On Tab Regression Controls, parameters for the numerical methods and grouping options are entered. Under Numerical Controls the following information is entered:
Convergence tolerance If the change in the objective function between two iterations, or the absolute value of the objective function, is less than this value, the regression stops.
Maximum number of iterations
The regression stops after the specified number of iterations.
Number of simultaneous regression parameters
Number of parameters to be regressed on at one time. The default value is 5. If the number of regression parameters is less than this number, the former will be used instead. Note that increasing this value can significantly increase the run time for the regression.
Under Grouping Controls an option is given to specify how the members of a group are varied during regression. Selecting Vary group variables by equal increments specifies that a change Δx will be applied to all group members as xnew = xold + Δx. Selecting Vary
group variables by equal ratios specifies that all group members will be multiplied by a
common factor as xnew = xold x FΔ. The default method is to vary the group members by equal increments.
Transferring Results to Other Data Sets
The results of the regression option are component properties that will be used in subsequent calculations. If calculation options are appended after the End Regression form then the component properties used will correspond to values modified by the regression procedure. However, it is prudent to examine the results of the regression calculation before proceeding further. This can be done easily using WinProp’s Update component properties feature. For example, when a regression is performed with a file named regress.dat, besides the standard output regress.out, WinProp also outputs a file named regress.rls. This (.rls) file contains the component properties from the regression process in a format readable by WinProp.
User's Guide WinProp Regression • 117 The contents of the (.rls) file can be used to update the component properties in the current data set by selecting File|Update component properties. Three forms: Titles/EOS/Units,
Component Specification/Properties and Composition forms are updated. The Regression Parameters and End Regression forms can now be removed from the file, and prediction of
phase behavior using the tuned model can be performed. To keep a record of the work done use File|Save as... to save this file with a different name, e.g. regress1.dat. Note that a number of back to back regression runs can also be performed in this way with same data but using different regression variables. A similar procedure applies to Plus Fraction Splitting and
User's Guide WinProp Compositional Grading • 119
Compositional Grading
Overview
The compositional grading phenomenon refers to a variation in fluid composition with depth in a reservoir. As depth increases the mole fraction of light components decreases, density increases and GOR decreases. Near critical oils and volatile fluids exhibit the largest compositional grading effects, while black oils have the least variation in properties with depth. Compositional grading is reduced if the system is highly undersaturated.
Assessment of compositional grading is important in estimation of fluid in place, initialization of reservoir simulators and consideration of production alternatives. For example, when considering gas injection in a reservoir with compositional grading the solvent composition required to achieve miscibility will vary with depth. There are two model formulations available for performing the compositional gradient calculation: the isothermal model or the thermal model.
The isothermal compositional gradient calculation solves the gravity/chemical equilibrium problem. Given the composition and pressure at a reference depth, the composition and pressure at any other specified depth can be determined. The saturation pressure at the specified depth is also calculated. If there is transition from bubble point to dew point saturation conditions over the calculation interval, the GOC depth will be estimated. This is done with a simple halving algorithm to locate the depth at which the transition from bubble point to dew point occurs. This ultimately requires saturation determination in the vicinity of the critical point, which can cause failure of the saturation calculation. The GOC calculation continues until an interval of 0.1m is reached or until the saturation calculation fails. For this reason, the accuracy to which the GOC depth was determined is reported in the summary table. Formulation of the problem and the required solution algorithms are given in Whitson and Belery [39].
The thermal model incorporates the effect of the geothermal temperature gradient on the compositional gradient. Thermal diffusion effects as well as the variation of fluid properties as a function of temperature can be included in the model. As for the isothermal model, the location of the GOC will be estimated if it exists. When the temperature is not constant, the system is not in equilibrium. The model solves for a stationary state, or zero mass flux condition, as described in Hoier and Whitson (SPE 63085).
Please note that the equation of state must predict a single-phase system for the reference composition at the reference pressure. If the system is unstable, the calculation cannot be performed. If experimental data indicate that the initial condition should be stable, some EOS tuning may be required before the compositional gradient calculation can be carried out.
120 • Compositional Grading User's Guide WinProp With the default output level of 1, only the summary table is shown in the output (.out) file. This gives the reservoir pressure, saturation pressure, density and two key mole fraction values as a function of depth. With output level 2, for each depth the full phase property table and the saturation calculation results are printed in addition to the summary table. When the detailed output is requested it will be printed in the order the calculation is carried out which is described below.
The calculation is carried out in the following order:
1. The first depth level above the reference depth is calculated, using the reference conditions as the initial guess for the calculation.
2. Continuing for each depth level from the first calculation to the top of the interval, each calculation is performed using the previous converged results as the initial guess.
3. The first depth level below the reference depth is calculated, using the reference conditions as the initial guess.
4. Continuing for each depth level from the calculation in step 3 to the bottom of the interval, each calculation is performed using the converged results from the previous calculation as the initial guess.
Data Input
Example data sets for the compositional grading calculation are given in compgrad-blackoil.dat and compgrad-voloil.dat. For field units, temperature is entered in °F, pressure in psia and depth in feet. For SI units, temperature is entered in °C, pressure in kPa and depth in meters. For Feed, K-values, Output level and Stability test level specifications, see the Chapter “Common Data Required for all Options”.
Specification of the primary calculation options is done on tab General. Enter the reservoir temperature at the reference depth in the text box Reference Temperature. In the text box
Reference Pressure enter a value for the pressure corresponding to the reference depth entered
in text box Reference Depth.
Enter the depth to the top and bottom of the formation in text boxes Depth to Top and Depth to
Bottom respectively. The total height of the fluid column as defined by these depths is divided
by the number of calculation intervals specified in the text box No. of Calculation Intervals to determine the evenly spaced points at which the calculation is performed. The default value is ten. If the user desires the calculation to be performed at certain specific depths, these can be entered in the table provided. Enter each depth in the column headed Depth Value.
The user can monitor the composition changes with depth for a given component or a range of components. This information will be printed in the summary table in the output file. When a range is selected the mole fractions of the specified components are summed and the total reported. For the first component or range of components to be tracked select the lower and upper limits through the combo boxes located next to the label Key Component 1. For the second key component or range select the lower and upper limits through the combo boxes located next to the label Key Component 2. The upper component must have a component index greater than or equal to the index for the lower component.
User's Guide WinProp Compositional Grading • 121 The thermal model data is specified on tab Thermal. To activate the thermal model check the box labelled Use Thermal Model. The temperature gradient imposed is constant and is entered in the textbox labelled Temperature Gradient. Entering a positive value for the thermal gradient implies increasing temperature with depth. The units are °F/ft for field units or °C/m for SI and modified SI. Various models for calculating the thermal diffusion
coefficients can be selected. In addition, constant thermal diffusion coefficients terms for each component can be entered in the table labelled Thermal Diffusion Coefficient Terms. Note that values entered in this table are not the thermal diffusion coefficients usually defined in the literature, but are the terms identified as Ft in Hoier and Whitson (SPE 63085). This table can also be used to enter multiplying factors for each component which will multiply the thermal diffusion coefficients calculated from the chosen model.
CMG’s GEM compositional simulator allows input of tables of composition vs. depth for initialization of the reservoir via the keyword *ZDEPTH. The results of the compositional grading calculation can be written out with this keyword in the format expected by GEM. The data will be written to a file with the same root name as the data file and the extension (.gmz). This option is activated by selecting the check box labeled “Write GEM *ZDEPTH
User's Guide WinProp STARS PVT Data Generation • 123
STARS PVT Data Generation
Overview
You can use this option of WinProp to generate the complete PVT data required by CMG’s steam and additives thermal simulator STARS. The data which may be generated includes:
1. Initial composition data
2. Liquid component densities, compressibility and thermal expansion coefficients, plus nonlinear mixing function data for density
3. Liquid component viscosity tables or correlation coefficients, plus nonlinear mixing function data for viscosity
4. Simple analytical correlation for component vapor-liquid K-values 5. Tabular gas-liquid K-values
6. Tabular liquid-liquid K-values 7. Tabular solid-liquid K-values
8. Gas-liquid and liquid-liquid K-values at surface conditions