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The paper was presented at the Annual Technical Meeting of Geothermal Resources Council, in San Diego, CA, September 1998.

A Computer Program for Geothermal Decline Curve Analyses

M. Ali Khan
Department of Conservation - Division of Oil, Gas, and Geothermal Resources
Keywords: The Geysers, Production, Injection, Superheat, Decline Curve, Data Reduction, Visualization

The most widely used technique for oil and gas reserve estimation has been the decline curve method, which also has geothermal applications. Prior to the widespread use of PCs, production data were plotted and a French curve was used to extrapolate the remaining reserves.

A PC-based program, which takes full advantage of the Window's graphics interface, has been developed. This QuattroPro© program is graphically oriented, making it easy to use and interpret results for the novice and the expert, alike. The data may be imported and updated, either for individual wells or fields using standard spreadsheets, or for large groups of wells, using standard database files, such as those used by the Division of Oil, Gas, and Geothermal Resources. Standard decline methods (exponential, harmonic, and hyperbolic), manual overrides, and nonlinear-offset functions are available. Results may be printed in graphic and tabular formats or exported for financial or reservoir modeling. Some examples are presented from geothermal fields.

Decline curve analysis has been a mainstay of the oil and gas industry for the last 90 years, but its application to the geothermal industry is more recent. Application to declining production at The Geysers Geothermal field is of particular interest. Dykstra (1981) discusses the observed rate of decline in the 1970s and early 1980s. S. Enedy (1987), K. Enedy (1989), and Sanyal et al. (1989) describe approaches to and the role of decline curve analysis at The Geysers.

In recent years, the mainframe computer and the personal computer (using DOS) have been used to solve decline curve problems, with analytical algorithms developed over 50 years ago. In decline curve analysis, the historical relationship of an independent variable (i.e., time or cumulative production) and a dependent variable (i.e., production rate, p/z, p, t, GOR, GWR, or OWR) is plotted or entered on a spreadsheet and the best-fit curve is extrapolated to an economic limit. The underlying assumption is that the past relationship of the dependent variable to the independent variable will continue in the future. The analysis yields an estimate of remaining reserves and the productive life of a well or group of wells, and production rate at some future date.

A QuattroPro© program named DOGGR-CF has been developed by the author to allow Division of Oil, Gas, and Geothermal Resources (DOGGR) engineers the ability to apply these concepts to reserve estimates and other needs of the Division. Enhancements and improvements are being made.

Decline Curve Method
Towler and Chakmakian (1994) and Masoner (1996) presented iterative numerical methods for use on a personal computer to find the values for initial production and decline rates, and the hyperbolic constant. DOGGR-CF initially places no limits on the values of qi, Di, or b, and the program runs iterations until it finds the best curve fit with least-square summation for the hyperbolic equation:

qt = qi ^ (-1/N)

  qt= Production @ time t
   qi= Initial Production
    Di= Instantaneous Decline Rate (to be determined by the curve-fit)
     N= Exponent (to be determined by the curve-fit)

The ideal curve-fit will have a value of r =1.00
The three variables in the curve-fit are:
  qi, N and Di
     r 1.00


  Pq=Production rate
   Eq=Extrapolation rate
    Qa=Average production rate
     to= Start of curve-fit time
      tn= End of curve-fit time

Options for curve-fits within the exponential, hyperbolic, and harmonic envelopes are provided in the program. In the exponential selection, iterations are run while the hyperbolic constant b is restricted to values near 0.0; in the hyperbolic case, b may be any value between 0.0 and 1.0; and in the harmonic case, b may be any value greater than 1.0. The user may even assign values to either b or Di and let the program find the best fit within these constraints.

Program Benefits and Uses
DOGGR-CF is easy to use, gives results that are reproducible, does not require subjective interpretation (but still the allows the user to get a feel for reservoir behavior and override results); and features input and output screens that are portable and reusable in financial and mapping modules. The program has been tested with oil and gas production data by DOGGR engineers. Additional functionality is being added.

Author at the Geothermal Resources Council Annual Technical Meeting.

Geothermal Field Examples
The Division of Oil, Gas, and Geothermal Resources database of geothermal production and injection data is complete for all geothermal fields from 1970 to present. The data used in DOGGR-CF can be monthly, quarterly, or yearly. The following examples represent typical production wells with production summed by quarter.

In Example A, we arbitrary decided to use first third of the field data, and ran the best unrestrained curve-fit. The resulting curve-fit was reasonably close to the remaining two-thirds of actual production. Of course, having a steady-state withdrawal and long producing life lent itself to such good prediction. The example shows the type of best-fit curve (harmonic) and the chosen economic limit (525 * 10^3 kg/day) that is calculated to be achieved in the 10th month of the year 2031. The remaining reserves are calculated to be about 214,000 * 10^3 kg. The best-fit curve yielded a fit of 0.877, with the hyperbolic constant N (same as b) = 2.382, and an initial decline rate D (same as Di) = 10.73 percent.

In Example B, the offset function is applied twice (approximately at years 1980 and 1995). Each time after the offset, the curve fit well without any other adjustment. The value of the hyperbolic constant and initial decline rate remain the same as before the offset.

A new, easy to use QuattroPro© program has been developed. The program has been tested on oil and gas applications. Although it has only recently applied to geothermal data, early results are positive.

I would like to thank my many colleagues in the Division of Oil, Gas, and Geothermal Resources who helped with this project.

Dykstra, H., 1981. A Reservoir Assessment of The Geysers Geothermal Field, A.D. Stockton, Principal Investigator, California Division of Oil and Gas Publication TR27, Sacramento, California.

Enedy, K.L., 1989. The Role of Decline Curve Analysis at The Geysers, Geothermal Resource Council Trans., v. 13, pp. 383-391.

Enedy, S. L., 1987. Applying Flowrate Type Curves to Geysers Steam Wells, Proceedings of the Twelfth Workshop on Geothermal Reservoir Engineering, Stanford Univ., January 20-22, pp. 29-36.

Faulder, D.D., 1997. Advanced Decline Curve Analysis in Vapor-Dominated Geothermal Reservoirs, SPE 38763, SPE Annual Tech. Conf., San Antonio, TX, October 5-8, pp. 139-150.

Masoner, L.O., 1996. A Decline Analysis Technique Incorporating Corrections for Total Fluid Rate Changes, SPE 36695, SPE Annual Tech. Conf., Denver, CO, October 6-9, pp. 171-182.

Sanyal, S.K., Menzies, A.J., Brown, P.J., Enedy, K.L., and Enedy, S. L., 1989. A Systematic Approach to Decline Curve Analysis for The Geysers Steam Field, California, Geothermal Resources Council Trans., v. 13, pp. 415-421.

Towler, B.F. and Bansal, S., 1993. Hyperbolic Decline-Curve Analysis Using Linear Regression, Journal of Petroleum Science and Engineering, v. 8, pp. 257-268.

Towler, B.F. and Chakmakian George G., 1994. Spreadsheet Determines Hyperbolic-decline Parameters, Oil and Gas Journal, March 14, pp. 61-64.