A new method for identifying reservoir fluid properties based on well logging data: A case study from PL block of Bohai Bay Basin, North China

2.1 Overview of the study area

The Bohai Bay Basin, situated in eastern China, is a characteristic Cenozoic terrestrial oil-bearing basin, encompassing an area of 20 × 10 4 km 2 [34,35,36]. The Bozhong depression, a notably hydrocarbon-rich area within the Bohai Bay Basin [37,38], is bordered by the Jiao Liao Rise to the east, the Cheng Ning Rise to the west, the Liaodong Bay Depression to the north, and the Jiyang Depression to the south, covering an area of 2 × 10 4 km 2 (Figure 1a) [39,40,41,42], The Bohai Oil Region, situated in the east-central portion of the Bohai Bay Basin, is developed atop the Cenozoic Craton Rift Basin above the Meso-Paleozoic boundary in North China. Adjacent to this, the Bohai Sea, a semi-enclosed sea bordered by the Shandong and Liaodong Peninsulas, defines the region’s maritime boundaries. The PL oil field is positioned north of the Miaoxi Rise within the Bohai Central Depression, covering an area of approximately 450 km 2 . In the PL oilfield, the principal oil-producing strata are located in the lower segments of the Neoproterozoic Minghuazhen Formation and the Guantao Formation. Notably, the L50-L100 oil group within the Guantao Formation constitutes the primary productive layer. The deposition of the Guantao Formation was primarily driven by the Himalayan orogeny, occurring on a foundation of regional denudation within the Tertiary strata. The sedimentary layers developed inheritably from fault depressions to basinal depressions, with thicknesses ranging from 150 to 400 m. Currently, the comprehensive water saturation level is 80%; this layer constitutes the primary focus of the current study.

Figure 1

Regional location of the PL field and the integrated geological column of the PL field (a) show the location of the PL oilfield. (b) Comprehensive geological column showing the PL oil field. (c) Granularity statistics according to the Udden-Webtworth classification. (d) The mineral content of the study area (XRD).

In the PL oilfield, the Guantao Formation exhibits an average stratigraphic thickness of 561 m, primarily composed of thick-bedded mudstone interspersed with thin-bedded sandstone. The formation’s lithology predominantly consists of medium-grained and fine-grained sandstones that are conglomerate-bearing, with local variations including conglomerates. The stratigraphy of the Guantao Formation is vertically segmented into upper and lower sections. The upper section ranges from 150 to 200 m in thickness and is primarily composed of medium to fine sandstone, interspersed with thin mudstone and gravel-bearing medium-coarse sandstone. The sandstone reservoirs typically exceed 2 m in thickness, with the predominant reservoir types being medium-thick and thick. The lower section of the Guantao Formation has a thickness ranging from 300 to 450 m, predominantly comprising conglomerate-bearing medium-coarse sandstone, interspersed with medium-fine sandstone and mudstone. The sandstone layers vary in thickness from 1.5 to 9.5 m, primarily consisting of thin to medium-thick strata. Integrating core and logging data analyses, the Guantao Formation in the PL Oilfield is characterized as a typical discursive river deposition. It features extensively developed trough-like interbedded laminations and natural gamma curves predominantly displaying bell-type and box-type patterns. The grain sequence exhibits a positive rhythmic pattern, and the sandstone displays poor lateral contrast [43].

2.2 Data analysis

Following core pore penetration experiments on three wells and subsequent statistical analysis of grain size within the target layer, porosity was found to range from 7.3 to 36.3%, averaging 22.65%. Similarly, permeability varied from 0.336 to 9,930 mD, with a mean value of 283.39 mD (Figure 2). The reservoir exhibits a broad distribution of porosity and permeability, with marked variability and complex physical properties. The grain size analysis data include 157 individual analyses. Figure 1c illustrates the distribution of grain sizes in the Guantao Formation’s reservoirs within the PL block, accompanied by a classification table (Table 1) that correlates sandstone types with their respective grain sizes. Analysis of these data indicates that grain sizes in the Guantao Formation predominantly fall within the range of 1–8 phi, with an average value of 3.25 phi.

Figure 2

Porosity and permeability of the study block.

A development well from the study area was selected, and the perforated interval was analyzed to assess the logging response. As depicted in Figure 3, the black section represents the perforated interval, which measures 15 m in length. The resistivity curve exhibits substantial fluctuations, while the natural gamma curve is attenuated. A pronounced decrease in resistivity occurs at the junction between the 5th and 6th layers, confirming a change in the reservoir fluid characteristics at this location.

Figure 3

Logging response logging map of shot hole sections of development wells in the study area.

2.3 Difficulties in evaluation

In the study block, several traditional water-flooded layer interpretation methods, which rely on the spontaneous potential curve and acoustic time-difference curve – such as the baseline offset method derived from the spontaneous potential curve – are inapplicable due to the absence of these curves in most wells. Additionally, determining formation water resistivity remains a critical issue in interpreting water-flooded layers. Current methods primarily involve experimental measurements, calculations of spontaneous potential, or apparent resistivity techniques. However, most wells in the study block lack spontaneous potential curves and have high mud content. These conditions significantly affect the reliability of these methods, leading to poor applicability in the study block. Moreover, techniques such as the use of rendezvous plates for qualitatively identifying water-flooded layers in the PL block exhibit low accuracy and do not correlate well with production data obtained from perforations.

3.1 Markov transformation field (MTF)

MTF is a technique that converts time-series data into image data, encapsulating the data in a format that illustrates the probability of state transitions, thereby enabling two-dimensional observation and analysis [44]. Utilizing the collected geophysical logging data, data from each sampling point are employed as input groups. These are then classified according to fluid properties inferred from sealed core and production data to facilitate state discretization. Following this, the transfer probabilities of these discretized states are computed, leading to the creation of a transfer matrix. The feature images derived from this matrix vary according to the specific data of each sampling point. Unlike time series, under this definition, logging data are considered spatial data, prompting a modification of the standard Markov Transition Field in this article. Conventionally, state transitions in time series depend on temporal shifts, whereas, in Markov Transition Fields derived from logging data, the transitions depend on spatial location shifts. As the sampling intervals for each data point in logging data are consistent, the introduction of additional spatial distance weights does not significantly impact the results. Thus, the non-standard Markov transition matrix can be expressed as follows [45,46] (Figure 4):

Figure 4

The UMTF conversion process.

Then, the process of mapping the logging data according to the non-standard Markov variation field is represented as:

3.2 Quantum computing and HQNNs

A quantum bit, or qubit, serves as the fundamental unit of information in quantum computing, distinct from the classical binary digit, or bit, which exists solely in the states of 0 or 1. A qubit, however, can simultaneously occupy both the 0 and 1 states, a phenomenon known as superposition. Moreover, qubits can exhibit entanglement, where the state of one qubit can instantaneously influence another with which it is entangled. These two pivotal properties – superposition and entanglement – underpin quantum computing. In binary systems, unlike qubits, bits are confined to discrete states of “0” or “1,” but qubits can also exist in a superposition, mathematically represented as follows [47,48]:

a, b denote the probability amplitude, satisfies | a | 2 + | b | 2 = 1 , this means { ∣ 0 〉 , ∣ 1 〉 } acts as the basis. Therefore, the quantum state of any individual quantum bit may be succinctly expressed as a vector:

In quantum computing [49], quantum gates can transform the quantum states of quantum bits, functioning similarly to classical logic gates in classical computing. According to quantum mechanics, any quantum gate corresponds to a unitary operator U , satisfying U U † = I , where U † represents the conjugate transpose of U . Transforming the initial quantum state ∣ ψ 〉 = ∑ i = 0 2 n − 1 α i ∣ i 〉 by U results in the quantum state:

In the HQNN, the architecture integrates convolutional, pooling, and fully connected layers. These components collectively facilitate the execution of classification and recognition tasks through a systematic training process, encompassing data preprocessing, quantum state preparation, construction of neural network structures, and network optimization. The comprehensive architecture of the HQNN is depicted in Figure 3.

4.1 Data processing

Organizing the collected geophysical logging data from the study area revealed that most wells lacked spontaneous potential and acoustic time-difference curves. Consequently, this analysis incorporated natural gamma (GR), density (RHOB), neutron (TNPH), various resistivity (RDEEP, RMED, RSHALLOW), and porosity (PHIE) logging curves as the primary input data. Logging data from six wells in the study area were used as input data, and the range of logging response values with curve types is given in Table 3. This study further synthesized sealed coring results and production data analysis to identify 64 strongly, 77 moderately, and 53 weakly water-flooded formations, summing up to a total of 194 water-flooded formations. Information entropy reflects the uncertainty of the transfer matrix, higher entropy values indicate more uniform state transitions, and results with high entropy suggest more complex changes in logging data. Conversely, lower entropy values denote more concentrated state transitions, and results with low entropy imply simpler changes in the logging data [50]. The variability of transfer probabilities, measured as the variance of these probabilities within the transfer matrix, indicates that higher variances correspond to greater variations in state transitions. As illustrated in the table, the RDEEP curve demonstrates the most significant contribution to the mapping process. This finding aligns with the established understanding that the primary alteration in water-flooded layers pertains to the reservoir’s resistivity. Consequently, employing a non-standard MTF model to map geophysical logging data into feature images is deemed appropriate. Formulations for calculating the variability of information entropy and transfer probability are as follows:

Table 2 delineates the contribution scores within the UMTF modeling process, utilizing two distinct evaluation metrics. The accompanying figure displays the feature images alongside their respective state transfer matrices, generated by the UMTF model. This model efficiently transforms raw geophysical logging data into 2D images, subsequently computing state transfer matrices that effectively capture the intricate patterns of change inherent in the data.

The distribution of logged values for various fluid properties is depicted in the box-line diagram, where trends in the logged responses to different fluids are evident. Notably, resistivity decreases with escalating levels of water flooding, whereas no discernible trends are observed in the logged changes for natural gamma, neutron, and density measurements. Additionally, considerable overlap exists among the data corresponding to different water-flooded levels.

Due to variations in magnitude and dimension across the geophysical logging data from each sampling point – from unflooded formations to purely water-saturated and water-flooded formations – standardization was imperative. Data normalization, a critical preparatory step for modeling, significantly enhances the precision of training and the accuracy of predictions. Consequently, each set of input data was normalized to a range of [0, 1] using the minmax_scale function from the sklearn library in PyCharm. The normalization formula employed is as follows:

where Y is the normalized logging data and X is the original logging data, and X max , X min are the maximum and minimum values of the logging data. Following normalization, the data underwent processing, and transfer matrices for five distinct state classes were computed in accordance with the workflow specified by the non-standard MTF model. Subsequently, this approach facilitated the generation of 8,786 feature images, representing transformations across three classifications of layers: flooded, unflooded oil, and pure water.

4.2 Partition of the training and testing data

Given the potential for significant variability in outcomes based on different training and testing set division ratios, and the propensity for overfitting within deep learning tasks, it was necessary to investigate the impact of data distribution on the UMTF-HQNN model. To mitigate overfitting and explore this effect, the training and test set ratios were systematically adjusted to 8:2, 7:3, and 6:4, respectively. This study did not employ the 9:1 and 5:5 data division ratios for the following reasons: the 9:1 ratio, despite offering abundant training data, fails to adequately assess the generalization ability of the UMTF-HQNN model due to the limited test data. Conversely, the 5:5 ratio, while providing ample test data, significantly reduces the training dataset, potentially leading to inadequate model training and suboptimal performance. Consequently, ratios of 8:2, 7:3, and 6:4 were selected to balance substantial training data with sufficient test data, facilitating a thorough evaluation of model performance. These division ratios are well-established in prior research and practical applications, having demonstrated their efficacy in optimizing the balance between training and evaluation demands of models. Consequently, the adoption of these ratios is pragmatically justified and contributes to achieving stable and reliable experimental outcomes.

As the fundamental unit of quantum information, quantum bits (qubits) are crucial in determining the complexity and computational efficiency of quantum computing tasks. Prior research has established that an increased number of qubits can enhance computational power and capacity for more complex model representations in quantum machine learning. However, this increase also potentially raises the system’s noise and complexity levels [51]. To optimize computational efficiency and model performance, this study experimentally evaluates various quantum bit configurations to determine the ideal number for identifying reservoir fluid properties, given the available technology. Citing Rispoli, M., and Wu, S., [52,53] it is noted that certain quantum algorithms may achieve significant performance enhancements or resource utilization efficiencies with up to eight qubits. Consequently, this research includes a comparative analysis of 4, 8, and 12 qubits to discern trends in model performance as the number of qubits increases (Figure 5).

Figure 5

(a) The overall architecture of HQNN, (b) HQNN structure.

Within the UMTF-HQNN model framework, both the convolutional kernel size and the stride are configured to 2. The architecture incorporates a quantum convolutional layer, followed sequentially by a quantum pooling layer and a quantum fully-connected layer. To ensure robust optimization, the Adam optimizer is employed with a set learning rate of 0.001, widely acknowledged as optimal for balancing training speed with convergence. Following transformation via the UMTF model, the reservoir fluid property identification task is reformulated as an image classification challenge, for which a cross-entropy loss function is utilized to enhance classification accuracy. Figure 6. illustrates the workflow for identifying reservoir fluid properties using the UMTF-HQNN method, comprising four phases: data preparation, data mapping, model optimization, and validation.

Figure 6

The transfer matrices corresponding to the feature images of different fluid properties: the left side is the feature image transformed by UMTF, and the right side is the feature matrix of UMTF, (a) and (b) are oil layers, (c) and (d) are pure water layers, (e) and (f) are weakly flooded layers, (g) and (h) are moderately flooded layers, (i) and (j) are strongly flooded layers.

4.3 Model optimization

To achieve optimal model performance in practical applications, this study first optimized the split ratio of the training and test sets prior to model training. Initial manual experiments revealed that a 7:3 split between the training and test sets, along with 4 qubits, yields higher model accuracy. To further validate the effectiveness of this partition ratio and optimize the relevant hyperparameters, random sub-sampling cross-validation was employed for optimization. Random sub-sampling cross-validation independently trains and evaluates the model by repeatedly splitting the dataset into training and test sets. This approach effectively mitigates potential bias caused by data partitioning, allowing for a more accurate evaluation of the model’s performance and stability. In this study, after setting the data partition ratio to 7:3, we optimized key hyperparameters in the model, including convolution kernel size, convolution stride, batch size, and learning rate (the schematic diagram illustrating the random sub-sampling cross-validation process is provided in the Fig, while the optimal parameter combinations obtained from cross-validation are presented in the Table). We adjusted these parameters and, through five experiments, determined the optimal combination of hyperparameters. After each experiment, the model is trained on the training set and its performance is evaluated on the test set. By comparing model performance across different hyperparameter configurations, the configuration with the highest average accuracy on the test set was selected. This process not only validates the effectiveness of the data partitioning strategy but also facilitates the fine-tuning of hyperparameters to ensure the model’s generalization ability and stability on unseen data. Through this systematic optimization process, the model demonstrated significant improvements across various performance indicators. A detailed list of hyperparameters and their respective settings for the final model configuration is provided in the appendix. This stage of research has laid a solid foundation for the practical deployment of the model, ensuring high accuracy and reliability during real-world operation (Figure 7).

Figure 7

Box line plots of logging response for different fluid properties (a) logging response for natural gamma, (b) logging response for deep resistivity, (c) logging response for compensated density, and (d) logging response for compensated.

5.1 Analysis of experimental results

In this study, eight experimental sets, each consisting of 30 epochs, were conducted using Pytorch 1.13.1 and Pennylane 0.31.0. The objective was to assess whether optimal data partitioning ratios, quantum bit counts, and the application of the UMTF model for mapping geophysical logging data to feature images could enhance training outcomes. All comparative experiments were performed in Pycharm (Figure 8).

Figure 8

Schematic representation of the random subsampling cross-validation process.

Table 3 presents the confusion matrix of the UMTF-HQNN model for the test set. It illustrates that the model accurately identifies the oil and medium water-flooded layers. However, there is some misclassification between the strongly water-flooded layer and the pure water layer, as well as occasional misclassification of the weakly water-flooded layer due to its resistivity being close to that of the oil layer. Overall, the model demonstrates satisfactory performance on the test set.

5.2 Application results

The described methodology was employed to evaluate the reservoir performance of well X9 in block PL, as depicted in Figure 9, with the results integrated with production data for a comprehensive assessment. Predictions for pure water layers by the UMTF-HQNN model were omitted from the figure as they are not pertinent to actual production. The figure displays the prediction results for the shot hole section of well X4 in block PL, which can be verified against the available actual production data (Tables 4 and 5).

Figure 9

Flow of the UMTF-HQNN workflow.

The UMTF-HQNN prediction results divided one shot hole section into two distinct oil and water systems. Actual production data show that the L50 oil group produces 128.82 m³ of fluid and 25.75 m³ of oil per day, with a combined water content of 80.01%. The UMTF-HQNN model predicts strong and medium water-flooded, which aligns with the actual data, indicating the prediction’s accuracy. (The predicted results relate only to the fluid properties of the reservoir at that depth and not to the effective thickness of the formation) (Figure 10).

Figure 10

The UMTF-HQNN predictions for well X4 show different fluid properties: green for reservoirs, red for weak water-flooded, pink for medium water-flooded, light blue for strong water-flooded, and grey for ineffective reservoirs.

6.1 Method comparison

This study includes multiple comparative analyses, Figures 11 and 12 present the accuracy and loss curves for each comparison experiment, respectively: (1) The impact of different training-to-test set ratios (8:2, 7:3, and 6:4) on accuracy is depicted in Figure (a). (2) The effect of varying quantum bit counts (4, 8, and 12) within the UMTF-HQNN model is shown in Figure (b). (3) The training performance of standardized geophysical logging data as input for the Quantum Neural Network (QNN) and LSTM models is presented in Figure (d). (4) The efficacy of feature images derived from geophysical logging data via the UMTF model, processed using the ResNet and LSTM models, is also illustrated in Figure d. (5) A further comparison involving the ResNet18 and UMTF-HQNN models using feature images mapped by the UMTF model is detailed in Figure 11c. The study reveals that the model achieves its highest accuracy of 90.85% at the 27th Epoch under a 7:3 training-to-test set ratio. Conversely, the least effective training occurs with a 6:4 ratio, likely due to an excessive allocation of data to the test set, diminishing the training set’s capacity to fully capture the data’s features. Figure (a) distinctly demonstrates the convergence speeds of the UMTF-HQNN model across the three tested ratios. Notably, the model’s convergence speed is significantly slower at an 8:2 ratio compared to the other configurations, whereas it begins to converge earlier with the 6:4 ratio.

Figure 11

Accuracy curves of the comparison experiments in the study (a) Comparison of training accuracies with different quantum bits (b) Division of the three datasets of the HQNN model at 4 Bit (c) Comparison of the accuracies of the HQNN and the Resnet model at 4 Bit and 8:2 (d) Comparison of the accuracies of the HQNN with the QNN and the LSTM models without passing through the mapped data at 4 Bit and 8:2.

Figure 12

(a) Comparative analysis of the loss functions across varying quantum bit configurations; (b) Partitioning of the three datasets utilized in the HQNN model with a 4-bit configuration; (c) Comparative assessment of the loss functions between the HQNN and ResNet models at 4-bit and 8:2 configurations; (d) Comparison of the loss functions of the HQNN, QNN, and LSTM models without passing through mapped data at 4-bit and 8:2 configurations.

Optimal training outcomes were achieved with a 7:3 data division ratio, which was subsequently selected for comparative experiments involving various quantum bit counts. As depicted in Figure 11a, the accuracy curves for configurations of 4, 8, and 12 quantum bits indicate a deviation from prior studies. While earlier research suggested optimal performance at 8 bits, our findings reveal superior results at 4 bits and the least effective training at 12 bits. Analysis indicates that an escalation in the number of quantum bits might engender increased complexity in the model and a heightened risk of overfitting. Following the transformation of geophysical logging data into feature images via the UMTF model – which incorporates seven distinct curves – the principles of quantum computing dictate that n quantum bits encode 2 ⁿ independent states. Consequently, 4 quantum bits can effectively encode 16 independent states [49,50,54,55]. When the effective dimensionality of the data aligns closely with that represented by 4 quantum bits, an optimal fit is often achieved – here, the model’s complexity is well-suited to the data’ s own complexity, allowing it to capture essential data features without overfitting or underfitting. Moreover, an increase in the number of quantum bits typically enhances the model’s sensitivity to noise and errors, potentially reducing training accuracy as more quantum bits are employed. This heightened sensitivity can diminish the model’s training accuracy as the number of quantum bits increases.

Figure 11c illustrates the accuracy comparison between the UMTF-HQNN and Resnet18 models, with the UMTF-HQNN model demonstrating superior training performance, particularly in handling high-dimensional and complex data. From a data-driven perspective, the UMTF-HQNN model outperforms the classic convolutional neural network, Resnet18, which is well-suited for large-scale, medium to low-dimensional complex datasets due to its residual components. However, with only 8,786 feature images derived from the UMTF model, the dataset size remains relatively small compared to typical large-scale datasets. Consequently, the Resnet18 model may require training on more extensive datasets to optimize its performance fully.

To assess whether employing the UMTF model to map geophysical logging data enhances training effectiveness, standardized logging data were utilized as input for training the QNN and LSTM models. Accuracy curves displayed in Figure 11d reveal that the UMTF-HQNN model consistently achieves superior training accuracy compared to the QNN and LSTM models, with the QNN model showing the poorest performance in all comparative sets. This underperformance may stem from the high complexity inherent in QNN’s pure quantum computation units, leading to training instability and pronounced fluctuations. Conversely, while the LSTM model excels in capturing long-term dependencies in time-series data, it struggles with the nonlinear relationships characteristic of geophysical logging data.

6.2 Advantages of the UMTF-HQNN method

In this study, the reservoir fluid property identification method, integrating the HQNN and the UMTF model, demonstrated promising application results within a specific geological context. Notably, in the PL block of the Bohai Bay Basin, this approach effectively addresses complex formation fluid variations induced by waterflood development. Moreover, it leverages alternative geophysical logging data (such as resistivity, density, and natural gamma) for fluid identification, even in the absence of conventional acoustic lag curves and SP curves. As a result, this method holds potential for application in reservoirs at similar stages of mid- to late-phase waterflood development. Furthermore, due to its foundation in nonlinear feature extraction and pattern recognition using logging data, this approach exhibits generalizability across porous media formations with varying pore structures and permeability.

Additionally, this method introduces a novel tool for analyzing reservoir fluid characteristics by transforming one-dimensional log data into two-dimensional feature images and utilizing quantum neural networks for classification and recognition. This approach has potential applications in other domains characterized by complex logging responses, particularly in cases of intricate geological changes that challenge traditional techniques. Furthermore, the integration of advanced machine learning methods could significantly enhance the accuracy of fluid identification.

Traditional evaluations of water-flooded layers depend heavily on the accurate calculation of both water saturation [56,57,58] and irreducible water saturation [59], a process that is often complex and challenging. The predictive method proposed in this research effectively circumvents the need for such calculations.

6.3 Limitations of the UMTF-HQNN method

As geophysical logging data are sourced directly from specific formations, the model’s applicability is inherently limited to those particular geological blocks. For example, changes in lithology. Consequently, while the model demonstrates high accuracy and reliability within these blocks, its predictive capabilities may diminish when applied to different blocks due to variations in geological characteristics and logging conditions. To enhance the model’s accuracy and practicality across diverse blocks, independent data collection and tailored model training for each block are imperative. Additionally, the timeliness of geophysical logging data necessitates the selection of wells with closely aligned drilling and logging times for analysis. This alignment ensures that the data maintain a strong correlation with the current geological conditions, thereby enhancing the model’s accuracy and reliability. The significance of data timeliness is underscored by the dynamic nature of geological parameters, such as fluid properties, porosity, and permeability, which can alter significantly over time, potentially leading to discrepancies between historical data and actual formation conditions.

6.4 The future of the UMTF-HQNN method

Future research can enhance the generalization capability of the UMTF-HQNN model under complex geological conditions by further refining critical model parameters, including quantum bits, network layers, and training datasets. Additionally, incorporating a wider variety of logging data, such as nuclear magnetic resonance logging and acoustic logging, will diversify the model’s input, thereby enhancing its adaptability to reservoirs with varying lithological characteristics. Moreover, advancements in quantum computing algorithms and hardware technologies will play a crucial role in reducing computational resource consumption, making this approach more practical for industrial applications.