PDF -Vicky Athanasiou WELCOME & WHAT’S NEW WITH 27 Oct 2016 UNISIM - PVTsim Tutorial Calsep
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calsep uploads Modules Footerbrochure technical pdf PVTsim is a versatile equation of state (EOS) modeling software that allows the user to simulate fluid properties and experimental PVT data PVTsim is the primary commercial software owned, marketed and developed by Calsep thereby ensuring continued and long term improvements

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ftp pwg pub pwg ipp wd wd ippauth 20190328 pdf ALL FAULTS, and the authors and developers of this material and the Printer Working Group and its members hereby disclaim all warranties and conditions, either expressed, implied or statutory, including, but not limited to, any (if any) implied

Description

Pure Component Database

- 6 Component Classes
- 6 Component Properties
- 9 User Defined Components
- 10 Missing Properties

Composition Handling

- 13 Types of fluid analyses
- 13 Handling of pure components heavier than C6
- 14 Fluid handling operations

15 Mixing

15 Weaving

- 15 Recombination
- 15 Characterization to the same pseudo-components

Flash Algorithms

- 17 PT Flash
- 17 Flash Algorithms
- 17 Other Flash Specifications
- 22 Phase Identification
- 22 Components Handled by Flash Algorithms
- 23 References

- 25 No aqueous components
- 25 Mixtures with Aqueous Components
- 26 Components handled by Phase Envelope Algorithm
- 26 References

Equations of State

- 28 SRK Equation
- 28 SRK with Volume Correction
- 30 PR/PR78 Equation
- 31 PR/PR78 with Volume Correction
- 31 Classical Mixing Rules
- 32 The Huron and Vidal Mixing Rule
- 33 Phase Equilibrium Relations
- 34 References

Characterization of Heavy Hydrocarbons

Characterization of Heavy Hydrocarbons

- 37 Classes of Components
- 37 Properties of C7+-Fractions
- 38 Extrapolation of the Plus Fraction
- 39 Estimation of PNA Distribution
- 39 Grouping (Lumping) of Pseudo-components
- 40 Delumping
- 42 Characterization of Multiple Compositions to the Same Pseudo-Components
- 43 References

45 Density

- 45 Enthalpy
- 45 Internal Energy

46 Entropy

- 47 Heat Capacity
- 47 Joule-Thomson Coefficient
- 47 Velocity of sound
- 48 References

- 49 Viscosity
- 49 Thermal Conductivity
- 55 Gas/oil Interfacial Tension
- 57 References

- 60 Constant Mass Expansion
- 60 Differential Depletion
- 61 Constant Volume Depletion
- 61 Separator Experiments
- 62 Viscosity Experiment
- 62 Swelling Experiment
- 62 References

Compositional Variation due to Gravity

Compositional Variation due to Gravity

- 63 Isothermal case
- 64 Systems with a Temperature Gradient
- 65 Prediction of Gas/Oil Contacts
- 66 References

Regression to Experimental Data

Regression to Experimental Data

- 68 Experimental data
- 68 Object Functions and Weight Factors
- 69 Regression for Plus Compositions
- 70 Regression for already characterized compositions
- 71 Regression on fluids characterized to the same pseudo-components
- 72 Regression Algorithm
- 72 References

Minimum Miscibility Pressure Calculations

- 73 Minimum Miscibility Pressure Calculations
- 73 Combined drive mechanism
- 75 References

Unit Operations

- 77 Compressor
- 77 Expander

79 Cooler

80 Heater

80 Pump

80 Valve

- 80 Separator
- 80 References

Hydrate Formation

- 81 Types of Hydrates
- 81 Hydrate Model
- 82 Hydrate P/T Flash Calculations
- 85 Calculation of Fugacities
- 86 Fluid Phases
- 86 Hydrate Phases

87 Salts

- 87 References

Modeling of Wax Formation

- 90 Vapor-Liquid-Wax Phase Equilibria
- 90 Extended C7+ Characterization
- 92 Viscosity of Oil-Wax Suspensions
- 93 Wax Inhibitors
- 94 References

Asphaltenes

Asphaltenes

- 96 Asphaltene Component Properties
- 96 References

H2S Simulations

H2S Simulations

Water Phase Properties

- 99 Properties of Pure Water
- 99 Properties of Aqueous Mixture
- 108 Viscosity of water-oil Emulsions
- 111 References

Thermodynamic equilibria

- 114 Amounts of CO2 and H2S in water
- 118 Activity coefficients of the ions
- 118 Calculation procedure
- 125 References

- 128 Discretization of the Pipeline into Sections
- 128 Energy balance
- 129 Overall heat transfer coefficient
- 130 Inside film heat transfer coefficient
- 130 Outside Film Heat Transfer Coefficient
- 132 Pressure drop models
- 132 Handling of an aqueous phase in the model
- 132 Wax deposition
- 133 Boost pressure
- 134 Porosity
- 134 Boundary conditions
- 134 Mass Sources
- 135 References

Clean for Mud

- 137 Cleaning Procedure
- 137 Cleaning with Regression to PVT Data

When installing PVTsim the Method Documentation is copied to the installation directory as a PDF document (pvtdoc

It may further be accessed from the menu in PVTsim

Pure Component Database The Pure Component Database contains approximately 100 different pure components and pseudo-components

The different component classes are described in the following

Component Classes PVTsim distinguishes between the following component classes • • • • • •

The program is delivered with a pure component database consisting of the following components Short Name Water H2O Hydrate inhibitors MeOH EtOH PG DPGME MEG PGME DPG DEG TEG Glycerol Salts NaCl

Systematic Name

Methanol Ethanol Propylene-glycol Di-propylene-glycol-methylether Mono-ethylene-glycol Propylene-glycol-methylether Di-propylene-glycol Di-ethylene-glycol Tri-ethylene-glycol Glycerol

CH4O C2H6O C6H8O2 C7H16O3 C2H6O2 C7H10O2 C6H14O3 C4H10O3 C6H14O4 C3H8O3

Sodium chloride

KCl NaBr CaCl2 HCOONa HCOOK KBr HCOOCs CaBr2 ZnBr2 Other inorganic He H2 N2 Ar O2 CO2 H2S Organic defined C1 C2 C3 c-C3 iC4 nC4 2,2-dim-C3 c-C4 iC5 nC5 c-C5 2,2-dim-C4 2,3-dim-C4 2-m-C5 3-m-C5 nC6 C6 m-c-C5 Benzene Napht c-C6 223-tm-C4 3,3-dim-C5 2-m-C6 c13-dm-cC5 t13-dm-cC5 3-m-C6 t12-dm-cC5 nC7 m-c-C6 et-c-C5 113-tr-cC5

Potassium chloride Sodium bromide Calcium chloride (anhydrous) Sodium formate (anhydrous) Potassium formate (anhydrous) Potassium bromide Caesium formate (anhydrous) Calcium bromide (anhydrous) Zinc bromide

Methane Ethane Propane Cyclo-propane Iso-butane Normal-butane 2,2-Dimethyl-propane Cyclo-propane 2-methyl-butane Normal-pentane Cyclo-pentane 2,2-Dimethyl-butane 2,3-Dimethyl-butane 2-Methyl-pentane 3-Methyl-pentane Normal-hexane Hexane Methyl-cyclo-pentane Benzene Naphthalene Cyclo-hexane 2,2,3-Trimethyl-butane 3,3-Dimethyl-butane 2-Methyl-hexane Cis-1,3-Dimethyl-cyclo-pentane Trans-1,3-Dimethyl-cyclo-pentane 3-Methyl-hexane Trans-1,2-Dimethyl-cyclo-pentane Normal-heptane Methyl-cyclo-hexane Ethyl-cyclo-pentane 1,1,3-Trimethyl-cyclo-pentane

CH4 C2H6 C3H8 C3H6 C4H10 C4H10 C5H12 C4H8 C5H12 C5H12 C5H8 C6H14 C6H14 C6H14 C6H14 C6H14

- -------C6H12 C6H6 C10H8 C6H12 C7H16 C7H16 C7H16 C7H14 C7H14 C7H16 C7H14 C7H16 C7H14 C7H14 C8H16

Toluene 2-m-C7 c-C7 3-m-C7 11-dm-cC6 c13-dm-cC6 t12-dm-cC6 nC8 c12-dm-cC6 Et-cC6 et-Benzene p-Xylene m-Xylene 2-m-C8 o-Xylene 1m-3e-cC6 1m-4e-cC6 c-C8 4-m-C8 nC9 Mesitylene Ps-Cumene nC10 Hemellitol nC11 nC12 nC13 1-m-Napht nC14 nC15 nC16 nC17 nC18 nC19 nC20 nC21 … nCn … nC40

Toluene 2-Methyl-heptane Cyclo-heptane 3-Methyl-heptane 1,1-Dimethyl-cyclo-hexane Cis-1,3-Dimethyl-cyclo-hexane Trans-1,2-Dimethyl-cyclo-hexane Normal-octane Cis-1,2-Dimethyl-cyclo-hexane Ethyl-cyclo-hexane Ethyl-Benzene Para-xylene Meta-xylene 2-Methyl-octane Ortho-xylene 1-Methyl-3-Ethyl-cyclo-hexane 1-Methyl-4-Ethyl-cyclo-hexane Cyclo-octane 4-Methyl-octane Normal-nonane 1,3,5-Tri-methyl-Benzene 1,2,4-Tri-methyl-Benzene Normal-decane 1,2,3-Tri-methyl-Benzene Normal-undecane Normal-dodecane Normal-tridecane 1-methyl-Naphthalene Normal-tetradecane Normal-pentadecane Normal-hexadecane Normal-heptadecane Normal-octadecane Normal-nonadecane Normal-eicosane Normal-C21 … Normal-Cn … Normal-C40

C7H8 C8H18 C7H14 C8H18 C8H16 C8H16 C8H16 C8H18 C8H16 C8H16 C8H10 C8H10 C8H10 C9H20 C8H10 C9H18 C9H18 C8H16 C9H20 C9H20 C9H12 C9H12 C10H22 C9H12 C11H24 C12H26 C13H28 C11H10 C14H30 C15H32 C16H34 C17H36 C18H38 C19H40 C20H42 C21H44 … CnH2n+2 … C40H82

The database furthermore contains the carbon number fractions from a C21 fraction to a C100 fraction

Each fraction Cn consists of all components with a boiling point in the interval from that of nCn-1 + 0

- 9°F to that of nCn + 0

Finally the database contains the components CHCmp_1 to CHCmp_6,

which are dummy pseudo-components

The only properties given in the database are the molecular weight,

and the molecular weight will usually also have to be modified by the user

Other component properties must be entered manually

Component Properties For each component the database holds the following component properties • • • • • • • • • • • •

- 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 either the SRK or PR equations

- • • • •

- 15 K/0°C/32°F (Href) Coefficients in ideal gas heat capacity (Cp) polynomial Melting point temperature (Tf)

• • • • • • • • • •

Enthalpy of melting ( ) 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,

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)

- in the SRK and PR equations

The component properties needed to calculate various physical properties and transport properties will usually be established as a part of the fluid characterization

also possible to input new components without entering all component properties and it is possible to input compositions in characterized form

and molecular weight are required input for all components to perform simulations

Whether the remaining component properties are needed or not depends on the simulation to be performed

The below table shows what component properties are needed to calculate a given property for gas and oil phases

Physical or transport property Volume Density Z factor Enthalpy (H) Entropy (S) Heat capacity (CP) Heat capacity (CV) Kappa (CP/ CV) Joule-Thomson coefficient Velocity of sound Viscosity Thermal conductivity Surface tension

Component properties needed Peneloux parameter*1) Peneloux parameter*1) Peneloux parameter*1) Ideal gas CP coefficients,

Peneloux parameter*1) Ideal gas CP coefficients,

Peneloux parameter*1) Peneloux parameter*1) Weight average molecular weight*2),

Peneloux parameter*1)

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

- • •
- and Molecular weight (M)

Missing Properties PVTsim has a option for estimating missing component properties for a fluid composition entered in characterized form

and molecular weight have all been entered

Below is shown what other properties are needed to estimate a given missing property and a reference is given to the section in the Method Documentation where the property correlation is described

Property

Section where described

needed for estimation T independent term of Peneloux parameter None Assumed equal to number average molecular weight None

Liquid density Normal boiling point Weight average molecular weight Critical volume Vapor pressure model Mathias-Copeman coefficients T-independent term of SRK or PR Peneloux parameter T-dependent term of SRK or PR Peneloux parameter Melting point depression (

Ideal gas absolute enthalpy at 273

- 15 K/0°C/32°F (Href) Ideal gas Cp coefficients Melting temperature (Tf)

PNA distribution Wax fraction Asphaltene fraction Parachor Hydrate former or not Hydrate Langmuir constants Number of ions in aqueous solution (only for salts) Number of crystal water molecules per salt molecule (only for salts)

Liquid density for pseudocomponents Not estimated for defined components

Liquid density for pseudo-components Only for pseudo-components

Viscosity data for an uninhibited/inhibited fluid

None for pseudocomponents Irrelevant for defined components

None for pseudocomponents Irrelevant for defined components

Liquid density for pseudo-components Irrelevant for defined components

None for pseudocomponents

Irrelevant for defined components

Liquid density for pseudo-components Not estimated Not estimated Not estimated Not estimated

PR with Volume Correction

Lohrenz-Bray-Clark (LBC) part of Viscosity section

SRK with Volume Correction or PR with Volume Correction SRK with Volume Correction or PR with Volume Correction

Compositional variation due to gravity Enthalpy Extended C7+ Characterization Extended C7+ Characterization Estimation of PNA Distribution Extended C7+ Characterization Asphaltenes Gas/Oil interfacial tension

Extended C7+ Characterization

Composition Handling PVTsim distinguishes between the following fluid types •

Characterized compositions

Compositions with plus fraction are compositions as reported by PVT laboratories where the last component is a plus fraction residue

For this type of compositions the required input is mol%’s of all components and molecular weights and densities of all C7+ components (carbon number fractions)

In this case the heaviest component is not a residue but an actual component or a boiling point cut and no extrapolation is performed

Gas mixtures with only a marginal content of C7+ components are usually classified as compositions with No plus fraction

Types of fluid analyses When considering fluid composition input a distinction is made between the light components up to C6 which are always identified by gas chromatographic analysis,

and the components heavier than C6 which may be analyzed in different ways

both of which must deal with the fact that the number of isomeric components for the larger molecules makes a detailed analysis of all chemical species impossible

GC analysis The GC analysis in various modifications is often used as it is relatively cheap,

- very fast,

and because only a very small sample volume is required

Furthermore the GC analysis is much more detailed than a TBP analysis

heavy ends may be lost in the analysis,

especially heavy aromatics such as asphaltenes

The main problem with a GC analysis is however that no information is retained on molecular weight (M) and density of the cuts above C6

which are essential for a proper representation of the heaviest constituents of the fluid

Often a set of residue properties is available say for the C7+ fraction,

while the measured GC composition often extends to e

In this case one may enter the mol%'s to C30 together with the M and density of the total C7+ fraction leaving the M and density fields blank for the higher C8

- - C30 fractions

With this input,

the program will be extrapolating from the C7+ fraction properties,

while honoring the reported composition for the fractions up to C30 under the mass balance constraints

one may as an alternative lump back the composition to C7+ and estimate properties from there,

which will often provide equally accurate simulation results as with the detailed GC composition

TBP Distillation The TBP distillation requires a larger sample volume,

typically 50 – 200 cc and is more time consuming

The method separates the components heavier than C6 into fractions bracketed by the boiling points of the normal alkanes

the C7 fraction refers to all species,

which distil off between the boiling point of nC6 + 0

and the boiling point of nC7 + 0

regardless of how many carbon atoms these components contain

Each of the fractions distilled off is weighed and the molecular weights and densities are determined experimentally

The density and molecular weight in combination provide valuable information to the characterization procedure on the PNA distribution

These properties are important in the characterization procedure

it is recommended that input for PVTsim is generated based on a TBP analysis

The accuracy of the 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 input densities,

and consequently the quality of the input directly affects the density predictions of the equation of state (EOS) model

they can never be expected to match the characteristics on any given crude exactly,

and thus experimental values are much to be preferred

Handling of pure components heavier than C6 When the compositional input is based on a GC analysis,

there will often be defined components (pure chemical species) reported,

which in the TBP-terminology would belong to a boiling point fraction because it has a boiling point higher than nC6 + 0

Such components may be entered alongside with the boiling point fraction,

which then represents the remaining unresolved species within that boiling point interval

the pure species are lumped into their respective boiling point fraction and the properties of that fraction adjusted accordingly

the pure species are split from the pseudo-component it ended up in,

- and the properties adjusted
- accordingly

This procedure ensures that discrepancies between different component classes are avoided in the characterization

Fluid handling operations Quite often it becomes practical to mix two or more fluids and continue simulations with the mixed composition

- ‘Weaving’,

‘Recombination’ and ‘Characterization to the same Pseudocomponents’

Averaging the properties of the pseudo-components in the individual compositions generates new pseudocomponents

For fluids characterized in PVTsim mixing is done on the level where the fluid has been characterized but not yet lumped

Each set of discrete fractions is mixed and the properties of the mixed fraction averaged on a mass basis

If the total number of C7+ components in the fluids to be mixed exceeds the defaults number of pseudocomponents (12),

pseudo-components of approximately the same weight are lumped to get down to the desired number of pseudo-components in the mixed fluid

Weaving Weaving will maintain the pseudo-components of the individual compositions and can only be performed for characterized compositions

all pseudo-components from all the original fluids are maintained in the resulting weaved fluid

This may lead to several components having the same name,

and it is therefore advisable to tag the component names in order to avoid confusion later on

The weaving option is useful to track 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)

- an oil and a gas composition

The recombination option is often used to combine a separator gas phase and a separator oil phase to get the feed to the separator

the GOR and liquid density at separator conditions must be input

Alternatively the saturation point of the recombined fluid can be entered along with the liquid density

the program determines the number of mols corresponding to the input volumes and simply mixes the two fluids based on this

the recombination is iterative (i

how much of the gas should be added to yield this saturation pressure)

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 all represented by the same component set

fashion as the mixing operation with the only difference that the same pseudos logic keeps track of the molar amount of each pseudo-component contained in each individual fluid

and can be applied for a number of tasks

In compositional pipeline simulations where different streams are mixed during the calculations or in compositional reservoir simulations where zones with different PVT behavior are considered,

mixing is straightforward when all fluids have the same pseudo-components

It is furthermore possible to do regression in combination with the characterization to the same pseudos,

in which case one may put special emphasis on fluids for which PVT data sets are available

In this case the data sets will also affect the characterization of the fluids for which no PVT data exist

Characterization to same pseudo-components is described in more detail in the section of Characterization of Heavy Hydrocarbons

Flash Algorithms

Flash Algorithms The flash algorithms of PVTsim are the backbone of all equilibrium calculations performed in the various simulation options

The terminology behind the different flash options are described in the following

Molar composition of feed (z) Pressure (P) and temperature (T)

A flash results consists of • • •

Number of phases Amounts and molar compositions of each phase Compressibility factor (Z) or density of each phase

- and aqueous)

- two oils,
- and aqueous)

- and aqueous)

- and aqueous)

- and aqueous)

UV (Gas,

- and aqueous)

- and aqueous)

Specific PT flash options considering the appropriate solid phases are used in the hydrate,

- and asphaltene options

A flash calculation assumes thermodynamic equilibrium

The thermodynamic models available in PVTsim are the Soave-Redlich-Kwong (SRK) equation of state,

the Peng-Robinson (PR) equation of state,

and the Peng-Robinson 78 (PR78) equation of state

These equations are presented in Equation of State section

To apply an equation of state,

a number of properties are needed for each component contained in the actual mixture

These are established through a C7+characterization as outlined in the section on Characterization of Heavy Hydrocarbons

They are based on the principle of Gibbs energy minimization

is the chemical potential is at a minimum

ni is the number of mols present of component i and of component i

The chemical potential can be regarded as the “escaping tendency” of component i,

and the way to escape is to form an additional phase

Only one phase is formed if the total Gibbs energy increases for all possible trial compositions of an additional phase

if it is possible to separate the mixture into two phases having a total Gibbs energy,

lower than that of the single phase

each component will have equal chemical potentials in each phase µ iI = µ iII The final number of phases and the phase compositions are determined as those with the lowest total Gibbs energy

The calculation of whether a given mixture at a specified (P,T) separates into two or more phases is called a stability analysis

The starting point is the Gibbs energy,

of the mixture as a single phase G0 = G(n1,

- n3,……,nN) ni stands for the number of mols 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

nN ) and ( ,

- ……,
- ) where is small

The Gibbs energy of phase I may be approximated by a Taylor series expansion truncated after the first order term

N ∂G G1 = G 0 − ∑ ε i i i =1 ∂n i n

- ,……,

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

∆G = G I + G II − G 0 = ∑ ε i ((µ i )II − (µ i )0 ) = ε ∑ yi ((µ i ) II − (µ i ) 0 )

and yi is the mol fraction of component i in phase II

- respectively

expressed in terms of the fugacity,

- as follows

µ i = µ i0 + RT1n f i = µ i0 + RT(1n z i + lnϕ i + 1n P ) is a standard state chemical potential,

- a fugacity coefficient,
- z a mol fraction,

P the where pressure,

and the sub-index i stands for component i

The standard state is in this case the pure component i at the temperature and pressure of the system

The equation for may then be rewritten to ∆G N = ∑ y i (1n y i +1n(ϕ i ) II − ln z i − 1n(ϕ i )0 ) εRT i =1

where zi is the mol fraction of component i in the total mixture

The stability criterion can now be expressed in terms of mol fractions and fugacity coefficients

Only one phase exists if N

- ∑ y (ln y + ln(ϕ ) i =1

− ln z i − ln(ϕ i ) 0 ) > 0

for all trial compositions of phase II

A minimum in G will at the same time be a stationary point

A stationary point must satisfy the equation ln yi + ln(ϕ i ) II − lnzi − ln(ϕ i )0 = k where k is independent of component index

given by ln Yi = ln yi – k the following equation may be derived

- 1n Yi = 1n zi + 1n(

)0 – 1n(

PVTsim uses the following initial estimate for the ratio Ki between the mol fraction of component i in the vapor phase and in the liquid phase Ki =

Pci T exp 5

- 42 (1 − ci ) P T

where Ki= yi/xi and Tci is the critical temperature and Pci the critical pressure of component i

if phase 0 is a liquid and zi/Ki,

- if phase 0 is a vapor

corresponding to the initial estimates for Yi are determined based on these fugacity coefficients,

- new Yi-value are determined,
- and so on

For a single-phase mixture this direct substitution calculation will either converge to the trivial solution (i

to two identical phases) or to Yi-values fulfilling the criterion N

- ∑Y ≤1 i =1

which corresponds to a non-negative value of the constant k

In the two-phase case the molar composition obtained for phase II is a good starting point for the calculation of the phase compositions

For two phases in equilibrium,

three sets of equations must be satisfied

- βyi + (1 − β )x i = zi ,
- (i = 1,2,3,

- (i = 1,2,3,

- ∑ (y − x ) = 0,
- (i = 1,2,3,

N ) i =1

yi and zi are mol fractions in the liquid phase,

the vapor phase and the total mixture,

- respectively

is the molar fraction of the vapor phase

and are the fugacity coefficients of component i in the vapor and liquid phases calculated from the equation of state

- namely (x1,

x3,…,

the number of variables equals the number of equations

The equations can be simplified by introducing the equilibrium ratio or K-factor,

- 1 + β(K i − 1)
- (i = 1,2,3,
- (i = 1,2,3,
- yi = K i x i ,
- and for Ki
- ϕ iL Ki = V ,
- (i = 1,2,3,

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

- ln ϕ iL ,
- ln ϕ iV
- (i = 1,2,3,
- ∑ (y − x ) = ∑ z (K i

− 1)/(1 + β(K i − 1)) = 0

- a given (T,

- an estimate of
- may be derived

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

- zi (K im − 1) =0 Hi i =1 N
- where j −1

β is the molar fraction of phase m

equals the ratio of mol fractions of component i in phase m and phase J

- z i K im ,
- (i = 1,2,3,
- m = 1,2,3,
- (i = 1,2,3,

are the mol fractions of component i in phase m and phase J,

- respectively

Passage of a valve may for example be approximated as a constant enthalpy (H) process and a compression as a constant entropy (S) process

The temperature after a valve may therefore be simulated by initially performing a PT flash at the conditions at the inlet to the valve

the temperature at the outlet can be found from a PH flash with P equal to the outlet pressure and H equal to the enthalpy at the inlet

A PT flash followed by a PS flash may similarly be used to determine an approximate temperature after a compressor

To perform a PH or a PS flash an estimate has to be provided for the temperature

85°C/80

Two object functions are defined

These are for a two-phase PH flash N

- g1 = ∑ z i (K i − 1)ζ i i =1
- g 2 = H − H spec

ς i = 1 + β(K i − 1) H is total molar enthalpy for the estimated phase compositions,

and Hspec is the specified molar enthalpy

The iteration procedure is described in Michelsen (1986)

UV and HS

A VT specification is useful to for example determine the pressure in an offshore pipeline during shutdown

Phase Identification If a PT flash calculation for an oil or gas mixture shows existence of two phases,

the phase of the lower density will in 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 generally accepted definition to distinguish a gas from a liquid

a criterion is needed for distinguishing between the two types of phases

The following phase identification criteria are used in PVTsim 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 1

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 mol% total of the components water,

hydrate inhibitors and salts is identified as an aqueous phase

Components Handled by Flash Algorithms The non-aqueous PT-flash algorithm handles the following component classes • • •

Other inorganic Organic defined Pseudo-components

The PT aqueous and multiflash algorithms handle • • • • • •

The PH,

and HS flash algorithms handle • • • • •

“The Isothermal Flash Problem

Michelsen,

“The Isothermal Flash Problem

“Multiphase Isenthalpic and Isentropic Flash Algorithms”,

Phase Envelope and Saturation Point 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 equals a specified value

The phase envelope option in PVTsim (Michelsen,

- 1980) may be used to construct dew and bubble point lines,

corresponding values of T and P for which

- equals 1
- respectively

Also inner lines (0< 1 It is seen that the proposed temperature dependence reduces to the default (classical) one for C1 = m and C2 = C3 = 0

In general the Mathias-Copeman (M&C) expression offers a more flexible temperature dependence than the classical expression

It can therefore be used to represent more complicated pure component vapor pressure curves than is possible with the classical expression

M&C is not used default in PVTsim,

but is it possible for the user to change temperature dependence from classical to M&C and to enter M&C coefficients (C1,

RT a − V − b (V + c')(V + b + 2c )

The SRK molar volume,

and the Peneloux molar volume,

- are related as follows

is similarly related to the SRK b-parameter as

- ~ b= b −c

and it is given by the following equation c'= c’ + c’’ (T – 288

- 15) where T is the temperature in K

The parameter c’ is the temperature independent volume correction and c’’ the temperature dependent volume correction

Per default the temperature dependent volume correction c’’ is set to zero unless for C+ pseudo-components

In general the temperature independent Peneloux volume correction for defined organics and “other organics” is found from the following expression c' = 0

- 29441 − ZRA ) Pc

- 29056 – 0
- 08775 For some components,
- and CO2,

the values have been found from pure component density data

The liquid density is known at 15°C/59°F from the composition input

the c’ parameter can be found as the difference between this molar volume and the SRK molar volume for the same temperature

Similarly c’’ is found as the difference between the molar volume at 80°C/176°F given by the ASTM 1250-80 density

correlation and the Peneloux molar volume for the same temperature,

where the Peneloux volume is found assuming c=c’

- where a(T) = ac a c'= Ωa

- T 0
- 5 α(T) = 1 + m1 − Tc R Tc b = Ωb Pc
- where Ω a = 0
- 45724 Ω b = 0
- 07780 The parameter m is for the PR equation found from m = 0

37464 + 1

379642 +

- 48503 − 0

at equilibrium at those conditions no hydrate can exist and the water will be in the form of either liquid or ice

Hydrate P/T Flash Calculations Flash calculations are in PVTsim performed using an ”inverse” calculation procedure as outlined below

Initial estimates are established of the fugacity coefficients of all the components in all phases except in the hydrate phases and in any pure solid phases

This is done by assuming an ideal gas and ideal liquid solution,

neglecting water in the hydrocarbon liquid phase and by assuming that any water phase will be pure water

The results of this calculation will be the compositions and amounts of all phases (except any hydrate and pure solid phases) based on the guessed fugacity coefficients,

- : xKj and

- j ≠ hyd and pure solid

subscript K is a component index,

- j a phase index,

stands for phase fraction and N for number of components

the fugacities of all components in all the phases except the hydrate and pure solid phases are calculated,

- j ≠ hyd and pure solid)

- j≠ hyd and pure solid),

mixture fugacities are calculated

For the non-water components,

a mixture fugacity is calculated as the molar average of the fugacities of the given component in the present hydrocarbon phases

For water the mixture fugacity is set equal to the fugacity of water in the water phase

is a correction term identical for all components

from where w stands for water and empty hydrate lattice

The hydrate compositions are calculated using the expression

- is found refers to the

which enables calculation of the fugacity coefficients as described below

Non-hydrate formers are assigned large fugacity coefficients (ln = 50) to prevent them from entering into the hydrate phases

Based on the actual values of the fugacity coefficients for all the components in all the phases ( Kj) and the total overall composition zK an ideal solution (composition independent fugacity coefficients) a multi phase flash is performed (Michelsen,

- : xKj and 1,…,
- number of phases)

Calculation of Fugacities Fluid Phases To use the flash calculation procedure outlined above,

expressions must be available for the fugacity of component i in each phase to be considered

The fugacity of component i in a solution is given by the following expression

- fi = ϕi x i P where
- is the fugacity coefficient,

xi the mol fraction and P the pressure

is calculated from the selected equation of state

Hydrate Phases The fugacities of the various components in the hydrate phases are calculated as described by Michelsen (1991) Water:

N (1 − θ ) N 0θ ln f wH − ln f wβ = v i ln 0 + v 2 ln v1 v2 Other Hydrate Formers:

vi = number of cavities of type i N0 = number of empty lattice sites

θ = ratio of free large lattice sites to total free lattice sites NK = content of component k per mol of water Cki = Langmuir constant

α k = Ck1/Ck2 The determination of and N0 follows the procedure described by Michelsen

the hydrate model parameters are equation of state specific in order to ensure comparable model performance for both SRK and PR

- 15 273

15 0

- 0390 P f ice = − 2
- 064 1− − 4
- 710 ln + T T T + 273

where P is the pressure in atm and T the temperature in K

Salts The fugacities of a salt in pure solid form is assumed to be equal to the fugacity of the mentioned salt in saturated liquid solution in water

The solubilities in mol salts per mol water are found from the following expressions (with T in °C) Sodium Chloride,

108 + 0

- 000125 T Mol water

- 91°C : Solubility in wgt% =
- 91°C ≤ T < 30
- 35°C : Solubility in wgt% = 30
- 35°C ≤ T : Solubility in wgt% = 3
- 85 Potassium Chloride,

KCl Mol salt = 0

0674 + 0

- 000544 T Mol water

Sodium Formate,

Mol salt = 0

145 + 0

- 00355 T Mol water

Mol salt = 0

- 313 Mol water

712 + 0

- 00705 T Mol water

-20°C :

Mol salt = 0

964 + 0

- 0174 T Mol water

-6°C :

Mol salt = 0

0248 + 0

- 00143 T Mol water
- -6°C ≤ T < 50°C :
- 50oC ≤ T :

272 + 0

- 006 T Mol water

Mol salt = 0

- 572 Mol water

if they consist of 3 ions and the solubility of NaCl,

if they consist of a number of ions different from 3

Burgass,

- and Todd,

IChemE,

- 71 (Part A),

457-459,

”Development of a Natural Gas Hydrate Prediction Computer Program”,

- thesis,

- and Michelsen,

”Modeling of Structure H Hydrates using a Langmuir Adsorption Model”,

1111-1114

”Calculation of Multiphase Equilibrium in Ideal Solutions”,

”Calculation of Hydrate fugacities ”,

1192-1193

Skjold-Jørgensen S

- and Rasmussen,

”Computations of the Formation of Gas Hydrates”,

2661-2672

- and Pedersen,

“Challenges in Modeling of Gas Hydrate Phase Equilibria”,

- 4th International Conference on Gas Hydrates Yokohama Japan,

- and Todd,

“Equilibrium Data and Thermodynamic Modelling of Cyclohexane Gas Hydrates”,

159-163,

Danesh,

- Østergaard,

241-250,

Modeling of Wax Formation The wax module of PVTsim may be used to determine the wax appearance temperature (cloud point) at a given pressure,

the wax appearance pressure at a given temperature and to perform PT flash calculations taking into consideration the possible formation of a wax phase in addition to gas and oil phases

The wax model used is that of Pedersen (1995) extended as proposed by Rønningsen et al

Vapor-Liquid-Wax Phase Equilibria At thermodynamic equilibrium between a liquid (oil) and a solid (wax) phase,

- the fugacity,

of component i in the liquid phase equals the fugacity,

of component i in the solid phase

f iL = f iS When a cubic equation of state is used for the liquid phase it is practical to express the liquid phase fugacities in terms of fugacity coefficients f iL =x iL ϕ iL P is the liquid phase mol fraction of component i,

the liquid phase In this expression fugacity coefficient of component i and P the pressure

the solid phase fugacity of component i can be expressed as f iS = x Si f ioS the solid standard state fugacity where x Si is the solid phase mol fraction of component i,

- and of component i

The solid standard state fugacity is related to the liquid standard state fugacity as f ioS (Pref ) ∆G = RT ln oL ( ) f P re