SPREADSHEET PROGRAM FILE QUICKLY EVALUATES GAS PROPERTIES

Brij Agrawal
Victoria Department of Energy & Minerals
East Melbourne, Australia

A spreadsheet program file has been developed to estimate many of the gas properties required by reservoir engineers in their day to day work. This file eliminates the need for published correlations requiring charts or sophisticated fluid property programs that are tedious and time consuming to use.

Many existing PC-based spreadsheet program files require more than one operation or spreadsheet to calculate gas parameters. Also, once calculated the results are often difficult to transfer to other pro,-rams for calculating other parameters.

The gas parameters, calculated by the new spreadsheet program file, include the gas deviation factor Z, compressibility cg expansion factor Eg, and viscosity ug at various pressures and initial reservoir gas gradient.

If partial gas analysis (from C, to Cg) is available, the program also calculates the dry and wet gas heating value. Calculated results are automatically plotted, and tabulated and graphical data can be printed for further use.

SYSTEM REQUIREMENTS

The system requirement for this spreadsheet is a 386/486 PC with 4 megabytes of RAM (random access memory), MSDOS 5+ operating system, Microsoft Windows version 3+, and Lotus 123 version 3 + with Wysiwyg (What you see is what you get) or Lotus for Window'S. A different version is needed for the program file to run under Excel 3 +.

Also needed is a laser printer or other printer capable of printing graphs.

INPUT DATA

The program is for cases where a complete gas analysis is not available and the gas gravity is equal to or greater than 0.55.

The required input data include:

• Gas gravity

• Mole percentage of nitrogen, carbon dioxide, and hydrogen sulfide

• Reservoir pressure and temperature.

When calculating the dry and wet gas heating values, if the C1 to C5+ component analysis is available, the total mole percentages of all components must equal 100%.

GAS DEVIATION FACTOR

To calculate the gas deviation factor Z, the method of Hall-Yarborough 1 developed using the Standing-Carnahan equation of state has been used. The accuracy of calculating Z was analyzed by Takacs who found that the average difference between the Standing-Katz charts and the Hall-Yarborough method is -0.158% and the average absolute difference is 0.518%. 2 The accurate was further discussed by Cox 3 who found the Hall-Yarborough method to have unparalleled accuracy in the specified range of 0.20 Ppr 24.0 and 1.15 Tpr 3.00. Also, because the method is based on a hard sphere equation of state, it may be used for reduced pressures outside the range of the Standing chart.

The correction for non-hydrocarbon gases using the Wichert-Aziz 4 method has been applied during calculation of Z. The Z factor is obtained as follows:

• Gas gravity for the pure hydrocarbon portion of the mixture Gghc is first calculated using Equation 1 (see equation and nomenclature box.

• Pseudocritical pressure and temperature, Ppchc and Tpchc for the hydrocarbon portion of the condensate and miscellaneous reservoir gases are then calculated with Equations 2-5 .5

• Pseudocritical pressure and temperature for the whole gas mixture are found with Equations 6 and 7.

• The Wichert-Aziz correction, CWA, for non-hydrocarbon gases is then calculated by Equation S. The Wichert-Aziz correction has an average absolute error 6 of 0.97% within the limits of 150 and 7,026 psi, 40 and 300 F., CO2 up to 54.4%, and H2S UP to 73.8%.

• Pseudocritical pressure and temperature for the gas after applying Wichert-Aziz correction are determined with Equations 9 and 10.

• Pseudoreduced pressure and temperature are calculated with Equations 11 and 12.

• In Equation 13 for the gas deviation factor Z, the t is the reciprocal of pseudoreduced temperature (1/Tpr). The reduced density Y is obtained by solving Equation 14, a non-linear equation. The solution uses the Newton-Raphson iterative technique with five steps:
  1. An initial estimate of Y is made, k being the iteration counter. The initial value of k is 1.

  2. The value of YK if substituted in Equation 2 will result in a small non-zero value F.

  3. A better estimate of yk is made by the use of the first order Taylor series expansion, Equation 15. The derivative of Equation 14 results in a general expression of dF/dY as shown in Equation 16.

  4. Equations 14 and 15 are used to iterate until a value of Fk = 0 is obtained. In the spreadsheet, 10 iterations are used to be an acceptable value of Fk.

  5. Substitution of the correct value of Y in Equation 13 will give the gas deviation factor, Z.

OTHER FACTORS

Equation 17 7 calculates the gas expansion factor E, (inverse of gas formation volume factor Eg). The units are gas volume at standard temperature and pressure divided by one volume of gas at the reservoir temperature and pressure.

Isothermal gas compressibility c, is calculated by the Trube method.6 First, the pseudoreduced compressibility, c, is calculated by Equation 8. Then, it is divided by the pseudocritical pressure to obtain the isothermal compressibility by Equation 19.

The Lee method, 8 Equation 20, is used to calculate the gas viscosity. The parameters in Equation 20 are obtained from Equations 21-25.

The standard deviation 9 for the calculated gas viscosity is 2.69% in the pressure range of 100-8,000 psi, temperature range of 100-340 F., and CO2 between 3.2 and 0.9 mole %.

Equation 26 is used to calculate the initial reservoir gas gradient. In this equation, Dg,sc = 0.0763 Gg and 0.0763 is the air density, at 14.7 psi and 60 F. in lb/cu ft.

Heating value of the gas is calculated on the dry and wet basis. Equation 27 is for dry. On a wet basis, a correction is applied to the dry gas heating value DHV for the partial pressure of water vapor at standard temperature and pressure, Equation 28.

SPREADSHEETS

All cells in the spreadsheet, except those where data are entered, are protected. The input data (i.e., gas gravity, mole percentages of non-hydrocarbon gases, and the reservoir pressure and temperature) are entered in the highlighted area. If the C1 to C5+ component analysis is available, it should also be entered for calculating the heating value.

In addition, an entry is required to identify whether the gas is dry or with condensate (1 if associated with condensate) and whether the reservoir pressure and temperature are entered in metric or field units (metric = 1). The program then automatically calculates 13 pressures (in addition to the initial pressure).

If the initial pressure is less than 2,000 psia, some cells in the A24 to L37 range where pressures and the other gas parameters are calculated will indicate error message (ERR) and some cells in the A column may show negative values. In this situation, it is advisable to recall the spreadsheet file from the floppy/ hard disk and enter the actual values of pressures at which gas properties are to be calculated in the A24 to A37 cells.

A summary of the calculated results is provided.

There are two macros in the spreadsheet. The first prints the results of the calculation in landscape format. The other prints the two graphs where the calculated results are plotted.

Table 1 and Fig. 1 are examples of the spreadsheet and the two graphs.

REFERENCES

1. Hall, K.R, and Yarborough, L., "How to Solve Equation of State for Z-Factors," OGJ, Feb. 18, 1974, pp. 86-88.

2. Takacs, G., "Comparisons made for Computer Z-Factor Calculations," OGJ, Dec. 20, 1976, pp. 64-66.

3. Cox, J.C., "What you should know about gas compressibility factors," World Oil, April 1988, pp. 69-72.

4. Wichert, E., and Aziz, K., "Calculate Z's for Sour Gases," Hydrocarbon Processing, May 1972, pp. 119-122.

5. Farrar, R.L., Applied Reservoir Engineering, Course notes, 1990.

6. Trube, A.S., "Compressibility of Natural Gases," Trans. AIME, Vol. 210, No. 61.

7. Dake, L.P., Fundamental of Reservoir Engineering, Elsevier, 1978.

8. Lee, A.L., Gonzalez, M.H., and Eakin, B.E., "The Viscosity of Natural Gases,". JPT, August 1966, pp. 997-1000.

9. Craft, B.C., and Hawkins, M., Applied Petroleum Reservoir Engineering, Prentice Hall, 1991.

Copyright 1993 Oil & Gas Journal. All Rights Reserved.