Evaluation of artificial neural networks for the prediction of deep reservoir temperatures using the gas-phase composition of geothermal fluids

Abstract Three-layer artificial neural networks were used for the multivariate analysis of the gas-phase composition of fluids, and the prediction of geothermal reservoir temperatures. The major gas-phase composition of geothermal fluids (CO 2 , H 2 S, CH 4 , and H 2 ) was defined as input variables whereas the measured bottomhole temperatures were used as output. Multivariate statistical analysis and log -ratio transformations were used for the normalization of input variables. These data sets were randomly divided into training (80%), validation (10%) and testing (10%). Matlab script algorithms based on a learning process of artificial neural networks (ANN) were programmed. The ANN architectures were determined by using up to five input neurons with thirteen different combinations of the input normalized variables for the input layer, a variable number of neurons for the hidden layer ranging from 1 to 35, and one neuron for the output layer. The Levenberg-Marquardt algorithm, the hyperbolic tangent sigmoid, and linear transfer functions were used for the training of the neural networks with tuned learning rates after using some initialization values (ranging from 0.01 to 0.00001). A sensitivity analysis to evaluate the relative importance of input variables on the output was also performed. Six ANN architectures were selected as the best from a comprehensive geochemometric analysis based on a statistical comparison and linear regressions between simulated and measured data. From an additional external validation (using a different geochemical database containing 13 samples from the Olkaria, Kenya geothermal field), the most efficient ANN made possible to predict geothermal reservoir temperatures with an acceptable accuracy (with mean error differences between simulated and measured data ranging from 2 to 11%). The best neural network was given by the ANN-33 architecture [ 3-8-1 ] which was characterized by three variables in the input layer [ ln ( H 2 S/CO 2 ), ln ( CH 4 /CO 2 ), and ln ( H 2 /CO 2 )], 8 neurons for the hidden layer and one neuron for the output layer. These results support, for the first time, the use of ANN as a gas geothermometry tool to predict geothermal reservoir temperatures.