Research on the Declining Trend of Shale Gas Production Based on Transfer Learning Methods

Abstract

With the development of artificial intelligence technology, machine learning-based production forecasting models can achieve the rapid prediction and analysis of production. However, these models need to be built on a large dataset, and having only a small amount of data may result in a decrease in prediction accuracy. Therefore, this paper proposes a transfer learning prediction method based on the hierarchical interpolation model. It uses data from over 2000 shale gas wells in 22 blocks of the Marcellus Shale formation in Pennsylvania to train the transfer learning model. The knowledge obtained from blocks with sufficient sample data is transferred and applied to adjacent blocks with limited sample data. Compared to classical production decline models and mainstream time-series prediction models, the proposed method can achieve an accurate production decline trend prediction in blocks with limited sample data, providing new ideas and methods for studying the declining production trends in shale gas.

1. Introduction

With the increasing global demand for clean energy, shale gas has attracted considerable attention as a new type of clean energy [1,2,3]. Compared to conventional natural gas extraction, shale gas exploration has a long cycle, requires significant investment, and involves high risks. Therefore, the accurate prediction of a declining production trend is crucial for the development of shale gas [4,5]. By precisely forecasting the decline in shale gas production, better production planning, rational resource allocation, and improved exploration and development efficiency can be achieved while reducing environmental pollution and ecological damage.

In recent years, Petroleum Data Analysis (PDA) has gained increasing attention. PDA utilizes data collected in the petroleum and natural gas industry to analyze, simulate, and optimize production operations. It is a branch of data science that involves data mining, artificial intelligence, machine learning, and pattern recognition. Machine learning is defined as the study of computer algorithms that enable them to learn from data and extract predictive models. Sagheer et al. [6] proposed a Deep Long Short-Term Memory (DLSTM) architecture for oilfield production data prediction, optimizing the DLSTM’s structure and using genetic algorithms to address the limitations of traditional prediction methods. Yuan et al. [7] introduced a Hybrid Deep Neural Network (HDNN) for reservoir production forecasting, establishing complex nonlinear relationships between target production and various features through a blended network structure. Zhang et al. [8] proposed an oil well production forecasting method based on multivariate time series (MTS) and vector autoregression (VAR) machine-learning models, mining linear relationships from MTS data and predicting oil well production through model fitting.

However, the above-mentioned prediction methods are only applicable in cases with comprehensive datasets, which means having an ample history of production data and relevant information. Nevertheless, due to the complexity of shale gas reservoirs, the difficulty of data acquisition, and sparse data samples [9,10], missing data can significantly impact the accuracy of predictions. In severe cases of data deficiency, the aforementioned methods may not be able to perform predictions smoothly. In this context, improving the accuracy and efficiency of declining shale gas production trend predictions is an urgent issue [11,12,13,14]. To address this problem, researchers propose the following solution: utilizing transfer learning to compensate for low data and fundamentally overcome the data insufficiency problem, enabling the prediction process to proceed smoothly.

Transfer learning, as an emerging machine-learning method, has been widely applied to solve problems in fields such as oil and gas field development, stock prediction, furnace temperature prediction, and power load forecasting [15,16,17,18,19]. Its core idea is to utilize knowledge from a source domain to assist learning in the target domain, thereby enhancing the predictive ability of the model. Felix et al. [20] addressed the issue of improving the prediction performance of drilling speed in actual drilling operations when there is a lack of available training data. They proposed a drilling speed prediction method based on continuous transfer learning, which achieved a higher prediction accuracy than current mainstream methods. Fu et al. [21] employed a deep forest model to construct a transfer learning model to detect doglegs in the oil drilling process. Yao [22] and colleagues aimed to enhance the accuracy and reliability of oil and gas pipeline defect detection in scenarios with small and poor-quality data. They utilized a method based on deep learning transfer models for defect diagnosis in oil and gas pipelines. Zhang et al. [23] conducted research on using meta-transfer learning to diagnose the functionality of rod pumps in oil wells under small sample conditions.

To address the issue of low accuracy in shale gas production forecasting under conditions of sparse data samples, this paper proposes a transfer learning method based on the hierarchical interpolation model. First, the abundant data samples in certain blocks are used as the source domain to pre-train the hierarchical interpolation model, resulting in a source domain model. Then, the training parameters of the source domain model are transferred to the target block with limited data samples. By fine-tuning the model parameters, the aim is to improve the accuracy of production forecasting. The proposed method provides strong support and assistance for the exploration and development of shale gas. The rest of this paper is structured as follows: Section 2 describes the composition of the proposed model. Section 3 presents the test results and discussion. Section 4 concludes the paper and proposes future research directions.

2. Methods Section

2.1. Classic Decline Production Model

2.1.1. Arps Model

The Arps prediction model is a common empirical model used for forecasting oil and gas well production [24]. It is suitable for oil and gas wells with exponential decline characteristics. It was proposed by J. J. Arps, an American petroleum engineer, in the 1950s. This model fits historical data to a three-parameter model and empirically predicts the decline in production for a specific oil well, as shown in Equation (1):

$$Q_t=\frac{Q_i}{{(1+n\times d\times t)}^{1/n}}$$

(1)

where $Q_t$ refers to the production quantity in the t-th month, $Q_i$ represents the initial production quantity, $t$ denotes time, $d$ represents the decline rate, and $n$ is a constant.

For the decreasing production prediction of shale gas wells, the hyperbolic decreasing model is more often applied. To fit the transient flow of shale gas reservoirs during the production process, the decrement exponent of the hyperbolic decrement curve is often greater than 1, and since its decrement rate decreases with the increase in time, it can result in a high production prediction in the later stage. In the application process of this article, the parameter estimation of the Arps hyperbolic decline model is conducted using the method of linear fitting between cumulative production and production. The specific steps for parameter calculation and production forecasting are as follows:

(1)

The removal of outliers in production data

To ensure the quality of raw data, it is necessary to exclude some data points with zero gas production and outliers caused by external factors. For the treatment of outliers, the Z-score method is used; if the Z-score of a data point is greater than 3, it indicates that the data value is significantly different from other values and is considered an outlier. As shown in Equation (2):

$$z=\frac{X-Mean}{SD}$$

(2)

where $X$ denotes the current value, $Mean$ denotes the mean of the overall data, and $SD$ denotes the standard deviation of the overall data.

(2)

Determining the values of decline rate ‘$d$’, decline exponent ‘$n$’, and initial production ‘$Q_i$’

Based on the relationship between cumulative production ‘$N_p$’ and production ‘$q$’ given by $N_p=\frac{q_i}{d}\frac{1}{1-n}-\frac{q_i^n}{d}\frac{1}{1-n}{q}^{1-n}$. Let $x=q^{1-n}$, $y=N_p$, $b_0=\frac{q_i}{d}\frac{1}{1-n}$, $b_1=\frac{q_i^n}{d}\frac{1}{1-n}$. Thus, the linear regression equation is given by $y=b_0+b_{1}x$. The production data are then fitted using this equation to obtain the regression coefficients $b_0$ and $b_1$. From $b_0$ to $b_1$, the values of $n$, $Q_i$, and $d$ are calculated.

2.1.2. Duong Model

In 2010, based on a large amount of actual production data, Duong identified the production flow regime of shale gas wells and proposed an analytical method for the production decline in shale gas reservoirs, known as the Duong model [25]. The production expression of the Duong model is given by Equation (3):

$$Q_t=Q_i{t}^{-m}{exp}^{\frac{a}{1-m}(t^{1-m}-1)}$$

(3)

where $Q_t$ represents the production quantity in the t-th month, $Q_i$ is the initial production quantity, $t$ represents time, $a$ is the decay coefficient, and $m$ is the exponential coefficient.

The Duong model is an experiential analysis method for decreasing production from gas wells in fractured shale reservoirs. In the application process of this article, the parameter estimation for the Duong model was performed using the linear fitting method. The specific steps for parameter calculation and production forecast are as follows:

(1)

The removal of outliers from production data

Refer to the steps of fitting the Arps model for detailed procedures.

(2)

Determining the values for the decline coefficient ‘a’ and the exponential coefficient ‘m’

Based on the relationship between production rate ‘$q$’ and cumulative production ‘$N_p$’ given by $\frac{q}{N_p}=a{t}^{-m}$, it is known that in a double-logarithmic coordinate system, $\frac{q}{N_p}~t$ follows a linear relationship ${ln}^{\frac{q}{N_p}}=-m{ln}^t+{ln}^a$. Let $y={ln}^{\frac{q}{N_p}}$, $x={ln}^t$, $b={ln}^a$. Thus, the linear regression equation is given by $y=-mx+b$. Using this equation, the production data are linearly fitted to obtain the values of parameters ‘$a$’ and ‘$m$’.

2.1.3. PLE Model

In response to the limitations of the Arps hyperbolic decline method in predicting the production of shale gas wells, D. Ilk et al. proposed a power–law exponent model, known as the PLE model [26]. The specific formula is shown in Equation (4):

$$Q_t=Q_i\mathrm{e}\mathrm{x}\mathrm{p}(-D_{\mathrm{\infty }}t-D_i{t}^n)$$

(4)

where $Q_t$ represents the production in the t-th month, $Q_i$ is the initial production, t denotes time, $D_i$ is a constant, $D_{\mathrm{\infty }}$ is the decay rate as t approaches infinity, and n is the decay exponent.

The PLE model can be used to analyze different production flow stages of shale gas wells, including the unstable flow stage, the transitional flow stage, and the boundary flow stage. The PLE model is suitable for wells with a longer production history, and the prediction results are more uncertain for wells with a shorter production history. In this paper, the parameter estimation for the PLE model was carried out using a nonlinear fitting method, and the specific steps for parameter calculation and production forecasting are as follows:

(1)

Outlier removal from production data

Refer to the steps of fitting the Arps model for detailed procedures.

(2)

The nonlinear fitting of production parameters

From Equation (4), it can be observed that there are several key parameters in the formula, leading to considerable uncertainty in the forecasting results. Direct solving or linear fitting can be challenging. Therefore, a nonlinear fitting method was adopted to estimate the corresponding parameter values.

2.2. Hierarchical Interpolation

In pursuit of achieving enhanced performance in long-term production prediction, this study employed a hierarchical interpolation method, utilizing multiple levels of temporal information to improve the prediction accuracy. The architecture comprises three primary components as follows: Multi-Rate Signal Sampling, nonlinear regression, and an interpolation layer. The model structure is illustrated in Figure 1.

(1)

Multi-Rate Signal Sampling

Using temporal max-pooling, which involves downsampling the data, time series are sampled into sequences of multiple granularities. The larger the pooling layer used for sampling, the lower frequency/larger scale the resulting sequences have; conversely, smaller pooling layers yield higher frequency/smaller scale sequences. However, after sampling, these sequences have a lower frequency/larger scale compared to the original sequence. The kernel size for each stack is chosen using an exponentially decreasing approach.

After downsampling, the sequence length becomes shorter, reducing the model’s complexity and increasing efficiency. Additionally, it reduces the number of model parameters, mitigating the risk of overfitting while preserving the original receptive field. The formula expression is as follows:

$$y_{t-L:t,l}^p=MaxPool(y_{t-L:t,l},k_l)$$

(5)

where $y_{t-L:t,l}$ represents the input data for block l, $k_l$ represents the kernel size, and $y_{t-L:t,l}^p$ represents the sampled data.

(2)

Nonlinear Regression

After sampling, sampled data are predicted via multi-layer perceptron (MLP), and nonlinear regression is performed on the interpolation coefficients for both the forward and backward. The formula expression is as follows:

$$h_l={MLP}_l\left(y_{t-L:t,l}^{\left(p\right)}\right)$$

(6)

$${\theta }_l^f={LINEAR}^f\left(h_l\right)$$

(7)

$${\theta }_l^b={LINEAR}^b\left(h_l\right)$$

(8)

where $h_l$ represents the hidden vector of block L, the forward ${\theta }_l^f$ and backward ${\theta }_l^b$ correspond to the nonlinear regression of MLP coefficients, and $y_{t-L:t,l}^{\left(p\right)}$ represents the values of block L between time t-L and time t, which serve as the training data.

(3)

Interpolation layer

Due to the downsampling of each input sequence by every block, the corresponding output is naturally shorter than the target Horizon. Thus, an upsampling operation is necessary for the prediction results. For instance, when the downsampling kernel size increases, the input sequence becomes shorter, and the scale becomes larger. Consequently, the predicted future sequence becomes shorter as well. In order to achieve the desired length similar to the target Horizon, an upsampling process is performed using linear interpolation. This interpolation ensures that the final output count matches the expected Horizon count. Each stack of the model is responsible for predictions at different scales. Ultimately, the prediction sequences of various scales are interpolated to the same count (equivalent to the desired prediction Horizon) and then combined to yield the final output. The interpolation formula is expressed as follows:

$$y_{T,l}=g\left(T,{\theta }_l^f\right),T\in \{t+1,\dots ,t+H\}$$

(9)

$$y_{T,l}=g\left(T,{\theta }_l^b\right),T\in \{t-L,\dots ,t\}$$

(10)

$$g\left(T,\theta \right)=\theta \left[t_1\right]+\left(\frac{\theta \left[t_2\right]-\theta \left[t_1\right]}{t_2-t_1}\right)(T-t_1)$$

(11)

$$t_1=arg{min}_{t\in T:t\le T}T-t,t_2=t_1+1/r_l$$

(12)

where $y_{T,l}$ represents the result of interpolation, g represents the function of interpolation, T represents the time partition and $r_l$ represents the expressiveness ratio that controls the number of parameters per unit of output time.

This paper proposes a model that employs a hierarchical interpolation approach, which can capture temporal trends in time series data across multiple time scales while mitigating the issue of multicollinearity commonly observed in traditional time series methods. The proposed model exhibits good interpretability and generalization performance while also demonstrating efficient training and prediction capabilities. For further insights into the hierarchical interpolation model, one can refer to the work of Challu et al. [27].

2.3. Transfer Learning Model

Transfer learning is a machine-learning technique that effectively utilizes pre-trained models to make predictions on new datasets in relation to a specific problem [28,29,30,31]. In this paper, transfer learning is employed to address the issue of yield prediction in sparse sample regions. The implementation involves removing the output layer of the pre-trained source domain model while retaining the previous layers (knowledge transfer layer), as shown in Figure 2. Subsequently, a new target domain model is designed by incorporating the knowledge transfer layer and adding a new untrained output layer. The new model is trained only on new data. During the training of the target domain model, knowledge transfer layers remain untrained to preserve the knowledge they acquire during the training of the source model.

3. Results

3.1. Data and Model Parameters

3.1.1. Data

The data used in this paper are from the Marcellus Shale in Pennsylvania, which has 13,344 gas wells, and the distribution of Marcellus Shale gas wells is listed in

Table 1. Distribution of data-rich blocks.

Washington	Susquehanna	Greene	Bradford	Tioga	Lycoming	Butler	Westmoreland	Fayette	Wyoming	Armstrong
2001	2000	1633	1593	1134	1105	684	388	357	353	339

and

Table 2. Distribution of data-scarce blocks.

Allegheny	Mercer	Jefferson	Indiana	Clarion	Somerset	Forest	Blair	Cambria	Venango	Warren
188	58	53	51	44	20	18	6	5	5	4

, respectively. We selected 1357 wells in which there were cumulative monthly production data for a total of 84 months from 2016 to 2022, with a total of 113,988 records, and the cumulative production is all in thousands of standard cubic feet. Figure 3 shows the location of the dataset in this paper. Figure 4 illustrates production data from selected wells (sample-rich blocks) in the GREENE. Figure 5 shows production data from selected wells in ALLEGHENY, MERCER, JEFFERSON, and INDIANA (sample-poor blocks). (Source: https://www.depgreenport.state.pa.us/ReportExtracts/OG/OilGasWellProdReport, accessed on 1 May 2023).

To facilitate the training of the model, the selected source domain data in this study were subjected to standardization processing, as described by Equation (13):

$${\mathrm{X}}_{\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}}=\frac{\mathrm{X}-{\mathrm{X}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}}{\mathsf{\sigma }}$$

(13)

where ${\mathrm{X}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$ represents the mean value of a selected set of data, σ represents the standard deviation of each group of eigenvalues, $\mathrm{X}$ represents each value, and ${\mathrm{X}}_{\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}}$ represents the normalized eigenvalue.

3.1.2. Model Prediction Structure

The prediction structure of the model in this paper uses multi-step prediction in the form shown in Figure 6. where n denotes the number of input variables and i denotes the number of output variables.

3.1.3. Model Parameters and Error Evaluation

(1)

The evaluation indicators of prediction result error are the mean absolute error (MAE) and the mean absolute percentage error (MAPE). The formulas are shown in Equations (15) and (16):

$$R^2=1-\frac{{\sum }_{i=1}^m{(y_i-\hat{\mathrm{y}})}^2}{{\sum }_{i=1}^m{(y_i-y_{mean})}^2}$$

(14)

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{\mathrm{m}}{\sum }_{\mathrm{i}=1}^{\mathrm{m}}|{\mathrm{y}}_{\mathrm{i}}-\hat{\mathrm{y}}|$$

(15)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\frac{1}{\mathrm{m}}{\sum }_{\mathrm{i}=1}^{\mathrm{m}}\frac{|{\mathrm{y}}_{\mathrm{i}}-\hat{\mathrm{y}}|}{{\mathrm{y}}_{\mathrm{I}}}$$

(16)

where ${\mathrm{y}}_{\mathrm{i}}$ is the real value, $\hat{\mathrm{y}}$ is the predicted value, $y_{mean}$ is the mean value, and $\mathrm{m}$ is the sample size.

(2)

The parameters of the model are shown in

Table 3. Model parameters.

Parameter	Values
Stacks	3
block	Stacks × [1]
MLP_hidden	[256,256]
Pool_kernel-size	Stacks × [1]
Activation	ReLU
Epoch size	100
Batch size	32
optimizer	Adam
Input size	24
Output size	60

. where the input dimension and output dimension, respectively, represent the input duration required by the model and the prediction duration of the model.

3.2. Results and Discussion

3.2.1. Results of Classic Decline Production Model

In this section, for the Arps, Duong, and PLE decreasing production models, 1/4 and 4/4 of the historical data of well 003-22278 in the ALLEGHENY block and well 063-37010 in the INDIANA block were selected to fit the parameters of the equations, respectively. This was conducted to demonstrate the predictive accuracy of classical decline models under conditions of both sufficient and insufficient historical production data. The left graph represents the decline trend prediction, while the right graph represents cumulative production prediction.

(1)

Discussions of Well 003-22278

As seen in Figure 7, it can be observed that the Arps model achieved an R² score of 0.84 with only 1/4 of the data, indicating a lower accuracy in predicting cumulative production in the later stages. When the dataset increased to 4/4, the R² score improved to 0.9, and the predicted cumulative production aligned with the expected values. According to Figure 8, the Duong model obtained an R² score of 0.67 with only 1/4 of the data, indicating a lower prediction accuracy. The predicted cumulative production tended to be higher in the later stages. However, when the dataset increased to 4/4, the R² score improved to 0.86, but the predicted cumulative production still remained lower than expected. Figure 9 shows that the PLE model achieves an R² score of 0.86 with only 1/4 of the data, indicating a lower accuracy when predicting cumulative production in the later stages. When the dataset increases to 4/4, the R² score improves to 0.9, and the predicted cumulative production aligns with the expected values.

(2)

Discussions of well 063-37010

As seen in Figure 10, it can be observed that the Arps model achieved an R² score of 0.77 with only 1/4 of the data. When the dataset increased to 4/4, the R² score improved to 0.94, and the predicted cumulative production aligned with the expected values. According to Figure 11, the Duong model obtained an R² score of 0.87 with only 1/4 of the data. However, when the dataset increased to 4/4, the R² score improved to 0.93. Figure 12 shows that the PLE model achieved an R² score of 0.77 with only 1/4 of the data. When the dataset increased to 4/4, the R² score improved to 0.91, and the predicted cumulative production aligned with the expected values.

Based on the predicted results of the Arps, Duong, and PLE decline models, it can be concluded that the accuracy of the classical decline model’s predictions can only be guaranteed under conditions of sufficient data. When data are lacking, the model parameters are difficult to fit, and the predicted decreasing production trend is, thus, not in keeping with the expected results.

3.2.2. Results of Transfer Learning Model

In this article, the model was trained via cross-validation on the blocks with sufficient samples in Table 1 to obtain the training parameters of the model, and the model trained in the source domain was transferred to the target domain (as shown in Table 2) for prediction. Figure 13 and Figure 14 illustrate the prediction results for well 003-22278 and well 063-37010, respectively, based on the transfer-learning model. In Figure 13 and Figure 14, the gray region represents the data points used for generating predictions, i.e., input months, while the remaining part represents the model’s prediction results. To demonstrate the advantages of the transfer learning model, only production wells in blocks with scarce neighboring samples were selected, and only 1/4 of the historical production data were used for fitting and prediction.

From Figure 13 and Figure 14, it can be observed that under the condition of scarce samples, the proposed model outperforms the classical production decline model with an R² score of 0.93 and 0.99. The prediction accuracy of the proposed model is the same as that of the classical production decline model under the condition of using 4/4 of the data, and there is even a slight advantage. Additionally, the predicted trend of cumulative production aligns with the expected results.

Meanwhile, other production wells were selected from the sparsely sampled blocks to validate the generalization capability of the model proposed in this paper. As shown in Figure 15, the R² scores of well 003, well 063, well 065, and well 085 were 0.93, 0.99, 0.9, and 0.87, respectively. Thus, the proposed model demonstrates a certain degree of generalization.

3.2.3. Comparative Analysis of Mainstream Predictive Models

This paper employs three mainstream time series forecasting methods, namely LSTM [33,34], GRU [35], and TCN [36], to validate the effectiveness of the proposed model. The test results are shown in Figure 16 (refer to Section 3.2.2 for the tested samples). In Figure 9, the gray area represents the data points used for generating predictions, while the remaining parts represent the model’s predicted results. It is evident from Figure 9 that the proposed model achieved the best-fitting effect between the predicted shale gas production values and the true label values.

To highlight the differences in the models more intuitively, the average absolute error (MAE) and average absolute percentage error (MAPE) were separately calculated for this model alongside three mainstream models. The results are shown in Figure 17. The results in Figure 10 indicate that the MAE values of this model for wells 1(003), 2(063), 3(065), and 4(085) were 2.24, 1.01, 0.85, and 1.35, respectively. The errors in MAPE were 16%, 2%, 8%, and 19% for the respective wells. These error values are significantly lower than those of the other mainstream models, indicating that the model proposed in this paper can provide stable prediction performance.

The further results of the transfer learning model at different input time steps are shown in Figure 18. When using 6 months of input data, the errors in terms of MAPE and MAE were 27% and 4.38, respectively. When using 12 months of input data, the errors were 34% and 5.74. When using 18 months of input data, the errors were 31% and 4.97. When using 24 months of input data, the errors were 17% and 2.25. From the above data, it can be observed that when the available historical production data exceeds 12 months, as the production time increases, the model’s errors are further improved.

3.2.4. Discussion

As shown in Section 3.2.1, the results indicate that when using the classical decline curve model for prediction, the longer the production history data, the higher the accuracy of the model’s predictions. Conversely, with fewer production history data, this model’s prediction accuracy decreases. Therefore, it can be concluded that the classical decline curve model is suitable for wells with a longer production history, while it performs poorly when predicting wells with a shorter production history.

According to the results presented in Section 3.2.2, the transfer learning model based on the hierarchical interpolation model can generate more accurate decline trend predictions for blocks with limited sample data, reducing prediction errors. The proposed transfer learning model achieves accurate predictions even with limited samples due to two main reasons. First, the model has a larger number of parameters compared to the classical decline curve model, which usually has only 3–4 parameters. Secondly, the transfer learning model adjusts its parameters directly from a large amount of data during the training process to generate a model that has good generalization in out-of-sample testing data, enabling it to adapt to different types of data fluctuations.

The results presented in Section 3.2.3 demonstrate that the proposed model outperformed several mainstream time series prediction models in terms of the mean absolute error (MAE) and mean absolute percentage error (MAPE) evaluation metrics. The main reason for this is that the model combines the advantages of multiple models. This combination ensures the further improvement of prediction efficiency.

By employing transfer learning methods, the issue of data scarcity can be addressed. Despite having different geological structures, adjacent blocks still exhibit similar characteristics in production decline patterns. Transfer learning utilizes these extracted similar features from the source model to enhance the prediction of the target model, even when dealing with different blocks. Meanwhile, the transfer learning model in this paper can also be built and trained based on shale gas datasets from other regions, so it has a certain degree of universality.

4. Conclusions

The research findings of this paper demonstrate that the performance of the proposed model, developed using transfer learning to address the issue of limited sample data in production decline modeling, outperforms classical decline models and several mainstream models. This newly proposed approach improves the existing prediction techniques, which is crucial for decision making and calculating investment returns. Furthermore, the results indicate that transfer learning can solve the problem of a declining yield trend prediction with limited sample data by leveraging the knowledge acquired from data-rich blocks.

Compared to classical decline models, the prediction of the proposed model in this paper requires the design of different models based on the input months. During the training period, the model specifically adjusts its weight to map a certain length of input data to the output data. For example, if a well has seven months of data and the goal is to predict the yield decline trend for the next ten years, only the model trained with the input data of seven months can be used. Although building a transfer learning model requires more work compared to classical decline models, the training process of the model is easy to automate and only needs to be performed once at the beginning, enabling these models to be effectively used for a declining yield trend prediction.

The transfer learning method employed in this study also has certain limitations. First, transfer learning requires a certain degree of similarity between the data distributions of the source domain and the target domain. If the data distribution in the target domain significantly differs from that of the source domain, transfer learning may not exhibit a good performance. Second, different shale gas wells may have distinct geological and operational conditions. Therefore, it is essential to ensure that the transfer learning model can adapt to various well conditions.

Future research directions are suggested as follows: (1) Domain adaptation technology can be used to solve the data mismatch problem to adapt to the data distribution of the target domain. (2) Considering knowledge from multiple source fields can improve the performance of transfer learning. (3) Using online transfer learning technology can enable the transfer learning model to continuously adapt to new data in real-time data streams.