PVT and rheology investigation

C H A P T E R

3 PVT and rheology investigation O U T L I N E Phase behavior

Fluid characterization Viscosity Lumping for different fluids Solid-liquid equilibrium Additional laboratory studies PVT tuning

43

Fluid sampling 44 Onshore vs deepwater 44 Special considerations for H2S samples 44 Special considerations for mercury samples 44 Sampling hydrocarbon fluid 45 Quality of fluid samples Oil sample quality checks Hydrocarbon fluid sample quality checks Water sample quality checks

45 45 45 50

Drilling and wellwork fluids formulation and safety 51 Fluid characterization Fluid properties and measurements

51 51

52 56 56 57 59 60

Fluid physical properties

61

Non-Newtonian behavior

63

Emulsion characteristics

64

Biodegradation

65

References

65

Further reading

66

This chapter is at the beginning of the book because thermodynamic fluid characterization also known as PVT represents the third most important characteristic of petroleum production after reservoir characterization and well drilling, and the most important one for flow assurance and for production chemistry. Good understanding of fluid properties allows a flow assurance engineer to develop a technically feasible and economically optimal set of strategies to overcome a variety of problems listed in the first two chapters.

Phase behavior Flow assurance analyzes the flow of fluids and associated solids at a range of pressure and temperature conditions. Properties of fluids vary with both temperature and pressure.

Handbook of Multiphase Flow Assurance https://doi.org/10.1016/B978-0-12-813062-9.00003-8

43

© 2019 Elsevier Inc. All rights reserved.

44

3.  PVT and rheology investigation

Pressure Undersaturated Liquid

Reservoir Early Life

Dense Phase

Wellhead Early Life

Reservoir Late Life Vapor + Saturated Liquid

Separator Separator Late Life Early Life

Vapor

Wellhead Late Life Temperature

FIG. 3.1  Fluid behavior shown on a phase diagram versus time and location in the production system.

A phase diagram in Fig. 3.1 helps illustrate fluid phases which are stable at different temperatures and pressures. A simple vapor-liquid equilibrium or VLE phase diagram is usually plotted in two dimensions on the scales of pressure and temperature, and illustrates just two phases, liquid and gas.

Fluid sampling Onshore vs deepwater Majority of onshore fluid samples are collected at the surface. Sampling conditions at the test separator should always be recorded. Deepwater exploration fluid samples are normally collected downhole to preserve the fluid phase state. A number of special containers are used for sampling such as MPSR, etc.

Special considerations for H2S samples Containers for H2S collection should have internal lining which prevents H2S adsorption on steel. Without such lining the H2S molecules adsorb on container walls and subsequent sample analysis may show little or no H2S present in the fluid whereas in the reservoir H2S would be in greater quantity.

Special considerations for mercury samples Sample containers for fluids which may contain mercury should also be specially prepared. Mercury similarly may adsorb on container walls making the fluid sample not representative. A good summary of sampling techniques and in situ analysis is provided by Fiotodimitraki (2016).



Quality of fluid samples

45

Laboratories for the sample collection should be validated, and personnel involved in actual sampling should be aware of the proper well flow duration requirements before the sampling takes place, to ensure that the sample is not contaminated with drilling mud and that sample itself is uniform and representative of the reservoir fluid.

Sampling hydrocarbon fluid API Recommended Practice 44 provides detailed recommendations on how to conduct the sampling for typical hydrocarbon fluids. Sampling specialists and laboratories would have additional procedures on how to properly collect and transport samples of fluids which may contain small amounts of hydrogen sulfide or mercury. Information whether a sampling program should have provisions for H2S or mercury may be obtained from regional analog fluids, from the analysis of samples collected earlier in the same region about which published information is available or from geologic analysis which provides indications whether similar rock structures may contain certain minerals which get dissolved by the reservoir fluid.

Quality of fluid samples Quality of the samples is of the most critical importance to the preconcept and concept evaluation phases of a project when the technical feasibility of developing an asset is evaluated. A flow assurance specialist should be able to use a few simple quality checks to find the most representative samples or to compensate for sample contamination.

Oil sample quality checks Collecting a surface sample from a separator onshore is much simpler than collecting a downhole sample from an openhole wellbore in deepwater. Thus a close attention must be paid to quality checks of the samples collected downhole. Several initial checks are described below. These checks omit the sampling process and conditions, container preparation and sample transfer and instead focus on the measured properties control which allows the flow assurance specialist to review data in the laboratory reports for the factors which can affect flow assurance work.

Hydrocarbon fluid sample quality checks 1. Check for GOR range GOR of the samples collected from similar depths of the same reservoir should be fairly constant, within a few hundred scf/stb. If GOR of some of the samples differs significantly from the rest, particularly if GOR is lower than the average, it may indicate that some of the gas was lost during downhole sample collection or transfer. In this case the reservoir fluid sample composition should be checked for methane content.

46

3.  PVT and rheology investigation

If the low GOR sample shows methane content relatively lower than in other samples, this may indicate gas loss during sample recovery to surface. Usually the low quality samples are not used. However, if very few samples are available, it may be possible to offset the loss of gas which could occur during or after sampling and see if GOR may be matched by adding methane back to the composition. Conversely, if GOR of a downhole sample is significantly higher than the rest of the samples, it may indicate gas coning and intake at the sampling depth. This may happen in saturated reservoirs where a gas cap is present or pressure is at or below the bubble point, and should not be the case in reservoirs with undersaturated fluid or dense phase. If GOR of one of the samples is higher than the average, the sample may have been collected near a gas cap if reservoir is saturated and free gas exists. An example of a GOR check is shown below. Fluid A-1 from 3050 m depth in well A has a GOR of 800 scf/stb, fluid B-2 from 3060 m in well B has a GOR of 810 scf/stb. Fluid B-1 from 3055 m in well B has a GOR of 600 scf/stb. It is possible that the sample container B-1 lost some gas during sample transfer from well bottomhole to the lab. Laboratories record and report the pressure which the beneficiated sample exhibited at opening of the container to verify whether pressure is similar to the other containers and if any part of the sample may have been lost. 2. Check for drilling mud contamination Oil based drilling muds typically are formulated with diesel fuel, kerosene or another available fraction of hydrocarbons. This hydrocarbon base of the mud would usually have increased content of hydrocarbons in the range between C16 and C20. Some synthetic muds can be formulated to have only even-numbered paraffins such as C16 and C18 dominate the composition. The presence of these paraffins can be noticed in gas chromatography analysis as an increased content relative to the composition of all paraffins on a logarithmic plot. These components are not expected to be present at the increased content in a reservoir fluid and can affect its properties. Additional steps are required to de-contaminate the sample or to find the sample with the least drilling mud contamination. Contamination level with a drilling mud below 1–2 wt% is considered acceptable for a PVT analysis. An example of a mud contamination check is shown below. Log10 plot of a GC analysis of sample A-1 composition in Fig. 3.2 shows a linear trend of C10+ component mass percent versus carbon number. Log10 of A-1 component mass % 0.6 0.5 0.4 0.3 0.2 0.1 0

C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35

FIG. 3.2  Example of a fluid with little to no contamination with oil-based drilling mud.



47

Quality of fluid samples

Log10 of A-2 component mass % 0.6 0.5 0.4 0.3 0.2 0.1 0

C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35

FIG. 3.3  Example of a fluid with some contamination with oil-based drilling mud seen as peaks at C16 and C18. Note that mud carbon numbers may vary such as C14 and C16 or C18 and C20, etc.

Log10 plot of a GC analysis of sample A-2 in Fig. 3.3 has two significant deviations from a linear trend at carbon numbers C16 and C18. It is known that the wells were drilled with an oil-based mud. The sample A-2 is likely contaminated with hydrocarbon components from the drilling mud. This is important for reservoir modeling because PVT properties of a sample contaminated with drilling mud would differ from the properties of the reservoir fluid. This is also important for flow assurance because components C16 and C18 would affect solubility of wax components C18 and C20, so prediction of wax deposition using data from a contaminated sample would be less accurate. For the purpose of wax deposition analysis it is possible to remove the artificially introduced parts of the components from the composition analysis to get a better prediction of wax deposition from a decontaminated sample. However, reservoir modeling requires a more thorough process of removing the oil-based mud contamination and tuning the fluid properties. 3. Quality of PVT analysis can be examined by checking material balance of components in the Differential Liberation or multistage separation tests for oil-dominated fluids or in the constant volume depletion for gas condensates and volatile oils Amounts of mass or moles of individual components from separated gas and liquid should add up to the amounts in the original sample. Also a mass balance or mole balance check may also be used to verify that measured oil density and calculated gas density are consistent with the measured GOR. An example of a material balance check for a typical PVT report is shown below. Usual reservoir fluid composition as in Table 3.1 and PVT summary provides mole percentages for an oil sample from a differential liberation test. TABLE 3.1  Example fluid composition as a reservoir fluid, liquid and gas Reservoir fluid

Liquid

Gas

Symbol

Component Name

Mole %

Mole %

Mole %

N2

Nitrogen

0.41

0.00

0.69

CO2

Carbon dioxide

0.29

0.01

0.48 (Continued)

48

3.  PVT and rheology investigation

Component

Reservoir fluid

Liquid

Gas

Mole %

Mole %

Symbol

Name

Mole %

C1

Methane

41.53

0.25

69.99

C2

Ethane

5.40

0.29

 8.92

C3

Propane

6.60

1.32

10.24

iC4

i-Butane

1.31

0.59

 1.80

nC4

n-Butane

3.38

2.13

 4.24

iC5

i-Pentane

1.35

1.59

 1.18

nC5

n-Pentane

1.68

2.32

 1.23

iC6

i-Hexanes

3.04

6.20

 0.86

C7+

Heptanes +

35.00

85.31

 0.36

Gas-oil ratio

876

scf/stb

Gas gravity

0.874

(Air = 1.00)

Gas MW

25.2

g/mol

Oil density

884

kg/m3

28.5

°API

Oil MW

194.9

g/mol

TABLE 3.2  Quality check example x/z

y/z

C1

0.00602

1.685288

C2

0.053704

1.651852

C3

0.2

1.551515

iC4

0.450382

1.374046

nC4

0.630178

1.254438

iC5

1.177778

0.874074

nC5

1.380952

0.732143

Component mole % in liquid relative to % in total fluid, and mole % in vapor relative to % in total fluid.

From the PVT report we can prepare a table as in Table 3.2 of vapor Y relative to reservoir fluid Z and of liquid X relative to reservoir fluid Z components. The plot of the vapor (y/z) vs liquid (x/z) in Fig. 3.4 should be close to linear if sampling in the well, sample beneficiation in the lab, and the lab tests were all performed correctly. If there are significant deviations, particularly in the light hydrocarbons, this may indicate a low quality sample and possible loss of light ends, if there is too little methane, or sampling of only gas if there is too much methane. In such case the history of sample collection should be reviewed to see if sufficient time was allowed for a well flow before sample collection (also called conditioning a well).



49

Quality of fluid samples

Material Balance Plot for C1-C5 components mole % in vapor vs in liquid. Slope ~1/GOR 1.8 1.6 1.4

y/z

1.2 1 0.8

y = -0.6926x + 1.6891

0.6 0.4 0.2 0

0

0.5

1

1.5

x/z

FIG. 3.4  Material balance plot for methane to pentane. Abscissa shows mole % ratio from Table 3.2 of each component in liquid. Ordinate shows mole % ratio from Table 3.2 of each component in vapor.

Linearity of the plot confirms that the sample quality is good and it can be used for flow assurance analysis. It is also possible to verify the gas oil ratio measured in the lab using information from the plot. A linear curve fit for the plot provides a slope. This slope is a ratio between vapor components and liquid components. The slope is inversely proportional to the GOR, which can be estimated using the following equations. Units of each parameter are presented for clarity. GOR ( scf / stb ) = 0.159 ( m 3 / bbl ) 35.3 ( scf / m3 ) Volumetric gas ratio ( m 3 gas / m 3 oil ) ∗

∗

Volumetric gas ratio ( m 3 gas / m 3 oil ) = Molar vapor ratio ( mol gas / mol oil )

∗

Gas molar volume ( L gas / mol gas ) / Oil molar volume ( L oil / mol oil ) Molar vapor ratio ( mol gas / mol oil ) = −1 / slope Gas molar volume ( L gas / mol gas ) = Gas MW ( g gas / mol gas ) / Gas density ( g gas / L gas ) Oil molar volume ( L oil / mol oil ) = Oil MW ( g oil / mol oil ) / Oil density ( g oil / L oil ) Gas density ( g gas / L gas ) = Gas gravity ( ( g gas / L gas ) / ( g Air / L air ) ) ∗11.225 ( g Air / L Air ) Oil density ( g oil / L oil ) = 141.5 / ( Oil API° + 131.5 ) ∗ 1000 Calculation of GOR is provided below: Slope = −0.692 Molar vapor ratio = −1 / −0.692 = 1.445 ( mol gas / mol oil )

50

3.  PVT and rheology investigation

Gas molar volume = 25.2 / ( 0.874∗1.225 ) = 23.5 ( L gas / mol gas ) Oil molar volume = 194.9 / ( 141.5 / ( 28.5 + 131.5 ) ∗ 1000 ) = 0.220 ( L oil / mol oil ) Volumetric gas ratio = 1.445∗ 23.5 / 0.220 = 154.3 ( m 3 gas / m 3 oil ) GOR = 0.159∗ 35.3∗ 154.3 = 866 ( scf / STB ) . The value of GOR estimated from the material balance is in fair agreement with the ­reported value of 876 scf/STB. This also confirms quality of the sample.

Water sample quality checks The quality of the water sample is important for various production chemistry analyses. The following initial quality checks may be done by a specialist to verify sample data. 1. Ionic balance Ionic balance is the similarity of the combined weight of positive ions and the combined weight of negative ions. Ionic balance indicates that sampling and lab analysis of the water was performed correctly. 2. Drilling mud contamination Most modern deepwater wells are drilled using an oil-based drilling mud, which keeps water emulsified. This limits the exposure of water-sensitive rock such as water-swelling clays to water, and also limits the exposure of the sample water to the mud water. Most non-deepwater wells are drilled using a simpler water-based drilling mud. If a water based drilling mud was used, brines used to weigh the mud could contact and contaminate the downhole water sample with ions such as sulfate which originates from seawater carrier for salt, and with barite from salts which do make the mud heavy. Typical reservoir water would have sulfate SO42− under 200 mg/L because sulfate SO42− ions convert to sulfide S2− and precipitate as iron sulfide FeS, zinc sulfide ZnS or other minerals in reservoir over geologic times. Seawater would typically have around 2600 mg/L SO42−. Any reservoir water with SO42− greater than 200 mg/L may be contaminated with water from the drilling mud. The reservoir water samples with the lowest SO42− concentration should be selected for further analysis. 3. Other salts The following salts may be used to weigh the mud: calcium chloride CaCl2 calcium bromide CaBr2 zinc bromide ZnBr potassium formate KHCO2 cesium formate CsHCO2 for HPHT wells and reservoirs Scale saturation index may be used to check water sample quality. Downhole samples with scale saturation index below zero or saturation ratio below one calculated at reservoir conditions should be used as this indicates that water sample is not oversaturated with minerals. The saturation index is calculated using any of the available scale prediction methods. Bicarbonate HCO3 concentration will decrease after sampling due to HCO3 conversion to carbonic acid H2CO3 and to CO2 and evolution of CO2.



Fluid characterization

51

Extreme cases In rare cases the bicarbonate concentration may reach nearly 10,000 mg/L in some reservoirs which have high CO2 content. This indicates that reservoir water is saturated with CO2. Reservoir water chemistry may change if seawater is introduced. CO2 will dissolve in seawater lowering its pH and making it acidic. Acidic seawater can dissolve carbonate minerals in the reservoir and as pressure drops in or near the wellbore, dissolved minerals can precipitate out of water solution causing solid scale deposition.

Drilling and wellwork fluids formulation and safety Salts make the drilling muds and completion or wellwork fluids heavy in order to use hydrostatic pressure of the mud to counteract the potentially high pressure of reservoir fluids. Overbalanced and underbalanced drilling are not in the scope of this work. Salts also help control hydrate formation which can plug flow paths and stop circulation during wellwork. All reservoirs differ in their many parameters. The two parameters we review in this section are rock consolidation and pressure. Consolidation defines how strong is the rock and how much pressure it takes to fracture it. Consolidation of mudstone or sandstone may be weak. Pressure in some known reservoirs can be very high, up to 29,000 psi or almost 2000 bar. When well and reservoir pressure dictate the need to prevent hydrate formation yet the consolidation of the reservoir rock is weak, then the use of salt may create a wellwork fluid which is too heavy and could lead to an uncontrolled fracture of the weakly consolidated rock. In extreme cases this is manifested as hydrocarbon seeps at seabed around the wellbore. To avoid such events, the wellwork fluid has to be formulated with both salts and other hydrate inhibitors to maintain both the desired mud weight and the hydrate inhibiting properties. A specialized series of lab measurements at up to 30,000 psi (2000 bar) were completed at the Colorado School of Mines (Hu et al., 2017a,b) which provide hydrate stability conditions with a variety of salts and inhibitors commonly used in wellwork fluids.

Fluid characterization After the sample quality is verified, a flow assurance specialist can use the PVT report information to characterize the fluid for predictive use with an equation of state. The objective for the fluid characterization process is to find the parameters for the selected equation of state which will accurately predict properties of vapor, liquid and undersaturated fluid phases along the range of temperature and pressure of interest for the subsequent multiphase flow assurance analysis. Key predicted parameters which must match the laboratory measurements closely include density, saturation pressure, gas oil ratio and viscosity.

Fluid properties and measurements Selection of the equation of state most appropriate for fluid characterization would determine the accuracy of fluid properties calculation. Equations of state are cubic equations relating pressure (P), volume (V) via compressibility (Z) and temperature (T) in a mixture of

52

3.  PVT and rheology investigation

components as a function of energy of interaction between components (A) and of molecular size (B). Peng Robinson or PR EOS and its updated versions PR78, PR78 Peneloux work more accurately with liquid-dominated systems and are equally as good for gas systems. Most hydrocarbon reservoir fluids are at present characterized using the PR78 EOS with the density correction developed by Peneloux and coauthors in Peneloux et al. (1982). Soave Redlich Kwong or SRK EOS works well for gas dominated fluids because the Soave variant of the Redlich Kwong EOS can underpredict liquid compressibility by 10–20% whereas the PR EOS predicts liquid compressibility a little better. Polynomial form of P-R E.O.S. is Z 3 + ( B − 1) Z 2 + ( A − 3B2 − 2B ) Z + ( B3 + B2 − AB ) = 0

(

A = 0.45724α Pr / Tr2

α = 1 + ( 0.37464 + 1.54226ω − 0.26992ω 2 ) ( −1Tr0.5 ) B=

)

2

P bP = 0.07780 r RT Tr P Pr = Pc T Tr = Tc

Values of acentric factor w, critical pressure and temperature Tc and Pc are known for each component. EOS calculates compressibilities of vapor and liquid for a given pressure and temperature. Fluids with high CO2 or other polar or associating components content may be modeled with specialty variants of the equations of state. Recent equations of state CPA (cubic plus association) and SAFT (self associating fluid theory) include an additional parameter of association between molecules. These methods are useful for polar components such as water, CO2, aromatics and asphaltenes. Other more complex equations of state are seldom used because a fully compositional model requires fast calculation of fluid properties, and the main demand for fluid properties is in reservoir simulation. Fluid characterization used for reservoir simulation is then usually transferred for further fluid analysis in flow assurance and in production chemistry in order to assure flow in the multiphase production system and surface process facilities.

Fluid characterization Sometimes the composition analysis data are limited and reported in a form of true boiling point analysis of volume % hydrocarbon vs temperature, with density data for the fractions unavailable. In order to model such fluid with EOS, it has to be converted from volume % to mass % distribution for hydrocarbon fractions.



53

Fluid characterization

Group contribution method (Joback and Reid, 1987) may be used to estimate boiling point of a one specific hydrocarbon molecule. However, this method would require estimating properties for hundreds of hydrocarbon molecules to find boiling point cuts which would introduce inaccuracy by developing a correlation from a correlation. Katz and Firoozabadi (1978) report boiling points for up to C45 and interaction coefficients for n-C4 and heavier for use with Peng-Robinson-AGA procedure to find fluid properties. This method was adopted by Pedersen (Pedersen, 1989) to correlate Tb with MW and SG. Correlation is used up to C45, then adds 6K for each carbon number. Tb  ° R  = 97.58 MW ^ 0.3323 SG ^ 0.04609 However, this method does not provide a formula directly usable by an engineer to correlate carbon number with boiling point as it requires density of each fraction. An additional correlation was developed here based on 188 hydrocarbons including n-­alkanes, isoalkanes and aromatics which relates carbon number to boiling point, applicable to C5+. Tb [ K ] = 240.71∗ LN ( carbon # ) − 90.5, for C 5 +

Boiling temperatures [K] for C1–C4 are 111.15, 180.82, 236.75, 276.15. This formula may be used when composition analysis is reported in a form of true boiling point analysis of volume % hydrocarbon vs temperature. Conversion of TBP data from volume to weight fractions facilitates the further fluid characterization by permitting conversion of boiling point to carbon number. Inverse form of the correlation shown in Fig. 3.5 is: carbon # = 1.455 exp ( Tb [ K ] / 240.69 ) , for C 5 + or

(

)

carbon # = exp ( Tb [ K ] + 90.5 ) / 240.69 . 1000 y = 240.69ln(x) - 90.295 R² = 0.969

Boiling Temperature, K

900 800 700 600 500 400 300 200 100 0 1

10

100

Carbon Number

FIG. 3.5  Correlation of boiling temperature versus carbon number for pentane and heavier hydrocarbons.

54 Correlation Boiling Temperature, K

3.  PVT and rheology investigation

1200 1000 800 600 400 200 0

0

200 400 600 800 1000 Data Boiling Temperature, K

1200

FIG. 3.6  Comparison of boiling temperature from correlation vs from data.

The correlation performs fairly well, within ±20% error vs data as shown in Fig. 3.6. Density can be related to carbon number either by method of Whitson and Brule (2000) or Pedersen (1989). Additional correlation in Fig. 3.7 for 115 n-alkanes, isoalkanes and aromatics is proposed, applicable to C5+: SG at 20° C  = 0.0661∗ Ln ( carbon # ) + 0.59 for C5 + Specific gravities for C3–C4 are 0.504, 0.63. Inverse form of the correlation is: or

(

)

carbon # = exp 15.129 SG at 20° C  / 7501, for C5 +

((

)

carbon # = exp SG at 20° C  − 0.59 / 0.0661

)

1.2

Density at 20°C, g/cm3

1 0.8 0.6 0.4 0.2 0

0

10

20 30 40 Carbon Number

FIG. 3.7  Correlation for hydrocarbon density vs carbon number.

50

60



55

Fluid characterization

Correlation Density at 20°C, g/cm3

1.2 1 0.8 0.6 0.4 0.2 0

0

0.2

0.4 0.6 0.8 1 Data Density at 20°C, g/cm3

1.2

FIG. 3.8  Comparison of hydrocarbon density from correlation vs from data.

The correlation performs fairly well for paraffins and overall reasonably, within ±20% error vs data, except for heavy components such as fused polyaromatics like naphthalene, anthracene, or pyrene as shown in Fig. 3.8. Combining the two equations,

(

((

)

)

exp ( Tb [ K ] + 90.5 ) / 240.69 = exp SG at 20° C  − 0.59 / 0.0661 or

)

( Tb [ K ] + 90.5 ) / 240.69 = ( SG at 20 C  − 0.59 ) / 0.0661 °

we get a simplified relationship between specific gravity at 20 °C and boiling temperature of a hydrocarbon fraction at 1 atm, for C5+ or Tb > 309 K. SG at 20° C  = 0.615 + Tb [ K ] / 3642 for C5 + or Tb > 309K Once the specific gravity information is derived from the True Boiling Point analysis, the critical properties for the Equation of State may be estimated by method of Riazi and Daubert (1980) Tc  ° R  = 24.2787 Tb  ° R 

0.58848

Pc [ psia ] = 3122810000Tb  ° R 

∗ SG  at 60° F 

−2.3125

0.3596

∗ SG at 60° F 

2.3201

Molecular weight may be estimated from SG using Pedersen (1989). MW = 14∗ carbon number − 4

56

3.  PVT and rheology investigation

Viscosity A number of correlations exist for dead oil viscosity as function of temperature and density. A summary overview of these correlations is provided in Bergman and Sutton (2007). Based on over 9000 viscosity measurements from over 3000 oil samples, they proposed a correlation:

(

)

Viscosity [ cP ] = exp exp ( 22.33 − 0.194 ∗ ρ + 0.00033 ∗ ρ 2 − ( 3.2 − 0.0185 ∗ ρ ) ∗ Ln ( TLM + 310 ) ) − 1 ρ = density, [API°], TLM = log-mean temperature [°F] for fluid between inlet and outlet. TLM = exp(average(Ln(TINLET),Ln(TOUTLET))). A simplified correlation is proposed here for stock tank oil viscosity at 60 °F for initial estimates, based on their correlation. Measured data should be used when available.

(

)

STO Viscosity [ cP ] = exp 194.3 / ρ  API°  / 27.47 Pseudocomponents and lumping In order to speed up the compositional analysis reservoir simulation specialists lump multiple components together. For example, components C12 through C15 may be lumped into a single pseudo-component C12–C15, etc. Properties of such pseudocomponents including critical temperature, critical pressure, acentric factor, molecular weight, boiling temperature etc. are calculated using the EOS tuning process. In early days of computer application for reservoir simulation as few as three or four components were used, as C1–C2, C3–C6 and C7+ in order to accelerate the vapor liquid equilibrium computation. Today using 15 pure components and 10 pseudocomponents is not uncommon. When two or more zones produce into the same well tubing, each zone gets characterized with a different set of pseudocomponents. This progressively increases the number of pseudocomponents and decreases the speed and accuracy of fluid property prediction. Typically five or more pseudocomponents, in addition to pure components (from C1 to C7) provide adequate ability to characterize a hydrocarbon fluid while maintaining reasonable computation speed. Usually software optimizes the lumping and pseudocomponent selection automatically, but this can be changed if necessary.

Lumping for different fluids It is preferred to have the same set of pseudocomponents for all fluids. Dedicated PVT tools which are used for fluid characterization for reservoir simulation have the capability to lump and tune different but similar fluids using the same set of pseudocomponents, which is preferred because it improves accuracy of blended fluid properties and improves computation speed. The accuracy of fluid behavior prediction improves substantially if the binary interaction parameters or kij are also supplied along with the properties of pseudocomponents and entered in the PVT simulation software. The binary interaction parameters are the additional adjustable coefficients in the equations of state which allow a more accurate prediction of fluid properties in multi-component mixtures. Flow assurance specialists usually receive fluid characterization information from the reservoir engineers who used the fluid properties to model the multiphase flow in the reservoir. The range of temperatures of interest to reservoir engineers is usually different from that of the flow assurance engineers. While XHPHT or extra high pressure high temperature



57

Fluid characterization

r­eservoirs may be as warm as 350–400 °F, the flow assurance systems may be exposed to temperatures as low as 0°C to −40°C in Arctic onshore or subsea environments. Typical deepwater temperature is near +4 °C or 40 °F, and the fluid characterization developed for the reservoir engineers may predict fluid properties accurately at high temperatures, but noticeably less accurately at lower temperatures. Fluid characterization should be done with both temperature ranges in mind so that the same parameters of the equation of state could apply to fluid property prediction by both reservoir and flow assurance disciplines. It is advisable to keep the same characterization of the fluid as the one used for reservoir analysis even if there are some inconsistencies in the VLE or other properties of the fluids at a different conditions, in order to maintain consistency of the project analysis. However, if the discrepancy is very significant and the flow assurance results would be significantly improved with more accurate fluid properties, the fluid may need to be re-characterized for flow assurance analysis using the laboratory data from the PVT report. The degree of discrepancy is to be determined by each individual project.

Solid-liquid equilibrium Flow assurance and production chemistry add a number of other liquid and solid phases to the diagram such as water, sand, hydrate, asphaltene, scale. The graph below illustrates a diagram where various phases coexist. Each phase has a label on the side of the boundary curve where the phase or a phenomenon appears, for example ice is on the colder side of the ice phase boundary. A flow assurance specialist or a production chemist could use the phase diagram in Fig. 3.9 like a map in order to get reservoir fluids efficiently from point A (well perforations) to point B (the separator). Fluid temperature is shown as increasing from reservoir past the wellhead and to the phase envelope to illustrate that in dense phase fluids Joule-Thompson effect causes Pressure Reservoir Early Life Wellhead Early Life

Reservoir Late Life

Separator Separator Late Life Early Life

Wellhead Late Life Temperature

FIG. 3.9  Phase diagram for various flow assurance issues. Fluid behavior and solid phases appearance are shown on a phase diagram versus time and location in the production system. Each phase is expected to appear on the labeled side of the curve.

58

3.  PVT and rheology investigation

heating. This effect can cause a hot reservoir fluid become even hotter during production and has to be taken into account for material selection and well design. In late life reservoir pressure declines but reservoir temperature remains the same so additional phases may become stable or unstable. Several solid phases can be present simultaneously if there are both sufficient fluid and appropriate conditions present to form those solids. Solids usually form from liquids by crystallization or by amorphous freezing. Examples of crystals are hydrate, ice, paraffin wax. Examples of amorphous solids are asphaltenes and some forms of wax and naphthenates. Scales are also crystals. In some cases petroleum solids can form from the gas phase such as diamondoids composed of adamantane, diamantane and heavier molecules. Diamondoids are also crystals and they photoluminesce (Clay et al., 2011) which may help identify them among other petroleum solids. Naphthenates are liquid crystals or micelles (Havre, 2002). Naphthenates have complex and little studied phase diagrams, and also can form amorphous solid films (Magnusson and Sjöblom, 2008). Two structures of hydrate commonly occurring in production operations are shown in the figure above to illustrate that when water is abundant for a hydrate to form, the propane and heavier components will be depleted first to form structure II hydrate, and if pressure is still sufficient to form more hydrate, the lean gas can keep forming structure I. This can happen when the number of moles of water is approximately six or more times greater than the combined number of moles of light hydrate forming hydrocarbons such as methane, ethane and propane. Similarly, if all gas is consumed into an exothermic hydrate and water is still present, ice can form if temperature is below freezing. Thermodynamically hydrate is more stable than ice at higher pressure because pressure helps water molecules in hydrate stay connected at higher temperatures, whereas in ice pressure distorts the crystal. However, kinetically ice forms faster than hydrate because it takes several types of molecules to get organized in order to form a hydrate crystal, while ice crystal forms with just water. Thus in an LNG process ice can form together with hydrate from an off-spec stream of hydrocarbon with a sufficient moisture content. Furthermore, in colder arctic environments hydrate can be dissociated by pressure reduction, while ice cannot if ambient temperature is below 0 °C. Depressurization is endothermic or consuming heat and should be done with care if ambient temperature is below freezing as hydrate upon dissociation releases mainly pure water. If fresh water released from dissociated hydrate converts into an ice blockage one would need to wait for the summer. Phase boundaries in the figure above are qualitative and intend to highlight the relative dependence of phase stability on changes in pressure or in temperature. For example, BaSO4 scale is less sensitive to changes in pressure than to changes in temperature. As pressure increases, less barite forms and as temperature increases, less barite forms. CaCO3 scale is sensitive to changes in both temperature and pressure. As temperature increases, more calcite would form. Also as pressure drops more calcite forms, mainly due to CO2 evolving from water and hydrocarbon phases. Carbon dioxide, if present in water and hydrocarbons, helps dissolve calcite in water, not too dissimilar from resins stabilizing asphaltene in oil. CaCO3 also can form a film on pipe surface which can reduce corrosion, unless the film gets sheared away by the flow. There is a continuous interaction between solid and fluid phases. Solids can act as diffusion barriers or as capillary channels to conduct less or more molecules in the liquid or gas



Fluid characterization

59

phases. This alters the rate of processes such as corrosion or formation of hydrate, deposition of wax or asphaltene. One should keep in mind that predicted stability of a solid phase does not guarantee solid formation at exactly the predicted condition because nucleation kinetics may be delayed, and formation of a solid does not always lead to a deposition and a blockage. At the same time, if a phase is not stable, it does not mean that it could not form in real operations. The software predictions and laboratory measurements can provide a warning for a specific set of conditions and fluid compositions. However, operations in the field can show that reality is more complex because not all factors and phase transitions were taken into account by a software or a lab such as reaction kinetics, solids nucleation and metastability, and the influence of one solid phase on another. As an example of such influence, in a system where scale is not stable, a hydrate formation can remove some water from a system. Hydrate consumes pure water and leaves salt in the remaining water. If a nearly saturated brine is present and the hydrate forms, it will cause water to become supersaturated with salt, leading to scale precipitation and deposition. Similarly, injection of methanol to inhibit hydrate into a produced fluid, which included a brine nearly saturated with NaCl, had led to a change is salt solubility and an unexpected halite scale blockage in a North Sea pipeline.

Additional laboratory studies Additional laboratory studies which may accompany a PVT report may include: Oil pour point temperature Oil HTGC or high-temperature gas chromatogram to resolve amounts of wax-forming components Oil emulsion stability study Oil TAN total acid number and TBN total base number analysis Oil SARA or saturates, aromatics, resins, asphaltenes content analysis Oil foaming study Wax appearance temperature measurement in CPM or cross-polarized microscope or DSC differential scanning calorimeter at stock tank conditions Wax appearance temperature measurement at pressurized conditions with reservoir fluid with either DSC or CPM Wax deposition study in a bench-scale mini-loop or a filter-plug apparatus Wax deposition study in a pilot-scale loop Wax deposition study in a cold finger apparatus with effect of chemical inhibitors Wax deposition study in a pressure cell Wax content from a cold solvent filtration study Wax dissolution study with dispersant chemicals or solvents Wax melting study for hot-oiling process Waxy gel strength test in a small diameter tube Asphaltene titration study for stock tank oil Asphaltene isothermal depressurization for live reservoir fluid under pressure

60

3.  PVT and rheology investigation

Asphaltene deposition study in a pressure cell Asphaltene deposition study in a mini-loop or a filter-plug apparatus Corrosion rate metal loss study with a static cell Corrosion rate study with a rotating linear polarization electrode at atmospheric pressure to measure the effect of shear on chemical performance Corrosion rate with a rotating electrode under high temperature and high pressure Corrosion rate from analog field metal coupon weight loss Scale precipitation study in a static cell Scale deposition in a mini-loop at high temperature to mimic reservoir condition Scale deposition in a mini-loop at low temperature to mimic wellhead & flowline condition Hydrate stability study with reservoir fluid and formation water Hydrate stability study with reservoir fluid and wellwork fluid Hydrate deposition study in a pressure autoclave, a rocking cell, a flow wheel or a flow loop, with or without chemical thermodynamic or kinetic inhibitors Hydrate dispersion study in a rocking cell with antiagglomerant chemicals Among the above tests, there are some indirect correlations: Hydrate nonplugging oil tendency may be related to TAN acids content and surfactants content as investigated by J. Sjoblom, where surfactants content may be analyzed based on emulsion stability study Naphthenate tendency may be related to TAN acids content Asphaltene tendency may be determined from SARA analysis Production chemicals viscosity as function of pressure and temperature Production chemicals vapor pressure analysis There are numerous alternatives available to measure wax appearance and wax disappearance temperatures, which should be used depending on fluid type (e.g. regular or biodegraded): - - - - - - -

CPM—visual detection of microscopic crystals assisted by polarized visual or IR light DSC—exothermic detection of solids, applicable to regular or biodegraded oils Viscometer or rheometer—detect a change in slope of Ln(viscosity) vs temperature Cold finger—visual detection of solids Cold filter plug—pressure differential detection of solids Cloud point—visual detection of crystals by eye—less accurate but field-usable Ultrasound change in wave frequency with temperature—applicable to live oil (Jiang et al., 2014) - Light scattering—applicable to wax appearance and wax disappearance Compressibility.

PVT tuning Binary interaction parameters kij serve as the tuning factors for the equations of state when properties of multicomponent mixtures are calculated. These BIPs are regressed for multiple



61

Fluid physical properties

(pseudo)component—(pseudo)component pairs to achieve the best fit between measured data and predicted values. Each group of regression, such as on liquid density, can have its own regression tolerance. Typical tolerance targets for regression during PVT tuning shown in Table 3.3 are as follows: TABLE 3.3  Tuning target tolerances Density

+/− 1–5%

Pressure of liquid saturation with gas

+/− 2–10%

Gas-oil ratio or RS (solution ratio)

+/− 1–5%

Liquid viscosity

+/− 5–20%

Parameters and acceptable tolerances of the fluid characterization are also illustrated in section 4.7 of the Phase Behavior monograph by Whitson and Brule. Fluid tuning process is available in multiple commercially available software packages. One would normally start with the most relaxed tolerances and repeat tuning the fluid several times while reducing the tolerance and noting the overall errors in property prediction at different temperatures and pressures. Default value for kij is zero because kij enters the equation of state in a form (1−kij), so a default value gives a complete contribution of a given pair of components to the interaction energy parameter in the equation of state. Normally the values of interaction energy (a) and molecule size (b) are calculated from the properties of components such as critical pressure and critical temperature which can be measured in the laboratory and acentric factor which can be calculated from the molecular structure. BIPs (kij) provide the ability to adjust the contribution of each component's interaction energy (a). Besides kij, there are also characteristic constant (kappa), volume shift parameters for density match improvement and other methods. As a final resort, when tuning of the GOR or density cannot be achieved with the provided composition, some of the component contents may be varied by 1–5%. This variation must be documented in the fluid characterization report. Example component properties are shown in Table 3.4.

Fluid physical properties TABLE 3.4  Component properties Formula

Name

Molecular weight

Density (g/L)

V (L/mol)

Melting point

g/mol

at 1 atm, 15.5 °C

Air

29

1.225

23.67

−215

N2

Nitrogen

28

1.183

23.68

−210

CO2

Carbon dioxide

44

1.869

23.55

−56.6

H2S

Hydrogen sulfide

34.1

1.451

23.49

−82

°C

(Continued)

62

3.  PVT and rheology investigation

TABLE 3.4  Component properties—cont’d Formula

Name

Molecular weight

Density (g/L)

V (L/mol)

Melting point

C1

Methane

16

0.679

23.63

−182.5

C2

Ethane

30.1

1.281

23.47

−182.8

C3

Propane

44.1

1.896

23.26

−188

iC4

i-Butane

58.1

2.524

23.03

−159.6

nC4

n-Butane

58.1

2.531

22.96

−140

iC5

i-Pentane

72.2

623.9

0.116

−160

nC5

n-Pentane

72.2

629.7

0.115

−130

iC6

i-Hexane

86.2

657.1

0.131

−153

nC6

n-Hexane

86.2

662.2

0.130

−95

C6

Methylcyclopentane

84.2

753.3

0.112

−142

C6

Benzene

78.1

885.3

0.088

5.5

C6

Cyclohexane

84.2

782.2

0.108

6.5

C7

Heptane

100

687.0

0.146

−90.5

C7

Methylcyclohexane

98.2

774.1

0.127

−126

C7

Toluene

92.1

870.1

0.106

−95

iC8

Iso-octane

114

702.6

0.163

−107

C8

Octane

114

706.0

0.162

−57

C8

Ethyl benzene

106

873.0

0.122

−95

C8

m-Xylene

106

866.9

0.122

−48

C8

p-Xylene

106

866.9

0.122

13

C8

o-Xylene

106

882.9

0.120

−25

C9

Nonane

128

720.7

0.178

−51

C10

Decane

142

732.6

0.194

−30

C11

Undecane

156

742.5

0.211

−26

C12

Dodecane

170

750.4

0.227

−10

C13

Tridecane

184

758.3

0.243

−5.5

C14

Tetradecane

198

765.2

0.259

5.9

C15

Pentadecane

212

771.2

0.275

10

C16

Hexadecane

226

775.1

0.292

18.2

C17

Heptadecane

240

779.5

0.309

22

C18

Octadecane

255

783.4

0.325

28.2

C19

Nonadecane

269

787.3

0.341

32.1

C20

Eicosane

283

785.6

0.360

36.8



63

Non-Newtonian behavior

TABLE 3.4  Component properties—cont’d Formula

Name

Molecular weight

Density (g/L)

V (L/mol)

Melting point

C21

Heneicosane

297

793.5

0.374

40.5

C22

Docosane

311

795.6

0.390

44.4

C23

Tricosane

325

798.7

0.406

47.6

C24

Tetracosane

339

800.8

0.423

50.9

C25

Pentacosane

353

802.3

0.440

53.7

C26

Hexacosane

367

805.9

0.455

56.4

C27

Heptacosane

381

807.1

0.472

59

C28

Octacosane

395

806.9

0.489

61.4

C29

Nonacosane

409

808.5

0.506

64

C30

Triacontane

423

811.5

0.521

66

C40

Tetracontane

563

817.0

0.689

82

C50

Pentacontane

703

824.0

0.854

91

CH3OH

Methanol

32

795

−98

C2H6O2

MEG

62.1

1117

−12.9

Hydrate structure1

17.7

916 at 129 atm

−81 at 1 atm

Hydrate structure2

19.1

958 at 22 atm

−44 at 1 atm

Light n-paraffin wax

400

910

66

Microcrystalline wax

800

940

78

Asphaltene

700

1100

not applicable, pyrolizes on heating

Non-Newtonian behavior Viscosity of oil is measured at a range of temperatures and pressures. Viscosity of gas is usually calculated using a correlation. Waxy crudes may also exhibit a pour point which can be measured and reported. The pour point is a measure of temperature at which a fluid in an inclined flask does not flow for a prescribed period of time. Non-Newtonian fluid rheology behavior is observed in viscosity measurement if solids such as wax precipitate in the liquid. If viscosity is plotted against temperature for a Newtonian fluid, usually a plot of natural logarithm of viscosity vs temperature is linear. When solids are introduced, the viscosity increases. This is exhibited as a nonlinear plot of logarithm of viscosity versus temperature. This nonlinearity may be used as one of the methods to determine wax appearance temperature of the fluid if more accurate data are not available.

64

3.  PVT and rheology investigation

There are various correlations for the effect of slurry solids volume fraction on viscosity. Nuland and Vilagines (2001, BHRG) proposed to use such correlation for hydrate slurries, which is based on the correlation by Mills (1985) for apparent shear viscosity, which in turn was based on the works of Einstein and Batchelor.

µr =

1 −Φ  Φ  1−  Φ max  

where µ r = µslurry / µ fluid , Φ = solid volume fraction , Φmax = maximum packing solids colume fraction = 4 / 7 for spheres. Other non-Newtonian behavior is also associated with wax crystals forming a gel. When slurry becomes so concentrated that crystals overlap and form a network, a waxy “gel” forms. The term gel is used in this context to signify that the whole fluid becomes nonflowing and non-Newtonian in its rheology. A gel exhibits a yield stress, which means that some force needs to be applied to disrupt the network before a gelled fluid starts to flow. In some cases waxy crudes with 3% or greater wax content (measured by cold filtration) may exhibit gelling behavior. Gel strength may vary depending on the cooling rate of the fluid. So, faster cooling (near a pipe wall) results in smaller wax crystals and a weaker network. Conversely, core of the gelling waxy oil cools at a relatively slower rate and grows larger crystals which form a stronger network. This effect becomes most pronounced in larger pipelines. It is not uncommon to see in a medium-diameter 2-in. pipe gel test that gel breaks near the pipe wall circumference, and the gelled oil core is extruded from the test pipe. To overcome the discrepancy between gel strength measured in a small laboratory tube and observed in a large diameter pipeline, gel strength may also be measured in a temperature-controlled rheometer with a cone-and-plate geometry to accurately reproduce the cooling rate history of a large diameter pipeline to obtain a more accurate gel strength reading. Alternatively, larger size test tubes or field pilot test sections may be used.

Emulsion characteristics Emulsion stability is commonly measured and reported for new oil samples. The time it takes to resolve an emulsion by gravity into oil and water layers is reported. Emulsion stability is particularly important for offshore operations as residence time in a separator is limited by size and weight of the separator to 5–10 min. Water-in-oil emulsions are prepared by mixing for a prescribed time at several shear rates and different water cuts and are allowed to resolve at different temperatures. Foaming of the oil may also be reported if observed. Formation of slop or solids-stabilized layer between oil and water layers may be reported if observed. Inversion point for an emulsion may be reported if observed at some water cut.

References 65

Oil-in-water emulsions are prepared at different water cuts between 50% and 90% at different shear rates for a prescribed time, and oil content of water is reported in ppm. The reported oil content should include both oil and water-soluble organic components. Rheology or viscosity of emulsions formed at different shear rates is reported for different temperatures and water cuts.

Biodegradation Crude biodegradation may be exhibited by the absence of n-paraffin peaks in gas chromatogram or in high-temperature gas chromatogram. Bacteria present in the reservoir consume normal paraffins and only branched or isomerized paraffins remain. This makes wax deposition prediction more complex as most modern wax deposition models are based on a solubility prediction method developed by Erickson (Erickson et al., 1993) which is applicable to n-paraffins. It also makes some laboratory studies such as CPM more complex as isomerized paraffins may form less crystalline and more amorphous solids which would not rotate the plane of light polarization. DSC or other methods to detect wax onset may then be used. Laboratory studies for the wax deposition then become necessary if wax appearance temperature is in the range of operating temperatures.

References Bergman, D.F., Sutton, R.P., 2007. A consistent and accurate dead-oil-viscosity method, SPE110194. In: SPE Annual Technical Conference and Exhibition, Anaheim, 11-14 November. Clay, W.A., Sasagawa, T., Iwasa, A., Liu, Z., Dahl, J.E., Carlson, R.M.K., Kelly, M., Melosh, N., Shen, Z.-X., 2011. Photoluminescence of diamondoid crystals. J. Appl. Phys. 110 (9), https://doi.org/10.1063/1.3657522. Erickson, D.D., Niesen, V.G., Brown, T.S., 1993. Thermodynamic measurement and prediction of paraffin precipitation in crude oil. In: SPE 26604, Annual Technical Conference and Exhibition, Houston, 3–6 October. Fiotodimitraki, T., 2016. Quality controlled oil reservoirs PVT data. Masters thesis, University of Crete. Accessed 12/12/2018, dias.library.tuc.gr/view/manf/63591. Havre, T.E., 2002. Formation of Calcium Naphthenate in Water/Oil Systems, Naphthenic Acid. Chemistry and Emulsion Stability. Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of DOKTOR INGENIØR Department of Chemical Engineering. Norwegian University of Science and Technology, Trondheim. Hu, Y., et al., 2017a. Gas hydrates phase equilibria for structure I and II hydrates with chloride salts at high salt concentrations and up to 200 MPa. In: Physical Chemistry Chemical Physics. Royal Society of Chemistry. Hu, Y., et al., 2017b. Gas hydrates phase equilibrium with CaBr2 and CaBr2 +MEG at ultra-high pressures. In: Physical Chemistry Chemical Physics. Royal Society of Chemistry. Jiang, B., et al., 2014. Measurement of the wax appearance temperature of waxy oil under the reservoir condition with ultrasonic method. Petroleum exploration and Development 41 (4). Joback, K.G., Reid, R.C., 1987. Estimation of pure-component properties from group-contributions. Chem. Eng. Commun. 57, 233–243. Katz, D.L., Firoozabadi, A., 1978. Predicting phase behavior of condensate/crude oil systems using methane interaction coefficients. J. Petrol. Tech. 20, 1649–1655. SPE-6721. Magnusson, H., Sjöblom, J., 2008. Characterization of C80 naphthenic acid and its calcium. J. Dispers. Sci. Technol. 29 (3), 464–473. Mills, P., 1985. Non-Newtonian behavior of flocculated suspensions. J. Physique Lett. 46, L-301–L-309. Nuland, S., Vilagines, R., 2001. Gas hydrate slurry flow – A flow modeler looks at the state of slurry rheology modelling. In: BHRG Multiphase International Conference proceedings, Cannes, France.

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3.  PVT and rheology investigation

Pedersen, K.S., et al., 1989. Characterization of gas condensate mixtures. In: Chorn, L.G., Mansoori, G.A. (Eds.), C7+ Fraction Characterization. Taylor & Francis, New York, pp. 137–152. Peneloux, A.E., Rauzy, E., Freze, R., 1982. Fluid Phase Equilib. 8, 7–23. Riazi, M.R., Daubert, T.E., 1980. Prediction of the composition of petroleum fractions. Ind. Eng. Chem. Process. Des. Dev. 19, 289–294. Whitson, C.H., Brule, M.R., 2000. Phase Behaviour, Richardson (TX). Society of Petroleum Engineers.

Further reading Landt, L., Kielich, W., Wolter, D., Staiger, M., Ehresmann, A., Möller, T., Bostedt, C., 2009. Intrinsic photoluminescence of adamantane in the ultraviolet spectral region. Phys. Rev. B 80, 205323. Pedersen, K.S., et al., 1991. Wax precipitation from North Sea crude oils. 4: Thermodynamic modelling. Energy Fuel 5, 924–932. Riazi, M.R., 1979. Prediction of Thermophysical Properties of Petroleum Fractions. PhD Thesis The Pennsylvania State University, PA.