Estimation of static formation temperatures in geothermal wells by using an artificial neural network approach

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An artificial neural network (ANN) approach was used to develop a new predictive model for the calculation of static formation temperature (SFT) in geothermal wells. A three-layer ANN architecture was successfully trained using a geothermal borehole database, which contains “statistically normalised” SFT estimates. These estimates were inferred from seven analytical methods commonly used in geothermal industry. Bottom-hole temperature (BHT) measurements and shut-in times were used as main input variables for the ANN training. Transient temperature gradients were used as secondary variables. The Levenberg–Marquardt (LM) learning algorithm, the hyperbolic tangent sigmoid transfer function and the linear transfer function were used for the ANN optimisation. The best training data set was obtained with an ANN architecture composed by five neurons in the hidden layer, which made possible to predict the SFT with a satisfactory efficiency ( R 2>0.95). A suitable accuracy of the ANN model was achieved with a percentage error less than ±5%. The SFTs predicted by the ANN model were statistically analyzed and compared with “true” SFTs measured in synthetic experiments and actual BHT logs collected in geothermal boreholes during long shut-in times. These data sets were processed both to validate the new ANN model and to avoid bias. The SFT estimates inferred from the ANN validation process were in good agreement ( R 2>0.95) with the “true” SFT data reported for synthetic and field experiments. The results suggest that the new ANN model could be used as a practical tool for the reliable prediction of SFT in geothermal wells using BHT and shut-in time as input data only.