluation Mandatory Optional

1 STO Oil Density X

2 Separator GOR X

3 Separator Conditions X

4 Separator Gas Saturation Temperature X

5 Separator Oil Saturation Pressure X

6 K-Factor Plot X

7 Mass Balance Closure Plot X

8 Hoffmann Plot (X)

9 Logarithmic Mole Fraction vs. Carbon Number X

10 Plus Component Amount X

11 Plus Component Molecular Weight X

12 Plus Component Density X

13 Critical Point/Fluid Type X

In the following the QC evaluations are described in terms of

Simulation method

Accepted deviation between measured and simulated results

Possible key sources in case of failure are listed in the QC report with suggestions on how to correct the sample topass the QC.

STO Oil Density (separator)

The recombined separator sample is flashed to at standard conditions (typically 1.01 bara/15C or 14.7 psia/59F),and the density of the flashed liquid compared with the input STO Oil density.

The fluid fails the QC test if the deviation exceeds 3%.

Separator GOR (separator)

The separator oil is flashed to standard conditions (typically 1.01 bara/15C or 14.7 psia/59F). The volume of thegas from this flash is added to the volume of the gas from flashing the separator gas to standard conditions and thetotal gas volume divided by the volume of the oil at standard conditions.

The fluid will fail the test if the simulated separator GOR deviates by more than 10% from the reported separatorGOR.

Separator Conditions (separator)

Phase envelopes for the separator gas and the separator oil should ideally meet at the separator P and T. In the QCmodule the deviation between the simulated separator P and T and the reported separator conditions are defined as


2

Reported

ReportedSimulated

2

Reported

ReportedSimulated% T

TTP

PP100Deviation

The criterion for passing the test depends on whether the simulated separator T is higher or lower than the reportedseparator T

TSimulated > TReportedAccept criterion is 5% (deviation most likely caused by liquid carryover)

TSimulated < TReportedAccept criterion is 20% (deviation most likely caused heavy components in gas not analyzed for, which willhave little influence on the properties of the recombined fluid)

The test will fail if the phase envelopes do not intersect.

Saturation Temperature Separator Gas (separator)

Ideally the dew point temperature of the separator gas at the separator pressure should be equal to the separatortemperature. The fluid will fail the QC if the simulated saturation temperature for the separator gas at the separatorpressure deviates by more than 10% from the separator temperature.

Saturation Pressure Separator Oil (separator)

Ideally the bubble point pressure of the separator oil at the separator temperature should be equal to the separatorpressure. The fluid will fail the QC if the simulated saturation pressure for the separator oil at the separatortemperature deviates by more than 10% from the separator pressure.

K-Factor Plot (separator)

The K-factor is determined through

i

ii x

yK

where Ki is the K-factor of component i, yi is the mole fraction of the ith component in the separator gas, and xi isthe mole fraction of the ith component in the separator oil.

To check whether the sampled separator compositions were at equilibrium at separator conditions the K-factors ofthe sampled compositions may be compared with the K-factors of the compositions from a flash of the recombinedfluid to separator conditions.

The test should yield a straight line (y=x) when plotting the simulated K-factors against the reported K-factors. Onlydefined components are included in the test since heavier components are not always contained in both separator gasand separator liquid analysis. N2 is not included in this evaluation, the reason being that sample cylinders may becontaminated by N2.

The line coefficient R2 must be above 0.98 to pass the K-Factor Plot test.

Mass Balance Closure Plot (separator)

A recombination of the separator gas and oil according to the separator GOR should give the composition of therecombined reservoir fluid composition in the PVT report. The mass balance over a separator is given by

iii x1yz


where zi is the mole fraction of component i in the feed to the separator, yi is the mole fraction of the ith componentin the separator gas, xi is the mole fraction of the ith component in the separator oil, and is the molar fraction ofthe feed that ends up in the separator gas.

Watanasiri et al. (1982) rewrites this equation to

1zx1

zy

i

i

i

i

which shows that plotting yi/zi against xi/zi should yield a straight line. The line should be downward sloping as 0 1. Only defined components are included in the test since heavier components are not always contained in bothseparator gas and separator liquid analysis.

The line coefficient R2 must be above 0.85 for the fluid in order to pass the Mass Balance Closure Plot evaluation.

Hoffmann Plot (separator)

The Hoffmann Plot (Hoffmann et al. (1953)) is an alternative/supplement to the K-factor plot for determiningwhether the given separator gas and oil compositions are in equilibrium at separator conditions.

The correlation is given by

T

1T1b

PP

KLogSeparatorb,idardtanS

Separatori

where Ki is the K-factor for component i, PSeparator is the separator pressure, PStandard is the standard pressure (typically1.01 bara/14.7 psia), is the slope of the straight line, b is a parameter given by

i,ci,b

dardtanS

i,c

T1

T1

PP

Logb

where Pc,i is the critical pressure of component i, Tb,i is the normal boiling point of component i, Tc,i is the criticaltemperature of component i, TSeparator is the separator temperature, and is the intercept of the straight line.

The Hoffmann Plot is included in the QC module because it is an accepted QC standard in the oil industry, Whitsonand Brul (2000) have shown that the Hoffmann correlation can be derived from the Wilson Equation forapproximate K-factors (Wilson, 1966) when the Edmister correlation (Edmister, 1958) is used to determine theacentric factor in the Wilson equation. Being an approximate correlation it is less refined than the K-factor plot andnot assigned any importance in the overall QC evaluation.

C7+ Molar Distribution (separator)

For most reservoir fluids the logarithm of the mole fraction of C7+ fractions (except plus component) versus carbonnumber will follow an almost straight line (Pedersen et al., 1992). With a fluid composition to for example C20+ analmost straight line is to be expected for logarithm of the mole%s of C7-C19 versus carbon number.

A best fit should have a coefficient R2 above 0.80 for the fluid pass the test. Before the test is performed, defined C7+components as for example benzene and toluene are added to the appropriate carbon number fraction.

For heavy oils, the carbon number, at which the logarithmic decay starts, is dependent on the STO API Gravity ofthe heavy oil. Based on the findings by Krejbjerg and Pedersen (2006), the following equation can be derived

918.22API5492.0CN B

where CNB is the carbon number where the logarithmic decay begins for heavy oils, and API is the API gravitymeasured for the heavy oil. The fluid analysis must be to at least CNB + 4.

Plus Component Amount (separator)

By extrapolation the best-fit line generated in the C7+ Molar Distribution analysis, an estimate can be provided of themolar amount contained in the plus fraction (C20+ molar amount if compositional analysis ends at C20+).


The extrapolation is continued to C80 (C200 for heavy oil). The simulated plus fluid molar amount found by thisextrapolation should agree with the reported plus molar amount within 100% for the fluid to pass the test.

Plus Molecular Weight (separator)

An extrapolation the best-fit line generated in the C7+ Molar Distribution analysis enables the reported plusmolecular weight to be checked. The plus molecular weight can be calculated from

maxC

Cii

i

maxC

Cii

z

MzM

where C+ is plus fraction carbon number. Cmax is C80 (C200 if the fluid is a heavy oil). The molecular weights of thecarbon number fractions contained in the plus fraction are found from

M = 14 CN 4

where CN is carbon number.

A deviation of more than 25% from the reported plus molecular weight will make the QC test fail.

Plus Fluid Density (separator)

An extrapolation the best-fit line generated in the C7+ Molar Distribution analysis enables the reported plus densityweight to be checked. The plus density is calculated from

maxC

Ci i

ii

maxC

Ciii

Mz

Mz

where C+ is plus fraction carbon number and CMax is either C80 (C200 for heavy oils). The densities of the carbonnumber fractions contained in the plus fraction are found from

NCNlnDC

where CN is carbon number and the constants C and D are found from a best-fit line for through density versusln(carbon number) for the carbon number fractions except the plus fraction.

The fluid fails the plus fraction density check if the simulated plus density deviates by more than 5% from the plusdensity input for the fluid.

The test is not performed unless C7+ densities are given to at least C20+.

Critical Point/Fluid Type (separator)

The following should apply

Critical temperature less than reservoir temperature -> Fluid Type: Gas or gas condensate.

Critical temperature higher than reservoir temperature -> Fluid Type: Oil or heavy oil.

The test is only performed if the reservoir temperature is input.

A mismatch between the reported and simulated fluid type should only be observed for near critical fluids (typicallyheavy gas condensates or volatile oils), i.e. fluids for which the reservoir temperature and the critical temperature arevery close. In this case only a small change in the fluid description (e.g. a different lumping) may cause the fluidtype to shift.

PVTsim Method Documentation Flash Algorithms 27

If no or more than one critical point is simulated for the recombined fluid composition, the test is not performed.

ReferencesEdmister, W.C., Applied Hydrocarbon Thermodynamics, Part 4: Compressibility Factors and Equations of State,Pet. Ref., April, 37, 1958, p.173.

Hoffmann, A. E., Crump, J. S. and Hocott, C. R., Equilibrium Constants for a Gas condensate System, PetroleumTransactions, AIME 198, 1953, pp. 1-10.

Katz, D.L. and Firoozabadi, A., Predicting Phase Behavior of Condensate/Crude-Oil Systems Using MethaneInteraction Coefficients, J. Pet. Technol. 20, 1978, pp. 1649-1655.

Krejbjerg, K., Pedersen, K.S., Controlling VLLE Equilibrium With a Cubic EoS in Heavy Oil Modeling,Presented at the 7th Canadian International Petroleum Conference, Calgary, Alberta, Canada, June 13-15, 2006.

Pedersen, K.S., Blilie, A.L., Meisingset, K.K., PVT Calculations on Petroleum Reservoir Fluids Using Measuredand Estimated Compositional Data for the Plus Fraction, I&EC Research, 31, 1992, pp. 1378-1384.

Watanasiri, S., Brul, M.R., Starling, K.E., Correlation of Phase-Separation Data for Coal-Conversion Systems,AIChE Journal, 28, 1982, pp. 626-637.

Whitson, C., Brul, M.R., Phase Behavior, SPE Monograph, Volume 20, SPE, 2000, pp. 41-42.

Wilson, G. M., "A Modified Redlich-Kwong Equation of State, Application to General Physical Data Calculation",Paper No. 15C presented at the 1969 AIChE 65th National Meeting, Cleveland, Ohio, March 4-7, 1969.

Flash Algorithms

Flash Algorithms

The flash algorithms of PVTsim are the backbone of all equilibrium calculations performed in the various simulationoptions. The different flash options are described in the following. A more detailed description can be found inMichelsen and Mollerup (2004).

The input to a PT flash calculation consists of

Molar composition of feed (z)

Flash specifications (e.g. Pressure (P) and temperature (T))


The flash result consists of

Number of phases

Amounts and molar compositions of each phase

Physical properties and transport properties of each phase.

Flash Options

PVTsim supports the flash options

PT non aqueous (gas and oil)

PT aqueous (gas, oil, and aqueous)

PT multi phase (gas, max. two oils, and aqueous)

PH where H is enthalpy (gas, oil, and aqueous)

PS where S is entropy (gas, oil, and aqueous)

VT where V is molar volume (gas, oil, and aqueous)

UV where U is internal energy (gas, oil, and aqueous)

HS (gas, oil, and aqueous)

P where is hydrocarbon vapor mole fraction of total hydrocarbon phase(s) (gas, oil, and aqueous)

T (gas, oil, and aqueous)

K - factor (gas and oil)

Split - factor (gas and oil)

Specific PT flash options considering the appropriate solid phases are used in the hydrate, wax, and asphalteneoptions.

Flash Algorithms

PVTsim uses the PT flash algorithms of Michelsen (1982a, 1982b). They are based on the principle of Gibbs energyminimization. In a flash process a mixture will settle in the state at which its Gibbs free energy


N

1iiinG

is at a minimum. ni is the number of moles present of component i and i is the chemical potential of component i.The chemical potential can be regarded as the escaping tendency of component i, and the way to escape is to forman additional phase. Only one phase is formed if the total Gibbs energy increases for all possible trial compositionsof an additional phase. Two or more phases will form, if it is possible to separate the mixture into two phases havinga total Gibbs energy, lower than that of the single phase. With two phases (I and II) present in thermodynamicequilibrium, each component will have equal chemical potentials in each phase

IIi

Ii

The final number of phases and the phase compositions are determined as those with the lowest total Gibbs energy.

The calculation that determines whether a given mixture at a specified (P,T) separates into two or more phases iscalled a stability analysis. The starting point is the Gibbs energy, G0, of the mixture as a single phase

G0 = G(n1, n2, n3,,nN)

ni stands for the number of moles of type i present in the mixture, and N is the number of different components.

The situation is considered where the mixture separates into two phases (I and II) of the compositions (n1 -1 , n2 --,n3 - -3 ., nN-N) and (1 , 2 , 3,,N) where i is small. The Gibbs energy of phase I may be approximated by aTaylor series expansion truncated after the first order term

N

1ini

ii01 n

GGG

The Gibbs energy of the second phase is found to be

GII = G ((1 , 2 , 3,,N)

The change in Gibbs energy due to the phase split is hence

N

1i0iIIii0iIIi

N

1ii0III ))()((y))((GGGG

where

N

1ii and yi is the mol fraction of component i in phase II. The sub-indices 0 and II refer to the single

phase and to phase II, respectively. Only one phase is formed if G is greater than zero for all possible trialcompositions of phase II. The chemical potential, i, may be expressed in terms of the fugacity, fi, as follows


)P1nlnzRT(1nf1nRT ii0ii

0ii

where 0 is a standard state chemical potential, a fugacity coefficient, z a mole fraction, P the pressure, and thesub-index i stands for component i. The standard state is in this case the pure component i at the temperature andpressure of the system. The equation for G may then be rewritten to

N

1i0iiIIiii ))1n(zln)1n(y(1ny

RTG

where zi is the mole fraction of component i in the total mixture. The stability criterion can now be expressed interms of mole fractions and fugacity coefficients. Only one phase exists if

N

1i0iiIIiii 0))ln(zln)ln(y(lny

for all trial compositions of phase II. A minimum in G will at the same time be a stationary point. A stationary pointmust satisfy the equation

k)ln(lnz)ln(yln 0iiIIii

where k is independent of component index. Introducing new variables, Yi, given by

ln Yi = ln yi k

the following equation may be derived

1n Yi = 1n zi + 1n(i)0 1n(i)IIPVTsim uses the following initial estimate (Wilson, 1969) for the ratio Ki between the mole fraction of component iin the vapor phase and in the liquid phase

)

TT(15.373exp

PPK cicii

where

Ki= yi/xiand Tci is the critical temperature and Pci the critical pressure of component i. As initial estimates for Yi are used Kizi,if phase 0 is a liquid and zi/Ki, if phase 0 is a vapor. The fugacity coefficients, (i)II, corresponding to the initialestimates for Yi are determined based on these fugacity coefficients, new Yi-value are determined, and so on. For asingle-phase mixture this direct substitution calculation will either converge to the trivial solution (i.e. to twoidentical phases) or to Yi-values fulfilling the criterion

N

1ii 1Y

which corresponds to a non-negative value of the constant k. A negative value of k would be an indication of thepresence of two or more phases. In the two-phase case the molar composition obtained for phase II is a good startingpoint for the calculation of the phase compositions. For two phases in equilibrium, three sets of equations must besatisfied. These are

1) Materiel balance equations

N1,2,3,...,i,zx1y iii

2) Equilibrium equations

N1,2,3,...,i,xy LiiVii


3) Summation of mole fractions

N

1iii 0)x(y

In these equations xi, yi and zi are mole fractions in the liquid phase, the vapor phase and the total mixture,respectively. is the molar fraction of the vapor phase. Vi and

Li are the fugacity coefficients of component i in the

vapor and liquid phases calculated from the equation of state. There are (2N + 1) equations to solve with (2N + 3)variables, namely (x1, x2, x3,, xN), (y1, y2, y3,.,yN), , T and P. With T and P specified, the number of variablesequals the number of equations. The equations can be simplified by introducing the equilibrium ratio or K-factor, Ki= yi/xi. The following expressions may then be derived for xi and yi

N1,2,3,...,i,xKy

N1,2,3,...,i,1K1

zx

iii

i

ii

and for Ki

N1,2,3,...,i,K Vi

Li

i

The above (2N+1) equations may then be reduced to the following (N+1) equations

N1,2,3,...,i,lnln

Kln Vi

Li

i

i

N

1iiiiii 01))(K1)/(1(Kz)x(y

For a given total composition, a given (T, P) and Ki estimated from the stability analysis, an estimate of may bederived. This will allow new estimates of xi and yi to be derived and the K-factors to be recalculated. A new value of is calculated and so on. This direct substitution calculation may be repeated until convergence. For more details onthe procedure it is recommended to consult the articles of Michelsen (1982a, 1982b).

For a system consisting of J phases the mass balance equation is

0H

1)(KzN1i i

imi

where

1)(K1H1j

1m

mi

mi

m is the molar fraction of phase m. miK equals the ratio of mole fractions of component i in phase m and phase J.

The phase compositions may subsequently be found from

N1,2,3,...,i,Hz

y

J1,2,3,...,mN;1,2,3,...,i,HKz

y

i

iJi

i

miim

i

where miy andJiy are the mole fractions of component i in phase m and phase J, respectively.

K-factor Flash


The Flash option and some of the interface options in PVTsim support K-factor and Split-factor flashes. The K-factor of component i is the mole fraction of component i in the vapor phase (yi) divided by the mole fraction (xi) ofcomponent i in the liquid phase (i.e. Ki=yi/xi). The Split-factor of component i equals the molar amount ofcomponent i in the vapor phase divided by the molar amount of component i in the feed composition. Split-factor areconverted to K-factors and the below N+1 equations solved.

1) Materiel balance equations

N1,2,3,...,i,zx1y iii

2) Summation of mole fractions

N

1i

N

1i i

iiii 0)1(K1

)1(Kz)x(y

In the multiphase meter interface in PVTsim full flash calculations are carried out for the individual separator stages.The total separation is then converted to overall K-factors and these are used to calculate the black oil propertieswritten out by this interface option.

Other Flash Specifications

P and T are not always the most convenient flash specifications to use. Some of the processes taking place during oiland gas production are not at a constant P and T. Passage of a valve may for example be approximated as a constantenthalpy (H) process and a compression as a constant entropy (S) process. The temperature after a valve maytherefore be simulated by initially performing a PT flash at the conditions at the inlet to the valve. If the enthalpy isassumed to be the same at the outlet, the temperature at the outlet can be found from a PH flash with P equal to theoutlet pressure and H equal to the enthalpy at the inlet. A PT flash followed by a PS flash may similarly be used todetermine an approximate temperature after a compressor.

To perform a PH or a PS flash, PVTsim starts with a temperature of 300 K/26.85C/80.33F. Two object functionsare defined. These are for a two-phase PH flash

N

1iiii1 1)(Kzg

spec2 HHg

where

1K1 ii

H is total molar enthalpy for the estimated phase compositions, and Hspec is the specified molar enthalpy. Atconvergence both g1 and g2 are zero.

Other flash specifications are VT, UV and HS. V is the molar volume and T the absolute temperature. A VTspecification is useful to for example determine the pressure in an offshore pipeline during shutdown. U is the


internal energy. A dynamic flow problem may sometimes more conveniently be expressed in U and V than in P andT.

Michelsen (1999) has given a detailed description on how to perform flash calculations with other specificationvariables than P and T.

Phase Identification

If a PT flash calculation for an oil or gas mixture shows existence of two phases, the phase of the lower density willin general be assumed to be gas or vapor and the phase of the higher density liquid or oil. In the case of a single-phase solution it is less obvious whether to consider the single phase to be a gas or a liquid. There exists no generallyaccepted definition to distinguish a gas from a liquid. Since the terms gas and oil are very much used in the oilindustry, a criterion is needed for distinguishing between the two types of phases.

The identification criterion used in PVTsim is

Liquid if

The pressure is lower than the critical pressure and the temperature lower than the bubble point temperature.

The pressure is above the critical pressure and the temperature lower than the critical temperature.

Gas if

The pressure is lower than the critical pressure and the temperature higher than the dew point temperature.

The pressure is above the critical pressure and the temperature higher than the critical temperature.

In the flash options handling water, a phase containing more than 80 mole% total of the components water, hydrateinhibitors and salts is identified as an aqueous phase.

Components Handled by Flash Options

The non-aqueous PT-flash option handles the following component classes

Other inorganic

Organic defined

Pseudo-components

The PT aqueous and multiflash options handle

Water

Hydrate inhibitors

Other inorganic

Organic defined


Pseudo-components

Salts

The PH, PS, and HS flash options handle

Water

Hydrate inhibitors

Other inorganic

Organic defined

Pseudo-components

Salts

The VT and UV flash options handle

Water

Hydrate inhibitors

Other inorganic

Organic defined

Pseudo-components

The T and P flash options handle

Water

Hydrate inhibitors

Other inorganic

Organic defined

Pseudo-components

Salts

References

Michelsen, M.L., The Isothermal Flash Problem. Part I: Stability, Fluid Phase Equilibria 9, 1982a, 1.

Michelsen, M.L., The Isothermal Flash Problem. Part II: Phase-Split Calculation, Fluid Phase Equilibria 9, 1982b,21.

Michelsen, M.L., State Based Flash Specification, Fluid Phase Equilibria 158-161, 1999, pp. 617-626.

Michelsen, M. L. and Mollerup, J., Thermodynamic Models: Fundamental and Computational Aspects, Tie-LinePublication, Holte, Denmark, 2004.


Wilson, G. M., A Modified Redlich-Kwong Equation of State, Application to General Physical Data Calculation,Paper No. 15C presented at the 1969 AIChE 65th National Meeting, Cleveland, Ohio, March 4-7, 1969.

PVTsim Method Documentation Phase Envelope and Saturation Point Calculation 36

Phase Envelope and SaturationPoint Calculation

Phase Envelope and Saturation Point Calculation

No aqueous components

A phase envelope consists of corresponding values of T and P for which a phase fraction of a given mixture equalsa specified value. The phase fraction can either be a mole fraction or a volume fraction. The phase envelope optionin PVTsim (Michelsen, 1980) may be used to construct dew and bubble point lines, i.e. corresponding values of Tand P for which equals 1 or 0, respectively. Also inner lines (0 < < 1) may be constructed.

The construction of the outer phase envelope ( = 1 and = 0) and inner molar lines follows the procedure outlinedbelow. The first (T, P) value of a phase envelope is calculated by choosing a fairly low pressure (P). The default inPVTsim is 5 bara/4.93 atm/72.52 psia. An initial estimate of the equilibrium factors (Ki = yi/xi) is obtained from thefollowing equation

)

TT

5.42(1expP

PK cicii

This relation and the mass balance equation

N

1i

N

1iiiiii 01))(K1)/(1(Kz)x(y

are solved for T and equal to the specified vapor mole fraction. The correct value of T is subsequently calculatedby solving this equation in conjunction with

Vi

Li

i lnlnlnK

where the liquid (L) and vapor (V) phase fugacity coefficients, , are found using the equation of state.


An initial estimate of the second point on the phase envelope is calculated using the derivatives of T and Ki withrespect to P calculated in the first point. The correct solution is again found by solving the above equations.

From the third point and on the extrapolation is based on the two latest calculated points and the correspondingderivatives. This stepwise calculation is continued until the temperature is below the specified lower temperaturelimit.

In simulations of PVT experiments, knowledge of the complete phase envelope is not needed but only the saturationpressure at the temperature of the experiment. A saturation point is also located through a phase envelopecalculation. A critical point may be considered a special type of saturation point, and the critical point is easilyidentified as a point where the lnKi changes sign. Some fluids have more than one critical point. The critical point isfurthermore verified by a more direct method as described by Michelsen and Heidemann (1981).

The basic phase envelope option only considers two phases (one gas and one liquid). For many reservoir fluidmixtures a PT-region exists with 3 phases (1 gas and 2 liquids). This is for example often the case for gas condensatemixtures at low temperatures. The phase envelope option in PVTsim allows a check to be performed of the possibleexistence of a 3-phase region.

For fluids with no aqueous components (i.e. water, hydrate inhibitors or salts) it is possible to obtain other phaseenvelope diagrams than the traditional PT-phase envelope diagram. PVTsim allows combinations of the followingproperties on the axes of the phase envelope diagram

Pressure (P)

Temperature (T)

Enthalpy (H)

Entropy (S)

Volume (V)

Internal Energy (U)

Mixtures with Aqueous Components

Only the outer lines (=1 and 0) will be located for mixtures containing aqueous components. The phasesconsidered are (hydrocarbon) gas, (hydrocarbon) liquid and aqueous. The mutual solubility between all phases istaken into account. The algorithm is described by Lindeloff and Michelsen (2003).

Components handled by Phase Envelope Algorithm

The algorithm handles components belonging to the classes

Other inorganic

Organic defined

Pseudo-components.


Water (no inner lines)

Hydrate inhibitors (no inner lines)

The saturation point algorithm used in the saturation point option and the PVT simulations is also based on the phaseenvelope algorithm, but does not handle water and hydrate inhibitors.

References

Lindeloff, N. and Michelsen, M.L., Phase Envelope Calculations for Hydrocarbon-Water Mixtures, SPE 85971,SPE Journal, September 2003, pp. 298-303.

Michelsen, M.L., Calculation of Phase Envelopes and Critical Points for Multicomponent Mixtures, Fluid PhaseEquilibria 4, 1980, pp. 1-10.

Michelsen, M.L. and Heidemann, R.A., Calculation of Critical Points from Cubic Two-Constant Equations ofState, AIChE J. 27, 1981, pp. 521-523.

PVTsim Method Documentation Equations of State 39

Equations of State

Equations of State

The phase equilibrium calculations in PVTsim are based on one of the following equations

Soave-Redlich-Kwong (SRK) (Soave, 1972)

Peng-Robinson (PR) (Peng and Robinson, 1976)

Modified Peng-Robinson (PR78) (Peng and Robinson, 1978)

All equations may be used with or without Peneloux volume correction (Peneloux et al., 1982). A constant or atemperature dependent Peneloux correction may be u

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