Finite Elements Based on Deslauriers-Dubuc Wavelets for Wave Propagation Problems

This paper presents the formulation of finite elements based on Deslauriers-Dubuc interpolating scaling functions, also known as Interpolets, for their use in wave propagation modeling. Unlike other wavelet families like Daubechies, Interpolets possess rational filter coefficients, are smooth, symmetric and therefore more suitable for use in numerical methods. Expressions for stiffness and mass matrices are developed based on connection coefficients, which are inner products of basis functions and their derivatives. An example in 1-D was formulated using Central Difference and Newmark schemes for time differentiation. Encouraging results were obtained even for large time steps. Results obtained in 2-D are compared with the standard Finite Difference Method for validation.

Selecting Oil Wells for Hydraulic Fracturing: A Comparison between Genetic-Fuzzy and Neuro Fuzzy Systems

Hydraulic fracturing is widely used to increase oil well production and to reduce formation damage. Reservoir studies and engineering analyses are carried out to select the wells for this kind of operation. As the reservoir parameters have some diffuse characteristics, Fuzzy Inference Systems (FIS) have been tested for these selection processes in the last few years. This paper compares the performance of a neuro fuzzy system and a genetic fuzzy system used for selecting wells for hydraulic fracturing, with knowledge acquired from an operational data base to set the SIF membership functions. The training data and the validation data used were the same for both systems. We concluded that, despite the genetic fuzzy system being a newer process, it obtained better results than the neuro fuzzy system. Another conclusion was that, as the genetic fuzzy system can work with constraints, the membership functions setting kept the consistency of variable linguistic values.

Unsupervised Methods to Classify Real Data from Offshore Wells

In the petroleum industry, sensor data and information are valuable. It can detect, predict and help to understand processes during oil production. Offshore wells require more attention. Once workovers, maintenance, and intervention are more costly than onshore wells. Coupling data-driven methods for well-monitoring applications, two unsupervised classification methods, one statistical and one machine learning-based, are proposed to detect anomalies in well data. The novelty is presented by applying a Control Chart using a 3 standard deviations window for the Permanent Downhole Gauge Pressure sensor (P-PDG), and a Fuzzy C-means algorithm to classify data from pressure and temperature sensors in an offshore field. The main goal in structuring a classified data set is using it to train machine learning models to monitor and manage petroleum production. Modeling applications for early fault detection systems in offshore production, based on real-time data from production sensors, require classified data sets. Then, labeling two target classes: “normal” and “fault” is a key step to be implemented in order to train the machine learning models. Therefore, this paper applies two methodologies to classify a real-time data set to create a training data set divided into “normal” and “fault” classes. Thus, it is possible to visualize the abnormal events pointed out by the methodologies and compare how sensible is each method. In addition, it is proposed a random forest application to test the performance of the classified data sets from both methods. The results have shown that the control chart method presents higher sensibility than fuzzy c-means, however, the differences between are insignificant. The random forest performance displayed sensitivity and specificity values of 99.91% and 100% for the data set classified by the control chart method and 94.01% and 99.98% for the data set classified by fuzzy c-means algorithm.