Estimation of static formation temperatures in geothermal wells by using an artificial neural network approach
Introduction
The exploitation of geothermal resources for producing electricity requires the drilling of deep boreholes in the most suitable thermal regions of geothermal fields (Saito et al., 1998, Davis and Michaelides, 2009). The borehole drilling is a complex process in which a constant thermal anomaly (added to a circulating drilling mud) affects the original rock-formation temperature surrounding the borehole (Fomin et al., 2003, Fomin et al., 2005). Once the borehole drilling is completed, the resulting thermal recovery is evaluated by analyzing build-up bottom-hole temperature (BHT) and shut-in time measurements (Santoyo et al., 2000). BHT data are measured at different shut-in times during the borehole drilling operations (Espinosa-Paredes and Espinosa-Martinez, 2009). BHTs are usually costly due to the use of sophisticated logging equipment, but mostly, because the borehole drilling progress needs to be stopped (Wisian et al., 1998, Fomin et al., 2005).
The determination of the static formation temperatures (SFTs) from BHT measurements constitutes a crucial task for the evaluation of geothermal systems (Espinosa et al., 2001, Kutasov and Eppelbaum, 2003). The estimation of SFT from BHT data at early drilling times offers the chance to know the virgin formation temperature several months before it can be measured with accuracy. This approach is valuable in terms of planning, exploration, developing, and exploitation programmes. The knowledge of the SFT is required for the: (1) determination of geothermal gradients for exploration mapping; (2) determination of heat flows of promising geothermal zones; (3) interpretation of borehole logging; (4) optimal design of borehole drilling and completion programs; (5) location of permeable or lost circulation zones; (6) evaluation of in-situ thermophysical formation properties; and (7) for the estimation of the heat reserves in geothermal systems.
The estimation of SFT in geothermal boreholes is usually performed by using simplified analytical methods based on complex heat transfer models concentrated at the bottom-hole conditions, where BHTs are actually measured. The BHT measurements tend to reflect the thermal anomalies caused by the drilling mud circulation to the rock-formation.
The most common analytical methods include: (i) the radial source with a conductive heat flow or Brennand method (BM: Brennand, 1984); (ii) the cylindrical heat source with a conductive-convective heat flow method (CSM) proposed by Hasan and Kabir (1994); (iii) the line-source or the well-known Horner-plot method (HM: Dowdle and Cobb, 1975); (iv) the generalized Horner or the Kutasov–Eppelbaum method (KEM: Kutasov and Eppelbaum, 2005); (v) the cylindrical source with a conductive heat flow or Leblanc method (LM: Leblanc et al., 1981); (vi) the cylindrical source with a conductive heat flow or Manetti method (MM: Manetti, 1973); (vii) the spherical and radial heat flow method (SRM) proposed by Ascencio et al. (1994); among others.
Most of these analytical methods require at least three or more BHT measurements carried out at the same borehole depth but at different shut-in times. The SFT is determined through the mathematical solution of each analytical method, using BHT and shut-in time measurements as input data, and the linear or nonlinear regressions between BHT data and the time functions of each method (Verma et al., 2006a, Verma et al., 2006b).
Although considerable progress has been achieved in this area over recent years, large discrepancies among the SFT results provided by different methods have been reported (Andaverde et al., 2005). Therefore, the development of new reliable methods to estimate SFT is still a challenging area. The geothermal industry is interested in estimating SFT in systems where heat convection dominates. Heat convection is attributed to the presence of permeable zones in reservoirs and drilling mud losses into the formation. The determination of SFT under such conditions requires the use of complex analytical methods or wellbore simulators. These tools need thermophysical and transport properties of drilling, cementing, and formation materials, which are rarely available in the literature. In addition, the accurate knowledge of the mud circulation time, which is generally unknown or difficult to determine under drilling conditions, is also needed by most analytical methods (Hermanrud et al., 1990).
Considering this complex scenario, the geothermal industry requires new practical tools that use the commonly available data (i.e., BHT and shut-in time) to estimate the SFT with an acceptable accuracy. In this regard, a new application of artificial neural networks (ANN) is here proposed for developing a new reliable method for the calculation of SFTs in geothermal wells.
ANN have been suggested as powerful computational tools in many sciences for modelling and solving complex real-world problems, and mainly for forecasting applications (Zhang et al., 1998). The use of ANN is increasingly in Earth Sciences (e.g., Goutorbe et al., 2006, Hsieh et al., 2009, Leite and Filho, 2009a, Leite and Filho, 2009b, Morton, 2009). In recent years, the application of ANN to geothermal and petroleum engineering problems has also been the subject of study (e.g., Farshad et al., 2000, Bayram, 2001, Can, 2002, Yilmaz et al., 2002, Spichak and Goidina, 2005, Spichak, 2006, Díaz-González et al., 2008, Serpen et al., 2009).
In this work, a three-layer ANN approach was successfully trained for obtaining a new predictive model to estimate SFT in geothermal wells. The new ANN model requires BHT and shut-in time measurements (as main input data), normalised SFT estimates (inferred from seven analytical methods), and transient temperature gradients.
Section snippets
Methodology
The ANN model was trained with a geothermal borehole database containing SFT estimates (statistically normalised). The geothermal database also contains build-up thermal recovery logs recorded during drilling operations carried out in some geothermal boreholes of the world. Build-up thermal recovery logs consist of BHT and shut-in time measurements, and transient temperature gradients, together with SFT estimates inferred from the regression analysis of curvilinear relationships between BHT and
Neural network learning and testing
A learning (or training) algorithm is defined as a process that consists of adjusting the coefficients (weights and biases) of a network, to minimize an error function (usually a quadratic one) between the network outputs (for a given set of inputs) and the correct outputs (already known). If smooth non-linearities are used, the error function gradient can be computed by the classical back propagation model (Rumelhart et al., 1986).
Previous learning algorithms have used this gradient directly
Conclusions
A new ANN model was successfully developed to predict the SFT in geothermal boreholes. It only requires BHT and shut-in time measurements as main input data. This feature makes it an advantageous tool over current available analytical methods that strongly depend on other complex input variables, such as the drilling mud circulation time. The ANN model was effectively trained with an experimental database, and validated with an unbiased testing database. The validity of the SFT computed by the
Acknowledgements
The authors wish to thank to the Engineering Ph.D. Programme of UNAM and to CONACyT for the financial support provided. Thanks are also due to Dr. A. Santoyo-Castelazo (University of Liverpool) for her valuable comments. We are grateful to the anonymous reviewer, Dr. Viacheslav V. Spichak, and Prof. Dr. E.C. Grunsky (Editor in Chief) for their helpful comments on an earlier version of this paper.
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