Szilas A.P. Production and transport of oil and gas, Gathering and Transportation

50

6.

GATHERING AND SEPARATION

OF

OIL

AND GAS

The mole number of gas discharged from the second separator is

nv2=zv2nLl=Zv2zLl"l.

The mole number

of

the hydrocarbon vapour discharged from the third separator

(or simply evaporating from it,

if

the tank is open) is

nv3

=Zv3nL2=Zv3ZLlZL2nl

'

In three-stage separation, the gas-oil ratio is generally the volume ratio of the gas

discharged from the first two stages to the liquid collecting in the third stage (stock-

tank oil), that is,

where

Vmo,

is the molar volume of the gas molecules in the standard state, in

m3/kmoles;

M,,

is the molar mass of the liquid collecting in the third stage, in

kg/kmoles; and

pL3

is the density of the liquid collecting in the third stage, in kg/m3.

Dividing both the numerator and denominator of the above formula by

n,

,

we get

and for two-stage separation,

6.4

-

9

The practical usefulness of equilibrium calculations depends first and foremost on

the accuracy

of

the equilibrium ratios

Ki.

The equilibrium ratio of the ith

component depends, in addition to separator temperature and pressure, also on the

composition

of

the well fluid, and accurate values may only be expected from the

laboratory testing of the fluid to

be

treated. The values

of

Ki

may, however, be

determined in a fair approximation also by various methods based on auxiliary

diagrams. The processes in current use relate the composition of the system to

convergence pressure. It is assumed that

if

two systems

of

hydrocarbons agree as to

convergence pressure, then the equilibrium ratios

of

their components will likewise

be equal at the given pressure and temperature. Hence, in order to find

Ki,

it

is

necessary to know the convergence pressure

of

the system and the equilibrium ratios

belonging to various convergence pressures. Determining in the laboratory the

equilibrium ratios of the components of a given hydrocarbon system at various

pressures and at a given temperature, one obtains families

of

curves similar to the

two families shown in Fig.

6.4

-

2.

These curves all end in one point, lying on the line

K

=

1

and characterized by a certain pressure. The pressure thus determined is the

6.4.

SEPARATION

OF

OIL

AND

GAS

51

apparent convergence pressure. It is

69

bars for the first family shown in the Figure,

and

345

bars for the second (Amyx

et

al.

1960).

If

the laboratory experiment is per-

formed at the critical temperature of the system, then the apparent convergence pres-

sure agrees with the critical pressure.

At

any other temperature, convergence is merely

apparent, because the system has its bubble point at a pressure lower than the

100

K

10

0.1

0.01

0

001

1

10

loo

p,bars

Fig.

6.4-2.

Equilibrium ratios

of

components

of

hydrocarbon systems

of

69

and

345

bars, apparent

convergence pressure; from Natural Gasoline Association

of

America’s

Equilibrium

Ratio

Data

Book

(1957;

used with permission

of

Natural Gas Processors Association)

apparent convergence pressure and there is just one phase instead of two at the

point of convergence. In the zone between the critical pressure and the apparent

convergence pressure, then, the equilibrium constant lacks a physical meaning: the

corresponding curve sections and the point

of

apparent convergence itself are

merely the results

of

extrapolation. The apparent convergence pressure of a given

system

of

hydrocarbons can

be

determined by various means. Its importance is

substantial especially at high pressures.

At

pressures below cca

7

bars, however, the

system’s composition, and hence, knowledge of its exact convergence pressure, lose

much of their importance. Experiment has shown that in establishing the

K

values

required for calculating equilibria in low-pressure separators, a satisfactory

accuracy will be achieved

if

convergence pressure

is

simply assumed to equal

345

bars

(5000

psia). K-isotherms may be found in the NGAA

Equilibrium Ratio

Data

Book

(1957).

Figure

6.4-3

shows the K-isotherms

of

isobutane for an example.

In the usual laboratory-analysis report, it is usual

to

state the content

or

mole

fraction

of

all components heavier than hexane by a single figure denoted

C,,

(heptane-plus). The composition of this mixture of hydrocarbons may vary widely,

52

10

100

500

1000

3000

10000

P,

prio

b’ig.

6.4

3.

liquilihriuni ratios of iwhutane at

So00

psia

apparent convergence pressure; from Natural

(iasoline

Association of America’s

Eyuilihriirn~

Rtrlio

Dtrrci

Book

(1957;

used with permission of Natural

Gas Processors Association)

depending on the composition of the crude in hand. Since, however, the pressure

curves and critical parameters

of

components heavier than hexane differ very little,

the system may be satisfactorily characterized by a median K-value. The

equilibrium ratios

of

this fraction can be estimated using the graphs in

Fig.

6.4-4

(after Katz and Roland in Amyx

et

al.

1960).

Let us finally point

out

that, even

though both the density and molar mass

of

the

C,,

fraction are required

for

equilibrium calculations, only one

of

the two data need be established in the

laboratory, as the other one can be calculated using Cragoe’s formula:

6.4-

10

6.4.

SEPARATION

OF

011

AND

(;AS

53

For the approximation

of

the equilibrium ratios, on the basis

of

the

NGAA

diagrams, numerical relations were elaborated by Canfield and Rowe. Canfield

(1971)

gives the

Ki

equilibrium ratio of the

ilh

component

in

the function

of

the

following parameters:

p,,

apparent convergence pressure; the

p/p,,

pressure ratio

and

TIT,,

temperature ratio; and the

zCi

critical deviation factor:

P

6.4-

11

where

Ai

=

8.0272

-

In

pE,,

-

4.46

1

3

T

and

Bi

=

6.3816

-

29.0020

zCi

+

35.3443

z:i

The correlation, elaborated by Rowe (1978), is based on the fact, that, in case of a

system characterized by a given convergence pressure, the logarithm of the

0

1

10

100

p,bors

Roland

---

Kotr

-

Fig.

6.4

-

4.

Equilibrium ratio

ofC,,

,according

lo

Katz

and Roland (Amyx

ci

ti/.

1960,

p.

341;

used with

permission

of

McGraw-Hill

Book

Company)

equilibrium constants

of

the hydrocarbon components, at any constant pressure

and temperature, changes in a linear way with the square

of

the critical temperature

of the components.

Recently,

to

determine the phase equilibria

of

light hydrocarbons, several

calculation methods, based on the equation

of

state, were elaborated (Kaufmann

1968; Starling 1973; Fussel and Yanosik 1978; Conrad and Gravier 1980). For

hydrocarbon systems, containing also oil, development of such a system seems

to

be

.

54

6.

<iATHIiKING AND SEPARATION

OF

OIL

AND GAS

Molar

mass

Critical temperature

Critical pressure

Critical density

Critical molar

vol.

<;as density (std)

Gas density (rel.)

Liquid density

III

Symbol Unit

M

I

kg

kmole

Tahle

6.4

~

1,

Physical parameters

of

hydrocarbons

CH,

16.042

190.6

46.4

161.9

0.0990

I

0.6750

0.554

299.5*

30.068

305.5

4R.X

203.1

0.

I480

I

.265

1.038

312.6

44.094

370.0

42.6

226.2

0.

I950

1.855

1.522

506.X

*

I'seudo-gravity

Standard

state

is at

7,

=

15.6

C,

pn

=

1.01

bar

irrational, since the quantitative analysis and

so

the characterization of the crude

in

hand is rathcr complicated and expensive.

In

case

of

the

direct use

of

the

NGAA

curves the process

of

calculating the

equilibrium at

low

pressure separation is, as follows:

Equilibrium calculation at low-pressure separation proceeds as follows:

(i)

The

K,

values for the prevailing temperature and pressure are read

off

the

NGAA

graphs

for 345 bars convergence pressure,

(ii)

the equilibrium ratio of the

C,

+

fraction is

read off

Fig.

6.4-4,

(iii)

a value for

zy

is estimated, and

xi

is calculated

for

each

component using Eq. 6.4

-

6.

(iv)

If

1

xi

is unity, then the assumed

zy

is correct, and

so

is, of course,

(1

-z,)=z,,

.

If

xi

differs from unity, the calculation has to be

repeated with a different

zy

.

Equilibrium calculations are usually performed by

computer nowadays, thus bypassing the time-consuming successive approximation

by pencil and paper.

Tah/e

6.4

-

I

contains physical constants published by

CNGA

and

NGAA

for

equilibrium calculations.

Example

6.4

-

I.

With reference to the hydrocarbon system characterized

by

Columns

1

and

2

of

Table

6.4-2,

and assuming three-stage separation,

(1)

what are

the compositions of the gas etluents

of

the individual separator stages?

(ii)

what

will

be the composition of the stock-tank oil collecting in the atmospheric-pressure

stock-tank?

(iii)

what will be the 'useful'

GOR,

that is, the volume

of

gas discharged

from the first two stages

of

separation per m3

of

stock-tank oil? Let separation

temperature be

4

"C

in all three stages, and let pressure be

6

bars in the first stage,

2.1

bars in the second, and

1.01

bar

in

the third. The standard state is at

p.

=

1.01

bar and

T,=

15.6

"C.

The main results of the equilibrium calculation for the three separator stages are

presented

in

Tables

6.4

-

2

-

6.4

-

4.

The

K

values were taken from the diagrams

for

5000

psia convergence pressure

of

the

NGAA

Equilibrium Data Book; the values

m

i-

I

m

i=

I

6.4.

S1:l’AKATION

01-

011

ANI)

(;AS

55

i-C,H,, n-C4Hlc,

58-

120

58.

1

20

407.2 425-0

36.6

38-0

233.0

226.6

0.249

I

0.2578

2.446 2.446

2.006

24.N6

56

1.9

582-3

i-C’sH12

72. I46

461.1

33-2

234.2

0.3078

3.036

2.49

1

623.1

Component

I

CI

c2

C,

I-C,

n-C,

I-C,

n-C,

(-h

C,

+

Total

72.146

470.6

33.5

23

I

.9

0.3

109

3.036

2.491

629.0

114

‘(,ti

]

J

86171

507.8

29

9

234.6

0.367

I

3.626

2-975

662.5

Tahlc

6.4- 2.

First separator stage;

pI

:

6 hars.

1;=~4

(

2

0.7354

0.1

503

0.0

1

20

0.00X7

0.0273

0.0036

0.0045

0.0

I04

09478

3

28.0

3.80

0.94

0.325

0.222

0.080

0.065

0.026

0~0015

I,

I

=

0

0742

z,

,

:

0

925x

____

.y,

I

4

~-

__-_

0.02~3

0.04

I

8

0.0

I

27

0.0232

0.0976

0.0243

0.0335

0.1059

0.6327

1

.oooo

5

for

C,

+

were read

off

Fig.

6.4

-

4.

The composition

of

gas discharged from the three

separator stages is given

in

Columns

5

of

said Tables, whereas the composition

of

the stock-tank

oil

is given in Column 4

of

Table 6.4-4. The useful

GOR

can be

calculated using

Eq.

6.4-8.

In

that relationship, the molar gas volume at the given

parameters

of

state is

R’T,

8.3 14

x

288.8

- -

=

0.02377

m3/mole

=

23.77

m3/kmole

1.01

x

105

Vmo,=

~

Pn

56

6.

GATHERING AND SEPARATION

OF

OIL

AND GAS

1

Let

us

point out that the exact value of the molar gas constant

in

the

S1

system is

R

=

8.3 I433

f

040044

J/mole

K.

We have used the value

8.3

14,

of sufficient accuracy

for

the task

in

hand. We have neglected

z,

,

the compressibility factor

in

the standard

state,

or

have put

it

equal to unity.

For

finding liquid density

pL3

we have used

Fig.

6.4-5,

which is Standing's

nomogram

(1952)

transposed into the

SI

system.

It

furnishes density of a liquid

2 3

Tahle

6.4

-

3.

Second separator stage;

p2

=

2.1

bars,

T2

=

4

'

C

z~.~

=

0.961

2

zv,

=

o.o3xx

Component

zt2

=

x,

I

K,2

3

Y,,

1

2

4

5

05533

03210

0.031

1

0.0196

0.0556

00050

0.0052

0.0066

0.0026

I

~oooo

Cl

c2

c3

i-C,

n-C,

i-C,

n-C,

c6

c,

+

Total:

0.0283

0.04

18

0.01

27

0,0232

0.0976

0.0243

00335

0.1059

0.6327

7x.o

10.5

2.60

0x40

0.560

0200

0.

I

50

0.060

0,004

0.007

1

0.0306

0.0

1

20

0.0233

0,099 3

0.025

1

0.0346

0.1099

0.658

I

1

~oooo

Tahle

6.4-4.

Third separator stage;

p,

=

1.01

bar.

T3=4'C

zI,

,,

=

0.9798

zy

3

=

0.0202

YO3

5

4

0.0016

0.02

I

5

001

10

0.0230

0.0989

0.0254

0.035

I

0.1

I19

0.67 I6

02718

0.4695

0,0593

0.04

I

3

0.1

187

0.0

I09

0.01

I I

0.0

I29

0.0045

Cl

c2

c3

i-C,

n-C,

i-C,

n-C,

c6

c,

+

Total:

0007

1

0.0306

0.0

1

20

00233

0,0993

0.025

1

0.0346

0.

I099

0.693

I

165.0

21.8

5.40

1

.80

1.20

0430

0.3

I5

0.115

0.0067

64

SEPARATION

OF

OIL

AND

GAS

57

1000

,

900

L

?I

E

l

-01

800

1

>

7001

i:

0-

i

600

;

500

400

1

300

1

200

*

I

"00

'OOO

900

..I

PO9

-5

01

1

%C

FOC

500

kCC

300

c-

I

200

Fig.

6.4-

5.

Apparent density

of

crude containing methane and ethane, at

7-

15.6

C and

I)=

1.01

bar.

after Standing

1952

(reproduced by permission

of

the copyright owner -apyright

'('

Chevron Research

Company

1951:

hydrocarbon containing

C,

and

C,.

The starting data are listed

in

Tuhlc

6.4-5.

The density

of

thc liquid containing

C,,

is then,

Mixi3

'+

Mixi3

=

688 kg/m3.

i=3

PLC3

+

=

i

c--

=

3

The content

of

C,

in

the liquid

C,

+

is 0.65 mass percent, and that

of

C,

in

the liquid

C,

+

is 0.03 mass percent. Owing

to

the low values

of

C,

+

and

C,

+,

Fig.

6.4-

5

gives

no

deviation; that is, we may retain

pL3

=

688 kg/m3. From Table 6.4

-

5,

M,,

is

99.48 kg/kmole.

Introduced into

Eq.

6.4-8, the data thus obtained give a

GOR

of

R=

=2185 m3/m3.

(0.9258

+

0.0388

x

00742)

x

23.77

x

688

00742

x

0.96 12

x

0.9798

x

99.48

If

separator pressure exceeds 7 bars,

or

separator temperature is below

-

5

"C,

then it will in general be necessary to determine the apparent convergence pressure

58

6.

GATHERING AND SEPARATION

OF

OIL

AND GAS

Component

I

c,

cz

c,

I-c,

n-C,

I-c,

c,

C,

t

Total:

n-C,

Table 6.4 ~

5.

2

0.00

I6

0.02

1

5

001

10

0.0230

0.0989

0.0254

0.035

1

0.1

119

0.67 16

1

~oooo

30.07

58.12

sx-

12

72.1

5

72.

I5

86. I7

115.0

4

0.03

0.65

0.48

I

.34

5.75

1.83

253

9.64

17.23

99.48

5

506.8

561.9

623.

I

629.0

662.5

7

10.0

582.3

00010

00024

oQo99

0.0029

0.0040

00

146

010x8

01436

and to read the

Kis

off

the corresponding

NGAA

curve family. Since equilibrium

calculations are rather time-consuming,

it

is recommended to find out beforehand

whether two separate phases do exist at all at the temperature and pressure in

question.

If

the well fluid is composed purely of hydrocarbons, this may be found out

as follows.

On

reducing the temperature

of

the mix at a given pressure, the dew point

(E)

is reached first and the bubble point

(H)

is reached thereafter

(Fig.

6.4-6).

If

therefore, e.g.

in

so-called low-temperature separation, well fluid is introduced into

the separator after cooling, it is necessary to examine whether the temperature

before cooling is below the dew point and the temperature after cooling is above the

bubble point.

If

both answers are yes, then the mix is two-phase

in

both cases and

it

P

t

ML

?t

A

Fig.

6.4-6.

Phase diagram

of

natural gas containing

a

significant amount

of

condensate

6.4.

SEPARATION

OF

OIL

AND GAS

59

is worth while to perform the equilibrium calculation.

At

the

dew

point,

one mole

(say)

of

vapour keeps equilibrium with a liquid drop

of

evanescent size. Hence, in a

very good approximation,

z,.

=

0

and

zy

=

1,

and by

Eqs

6.4

-

4 and 6.4

-

6,

m

5

xi=

c

zilKi=l.

6.4-

12

i-

1

i=

1

If

the value obtained is greater than

unity,

the mix is two-phase, because

in

order to

make said value approach unity

it

is necessary to increase the

Kis

and, by

Fig.

6.4

-3.

this requires raising the temperature

if

the pressure is fixed. Now by

Fig.

6.4-6,

this is possible only

if

the mix is

in

the two-phase domain.

At

the

bubble

point,

one

mole (say) of liquid keeps equilibrium with a gas bubble ofevanescent size. Hence,

in

a very good approximation,

zL

=

1

and

zy

=

0,

and Eqs 6.4

-

4 and 6.4

-

7

yield

m

1

yi=

c

ziKi=l.

i-

I

i:

I

6.4

-

13

If

the value of

the

equation is greater than unity, this means once more that the mix

is two-phase. because

in

order to make said value approach unity

it

is necessary to

reduce the

Kis:

now, by

Fig.

6.4-3,

this requires lowering the temperature

if

the

pressure is fixed, and by

Fig.

6.4

-6

this is possible only

if

the

mix

is in the two-phase

domain.

The well fluid often contains some water, too.

It

is necessary to keep

in

mind when

performing calculations concerning such

a

fluid that

the

common

vapour

pressure

qf

immiscible

liquids

is entirely independent of the proportion of the components

in

the

liquid phase, being equal

to

the sum of the vapour pressures of the components,

taken separately at the temperature considered.

Example

6.4-2.

Find the vapour pressure of a water-pentane mix at

50

"C.

H,O

1

~apou;.;;sure

bars

Component

CSH

I2

1.60

On heating this mix, the bubble point will occur at that temperature where the

sum

of

the two vapour pressures equals the external pressure. The bubble-point

temperature of the mix is, then, lower than that of any individual component (water-

vapour distillation). It is often necessary to determine the temperature at which

water starts to condense out

of

the hydrocarbon-water system (that is, to establish

the dew point

of

the mixture.) Since each component generates its partial vapour

pressure independently of the other components, the task is essentially

to

find the

temperature at which the sum

of

partial pressures equals the vapour pressure.

Szilas A.P. Production and transport of oil and gas, Gathering and Transportation

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