11 HC Phase Behavior

8/16/2019 11 HC Phase Behavior

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SKPP 2313RESERVOIR ROCK & FLUID PROPERTIES

Ch. 11a – Qualitative Hydrocarbon Phase

Behavior

Assoc. Prof. Abdul Razak Ismail

Petroleum Engineering Dept.Faculty of Petroleum & Renewable Energy Eng.

Universiti Teknologi Malaysia

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Assoc. Prof. Abdul Razak Ismail, UTM


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Contents

• Single component

• Two Components

• Multi-Components


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Three factors are important to the behavior of molecules:

1. Pressure - a reflection of the number of molecules present and their motion. P is a

reflection of the number of times the molecules of a gas strike the walls of the container.

As the molecules are forced closer together the P increases.

2. Temperature - a reflection of the kinetic energy of the molecules. T is simply a physical

measure of the average kinetic energy of the molecules of the material. As heat is added tothe material the kinetic energy of the molecules is increased, and, as a result, T is increased.

The increase in kinetic energy causes an increase in molecular motion which results in a

tendency for the molecules to move apart.

3. Molecular attraction and repulsion. Intermolecular forces change with distance between

the molecules. The attractive force increases as the distance between the molecules

decreases until the molecules get so close together that their electronic fields overlap. Anyfurther decrease of the distance between the molecules will cause a repulsive force between

them. This repulsive force will increase as the molecules are forced closer together

P and molecular attraction tend to confine the molecules and pull them together,

whereas T and molecular repulsion tend to separate the molecules.

Pressure, Temperature and Intermolecular Forces


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• Phase - any homogenous and physically distinct part of a system which is separated

from other parts of the system by definite bounding surfaces.

– For example, ice, liquid water, and water vapor are three phases.

– Each is physically distinct and homogenous and there are definite boundaries

between ice and water, between ice and water vapor, and between liquid water

and water vapor. – It is not necessary for any one particular phase to be continuous. For example,

the ice may exist as several lumps in the water.

– Thus, we say that we have a three-phase system: solid, liquid, and gas.

• Component - the smallest number of independently variable constituents by means

of which the composition of each phase can be expressed for a system at

equilibrium.

– For example, the ice-water-water vapor system mentioned above consists of one

component.

– On the other hand, the single phase consisting of natural gas may contain eight

or more components.

Definition of Phase and Component


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• Intensive properties are independent of the quantity of material present.

– Examples: density, specific volume, and compressibility factor

• Extensive Properties are determined by the total quantity of matter present

such volume and mass

Definition of Intensive and Extensive properties


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Phase diagram for single component (pure substance)

• A phase diagram is a graph of P vs T which shows the conditions underwhich the various phases of a substance may be present.

• Phase diagrams are often called P-T diagrams.

The vapor-pressure line (line TC):

This line divides the liquid region from

the gas region. Points which fall on theline indicate conditions of both gas and

liquid coexist.

The critical point (C):

The upper limit of the vapor-pressure

line, critical temperature, Tc and thecritical pressure, Pc. Temperature above

Tc, a gas cannot be liquefied, regardless

of the pressure applied. Similarly,

pressure above Pc, liquid and gas cannot

coexist regardless of the temperature.


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The triple point (T):

This point represents the P & T at which

solid, liquid, and gas coexist underequilibrium conditions.

The sublimation pressure line:

At temperatures below the triple-point, the

vapor-pressure line divides the region

where the substance is solid from theregion where the substance is gas.

Theoretically this line extends to a

temperature of absolute zero.

The melting-point line:

The nearly vertical line above the triple point separates the solid region from theliquid region. Again, pressure-temperature points which fall exactly on this line

indicate a two-phases system; in this case coexistance of solid and liquid. Phase

diagrams for some pure materials show other lines within the solid region indicating

a change of phase of the solid brought about by a change in crystalline structure.

The upper end of the melting-point line has not been obtained experimentally.


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Vaporization of a pure substance at constant T

Phase diagram for a pure substance at isothermal expansion• Line 1-2: As mercury is removed the P will decrease until

it reaches a value of Pv.

• At this point a gas phase will begin to form as molecules

leave the liquid.

• As mercury removal continues, the gas phase volume

will increase and the liquid phase volume will decrease.

However, the pressure will remain constant at pv.• Once the liquid phase disappears, further mercury

removal causes a decrease in pressure as the gas phase

expands.

• Above the Tc, i.e. line 3 - 4, the removal of mercury will

cause a decrease in pressure; however, there will not be

an abrupt change in the density., and no phase change.

• Consider a cylinder in which the temperature can be

controlled and the volume varied by injection ofmercury as shown.

• Figure shows that a pure substance has been trapped in

the cylinder at pressure P1 and T < Tc.

• Remove mercury at constant temperature, thereby

causing the pressure to be reduced.


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Phase diagram at isobaric temperature change

• Increasing the temperature from T1 to T2 at a constant

pressure. T increases by the addition of heat and maintain

the P constant by removal of mercury as required. Cell A

full of liquid at temperature T1 (less than the vapor-pressure

temperature of the substance).

• In cell B the substance has been heated at constant pressure

to the vapor-pressure temperature. A gas phase has formed

and gas and liquid coexist. The injection of heat has causedthe kinetic energy of the molecules to increase so that the

molecules with the highest kinetic energy can escape the

attractive forces and pressure and form a gas phase.

• After the vapor-pressure temperature is reached, heat that is

put into the cylinder causes vaporization of the liquid rather

than increase of the temperature. The temperature will

remain constant as long as gas and liquid co-exist.• Cell D indicates that enough heat has been put into the

cylinder to evaporate all the liquid and additional heat has

caused an increase in temperature to T2.

• The same process at pressures above the critical pressure,

for example line 3-4 , will not show the abrupt change in

phase that the process below the critical pressure shows.


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Vapor Pressure of Normal Paraffins

(Data from M. W. Kellogg Co.)


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Vapor Pressure of Isomeric Paraffins

(Data from M. W. Kellogg Co.)


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Typical Pressure-Volume diagram for a

pure substance

Two isotherms:

• 1 - 2 below critical temperature

• 3 - 4 above critical temperature.

Bubble point and dew point

• At point 1 the substance is in liquid phase, at constant T, the P is

reduced from P1 to vapor P (Pv) by removal of mercury.

• A relatively large change in P results from a small change in

volume. This is because liquids are relatively incompressible.

• When the P is reduced to the Pv, gas begins to form and further

removal of mercury causes vaporization of the liquid. This

continues at constant P until all the liquid is vaporized (a straight

horizontal line)• After all the liquid is vaporized, continued removal of mercury

causes expansion of the gas and reduction in P. Since the gas is

highly compressible, the slope of the gas line is much less steep

than the slope of the liquid line.

• Line 3- 4 illustrates the same process at a T above Tc. The line

shows that there is simply an expansion of the substance

and that no phase change occurs.• Point where the first few molecules leave the liquid and form a

small gas bubble is the bubble point.

• Point where only small drop of liquid remains is the dew point.

• The sharp breaks in the line represent the bubble point and

dew point.

• For pure substance the P at the bubble point and dew point are

equal to the Pv

at T.


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Phase behavior of a single component HC 3D diagram of a single component system


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Density-temperature diagram for a pure substance

• The shape of a typical density-temperature

diagram.

• The line shows the densities of the liquid

and gas phases that coexist in the two-

phase region. Often these are called the

saturated densities.

• Notice that the density of the liquid and

gas become the same at the critical point.

• The average densities (dashed line) of the liquid and vapor will plot as a straight line which passed

through the critical point.

• Known as the Law of Rectilinear Diameters.


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Two component systems (binary system)

P-T diagram for mixtures of two component system: ethane (C2)

and n-heptane (nC7)

A - 90% weight ethaneB - 50 % weight ethane

C - 10 % weight ethane

Each individual mixtures hasits own phase diagram.


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• Phase data on seven mixtures of methane and ethane along with the vapor-pressure lines

for pure methane and pure ethane.

• Observe that the two-phase region of each of the mixtures lies between the vapor

pressures of the two pure substances and that the critical pressures of the mixtures lie

well above the critical pressures of the pure components.

• The dashed line is the locus of critical points of mixtures of methane and ethane.

The critical point for two-component systems


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• The behavior of a mixture of two

components is not as simple as the behavior of a pure substance.

• Instead of a straight line representing

the vapor-pressure curve there is a broad

region in which two phases coexist.

• The two-phase region of the phase

diagram is bounded on one side by a

bubble-point line and the other side by a

dew-point line.

• The two lines join at the critical point.Typical shape of the phase diagram for a mixture of equal

amounts of two components.

Vapor pressure bubble point and dew point of two-component systems

• Consider line 1 – 2 at constant temperature expansion.

• At pressure P1 the substance is a liquid.

• As P is decreased the liquid expands until the P reaches a point at which a few molecules

are able to leave the liquid and form a small gas phase.

• The P at which the first bubble of gas is formed known as the bubble point pressure, P b.

• As P is decreased below the P b, liquid and gas coexist.

• Finally, only a minute amount of liquid remains. This is known as the dew-point and the

P at this point is known as the dew-point pressure, Pd.

• Further reduction of P simply causes an expansion of the gas.


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Phase behavior of two-component systems

• The dew point and bubble point curves meet at the critical point, which is defined

as that T and P at which the liquid and vapor (gas) phases have identical intensive

properties (density, specific volume, etc)

• Fluid above the bubble point is in the liquid state and fluid below the dew point is

gas

• In the space enveloped between the two lines, liquid and gas are in equilibrium

• Referring to the figure,the vapor pressure and

bubble point lines do not

coincide but form an

envelope enclosing a

broad range of T and P at

which two phases (gasand oil) exist in

equilibrium.

Phase behavior of a 50:50 mixture of two pure HC components


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• The critical loci of binary

systems composed of normal

paraffin HC are shown.

• Obviously the critical

pressures of mixtures areconsiderably higher than the

critical pressures of the

components of the mixtures.

• In fact, the difference in

molecular size of thecomponents greatly

increases the critical

pressures of the mixtures.

The critical point for two-component systems


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A single isotherm on a pressure-volume

diagram of a two-component mixture with a

constant over-all composition.

The feature that distinguishes this diagram

from a pressure-volume diagram of a pure

substance is that the P decreases as the

process passes from the bubble point to the

dew point. This decrease is caused by the change in

composition of the liquid and the vapor as

the process passes through the two-phase

region.

Pressure-volume diagram for a two-component system

At the bubble point the composition of the liquid is essentially equal to the overall

composition of the mixture but the infinitesimal amount of gas is richer in the morevolatile component

Likewise, at the dew point the composition of the vapor is essentially equal to the overall

composition of the system and the infinitesimal amount of liquid is richer in the less

volatile component

The breaks in the line at the bubble point and dew point are not as sharp as for a pure

substance. Assoc. Prof. Abdul Razak Ismail, UTM

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• Pressure-volume diagram for amixture of ethane and n-heptane.

• Showing several isotherms and the

saturation envelope.

• Notice that at the lower temperatures

the dew point breaks in the isotherms

are almost non-existant.

• Also notice that the critical point is

not at the top of the saturation

envelope as it was for pure substances

but appears somewhat to the right of

center .• This is a result of the slope of the

isotherms through the two-phase

region.

Pressure-volume diagram for a two-component system


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The T above which liquid cannot be formed regardless of the P

attained is known as the cricondentherm.

The P above which no gas can be formed regardless of the T is

known as the cricondenbar .

Cricondentherm and Cricondenbar


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Retrograde condensation • Another unusual feature of the two-component

system is illustrated by the shaded portion.• For a pure substance a decrease in P causes a

change of phase from liquid to gas at the Pv line.

• Likewise, in the case of the two-component

system a decrease in P causes a change of phase

from liquid to gas at temperatures below the

critical T.

• However, consider the isothermal decrease in P

illustrated by line 1—3.

• As P is decreased from point 1, the dew-point line

is reached and liquid begins to form.

• At the position indicated by point 2 the system is

5% liquid and 95% gas.

• P decrease has caused a change from gas to liquid. This is exactly the reverse of the behavior one

would expect.

• This behavior is called retrograde condensation.

• As P is decreased from point 2 toward point 3 the amount of liquid decreases; the dew-point line is

reached and the system again becomes gas.

• The region of retrograde condensation occurs at T between the Tc and the cricondentherm.

• A similar retrograde situation occurs when T is decreased at constant P between the Pc and the

cricondenbar.


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Definition of Solution

Solution : A homogeneous mixture of two or more

substances, which have the same chemical

composition and the same physical properties

throughout.

Ideal solution : In an ideal solution there are no forces of

attraction between the constituent molecules.


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Vapor pressure of an ideal liquid solution

i i viP x P

T i viP x P

ii i T i

T

PP y P or y

P

Raoult’s law states that for an ideal solution, the partial pressure of a

component in the vapor is equal to the product of the mole fraction of that

component in the liquid and the vapor pressure of the pure component.

where Pi = partial pressure of the ith component in the vapor

xi = mole fraction of the ith component in liquid solutionPvi = vapor pressure of the pure i

th component

where PT = total pressure of exerted by the vapor

= vapor pressure of the solution

= bubble point pressure

Dalton’s law states that for an ideal gas the partial pressure of a component inthe vapor is equal to the product of the mole fraction of that component in the

vapor and the vapor pressure of the solution.


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Example

Component Pi xi Pi = xiPvi yi = Pi/PT

C3H5 38.20 0.50 19.10 0.840

C4H10 7.30 0.50 3.65 0.160

At 0oF calculate the bubble-point pressure and the composition of the vapor at the bubble point for a two-

component solution having a mole fraction of propane equal to 0.5 and a mole fraction of butane equal to 0.5.Repeat these calculations for a solution whose mole fraction of propane is 0.25 and whose mole fraction of butane

is 0.75. The vapor pressures of pure propane and butane at 0oF are 38.20 psia and 7.30 psia, respectively.

For the solution of propane and butane of each 0.5 mole fraction:

PT = 22.75 psia

Thus, bubble-point pressure for this solution is 22.75 psia at 0oF, and the mole fractions of propane and butane are

0.840 and 0.160, respectively

For the solution of propane = 0.25, and butane = 0.75 mole fractions:

PT = 15.03 psia

Thus, bubble-point pressure for this solution is 15.03 psia at 0oF, and the mole fractions of propane and butane are

0.635 and 0.365, respectively

Component Pi xi Pi = xiPvi yi = Pi/PT

C3H5 38.20 0.25 9.55 0.635

C4H10 7.30 0.75 5.48 0.365


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28Liquid and vapor composition of two-component system

in the two-phase region

1 v1 2 v2 T

1 2 2 1

1 v1 1 v2 T

T v2 T v11 2 1

v1 v2 v2 v1

1 v1 2 v21 21 2 2

T T T

T

T

Dalton’s Law for the vapor :

(

(1) x P x P P

but, x x 1 x 1 x

(2) x P 1 x P P

P P P P

(3) x , and x 1 xP P P P

x P x PP Py , and y 1 y

P P P4)

where P pressure in the l

P

iquid

phase

Note: Equations (1) to (4) are applicable anywhere in the two-phase region,

including at the bubble point and dew point.


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Example

c 4 vC 4C4

T

C5 C4

x P 0.394x160y 0.665

P 95

y 1 y 1 0.665 0.335

Assuming ideal solution behavior for a system of one mole n-butane and one mole n-pentane.

a. Calculate the composition of the liquid and vapor at 180oF and 95 psia. b. Calculate the bubble point and the composition of the vapor at 180oF.

c. Calculate the dew point pressure and the composition of the liquid at the dew point at 180oF.

T vC5C4

vC4 vC5

C5 C4

P P 95 54x 0.394

P P 160 54

x 1 x 1 0.394 0.606

a. From graph (page 10), at 180 oF: PvC4 = 160 psia, and PvC5 = 54 psia

Mole faction in the liquid (Eq. 3):

Mole faction in the vapor (Eq. 4):


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c4 v4C4

T

C5 C4

x P 0.5x160y 0.747

P 107

y 1 y 1 0.0.747 0.253

T TP 54

From Eq. (3) : 0.5 P 107psia bubblepoint pressure160 54

b. The bubble point and the composition of the vapor at 180oF?

Since the overall composition and the composition of liquid are equal at bubble point,

xC4 = xC5 = 0.5

From Eq. (4): Mole faction of the vapor at bubble point pressure:


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c. The dew point pressure and the composition of the liquid at the dew point at 180oF?

Since the overall composition and the composition of vapor are equal at dew point,

yC4 = yC5 = 0.5.

c4 v4C4

T

T vC5

v4vC4 vC5T vC5

C4 C4

vC4 vC5 T

T

C4 T

T

T

x PFrom Eq.(4) : y

P

P P

PP PP Px Eq.(3) in (4) : y

P P P

P 54(160)

160 54y 0.7

where P dew point pressure

FromEq.

47 P 80.8 psia (dew point pressur

(

e

3

)P

) :

C4

C5

Mole faction of the liquid at dew poinFrom Eq. (3)

80.8 54x 0.24

t press

3160 54

x 1 0.243 0.7

ure:

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For a system composed of 1 mole of n-butane and 1 mole of n-pentane at 180oF.

Calculation Summary

Bubble point pressure (P b) = 107 psia

Composition of vapor at P b: yC4 = 0.747 , yC5 = 0.253

Compositions of liquid and vapor at 95 psia:

xC4 = 0.394, xC5 = 0.606;

yC4 = 0.665, yC5 = 0.335

Dew point pressure (Pd) = 80.8 psia

Composition of liquid at Pd: xC4 = 0.243, xC5 = 0.757

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11 HC Phase Behavior