resengch12.pdf

CONTENTS

1 INTRODUCTION - THE IMPORTANCE OFVAPOUR-LIQUID EQUILIBRIUM

2 IDEAL SOLUTIONS2.1 Raoult's Law2.2 Dalton's Law2.3 Ideal Equilibrium Ratio

3 NON IDEAL SYSTEMS

4 EQUATIONS FOR CALCULATINGEQUILIBRIUM RELATIONS4.1 Vapour - Liquid Calculations4.2 Dew - Point Calculation4.3 Bubble Point Calculation

5 SEPARATOR PROBLEMS5.1 Gas / Oil Ratio5.2 Oil Formation Volume Factor5.3 Optimum Pressure of Separator System5.4 Example of Separator Problem

1212Vapour Liquid Equilibria

2

LEARNING OBJECTIVES

Having worked through this chapter the Student will be able to:

Define equilibrium ratio.

Derive equations for vapour-liquid equilibrium calculations for real systemsand explain the application of the equations.

Derive and explain the use of equations to determine the dew point pressure andbubble point pressure of a fluid mixture.

Describe in general terms the impact of separator conditions the gas-oil ratioand oil formation volume factor.

Department of Petroleum Engineering, Heriot-Watt University 3


1 INTRODUCTION - THE IMPORTANCE OF VAPOUR-LIQUIDEQUILIBRIUM

The multiphase perspectives of hydrocarbon mixtures in and produced from reservoiraccumulations are an important aspect in reservoir management, well productivity,facility design and pipeline transport.

Predicting the relative amount of the phases and their respective physical propertiesis an essential element in all of the above operations. The topic of vapour-liquidequilibria is also at the heart of many subsequent and other process operations andtherefore there have been a range of approaches into the solution of the problem.

The behaviour in reservoirs of multicomponent mixtures and their production tosurface has provided one of the most rigorous challenges to design engineers becauseof the complex and unique nature of the fluids and in many cases their behaviour nearthe critical point.

Figure 1, and 2 illustrate the complex nature of oil and gas production where,particularly in a major offshore province, as well as onshore, a number of reservoirsproduce into a common transport line and associated treatment facilities (Figure 1).Each of the fields with their unique composition clearly contribute to a compositionalblend entering a treatment facility (Figure 2), where further separation occurs.

CUSTOMERS

ONSHORE FACILITIES

OFFSHORE FACILITIESOFFSHORE FACILITIES

RESERVOIRRESERVOIR

WELLS WELLS

Figure 1

The total system

4

CHEMICALFEEDSTOCK

FUEL OIL SALES& TAXES

FIELD B

Composition = (TA*CA)*(TB*CB)+(TC*CC)

Throughput = TA + TB + TC

TA + TB + TC

Composition CBThroughput TB

FIELD A

Composition CAThroughput TA

FIELD C

Composition CCThroughput TC

TERMINAL

The allocation of revenue based on quality of product and oil injected into a commonpipeline provides a considerable challenge to metering and compositional analysis.

To the reservoir engineer, the main issues are the multiphase behaviour in theformation and the relationship between the fluids in the reservoir and those producedat surface conditions.

The critical element in reservoir simulation is the grid block where the saturations andflow behaviour of the respective fluids; gas, oil and water are required. The grid blocktherefore can be considered as a separator and vapour-equilibrium calculations arerequired out to determine the relative amounts of the phases which lead to saturationvalues and relative permeability of the phases, and the composition of these phaseswhich lead to important physical property values of density, viscosity and interfacial tension.

In the previous chapter the considerations of the relative amounts of gas and liquidwere considered in the simplistic two component black oil approach. In this chapterwe will consider approaches to vapour-liquid equilibrium from a compositionalmodel consideration both from an ideal behaviour perspective and then the considera-tion of real systems.

Figure 2

Complexity of allocation of

produced oil to supply fields



On a pressure temperature phase diagram of a multi-component mixture, the areabounded by the bubble point and dew-point curves defines the conditions for gas andliquid to exist in equilibrium. It is an over-simplification to describe the system asinvolatile oil with associated solution gas. The behaviour of the individual compo-nents and their influence on the composition of the mixture need to be considered.

If a sample of bubble point fluid is brought to surface to separator conditions, the fluidenters the two phase region at a temperature and pressure much lower than reservoirconditions. In the separator the liquid and gas phases, in equilibrium, are withdrawnseparately. Large volumes of gas are formed at these separator conditions, and theliquid volume shrinks substantially because of decreased temperature and conversionof some of the fluid into the gas phase. The separator liquid is collected in the stocktank, at which additional temperature and pressure drop may occur, more gas may bereleased depending on the separator conditions to stock tank conditions.

If Vo is the volume of liquid at reservoir conditions and V

st is the volume of stock tank

oil. The oil formation volume factor Bo is :

BV

Voo

st

=

If Vg and V

st are the total volume of gas and oil collected from the separator and stock

tank. The solution gas to oil ratio is :

RV

Vsg

st

=

The volume factors can be determined directly in the laboratory or from equilibriumcalculations.

In addition to separator calculations vapour liquid equilibrium data can be used for:

Reservoir calculations

Two phase pipeline flow calculations

Process calculations

Although phase behaviour considerations are required throughout the productionprocess from reservoir to refinery the context of this particular chapter is in relationto reservoir predictions. When reservoir fluids undergo phase alteration as a result ofchanges in pressure, temperature or composition it is considered that these changes areslow and therefore the resulting separate phases are in equilibrium, i.e the propertiesof the phases are not changing with respect to time.

For multicomponent phase behaviour predictions thermodynamic principles havebeen applied to provide the predictive tools. Many works have been written which

6

provide the foundation of the topic. Danesh1 in his text provides a good review of thetopic both with respect to the foundation principles and the equations used.

Vapour-liquid equilibrium calculations have been somewhat restricted to analysis ofbehaviour with the separate areas, i.e. reservoir and wells, surface separation,pipelines, onshore treatment and refininery operations. Increasingly in the modernmultidisciplinary approach to technical management there is an interest in theintegrated perspective of vapour liquid equlibrium. For example, what is the impacton the quality of product exiting from a multifield oil transport line of a pressurechange in field X. Such integrated perspectives provide a considerable technical andcommercial challenge to the various technical disciplines which have been separatelyinvolved.

2 IDEAL SOLUTIONS

Before we consider the behaviour of real systems we will first examine the behaviourof an ideal solution, where no chemical interaction occurs and where no inter-molecular forces occur when mixing components.

These ideal solutions result in no heating effects when ideal solutions are mixed andthe volume of the mixture equals the sum of the volumes the pure components wouldoccupy at the same pressure and temperature.

2.1 Raoults LawRaoults equation states that the partial pressure of a component in the gas is equalto the product of the mole fraction, x

j in the liquid, multiplied by the vapour pressure

of the pure component pvj.

pj = x

jp

vj(1)

where pj is the partial pressure of component j in the liquid with a composition x

j and

pvj is the vapour pressure of the pure component j.

2.2 Daltons LawDaltons law states that the partial pressure of a component p

j is equal to the mole

fraction of that component in the gas, yj times the total pressure of the system p, i.e.

pj = y

jp

(2)where y

j is the composition of the vapour and p is the pressure of the system

2.3 Ideal Equilibrium RatioBy combining the above two laws,

yjp = x

jp

vj(3)

y

x

p

pj

j

vj= (4)



i.e. the ratio of the component in the vapour and liquid phases is given by the ratio ofthe vapour pressure of the pure component to the total pressure of the system. Thisratio is termed the Equilibrium ratio, Kj .

If n is the total number of moles of mixture and zj is the mole fraction of component

j in the mixture.

zjn = x

jn

L + y

jn

g(5)

where nL and n

g are the moles of liquid and gas such that n

L + n

g = n

From equation 4.

z n x n xp

pn

xz n

np

pn

j j L jvj

g

jj

Lvj

g

= +

=+

(6)

xj by definition = 1.0

xz n

np

pn

jj

cj

Lvj

gj

c

=+

== =

1 1

1 0.

. (7)

Similarly:

yz n

np

pn

jj

cj

gvj

Lj

c

=+

== =

1 1

1 0.

. (8)

If a basis of one mole of mixture is used i.e. n g + n

L = 1.0

xz

j = jjg

vjnp

p1 1

1 0

+

= . (9)

jj

L

vj

yz

np

p1 1

1 0=

+

= . (10)

Using these equations in a trial and error method the compositions of vapour and liquidstreams in a flash separation can be determined.

8

The equilibrium ratio Kj is defined as the ratio of the composition of j in the vapour

to liquid phase, i.e.

jj

j

Ky

x= (11)

Clearly Kj is defined at a particular pressure and temperature.

Other names for Equilibrium ratio, include K-factors, K-values, equilibrium vapour-liquid distribution ratios.

FugacityLewis2 introduced the concept of fugacity, for use in equilibrium calculations, toextrapolate or correct vapour pressures. This is required since a pure component onlyhas a vapour pressure up to its critical point. The fugacity is a thermodynamic quantitydefined in terms of the change in free energy in passing from one state to another.

For an ideal gas , the fugacity is equal to its pressure, and the fugacity of eachcomponent is equal to its partial pressure. The ratio of fugacity to pressure is termedthe fugacity coefficient, . For a multicomponet system,

i

i

f

Pz= (12)

All systems behave as ideal gases at very low pressures, therefore > 1 when P > 0

When fugacities are not 1 , then this gives an indication of non-ideality.

Fugacity has been imagined (Danesh)1 as a measure of the escaping tendency ofmolecules from one phase to an adjacent phase. In multicomponent systems, if thefugacity of a component in adjacent phases is the same, the two phases will be inequilibrium with no net transfer of molecules from one phase to another. Atequilibrium therefore

fg = f

L. (13)

The fugacity coefficient, of a pure component can be calculated from the followinggeneral equation (Danesh).

ln ln =

= ( ) +

zp

dp z zRT

RTv

P dvo

p v11

1 (14)

The ratio of the fugacity at the state of interest to that at a reference state is called theactivity

i = f

i/f

io

The activity is a measure therefore of the fugacity contribution or activeness of thecomponent in a mixture. f

i =

if

io .

The ratio of activity to concentration is called the activity coefficient i, where



i =

i/x

i

Therefore fi=

ix

if

io (15)

3 NON IDEAL SYSTEMS

Ideal solution assumptions cannot be applied to the systems relevant to multicomponenthydrocarbon fluids in reservoir flow, transport and processing conditions. The idealassumptions only apply to low pressures and moderate temperatures, chemically andphysically similar components and behaviour below the critical point.

Different methods have been developed for treating vapour-liquid equilibrium for nonideal systems.

The previous K value is based on both ideal and ideal solutions laws. To extend theprinciple of equilibrium ratio to multicomponent hydrocarbon mixtures to thepressures and temperatures relevant to petroleum engineers, methods of treating nonideal systems need to be established.

The subject of non ideal equilibrium ratios are treated later in the text. We assume inthis section that K values are available either from whatever source, experimental,NGPSA data charts, or from equations of state and other predictive methods.

4 EQUATIONS FOR CALCULATING EQUILIBRIUM RELATIONS

4.1 Vapour-Liquid CalculationsThe calculations for determining the amount of liquid and vapour present in a mixturewhen the pressure and temperature is known are obviously important, for example, inoptimising the performance of a separator process.

The equilibrium equations which are used for a process separator are the same as thosewithin a grid block or element of a reservoir simulator.

Figure 3 represents such a separation element.

T & PF

zj

V

yj

L

xj

Figure 3

Vapour-liquid separation in

an element

10

F = total moles of system both liquid and gasL = total moles of material within liquid phaseV = total moles of material within vapour phasez

j= mole fraction of jth component in the mixture

xj

= mole fraction of jth component in the liquidy

j= mole fraction of jth component in the vapour

It is common to express the feed F as 1.0 or 100 moles and express L and V as fractionsor percentages of F.

i.e. F = 1 = L + V (16)

For component j

zjF = x

jL + y

jV

For F = 1.0 mole

zj = x

jL + y

jV (17)

The equilibrium ratio:

jj

j

Ky

x= (18)

By definition:

jj

m

jj

m

jj

m

x y z1 1 1

= = = = =

=1 (19)

where m is the number of components.

Replacing yj by K

jx

j in (17)

zj = x

jL + x

jK

jV

zj = x

j (L + K

jV)

dividing both sides by L + KjV

xz

L K Vjj

j

=+ (20)

and:

jj

mj

jj

m

xz

L K V1 0

1 1

=+

= = =

. (21)

similarly:



yz

V L Kjj

mj

jj

m

= = = + =1 1

1 0. (21a)

by multiplying (21) by V we get:

zLV

KVj

jj

m

=

+=

1

(22)

and (21a) in the same way:

zL

K V

Vj

j

j

m

=

+=

1 1

(22a)

These equations are the key equations in vapour-liquid equilibrium calculations andtheir use is the same whether in those calculations to determine phase behaviour in aseparator or those which take place within the numerous grid blocks of a reservoirsimulator. Clearly in the latter the amount of calculations is considerable since eachgrid block can be considered a separator. In a large compositional based simulationa study thousands of grid blocks will be used.

The method of calculation is therefore as follows for each separation element:

(1) Select Kj for each component at the temperature and pressure of the system;

(For the determination of K see the later section.)

(2) Assume a vapour liquid split i.e. V&L such that V + L = 1.0;

(3) Calculate either V, L, xj or y

j from equation 21, 21a, 22 and 22a;

(4) Either:(i) check V&L calculated against assumed V or L;(ii) determine if x

j or y

j = 1.0;

(5) Repeat the calculation until assumed value is calculated value or until xj and

yj = 1.0.

It can be understood therefore that in a compositional reservoir simulator a consider-able amount of computational time is taken up because of these iterative calculationsat each grid block. In a black oil simulator no such iteration takes place the specificpressure and temperature provide the direct phase values either from a PVT report oran empirical black oil correlation.

This phase equilibrium perspective can also be used to calculate the reservoirsaturation pressures for a particular temperature, ie. the dewpoint and bubble pointpressures.

12

4.2 Dew-Point CalculationThe dew-point is when the first drop of liquid begins to condense. At this point thecomposition of the liquid drop is higher in heavier hydrocarbons whereas thecomposition of the vapour is essentially the composition of the system: Figure 4.

Vapour yj = Zj

Liquid Xj VapourLiquid

At the dew point therefore:

zj = y

j(22)

or: zj = x

jK

j

The mixture at the dew-point is therefore in equilibrium with a quantity of liquidhaving a composition defined by the above equation. Clearly:

xz

Kjj

mj

jj

m

= = = =

1 1

1 0. (23)

Similarly for the bubble point.

4.3 Bubble Point CalculationThe bubble point is when the first bubble of gas appears. At this point the compositionof this bubble of gas is higher in lighter hydrocarbons whereas the composition of theliquid is essentially the composition of the system. Figure 5.

Vapour = Yj

Liquid Xj = Zj Vapour

Liquid

At the bubble point therefore:

zj = x

j(24)

or:

zy

Kjj

j

=

The mixture at the bubble point is therefore in equilibrium with a quantity of liquidhaving a composition defined by the above equation.

Figure 4

Conditions at the Dew

Point

Figure 5

Conditions at the Bubble

Point.



Also:

y z Kjj

m

j jj

m

= = = =

1 1

1 0. (25)

The dew-point and bubble point when either temperature or pressure are known aredetermined by trial and error techniques until the above relationships are satisfied.

The dew-point pressure or bubble point pressure are estimated, K values obtained andequations 23 or 25 checked. If the summation 1, different pressure values are trieduntil convergence is reached. When convergence is reached the respective dew pointor bubble point pressure has been obtained.

5 SEPARATOR PROBLEMS

In a separator a stream of fluid is brought to equilibrium at separator temperature andpressure. Vapour and liquid are separated within the unit and continue as separatestreams. Several separators can be operated in series each receiving the liquid phasefrom the separator operating at the next higher pressure.

Each condition of pressure and temperature at which vapour and liquid are separatedis called a stage-separation. Hence a process using one separator and a stock tank isa two stage process a three stage process has two separators and one stock tank. (Figure 6).

Separator calculations are performed to determine the composition of products, the oilformation-volume factor and the volume of gas released per barrel of oil and todetermine the optimum separator conditions for the particular conditions of fluid.

Using equilibrium calculations already derived we can calculate the separationachieved at each stage, the composition of the phases separated, the gas/oil ratio, andthe oil formation volume factor.

14

Feed

Vapor Vent

Liquid

To pipeline / tanker

Separatorat Psep and Tsep

Stocktankat Pst and Tst

Two-stage separation

Feed

1st stage vapor Vent

Liquid

2nd stage vapor

Liquid

To pipeline / tanker

1st stage separatorat (Psep)1 and (Tsep)1

2nd stage separatorat (Psep)2 and (Tsep)2

Stocktankat Pst and Tst

Three-stage separation

5.1 Gas/Oil RatioGas is removed from each stage so that the solution GOR can be calculated for eachstage or combination of stages.

Total gas / oil ratio =sum of gas volumes (SCF)

volume of stock tank oil (bbl)= RT

(a) Calculation for Stock Tank Oil, STO.

If n1 moles enter first stage, moles of liquid entering 2nd = n

2 = n

1L

1.

where L1 = separation in stage one based on basis of one mole feed.

Number of moles entering third stage n3 = n

2L

2 = L

2L

1n

1

If third stage is the stock tank then:

nST

= L3n

3 = L

3L

2L

1n

1

nST

is the moles of liquid in stock tank for n1 moles into first separator:

n n LST ii

m

= = 1

1

(26)

m = number of stagesL

i= mole fraction of liquid off ith stage

n1

= moles of feed to first stage

Figure 6

Schematic drawing of

separation process.



If n1 = 1

then:

nST ===Lii

m

1

(27)

nST ===Lii

m

1

= mole fraction of STO in the feed.

(b) Calculation of Total Gas

ngi = number of moles off stage i

ng1

= V1n

1

ng2

= V2n

2 = V

2L

1n

1

ng3

= V3n

3 = V

3L

2L

1n

or in general for total gas:

= == = =

n n n V LgT gii

m

ii

m

jj

i

11

1 1

1

If nj = 1

== =

n V LgT ii

m

jj

i

1 1

1(28)

ngT

= mole fraction of total gas in the feed

Total gas volume per mole of feed =ngT

Vmcu ft where V

m is the molar volume

5.2 Oil Formation Volume FactorVolume of stock tank oil per mole of feed

( ) =V n MST mST ST

ST(29)

MST

= molecular weight of stock tank oil

n sT

= moles of STO per mole of feed

ST

= density of STO at standard conditions lb/bbl

Total gas to oil ratio RT =

16

=( )

=Rn VV

n Vn MT

gT m

ST m

gT m ST

ST ST

(30)

where RT is the total gas - oil ratio.

If the feed to the first stage is a single-phase liquid into its point of entry into theproduction stream then B

o can be calculated.

res.

= density of feed (lb/bbl)

Volume of reservoir oil per mole = Vres

= Mres

/res

Oil formation volume factor Bo =

=( )

=BV

VM

M nores

ST

res ST

res ST ST

(31)

where

=Mres molecularmolecular weight of reservoir fluidlb res

lb mol

..

=

and

nlb mol stock k fluid

lb mol res fluidST. . tan

. . .=

5.3 Optimum Pressure of Separator SystemThe operating conditions of pressure and temperature of a separator influence theamount of gas and stock tank oil produced. Change in these valves will change theGOR and the Bo. In quoting these values therefore it is important to keep note of theassociated separation conditions of pressure and temperature. A number of units inseries also influence these parameters. It is the role of the process designers tooptimise the operating conditions of such limits and the number of units required.

It is the equilibrium characteristics of the individual components as a function oftemperature, pressure and composition which influence these total separationcharacteristics for the mixtures at each separation stage.



1.36

1.34

1.32

1.30

1.28

1.26

1.24140120100806040200

480

500

520

540

560

580

600

32.4

32.6

32.8

33.0

33.2

33.4

33.6

First-stage separator pressure, psi

Sep

arat

or +

sto

ck ta

nk g

as-o

il ra

tio, s

cf/b

bl

stoc

k ta

nk g

ravi

ty,

AP

I at 6

0F

Form

ation volume factor

Total gas-oilratioA

PI g

ravi

ty

Formation volum

e factor

Figure 7 illustrates the influence of a change of pressure for a two-stage separationprocess on GOR, B

o and the density of stock tank oil.

Equilibrium flash calculations, which the above are called, are used in many otherapplications. In reservoir engineering, flash calculations are at the core of compositionalsimulation.

5.4 Example of Separator Problem (McCain)4

The following example is taken from McCains text on Petroleum Fluids and thevalues for K used in the calculations come from the NGPSA sources5.

Calculate the gas-to-oil ratio, stock-tank oil gravity and formation-volume factorwhich will result from a two-stage separation of the hydrocarbon mixture below. Useseparator conditions of 76F and 100 psig. Assume that the mixture is a liquid at itsbubble point at reservoir conditions of 2,695 psig and 220F.

Component Mole Fraction Gravity API at 60F Molecular 60/60 WeightMethane 0.3378Ethane 0.0694Propane 0.0982i-butane 0.0133n-butane 0.0299i-pentane 0.0125n-pentane 0.0193Hexanes 0.0299Heavier 0.3897 0.8859 28.2 263 1.0000

Figure 7

Effect of separator pressure

in a two-stage separation

process

(Amyx, Bass & Whiting)

18

Step 1: Calculate the composition and quantities of separator gas and liquidusing equation 21.

xz

L K Vjj

j = + = 1 0.

Component Component, Equilibrium zjof feed to mole ratio at L+KjV separator fraction zj 114.7 psia V=0.43 and 76F Kj V=0.42 V=0.4291C1 0.3378 20.8 0.03626 0.03551 0.03557C2 0.0694 4.07 0.03031 0.02991 0.02995C3 0.0982 1.16 0.09202 0.09188 0.09189i-C4 0.0133 0.495 0.01688 0.01699 0.01698n-C4 0.0299 0.343 0.04129 0.04167 0.04164i-C5 0.0125 0.142 0.01954 0.01985 0.01978n-C5 0.0193 0.108 0.03086 0.03131 0.03127C6 0.0299 0.0334 0.05033 0.05117 0.05109C7+ * 0.3897 0.00150* 0.67117 0.68291 0.68184 1.000 0.98866 1.0015 1.00001* Used K for C9

x=

The summation equals 1.0 when V1 = 0.4291 and L

1 = 0.5709 and the compositions

of the separator gas and liquid are:

Component xj = zj L+KjV yj=kjxj

C1 0.0356 0.7399C2 0.0299 0.1219C3 0.0919 0.1066i-C4 0.0170 0.0084n-C4 0.0416 0.0143i-C5 0.0198 0.0028n-C5 0.0313 0.0034C6 0.0511 0.0017C7+ 0.6818 0.0010 1.0000 1.0000

Step 2: Calculate the compositions and quantities of stock tank and liquid usingequation 21, noting that the composition of the feed to the stock tank is the compositionof the liquid from the separator.



Component Component, Equilibrium zjof feed to mole ratio at V=0.13 L+KjV V=0.1351separator fraction zj 14.7 psia V=0.14 and 76F, KjC1 0.0356 161 0.00163 0.00152 0.00157C2 0.0299 30.7 0.00615 0.00580 0.00597C3 0.0919 8.15 0.04763 0.04593 0.04674i-C4 0.0170 3.27 0.01313 0.01290 0.01301n-C4 0.0416 2.30 0.03559 0.03519 0.03538i-C5 0.0198 0.90 0.02006 0.02008 0.02007n-C5 0.0313 0.675 0.03286 0.03279 0.03274C6 0.0511 0.20 0.05703 0.05755 0.05729 C7+* 0.6818 0.0089* 0.78264 0.79164 0.78720 1.0000 0.99654 1.00340 1.00000

* Used K for C9

xj=

The summation equals 1.0 so VST

= 0.1351 and LST

= 0.8649 and the compositions ofthe stock tank gas and liquid are:

xj yj = Kjxj0.016 0.25340.0060 0.18310.0467 0.38100.0130 0.04250.0354 0.08140.0201 0.01810.0327 0.02210.0573 0.01150.7872 0.00701.0000 1.0001

Step 3: Calculate the density and molecular weight of the stock tank oil.

Component Component, Molecular Weight Liquid Liquidof stock mole weight density at volume attank oil fraction 60F and 60F and xj Mj xjMj 14.7 psia 14.7 psia oj xjMj / ojC1 0.0016 16.0 0.026 C2 0.0060 30.1 0.181 C3 0.0467 44.1 2.059 31.66 0.0650i-C4 0.0130 58.1 0.755 35.12 0.0215n-C4 0.0354 58.1 2.057 36.45 0.0564i-C5 0.0201 72.2 1.451 38.96 0.0372n-C5 0.0327 72.2 2.361 39.35 0.0600C6 0.0573 86.2 4.939 41.30 0.1196 C7+ 0.7872 263 207.034 55.25 3.7472 Total 1.0000 220.863 4.1069 cu.ft. C3+ C3+ = 220.656 lb.mole STO C2+ = 220.837 MSTO = 220.863 lb lb mole

20

Density of propane plus = =220 6564 1069

53 73.

..

lbcu ft

Weight fraction ethane in ethane plus = =0 181

220 8370 001

..

.

Weight fraction methane in STO = =0 026

220 8630 0001

..

.

= 53.73lb

cu.ft.STO From chapter 6, figure 13.

= =53.7362.4

0.86STO

= =API141.50.861

131.5 32.8o

Step 4: Calculate gas to oil ratio

=

R

VL L

lb moles sep gaslb mole STO

379SCF sep gas

lb mole sep gas5.615M

lb mole STOSTBSP

1

1 ST STOSTO

RSPSPSTO

ST STO

VL L M

= 2130 11

Similarly:

STSTO

STO

RV

L M=

2130 22

RT = R

ST + R

SP

SPRSCFSTB

=( )( )( )

( )( )( )=

2130 0 4291 53 730 5709 0 8649 220 9

450. .

. . .

STRSCFSTB

=( )( )( )

( )( )=

2130 0 1351 53 730 8649 220 9

81. .

. .

TRSCFSTB

= 531

Step 5: Calculate the density and molecular weight of the reservoir liquid at reservoirconditions.



Component Component, Molecular Weight xjMj Liquid Liquidof reservoir mole weight Mj density at volume atliquid fraction xj 60F and 60F and 14.7 psia 14.7 psia j xjMj / jC1 0.3378 16.0 5.405 C2 0.0694 30.1 2.089 C3 0.0982 44.1 4.331 31.66 0.1368i-C4 0.0133 58.1 0.773 35.12 0.0220n-C4 0.0299 58.1 1.737 36.45 0.0477i-C5 0.0125 72.2 0.902 38.96 0.0232n-C5 0.0193 72.2 1.393 39.35 0.0354C6 0.0299 86.2 2.577 41.30 0.0624 C7+ 0.3897 263 102.491 55.25 1.8550 1.0000 Mor =121.699 2.1825 cu.ft.C3+ lb / lb mole res oil lb.mole res oil C2+ = 116.294 C3+ = 114.205

Density of propane plus = =114.2052.1825

52.33lb

cu ft

Weight fraction ethane in ethane plus = =2 089

116 2940

..

.018018

Weight fraction methane in reservoir oil = 5 405

121 6990 044

..

.=

po

= 49.1 lb.cu ft. From figure 13, Chapter 6.

From figure 14 chapter 6compressibility correction 49.1 + 0.8 = 49.9 at 60F and 2710 psia.

From figure 15 chapter 6thermal expansion correction 49.19 - 3.86 = 46.04 at 220F and 2710 psia.

or = 46.04 lb/cu ft.

Step 6: Calculate formation volume factor using equation:

BMM L L

B 1.302res bblSTB

ores STO

res STO 1 ST

o

=

=( )( )

( )( )( )( )

=

Bo121 7 53 73

46 04 220 9 0 5709 0 8649. .

. . . .

22

Integration of the Black-Oil and Compositional ApproachThe example above illustrates the combination of the compositional based predictionof phase volumes and associated properties and that based around the black-oil model,centered around parameters of oil formation volume factor and gas-oil ratio. By sucha combination, the weaknesses of the simple two component black-oil model whichis at the heart of describing oil field parameters, can be overcome by using compositionalderived values rather than using perhaps inappropriate empirical correlations andcharts.

Determination of K valvesIn the procedures developed, it has been assumed that values for K are available. Inthe next chapter we will examine the procedures for determining K.



REFERENCES

(1) Danesh, A, "PVT and Phase Behaviour of Petroleum Reservoir Fluids." 1998Elsevier. pp 105-206

(2)Prausnitz,J.M., Lichtenthaler,R.N., and d Azevedo,E.G. MolecularThermodynamic of Fluid -Phase Equilibria 2nd Edition, Prentice Hall Inc, NY.,(1986)

(3) Smth,J.M. and Van Ness,H.C. Introduction to Chemical EngineeringThermodynamics, Third Edition, McGraw-Hill ( 1975)

(4) McCain,W.D. The Properties of Petroleum Fluids Petroleum Publishing Co.Tulsa 1973

(5) GPSA: Engineering Dat Book, Gas Processors Association. Tulsa Oklahoma, GnEducation 1972

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