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This option is invoked be selecting Characterization|Plus Fraction Splitting. An example data set for this option is split-mwsg_plus.dat.
General splitting model controls are entered on Tab General of the Plus Fraction Splitting calculation form as described below.
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Distribution Function Type
Three choices are available for the distribution function for splitting the plus fraction: Exponential Exponentially decreasing function appropriate for gas
condensates and lighter fluids
2-Stage Exponential Approximation to the gamma function suitable for black oil type fluids
Gamma Three-parameter gamma distribution suitable for all fluid types
Number of Fluid Samples
If the gamma distribution is chosen, up to 8 related fluid samples may be characterized simultaneously. If the exponential distributions are chosen, this text box is not enabled.
First Single Carbon Number in Plus Fraction
Enter the carbon number of the lightest SCN in the plus fraction (e.g. enter 6 to characterize a C6+ fluid fraction).
Number of Pseudo-Components
The SCNs can be used as is in subsequent calculations or lumped into pseudo-components right after the splitting procedure. The following options are available:
No lumping The SCNs will be used as is.
Determined internally WinProp will estimate internally the number of pseudo- components for the plus fraction.
Input value Specify the desired number of pseudo-components.
When using the gamma distribution and gaussian quadrature without extended analysis, the number of pseudo-components cannot be estimated via correlation and will be set equal to 3.
Lumping Method
Log(K) lumping is available when characterizing a single sample with any of the distribution functions. Gaussian quadrature lumping may be used with the gamma distribution, and is required for characterizing multiple samples. Log(K) lumping defines pseudo-components as having equal ranges of log(K). Gaussian quadrature lumping defines pseudo-components via analytical integration of the gamma distribution.
Critical Properties Correlation
Three correlations are available to calculate the critical properties of the SCNs. 1. Lee-Kesler (Kesler and Lee [12])
2. Riazi (Riazi and Daubert [34]) 3. Twu (Twu [36])
On the Distribution Tab, parameters relating to the chosen distribution are entered. Three of these properties are common to both exponential and gamma distribution types, as follows.
80 • Component Splitting and Lumping User's Guide WinProp
SCN Fraction MW Interval
This corresponds to the interval in molecular weight for each single carbon number group. For the gamma distribution, if a variable MW is selected this value is ignored. The default is 14.026.
“Bias” Parameter for SCN MW End Points
This parameter is used for setting the minimum molecular weight for the plus fraction distribution. A value of 0 means that the minimum MW will be equal to the normal alkane MW of the same carbon number as the first SCN fraction in the plus fraction. A value of 1 means that the minimum MW will be equal to the normal alkane MW of one lower carbon number than the first SCN fraction in the plus fraction. The default value is 0.75.
Distribution Function Cutoff
This parameter is used in determining the number of pseudo-components for lumping. This calculation requires specification of a maximum SCN number. Setting the cutoff to 1.0 means that the maximum SCN number will be set equal to the last SCN number in the analysis. This often leads to over-prediction of the required number of pseudo-components. Setting the cutoff less than 1.0 indicates that the maximum SCN number will be taken as the one at which the ratio of the sum of the individual SCN mole fractions to the total plus fraction mole fraction exceeds the cutoff. The value should be less than 1. The default is 0.95.
Parameters specific to the exponential distributions are:
Mole Fraction of Component Preceding Plus Fraction
This value is used to set the “Y-Axis” intercept of the two-stage exponential distribution function. For C6+ fraction characterization, this value should be set equal to the mole fraction of the C5 components, for C7+ fraction characterization, this value should be set equal to the mole fraction of the C6 components, etc.
“Y” Axis Intercept of the Distribution Function
This is usually set equal to the mole fraction of the component preceding the plus fraction (default).
Parameters specific to the gamma distribution are:
SCN MW Interval Type
When fitting the gamma distribution to extended analysis data, the SCN fractions can have fixed or variable intervals in molecular weight. Choosing Constant sets the MW interval equal to the value entered under SCN fraction MW interval. Choosing Variable (match
mole fraction) or Variable (match weight fraction) indicates that the upper MW boundary
of the SCN fraction is varied until either the experimental mole fraction or the experimental weight fraction (default) of the SCN is matched.
Eta Parameter (Minimum MW in Distribution)
The eta (η) parameter specifies the minimum molecular weight in the gamma distribution. By default, it will be calculated as described under “Bias” parameter for SCN MW end points.
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MW of Heaviest Pseudo-Component
The choices for molecular weight of the heaviest pseudo-component are No Restriction,
Internal Default or entering a value. Specifying No Restriction implies no upper limit in
MW on the gamma distribution, and is not recommended. It leads to prediction of very high molecular weights for the heaviest pseudo-component. The default setting obtained by selecting Internal Default sets the heaviest pseudo-component MW equal to 2.5 times the MW of the plus fraction. If multiple samples are used and No Restriction is selected, it will automatically be reset to Internal Default.
SG-Tb-MW Correlation
When Gaussian quadrature is used with the gamma distribution, the following correlations are available for determining pseudo-component boiling point from specific gravity and molecular weight.
1. Twu (Twu [36])
2. Goossens (Goossens [7]) 3. Riazi (Riazi and Daubert [34])
The controls available for determining gamma distribution parameters by minimization are:
Residual Value
The choices for residual value depend on what is selected under SCN MW interval type. The residual value setting indicates what experimental data for each SCN is used in defining the error function to be minimized. The choices are Molecular Weight, Mole Fraction and Weight
Fraction. If a constant MW interval is chosen, then molecular weight is not available as a choice
of residual value. Similarly, if a variable MW interval is chosen to match the mole fraction, then mole fraction is not available as a choice of residual value. The default is to vary the MW interval to match the weight fraction of the SCN, and adjust the distribution α parameter to minimize the error function defined in terms of the molecular weights.
Residual Type
The choices for residual type are Sum of Squares, Chi Square Goodness-of-Fit Test or
Sum of Scaled Squares. The default is sum of squares. For most applications, the difference
in minimization results between the residual types will be small.
Final SCN Fraction Data
The residual calculation can be specified to include or not include the data from the final SCN fraction in the analysis.
On each Sample Tab, the properties of the plus fraction are entered. The number of sample tabs appearing is set according to the Number of Fluid Samples entered on the General tab. If extended analysis data is available from a true or simulated boiling point (distillation) analysis, the data can be entered in the table on the Sample tab. In column 2 enter the mole fraction of each fraction. In column 3 enter the average molecular weight of the fraction. Note that if any extended analysis data are to be entered, mole fraction and molecular weight are required for each cut. If data is available then values for the specific gravity can be entered in column 4 and normal boiling point in °C in column 5. Please note that if data for normal boiling point is
82 • Component Splitting and Lumping User's Guide WinProp entered then data for specific gravity must also be entered. Sample data sets with extended analysis data are split-mw_analysis, split-mwsg_analysis and split-mwsgtb_analysis.
Number of SCN Fractions
If this entry is left blank, the value will default to the number of fractions in the analysis, or to 25 if there is no extended analysis. If the exponential distributions are used with extended analysis, and a value for number of SCN fractions is entered, it will be ignored. If the gamma distribution is used with extended analysis, and a value for number of SCN fractions is entered that is greater than the number of fractions in the analysis, the analysis will be extended using the distribution function to the specified SCN number.
MW+
Molecular weight of the plus fraction must be entered in the text box unless extended analysis data is given.
SG+
Specific gravity of the plus fraction must be entered in the text box unless SG data is given in the extended analysis table.
Z+
Mole fraction of the plus fraction must be entered in the text box unless extended analysis data is given.
If one of the exponential distribution function types is selected then the following data entry box will be available:
Slope
This is the slope of the exponentially decreasing curve of the distribution function. If not specified then it is determined internally based on data for a typical oil.
If the gamma distribution function is selected then the following data entry box will be available:
Alpha
This parameter is analogous to the slope parameter used for the exponential distribution types. If α>1, the distribution has a peak in mole fraction for an SCN greater than the initial SCN in the distribution. If α=1, the gamma distribution reduces to an exponential distribution, and if α<1 the function decreases more rapidly than an exponential distribution. In general, α is larger for heavier fluids, and smaller for lighter fluids. The normal range is from 0.5 to 2.5. If extended analysis data is available and α is not specified, it is determined by minimization to best fit the experimental data. If extended analysis data is not available and α is not specified, an estimate is determined internally based on plus fraction SG and MW.