1.1 Composition and physical properties of hydrocarbons...saturated hydrocarbons with straight...

1.1.1 Introduction

Petroleum is a naturally occurring liquid, gaseous or even solid mixture, composed principally of hydrocarbons, that accumulates in subterraneanreservoirs. As a generic term that keeps varying with time, petroleum is difficult to define precisely.In this text, it is used interchangeably with hydrocarbons when these compounds representthe predominant portion in the mixture. However, our discussion will not be exclusive to hydrocarbons but will also include relevant non-hydrocarbons.

The constituents of a natural reservoir fluid forman almost continuous hydrocarbon spectrum from the lightest one, methane, through intermediatemolecular weights and up to very large molecules.The relative proportion of these different parts can vary in a large range, which results in petroleumfluids showing very different features. For instance, the simplest reservoir fluids are natural gas, while the most complex molecularmixtures are those of black oil and bitumen. As can be seen from this example, the physicalproperties of a petroleum fluid are determined by its composition and, moreover, many of these vary significantly as a function of temperature and pressure. Petroleum reservoirs have temperaturesthat vary from ambient to more than 200°C and a pressure that can be as high as 150 MPa. The reservoir conditions depend on the depth of the reservoir and on the geological processes that the reservoir has experienced since it was filledby the reservoir fluid.

The temperature and pressure change dramatically,relative to the reservoir conditions, during productionwhere the pressure is lowered to fulfil transport and storage conditions. These changes in temperature

and pressure will often lead to a change in the state ofthe mixture from a single phase state to a two-phasestate where the two phases will each have a differentcomposition in comparison to the original petroleumfluid. Therefore, the properties of the new phases will change with the change in composition,temperature and pressure. Even within the reservoirthe physical state of the mixture (gas, liquid or solid)can change due to varying composition, temperatureand pressure.

1.1.2 Composition of petroleumfluids

Two important questions regarding the composition of petroleum fluids are “what is in the mixture?”(qualitative chemical analysis) and “how can theamount of each component be quantitativelydetermined?” (quantitative chemical analysis). The chemical composition of petroleum is largelyspeculative due to the difficulty of a completeidentification caused by the enormous number of components. For a hydrocarbon with a givenmolecular formula CxHy, the number of possibleisomers increases dramatically as the moleculebecomes larger. To illustrate this point, Fig. 1 showshow drastically the number of possible isomersincreases in the paraffin group alone. Even though notall of them exist in real oils, the presence of otherhydrocarbon groups and heterocompounds will complicate the task. Even for the paraffins in theC5-C12 range, the number of possible isomers isgreater than 600 (Altgelt and Boduszynski, 1994),around 200-400 of which have been experimentallyobserved (though not all identified).

Fortunately, in most cases, we do not need an all-out effort to identify and quantify all of the

31VOLUME I / EXPLORATION, PRODUCTION AND TRANSPORT

1.1

Composition and physical propertiesof hydrocarbons

components. Hydrocarbons up to and including C5are easily determined on a molar basis. The remaining identified components, whichnormally go up to 20, or in some cases 30, carbonatoms, are not individual molecular compounds but rather fractions defined by a normal boilingpoint range. These fractions are defined based on the normal boiling point of the normal alkanes andare called the C6, C7, etc. fractions (or components)according to the carbon number of the normal alkanewithin the fraction. Finally, the part of the oil that cannot be analysed is called the residue or plus fraction: for example, the symbol C20�

indicates the residue that includes the C20 fractionand all of the material in the oil less volatile thanthis. The above compositional analysis is generallyconsidered to be sufficient in terms of oilcharacterization for physical property studies.However, some laboratories systematically identifyall components up to C12 by the use of gaschromatography combined with mass spectroscopy.

Chemical composition

Gases produced from a petroleum reservoir mainlycontain alkanes lighter than heptane, with methane andethane being the predominant components. However,light non-hydrocarbons including nitrogen, carbondioxide, and hydrogen sulphide are also common, theirproportions being related to the reservoir where theyoriginate from.

Petroleum liquid, or crude oil, contains largermolecules and its appearance, composition, and other properties vary a lot with differentpetroleum reservoirs. Nevertheless, nearly all naturally occurring petroleum liquids have fairlynarrow limits of elemental composition

(Speight, 2001) as shown by the following values of percentage weight:

Carbon: 83.0-87.0%Hydrogen: 10.0-14.0%Nitrogen: 0.1-2.0%Oxygen: 0.05-1.5%Sulphur: 0.05-6.0%

The narrow range of the carbon to hydrogen ratioreflects the fact that �CH2� group is the primaryunit in various organic molecules in crude oils.

Generally speaking, components in petroleumliquids can be classified into hydrocarbonsand heterocompounds. The term hydrocarbon is used for molecules made up only of carbon and hydrogen atoms. On the other hand,heterocompounds are compounds which, in additionto carbon and hydrogen, also contain one or moreheteroatoms such as sulphur, nitrogen, oxygen,vanadium, nickel or iron.

The principal chemical and physical characteristicsof three crudes originating from three differentoilfields and the hydrocarbon fractions obtained from these using the true boiling point distillationmethod (see below) are reported in Table 1.

Hydrocarbon componentsThe hydrocarbon components of petroleum fall

into three groups: paraffins, naphthenes and aromatics.Olefins (also called alkenes) are so scarce in naturallyoccurring petroleum that they may be neglected.Also, the presence of dienes (R�CH�CH�R')and acetylenes (RC�CR') is considered to beextremely unlikely.

Paraffins, also known as acyclic alkanes, aresaturated hydrocarbons with straight (normal paraffin)or branched (isoparaffin) chains, but without any ringstructure. Both normal and isoparaffins have the samemolecular formula CnH2n+2.

Naphthenes, also known as cycloalkanesor alicyclic hydrocarbons, are saturated hydrocarbonscontaining one or more rings, each of which may haveone or more paraffinic side chains. Naphthenes are present in all fractions in which the constituentmolecules contain more than five carbon atoms.

Aromatics are compounds containing at least one benzene ring. Many of the aromatic hydrocarbonsin petroleum consist of aromatic and naphthenic rings and bear normal and/or branched alkane sidechains.

The proportions of the above three groups varywith the type of crude, but within any crude oil, the proportion of paraffinic hydrocarbons usuallydecreases with increasing molecular weight or boiling

32 ENCYCLOPAEDIA OF HYDROCARBONS

GEOSCIENCES

num

ber

of is

omer

s

carbon number10 20 30

3753.66.103

4.11.1091010

1020

1030

1040

6.24.1013

2.21.1022

1.06.1031

5.92.1039

40 50 60 70 80 90 100 11001

Fig. 1. Increase in the number of isomers with carbon number in paraffin.


COMPOSITION AND PHYSICAL PROPERTIES OF HYDROCARBONS

Tabl

e 1.

Che

mic

al a

nd p

hysi

cal c

hara

cter

isti

cs o

f th

ree

crud

es o

rigi

nati

ng in

dif

fere

nt f

ield

s

Cru

de A

Cru

de

Yie

lds

an

d c

ha

ract

eris

tics

of

pro

du

cts

Oil

Ga

sN

aph

tha

sK

ero

sin

esG

aso

ils

V. D

ist.

Res

idu

es

TB

P r

ange

C1-

C4

C5-

8080

-160

80-1

8016

0-23

018

0-23

023

0-37

037

0-41

637

0-53

037

0+41

0+53

0+

TB

P y

ield

% w

t0.

290.

972.

043.

127.

186.

1024

.23

5.14

21.4

765

.31

60.1

743

.84

TB

P y

ield

% v

ol0.

501.

372.

653.

988.

547.

2026

.71

5.35

21.5

260

.28

54.9

338

.77

Den

sity

at 1

5°C

kg/l

0.96

240.

5491

0.68

000.

7408

0.75

310.

8090

0.81

490.

8730

0.92

480.

9603

1.04

261.

0541

1.08

83

AP

I G

ravi

ty a

t 60°

F15

.5

Vis

cosi

ty a

t 20°

CcS

t15

85.9

4

Vis

cosi

ty a

t 50°

CV

BN

4.31

5.25

15.8

025

.69

32.1

248

.76

50.7

356

.90

Sul

phur

% w

t6.

700.

0500

0.38

500.

4506

1.76

501.

8700

3.35

4.85

6.22

8.66

8.99

9.36

Mer

capt

an s

ulph

urpp

m31

016

810

893

5236

Hyd

roge

n su

lphi

de%

wt

�0.

001

Aci

dity

mgK

OH

/g2.

130.

770.

790.

781.

501.

62

Para

ffin

s%

vol

82.2

70.7

66.1

Nap

hthe

nes

% v

ol13

.821

.122

.9

Aro

mat

ics

% v

ol4.

08.

211

.023

.825

.1

N+

2A in

dex

21.7

37.5

44.9

Sm

oke

Pt.

mm

2423

Free

zing

Pt.

°C�

56�

53

Clo

ud P

t.°C

�6

21

Pour

Pt.

°C�

15�

918

5368

>10

0

Cet

ane

inde

x46

.748

.5

Tota

l nit

roge

n%

wt

�0.

0000

3�

0.00

003

�0.

0000

3�

0.00

003

0.38

540.

4796

Bas

ic n

itro

gen

ppm

399

521

Nic

kel

ppm

75.8

�0.

1416

.112

6.0

172.

9

Van

adiu

mpp

m10

5.3

�1.

916

1.2

175.

024

0.2

P. V

alue

3.0

3.3

2.9

Asp

halt

enes

% w

t12

.89

19.7

321

.42

29.4

0

R.C

.C.

% w

t8.

661.

0713

.26

14.7

819

.76

Pene

trat

ion

at 2

5°C

dmm

UO

P K

fac

tor

12.0

511

.89

11.4

011

.30

TB

P D

isti

lla

tio

n A

Cu

t%

Wt

Cu

mpo

int

C1

C2

C3

0.08

i-C

40.

16

n-C

40.

28

i-C

50.

40

n-C

50.

55

801.

25

100

1.45

120

1.81

140

2.45

160

3.29

180

4.37

210

7.91

230

10.4

7

250

13.3

3

270

16.8

2

290

20.6

7

320

26.7

5

350

31.3

4

370

34.6

9

390

37.3

9

410

39.8

3

530

56.1

6

550

61.8

9


GEOSCIENCES

Tabl

e 1.

Che

mic

al a

nd p

hysi

cal c

hara

cter

isti

cs o

f th

ree

crud

es o

rigi

nati

ng in

dif

fere

nt f

ield

s

Cru

de B

Cru

de

Yie

lds

an

d c

ha

ract

eris

tics

of

pro

du

cts

Oil

Ga

sN

aph

tha

sK

ero

sin

esG

aso

ils

V. D

ist.

Res

idu

es

TB

P r

ange

C1-

C4

C5-

8080

-160

80-1

8016

0-23

018

0-23

023

0-37

037

0-41

637

0-53

037

0+41

0+53

0+

TB

P y

ield

% w

t1.

114.

3913

.78

17.7

913

.40

9.39

24.7

25.

0521

.55

42.6

136

.56

21.0

6

TB

P y

ield

% v

ol1.

725.

7416

.19

20.6

614

.70

10.2

324

.78

5.71

19.7

337

.15

31.4

417

.42

Den

sity

at 1

5°C

kg/l

0.86

520.

5549

0.66

060.

7368

0.74

490.

7883

0.79

450.

8630

0.91

700.

9452

0.99

241.

0061

1.04

60

AP

I gr

avit

y at

60°

F32

.0

Vis

cosi

ty a

t 20°

CcS

t8.

77

Vis

cosi

ty a

t 50°

CV

BN

2.81

4.23

15.2

525

.08

30.6

238

.57

40.8

046

.70

Sul

phur

% w

t2.

800.

0350

0.03

800.

0787

0.18

500.

2250

2.25

3.46

3.72

5.06

5.33

6.44

Mer

capt

an s

ulph

urpp

m18

626

422

424

130

630

5

Hyd

roge

n su

lphi

de%

wt

�0.

001

Aci

dity

mgK

OH

/g0.

090.

110.

140.

070.

080.

06

Para

ffin

s%

vol

90.4

74.2

70.5

Nap

hthe

nes

% v

ol7.

413

.415

.7

Aro

mat

ics

% v

ol2.

312

.413

.821

.021

.9

N+

2A in

dex

11.9

38.2

43.3

Sm

oke

Pt.

mm

2625

Free

zing

Pt.

°C�

54�

48

Clo

ud P

t.°C

�4

25

Pour

Pt.

°C�

15�

924

3033

67

Cet

ane

inde

x49

.752

.2

Tota

l nit

roge

n%

wt

�0.

0000

3�

0.00

003

�0.

0000

3�

0.00

003

0.24

460.

3329

Bas

ic n

itro

gen

ppm

190

302

Nic

kel

ppm

4.8

�0.

1411

.213

.022

.6

Van

adiu

mpp

m2.

9�

1.9

6.9

8.0

13.9

P. V

alue

4.8

�5

Asp

halt

enes

% w

t0.

561.

321.

542.

67

R.C

.C.

% w

t4.

390.

4410

.31

12.2

820

.87

Pene

trat

ion

at 2

5°C

dmm

UO

P K

fac

tor

12.3

812

.02

11.7

311

.89

TB

P D

isti

lla

tio

n B

Cu

t%

Wt

Cu

mpo

int

C1

0.00

C2

0.02

C3

0.30

i-C

40.

46

n-C

41.

10

i-C

51.

69

n-C

52.

75

805.

49

100

8.52

120

11.7

4

140

15.4

2

160

19.2

7

180

23.2

8

210

29.0

6

230

32.6

7

250

36.3

9

270

40.2

6

290

43.8

2

320

48.1

3

350

54.2

1

370

57.3

9

390

60.4

5

410

63.4

4

530

78.9

4

550

81.9

0



Tabl

e 1.

Che

mic

al a

nd p

hysi

cal c

hara

cter

isti

cs o

f th

ree

crud

es o

rigi

nati

ng in

dif

fere

nt f

ield

s

Cru

de

CC

rud

eY

ield

s a

nd

ch

ara

cter

isti

cs o

f pr

od

uct

s

Oil

Ga

sN

aph

tha

sK

ero

sin

esG

aso

ils

V. D

ist.

Res

idu

es

TB

P r

ange

C1-

C4

C5-

7070

-160

160-

230

180-

230

230-

370

370-

416

370-

530

370+

410+

530+

TB

P y

ield

% w

t2.

604.

8017

.57

16.2

511

.57

29.5

66.

6419

.91

29.2

222

.58

9.31

TB

P y

ield

% v

ol3.

865.

9519

.49

16.8

411

.89

28.6

66.

1618

.09

25.8

119

.65

7.72

Den

sity

at 1

5°C

kg/l

0.81

100.

5447

0.65

440.

7311

0.78

250.

7894

0.83

640.

8741

0.89

260.

9181

0.93

200.

9780

AP

I gr

avit

y at

60°

F42

.9

Vis

cosi

ty a

t 20°

CcS

t3.

56

Vis

cosi

ty a

t 50°

CV

BN

4.99

15.5

624

.28

28.4

332

.96

35.5

242

.67

Sul

phur

% w

t0.

240.

0009

0.00

060.

0156

0.02

100.

190.

420.

460.

620.

680.

98

Mer

capt

an s

ulph

urpp

m10

�3

Hyd

roge

n su

lphi

de%

wt

Aci

dity

mgK

OH

/g�

0.05

0.04

0.04

0.03

Para

ffin

s%

vol

93.7

74.3

Nap

hthe

nes

% v

ol4.

121

.0

Aro

mat

ics

% v

ol2.

24.

78.

59.

1

N+

2A in

dex

8.5

30.4

Sm

oke

Pt.

mm

3230

Free

zing

Pt.

°C�

51�

45

Clo

ud P

t.°C

�2

Pour

Pt.

°C�

�36

�5

2630

3339

Cet

ane

inde

x61

.372

.3

Tota

l nit

roge

n%

wt

�0.

0001

�0.

0001

0.00

530.

0274

0.03

030.

1300

0.16

000.

3200

Bas

ic n

itro

gen

ppm

104

162

Nic

kel

ppm

0.5

1.5

2.0

4.8

Van

adiu

mpp

m3.

412

.015

.035

.0

P. V

alue

�1.

1�

1.1

1.2

Asp

halt

enes

% w

t0.

732.

507.

90

R.C

.C.

% w

t1.

460.

0550

.01

6.48

15.6

0

Pene

trat

ion

at 2

5°C

dmm

UO

P K

fac

tor

12.1

512

.00

11.9

011

.90

TB

P D

isti

lla

tio

n C

Cu

t%

Wt

Cu

mpo

int

C1

C2

C3

0.05

i-C

40.

90

n-C

41.

67

i-C

52.

60

n-C

53.

66

705.

03

100

7.40

120

11.8

7

140

15.7

4

160

20.2

4

180

24.9

7

210

29.6

5

230

36.9

9

250

13.3

3

270

41.2

2

290

45.7

3

320

50.5

6

350

54.8

0

370

61.6

9

390

67.0

5

410

73.9

9

530

77.4

2

530

90.6

9

point (Fig. 2). As the boiling point of the petroleumfraction increases, not only will the number ofconstituents increase but so also will the molecularcomplexity of the constituents.

Non-hydrocarbon components (heterocompounds)

The non-hydrocarbon components of petroleumconsist of: sulphur compounds commonly includingthiols, sulphides, cyclic sulphides, disulphides,benzothiophene, dibenzothiophene andnaphthobenzothiophene; oxygen compoundsincluding alcohols, ethers, carboxylic acids, esters,ketones and furans; and nitrogen compoundsincluding pyrrole, indole, carbazole,benzo(a)carbazole, pyridine, quinoline, indoline, andbenzo(f)quinoline. Among the non-hydrocarbonspecies present in petroleum certain metals can alsobe found. These heterocompounds, as well as metals,are generally found only in the non-volatile portionof crude oil (Speight, 2001).

The concentration of these heterocompounds isusually quite small, although it tends to increase withincreasing boiling point (see again Fig. 2).Furthermore, their presence mainly influences theprocessibility of the crude oil and the quality of thepetroleum products rather than the physical propertiesof petroleum.

Compositional analysis

Reservoir fluid samples at elevated pressure cannotbe introduced into a Gas Chromatography instrumentfor direct analysis unless a special high pressureinjection technique is employed. Therefore, the highpressure samples are generally separated intoatmospheric gas and oil which are analysed separately.Sampling, recombination and analysis of hydrocarbon

gases and oils constitute the main aspects in obtainingthe representative overall composition of a reservoirfluid. For a discussion of the sampling andrecombination procedures, see chapters 3.3 and 4.2.

Analysis of hydrocarbon gases and oils

The composition of hydrocarbon gases can bedetermined by Gas Chromatography (GC) and that ofoils by True Boiling Point (TBP) distillation orsimulated distillation. Furthermore, MassSpectroscopy (MS) can be used together with GC forthe most detailed analysis.

Gas Chromatography. GC is a chromatographicmethod for separating volatile components using a gasas a mobile phase. A small amount of sample isintroduced into the gas chromatograph through aheated injection port, where the liquid (if any) isvaporized. This sample is then transported by a carriergas, e.g. helium, into a column coated or packed witha stationary phase. Components in the sample areretained by the stationary phase, then released anddisplaced forward by the upstream carrier gas, and,finally, elute in the reverse order of their affinity to thestationary phase, that is, with respect to the force withwhich they are retained. Gas chromatography can haveup to one million theoretical equilibrium stages andthus has a high separation ability. The elutedcomponents can be identified by their retention times,which are calibrated in advance, and quantified bydifferent detectors. The two most commonly useddetectors are the Flame Ionization Detector (FID) andthe Thermal Conductivity Detector (TCD), where theformer is usually employed for hydrocarbons and thelatter for non-hydrocarbons.

True Boiling Point (TBP) distillation. True BoilingPoint distillation is traditionally used in analysing oilby fractionating it into relatively narrow fractions orcuts. These TBP fractions can then be treated ascomponents with specific boiling points, molecularweights and critical properties, that is, in the same wayas a pure component.

Distillation separates molecules by their differencein volatility (vapour pressure, boiling point). However,it cannot be taken for granted that distillation is basedon molecular weight difference. Although the volatilityof hydrocarbons decreases with molecular weightwithin each homologous series, the difference betweenboiling points in the different homologous series isquite substantial. An increase in aromaticity andpolarity decreases the volatility and increases theboiling point.

TBP distillation consists of distillations both atatmospheric pressure and at reduced pressure.Atmospheric distillation is confined to a maximum

36

GEOSCIENCES

ENCICLOPEDIA DEGLI IDROCARBURI

wei

ght (

%)

paraffins

naphthenes

naphtheno-aromatics

aromatics

boiling point

heteroatomiccompounds

Fig. 2. Distribution of various compound types throughout petroleum (Speight, 2001).

reboiler temperature of 345°C to avoid decomposition.Subsequently, vacuum distillation at pressures rangingfrom 5 to 200 mmHg (~0.7-27 kPa) is usually used toseparate higher fractions. The boiling pointsdetermined at reduced pressure are converted to so-called Atmospheric Equivalent Temperatures (AET),which are hypothetical boiling points at atmosphericpressure if decomposition could be avoided.

The standard American Society for TestingMaterials (ASTM) D-2892 describes the TBPdistillation procedure in detail. In practice, differentvariations can be implemented.

In general, TBP distillation is a standard method ofoil analysis, which fractionates oil truly according totheir boiling points. Moreover, physical samples ofeach fraction can be obtained and furtherdetermination of their physical properties, e.g.molecular weight and specific gravity, is possible.However, the drawback of TBP distillation is that itrequires large amounts of sample (1-10 litres) and along analysis time (100 hours). Pedersen et al. (1989b)suggested using a mini-distillation apparatus whichonly requires 100 ml sample.

The normal boiling points of paraffin plus 0.5°C,as suggested by Katz and Firoozabadi (1978), aregenerally accepted as boundaries between differentfractions, and the resulting narrow fractions are oftencalled Single Carbon Number (SCN) fractions, toemphasize that they contain compounds whose boilingpoints fall within a narrow range. Each of these SCNfractions is named after the number of carbon atoms ofthe n-alkane in the fraction, e.g. C7, C8, etc.

Simulated distillation. Simulated distillation isessentially a low resolution gas chromatographymethod. The method is based on the observation thathydrocarbons are sequentially eluted from a non-polarcolumn almost in the order of their boiling points.After calibration with normal alkanes, the retentiontimes for an oil sample can be readily converted toboiling points. In the case where complete elution ofheavy ends is impossible, an internal standard must beused to determine the amount of eluted fractions.

Simulated distillation is preferred to the TBPmethod since it is quick and requires only a smallamount of sample. On the other hand, no physicalfractions can be obtained with this method andtherefore their molecular weights and specificgravities are unavailable.

ASTM D-2887 is a simulated distillation standardup to approximately 540°C (1,000°F) atmosphericequivalent boiling point. However, recent efforts havefocused on extending the range up to 800°C (1,470°F).

Gas Chromatography coupled to MassSpectrometry (GC-MS) and others. In the GC-MSmethod, a gas chromatography instrument and a mass

spectrometer are employed in series. GC serves as aseparation procedure of different compounds,whereas MS provides the molecular weight, thechemical formula and the amount of each compound.The GC-MS analysis can be applied to gas or oilsamples. Using this method, each individualsubstance in the mixture can, in principle, bedetected quantitatively if the amount is above thedetection limit. However, with increasing boilingpoint, the number of possible molecular structuresincreases dramatically, while the concentration of thecompounds generally decreases, and thus the MSanalysis becomes increasingly difficult. Therefore, asignificant fraction of the oil will be unrecognized bythe GC-MS and its amount will be determined by amass balance in which all of the detected compoundsare subtracted from the total oil.

GC-MS can determine the distribution of paraffins,naphthenes and aromatics (indicated by the acronym:PNA) in a SCN fraction. Information about the PNAdistribution can be used to improve the C7+characterization. However, a complete PNAdistribution of the whole oil is difficult to obtain andeven if it is available, many uncertainties still exist inevaluating the properties of heavy components. In thissense, PNA analysis has limited usefulness in practicalcharacterization.

A more detailed discussion of different analysismethods, especially for heavy petroleum fractions canbe found in Altgelt and Boduszynski (1994).

1.1.3 Physical properties of hydrocarbons

In quantitative simulations of the production andprocessing of petroleum fluids, two approaches tothe description of petroleum fluids are usuallyemployed: the black oil approach, where the fluid isdescribed by only two components, oil and gas, andthe compositional approach, where the fluid isdescribed by a number of components. The black oilapproach is directly based on Pressure-Volume-Temperature (PVT) experiments (see Chapter 4.2),however, its modelling of phase equilibria andphysical properties is approximate. On the otherhand, the compositional approach employsEquations Of State (EOS) and provides a moreaccurate fluid estimation.

EOS modelling requires a detailed knowledge ofthe molar composition of the mixture and the criticalproperties and the acentric factor of all thecomponents. The next section discusses how to obtainthe required information either experimentally orthrough a characterization procedure.



A major step in modelling the physical propertiesof reservoir fluids is to calculate volumetric propertiesand associated phase equilibria (PVT modelling) aswell as other important physical properties such asviscosity and interfacial tension. A discussion of theseissues is presented in the following.

Physical properties of narrow distillationcuts and their characterization

The compositional analysis cannot provide therequired information for all of the real components ina petroleum mixture. The compositional informationobtained varies with boiling point range. Hydrocarboncomponents up to C6 and non-hydrocarbon gases (N2,CO2 and H2S) can be quantified discretely and theproperties of these well-defined components arereadily found in handbooks. The low boiling range inthe C7+ fractions (e.g. up to C30) can be fractionated interms of narrow TBP fractions and their molecularweights and specific gravities can be experimentallydetermined. For the heavy end of the C7+ fractions,TBP residue, no further analysis of the molardistribution is made and only the molecular weight andspecific gravity of the whole residue areexperimentally determined. It is also very commonthat the only available information about the C7+fraction is its molar composition, specific gravity andmolecular weight.

To create a set of components, which can bedirectly used by the EOS method, from the limitedcompositional information, proper characterization ofthe C7+ fraction is needed. This characterizationroughly includes two steps: determination of the molarcomposition of all components (including the C7+fractions) and estimation of the critical properties andthe acentric factor (see below) of the C7+ fractions. Inpractice, the number of components in a characterizedoil is too high for simulation purposes and lumping toa lower number of pseudocomponents is generallyundertaken. Each pseudocomponent is a mixturerather than a pure compound, however, they are treatedas pure compounds with specific physical propertiesin the calculations.

The properties involved in characterization includethe molecular weight, M, the normal boiling point Tb,the specific gravity g, the critical temperature Tc, thecritical pressure Pc, and the acentric factor w. M isused to convert weight fractions from compositionalanalysis to molar fractions. Tb and g are used forestimating Tc, Pc and w, which are used almostexclusively for EOS modelling. In the followingsections, the properties mentioned above will bedefined and the experimental methods used todetermine the measurable properties will be described;

moreover, correlations between these properties willbe discussed, and different characterization methodswill be introduced.

Properties Molecular weight (M). For well defined molecular

structures the molecular weight is easily calculatedfrom the atomic masses of the constituents. In the caseof the fractions, the average molecular weight can bemeasured by the following methods: vapour pressureosmometry, freezing point depression, boiling pointelevation, gel permeation chromatography and non-fragmenting mass spectrometry (Speight, 2001). Thedifferent methods have advantages and drawbacks,which make them suitable for different molecularweight ranges.

Vapour pressure osmometry, freezing pointdepression and boiling point elevation are all based onthe assumption that the change in the correspondingproperties (vapour pressure, freezing point, andboiling point) in a pure solvent caused by introductionof a solute at low concentration is directly proportionalto the concentration of the solute. Gel permeationchromatography, also known as size exclusionchromatography, takes advantage of the difference inelution time between molecules with different sizes.Non-fragmenting mass spectrometry principallyprovides detailed information of the hydrocarbontypes, the formulae and the concentration of all thecomponents in a fraction.

Normal boiling point (Tb ). The normal boilingpoint of a pure substance is the temperature at whichthe substance changes state from liquid to vapour at apressure of 1 atm (0.1013 MPa). This property isknown and tabulated for all the pure componentsnormally considered in petroleum engineering exceptfor the high boiling substances that do not have aboiling point at atmospheric pressure. For thedistillation fractions the normal boiling point isusually chosen to be a certain average value of thetemperature interval of the distillation fraction.

Density (r) and specific gravity (g). The density ris defined as the mass divided by the volume at acertain temperature and pressure. This can bemeasured for pure components, fractions andpetroleum fluids by different methods. The mostwidely used techniques are the following:• Pycnometry, where the mass of a calibrated volume

is determined before and after filling with thesubstance to be investigated. Pycnometers for highpressure and high temperature are available but haveto be calibrated carefully at the relevant conditions.

• Oscillating tube or vibrating tube densimetry,where a tube of glass, for low pressure, and of metal, for high pressure, is exposed to forced


GEOSCIENCES

oscillations. The resonance frequency is measuredand if the apparatus has been calibrated with a fluidof similar density, the resonance frequency of thesample can be converted into its density. Themethod is convenient for high pressure measurementssince it can be connected directly to other high pressureequipment. It should be noted that for measurements at very high pressure and high temperature thecalibration has to be repeated frequently.

• Displacement method, where a known volume istransferred into a vessel that is weighed before andafter the transfer. This method can be used at highpressure and high temperature conditions.Specific gravity g, or relative density, is the ratio

of the density of a material at temperature T andpressure P to the density of a reference material atreference temperature Tref and reference pressure Pref :

[1] g�r(P,T )/rref (Pref ,Tref)

Specific gravities of oil and gas are measured atstandard conditions of 14.7 psia (0.1013 MPa) and 60°F (15.6°C) with respect to water and air at thesame conditions. In the petroleum industry, APIgravity is often used:

[2] API�141.5/go�131.5

where go is the specific gravity of the oil measured atstandard conditions.

Figs. 3 and 4 show change of density and ofmolecular weight, respectively, versus carbon numberfor different oils. It can be seen that the density varies

considerably with the PNA distribution of thehydrocarbon fraction as compared to the molecularweight. The narrow range of molecular weight for agiven carbon number has been used as a basicassumption in Pedersen’s characterization method (seebelow). However, other studies show that themolecular weight can also vary considerably(Dandekar et al., 2000).

Critical temperature (Tc ). For a pure componentthe critical point is the point that terminates the vapourpressure curve, while the critical temperature Tc is thehighest temperature at which the substance can existsimultaneously as vapour and liquid. Therefore, attemperatures above Tc no phase transition can occurbetween vapour and liquid. For pure components, Tccan be measured in principle and compilations of Tcare readily available (Poling et al., 2000). Criticalpoint measurement of heavy hydrocarbons is hinderedby their decomposition temperature. Recentlydeveloped techniques, using extremely short exposureto high temperature (a few milliseconds), make itpossible to measure the critical temperature of n-alkanes (Nikitin et al., 1994) up to tetracosane (n-C24). Fig. 5 shows how Tc increases with carbonnumber in the n-alkanes.

Critical pressure (Pc ). Similarly the criticalpressure Pc of a pure component is the highestpressure at which the pure component has a vapour-liquid phase transition or, in other words, the highestpossible vapour pressure of the component. For thesame reasons explained above for the critical



dens

ity

(g/c

m3 )

carbon number

aromatic oilsmedium paraffinic oils

paraffinic oils

Katz and Firoozabadi (1978)

aromaticsaliphatics

1

0.98

0.96

0.94

0.92

0.90

0.88

0.86

0.84

0.82

0.80

0.78

0.769 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Fig. 3. Density versus carbonnumber for North Sea oils and condensates (Pedersen et al., 1989a).

temperature, the critical pressure cannot be measuredfor large hydrocarbon molecules. Pc decreases withcarbon number in n-alkanes after ethane (see againFig. 5).

Acentric factor (w). The acentric factor w isdefined as follows:

[3] w��log(Prsat)Tr�0.7�0.1

where Prsat is the reduced vapour pressure and Tr is the

reduced temperature. The value of w reflects adeviation in the vapour pressure compared to thebehaviour of ideal spherical molecules (e.g. noblegases) for which w is always zero. The factor w can beexplained as the non sphericity of a molecule andgenerally increases with increasing molecular weight.Tc, Pc and w are the three basic input parameters for thecubic equations of state which are widely used in thepetroleum industry (see below).

Critical volume (vc ). The critical volume vc is themolar volume of a component at its Tc and Pc.Experimental values of vc are fewer and less accuratethan Tc and Pc. The volume vc is generally not used asan input parameter in the EOS method, but it is usedby some property estimation semiempirical models,e.g. the Lohrenz-Bray-Clark (LBC) correlation forviscosity estimation (see below).

Correlations between propertiesEstimation of the missing quantities: g, M and Tb.

The specific gravity g, the molecular weight M, andthe normal boiling point Tb form the minimum set

required for the characterization of a narrow petroleumfraction. Sometimes, experimental values of two ofthem (typically Tb and g, or M and g), are unknownand have to be estimated. TBP data for oils from asimilar region can be used as a good reference. Thegeneralized properties up to C45 proposed by Katz andFiroozabadi (1978) can be used as a rough estimationbut caution must be taken since g is usuallyoil-specific. In any case, properties for C45 are stillneeded if the oil is heavy.

Pedersen et al. (1989a, 1992) have assumed a verysimple molecular weight correlation for SCNfractions:

[4] MCi�14i�4

where i is the carbon number. The SCN fractions


GEOSCIENCES

400

380

360

340

320

300

280

260

240

220

200

180

160

140

1209 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

aromatic oilsmedium paraffinic oils

paraffinic oilsaromaticsaliphatics

Katz and Firoozabadi (1978)

carbon number

mol

ecul

ar w

eigh

t

crit

ical

tem

pera

ture

(K

)

100

200

300

400

500

600

700

800

carbon number5 10 15 20 25

crit

ical

pre

ssur

e (b

ar)

10

20

30

40

50

Fig. 5. Change of critical temperature and critical pressure with carbon number in n-alkanes.

Fig. 4. Molecular weight versuscarbon number for North Sea oils

and condensates (Pedersen et al., 1989b).

are defined using Katz and Firoozabadi’s Tbup to C45 and extrapolating the successive values byadding 6 K for each carbon number from C45 to C80.Pedersen et al. also suggested a logarithm distribution for g:

[5] gCi�C+Dlni

where the two coefficients C and D are determined bya measured or assumed gCn

and the volume additivityconstraint on the experimental gCn�

[6] zCn�MCn�

gCn�

�1�i�n�zCi

MCigCn

�1

where z is the molar composition.Another approach to estimating g is to relate

g to M through a unique characterization factor(Whitson and Brule, 2000), which can be determinedby the constraint in (6). Several empirical correlations employed when estimating Tbare also reviewed in detail by Whitson andBrule (2000).

Correlations between Tc, Pc and w. Abundantcorrelations exist for the estimation of criticalproperties. The most popular of these include the Lee-Kesler correlations (Kesler and Lee, 1976;Lee and Kesler, 1980), the Riazi-Daubert correlations (1980) and Twu’s perturbation expansion correlations (1984). All of thesecorrelations express Tc and Pc in terms of Tb and g. At the same Tb, the difference in g reflects thedifference in aromaticity. Furthermore, fractions withhigh aromaticity tend to have higher g, Tc and Pc. InTwu’s correlations, critical properties of normalalkanes are correlated only in terms of Tb, while gonly appears in the perturbation step to correct for thedeviation of the critical properties from those of n-alkanes.

Acentric factors can be estimated using either theLee-Kesler correlations or the Edmister correlation(1958).

Pedersen et al. (1989a) argued that using Tb as anintermediate variable to estimate Tc and Pc is notnecessary and expressed Tc and Pc directly in terms ofg and M. Instead of correlating w, they directlycorrelate the m parameter in the SRK EOS (seebelow). Recently, another set of correlations for hightemperature high pressure reservoirs were proposed byPedersen et al. (2002).

Due to the intrinsic limitation of any EOS, the true Tc, Pc and w will not necessarily give areasonable reproduction of the vapour pressure forheavy components. Soave (1998) proposed a set ofcorrelations in which the values of Pc are adjusted sothat boiling points at both 10 and 760 mmHg can bereproduced.

CharacterizationFor Cn�where the molar distribution is unknown or

incomplete, different distribution functions can beassumed. A simple approach adopted by Pedersen et al.(1989a, 1992) is to assume an exponential molardistribution:

[7] zCi�Aexp(Bi)

where i refers to the carbon number, and A and B aretwo constants determined by the two constraints onzCn�

and MCn�:

[8] zCn��

i�n�zCi

[9] zCn�MCn�

�i�n�zCi

MCi

Whitson (1983; Whitson and Brule, 2000)suggested a more general three-parameter gammadistribution. Therefore, after determination of themolar distribution, Tc, Pc and w of each SCN fractioncan be evaluated using the correlations introduced inthe previous section.

The characterized SCN components are usuallytoo numerous and thus are grouped into a number ofpseudo components which are manageable for processor reservoir simulations. For reservoir simulations thenumber is currently limited to around 10 components,while for process simulations it is in general limitedto around 50 components, even though for someprocess calculations it can be feasible to use up to 100components for the description of the oil. Eachlumped fraction can contain several SCN fractionsand its properties are obtained using differentaveraging methods: from the simple weight or molaraverage to very sophisticated ones (Montel andGouel, 1984; Leibovici, 1993). As a reversal processof lumping, delumping can be performed to retrievethe detailed compositional information after asimulation with lumped components (Leibovici et al.,1996).

PVT experiments

In the case of petroleum fluids in reservoirs underpressure, it is essential to know very early in theproduction phase how the fluid will respond to thepressure reduction that will occur when the reservoir isdepleted. A set of simple, yet informative experimentsare used to reveal the nature of the fluid. Theexperiments have the common name PVT experimentssince they investigate the relationship between thepressure and the phase volumes at one or moretemperatures. During each experiment the temperatureis kept constant. Further details on these types ofexperiments can be found in chapter 4.2.




GEOSCIENCES

PVT modelling

Empirical correlationsEmpirical correlations were extensively used in

calculating PVT properties before the widespreadapplication of more theoretically sound models basedon EOS. Unlike general EOS models, empiricalcorrelations usually treat gas properties and oilproperties as two separate categories. The properties ofmajor concern include the volumetric property and theviscosity for both gas and oil, gas solubility, as well asbubble point pressure and surface tension in the caseof oils. An extensive description of these empiricalcorrelations can be found in chapter 4.2.

Basics of phase equilibriumFor a heterogeneous closed system consisting of Nc

components and Np phases, it can be proven that thetemperature T and the pressure P must be uniformthroughout the system and that the chemical potentialm of the individual components must be the same in allof the phases at equilibrium:

[10] mij�mi

k i�1,…,Nc, j,k�1,…,Np with j�k

The chemical potential of component i, mi, isusually expressed as ( ∂ G/∂ ni)T,P,nj�i

o ( ∂ A/ ∂ ni)T,V,nj�i,

where V is the total volume, ni is the molar number ofcomponent i, and G and A are the Gibbs energy andthe Helmholtz energy respectively. In practicalequilibrium calculation, a less abstract concept,fugacity, is often used instead of chemical potential.Fugacity, literally meaning ‘escaping tendency’, isrelated to chemical potential by the followingdefinition:

[11] mi�mi°�RT ln

fi1

fi°with

fi13

yi P→ 1 as P→ 0

where mi° and fi

° are the chemical potential and thefugacity of component i, respectively, at a referencestate of the same temperature, and yi is thecomposition of component i in the mixture. Fugacitycan be understood as a ‘corrected pressure’. Thedimensionless ratio /i�fi / yiP is called the fugacitycoefficient. The ratio ai�fi /fi

° is known as the activityof component i and gi�ai/xi is called the activitycoefficient where xi is the molar fraction.

If the reference states for different components areat the same temperature, it can be shown that Eq. [10]is equivalent to the equality of the fugacities:

[12] fij�fi

k i�1,…,Nc, j,k�1,…,Np with j�k

The fugacity and other thermodynamic functions,such as the internal energy and the enthalpy, can beexpressed rigorously in terms of volumetricproperties, e.g.:

[13] ln/i�lnfi13

yi P�

11

RT�

V

��∂ P1

∂ ni�T,V,nj

�RT1

V �dV�lnZ

where Z is the compressibility factor given byZ�Pv/RT, in which v is the molar volume.

In principle, all of the thermodynamic propertiescan be calculated if the necessary volumetric data areavailable. However, experimental measurement ofvolumetric data over the full range of the integral inEq. [13] is unrealistic in most cases. The necessaryvolumetric data are usually provided by an EOS whichdescribes the mathematical relation between pressure,temperature, volume, and composition.

Finally, it should be noted that criteria [10] and[12] are only necessary conditions (and not sufficient)for phase equilibrium since a stable equilibrium stateis not only a stationary point but also a globalextremum, e.g. dAT,V≤ 0, dGT,P≤ 0.

Equations of state (EOS)Since the introduction of the van der Waals EOS

in 1873, numerous EOS have been proposed. Generalreviews of EOS are readily available in the literature(Anderko, 1990; Wei and Sadus, 2000). The EOSencountered in modelling petroleum fluids roughlyfall into three families: vdW (van der Waals) -typeEOS, the virial EOS and its modifications, and EOSbased on the Principle of Corresponding States(PCS).

All vdW-type EOS consist of a repulsive term andan attractive term like their common predecessor vander Waals EOS:

[14] P�RT12

v�b�

a1

v2

repulsiv attractiveterm term

where b is a co-volume parameter and �a/v2 is anexpression for the attractive pressure. Many vdW-typeEOS, including the vdW EOS itself, take a cubic formin terms of the volume or the compressibility factor Zand are referred to as cubic EOS. Despite theirsimplicity and empirical nature, cubic EOS are themost widely used EOS in the petroleum industry. Thetwo most successful examples are the Soave’smodification of the Redlich-Kwong EOS i.e. the SRKEOS (Redlich and Kwong, 1949; Soave, 1972) and thePR EOS (Peng and Robinson, 1976), which will bediscussed in detail below.

The virial EOS can be expressed as an expansionin terms of molar density r:

[15] Z�1�Br�Cr2�…

or pressure P:

[16] Z�1�B�P�C�P2�…

where coefficients B, C, etc. are called the second,third, etc. virial coefficients, and B�, C�, etc. are coefficients related to B, C etc. Since the thirdand higher virial coefficients are generallyunavailable from experimental data, application ofthe virial EOS is limited to the low density regionand, thus, is of little use in most practicalapplications. However, the rigorous statisticalmechanics basis of the virial EOS has inspired manyempirical extensions which are valid over wideranges of density. Amongst these extensions are theBenedict-Webb-Rubin EOS i.e. BWR EOS (Benedict et al., 1940) and Starling’s modification(1973) of this EOS (BWRS EOS).

The third class of EOS is based on PCS. The classical two-parameter PCS assumes that two different systems have the same reducedpressure if they are at corresponding states, i.e. if they have the same reduced volume andtemperature. Depending on the number of parameters used in defining the correspondingstates, there are three-parameter and even four-parameter PCS. The PCS is actually implicatedin most EOS, while it is in this third family that EOS are formulated explicitly using the PCS.The EOS in this family usually employ very accurate equations for suitable reference fluidsand relate the final fluid properties with the properties of reference fluids by the shapefactor method or the perturbation method. The main advantage of this family of EOS is that theproperties of the fluid of interest can be accuratelyreproduced provided the substance is not verydifferent from the reference fluids. The EOSproposed by Mollerup and Rowlinson (1974) forliquefied natural gas and low molecular weighthydrocarbon mixtures, and that proposed by Lee and Kesler (1975), for hydrocarbons and their mixtures, belong to this family.

Cubic equations of state: the SRK EOS and the PR EOS. These EOS can be written in a general form:

RT a(T)[17] P�11�1111121

n�b (n�d1b)(n�d2b)

where a(T) and b are two EOS parameters. d1 and d2are constants: d1�1 and d2�1 for the SRK EOS, whiled1�1�62 and d2�1�62 for the PR EOS.

Since the critical point of a pure component is aninflexion point of the pressure-volume isotherm,which requires the first and second derivatives to beequal to zero, the two parameters ac�a(Tc) and b canbe determined through these two constraints and,finally, expressed in terms of critical temperature andpressure as follows:

[18] ac�WaR2Tc2/Pc

[19] b�WbRTc/Pc

where Wa�0.42747 and Wb�0.08664 for the SRK EOS, and Wa�0.45724 and Wb�0.07780for the PR EOS. The temperature dependency of a(T) is expressed by the following functional form:

[20] a(T)�aca(Tr,w)where the temperature function a(Tr,w) is assumed to be a function of the reduced temperature Trand the acentric factor w has the following form:

23

[21] a(Tr,w)�[1�m(1��Tr)]2

[22] mSRK�0.480�1.574w�0.175w2

[23] mPR�0.37464�1.54226w�0.26992w2

The function a(Tr,w) can be determined by fittingthe pure component vapour pressures. Finally, Eq. (17) can be expressed in terms of the compressibility factor as

[24] Z3�[1�(1�d1)B]Z2�[A�d1B�B2(d1�d2)]Z�

(AB�d2B2�d2B3)�0

where d1�d1�d2, d2�d1d2 and two dimensionlessparameters, A and B, are defined as:

A�aP/(RT )2

[25]B�bP/RT

Eq. [24] is in cubic form and can be solvedanalytically, which is generally believed to be anadvantage of the cubic EOS. In fact, numericalsolutions using the Netwon-Raphson method can beequally efficient.

Quadratic mixing rules, also known as van derWaals one-fluid mixing rules or random mixing rules,are generally used for a and b in an Nc componentmixture:

[26] b�i�1

Nc

�xibi

[27] a�i�1

Nc

�j�1

Nc

�xixjaij

where aij�5

aiaj (1�kij) e kij is the binary interactionparameter with kii�0 and kij�kji. The value of kij canbe obtained by fitting binary vapour-liquidequilibrium data. Usually, kij�0 is a goodapproximation for most hydrocarbon-hydrocarbonpairs except for C1-C7+ pairs.

Fugacity coefficients of component i in a mixtureare given by:



fi bi[28] ln/i�ln12�32 (Z�1)�ln(Z�B)�yiP b

A2

j�1

Nc

�xjaij bi Z�d1B1212333�12123�32 ln�1212 (d2�d1)B a b Z�d2B

Expressions for other thermodynamic propertiesare easily found in the original papers. The aboveexpressions are commonly adopted in phaseequilibrium calculations. However, a more systematicand efficient way to formulate these properties exists,especially when a large number of thermodynamicproperties, including derivatives of fugacitycoefficients, are required (Michelsen and Mollerup,1986; Mollerup and Michelsen, 1992).

The SRK and PR EOS give similar vapour-liquidequilibrium calculation results, however, the majorimprovement offered by the PR EOS is in the liquiddensity calculation. This can be attributed to the factthat the critical compressibility factor predicted by thePR EOS (0.307) is closer to the real hydrocarbon value(<0.290) than that determined by the SRK EOS(0.333). On the other hand, volume translation (seebelow) can improve the density prediction in the SRKEOS and, in many cases, it is required by both types ofEOS to obtain acceptable volumetric results. Inconclusion, the choice of the SRK or PR EOS islargely determined by personal preference.

Improvement of cubic EOS. Modifications of cubicEOS have been performed mainly in two directions.The first is to introduce a better temperaturedependency a(T) in order to improve the reproductionof the vapour pressure; the second is to modify thefunctional form of the EOS in order to improve liquiddensity prediction.

It should be noted that Soave’s modification of theRK EOS is actually a modification of the a(T)function. In a similar way Mathias and Copeman(1983), and Stryjek and Vera (1986), have proposedbetter a(T) functions for the RK and the PR EOS,respectively. Recently, Twu et al. (1995a, 1995b)proposed new a(T) functions for both the RK and thePR EOS. These modifications usually incorporatecompound specific parameters which significantlyimprove the vapour pressure accuracy, especially forpolar molecules. However, their effect on supercriticaltemperatures is still open to question.

The PR EOS improves the density calculation bymodifying the attractive form in the SRK EOS.Further improvement of density prediction can beachieved by introducing additional EOS parameters.The Schmidt-Wenzel EOS (1980) and the Patel-TejaEOS (1982) are two commonly used three-parameterEOS.

An alternative to three-parameter cubic EOS is thevolume translation method which can be used toseparate the application of an EOS to vapour-liquidequilibrium calculations from the application to densitycalculations. The method proposed by Martin (1979),and elaborated further by Peneloux et al. (1982),consists in translating the molar volume from theoriginal EOS, vEOS along the volume axis as follows:

[29] nCOR�nEOS�c

The mixture translation parameter c is calculatedfrom the pure component translation parameters cithrough a linear mixing rule:

[30] c�i�1

Nc

�xici

where ci can be determined by matching the measuredsaturated liquid volumes at Tr�0,7 or from differentcorrelations (Peneloux et al., 1982; Jhaveri andYoungren, 1988). ci can also be treated as tuningparameters to match experimental densities.

Since vapour volume is generally much larger thanliquid volume, the above translation will mainlyimprove the liquid density without much affecting thegas density. The elegance of this method is found inthe fact that the translation will increase the fugacityof component i in all the phases by the same factorexp(�ci P/RT) and thus will not affect the phaseequilibrium calculations. Also, the same formulationand code for the original EOS can be utilized directly.

Phase equilibrium calculationSeveral frequently used phase equilibrium

calculations are introduced below. More detaileddiscussion can be found in the work by Michelsen andMollerup (2004).

T-P flash calculation. In an isothermal flash (or T-P flash) calculation, a feed with a givencomposition is brought to a specified T and P, theresultant number of phases, and the amount andcomposition of each phase, then need to bedetermined. The isothermal flash is probably the mostcommon and important equilibrium calculation.Therefore, robust and reliable algorithms are availablefor this type of calculation.

In many practical calculations, it is either assumedor can be known in advance that there are, at most, oneliquid phase and one vapour phase. The two-phaseflash calculation for these situations consists of astability analysis step and a phase split calculationstep (Michelsen, 1982a and 1982b). Multiphaseisothermal flash calculations also have similar steps,but they require more extensive stability analysis andmore demanding phase split calculation. Thediscussion here is limited to two-phase equilibrium.


GEOSCIENCES

The stability analysis step is carried out as follows:a stable equilibrium mixture of molar composition z issubject to the following TPD (Tangent Plane Distance)criterion:

[31] TPD(w)�i�1

Nc

�wi[mi(w)�mi(z)]�0

which means that the appearance of any infinitesimalamount of a new phase of any molar composition wshould always increase the Gibbs energy.

Fig. 6 shows the geometric meaning of TPD(w). Atangent plane (line) to the Gibbs energy surface(curve) can be made at composition z, while TPD(w)is the distance from the tangent plane (line) to theGibbs energy surface (curve) at composition w.Stability requires that all points on the tangent planeare lower than the Gibbs energy surface, in otherwords, that TPD(w) is always positive. In realcalculations, it is impossible and also unnecessary tocheck all of the compositions. Only the stationarypoints (possible minima) of the tangent planedistances are checked. The search for stationarypoints should start from a set of initial estimatesrepresenting a possible incipient phase. At highpressures, a priori phase identification is difficult.Therefore, both vapour-like and liquid-like initialestimates are used in the stability analysis for a two-phase vapor-liquid flash calculation. Once instabilityis found in the located stationary point, the fugacitycoefficients at this point are used to generate theinitial estimates for the equilibrium factors Ki in thephase split calculation step. Ki is defined as the molefraction ratio of component i between vapour andliquid phases.

Whereas the TPD criterion specified by Eq. (31)requires constraint minimization, in practice, it ismodified to a form which only needs unconstrainedminimization.

The phase split calculation is usually started with asuccessive substitution algorithm. This algorithmconsists of an inner loop, which solves for phaseamounts and compositions at fixed Ki, and an outerloop, which updates the K-factors using the new phasecompositions. The equation solved in the inner loopcan be written as follows:

zi(Ki�1)[32]

i�1

Nc

�11111�01�(Ki�1)b

and is known as the Rachford-Rice equation. b is themolar amount of vapour phase. The Rachford-Riceequation can readily be solved by the Newton-Raphson method.

Successive substitution can be accelerated by thegeneral dominant eigenvalue method. If the iterationdoes not converge after two or three accelerations, it is

recommended to switch to a second orderminimization of the Gibbs energy.

Saturation points and the phase envelope. In theearly days, saturation points (the bubble point and thedew point) calculations were thought to be simple andwere even used to initiate a flash calculation bychecking if the specified condition is situated in thetwo-phase region. The true situation, however, is justthe opposite: calculations of bubble or dew points atelevated pressures are much more difficult. Oneobvious difficulty is that the number of solutions tothe saturation point calculation is not known inadvance. For example, there is no dew point attemperatures higher than the cricondentherm while thenumber of dew points increases to two below thecricondentherm. Furthermore, stability analysis cannotbe performed in an easy and reliable manner as in thecase of an isothermal flash calculation since a primaryvariable, T or P, is always missing. Currently, there isno entirely satisfactory method for calculation ofsaturation points at arbitrary conditions.

With proper initial estimates, saturation pointcalculations can be performed using a partial Newton’smethod, in which saturation T or P converges fasterthan composition. Wilson K-factors can be used asinitial estimates, however, their accuracy is poor athigh pressure or near the critical point. Dew pointcalculation is generally more difficult than bubblepoint calculation due to the non-ideality of theincipient liquid phase. A search of the unstable P (orT) range by stability analysis can also be used toinitiate the saturation calculation. This procedure



TPD(wsp)

zwwspmole fraction

mol

ar g

ibbs

ene

rgy

of m

ixin

g

TPD(w)

Fig. 6. Illustration of Tangent Plane Distance (TPD) concept. TPD at composition w for the feed composition zis shown as TPD(w). TPD at the stationary point wsp is TPD(wsp). The dashed tangent at wsp is parallel to the tangent at z.

obviously needs more computation effort and a prioriknowledge of a reasonable search region.

A more reliable procedure to locate all saturationpoints is to perform phase envelope calculation. Thephase envelope is a curve in the pressure-temperatureplane showing the transition boundary between thevapour and the liquid phase. Further explanation ofphase envelopes for multicomponent systems is givenin Section 1.1.5. Michelsen (1980) developed anefficient algorithm to construct the entire phaseenvelope. The calculation starts at readily obtained lowpressure saturation points, while the subsequentsaturation points are generated by a full Newton’smethod using initial estimates generated frominformation obtained in earlier steps. This type ofcalculation can cross the critical point smoothly.

Critical point. A preferable algorithm, proposed byHeidemann and Khalil (1980), expresses the criticalpoint criteria in terms of the Helmholtz energy insteadof the Gibbs energy, as had been done in earlier work(Peng and Robinson, 1977). After further improvementby Michelsen and Heidemann (1981), the critical pointcalculation algorithm is comparable to flashcalculation in computation time.

PVT simulation and EOS tuningAll of the conventional PVT experimental results

can be simulated based on an EOS model. Simulationof a specific PVT experiment is simply one of, or acombination of, several phase equilibrium calculationsdescribed above. Commercial PVT softwares arewidely available nowadays. Calculations using cubicEOS with a proper characterization procedure cangenerally reproduce the experimental dataqualitatively. Quantitatively, several percent errors arecommon in calculated saturation pressures, densities,and mole percent of key components (Whitson andBrule, 2000; Pedersen et al., 1989b). Near the criticalregion, it is likely that the EOS method will incorrectlyidentify dew points or bubble points even if there isonly a small calculation error.

The disagreement between the measured and thecalculated results may originate from inaccurateproperties deduced from characterization, limitationsof the cubic EOS, incomplete compositional analysis,and last but not least, erroneous experimental data.Nearly all PVT reports are flawed to some extent,however, consistency checks before a PVT simulationcan help to rule out some poor experimental data. Theremaining deviations between predictions andmeasurements can be reduced further by adjusting theparameters entering the calculation model. Thismethod is known as EOS tuning.

Tuning of EOS parameters is not an exact sciencein the sense that there is no unique way of tuning, and

the engineer decides how much and which parametersto tune based on his experience. However, we attemptto give some guidelines to tuning below:• The common tuning parameters are the properties

of C7+ fractions including critical properties,acentric factors, their interaction coefficients withmethane, and volume shift parameters. Coats andSmart (1986) suggested direct tuning of Wa andWb, both for methane and the heaviest C7+ fraction.However, the magnitude of tuning is generallylarge and may cause undesirable results outside theregression region.

• The properties of the greatest interest in terms offurther application and those of higherexperimental accuracy should be assigned a higherweighting factor. Saturation pressure, densities,and gas/oil ratio are examples of importantproperties for reservoir simulation. Coats andSmart’s suggestion (1986) of a weighting factor of40 for saturation pressures, around 10 for densitiesand 1 for composition can serve as a rough guideto the setting of weighting factors.

• The number of parameters tuned and the extent oftuning should be as few as possible. Tuning shouldbe focused on the most sensitive parameters, whilethe insensitive ones can be removed. Furthermore,one should be aware of the errors in experimentaldata and avoid overfitting.

• Although automatic non-linear regression is theprevailing technique, common sense should be theguide throughout and ‘manual’ trial-and-errorshould also be attempted. The tuning of parametersshould correspond to reasonable trends inproperties, such as the increase of Tc, Pc with thecarbon number.

• Pedersen et al. (1989b) suggested tuning of the C7+molecular weight by arguing that the molecularweight measurement usually suffers from an errorof 5-10%. The overall composition must bechanged after C7+ tuning since the molarcomposition is actually converted from the originalweight composition data using molecular weights.For a sample from a well-studied reservoir,however, the range of molecular weight isrelatively certain.

• A consistent way of tuning kij between the C7+fraction and methane is preferred, i.e. tuning of thecoefficients of the empirical correlation whichgenerates these kij instead of tuning themseparately. It should be realized that kij tuning maycause spurious results at other temperatures.

• Volume shift parameters will not change phaseequilibrium calculation. Also, the critical volumewill only influence viscosity calculation throughthe LBC correlation (see below).


GEOSCIENCES

Viscosity, interfacial tension and diffusion

ViscosityViscosity is a measure of the resistance which a

fluid exhibits to flow. The dynamic viscosity, h, of aNewtonian fluid is defined as the ratio of the localshear stress driving the fluid flow to the velocitygradient in its perpendicular direction. Viscosity is notan equilibrium property. However, the viscosity of aNewtonian fluid is still a state function and has adefinite value once the state is fixed. The mostcommon unit of h used in the oil industry is the poise(P), which is equivalent to 0.1 Pa·s, and its submultiplethe centipoise (cP), 1 cP�1 mPa·s. The kinematicviscosity is the ratio of the viscosity to density and itsunit is the stoke (St), where 1 stoke �10�4 m2/s.

Fig. 7, a generalized viscosity plot calculated usingLucas’ corresponding-states viscosity correlation, andFig. 8, the smoothed viscosity of propane, illustratehow fluid viscosity varies with pressure andtemperature. An increase in pressure always increasesthe fluid viscosity; however, the influence oftemperature is different for liquid and gas, and in thelatter case depends on the pressure. For a liquid phase,or a gas phase at relatively high pressure, an increasein temperature will reduce the viscosity. For a gasphase at low pressure or a dilute gas, viscosity willincrease with temperature.

Abundant viscosity models, ranging from highlytheoretical ones to simple empirical correlations, areavailable in the literature. Many of them are onlysuitable for predicting either the liquid or the gasphase viscosity. However, viscosity calculation forboth hydrocarbon gas and liquid using a single modelis often required in the petroleum industry, especiallyin processes involving high pressure phaseequilibrium. The following discussion will focus onlyon this type of model. Reviews of other viscositymodels can be found in the literature (Monnery et al.,1995; Poling et al., 2000).

The Lohrenz-Bray-Clark correlation (LBC,Lohrenz et al., 1964) is traditionally used in the oilindustry. Nevertheless, a number of new viscositymodels appeared recently, including the model basedon the corresponding states principle (Aasberg-Petersen et al., 1991), the model based on the graphicalsimilarity between P�v�T and T�h�P plots (Guo etal., 2001) and the friction-theory (f-theory) viscosity model (Quiñones-Cisneros et al.,2000; Quiñones-Cisneros, 2001). Only the LBCcorrelation and the f-theory model are discussed below.

Both the LBC correlation and the f-theory modelincorporate the dilute gas viscosity as the lowerdensity limit. Actually, only the viscosity of the dilute

gas can be evaluated strictly based on gas kinetictheory. On the other hand, viscosity models for densefluids, including the LBC correlation and the f-theory,are generally semi-empirical in form.

The Lohrenz-Bray-Clark (LBC) correlation. TheLBC correlation is given by:

[33] [(h�h*)x�10�4]1/4�a0�a1rr�a2rr

2�a3rr3�a4rr

4

where a0�a4 are empirical coefficients, rr�vc/v is thereduced density, x�Tc

1/6M�1/2Pc�2/3 is the viscosity-



Pr�0

Pr�0

66

56

46

36

26

16

6

1

2

3

4

5

5

4

3

hx

hx

0.50.8

2.01.71.41.21.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5reduced temperature

reduced temperature

100

70

50

40

3025

2015

108.0

6.0

3.04.0

5 6 7 8 9 10 11 12 13 14

100

70

5040

302010

Fig. 7. Generalized viscosity plot based on Lucas’corresponding states correlation (Poling et al., 2000). The vertical axis represents the product of the dynamic viscosity h and the parameter x�0.176 Tc

1/6M�1/2Pc�2/3,

where h is given in mP, Tc in K, and Pc in bar.The lower part of the figure shows the behaviour for high temperature values.

reducing parameter and h* is the low-pressure gasmixture viscosity.

When the LBC correlation is applied to amixture, linear mixing rules are used for M, Tc, Pcand vc , and the following special mixing rule isapplied to h*:

[34] h*�i�1

Nc

�zihi*Mi1/2/

i�1

Nc

�ziMi1/2

Lohrenz et al. (1964) also suggest a correlation forthe critical molar volumes of the C7+ fractions.However, in practice, the C7+ critical volumes aregenerally treated as tuning parameters.

As can be seen from Eq. [33], the LBCcorrelation actually expresses h as a 16-degreepolynomial in the reduced density and thus is verysensitive to the density calculation results. It tends tounderpredict viscosities especially for highly viscousfluids.

The friction theory viscosity model (f-theory).The friction theory considers dense fluid viscosity asa mechanical property rather than a transportproperty. It is not until the dilute gas limit that thekinetic theory of gases becomes important.According to f-theory, the total viscosity h of densefluids can be separated into a dilute gas term h0 anda friction term hf :

[35] h�h0�hf

where the dilute gas model of Chung et al. (1988) isused to calculate h0.

By analogy with the Amontons-Coulomb frictionlaw, the viscosity friction term has been related to therepulsive pressure term Prep and the attractive term Pattrin a vdW type EOS (e.g. the SRK EOS or the PR

EOS) by means of three temperature dependentfriction coefficients as follows:

[36] hf�kr Prep�krrPrep2�kaPattr

Quiñones-Cisneros et al. (2001) further introduced theconcept of corresponding states into the model anddeveloped a general one-parameter f-theory. The one-parameter f-theory expresses the friction term °ofa pure component in the reduced form:

[37] hf�hf /hc

where hc is the characteristic critical viscosity. hf isrelated to Prep and Pattr in a way similar to that shown inEq. [36]:

[38] hf�kr�Prep12

Pc �krr�Prep

12

Pc 2

�ka�Pattr12

Pc

where kr, krr, ka are EOS-specific andtemperature dependent coefficients.

For mixtures, the h0 is calculated by:

[39] lnh0�i�1

Nc

�xi lnh0,i

and the hf is calculated using Eq. [36], while kr,krr, ka are calculated from the following mixingrules:

xi hc,i kr,i xi[40] kr��

i�1

Nc

�111 �i�1

Nc

�12 �1

M 0.3Pc,i M 0.3

xi hc,i ka,i xi[41] ka��

i�1

Nc

�111 �i�1

Nc

�12 �1

M 0.3Pc,i M 0.3

xi hc,i krr,i xi[42] krr��

i�1

Nc

�111 �i�1

Nc

�12 �1

M 0.3Pc,i2 M 0.3


GEOSCIENCES

Tc�369.82 KPc�42.4953 bar

10,000

1,000

100

dyna

mic

vis

cosi

ty (

mP

)

0 2 4 6reduced pressure

8 10

0.7

0.91.01.11.2

0.8

0.4

0.5

0.6

Tr�0.3

1.29

Fig. 8. Viscosity of propane at different reduced pressuresand temperatures.

Although the one-parameter f-theory losessome accuracy in comparison to the original f-theory, it reduces the required number ofinput parameters to a single compound-specifichc. For normal alkanes, hc can be evaluated bythe following empirical equation:

[43] hc�7.94830·10�4 1321�1

MPc2/3

Tc1/6

where the units are M in g/mol, Pc in bar, Tc in K and hcin cP. The f-theory has also been extended to modelviscosities of petroleum fluids (Quiñones-Cisneros etal., 2004).

Interfacial tensionInterfacial tension σ originates from the

unbalanced force at the interfacial layer between twophases. For molecules in the surface layer between alow dense gas phase and a high dense liquid phase, theattraction from neighbouring gas molecules is lessthan that from neighbouring liquid molecules. Inmacroscopic terms, the result is a tension at theboundary, pointing inside the bulk liquid phase.

The tension between a pure liquid and its vapour (orair saturated with its vapour) is referred to as surfacetension, while that between two liquids is referred to asinterfacial tension. However, both terms have beenapplied to other situations and a consistentnomenclature does not seem to exist. Here, interfacialtension is accepted as a general term for all situationsand surface tension specifically refers to a purecomponent.

Interfacial tension is closely related to the flowbehaviour of reservoir fluids at the pore level, e.g.the important capillary function is determined bothby the interfacial tension and the porecharacteristics.

Surface or interfacial tension is interpreted as thetension force on a unit length on the surface, or theGibbs energy change with unit increase in surfacearea. Traditionally, the units corresponding to theabove two definitions are the dyne/cm and theerg/cm2, respectively. In SI unit, 1 dyne/cm=1erg/cm2=1 mN/m.

Interfacial tension is roughly related to the densitydifference between two phases and vanishes at thecritical point. For a gas-oil system, interfacial tensionusually decreases with increasing pressure, whereas thetemperature effect depends on the position relative tothe critical point. For example, for gas condensates, sis expected to decrease with decreasing temperature,while the opposite is expected for an oil sample.

Interfacial tension at high pressure is commonlymeasured using the pendant drop method, whichconsists of measuring the shape of a suspended drop

of the heavier phase (or a standing bubble of thelighter phase) formed in its equilibrium phase, asshown in Fig. 9. The interfacial tension is related tothe drop dimensions by:

Drgde2

[44] s�111H

where Dr is the density difference between twophases, de is the equatorial diameter, and 1/H is atabulated function of ds /de, where ds is the diameter ofthe drop measured at the height de above the bottom ofthe drop (see again Fig. 9). In the case of smallinterfacial tension near the critical point, laser lightscattering techniques are preferred (Fotland andBjorlykke, 1989; Haniff and Pearce, 1990).

Traditional interfacial tension modelling consistsof relating surface tensions of pure compounds tovarious properties, such as density, compressibilityand latent heat of vaporization and then extending thisconcept to mixtures by some arbitrary mixing rules. Amore recent attempt is to use a theoretically soundgradient theory and its simplifications.

Parachor method. The Macleod-Sugden equation(Poling et al., 2000), which is widely employed toestimate the vapour-liquid interfacial tension, is given by:

[45] s1/4��Ps�(rML �rM

V )

where rML and rM

V are the molar densities of the liquidand vapour phase, respectively. [Ps] is known as theparachor, which is supposed to be temperatureindependent. Eq. (45) has been extended to mixturesby Weinaug and Katz (1943) using simple molaraveraging for the parachor:

[46] s1/4�rML

Nc

i�1�xi �Ps�i�rM

VNc

i�1�yi �Ps�i�

Nc

i�1��Ps�i (xir

LM�yir

VM )



dede

ds

Fig. 9. The principle of the pendant drop method for the measurement of the surface tension.

The above equation is widely used in the petroleumindustry.

Parachor values can be estimated by groupcontribution methods. Ali (1994) also reviews theparachor values reported by different investigators. Forhomologous hydrocarbons, an almost linearrelationship with molecular weight is usually found.However, in real oils, the PNA distribution varies invarious SCN groups and the linearity is distorted.Firoozabadi et al. (1988) give an equation that can beused to approximate the parachor of purehydrocarbons from C1 through C6 and for C7+fractions.

It should be noted that since s is proportional to�Ps�4(rL

M�rVM )4, the result obtained from Eq. [45] is

very sensitive to the density calculation and the choiceof parachor values.

Other modifications of Weinaug and Katz’sparachor method have been made, includingmodification of the exponent 1/4 on the left-hand sideof Eq. [46] and improvement of the parachor mixingrule. However, Firoozabadi et al. (1988) comment thatfor reservoir fluid without asphaltene, the Weinaug-Katz correlation is sufficient.

Finally, it should be noted that generalizedcorrelations are not expected to provide a reliableparachor value for the oil heavy end, which generallycontains a high concentration of asphaltic and surfaceactive materials. Therefore, it is advisable to determineit experimentally.

The gradient theory and its simplification. Thegradient theory (Carey et al., 1978, 1980; Guerreroand Davis, 1980) assumes that there is a continuousdensity variation for each component across theinterface between two equilibrium bulk phases. Thedensity profiles of all the components must takespecific forms in order to minimize the Helmholtzenergy at fixed T, V and N. Interfacial tension is bydefinition the partial derivative of the minimizedHelmholtz energy with respect to surface area. Aftersome derivation, it can be expressed in terms of thedensity profiles of all of the components:

[47] s��i

�j�−∞

�∞C(n)� dni

11

dx � dnj11

dx dx

where C(n) is the influence parameter forinhomogeneous fluid, ni is the number density ofcomponent i and x is the distance from the interface.

When combined with a specific EOS to calculateσ , the density profiles are first calculated by solving aset of partial differential equations or algebraicequations. The interfacial tension is then readilyobtained using Eq. [47].

To avoid the difficulty in the density profilecalculation, Zuo and Stenby (1996a, 1996b, 1998)

proposed a linear gradient theory, which assumes that the number densities of each component arelinearly distributed across the interface. These authors have applied this model to a variety of mixtures including hydrocarbon-water mixtures.

Diffusion and thermodiffusionDiffusion describes the process of relative motion

of different components in a mixture in the absence ofmixing. Diffusion fluxes are determined as relativefluxes of different components in a mixture. Forexample, if Ji is the molar flux of component i in amixture of Nc component, then one determines themolar convective flux using (Haase, 1969):

[48] Jc�Nc

i�1�Ji

and the diffusive flux of component i using:

[49] JD,i�Ji�zi Jc

where zi is the molar fraction of component i. Themass flux of each component can be similarly defined.Fick’s law expresses the molar diffusion fluxes interms of the gradients of the molar fractions:

[50] JD,i�rNc�1

k�1�Dikzk

where r is the molar density and Dik is the Fickianmolar diffusion coefficient of component i. AlthoughD12�D21 holds for binary systems, it is seldompointed out that Dij is not necessarily equal to Dji forn�3. On the other hand, the study onmulticomponent diffusion is rare, bothexperimentally and theoretically, in contrast to thefact that large databases of experimental values, andmany models and correlations for diffusioncoefficients exist for binary mixtures (Hsu and Chen,1998; Poling et al., 2000).

For dilute gases, diffusion coefficients can easilybe evaluated based on the strict framework of gaskinetic theory. For liquids, only approximate modelsare available and their prediction ability is difficult toverify due to the lack of experimental data ondiffusion coefficients in multicomponent mixtures.The free volume theory has been used in modellingliquid diffusion coefficients for a long time(Hirschfelder et al., 1954; Bondi, 1968) and recentmodels for multicomponent diffusion are available(Wesselingh and Bollen, 1997). In engineeringpractice, effective diffusion coefficients estimatedfrom binary diffusion coefficients are often used(Whitson and Brule, 2000). Estimation of liquiddiffusion coefficients is believed to have only orders ofmagnitude accuracy.


GEOSCIENCES

Thermodiffusion, or the Soret effect, which isinduced by temperature gradients, is analogous todiffusion induced by concentration gradients.Thermodiffusion is often negligible but it can beimportant under specific situations, e.g. thecompositional grading of thick oil reservoir (Georis etal., 1998). Accurate measurements of thermodiffusionare rare since they are easily ruined by the naturalconvection which occurs under the gravityenvironment.

1.1.4 Heavy petroleum fraction

The most complex chemistry of petroleum is foundin the heavy fraction. This part contains severalclasses of compounds. The detailed molecularstructure cannot always be determined and it may benecessary to define a group of compounds as asolubility class rather than a class of molecularstructures. From a technological point of view themost important heavy fractions are waxes andasphaltenes, but resins also play a significant role.These three classes of compounds will be definedand described below.

Wax

Definition and chemical structure Waxes are crystalline materials separated from

petroleum by cooling a mixture of the oil, a ketone,and another polar or aromatic solvent. Severaldifferent solvent types and solvent pairs are used in theliterature, such as acetone-toluene,methylisobutylketone (MIBK)-methylene chloride,etc. Due to the differences in the solvent pairs andother conditions the wax content will vary accordingto the method employed, and may even contain co-precipitated and entrapped oil and asphaltenes. Asthe separation temperature decreases the amount ofsolid material recovered increases.

The term paraffins is often used synonymouslywith waxes since the long chain normal alkaneslargely dominates the composition of waxes. Mostwaxes consist of normal alkanes with a carbon numberin the range from 20 to 50, but there is discussion inthe scientific community whether a different class ofwaxes exists, namely, the so-called microcrystallinewaxes. To avoid confusion the term paraffin waxeswill be used in the following. Branched alkanes do notfit into the crystal structures formed by the normalalkanes and, therefore, are not found in paraffin wax.As a result, the class of molecules are generally verywell defined when paraffin wax problems have to beaddressed.

Paraffin waxes in petroleum production The fraction referred to as paraffin waxes is

important because it represents a potentialproduction or transport problem in relation to oil andgas condensate production. As commercial products,paraffin waxes are valuable, for instance, aslubricants; however, this will not be covered furtherin this section. Paraffin wax formation in apetroleum fluid is observed as a solid phase thatappears when the fluid is cooled down. Thetemperature at which the first paraffin wax isobserved is called the Wax Appearance Temperature(WAT). In Fig. 10, a temperature-pressure diagram isshown for a petroleum fluid where both the solid-liquid phase transition boundary and the vapour-liquid phase envelope are reported (for a detaileddiscussion of the latter, see Section 1.1.5). The slopeof the solid-liquid curve is rather steep, whichindicates that the WAT is neither very sensitive tothe pressure nor to the dissolved gas in the oil. If theWAT is higher than the process or transporttemperature there will be precipitation anddeposition of paraffin wax in the process equipmentor transport pipelines. Therefore, the control ofparaffin wax is covered by the term flow assurance.Since deposited paraffin wax can only be removedmechanically or by heating, it is crucial that thedeposition of paraffin wax does not get out ofcontrol. Off shore pipelines are particularlyvulnerable since the costs of remediation areconsiderable. The level of paraffin wax deposition inpipelines is controlled mechanically by pigging; aprocess in which a tool with a diameter slightlysmaller than the inner pipe diameter – also known as



500

400

300

200

100

00 100 200 300 400

temperature (K)

pres

sure

(ba

r)

500 600 700

700

600

liquid�vapour

liquid

solid�liquid�vapour

solid�liquid

model

data

Fig. 10. Entire phase envelope with consideration of the wax precipitation (Lindeloff et al., 1999).

the ‘pig’ – is pushed through the pipeline. The pigscrapes the paraffin wax off the pipe walls andpushes it to the end of the pipeline where it iscollected. Another way to secure flow assurance isthe use of chemical additives that affect the paraffinwax precipitation, or the growth or agglomeration ofparaffin wax crystals. Such chemicals can keep theparaffin wax dispersed as small crystals that will becarried along with the flowing oil. The basicmechanisms are not completely understood and theuse of these chemical additives requiresexperimental testing for each specific oil. Differentoils will contain a varying amount of paraffin waxcomponents but since accumulation over time willoccur in pipelines, even small amounts of paraffinwax in an oil can represent a significant risk for theflow assurance.

Experimental determination of the wax appearancetemperature

A number of methods can be used to determine theWAT, including differential scanning calorimetry,visual observation using microscopy, cross polarmicroscopy, light transmittance or scattering,viscometry, cold finger, and filter plugging. Only themicroscopy, light transmittance and filter pluggingmethods are briefly introduced below.

In general, microscopy is only used at atmosphericpressure. A small fluid sample is studied under themicroscope while being either heated or cooled. Sincesubcooling will occur, the most accuratemeasurements are obtained when a cold fluid sampleis melted. The WAT can be identified as thetemperature at which the last crystal melts. Sinceparaffin wax is a multicomponent mixture, the meltingor freezing will take place over a range oftemperatures and not at a single temperature as for apure substance.

Laser light of different wavelengths can easily betransmitted through petroleum fluids if a small lightpath is chosen. If the fluid is cooled uniformly, andis mixed well, the WAT can be determined by thefact that the transmitted light is disturbed byscattering from the paraffin wax crystal in the fluid.This method has been developed for high pressureapplications.

In the filter plugging method, petroleum fluid ispumped or circulated through a filter while the wholesetup is cooled down in a controlled manner. The WATcan be detected by a sudden resistance to the flowthrough the filter. This method has also beendeveloped for use at high pressure. It is possible todesign the setup in such a way that the paraffin wax onthe filter can be collected and its compositionanalysed.

Modelling of wax precipitation Accurate thermodynamic modelling of paraffin

wax precipitation is possible. The requirement is thatthe balance between the paraffins, naphthenes, andaromatic compounds is known for the fraction of thefluid in which the paraffin wax components arepresent.

The fugacity equality condition for the solid-liquidequilibrium between solid wax and liquid hydrocarboncan be written as

xSi gL

i fi°L PnL

i �nSi[51] 1�1 12 exp�� 112 dP xL

i gSi fi°

SP° RT

where xi is the mole fraction, giis the activitycoefficient, fi° is the fugacity at the reference state (T,P°), and vi is the molar volume. The superscripts L andS represent the liquid and solid phases, respectively.The exponential term in Eq. [51] corrects the effect ofpressure on the fugacity. The fugacity ratio fi°

L/fi°S can

be expressed as:

[52] lnfi°

L

fi°S

11�Dhf

RT11 �1�1

T

Tf �

ht11

RT �1�1T

Tt �

Cp1222

R �1�1T

Tf

�ln1T

Tf

where Dhf is the molar heat of fusion or meltingenthalpy at the melting temperature of the solute Tf ,Dht is the molar enthalpy change of phase transitionat the temperature of phase transition Tt and DCp isthe difference between the heat capacity of the liquidphase and that of the solid phase. The Dht term isimportant in modelling wax precipitation since thesolid-solid phase transition usually occurs below themelting temperature for heavy n-alkanes. Thecontribution from the DCp term is usually small andoften neglected.

Eq. [51] and Eq. [52] provide the framework ofmodelling wax precipitation in terms of the activitycoefficients model. Early wax models (Won, 1986;Pedersen et al., 1991; Coutinho and Stenby, 1996;Coutinho et al., 1996) have been developed mainly forlow pressure applications. The key problem lies inproper modelling of the activity coefficients inaddition to reasonable estimation of Tf , Tt, Dhf and Dhtfor the n-alkanes in the oil. Coutinho et al. (1995) gavea comprehensive evaluation of the different activitycoefficient models utilized in the prediction of alkanesolid-liquid equilibria.

To model the precipitation in live oils, where theeffects of pressure and dissolved gas are present, it isconvenient to modify the above framework bymodelling the vapour and liquid phase using an EOS(Pedersen, 1995; Lindeloff et al., 1999; Pauly et al.,2000; Daridon et al., 2001). In this method the liquid


GEOSCIENCES

activity coefficients terms are replaced by liquidfugacities.

Asphaltene and resin

Definition, composition and structure Asphaltenes are operationally defined as the solid

material precipitated from crude when mixed with anexcess of a low boiling hydrocarbon, such as n-heptane or n-pentane. This fraction should besoluble in toluene or benzene (Fig. 11). The amount ofasphaltene separated is a function of the n-alkanecarbon number, the time of contact (especially forviscous heavy oils), the ratio of oil to solvent, and thetemperature. Although some standards, such as theInstitute of Petroleum (IP) 143, are prevailing in thedetermination of the asphaltene content of crudes,most of the above separation conditions are oftenvaried in the literature on asphaltene research. Thisleads to some additional confusion regarding theactual behavior and nature of this fraction, as the grosscomposition of the asphaltene will vary considerably.

The number of different compounds inside theasphaltene fraction is estimated to be over 100,000.These compounds are characterized by high molecularweight, polarity and aromaticity. Despite thecomplexity of asphaltene fractions, their ratio ofhydrogen to carbon varies only in a narrow range, say,around 1.0 to 1.2. The heteroatoms N, S, O and tracemetals are concentrated in the asphaltene fraction,while their quantity can vary from oil to oil in almostone order of magnitude. Sulphur is usually the mostconcentrated among all heteroatoms.

The molecular weight of asphaltene is directlyrelated to the molecular size of asphaltene and is acrucial parameter in any asphaltene model.Unfortunately, its experimental determination isdifficult. Asphaltenes tend to self associate even indilute solution. The mechanism is not wellunderstood but hydrogen bonding and charge-transferare believed to be responsible. The association isinfluenced by solvent polarity, asphalteneconcentration, and the temperature at which thedetermination is made (Speight, 1999). Methods likevapour pressure osmometry are only able to providethe molecular weights of aggregates and themeasured values are dependent on the abovementioned factors. Other methods have their ownspecific problems. In general, none of the currenttechnologies can answer the challenge of determiningthe true molecular weights of asphaltenes. Valuesfrom different methods differ significantly, even byorders of magnitude.

Not much is known about the asphaltenestructure. Investigations have shown that asphaltenesconsist of condensed aromatic nuclei that carry alkyland alicyclic systems with heteroelements scatteredthroughout in various locations (Speight, 1999).However, the formulation of the individualmolecular structure is still impossible. An exampleof a hypothetical asphaltene molecule is given in Fig. 12. Different types of structures haveappeared in the literature.

Generally, resins refer to the more stronglyadsorbed oil fraction in a deasphaltened oil which issubject to subdivision using a surface active



1. heptane 2. benzeneor toluene

benzene or toluene

carbon disulphideor pyridine 3. benzene

and methanol

saturates

insolubles asphaltenes

carboids(insolubles)

carbenes(solubles)

aromatics resins

feedstock

insolubles deasphaltenedoil

n-heptane

silica or alumina

Fig. 11. Simplified representation of the separation of petroleum into six major fractions according to the solubility in differentsolvents (n-heptane, benzene, etc.) or the adsorption on solid substrates (Speight, 1999).

material, such as fuller’s earth or alumina. Theabsorbed resin is recovered by a more polar solventand, therefore, eluted last (see again Fig. 11). Resinsare believed to have molecular structures similar toasphaltenes but with longer alkyl non-polar chainsand smaller aromatic rings. The molecular weight ofresins is in the range of 100-600 u, according tovapour pressure osmometry measurements (Speight,1999). These resins can be considered to be atransition type between asphaltenes and the simplerfractions, and hence an overlap between resins andasphaltenes is expected.

Resins play an important role in dispersingasphaltenes in crude oil (Andersen and Speight,2001). It is generally believed that asphaltenes aredispersed in crude oil as centres of micellessurrounded by resins and other lighter and lessaromatic molecules. The transition from theasphaltene centres to the bulk phase oil is gradual,with the size and aromaticity decreasing outwardsfrom the aggregate. The concept of Critical MicellarConcentration (CMC) has been widely used indescribing the association of asphaltenes. However,recent studies suggest a step-wise mechanism ratherthan the formation of finite-size micelles (Andersen,1994; Acevedo et al., 1999; Groenzin and Mullins,2000).

Asphaltene precipitation The importance of asphaltene is unfortunately

justified by the many problems it causes. Apartfrom poisoning of catalysts and destabilization ofproducts in the refining process, the major problemcaused by asphaltene in oil production and transportis its precipitation. Asphaltene precipitation is

complex, and the possibility of precipitation is notnecessarily proportional to the content of theasphaltene. For example, oils with a smallerpercentage of asphaltene may be more likely toprecipitate. Both depletion and gas injection cantrigger precipitation of asphaltene. The reason isusually attributed to unfavourable changes insolvent properties with a change in pressure or theaddition of injection gas.

Experimental data on the onset of asphalteneprecipitation are scarce in the literature. The data canbe measured by different methods, e.g. visualobservation through microscopy, light transmissionor scattering, electrical conductivity, viscometry, andcapillary flow measurements.

The modelling of asphaltene precipitation is lessdeveloped in comparison to the modelling of waxprecipitation. Among the major difficulties is thelack of understanding of the actual mechanismsresponsible for the precipitation. Moreover, little isknown about the true dispersion state of asphaltene inoil, while data on the physical properties ofasphaltene are virtually unavailable. There is evendebate on whether the precipitation is a reversibleprocess. The limited experimental data make it moredifficult to evaluate the existing models.

1.1.5 Reservoir fluids

This section describes the different types ofpetroleum reservoir fluids which are commonlyencountered by exploration. A proper classificationof a reservoir is important since the fluid type is adeciding factor in the production scheme. Theproperties of interest also differ between differenttypes of reservoirs. As will be seen below, theclassification of reservoir fluids is closely related tothe Pressure-Temperature (P-T) phase diagram ofmulticomponent mixtures.

The P-T phase diagram of a multicomponent system

Fig. 13 shows a typical pressure-temperaturephase diagram of a multicomponent system with aspecific overall composition. In the phase diagram,the two-phase region is enclosed by a continuousboundary called the phase envelope. This phaseenvelope consists of a bubble point branch and a dewpoint branch, with the two branches connected at thecritical point where the coexisting liquid and vapourbecome identical in terms of intensive properties. Incontrast to a single component system, the criticalpoint of a multicomponent system is generally not


GEOSCIENCES

S

N

S

OH

mole

Fig. 12. A hypotheticalasphaltene molecule(Speight, 1999).

C 84.9%H 8.2%N 1.0%O 1.2%S 4.7%H/C 1.15

molecular weight: 1,370

the maximum temperature and the maximumpressure of the two-phase region. The maximumtemperature point and the maximum pressure pointare called the cricondentherm and the cricondenbar,respectively.

In the two-phase region, a set of quality lines(dashed lines) can be drawn to indicate constantpercentage liquid volume. The bubble point and thedew point branches correspond to the two specialquality lines with 100% and 0% liquid, respectively.All of the quality lines converge to the critical point.

The single phase region can be further dividedinto a liquid region and a gas region, where theformer refers to the region above the bubble pointcurve with temperatures lower than the criticaltemperature and the latter refers to the remaining partof the diagram.

A special phenomenon called retrogradecondensation can be observed for mixtures due to theexistence of two dew point pressures at temperatureshigher than the critical temperature but lower thanthe cricondentherm. As shown in Fig. 13, both a lowpressure dew point D1 and a high pressure dew pointD2 exist at temperature T1. For a depletion processA → D2 → B → C → D1 at constant temperature T1, aninfinitesimal amount of liquid will form when thesystem reaches D2, and a further decrease in pressurewill increase the liquid volume fraction until itreaches its maximum at B. The increase of thecondensed liquid (usually called the liquid dropout)with decreasing pressure is contrary to the commonintuition and named retrograde condensation. Itshould be noted that B is only the maximum in theliquid volume fraction rather than the absolute

amount of the liquid dropout. The absolute liquiddropout can still increase after B but the increase isnot enough to counteract the expansion effect so thatthe liquid volume fraction decreases. After C, furtherdecrease in pressure will reduce the absolute liquiddropout due to the re-vaporization. The decreasecontinues until an infinitesimal amount of liquid isleft at D1.

Classification of reservoir fluids

Petroleum reservoirs are described or classifiedbased on the composition of the petroleum fluid, andthe temperature and pressure prevailing in thereservoir. However, the dimensions of a petroleumreservoir are large and the composition of thepetroleum fluid varies depending on the location in thereservoir due to the influence of gravity, thegeothermal gradient and the geologic history of thereservoir. The classification, into the categoriesdescribed below, is therefore a simplification whichshould be kept in mind.

When a petroleum reservoir is discovered, it iscommon practice to classify the reservoir into one ofthe following types: natural gas, gas condensate,volatile oil or black oil, based on the location of initialreservoir conditions with respect to the phase envelopeof the reservoir fluid. Natural gas is further subdividedinto wet gas and dry gas, while black oil will, here,also cover heavy oil and extra heavy oil. Theclassification has a direct impact on the economicaland technical evaluation, and thereby on theproduction strategy. For example, some aspects of thefluid properties, such as volumetric properties, are



100

80

0

12

5

101520

30pres

sure

temperature

single phaseregion(liquid)

single phaseregion(gas)

cricondenthermtwo-phase

region

cricondenbar

critical point

% liquid

A

B

C

D2

D1

T1

Fig. 13. Typical pressure-temperature phase diagram for a multicomponent system.The quality lines can be moreevenly spaced for other systems.

important for the estimation of the petroleum reserves.Others are of importance for the flow assurance.Potential production problems have to be addressed asearly as possible.

Table 2 shows the typical molar composition ofpetroleum reservoir fluids and the correspondingcalculated phase envelopes are shown in Fig. 14. Itshould be noted that the same initial reservoirconditions and separator conditions are used for allfluids in Fig. 14, whereas in fact, they vary from fieldto field.

Dry gas and wet gasFor both dry gas and wet gas, the initial reservoir

temperature is higher than the cricondentherm of thereservoir fluid and the reservoir conditions never fallinside the two-phase region during a depletionprocedure (the vertical line in Fig. 14). Furthermore,for a dry gas, the process conditions are typicallyoutside the two-phase envelope. Compared with a drygas, a wet gas contains a larger fraction of C2-C6components, and its phase envelope is larger andreaches higher temperatures. The separator conditionsare inside the two-phase region for a wet gas. Thetypical gas/oil ratio of a wet gas is 60,000-100,000scf/stb (11,000-18,000 sm3/m3) and its stock tank oil isusually water-white with a specific gravity higher than60° API.

It can be seen that there is no gas-liquid criticalpoint on the phase envelope of the wet gas in Fig. 14. This is due to the three-phase equilibrium atthe low temperature. Actually, phase envelopes inreal hydrocarbon mixtures can be much morecomplicated than the phase envelops shown in Fig. 13. For example, multiphase equilibria as wellas multiple critical points or no critical point are

very common in reality, and at low temperature oneor more solid phases will usually form. These pointsare not considered in the two-phase envelopes in Fig. 14.

Gas condensateThe initial temperature of a gas condensate

reservoir lies between the critical temperature and thecricondentherm of the reservoir fluid. In such a casethe fluid exists as a gas at initial conditions, butduring pressure depletion, liquid will drop out due toretrograde condensation below the high pressure dewpoint. A typical gas condensate has a gas/oil ratio inthe range 8,000-70,000 scf/stb (1,400-12,000sm3/m3). The stock tank oil is usually slightlycoloured and its API gravity is usually greater than50°.

Volatile oil and black oilIn the case of both volatile oil and black oil, the

initial reservoir temperature is below the criticaltemperature of the reservoir fluid. The fluid thereforeexists as a liquid at initial conditions, however, onpressure depletion, the bubble point will eventuallybe reached.

Volatile oil differs from black oil quantitativelyonly in terms of having a relatively larger fraction of light and intermediate hydrocarbon components.As a result, its critical temperature is much closer to the reservoir temperature. During the depletion,volatile oils show a larger shrinkage factor due to the large amount of gas released. The typicalgas/oil ratio for a volatile oil is 2,000-3,500 scf/stb(360-620 sm3/m3). Its stock tank oil is usuallygreenish to orange in colour with an API gravitybetween 45 and 55°.


GEOSCIENCES

Table 2. Typical molar composition of petroleum reservoir fluids

Component Dry gas Wet gas Gas Volatile Blackcondensate oil oil

N2 0.0292 0.0150 0.0050 0.0161 0.0070CO2 0.0107 0.0100 0.0393 0.0217 0.0200C1 0.8763 0.9010 0.7257 0.6065 0.3300C2 0.0477 0.0420 0.0850 0.0796 0.0660C3 0.0185 0.0210 0.0493 0.0471 0.0700

i-C4 0.0049 0.0020 0.0102 0.0210 0.0240n-C4 0.0058 0.0015 0.0105 0.0220 0.0280i-C5 0.0020 0.0021 0.0035 0.0210 0.0180n-C5 0.0020 0.0024 0.0045 0.0110 0.0170C6 0.0029 0.0020 0.0050 0.0190 0.0290C7+ 0.0010 0.0620 0.1350 0.3910

C7+ molecular weight 128 182 199 249C7+ specific gravity 0.750 0.807 0.802 0.853

The gas/oil ratio for a black oil is usually below700 scf/stb (120 sm3/m3) and the stock tank oilcolour can range from brown to black with an APIgravity between 15° to 40°. Black oils with a gas/oilratio less than 200 scf/stb (36 sm3/m3) and an APIgravity less than 15° are sometimes known as lowshrinkage oils.

Heavy oils and extra heavy oilsThe definition of heavy oil is quite arbitrary.

Generally, it refers to petroleum with an API gravity ofless than 20° and usually, but not always, a sulphurcontent higher than 2 wt% (Speight, 1999). The termheavy oil has also been arbitrarily used to describeboth heavy oils that require thermal stimulation ofrecovery from the reservoir and bitumen in bituminoussand (tar sand) formations from which the heavybituminous material is recovered by a miningoperation. Speight (1999) gives a detailed discussionof the difference between the terms heavy oil,bitumen, mineral wax, asphaltite, asphaltoid, andbituminous sand.

Near critical fluidA reservoir fluid with its critical temperature very

close to the reservoir temperature is called a nearcritical fluid. Such a near critical fluid can be either agas condensate or a volatile oil, and is characterized bya dramatic change in the liquid volume fraction justbelow the saturation pressure. For the near critical gas

condensate, as shown in Fig. 15, a small pressure dropbelow the dew-point will give rise to a large amount ofliquid dropout.

Compositional grading

A reservoir at static equilibrium can showsignificant compositional variations known ascompositional grading. Compositional grading ismainly due to gravity, as the temperature gradient in areservoir is usually small (0.025 K/m), and thereforeplays a less important role. However, the temperaturecan significantly influence the fluid distribution insome specific situations (Georis et al., 1998).

The isothermal compositional grading can bedescribed by

[53] mi(Pref ,zref ,T )�Mi ghref�mi(P,z,T )�Mi gh

i�1,…,Nc

where mi is the chemical potential of component i, Miis the molecular weight, zref is the known compositionof a single phase fluid at reference depth href withreference pressure Pref , and P and z are the pressureand composition at depth h.

In general, the heavy components tend toaccumulate at the bottom while the light componentstend to accumulate in the top. Therefore, saturationpressure and solution gas/oil ratio can changeconsiderably as they are associated withcompositional change. Fig. 16 shows two typical



pres

sure

(M

Pa)

0�100 0 100 200 300 400 500

10

20

30

40

50reservoir conditions

reservoirtemperature

separatorconditions

dry gas

wet gas

temperature (° C)

gascondensate

volatile oil

phase envelope

gas-liquid critical pointthree-phase point

black oil

Fig. 14. Phase envelopes fordifferent types of reservoir fluids.

The dashed line indicates thedepletion line for an isothermal

reservoir. Fluids with critical pointsto the right of the depletion line

belong to oil reservoirs, while therest belongs to gas reservoirs.

profiles of saturation pressure and reservoirpressure. On both profiles, the dew point pressureincreases with depth (i.e. with an increasing amountof heavy components) and the bubble pressuredecreases with depth (i.e. with decreasing methanecontent). The reservoir pressure increases with depthand shows different slopes in the gas and oil regions.The difference between two profiles is that in theleft-hand profile, the saturation pressure reaches thereservoir pressure at a depth where a clear Gas Oil

Contact (GOC) is formed, whereas in the right-handprofile, the saturation pressure is always below thereservoir pressure and the transition from oil to gastakes place through a local critical point.Compositional change is discontinuous at the GOCin the left-hand profile while that in the right-handprofile is always continuous.

1.1.6 Formation water

Water is always associated with petroleumhydrocarbons in their production. Not only is waterfound almost invariably in reservoirs in appreciablequantities as connate, interstitial, or formation water,but it is also deliberately injected to improve oilrecovery. Water interacts with hydrocarbon fluids interms of flow, expansion, and sometimes dissolutionand release of soluble gases. Furthermore, solidprecipitation including scaling and hydrate formationdue to temperature and pressure change may causeconsiderable damage during the production process.Knowledge of the physical properties of the formationwater and its phase equilibrium is therefore importantto petroleum engineers. Some of these aspects arediscussed in the following paragraphs. Further detailson the characteristics of the layer waters (salinity,solubility of gas in the water, volumetric parametersand viscosity) are reported in chapter 4.2.

CompositionFormation water contains dissolved salts

(primarily sodium chloride) and dissolved gases(primarily methane and ethane). It bears littlerelationship to sea water although both are generallycalled brine or salt water. The formation water hasmuch higher salinity, ranging from 200 to 300,000ppm (around saturation), compared with around35,000 ppm of sea water.

The cations dissolved in formation waters usuallyinclude Na�, Ca2� and Mg2�, and occasionally K�,Ba2�, Li�, Fe2� and Sr2�. The anions commonlyinclude Cl�, SO4

2� and HCO3�, while CO3

2�, NO3�,

Br�, I�, BO33� and S2� are also often present.

Finally, the concentration of salts in formationwater is called salinity and can be specified usingdifferent quantities. Table 3 gives definitions of someof the most commonly used quantities.

Volumetric property of formation waterUnlike water density, which is only a function of

temperature and pressure and can be easily determinedwith high accuracy, formation water density is alsoinfluenced by the amount and composition ofdissolved salts and gases. The large range of dissolved


GEOSCIENCES

pres

sure

(ps

i)pr

essu

re (

psi)

temperature (° F)a

b

2,600

2,400

2,200

2,000

1,800

1,600

1,400

60 80 100 120 140 160 180 200 220 240 260

critical point

100%90%80%70%60%

50%

40%

30%

20%10%

0%

% liquid by volume

2,700

2,600

2,500

2,400

2,300

2,200

2,100

2,000

1,900

1,800

1,700

1,600

1,500

1,400

1,300

1,200

percent liquid by volume0 10 20 30 40 50 60 70 80 90 100

85° F

102 ° F

145°

F

166° F171° F 169° F

212 ° F

192 ° F

181 ° F119 ° F

Fig. 15. P-T phase diagram for a near critical gas condensate fluid (A) and its corresponding volume isotherms (B)(Katz et al., 1959).

B

A

components brings difficulty in developing a generalmodel. Fortunately, the volumetric property offormation water varies within a relatively small range,with the isothermal compressibility being typically2-4 �10�6 psi�1 (3-6 �10�10 Pa�1) and the formationvolume factor, which is defined as the volume of theformation water at reservoir conditions divided by thevolume of the water produced from the formationwater at surface conditions, typically ranging from1.00 rm3/m3 at high pressure to 1.07 rm3/m3 at lowpressure. Engineering correlations (McCain, 1990;Whitson and Brule, 2000) can give reasonableestimations in practice when experimental data are notavailable. These engineering correlations oftensimplify the dissolved salts to NaCl or neglect the salteffect on the formation volume factor.

Mutual solubility of formation water and hydrocarbons

The solubility of hydrocarbons in water is verylow, while that of methane in water is no more than 1 mol% at common reservoir conditions. From methaneto propane, the solubility decreases by a factor of twoto three on going from one hydrocarbon gas to the next

heavier one, and the solubility of heavier liquidhydrocarbons is much smaller. Furthermore, thesolubility of hydrocarbons increases with pressure, thiseffect being more prominent for lighter hydrocarbonsand at low pressures. On the other hand, at constantpressure, the solubility of hydrocarbons has atemperature minimum, before which it decreases withtemperature and after which it increases. Withincommon reservoir temperature and pressure ranges, anincrease in hydrocarbon solubility with temperature isusually observed. Finally, the solubility of CO2 inwater is almost one order of magnitude larger than thatof methane.

The equilibrium water content in hydrocarbons isgenerally larger than the corresponding hydrocarbonsolubility in water, especially at low pressure andhigh temperature. Therefore, in the case of liquidhydrocarbons, the water content can be orders ofmagnitude higher. However, since the water contentdecreases with pressure and increases dramaticallywith temperature, the water content in lighthydrocarbon gases can be lower at low temperatureand high pressure. Fig. 17 illustrates the mutualsolubility of methane and water within the usualreservoir temperature and pressure ranges. Thepresence of salt reduces both the solubility of thehydrocarbons and the equilibrium water content.

The plot of methane solubility in water prepared byCulberson and McKetta (1952) is commonly used toestimate the solubility of natural gas in water.Application of the salinity correction can beperformed subsequently by introducing salting outcoefficients (Whitson and Brule, 2000). The solubilityof CO2 in brine can be estimated by the empiricalcorrelation of Chang et al. (1996), while that of waterin natural gas and hydrocarbon liquids can beestimated using empirical charts (Hoot et al., 1957;McKetta and Wehe, 1962; GPA, 1980).

Cubic EOS with the conventional quadraticmixing rules cannot simultaneously correlate the



pressure

bubb

le p

ress

ure

bubb

le p

ress

ure

reservoir pressure

dew pressure

dew pressure

gas

oiloil

gas

dept

h gas/oil contact criticalpoint

reservoirpressure

dept

h

pressure

Fig. 16. Typical saturationpressure and reservoirpressure change withdepth.

Table 3. Different commonly used expressions of salinity.

Term Definition

Molality moles of solutemass of pure water (kg)

Molarity moles of solutevolume of brine (l)

Weight percent mass of solute�100

mass of brine

Parts per million (ppm) mass of solute (g)mass of brine (t)

Milligrams per liter mass of solute (mg)mass of brine (l)

composition both in the hydrocarbon phase and inthe aqueous phase. Therefore, when the watercontent in the hydrocarbon phase is accuratelycorrelated, the solubility in the acqueous phase willoften be underestimated by orders of magnitude. Aconventional engineering solution to the aboveproblem is to use different sets of interactionparameters for the hydrocarbon phase and theaqueous phase, where the interaction parameter inthe aqueous phase is usually assumed to betemperature dependent. Søreide and Whitson’smodification (1992) of the PR EOS is such anexample. Unconventional mixing rules can also beapplied to the problem (Kabadi and Danner, 1985).Søreide and Whitson’s model only accounts for thesalt effect empirically by constricting the interactionparameters to be salinity dependent. More rigorous

inclusion, using Debye-Hückel terms, isimplemented in other engineering models (Zuo andGuo, 1991; Zuo et al., 1996).

In the production process, the hydrocarbons andwater may coexist with glycols, which are added forthe purposes of inhibiting hydrate formation,depressing water freezing point, and dehydratingnatural gas. Modelling glycol-hydrocarbon-watersystems is theoretically difficult due to the selfassociation and cross association in these systems. TheCubic-Plus-Association (CPA) EOS (Kontogeorgis etal., 1999), a recent EOS, developed by combination ofthe SRK EOS and the Wertheim association term, hassucceeded in the description of this system. The mostimpressive aspect of the CPA EOS is its ability tosimultaneously describe hydrocarbon-water mutualsolubility using a single interaction parameter and toaccurately predict multicomponent phase behaviour(Derawi et al., 2003).

ViscosityThe viscosity of formation water at reservoir

conditions is virtually less than 1 cP, generally lowerthan the viscosity of oil. Within the normal reservoirtemperature and pressure ranges, the viscosity offormation water increases with pressure and decreaseswith temperature. Furthermore, an increase in salinitywill increase the viscosity, while the effect ofdissolved gas is also believed to increase the viscosity.To account for this Whitson and Brule (2000)recommend a modified version of the empiricalcorrelation by Kestin et al. (1981) for brine viscositycalculation.

Interfacial tension between hydrocarbon and formation water

The interfacial tension of water/hydrocarbonsystems varies from approximately 72 mN/m for water/brine/gas systems at surface conditions to 20 to 30 mN/m for water/brine/stock-tank-oilsystems at reservoir conditions. Fig. 18 shows the experimental data on the interfacial tensionbetween methane and water, which is largelyrepresentative of the case of reservoir gas andformation water. The interfacial tension decreaseswith pressure and temperature in the tested region.Due to the experimental difficulty, the published data are often in significantdiscrepancy as indicated by Fig. 18. The interfacialtension between liquid hydrocarbon and waterdecreases with temperature but slightly increaseswith pressure, while it generally increases in thepresence of salts.

The parachor method is not suitable to modelinterfacial tension between hydrocarbons and water.


GEOSCIENCES

1

mol

e fr

acti

on

pressure (bar)0 200 400 600 800 1,000

10-1

10-2

10-3

10-4

37.78° C

71.1° C

104.44° C

150° C

200° C

Fig. 17. Solubility of methane in water (solid lines) and water content in methane (dashed lines) (Olds et al., 1942; Culberson and McKetta, 1951; Sultanov et al., 1971; Sultanov et al., 1972).

inte

rfac

ial t

ensi

on (

mN

/m)

30

35

40

45

50

55

60

65

70

75

pressure (bar)0 200 400 600 800 1,000

Sachs and Meyn (1995)

Jennings and Newman (1971)25° C

23.3° C106.0° C176.7° C

Fig. 18. Pressure and temperature dependency of interfacial tension in the methane-water system (Jennings and Newman, 1971; Sachs and Meyn, 1995). Obvious disagreement can be observed between the data at 23.3°C and 25°C.

On the other hand, Firoozabadi and Ramey (1988)suggested a graphical relation with limited success.The empirical correlation uses density difference andreduced temperature as correlation parameters. Finally,more recently, Zuo and Stenby (1998) applied thelinear gradient theory to the modelling of interfacialtension between hydrocarbon and formation water andobtained fairly good results.

Mineral scalingScale formation, the precipitation of inorganic

minerals from brine, either in production facilities orin reservoir pores, is a serious problem in oilproduction. As an example, Fig. 19 illustrates the resultof serious scale formation in a well tube.

The most common types of scale found areCaCO3, BaSO4, SrSO4, CaSO4 and CaSO4·2H2O.Formation of these scales is usually caused bytemperature and pressure change during production,which not only induces supersaturation of one orseveral dissolved minerals, but also changes thesolubility of CO2 and H2S, and thus modifies the pHin the aqueous phase. The solubility of minerals suchas carbonates is dependent on the pH and, therefore,scale may be formed after a change in the pH. Anothercommon reason for scale formation is the mixing ofincompatible water, which can happen during seawater injection.

Thermodynamic modelling of scale formationmainly concerns whether, and how much, scale willform under certain conditions. Most of the modellingwork uses a general model for electrolyte solutions(Atkinson et al., 1991; Yuan and Todd, 1991;Haarberg et al., 1992; Atkinson and Mecik, 1997;Kaasa, 1998). Scale formation modelling ofsulphates is relatively simple while that of carbonatesneeds additional consideration of the pH and thephase distribution of CO2.

References

Aasberg-Petersen K. et al. (1991) Prediction of viscositiesof hydrocarbon mixtures, «Fluid Phase Equilibria», 70,293-308.

Acevedo S. et al. (1999) Thermo-optical studies of asphaltenesolutions. Evidence for solvent-solute aggregate formation,«Fuel», 78, 997-1003.

Ali J.K. (1994) Prediction of parachors of petroleum cuts andpseudocomponents, «Fluid Phase Equilibria», 95, 383-398.

Altgelt K.H., BODUSZYNSKI M.M. (1994) Composition andanalysis of heavy petroleum fractions, New York, MarcelDekker.

Anderko A. (1990) Equation of state methods for the modellingof phase equilibria, «Fluid Phase Equilibria», 61, 145-225.

Andersen S.I. (1994) Concentration effects in HPLC-SECanalysis of petroleum asphaltenes, «Journal of LiquidChromatography», 17, 4065-4079.

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Erling Halfdan Stenby

Wei YanDepartment of Chemical Engineering

Technical University of DenmarkLyngby, Denmark


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1.1 Composition and physical properties of hydrocarbons...saturated hydrocarbons with straight...

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