Abdurrahman SATMAN, Mustafa ONUR, Hülya SARAK

Düşük sıcaklıklı jeotermal rezervuarlar için boyutsuz rezervuar modelleri

Bu çalışmada, düşük sıcaklıklı jeotermal rezervuarların üretim davranışı analitik olarak modellenmektedir. Modellerde üretim, enjeksiyon ve doğal beslenmenin, düşük sıcaklıklı ve sıvının etken olduğu bir jeotermal rezervuarın basınç veya su seviyesi üzerindeki etkileri göz önüne alınmaktadır. Modellemede rezervuar ve akifer ayrı ayrı tanklar olarak temsil edilmekte ve beslenme kaynağının etkisi incelenmektedir. Model sonuçları sabit debide üretim/tekrar-basma durumunda analitik ifadeler şeklinde verilmekte, debi değişimleri Duhamel ilkesi yaklaşımıyla modellenmektedir. Rezervuar ve akifere ait model parametrelerinin tahmin edilmesinde, doğrusal olmayan ağırlıklı en küçük-kareler parametre yöntemi kullanılmaktadır. İzlanda’daki düşük sıcaklıklı jeotermal sahalardan biri olan Laugarnes jeotermal sahası ile Türkiye’den bir örnek olarak Balçova-Narlıdere jeotermal sahasına ait üretim ve su seviyesi verileri kullanılarak modelleme çalışması yapılarak, model sonuçları ile saha verileri karşılaştırılmaktadır.

Lumped parameter reservoir models for low-temperature geothermal reservoirs

In this study, the production behavior of low-temperature geothermal reservoirs is simulated by analytical models. Models consider the effects of production and injection rates and natural recharge on the pressure or water level behavior of a low-temperature, liquid dominated geothermal reservoir. Reservoir and aquifer are represented by different tanks and the effect of recharge source is studied. Tank systems used in the modeling and represent the geothermal system, can be classified as 1 reservoir tank with recharge; 1 reservoir, 1 aquifer with recharge; 1 reservoir, 2 aquifers with recharge; 1 upper reservoir, 1 lower reservoir with recharge; 1 upper reservoir, 1 lower reservoir, 1 aquifer with recharge. The reservoir in which the production/reinjection occurs represents the innermost part of the geothermal system. The aquifer in which neither production nor reinjection occurs, recharges the reservoir. The recharge source represents the outermost part of the geothermal system. Model results for constant production/reinjection flow rates are given in the form of analytical expressions. Variable flow rate case is modeled by Duhamel’s principle. By using nonlinear weighted least-squares parameter estimation technique, measured field data are matched to model results, and thus reservoir and aquifer parameters are estimated. Model results are compared with the measured data for Laugarnes geothermal field located in Iceland. As an example from Turkey, Balcova-Narlidere geothermal field is investigated.

PDF

___

Alkan, H., Satman, A., (1990). A new lumped parameter model for geothermal reservoirs in the presence of carbon dioxide, Geothermics, 19-5, 469-479.
Axelsson, G., (1989). Simulation of pressure response data from geothermal reservoirs by lumped parameter models, 14th Work-shop on Geothermal Reservoir Engineering, Stanford University, USA, 257-263.
Axelsson, G., Gunnlaugsson, E., (2000). Long-term monitoring of high- and low-enthalpy fields under exploitation, International Geothermal Association-International Institute for Geothermal Research, Auckland, New Zealand.
Bard, Y., (1974). Nonlinear Parameter Esti-mation, Academic Press, San Diego.
Brigham, W.E., Ramey, H.J.Jr., (1981). Material and energy balance in geothermal reservoirs, Reservoir Engineering Assessment of Geothermal Systems, Ramey, H.J.Jr. (editor), Petroleum Engineering Department, Stanford University.
Castanier, L.M., Sanyal, S.K., Brigham, W.E., (1980). A practical analytical model for geothermal reservoir simulation, SPE 8887, SPE Caifornia. Regional Meeting, Los Angeles, Ca, Nisan 9-11.
Dogru, A.H., Dixon, T.N., Edgar, T.F., (1977). Confidence limits on the parameters and predictions of slightly compressible, single phase reservoirs, Society of Petroleum Engineering Journal, Şubat 42-56.
Garbow, B. S., Hillstrom, K. E., More, J. J., (1980). Subroutine LMDER, Argonne National Laboratory, MINPACK project.
Grant, M.A., (1977). Approximate calculations based on a simple one phase model of a geothermal reservoir, New Zealand Journal of Science, 20, 19.
Kuchuk, F.J., Ayestaran, L., (1985). Analysis of simultaneously measured pressure and sandface flow rate in transient testing, Journal of Petroleum Technology, Şubat, 323-334.
Olsen, G., (1984). Depletion modeling of liquid dominated geothermal reservoirs, Technical Report SGP-TR-80, Stanford Geo-thermal Program, Stanford University, USA.
Onur, M., Kuchuk, F. J., (2000). Nonlinear regression analysis of well-test pressure data with uncertain variance, SPE 62918, SPE Annual Technical Conference and Exhibition, Dallas, Ekim 1-4.
Sarak, H., Onur, M., Satman, A., (2003). New lumped parameter models for simulation of low-temperature geothermal reservoirs, 28th Stanford Workshop on Geothermal Reservoir Engineering, Stanford University, USA, Ocak 27-29.
Sarak, H., Onur, M., Satman, A., (2003). Applications of lumped parameter models for simulation of low-temperature geothermal reservoirs, 28th Stanford Workshop on Geothermal Reservoir Engineering, Stanford University, USA, Ocak 27-29.
Satman, A, Onur, M., Serpen, U., (2002). İzmir Balçova-Narlıdere jeotermal sahasının rezervuar ve üretim performansı projesi, İstanbul Teknik Üniversitesi, Petrol ve Doğal Gaz Mühendisliği Bölümü.
Schilthuis, R.J., (1936). Active oil and reservoir energy, Transaction Amrican Institute of Mining Engineering, 118, 33-52.
Thompson, L.G., Reynolds, A.C., (1986). Analysis of variable rate well-test pressure data using Duhamel’s Principle, Society of Petroleum Engineering Formation Evaluation, Ekim, 453-469.
Whiting, R.L., Ramey, H.J.Jr., (1969). Application of material and energy balances to geothermal steam production, Journal of Petroleum Technology, Temmuz, 893-900.