La competencia como contraposición y capacidad

You can model asphaltene or wax precipitation by selecting Calculations|Asphaltene/Wax

Modelling. The approach is described in detail in references cited above. It is recommended

that you go through the example data sets solid-asph1.dat, solid-phenanthrene.dat, solid- wax.dat and solid-asph2.dat to get familiar with the approach.

For specification of data on the Calculations tab and the Plot Control tab, please see the section “Common input for two-phase flash, multiphase flash and asphaltene/wax

modelling calculations” at the beginning of this chapter.

Additional plotting options are available on the tab Plot Control for Asphaltene/Wax modelling. If X-Y Plots is selected, the amount of solid in terms of weight percent precipitated can be plotted in addition to three other phase properties.

Selecting Pseudo-Ternary Phase Diagram allows creation of a triangular diagram, displaying the results of flash calculations in terms of phase split (e.g. liquid-vapor, solid-liquid-vapor, solid- liquid, etc.) along dilution lines. The first step is to assign each component to one of three

pseudo-components by entering the number 1, 2 or 3 in the column labeled “Pseudo” in the table. Pseudo-component 1 is at the lower left apex of the triangle, 2 is at the lower right and 3 is at the top. Definition of the dilution lines is done by first selecting which two pseudo-components will be held at a fixed ratio along each dilution line. For example, setting pseudo-components A to 1 and B to 2 indicates that the base of the dilution lines will be along the bottom of the diagram, between apexes 1 and 2, and the lines will terminate at the top of the diagram at apex 3. The molar ratios of the two pseudo-components along each dilution line are then defined by entering the mole fraction of pseudo-component B for each desired line in the table under Dilution Line

Definition. The number of flashes desired on each dilution line must also be specified.

On Tab Ref. State, the following information is entered:

Calculation Method Identifier

The three-phase flash algorithm performs flash and stability calculations in an alternating sequence. The calculation begins with a stability test on the single-phase fluid. If the phase is unstable, a two-phase flash calculation is performed, followed by a stability test on the converged two-phase system and so on. Three calculation methods are available. They differ in the sequence in which the stability tests are performed. In Method 1, the stability test is performed first with respect to the solid phase. In Method 2 (default), the stability test is performed with respect to all fluid phases prior to a stability test with respect to the solid phase. Method 3 is a special case of Method 1; with Method 3, a stability test on the converged two- phase fluid-solid system is not performed. Thus, Method 3 is more efficient but not as rigorous as Method 1. For most cases, Methods 1 and 2 converge to the same results. In exceptional cases, it has been found that only one method converged while the other one failed.

68 • Flash Calculations User's Guide WinProp

Number of Solid Forming Components

Of the Nc total components, the user may specify the last N1 as the number of solid forming components. The default is set to 1, that is only component number Nc can precipitate. Once this number is specified in the text box provided, the component number and name for all the precipitating components are shown on the first and second columns of the table on this tab. Depending on the method selected for computing the reference fugacity, columns 3-5 of this table will also be updated automatically.

Reference Fugacity (ln (solid fugacity (atm)))

Four options are available for specifying the reference fugacity through the Reference fugacity combo box:

CALCULATE The reference fugacity at the specified pressure and temperature is set equal to the fugacity of the solid forming component after the system has converged to a single liquid phase or a two-phase vapor-liquid system.

LCORRELATE This is used for wax only. The reference fugacity at the specified

pressure and temperature will be correlated with the pure component liquid fugacity at the same pressure and temperature.

PREVIOUS Use the value for the reference fugacity from a previous multiphase

solid flash calculation.

USER INPUT This selection implies that the value of the natural logarithm of the reference fugacity in units of atmospheres as well as the corresponding reference pressure and temperature will be input by the user for each precipitating component on the table provided. The user must select this option before the values can be entered in the table

If the reference fugacity specification is set to CALCULATE, solid onset pressures for the same mixture but at different temperatures may be specified in the Additional Onset Points table. ΔCp and ΔHtp (optionally vs) can be calculated so the solid model will match these onset points.

Additional Onset Points

Solid onset pressures at different temperatures may be used to calculate parameters in the solid model for performing temperature-dependent precipitation predictions.

The requirements for doing this calculation are:

• Two, three or four solid precipitation onset pressures at different temperatures must be known for one fluid composition.

• The solid phase must be modelled with a single component, as is normally done for asphaltene precipitation modelling.

The pressure and temperature for one of the onset points must be entered on the Calculations tab as the pressure and temperature for the flash. This will be used as the reference condition, and will define the reference fugacity. Calculation of the other parameters will depend on the number of additional onset points entered, as described below. Normally vs is adjusted to match a known amount of solid at a given condition (bulk precipitation experiment) otherwise it will default as described under Solid-Phase Molar Volume.

User's Guide WinProp Flash Calculations • 69 • 1 additional onset point – ΔCp is set to the user-input value or defaults to zero. ΔHtp is

calculated to match the specified onset point.

• 2 additional onset points – ΔCp and ΔHtp are calculated to match the specified onset points.

• 3 additional onset points – ΔCp, ΔHtp and vs are calculated to match the specified onset points. This is not normally done, as it is preferable to use vs to match a bulk

precipitation experiment.

Reference Pressure (psia | kPa | kg/cm2)

This corresponds to the reference pressure for calculating reference fugacity. This pressure is required only if a reference fugacity is actually entered. If Field units is selected enter value in psia, for SI units in kPa and for modified SI units in kg/cm2. When the CALCULATE,

PREVIOUS or LCORRELATE options are selected for the reference fugacity, the

reference pressure is set internally by the program and need not be entered on the table.

Reference Temperature (°C for SI or °F for field units)

This corresponds to the reference temperature for calculating the reference fugacity. This temperature is required only if a reference fugacity is actually entered. When the

CALCULATE, PREVIOUS or LCORRELATE options are selected for the reference

fugacity, the reference temperature is set to appropriate values internally by the program and need not be entered on the table.

Solid-Phase Molar Volume (l/mol)

This corresponds to the component solid-phase molar volume for the calculation of the component solid-phase fugacity. If the molar volume is not specified, the following value is assigned:

• If the reference fugacity option is CALCULATE, the solid-phase molar volume is calculated from the EOS, unless 3 additional onset points have been specified. • If the reference fugacity option is LCORRELATE then the molar volume is

obtained from a correlation by Won (1986).

• If the reference fugacity option is PREVIOUS, the solid-phase molar volume from the previous calculation is used.

• If a value for the reference fugacity is entered, the solid-phase molar volume is calculated from the EOS.

Heat Capacity (cal/K/mol)

This corresponds to the component solid-liquid heat capacity difference for calculation of the component solid-phase fugacity. If this quantity is not explicitly specified for each

precipitating component, the following value is assigned:

• If the reference fugacity option is CALCULATE, the solid-liquid heat capacity difference defaults to zero, unless 2 or more additional onset points have been specified.

• If the reference fugacity option is LCORRELATE then the heat capacity difference is obtained from a correlation by Pedersen (1991).

70 • Flash Calculations User's Guide WinProp • If the reference fugacity option is PREVIOUS, the solid-liquid heat capacity

difference from the previous calculation is used.

• If a value for the reference fugacity is entered, the solid-liquid heat capacity difference defaults to zero.

Heat of Fusion (cal/mol)

This corresponds to the component heat of fusion for the calculation of the component solid- phase fugacity. If this quantity is not explicitly specified for each precipitating component, the values are obtained from a correlation by Won (1986).

Triple Point Pressure (psia | kPa | kg/cm2)

If the triple point pressure for each precipitating component is known then these may be specified under the column heading Triple Pres. If Field units is selected enter value in psia, for SI units in kPa and for modified SI units in kg/cm2. If the triple point pressure is not known then the default is a value of zero, which is realistic for high molecular weight compounds.

Triple Point Temperature (°C for SI or °F for field units)

If the triple point temperature for each precipitating component is known then these may be specified under the column heading Triple Temp. If not known then the values are estimated from an internal correlation that was developed by Won (1986).

Ratio of reverse over forward rate for conversion to irreversible solid

This is the equilibrium constant “K” described above under “Irreversible Asphaltene Calculations”.