Because carbonate rocks have a wide range of reservoir forms, a low matrix permeability, and a complicated seam hole formation, using traditional capacity prediction methods to estimate carbonate reservoirs can lead to significant errors. We propose a machine learning-based capacity prediction method for carbonate rocks by analyzing the degree of correlation between various factors and three machine learning models: support vector machine, BP neural network, and elastic network. The error rate for these three models are 10%, 16%, and 33%, respectively (according to the analysis of 40 training wells and 10 test wells).
At the moment, carbonate reserves are found around the planet. Around 40% of the world’s 236 big oil and gas fields are carbonate reservoirs, with 96 being carbonate reservoirs dominated by chert and dolomite reservoirs. Until present, carbonate oil and gas fields have been located and developed in almost 40 countries and over 60 sedimentary basins worldwide, and the reserves of these exploited carbonate fields have accounted for up to 65 percent of the world’s total original reserves.
Despite the fact that numerous scholars have investigated the oil and water dynamics of this sort of reservoir [
We investigated the variation in output from production wells in multi-media reservoirs and multi-media composite reservoirs. However, due to the difficulties associated with poor matrix permeability and complex seam development in carbonate reservoirs, the application of these conventional production forecast methodologies frequently results in significant mistakes when estimating carbonate reservoirs. As a result, oilfield workers employ a variety of machine learning techniques in the fracturing process. For example, some scholars used a support vector machine algorithm to develop a quantitative prediction model of daily fluid production following fracturing, which serves as an effective reference for field fracturing work [
Beginning with the current state of carbonate reservoirs, the paper integrates and compares three machine learning methods, namely evaluation of support vector regression, BP neural network, and elastic network, in order to propose a carbonate production capacity prediction method based on support vector regression. This method can be used to forecast the future production capacity of carbonate development wells using geological and engineering data from existing carbonate wells.
The gray correlation method is based on gray system theory and can be used to determine the degree of connection between numerous variables. The degree of correlation between several variables is determined by the correlation coefficients of the reference and comparison series. If the change trends of the reference and comparison series are inconsistent, the correlation degree is low; conversely, if the change trends of the reference and comparison series are consistent, the correlation degree is strong.
Gray correlation analysis is used to examine the gray correlation of each influencing parameter in order to determine the numerical link between the system’s parameters using a specific method. It is based on each factor’s sample data and uses gray correlation to quantify the strength, magnitude, and order of the link between components. The advantage of this strategy is that the concepts are straightforward, the loss caused by knowledge asymmetry may be significantly reduced, and the data requirements and workload are little. The following are the specific steps in the analysis.
Let
(1) Data causelessness
(2) Difference sequence notation
(3) Calculate the maximum difference
(4) Calculate the number of correlation coefficients
where
(5) Calculate the gray correlation
The
Since the actual fracturing sample data set is small and not suitable for machine learning methods based on large data samples, the three algorithms used are support vector machine regression, elastic network regression, and BP neural network for preferences, and the three models and parameter settings are briefly described below.
Elastic network regression (EN) is a fusion of Lasso regression and ridge regression, which is a standard linear regression with a canonical term, the squared deviation factor, added to make the optimization function into
An artificial neural network is a novel type of information processing network system developed on the basis of biological research that is capable of acquiring knowledge and solving problems through learning. It is an effective method for solving complex nonlinear problems
The core of support vector regression (SVR for short) is to discover the intrinsic connection between different data, and by fitting the data at high latitudes, the algorithm can obtain a formula that yields a new output value when the input value is changed. the major difference between SVR regression and traditional regression methods is that traditional regression methods require that the prediction is considered correct when and only when the
For SVR, the most important parameter is the kernel type, which generally includes linear kernel, polynomial kernel, hyperbolic tangent kernel, and Gaussian Radial Basis Function. Because of the nonlinearity problem of reservoir data,
As shown in the figure, the method in Grid Search is used to determine the optimal penalty factor
To evaluate the strengths and weaknesses of the regression effects of the three models for the fracturing optimization problem, a cross-validation approach was utilized. Fifty wells were selected, 40 of which were used as training set data, and the remaining 10 wells were used as test set data. The support vector machine model, BP neural network model, and elastic network model were trained respectively, and the 10 wells data were used as input to predict their post-frac production, and the model regression prediction results are shown in
Well | Cumulative oil production/(10^{5}t) | Predicted cumulative oil production/(10^{5}t) | |||||
---|---|---|---|---|---|---|---|
SVR | err/% | EN | err/% | BP | err/% | ||
Well# 1 | 0.35892377 | 0.31178 | 13.134758 | 0.57549 | 60.3379459 | 0.41278 | 15.004921 |
Well# 2 | 0.06160603 | 0.07123 | 15.629914 | 0.07493 | 21.6358204 | 0.056452 | 8.366112 |
Well# 3 | 0.23428876 | 0.21118 | 9.861659 | 0.31208 | 33.2044269 | 0.326738 | 39.459528 |
Well# 4 | 0.29248092 | 0.30511 | 4.319283 | 0.34844 | 19.1335831 | 0.237948 | 18.644949 |
Well# 5 | 0.48181047 | 0.49549 | 2.841061 | 0.52428 | 8.815402 | 0.567512 | 17.787394 |
Well# 6 | 0.91576303 | 0.58791 | 35.80064 | 0.55115 | 39.8152162 | 0.774259 | 15.452035 |
Well# 7 | 0.32894596 | 0.32289 | 1.841019 | 0.38692 | 17.6253996 | 0.247948 | 24.623485 |
Well# 8 | 0.79564272 | 0.80546 | 1.234885 | 0.81001 | 1.8061222 | 0.785369 | 1.291247 |
Well# 9 | 0.16847716 | 0.15452 | 8.282523 | 0.37874 | 124.8037657 | 0.234313 | 39.077012 |
Well# 10 | 0.75204001 | 0.64891 | 13.712303 | 0.73315 | 2.5115698 | 0.704973 | 6.258577 |
Variance | Mean absolute error | Mean square error | r^{2} | |
---|---|---|---|---|
0.86047252 | 0.0642232 | 0.01484464 | 0.83686 | |
0.69820864 | 0.10888234 | 0.02598688 | 0.68576 | |
0.94611346 | 0.05631742 | 0.00696892 | 0.94377 |
Based on the above-evaluated results, the support vector machine algorithm has the best overall performance, so the support vector machine algorithm was selected for exploratory analysis of fracturing effects in carbonate reservoirs.
One well data was selected and the existing formation and construction parameters of the well were input into the completed production prediction model trained using the SVR algorithm. It is known that the actual production capacity of the well is about 0.594365 (10^{5} tons/year), while the model predicts the production value of 0.624246 (10^{5} tons/year), and the comparison shows that the actual value is close to the model prediction, and the prediction error is about 5%. According to the above analysis of model input parameters and yield, we choose to adjust the model input parameters, including adjusting the segment spacing from 58 m to the optimal segment spacing of 40 m and adjusting the cluster spacing from 20 m to the optimal cluster spacing of 10 m, then the prediction result is 0.657372 (million tons/year) when the input parameters are brought into the model at this time, which can improve the cumulative oil production by about 10.6% after optimization.
The magnitude of the factors impacting the capacity of carbonate wells was calculated using the gray correlation approach. Correlation coefficients for four criteria, including discharge volume, horizontal section length, number of broken sections, and total production months, were larger than 0.6, indicating the largest effect.
The three machine learning methods of support vector regression, BP neural network, and elastic network were compared and evaluated, and the results indicated that the support vector machine algorithm performs the best overall and offers the most unique advantages for small samples and non-linear complex data.
Using an actual oil well as input to a support vector regression-trained production prediction model, it was determined that the error between predicted and actual production was approximately 5%, while cumulative oil production could be increased by approximately 10% after optimization by modifying the construction parameters.