A Functional Networks Softsensor for Flowing Bottomhole Pressures and Temperatures in Multiphase Flow Production Wells
Authors: Bello Oladele , Asafa Tesleem 
Published: June 2014

Abstract
Many production and injection wells completed with intelligent (smart) systems are operating around the world. These wells are more economical and efficient than conventional wells. Computational tools for predicting bottomhole flowing pressure and temperature can provide valuable information for engineers and operators when making decisions regarding the use of production optimization technologies and reservoir management operations in the future. As such, improved predictions of bottomhole flowing pressures and temperatures are quite critical in minimizing well production losses. This paper presents functional networks as a novel modeling method to forecast bottomhole flowing pressures and temperatures in vertical multiphase production wells using over 700 multiple field data. The new approach helps to overcome the most common limitations of the existing predictive techniques such as empirical correlations, multiple regressions and artificial neural networks.
The functional network models were trained and tested using 70% and 30% of the available datasets, respectively. Trainings were conducted with associativity functional networks models with families of linearly independent learning functions such as polynomial, logarithm, Fourier and exponential basis. By using backward-forward search based on minimum description length criterion or the least-square optimization technique, the best functional networks models were selected and tested. To demonstrate the robustness of the developed models, the optimized networks were used for time series analysis (using data obtained every three minutes, every hour and every six hours) and trend evaluation to forecast and monitor the influence of changing input values. After optimization, logarithm basis of order three gave the best line-of-fit with correlation coefficients R2 &gt; 0.99 for training and testing sets and for bottomhole flowing pressure and temperature data. The models results are accurate, reliable and can be used for forecasting. For the times series analyses, the models perform excellently with R2 &gt; 0.99 for the hourly and 6-hourly data while R2 &gt; 0.96 for the data obtained every three minutes. In addition, trend analysis shows that the predictive models are physically correct and justified by the field data. As examples, temperature and pressure decrease with increased oil flow rate or with increased gas flow rate, while they are less significantly influenced by increased water flow rate. Finally, the current models outperform the artificial neural network models in both time series and trend analyses.
This is the first reported study where functional network is used to simultaneously forecast bottomhole flowing pressures and temperatures with such a high accuracy. This work also holds a significant contribution to authenticating operational state and diagnosing future malfunction of downhole pressure and temperature sensors in intelligent well system operations in petroleum and geothermal industry.