A comparative study between proposed hybrid and known decline curve models and financial impacts

Manda, Prinisha
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The development of prediction tools for production performance and the lifespan of shale gas reservoirs has been a focus for petroleum engineers. Several decline curve models have been developed and compared with data from shale gas production. Initially in this study, the current or existing decline curve models were evaluated using the goodness of fit as a measure of accuracy with field data. The evaluation found that there are advantages in using the current decline curve models; however, they also have limitations associated with them, which have to be addressed. A new hybrid model, which incorporates the Autoregressive Integrated Moving Average (ARIMA), and the Artificial Neural Network (ANN), was examined and reasoned from literature to provide a higher level of accuracy. Based on the accuracy assessment conducted on the different models, the Stretched Exponential Decline Model (SEDM) and Logistic Growth Model (LGM), followed by the Exponential Decline Model (EDM), the Power Law Exponential Model (PLE), the Duong Model and, lastly, the Arps Hyperbolic Decline Model provide the best fit with production data. The coefficient of variance (R2) values were, 0.9672, 0.9627, 0.9528, 0.9512, 0.9382 and 0.8849, respectively. Secondly, the study used the hybrid model philosophy to develop, predict and validate shale gas decline. The results indicated that the PLE and Duong model provided the best-fit and R2 with the estimated data. The use of hybrid models provides a more precise predicting model for forecasting time series data, as compared to an individual model. The forecasting performance of decline curve hybrid models and ANN-ARIMA hybrid models are evaluated and compared with Arps, Duong, PLE,ARIMA and ANN models, respectively. The variable used to assess the models was the respective flow rate, q(t) monitored over a period of time (t). The results have shown that the Arps-PLE hybrid decline model had the lowest root mean square (RMSE) and good R2 followed by the ANN and ARIMA models. The result provided a significant contribution to the prediction of shale gas production. The Arps-PLE hybrid decline model is a good model predictor for shale gas production. The contributing factor is the dominance of the PLE parameters i.e., Di changes at early stages and D∞ become constant at late time in the model. This caters for the transient flow regime (TFR) which the Arps decline model did not consider. Thirdly and lastly, the study evaluated the EUR, and it was found that different values are obtained from the various models. The EUR is either over or underestimated. The Arps-PLE hybrid decline and ANN models, which were found to be the best models in predicting values closest to the actuals, were used to calculate the EUR and to compare with other decline curve models. The results clearly show the overestimation of the EUR values for the different shale plays using the Arps, Duong and PLE decline models, compared to the Arps-PLE hybrid decline and ANN models. Evaluating the EUR accurately would then allow for the accurate estimation of the total net revenue generated from a shale play
A thesis submitted to the School of Chemical and Metallurgical Engineering, Faculty of Engineering and the Built Environment, University of the Witwatersrand in fulfilment of the requirements for the degree of Doctor of Philosophy (PhD), 2021