The Bakken and Three Forks Formations Daily Crude Oil Production per Well Prediction Based on Support Vector Regression

Introduction

The knowledge of Daily oil production per well is important to America. Because America leads the world in the production of oil and gas. The oil production rate is defined as the rate per unit time at which oil is produced in a well. Productivity index is used to estimate the performance of an oil well. Oil production is measured in barrels and the production rate is measured in barrels per day. When the rate of oil production drops, Artificial lift technique is used to increase its productivity. Over the years, the oil production in North Dakota has generated more than $12 billion of economic activity and it is said to be the second-largest state in terms of oil production in the USA. Numerous jobs have been created for direct and indirect workers across the state. The energy costs for the country are lower because of daily production of the wells. It is worth mentioning that an estimated of about $1.6 trillion of federal and state tax can be generated to support government projects such as hospitals, schools, infrastructure, etc. between 2012 and 2025. The data used for this study was obtained from North Dakota Industrial Commission (NDIC) website. A typical Bakken well drilled today may produce for 45 years which could generate about $20 million net profit.

Machine learning is a field that utilizes the ability to learn from a developed model to improve the performance of the targeted tasks. Numerous research has been done using machine learning in the field of Medicine, Petroleum, Economics, Microbiology, Agriculture Mathematics and Statistics. Fisher [1] developed the first pattern recognition algorithm, thereafter, Rosenblatt [2] modeled the Perceptron also known as neural network. More research was done to minimize errors relating to pattern recognition [3, 4, 5, 6]. Ali [7] and Mohagheh [8] applied Artificial Neural Networks (ANN) in characterization of oil and gas reservoirs. Cortes, et al. [9] developed a linear decision surface. Tong, et al. [10] classified text using support vector machine active learning. Basak, et al. [11] affirmed that SVM minimizes the generalization error rather than just the observed training error.

SVM is highly applied in data analysis as Auria, et al. [12] used it as a technique to analyze solvency. Comparison of SVM with Logistic regression and discriminant analysis was made. Several papers use SVM in their projects [13, 14, 15]. In the advancement of research, Chia-Hua, et al. [16] made a progression from linear SVC to Linear SVR. Zhang [17] classified Support Vector machine and its Prospect application Falode, et al. [18] uses artificial neural networks (Machine Learning) to predict the amount of scale precipitated in the oilfield. Huibing, et al. [19] conducted a research survey on SVM. Ruidong, et al. [20] reconstructed the Field-Programmable Gate Array (FPGA) to reduce the total latency. Xuehua, et al. [21] did research that predicted Water Quality by improving the Sparrow search algorithm using Support vector regression.

It is noted that the Bakken Petroleum System of the Williston Basin (North Dakota and Montana, USA) consists of the Late Devonian to Early Mississippian Bakken Formation, the underlying Three Forks Formation, and the overlying lower Lodgepole Formation (Early Mississippian). The Bakken Formation is stated to compose of four distinct informal members which include the Pronghom member formerly defined as Sanish sand, the lower shale member, the middle Bakken member, and the Upper shale Member [22]. It was confirmed that the primary reservoir targets are the low porosity and low permeability members of the middle Bakken and upper Three Forks with continued exploration into the middle and lower intervals of the Three Forks Formation and the Pronghorn member [23, 24].

Oil production in the Bakken and Three Forks Formations began in the early 1950s at Antelope Field (North Dakota). Oil drilling was shifted to the Billings Nose area (North Dakota), where the upper Bakken shale was exploited. It was recorded that the first horizontal well was drilled in this region in 1987. As drilling continues in the Three Forks Formation, it has expanded north and south along the main structure of the Nesson anticline, as well as east into the Parshall Field region and the central Williston Basin (North Dakota) [23, 25, 26, 27] (Figure 1).

The Bakken and Three Forks Formations were evaluated by the U.S. Geological Survey (USGS) in 2013, resulting in unexplored, technically recoverable mean resource estimates of 3.65 billion barrels of oil (BBO) for Bakken Formation and 3.73 BBO for the Three Forks Formation (total mean resource estimate of 7.38 BBO; Gaswirth and Marra [23]). IHS Markit® [27] reports that more than 6,400 wells have been drilled in the Bakken Formation since the 2013 assessment. It is also worth mentioning that about 4,100 wells have been drilled in the underlying Three Forks Formation and an estimated 4 billion barrels of oil have been produced from the Bakken and Three Forks Formations [27] (Figure 2).

It was stated that since 2010, the production in the Bakken has generally increased, with various declines beginning in 2014 due to a drop in oil prices and in mid-2020 due to the decrease in demand during the ongoing COVID-19 pandemic. Also, due to drop in well completions, production growth may not rebound until 2022 [29]. Overall, oil production has remained high, and North Dakota continues to be the second largest oil producing state in the country.

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Methodology

The Support vector Regression was used in Python to predict the Daily Oil per well of the Bakken and Three Forks Formations. The result obtained was validated using the Orange-Linear regression algorithm Software. The dataset obtained from North Dakota Industrial Commission (NDIC) has 817 total instances with both independent variables and dependent value (Figures 3 & 4).

Support vector machine (SVM) is a learning machine that can be used for both classification and regression problems [9]. Support vector regression (SVR) is becoming increasingly popular as a method of curve fitting in linear and non-linear regression problems. Based on the principles of support vectors, SVR operates in the areas of SVM where data points are analyzed in n-dimensional feature space along the hyperplane.

To predict continuous output, hyperplanes are used as decision boundaries. Kernel was employed as the mathematical function that transforms data input into the desired form.

The generalized equation for hyperplane may be represented as:

y = wX + b (1)

where w is weights and b are the intercept at X = 0.

The SVR regression model is imported from SVM class of sklearn python library.

The regressor is fit on the training dataset. The model parameters as chosen here for analysis is shown below.

SVMClass = svm.SVR(kernel=’rbf’, C= 2777.777777777778 , gamma= 0.6444444444444445 ,epsilon= 0.17777777777777778 ). The margin of tolerance is represented by epsilon ε.

In this study, the Support Vector Machine with RBF kernels is used.

In general, the class predictor trained by SVM has the form [equation]

(2) but in the case of a linear kernel K(x, z) = xTz this can be rewritten as [equation]

(3) where the vector of weights w = (w1,...,wd) can be computed and accessed directly. Geometrically, the predictor utilizes a hyperplane to differentiate the positive from the negative instances, and w is the normal to the hyperplane.

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Data Pre-Processing

The dataset was processed after importing the data. The aim is to transform the raw data into an understandable format for analysis by a machine learning model. To improve the quality of the result, the dataset was preprocessed in the following order. Data Cleaning: Filling the missing values, smooth noisy data, identify or remove outliers, and resolve inconsistencies. Data Integration: At this point, integration of multiple databases, data cubes, or files was carried out. Data Transformation: This stage involves the normalization and aggregation of the obtained dataset. Thus, the process of converting data to a different format, structure, or value. Normalization is the Data transformation method used for scaling in this project. Data Reduction: The data volume was reduced but the same or similar analytical results were also obtained. Data discretization: The numerical and categorical data at this point was also reduced. In this project three different packages (Microsoft Excel, Python, and Orange) were utilized to obtain the desired accurate results. Data preprocessing for this project is very important because it made the quality of the raw data to be improved.

Visualization of Data

The visual representation of data and information is called data visualization. Data visualization tools utilize visual elements such as charts, graphs, maps, etc. to provide an accessible way to see and understand trends, outliers, and patterns in data (Figure 5).

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Support Vector Regression and Linear Regression

Support vector regression is an algorithm that predicts discrete values through supervised learning. SVR works by finding the hyperplane with the most points, which is the best fit line. In the development of this model in Python, the following steps were followed. First, all the required data was imported and visualized. Featured engineering was then employed and this basically uses the main knowledge to the needed features from the primary data using data mining techniques. The train_test_split was imported from sklearn library which I used to split the dataset into training and testing data. After I succeeded with the splitting of the dataset, I imported the SVR from sklearn.svm library and the model is fitted over the training dataset. In this project, I used the RBF Kernel which gave an accurate prediction.

In linear regression, the relationship between a scalar response and one or several explanatory variables (dependent and independent variables) is modeled linearly.

0 1 ( ) f x b b x = + (4)

To fit a predictive model to observed data sets of response and explanatory variables, linear regression is used. It can be said that when the model has been developed, predictions can be made of the response by using the fitted model when additional explanatory variables are collected without a response value.

Model Evaluation

This project was evaluated using the R2, RMSE, MAE and MSE to measure the performance of the developed model.

R-Squared (R2) is simply a measure of a goodness of fit for Linear regression model. It shows the strength of the relationship between the model developed and the dependent variable on a convenient 0-1 scale.

SSregression R Squared SStotal − = (5)

Where: SSregression is the sum of squares due to regression and SStotal is the total sum of squares.

Root Mean Square Error (RMSE) is defined as the prediction errors (residuals). Which is a measure of how far from the regression line data points.

2 ( ) RMSE f O = − (6) Where f is the forecasts (expected values or unknown results), and 0 is the observed values (known results).

Mean Absolute Error (MAE) is defined as a measure of errors between paired observations expressing the same phenomenon.

i MAE yi xi n = = − ∑ (7)

1 / n Where yi= prediction, xi= true value, n= total number of data points Mean Squared Error (MSE) measures the average of the squares of the errors.

i MSE n yi y i = = ′ − ∑ (8)

( ) 2

1 1/ n Where n=number of data points, yi=observed values and =predicted values

Conclusion

It was shown with these models developed that the Daily Oil production per well can be accurately predicted as the dependent variable using the independent variables (Year, Month, BBLs oil, Daily Oil, Wells producing, and BBLs per well) by applying the knowledge of Data mining in petroleum Engineering gained in the lectures and tutorials. The model development started by collecting the dataset from the North Dakota Industrial Commission (NDIC). Followed by Preprocessing (Cleaning, Integration, Transformation, Reduction and Discretization) of the dataset. Data splitting which was basically to partition the dataset into 70% training and 30% testing. Normalization of the dataset was done by using the MinMax scaler. The Support Vector regression was tested using the 70% trained model partitioned.

The result obtained at first didn’t match the trained dataset well enough until the SVR model was developed with values of C, gamma and Epsilon clearly stated. The values for R2 became 0.99 from its initial value of 0.35. Likewise, the values of RMSE reduced to 16.593 and MAE reduced to 10.593. This project used both the Python-Support vector regression and Orange-Linear regression algorithm to predict the Daily oil production per well by Bakken and Three Forks formations. This machine learning algorithm was able to accurately forecast the daily oil production per well from the given datasets. Comparing the results obtained from both software, it is seen that the values obtained from the Orange-Linear regression show better performance which also validates the values obtained from the Python Support Vector Regression.

Application of this algorithm is not limited to just research; it can be generally used for all forecasting and prediction related problems in all fields given that there is a relationship between the dependent variable and the independent variables.