Sains Malaysiana 36(2): 207-211 (2007)

Structural Analysis of Geothermal Decline Rate

(Analisis Struktur Kadar Penurunan Geotermal)

Sutawanir Darwis

Department of Mathematics, Institut Teknologi Bandung

Bandung, Indonesia

Isnani

Deptartment of Mathematics, Universitas Pancasakti

Tegal, Indonesia

Ali Ashat

Department of  Petroleum Engineering

Institut Teknologi Bandung, Bandung, Indonesia

Received  :  26 January 2006 / Accepted :  29 Mac 2007

ABSTRACT

The aim of semivariogram modeling is to infer the structure of spatial continuity of the measurements. Practical experiences show that semivariogram modeling is an important step in spatial interpolation. The usual empirical semivariogram is sensitive to extreme data and shows a noised pattern.  Some robust empirical semivariogram was proposed. This paper reports the application of pairwise relative empirical semivariogram to Kamojang geothermal decline rate.  Using the same data, the usual empirical semivariogram and pairwise semivariogram are compared.  Comparative study shows that the empirical pairwise relative semivariogram   is able to infer the structure of spatial continuity of the process.

Keywords: Semivariogram; pairwise semivariogram; decline rate

ABSTRAK

Pemodelan semivariogram bertujuan meneliti kontinuitas spatial dari pengukuran.  Pemodelan semivariogram merupakan langkah penting dalam interpolasi spatial.  Semivariogram peka terhadap data ekstrim dan memperlihatkan pola tidak teratur (noised).  Beberapa semivariogram kekar (robust) telah diusulkan. Makalah ini  melaporkan aplikasi semivariogram pairwise relatif  emperikal pada kadar penurunan geotermal Kamajong. Dengan menggunakan data yang sama, semivariogram biasa dengan semivariogram pairwise dibandingkan. Perbandingan menunjukan bahawa semivariogram pairwise relatif emperik mampu memperlihatkan kontinuitas struktur proses tersebut. 

Kata kunci: Semivariogram; pairwise semivariogram; kadar penurunan

REFERENCES/RUJUKAN

Arps, J. J. 1945. Analysis of decline curves, Trans. AIME: 228-247.

Armstrong, M & Diamond, P. 1984. Testing variograms for positive-definiteness. Mathematical Geology 16(4): 407-421.

Deutsch, C. V., & Journel, A. G. 1997. GSLIB : Geostatistical Library and User’s Guide. New York: Oxford University Press.

Fairley. J., Heffner, J., & Hinds, J. 2003. Geostatistical evaluation of permeability in an active fault zone. Geophysical Research Letters 30(18): 5.1-5.4

Gentry, R. W. 1972. Decline curve analysis, Journal of Petroleum Technology  SPE 3356: 38-41.

Hewett, T. A. 1986. Fractal distributions of reservoir heterogeneity and their influence on fluid transport. Society of Petroleum Engineers SPE 15386: 1-13.

Kamah, M. Y., Dwikorianto, Zuhro, A. A., Sunaryo, D., & Hasibuan, A. 2005. The productive feed zones identified based on spinner data and application in the reservoir potential review of Kamojang geothermal area Indonesia. Proceedings World Geothermal Congress, Turkey, 1111, pp 1-6.

Saptadji, N. M., Ashat, A., Syihab, Z., & Setiadi, D. 2005, GeTools: geothermal engineering tools. Proceedings World Geothermal Congress, Turkey, 1707, pp 1-10.

Sasradipoera, D. S., Sujata, I. K., and Komaruddin, U. 2000. Evaluation of steam production decline trends in the Kamojang geothermal field. Proceedings World Geothermal Congress, Japan, 2857-2862.

Shoji, T. 2000. Statistical and geostatistical analysis of temperature profile in the Yanaizu-Nishiyama geothermal fields NE Japan.  Proceedings World Geothermal Congress, Japan,  1753-1757.

Spivey, J. P. 1986. A new algorithm for hyperbolic decline curve fitting. Society of Petroleum Engineers, SPE 15293: 89-97.