A machine learning-based production prediction method for offshore deep low-permeability to tight reservoirs based on reservoir classification: a case study from the western south China sea

Abstract

Introduction:

Developing offshore deep low-permeability to tight reservoirs faces inconsistent success due to ambiguous reservoir classification and inaccurate production evaluation. This study addresses these issues by analyzing oil wells in the western South China Sea.

Methods:

The target reservoir was classified into four types using a flow zone indicator method, and permeability conversion models were established accordingly. Using tNavigator, numerical reservoir models were constructed to evaluate the effects of permeability contrast, sedimentary rhythm, interlayers, and oil saturation on initial oil production. Key production factors were identified through Pearson analysis and grey relational analysis of test data. Production allocation was then performed for each sublayer within the test interval using the formation coefficient method. Subsequently, K-nearest neighbor (KNN) and back-propagation (BP) machine learning models were developed to predict production for different reservoir types.

Results:

Types II and III reservoirs, distinguished mainly by effective permeability, make the dominant contribution to total well production, whereas Type IV reservoirs contribute little. Between the two machine learning approaches evaluated, the back-propagation model offered the best predictive accuracy.

Discussion:

This study establishes a targeted prediction workflow that clarifies the contribution of individual reservoir types to total well production. It helps fill the gap in production prediction for offshore deep low-permeability to tight reservoirs and provides reliable support for oil-well stimulation design.

1 Introduction

Offshore low-permeability to tight reservoirs have become increasingly important targets for reserve growth and production replacement as offshore exploration and development continue to expand (Sun et al., 2013; Sun et al., 2010; Zhu et al., 2023). However, these reservoirs commonly exhibit complex lithology, strong heterogeneity, complicated pore-throat structures, and highly variable fluid distributions, which make reservoir evaluation and production testing difficult (Ding et al., 2020; Jia et al., 2012; Liu Z. et al., 2022). In offshore test wells, production is often obtained from multilayer commingled test intervals rather than from individually isolated sublayers, and the limited number of formation tests further increases the uncertainty of production evaluation. As a result, accurate reservoir characterization, sublayer-level production evaluation, and reliable productivity prediction remain challenging in offshore low-permeability to tight reservoirs.

Reservoir classification is a fundamental step in the evaluation of heterogeneous reservoirs because it helps identify flow units with similar storage and seepage capacities and supports the selection of favorable test intervals. Previous studies have proposed a variety of reservoir classification methods based on petrophysical properties, pore structure, core analysis, and integrated geological indicators (C et al., 2019; Gao et al., 2021; Deng et al., 2024; Cui et al., 2024). Among these approaches, flow-unit-based methods, including the flow zone indicator (FZI), have been widely used to distinguish reservoirs with different seepage behaviors and to improve the interpretation of porosity-permeability relationships (Cullender, 1955; Joshi, 1988; Zhang et al., 2013). These studies demonstrate that reservoir classification can effectively reveal heterogeneity and provide a basis for reservoir evaluation. In recent years, advanced data-driven methods have also been introduced into reservoir quality evaluation. For example, Rashid et al. applied self-organizing maps (SOM) and cluster analysis to predict reservoir quality in gas-bearing carbonate sediments, demonstrating the potential of machine-learning-assisted classification for heterogeneous reservoirs (Rashid et al., 2023). In addition, petrophysical correlations in reservoirs with complex void structures may be highly uncertain when a single generalized porosity-permeability relationship is used. Ponomareva et al. showed that more detailed characterization of reservoir void structure can substantially improve the correlation between filtration and capacitance characteristics and enhance the predictive performance of geological-hydrodynamic models (Ponomareva et al., 2025). Recent international studies also suggest that reservoir characterization workflows need to be adapted to the geological setting and data conditions of the target reservoir. Wang et al. emphasized the difficulty of offshore reservoir prediction under sparse-well conditions (Ismail et al., 2026), Yarmohammadi et al. showed that heterogeneity characterization requires integrated multi-scale workflows that remain strongly reservoir-specific (Yarmohammadi et al., 2025), and recent field-scale characterization work in the Temsah gas field likewise relied on field-specific seismic–geological integration rather than generalized evaluation schemes (Aghli et al., 2020). Therefore, many existing classification and evaluation schemes are still established for specific reservoir types, blocks, or datasets, and their direct applicability to offshore low-permeability to tight reservoirs may remain limited, especially under conditions of scarce test data, multilayer commingled production, and strong vertical heterogeneity.

Production prediction methods for oil and gas reservoirs have evolved from analytical and seepage-theory-based models to logging-based methods, statistical models, and, more recently, machine-learning-based approaches (Xie et al., 2022; Zhang et al., 2023; Liu et al., 2020; Fan et al., 2025; Fang et al., 2024; Bai et al., 2024; Gao et al., 2020). Analytical or semi-analytical productivity models are useful for understanding the effects of seepage mechanisms and fracture parameters, but they often rely on idealized assumptions and simplified boundary conditions, which restrict their application in geologically complex reservoirs (Xie et al., 2022; Zhang et al., 2023; Liu et al., 2020). Production behavior in complex reservoirs is strongly influenced by internal flow mechanisms. Martyushev et al. showed that interporosity flow between matrix and fractures can significantly affect oil production in carbonate reservoirs, indicating that production prediction in heterogeneous reservoirs should account for physically meaningful reservoir differences rather than relying solely on generalized empirical relationships (Martyushev et al., 2025). Logging-based and statistical methods can provide rapid productivity estimates, yet they are often limited in their ability to capture strongly nonlinear relationships among geological, petrophysical, and dynamic production factors (Fan et al., 2025; Fang et al., 2024). In recent years, a variety of machine-learning-based methods, including support vector machines, random forests, gradient boosting, and artificial neural networks, have been increasingly applied to production prediction because of their ability to capture nonlinear relationships among geological and engineering variables. Jin et al. improved the model’s capability to extract dynamic features and enhanced its generalization performance through feature selection and sample-structure optimization (Jin et al., 2024). Al-Shabandar et al., Bao et al., and Song et al. applied GRU, RNN, and PSO-optimized LSTM models, respectively, to production performance prediction, demonstrating the advantages of deep sequential models in terms of predictive accuracy and application potential (Al-Shabandar et al., 2021; Bao et al., 2020; Song et al., 2020). Pan et al. further integrated CNN, LSTM, and a self-attention mechanism to achieve comprehensive extraction of spatiotemporal features from oil well production data and to predict production behavior (Pan et al., 2023). In addition, Duplyacov et al., Du et al., and Fan et al. improved prediction performance from the perspectives of fracturing optimization, interwell spatial relationship characterization, and hybrid linear–nonlinear modeling, respectively, thereby further extending the application scope of related methods (Ma et al., 2024; Du et al., 2022; Ismail et al., 2026). However, many existing machine-learning-based studies still focus on direct well-level production prediction and do not explicitly address multilayer commingled intervals, sublayer-level production allocation, or reservoir-type-specific heterogeneity under limited-data offshore conditions (Bai et al., 2024; Gao et al., 2020; AI-Jawad and Saleh, 2020; Dezfoolian, 2013; Liu R. et al., 2022). For offshore low-permeability to tight reservoirs, such direct prediction may obscure the contribution of individual sublayers within a test interval and may not fully account for the strong heterogeneity between different reservoir types.

Therefore, a key research gap remains in establishing an integrated production-prediction workflow for offshore low-permeability to tight reservoirs under limited-data conditions. Unlike conventional machine-learning-based studies that directly map reservoir and engineering parameters to total well production, the novelty of this study lies in the integration of reservoir classification, physical modeling, dominant-factor screening, sublayer-level production allocation, and reservoir-type-specific machine-learning prediction into a unified workflow. First, the target reservoir is classified using the FZI method, and permeability conversion relationships are established for different reservoir types. Second, numerical forward models are constructed to analyze the effects of permeability contrast, sedimentary rhythm, interlayers, oil saturation, and thickness on production behavior. Third, key production-controlling factors are identified through statistical and grey relational analyses, and the production of each sublayer within a test interval is allocated using the formation coefficient method. Finally, K-nearest neighbor (KNN) and back-propagation (BP) models are developed to predict production for different reservoir types in offshore low-permeability to tight reservoirs. This workflow combines geological classification and physically guided production allocation with data-driven prediction, and is intended to provide a more suitable framework for offshore test wells characterized by limited data and multilayer commingled production.

2 Regional geological conditions

The Beibu Basin, located at approximately 19°21′6.00″N and 108°38′36.00″E, covers an area of about 3.9 × 10⁴ km². This Cenozoic sediment-dominated extensional rift basin, bounded by the Hainan Uplift to the southeast and the Yinggehai Basin to the west, is an important offshore oil-rich area (Gao et al., 2020). The basin comprises three primary tectonic units: the northern depression, the Qixi uplift, and the southern depression, exhibiting an alternating uplift-depression structure.

The Weixinan Sag (Figure 1), a NEE-SWW trending, 0.38 × 10⁴ km² half-graben basin in the northern Beibu Basin’s northeastern depression, formed through three rifting and post-rift subsidence phases during the Cenozoic (Gao et al., 2020). Characterized by a north-faulted and south-overlapped structure, it contains Paleogene sediments including the Changliu, Liushagang, and Weizhou formations. The Liushagang formation, primarily composed of medium-deep lake sediments, is the focus of this study. The Liushagang Formation can be divided vertically into three members: the first member, primarily sub-lacustrine fan and fan-delta deposits; the second member, shore-shallow lake, deep lake or semi-deep lake, sub-lacustrine fan, and braided-river delta deposits; and the third member, primarily fan-delta deposits. Despite the Weixinan Sag’s substantial oil production (8.0 × 10⁹ t), proven geological reserves are only 1.3 × 10⁸ t, indicating significant exploration and development potential.

FIGURE 1

3 Reservoir model construction

3.1 Reservoir classification by FZI method

The FZI (flow zone indicator) formula is based on the modified Carmen-Kozeny formula (AI-Jawad and Saleh, 2020; Dezfoolian, 2013; Liu R. et al., 2022; Liang et al., 2024; Soleymanzadeh et al., 2019) (Equation 1):where K: permeability, mD; φ_e: effective porosity, %; F_s: shape coefficient; τ: tortuosity of porous media; S_gv: unit volume particle surface area, μm².

Define normalized porosity (AI-Jawad and Saleh, 2020; Dezfoolian, 2013; Liu R. et al., 2022; Liang et al., 2024; Soleymanzadeh et al., 2019) (Equation 2):where φ_z: normalized porosity, %.

Define reservoir quality index (AI-Jawad and Saleh, 2020; Dezfoolian, 2013; Liu R. et al., 2022; Liang et al., 2024; Soleymanzadeh et al., 2019) (Equation 3):where RQI: reservoir quality index, dimensionless.

Based on the above formulas, the FZI formula can be constructed (AI-Jawad and Saleh, 2020; Dezfoolian, 2013; Liu R. et al., 2022; Liang et al., 2024; Soleymanzadeh et al., 2019) (Equation 4):where FZI: flow zone indicator, dimensionless.

In order to reduce the error influence of core data, the cumulative distribution function is introduced to divide the flow units (Equation 5):where Ф (x)∈ [0, 1]; x, t: real number, x, t∈ [, ].

Based on the 327 core samples with depth ≥2800 m, low to ultra-low porosity and permeability in the Weixinan Sag, calculated FZI and its cumulative probability (Figure 2). According to the FZI cumulative probability cure, the low-permeability to tight reservoirs are divided into four types (Figure 2a) and (Table 1). After reservoir classification, the porosity-permeability relationships for different reservoir types are shown in Figure 2b and summarized in Table 2.

FIGURE 2

It should be noted that the classified samples span a range from low-permeability to tight reservoirs; therefore, the term used in this study refers to the overall reservoir system under investigation rather than a single strict cutoff-based definition.

Table 1 indicates that reservoir types II and III are dominant in the Weixinan Sag. Type I reservoirs (FZI≥3.07) exhibit permeability ranging from 0.008 mD to 49.100 mD (average 8.675 mD) and porosity from 0.131% to 12.603% (average 5.063%). Type II reservoirs (0.83 ≤FZI <3.07) exhibit permeability ranging from 0.010 mD to 40.992 mD (average 4.93 5 mD) and porosity from 2.160% to 14.709% (average 10.182%). Type III reservoirs (0.24 ≤FZI <0.83) exhibit permeability ranging from 0.010 m D to 2.728 mD (average 0.551 mD) and porosity from 2.821% to 14.844% (average 10.947%). Type IV reservoirs (FZI <0.24) exhibit permeability ranging from 0.012 mD to 0.196 mD (average 0.092mD) and porosity from 9.422% to 14.779% (average 11.858%).

According to Table 2, reservoir classification helps establish type-specific porosity-permeability relationships, although the goodness of fit varies among reservoir types.

3.2 Physical modeling of reservoir heterogeneity

tNavigator (Rock Flow Dynamics, 2024) is an integrated reservoir modelling and simulation platform developed by Rock Flow Dynamics (Rock Flow Dynamics, 2024). The software provides a unified workflow for geoscience, reservoir engineering, and production engineering, and supports static and dynamic reservoir analysis within a single environment. Because this study required forward simulations under different reservoir configurations, tNavigator was selected to evaluate the effects of permeability contrast, sedimentary rhythm, interlayers, and oil saturation on production behavior. Using tNavigator software, reservoir forward models were constructed based on seepage mechanisms to assess the impact of permeability gradients, sedimentary rhythms, interlayers, and oil saturation on initial oil well production. Model parameters (Table 3) were selected based on Weixinan Sag Liushagang formation test data and reservoir classification results (Table 1). Oil and water PVT properties are detailed in Tables 4, 5.

3.2.1 Reservoir models without interlayers under different permeability contrasts

Considering the influence of sedimentary conditions on permeability difference, reservoir physical models under positive rhythm, inverted rhythm and composite rhythm conditions are constructed respectively. Positive rhythm describes a reservoir with decreasing permeability from bottom to top due to gravity-driven deposition of fine grains at the bottom and coarse grains at the top, typical of fan-delta front underwater distributary channels. Reverse rhythm describes a reservoir with increasing permeability from bottom to top, influenced by water erosion and sorting. High-permeability, coarse-grained sediments accumulate at the reservoir bottom, while low-permeability, fine-grained sediments deposit at the top, characteristic of fan-delta front mouth bar microfacies. Compound rhythm, reflecting complex permeability variations (positive and composite rhythm), results primarily from the superposition of underwater distributary channels and multi-stage estuary dams.

FIGURE 3

FIGURE 4

FIGURE 5

Figure 6 shows that the cumulative oil production of groups A and B depends primarily on permeability, with higher permeability leading to greater cumulative production and daily increases. At a permeability ratio of 10, the cumulative production differs by roughly 10 times. In early production stages, with equal permeability, groups A and B show similar cumulative oil production. However, the composite rhythm without interlayer yields significantly less than the positive and reverse rhythms without interlayer, indicating that the composite rhythm tends to reduce cumulative oil production.

FIGURE 6

3.2.2 Reservoir models with interlayers under different permeability contrasts

Figure 7 shows that in rhythmic reservoirs with interlayers, cumulative oil production depends primarily on permeability. Higher permeability leads to greater cumulative production and daily increases, particularly at 35mD and 50mD, where the rise is most pronounced. Early production stages reveal minimal differences in cumulative output across rhythmic modes with interlayers at equal permeability, suggesting that, under the current model settings, interlayers and rhythmic patterns have a relatively limited effect on production.

FIGURE 7

3.2.3 Physical model for oil saturation and reservoir thickness

The reservoir is modeled as a 200 m × 200 m × 29 m cuboid, accounting for thickness, interlayers, and oil saturation.

The physical model has layers of 2m, 5m, 8m, and 11 m from top to bottom. Permeability is 11mD in the X and Y directions and 0.1mD in the Z direction, with a porosity of 0.15. Oil saturation values are 55%, 60%, 70%, 80%, and 85%.

The reservoir simulation results display cumulative oil production for different oil saturation levels and reservoir thicknesses, using data collected 5 days before production. Figure 8 shows the correlation between oil saturation and single-well oil production. Figure 8a shows a power function relationship between oil saturation and cumulative oil production. While the exponent remains nearly constant with reservoir thickness, the variable x changes significantly, indicating that thicker reservoirs yield higher cumulative production. Figure 8b demonstrates a linear increase in cumulative production with reservoir thickness, where higher oil saturation produces a steeper slope.

FIGURE 8

4 Machine learning-based production prediction methods

This section presents two machine-learning models for production prediction: one based on the K-nearest neighbor (KNN) algorithm and the other on the back-propagation (BP) algorithm. The detailed procedures are illustrated in Figure 9 and are described as follows:

FIGURE 9

(1) Reservoir Classification: According to the reservoir classification criteria of the flow zone indicator (FZI) method (Table 1), the reservoir type of each sublayer in the single well sublayer is identified. (2) Effective Permeability Calculation: Based on the reservoir classification results (Table 1), the effective permeability of each layer is determined using the permeability models (Table 2) specific to different reservoir types. (3) Training Variable Selection: Effective permeability, porosity, and oil saturation are selected as the training variables for the machine learning production prediction method, based on the Pearson correlation analysis results of key production factors. (4) Production Allocation Using the KH Method: The formation coefficient (KH) method is employed to split production based on the effective permeability and effective thickness of each layer in the single well sublayer. (5) Construction of the KNN and BP Production Prediction Model: A KNN-based production prediction model is built to estimate output for four reservoir types, followed by a BP-based model for the same reservoirs. (6) Model Verification: The accuracy and reliability of the constructed models are verified through validation techniques. (7) Error Analysis: A thorough error analysis is conducted to assess the differences between the predicted and actual production values. (8) Model Selection: The most suitable model is selected based on the results of the verification and error analysis.

This structured approach ensures a comprehensive evaluation and selection of the best machine learning model for accurate production prediction.

4.1 Main factors controlling oil well production

4.1.1 Pearson correlation analysis

The Pearson correlation coefficient is (Tong et al., 2024; Tian et al., 2024; Wang et al., 2020):where P_x,y: Pearson correlation coefficient, p_x,y∈ [-1, 1]; cov (x, y): covariance of x and y; σx: variance of x; σy: variance of y.

The greater the Pearson correlation coefficient, the stronger the correlation between the two variables (Table 6).

Pearson correlation coefficients, calculated using Equation 7 for ten wells of Weixinan Sag, reveal the relationship between seven production factors (effective permeability, porosity, oil saturation, argillaceous content, skin coefficient, viscosity, and well radius) and production (Figure 10a). The ranking of these factors is illustrated in Figure 10b.

FIGURE 10

Based on Table 6, with |Px,y|≥0.5 as the standard, the key production factors of Weixinan Sag are effective permeability, porosity and oil saturation.

4.1.2 Grey relational analysis

Grey correlation analysis assesses factor correlation by comparing the similarity of their development trends. Using specific oil production as the reference sequence, seven production factors (effective permeability, porosity, oil saturation, shale content, skin factor, viscosity, and well radius) are compared. Production factors are averaged to mitigate dimensional influences (Equation 8):

Where ave (x_i): the mean of x_i.

The formula of grey correlation coefficient is:

Where ζi (k): grey correlation coefficient; mini: the minimum value of i; mink: the minimum value of k; Δi (k): sequence difference, ; ρ: resolution coefficient, ρ = 0.5; max_i: the maximum value of i; max_k: the maximum value of k.

The formula of grey correlation degree is Equation 10:

The grey correlation coefficient is calculated using Equation 9, and the results are weighted to obtain the grey correlation degree. A higher grey correlation degree indicates a stronger correlation with the reference column. Table 7 shows the ranking of the seven production factors based on their grey correlation degrees.

For the seven production factors, the correlation between effective permeability and specific production index is the highest (0.908), followed by oil saturation (0.815) and porosity (0.814).

4.1.3 Optimization of main production factors

Based on Pearson correlation analysis and grey correlation analysis, the comparison results of the ranking of production factors are as shown in Table 8, and the results obtained by the two analysis methods are basically the same. The key production factors of Weixinan Sag are effective permeability, porosity and oil saturation.

4.2 Production allocation method

After the oil test, only the total production of the test interval is obtained. Since a test interval typically consists of multiple sublayers with different contributions to total production, production allocation is required to quantify the contribution of each sublayer.

The formation coefficient method (KH method) is a widely used method for production allocation (Yang et al., 2018). Its calculation formula is:where Y_i: formation coefficient, dimensionless; k_i: dynamic permeability of the i-th layer, mD; h_i: effective thickness of the i-th layer, m.

It can be seen from Equation 11 that the larger the product of the dynamic permeability of the reservoir and the effective thickness, the higher the contribution of the layer in the total production.

The allocated production of each layer can be calculated as follows (Yang et al., 2018):where q_i: production of the i-th layer after splitting, m³/d.

Using the DST1 interval of Well X12-1S-1 in Weixinan Sag as an example (Equation 12), the total production is 10.40 m³/d. As shown in Table 9, the production allocation aligns with reservoir classification: higher-quality reservoirs contribute more, while the IV reservoir contributes almost nothing.

4.3 Production prediction model

4.3.1 Data normalization

To eliminate the influence of differences in variable magnitude and dimension, the selected variables were normalized using Min–Max normalization, as expressed in Equation 13:where is the normalized production-controlling factor (dimensionless), is the original factor, and and are the minimum and maximum values of that factor, respectively. The specific normalizations for permeability, porosity, and oil saturation are as follows Equations 14–16:

This preprocessing step was necessary because the input variables differ in physical meaning and numerical scale, and unscaled features may affect distance calculation in the KNN model as well as training efficiency and convergence behavior in the BP neural network.

4.3.2 K-nearest neighbor (KNN) algorithm

The K-nearest neighbor algorithm is a fundamental supervised learning method in machine learning (Niu et al., 2022; Liu et al., 2023; Wang et al., 2021). It works by training a model on labeled data, then classifying new data points based on their similarity to known samples. The approach measures distance between points to determine similarity, assigning each new sample to the category of its nearest neighbors.

To construct a production prediction model using the K-nearest neighbor algorithm, we first establish a training set using key production factors. Based on Pearson correlation analysis in the Weixinan Sag, effective permeability, porosity, and oil saturation are identified as the main production-controlling factors. Therefore, these three variables are used to form the training set. The selected production-controlling factors were normalized before KNN modeling using the preprocessing procedure described in Section 4.3.1.

Then, construct training data with known categories. Based on the three key production controlling factors, create three-dimensional vector training sets for I, II, III, and IV reservoirs, respectively (Equation 17).

Euclidean distance measures the distance between variables and is a specific case of Minkowski distance where P = 2 (Niu et al., 2022; Liu et al., 2023; Wang et al., 2021).

The Mankowski distance (Equation 18):

The Euclidean distance (Equation 19):

To ensure the generalization capability of the KNN model and mitigate the risk of overfitting, a well-based 5-fold cross-validation procedure was implemented to determine the optimal value of the hyperparameter K (number of nearest neighbors). Specifically, tested-interval samples from ten test wells in the Weixinan Sag—including X11-6-5d, X6-3-2, X11-2-2, X11-2-3, X11-8-1, X12-1S-1, X12-1W-1, X6-3-1, X12-1-3, and X11-8-2—were utilized as the dataset. These wells were divided into five mutually exclusive subsets. In each validation round, the tested-interval samples from one subset of wells were used as the validation set, while the samples from the remaining wells constituted the training set. KNN models with varying values of K (K ∈{1, 2, 3, 4, 5}) were then constructed, and their predictive performances were evaluated using the coefficient of determination (R²), mean absolute error (MAE), and mean squared error (MSE). This procedure was repeated across all five folds, and the arithmetic mean of the evaluation metrics from the validation rounds was calculated to represent the model’s overall performance for each K setting. As summarized in Table 10, comparing the averaged validation results across different K values reveals that the model achieved the optimal bias-variance trade-off at K = 3. Therefore, K = 3 was selected as the final model parameter for subsequent production prediction.

4.3.3 Back-propagation (BP) algorithm

Back-propagation is a supervised learning algorithm used to train multilayer feedforward neural networks (Bai et al., 2024; Zhang et al., 2024; Wu et al., 2020). It adjusts model weights to minimize the difference between predicted and actual outputs, thereby improving the accuracy of the non-linear prediction function.

The process of constructing a production prediction model using the backpropagation algorithm involves the following steps:

First, the training and test sets are constructed based on the main production-controlling factors, namely effective permeability, porosity, and oil saturation. Both the training and test sets were preprocessed using the normalization procedure described in Section 4.3.1 before BP model construction. Then, initial prediction function models are constructed separately for the four reservoir types: I, II, III, and IV.

Next, the model weights are iteratively updated during the training process. The hidden-layer transformation can be expressed as follows (Equation 20):where w: weight; α: bias, assuming that the model has j layers, j = 1, 2, 3, … … , l and each layer has i weights; w_ij: the i weight of the j layer, and each layer shares a bias α_j.

The prediction performance is assessed after each weight update, with the coefficient of determination R² serving as the evaluation criterion for the model’s predictive accuracy (Equation 21).where R²: the coefficient of determination, that is, the degree of interpretation of the variance variable, the closer R² is to 1, the closer the predicted production is to the real production; N: mber of samples; y_i: actual value; : predictive value; : the average of the true value.

In BP neural networks, the sigmoid function is a commonly used activation function. It maps arbitrary real-valued inputs into the interval between 0 and 1 and is differentiable, making it suitable for gradient-descent-based optimization of network parameters. The expression of the sigmoid function is given in Equation 22, and its functional curve is shown in Figure 11.

FIGURE 11

During the training process, the input data are first fed into the neurons of each layer. The output of each neuron is then calculated from the corresponding connection weights and thresholds. These outputs are subsequently passed to the next layer as input, and this process continues layer by layer until the final prediction is generated at the output layer. For the training set the training of the BP neural network can be formulated as an optimization problem, as shown in Equation 23.

Here, : the weight matrix; : the bias vector; : the predicted value of the -th sample; : the actual value of the -th sample, and : the number of samples.

To evaluate the prediction accuracy and generalization performance of the BP neural network model in production prediction, the root mean square error (RMSE) and the coefficient of determination were selected as the main evaluation metrics. RMSE reflects the overall magnitude of the prediction error between predicted and observed values, whereas measures the degree of correlation between the model output and the target value. When the RMSE of the test data is low and the value is close to 1, the model is considered to have good predictive performance; otherwise, further adjustment is required. The formulas for RMSE and are given in Equations 24, 25, respectively.

In these equations, is the actual production of the -th sample, is the number of samples, is the production predicted by the BP neural network for the -th sample, and is the average actual production of all samples.

After multiple rounds of training, the weights that yield the best prediction performance are selected and loaded into the model. The input layer receives three-dimensional data, and the production prediction value is ultimately output from the output layer through the hidden layer.

The BP neural network used in this study consisted of an input layer, a hidden layer, and an output layer. The input variables were effective permeability, porosity, and oil saturation; therefore, the numbers of neurons in the input layer, hidden layer, and output layer were 3, 7, and 1, respectively. The network was trained using the Sigmoid function. The learning rate was set to 0.0001, the maximum number of training epochs was 2000, and the target error was 0.0001. Before training, the input and output data were normalized, and the trained network was then used for production prediction.

4.4 Validation and optimization

The coefficient of determination (R²), mean absolute error (MAE), and mean squared error (MSE) are statistical metrics used to evaluate algorithm performance (Li et al., 2024).

The mean absolute error (Li et al., 2024) (Equation 26):where MAE: the average absolute error, that is, indicating prediction deviation, and lower MAE signifies greater prediction accuracy; n: the number of samples; y_i: the actual value; : the predicted value.

The mean squared error (Li et al., 2024) (Equation 27):where MSE: mean square error, the average squared difference between predicted and actual values, and lower MSE indicates higher prediction accuracy.

Table 11 and Figure 12 present the effect evaluation of two machine learning-based production prediction models for the Weixinan Sag.

FIGURE 12

In I reservoirs (Table 10, Figure 12a), the actual specific oil production index ranges from 0.0239 to 2.5906 m³/d/MPa, averaging 0.2255 m³/d/MPa. The K-nearest neighbor algorithm predictions within this range are 0.0388–0.6235 m³/d/MPa, with an average of 0.1275 m³/d/MPa (R² = 0.3480, MAE = 0.1302, MSE = 0.1954). The back-propagation algorithm predicts oil production ranging from 0.0233 to 2.3176 m³/d/MPa, with a mean of 0.2167 m³/d/MPa. Performance metrics indicate that: R² = 0.9497AE = 0.0498, and MSE = 0.0061.

In II reservoirs (Table 10, Figure 12b), the actual specific oil production index ranges from 0.0009 to 0.2653 m³/d/MPa, averaging 0.0514 m³/d/MPa. The K-nearest neighbor algorithm predictions within this range are 0.0038–0.1972 m³/d/MPa, with an average of 0.0491 m³/d/MPa (R² = 0.8620, MAE = 0.0186, MSE = 0.0008). The back-propagation algorithm predicts oil production ranging from 0.0023 to 0.2469 m³/d/MPa, with a mean of 0.0513 m³/d/MPa (R² = 0.9195, MAE = 0.0156, MSE = 0.0005).

In III reservoirs (Table 10, Figure 12c), the actual specific oil production index ranges from 0.0001 to 0.0404 m³/d/MPa, averaging 0.0103 m³/d/MPa. The K-nearest neighbor algorithm predictions within this range are 0.0001–0.0301 m³/d/MPa, with an average of 0.0113 m³/d/MPa (R² = 0.5851, MAE = 0.0056, MSE = 0.0001). The back-propagation algorithm predicts oil production ranging from 0.0007 to 0.0346 m³/d/MPa, with a mean of 0.0107 m³/d/MPa (R² = 0.9224, MAE = 0.0025, MSE = 0.0001).

In IV reservoirs (Table 10, Figure 12d), the actual specific oil production index ranges from 0.0001 to 0.0017 m³/d/MPa, averaging 0.0002 m³/d/MPa. The K-nearest neighbor algorithm predictions within this range are 0.0001–0.0023 m³/d/MPa, with an average of 0.0003 m³/d/MPa (R² = 0.8213, MAE = 0.0001, MSE = 0.0001). The back-propagation algorithm predicts oil production ranging from 0.0001 to 0.0018 m³/d/MPa, with a mean of 0.0004 m³/d/MPa (R² = 0.6381, MAE = 0.0002, and MSE = 0.0001).

Overall, back-propagation outperformed the other algorithm in predicting test production for low-permeability to tight reservoirs in the Weixinan Sag.

4.5 Application

Wells X6-3-7 and X-6 serve as model application wells. Table 12 presents reservoir classification and dynamic/static parameter conversion results for two wells. In well X6-3-7, within the perforated interval (3551.20m–3621.38 m), III reservoirs dominate. Specifically, there are no I reservoirs; II reservoirs constitute 8% (cumulative thickness: 4.62 m); III reservoirs constitute 54% (cumulative thickness: 33.99 m); and IV reservoirs constitute 38% (cumulative thickness: 2.76 m). In well X-6, within the perforated interval (2929.06m–3010.68 m), III reservoirs dominate. Specifically, there are no I reservoirs; II reservoirs constitute 13% (cumulative thickness: 2.9 m); III reservoirs constitute 56% (cumulative thickness: 13.35 m); and IV reservoirs constitute 31% (cumulative thickness: 3.20 m).

According to Table 12, the data of the same type of reservoir are combined by thickness weighting, and the prediction results obtained using the machine-learning-based back-propagation model are shown in Table 13.

5 Discussion

Compared with conventional production prediction methods, production prediction in offshore low-permeability to tight reservoirs is more challenging because of strong heterogeneity, limited well-test data, and multilayer commingled production. Traditional empirical formulas and single-factor approaches often rely on simplified assumptions and cannot adequately capture the combined effects of reservoir quality, dynamic seepage characteristics, and engineering factors. Although numerical simulation methods are physically meaningful, they are still sensitive to model assumptions, boundary settings, and parameter uncertainties. In contrast, purely data-driven approaches are constrained by sample size, data representativeness, and the quality of input parameters.

To address these challenges, this study developed an integrated workflow that combines reservoir classification, dynamic–static parameter conversion, dominant-factor identification, production allocation, and machine-learning-based prediction. The results indicate that reservoir classification provides an effective basis for distinguishing the production contributions of different reservoir types. Furthermore, effective permeability, porosity, and oil saturation were identified as the main factors controlling single-well productivity in the study area. The dynamic–static permeability conversion models also improved the consistency between well-logging-derived and well-test-derived parameters, which is important for subsequent production prediction.

The better performance of the BP model may be attributed to its stronger ability to approximate nonlinear mappings between reservoir parameters and productivity. In contrast, the KNN model relies on local similarity in the feature space and is therefore more sensitive to sample distribution, data sparsity, and local fluctuations. Under the present dataset, which is characterized by limited sample size and strong heterogeneity among reservoir types, the BP model appears to provide a more robust representation of the relationship between production-controlling factors and productivity.

The present results further suggest that the applicability of different prediction methods is not identical. Under the current dataset, physics-based and statistical interpretations remain important for production evaluation, whereas machine-learning models can provide useful supplementary predictive capability after reservoir-type-specific classification and parameter screening. Among the evaluated algorithms, the BP model showed better overall predictive performance than the KNN model under the present dataset. However, the performance of machine-learning-based prediction remains constrained by sample size and data representativeness, and the relevant conclusions should therefore be interpreted with appropriate caution. In addition, the dynamic–static parameter conversion relationships and the numerical simulation results in this study are established under the geological conditions and parameter settings of the study area, and their direct application to other offshore blocks may require recalibration and further validation.

From an engineering perspective, the proposed workflow is useful not only for production prediction of offshore test wells, but also for reservoir quality evaluation, sublayer-level production interpretation, and productivity-enhancement decision-making. The results show that higher-quality reservoir types make a greater contribution to total production, whereas lower-quality reservoirs contribute little under the current development conditions. This provides a practical basis for identifying favorable test intervals and selecting appropriate stimulation strategies for offshore low-permeability to tight reservoirs. Although a detailed economic evaluation is beyond the scope of this study, improved production prediction accuracy may still have practical economic value by reducing uncertainty in test-well evaluation, supporting the selection of more favorable intervals, and helping avoid ineffective engineering measures. In this way, the proposed workflow may contribute to more efficient use of testing and stimulation resources in offshore low-permeability to tight reservoirs. Future work should focus on expanding the dataset, comparing alternative validation strategies and prediction methods, and testing the applicability of the proposed workflow in other offshore blocks.

6 Conclusion

References

• 1

  AghliG.Moussavi-HaramiR.MohammadianR. (2020). Reservoir heterogeneity and fracture parameter determination using electrical image logs and petrophysical data (a case study, carbonate asmari formation, zagros Basin, SW Iran). Pet. Sci.17, 51–69. 10.1007/s12182-019-00413-0

  • CrossRef
  • Google Scholar
  • View reference in article

• 2

  Ai-JawadS.SalehA. (2020). Flow units and rock type for reservoir characterization in carbonate reservoir: Case study, south of Iraq. J. Petroleum Explor. Prod. Technol.10, 1–20. 10.1007/s13202-019-0736-4

  • CrossRef
  • Google Scholar
  • View reference in article

• 3

  Al-ShabandarR.JaddoaA.LiatsisP.HussainA. J. (2021). A deep gated recurrent neural network for petroleum production forecasting. Mach. Learn Appl.3, 100013. 10.1016/j.mlwa.2020.100013

  • CrossRef
  • Google Scholar
  • View reference in article

• 4

  BaiW.ChengS.GuoX.WangY.GuoQ.TanC. (2024). Oilfield analogy and production prediction based on machine learning: field cases in PL oilfield, China. Petroleum Sci.21, 2554–2570. 10.1016/j.petsci.2024.02.018

  • CrossRef
  • Google Scholar
  • View reference in article

• 5

  BaoA.GildinE.HuangJ. (2020). “Data-driven end-to-end production prediction of oil reservoirs by EnKF-enhanced recurrent neural networks,” in In proceedings of the SPE Latin American and Caribbean petroleum engineering conference.

  • Google Scholar
  • View reference in article

• 6

  ChengZ.LiW.XueH.LuS.TanZ. (2019). Grading evaluation criteria of tight sandstone reservoir based on high pressure Mercury injection technology and fractal theory. J. Northeast Petroleum Univ.43, 50–59+8. 10.3969/j.issn.2095-4107.2019.01.006

  • CrossRef
  • Google Scholar
  • View reference in article

• 7

  CuiY.YangJ.RaoL.YangS.JiangJ.LuK.et al (2024). Classification and evaluation of flow units in tight sandstone reservoirs based on neural network model: a case study of chang 6 oil reservoir in northern WQ area of ordos Basin. J. Xi'an Shiyou Univ. Nat. Sci. Ed.39, 22–30. 10.3969/j.issn.1673-064X.2024.02.003

  • CrossRef
  • Google Scholar
  • View reference in article

• 8

  CullenderM. (1955). The isochronal performance method of determining the flow characteristics of Wells. Soc. Petroleum Eng.204, 137–142. 10.2118/330-g

  • CrossRef
  • Google Scholar
  • View reference in article

• 9

  DengY.YinS.LiB.NieX. (2024). High resolution characterization and evaluate of pore structure of tight sandstone based on digital core technology. Geol. Rev.70, 1377–1390.

  • Google Scholar
  • View reference in article

• 10

  DezfoolianM. (2013). Flow zone indicator estimation based on petrophysical studies using an artificial neural network in A southern Iran reservoir. Petroleum Sci. Technol.31, 1294–1305. 10.1080/10916466.2010.542421

  • CrossRef
  • Google Scholar

• 11

  DingX.ZhangF.ZhangG. (2020). Modelling of time-dependent proppant embedment and its influence on tight gas production. J. Nat. Gas Sci. Eng.82, 103519. Article ID 103519. 10.1016/j.jngse.2020.103519

  • CrossRef
  • Google Scholar

• 12

  DuE.LiuY.ChengZ.XueL.MaJ.HeX. (2022). Production forecasting with the interwell interference by integrating graph convolutional and long short-term memory neural network. SPE Reserv. Eval. Eng.25, 197–213. 10.2118/208596-PA

  • CrossRef
  • Google Scholar

• 13

  FanD.LaiS.SunH.YangY.YangC.FanN.et al (2025). M.H. review of machine learning methods for steady state capacity and transient production forecasting in oil and gas reservoir. Energies18, 842. 10.3390/en18040842

  • CrossRef
  • Google Scholar

• 14

  FangM.ShiH.LiH.LiuT. (2024). Application of machine learning for production prediction in tight gas reservoirs. Energies17, 1916. Article ID 1916. 10.3390/en17081916

  • CrossRef
  • Google Scholar

• 15

  GaoG.XuX.QuT.GanJ.DangW.ZhouX.et al (2020). Petroleum origins and accumulation patterns in the weixinan sag in the beibu gulf Basin, using subsag B as an example. Acta Geol. Sin.94, 1515–1530. 10.1111/1755-6724.14371

  • CrossRef
  • Google Scholar

• 16

  GaoM.LuY.DuX.MaY.ZhangJ.DengK. (2021). Multi-factor evaluation for fine grading of tight sandstone reservoirs: a case study from H3 sand group in the upper section of Oligocene huagang formation, Xihu Sag, East China Sea Basin. Petroleum Geol. and Exp.43, 1097–1106. 10.11781/sysydz2021061097

  • CrossRef
  • Google Scholar

• 17

  IsmailH.LatiffA. H. A.RashidA.JamaludinS. N. F. (2026). Seismic reservoir characterization framework for geological modeling input of carbonate flank deposits (CFD) in central luconia, sarawak. Geomech. Geophys. Geo-energ. Geo-resour.12, 32. 10.1007/s40948-025-01095-2

  • CrossRef
  • Google Scholar

• 18

  JiaC.ZhengM.ZhangY. (2012). Unconventional hydrocarbon resources in China and the prospect of exploration and development. Petroleum Explor. Dev.39, 139–146. 10.1016/S1876-3804(12)60026-3

  • CrossRef
  • Google Scholar

• 19

  JinY.GuoK.GaoX.LiQ. (2024). Tight oil well productivity prediction model based on neural network. Processes12, 2088. 10.3390/pr12102088

  • CrossRef
  • Google Scholar

• 20

  JoshiS. (1988). Augmentation of well production with slant and horizontal Wells. J. Petroleum Technol.40, 729–739. 10.2118/15375-pa

  • CrossRef
  • Google Scholar

• 21

  LiQ.GuoK.GaoX.ZhangS.JinY.LiuJ. (2024). Production prediction model of tight oil reservoir based on particle swarm optimization-back propagation neural network. Processes12, 1890. Article ID 1890. 10.3390/pr12091890

  • CrossRef
  • Google Scholar

• 22

  LiangZ.LiX.SunA.HouF.ZhaiZ.SuiQ. (2024). Nuclear magnetic resonance logging-based permeability classification modeling for tight sandstone reservoirs. Processes12, 1309. Article ID 1309. 10.3390/pr12071309

  • CrossRef
  • Google Scholar

• 23

  LiuS.ChenG.LouY.ZhuL.GeD. (2020). A novel production evaluation approach based on the morphological analysis and fuzzy mathematics: insights from the tight sandstone gas reservoir in the ordos Basin, China. J. Petroleum Explor. Prod. Technol.10, 1263–1275. 10.1007/s13202-019-00822-2

  • CrossRef
  • Google Scholar

• 24

  LiuZ.QinM.ZhangJ.LiZ.SongP. (2022a). Mechanism and adaptability evaluation of well soaking in tight reservoir. Chem. Technol. Fuels Oils58, 181–184. 10.1007/s10553-022-01365-9

  • CrossRef
  • Google Scholar

• 25

  LiuR.SunY.YaoX.YanB.MaJ.GuoC.et al (2022b). Dynamic evaluation of flow unit based on Reservoir evolution: a case study of Neogene guantao Ng3 formation in M area, Gudao, Bohai Bay Basin. Geofluids2022, 1–19. Article ID 6249369. 10.1155/2022/6249369

  • CrossRef
  • Google Scholar

• 26

  LiuW.ChenZ.HuY.XuL. (2023). A systematic machine learning method for reservoir identification and production prediction. Petroleum Sci.20, 295–308. 10.1016/j.petsci.2022.09.002

  • CrossRef
  • Google Scholar

• 27

  MaX.ZhangL.ZhanJ.ChangS. (2024). Application of dual-stage attention temporal convolutional networks in gas well production prediction. Mathematics12, 3896. 10.3390/math12243896

  • CrossRef
  • Google Scholar

• 28

  MartyushevD. A.PonomarevaI. N.DavoodiS.KadkhodaieA. (2025). Interporosity flow between matrix and fractures in carbonates: a Study of its impact on oil production. Arabian J. Sci. Eng.50, 4963–4977. 10.1007/s13369-024-09533-1

  • CrossRef
  • Google Scholar

• 29

  NiuW.LuJ.SunY. (2022). Development of shale gas production prediction models based on machine learning using early data. Energy Rep.8, 1229–1237. 10.1016/j.egyr.2021.12.040

  • CrossRef
  • Google Scholar

• 30

  PanS.YangB.WangS.GuoZ.WangL.LiuJ.et al (2023). Oil well production prediction based on CNN-LSTM model with self-attention mechanism. Energy284, 128701. 10.1016/j.energy.2023.128701

  • CrossRef
  • Google Scholar

• 31

  PonomarevaI. N.NovikovV. А.MartyushevD. A.RaznitsynA. V. (2025). Study of correlations between filtration and capacitance characteristics of carbonate reservoirs with complex void structure. Georesursy27 (3), 221–232. 10.18599/grs.2025.3.16

  • CrossRef
  • Google Scholar

• 32

  RashidM.LuoM.AshrafU.HussainW.AliN.RahmanN.et al (2023). Reservoir quality prediction of gas-bearing carbonate sediments in the qadirpur field: insights from advanced machine learning approaches of SOM and cluster analysis. Minerals13, 29. 10.3390/min13010029

  • CrossRef
  • Google Scholar

• 33

  Rock Flow Dynamics (2024). tNavigator. Available online at: https://rfdyn.com/(Accessed March 18, 2026).

  • Google Scholar

• 34

  SoleymanzadehA.ParvinS.KordS. (2019). Effect of overburden pressure on determination of reservoir rock types using RQI/FZI, FZI* and winland methods in carbonate rocks. Petroleum Sci.16, 1403–1416. 10.1007/s12182-019-0332-8

  • CrossRef
  • Google Scholar

• 35

  SongX.LiuY.XueL.WangJ.ZhangJ.WangJ.et al (2020). Time-series well performance prediction based on long short-term memory (LSTM) neural network model. J. Pet. Sci. Eng.186, 106682. 10.1016/j.petrol.2019.106682

  • CrossRef
  • Google Scholar

• 36

  SunL.FangC.LiF.ZhuR.HeD. (2010). Petroleum exploration and development practices of sedimentary basins in China and research progress of sedimentology. Petroleum Explor. Dev.37, 385–396. 10.1016/S1876-3804(10)60040-7

  • CrossRef
  • Google Scholar

• 37

  SunL.ZouC.ZhuR.ZhangY.ZhangS.ZhangB.et al (2013). Formation, distribution and potential of deep hydrocarbon resources in China. Petroleum Explor. Dev.40, 687–695. 10.1016/S1876-3804(13)60093-2

  • CrossRef
  • Google Scholar

• 38

  TianF.FuY.LiuX.LiD.JiaY.ShaoL.et al (2024). A comprehensive evaluation of shale oil reservoir quality. Processes12, 472. Article ID 472. 10.3390/pr12030472

  • CrossRef
  • Google Scholar

• 39

  TongS.WangF.GaoH.ZhuW. (2024). A machine learning-based method for analyzing factors influencing production capacity and production forecasting in fractured tight oil reservoirs. Int. J. Hydrogen Energy70, 136–145. 10.1016/j.ijhydene.2024.05.036

  • CrossRef
  • Google Scholar

• 40

  WangY.LuoT.GaoY.YuS.WangS.ZouY. (2020). Pearson correlation analysis of factors controlling the high abundance of rearranged hopanes in crude oils from the southwest depression of the Tarim Basin, China. Geochem. J.54, 105–115. 10.2343/geochemj.2.0592

  • CrossRef
  • Google Scholar

• 41

  WangH.ChenZ.ChenS.HuiG.KongB. (2021). Production forecast and optimization for parent-child well pattern in unconventional reservoirs. J. Petroleum Sci. Eng.203, 108899. Article ID 108899. 10.1016/j.petrol.2021.108899

  • CrossRef
  • Google Scholar

• 42

  WuC.WangS.YuanJ.LiC.ZhangQ. (2020). A prediction model of specific production index using least square support vector machine method. Adv. Geo-Energy Res.4, 460–467. 10.46690/ager.2020.04.10

  • CrossRef
  • Google Scholar

• 43

  XieY.HeY.HuY.JiangY. (2022). Study on production prediction of multi-stage fractured horizontal well in low-permeability reservoir based on finite element method. Transp. Porous Media141, 629–648. 10.1007/s11242-021-01739-3

  • CrossRef
  • Google Scholar

• 44

  YangZ.YueS.ZhengC.LiuX.ChenG. (2018). Production split method restricted synthetically by multi-factors in thin interbed sandstone reservoirs. Lithol. Reserv.30, 117–124.

  • Google Scholar

• 45

  YarmohammadiS.JavaherianA.SharifiM.SaberiM. R.BasirH. M. (2025). Investigating the vertical and lateral heterogeneity in an Iranian carbonate reservoir using advanced petrophysical logs, petrographic data and image processing techniques. J. Petrol Explor Prod. Technol.15, 141. 10.1007/s13202-025-02057-w

  • CrossRef
  • Google Scholar

• 46

  ZhangD.ZhangL.ZhaoY.LiuQ. (2013). Study on steady productivity of fractured horizontal well in low permeability gas reservoir. Petroleum Geol. Recovery Effic.20, 107–110+118.

  • Google Scholar

• 47

  ZhangS.GuoK.YangH.GaoX. (2023). The production segmented calculation model of perforated horizontal Wells considering whether to penetrate the contaminated zone. Front. Earth Sci.11, 1270662. Article ID 1270662. 10.3389/feart.2023.1270662

  • CrossRef
  • Google Scholar

• 48

  ZhangY.ChenJ.WuZ.XiaoY.XuZ.ChengH.et al (2024). Effect evaluation of staged fracturing and production prediction of horizontal Wells in tight reservoirs. Energies17, 2894. Article ID 2894. 10.3390/en17122894

  • CrossRef
  • Google Scholar

• 49

  ZhuG.JiangH.HuangS.MaD.ZhangM.ChenW.et al (2023). New progress of marine hydrocarbon accumulation theory and prediction of super large oil and gas areas in China. Acta Pet. Sin.44, 1–25.

  • Google Scholar