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# PVT and Flow course - K Values

### More By Petro Engineer

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## K Values - Part 1

### Phase equilibrium

We are talking about having a some volume at some point in the system: reservoir and the production pipe going to the surface or at the surface gathering pipe lines maybe, at the separator, basically at some point in the system having a known pressure and temperature of that particular point and wanting to identify whether we have oil and/or gas for a given condition. In addition to having the known pressure and temperature, we're going to assume that we also know the overall mixture composition at that point, the molar amount of methane, ethane, CO2 and so forth. That composition is is known as well as the pressure and temperature. And then the question is: how much oil, how much gas in terms of moles mass and volume exist? What is the composition? So for example the moles of oil, the moles of gas and the molar composition of the gas and the molar composition of the oil.
For right now we're going to ignore water as a phase we might very well have and often we'll have water in the system. It will generally be contacting both the gas and the and the oil. But we typically don't do three phase calculations including water.

Ki is defined as the ratio of mole fractions of the component i in the equilibrium gas phase divided by the mole fraction of the component in the equilibrium oil phase:

```Ki = yi / xi
```

Note: if you have two phases together then we know the two phases each are saturated. It's a saturated oil and a saturated gas.

We're going to talk about the dependence of these K values on pressure, on temperature and on the overall composition. Ki value is not dependent only on the mole fraction of that i component it's it's dependent on the mole fraction of all of the components, the total composition.
Once we understand that basically how theydepend on pressure, temperature and composition and why they depend in a certain way on pressure, temperature and composition then the actual computation of this two-phase calculation will have more meaning. It's just pure mathematics.

The composition that is flowing in at the wellbore will be the same composition in the wellbore, pipeline and entering the separator. That will be a composition that doesn't really change. What's going in is going out - averaged over some time period.
The composition in the reservoir which is flowing into the wellbore, this composition might be changing as it's flowing in towards the wellbore. If it goes from being single-phase into being two-phase, may be the one phase has more mobility than the other phase, the one phase lags behind the other phase, moves forward more quickly. So, the composition of what we'll call the in situ reservoir composition may be equal or it may not be equal to what we call the wellbore composition (or well stream composition).
But generally speaking, after the wellbore we can say, that wherever we are, we know the composition. And now we're interested in how that composition partitions into phases and how the individual components partition into the two phases.

### Behavior of Ki

Ki represent (in lay terms) a quantity that gives a relative preference of the component i to be in the gas phase or the oil phase. It's not an on/off switch, but it's a relative tendency. Showing, does it prefer going to the gas phase as a point as opposed to go into the oil phase.
Basically if it's the gas phase, if it has a relative preference to be in the gas phase then the K value will be greater than one: K>1.
And if it has a relative preference to be in the oil phase that will have the K value less than one: K<1.

Note: the company is going to make more money by selling component i (propane, butane, pentane these components) as part of the ultimate processed surface liquid phase. If we can keep that component in the liquid as it is processed down to this ultimate surface phase then we're going to make a lot more money, somewhere between five and ten times as much, for every molecule of component you can keep in that phase than if it ends up in the gas phase, being sold or burned or given away.

So, from the reservoir until the entry to the separator we don't really have much control over the composition. We might have a little bit control in the reservoir in some situations, but, basically, once it hits the wellbore until it reaches the separator it's just the composition the reservoir is giving up, and we don't have any control. We can change the pressure and temperature as we like from the wellbore to the entry to the separator, nothing's going to change the composition, nothing's going to change the K values. But what we can control is all of this surface process. And we try to do that to keep as many of the components as possible in the ultimate stock tank oil.

If we have the vapor pressure of a given component as a function of temperature, we automatically have the K value of that component as a function of pressure less than probably about 100 bar in any temperature.
K value is equal to vapor pressure over pressure:

```K = Pv(T) / P
```

Note: in the low pressure region the K value is basically independent of the overall composition. But in the reservoir and in some of the production tubing, where you have high pressures, there heptane behave differently in the Troll oilfield and the Qatar North field, in the Oklahoma City field, it starts depending on the overall mixture composition.

## K Values - Part 2

### Surface processing

In petroleum engineering calculations we typically ignore the fact that some of the gas from the separation you may be able to extract back into the liquid stream. But we generally don't make that assumption. We just assume that each stage gas remains as a "surface gas". So we simply add together all of the moles of gas coming off at each separation stage.
One important characteristic of stock tank oil is that it needs to be stable, it needs to be a liquid at one atmosphere and atmospheric temperature so it needs to be stabilized. If it's not stabilized and you put it in those conditions a lot of those lighter components will just evaporate off and disappear into the atmosphere which is both not good environmentally and it's not good because the volume of oil is shrinking.

From an engineering point of view we have different pressure and temperature at each of separator stages, we have a different set of K values for stage 1, stage 2, stage 3, etc. Those are all basically only a function of pressure and temperature, because we're in this low pressure-temperature range.
The thing is what one may do or sometimes try to do is to find an optimal set of separator pressures and temperatures. We don't really have control of the last pressure and temperature. So, for example in this case of a three-stage separation process we have four numbers that we might be able to manipulate with some cost. And what we'd like to do is to manipulate those in a way that we maximize the stock tank well volume.

K value is typically at approximately somewhere between 50 and maybe a 120 bar, it depends on each component.These pressure range give us the lowest K values, so intuitively you think some of the separators should be at those conditions. But in reality what we're trying to maximize is for the most part it's the moles of stock tank oil. We want to get as many of these moles that come from the well to end up as moles in liquid at standard conditions.
What controls the ultimate moles of component i that ends up in the stock tank oil:

• individual K value
• overal mixture K value

And this optimization of of the pressure and temperature will affect all of the K values.

### Water-Gas-Oil Phase Equilibria

In general the gas-oil K value as the function of pressure, temperature and total composition is for practical purposes (a magnitude of difference or error that is insignificant) equal to gas-oil-water K value. And as a result of that we can generally ignore the H2O component and the aqueous phase when doing gas oil phase equilibria calculations.

Note: when our overall system contains all of components (C1, C2, C3..., H2O, etc) and we bring them to equilibrium at pressure and temperature - each and every component you will find in all three phases. That means that for example a lot of the methane will end up in gas because the K values are greater than 1 but we can have a substantial amount of methane in the oil. You're also going to have some methane in the water.

## Convergence Pressure

One more video, explaining convergence pressure.

## 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/