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 AnalysesM. Ali KhanDepartment of Conservation - Division of Oil, Gas, and Geothermal Resources |

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

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

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

When 0

Where

Pq=Production rate

Eq=Extrapolation rate

Qa=Average production rate

to= Start of curve-fit time

tn= End of curve-fit time

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.

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

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.