In this Case Study, the Peng-Robinson equation of state will be tuned via regression to match the PVT behavior of a Gas Condensate fluid. Data for this example are taken from the Petroleum Engineering Handbook (H.B. Bradley, Editor-in-Chief, Society of Petroleum Engineers, 1987, pp. 39-6 to 39-9). The data given are typical for a fluid of this type, including hydrocarbon analyses of separator products, and results of constant composition expansion and constant volume depletion laboratory experiments.
Create Data Set for Splitting Calculation
Begin by double-clicking the WinProp icon in the CMG Technologies Launcher (accessed from the Windows Start Menu). This will open WinProp with a new blank data set ready for editing. The required forms Titles/EOS/Units, Component Selection/Properties and
Composition are placed in the new data set by default.
The first step in modelling the condensate fluid will be to split the heptanes plus fraction. The splitting calculation is inserted into the data set by selecting Characterization|Plus
Fraction Splitting from the main menu or by clicking on the SPLT button on the options
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Set EOS Model and Unit System
Double-clicking on the row labelled Titles/EOS/Units opens the form for selecting the EOS model and units system. Text to appear on the main form for the data set can be typed in the text box labelled Comments, while text to appear in the output file can be entered into the text boxes labelled Title 1 - 3. The text from Title 1 will also be used to label any plots that are created. The EOS and Units selection may be left at the default values as shown below.
Specify System Components to C6
Click OK to accept the data on the form and return to the main WinProp form. Specification of the system components is done by double-clicking on the row labelled Component
Selection/Properties. In this case all components up to hexane may be selected from the
WinProp component library. From the Component Selection/Properties form menu, select
Options|Insert library component and then use the mouse to choose the system components
User's Guide WinProp Appendix A • 155 Again, click OK to accept the selection and return to the Component definition form. All other information on this form can be left at the default values. Please refer to the “Components” section for information on modifying any of the default component properties. Click OK to return to the main form.
Specify System Composition
Composition for the selected components is specified by double-clicking on the row labelled
Composition and entering the values in mole % as shown on the following form.
A message will be issued when this form is closed, warning that the composition does not sum to 1 or 100. Since the heptane plus fraction has not yet been included in the system, this warning can safely be ignored.
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Specify C7+ Fraction Properties
Now that all of the light and intermediate components have been defined, all that remains is to characterize the heavy fraction as several pseudo-components. Specification of the heavy fraction properties, splitting into single carbon number fractions, and lumping into pseudo-components is easily done in a single step with WinProp’s splitting option. From the main form, open the Plus
Fraction Splitting form and enter the plus fraction properties on the third tab as shown below.
Specify Plus Fraction Splitting and Lumping Calculation
Now, click on the General tab to view the default parameters to be used for the splitting and lumping calculations. The plus fraction will first be split into 25 single carbon number fractions. Select Lee-Kesler as the critical property correlation to be used to generate the properties of these fractions. By default, WinProp will automatically determine the number of pseudo-components to lump into. It is also possible to select no lumping, or the user can enter the desired number of pseudo-components. The mole fraction of the component immediately preceding the plus fraction also has to be entered on tab 2, Distribution. In our case the component is FC6 with mole fraction equal to 0.0173. Information on the other tabs can be found in the “Component splitting and lumping” section. Click OK to return to the main form.
Save the Data Set and Run the Splitting Calculation
The splitting calculation is now ready to run. Select File|Save and enter a file name. The file extension (.DAT) will be added automatically if it is not specified. Now select File|Run to run the data set. When control returns to WinProp, the output file can be viewed by selecting
File|View output. The distribution of single carbon number fractions and the final properties
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Update the System Component Specification
The next step in the tuning process is to match the available experimental data via
regression. First, the component specification must be updated to reflect the results of the splitting calculation. This is done by selecting File|Update component properties from the main menu, which will modify the first three forms in the data set. Open the
Titles/EOS/Units form and enter a new comment and descriptive title for this data set. On
the Component Selection/Properties form the properties of the full component
specification, including the heavy pseudo-components, can be viewed and a new comment entered. Open the Composition form to verify that the mole fractions now sum to one. At this point the splitting calculation can be removed from the data set by selecting the row labelled Plus Fraction Splitting on the main form and pressing the Delete key or selecting
Edit|Delete from the main menu. To avoid overwriting the original data set, select File|Save As … and enter a new name for the data set.
Set Up the Regression Data Set
To begin setting up the regression run, make sure the row directly under the row labelled composition is selected. From the main menu select Regression|Start. The data set should now look like the following:
Copy the Data for Regression
The saturation pressure, constant composition expansion and constant volume depletion specification experimental data can now be copied from the template file Case_study-1.dat. This file is located in the WinProp templates directory, for example cmg\WinProp\1999.10\Tpl. Open the Case_study-1.dat data file, and select the rows from Saturation Pressure through
Constant Volume Depletion using the mouse. The WinProp window should appear as
158 • Appendix A User's Guide WinProp Select Edit|Copy from the main menu to copy these calculation options to the clipboard. Close the Case_study-1.dat file, then make sure that the row directly underneath Regression
Parameters in your data file is selected and choose Edit|Paste to paste the contents of the
clipboard into your data file. Next, click on the row underneath Constant Volume
Depletion, then select Regression|End to indicate the end of the calculation options to be
included in the regression. View the calculation specifications and experimental data by double-clicking on the appropriate row.
Select Initial Regression Parameters
The parameters to be used in the regression can now be selected by double-clicking on the
Regression Parameters row. To begin, select the critical pressures of the C7+ pseudo- components as regression variables. This is done by clicking on the cells in the first column (labelled Pc) for the last 5 components in the system. The first tab on the Regression
User's Guide WinProp Appendix A • 159 Click on the tab labelled Interaction Coefficients and in the same manner as for the critical pressures, select the Hydrocarbon Interaction Coefficient Exponent and the interaction coefficients between CO2 and Methane, and between CO2 and the C7+ pseudo-components. Select OK. Before the Regression Parameters form closes, a message box appears asking if you would like to change the value for the number of simultaneous regression parameters. Click No to accept the default value of 5. This means that a subset of the 5 most sensitive regression parameters will be used at each regression iteration. For more details please refer to the “Regression” section of the manual.
Run the Regression Data Set
The regression data set is now ready to run. Select File|Run; since the data set has changed since it was last saved, a message box appears asking if you would like to save the data set before running. Click Yes to save your changes.
While the data set is running, the progress of the regression can be tracked by noting the values of the residuals in the window displaying the run status messages. This information is also echoed to the output file. It is important to note that the magnitude of the change from the initial value of the residual is more important than the values of the residuals themselves.
Create Regression Summary Plots
Summary plots of the before regression and after regression results, along with the
experimental data, can be created by selecting File|Create Excel plots from the main menu. This will create an Excel workbook with individual plots of all of the simulated results, as well as the summary plots. Viewing the summary plots for this run quickly shows that only minimal improvement in the fit was obtained. Note particularly that the liquid dropout values for the constant volume depletion have large errors.
Check the Regression Summary Table
To check the numerical values for the before and after regression calculation errors, open the output file by selecting File|View output from the main menu. At the end of this file is a table with a summary of the regression results. Check if there has been any improvement of the match to the saturation pressure, shown in the first row of the summary table.
Modify the Regression Specification
Modifications to the data set can now be made to improve the predictions of the volumetric data and the saturation pressure.
Begin by opening the Component Selection/Properties form and viewing the column for the Volume Shift parameters. Note that all components have a default volume shift of zero. Select Volume Shift|Reset to correlation values from the menu to insert values correlated with component molecular weight for all components.
Next, open the Saturation Pressure form, and on the tab Calculations, enter a value of 50.0 for the weight associated with the experimental saturation pressure value. This is to ensure that the saturation pressure is more closely matched. On the Constant Volume Depletion form, Pressure Levels tab, enter a weight of 5.0 for the liquid dropout values.
Now, open the Regression Parameters form and add the volume shift parameters for methane and the C7+ pseudo-components as regression variables.
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Run the Modified Regression Data Set
Save and run the data set again. Note the decrease in the residual values. Create the Excel plots again. Check the match to the liquid dropout on the CVD summary plot. View the summary table in the output file to observe the effect of increasing the weight for the saturation pressure experimental data.
Specify Group Variables for Regression
Further improvement of the fit can be attempted using WinProp’s regression variable grouping method. The grouping method ensures that existing trends in the original
component properties are maintained, by incrementing or decrementing all of the members of a group by the same amount during regression. Since each group is treated as a single regression variable, this also provides a method for varying a large number of component properties without having to select them all as individual regression parameters.
Open the Regression Parameters form, and clear the selection of the critical pressures and volume shifts for the components C07-C09 through C15-C17 by clicking on the cells marked with an “X” for those components. Leave Pc and Vol shift selected for component C18+, and then select critical temperature and acentric factor for C18+. From the menu, select
Grouping|Start group selection, then click on the cells for components C07-C09 through C15- C17 in the critical pressure column then select Grouping|End group selection from the menu. In the same manner, select regression variable groups for the components C07-C09 through C15-C17 for properties: critical temperature, acentric factor and volume shift. On completion, the form should appear as follows:
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Run the Data Set and Create Final Summary Plots
Save and run the data set with the new regression specification.
In this case, the residual is reduced significantly, indicating that a much better fit has been obtained. Check the output file to verify that the predicted saturation pressure now matches the experimental value quite closely. Create the Excel plots and view the regression summary plots. The CVD summary should now show a good match of the liquid dropout as shown below.
CVD pressure levels and depletion data : CVD Calc. Regression Summary 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 0 1000 2000 3000 4000 5000 6000 7000 Pressure (psia) Li qu id V ol um e , % o rig in a l v o l. 0.0 20.0 40.0 60.0 80.0 P ro d u ced G as, % o rig in a l m o l
Final Liq. Vol. Init. Liq. Vol. Exp. Liq. Vol.
Final Prod. Gas Init. Prod. Gas Exp. Prod. Gas
Predict VLE Behavior with Tuned Model
Now that the EOS is tuned, it can be used to predict the phase behavior of the gas condensate. Begin by updating the component properties in the data set to reflect the results of the regression as was done after the splitting calculation. Select File|Update component properties, delete all of the rows underneath the Composition row, then save the file under a new name.
Specify a Two-Phase Envelope Calculation
Click on the row underneath the Composition row. Select Calculations|Two-phase
Envelope from the main menu, or click on the toolbar button labeled 2P ENVP, then open
the data entry form for the envelope calculation. On the first tab, change the pressure specification to UNKNOWN, the temperature specification to 60, and change the minimum temperature for the X-Axis to 32; leave all of the other envelope specification controls on this tab at the default values. The first tab should now appear like the one below.
162 • Appendix A User's Guide WinProp On tab Envelope Construction Controls, the phase boundary and quality line calculation can be specified. A value of 0.0 is already entered in the grid for Vol. frac. vapor phase. Below this row, enter values of 0.1, 0.2 and 0.3 to generate quality lines. Also set the Initial step size to 0.1. Save and run the data set to perform the envelope calculation.
In the output file, a table showing the Pressure, Temperature, Z-factors and K-values at all points for the two-phase boundary and all of the specified quality lines is given. Select
File|Create Excel plots to generate the diagram as shown in the figure below.
Tuned condensate model P-T Diagram 0 1000 2000 3000 4000 5000 6000 7000 0 100 200 300 400 500 600 700 800 Temperature (deg F) P ressu re ( p si a)
2-Phase boundary 90.000 volume %
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