Damage Evaluation of Unconsolidated Sandstone Particle Migration Reservoir Based on Well–Seismic Combination

Abstract

The primary factor constraining the performance of unconsolidated sandstone reservoirs is blockage from particle migration, which reduces the capacity of liquid production. By utilizing logging, seismic, core–testing, and oil–well production data, the reservoir damage induced by particle migration in the Bohai A oilfield was characterized and predicted through combined well–seismic methods. This research highlights the porosity, permeability, median grain diameter, and pore structure as the primary parameters influencing reservoir characteristics. Based on their permeability differences, reservoirs can be categorized into Type I (permeability ≥ 800 mD), Type II (400 mD < permeability < 800 mD), and Type III (permeability ≤ 400 mD). The results of the core displacement experiments revealed that, compared to their initial states, the permeability change rates for Type I and Type II reservoirs exceeded 50%, whereas the permeability change rate for Type III reservoirs surpassed 200%. Furthermore, by combining this quantitative relationship model with machine learning techniques and well–seismic methods, the distribution of permeability change rates caused by particle migration across the entire region was successfully predicted and validated against production data from three oil wells. In addition, to build a reliable deep learning model, a sensitivity analysis of the hyperparameters was conducted to determine the activation function, optimizer, learning rate, and neurons. This method enhances the prediction efficiency of reservoir permeability changes in offshore oilfields with limited coring data, providing important decision support for reservoir protection and field development.

1. Introduction

Unconsolidated sandstone reservoirs are distributed in various oilfields throughout the world. This kind of oil reservoir usually has a shallow burial depth (burial depth of <1800 m), a high porosity and permeability, a coarse lithology, and a loose cementation. In unconsolidated sandstone reservoirs, a reduction in permeability caused by particle migration is the most prevalent form of reservoir damage. Particle migration is a type of velocity–sensitive reservoir damage. As the particles adhered to the rock surface move, the permeability of the reservoir diminishes. These particles typically settle at constriction points in the rock, often through bridging mechanisms. Consequently, this phenomenon results in a decline in the production capacity of oil wells [1,2] or the injection capacity of water injection wells [3,4,5,6]. The particles within a reservoir are predominantly composed of clay minerals, notably kaolinite, chlorite, and illite [7,8]. Quartz and silica particles also migrate easily in unconsolidated sandstone and their particles are generally less than 37 μm in diameter [9,10].

At present, there are three main categories of research methods that are used to study reservoir damage due to particle migration. The first category involves theoretical mathematical models, with the deep–bed filtration model being the most prominent. This model is recognized as a foundational theoretical framework and it describes the process of particle entry and capture within porous media [11]. Furthermore, this model integrates the principles of particle mass conservation and trapping theory and has been refined and expanded upon by numerous scholars. The common theoretical models currently in use include phenomenological models, models based on trajectory analyses, network models, and random models [12]. The second research category is experimental evaluation. Presently, the evaluation of reservoir damage caused by particle migration relies on indoor core displacement experiments, with the change in permeability before and after core displacement serving as the evaluation index [13,14,15]. The third category is numerical simulation, which encompasses various methods such as the two–fluid model (TFM), the discrete phase model (DPM), the computational fluid dynamics–discrete element method (CFD–DEM), the particle–tracking method, and the Brownian motion simulation [16,17,18,19,20].

In the process of particle migration and sand production, the permeability of rock is changed. The permeability increases or decreases under different mechanism conditions. For example, volumetric dilation can lead to a permeability increase, whereas strain localization and shear band formation may increase or decrease the permeability depending on the state of compaction and the level of grain breakage inside the band [21,22]. In addition, the migration of particles in porous media can lead to the blockage of the pore throat, resulting in a reduction in permeability. Permeability changes during sand production have been demonstrated in fields such as the Chestnut Field, located in the UK North Sea [23], and the McMurray Field [24], where well–test analysis reports have shown that sand production has increased the permeability. The permeability of the Penglai Oilfield in China has been reduced due to the particle migration of unconsolidated sandstone [25].

In summary, particle migration significantly impacts the performance of unconsolidated sandstone reservoirs. At present, most evaluation methods for particle migration and reservoir damage are based on core displacement. However, these evaluation methods can only characterize the effect of particle migration on the permeability at core test points. They lack continuous characterization methods that consider the microscopic characteristics of reservoirs in the longitudinal and horizontal directions.

An offshore oilfield has the characteristics of a large well spacing and little coring data. At present, most of the research on the damage of particle migration to reservoirs is limited to core displacement experiments, which are relatively limited. In this study, the loose sandstone of Oilfield A in the Bohai Sea was selected as the research object and the evaluation parameters characterizing the reservoir characteristics were optimized by means of data mining. A quantitative relationship was established between the change rate of the particle migration permeability, obtained using core displacement, and the reservoir’s characteristic parameters. A deep neural network combined with seismic attributes was used to constrain the wells. The damage degree of fine particle migration to the reservoir was predicted both vertically and horizontally, which breaks through the limitation of the core scale and provides a new scientific basis for reservoir protection and oil and gas development.

2. Geological Background

Bohai Oilfield A is located on the Bonan low bulge of the Tanlu strike–slip fault zone in the central and southern Bohai Sea area of China (Figure 1a). This structure is a faulted anticline developed on the background of basement uplift and controlled by two sets of north–south strike–slip faults [26,27,28]. The oil layers consist of the Neogene Guantao Formation and the lower Minghuazhen Formation. The Guantao Formation is segmented into 13 oil–bearing groups, which are further subdivided vertically into 47 smaller layers (Figure 1b). The thickness of the oil layer ranges from 63 to 151 m and the oil–bearing area extends over 50 km² [25,29]. The central and southern areas of Oilfield A are affected by a gas cloud belt, resulting in poor seismic data quality. Oilfield A is characterized by a series of north–east- and east–west—trending normal faults, with the structural inclination being gradual in the west and steeper in the east. The trap area spans approximately 125 km².

The plane of Oilfield A is divided into several development zones based on the fault distribution. This study focused on zone 4, which is situated in the north [25,29] (Figure 1c). The principal reservoir in zone 4 is the L74 Formation, which is also the focal point of this investigation. Identified as a shallow–water braided river delta deposit, the depositional facies type is predominantly characterized by distributary sandbars and distributary channel depositional microfacies. With an average porosity of 27% and a permeability of 1300 mD, the reservoir is primarily composed of lithic feldspar sandstone and feldspar sandstone [29].

3. Samples and Methodology

3.1. Experimental Samples

In this study, the reservoirs were divided into three types. The reservoir classification results are shown in

Table 1. Reservoir classification evaluation.

Reservoir Classification	Porosity (%)	Permeability (mD)	Vsh 1 (%)	R35 2 (μm)
Type I	≥25	≥800	≤15	≥10
Type II	20~25	300~800	15~25	3~10
Type III	<20	<300	>25	<3

¹ Volumetric shale content. ² The pore throat radius that corresponds to 35% mercury saturation.

.

Eleven core samples, representing three different categories, were selected from the reservoir coring well of the Guantao Formation. The depth of the core samples ranged from 1286 m to 1621 m. The measured parameters are presented in

Table 2. Reservoir parameters of 11 samples from the Guantao Formation in Bohai Oilfield A.

Sample	Depth/m	Member	Reservoir Type	Poro./%	Perm./mD	Md/μm	R35/μm
2—009	1286.73	L60	I	34.70	1772.65	224.73	20.66
2—028	1289.33	L60	I	32.60	1357.52	201.55	19.12
3—038	1306.6	L62	I	29.70	2539.08	356.94	11.24
4—029	1333.19	L64	I	31.90	3118.01	479.35	15.06
5—002	1340.46	L70	III	27.60	112.14	73.96	0.11
5—024	1344.54	L70	I	34.50	3137.97	385.56	25.73
6—024	1378.94	L76	III	28.90	331.23	90.71	0.41
7—024	1406.3	L82	III	21.00	166.03	120.17	0.02
8—036	1450.42	L88	II	26.60	537.90	238.38	5.70
9—038	1479.89	L92	II	26.10	446.94	111.25	0.17
11—009	1621.36	L112	I	32.50	1556.47	426.02	15.07

. All the samples were tested using industry-standard methods. The test equipment was provided by the State Key Laboratory of Oil and Gas Reservoir Geology and Exploration of Southwest Petroleum University. The core porosity and permeability are tested by permeability Gas Measurement 700 unit made by Sanchez Technologies. The PoreMaster60 (Quantachrome Instruments, Boynton Beach, FL, USA) was used to measure the mercury injection of sandstone samples and characterize the pore structure of the reservoir.

For the experiment, formation water was simulated with similar properties as the field fluid and was used as the displacement medium. The advection pump adopts the CX-HL-0100 model (China). The experiment process conforms to the Chinese national standard, the accuracy of pressure gauge is 0.001 MPa, the accuracy of flowmeter is 0.01 L/min. The experimental procedure was as follows:

• The core was displaced with formation water. Then, the core was dried and the permeability ($K_g$) of the core was measured.
• The natural core was saturated with the simulated formation water and soaked for more than 24 h.
• The saturated natural core sample was placed into the core holder and the confining pressure was set to 2.0 MPa.
• Formation water was injected into the core at the following flow rates: 0.25 mL/min, 0.5 mL/min, 1 mL/min, 1.5 mL/min, 2 mL/min, 3 mL/min, 4 mL/min, 6 mL/min, 8 mL/min, 10 mL/min, or 12 mL/min.
• The core permeability $K_n$ (n = 1, 2, 3, 4…) was identified for different displacement velocities. The degree of permeability damage was calculated as shown in Equation (1).

Based on the relationship between the injection velocity and the permeability, the sensitivity of the oil and gas core to the flow rate was analyzed. The critical flow rate was then determined based on where a significant decrease in permeability occurred. If the rate of change of the rock permeability $D_{vn}$ exceeded 20% at a high flow velocity, then the velocity of the previous point was considered as the critical velocity:

$$D_{vn}={\displaystyle \frac{\left|K_n-K_i\right|}{K_i}}\times 100\%$$

(1)

where $D_{vn}$ represents the rate of rock permeability change at various flow rates (%); $K_n$ represents the permeability of the rock samples at different flow rates (mD); and $K_i$ is the initial permeability (mD).

The permeability damage is given by Equation (2):

$$D_v=\max (D_{v2},D_{v3},\dots ,D_{vn})$$

(2)

where $D_v$ represents the permeability damage rate (%) and $D_{v2}$, $D_{v3}$, …, and $D_{vn}$ represent the permeability damage rate at different flow rates (%).

The critical flow rate, measured in the laboratory core displacement experiment, had units of mL/min, which were then converted into m/d as those are the units commonly used in oilfields. The equation for the unit conversion is as follows:

$$v_c={\displaystyle \frac{14.4Q_c}{A\cdot \varphi }}\times 100\%$$

(3)

where $v_c$ represents the critical velocity (m/d); $Q_c$ denotes the critical flow for the laboratory experiments (mL/min); $A$ stands for the core cross–sectional area (cm²); and $\varphi$ signifies the core porosity (%).

3.2. Seismic Attribute Fusion

The petroleum industry began to search for applications for seismic properties during the 1960s and 1970s. With the advancement of computer technology, over 200 types of seismic properties have been investigated to enhance oil exploration and production. However, there is no standard classification system for these seismic attributes. Currently, seismic attributes are primarily classified into eight types: amplitude, waveform, frequency, attenuation, phase, correlation, energy, and ratio attributes [30,31].

There are numerous techniques for seismic attribute fusion, from traditional linear fusion to the presently prevalent nonlinear intelligent fusion [32]. Each fusion method has a specific range of applicability. The specific advantages and disadvantages of each method are outlined in

Table 3. Applicability of common seismic attribute fusion methods.

Method	Advantages	Disadvantages
RGB seismic attribute fusion	Although this method can overcome single attribute colors, it cannot highlight the shortcomings of regional anomalies.	This technology is only applicable to a few attributes for fusion and should be combined with data–mining methods.
Clustering analysis of seismic attribute fusion	Suitable for classifying seismic attributes from large amounts of data.	Limited application conditions.
Multiple linear regression seismic attribute fusion	Can overcome the limitations of single earthquake attributes.	Simple linear model with limited room for improvement of the coincidence rate. Has high requirements for the selection of attribute types.
Seismic attribute fusion based on well data	Can make full use of logging data and assign weight coefficients to each seismic attribute to improve the prediction accuracy.	Weightings are difficult to determine, which will affect the final result.
Neural network seismic attribute fusion	Can handle complex nonlinear data. Has a high prediction accuracy and a wide range of applications.	Seismic attributes need to be optimized using data–mining methods and the neural network model needs a large amount of training data.

.

3.3. Deep Neural Network

A deep neural network (DNN) is a kind of artificial neural network with multiple hidden layers. A DNN is composed of an input layer, multiple hidden layers, and an output layer. The input layer receives the original data and transmits them to the hidden layer. The hidden layer extracts features using a nonlinear transformation of the input data and the output layer has different forms according to different tasks. Its training is the process of minimizing loss functions by adjusting the network parameters, including defining loss functions, updating parameters using optimization algorithms, performing data preprocessing, and adjusting hyperparameters.

This study employed the multiseismic attribute fusion method using a DNN. Schmidhuber (2015) argued that there is currently no clear agreement regarding the differences between shallow neural networks and DNNs [33]. However, most scholars generally agree that shallow neural networks typically only have a single hidden layer between the input and output layers, whereas DNNs incorporate multiple hidden layers. Figure 2 provides a schematic representation of shallow and DNN architectures. In neural network models, it is necessary to assign activation functions. This gives the model the capability of handling complex nonlinear data. These nonlinear functions can represent curves, which enables the network to capture complex relationships within the data. As the neural network incorporates more layers, it becomes capable of representing increasingly intricate curves, enhancing its ability to effectively address practical problems.

3.3.1. Activation Functions

Activation functions are a critical component of neural network models. Without them, neural network models can only handle simple linear relationships. The

Table 4. Activation function expressions.

Activation Function	Expression
Linear	$f\left(x\right)=x$
Sigmoid	$f\left(x\right)={\displaystyle \frac{e^x}{1+e^{-x}}}$
Tanh	$f\left(x\right)={\displaystyle \frac{e^x-e^{-x}}{e^x+e^{-x}}}$
ReLu	$f\left(x\right)=\mathrm{m}\mathrm{a}\mathrm{x}(x,0)$
Softplus	$f\left(x\right)=\mathrm{l}\mathrm{o}\mathrm{g}(1+e^x)$

lists commonly used activation functions.

ReLu is an activation function that is currently widely used. It addresses the gradient–vanishing issue encountered in sigmoid and tanh activation functions. When processing large datasets, the computational speed of sigmoid and tanh functions tends to be slow. Figure 3 graphically represents the three activation functions. As the input values increase, the slopes of the sigmoid and tanh functions gradually decrease. Hence, the ReLu function effectively resolves the gradient–vanishing problem, significantly improving the computational efficiency.

3.3.2. Adam Optimizer

To enhance the performance of neural network models, researchers have developed numerous optimization algorithms such as the momentum gradient descent algorithm and the root mean square propagation method [34]. However, each of these methods has limitations. The Adam optimizer combines the advantages of the aforementioned two algorithms [35] and is currently one of the most commonly used optimization algorithms. The iterative formula of the Adam optimizer is as follows:

$$\Delta x_t=-{\displaystyle \frac{\eta }{\sqrt{{\displaystyle {\sum }_{\tau =1}^t{\mathrm{g}}_{\tau }^2}}}}{g}_t$$

(4)

where $\eta$ represents the initial learning rate, $g_t$ denotes the gradient of the parameters in the t-th iteration, and $\mathsf{\Delta }{x}_t$ represents the change in the parameters in the t-th iteration. The denominator is the L2 norm for all the gradients in each dimension.

3.3.3. Data Preparation

The stratum studied in this research was the Neogene Guantao Formation. The sandstones of the Guantao Formation are mainly lithic feldspathic sandstone and feldspathic sandstone. The main pore type is primary intergranular pores. A total of 220 data points from 40 oil production wells were collected in this study, mainly including the geological parameters, reservoir parameters, and seismic data (

Table 5. Deep neural network data.

Well	Porosity/%	Permeability/mD	R35/μm	Md/μm	Vsh/%
1	24.11	486.69	10.61	53.77	44.62
2	25.06	835.40	12.15	127.57	27.89
3	30.47	1366.58	15.26	135.89	21.62
4	32.35	1283.12	13.12	141.58	23.83
……
40 wells (mean)	25.93	680.45	11.12	88.85	35.27

). The parameters include the porosity, permeability, pore throat radius (R35) at a 35% mercury injection saturation, median grain diameter (Md), and shale content (Vsh). Most of the above data were obtained from logging interpretation results and indoor experimental data.

3.4. Reservoir Modeling

A 3D geological model is the core of reservoir descriptions [36,37]. There are many methods for reservoir stochastic modeling, including sequential Gaussian simulation, sequential indication simulation, and fractal stochastic simulation. At present, the commonly used method is the sequential Gaussian simulation. The sequential Gaussian simulation is based on the basic Kriging method and mainly consists of well data modeling without considering trends or second–order variables (such as seismic information). The sequential Gaussian simulation of the integrated trend is based on Kriging with the trend, so as to simulate the reservoir parameters by integrating the trend. Model configuration involves adding the random seed number, normal score transformation, simulation time, and sequential parameter settings on the basis of the trend in Kriging setting. The simultaneous cooperative Gaussian simulation is based on simultaneous cooperative Kriging and integrates second–order variables for a random simulation, which can fully tap the information carried by the second–order variables and reflect the reservoir variation law between wells.

Offshore oilfields generally have a large well spacing and low well control. Under the condition of a thin well pattern, three–dimensional seismic data should be fully used for fine reservoir characterization. In this study, a 3D geological model of reservoir parameters was established with the help of a parallel collaborative sequential Gaussian simulation under the constraint of seismic attributes. With downhole information as the control point, a deep learning machine model was used to establish a geological model of the reservoir parameters by simultaneously using the spatial variation characteristics of seismic and logging data and the cross–variation relationship between them under the constraint of seismic attributes. The study was based on Schlumberger’s petrel platform.

4. Results

4.1. Experimental Results

The experimental results were significantly different for the different reservoir types. The results from flooding the natural cores with simulated formation water indicated that the rate of permeability damage in the Type I reservoir (K > 1000 mD) ranged from 43 to 55%, while for the Type II reservoir (400 mD < K < 1000 mD), the rate of damage varied between 70 and 201%. Type III reservoirs (K < 400 mD) exhibited a higher rate of permeability damage, ranging from 222% to 410%. Comparatively, the degree of permeability damage in Type I and II reservoirs was less pronounced than that in Type III reservoirs, with a critical flow rate ranging from 6 to 10 m/d (Figure 4).

4.2. Optimization of Reservoir Characteristic Parameters

The highly heterogeneous nature of reservoir characteristics plays a pivotal role in governing particle migration and the plugging phenomena. The selection of characteristic reservoir parameters necessitates a comprehensive consideration of the physical property, pore structure, and rock structure attributes. Moreover, these parameters should be readily accessible within the study area and have good reproducibility.

Unconsolidated sandstone, which is characterized by weak cementation, is susceptible to particle migration and throat blockage. Among the reservoir particle parameters, the median particle size was selected due to its significance. The porosity and permeability, representing essential physical properties, were also chosen as conditional parameters for the evaluation due to their accessibility and indicative nature.

The heterogeneity of the pore structure plays a significant role in particle migration within porous media. Parameters such as the pore throat radius (R35) and median saturation pressure are commonly employed to characterize rock pore structures since they directly reflect the connectivity of the reservoir. R35 denotes the pore throat radius corresponding to a mercury saturation of 35% [38,39,40,41,42]. Among the various pore structure parameters, R35 exhibited the best correlation with the permeability, indicating that R35 not only characterizes the pore structure but also effectively characterizes the percolation effect. The pore structure characteristics can affect the reservoir’s capacity and seepage, which then affect the ultimate oil recovery. As can be seen from the pore structure correlation matrix (Figure 5), R35 exhibited a strong correlation with the other pore structure parameters, which indicates that R35 can comprehensively characterize the pore structure characteristics. Hence, R35 was chosen as the parameter used to characterize the pore structure in this study.

4.3. Neural Network Reservoir Characteristic Parameters

4.3.1. Optimization of Seismic Attributes

Zone 4 in the northern region is characterized by the prominent L74 reservoir. Because the quality of seismic data in the central and southern areas of Bohai Oilfield A is affected by the gas cloud belt, the northern 4 region, which is not affected by the gas cloud belt, was chosen as the focus area of this study. Seismic attributes, including amplitude, energy, and impedance, were extracted and transformed into the depth domain through the establishment of a velocity model. These attributes were then correlated with well data, incorporating gamma ray and resistivity logs to ensure calibration accuracy.

Seismic attributes from the well side were extracted for each well and a correlation analysis was conducted with reservoir microparameter logging curves. Attributes that exhibited a high correlation were selected for further analysis. The seismic attributes considered for correlation were the original amplitude; the 30 Hz, 40 Hz, 50 Hz, and 60 Hz divider amplitudes; the relative impedance; the reflection intensity; the RMS amplitude; and the sweetness attribute. Through a correlation analysis, the original amplitude, the 50 Hz frequency division amplitude, and the 60 Hz frequency division amplitude emerged as the preferred attributes for multiseismic attribute fusion (Figure 6).

4.3.2. Seismic Attribute Fusion Based on Deep Learning

• Optimization of DNN hyperparameters

Three DNN hyperparameters were optimized before the deep neural network model was constructed. The specific hyperparameters selected for this study are listed in the

Table 6. Selected DNN hyperparameters.

Hyperparameter	Classification
Optimizer	SGD, Adam, RMSprop
Neuron	[5,10,1], [5,10,5,1], [5,10,20,10,1]

.

The optimizer influences how the parameters are updated during the backpropagation process of deep neural networks, thereby affecting the prediction accuracy of the neural network model. Three optimizers were selected for comparison, as shown in Figure 7. The number of neurons and layers controls the scale of the neural network model, thereby influencing the learning capacity of the model and the prediction accuracy. Three scenarios were designed, with each bracket representing the scale of a model. The elements within the brackets indicate the number of neurons (Figure 8). Additionally, the learning rate signifies the magnitude of parameter updates during backpropagation (Figure 9). An excessively large or small learning rate can hinder the network’s ability to update parameters and converge, thus impeding its capacity to find the global minimum point and optimize the prediction performance.

Next, the mean square error (MSE) method was utilized to evaluate the prediction accuracy of the deep neural network. The equation is as follows:

$$MSE={\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m{(y_i-{\widehat{y}}_i)}^2}$$

(5)

where $y_i$ is the actual parameter and ${\widehat{y}}_i$ is the predicted parameter.

Based on the above analysis, the hyperparameters shown in

Table 7. Results of hyperparameter optimization.

Hyperparameter	Classification
Optimizer type	Adam
Number of neurons	[5,10,5,1]
Learning rate	0.01

were selected.

2.

Seismic attribute fusion

In multiseismic attribute fusion based on deep learning, microfeature data from key wells are utilized as sample wells for learning and training purposes. Various attributes are extracted and optimized from the local area in a targeted manner, eliminating irrelevant or outlier attributes from the predicted object. The seismic prediction objective function of the reservoir’s microcharacteristic parameters was established using the optimized multiple attributes. After detection, correlation was achieved, and, then, multiattribute machine learning was conducted and predictions were made (Figure 10). First, the seismic attribute parameters and reservoir characteristic parameters were extracted from seismic traces near the wells to be used as inputs. Through deep learning neural network training, the network gradually adjusted the connection weights to bring the output values closer to the actual values, thereby predicting the reservoir’s microcharacteristics. This process optimized the selection and calculation of seismic attributes with the goal of improving the prediction accuracy (Figure 11).

The microscopic characteristics of the reservoir in Oilfield A are complex and a single seismic attribute may not accurately predict the entire microgeology. Deep neural networks are effective at expressing and predicting nonlinear structured data. Based on the optimization results of the seismic attributes, the original amplitude, the 50 Hz frequency division amplitude, and the 60 Hz frequency division amplitude seismic attributes were used as the inputs. The learning process of the deep neural network was executed using the reservoir’s microscopic characteristics from the single–well data. A multiseismic attribute fusion model was obtained for the microcharacteristics (porosity, permeability, median particle size, and R35) of the well reservoir, which were fitted with multiple seismic attributes (Figure 12). The seismic attribute fusion integrated the advantages of several attributes and was highly correlated with the well data (R² = 0.53). The accuracy of linear fusion was 0.32 (R² = 0.32). The model adopted a 12.5 m × 12.5 m grid in the horizontal direction and the grid step size was 0.25 m in the vertical direction. The model grid number was 363 × 185 × 66 = 4,432,230.

3.

Characterization of reservoir’s characteristic parameters

Once the reservoir parameter model was derived using the deep learning approach, it was then possible to obtain a rough understanding of the distribution of the reservoir parameters. However, at that stage, the model required correction by integrating the results from individual well evaluations. By incorporating multiple seismic attribute fusion bodies as constraints, a more representative model of the reservoir’s microparameters was established.

A 3D model of the reservoir’s microparameters was established using parallel collaborative sequential Gaussian simulations. This method incorporated constraints derived from the seismic attribute fusion of reservoir microparameters. Utilizing the control points of well parameters, a multiseismic attribute fusion body was employed as the trend between wells. The spatial variation characteristics of seismic data and logging data, as well as the cross–variation relationship between them, were also considered. The well points were consistent with the well log data and the prediction accuracy was relatively good in the area without well control.

5. Discussion

5.1. Permeability Variation Characteristics of Different Reservoir Types

The experimental evaluation of the reservoir sensitivity flow (SY/T 5358-2010) suggests that the rate of change in rock permeability should be selected as the characteristic parameter to indicate the degree of reservoir damage. These experimental findings illustrate that the rate of change in rock permeability increased after the core samples were flooded with the formation water. This phenomenon arose because the concise nature of the loose core plunger samples discharged most of the displaced particles. This effect led to an augmentation of the reservoir pore volume, which consequently increased the rock permeability. The permeability of loose sandstone can change during sand production. This phenomenon has been demonstrated in many oilfields, such as the Chestnut oilfield in the central North Sea [23], the Gudong oilfield in China [43], and the McMurray oilfield [24]. Production reports from these fields indicate that sand production changes the reservoir permeability and that the main influence of particle migration on the fluid flow in unconsolidated sandstone reservoirs is concentrated in a 1 m radius around the wellbore [44]. Previous experimental studies also support these findings [24,43,45]. Zivar et al. (2019) studied the permeability changes in unconsolidated sandstone samples during the sand production process [45]. Their study found that there were certain differences among different cores but, overall, the permeability of the cores increased. Nie et al. (2014) analyzed the change characteristics of permeability under different displacement times and found that the permeability fluctuated in the initial phase of displacement while the overall permeability increased in a later phase of displacement [46]. The results of previous experiments are mostly consistent with those of this experiment. Both this study and previous studies are based on core–scale displacement experiments. However, the greater the permeability variation in the macroscopic stratigraphic background, the more likely it is for such reservoirs to have particle migration, which leads to pore throat blockage and reservoir damage.

Previous research has focused on the variation in permeability but this study also highlights the influence of different types of reservoirs on the variation characteristics of permeability. Reservoirs characterized by a high permeability (Type I and Type II reservoirs) have fewer clay minerals, fewer mobile particles, larger pore throats, and a lower rate of permeability change following formation water displacement. In contrast, reservoirs characterized by a low permeability (Type III reservoirs) contain an abundance of clay minerals and mobile particles, resulting in a substantial alteration to the pore structure and the rate of permeability change postdisplacement. Under infinite formation conditions, Type III reservoirs may experience the most severe degree of damage.

5.2. Seismic Attribute Fusion Body Distribution Characteristics

In terms of the seismic profile, the robust reflection aligned well with the oil reservoir’s development position, exhibiting a high correspondence between wells A2 and A3, while the weaker reflection corresponded to well B1. The distribution of strong reflection in the frequency division amplitude profile mirrored that of the original amplitude, albeit with a higher vertical resolution, and demonstrated a good alignment with thin sand layers. Notably, there was an increased disparity between the relative impedance profile and the amplitude class profile. From the profile, there was a slightly inferior degree of alignment with the well reservoir; however, there was a good response to the development of high–quality oil reservoirs (Figure 13).

From the planar perspective, the overall distribution of the original amplitude and the frequency division amplitude appears to be similar across the plane. Spatially, the seismic attribute characteristics indicate lower values in the west, higher values in the northeast direction, and significant variations in localized areas. Seismic attribute fusion enables the exploration of the diverse advantages offered by different types of seismic attributes (Figure 14).

5.3. Correlating Reservoir Characteristic Parameters with Particle Migration

Based on the experimental findings for the reservoir parameters and the damage caused by particle migration to the reservoir, a correlation between the rate of permeability damage and the reservoir’s characteristic parameters was established. The experimental procedure involved determining the rate of permeability damage across various flow rates. Subsequently, the reservoir’s microscopic parameters (including the porosity, permeability, median particle size, and R35) were extracted from the core samples for each flow rate condition. Empirical formulas (R² > 0.8) for the rate of permeability damage and reservoir microscopic parameters at different linear flow rates were constructed using the empirical formula method (

Table 8. Reservoir microscopic parameters and rate of permeability damage: fitting formula for different flow rates.

Flow Velocity (m/d)	Linear Fitting Formula	R2
2	y = −92.07 × $R_{35}$ + 0.76 × $K$ + 45.97 × $M_d$ + 2652.33 × $\varphi$ − 341.93	0.83
6	y = −24.74 × $R_{35}$ + 0.24 × $K$ − 430.30 × $M_d$ − 317.66 × $\varphi$ + 230.35	0.94
10	y = 70.34 × $R_{35}$ − 0.57 × $K$ + 9.28 × $M_d$ − 2111.87 × $\varphi$ + 233.13	0.82
15	y = −7.00 × $R_{35}$ + 0.12 × $K$ − 309.39 × $M_d$ − 1732.94 × $\varphi$ + 524.79	0.80
20	y = 21.94 × $R_{35}$ − 0.19 × $K$ + 187.15 × $M_d$ − 1793.72 × $\varphi$ + 398.79	0.83
25	y = 27.76 × $R_{35}$ − 0.28 × $K$ + 194.86 × $M_d$ − 2017.01 × $\varphi$ + 504.00	0.80

$R_{35}$ = pore throat radius corresponding to 35% mercury saturation, μm; $K$ = permeability, mD; $M_d$ = median grain diameter, mm; and $\varphi$ = porosity, df.

).

Based on the empirical formula for the rate of reservoir damage shown in Table 5 and, using coring well P25-C as an example, the damage rate curve was fitted according to the empirical formula, accurately describing the changes in the rate of longitudinal reservoir damage. The results indicate a significant negative relationship between the rate of permeability damage and the reservoir quality. The physical characteristics, pore structure, and particle size differ significantly among different categories of reservoirs. As the reservoir quality improves, the potential degree of particle damage to the reservoir decreases. However, with an increase in flow velocity, the rate of permeability damage gradually increases (Figure 15).

5.4. Prediction of Reservoir Damage Caused by Particle Migration

Although the logging data had a high longitudinal resolution, they can only reflect the formation characteristics at the well point and the prediction accuracy was low for inter–well interpolation methods relying solely on well data. The seismic data exhibited a high predictive accuracy on the plane, providing a better reflection of the distribution of the reservoir characteristics. After obtaining the trends for the reservoir’s characteristic parameters, a geological model of the parameters was constructed with a collaborative Gaussian simulation using the well as the control point and the multiseismic attribute fusion body between wells as the constraint (Figure 16). An advantage of this method is that the complete consistency of data is ensured at the well points. Additionally, due to the constraint provided by the seismic properties, a good predictive performance was achieved, even in areas where there were no wells. On this basis, the formula in Table 5 was used to perform calculations between the reservoir parameter attribute models. The model was then used to predict the rate of permeability damage due to particle migration under different flow rates constrained by seismic attributes. Figure 17 shows a plane diagram of the reservoir damage rates at different flow rates.

(1)

The rate of change in permeability exhibited significant planar heterogeneity. As the quality of the reservoir improved, the rate of permeability damage decreased. High–quality thick reservoirs typically contain a lower clay mineral content, a lower content of mobile particles, and a larger pore throat. These characteristics impart the reservoirs with a greater resistance to particle migration–induced damage.

(2)

As the flow velocity increased, the rate of permeability damage gradually intensified. As illustrated in Figure 17, even at a flow velocity as low as 2 m/d, certain regions exhibited a rate of permeability damage exceeding 50%.

(3)

Comparing the degree of damage of the reservoirs at different flow rates revealed substantial variation, particularly within the displacement velocity range of 10 m/d to 15 m/d. Therefore, according to the definition of the critical flow rate, the critical damage velocity was estimated to be between 6 m/d and 10 m/d.

Figure 16. The data for the model to predict the degree of damage from particle migration. (a) Porosity model. (b) Permeability model. (c) Median grain diameter model. (d) R35 model. (e) Permeability change rate model.

Figure 16. The data for the model to predict the degree of damage from particle migration. (a) Porosity model. (b) Permeability model. (c) Median grain diameter model. (d) R35 model. (e) Permeability change rate model.

Figure 17. Prediction of rate of permeability damage from particle migration at different flow rates.

Figure 17. Prediction of rate of permeability damage from particle migration at different flow rates.

5.5. The Effect of Particle Migration Reservoir Damage on Oil Well Production

Three new horizontal wells (H1, H2, and H3) drilled into the L74 formation were selected to illustrate the damage from particle migration to oil well production. The fluid production data of each well during a stable production period six months before operation were used for the analysis. Equation (3) was used to calculate the critical flow rate corresponding to the current production status, which was then converted into a linear flow rate. The permeability damage flow rate of all three production wells was found to be 10 m/d. Subsequently, the attribute graph for the corresponding rate of permeability damage for 10 m/d was extracted for the dynamic analysis.

According to the sedimentary facies diagram and prediction diagram of permeability damage due to particle migration (10 m/d) (Figure 18a), the H1 production well was located in an area with a permeability damage rate of less than 15% (Figure 18b). This well experienced minimal impact from migrating particles, thus leading to stable fluid production (Figure 19a). The predicted permeability damage aligned with the actual production levels of the oil wells. However, for well H2, which was located in the same sandbar as the W1 injection well (Figure 17a), its water content increased from 20% to 80% within three months. The well trajectory of H2 is located in the green area with a 25% rate of permeability damage in the southwest part, while the majority of the well trajectory lies in the blue area with a rate of permeability damage < 10%. Therefore, at a flow rate of 10 m/d, well H2 suffered less damage from particle migration and produced a relatively stable fluid volume (Figure 19b). The production well H3 and the injection well W1 belong to different sedimentary microfacies, resulting in poor sand body connectivity (Figure 18a). Consequently, the water influx was relatively slow. From Figure 17b, it can be observed that the trajectory of well H3 mostly lies within areas where the rate of permeability damage exceeded 50%, indicating that, among the three wells, H3 experienced the most significant permeability damage due to particle migration. Additionally, Figure 17c shows that the liquid production capacity of well H3 declined rapidly, decreasing by 75% within the first three months of production, which aligns with the predicted rate of permeability damage (Figure 19c).

6. Conclusions

Unconsolidated sandstone reservoirs are widely distributed in major oil–bearing regions worldwide and they exhibit a high heterogeneity. Through data–mining technology, in this study, we selected parameters to characterize the macro- and microcharacteristics of unconsolidated sandstone reservoirs, providing effective methods for the characterization of other such reservoirs. Furthermore, this study combined machine learning with well–seismic methods to offer a new perspective and method for offshore oilfields with limited core wells. More importantly, in this study, we predicted the permeability changes caused by particle migration at different flow rates and verified the initial productivity of actual production wells, providing a new scientific basis for reservoir protection and oil and gas development. The following insights were obtained:

(1)

The porosity, permeability, R35, and median grain size selected through data–mining methods effectively characterized the macroscopic and microscopic features of unconsolidated sandstone reservoirs.

(2)

Offshore oilfields often lack sufficient core data. This study combined machine learning with well–seismic methods, inputting well logging curves and core test information at the wells and utilizing the seismic attribute fusion constraints between wells to successfully characterize the distribution of the reservoir feature parameters (porosity, permeability, R35, and median grain size) in the region. This method enhances the effectiveness of predicting reservoir feature parameters in offshore oilfields with limited core data.

(3)

Unconsolidated sandstones are widely distributed in major oil–bearing regions in the world. This study compared the experimental results of other scholars and found that the permeability of unconsolidated sandstones would increase due to particle detachment. The core displacement experimental results indicated significant differences in permeability changes among different types of reservoirs after formation water displacement. The variation range for Type I reservoirs is 43% to 55%; for Type II reservoirs, it is 70% to 201%; and the change is most pronounced for Type III reservoirs, ranging from 222% to 410%. The critical flow velocity is estimated to be between 6 and 10 m/d.

(4)

Based on the experimental results, a quantitative relationship model between the permeability change rate induced by particle migration and the reservoir’s characteristic parameters (porosity, permeability, R35, and median grain size) was established. This model could quantitatively predict the permeability change rates in both vertical and horizontal planes at different flow rates within the region. Ultimately, the prediction results were successfully validated by the initial production performance of three horizontal wells, providing new scientific evidence for reservoir protection and oil–gas development.