Cementing Quality Prediction in the Shunbei Block Based on Genetic Algorithm and Support Vector Regression

Abstract

There are a number of factors that can affect the quality of cementing, and they constrain each other. Current cementing quality prediction methods are still in the stage of development, and it is difficult to establish an analytical model for cementing quality prediction that meets the strict requirements of cementing design. In order to accurately predict the cementing quality in the Shunbei block of the Northwest Oilfield, in this study, we established a cementing quality prediction model based on support vector regression (SVR) and optimized the penalty parameter and kernel parameter by using grid search (GS), a Bayesian optimization algorithm (BOA), and a genetic algorithm (GA), which improve the prediction accuracy of SVR. The results show that the smallest root-mean-square error and average relative error (2.318% and 7.30%, respectively) and the highest accuracy are achieved when using GA–SVR as compared to SVR, GS–SVR, and BOA–SVR. Therefore, GA–SVR is suitable for cementing quality prediction in the Shunbei block.

1. Introduction

Cementing is an important and indispensable part of drilling and completion operations. The purpose of cementing is to protect and support the casing in oil and gas wells and to seal off oil, gas, and water formations. The quality of cementing has an important impact on the production of oil and gas wells. If the quality of cementing is low, it may lead to a decline in oil and gas well production, shorten the service life, and even cause accidents. Therefore, improving the quality of cementing is a very important task in drilling engineering. By predicting the quality of cementing, it is possible to optimize measures to put new wells into production, improve the quality of cementing, and prolong the service life of oil, gas, and water wells. Therefore, many domestic and foreign experts are attempting to improve the quality of cementing [1,2]. There are many factors affecting the quality of cementing, such as the geological environment, construction conditions, and material properties. The mutual constraints and uncertainties among these factors increase the difficulty of implementing traditional cementing quality analysis and even affect the analysis results. Therefore, it is very difficult to establish a cementing quality prediction model under multifactorial conditions. Scholars at home and abroad are using different methods to analyze the correlation between the main influencing factors and initially establish some cementing quality evaluation methods [3,4]. However, there are some shortcomings in the accuracy and stability of these methods; thus, further research is necessary. Nezhad et al. proposed a convolutional neural network (CNN) approach to evaluate the performance of neural networks in automatic interpretation and combined it with fuzzy systems [5]. Viggen et al. proposed an assisted cement log interpretation tool based on supervised ML, and the implemented tool, which can be used for cementing quality evaluation, allows the interpretation of logging results to be automated [6]. Fang Chunfei et al. proposed a multi-scale perceptual convolutional neural network with kernels of different sizes, which is suitable for recognizing logging variable density images and evaluating cementing quality [7]. Souza et al. combined an experimental setup simulating several well conditions with machine learning as a diagnostic tool to demonstrate that support vectors are more suitable than other vectors for cementing quality evaluation [8]. Kinoshita et al. investigated a method of evaluating the quality of cementing with an acoustic quantitative model [9,10]. Sun Zhicheng et al. used gray relational theory for multifactorial statistics on cementing quality [11].

An analysis shows that current cementing quality evaluation methods mainly rely on amplitude logging, whereas cementing quality prediction mainly relies on fuzzy evaluation theory and neural network theory to establish relevant models [12]. For the current situation, the existing cementing quality prediction methods do not satisfy the requirements of cementing design. In recent years, support vector regression (SVR) has proven to be a reliable machine learning algorithm that can overcome the many shortcomings of artificial neural networks; thus, it has been widely applied in many scientific and engineering fields [13,14]. In this paper, a method for cementing quality prediction based on a genetic support vector regression machine is proposed. Based on the cementing historical data of the Shunbei block in the Northwest Oilfield, a cementing quality prediction model is established and optimized. This method has high prediction accuracy and can be used to predict the cementing quality in the Shunbei block.

2. Background

2.1. Analysis of Cementing Quality Influencing Factors

Located in the hinterland of the Taklamakan Desert, the Northwest Oilfield is the basin with the largest remaining oil and gas resources in China. The Northwest Oilfield is characterized by a special geographic location, abundant oil and gas resources, and leading technology for drilling ultra-deep wells. The Shunbei block in the Northwest Oilfield is a carbonate formation that is structurally characterized by fractured formations, large well slopes, and leaky conditions. The Shunbei block of the Northwest Oilfield has deep wells, a long cement section, a high bottomhole temperature, and a small annular space gap. In the process of cementing, the annular space can be easily blocked, resulting in downhole leakage and well collapse. In addition, the horizontal casing center is difficult to set, and the displacement is limited, so it is difficult to ensure the quality of cementing. According to the existing literature, the main factors affecting the quality of cementing include the inclination angle, total angle change rate, borehole diameter enlargement rate, casing centers, grouting return rate, mud displacement return rate, and cement slurry contact time. When the inclination angle is large, the casing tends not to be centered, and when the total angle change rate is large, the casing tends to stick to the edge of the casing, which makes it difficult to drive away chips and mud effectively. It also tends to flow, which affects the cementing quality. In addition, the grout reflux rate, mud replacement reflux rate, and cement slurry contact time are key factors affecting replacement efficiency. In particular, they directly affect the efficiency of the replacement of cementing fluid with cement slurry, which in turn affects the quality of cementing. The borehole expansion rate directly affects the grout reflux rate and mud replacement rate, which indirectly affects the cementing quality.

2.2. Relevant Works

Many scholars have applied machine learning algorithms to the field of cementing quality prediction. For example, cementing quality prediction can be performed using a multi-scale perceptual convolutional neural network model. It is a deep learning model; specifically, it can utilize convolutional kernels of different scales to perform convolutional operations on the feature maps obtained at a certain moment to obtain new feature maps of different scales and then later up-sample the feature maps of different scales according to the scales of the input feature maps. In addition to this, there are other types. Deepak Kumar Voleti et al. examined the efficacy of random forest classification and neural network models in cement evaluation and proposed the use of nested models that have low bias, improving interpretation accuracy and cement evaluation in onshore wells; however, the work did not address the issues of model generalizability, data dependency, or potential overfitting [15]. Ni Hongmei et al. introduced a particle swarm optimization algorithm based on stochastic global optimization in neural network training. This method was used to improve defects, which include the slow convergence speed of the traditional BP network in cementing quality prediction. This work reduced the training time and improved the accuracy of cementing quality prediction, but it was not time-effective [16].

2.3. SVM Algorithm

The main idea of SVMs (support vector machines) is to minimize the structural risk and VC dimensionality theory in statistical learning [17,18]. The SVM algorithm can be used to solve small sample problems and nonlinear regression models, which can overcome the problems of “dimensionality catastrophe” and “overlearning” to a large extent [19,20].

For example, taking two types of data classification and letting the sample set be $\left\{\left(x_1,y_1\right),\left(x_2,y_2\right),\cdots ,\left(x_i,y_i\right)\right\}$, the optimal interface linear equation for the sample space can be expressed as follows:

$${\omega }^T\cdot x+b=0$$

(1)

where ω denotes the normal vector and b denotes the displacement term [21,22].

ω^T⋅x: This is the inner product (dot product) operation, which multiplies the weight vector ω and the eigenvector x and adds their corresponding elements. The result of this part of the computation represents a linear combination between the hyperplane and the eigenvector x. The result of this part of the computation represents a linear combination between the hyperplane and the eigenvector x.

= 0: This is the equational part of the equation. The regression hyperplane is defined as the hyperplane that satisfies this equation. In SVR, the goal of this equation is to make the hyperplane fit the training data points as closely as possible, and data points within the ε-tube are considered to fall on the hyperplane, with ε being a user-defined parameter.

The goal of SVR is to minimize the error term and find a regression hyperplane such that the sum of its residuals with respect to the data points is as small as possible. This is why the SVR model uses this linear equation to describe the regression hyperplane, but by adjusting the weight vector ω and the bias term b it can fit nonlinear data relationships.

In summary, ω^T⋅x + b = 0 is the equation used in the SVR model to describe the regression hyperplane, where the weight vector ω and the bias term b are determined by training the model to fit the training data and perform the regression.

To ensure that the hyperplane (ω, b) can classify the training sample normally, the following should be satisfied:

$$\left\{\begin{array}{c}{\omega }^T\cdot x_i+b\ge +1,y_i=+1\\ {\omega }^T\cdot x_i+b\le -1,y_i=-1\end{array}\right.$$

(2)

The exact derivation of the algorithm is described in Appendix A.

Essentially, the SVR in the SVM is used to establish the margin of error, and predictions that fall within the margin of error are considered to be correct, which is different from the principle of the SVM model (maximum spacing between sample points closest to the hyperplane). The purpose of the SVR is to minimize the distance between the farthest sample point to the hyperplane.

Support vectors can be categorized into two types, depicted as the first kind and second kind in Figure 1. The first kind of support vectors are data points that lie within the ε-tube, which is a user-defined width parameter used to determine the threshold of prediction error allowed by the model. The second kind of support vectors are data points that lie outside the ε-tube, i.e., those that are more than ε away from the regression hyperplane. It is important to help regularize the model, avoid overfitting, and maintain the complexity of the model.

In summary, the first kind of support vectors and the second kind of support vectors represent different data points in SVR, and they are important for both model fitting and generalization performance. The first type of support vectors are used to construct regression hyperplanes, while the second type of support vectors help regularize the model and control the complexity of the model.

3. Data and Methods

3.1. Datasets

In this model training, 48 sections of historical cementing data of the Shunbei block were used, and each section included cementing quality (CBL acoustic amplitude) and its influencing factors: inclination angle, overall angle change rate, borehole diameter enlargement rate, casing centralizer, grouting return velocity, mud replacement return velocity, and cement slurry contact time. Various factors interacted, inhibited, or depended on each other, and an accurate cementing quality prediction model was obtained by substituting the model for post-training evaluation.

Here are histograms of the relevant parameters, as shown in Figure 2.

3.2. Data Preprocessing

The max–min method in the standardized method was used to process 48 datasets to prevent excessively large data dimensions, which can affect the prediction results. The max–min method can be expressed as Equation (3):

$$x_i^{\prime }=\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}$$

(3)

Overall, 40 groups were randomly selected from the processed data and set as training data; the remaining 8 groups were used as prediction data. To verify the accuracy of the model, the root-mean-square error (RMSE) and average relative error (MRE) for the prediction data were calculated. The calculation formulas for RMSE and MRE are shown in Equation (4) and Equation (5), respectively:

$$RMSE=\sqrt{{\displaystyle \sum _{i=1}^n\frac{{\left(p_i-o_i\right)}^2}{n}}}$$

(4)

$$MRE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\frac{\left|o_i-p_i\right|}{{\mathrm{o}}_i}}$$

(5)

where O_i denotes the true value of cementing quality, p_i denotes the prediction value of the cementing quality, and n denotes the number of the predicted data group.

3.3. Model Training

A cementing quality prediction model was established based on SVR. The inclination angle, overall angle change rate, borehole diameter enlargement rate, casing centralizer, grouting return velocity, mud replacement return velocity, and cement slurry contact time are the input values; cementing quality is the output value. The processed data were used by the SVR model to build a model, in which the penalty coefficient takes 1, and the kernel function g takes 1/n.

Table 1. Test set of random partition and model prediction evaluation.

Number	Actual Cementing Quality/%	SVR Predicted Cementing Quality/%	Relative Error	RMSE	MRE	Time/s
14	13.37	13.92	0.0411	2.851	0.0980	<1
16	19.34	20.49	0.0595
17	17.29	21.33	0.2337
20	22.31	22.54	0.0103
26	20.19	21.21	0.0505
42	28.34	23.69	0.1641
43	29.76	25.07	0.1576
44	21.39	22.76	0.0640

shows the divided test set as well as the RMSE and MRE values for the prediction results.

From Table 1, it is evident that that the MRE between the SVR predicted cementing quality and actual cementing quality is roughly 9.80%. Accordingly, the SVR parameters must be optimized to increase the accuracy of the model.

As can be seen in Table 1, there is a large difference between entries 14 and 17. This is due to the fact that a lack of cementing data samples from a certain rare and specific environment can lead to a larger relative error.

3.4. Model Optimization

For the SVR algorithm, the penalty parameter and kernel parameter both directly affect the prediction error. Researchers have studied SVR regression and put forward some suggestions, but many contradictory opinions still exist. In this study, to reduce the SVR prediction error, the grid search (GS) method [24], Bayesian optimization algorithm (BOA) [25,26,27], and genetic algorithm (GA) [28,29] were used to optimize the penalty and kernel parameters, after which the optimized SVR algorithm was used to train and predict the relevant data. In this study, RBF was specified as the kernel function in Python, the scope of the penalty coefficient was [0.1, 100], and the range of the kernel parameter was [0.01, 1].

3.4.1. Grid Search Method to Optimize the Support Vector Regression Model

The GS method is one of the easiest methods in the global optimization algorithm, which is a learning method to optimize the model performance by traversing the given parameter combinations. Its principle is to determine the search range of the model, separate the possible values of the parameters to be searched in accordance with a certain step length, and generate a “grid”. Then, it searches for each node of the grid one by one, uses the objective function to make judgments, and adjusts the search range and the step length according to the value of the objective function until it reaches the optimal solution.

The optimization flow chart of the GS method is shown in Figure 3.

From

Table 2. Optimization results and model evaluation of GS method.

Penalty Coefficient C	Kernel Function Parameter g	Number	Actual/%	GS–SVR Prediction Cementing Quality /%	Relevant Error	RMSE	MRE	Time/s
25.1	0.13	14	13.37	13.65	0.0209	2.653	0.0846	44.8
		16	19.34	20.60	0.0652
		17	17.29	21.32	0.2331
		20	22.31	22.57	0.0117
		26	20.19	20.19	0.0005
		42	28.34	24.48	0.1362
		43	29.76	25.04	0.1586
		44	21.39	22.47	0.0505

, it is evident that the MRE between GS–SVR and the actual cementing quality is 8.46%, and the RMSE is 2.653, which suggests a certain optimization effect.

3.4.2. Bayesian Optimization Algorithm for the Support Vector Regression Model

The BOA [30,31] involves testing each sample point according to prior knowledge and updating prior distributions to identify the global optimal value.

Assume that a sample S is present, including t parameter groups and corresponding objective function value. Firstly, the posterior probability distribution D_t (namely, joint normal distribution) is calculated by the Gaussian process, and then a function a(x|D_t) is selected to collect a new parameter value x_t+1 so as to satisfy Equation (6):

$$x=\arg \max E\left(\max \left\{0,f_{t+1}\left(x\right)-\left.f_{best}\right|D_t\right\}\right)$$

(6)

Thus, in the distribution, D_t is able to make the expected difference between the new estimate objective function value f_t+1(x) and current maximum objective function value f_best the largest, the new parameter is used to calculate the new actual objective function value and update the corresponding Gaussian process, and a new posterior distribution is obtained. The above process is repeated until the stop condition is satisfied.

The optimization flow chart of the BOA is shown in Figure 4.

From

Table 3. BOA results and model evaluation.

Penalty Parameter C	Kernel Function Parameter g	Number	Actual Cementing Quality /%	BOA–SVR Predicted Cementing Quality /%	Relevant Error	RMSE	MRE	Time/s
47.38	0.07635	14	13.37	13.52	0.0112	2.533	0.0800	19.8
		16	19.34	20.51	0.0605
		17	17.29	21.21	0.2267
		20	22.31	22.49	0.0081
		26	20.19	20.24	0.0025
		42	28.34	24.83	0.1239
		43	29.76	25.18	0.1539
		44	21.39	22.53	0.0533

, it is evident that the MRE between the predicted cementing quality of BOA–SVR and the actual cementing quality is 8.00%, and the RMSE is 2.533, which suggests good optimization.

3.4.3. Genetic Algorithm Optimization for the Support Vector Regression Model

The GA [32,33] is an efficient stochastic search and optimization method based on natural genetic mechanisms and biological evolution. The GA exhibits a global optimization performance and can find the most appropriate values of the penalty and kernel function parameters for the SVM, by which the SVM can achieve the optimal configuration to accurately predict cementing quality.

The optimization flow chart of the GA method is shown in Figure 5.

The GA–SVR code is run in Python, and the optimization results and model evaluation are shown in

Table 4. GA optimization results and model evaluation.

Penalty Parameter C	Kernel Function Parameter g	Number	Actual Cementing Quality /%	GA–SVR Predicted Cementing Quality /%	Relevant Error	RMSE	MRE	Time /s
85.08	0.0238	14	13.37	13.56	0.0142	2.318	0.0730	36.3
		16	19.34	20.09	0.0388
		17	17.29	20.63	0.1932
		20	22.31	22.06	0.0112
		26	20.19	20.30	0.0054
		42	28.34	25.09	0.1148
		43	29.76	25.41	0.1462
		44	21.39	22.67	0.0598

, from which it is evident that the prediction accuracy of the SVR model constructed after GA optimization is higher than that of SVR, GS–SVR, and BOA–SVR. The MSE is 7.30%, and the RMSE is 2.318, which suggests that the optimization effect is the best.

3.5. Analysis of Cementing Quality Prediction Results

In this study, a cementing quality prediction algorithm was established based on SVR, and the penalty parameter and kernel function parameter were optimized. The parameter optimization process was carried out via Python programming, and the GA, GS, and BOA optimization methods were adopted. The prediction results of the four algorithms are shown in

Table 5. Evaluation before and after model optimization.

Model	MRE	RMSE	Time
SVR	0.0980	2.851	<1
GS–SVR	0.0846	2.653	44.8
BOA–SVR	0.0800	2.533	19.8
GA–SVR	0.0730	2.318	36.3

.

From Table 5 and Figure 6 and Figure 7, it is evident that the MRE of GA–SVR is 7.30%, and the RMSE is 2.318, both of which are far smaller compared with SVR, GS–SVR, and BOA–SVR, indicating that this algorithm is the most suitable for cementing quality prediction. Table 5 indicates that GA–SVR is the least time-effective method. This suggests that, compared with SVR and BOA–SVR, it is more complex and takes more comprehensive factors into consideration. Meanwhile, there are nonlinearities and uncertainties in the influencing factors of cementing quality; while GA–SVR performs better in dealing with high-dimensional, multimodal, and nonlinear problems, GS–SVR is more suitable for dealing with large-scale datasets, and BOA–SVR is suitable for the problems that need to find the global optimal solution. Based on this property, it is more appropriate to use the GA–SVR algorithm.

4. Results and Discussion

Pearson correlation, which is a method that measures the degree of correlation between two variables X and Y, was adopted to verify the example. The Pearson correlation coefficient between X and Y is defined as the quotient of the covariance and standard deviation of the two variables, as shown by Equation (7). The Pearson correlation coefficient ranges between $-$1 and 1, where 1 suggests complete positive correlation of variables, 0 indicates irrelevance, and $-$1 means complete negative correlation [34].

$${\rho }_{X,Y}=\frac{\mathrm{cov}(X,Y)}{{\sigma }_X{\sigma }_Y}=\frac{E[(X-{\mu }_X)(Y-{\mu }_Y)]}{{\sigma }_X{\sigma }_Y}$$

(7)

Equation (7) defines the population correlation coefficient and estimates the sample covariance and standard deviation. The calculation method is expressed by Equation (8).

$$r=\frac{{\displaystyle \sum _{i=1}^n(X_i-\overline{X})(Y_i-\overline{Y})}}{\sqrt{{\displaystyle \sum _{i=1}^n{(X_i-\overline{X})}^2}}\sqrt{{\displaystyle \sum _{i=1}^n{(Y_i-\overline{Y})}^2}}}$$

(8)

The completion depth of a well in the Shunbei block of the Northwest Oilfield is 8725 m, the maximum deviation angle is 86.01°, the maximum angle change rate is 0.6127°/m, the maximum diameter expansion rate is 12%, the mud density is 1.68 g/cm³, and the plastic viscosity is 36 mPa$·$s. For the 139.7 mm liner cementing of the well, the centralizer cannot be placed in case the straight casing is upset. The casing is close to the lower shaft wall, and the casing is basically zero in the medium range. The displacement flushing fluid (1.05 g/cm³) is designed to be 7 m³, the weighted isolation fluid (1.75 g/cm³) is 4 m³, the cement slurry (1.88 g/cm³) is 11 m³, and the designed injection displacement is 0.6–0.8 m³/min. The sound amplitude logging of the 139.7 mm liner well cementing is shown in Figure 8, from which it is evident that the sound amplitude of the CBL logging in the whole sealing section is between 10% and 30%, and the cementing quality for 7850–8000 m is excellent.

Using GA–SVR to predict the cementing quality of the cementing data, the comparison between the predicted values and the actual values is shown in Figure 9, from which it can be seen that Pearson’s correlation coefficient is 0.9781; in addition, the predicted values of GA–SVR have a good correlation with the actual cementing quality values.

In order to further analyze the deviation between the predicted values of the GA–SVR model and the actual cementing quality values, the relative errors of the prediction results were analyzed, and the results are shown in Figure 10, from which it can be seen that the sixth data group has the largest relative error of 9.16%. The first data group has the smallest relative error of 1.27%. The prediction errors of most subgroups are concentrated around 5.5%, with MRE of 5.27% and RMSE of 1.166. The results show that the predicted values of GA–SVR match the actual cementing quality values to the greatest extent and have the smallest errors, which indicates that this method is suitable for predicting the cementing quality of the Shunbei block. GA–SVR is a complex model, which will always have some uncertainty in predicting future situations. For example, many factors, such as the environment, can affect the prediction results. In addition, there is randomness and noise in the data, which will have an impact on the prediction results. This method is more suitable for situations where the environment is similar, and it may not be able to adapt quickly to changes in the data when the conditions differ.

5. Conclusions

In this study, a cementing quality prediction model was established based on SVR. In the process of using SVR, the penalty coefficient and kernel coefficient have an important impact on data learning and prediction results, so the model was optimized using GS, BOA, and GA, and the cementing quality was predicted using SVR, GS–SVR, BOA–SVR, and GA–SVR in combination with the historical cementing data of a block in Shunbei. The prediction results show that the MRE and RMSE of GA–SVR are relatively small. This proves that the algorithm has high prediction accuracy and can be used to predict cementing quality in the Shunbei block. In addition, this method is suitable for the case of similar environments, and, when the environments differ, this method cannot adapt to the data changes quickly, so we plan to use incremental learning for the next optimization in the future.