## Phase Behavior and Phase separation - Chapter 2

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### Phase Behavior and Phase separation - Chapter 2

Fundamentals of Oil and Gas Processing Book
Basics of Gas Field Processing Book
Prediction and Inhibition of Gas Hydrates Book
Basics of Corrosion in Oil and Gas Industry Book

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Chapter 2 45
Phase Behavior and Phase separation 45
2.1: Phase Behavior 45
2.1.1: Introduction 45
2.1.2: System Components 45
2.1.4: Single-Component Systems 46
2.1.5: Multicomponent Systems 49
2.1.6: Prediction of phase envelope 50

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Chapter 2

Phase Behavior and Phase separation

2.1: Phase Behavior

2.1.1: Introduction
Before studying the separation of gases and liquids, we need to understand the relationship between the phases. Phase defines any homogeneous and physically distinct part of a system that is separated from other parts of the system by definite bounding surfaces:
The matter has three phases, the simplest example is water.
• Solid (ice),
• Liquid (liquid water),
• Vapor (water vapor).
Solids have a definite shape and are hard to the touch. They are composed of molecules with very low energy that stay in one place even though they vibrate. Liquids have a definite volume but no definite shape. Liquids assume the shape of the container but will not necessarily fill that container. Liquid molecules possess more energy than a solid (allows movement from place to another). By virtue of the energy, there is more space between molecules, and liquids are less dense than solids. Vapors do not have a definite volume or shape and will fill a container in which they are placed. Vapor molecules possess more energy than liquids (very active) and are less dense than liquids.
Our primary concern in this section is the difference in energy level between phases.
Energy is added to melt a solid to form a liquid. Additional energy will cause the liquid to vaporize. One needs to know the phase or phases that exist at given conditions of pressure, volume, and temperature so as to determine the corresponding energy level, to do this we need to study the phase diagram or phase behavior, but first we have to separate components into three classifications:
• Pure substance (single-component systems),
• Two substances,
• Multicomponent.
Phase diagrams illustrate the phase that a particular substance will take under specified conditions of pressure, temperature, and volume.

2.1.2: System Components
Natural gas systems are composed primarily of the lighter alkane series of hydrocarbons, with methane (CH4) and ethane (C2H6) comprising 80% to 90% of the volume of a typical mixture. Methane and ethane exist as gases at atmospheric conditions.
Propane (C3H8), butane (n-C4H10 and i-C4H10), and heavier hydrocarbons may be extracted from the gas system and liquefied for transportation and storage. These are the primary components of liquefied petroleum gas, or LPG.
The intermediate-weight hydrocarbons (pentane through decane) exist as volatile liquids at atmospheric conditions. These components are commonly referred to as pentanes-plus, condensate, natural gasoline, and natural gas liquids (NGL).
Natural gas systems can also contain non-hydrocarbon constituents, including hydrogen sulfide (H2S), carbon dioxide (CO2), nitrogen (N2), and water vapor. These constituents may occur naturally in gas reservoirs, or they may enter the system as contaminants during production, processing, and transportation. In addition, operators may intentionally add odorants, tracers (such as helium), or other components.
Dry, or lean, natural gas systems have high concentrations of the lighter hydrocarbons (methane and ethane), while wet, or rich, gas systems have higher concentrations of the intermediate-weight hydrocarbons. Lean gases burn with a low air-to-gas ratio and display a colorless to blue or yellow flame, whereas rich gases require comparatively higher amounts of air for combustion and burn with an orange flame. Intermediate-weight hydrocarbons may condense from rich gases upon cooling.

2.1.4: Single-Component Systems
A pure component of a natural gas system exhibits a characteristic phase behavior, as shown in Fig. 2-1. Depending on the component’s pressure and temperature, it may exist as a vapor, a liquid, or some equilibrium combination of vapor and liquid Figure 2-1 P-T Diagram for pure component.

Lines HD, HC, and FH are the equilibrium lines - combinations of pressure and temperature at which the adjoining phases are in equilibrium. At equilibrium, one can change phase, by simply adding or removing energy from the system. Point H, the triple point, is the only combination of pressure and temperature at which all three phases can exist together.
Along line FH no liquid phase is ever present and solid sublimes to vapor. The use of "dry ice" for cooling is an example of this. Line HD is the equilibrium line between solid and liquid. Ice water at 0°C [32°F] and atmospheric pressure occurs on this line. Line HD can have a positive or negative slope depending on whether the liquid expands or contracts on freezing. The energy change occurring along line HD is called the heat of fusion. At any P and T along this line the system can be all solid, all liquid or a mixture of the two depending on the energy level.
This line could be called the solid-liquid saturation or solid-liquid equilibrium line.

Line HC is the saturation or equilibrium curve between vapor and liquid. It starts at the triple point and terminates at the critical point "C." The pressure and temperature conditions at this latter point are known as critical temperature (Tc) and critical pressure (Pc).
At this point the properties of the liquid and vapor phases become identical. For a pure substance the critical point can be defined as that point above which liquid cannot exist as a unique separate phase. Above (Pc), and (Tc), the system is often times referred to as a dense fluid to distinguish it from normal vapor and liquid.
Line HC is often referred to as the vapor pressure curve. Such vapor pressure curves are available from many sources. Line HC is also the bubble point and dew point curve for the pure substance.
The vapor pressure line in Figure 2-2 divides the liquid region from the vapor region.

In figure 2-1, consider a process starting at pressure P1, and proceeding at constant pressure.
From "m" to "n" the system is entirely solid. The system is all liquid for the segment o-b. At "b" the system is a saturated liquid - any further addition of energy will cause vaporization. At "d," the system is in the saturated vapor state. At temperatures above "d," it is a superheated vapor.
Line HC is thus known by many names - equilibrium, saturated, bubble point, dew point and vapor pressure. For a pure substance these words all mean the same thing.

At the pressure and temperature represented by HC the system may be all saturated liquid, all saturated vapor or a mixture of vapor and liquid.
The rectangle "bfghd" illustrates another important phase property that is confirmed experimentally.
Suppose we place a liquid in a windowed cell at condition "b" and light it so it is easily visible.
We then increase pressure at constant temperature (isothermally). As we proceed toward point “f” the color will begin to fade. At some point, the color disappears completely. The cell now contains what looks like a vapor, but no bubble of vapor was ever seen to form.
At “ f ” (above the critical) the system is in a fourth phase that cannot be described by the senses. It is usually called dense phase fluid, or simply fluid. The word "fluid" refers to anything that will flow and applies equally well to gas and liquid.
This fluid at "f' looks like a gas but possesses different properties from regular gas found to the right of line HC and below the critical pressure. It is denser than regular gas but is more compressible than a regular liquid. “Properties of the liquid and vapor phases become identical”.

Table 1-3 lists Critical pressures and critical temperatures, along with molecular weights, of some pure components present in many natural gas systems.
Figure 2- 2 shows vapor pressure line for light hydrocarbons, where the left part of any component line, represents its liquid phase while the right part represents its gas phase. Figure 2-2 Vapor pressure for light hydrocarbons.

2.1.5: Multicomponent Systems
In reality, natural gas systems are not pure substances. Rather, they are mixtures of various components, with phase behavior characteristics that differ from those of a single-component system. Instead of having a vapor pressure curve, a mixture exhibits a phase envelope, as shown in Figure 2-3. Figure 2-3 typical phase envelop of hydrocarbon mixture.

The phase envelope (curve BCD in Figure 2-3) separates the liquid and gas phases. The area within this envelope is called the two-phase region and represents the pressure and temperature ranges at which liquid and gas exist in equilibrium.
The upper line of the two-phase region (curve BC) is the bubble-point line. This line indicates where the first bubble of vapor appears when the pressure of the liquid phase mixture is lowered at constant temperature, or when the temperature increases at constant pressure.
The lower section of the phase envelope (curve CD) is the dewpoint line. When the pressure of a mixture in the gaseous phase is decreased at constant temperature, or when the temperature is lowered at constant pressure, the first drop of liquid forms on this line. The bubble-point line and the dewpoint line meet at the critical point (C).
The highest pressure in the two-phase region is called the cricondenbar, while the highest temperature in the two-phase region is called the cricondentherm.

Figure 2-4, is another example of phase envelope, where:
Cricondenbar - maximum pressure at which liquid and vapor may exist (Point N).
Cricondentherm - maximum temperature at which liquid and vapor may coexist in equilibrium (Point M).
Retrograde Region - that area inside phase envelope where condensation of liquid occurs by lowering pressure or increasing temperature (opposite of normal behavior).
Quality Lines - those lines showing constant percentages which intersect at the critical point (C) and are essentially parallel to the bubble point and dew point curves. The bubble point curve represents 0% vapor and the dew point curve 100% vapor.
Line ABDE represents a typical isothermal retrograde condensation process occurring in a condensate reservoir. Point A represents the single phase fluid outside the phase envelope. As pressure is lowered, Point B is reached where condensation begins. As pressure is lowered further, more liquid forms because of the change in the slope of the quality lines. As the process continues outside the retrograde area, less and less liquid forms until the dewpoint is reached (Point E). Below E no liquid forms. Figure 2-4 shows another phase envelope for hydrocarbon mixture.

2.1.6: Prediction of phase envelope
The location of the bubblepoint and dewpoint lines may be calculated using vapor-liquid equilibrium (VLE) methods. For most naturally occurring systems above about [2000 psia], the validity of the standard calculation becomes questionable.
The application of K-values to calculate phase quantities and compositions proceeds as follows.
For any stream (F) with mole fractions of components (Z1+Z2+Z3,.., etc.) entering a vessel at certain pressure and temperature, the stream will be divided into Vapor stream(V) with mole fractions of components (Y1+Y2+Y3,.., etc.), and into a liquid phase (L) with mole fractions of components (X1+X2+X3,.., etc.).

Component balance:

Fzi = Vyi + Lxi Eq. 2-1 Figure 2-5 flash separation for hydrocarbon mixture.
where
zi = mol fraction of any component in total feed stream to separation vessel
yi = mol fraction of any component in the vapor phase
xi = mol fraction of any component in the liquid phase
Ki = equilibrium vaporization ratio (equilibrium constant) = yi/xi
F = total mols of feed
V = total mols of vapor
L = total mols of liquid

If we set F = 1.0 so that L and V are now liquid and vapor-to-feed ratios
then zi = Vyi + Lxi
Since yi = Kixi
So, zi = V Ki xi + L xi

xi = zi / ( L + V Ki) Eq. 2-2

Since the summation of liquid fractions must equal one, we can write the following equation.

∑ xi = ∑ zi / ( L + V Ki) = 1 Eq. 2-3

The equation serves as the objective function in an interactive calculation to determine the quantity of L or V. The calculation procedure is as follows:
1. Determine K values of each component at the temperature and pressure of the system.
2. Assume a value of L (remember, V = 1 - L)
3. Solve the equation Eq. 2-3. If ∑xi ≠ 1.0 assume a new value of L and repeat step 2.
4. When ∑ xi = 1.00, the phase quantities L and V are known as well as the liquid phase composition. Vapor phase compositions may be calculated by remembering that yi = Kixi,

The foregoing calculations is known as a flash calculation and is used to predict the equilibrium quantities and compositions of two phase systems.

Special cases of a flash calculation include bubble point (V = 0, L = 1) and dew point (V = 1, L = 0), calculations. Equations for bubblepoint, and dewpoint are as follows:

Bubblepoint condition:

∑ Ki xi = 1.0 Eq. 2-4

Dewpoint condition:

∑ yi/Ki = 1.0 Eq. 2-5

Flash calculation are usually made by computer software, but knowing the basic of calculations is important in understanding the gas-liquid separation process.

Example 2- 1: Calculate the bubblepoint and dewpoint temperature at 250 psia of the following hydrocarbon mixture. Then calculate the amount of vapor and liquid and the composition of the two phases if these feed entered a vessel @ 250 psia and 150 0F. Table 2-1 hydrocarbon component for example 2-1.

Solution:
Bubblepoint calculation : To calculate the bubblepoint temperature at certain pressure, (All the components are in liquid phase xi = 1).
From eq. 2-4, the bubblepoint will be reached when ∑ Ki xi ≅ 1
Solution Steps:
Assume a temperature value (100 0F), for example.
From the K chart of each compound, find the K value at the system pressure and assumed temperature.
Multiply mole fraction xi of each component by its equilibrium value taken from the table Ki.
Take the sum ∑ Ki xi , if it’s less than 1, choose higher temperature, (150 0F for example), and repeat as in the table.
If, ∑ Ki xi is higher than 1, choose a lower temperature.
Repeat till ∑ Ki xi ≅ 1. Table 2-2 bubblepoint calculation for example 2-1.

We assumed two values of temperature , we found the first value (100 0F) is lower than the bubble point since ∑ Ki xi < 1.00 , and the second value (150 0F) is higher than the bubble point since ∑ Ki xi > 1.00 , the bubble point will be between the two values where ∑ Ki xi ≅ 1.
The Ki values in previous table where collected from “ Design operation and maintenance of gas plants - John Campbell Co.” , since it’s hard to obtain Ki numbers at temperature rather than the pre-drawn temperature lines in K-Charts.
The Values of Ki can be extracted from individual component charts (figures 2-6 to 2-10) (Methane K-chart, Ethane K-chart ….etc.), or can be extracted from “DePriester” chart, fig 2-11.

Dewpoint calculation: To calculate the dewpoint temperature at certain pressure, (All components are in gas phase yi = 1). From eq. 2-5, the dewpoint will be reached when ∑ yi /Ki ≅ 1
Solution Steps:
Assume a temperature value (150 0F), for example.
From the K chart of each compound, find the K value at the system pressure and assumed temperature.
Divide mole fraction Yi of each component by its equilibrium value taken from the table Ki.
Take the sum ∑ Yi /Ki , if it’s higher than 1, choose higher temperature, (2000F for example), and repeat as in the table.
If, ∑ Yi /Ki is less than 1, choose a lower temperature.
Repeat till ∑ Yi /Ki ≅ 1. Table 2-3 dewpoint calculation for example 2-1.

We assumed two values of temperature , we found the first value (150 0F) is lower than the dewpoint since ∑ yi /Ki > 1.00 , and the second value (200 0F) is higher than the bubble point since ∑ yi /Ki value is < 1.00 , the dewpoint will be between the two values where ∑ yi /Ki ≅ 1 .
The Ki values in previous table where collected from “ Design operation and maintenance of gas plants - John Campbell Co.” , since it’s hard to obtain Ki numbers at temperature rather than the pre-drawn temperature lines in K-Charts.
The Values of Ki can be extracted from individual component charts (Methane K-chart, Ethane K-chart ….etc.), or can be extracted from “DePriester” chart, fig 2-11.

Flash calculations:
Different values of “L” will be assumed (remember, V = 1 - L), and accordingly Xi will be calculated till we obtain ∑ xi = 1.00.
Ki from chart at 250 psia and 150 0F
Using Eq. 2 -2 xi = zi / ( L + V Ki)
Component Zi Ki Assume
L=0.5
Xi = Assume
L = 0.75
Xi = Assume
L= 0.649
Xi =
Yi = Ki Xi Table 2-4 flash calculations for example 2-1.

The assumed value of L=0.5, found to be lower than the correct value, and the assumed value of L= 0.75 found to be higher than the correct value.
The correct value must be in between the two previous assumed values, and found to be 0.649.
Flash calculations usually performed by computer software, for manual calculations, some K value charts are included in this chapter for the illustration of manual calculations for the previous example. (Figures 2-6 to 2-10)
Other K-values are included in Chapter 25 “Equilibrium Ratio (K) Data” in the “GPSA Engineering Data Book”, or Appendix 5A Volume 1 “Gas conditioning and Processing – The Basic Principles,” Campbell Petroleum Series. In the other hand, the DePriester Chart Figure 2-11, may be used for all hydrocarbon components.

K Value charts: Figure 2-6 Equilibrium ratio (K) for Methane. Figure 2-7 Equilibrium ratio (K) for Ethane. Figure 2-8 Equilibrium ratio (K) for Propane. Figure 2-9 Equilibrium ratio (K) for i-Butane. Figure 2-10 Equilibrium ratio (K) for n-Butane. Figure 2-11 the DePriester (K) Chart for hydrocarbon components.