A Machine Learning Approach to Modeling Pore Pressure

Introduction

Machine learning models are nowadays essential and commonly useful means for forecasting vital variables for complex oil and gas systems with numerous influencing variables displaying highly irregular and/or non-linear relationships. Their application and diversity are growing by Schmidhuber J [1]. Machine learning methods have caught the eyes of engineers thanks to their ability to associate input data to the output data.

Machine learning methods were utilized expansively in the majority of petroleum engineering purposes, such as, drilling, reservoir, production and engineering, as well as petrophysics, rock mechanics and exploration [2]. One of such is the Response Surface Model which is utilized in numerous facets of reservoir engineering such as history matching [3, 4], determining the initial uncertainty of hydrocarbons [5], locating spots for well placement [6] and estimating initial hydrocarbon uncertainty. Production variation has been forecasted with the aid of pattern recognition based on the well locations. Mohaghegh SD, El-Sebakhy E introduced a novel computational intelligence modeling plan founded on the support vector machines SVR system to forecast both bubble point pressure and oil formation volume factor [7, 8, 9, 10]. They utilized solution gas-oil ratio, reservoir temperature, oil gravity, and gas relative density as input parameters. Oloso (2009) established two novel models for assessing the viscosity and solution gas/oil ratio (GOR) [11].

Artificial Neural Networks are computational techniques that mimics the human brain in unraveling solutions to problems. It consists of a series of interconnected nodes, which are more or less the artificial versions of the neurons in the brain. Each node symbolizes the artificial neuron, while the arrows symbolize the link from an output node to an input node.

Usually, the most common methods used to predict formation pressure prior to drilling is by using correlations that require well logs or seismic analysis data as input parameters. However, these correlations have their limitations in that they are based on limited data sets that are not readily available, thus making such predictions somewhat tedious. Consequently, the oil and gas industry is constantly seeking for alternative techniques of forecasting pore pressures that are not so dependent on well log data. It is on this account that we adopt and assess the machine learning approach so as to ascertain their suitability to formation pressure prognosis.

Methodology

The methodology implemented for the work involved using 80% of the actual pore pressure data in training the three models while the remaining 20% was used for testing of the models. A sensitivity analysis was carried out in this work using scatter plots. This involved plotting the variables (hydrostatic pressure, lithostatic pressure, observed sonic compressional velocity Vp, and normal compacted shale velocity Vn) against one another. These plots give a very vivid and simplified illustration of the variables’ sensitivity. The strength of the correlations between the variables was computed using the linear correlation coefficient [12].

− − − − ∑ x x y y i i s s x y r n ( )( )

(1) = −

1 − x = sample mean of the predictor variable Where

xs = standard deviation of the predictor variable −y = sample mean of the response variable xy = standard deviation of the response variable n=sample size

Results and Discussion

The outcome of the pore pressure modeling are presented below. Results reveal that the Multilayer Perceptron (ANN) accurately predicted pore pressure across most instances. This is evidenced by the low Relative absolute error of

5.77%. The decision stump also yielded good predictions with Relative absolute error of 54.41%. The simple linear regression model yielded the least accuracy of the three models with a Relative Absolute Error of 67.93% (Table 1-2).

Conclusion

Machine Learning algorithms can be realistically trained and utilized to direct pressure measurements in other to forecast pore pressure. In this work, the pore pressure of a formation was predicted using existing pore pressure data with the aid of three machine learning models namely, Simple Linear Regression, Decision Stump and Multilayer Perceptron. The models were trained with Eighty percent of the dataset after which the remaining twenty percent was utilized in the validation of the models’ accuracies. Results obtained showed that the Multilayer Perceptron model has a laudable prediction accuracy. The Decision Stump model equally showed a good prediction performance. The Simple Linear Regression had the highest Relative Absolute Error. Furthermore, sensitivity analysis of the data used in the work showed that the hydrostatic pressure, overburden pressure and normal compacted sonic velocity have best correlations with the pore pressure as their values are closest to 1. On the whole, it can be surmised that the Multilayer Perceptron can be successfully utilized in the projection of pore pressures as demonstrated by the end result.