Case studies - Phase equilibria
Introduction............................................................................................................................................... 1
Oil and gas systems................................................................................................................................. 1
Calculating the
bubble point curve........................................................................................ 3
Calculating the dew
point curve............................................................................................. 3
Phase envelope......................................................................................................................... 4
Adding water to the
system.................................................................................................... 5
Including a
petroleum fraction................................................................................................ 6
Other flash
calculations........................................................................................................... 8
PVT Analysis............................................................................................................................................ 9
Black Oil Analysis.................................................................................................................................. 14
Refrigerant mixtures................................................................................................................................ 16
Polar systems.......................................................................................................................................... 17
Modelling a polar
mixture...................................................................................................... 18
Liquid-liquid
equilibria........................................................................................................... 21
Vapour-liquid-liquid
equilibria.............................................................................................. 22
Azeotropes.............................................................................................................................. 22
Eutectics................................................................................................................................... 23
Polymers................................................................................................................................................... 24
Data input................................................................................................................................ 24
Co-Polymers............................................................................................................................ 26
The main purpose of Multiflash is to determine the phase equilibria and thermodynamic properties of complex mixtures. The simple tutorial shown earlier, see “Simple Tutorial” on page 19. was based on calculating the phase equilibria of a binary hydrocarbon system. Here we will look at a more complex hydrocarbon system and the phase equilibria of a polar mixture.
Initially we will look at the phase envelope of a system which contains six components: methane, ethane, propane, butane, hexane and decane.
As with the pure component data system discussed earlier the case study can be set up interactively or by using a problem setup file. Only the former will be discussed in detail, but the setup file, hycbvle.mfl, is provided and may be used to load models and components or as an example for writing or editing your own files for handling similar cases.
Specify the model
Any of the equation of state models would be suitable for handling this problem. We have chosen the advanced version of RKS but very similar results would be expected using advanced PR, PR or RKS.
Select Select, then
Select Model set from the sub-menu, followed by
Selecting Equations of state from the Select Model set dialogue box and again,
Selecting RKS (Advanced) with the default option for transport property models.
Finally, click on OK in the message box and Close in the Model set dialogue box.
Specify the components
The INFODATA databank will be the default data source and this is acceptable for this case study, so we can move directly to specifying the components. You can activate the Select Components dialogue box by either
Clicking on the
select components button 
or
Selecting Select from the menu bar and
Selecting Components from the sub-menu
The various methods for selecting or searching for components have been shown before, see “Selecting components” on page 87. As our current system contains simple well known compounds they have been selected by
Highlighting the Name option button
Typing the component name in the Enter name text box
and pressing the enter key after the name to load it for Multiflash
or
Clicking on Add to load the component.
Click on Close to load the components
Define the composition
Click on Compositions in the Conditions section, and
Type in the compositions in the drop down table. For our example they are:
Methane 0.45
Ethane 0.20
Propane 0.10
Butane 0.10
Hexane 0.10
Decane 0.05
Calculating the bubble point curve
You can calculate the bubble point curve using a series of flash calculations or by generating the phase envelope. Individual calculations may be a series of bubble point calculations at either fixed temperature or fixed pressure. Technically there is no particular reason to prefer one over the other; for this particular example we will fix temperature and have our output pressure in bar.
To change the pressure units,
click on the Select input and output units button
, then in the
Tab control click on Pressure
and click in the
Output option button box against bar. (You can also change the input units for
pressure if you wish.)
Having specified the model, components, compositions and units,
Enter the first temperature, 250K, in the Conditions section and
Click on the T,
Bubble button, 
.
Repeat the last two steps increasing the temperature by 25K each time. At 375 you still have a stable solution reported but by 400K the solution is reported to be “marginally stable” but by you will notice a failure message
Bubble point at fixed T:
*** WARNING -20323
***
Possible instability in solution (constrained flash)
*** ERROR 20334 ***
Constrained flash solution unstable
*** ERROR 20028 ***
Cannot solve flash problem - other unspecified error
*** ERROR 344 ***
The flash calculation has not converged
Investigating the bubble point curve using reduced temperature steps you will see that at 403K the solution is at the stability limit and the compositions of the liquid and gas phases are very similar, indicating that we are probably close to the critical region. You can either investigate this area of the phase envelope further using P,T flashes or move to calculating the dew point curve to formulate a view of the phase envelope.
Calculating the dew point curve
As with the bubble point curve, the dew point curve can be calculated from a series of dew point calculations at either fixed temperature or pressure. Again we will use dew point calculations at fixed temperature for this example
As with the bubble point curve, start at
275K and calculate the dew point at 25K intervals using the T, dew point button, 
.
This time the dew point calculation fails to converge at 475K. Returning to the last successful convergence at 450K, increase the temperature in 5K steps. This time the first failure to converge occurs at 470K.
We know that it is probable that the critical point is around 400K so it is a reasonable assumption that this system has a significant retrograde region. Check this by repeating the dew point calculation at 450K but this time by using the fixedphase fraction route and looking for the upper retrograde solution.
To do this:
Click on the
fixedphase flash at fixed temperature button, 
’
In the dialogue box which is then activated,
Click on the roll down arrow to the right of Select phase and from the drop down menu click on GAS. Choose Mole Fraction under Select Basis and enter a phase fraction of 1.0 in the text box and click on the Upper retrograde type of solution. This fixedphase flash simulates a dew point calculation.
Click on Do flash.
The calculated dew point pressure is now 114.527 bar for the retrograde region, whereas for the “normal” dew point the calculated pressure was 28.1796 bar. This confirms that we have a retrograde region for this system.
To calculate the full dew point curve you therefore need to increase the temperature at 1K intervals above 460K, using the normal T, dew point flash, until you meet the first convergence failure, at which point you are just beyond the cricondenbar. You should now switch to fixedphase fraction flashes at fixed temperature, set the options as described and reduce the temperature in small steps. This will define the retrograde dew point curve to 402K.
Phase envelope
The same problem can be investigated more easily using the phase envelope calculator. Set up the problem as before, but instead of carrying out individual dew and bubble point calculations
Select Calculate/Phase Envelope or click on the Phase Envelope button
Click on V/L Autoplot and Click on Yes when the message box appears asking if more points should be calculated. The resulting plot includes the dew and bubble point lines and the critical point is labelled.
The output in the results window will allow you do identify the critical point explicitly
53C 402.732 147.11
Adding water to the system
It is quite common in the oil and gas industry to find some water present with hydrocarbon systems, which will probably form a separate liquid phase. In this case study we can add water and look for the water dew point line.
To add water to the input stream
With the hydrocarbon case study defined,
Click on the Select component button
In the Select components dialogue box, enter water in the Enter name text box then press the enter key or click on Add
Click on Close
In the main window, click on composition and in the drop down table enter a composition for water, say 0.2.
Calculating the water dew point line
If there are more than two liquid phases present then using Multiflash to calculate the dew point, defining either temperature or pressure, will result in finding the primary dew point, in this case the hydrocarbon liquid dew point. To find the dew point for the second liquid phase, in this case water, you must use the fixed phase fraction flash and look for the temperature or pressure where there is a zero amount of that phase. Therefore, for the water dew point,
Enter the first temperature in the Conditions section of the main window.
Click on the
fixedphase fraction flash at fixed temperature button, 
.
In the resulting dialogue box, click on the arrow under Select phase and select water. Under Select basis choose Mole Fraction and enter a phase fraction of 0.0. The “normal” type of solution should be satisfactory for the water dew point.
Click on Do flash
Repeat the calculation at increasing temperatures to obtain the water dew point line.
Alternatively, plot the water dew point line using the Phase Envelope calculator by selecting the water phase at 0.0 molar phase fraction.
Including a petroleum fraction
The heaviest component in our hydrocarbon stream is decane, but often the heavier end of oil or gas condensate systems is defined as a petroleum fraction rather than as a single specified component. Each petroleum fraction will consist of a mixture of components and the fraction as a whole will be defined in terms of its molecular weight, density and possibly boiling point, although the first two properties are the most likely to be reported. Often the heavy end will be reported as a single fraction, e.g. C7+, although sometimes a more detailed analysis may be available breaking the heavy end down into several fractions.
Multiflash includes petroleum fraction correlations which may be used to predict the thermodynamic and transport properties of the fraction based on the data available, see “Calculating petroleum fraction properties” on page 118 .
For this case study we will remove decane and water from our stream and replace decane with a petroleum fraction of molecular weight 234 and specific gravity 0.838.
To delete components
Assuming the stream definition for the last case study is loaded
Click on Select components button
In the Select Components dialogue box, select water in the list of components selected for Multiflash, then click on Delete. This will remove water from the list. Repeat this for decane. You should now be left with methane, ethane, propane, butane and hexane.
To add the petroleum fraction
In the Select components dialogue box
Click on the arrow to the right of the Data source list box, then select Petroleum fractions correlations.
In the dialogue box then activated:
Enter C7+ in the Name box, enter 234 for Molecular Weight and enter 0.838 for specific gravity.
Click on Add to include the fraction in the defined stream.
Alternatively you could use the Replace option to replace decane with C7+.
Click on Close
In the main window click on Composition and enter 0.05 for the amount of C7+.
The petroleum fraction is now included in the stream definition and the phase envelope calculation may be repeated with the new stream, although the cricondenbar, cricondentherm and retrograde regions will now be different.
If you only know that the petroleum fraction is C7+ but do not have a reported MW or specific gravity you can simply fill in 7 as the Carbon number
and Multiflash will determine the properties from a set of standard tables.
Other flash calculations
Many engineering applications involve a wide range of flash calculations, not just those related to determining the phase envelope. For example, an isenthalpic flash at fixed pressure can be used to simulate the expansion of a stream through a valve
Basing this case study on the simple hydrocarbon stream (and model) we first defined
Methane 0.45
Ethane 0.20
Propane 0.10
Butane 0.10
Hexane 0.10
Decane 0.05
we must initially carry out a P,T flash at the upstream conditions to determine the enthalpy and then a P,H flash at the exit pressure.
Having loaded the model set and stream information
Enter the upstream temperature, 300K and pressure, 50 bar
Click on the P,T flash button
The calculated total enthalpy is -10912.3 J/mol
The stream is then throttled isenthalpically to 10 bar, by
Entering the new pressure, 10 bar under Conditions
[CText1] Entering the calculated enthalpy under Conditions
Clicking on the P,H flash button
The calculated temperature at outlet has dropped to 276.468K.
You can also add the isenthalpic boundary for -10912.3 J/mol to your phase envelope.
Many users will receive a PVT Analysis for the composition of an oil or gas from one of the PVT laboratories and wish to use this as input to Multiflash. These reports follow a fairly standard format and the PVT Lab Analysis form endeavours to reproduce this to make entering information as easy as possible. The facility to add or delete components from the generated list is also useful. The form is discussed in detail in section “PVT Analysis” on page 110.
The case study we are considering here is based on a problem setup file called pvt1_new.mfl, which uses the Revised Analysis method.
To enter a PVT Analysis either choose the Select/PVT Lab Input menu option or click on the 
icon.
The Lab Analysis form will then be displayed.
Initially we will consider a case where you only have a single fluid composition. First select the datasource for your discrete (i.e. well-defined) pure components. This can be Infodata or DIPPR and we have chosen Infodata. Next at the top of the column headed Single fluid choose either mass or mol % as appropriate by clicking on the down arrow. If your PVT report offers a choice of mole or mass % it is the mass % that is the experimentally measured data and should be given preference for separator oils. Next enter the compositions of the discrete components and the compositions of the petroleum cuts. In the form the pseudocomponents or single carbon number (SCN) cuts are labelled C6, C7 etc. In your PVT Laboratory report they may be referred to as hexanes, heptanes etc., with the heaviest being labelled as a plus fraction such as C20+ or eicosanes+. In our example the heaviest SCN is C20.
The overall percentage will be totalled as you enter the compositions. If the final total is not 100 you will be offered the opportunity to normalise the compositions when you characterise the fluid.
You can enter further information to define the stream, such as the molecular weight of the Stock Tank Oil (STO), the total fluid or the heaviest SCN or the specific gravity of either the heaviest SCN or the STO. We have provided general advice on when such data should be supplied in “Fluid composition” on page 113. As the fluid in question has a heavy end (C6+) which comprises more than 50% of the stream we should supply this information if possible. We have therefore entered the molecular weight of the heaviest SCN but if you have the molecular weight of the total fluid available this may be preferable as this is again the measured quantity.
We will use the default distribution method, Infoanal2.
You are now ready to define the basis of your characterisation by choosing where in your existing analysis you want to start redistributing the remaining fluid into new pseudocomponents and how many pseudocomponents you want to split this heavy end into. We’ve started with the simplest case where we have chosen to start the split at the heaviest SCN and only allocate one pseudocomponent. Effectively we are only allocating physical properties to the existing SCNs. Click on the Do Characterisation button and you will see a message box such as
followed by a screenshot of the experimental data and the fitted distribution
Click on OK and Close to return to the main window where the new fluid composition will be reported
Properties of the individual pseudocomponents may be viewed using Tools/Pure Component Data as usual and further calculations can be carried out on the basis of this characterisation.
At this point, having successfully characterised the fluid, you can also save the input as an .mfl file.
A useful way of seeing how changing characterisations alter the results of phase calculations is to use the phase envelope generator. For instance, plot the phase envelope of this fluid.
You can investigate various aspects of the characterisation and the sensitivity of the phase envelope to changing these. For instance you can change the distribution method to Infoanal1 and re-plot the phase envelope, do this and also include a n-paraffin distribution by ticking the Estimate Wax Content box. In the latter case the names and compositions of the fraction cuts will differ,
but the phase envelope is not significantly affected.
If you return to the PVT Lab Analysis form and instead of the heaviest SCN choose total liquid and enter a MW of 68. Do the characterisation and plot the phase envelope. Then see what the effect is of extending the heaviest SCN to further fractions, by leaving C20 as the start of the pseudocomponents but choosing to split it into 5 pseudocomponents. Alternatively you can group the components by starting the pseudocomponent split at C8 and grouping the plus fraction into 15 pseudocomponents. You can see that this alters the cricondenbar but the major effect is on the cricondentherm.
Next, return to the original fluid definition and re-plot the phase envelope, then in the PVT Analysis form enter a watercut. This is defined in terms of the volume percentage of the total fluid that is water. In this case choose 3 %. In the main window plot the new phase envelope and the water phase. boundary.
Finally, return to the original fluid analysis again and this time add a separator gas. Here we will look at a simple problem where the gas is 100 % methane added at a GOR of 100 m3/m3. Move to the Liquid + Gas tab and enter 100 next to methane in the left hand column headed separator gas and in the Recombined fluid section of the PVT form set the GOR units to m3/m3 and enter 100. Do the characterisation and return to the main window and plot the new phase envelope.
The black oil analysis offers the user an opportunity to take a very limited input specification (known as Black Oil input) for a condensate or oil and from this generate a normal compositional analysis. Our example is based on the blackoil.mfl file.
The minimum required input is the gas gravity(relative to air), the STO specific gravity(relative to water) at 60F and 14.7 psi and the solution GOR. The latter is the volume of gas produced at surface standard conditions divided by the volume of oil entering the stock tank at standard conditions. It is often referred to as Rs.
The remainder of the form is the standard PVT, except that you do not provide molecular weight or specific gravity. You can choose the pseudocomponent distribution as normal, depending on the final application. In this case the split is five fractions from C6+. Clicking on Do Characterisation generates the message that the characterisation has been successfully completed – in this case there is no compositional information to generate the compositional plot. The new composition is echoed in the main window and the phase envelope can be plotted as before.
Additional data can be added such as the Watson K-factor and/or the Gas analysis. Plotting the phase envelopes shows the effect of including this data.
To determine the properties of any refrigerant mixture, first load refrig.mfc using File/Load problem setup. The refrigerant mixture can then be defined as normal using Select Components and providing the composition. However, there are several well defined refrigerant mixtures which have been allocated refrigerant numbers e.g. R407A. This is a mixture of the pure refrigerants, R32, R125 and R134A, with a fixed composition (in mass percentages) of 20/40/40. To help our users we have set up .mfl files defining components/compositions for
R401A
R401B
R401C
R402A
R402B
R404A
R405A
R406A
R407A
R407B
R407C
R407D
R407E
R408A
R409A
R410A
R411A
R411B
R414B
R417A
R500
R501
R502
R503
R504
R507A
R508A
R508B
To determine the dew point properties of R407A
Load refrig.mfc
Load R407A.mfl
Specify pressure, e.g. 25 bar or 25e5 Pa
Click on the P, Dew point flash icon or menu item
And the results will be displayed in the results window
Dew point at fixed P:
Multiflash is equally applicable to polar mixtures, although for systems of this type an activity model, such as Wilson-E, NRTL, UNIQUAC or UNIFAC, plus binary interaction parameters is usually needed to obtain accurate results. For the first three models, Multiflash has BIPs available for many binary pairs but where these are missing you need to supply them. For UNIFAC BIPs are generated from group structure. Before carrying out phase equilibrium calculations for polar streams using an activity coefficient model we recommend that you check the availability of BIPs for your system and look up interaction parameters for the binary pairs where none are available from INFOBIPs. An alternative is to fit experimental data to a model used in Multiflash or generate data from UNIFAC and fit this to the model of your choice. We have provided sample spreadsheets which allow you to do both using the Excel interface.
|
Reference: Dechema Chemistry Data Series Vols I to XIV, Dechema |
A good source of experimental data and BIPs is the series of volumes in the “Chemistry Data Series”, published by Dechema. The UNIFAC model will provide estimates of vapour-liquid and liquid-liquid equilibria without the need for BIPs. |
Modelling a polar mixture.
Using INFOBIPS
As polar mixtures are usually non-ideal you may have some information on their phase behaviour and wish to know how best to reproduce this. A simple example is the acetone/water mixture. The Dechema data series referred to has several sets of data for this system. We have taken, at random, the data by Kojima et al, Kagaku Kogaku 32, 149 (1968) and based the example on one experimental point
Pressure 760 mmHg
Temperature 60.39 degC
x(acetone) 0.4000
y(acetone) 0.8426
We can use Multiflash to see how well different models and different sets of parameters represent this data. Depending on the relative importance to your application of accurate temperature or phase composition we can fix P and x and calculate T and y using a bubble point calculation at fixed P or fix P and T and calculate x and y with a P,T flash.
We would usually suggest using activity coefficient models to predict phase behaviour for non-ideal mixtures. If you have BIPs available either from INFOBIPS or from any other source for any particular activity model then this is the model you should use.
Specify the mixture by
Clicking on the Select components button
With the
Type acetone in the Enter name text box and