Objetivos específicos 10

112 • Regression User's Guide WinProp Example data sets for regression begin with the word regress. There are 16 template cases that involve regression from regress-blackoil1.dat through regress-separator.dat. Please refer to the introduction section for a brief description of each of these data files.

Note the forms named Regression Parameters and End Regression in the “Forms” column. The calculation options between these two forms contain experimental data for regression. The form Regression Parameters is inserted by selecting Regression| Start while the form End

Regression is included by selecting Regression|End. The experimental data are entered on the

appropriate tables or text boxes in each calculation option. A weight is associated with each data item or group of data. The weights wi are used to assign a degree of importance to each data point. The default value is 1.0. A larger value gives more importance to the data while a lesser value gives less importance. The regression is performed by minimizing the objective function

(

)

[

]

∑

where xi,calc and xi,meas correspond to the calculated value and measured value respectively. To exclude any measured value from the regression, precede it with a negative sign ("-"). Please see the section on “Convention for experimental data input.”

All calculations before the form Regression Parameters use the parameter values before regression. All calculations after the form End Regression form use the parameter values after regression. For the calculation options that are included in the regression, the output and plots contain both results before and after regression.

In the above example, the CMG GEM EOS Model option was used to print component properties before and after the regression (see the section on “GEM fluid model generation

and component properties printing”).

Parameter Selection

Component properties for regression are selected on tab Component Properties of the

User's Guide WinProp Regression • 113 Select or unselect the component properties by clicking on the grid. Clicking the first time selects the property. Clicking a second time unselects that property.

If temperature dependent volume shifts have been activated on the component form, then volume shift will not be available as a regression parameter. Non-zero values of the aqueous phase solubility parameters, reference Henry’s constant and molar volume at infinite dilution, must be set on the component form to enable these variables as regression parameters. The mole fraction of the secondary stream used to define the feed for calculation options can be selected as a regression variable be clicking the checkbox below the grid.

Interaction coefficients are selected as regression parameters on tab Interaction Coefficients.

The interaction coefficients between hydrocarbon components are calculated from the

equation described in section “Interaction coefficients” in the Chapter “Components”. The HC-HC Int. Coef. Exponent is an important parameter for matching reservoir fluid saturation pressure. The list of HC-HC groups, defined earlier via the Component

Selection/Properties form is shown in the list box under the frame with the caption Hydrocarbon Groups. To select specific groups as regression parameters, first select the

option button labeled Select from list and then highlight entries from the list by holding down the CTRL key and clicking with the left mouse button. The interaction coefficients involving non-hydrocarbon components are selected by clicking on the grid.

Parameters specific to the viscosity correlations are selected on the tab Viscosity Parameters. As discussed in the “Components” chapter, there are two types of viscosity correlations available in WinProp: Jossi-Stiel-Thodos (JST) and Pedersen. When JST is being used, the correlation coefficients and the component critical volumes for viscosity are available to be selected as regression parameters. When the Pedersen correlation is active, only the correlation coefficients appear as possible regression variables on this tab. Both correlations also depend on the component critical pressures, critical temperatures and molecular weights. By leaving these values fixed, however, and regressing only on the parameters appearing on the viscosity parameters tab, the process of matching experimental viscosity data can be completely decoupled from the process of tuning the EOS to PVT data.

114 • Regression User's Guide WinProp Second set EOS parameters can be specified as regression variables in the same way as the first set. The user can toggle between the component properties and interaction coefficient tables belonging to the first and second set through the set selection menu. To activate second set when the first set is active select SetSelection|Second Set. The second set regression variables currently supported are the critical pressure, critical temperature, volume shift, omega A, omega B, interaction coefficient exponent and the binary interaction coefficients for pairs with a non- hydrocarbon species. The user does not need to enable the second EOS set through the

Component Selection/Properties form to specify second set regression parameters. The

second set is activated automatically when a second set regression variable is selected. The default variable bounds for a given property are the same regardless of which set the component belongs to. The selection of bounds is discussed in more detail below. The grouping feature discussed below can also be used for the second set parameters.