4.2 petroleum fluid properties - treccani, il portale del · pdf file ·...

4.2.1 Introduction

Reservoir fluids are composed of a large number ofcomponents. At ambient temperatures some of these arepresent in the gas phase, while others (resins andasphaltenes), due to their greater molecular weights, maybe present in solid phases. The ensemble of thesecharacteristics, related to phenomena of migration andheterogeneity of the formation, causes a non-homogeneous partitioning of the individual componentsin the reservoir, which must be taken into account in thedesign of the production process. Under certaintemperature and pressure conditions, solid phases maybe formed that strongly influence the production of fluid.

In addition, these fluids are always in contact withwater of a variable degree of salinity, which isproduced together with the crude, and at times in evenlarger quantities; this may cause problems due to saltprecipitation (when there is a mixture of differenttypes of water) and corrosion.

On the other hand, the development of ahydrocarbon field requires considerable investment,especially in the case of offshore fields. In order tofinalize the development scheme leading to optimalrecovery (cost, quantity and quality), it is necessary tohave an accurate knowledge of the thermodynamicbehaviour of the fluid. In fact, the surface facilitiesvary according to the type of fluid (oil or gas) and thetemperature and pressure conditions of the reservoir.When there is a risk of precipitation of heavycomponents, it is important to install suitableequipment or to use additives that can avoid suchproblems. Failing to recognize one of these processescan have serious economic and safety implications.

To predict the fluid’s thermodynamic evolutionunder the temperature and pressure conditionsencountered during production, mathematical modelsdesigned to calculate their behaviour are used. The

development of models capable of reproducing all ofthe physical phenomena requires knowledge of thefluid’s composition. Furthermore, laboratory data arerequired for the calibration of such models.

For this reason, fluid samples are taken as soon aspossible from the reservoir in order to performanalyses and thermodynamic experiments aimed atsimulating the temperature and pressure variations towhich the fluid will be subjected, so as to identifypotential problems. To be reliable, these experimentshave to be performed on samples representative of thereservoir fluid.

The discussion that follows will be dedicated tothese problems. After a brief account of thethermodynamic behaviour of pure components andbinary mixtures, the various types of reservoir fluidswill be classified. Subsequently, having described thereasons for which the composition of the reservoircomponents is not always homogeneous, the samplingprocedure will be described. A section is thendedicated to laboratory thermodynamic experimentsand finally some empirical correlations and equationsof state used to simulate the phase behaviour of thehydrocarbons will be presented.

4.2.2 Phase behaviour

The main components of petroleum fluids arehydrocarbons. Reservoirs also contain water, howeverits influence on the thermodynamic behaviour of thefluids is secondary, and consequently the oil and gasphases are generally treated separately from the waterphase. The behaviour of hydrocarbon mixtures in thereservoir and during production depends on thecomposition of the fluid as well as on the temperatureand pressure conditions it encounters. Understandingthis behaviour is of crucial importance to the

487VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT

4.2

Petroleum fluid properties

development of a hydrocarbon field, because it servesas the basis for the design of the production plan.

Even though the behaviour of these fluids is verycomplex, it can be explained on the basis of thebehaviour of simple fluids. As a result, the behaviourof pure components is covered first before going on tothat of binary mixtures, bearing in mind that the realfluids obey the same rules.

Pure componentsFig. 1 illustrates the behaviour of a pure component

by means of a pressure-volume diagram, which can bedescribed in the following way. Starting from point A(the component in the liquid state) and graduallyincreasing the volume (at constant temperature), thefollowing phenomena are observed: a) a rapiddecrease in pressure; b) the appearance of the firstbubbles of gas at point B; c) the increase in volume ofthe gas phase and the decrease in that of the liquidphase at constant pressure (line joining B to R); d ) thedisappearance of the last drop of liquid (point R); ande) the much slower decrease in pressure.

This series of phenomena occurs for alltemperatures below the critical temperature (TC). Abovethis temperature, the component remains in a singlephase and is referred to as being in the supercriticalstate. The set of bubble points form the bubble curve,while the dew points give rise to the dew curve.

It is also possible to represent the behaviour of apure component on a pressure-temperature diagram(Fig. 2).

All of the conditions at which the liquid and gasphases can co-exist are represented by the curve AC,where the bubble and dew curves are merged. In fact,according to the phase rule, at each temperature thereis only one pressure value for which the fluid can havetwo phases: if the number of components of a fluid isgiven by n and the number of phases is given by f,then the variance of the system (V), that is, the numberof intensive properties (temperature, pressure,composition of each phase) that need to be fixed inorder to determine the state of the system, is given by:

V�n�2�f

This curve is known as the vapour pressure curveand ends at the critical point (point C), beyond whichthe fluid always has a single phase. The line ASrepresents the liquid-solid equilibrium line, whichcorresponds to the line of melting points of the purecomponent. The curve AE is the line of sublimation;on this line the solid is in equilibrium with the vapour.The intersection of the line AC, AS and AEcorresponds to the triple point representing the onlypair of values of pressure and temperature at which thethree phases can co-exist.

Mixtures As with a pure component, the behaviour of a

mixture can be represented on a pressure-volumediagram (Fig. 3). Starting from point I (situated at atemperature below the mixture’s critical temperature),and moving towards larger volume, the followingphenomena can be observed: a) a rapid decrease of thepressure in the liquid phase; b) the appearance of the

488 ENCYCLOPAEDIA OF HYDROCARBONS

OIL FIELD CHARACTERISTICS AND RELEVANT STUDIES

T>TCT<TC

R

A

B

volume

pres

sure

Fig. 1. Pressure-volume diagram of a pure component. Two isothermal curves for temperature lower than the critical temperature and one (dashed line) for higher temperatures are shown. Points B and R are the bubble point and the dew point, respectively.

CS

AE

liquid

vapour

triple point

temperature

critical point

pres

sure

solid

Fig. 2. Pressure-temperature diagram of a pure component.

R

B

Iliquid

+vapour

vapour

volume

pres

sure

Fig. 3. Pressure-volume diagram of a mixture.

first bubbles of gas at point B, which represents thebubble point; c) the increase of the volume of the gasphase and the decrease of the volume of the liquidphase (but in this case, instead of remaining constant,the pressure decreases during the phase change); d )the disappearance of the last drop of liquid at point R(the dew point); and e) the slow decrease in pressurebeyond point R, where the entire mixture is in the gas.

If the behaviour of a mixture is represented on apressure-temperature diagram (Fig. 4), a two phaseregion appears and not simply a two phase line as inthe case of a pure component. The bubble and dewcurves no longer coincide, but instead intersect at thecritical point. The critical point can be situated eitherto the left or to the right of the maximum of thesaturation curve, and thus does not correspond to themaximum pressure and temperature of the twophases (in contrast to the case of a pure component).In fact, there is a pressure greater than the criticalpressure, above which the two phases can co-exist.This pressure is called the cricondenbar. In the sameway, the cricondentherm corresponds to themaximum temperature, above which the two phasescannot co-exist.

If the cricondentherm is greater than the criticaltemperature of the mixture, decompressing the gasstarting from point A, the dew curve is crossed at theupper dew point (Ru), where the first drop of liquidappears. Continuing the decompression, the volume ofthe liquid deposit goes through a maximum (point M)and then decreases before finally dropping to zero atthe lower dew point (Rl). This is the phenomenon ofretrograde condensation, which is frequentlyencountered in reservoir fluids such as gascondensates.

4.2.3 Fluid classification

Reservoir fluids behave in a similar way to binarymixtures. Depending on their composition and on thereservoir pressure and temperature, they may exist in

the reservoir in the liquid or gaseous state, or in stateof equilibrium between these two phases. Thereservoir fluids are composed of a wide range ofcomponents that can have a greatly variable number ofcarbon atoms. The lightest are gaseous under ambientconditions (CO2, N2, CH4), while the heaviest, whichcontain several hundred carbon atoms, are almostsolid. The crude also contains sulphurated compounds(mainly hydrogen sulphide and mercaptans), whichcause various types of problems, including problemsrelated to their toxicity.

Helium, heavy metals (mercury, nickel andvanadium) as well as traces of organo-metalliccompounds may also be present.

Reservoir classification Reservoir fluids can be conveniently classified by

referring to the characteristics of their phase envelopes(see also Chapter 1.1). Petroleum fluids are generallyclassified into two large families, depending onwhether the reservoir temperature is above or belowthe critical temperature of the fluid (Fig. 5).

The term oil is used to describe reservoir fluidswith a critical temperature higher than the temperatureof the reservoir, while the term gas is used to identifythose with a critical temperature lower than that of thereservoir.


PETROLEUM FLUID PROPERTIES

C

A

M

temperature

bubble point curve dew-point curve

cricondentherm

cricondenbar

liquid

pres

sure

liquid�vapour

Ru

Rl

Fig. 4. Phase envelope of a mixture.

C

TmaxTC

temperature

oil

gascondensate

dry gas

pres

sure


Fig. 5. Location of different types of fluid on the phase envelope.

Oils have the characteristic of liberating a certainquantity of gas, starting from the bubble point, whenthey are subject to an isothermal expansion. Dependingon whether the reservoir pressure is higher, lower orequal to the bubble point pressure, oils are classified asundersaturated, oversaturated or saturated.

An oil is referred to as a low or high shrinkage oildepending on the quantity of gas liberated underexpansion. Further distinctions are possible by takinginto account the composition of the gas. A lowshrinkage oil liberates a small quantity of gas, which isusually dry. A high shrinkage oil (or volatile oil)liberates a large quantity of gas, which generallycontains constituents that condense at surfaceconditions. The presence of a volatile oil is suspectedwhen the volumetric Gas/Oil Ratio (GOR) is greaterthan 200-300 and the API gravity of the oil is greaterthan 40°.

Gases can be classified into three subfamilies. Ineach of these cases, the reservoir temperature is abovethe critical temperature of the mixture, but may beabove or below the cricondentherm (Tmax in Fig. 5).

The reservoir contains a gas condensate if thereservoir temperature (TR) is lower than thecricondentherm and higher than the temperature at thecritical point, and the reservoir pressure (PR) is higheror equal to the saturation pressure. An isothermalexpansion of such a gas (Fig. 6), beginning from thesaturation pressure (upper dew point Ru), leads to theformation of a liquid phase. On reduction of thepressure, the volume of this liquid phase increases to amaximum (M), and subsequently decreases to zerowhen lower than the lower dew point (Rl). As alreadymentioned, this phenomenon is known as retrogradecondensation. It does not occur in the case of a purecomponent, in which an isothermal expansion of thegas phase never gives rise to a liquid phase, but insteadleads to direct vaporization. This behaviour ofvaporization is also observed in the case of a gascondensate, but only when the expansion is continuedabove point M. The main difference between a volatileoil and a gas condensate resides in the nature of theheavy fraction. The molar mass and quantity of the C7+fraction of a volatile oil are larger than those of a gascondensate; in general, it is rarely observed that a gascondensate contains a C7+ fraction with a molarpercentage greater than 15%.

If the reservoir temperature is higher than thecricondentherm and if the point representing thesurface conditions (Psep and Tsep, which are theconditions of the separator) reside within the phaseenvelope, the gas is said to be wet (Fig. 7). This meansthat liquid will be produced at surface conditions,without, however, the occurrence of retrogradecondensation in the reservoir. This situation veryrarely occurs. If, on the other hand, the pointrepresenting the surface conditions lies outside thephase envelope, the gas is said to be dry (Fig. 8) andwill not lead to the production of liquid at the surface.In this extreme case, the GOR is almost infinite.

4.2.4 Lateral and verticaldistribution of hydrocarbonsin reservoir

There are a number of theories regarding the formationof petroleum from organic matter, all of whichconverge on the conclusion that the composition of thereservoir fluid depends on its environment, itsgeological maturity and on the migration process fromthe source rock to the reservoir rock. These factors cancause significant variations in the lateral and vertical



C

TR

Psep

PR

Tsep

pres

sure

reservoir conditions

temperature

separator

Fig. 8. Phase envelope of a dry gas.

TR

C

Psep

PR

Tsep

pres

sure

reservoir conditions

temperature

separator

Fig. 7. Phase envelope of a wet gas.

C

M

TmaxTR

PR

temperature

pres

sure


reservoir conditionsRu

Rl

Fig. 6. Phase envelope of a gas condensate.

composition in reservoirs in different areas around theworld. Even though reservoirs are usually considered tohave reached a state of equilibrium, a significantnumber of these exhibit phenomena of lateral andvertical variations in composition (Hamoodi and Abed,1994; Hamoodi et al., 1996). In the well known case ofa reservoir in Abu Dhabi the fraction of H2S varieslaterally from 1% to 12% in spite of excellent reservoircommunication, and, therefore, this phenomenoncannot be explained by the subdivision of the reservoirinto separate zones (Firoozabadi et al., 1996). Anothersimilar example is a reservoir in the North Sea inwhich the methane concentration varies from 55% to73% along a depth interval of 81 metres (Danesh,2003). Volatile oils and fluids containing asphaltenesare particularly sensitive to these variations. The lack ofthe evaluation of such effects during the developmentstudy can lead to considerable errors in the estimationof the reservoir properties, the quantity of reserves inplace and the recovery factor. The margin of error mayreach 50% on the volume of the condensate in placeand up to 20% on the volume of gas, in the case of gascondensates. Similarly, the calculation of thecumulative production can be either under or over-estimated by more than 20% (Jaramillo, 2001).

The causes of this heterogeneity are numerous andmay be related to thermodynamic phenomena, reservoircharacteristics or the phenomena of generation,migration and accumulation of the hydrocarbons. Thethermodynamic processes of gravitational segregation,thermal diffusion (caused by the thermal gradient) andnatural convection lead to the creation ofheterogeneities, while molecular diffusion (caused byconcentration gradients) leads to homogenization of thefluid. Concerning the reservoir, the characteristicscapable of leading to a heterogeneous distribution arevariations in the permeability, porosity, wettability and,more generally, all of the reservoir heterogeneities.Finally, differences between source rocks andmaturation processes, as well as phenomena ofbiodegradation and precipitation of asphaltenes orresins may also contribute to the formation of aheterogeneous distribution of reservoir fluids.

All of these phenomena are very difficult to model.For this reason, it is necessary to take samples fromdifferent wells distributed over the entire area of thereservoir.

Regarding thermodynamic phenomena, the verticalthermal gradient, found in most parts of the reservoir,induces diffusion but not necessarily convection(Firoozabadi et al., 1996). In contrast, a lateral thermalgradient (observed in some reservoirs) cansimultaneously induce thermal convection anddiffusion phenomena. Constructing a model that takesthese phenomena into account is complex, and as far

as is known, will never succeed in taking all factorsinto account. The most important effects are related togravity. Gibbs (1961) proposed a mathematical modelcapable of evaluating the composition gradient causedby gravity in the absence of temperature gradients. Inthese conditions, the heavier components are found inthe lower part of the reservoir, while the lightest arefound in the upper part. Schulte (1980) and Montel(1993) proposed a model of this phenomenon based onthe equations of state. However, the quantification ofthese phenomena is very complex and the effects oftheir reciprocal influence is not precisely known. Forexample, some authors (Holt et al., 1983) sustain thatthe thermal effect may be of the same order ofmagnitude as the gravitational effect and that both actin the same direction, while other researchers havearrived at the opposite conclusion (Ghorayeb andFiroozabadi, 2001).

In any case, it is certain that the lateral and verticalvariations of the composition can be significant(especially in the case of volatile oils and gascondensates), and it is indispensable to take them intoconsideration during reservoir studies for thedevelopment of the field. As the factors for thesevariations are numerous and difficult to integrate intoa model, it is important to take samples from differentwells with the aim of calibrating the models.

4.2.5 Sampling

An accurate knowledge of a fluid’s thermodynamicbehaviour requires representative samples of thereservoir fluid to be taken. The study performed onthese samples provides data for the calculation of thereserves in place, the calculation of flow in the porousmedium, as well as for the design and thedetermination of the size of the surface facilities andthe development scheme that would allow an optimalrecovery of fluid. The necessity of havingrepresentative samples available appears even moreimportant when the investment required for the designprocess is taken into account, especially in the case ofoffshore fields. These studies should also enable theidentification of behaviour such as the precipitation ofasphaltenes and paraffins, or the formation ofhydrates.

The quantity of fluid required depends on the typeof laboratory study to be conducted. For example, if,on one hand, a classical PVT (Pressure-Volume-Temperature) analysis is to be carried out, a relativelysmall amount of fluid will be required, especiallyconsidering that modern PVT equipment is capable ofanalysing ever smaller samples. If, on the other hand, amore in-depth characterization (analytical and/or



thermodynamic) needs to be performed, acorrespondingly larger sample will be required. This isparticularly true in cases when the heavy fraction ofthe fluid needs to be accurately characterized. If thefluid to be sampled is a gas condensate in which theproportion of the heavy fraction is relatively low, itwill be necessary to take a significant amount of fluidin order to perform an accurate analysis of thecondensate. Also, in the case of the characterization ofthe heaviest fraction of oil containing asphaltenes orheavy paraffins, adequately large samples of fluid willbe required. Therefore, choosing of the type ofsampling is a function of the fluid, the well equipment,the production equipment at the surface and the typeof study to be performed.

There are two types of sampling procedures:bottomhole sampling (single phase) and surfacesampling. Surface fluids are generally sampled at theseparator. When the conditions of the wellhead aresuch that the fluid is in a single phase, samples can betaken at the wellhead. When large quantities of fluidare necessary, it is also possible to work with stocktank oil. The stock tank oil properties are used to studythe risk of deposits during transport, to performmeasurements in porous media, as well as for studiesconcerning the treatment of emulsions, thedehydration and the desalting.

Finally, the reservoir water is also sampled. Theknowledge of its properties is necessary for thecalibration of well logging, the definition of theproduction and process methods, the verification of itscompatibility with water to be used in a possible waterinjection, and for corrosion studies. Even though it isoften ignored, a water study is important: it should notbe forgotten that wells produce water after a certainperiod. At the end of the lifetime of a field, thequantity of water produced may even be larger thanthat of the oil.

Since the aim of the sampling procedure is toobtain a sample that must be representative of theoriginal reservoir fluid, it is indispensable to performthe sampling before the reservoir pressure reaches thesaturation pressure. In the case of a volatile oil or a gascondensate, below this threshold it is almostimpossible to obtain, either at the surface or at thebottomhole, a fluid representative of the originalmixture in the reservoir.

Bottomhole samplingThis type of sampling is performed using special

equipment lowered into the well. In general, thesampling is done during the production tests, beforeproduction has begun. Bottomhole sampling ispreferred in the following cases: undersaturated oils,fluids close to the critical point and rich gas

condensates. The possibility of maintaining thesamples in a single phase until the laboratory analysisdeters the precipitation of asphaltenes, whoseredissolution is always problematic. Bottomholesampling can be performed only when the pressure inthe well is greater than the saturation pressure of thereservoir fluid, otherwise the sample taken will not berepresentative of the original reservoir fluid. However,when this is the only type of sampling possible (whenthe reservoir pressure corresponds to the saturationpressure or when the flowing pressure in the well islower than this saturation pressure), one must try toattain well conditions that enable the sample collectedand the reservoir fluids to bear as many commoncharacteristics as possible. This can be achieved byreducing the production rate of the well.

It is important to suitably select the well where thesampling will be performed. The well should be locatedin an area of the reservoir where the reduction inpressure is minimal and it should have a highproductivity so as to maintain a sufficient pressure inthe surrounding region as well as to avoid the transitionto two-phase conditions. Furthermore, in order tominimize contamination of the sample, the well shouldnot produce water and should have been in productionfor a sufficiently long time in oder to avoidcontamination, for example, by the drilling fluid.Finally, the well should be connected to a separatorlocated as close to the wellhead as possible thusavoiding disturbances and excessively long stabilizationtimes. The choice of the well is made by studying thepast history of its production in order to ascertain that,in particular, the GOR of the fluid produced at thesurface remains constant over time, thus guaranteeing asingle-phase production. Before sampling, the rate ofthe well should be stabilized for a sufficient amount oftime to allow the GOR at the surface to become stable.This stabilization time can vary significantly (from afew hours to several days). The value of the GOR at theseparator should remain constant between tworeductions of the rate in order to be sure that theproducing horizon is indeed in a single phase.

In the case of sampling in a gas well, the rateshould be high enough to avoid an accumulation ofliquid at the bottom of the tubing.

Bottomhole sampling is performed by means ofsuitable instruments (samplers), which are loweredinto the well and vary according to the type of well.This type of sampling can be performed: • While drilling; in this case the samplers are fixed,

together with other equipment, to the end of thedrilling string. The most modern equipment makesit possible to obtain good quality samples with thistype of procedure (open hole sampling). Thismethod of sampling is becoming more and more



common especially in offshore fields because itsaves time considerably, with a correspondingreduction of costs. Furthermore, this equipmentpermits an accurate control of the sampling. Inparticular, using infrared measurements, it ispossible to verify that the sample is not toocontaminated by water or drilling mud. Equipmentcapable of measuring the viscosity and the densityof the fluid as well as taking samples at differentdepths, in order to measure the homogeneity of thecomposition, is presently being developed.

• In wells that are completed with production tubing.In this case, the sampler is most commonlylowered at the bottomhole by a cable.These samplers collect a certain volume of liquid

(generally between 500 and 1,000 cm3, depending onthe type) before being brought back to the surface. Thesamples are then transferred to suitable containers,which allow them to be transported in complete safety.This fluid transfer is performed under isobaricconditions. Finally, if the saturation pressure has beenreached, due to the pressure and temperature changesduring the ascent of the sampler to the surface, thesample must be restored to the reservoir temperaturebefore transfer. There is also a new type of sampler(SPMC, Single Phase Multisample Chamber), whichkeeps the sample above its saturation pressure in spiteof the temperature reduction due to the ascent of thesampler. The pressure is maintained (Fig. 9) by meansof a nitrogen chamber or a system of two pistonsallowing, in an initial stage, the sample to becompressed from the initial reservoir conditions (pointA) to a pressure higher than the sampling pressure(point B), and subsequently to limit the drop inpressure due to the ascent (point D). A samplercapable of simultaneously avoiding the drop inpressure and temperature has been put forward; thissampler thus eliminates any change in the temperature

and pressure conditions during the sample’s ascent tothe surface. After the transfer, the sample generallyexpands to a pressure lower than that of saturation insuch a way as to create a gas cap, which allows thesample to be transported safely. When the samplesarrive at the laboratory, they are brought back tosampling conditions.

Bottomhole sampling is the best method to obtainsamples, provided that the fluid is in a single phaseduring sampling. In particular, this is the onlytechnique that allows samples to be obtained withoutanti-hydrate additive contamination. Samples of thistype are also the most recommended for studies ofasphaltene containing fluids, since redissolving thesecomponents remains to this day very difficult andmuch debated. On the other hand, this method doesnot allow extensive studies to be performed, inparticular, on the liquid fraction of gas condensatesdue to the small volumes obtainable (generally lessthan one litre). In the case of saturated oils and poorcondensates, surface sampling methods arerecommended.

Surface samplingAt the surface, samples can either be taken directly

at the wellhead (if still in a single phase) or, morecommonly, at the separator. This method can be used foroils or gas condensates; in particular, when the fluidshave reached or are close to saturation pressure, orwhen the well produces a large quantity of water. Incontrast, the use of this technique is not recommendedwhen problems related to the crystallization of paraffinsor precipitation of asphaltenes are suspected to occur.Sampling at the separator consists of taking a gas and aliquid sample. The two samples must be taken at thesame time and the sampling time must be greater thanthe residence time in the separator. If there is more thanone separator, preferably the sampling should beperformed at the first separation stage in order to avoiderror accumulation. The two fluids, the gas and theliquid, are then recombined in the laboratory in such away as to synthesize a fluid representative of thereservoir fluid. When the saturation pressure of thereservoir fluid is known with precision, it is preferableto perform the recombination on the basis of the bubblepoint pressure rather than on the GOR (Danesh, 2003).The main difficulty with this type of sampling, whichassumes the use of a separator, lies principally in themeasure of the respective rates of the gas and the liquid.Furthermore, as the gas is at the dew point and theliquid at the bubble point, the slightest variation of thetemperature and pressure conditions during thesampling process can induce the transition to a two-phase state. In this case, there is a risk that the fluids areno longer representative. However, the advantage of this



A

B

D

pres

sure initial reservoir conditions

temperature

Fig. 9. Conservation of pressure in samplers.

type of sampling is that large quantities of fluid can betaken. Such large quantities are necessary for detailedstudies (this is especially true in the case of gascondensates that contain small quantities of heavycomponents). Nevertheless, in order to mix the gas andthe liquid in the proportions to generate a trulyrepresentative fluid, it is essential that the reservoir fluidis in a single phase at the depth of perforation (intervalopen to production), that the gas can lift the liquid in thetubing (if the pressure in the tubing is lower than thesaturation pressure), and that the gas and the liquid rateat the separator can be measured with maximumprecision.

The following measurements must be performedduring the sampling procedure: the rate of the gas andthe liquid at the separator; the sampling pressure andtemperature; the density of the gas at the separator;and the density of the oil at standard conditions.

There are several sampling methods for the gas andthe liquid at the separator. The gas can be transferredto a container under vacuum, or it may be transferredby displacement of a liquid (e.g. the container may befilled with water) or by displacement of a gas. In thelast two cases, it is advisable to transfer severalvolumes of gas in order to avoid the risk ofcontamination.

The liquid is transferred by displacement of aliquid (taking care that the liquid chosen is notmiscible nor reacts with the liquid being sampled), byequilibrium displacement of the separator gas (in thiscase, the bottle should be pre-filled with separatorgas), or by displacement of air.

4.2.6 PVT analyses (laboratory procedures and parameters measured)

Reservoir fluids contain several hundred components;therefore, it is impossible to identify all of thesecomponents in order to calculate the behaviour of afluid using a thermodynamic model. As a result, themethod used is to study, in the laboratory, thethermodynamic behaviour of representative samples ofthe reservoir fluids and to use the results obtained onthese samples to calibrate the thermodynamic model.This model can then be employed to forecast thebehaviour of the fluid throughout the productive life ofthe reservoir.

The experimental studies performed on thereservoir fluid allow the determination of theircomposition, their volumetric behaviour, as well astheir physical properties, such as density and viscosity.

The volumetric tests include a constant mass studyand a differential study (differential liberation or

vaporization). The constant mass study best representsthe behaviour of the fluid in the proximity of the well.Further from the well, where the pressure falls belowthe saturation point, a gas phase appears, which isproduced preferentially to the less mobile liquid phase.The study of differential liberation aims to simulatethe behaviour of the oil left in the reservoir, whichprogressively liberates the gas that was initiallydissolved within it. This gas does not remain in contactwith the oil and thus is no longer in equilibrium withit. As illustrated later, the measurements performed areslightly different depending on the type of fluidexamined.

In order to be useful, these tests must be performedon fluid samples representative of the reservoir fluids.Bottomhole samples or samples obtained byrecombination of separator fluids can be used. Ineither case, before beginning the analysis, it isessential to be certain that the sample is of goodquality. In the case of samples taken at the separator, itis preferable to ascertain that the saturation pressure ofthe oil does indeed correspond to the separatorpressure before performing the recombination. The gasobtained at the separator must be heated to a highertemperature than the separator temperature in order toavoid any condensation. Furthermore, the openingpressure of the bottle containing the gas must be equalto the closing pressure at the well site. The analysis ofthe separator gas is an important parameter whenverifying that the sample is representative (Williams,1994). The recombination of the gas and the oil mustbe performed in the proportions of their respectiverates measured at the separator so as to reproduce thesaturation pressure of the reservoir fluids. When thesaturation pressure is known with certitude, thisparameter should be given priority with respect to theGOR measured at the separator.

OilsOil is a fluid for which the reservoir temperature is

lower than the critical temperature of the mixture. Thedecompression of the fluid thus leads to theappearance of gas bubbles starting from the momentwhen the pressure is lowered below the saturationlevel, also known as the bubble point pressure (Pb).

The measurements performed during the testing ofoil samples include constant mass study, differentialstudy, separation tests and viscosity measurements.When a particular development scheme is planned(e.g. gas injection), further tests are required.

Constant mass studyConstant mass studies are performed by gradually

decompressing the fluid under isothermal conditionsuntil the appearance of the gas phase. Using this



method, it is possible to measure the saturation pressureof the oil (bubble point), the relative volume (i.e. theratio between the volume of the fluid, whether single-phase or two-phase, and the volume of the oil at thebubble point) and, in the case of undersaturated oils(when the pressure is higher than the bubble point), theisothermal compressibility coefficient. This study aimsto reproduce the behaviour of the fluid in areas wherethere is no flow, but where the fluid pressure falls belowthe saturation pressure (close to the well).

A sample of the recombined fluid is introducedinto an analysis cell at constant pressure. Havingstabilized the temperature at reservoir temperature, thepressure is reduced in successive steps. Afterstabilization of the pressure, the volume of the sampleis measured at each step. In this way, the variation ofthe volume with pressure at constant temperature isdetermined and the relative volume is calculated. Theresults of such an experiment are shown in Fig. 10.Using the data obtained in this way, thecompressibility coefficient of the fluid as a function ofpressure is determined:

1 DVCo��1�12�

TV DP

When the gas phase appears, a sudden change inthe slope of the curve is observed, from which thebubble point can be accurately determined. This study

can also be used to determine the density of the fluidat a given pressure and, subsequently, knowing therelationship between the pressure and the volume, thedensity can be calculated as a function of pressure.

Differential studyDifferential liberation (or vaporization) reproduces

the behaviour of the fraction of initial reservoir liquidthat is not produced at the surface during thedecompression of the reservoir. In fact, given that thegas is more mobile than the oil, it is preferentiallyproduced when the fluid is at a lower pressure than thebubble point. To simulate the true behaviour of thefluid, it would be necessary to remove the gas as it isproduced. Since this is not possible, one proceeds bysuccessive expansions and subsequent removals of thegas. In general, about ten stages between the reservoirand atmospheric pressure are employed during theanalysis. As in the constant mass study, the fluid isintroduced into the analysis cell at the reservoirtemperature and, when the temperature has stabilized,the pressure is reduced in steps. The gas phase appearswhen the saturation pressure has been reached, whichis then completely removed from the system atconstant pressure. The volume of the removed gas ismeasured by means of a gasometer. These operationsare then repeated until a pressure close to atmosphericpressure is reached. Having arrived at the last stage,the volume of the residual oil is first measured at thetemperature of the experiment and at atmosphericpressure, then at standard conditions (SC), 288 �15 Kand 1.013 bar.

Fig. 11 illustrates the evolution of the phaseenvelopes of the different saturated oils in the cellduring the course of the experiment. This figurehighlights how the oils obtained after removal of thegas are successively less volatile due to the reductionof the bubble point at the expansion temperature. Thesaturation pressure of the initial fluid at reservoirtemperature (TR) is represented by point A.Subsequently, the saturation pressures of the liquids inthe successive stages are represented by points B-E asthe pressure is progressively reduced. At each stage, itis necessary to measure the volume of the gas removedat the temperature and pressure conditions of the cell,as well as at standard conditions, the density of the gasand the volume of oil at cell conditions.

The properties calculated at the end of theexperiment are as follows:• Properties of the liberated gas: the total volume of

the gas produced, the volumetric factor Bg, thecompressibility factor Z and the composition of thegas from which the density is calculated; thevolumetric and compressibility factors are definedin the following way:



volume

pres

sure

bubble pressure

Fig. 10. Graph of the pressure as a function of the volume during a constant mass and temperature expansion.

TR

A

B

C

D

E

temperature

pres

sure

Fig. 11. Phase envelope of liquids in equilibrium during a differential study.

Vg(P,T)Bo�1111 (expressed in m3/m3)

Vg(SC)

288.15 PVg(P,T)Z�111112323

PatmTV(SC)

• Properties of the residual liquids at each pressurevalue: the relative volumes VR, the volumetricfactor Bo, the density r and the dissolved gas RS .These quantities are defined as follows:

Vo(P,T)VR�11133

Vo (Pb,T)

where Pb is the bubble point pressure of the oil attemperature T, and Vo is the volume of the liquidphase;

Vo(P,T)Bo�1111 (expressed in m3/m3)

Vo,res(SC)

where the volume of the residual oil Vo,resis the volume of the oil left at the last stage ofdecompression under standard conditions,

Vg,diss (P,T)RS�11111

Vo,res(SC)

where Vg,diss(P,T) is the volume of dissolved gas atthe pressure considered. This volume of gas isequivalent to the sum of the volumes of gasliberated in the successive stages and, therefore, iscalculated after the last stage.Furthermore, an analysis of the gas is performed at

each stage and an analysis of the residual liquid isperformed at the last stage.

Separation testsThis experiment consists of expanding the fluid

from its saturation pressure to the separator pressureso as to optimize the oil production. Depending on thefluid pressure at the wellhead case, one or severalstages of separation can be foreseen.

During this test, the volume and composition of thegas at each stage as well as the volume of the oil aremeasured. These two values are then converted to thevolume of oil under standard conditions. Furthermore,the density of the oil and the composition of the liquidare measured at standard conditions.

Viscosity of the reservoir fluid The viscosities of the fluid are necessary to define

the flow of the fluid in the rock. These viscosities aremeasured at the reservoir temperature conditions and

at different pressure values ranging from the reservoirpressure to atmospheric pressure, using either a ballviscosimeter (by measurement of the drop-time of asteel ball in a calibrated tube filled with the reservoirfluid) or a capillary viscosimeter (e.g. for a gascondensate).

Gas condensates As mentioned above, the reservoir temperature of a

gas condensate falls in the range between the criticaltemperature and the cricondentherm. Upon expansion,these fluids, which are initially gaseous, form a liquid(below the saturation pressure); the quantity of liquiddeposited reaches a maximum value before beingrevaporized. Laboratory tests aim to describe suchbehaviour on the basis of volumetric andcompositional measurements.

Constant mass studiesThe goal of this experiment is to determine the

dew point, the compressibility coefficient above thedew point and the volumes of liquid deposited belowthe dew point. To perform this experiment, therecombined fluid or the separator fluids (liquid andgas) are introduced into the PVT cell, which is thenbrought to reservoir temperature. The initial pressureis generally fixed to that of the reservoir.Subsequently, the fluid is gradually decompressed,thus increasing its volume until the dew pointpressure is reached. In most cases, the determinationof the dew point is made visually (either by eye or bymeans of a camera). The decompression is thencontinued in steps until revaporization begins. Ateach step, the pressure and volume of the liquiddeposited are measured. The parameters that can bedetermined by means of this procedure are: a) theupper dew point; b) the compressibility factor of thefluid as a function of pressure; c) the relative volumeVR�V(P,T)/V(PD,T), where PD is the dew pointpressure; d ) the density of the fluid as a function ofpressure; e) the percentage of condensate depositedas a function of the pressure (calculated using thesample volume at the dew point pressure as areference); and f ) the maximum quantity of theliquid deposited.

Constant volume studiesThis type of experiment is of fundamental

importance as it aims to reproduce the evolution ofthe reservoir fluid’s composition during the courseof the exploitation, thus allowing the estimation ofthe quality and quantity of the condensates whichwill remain in the reservoir. To perform thisanalysis, the fluid is recombined in the cell or isdirectly introduced (in the case of bottomhole



sampling), and the cell is subsequently brought tothe pressure and temperature conditions of thereservoir. The quantity of the fluid introduced mustbe measured with maximum precision in order toperform a material balance. To this end, it isimportant to know the density and composition ofthe fluid introduced. The volume of the recombinedsample, at the initial pressure and temperatureconditions, is chosen as the reference volume (V0).The pressure is then gradually reduced (in 10 to 15stages). At each stage, a part of the gas phase isremoved from the cell (at constant pressure) in orderto maintain the system at the reference volume V0.The information collected at each step includes thepressure, the volume of the liquid deposited, thevolume of gas extracted (at both the pressurecondition of the experiment and atmosphericpressures) and the composition of the gas. In thisway, it is possible to calculate the cumulativeproduction of gas, in terms of the cumulativenumber of moles of gas produced over the numberof moles of reservoir fluid at the initial pressure. Theparameters calculated at the end of the experimentare the following:• The volume of condensate deposited as a

function of pressure. The condensate curve willbe lower than that obtained from the constantmass study (Fig. 12) since the quantity ofmaterial in the cell diminishes at each stage. Thiscurve indicates the fraction of the condensatethat will remain in the reservoir. On the otherhand, the difference between the two curvesrepresents the condensates that will be producedat the surface.

• The compressibility factor Z of the gas produced,as already defined.

• The density of the gas relative to air. This can bemeasured by weighing a known volume of gas orcalculated from its composition.

• The composition of the gas produced.The principal difficulty of this study lies in the

recovery of the small volumes of condensates formedduring the expansion of the gas. The quantity of gasremoved must be sufficient to allow the measurementof the volume of the condensate; if this is not the case,the material balance between the quantity of materialintroduced and removed will not give satisfactoryresults. Danesh (2003) cites the work of Drohm et al.(1988) whose results show that of 80 studies of the gascondensates reported, 71 presented unsatisfactorymaterial balances. The development of injection valvesunder pressure for the direct gas chromatographicanalysis of the fluid should resolve this problem.

Composition of reservoir fluids In order to determine the composition of a

reservoir fluid, it is generally necessary to expand it toatmospheric pressure, as the techniques for gaschromatographic analysis available today can only beapplied under such conditions. The gas and liquidphases are then collected and analysed by means ofgas chromatography (see also Chapter 1.1). Theanalysis of the two phases obtained in this way arethen recombined in order to determine thecomposition of the original mixture. It is important toavoid the contamination of the sample with air at thetime of sampling as this can cause errors in themeasurement of nitrogen concentration. In addition tothe light components (up to C4), the heavy componentsin the gas (between C5 and C10) and especially in thecondensate should also be quantified, because the dewpressure value is strongly affected by theirconcentration.

The molar mass (or molecular weight) Mg of thegas can be calculated in the following way:

Mg�� yi Mii

where yi and Mi represent the molar fraction and molarmass of the component i.

The density of the gas can be measured byweighing a known volume of gas, or it can becalculated from the results of the gas chromatographicanalysis by means of the expression:

Patm Mgrg�11133

RT0

where rg is the density of the gas at atmosphericpressure Patm and at the standard temperature T0, and Ris the universal gas constant (equal to 0.0083144 ifPatm is expressed in MPa, T0 in K and r in kg/m3).

As far as the liquid phase is concerned, it can beanalysed by distillation or by means of gaschromatography on a capillary column. In either case,an unidentified residual heavy fraction remains, which



2

0

4

6

8

10

12

14

0 10 20 30 40 50 60pressure (MPa)

liqu

id d

epos

it (

100

V/V

sat)

constant volumeconstant mass

Fig. 12. Graph of the quantity of liquiddeposited as a function of the pressure in the constant mass and volume experiments.

can be analysed by liquid phase chromatography(Danesh, 2003).

The composition of the reservoir fluid is obtainedfrom the composition of the gas and the liquid on thebasis of the value of the GOR. The principal problemwith this method lies in the necessity to expand thefluid to atmospheric conditions before analysis. Infact, the expansion could cause a loss of heavycomponents, which are deposited on the walls of thecell, and a loss of part of the oil’s volatile components.As a result, the composition of the C5-C10 fractionscould be less accurate than that of the other fractionsin the fluid. To avoid this problem, methods ofinjection under pressure are presently being developed.These methods will allow the fluid (especially gascondensates) to be directly introduced into the gaschromatograph without the preliminary expansion,thus avoiding the loss of intermediate components.

4.2.7 Equations of state

An accurate knowledge of the thermodynamicbehaviour of the fluid is necessary in order to calculatethe reserves in place, to define the production designand to determine the size of the surface facilities thatwill guarantee an optimal recovery of liquid phase.The laboratory tests provide useful information on thethermodynamic behaviour of reservoir fluids, butunfortunately these experiments are long andexpensive, and cannot be performed in all of theconditions foreseen during the productive life of thereservoir. Therefore, the experimental studies are oftenused to calibrate the thermodynamic models integratedinto the reservoir, transport and process simulators.The models are either based on simple laws, whichallow the equilibrium constants and properties of thephases to be calculated, or on the use of equations ofstate. A detailed treatment of the application ofequations of state to petroleum fluids has already beengiven (see Chapter 1.1). To follow, only certainspecific aspects that are of particular interest forreservoir fluids are recalled.

Calculation of the equation of state parameters of mixtures

Equations of state used to describe the behaviourof reservoir fluids contain various parameters thatmust be determined or estimated. For example, two ofthe most commonly used equations of state in the oilindustry are the equation of Peng-Robinson and that ofSoave-Redlich-Kwong (see also Chapter 1.1):

RT aP�11�11111

V�b V 2�2bV�b2

RT a (T)P�11�11111113

V�b (V�c) (V�b�2c)

which contain the parameters a, b and c. For purecomponents, these parameters are calculated from thecritical properties or are modified in such a mannerthat the equation simulates in the best way thebehaviour of the fluid. In the case of a mixture,specific rules (mixing rules) are used to calculate theseparameters starting from those of the pure componentsthat make up the mixture. The classical mixing rulesused by the Peng-Robinson and Soave-Redlich-Kwongequations of state are the following:

a�� aij zi zji j

b��bi zii

2323

aij��ai aj (1�kij) with kij�kji

c��ci zii

where zi and zj represent the molar fractions of thecomponents i and j in the mixture. In theseexpressions, ai, bi and ci represent the parametersof the pure components. The calculation of aijrequires the use of a binary interaction parameterkij, which is usually determined by minimizing thedifference between the calculated and experimentaldata on the binary mixtures. At present, it is alsopossible to use pseudo-experimental datacalculated by means of molecular modelling,especially when it is necessary to characterize theheavy components of the mixtures, for whichminimal data are available, or the toxic components(Delhommelle et al., 1999). Moreover, there arenumerous publications in the literature where thevalues of kij for the Peng-Robinson and Soave-Redlich-Kwong equations can be found (Vidal,2003). In the case of a mixture containing largequantities of nitrogen or carbon dioxide, it isnecessary to use specific correlations for thebinary interaction parameters. The works ofMoysan et al. (1986) and Nishiumi et al. (1988)report such specific correlations for the cases ofcarbon dioxide and nitrogen, respectively.

Mixtures with acidic gases, water and alcohols When considering systems containing water,

gaseous acids (H2S or CO2) or alcohols (which usuallyare added in order to avoid the formation of hydrates)in addition to hydrocarbon, the classical mixing rulesdo not provide an accurate description of thebehaviour of the mixture. In such cases, it is advisableto use rules derived using the excess free energy(Huron and Vidal, 1979).



As far as equilibria with water are concerned, attimes it is necessary to take into account the salinity ofthe water, which is not considered in the formulationof the mixing rules outlined above. In this case, forhigh pressures, it is preferable to use another method(Soreide and Whitson, 1992), which consists ofmodifying the classical mixing rules associated withthe Peng-Robinson equation. This method usesdifferent interaction parameters for the hydrocarbonand liquid phases.

In the domains of gas transport and treatment,when the pressure and temperature conditions are suchthat there is risk of hydrate formation during transport,additives that inhibit such processes are usuallyemployed. Classical equations of state cannot describethe phase equilibria in which these components takepart. Therefore, new equations derived using statisticalmechanics are presently being developed(Kontogeorgis et al., 1999).

Grouping of componentsApplying equations of state to mixtures assumes

knowledge of the mixture’s composition (componentsand concentration) as well as of the chemical andphysical properties of each component (the criticaltemperature TC , the critical pressure PC and theacentric factor w for the Peng-Robinson and Soave-Redlich-Kwong equations; see Chapter 1.1).

As already mentioned, reservoir fluids (gases orliquids) are commonly analysed by means of gas phasechromatography and the analytical methods commonlyused provide very detailed information on theircomposition. Unfortunately, it is not possible to takeinto account all components, either individually or ingroups, during the modelling of the fluid behaviourusing basin or reservoir simulators, because thecalculation times are proportional to the number ofcomponents and these times rapidly becomeincompatible with the calculation capacity of presentday computers. For this reason, the fluids are generallyrepresented by a number of pseudocomponents (3 to10), each one grouping together an ensemble ofcomponents. There are various methods of grouping thecomponents; the simplest consists of gathering allcomponents eluted between two n-paraffins in the gaschromatography analysis. Furthermore, all componentswith the same number of carbon atoms can be groupedtogether. It is also possible to differentiate, on the basisof chemical families, components with a given numberof carbon atoms or within a given range of boilingtemperatures. This further subdivision results in a largernumber of pseudocomponents.

Finally, Montel and Gouel (1984) propose groupingtogether components in a 3 or 4 dimensional parameterspace, represented by, for example, the critical

temperature and pressure, the acentric factor and theboiling temperature. Ahmed (1989) described variousmethods of grouping together and characterizing thepseudocomponents of the heavy fraction.

The physico-chemical properties (TC , PC , w)attributed to each of these pseudocomponents aregenerally calculated from the properties of theconstituent pure components. The rule most commonlyused is that of Kay (1936), which is based on the linearweighting of the given property as a function of thecomponent’s molar fraction in the pseudocomponent.With regard to the heavy fraction, the literature containsnumerous studies on its characterization and, inparticular, on the influence of the method used on thepredictions of the reservoir fluid’s properties (Hamoodiet al., 1996). It has been demonstrated that even in thecase of a fluid containing only 0.01% in moles of theC6+ fraction, the adjustment of the properties of theheavy fraction can significantly modify the phaseenvelope of the fluid. Finally, Thomassen et al. (1987)indicated that an error of between 5 and 10% in themolar mass of the heavy fraction can cause an error of700 psi on the predictions of the dew point pressure of agas condensate.

The heavy fraction can be represented by purecomponents mixed in such a way as to reproduce themolecular mass and the division by chemical familyresulting from the compositional analysis, or by amixture of several pseudocomponents. The propertiesof the pseudocomponents can be quantified to a firstapproximation with the help of correlations, whichallow them to be calculated from the values of two ofthe following properties: the boiling temperature, thedensity and the molar mass. For example, it is possibleto cite the correlation proposed by Twu (1984), whichallows TC, PC, VC and M to be expressed as a functionof g0 (the relative density) and the boiling temperatureTb. This correlation is expressed using the followingfour parameters:

T0C�Tb�0.533272�0.191017�10�3Tb�0.779681�10�7Tb

2�

0.959468�1028

0.284376�10�10Tb3�111113��1

Tb13

VC0��1�(0.419869�0.505839a�1.56436a3�

9481.7 a14)��8

P0C�(3.83354�1.19629a0.5�34.8888a�

36.1952a2�104.193a4)2

S 0�0.843593�0.128624a�3.36159a3�13749.5a12

with a�1�Tb /T0

C, which allows the determination of:• The critical volume VC (in ft3/lb mol):



(1�2fv )VC�V0

C �11133�2

(1�2fv)

where

0.46659 3.01721fv�DSv�11133��0.182421�11133DSv�

Tb0.5 Tb

0.5

DSv�exp4[(S0)]2�g0 ��1;

• The critical temperature Tc (in °R):

(1�2fT)TC�TC

0 �11133�2

(1�2fT)

with0.362456 0.948125

fT�DST�11133��0.0398285�111332DST�Tb0.5 Tb

0.5

DST�exp[5(S0�g0)]�1;

• The critical pressure Pc (in psia):TC VC

0 (1�2fp)PC�PC

0 �12��12��121233�2

TC0 VC (1�2fp)

with

46.1955fp�DSp��2.53262�11133�0.00127885Tb�

Tb0.5

252.140��11.4277�11133�0.00230535TbDSpTb

0.5

DSp�exp[0.5(S0�g0 )]�1;

• The molar mass M:

(1�2fm)1nM�1nM0�132

2

(1�2fm)

with ln M0�q, q being defined by:

Tb�exp�5.71419�2.71579q�0.286590q2�

39.8544 0.1224881111�1111 �24.7522q�

q q2

35.3155q2

and with

0.193168fm�DSm��x��0.0175691�1111�DSm Tb

0.5

where

DSm�exp�5(S0�g0 ) �1

0.328086�x��0.0123420�1111�Tb

1/2

The characteristic values of the heavy fraction arethen optimized in such a way as to reduce to aminimum the differences between the data measuredat the reservoir temperature and the calculated data. Asan example, Fig. 13 illustrates the phase envelope ofthe oil, calculated with the initialization values used asparameters of the pseudocomponent of the heavyfraction and the phase envelope obtained aftercalibration of these parameters. This exampledemonstrates the necessity of laboratory experiments.

Representation of the heavy fraction The heavy fraction of the fluid, which is not

completely analysed, is represented by one or morepseudocomponents (usually two or three), the physicalproperties of which need to be determined. The use ofthree pseudocomponents has been proposed in orderrepresent, respectively, the paraffins, the napthenesand the aromatics present in the heavy fraction.Pedersen et al. (1992), on the other hand, propose amethod of representing the heavy fraction of gascondensates by means of a distribution function basedon the number of carbon atoms. In fact, this functionallows one to determine a concentration per number ofcarbon atoms, the final number of carbon atoms beingfixed with the help of the molar mass of the heavyfraction. Finally, Danesh (2003) describes thepossibility of using the mathematical distributionfunctions proposed by Cotterman (1985).

4.2.8 Empirical PVT correlations

As already mentioned, in order to correctly developa hydrocarbon field, it is necessary to know theproperties of the fluid under a wide range ofpressure and temperature conditions. The propertiescan be calculated by the equations of state orestimated with the help of empirical correlations.The latter are easier to use than equations of state,but they are generally only applied to the type offluids on which they were developed and cannot beextrapolated. The main properties that can becalculated using these correlations are the saturationpressure, the GOR, the formation volume factors,



pres

sure

after tuningbefore tuning

temperature

Fig. 13. Variation of a phase envelope beforeand after the calibration of the parameters of the heavy fraction.

the compressibility, the density and the viscosity.The correlations available in the literature have beenevaluated by numerous authors, however, it is stilldifficult to advise the use of one more than another.Therefore, in the following, only the most frequentlycited or the most recent correlations will be given asexamples, indicating where possible the nature ofthe fluids used in their derivation (Ahmed, 1989;Danesh, 2003).

McCain (1991) and, more recently, Valko andMcCain (2003) presented a summary of thecorrelations that can be used to calculate the propertiesof reservoir fluids.

Properties of oils

Bubble point pressureStanding’s correlation. This correlation was

established using data obtained on certain fluidsoriginating in California having bubble pointspressures between 900 and 48,300 kPa (i.e. between130 and 7,000 psia). It was first presented in the formof a graph without analytical formulation (Standing,1947) and later in the form of a computer usablecorrelation (Standing, 1977). It is presented below withparameters compatible with SI units:

GORPb�519.7�13

0.83

10 yg

gg

with

1.769yg�1.225�0.00164T �13

go

where the bubble point pressure Pb is expressed inkPa, the GOR in m3/m3 and the temperature T in K. ggand go are the density of the gas relative to air and thedensity of the oil relative to water.

From the many other correlations which have beendeveloped, that of Elsharkawy (2003) can be cited asan example. The input data of this correlation, basedon data obtained from fluids coming from the NorthSea, are the molecular weight and the density of theC7+ fraction, as well as a detailed composition of thefluid up to C6.

The GORIt is recalled that, for a saturated oil, the GOR

represents the quantity of gas dissolved in a unitvolume of the storage oil, where the volumes of gasand oil are those under standard conditions, that is288.15 K and 1.013 bar. The same correlations can beused to calculate the quantity of gas dissolved RS (seeabove) at all pressures below the bubble point, since atall of these pressures the oil is saturated (in the case ofa differential study).

volume of gas dissolved(SC)GOR1111111111

volume of the storage oil (SC)

Also, in this case, the correlations established byStanding will be examined.

Standing’s correlation. This correlation isapplicable to fluids with a GOR between 3.6 and 254sm3/m3 (i.e. between 20 and 1,425 sft3/stb):

PGOR�gg�113 1.204

519.710yg

with

1.769yg�1.225�0.00164T�133

go

where the GOR is expressed in sm3/m3 and the pressureP in kPa; gg and go are the density of the gas relative toair and the density of the oil relative to water.

Formation volume factorThe formation volume factor Bo is used to establish

the relationship between the volume of the oil underreservoir conditions and that under standardconditions. The correlations that allow the calculationof Bob (Bo at the saturation pressure) require the GOR,the density of the gas and the storage oil, and thetemperature to be known. As an example, Standing’scorrelation is discussed.

Standing’s correlation. It is expressed by

Bob�0.972�0.000147 F1.175

with

ggF�5.615 GOR�1�0.5

�2.25T�575go

where Bo and the GOR are expressed in m3/m3, and ggand go are the density of the gas relative to air and thedensity of the oil relative to water.

Compressibility factorThe isothermal compressibility factor of the

undersaturated oil Co (at pressures higher than thebubble point pressure) is defined in the following way:

1 �VCo��1 �1�

TV �P

where (�V/�P)T is the slope of the pressure-volumecurve. This factor is generally determined with thehelp of the experimentally defined pressure-volumecurves. However, it is also possible to evaluate itusing various correlations, among which that ofVasquez and Beggs (1980), which requiresknowledge of the density of the gas, the API gravityof the oil, the GOR, the temperature and the pressure,can be cited:



1,78428.1GOR�30.6T�1,180gg�112�10,910goCo�

111111111111111111

105P

where gg is the density of the gas relative to air andgo is the density of the storage oil relative to water;Co is expressed in kPa�1, GOR in m3/m3, P in kPaand T in K.

This correlation was established on the basis of2,000 experimental measurements performed on 600different fluids.

DensityThe density (r) of a fluid is defined as the mass of

a unit volume of fluid at the given pressure andtemperature conditions. The relative density of an oilis defined as the ratio between the density of the oiland the density of water at the same conditions ofpressure and temperature. In the case of gases, thedensity is given relative to that of air.

In the oil industry, the API gravity is alsofrequently used for storage oils. It is defined asfollows:

141.5gAPI�

1223�131.5go

where go is the density of the oil relative to water atstandard conditions (15.6°C, 1.013 bar).

The main methods for calculating the density of oilare those formulated by Katz (1942), by Standing(1977, 1981) and by Alani-Kennedy (1960).

Standing and Katz proposed a graphicalcorrelation to determine the density of oils for givenvalues of pressure and temperature (Gravier, 1986;Ahmed, 1989). This method is based on twoproperties: on the additivity of the partial volumes ofthe liquid components and on the apparent density ofmethane and ethane in solution in the liquid. Thedensity of the oil is determined in successive steps:• Determination of the density of the C3+ fraction at

15.6°C and atmospheric pressure using thefollowing relationship:

n

�xiMii�3rC3��111n xiMi�13i�3 ri

where rC3+ is the density of the C3+ fraction atstandard conditions, n is the number ofcomponents in the mixture, xi is the molar fractionof component i, Mi is the molar weight ofcomponent i, and ri is the density of component i.

• To determine the fictive density of the system at15.6°C and atmospheric pressure on the chart(abacus or monograph), it is necessary to know the

density of C3+ and the weight fraction of methaneand ethane as defined by:

x1M1 x2M21122 and 1122n n

�xiMi �xiMii�1 i�1

where x1 and x2 are the molar fractions of methaneand ethane, respectively, and M1 and M2 are theirmolecular weights.

• Correction of the fictive density at 15.6°C andatmospheric pressure, by the addition of acontribution related to the thermal expansion andthe compressibility. These contributions aredetermined graphically.Furthermore, Katz (1942) proposed a correlation

that does not require knowledge of the composition ofthe oil, but instead uses the density of the gas, the APIgravity of the oil and the GOR (Standing, 1977). It isalso worth mentioning the correlation proposed byStanding (1981), which allows calculation of thedensity of the oil from the GOR and the densities ofthe gas and the liquid:

62.4go�0.0136GORggro�11111111111111111111

gg0.972�0.000147�GOR�1�0.5�1.25(T�460) 1.175

go

where the density is expressed in lb/ft3, thetemperature in °R, the GOR in sft3/stb, and where go isthe density of the storage oil relative to water and gg isthe density of the gas relative to air.

The method of Alani-Kennedy, which was alsodescribed by Ahmed (1989), requires the molecularweight and the density of the C7+ fraction of the oil tobe known.

ViscosityAs in the case of the above properties, the viscosity

m of the reservoir fluid is measured at the reservoirtemperature and for pressures higher than the bubblepoint pressure. If this is not the case, it is possible toestimate its value by using a correlation. There arenumerous correlations that can be used to calculate theviscosities of the storage oil, the oversaturated oil, theoil at the bubble point pressure and the undersaturatedoil. However, as in the case of the previouscorrelations, their application is specific to the type offluids on which they were developed. In the following,one of each type of calculation is mentioned; thereader interested in the matter can refer to the work ofvarious authors (Ahmed, 1989; McCain, 1990;Danesh, 2003).

Viscosity of the storage oil: the correlation of Ngand Egbogah. This correlation, cited in McCain(1991), can be used to estimate the viscosity of astorage fluid (mod) at temperature T:





log[log(mod�1)]�1.8653�0.025086gAPI�0.5644logT

where mod is expressed in cP, T in °F and gAPI is the API gravity at temperature T.

This equation was derived from data on fluids withan API gravity between 5° and 58° and fortemperatures between 288.75 K and 352.55 K, that is,between 60°F and 175°F (Ng and Egbogah, 1983).

Viscosity below the bubble point pressure: Khan’scorrelation. It is expressed by

Pm�mob�1��0.14

exp[�2,5�10�4(P�Pb)]Pb

where mob is the viscosity at the bubble pressure in cP,Pb is the bubble point pressure in psia, and P is thepressure in psia (Khan et al., 1987).

Viscosity at the bubble point pressure: thecorrelation of Beggs and Robinson. This correlationfollows the expression

mob�ambod

with

a�10.715(GOR�100)�0.515

b�5.44(GOR�150)�0.338

where the GOR is expressed in sft3/stb, T in °F, andmob and mod in cP.

The viscosity of the fluid at standard conditionscan be obtained experimentally or calculated with thehelp of the correlation of Ng and Egbogah describedabove. At pressure below the bubble point value, theGOR is replaced by the Rs at the pressure underconsideration (Beggs and Robinson, 1975).

Viscosity at pressure above the bubble pointpressure: the correlation of Vazquez and Beggs. It isexpressed by

Pmo�mob�1�B

Pb

withB�C1P

C2 exp (C3+C4P)

C1�2.6, C2�1.187, C3�11.513 and C4��8.98�10�5

where mo is the viscosity of the oil in cP at the pressureP (expressed in psia) and Pb is the bubble pointpressure in psia (Vazquez and Beggs, 1980).

Properties of the gases

CompressibilityStanding and Katz (1942) proposed a graphical

method, which allows the estimation of thecompressibility coefficient of the gas from the

pseudo-reduced properties (Tpr and Ppr), estimated inthe following way:

TTpr�

1 with Tpc��yiTc,iTpc

PPpr�

1 with Ppc��yi Pc,iPpc

where yi is the molar fraction of the component i in thegas, Tc,i and Pc,i are the critical temperatures andpressure of the component i, Tpc and Ppc are thepseudo-critical temperature and pressure of the gas.

This graphical method was subsequently convertedinto the form of a correlation by Dranchuk (Dranchukand Abou-Kassem,1975; Danesh 2003):

C2 C3 C4 C5 C7 C8Z��C1�1�1�1�1 rr��C6�

1�1 rr2�

Tpr Tpr3 Tpr

4 Tpr5 Tpr Tpr

2

C7 C8 rr2

C9�1�1 rr5�C10(1�C11rr

2)13 exp[�C11rr2]�1

Tpr Tpr2 Tpr

3

with C1�0.3265, C2��1.0700, C3��0.5339,C4�0.01569, C5��0.05165, C6�0.5475,C7��0.7361, C8�0.1844, C9�0.1056, C10�0.6134,C11�0.7210.

The reduced density is calculated using:

0.27Pprrr�1123

ZTpr

To solve this system a Newton-Raphson iterationtechnique can be used, while to initialize the system avalue of Z=1 can be used. The correlations establishedfor hydrocarbon gases must be corrected whenworking with gases containing non-hydrocarbonsubstances such as N2, CO2 and H2S. Some suchcorrelations have been proposed by Ahmed (1989).

Takacs (1976) evaluated the performances of eightcorrelations, the most simple to use is presented below:

Ppr PprZ�1�12 �0.36748758�0.04188423�12� Tpr Tpr

Elsharkawy’s correlation. Recently Elsharkawy(2004) proposed a correlation that allows thecalculation of the compressibility coefficient of a gascontaining C7+ components. In this procedure, thecompressibility coefficient is calculated by means ofDranchuk’s equation, which, as mentioned, representsin analytical form the graphical method presented byStanding and Katz. On the other hand, in order tocalculate the pseudocritical properties, the use of thefollowing correlations is proposed:

T K2infTpr�

1 with Tpc�123

Tpc Jinf

P TpcPpr�1 with Ppc�

12

Ppc Jinf

where

yiTc yiTcJinf�a0��a1�123� H2 S��a2�1233� CO2

�Pc Pc

yiTc Tc�a3�123� N2

��a4�yi �12� C1�C6

��a5(yiM) C7�Pc Pc

with a0=0.036983, a1=1.043902, a2=0.894942,a3=0.792231, a4=0.882295, a5=0.018637, and

yiTc yiTcKinf�b0��b1�12� H2S��b2�12� CO2

�Pc

0.5 Pc0.5

yiTc Tc�b3�12� N2

��b4�yi �12� C12C6

��b5(yiM) C7�Pc

0.5 Pc0.5

with b0= –0.7765003, b1=1.0695317,b2=0.9850308, b3=0.8617653, b4=1.0127054, andb5=0.4014645. Finally, yi is the mole fraction ofcomponent i and M is the molecular weight of C7�.

Formation volume factorAs in the case of oil, the formation volume factor

(Bg) of gas is the ratio between the volume occupiedby the gas at the reservoir conditions and the volumemeasured at standard conditions:

VP,TBg�12VSC

ZnRT112

P PSC ZTBg�1211�1212ZSCnRTSC TSC P111

PSC

where ZSC , the compressibility factor at standardconditions, is equal to 1, and PSC and TSC are thestandard pressure and the temperaturerespectively.

ViscosityLee’s correlation. Lee et al. (1996) presented a

semiempirical correlation to calculate the viscosity µg,of natural gases:

µg�10�4D1exp(D2rgD3)

with

(9.379�0.01607M)T1.5D1�

1111111111

209.2�19.26M�T

986.4D2�3.448�1123�0.01009M

T

D3�2.447�0.224D2

where rg is the density of the gas at the reservoirtemperature and pressure in g/cm3, T is the

temperature of the reservoir in °R, and M is theaverage molecular weight of the gas in g/mol.

Elsharkawy’s correlation. Lee’s correlation wasmodified by Elsharkawy (2004) to take the heavyfraction, H2S and CO2, into account. Corrections madeto Lee’s expression can be calculated as follows:

Dmg�yH2S [�3.2268�10�3loggg�2.1479�10�3]

Dmg�yCO2

[6.4366�10�3loggg�6.7255�10�3]

Dmg�yC7�

[�3.2875�10�1loggg�1.2885�10�1]

where y is the molar fraction of the component in thegas and gg is the density of the gas relative to air.

4.2.9 Reservoir Water

In reservoirs, water is always associated with thehydrocarbons (see also Chapter 1.1). It is present inequilibrium in the reservoir both when productionbegins and during the course of the exploitation; it isproduced together with the hydrocarbons and itsproduction increases with time. Towards the end of theproduction life of the reservoir, the production ofwater may become larger than that of oil.

The water of the reservoir may be interstitial (i.e. itmay occupy the part of the pore volume not occupied bythe crude); on the other hand, when the water occupiesthe entire pore volume, it is considered to be an aquifer.

Knowledge of the water’s properties enables theidentification of the areas where it is permanentlypresent, the determination of the fraction of porevolume that it occupies and the prediction of its flowwithin the reservoir. The analysis of the reservoir wateralso allows one to identify potential problems due toscales in the well strings or in the surface equipmentduring the course of production, corrosion problems, aswell as to determine the size of the surface facilities. Ifthe decision is taken to inject water in order to maintainreservoir pressure, it is imperative to verify that thereare no incompatibilities between the reservoir waterand that which is to be injected, in order to avoid theformation of solid deposits. At certain pressure andtemperature conditions, the water and somecomponents of the gas may crystallize and formhydrates. Formation of these compounds may lead toserious safety problems and eventually to blockage ofthe pipes. When the production conditions arecompatible with the thermodynamic range of stabilityof these hydrates, it is necessary to perform adequatestudies and implement the required measures, both toavoid the formation of hydrates and control theirformation (Sloan, 1990a, 1990b).

Finally, the water sometimes forms an emulsionwith the oil. In these cases, it is necessary to perform a



systematic laboratory study in order to verify stabilityof the emulsion so as to ascertain that it is possible toseparate the oil from the water. When separation bymeans of simple settling is not possible, chemicaladditives may be used to facilitate the breakage of theemulsion.

SamplingThe composition of the water varies with depth,

but may also vary laterally as a function of differentsources. Therefore, it is important to take samples indifferent points in order to reconstruct the history ofthe reservoir. As in the case of reservoir fluids, it isimportant for the well to be in production for sometime before taking the sample, so as to avoidcontamination of the sample with the drilling fluids.The type of sampling varies as a function of the typeof analysis that is planned. If the aim of this analysis isto determine the quantity and composition of the gasdissolved in the water, the sampling must beperformed at the wellhead in order to avoid theexpansion of the water with the resulting loss of gas.If, on the other hand, the pH, the redox potential or thequantity of oxygen or CO2 dissolved in the water areto be determined, it is necessary to use a mobileanalyser capable of performing the analysis on site,thus avoiding the transport of the sample. In somecases, an isotopic analysis of the water is alsoperformed in order to determine its origin.

SalinityThe salinity of reservoir water is extremely

variable: it can range from water that is almost fresh tobrine solutions that may contain (Gravier, 1986) up to400 g of salt per litre (see also Chapter 1.1). Ingeneral, the salinity of the water increases with depth.The main cations present in reservoir water are sodium(Na�), potassium (K�), calcium (Ca2�), magnesium(Mg2�), barium (Ba2�) and, in smaller quantities,strontium (Sr2�). Occasionally, the presence of lithium(Li�), caesium (Cs�), rubidium (Rb�) and ammoniumions (NH4

�) are also observed. Furthermore, metalssuch as aluminium, iron and manganese are alsofound. Regarding anions, the main ones observed arechlorides (Cl�), sulphates (SO4

2�), bicarbonates(HCO3

�), carbonates (CO32�), S2� ions and, more

rarely, nitrates (NO3�), bromides (Br�), thiosulphates

(S2O32�), phosphates (PO4

3�) and silicates (SiO32�). The

composition of the water can be described in terms ofthe first and second salinity, and of the first andsecond alkalinity. The first salinity refers to NaCl andNa2SO4 salts, while the second refers to CaCl2,MgCl2, CaSO4 and MgSO4 salts. The first alkalinity ismainly concerned with CaCO3, Ca(HCO3)2, MgCO3and Mg(HCO3)2 (Koederitz et al., 1989). The

composition of the water varies according to its origin(marine or meteorological water). Sea water ischaracterized by a high content of chlorides, a weakconcentration of phosphates and the presence ofiodides. Water of meteorological origin is rich inoxygen (often in the form of CO2) and gives rise to theformation of sulphates following the reaction of theoxygen, as well as to carbonates and bicarbonatesrelated to the action of CO2. The quantity of alkaline-earth components is greater than that of the alkalines,while a very weak concentration of mineral salts ispresent. The salinity of water is generally expressed ing/l and corresponds to the quantity of salts dissolvedin a litre of water. Analysis of the water is used for thelog interpretation, water treatment and environmentalimpact.

Solubility of gas in the waterGases are easily soluble in water; the level of their

solubility depends on the temperature, on pressure andon the salt concentration. The solubility of gas in brineis smaller than that in fresh water. The bubble point ofthe reservoir water is the same as that of the fluid inequilibrium with the reservoir water. The Gas/WaterRatio (GWR) can be calculated using a correlation,such as that proposed by McCain (1991), which allowsthe estimation of the GWR in pure water and thenadds a correction in order to take into account thesalinity of the water:

GWRfresh water�A�BP�CP2

where the GWR is expressed in sft3/stb, P in psia andT in °F, and with

A�8.15839�6.12265�10�2T�

1.91663�10�4T 2�2.1654�10�7T 3

B�1.01021�10�2�7.44241�10�5T�

3.05553�10�7T 2�2.94883�10�10T 3

C��10�7(9.02505�0.130237T�

8.53425�10�4T 2�2.34122�10�6T 3�

2.37049�10�9T 4)This equation was obtained by means of interpolationof a correlation presented by Culberson and McKetta(1951) in graphical form and applicable between 310and 444 K and between 7 and 70 MPa. To take accountof the salinity of the water, it can then be corrected inthe following way:

GWRbrinelog�1211111 ��0.0840655ST �0.285854GWRfresh water

where S is the salinity expressed in weight percentage,T is the temperature expressed in °F and the GWR isexpressed sft3/stb.





Formation volume factorsThe formation volume factor (Bw) of water can be

calculated using the correlation proposed by McCain:

Bw�(1�DVwP)(1�DVwT)

where DVwP and DVwT represent the volume changesdue to the pressure and temperature, respectively,which can be expressed as follows:

DVwP��(3.58922�10�7�1.95301�10�9T )P�

(2.25341�10�10�1.72834�10�13T )P2

and

DVwT��1.0001�10�2�1.33391�10�4T �

5.50654�10�7T 2

This correlation is valid for temperatures below 400 Kand for pressures below 31 MPa.

CompressibilityMeehan’s correlation. According to Danesh

(2003), it is possible to calculate water compressibilityusing the correlation proposed by Meehan (1980). Inthis method, the compressibility of the water is firstcalculated without taking into account the quantity ofdissolved gas (Cwf):

Cwf�10�6(C0�C1

T�C2T 2)

where Cwf is expressed in psi-1, T in °F and the Ccoefficients depend on the pressure according to thefollowing relationships:

C0�3.8546�0.000134P

C1��0.01052�4.77�10�7P

C2�3.9267�10�5�8.8�10�10P

with the pressure expressed in psia. The dissolved gas is then taken into account by

using the following relationship:

Cw�Cwf (1�8.9�10�3GWR)

where the GWR is expressed in sft3/stb.Osif’s correlation. Osif (1988) proposed another

correlation to estimate the compressibility of water:

1Cw�11111111111111122

7.033 P�541.5 S�537.0 T�403.300�103

where S is the salinity expressed in g/l. This expressionis valid between 366 K and 405 K, for pressuresbetween 7 MPa and 14 MPa and salinity up to 200 g/l.

Density The density of salt water (rw) strongly depends on

the salinity. It is possible to evaluate this parameterfrom the density of the water in standard conditions(rw(SC)) and the formation volume factor Bw (McCain,

1991) previously defined. If the quantity of gasdissolved in the water is negligible under reservoirconditions, the density of the brine can be written inthe following way:

rw(SC)rw�111Bw

where rw(SC) is calculated from the expression:

rw(SC)�62.368�0.43603S�1.60074�10�3S 2

where S is the salinity expressed in percentage weightand r is expressed in lb/ft3.

Allen’s correlation. Allen et al. (1970) proposedanother correlation for the calculation of the density:

113�A(T)�PB(T)�P2C (T )�xD(T )�x2E(T )�rw 1

xPF(T )�x2PG(T )�1xP2H(T )2

where the density is expressed in g/cm3, thetemperature in K and the pressure in kg/cm2, andwhere x is the weight fraction of NaCl in solution. Thetemperature functions are as follows:

A(T)�5.916365�0.01035794T �

0.9270048�10�5T 2�1127.522T �1�

100674.1T �2

B(T)�0.5204914�10�2�0.10482101�10�4T �0.8328532�10�8T 2�1.1702939T �1�

102.2783T �2

C (T)�0.118547�10�7�0.6599143�10�10T

D(T)��2.5166�0.0111766T �0.170552�10�4T 2

E(T)�2.84851�0.0154305T �0.223982�10�4T 2

F (T)��0.0014814�0.82969�10�5T �0.12469�10�7T 2

G(T)�0.0027141�0.15391�10�4T �0.22655�10�7T 2

H(T)�0.62158�10�6�0.40075�10�8T �0.65972�10�11T 2

ViscosityMcCain’s correlation. To calculate the viscosity of

the water at reservoir temperature and atmosphericpressure, McCain proposed the following relationship:

mw (1atm)�AT�B

whereA�109.574�8.40564 S�0.313314 S2�

8.72213�10�3S3

and

B�1.12166�2.63951�10�2S�6.79461�10�4S2�

5.47119�10�5S3�1.55586�10�6S4

This correlation can be used between 310 and 477K, and for salinity up to 26% in weight. The viscosityobtained can be subsequently corrected by means ofthe following relationship, which allows the effect ofthe pressure to be taken into consideration:

mw (P)111�0.9994�4.0295�10�5P�µw (1atm)

3.1062�10�9P 2

This equation is valid between 303 and 440 K andfor pressures below 70 MPa; mw (P) and mw (1atm) areexpressed in cP, S in percentage weight, T in °F and Pin psia.

Kumagai’s correlation. When CO2 is injected, intothe reservoir, specific correlations have beendeveloped for the calculation of the viscosity of abrine containing CO2. The correlation proposed byKumagai (Kumagai and Yakoyama, 1999) is presentedbelow:

m�(a�bT)MNaCl�(c�dT)M1/2NaCl�(e�f T)MCO2

�

(g�hT)M 2CO2

�i(P�0,1)�mH2O (T,P�0.1MPa)

with

a�3.85971 e�8.79552

b��1.32561�10–2 f��3.17229�10–2

c��5.37539 g��7.22769

d�1.90621�10–2 h�2.64498�10–2

i��1.69956�10–3

where µ is expressed in mPa·s, T in K and P in MPa;MNaCl and MCO2

are the molalities of NaCl and CO2expressed in ml·kg�1, mH2O(T,P=0.1 MPa) is the viscosity ofthe water at temperature T and a pressure of 0.1 MPa.

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Véronique Ruffier-MerayInstitut Français du Pétrole

Reuil-Malmaison, France



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