Steve Furnival

PVT Analysis for Compositional Simulation

Oxford

February 2000

PVT Analysis

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PVT Analysis

Table of Contents

Table of Contents.................................................................................................................3Table of Figures...................................................................................................................61. Introduction......................................................................................................................72. Hydrocarbon Composition..............................................................................................9

2.1 The Atom....................................................................................................................92.1.1 The Carbon Atom...............................................................................................10

2.2 Basic Hydrocarbon Molecules the Alkanes...........................................................102.2.1 Isomerism...........................................................................................................132.2.2 Alkenes and Alkynes..........................................................................................14

2.3 Cycloalkanes.............................................................................................................152.4 Aromatics.................................................................................................................162.5 Polyaromatics...........................................................................................................172.6 Other Compounds.....................................................................................................172.7 Single Carbon Number Groups................................................................................17

Generalized SCN Physical Properties.........................................................................182.8 The Plus Fraction......................................................................................................19

Phase Behaviour................................................................................................................213.1 Pure Component Phase Behaviour...........................................................................21

3.1.1 p-T Projection.....................................................................................................233.1.2 p-V Projection....................................................................................................24

3.2 Binary Mixture Phase Behaviour.............................................................................253.3 Multi-Component Base Behaviour...........................................................................27

3.3.1 Dry and Wet Gas................................................................................................283.3.2 Gas Condensates................................................................................................283.3.3 Volatile Oils.......................................................................................................303.3.4 Crude Oils..........................................................................................................30

3.4 The Corresponding States Theorem.........................................................................31Z-Factor Correlations..................................................................................................33

Estimating Pseudo-Criticals.....................................................................................344. Sampling and Laboratory Analysis...............................................................................35

4.1 Sampling...................................................................................................................354.1.1 Well Testing.......................................................................................................35Conditioning................................................................................................................364.1.3 Down Hole Sampling.........................................................................................364.1.4 Surface Sampling...............................................................................................38

4.1.4.1 Liquid Loading in Gas Wells.......................................................................384.1.4.2 Taking Samples............................................................................................394.1.4.3 Metering.......................................................................................................394.1.4.4 Checking the Data........................................................................................414.1.4.5 Recombination Example..............................................................................41

4.2 Laboratory Analysis.................................................................................................454.2.1 Compositional Determination............................................................................45

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4.2.2 Saturation Pressure (SAT)..................................................................................474.2.2.1 The PVT Cell...............................................................................................47

4.2.3 Constant Composition Expansion (CCE)...........................................................504.2.4 Separator Test (SEP)..........................................................................................514.2.5 Differential Liberation (DLE)............................................................................52Constant Volume Depletion (CVD)............................................................................54

4.2.6.1 CVD Material Balance Check.....................................................................554.2.7 Other Experiments.............................................................................................56

5. Equations of State..........................................................................................................595.1 Development of the Ideal Gas Law..........................................................................59

5.1.1 The Mole............................................................................................................605.1.2 Deficiencies in the Ideal Gas Law.....................................................................615.1.3 The Real Gas Law..............................................................................................61

5.2 Cubic EoS.................................................................................................................625.2.1 Van der Waals EoS............................................................................................625.2.2 Redlich-Kwong Family of EoS..........................................................................64

5.2.2.1 Zudkevitch Joffe RK EoS............................................................................645.2.2.2 Soave RK EoS.............................................................................................65

Peng-Robinson EoS....................................................................................................65The Martins 2-Parameter EoS....................................................................................665.2.5 Other Cubic EoS................................................................................................66

5.3 Multi-Component Systems.......................................................................................675.4 Volume Translation..................................................................................................68

6. Flash Calculations..........................................................................................................696.1 Successive Substitution (SS) Method.......................................................................70

6.1.1 Rachford-Rice Equation.....................................................................................726.2 Stability Test.............................................................................................................726.3 Saturation Pressure...................................................................................................746.4 Composition versus Depth.......................................................................................75

7. Characterization.............................................................................................................777.1 Molar Distribution Models.......................................................................................77

7.1.1 Quadrature..........................................................................................................797.1.2 Modified Whitson Method.................................................................................80

7.2 Inspection Properties Estimation..............................................................................817.3 Critical Property Estimation.....................................................................................83

7.3.1 Normal Boiling Point Temperature....................................................................837.3.2 Critical Temperature, Critical Pressure..............................................................837.3.3 Critical Volume..................................................................................................837.3.4 Acentric Factor...................................................................................................84

8. Regression......................................................................................................................85Objective Function.........................................................................................................858.2 Variable Choice........................................................................................................868.3 Constraints................................................................................................................87

9. Export for Simulation....................................................................................................899.1 Black Oil Modeling..................................................................................................899.2 Compositional Modeling..........................................................................................92

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9.2.1 Grouping............................................................................................................929.2.2 Mixing Rules......................................................................................................93

References..........................................................................................................................95Appendix A: Classical Thermodynamics..........................................................................97

A.1 Abstractions.............................................................................................................97A.2 Chemical Potential...................................................................................................98

A.2.1 Fugacity.............................................................................................................99A.3 Equilibrium............................................................................................................100

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Table of Figures

Figure 1: The Total Production System...............................................................................8Figure 2: Schematic of Methane Molecule showing four C-H Bonds..............................11Figure 3: Schematic of Ethane Molecule...........................................................................12Figure 4: Schematic of Propane Molecule.........................................................................12Figure 5: Schematic Representations of Butane Isomers, nC4 and iC4............................14Figure 6: Schematic Representation of Pentane Isomers..................................................14Figure 7: Schematic of the Alkene Double Bond..............................................................17Figure 8: Schematic of the Alkyne Triple Bond................................................................18Figure 9: Schematic Representation of Cyclopentane and Cyclohexane..........................19Figure 10: Alternate Schematic Representations for Benzene Molecule..........................19Figure 11: The p-V-T Behaviour of a Pure Substance. [From Adkins]............................25Figure 12: p-T and p-V projections from the 3D p-V-T Surface [from Adkins]..............26Figure 13: p-T Projection for a Pure Component..............................................................26Figure 14: p-V Projection for a Pure Component..............................................................28Figure 15: Phase Envelopes of C2-C10 Binary Mixtures.................................................29Figure 16: Multi-Component Phase Envelope..................................................................30Figure 17: Schematic Phase Envelope of a Dry and Wet Gas...........................................31Figure 18: Liquid Dropout Profile from Gas Condensate [at constant composition]........32Figure 19: Standing Z-Factor Chart...................................................................................35Figure 20: Schematic of the Venturi Tube Rate Measurement.........................................42Figure 21: Schematic of an Orifice Plate Gas Rate Device...............................................42Figure 22: Surface Separator Analysis..............................................................................45Figure 23: Standing Analysis for the Separator Stage.......................................................47Figure 24: Schematic of a GC System...............................................................................48Figure 25: Schematic of the FID [from www.scimedia.com]...........................................49Figure 26: Freezing point depression diagram [from Pedersen et al.]...............................50Figure 27: Schematic of a Gas Condensate PVT cell........................................................51Figure 28: Change in Slope of p-V curve around the Bubble Point..................................51Figure 29: Liquid Dropout Tail Shown by Some Gas Condensates..............................52Figure 30: Schematic of CCE applied to Gas Condensate Fluid.......................................53Figure 31: Schematic of 2-Stage Separator Test...............................................................54Figure 32: Schematic of Differential Liberation Experiment............................................56Figure 33: Schematic of CVD Performed on Gas Condensate Fluid................................57Figure 34: Schematic of the Swelling Test........................................................................60Figure 35: Schematic of the Slim Tube Apparatus [ref. See Figure 27]...........................61Figure 36: Charles Law Behaviour for Water Implying Zero Temperature....................62Figure 37: p-V Behaviour for Pure Component with Cubic EoS Behaviour....................66Figure 38: Flow Diagram for the Successive Substitution Flash......................................74Figure 39: Gas-Oil Contact Figure 40: Critical Transition..............................................79Figure 39: Gas-Oil Contact Figure 40: Critical Transition..............................................79Figure 41: Whitson GDM for different values of ..........................................................81Figure 42: Schematic of the Generalized BO Table Construction....................................93

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1. Introduction

In order to perform flow simulation in the reservoir and production system, we need to know various physical properties of the fluid system. Firstly, what phases are present? Gas? Oil? Water? What are the relative proportions of these phases? What are the bulk phase properties, i.e. density, viscosity, thermal conductivity, etc.

In principle, we can and do take samples of the reservoir fluid and measure the quantities of interest at certain pressures and temperature. However, these experiments are both difficult and costly and cannot hope to cover the range of pressures, temperatures and compositions we are likely to encounter. Consider the following schematic of the total production system:

Figure 1: The Total Production System.

In mature areas such as the North Sea, petroleum accumulations are being sought at ever-greater depths: it is now common to find reservoirs at 20000-ft [6100 m] or more. At such depths, pressures can approach 16000 psia [1100 bars] and temperatures are close to 400 oF [205 oC]. Pressure can take any value between initial reservoir pressure and 1

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atmosphere in the stock tank, if one exists. Temperature will also vary between reservoir temperature and standard temperature although lower temperatures are possible in sub-sea flow lines and cryogenic coolers.

If the fluid composition was fixed, a set of pre-defined look-up tables could handle temperature and pressure variability. This is the black oil approach, which we will review later in this course.

Generally, the fluid composition within the production system is not fixed for a variety of reasons. Within the reservoir, the following changes can take place:

Composition varies with depth and areal location. The presence of high permeability streaks can then allow different fluids to mix.

As fluid drops below saturation pressure, one phase generally the gas will flow in preference to the oil so the produced well composition changes with time. This effect is particularly important for Gas Condensates and Volatile Oils near critical fluids.

Gas injection for pressure maintenance or miscibility processes.

Within the production system:

Fluids from different parts of the reservoir or reservoirs, can mix, i.e. Eastern Trough Area Project (ETAP).

Gas injection for Gas-Lift.

Changes in surface separation.

Phase slippage in long pipe and flow lines can cause formation of liquid slugs.

All these cases, and more, point to the need for a compositional treatment of the fluid system. These methods are computational expensive. However, with the rapid increase in computer power at reducing cost, they are all now achievable on a high-end PC.

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2. Hydrocarbon Composition

Hydrocarbons are molecules1 composed principally of Hydrogen and Carbon but also containing Sulphur, Nitrogen, Oxygen and various trace metals.

Carbon is unique amongst the elements in its ability to form not only strong Carbon-Carbon bonds but strong Carbon-OtherElement bonds also. Because of this ability, the number of naturally occurring molecules containing Carbon is vast. So much so that one of the main sub-disciplines within Chemistry is devoted to the study of Carbon compounds Organic Chemistry. In order to appreciate the richness of Carbon compounds, it is worth taking a short time to understand the nature of how atoms bind within molecules.

2.1 The Atom

Consists of a central positively charged nucleus of +Z units, comprising the majority of the atoms mass, surrounded by Z electrons, each of charge 1. Electrons are forced to occupy certain orbits or shells by the laws of quantum physics. The number of electrons that can occupy each shell is limited. The first can hold two, the second eight, etc. As the Z electrons are added to balance up the charge on the nucleus, they will fill the shells from the inside out.

When the outermost shell is not complete then the atomic species will try to bond with other atomic species to close the shell. Atomic species containing just one electron in their outermost shell, such as the Group I Alkali metals2 will donate their spare electron to atoms that are missing one in their outermost shell. Similarly, atoms such as the Group II Alkaline metals3 will donate their two spare electrons to atoms missing one or two electrons. Atoms missing one or two electrons in their outermost shell include the Group VII Halogens4 or Group VI atoms5. The exchange of electrons causes the donor become positively charged and the recipient ions to become negatively charged. The electrostatic attraction between the ions is what then provides the bonding mechanism. This is known as ionic bonding.The other way in which atoms can close their outermost shell is by sharing electrons with other atomic species that have vacancies in the outermost shell. This is known as covalent bonding and is the mechanism that dominates Carbon chemistry.

1 A molecule is the smallest sub-division of a chemical species which is representative of that species.2 Lithium, Sodium, Potassium, etc.3 Beryllium, Magnesium, Calcium, etc4 Fluorine, Chlorine, Bromine, etc.5, Oxygen, Sulphur, etc.

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2.1.1 The Carbon Atom

The nucleus of the most commonly occurring Carbon consists, in part, of six positively charged protons. Therefore, its six electrons are arranged in two shells; the inner shell of two electrons is full and the outer shell of four electrons is four short of being complete. Therefore, each Carbon atom requires other atomic species to share four electrons with it. Note the four electrons required do not have to come from four other atoms. Carbon-Carbon pairs can exchange one, 2 or 3 electrons with each other to form what are known as single, double and triple bonds. Naturally occurring hydrocarbons usually only consist of Carbon-Carbon pairs with single bonds.

These four other electrons can be donated by four other Carbon atoms in one of two different ways. When combined in a 2D planar lattice structure, the result is graphite - a soft powder that is used in pencils. When combined in a 3D tetrahedral structure, the result is diamond an ultra-hard crystal that is prized for its durability.

When Carbon combines with other atomic species, principally hydrogen, the result is the series of chemical compounds found in petroleum.

2.2 Basic Hydrocarbon Molecules the Alkanes

The most common hydrocarbon molecule by number is that of Methane. It consists of a single Carbon atom surrounded by 4 hydrogen atoms each of which shares its single electron thereby closing the Carbon outer shell of 8 and the single Hydrogen shell of 2. The Hydrogen atoms arrange themselves at the apexes of a tetrahedron with the Carbon atom at the centre of the structure. Symbolically Methane is represented by:

Figure 2: Schematic of Methane Molecule showing four C-H Bonds

The common shorthand representation is CH4: on PVT reports it will be denoted as C1.

If one of the C-H bonds is broken, the resulting Methyl radical is highly reactive and will look to fill the missing electron hole as quickly as possible. If another Methyl radical is close by, they will C-C bond to form Ethane, which is represented by:

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Figure 3: Schematic of Ethane Molecule

The common shorthand representation is CH3CH3 or C2H6: on PVT-reports it will be denoted C2.

A Methane molecule can lose two electrons to generate a CH2 radical. Now if the Ethane C-C bond is broken, the CH2 radical can be inserted between the 2 Methyl radicals and the Propane molecule is created which is represented by:

Figure 4: Schematic of Propane Molecule

The common shorthand representation is CH3 CH2CH3 or C3H8: on PVT-reports it will be denoted C3.

The process just described of inserting CH2 radicals can now be repeated ad-infinitum. The next few molecules in the series are Butane [C4H10 or C4], Pentane [C5H12 or C5] and Hexane [C6H14 or C6]. The generic formula for this series is CNH2N+2 where N is number of Carbon atoms.

Organic molecules that have a similar structure and consequently graded physical properties are known as a homologous series. This series is variously referred to as the Alkanes or Paraffins. Some physical properties of the normal-Alkanes are shown in Table 2.1 and its corresponding Chart.

Note the melting points of Methane and Ethane does not fit the trend; otherwise, a remarkably smooth set of trends is evident. The first four Alkanes are gases at room conditions: Alkanes with 18 Carbons or more are solids at room conditions.

Whether hydrocarbon molecules are found in gas, liquid or solid states depend on the inter-molecular force called the van der Waals force. Fluctuations in the distribution of the electron clouds gives rise to an electric field, which is the basis for the force. The smallest molecules are highly symmetric and hence the generated fields are weak: characteristics of a gas. The larger molecules are less symmetric and have a stronger field: characteristic of a liquid or solid.

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Table/Chart 2.1: Physical Properties of Normal-Alkanes

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Boil.Point Melt.Point Spec.Grav.N Name oF oF 60o/60o

1 Methane -258.7 -269.42 Ethane -127.5 -297.03 Propane -43.7 -305.7 0.5074 Butane 31.1 -217.1 0.5845 Pentane 96.9 -201.5 0.6316 Hexane 155.7 -139.6 0.6647 Heptane 209.2 -131.1 0.6888 Octane 258.2 -70.2 0.7079 Nonane 303.5 -64.3 0.722

10 Decane 345.5 -21.4 0.73411 Undecane 384.6 -15.0 0.74012 Dodecane 421.3 14.0 0.74915 Pentadecane 519.1 50.0 0.76920 Eicosane 648.9 99.030 Triacontane 835.5 151.0

Variation of Physical Properties with Carbon Number

-400.0

-300.0

-200.0

-100.0

0.0

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500.0

1 2 3 4 5 6 7 8 9 10 11 12

Carbon Number

Tem

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ture

/[deg

F]

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0.500

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0.600

0.650

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0.800

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ific

Gra

vity

Boil.PointMelt.PointSpec.Grav.

PVT Analysis

2.2.1 Isomerism

The structure of the Alkanes from C4 and above can vary from that implied above. In Figure 3 showing Propane, one of the Hydrogen atoms bonded to the central Carbon atom can be removed and replaced by a Methyl radical: this is known as iso-Butane or iC4.

It has the same number of Carbons and Hydrogens as its straight-chained equivalent that is generally known as normal-Butane or nC4 [or just C4].

Figure 5: Schematic Representations of Butane Isomers, nC4 and iC4.

Three possible structures are possible for Pentane. The straight-chained molecule called normal-Pentane, nC5 [or just C5]. A Butane chain with a Methyl radical attached to the 2nd Carbon called iso-Pentane, iC5. Finally, a Propane chain with two Methyl radicals attached to the central Carbon: the last structure called neo-Pentane is rarely found in petroleum mixtures.

Figure 6: Schematic Representation of Pentane Isomers.

As the Carbon number rises, the number of Isomers increases rapidly.

Question:How many isomers are there of Hexane [C6]? Estimate the number of isomers of Decane [C10] and Triacontane [C30].

Branch-chained Isomers do not exhibit the smooth variation in physical properties seen for the normal-Alkanes [see Table/Chart 2.1]. The physical properties of the Hexane Isomers are shown in Table 2.2, below.

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Table 2.2: Physical Properties of Hexane Isomers

Generally, an increase in the degree of branching causes a decrease in the inter-molecular attraction with the consequent lowering in boiling point. The variation of melting point is harder to predict. The way the different shapes can be slotted together is the main factor affecting the formation of the solid lattice.

2.2.2 Alkenes and Alkynes

Chemically the Alkanes are unreactive: the name Paraffin means not enough affinity. This is not true of straight-chained and branched hydrocarbons with double bonds the Alkenes: note each Carbon makes two conventional single bonds.

Figure 7: Schematic of the Alkene Double Bond.

Nor is it the case for triple bounds the Alkynes: note each Carbon can make only one conventional single bond.

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Isomer Structure Boil.Point Melt.Point Spec.Grav.oF oF 60o/60o

n-Hexane CH3CH2CH2CH2CH2CH3 155.7 -139.6 0.664

CH3

3-MethylPentane CH3CH2CHCH2CH3 145.9 -180.4 0.669

CH3

2-MethylPentane CH3CHCH2CH2CH3 140.5 -244.6 0.658

CH3 CH3

2,3-DiMethylButane CH3CH CHCH3 136.4 -199.4 0.666

CH3

2,2-DiMethylButane CH3CCH2CH3 121.5 -147.7 0.654

CH3

PVT Analysis

Figure 8: Schematic of the Alkyne Triple Bond.

These bonds are somewhat stretched compared with the equivalent single bond making them much more likely to break. Therefore, these compounds are rarely found in naturally occurring petroleum. That is not to ignore their importance in the Petrochemical industry. In particular, the polymerization6 of Ethene, C2H4, [or to give it its old name of Ethylene] gives rise to that most versatile of materials polyethylene. Similarly, polymerizing Ethyl Chloride gives PVC poly-vinyl-chloride.

The presence of a Carbon-Carbon double bond in the Alkenes eliminates the need for two Hydrogen atoms giving a generic formula of CNH2N. The corresponding Alkyne has the formula CNH2N-2.

2.3 Cycloalkanes

The Alkanes [Alkenes and Alkynes] are all straight or branched chains; with 3 or more Carbon atoms, other structures are possible. One of these alternatives is the homologous series called the Cycloalkanes. In the petroleum industry, the names Cycloparaffins or Napthenes are often used instead.Although they have the same general formula as the Alkenes, CNH2N, because they have a ring structure, their physical properties are very different. The two most common Cycloalkanes are Cyclopentane, C5H10, and Cyclohexane, C6H12: see figures below.

The lighter Cycloparaffins of Cyclopropane, C3H6, and Cyclobutane, C4H8, are both possible. However, they rarely occur in natural petroleum. The Carbon-Carbon bond angles of 60o and 90o are both very sharp making these bonds much weaker than their equivalents in the 5- and 6-Carbon ring structures. Ring structures with 7 or more Carbon atoms are chemically stable but again occur rarely in natural petroleum. This is probably because the probability a straight-chained molecule of 7 or more Carbons would lose a Hydrogen atom from both ends simultaneously is very low.

6 In the case of polymerization of Ethene, one of the C=C double bonds is broken in each molecule. The second Carbon in the first ethane-radical then bonds with the first Carbon in the second ethane-radical, etc. to form the long-chain polyethylene.

The Polymerization Process of Ethene.

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Figure 9: Schematic Representation of Cyclopentane and Cyclohexane.

As with the Paraffins, one or more Hydrogen atoms can be removed from any point on the ring to be replaced by Methyl, Ethyl, etc. radicals. Unlike the next series, the Aromatics, the central ring is referred to as saturated.

2.4 Aromatics

A third main homologous series are the Aromatics. The basis for the Aromatics is the Benzene molecule. Benzene contains six Carbons in a hexagonal ring with one Hydrogen atom attached to each Carbon. Initially it was thought that there were three single Carbon-Carbon bonds alternating with 3 double Carbon-Carbon bonds. However, the double bonds would be much weaker than their single bond equivalents making Benzene chemically reactive which is not the case. Clearly, the Carbon-Carbon bonds in Benzene are unlike anything considered to date.

Current thinking has it that the electrons are delocalized over all six Carbon atoms thus there are six hybrid bonds, or one-and-half bonds or benzene bonds.The common symbols used to depict the Benzene molecule are shown below:

Figure 10: Alternate Schematic Representations for Benzene Molecule

In the figure above, it is assumed there is a single CH group at each vertex of the hexagon. As with the Cycloalkanes, each of the Hydrogen atoms can be replaced by a Methyl, Ethyl, etc. radical. Replacing one Hydrogen atom by a single Methyl radical produces Toluene, C6H5.CH3. Replacing two Hydrogen atoms by Methyl radicals produces Xylene, C6H4.CH3.CH3.

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2.5 Polyaromatics

Most of the large molecules found in petroleum are linked multi-ring structures that are composed of Cycloalkanes and Aromatics, often with Sulphur, Oxygen and/or Nitrogen atoms replacing one or more Hydrogen atoms. They are often sub-divided into two classes called Resins and Asphaltenes. Resins readily dissolve in petroleum and are either heavy liquids or sticky solids. Asphaltenes are solids that are only weakly soluble in petroleum. An oil with a high Asphaltene content is a production nightmare since when the near well bore pressure drops, these molecules will precipitate, causing pore blocking and leading to a loss of Productivity Index (PI).

2.6 Other Compounds

The four main non-hydrocarbon or inorganics components of naturally produced petroleum are:

Nitrogen N2 Carbon Dioxide CO2 Hydrogen Sulphide H2S

Water H2O

Of these, it is generally assumed that water is mutually insoluble in hydrocarbon phases: this may not be true at high temperatures or in the presence of large concentrations of CO2 and/or H2S. However, we will not consider the effect of water other than as a stand-alone component during this course.

N2, CO2 and H2S are important constituents of most petroleum mixtures and are routinely considered when laboratory analyses of reservoir fluids are undertaken. Chemically, N2 behaves most closely to Methane. CO2 is most similar to Ethane and H2S to Propane.

2.7 Single Carbon Number Groups

If the presence of Isomers were not bad enough, we now have to contend with the different homologous series. Laboratory analysts could spend between now and eternity trying to isolate every different molecular species. Clearly an impossible task!

For petroleum engineering purposes, standard practice is to check for and measure the concentrations of the inorganics, N2, CO2 and H2S and the first few members of the Alkane series, C1, C2, C3, iC4, nC4, iC5 and nC5. Thereafter, boiling point cuts called Single Carbon Number (SCN) groups are used.

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SCN group N is taken to be all hydrocarbon molecules which boil at temperatures just above that of the normal paraffin CN-1 up to and including the normal paraffin CN. For example, consider some of the members of SCN group 7, denoted C7:

Name Tboil/Kelvin

normal-Hexane 341.9

Benzene 353.2

Cyclohexane 353.8

2-Methylhexane 363.2

normal-Heptane 371.6

Table 2.3: Some Members of SCN group C7 Shaded Area.

Clearly, the blend of Paraffins, Paraffin-Isomers, Cycloparaffins and Aromatics within any given SCN group will vary from fluid to fluid. As the blend varies from highly Paraffinic to highly aromatic, the average physical properties of the group can vary considerably. This can in turn, have a considerable effect on the ability of our models to predict fluid behaviour. We will reconsider this issue when we look at fluid characterization and regression. For now, we either take some average of a reasonably large set of test fluids or just use the paraffin properties.

Generalized SCN Physical Properties

The following table is re-produced from Whitson. Note the mole weights of the SCN components are less than the mole weights of the normal-Paraffins with the same number of Carbon atoms. This reflects the presence of Napthanic and Aromatic components within the blend.

Key: Tb Normal Boiling Point Temperature

Specific Gravity (60/60)Kw Watson Characterization Factor: see section 7.2

Mw Molecular Weight

Tc Critical Temperature

Pc Critical Pressure

Acentric Factor

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Tb Kw Mw Tc Pc SCN K oR K oR kPa psia

6 337 607 0.690 12.27 84 512 923 3340 483 0.250

7 366 658 0.727 11.96 96 548 985 3110 453 0.280

8 390 702 0.749 11.87 107 575 1036 2880 419 0.312

9 416 748 0.768 11.82 121 603 1085 2630 383 0.348

10 439 791 0.782 11.83 134 626 1128 2420 351 0.385

11 461 829 0.793 11.85 147 648 1166 2230 325 0.419

12 482 867 0.804 11.86 161 668 1203 2080 302 0.454

13 501 901 0.815 11.85 175 687 1236 1960 286 0.484

14 520 936 0.826 11.84 190 706 1270 1860 270 0.516

15 539 971 0.836 11.84 206 724 1304 1760 255 0.550

16 557 1002 0.843 11.87 222 740 1332 1660 241 0.582

17 573 1032 0.851 11.87 237 756 1360 1590 230 0.613

18 586 1055 0.856 11.89 251 767 1380 1530 222 0.638

19 598 1077 0.861 11.91 263 778 1400 1480 214 0.662

20 612 1101 0.866 11.92 275 790 1421 1420 207 0.690

21 634 1124 0.871 11.94 291 801 1442 1380 200 0.717

22 637 1146 0.876 11.95 300 812 1461 1330 193 0.743

23 648 1167 0.881 11.95 312 822 1480 1300 188 0.768

24 659 1187 0.885 11.96 324 832 1497 1260 182 0.793

25 671 1207 0.888 11.99 337 842 1515 1220 177 0.819

26 681 1226 0.892 12.00 349 850 1531 1190 173 0.844

27 691 1244 0.896 12.00 360 859 1547 1160 169 0.868

28 701 1262 0.899 12.02 372 867 1562 1130 165 0.894

29 709 1277 0.902 12.03 382 874 1574 1110 161 0.915

30 719 1294 0.905 12.04 394 882 1589 1090 158 0.941

2.8 The Plus Fraction

Depending on the nature of the fluid, there comes a point in the allocation of SCN groups where the law of diminishing returns takes over. That is, the error associated with measuring the concentration of SCN group N is bigger than that concentration. At some point before that, which usually depends on how much the owner of the fluid is prepared to pay the service laboratory, a cut-off in the analysis is made. The residual or plus

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PVT Analysis

fraction is what is left. Usually, just the molecular weight7 and sometimes the specific gravity of this fraction are measured are reported. As laboratory techniques have improved, so the typical Carbon number of the plus fraction has increased. In the 1960s, a plus fraction of C7+ was typical. During the 1970s and 1980s, C12+ was typical whereas C20+ would be the norm now. Some typical reservoir fluid analyses are shown below. Note the units are mole fractions. Moles and mole fractions will be discussed in some detail in section 5.1.

Comp NS GC Bah-GC NS-VO SWT-BON2 0.60 11.71 0.58 0.00CO2 3.34 6.50 3.27 0.00H2S 0.00 0.05 0.00 0.00C1 74.16 79.06 53.89 52.00C2 7.90 1.62 8.57 3.81C3 4.15 0.35 6.05 2.37iC4 0.71 0.08 1.05 0.76nC4 1.44 0.10 2.44 0.96iC5 0.53 0.04 0.88 0.69nC5 0.66 0.04 1.17 0.51C6 0.81 0.06 1.45 2.06C7 1.20 0.06 2.38 2.63C8 1.15 0.05 2.59 2.34C9 0.63 0.04 1.75 2.35C10 0.50 0.24 (+)195 1.50 29.52 (+)221C11 0.29 1.55C12 0.27 0.93C13 0.28 1.13C14 0.22 1.01C15 0.17 0.80C16 0.15 0.86C17 0.14 0.60C18 0.09 0.68C19 0.13 0.54C20 0.47 (+)362 4.34 (+)411

Table 2.4: Typical Fluid Analyses

Key: NS North Sea SWT South West Texas Bah Bahrain

GC- Gas Condensate VO Volatile Oil BO Black Oil

7 Molecular weight will be defined shortly. Note its measurement can be subject to an error of 10 %.

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Phase Behaviour

One of the first questions to ask of a petroleum mixture of known composition is how those components distribute themselves at some specified conditions. In particular, is the fluid a gas, oil or a mixture of the two?

Generally we will limit our interest to hydrocarbon mixtures which can form up to 2-phases which are usually denoted oil and gas, although it may be best to reserve those names for the phases at surface conditions. Under reservoir or production conditions, the names vapour and liquid will be used here. Wherever we find hydrocarbons, we usually find water also. Strictly, we should consider hydrocarbons and water together when we investigate fluid properties, however, their mutual solubility is generally very low and for most purposes, we can consider water independently. A notable exception is gas-water mixtures in production systems, especially long sub-sea flow lines. At low flow rates or shut-ins, the gas-water mixture is capable of forming a solid ice-like structure at temperatures above zero oC called a Gas Hydrate. Once formed, they are very difficult to get rid of. So much so those operators will add expensive Methanol at the earliest convenient point in the flow line to suppress hydrate formation.

Other pure hydrocarbon solids can be found. We have already seen when discussing petroleum composition that very heavy hydrocarbon molecules called resins and Asphaltenes can be found. These materials cause most problems in the production system but they can also be a problem in the near well bore region where they can drop out as pressure falls and effectively reduce the porosity. Again, expensive chemical treatments may be needed to remove them if they occur.

Carbon Dioxide injection is popular for many old oil fields in the Southern Continental USA. Large CO2 reservoirs mean there is a plentiful supply of material for injection and under the right conditions it can substantially enhance oil production. However, CO2 and to a lesser extent H2S are as soluble in water as they are in hydrocarbons. At relatively low pressures and temperatures, say 150 oF and 1500 psia; a four-phase system is seen consisting of an aqueous phase, a hydrocarbon vapour, a hydrocarbon liquid and a CO2 rich liquid. Given the narrow range of conditions under which this effect occurs, it is generally not modeled in reservoir simulation although it is studied as a PVT problem.

3.1 Pure Component Phase Behaviour

Before we attempt to consider the phase behaviour of petroleum mixtures, let us first consider a single pure component. The 3D image shown below shows axes for pressure p, volume V and temperature T.At high temperatures, the T5 isotherm approximates to Boyles Law, namely pV = constant, which we see in Section 5.1. As temperature is reduced, the isotherm becomes more distorted until at Tc the Critical Temperature at point C it becomes horizontal. At temperatures less than Tc there is a region in which liquid and vapour can co-exist

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region GCF. The point G is called the Triple Point, which is the unique point at which this component can co-exist as solid, liquid and vapour.

Figure 11: The p-V-T Behaviour of a Pure Substance. [From Adkins]

Although most general, the 3D image is difficult to work around. It is more useful to consider one of two possible projections take from this image, namely the p-T projection at constant volume and p-V projection at constant temperature. These projections can be seen on the next figure, below. Note that for a given temperature, liquefaction and solidification take place at a constant pressure, therefore, the mixed phase regions shown shaded project into lines on the p-T plot. Whereas on the p-V plane, the mixed phase regions continue to be visible.

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Figure 12: p-T and p-V projections from the 3D p-V-T Surface [from Adkins].

Using the projections derived from this figure, we can now give a clearer description of the fluid phase behaviour.

3.1.1 p-T Projection

Figure 13: p-T Projection for a Pure Component

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PVT Analysis

As described before, the two-mixed phase regions on the 3D-image project into two lines on this representation, the Vapour-Liquid-Equilibrium (VLE) line and the Solid-Liquid-Equilibrium (SLE) line. We will not consider the SLE any further except to note the dashed line GH which is that of water all other compounds behave like the line GH. One consequence of line GH for water is a skater is actually sliding on a film of water: the pressure caused by a skate causes the ice to melt [at constant temperature].

The VLE line GC defines the unique pressure versus temperature curve at which liquid and vapour can co-exist. For water at atmospheric pressure, this is 100 oC or 212 oF. The point C the critical point marks the highest temperature at variable pressure or the highest pressure at variable temperature at which this compound can exist as liquid and vapour. Furthermore, unlike other point along the VLE, the intensive properties of the liquid and vapour at the critical point, such as density, viscosity, specific heat, etc. are identical. At temperatures or pressures in excess of Tc and pc, the fluid can only ever exist as a single-phase of indeterminable type: some authors call this region supercritical.Previously in section 2.2, we saw how properties such as boiling point, melting point and specific gravity vary with Carbon number. Not surprisingly, the critical properties, including critical Volume, Vc, vary in a similar way:

Comp Tc Pc Vc-

oR psia ft3/lbmolC1C2C3C4C5C6C7C8C9C10

343.0549.8665.7765.3845.4913.4972.5

1023.91070.31111.8

667.8707.8616.3550.7488.6436.9396.8360.6332.0304.0

1.58992.36953.24994.08034.87025.92906.92427.88208.77299.6612

Table 3.1: Variation of Tc, pc and Vc with Carbon Number.

3.1.2 p-V Projection

In this projection, we have only highlighted the vapour-liquid two-phase region shaded.

Consider the sub-critical isotherm defined by the points MNOP. At point P we have a highly compressible vapour: small changes in pressure yield large changes in volume. At point O the Dew Point - the liquid phases appears. Now at constant pressure, the proportion of liquid and vapour changes along the line NO until at point N the Bubble Point all the vapour has disappeared and we have a single-phase liquid. Now along

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line MN we have the characteristic behaviour of a liquid in that large changes in pressure only cause a small change in volume.

Figure 14: p-V Projection for a Pure Component

The loci of points traced out by the dew point and bubble point lines define the two-phase region. As the temperature rises towards the critical temperatures, the [molar] volumes and other intensive properties of the saturated vapour and liquid come together until they are equal at the critical point, C. We will review this issue when we consider Cubic Equations of State (EoS) in section 5.2.

3.2 Binary Mixture Phase Behaviour

Consider a mixture of two pure components, say Ethane and Decane, (C2, C10). From Table 3.1, above, we can see that on a p-T plot, the critical points of Decane are displaced down [in pressure] and to the right [in temperature]. Generally, with increasing Carbon number, critical temperature increases and critical pressure decreases.

Now add a small amount of C10 to otherwise pure C2. The effect is to make the VLE line of C2 into a narrow envelope the two-phase region denoted 99/01. Note the critical point of the 99/01 mixture denoted as a black circle has a critical pressure greater than that of pure C2 whereas the critical temperature is intermediate between the Tc of C2 and C10. As the percentage of C10 is increased and therefore that of C2 reduced, the envelope initially broadens until as the percentage of C10 approaches 100%, it collapses onto the VLE line of C10. The critical pressure of the binary mixtures exceeds that of C2 for the

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90/10, 75/25 and 50/50 mixtures. The critical temperature of these and the remaining mixtures, 25/75 and 10/90 like their predecessors are intermediate between the Tc of C2 and C10.

Figure 15: Phase Envelopes of C2-C10 Binary Mixtures.

As a rule of thumb, the critical temperature of an N-component mixture may be estimated from:

(3.1) =

N

icii

mixc TzT

1

Tci is the critical temperature of the ith component and zi is that components mole fraction: we will explain moles and mole fractions in the next two sections. This expression is often referred to as Kays rule: experience has shown it is accurate to 10%. No such estimation technique is available for critical pressure.

Note that generally the critical point for a mixture is not the highest pressure and/or highest temperature at which a two-phase system can exist. For a mixture, we call the point corresponding to the highest saturation pressure [psat] the Cricondenbar [at which

0=dTdpsat ] and the highest temperature the Cricondentherm [at dTdpsat ]

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3.3 Multi-Component Base Behaviour

Adding more components to a mixture generally has the effect of broadening and raising the phase envelope. The extent of these changes depends primarily on the range of components in the mixture and their relative proportions [measured in moles see section 5.1]. The phase envelope for a hypothetical mixture is shown below.

Figure 16: Multi-Component Phase Envelope.

In addition to the Bubble point line [vapour fraction, V = 0%] and Dew point line [V = 100 %], we have plotted lines of constants vapour fraction for V = 10, 25, 50,75 and 90%. All these lines, including the Bubble and Dew point lines converge at the critical point [approximately 4100 psia and 250 oF]. Using this plot, we can make sense of the five standard fluid types:

Dry Gas

Wet Gas

Gas Condensate

Volatile Oil

Crude Oil

We will discuss each of these fluid types by looking at relationship between reservoir temperature and phase envelope.

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3.3.1 Dry and Wet Gas

Although not marked explicitly, the Cricondentherm for this fluid is about Tcri 525 oF: it is highly unlikely a hydrocarbon reservoir would be found at such a temperature. For a lighter fluid mixture, the Tcrit will be lower and it is common to find Tres > Tcri.If reservoir temperature is in excess of Tcri, under primary depletion where only pressure changes, at no point would the phase envelope be crossed: denoted 1 2 in the figure below. If surface conditions are at point 3d, still outside the two-phase region, the fluid is called Dry Gas.

Figure 17: Schematic Phase Envelope of a Dry and Wet Gas.

On the other hand, if surface conditions are at point 3w inside the two-phase region, then at some point in the production system liquid drop out will occur: this fluid is called Wet Gas.As a rough guide, it has been suggested that any fluid which produces more than 50 Mscf/STB [ 8900 sm3/sm3] may be considered a wet gas. This corresponds to the Heptanes plus fraction being 1.0 mole percent or less. For most purposes, dry and wet gases can be modeled using correlations: this will be discussed further when we look at reduced properties and the Corresponding States theorem [see section 3.4].

3.3.2 Gas Condensates

Imagine the reservoir temperature for our multi-component mixture lies between Tcrit [approximately 252 oF] and Tcri. Further, assume the initial reservoir pressure is 4500 psia - we have a single-phase fluid.

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PVT Analysis

Under primary depletion, pressure can fall to about 3675 psia whereupon we find the dew point at which the first drop of liquid [heavier phase] appears from what we can now assume to be the vapour [lighter phase].

Figure 18: Liquid Dropout Profile from Gas Condensate [at constant composition]

As the pressure continues to fall, the liquid fraction builds to a peak of about 19% [by moles!] at about 3200 psia. As the pressure continues to fall, some of the dropped-out liquid re-vapourizes so that as we approach abandonment pressure around 1000 psia, the liquid fraction has fallen back to about 10%.

Note the behaviour just described is an idealized representation, which is only seen in the laboratory. Within a reservoir, the dropped-out liquid will generally remain immobile because of relative permeability effects [we will discuss this effect later in section 4.2.6]. The vapour however, will flow and therefore the fluid composition at a point will change with time.

The effect where a heavier liquid phase is evolved from a lighter vapour phase goes against our normal expectation of fluid behaviour under pressure reduction. Hence, the name Retrograde Condensation was termed: some authors still prefer to call Gas Condensates Retrograde Gases.

As reservoir temperature approaches the critical temperature, we have already seen how the vapour fraction lines on the multi-component phase envelope are packing together. On the liquid dropout plot above, this would correspond to the slope of the curve becoming more nearly vertical and the maximum dropout approaching 50%. If the

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reservoir temperature is equal to the critical temperature, then as the pressure falls to equal the critical pressure, we immediately jump to a two-phase system [with 50% liquid and 50% vapour]. The two-phases will be identical and therefore indistinguishable.

Gas Condensates typically have GORs between 3.3 Mscf/STB [590 sm3/sm3] and 50 Mscf/STB [8900 sm3/sm3] although values up to 150 Mscf/STB have been reported. The stock tank oil derived from a gas condensate is usually lighter in colour than that derived from a crude oil. These rules are somewhat arbitrary. A more useful indicator is the mole fraction of the Heptanes-plus will be less than 12.5%.

3.3.3 Volatile Oils

If the reservoir temperature is less than the critical temperature, we get the expected fluid behaviour as pressure is reduced. An initially single-phase fluid, which we will subsequently label as liquid, on reaching the bubble point pressure yields a lighter vapour phase. The amount of vapour evolved depends on the proximity to the critical point. At temperatures just below the critical temperature, the amount of vapour produced approaches 50%. This vapour is rich in heavier hydrocarbons and will exhibit retrograde condensation as its produced. In some volatile oil reservoirs, it is common to find that half the produced stock tank oil entered the well bore as vapour. Because of this effect, the classical reservoir engineering material balance equations attributed to Schilthuis [see Dake, Chapter 3] will not work for a volatile oil.

GORs for volatile oils vary between 2.0 and 3.3 Mscf/STB. The Heptanes plus fraction varies between 12.5 and 20.0 mole percent. The liquid formation volume factor, denoted Bo [see section 4.2.5] will usually be greater than 2.0 RB/STB [2.0 m3/sm3].

3.3.4 Crude Oils

As the difference between reservoir temperature and critical temperature increases, with Tres < Tcrit, so the lines of constant vapour fraction spread out. Therefore, as pressure falls from the bubble point, the amount of vapour liberated falls. In addition, the liquid content of the liberated vapour is reduced. If the assumption that the liberated vapour can be treated as dry gas is acceptable, we can treat this fluid as a crude oil.

At pressures in excess of the bubble point, the crude will be referred to as being undersaturated, that is more vapour could be dissolved if it were present. At the bubble point, the crude is called saturated i.e. it holds as much vapour as it can. Strictly, at all pressures less than the bubble point pressure the liquid will be saturated, as vapour will continue to evolve.

Crude oils usually have GORs less than 2.0 Mscf/STB and their stock tank oil is often very dark in colour, usually black hence the alternative name of black oil. The Heptanes plus mole fraction will exceed 20%.

The relative simplicity of the crude oil phase behaviour has given rise to numerous correlations to describe their behaviour. These consist of expressions to calculate:

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Bubble point pressure, pb,

Liquid [Oil] Formation Volume Factor (FVF), Bo,

Solution GOR, Rs, and

Oil and Gas Viscosity, o and g.These correlations generally use the following set of parameters:

Oil API gravity8, API, Gas gravity9, g, Solution GOR at initial conditions, Rsi, and

Temperature, TR.The correlations are therefore of the form:

(3.2) ( )RsigAPIb TRfp ,,,=The more commonly known correlations are due to Standing, Lasater, and Vasquez and Beggs: for more details see Chapter 22 of Bradley.

3.4 The Corresponding States Theorem

As was evident from Table 3.1, the physical properties of hydrocarbons vary with molecular weight [and shape]. Therefore, derived properties such as density, viscosity, thermal conductivity, etc., cannot be easily be deduced for one species based on measurements of those properties for another species. However, it was observed that if we work in terms of reduced properties, such as reduced temperature, Tr, and reduced pressure, pr, where:

(3.3)c

r TTT =

cr p

pp = ,

then a more consistent picture emerges.

In particular, the Corresponding States theorem says all pure gases will have the same Z-factor10 at the same reduced temperature and reduced pressure: see the Real Gas Law in section 5.1.3.

The following figure, usually known as the Standing Z-Factor chart, shows the variation of Z-Factor with reduced pressure and reduced temperature.

8 API gravity is related to specific gravity, o, [density relative to water] by 5.131)5.141( = oAPI 9 Gas gravity is density relative to that of air. Since they are both measured at standard conditions, we assume the ideal gas law applies [see section 5.1] and therefore density is proportional to mole weight. Therefore, gas gravity can be equally well represented as the gas mole weight relative to that of air where Mair = 28.97.10 We will define Z-factor in section 5.2.

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Figure 19: Standing Z-Factor Chart

All hydrocarbon gases [up to C6] and the inorganics N2, CO2 and H2S obey this chart to within a few percent. Mixtures of these components can also have their Z-Factor computed from this chart if instead of the pure component critical pressure and temperature in (3.3), we use the pseudo-critical pressure, ppc, and pseudo-critical temperature, Tpc, defined by:

(3.4) =

=

N

iciipc pyp

1

=

=

N

iciipc TyT

1

Here yi is the mole fraction of the ith of the N components. In the absence of a compositional analysis, the pseudo-criticals can be estimated from correlations based on gas gravity: see Appendix B of McCain.

We will see later when we study Equations of State that both pressure and temperature enter these expressions as reduced quantities. Other models utilize the Corresponding States Theorem. Amongst them are the models for estimating viscosity and thermal conductivity of hydrocarbon mixtures due to Pedersen et al., in Chapter 11 of Pedersen et al.

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Z-Factor Correlations

One of simplest correlations for estimating Z-factors is due to Brill and Beggs [see Beggs for details]:

(3.5) DprCpBAAZ ++= )exp()1(

where:

(3.6)

( )( ) ( )[ ]

( )2

62

5.0

42.0128.1715.0exp

log32.0132.0

1723.20exp32.0037.0)86.0(

066.023.062.0

101.036.092.039.1

prpr

pr

prprpr

prprpr

prpr

TTD

TC

TpT

pTpB

TTA

+=

=

+

+=

=

This correlation is adequate (1-2%) provided the temperature is 80.0 < T (oF) < 340.0 and the pressure p < 10000.0 psia. The main advantage is the expression is explicit in Z.A more accurate expression, which can be used over a wider range of pressure and temperature, is credited to Hall and Yarborough. Here, the Z-factor is calculated from:

(3.7)yp

Z pr

=

where:

(3.8)( )[ ]

prTttt

112.1exp06125.0 2

=

=

In (3.7), y is the reduced density, which is found by solving the non-linear equation:

(3.9)( )

( )

0)4.422.2427.90(

)58.476.976.14(1

)(

82.218.232

2323

432

=

++

+

++++=

+ t

pr

yttt

yttty

yyyypyF

The derivative of (3.9) is calculated from:

(3.10) ( )( ) ( ) ( )tytttt

yttty

yyyydydF

82.218.132

324

432

3.422.2427.9082.218.2

)16.952.1952.29(1

4441

++++

+

+++=

An initial estimate of y=0.001 when used with the Newton procedure should achieve convergence in 3 to 10 iterations for F(y) = 10-8.

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Estimating Pseudo-CriticalsIn the absence of compositional information, the pressure and temperature pseudo-criticals (ppc, Tpc), can be estimate by correlations dependent on the [reported] gas gravity. Standing gives two sets of correlations, one for dry gases (gHC < 0.75):

(3.10) 2

2

5.370.15 0.667

5.120.3250.168

gHCgHCpHC

gHCgHCpcHC

p

T

+=

+=

and a second set for wet gas mixtures (gHC 0.75):

(3.11) 2

2

1.117.51 0.706

5.710.3300.187

gHCgHCpHC

gHCgHCpcHC

p

T

+=

+=

When significant quantities of the inorganics CO2 and H2S are present, the pseudo-criticals should be corrected to account for the mole fractions of these components. In particular,

(3.12) ( )

)1(22 SHSHpcHC

pcHCpcHCpc

pcHCpc

yyTTp

p

TT

+

=

=

where the -correction factor is calculated from:

(3.13) ( ) ( )[ ] ( )45.06.19.0222222

15120 SHSHSHCOSHCO yyyyyy +++=

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PVT Analysis

4. Sampling and Laboratory Analysis

Increasingly, we are using mathematical models encapsulated within software packages to predict the behaviour of hydrocarbon reservoirs and their associated production systems. The models require things:

1. Input and Initialisation

2. Calibration

For fluid property determination this necessitates we take samples of the fluids of interest. Next, we determine their composition. Finally, we perform a set of standard tests to produce data to calibrate our models.

4.1 Sampling

Before we can conduct any test, we have to acquire samples of the fluid of interest. Samples should be taken as part of the initial well testing program. There are usually conflicts in the well test program with the need to acquire reservoir parameters versus the collection of representative samples. Proper design and careful planning are the key to minimizing these conflicts.

A number of industry bodies have studied the problem of sampling, especially for more complex fluids such as gas condensates. Their recommendations can be found the reports from the API and UKOOA.

4.1.1 Well Testing

The main problems in well test design for sampling concern the producing interval and tubing size.

In large hydrocarbon columns, a significant variation in composition with depth is possible [we will discuss this effect in detail in section 6.4]. In this case, it is preferable to sample only a limited interval by restricting the perforations: the UKOOA report suggests intervals be restricted to 30-ft [10 m]. This then requires several tests be performed over a large column: over a 300-ft column, the UKOOA report suggests a minimum of three separate tests.

As we will see when we consider well conditioning, sample collection is best served by low flow rates. Low flow rates should be produced using small diameter tubing since low rate production in large diameter tubing gives rise to an unstable flow regime called slugging. However, the rate must be high enough to ensure that liquids are produced to surface: see Turner et al.: see section 4.1.4. If the flow rate of a condensate well being surface sampled is too low such that some of the liquid phase is not produced then an

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unrepresentative sample will be taken. If all the liquid falls back, the well may choke and die.

Technological advances in recent years have helped us here since it may be possible to run small diameter coiled tubing during the sampling phase, reverting back to the large diameter tubing for the other aspects of the well test.

Conditioning

As we shall discuss shortly, there are two ways of sampling:

Down Hole

Surface

In both cases, proper conditioning of well prior to taking the sample is essential.

Ideally, sampling should be done as soon as possible after the well is completed. The process of drilling and completion usually results in near well bore damage and contamination, which must be cleaned-up before the sample can be taken. This is best achieved by a high flow rate. However, a high flow rate may cause in a large pressure draw down that results in the bottom hole pressure falling below the saturation pressure. Then, depending on relative permeability effects, the fluid flowing into the well may be unrepresentative of the reservoir fluid.

Once the balance has been achieved between maximizing clean-up time and minimizing draw down the main aim is to achieve:

Uniform flow rate,

Uniform GOR,

Stable Top Hole Pressure (THP)

Stable Bottom Hole Pressure (BHP)

Stable bottom hole density, BH [to ensure no liquid build up], and Stable wellhead temperature, TWH. The UKOOA report suggests these stability conditions be satisfied for 6 hours prior to the sample being taken.

4.1.3 Down Hole Sampling

In this technique, a bottle is lowered down hole on a wire line and placed as close as possible to the open interval. At some pre-arranged time or on a command from the surface, the bottle is opened to the fluid flowing around it whereupon some of that fluid is allowed to enter the bottle.

Unlike surface sampling, the volume of fluid that can be collected is relatively small: typically 1 litre or so. Traditionally, this has precluded their use for gas condensate

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systems but with improving laboratory techniques requiring less fluid to perform the suite of analysis tests, this is less of a problem.

The sample bottle is returned to the laboratory and the fluid is flashed to atmospheric conditions. The volumes of stock tank gas and oil are measured (Vg, Vo). The normalized weight fractions of the stock tank gas and oil samples are found by gas chromatography, wgi and woi. The mole weight and density of the oil sample are measured, Mo and o. The flash GOR, Rs, in consistent units, i.e. ft3/ft3 or m3/m3, tells us:

(4.xxx)omo

gmg

o

gs Vn

VnVV

R ==

Vgm and Vom are the molar volumes of gas and oil and ng and no are the corresponding mole numbers: by definition, in field units, Vgm = 379.4 ft3/lbmole. If we assume 1.0 mole of feed then no = 1.0 ng. The oil molar volume is calculated from:

(4.xxx)o

oom

MV

=

Combining these results allows us to calculate the gas moles as:

(4.xxx)( )

( ) soogmsoo

g RMVRM

n

+

=

Meanwhile, the oil and gas weight fractions are converted to mole fractions using the component mole weights:

(4.xxx)

( )( ) ( )

( )( ) ( )

+

+

++

++

+=

+=

7

7

77

77

Cjggjgj

igii

Cjoojoj

ioii

MwMwMw

y

MwMwMwx

The surface gas usually contains 1.0 mole percent or less of C7+ so Whitson has suggested that a good estimate for the gas plus fraction mole weights is Mg7+ = 105.0. The oil sample plus fraction weight is calculated by material balance from:

(4.xxx) +

++

=

7

17

7

Cj j

oj

o

oo

Mw

M

wM

Finally, with the gas and oil sample compositions and the gas moles, the feed composition is calculated from:

(4.xxx) igigi xnynz )1( +=

We will see in section 4.2.1 that the measurement of mole weight is extremely difficult and can be subject to an error as large as 10.0%: this will clearly feed through into the determination of well stream composition. Whitson has suggested that the Watson

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characterization factor, Kw11, can be used to test the accuracy of the mole weight measurement.

4.1.4 Surface Sampling

This remains the dominant technique for collecting samples. A well is allowed to flow to surface where a fraction of the well stream fluid is re-directed to a test separator held at some pre-determined pressure and temperature. After ensuring the stability conditions outlined in section 4.1.2 are met, samples of the separator vapour and liquid are collected in a number of bottles. These are then sent to regional laboratories for analysis.

The main advantage of this technique over down-hole sampling is the ability to collect large volumes of fluid. However, there are a number of issues including:

Lifting all the produced fluids,

Ensuring a representative mix is taken from the flow line,

Accurate metering with the consequent problem of recombining the vapour and liquid streams to reconstitute the well stream fluid.

4.1.4.1 Liquid Loading in Gas WellsThe first issue is particularly important for gas wells that also produce condensate or water. The minimum [equivalent surface] rate for a given well head pressure and tubing size was predicted by Turner et al. from:

(4.xxx)TZApv

Q whminmin 06.3=

The surface flow is expressed in MMscf/day, the tubing area, A, in ft2, the well head pressure, pwh, in psia, the surface flowing temperature, T, is in degrees Rankine and Z is the gas Z-factor at (pwh, T). The minimum velocity, vmin, measured in ft/s, can be estimated from one of the two following equations depending on whether the liquid is water or condensate:

(4.xxx)

( )( )

( )( ) 50.0

25.0

min

50.0

25.0

min

0031.00031.00.45

02.4

0031.00031.00.67

62.5

wh

whcond

wh

whwat

pp

v

ppv

=

=

It has been reported that the Turner correlation works well for LGR ratios as high as 250 bbl/MMscf.

11 See section 7.2.

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PVT Analysis

4.1.4.2 Taking SamplesMost surface samples are taken via a test separator. Ideally, the inlet of to the test separator should be a probe inserted into the main flow line from the well head manifold. The probe should be preceded by a baffle arrangement to ensure the fluid is well mixed.

4.1.4.3 MeteringProbably the biggest source of error in surface sampling is associated with errors in metering the vapour and liquid streams emerging from the test separator.

The measurement of the gas rate is usually done by inserting a restriction into the gas flow line. The restriction is one of two types, the Venturi tube:

Figure 20: Schematic of the Venturi Tube Rate Measurement

Or the Orifice Plate:

Figure 21: Schematic of an Orifice Plate Gas Rate Device

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PVT Analysis

In both cases, the conservation of momentum is used to equate the change in pressure between the upstream [denoted 1] and throat [denoted 2] to the flow rate:

(4.xxx) 22222111 2

121 vPvP +=+

where the local velocity vj = Q/Aj and Aj = pidj2. After some algebra, the above equation becomes:

(4.xxx)( )

21

422

1

1 PP

FAQ

d

g

=

where A2 is the choke area, Fd = d/D and is the average density. The second term on the right side of this expression is often known as the Approach factor. The pressure difference is often expressed in terms of the height of a column of water, hw. In this case, the Orifice Plate Equation (OPE) is expressed as:

(4.xxx) fwg phCQ =

where pf is the flowing or down stream pressure and the Orifice constant C is given by:

(4.xxx) almpvrtjgtbpbb FFFYFFFFFFFC =

The set of F-multipliers correct for a series of assumptions which were made in the derivation of OPE. Of particular interest are:

The Specific Gravity-factor, Fg, which must be used when the gravity is other than 1.0: ( ) 5.01 ggF =

The Super Compressibility factor, Fpv, which accounts for deviations from the Ideal Gas law: ( ) 5.01 ZFpv =

Very often the during the laboratory report of the recombination process, it will be seen that the test separator or field GOR is corrected to lab conditions by the equation:

(4.xxx) Fieldpv

Fieldg

Labpv

LabgFieldLab

FFFF

GORGOR =

More information on the OPE and its various F-multipliers can be found in Chapter 13 of the Petroleum Engineers Handbook.

A well maintained, relatively new OP or Venturi Tube meter should be capable of predicting the gas rate to an accuracy of 5.0%. However, they are easily damaged if there is liquid carry over in the form of a liquid-in-gas mist into the gas line. Even worse damage will occur if the well stream fluid contains particulates, i.e. sand production.

Most liquid measurements are done via a turbine-based meter in which a spinner turns more or less slowly depending on the flow rate and fluid properties. A well maintained meter would be accurate to 5.0%.

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PVT Analysis

4.1.4.4 Checking the DataA number of analysis techniques can be employed to ensure any recombined sample is representative. Firstly, when the liquid bottle is opened back in the laboratory, the bubble point pressure should be the same as the separator pressure at which it was sampled, corrected for temperature12. Secondly, since we have a vapour and liquid composition, then we know the vapour and liquid mole fractions of all components, denoted ( )ii xy , , respectively. From the gas and oil compositions we can calculate the K-values:

(4.1)i

ii x

yK =

Standing suggested that these measured K-values should obey:

(4.2) ( ) isepi FAApK 1010log +=The Fi are given by:

(4.3)

=

sc

ci

cibi

bii p

pTTTT

F log1111

( )cicibi pTT ,, are the ith components normal boiling point temperature, critical temperature and critical pressure and psc is standard pressure in a consistent unit set. The constants (A0, A1) are calculated from:

(4.4) 2841

2840

105.3 107.1890.0

100.15105.4200.1

sepsep

sepsep

ppA

ppA

=

++=

The separator pressure must be measured in psia. Equation (4.2) is generally assumed valid for hydrocarbon mixtures at pressures up to 1000 psia and temperatures up to 200 oF.

4.1.4.5 Recombination ExampleThe well stream fluid is flashed via the test separator into gas and oil samples. The samples are collected in bottles and sent to the laboratory. The gas and oil flow rates from the test separator are noted to give a gas-oil-ratio for the subsequent recombination calculation. The gas sample is sent straight to compositional analysis via the gas chromatogram. The oil sample is flashed at ambient or Stock Tank Conditions (STC) with the stock streams then being analysed by gas chromatogram: again, the gas and oil volumes are noted to give the ST flash GOR.

The surface separation process can be illustrated in the following schematic.

12 As a rule, bubble-point pressure of separator liquid samples increase between 3 and 4 psia per degree Fahrenheit.

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PVT Analysis

Figure 22: Surface Separator Analysis.

The typical data looks like the following Excel chart: compositions, GORs, etc. taken from Table 2.15 of Pedersen et al.

The input data is highlighted in the bordered cells. This includes the stock tank oil and gas compositions, the separator gas composition, the stock tank oil plus fraction mole weight and stock tank oil density, the separator and ambient GORs and the separator FVF. The calculated reservoir composition is shown in the final column of the sheet.

The basis of the calculation is the assumption of 1.0 STB of stock tank oil. Given a density in lb/ft3, this is converted to lb./STB by multiplying by 5.615 ft3/STB. The stock-tank oil mole-weight is calculated via Equation 5.9 with the user-supplied value of plus fraction mole weight.

The moles of oil in 1.0 STB can now be calculated from the density [in lb./STB] divided by the mole weight.

The quoted separator GOR is the produced gas at standard conditions, per barrel of oil at separator conditions. To convert the separator GOR to oil at standard conditions, multiply by the separator oil FVF. Now since both GORs are quoted per stock tank barrel, we can assume the stated volumes of gas are to be added to our 1.0 STB. Standard volumes of gas can be converted directly to moles by dividing by 379.4 [scf/lbmole]. We can add the moles of stock tank oil, stock tank gas and separator gas directly. The stream mole fractions are just stream moles per total moles. Finally, we multiply the stream mole fractions by the stream compositions and add to yield the reservoir fluid composition. A similar calculation involving just the stock tank oil and gas streams will back calculate the pre-flashed separator oil composition.

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PVT Analysis

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Recombine Test Separator Streams to Calculate Reservoir Composition

Comp Mw ST Oil Mw ST Gas Mw Sep Gas MwN2 28.0 0.00 0.0 0.20 5.6 0.66 18.5CO2 44.0 0.00 0.0 3.96 174.2 5.65 248.6C1 16.0 0.00 0.0 24.85 397.6 68.81 1101.0C2 30.0 0.20 6.0 20.40 612.0 12.86 385.8C3 44.0 2.14 94.2 28.41 1250.0 7.94 349.4iC4 58.0 1.10 63.8 4.78 277.2 0.94 54.5nC4 58.0 4.25 246.5 10.97 636.3 1.96 113.7iC5 72.0 2.68 193.0 2.21 159.1 0.34 24.5nC5 72.0 4.32 311.0 2.53 182.2 0.42 30.2C6 96.0 6.66 639.4 1.05 100.8 0.22 21.1C7 110.0 11.90 1309.0 0.54 59.4 0.15 16.5C8 124.0 13.14 1629.4 0.10 12.4 0.05 6.2C9 138.0 7.73 1066.7 0.00 0.0 0.00 0.0C10+ 228.5 45.88 10483.6 0.00 0.0 0.00 0.0Sums 100.00 160.4 100.00 38.7 100.00 23.7

Dens (lb/ft3) 53.69(lb/stb) 301.47

Separator GOR 2482 scf/bblSeparator FVF 1.165 bbl/stb Separator GOR(*) 2891.53 scf/stbAmbient GOR 207 scf/stb

ST Oil ST Gas Sep Gas TotalMoles 1.8792 0.5456 7.6213 10.0461Mol% 0.1871 0.0543 0.7586

Comp ST Oil Mol ST Gas Mol Sep Gas Mol Res FluidN2 0.00 0.00 0.20 0.01 0.66 0.50 0.51CO2 0.00 0.00 3.96 0.22 5.65 4.29 4.50C1 0.00 0.00 24.85 1.35 68.81 52.20 53.55C2 0.20 0.04 20.40 1.11 12.86 9.76 10.90C3 2.14 0.40 28.41 1.54 7.94 6.02 7.97iC4 1.10 0.21 4.78 0.26 0.94 0.71 1.18nC4 4.25 0.79 10.97 0.60 1.96 1.49 2.88iC5 2.68 0.50 2.21 0.12 0.34 0.26 0.88nC5 4.32 0.81 2.53 0.14 0.42 0.32 1.26C6 6.66 1.25 1.05 0.06 0.22 0.17 1.47C7 11.90 2.23 0.54 0.03 0.15 0.11 2.37C8 13.14 2.46 0.10 0.01 0.05 0.04 2.50C9 7.73 1.45 0.00 0.00 0.00 0.00 1.45C10+ 45.88 8.58 0.00 0.00 0.00 0.00 8.58Sums 100.00 18.71 100.00 5.43 100.00 75.86 100.00

PVT Analysis

Using the Standing procedure discussed in the previous section, we can generate the following plot:

Figure 23: Standing Analysis for the Separator Stage.

There is some scatter of the points, especially for high F-factors, which correspond to the more volatile species. However, this particular analysis would be regarded as satisfactory.

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PVT Analysis

4.2 Laboratory Analysis

Having obtained what are hoped to be one or more representative samples, the next task is to analyse them. Here the first task is to perform a compositional determination to find which components are present and in what proportions. Then a set of standard experiments should be performed to determine a set of important parameters. The parameters measured depend on the nature of the fluid, i.e. reservoir liquid or vapour.

4.2.1 Compositional Determination

The workhorse in this area is the gas chromatogram. A gas chromatogram usually comes in one of two types, Packed or Capillary columns. The packed column consists of a glass or stainless steel coil, typically 1-5 m in length and 5 mm inner diameter. The capillary columns are thin fused silica, typically 10-100 m in length with an inner diameter of 250 m.

Figure 24: Schematic of a GC System.

The sample is injected into the column, which is housed in a temperature-controlled oven. As the temperature is increased on some pre-programmed schedule, the components will boil depending on their volatility. An inert carrier gas such as helium or argon then carries the components along the tube to a detector. The most popular types of detector are the Flame Ionization Detector (FID) and the Thermal Conductivity Detector (TCD).

The effluent from the GC mixes with the air/hydrogen mixture and passes through a flame. The resulting ions are collected between the electrodes to produce an electrical signal. The FID is very sensitive but it destroys the sample.

The TCD consists of an electrically heated wire whose resistance is effected by the thermal conductivity of the surrounding gas. The change in resistance can be correlated to the nature of the surrounding gas. The TCD is not as accurate as the FID but it is non-destructive.

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PVT Analysis

Figure 25: Schematic of the FID [from www.scimedia.com].

Liquid samples can be analysed up to C10+ using the same capillary column technique. If a breakdown of the C10+ fraction into C10, , C19, C20+ is required, mini distillation is required. The C10+ residue is heated at reduced pressure, to prevent thermal cracking, in a series of boiling point increments corresponding to those which define the Single Carbon Number groups, see section 2.7.

In a detailed study by Eyton, the repeatability and hence the accuracy of compositional measurements was evaluated. Eyton concluded that given a mole percentage of xi, the error bands would be:

(4.xxx) 43.007.0 ii xx =

Thus as the mole percentage of a component approaches 100.0%, the measurement error can be assumed to be 0.5% whereas if the mole percent is as low as 0.01%, the measurement error is of the same order.

Regardless of the technique employed, a residue or plus fraction will be left: see section 2.8. The density or specific gravity of the plus fraction should measured relatively accurately. The measurement of molecular weight is a lot more difficult and therefore prone to error. The most common technique is freezing point depression where a small amount of the plus fraction is added to a pure solvent such as benzene. The freezing point of the mixture will be depressed by some T, the value of which depends on the mole weight of the contaminant.

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PVT Analysis

Figure 26: Freezing point depression diagram [from Pedersen et al.]The apparatus must be calibrated with great care using substances of known molecular weight. Similarly, the solvent must be of the highest purity. Errors of 10% are common.

4.2.2 Saturation Pressure (SAT)

The bubble point pressure for a reservoir liquid or the dew point pressure for a reservoir vapour is one of the important measurements performed. The exact mechanics of the measurement depend on the fluid type but in both cases it begins by loading a volume of the reservoir fluid into a PVT cell. This cell is placed in chamber whose temperature can be set to the reservoir temperature. Pistons can raise and lower the pressure and valves allow fluid to be injected and removed from the top and bottom of the cell. Some cells contain a window, located towards the bottom of the cell to allow visual inspection of the contents.

4.2.2.1 The PVT CellBelow is a schematic representation of a Gas Condensate PVT cell. The solid black line surrounding the cell indicates the oven in which reservoir temperature can be simulated. The proportional mercury pumps allow the reservoir fluid to be pushed from above and below to allow the gas/oil interface to be located centrally where the cell contracts. A mica window allows a camera too see into the cell via a fibre optic cable. A stirring device is added to speed-up the equilibration process.

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PVT Analysis

Figure 27: Schematic of a Gas Condensate PVT cell13

For a liquid, the pressure is raised to some high pressure, generally slightly in excess of initial reservoir pressure. Then, the pressure is reduced in a series of stages, noting the volume of the fluid at each stage. If a plot of volume versus pressure is made, the behaviour on the following plot is observed.

Figure 28: Change in Slope of p-V curve around the Bubble Point.

13 See Heriot-Watt Petroleum Engineering web pages: http://www.pet.hw.ac.uk/3frame.html.

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PVT Analysis

In particular, note the change in slope this identifies the bubble point pressure since at pressures less than 3900 psia, the higher slope shows the presence of a more compressible system i.e. liquid and vapour.

This fluid was subsequently labeled a volatile oil and the change in slope is still evident. However, for very near critical liquids, this technique may not be sensitive enough and the technique used for gas condensates may be required.

The evolution of a liquid from a vapour will not produce any significant change in slope on the p-V plot like the one seen above: instead, a visual determination is required. Because of the hostile conditions, remote visual observation is made of the cell using a fibre optic cable. As pressure is reduced, a careful watch is made for the point when the first drop of dew [liquid] is seen.

This measurement is prone to error. There is considerable debate as to how long the cell should be left after each pressure reduction step before the observation is made: this is because equilibrium is not instantaneous. Various stirring or mixing techniques are used to try to speed up the process. Contamination such as grease on the seals and o-rings may cause early liquid formation. Finally, small droplets of liquid, which appear in the top of the cell, may not trickle down to the bottom of cell where the observation is usually made.

Some condensate samples exhibit an effect called the