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# PVT and Flow course - Multi-Component Phase Diagrams

### More By Petro Engineer

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## Multi-Component Phase Diagrams - Part 1

10 - 20 components is a very simple gas, very boring kind of gas, but much more often in the great majority of reservoir fluids will contain hundreds if not thousands of different compounds hydrocarbon compounds.

The calculations of flow through reservoir, flow through pipe, is strongly influenced by whether it's single phase or two phase. Generally two phase requires higher pressure drop and higher pressure drop requires in general more cost.

Everywhere inside the P-T envelope we have two phases and the start of two phases is the line itself. If you if you're on the line and you're about to falling into the evelope you'll see either the bubble appear or the droplet appear. You're at the point of a second phase. So we also consider the line itself part of the two-phase region even though the second phase is so small, you won't see it.
Everywhere outside that envelope it's single phase.

The critical point differentiates the line of bubble points from the line of dew points.

The critical point, the bubble point versus temperature, the dew point versus temperature make up the phase diagram. These are primarily function of the composition Zi. This whole pressure temperature diagram is for a constant or fixed composition Zi.
Zi it's both the molar quantities of each component and the list of components.

### Notes

If you have a single-phase mixture in the reservoir, what do you call it - oil or gas? The conventional way to say whether ts is a reservoir oil or gas in the petroleum industry is to say that if the average reservoir temperature is less than the critical temperature of that mixture then we're going to call this a reservoir oil. If the reservoir temperature for this mixture is greater than the critical temperature then we're going to call it a reservoir gas. But it's just convention.

Condensation: Appearance of a liquid phase from a gas phase.
Retrograde condensation: increasing liquid volume as pressure decreases.

## Multi-Component Phase Diagrams - Part 2

### Pressure-Volume Diagram

Pressure - % of Liquid Diagram. T1 < T2 <T3 < T4:

This diagram is the alternative to P-T diagram. In the P-T diagram, we have constant lines of percentage liquid. And in the P-V diagram we have constant lines of temperature. So, this is just a different way to represent the same information.

### Ternary Diagram

Ternary diagram, usually only used in the context of injecting a gas into an oil reservoir.

We take these literally hundreds if not thousands of compounds Zi and translate that into three pseudo components.

```Zi → 3 "Pseudo" components:
* Light  (C1, N2)
* Intermediate   (CO2, C2-C5)
* Heavy   (C6+)
```

The ternary diagram applies at a fixed pressure and temperature.

Let's say our mix Zi is ~ 30 mole% Light, ~25 mole% Intermediate and ~45 mole% Heavy.
A ternary diagram is a triangle with Zi inside the triangle:

A tie line joins the equilibrium gas yi, the equilibrium oil xi and the total mixture Zi.

If you have a 2-phase mixture at fixed pressure and temperature, and you remove 90% of the vapor (or gas), nothing would change in terms of the equilibrium of the system. The total composition has changed (point A on the diagram), but the system remains in equilibrium. The same with the oil - remove 90% of the liquid from the original mixture (point B on the diagram) and the equilibrium would remain the same. And that's the characteristic of this tie line: the chemical energy of the system doesn't change but that the same, equilibrium is always achieved with xi and yi filling the container in different amounts. And its independent of how much vapor or liquid you have.

We can draw the line where zi is equal to xi and the will be a bubble point line. And the second line where zi is equal to yi and the will be a dew point line.
Everywhere inside that envelope we have 2 phases and everywhere outside we have single phase.

In this diagram, the pressure and temperature are fixed, what has changed is the composition. The only way this diagram is correct is if the heavy is always the same heavy, the intermediate is always the same intermediate (same distribution of c2 through c5) and the light is always the same light.

Every point on this diagram will have a different pressure-temperature diagram.

### Note

Ternary diagram method is approximative, a kind of a guideline. It is violating that the 3 (pseudo) components are not the same. There's a limit to how much you can use this quantitatively. And because of that the ternary diagram can be very misleading if you try to use it quantitatively.

The entire oil industry was tricked by the ternary diagram until about 1986 in understanding how gas can displace oil efficiently. Because they used the ternary diagram religiously, they just didn't get it they didn't understand what was really going on. And only around 1985-86 where as a guy who came along and said: "we can't use this ternary diagram, we have to look at all the components and study the mixing of injection gas and reservoir, not with the ternary diagram but in some other way.

The ternary diagram is dangerous to use quantitatively.

## Multi-Component Phase Equilibria & Gibbs Energy

Injection gas:

• CO2
• N2
• Lean HC - C1 (+ small amount of C2 - C4)
• Separator gas
• Enriched gas (add C2 - C4)

The Pressure - Injected Gas Diagram at constant reservoir temperature would look like this:

The curve connects all bubble points and dew points of all compositions during gas injection.

The maximum pressure is the lowest pressure where the injection gas is directly (first contact) miscible with the reservoir oil. Or the minimum first contact miscibility pressure. So, if you happen to be able to inject at that pressure or above - wherever that injection gas slides through the oil reservoir - it's going to recover a hundred percent of the oil. Wherever that gas moves in the reservoir, it is going to clean it out completely 100 %, recovery, nothing's going to be left in the pores but the injection gas.

### Notes

You might have local regions with 3 phases:

• co2 rich gas phase
• co2 rich liquid phase
• hydrocarbon rich liquid phase

### Chemical energy

How does nature decide if a certain composition has certain pressure in temperature is single phase or two or more phases?

Nature always tries to minimize the system energy. And we've got these hundreds of components, we've got a total composition, we've got a pressure and temperature and nature can decide to keep it as a single phase and if it does that single phase will have a certain energy. But if nature can come up with some other configuration where some of the methane is put into a lighter phase and some of the methane is put into the heavier phase and likewise for every other component, if that configuration gives lower total energy, mother nature won't tolerate single phase.

```Single phase energy: μ = Σ(ni*μi)
Two phase energy: μ = nv*Σyi*μiv(y) + nL*Σxi*μiL(x)

where:
energy μi is a function of composition, pressure, temperature and moal volume
L - liquid phase
V - vapor phase

```

## Other lectures from the PVT and Flow course

Class notes developed during lectures are available as PDF files, named with the format yyyymmdd.pdf located on: http://www.ipt.ntnu.no/~curtis/courses/PVT-Flow/2016-TPG4145/ClassNotes/