*Article* **Characterization of Microstructures in Lacustrine Organic-Rich Shale Using Micro-CT Images: Qingshankou Formation in Songliao Basin**

**Yan Cao 1,2, Qi Wu 3, Zhijun Jin 1,2,\* and Rukai Zhu <sup>4</sup>**


**Abstract:** In order to explore the development characteristics and influencing factors of microscale pores in lacustrine organic-rich muddy shale, this study selected five shale samples with different mineral compositions from the Qingshankou Formation in the Songliao Basin. The oil content and mineralogy of the shale samples were obtained by pyrolysis and X-ray diffraction analysis, respectively, while the porosity of the samples was computed by micro-CT imaging. Next, based on the CT images, the permeability of each sample was calculated by the Avizo software. Results showed that the continuous porosity of Qingshankou shale in the Songliao Basin was found between 0.84 and 7.79% (average 4.76%), the total porosity between 1.87 and 12.03% (average 8.28%), and the absolute permeability was calculated between 0.061 and 2.284 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>μ</sup>m2. The total porosity of the samples has a good positive correlation with the continuous porosity and permeability. This means higher values of total porosity suggested better continuous porosity and permeability. Both total porosity and continuous porosity are positively correlated with the content of clay minerals. Moreover, the oil content of the samples (the S1 peak from programmed pyrolysis) exhibits a good positive correlation with the total porosity, continuous porosity, permeability, and clay mineral content. Therefore, pores that are developed by clay minerals are the main storage space for oil and flow conduits as well. Clay minerals were found to be the main controlling factor in the porosity, permeability, and the amount of oil content in the pores in the study area.

**Keywords:** organic-rich mud shale; Songliao Basin; Qingshankou Formation; micro-CT; simulation; porosity and permeability

#### **1. Introduction**

Shale oil and gas resources are abundant around the globe, and drilling horizontally and hydraulic fracturing have been applied successfully in North America, enabling large-scale commercial development of shale oil and gas [1,2], and accounting for a significant growth in hydrocarbon production. In 2018, the global crude oil production was 44.5 × <sup>10</sup><sup>8</sup> t, of which 14% was from unconventional shale plays. Additionally, natural gas production was 3.97 × <sup>10</sup><sup>12</sup> m3, with 25% from unconventional plays [3]. In addition to the US, China is also rich in plays with a huge exploration potential, heading towards large-scale production [1,2].

The shale oil–producing layers in North America are mainly distributed in marine or foreland basins, in a large depositional area, with good continuity, mostly over pressured and high thermal maturity. Conversely, in China, such plays are mostly distributed in depressions and rift basins of continental deposition, which are characterized by strong heterogeneity, low overall pore pressure, and lower thermal maturity [4]. Generally

**Citation:** Cao, Y.; Wu, Q.; Jin, Z.; Zhu, R. Characterization of Microstructures in Lacustrine Organic-Rich Shale Using Micro-CT Images: Qingshankou Formation in Songliao Basin. *Energies* **2022**, *15*, 6712. https://doi.org/10.3390/ en15186712

Academic Editors: Xingguang Xu, Kun Xie and Yang Yang

Received: 23 July 2022 Accepted: 7 September 2022 Published: 14 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

speaking, regardless of the basin in China, shale reservoirs have ultra-low permeability (1 × <sup>10</sup><sup>−</sup>9~1 × <sup>10</sup>−<sup>4</sup> <sup>μ</sup>m2), nanoscale pore diameter (1~200 nm), and complex pore structures [5]. The pore structure and permeability in shale are often considered key indicators of the storage space and flow capacity of shale oil and gas [1,2,5]. Therefore, the pore structure and permeability of Chinese terrestrial shales have been a hot topic of research [1,2,5].

A large number of research tools have been used to reveal the pores of shale, including scanning electric microscopes (SEM) [5], atomic force microscopes (AFM) [6], mercury intrusion porosimetry (MIP) [7], low-pressure gas adsorption [8], micro-CT and nano-CT [9,10], small-angle X-ray or neutron scattering [11], and so on. Loucks et al. (2009) [5] reported that the pores of Mississippian Barnett shale are mainly nanoscale (nanopores), and the pore size can be as low as 5 nm. Organic matter pore space is the dominant pore type in the shale and is strongly controlled by maturity, and pyrite and shale matrix can also provide some pore space for shale [5]. There are several factors that control the enrichment of gas in the marine shales, including well-developed micropores, a large surface area, and a high gas adsorption capacity [8]. Inter-particle pores between organic matter and clay minerals may be responsible for those three controls [8]. Sun et al. (2018) [11] reported that the storage and flow mechanisms of gas in shale reservoirs can be greatly affected by pore structure. There were rarely closed pores in illite but mainly in organic matter by means of small-angle neutron scattering (SANS) [11]. Moreover, geometrical tortuosity and matrix permeability are negatively correlated with the fraction of closed pores [11]. However, most of the current methods only reveal shale pore space but ignore the pore connectivity of shale; furthermore, shale oil and gas development depends heavily on pore connectivity [12]. Among those means, micro-CT and 3D reconstruction of pore spaces via digital rock physics (DRP) methods can effectively distinguish various type of pores, including the continuous pores and isolated ones [13].

In confined nanopores of shale, the solid-liquid intermolecular forces result in complex fluid properties which impact fluid flow. This means the traditional macroscopic Darcy flow equation is no longer applicable for accurately characterizing the fluid flow in such confined very fine spaces [13,14], which has encouraged a large amount of research [15–19]. Currently, the permeability of shales can be determined in the laboratory using three methods, including (i) gas measurements of plunger cores, (ii) gas analysis of particle samples, and (iii) the use of mercury (Hg) intrusion curves [20]. However, it is not feasible to measure shale permeability using steady-flow methods because of measurement of extremely small pressure drops or flow rates requires highly complex instrumentation. The development of pulse decay techniques followed, which could measure pressure decay on an upstream end of a confined core as well as pressure increase on the downstream end. As little as 10−<sup>9</sup> millidarcies (1 × <sup>10</sup>−<sup>15</sup> mD ≈ 1 m2) of permeability can be measured with pulse decay techniques in minutes to hours or even days, depending on the application [21]. Helium (He) is utilized for permeability measurements of granular samples of shale, and pressure decay is measured and quantified as permeability [22]. The particle density or skeletal density of the rock is obtained by He porosimetry using crushed samples, and the porosity of shale can also be calculated by combining the capacity of the impregnated mercury [23]. Numerous studies have examined the relationship between permeability and Hg injection curves [24,25]. Permeability is calculated based on Hg saturation and capillary pressure at the apex of the hyperbolic log-log Hg injection plot [26]. Although the above experimental methods can characterize the permeability of shale to some extent, there are still problems such as large errors and low reproducibility. Considering low saturation and mobility of oil in shale, it would be difficult to intuitively capture oil flow in shale samples in experimental studies. Therefore, theoretical methods via simulation of the flow process [19] were used to investigate permeability in our selected shales.

The shale of the Qingshankou Formation in the Gulong Sag is a key target for shale oil development in China. The relationship between total porosity, continuous porosity, and permeability in studied shale has not been previously revealed by the combination of micro-CT experiments and simulations. Therefore, it is necessary to reveal the characteristics

of porosity and permeability of shale in the region and its influence factors through a combination of experiments and simulations.

In this study, five shale samples from the Well Songyeyou 1HF, which was drilled through the Qing 1–3 Member in the Gulong Sag of the Songliao Basin, were selected for analysis and testing. Through micro-CT imaging combined with modeling, the difference in porosity, permeability, and oil content of the shale samples with different mineral assemblages is recognized first, then flow behavior in each is studied by simulation method to enable us to judge the possibility of commercial development of shale layers in the block.

#### **2. Geological Setting and Sampling**

The Songliao Basin is a large-scale lacustrine facies basin located in northeastern China (Figure 1A). There were three major tectonic stages in the formation of the basin: fault subsidence, thermal subsidence, and inversion [27]. The basin can be divided into 6 tectonic units: the western slope, northern steep slope, central depression, northeast uplift belt, southeast uplift belt, and southwest uplift belt (Figure 1B). The Gulong Sag is located in the western side of the Central Sag, which was formed during the depositional period of the Qingshankou Formation, the main source rock in the basin (Figure 1C). The point B' (i.e., red star), the well location of the studied samples, is located at the junction between profile AA' and BB' (Figure 1C).

**Figure 1.** Location of the Songliao Basin on a generalized map (**A**). Central Depression (**B**). Well locations in the study area (the Gulong Sag) (**C**). (Modified from Liu et al., 2019 [27]).

The Qingshankou Formation (K2qn), a moderately deep lacustrine environment, was influenced by periodic marine intrusions. The lithology divides the Qingshankou Formation (K2qn) into three subsections (K2qn1, K2qn2, and K2qn3) based on lithology (Figure 2). The first member of the Qingshankou Formation (section K2qn1) is widely distributed throughout the basin and is one of the most favorable hydrocarbon source rocks in the Songliao Basin [27]. The first member of the Qingshankou Formation (section K2qn1)

is up to 500 m thick, and formed during rapid, large-scale lake transgression. Lake levels rose several times due to stepwise subsidence of the basement during the emplacement of K2qn1, leading to the interbedded accumulation of dark shale and siltstone [27]. The first member of the Qingshankou Formation (section K2qn1) was selected as the target layer for this study, and five typical dark shale samples in this member were selected for our study.

**Figure 2.** The strata and sedimentary characteristics of the Qingshankou Formation in western Songliao Basin (modified from Liu et al., 2019 [27]).

#### **3. Experiments**

#### *3.1. Analysis of Oil Content and Mineral Content*

Oiliness analysis is performed following the ASTM standards [28]. Next, samples were powdered to the mesh size of 100 and were analyzed for thermal maturity with programmed pyrolysis. This procedure provided us the S1 peak (mg HC/g rock), which is the quantity of free hydrocarbons volatized at 300 ◦C. This peak can represent the oiliness of the sample. Furthermore, powder finer than 200 mesh (i.e., <0.075 mm) was analyzed by quantitative X-ray diffraction (XRD) to determine the mineral content of the studied samples. The D/max-2500 diffractometer was used for the measurements, following two separate CPSC procedures [29].

#### *3.2. Micro CT Experiment*

First, a cylindrical core plug with a diameter of 1 mm and a length of 1 mm parallel to the bedding from the main core was retrieved. The micro-CT imaging was completed in the China Petroleum Exploration and Development Research Institute using the Nano-CTX Radia scanning equipment (Model Ultra XRM-L200) from ZEISS, with a maximum resolution of 1μm. During the scanning process, the sample is rotated from −90 to 90◦ and the X-ray information is continuously acquired [30].

In the micro-CT experiment, the scanning voltage was set to 8 kV, at 20 ◦C, and the exposure time was 90 s. A total of 901 two-dimensional plane images along the Z-axis were obtained, which can be stacked to form a three-dimensional data volume with a diameter of 65 μm and a height of 60 μm [30]. Using the Avizo software, the 3D model of the sample can be reconstructed which is shown in Figure 3 for the S41 sample. In this study, we analyzed five shale samples from the Qingshankou Formation in the Gulong Sag labeled as: S41, S189, S201, S317, and S353.

**Figure 3.** 3D reconstruction of the S41 shale sample.

#### *3.3. Avizo Simulation Computing*

Avizo software was used to reconstruct the 3D shale models from cross-sectional images from the micro-CT data. To separate pores from the matrix, the threshold segmentation

method based on the gray scale was used to select using the Avizo software. To be more specific, the Gaussian deconvolution threshold segmentation method for identifying different phases in the CT images was employed which converts each image into binary mode and further will be used to reconstruct the pore structure network. Figure 4 represents the process that was performed for the S41 sample as an example, where the blue part is the pore distribution extracted from the area with higher values on the gray scale.

**Figure 4.** 3D reconstruction of S41 sample after threshold segmentation.

Th permeability of the reservoir refers to the property of the rock that allows fluid to pass through its continuous pores under a certain pressure difference. In other words, permeability refers to the conductivity of the rock to fluids. The permeability of the reservoir determines the ease of hydrocarbon penetration, which is one of the main parameters for evaluating reservoir quality. In the petroleum industry, absolute permeability is a common parameter that has been used frequently as a measure of the reservoir productivity. This parameter can be calculated from the CT-based 3D models which can be verified with experimental analysis as well. Flow experiments on core samples were conducted under steady state, and the following equation was used to calculate permeability using Darcy's law:

$$k\_{\mathcal{S}} = \frac{2p\_a \mu q\_{\mathcal{S}} \mathcal{L}}{P\_1^{\mathcal{L}} - P\_2^{\mathcal{L}} \mathcal{A}} \tag{1}$$

$$v\_{\mathcal{S}} = \frac{q\_{\mathcal{S}}}{A} = \frac{P\_1^{\cdot^2} - P\_2^{\cdot^2}}{L} \times \frac{k\_{\mathcal{S}}}{2p\_a\mu} \tag{2}$$

In order to make sure that the flow conditions satisfy Darcy's Law, tests were carried out under different flow rates. In practice, permeability is calculated from the slope of the curve of flow velocity, *vg* vs (*P*<sup>1</sup> <sup>2</sup> − *<sup>P</sup>*<sup>2</sup> <sup>2</sup>)/*L*. A similar approach can be followed in numerical simulation as well. In the simulation models, air density in the flow process was ignored and the flow was considered incompressible viscous, which satisfies the three laws of mass, momentum, and energy conservation. Therefore, the flow can be described by the Navier–Stokes equation, which is defined by the following formula:

$$
\rho \left[ \frac{\partial v}{\partial t} + (v \cdot \nabla) v \right] = \rho f - \nabla \mathbf{p} + \mu \nabla^2 v \tag{3}
$$

Using Equation (2), if *qg* is known, permeability *kg* can be computed. Hence, porous media parameters such as the pore structure and permeability can be easily estimated from the digital shale model.

#### *3.4. The Porosity and Permeability of the Sample by Conventional Method*

Based on a rock sample's bulk volume, grain volume, and pore volume, the porosity is calculated. Porosity studies were per-formed using typical equipment and conventional methods (i.e., GRI [31,32]).

Using virtually the same method as GRI, samples were analyzed in this laboratory [33]. Samples were weighed to a precision of 0.001 g and their bulk volumes measured to a precision of 0.001 cm3. In the next step, a core plug was drilled perpendicular to the lamination. After crushing the remaining sample with a mechanical rock crusher, the 20/35 US mesh fraction was sieved. In order to limit the evaporation of fluids from the sample, these steps were performed as quickly as possible. The 20/35 fraction was then divided into two subsamples and sealed in airtight vials. Using the GRI method, one subsample was measured for porosity and permeability. Afterwards, a second subsample was refluxed for 7 days in toluene in a Dean Stark apparatus. Water extraction was verified twice a day by checking fluid volumes. After being dried for 2 weeks at 110 ◦C, the samples were weighed until weight stabilization (0.001 g) was achieved. After that, the samples were kept in a desiccator. Helium gas at approximately 200 psig was used for measuring permeability. We measured pressure at 0.25 s intervals for a maximum of 2000 s. In the end, we measured the permeability of core plugs with the PDP technique described by Jones [34] at a helium pressure of 1000 psi and confining pressure of 5000 psi [33].

#### *3.5. Experimental Procedure for Studying Samples*

Combining above mentioned experiments, we summarize the schematic diagram of the experimental procedure of the studied sample in Figure 5. The porosity and permeability of the studied samples were obtained by means of micro-CT and simulation calculations, respectively. The reliability of micro-CT and simulation is verified by comparing the reservoir characteristics obtained above with the porosity and permeability measured by typical experimental equipment. Correlation of reservoir characteristics with XRD results and free hydrocarbon S1 to obtain control factors of shale reservoir.

**Figure 5.** The schematic diagram of the experimental procedure of the studied sample.

#### **4. Results**

#### *4.1. Mineral Composition and Oil Content*

XRD results confirm all five samples from the Qingshankou Formation in the Gulong Sag consisted of large amounts of clay, varying between 32.6 wt. and 42.3 wt.%, with an average value of 36.46 wt.%. In addition, quartz is also abundant in the samples ranging between 29.9 and 34 wt.%, with an average of 32.4 wt.%, and plagioclase (18.1–23.4 wt.%, with and average of 20.16 wt.%) was also detected in the samples. Other minerals, including calcite, siderite, and pyrite, were detected with different amounts in the samples. Movable hydrocarbon (S1) content was found relatively high, mainly at 1.36–8.54 mg/g, with an average of 5.67 mg/g. The detailed mineralogy and oil-bearing characteristics of all samples are summarized in Table 1.

**Table 1.** Mineralogy and oil-bearing characteristics of the studied samples.


#### *4.2. Porosity and Permeability*

Using DRP methods and the 3D model that was obtained by Avizo software, the total and effective porosity of five samples is calculated and reported in Table 2. Furthermore, the flow simulation module provided by the Avizo software can compute the permeability of the samples which is also listed in Table 2. Results showed that these values vary notably among the samples. The continuous porosity of these five samples was found between 0.84 and 7.79% (average 4.76%), the total porosity between 1.87 and 12.03% (average 8.28%), and the absolute permeability was calculated between 0.061 and 2.284 × <sup>10</sup>−<sup>3</sup> <sup>μ</sup>m2. Moreover, average open pores account for 55.79% of the total pores (Table 2), which means the average porosity in this area is relatively low, while the proportion of continuous pores is high, and the permeability is low. Based on the results we can categorize the shale samples in the study area as tight reservoir with low porosity and permeability.


The measured results of porosity and permeability of the samples using the typical equipment are shown in Table 3, and the above test results are similar to those obtained by micro-CT and simulation; the error produced by comparing the results of the two methods is acceptable (Tables 2 and 3). Therefore, the combination of micro-CT and simulation is a reliable method to reveal shale porosity and permeability.


**Table 3.** The porosity and permeability of the sample with typical equipment.

Based on the above summary, the low saturation and mobility of oil and gas in shale makes it difficult to obtain plausible permeability in shale samples in conventional experimental studies (i.e., gas measurements of plunger core, gas analysis of particle sample, and the use of mercury (Hg) intrusion curves). However, the combination of micro-CT and simulation calculation could obtain credible total porosity, continuous porosity, and permeability of shale samples, while avoiding the consumption caused by permeability experiments.

#### **5. Discussions**

#### *5.1. Relationship between Porosity and Permeability*

Previous studies have shown that porosity characterizes the storage capacity of the reservoir rock [35]. However, if the porosity of the tight reservoirs is too large, the porethroat ratio increases, which makes it difficult to establish an effective driving pressure difference during production. Therefore, it is necessary to comprehensively evaluate the porosity of the rock samples from the perspective of reservoir property and flow behavior during reservoir quality evaluation [35]. In this study, we found that the total porosity and the continuous porosity have a linear relationship (Figure 6a), which means higher total porosity leads to more developed continuous pores. Total porosity and continuous porosity were both significantly positively correlated with permeability (Figure 6b,c), which indicates higher values of total porosity and continuous porosity suggested better permeability. Findings from this study are also consistent with the results from Burnham (2017) [36], which studies shale samples from the Green River Formation. In addition, our study found no positive correlation between the total porosity of the studies samples and the burial depth (Figure 6d), which indicates the effect of formation compaction on the porosity of shale in the study area is not obvious. The possible reason is that the hydrocarbon generation of organic matter in the studied strata generates strong pressure, which could counteract the compaction of the overlying strata [37].

#### *5.2. Relationship between Porosity and Mineral Content*

Previous studies have explained that clay minerals are the main constituent component of shale and closely control the occurrence and enrichment of shale plays [38,39]. Considering clay minerals, their special crystal structure causes different types of pores to form between their crystal layers, also creating inter and intraparticle pore spaces. Furthermore, size, morphology and specific surface area of these pores determine the shale oil storage capacity. Previously it was documented that clay minerals are mostly composed of different types of porous structures, i.e., montmorillonite mostly develops in a circular and slit-like meso/micropores and has the largest total specific surface area. As the burial temperature increases, it transforms into mixed layers of other clay minerals, specifically illite, and the number of pores in the corresponding clay minerals gradually decreases [39]. Kaolinite is dominated by medium and large primary pores of 20–100 nm in size, which can be altered into illite in an alkaline environment [39]. Mesopores and macropores are mostly developed in illite and kaolinite. Additionally, it was found that the content of clay minerals in the same TOC range has a positive correlation with the pore volume and pore specific surface area of the organic-rich shale [40], and the pores between clay minerals can be filled with organic matter that migrates over a short distance. Therefore, pores of organo–clay mineral nanocomponents and organo–clay mineral complexes [41,42] can be considered as the main contributors to shale pore structure. Therefore, in general, pores of clay minerals are in general very well developed [43,44], which is the main controlling factor for the development of various types of pores in shale. In addition, previous studies found that

illite and kaolinite are the main clay types in the shales of the Qingshankou Formation of the Gulong Sag [45]. Comparing our results with previous studies confirm that the total and continuous porosity of the samples in this study have a linear relationship with the content of clay minerals (Figure 7a,b), which means clay minerals are providing adequate pore space to the for the fluid to flow as well as storing the generated hydrocarbons. Our findings echo, to some extent, those of previous studies that suggested the variation of shale permeability depends on the nature of the clay mineral surface [46], the presence of a large number of pore structures in typical clay minerals (i.e., illite and chlorite) in shale has a positive effect on permeability [47]. Notably, our porosity values are lower than the typical porosity range of shale in the depth, according to porosity data compilation in Kim et al. [48], which could be attributed to a sequential microquartz cementation process and the quartz cement preferentially blocked the small mudstone pores during diagenesis [49].

**Figure 6.** *Cont*.

**Figure 6.** Relationship between porosity and permeability in studied samples. (**a**) Relationship between total porosity and continuous porosity of the studied samples. (**b**) The crossplot of total porosity versus permeability for the studied samples. (**c**) The relationship between continuous porosity and permeability of the studied samples. (**d**) The relationship between total porosity and burial depth of the studied samples.

**Figure 7.** (**a**) Crossplot of total porosity versus clay content for the studied samples. (**b**) Continuous porosity versus clay content of the studied samples.

#### *5.3. Relationship between Porosity and Oil-Bearing S1*

High-yield shale oil formations are often accompanied by a variety of minerals such as kaolinite and Fe2O3 that can promote hydrocarbon generation and transformation [50]. Natural attapulgite, kaolinite, clinoptilolite, and other minerals can catalyze the in situ upgrading of oil shale. Moreover, clay minerals are naturally micro-mesoporous materials with good thermochemical stability and are widely used as catalyst carriers and adsorbents [51,52], which not only improves the hydrocarbon production from shale oil

but also reduces the activation energy [53–56], promoting the thermal maturity of oil shale kerogen and increasing the oil generation from the source rock. In this regard, simulation studies argue that montmorillonite has a catalytic effect on hydrocarbon generation from the organic matter [57], while the catalytic ability of illites is relatively small. These clay-based catalysts have good thermal stability and a simple development process and show significant potential in improving oil shale conversion efficiency and hydrocarbon yield [58] which makes us to conclude that the value of S1 with the amount of clay minerals in the samples should be closely related.

Shale oil mainly accumulates in matrix pores, and there is a positive correlation between pore development and the S1 peak [40,43]. Clay minerals have been shown to have a high adsorption capacity for shale oil [59]. In this regard, hydrocarbons show different adsorption properties in the pore structure of clay minerals where the adsorption capacity of montmorillonite for hydrocarbons is stronger than that of illite and kaolinite. In addition to the pore size of the adsorbent, the structure and morphology of hydrocarbon molecules also strongly affects the adsorption behavior [56]. However, clay mineral content and pore volume are negatively correlated, according to some studies, which indicates developing large pores or enriching movable oil in clay is not possible [60].

Here, we found that the oil content of the samples (S1) has a good linear relationship with the total and continuous porosity as well as the permeability and the clay content of the samples (Figure 8). Therefore, we can conclude the pores that are developed by clay minerals are the main storage space for oil in these samples.

**Figure 8.** *Cont*.

**Figure 8.** (**a**) The relationship between total porosity and oil content, S1 peak of the studied samples. (**b**) The relationship between continuous porosity and the oil-bearing capacity, S1, of the studied samples. (**c**) The relationship between permeability and the oil content (S1) of the studied samples. (**d**) The relationship between clay mineral content and the oil content (S1) of the studied samples.

#### **6. Conclusions**

In order to obtain the pore and permeability characteristics of the shales in the Qingshankou Formation and their relationship with oil-bearing, micro-CT and simulation calculations, instead of traditional experiments, were performed on five typical samples. Based on the results the following conclusions can be made:


**Author Contributions:** Conceptualization, Y.C.; Data curation, Y.C. and R.Z.; Formal analysis, Y.C.; Funding acquisition, Z.J.; Investigation, Z.J. and R.Z.; Methodology, Q.W. and R.Z.; Resources, Z.J. and R.Z.; Software, Q.W.; Supervision, Z.J.; Writing—original draft, Y.C.; Writing—review & editing, Y.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was jointly funded by the National Science Foundation of China (42090020/42090025) and the 2022 American Association of Petroleum Geologists Foundation Grants-in-Aid Program (Grants-in-Aid General Fund Grant).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Hongxia Zhang 1,\*, Kaijie Fu 1, Zhihao Lv 1, Zhe Wang 2, Jiqiang Shi 3, Huawei Yu 2,4 and Xinmin Ge 2,4**


**Abstract:** Predicting reservoir parameters accurately is of great significance in petroleum exploration and development. In this paper, we propose a reservoir parameter prediction method named a fusional temporal convolutional network (FTCN). Specifically, we first analyze the relationship between logging curves and reservoir parameters. Then, we build a temporal convolutional network and design a fusion module to improve the prediction results in curve inflection points, which integrates characteristics of the shallow convolution layer and the deep temporal convolution network. Finally, we conduct experiments on real logging datasets. The results indicate that compared with the baseline method, the mean square errors of FTCN are reduced by 0.23, 0.24 and 0.25 in predicting porosity, permeability, and water saturation, respectively, which shows that our method is more consistent with the actual reservoir geological conditions. Our innovation is that we propose a new reservoir parameter prediction method and introduce the fusion module in the model innovatively. Our main contribution is that this method can well predict reservoir parameters even when there are great changes in formation properties. Our research work can provide a reference for reservoir analysis, which is conducive to logging interpreters' efforts to analyze rock strata and identify oil and gas resources.

**Keywords:** reservoir parameter prediction; temporal convolutional network; porosity; permeability; water saturation

#### **1. Introduction**

Reservoir parameters are very important in petroleum exploration and development and also a significant reference foundation to analyze reservoir geology and evaluate oil and gas reservoirs accurately. In the actual exploitation process, obtaining reservoir parameters is expensive from core data, and the amount of data obtained is limited. At the same time, the actual development environment is changeable, and the underground geological situation is complex and diverse. Affected by the original data, logging cost, the level of explorers, the empirical coefficients, response logging curve selection, heterogeneous formation, depositional environment and tectonic location, it becomes extremely complex to obtain accurate reservoir parameters.

In recent years, artificial intelligence technology has provided a possibility for intelligent exploration [1]. Deep learning methods such as BP (back propagation) network [2], recurrent neural network (RNN) [3], long short-term memory (LSTM) [4] and gated recurrent unit (GRU) [5] have been applied to petroleum field by many researchers. Dos [6] proposed a computational system based on deep recurrent neural networks (RNNs) as an effective method to automatically identify lithofacies patterns from well logs. For forecasting petroleum production, a novel method based on a gated recurrent neural network has been proposed. It has multiple hidden layers, and each layer has a number of nodes.

**Citation:** Zhang, H.; Fu, K.; Lv, Z.; Wang, Z.; Shi, J.; Yu, H.; Ge, X. FTCN: A Reservoir Parameter Prediction Method Based on a Fusional Temporal Convolutional Network. *Energies* **2022**, *15*, 5680. https:// doi.org/10.3390/en15155680

Academic Editors: Xingguang Xu, Kun Xie and Yang Yang

Received: 14 July 2022 Accepted: 2 August 2022 Published: 5 August 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

<sup>1</sup> Qingdao Institute of Software, College of Computer Science and Technology, Qingdao 266580, China

The robustness of this model is very good [7]. Heghedus [8] concentrated on pressure-rate datasets accumulated with massive installation of permanent downhole gauge production and injection wells based on an LSTM network. The research results provide a basis for filling gaps in well monitoring data. Meanwhile, it also becomes a research hotspot for intelligent reservoir parameter prediction.

For the sake of enhancing the prediction results of reservoirs in intricate geology effectively, a new parameter prediction method named the fusional temporal convolutional network (FTCN) has been proposed. Firstly, the relationship between logging curves and reservoir parameters is analyzed deeply, and the logging curves, which are closely related to reservoir parameters, are obtained. We use the selected correlation logging curves to predict the reservoir parameters. Secondly, we present a fusion module on TCN to improve the affection of reservoir parameter prediction innovatively. We weigh the output of different network layers and combine the output to enrich the data characteristics obtained by the predictive network model. A fusion module is raised to utilize the information from different network layers adequately, which decreases the large deviation in the fluctuation of local peak values. Finally, experiments are set up on the actual logging data. Our method provides better support to understand and analyze reservoir conditions technically and thus provides a novel reference to the exact interpretation of the logging data.

There are a lot of measurement data in the petroleum industry. These data usually contain momentous information describing the characteristics of strata and reservoir properties and play an important role in production and reservoir management. Logging records provide a data source for logging interpretation experts to analyze reservoir properties. Logging experts can obtain the information of reservoir characteristics by analyzing logging records. Reservoir parameters are exceedingly significant for logging interpreters to analyze formation properties and reservoir capacity and are also the foundation for fine logging reservoir evaluation and analysis of oil-gas. Reservoir parameters, such as porosity, permeability and water saturation, reflect the reservoir's storing ability. Generally, the greater the porosity is, the more likely it is to store oil and natural gas in the pores. The higher the permeability is, the stronger the fluidity of oil, and the easier it is to be exploited. Predicting reservoir parameters effectively can provide a reference for analyzing reservoir properties, characterizing oil reservoirs and providing accurate interpretation of well logging data, which can assist logging interpreters in judging formation conditions and evaluating oil-gas potential. Thus, it provides a support for reserve calculation, flow unit identification and reservoir evaluation. Using the effective porosity parameter of the fracture and cavity reservoirs in combination with the effective thickness, oil-bearing area and other reserve calculation parameters, Kuanzhi [9] formulated a reserve estimation scheme for fractured vuggy carbonate reservoirs so as to guide the exploration and development of oil and gas reservoirs. In the research of reservoir flow unit identification in the North Rumaila Oilfield, according to the logging curve similarity, the porosity and permeability crossplot, the capillary pressure data, the porosity and water saturation and depth relationship and the flow zone indication method, Al-Jawad [10] subdivided the primary reservoir units in the oilfield, interpreted and classified the sub units and thus identified the good reservoirs. Therefore, reservoir parameters play an important role in the exploration and development of the petroleum industry.

The main contributions of this paper are as follows:


#### **2. Previous Work**

Complex reservoir analysis is a significant field in oil reservoir description. Well logging data involves abundant geological information. By analyzing logging data, logging interpreters can judge stratum properties and identify oil and gas reservoirs. In recent years, with the incessant development of machine learning, there have been many outstanding works in the field of engineering applications of deep learning or convolutional networks. For example, a novel method based on deep convolutional neural networks to identify and localise damages to building structures equipped with smart control devices has been proposed [11]. In addition, Yu [12] developed a vision-based crack diagnosis method using a deep convolutional neural network (DCNN) and enhanced chicken swarm algorithm (ECSA). It has also been applied in the domain of petroleum logging successfully [13]. Scholars have done a great deal of research and achieved many achievements in the integration of oil exploration and development and artificial intelligence [14]. For example, the porosity classification and quantification scheme [15] mainly introduces a thorough understanding of the carbonate pore system, which is essential to hydrocarbon prospecting and the prediction of petroleum reservoir properties [16]. Other examples include sedimentary facies classification, reservoir evaluation [17], and so on.

A variety of methods have been proposed to solve the problem of reservoir parameter prediction, which continuously promotes the development of reservoir analysis and logging interpretation technology and provides an important basis for geological experts to analyze reservoirs. In the early stage, based on years of experience in the analysis of reservoir parameters and geological conditions, researchers [18–20] established many empirical formulas to determine the reservoir parameters in the research field. However, because the geological conditions of the new and old exploration areas are different, there will be great differences. A new, undeveloped study area is likely to have rich potential oil and gas resources and good reservoir physical properties. However, in an old study area, due to long-term development, the physical properties and lithology of the reservoir will have changed, and the geological conditions become very poor, which brings challenges to the development of the remaining oil and gas resources. Some empirical coefficient values cannot be generalized, and the formula is also affected by the subjective factors of logging interpreters. Thus, the results are uncertain. Empirical formulas can only be used as a reference. In addition, cross plots can also be used to analyze reservoir properties in exploration and development [21]. The cross plot draws a two-factor or multi-factor rendezvous map using logging curve readings or calculation parameters. Geological experts interpret geological models and analyze and evaluate strata according to the observation of cross plots, which is also uncertain. Therefore, the above methods are influenced by the subjective factors of logging interpreters and the great changes in geological conditions, so the accuracy of the reservoir parameter prediction needs to be improved.

As mature oilfields turn into a later exploitation period of the ultra-high water cut stage, the geological situation becomes complex and changeable, and the quality of oil resources gradually deteriorates [22]. The search for oil and gas fields with complex reservoirs has become difficult, and traditional methods have been unable to meet the demand. The development of machine learning technology makes it possible to improve the effect of reservoir parameter prediction [23].

Through the analysis of tight sandstone reservoirs, Zhu [24] considered that the clay content, the irreducible water saturation, the porosity and the diagenetic coefficient were important factors affecting the reservoir parameter permeability. The studied samples of the model were selected based on the representative core analysis data. According to these influencing factors and samples, permeability was predicted based on an improved BP neural network. Mahdaviara [25] pointed out that the prediction of permeability was a challenge in carbonate heterogeneous rock and built a model to predict reservoir permeability based on Gaussian process regression. The evaluation of permeability in the southern Yellow Sea basin showed that it can be used as a supplement to the neural network prediction methods. In addition, researchers [26,27] have used machine learning methods, such as support-vector machines, particle swarm optimization algorithm [28], and artificial neural networks [29–31] to study and analyze reservoir parameters, achieving good results.

As a research hotspot in the domain of machine learning, deep learning has achieved fruitful results in many fields, such as agriculture [32], ultrasound imaging [33], smart cities [34] and so on. Many researchers have applied deep learning to the field of petroleum exploration and development [35,36]. In the study of predicting reservoir parameters, deep learning technology has been combined to improve the prediction accuracy. As two significant parameters of the oil and gas storage, porosity and shale content express the sedimentary characteristics of various historical stages and have an intense nonlinear mapping with logging parameters. Deep learning has a powerful data mining capacity. Therefore, AN [37] applied an LSTM network to predict the shale content and porosity of a reservoir. The prediction accuracy of this network was more superior than the conventional deep neural network. The hardship of gaining porosity increases gradually with increasing drilling depth, and the cost for gaining intact porosity by the conventional coring method is large comparatively. Thus, for the sake of achieving low-cost and high-efficiency porosity prediction, Chen [38] proposed a logging method found on a multi-layer LSTM network, which performs well for logging at different depths and predicts the changing trend of porosity in strata effectively. The logging curves gained from deep to shallow stratum indicate the sedimentary features of distinct geological stages. The porosity, as a vital reservoir parameter, reflects the capacity of the oil and gas storage. It is very meaningful for the exact description of a reservoir to use logging parameters to acquire reservoir porosity [39]. The application effect in a certain research region of the Ordos basin showed that a gated recurrent unit (GRU) network combined with various logging curves was more effective in predicting reservoir porosity than multiple regression analysis as well as RNN. In addition, convolution structures [40,41] also have certain advantages in predicting sequence tasks. However, although the above methods solve the problem of reservoir parameter prediction in some practical areas effectively, the effect on geological complex reservoir prediction is general, such as in an old oilfield with serious water flooding and intense inhomogeneity. The structure of the reservoir sand body is loose, and the lithology is complex. Development is difficult, and the effect needs to be further improved. The generalization of the model is limited to a certain extent, so these methods have some limitations in practical application and cannot meet the requirements of all kinds of fine reservoir prediction.

#### **3. Methodology**

LSTM [4] was first proposed by Hochreiter and Schmidhuber to solve the long-term dependence problem of general RNN, which can avoid gradient vanishing and gradient exploding. GRU [5] is an important variant of LSTM. It improves the design of gates in LSTM and optimizes the forgetting gate, input gate and output gate in LSTM into two gates called the reset gate and update gate, respectively. A temporal convolutional network (TCN) [40] is a special convolution network that has the advantages of a flexible receptive field and stable gradient.

#### *3.1. FTCN Network Model*

For the purpose of resolving problems of the resulting uncertainty, reservoir area limitation and low prediction accuracy, a fusional temporal convolutional network (FTCN) based on TCN is proposed in this paper by digging into the nonlinear relationship between logging curves and reservoir parameters in complex reservoirs. Firstly, the input curves are optimized by selecting the logging curves, which are sensitive to porosity, permeability and water saturation, and excluding the non-correlation curves. Then, a fusion module is designed to improve the prediction results of the inflection point of the curve, which can reduce the local deviation of reservoir parameter prediction parameters efficiently. The framework of FTCN is shown in Figure 1. A variety of logging curves are preprocessed. The middle part is the main structure of the prediction network. The right part shows the optimization of the network. Specifically, the original logging data mainly include acoustic travel time, density, compensated neutron logging, natural gamma ray, spontaneous potential, micro-potential resistivity, micro-gradient resistivity, and so on. We use the numerical values of these logging curves as the input data of the network model.

**Figure 1.** Framework of reservoir parameter prediction model named FTCN.

There are great differences in the value range of different logging curve data. For the sake of reducing the effect of different dimensions of the original logging data, the data are standardized and preprocessed as

$$y\_{ij} = \frac{\mathbf{x}\_{ij} - \mu\_i}{s\_i},\tag{1}$$

where *i* is the *i*th kind of curve parameter, *j* is the *j*th sample of the curve parameter, *xij* denotes the original data, *yij* denotes the standardized data, and *μ<sup>i</sup>* and *si* are the mean and standard deviation of data, respectively.

The standardized data are used as the input data of the predictive network model and first enter the convolution layers, where convolution and pooling operations are carried out, which are mainly used to obtain the low-level features of the network. Then, they enter the TCN network, including dilated causal convolution and residual connection blocks, and the deep-level features of the data are obtained through the TCN network. Then, they enter the fusional module. After passing the network fusional module and then going through the full connection layer, the predicted reservoir parameters are output. In the process of adjusting the training network, we chose the RMSProp algorithm [42] with adaptive learning rate. Through continuous iterative training, the reservoir parameter prediction model is established.

#### *3.2. Fusional Module*

The variation of well logging curves reflects the change in reservoir parameters in some ways, and it has a good correlation among adjacent wells in the same horizon. Convolution networks have strong data mining abilities. Dilated convolution expands the receptive field by introducing a dilation factor to the convolution. This dilation factor defines the distance between values when the network processes data. The dilated convolution obtains the information farther from the current input by skipping part of the input value. In order to make the network remember more effective information, we introduce dilated convolution that can expand the receptive field into our network. Thus, the network can pay more attention to global information and capture more feature information. However, with the increase in network depth, dilated convolution will lose the continuity of data information and weaken the attention to local information. To get the most out of the non-linear mapping relation between logging curves and reservoir parameters, we combine the output weighting of shallow convolution layer and deep TCN network to enrich the data information obtained by prediction network model, and a network fusional module is designed as

$$F(\mathbf{x}) = \frac{\left(1 + \boldsymbol{\alpha}^2\right) \* T(\mathbf{x}) \* \mathbb{C}(\mathbf{x})}{\left(\boldsymbol{\alpha}^2 \* T(\mathbf{x})\right) + \mathbb{C}(\mathbf{x})},\tag{2}$$

where *F*(*x*) is the output of the fusion module, *C*(*x*) and *T*(*x*) are the output of the convolution layer and after the TCN, and *α* is a balance factor, which is used to weigh the integration with the network layer.

This design considers the information of the deep and shallow network to enhance the prediction performance of the network comprehensively and maximize the characteristic information of the logging curves.

#### *3.3. TCN Network*

The network uses causal convolution to handle time series data. There is a causal relationship between different layers of the network, so that it does not have information leakage from the future into the past, as shown in Figure 2. At time t, the output is only convolved with t and earlier elements in an anterior layer. In order to make the network produce the same output as the input length, a one-dimensional fully convolutional network structure is used for TCN, in which the length of the hidden layer is the same as the input layer. In addition, it adds zero padding of kernel size 1 length to ensure that the length of the subsequent layer is equal to the preceding layers [40].

**Figure 2.** Causal convolution.

An ordinary causal convolution can merely review a history of linear size in the depth of the network, which results in difficulties when using causal convolution in assignments that require longer history. In order to remember long effective historical information, dilated convolution [43] is introduced into the network, which increases the receptive field of the kernel and maintains the parameters unchanged. Specifically, for a filter f: {0, ... , *<sup>k</sup>* − <sup>1</sup>} → *<sup>R</sup>*, a 1-D sequence input *<sup>X</sup>* ∈ *<sup>R</sup>n*, and sequence element *<sup>e</sup>*, the dilated convolution operational express *F* is denoted as

$$F(e) = (X \ast\_d f)(e) = \sum\_{i=0}^{k=1} f(i) \cdot X\_{e-d \cdot i \prime} \tag{3}$$

where *d* denotes the dilation factor. *k* denotes the filter size, and *e* − *d* · *i* indicates the direction of the past. Therefore, the dilation corresponds to bringing in a fixed step in the middle of every two contiguous filter taps. When the *d* value is 1, dilated convolution turns into

regular convolution. This utilization of greater dilation makes the top-level output express a broader input scope. Therefore, the receptive field in ConvNet is expanded effectively.

Dilated convolution obtains the information farther from the current input by skipping part of the input values. The dilation factor d(d = O 2i ) increases along with the depth of network exponentially. This is shown in Figure 3, which represents a dilated convolution when the filter size *k* = 3 and dilated factors *d* = 1, 2, 4. Therefore, with the increase in the network layer, the receptive field of the network continues to increase, thus ensuring that the network can remember more historical information while avoiding an excessively deep network.

**Figure 3.** Dilated convolution.

In general, the expression ability of neural networks increases with the increase in network depth, but a deeper and larger network can easily produce exploding gradients, vanishing gradients and so on. Residual connections are used in this network [44].

$$
\rho = \text{Activation}\left(x + \mathcal{F}(x)\right),
\tag{4}
$$

The residual block consists of a branch that leads to a train of transformations F(*x*), and its output is appended to input *x* of this block, which avoids the degradation of very deep networks. The left part of the FTCN framework shows the residual block, which contains two dilated causal convolution layers, weight normalization layers and rectified linear unit layers. The dropout is used to discard some neurons to prevent overfitting. In addition, 1 × 1 convolution is applied to assure the element-wise addition ⊕ takes over tensors which have an identical shape. This design can retain information as much as possible and improve the performance of the network model.

#### *3.4. FTCN Network Flow*

The RMSProp algorithm is an effective and practical depth network optimization algorithm. It adjusts changes in the learning rate by combining an exponential moving average of the square of the gradient and can converge well in the case of the unstable objective function. According to the mean absolute error loss calculated by the prediction network model, the algorithm updates the model parameters by computing the gradient of each weight to optimize the network. The pseudo-code of the FTCN algorithm flow is shown in Algorithm 1, in which AC, CNL, DEN, GR and SP represent acoustic travel time, compensated neutron logging, density, natural gamma ray and spontaneous potential, respectively, and POR, PERM and SW represent porosity, permeability and water saturation, respectively.

#### **Algorithm 1:** FTCN RP = FTCN(LCS).

**Input:** Logging Curves(AC, CNL, DEN, GR, SP ··· ).

**Output:** Reservoir Parameter(For example: POR, PERM, SW).


$$\Delta\theta = -\frac{\epsilon}{\sqrt{\delta+\gamma}} \odot \lg \cdot \left(\frac{1}{\sqrt{\delta+\gamma}} \text{ applied element } - \text{ wise }\right);$$


#### **4. Results and Discussion**

*4.1. Geological Setting and Data Source*

As shown in Figure 4, the experiment was set up on a real oil field reservoir, which is located in the east China. The Figure shows the relative position of the well. In this area, the braided river deposit is composed of a mid-channel bar and watercourse. The existence of different configuration units leads to the diversity and complexity of reservoir properties and development characteristics. In turn, the differences in reservoir properties and development characteristics also reflect the differences in sedimentary facies distribution or geological flow unit distribution. The oil field has entered the mid-to-late stage of development, and it is in the stage of high and ultra-high water cut. After long-term water flooding, the heterogeneity has become stronger, and the physical properties, electrical properties and oil-bearing properties of the reservoir have also changed.

**Figure 4.** Situation in the study area. (**a**) the map of the location of the study area; (**b**) the relative position of the well and architecture analysis.

Figure 5 shows different sedimentary facies in this study area. The thick oil layer in this area is a braided river reservoir, which mainly develops parallel-bedding sandstone facies, trough and plate cross-bedding sandstone facies and conglomerate, with a flushing surface at the bottom. Parallel bedding sandstone facies generally form the top of the braided river channel and the center beach of the braided river. In most cases, due to erosion, the preservation is incomplete, and the thickness is thin, so it is easy for a highpermeability layer to form. The study area is seriously flooded, and it is difficult to stabilize production. Affected by the development and distribution of sand bodies, the reservoir has serious heterogeneity, loose structure and easy sand production, so it is difficult to evaluate accurately. Therefore, the fine reservoir parameter prediction, such as porosity, permeability and water saturation, is important for the analysis of reservoir properties in the research region particularly.

**Figure 5.** Different sedimentary facies in the study area.

The actual exploration logging and core data of 6 wells in this area were used to study the reservoir parameter prediction in this paper. There are many kinds of logging curves. In our scenario and actual logging, based on actual engineering experience, we obtained acoustic travel time, density, compensated neutron logging, natural gamma ray, spontaneous potential, micro-potential resistivity, micro-gradient resistivity, deep investigation induction log, medium investigation induction log, induced conductivity, microspherically focused logging, high-resolution array-induced resistivity (M2R1, M2R2, M2R3, M2R6, M2R9, M3RX), and 4 m bottom gradient resistivity curves, which are considered to be important in the region. Our experiments are based on the field data. The above logging curves were used for predicting reservoir porosity, permeability and water saturation, and the true values of reservoir parameters were determined by core data in this area. Because different well logs may respond to each one of the predicted parameters differently, we used the logs showing direct responses to each one of the reservoir parameters. Specifically, we analyzed the correlation between logging curves and reservoir parameters and optimized the input logging curves during data preprocessing. Taking the analysis of porosity correlation as an example, as shown in Figure 6, the cross-plots show the relationship between input well logs and porosity. It can be seen that the tri-porosity logging curves are closely related to porosity. As the logging curves assist in calculating porosity, the natural gamma ray and the spontaneous potential are also related to porosity. Therefore, acoustic travel time, density, compensated neutron logging, natural gamma ray, and spontaneous potential were selected as the input data for predicting porosity. Similarly, micro-potential resistivity, micro-gradient resistivity, acoustic travel time, density, compensated neutron logging, natural gamma ray, spontaneous potential, deep investigation induction log, medium investigation induction log, and high-resolution array-induced resistivity were selected to predict permeability. Additionally, deep investigation induction log, medium investigation induction log, induced conductivity, high-resolution array-induced resistivity and 4 m bottom gradient resistivity were selected to predict water saturation. Among them, the porosity is about 18% to 46%, the permeability varies widely, from about

50 md to 18,000 md, and the reservoir water saturation is about 10% to 100%, which has the characteristics of strong watered-out layers such as high permeability and low water saturation. The depth of the well section in this area is 1240 m to 1350 m, and the lithology is complex, mainly sand-mudstone, sometimes bottom conglomerate or gravel-bearing sandstone, with vertical accretive sedimentary corrugated siltstone and silty mudstone interbedded at the top. As shown in Figure 7, the core images of well2 show its internal structure clearly.

**Figure 6.** The cross-plots of logging curve correlations. Shown are the AC-POR cross-plot, CNL-POR cross-plot, DEN-POR cross-plot, GR-POR cross-plot and SP-POR cross-plot, respectively. These show the correlation between different logging curves and POR.

**Figure 7.** The core images of well2. (**a**) trough cross-bedding gravelly sandstone facies; (**b**) massive bedding gravelly sandstone facies; (**c**) wavy cross bedding siltstone facies; (**d**) horizontal-bedding siltstone facies; (**e**) trough cross-bedding sandstone facies; (**f**) planar cross-bedding sandstone facies; (**g**) parallel-bedding sandstone facies; (**h**) massive mudstone facies.

The lithofacies types are trough cross-bedding gravelly sandstone facies (1343.40–1343.50 m), massive bedding gravelly sandstone facies (1334.81–1334.88 m), wavy cross-bedding siltstone facies (1330.31–1330.40 m), horizontal-bedding siltstone facies (1329.27–1329.36 m), trough cross-bedding sandstone facies(1343.20–1343.30 m), planar cross-bedding sandstone facies (1341.14–1341.29 m), parallel-bedding sandstone facies (1339.79–1339.91 m) and massive mudstone facies (1343.53–1343.70 m), respectively.

Additionally, as shown in Figure 8, we can analyse the sedimentary structures characteristics from the cored well5 further. According to the observation and analysis of well5, we know that the lithofacies types are retained conglomerate facies (1330.44–1330.53 m), trough cross-bedded sandstone facies (1329.96–1330.07 m), tabular cross-bedded sandstone facies (1329.26–1329.37 m), parallel-bedding sandstone facies (1331.37–1331.48 m), wavy-bedding siltstone facies (1327.03–1327.15 m) and massive mudstone facies (1340.35–1340.46 m). During the experiment, the logging data have been relocated deeply. Because there are some missing values in the original core data, and the data values of similar depth are very close, we complement the missing data with its nearest value so as to improve the missing data. The experimental dataset consists of 6734 groups of logging data samples. In this paper, we separated the dataset for network training and testing by the size of the data set and general experience. Then, 80% of logging data samples were randomly selected as the training set of FTCN prediction model, and 20% of the logging data samples were selected as the test set.

**Figure 8.** Sedimentary structure characteristics of cored well5. (**a**) retained conglomerate facies; (**b**) trough cross-bedded sandstone facies; (**c**) tabular cross-bedded sandstone facies; (**d**) parallelbedding sandstone facies; (**e**) wavy-bedding siltstone facies; (**f**) massive mudstone facies.

#### *4.2. Evaluation Metrics*

For estimating the prediction effect of FTCN model, mean absolute error (MAE), mean square error (MSE) and root-mean-square error (RMSE) are used as evaluating indicators. The calculation equations are as follows:

$$MAE = \frac{1}{n} \sum\_{i=1}^{n} |\mathcal{Y}\_i - \mathcal{Y}\_i| \,\tag{5}$$

$$MSE = \frac{1}{n} \sum\_{i=1}^{n} \left(\mathcal{y}\_i - y\_i\right)^2,\tag{6}$$

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (\hat{y}\_i - y\_i)^2} \,\tag{7}$$

where *y*ˆ*<sup>i</sup>* and *yi* are the predicted and actual values of the model, respectively, and *n* is the number of samples.

#### *4.3. FTCN Parameter Setting*

#### 4.3.1. Setting *α*

We define *α* in Equation (2). The *α* is a balance factor of the fusional module in the FTCN model, and it is used to weigh the integration with the network layers. Its value represents the integration degree of the network layers. By adjusting *α*, we can better realize the integration of the network layers. In order to study the effect of various *α* for the experimental prediction results, the experimental values of *α* were 0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8 respectively.

As shown in Figure 9, the MSE, MAE and RMSE of the FTCN model in the prediction of three kinds of reservoir parameters can reach lower values when *α* = 1. In the experiment of porosity prediction (shown as the blue line), changes in *α* have little influence on the prediction result except *α* = 1.8 and *α* = 1.6. The FTCN model is relatively stable when *α* <= 1.4. When *α* = 1.8, the errors of porosity, permeability and water saturation become larger in varying degrees, indicating that *α* = 1.8 is not conducive to the prediction of the FTCN model. This shows that the larger the *α* value is, the less the effectiveness of the fusion of different network layers will be. When predicting water saturation, the difference between *α* = 0.2 and *α* = 1 is very small, and when *α* = 1, the FTCN model performs best in permeability prediction. Considering three reservoir parameters, *α* = 1 is the optimal parameter for the FTCN model. In the follow-up experiments, *α* was set to 1.

**Figure 9.** The influence of different *α* on FTCN model.

#### 4.3.2. Verification of Fusional Module

For the sake of verifying the effect of the proposed fusional module, we compared it with the unimproved TCN and AddTCN, ConTCN and AveTCN combined with Add, Concat and Average fusion methods. Among them, Add, Concat and Average are all commonly used methods of network multi-layer feature fusion. In various network models, such as ResNet [44] and FPN [45], add is used to fuse features, while in DenseNet [46], concat is used to fuse features. Experiments were carried out in the prediction of three reservoir parameters that include porosity, permeability and water saturation. Among them,


As shown in Figure 10, the FTCN model is superior to the TCN model in predicting porosity (por), permeability (perm) and water saturation (sw) in MAE, MSE and RMSE. In the experiment of predicting porosity, the predictive result of the FTCN model is obviously better than AddTCN and is very similar to that of ConTCN and AveTCN. When predicting permeability, ConTCN has the best performance, and the evaluation metrics obtained by FTCN are slightly higher than ConTCN but also significantly lower than the TCN and AddTCN models. In the experiment of predicting water saturation, the performance of the FTCN model is superior to other models and achieves the best prediction effect. This may be because the fusional module is more suitable for the information fusion of different layers in the reservoir parameter prediction network compared with other fusional methods.

**Figure 10.** Influence of different fusion methods on the TCN model. (**a**) the MSE; (**b**) the MAE; (**c**) the RMSE.

#### 4.3.3. Influence of Filter Size k and Residual Block

We explore the influence of the filter size (k) and residual block in the FTCN model based on experiments. The effect of porosity predicted by the FTCN model is demonstrated in Figure 11.

**Figure 11.** Effect of different k and residual blocks on FTCN-predicted porosity. (**a**) the MAE; (**b**) the MSE; (**c**) the RMSE.

The MAE reaches the lowest level when *k* = 3 and the residual block exists. The MSE of the model with the residual block is significantly better than that of the model without the residual block when *k* = 3, *k* = 5 and *k* = 7. When looking at the RMSE, the performance is relatively better when *k* = 5, and the model with the residual block also has a better performance.

We also explore the performance of the FTCN model for predicting permeability. As illustrated in Figure 12, this model has the best effect when *k* = 3, and the performance of this model with the residual block is better as a whole.

**Figure 12.** Effect of different k and residual blocks on FTCN predicted permeability. (**a**) the MAE; (**b**) the MSE; (**c**) the RMSE.

We also explored the experiment of the FTCN model for predicting water saturation. As shown in Figure 13, when *k* = 3, the model performs better than *k* = 5 and *k* = 7 on MAE, MSE and RMSE, and the model with the residual block is better than the FTCN model without the residual block.

**Figure 13.** Influence of different k and residual blocks on FTCN-predicted water saturation. (**a**) the MAE; (**b**) the MSE; (**c**) the RMSE.

From the above experiments on the FTCN model predicting porosity, permeability and water saturation, it can be seen that the prediction effect of the model with *k* = 3 and the residual block is better. That is because it avoids the degradation of the very deep network and advances the effect of the network.

#### *4.4. Influence of Input Logging Curves*

For the purpose of estimating the validity of the optimized logging curves used for the reservoir parameter prediction, the effects of different input logging curves on the experimental prediction results are explored.

In logging interpretation, permeability is related to porosity, and the commonly used three-porosity logging includes acoustic travel time, density and compensated neutron logging curves. Acoustic logging mainly measures the time difference of formation sliding waves. Using the interaction between gamma ray and formation, density logging can reflect the formation porosity by measuring the gamma count of gamma rays emitted by the source and arriving at the detector after one or more scatterings through the formation. The compensated neutron logging mainly reflects the deceleration ability of the formation to fast neutrons and shows the change of hydrogen content in the formation. They have different responses in different formations, are closely related to the determination of porosity, and have great advantages in calculating porosity, permeability and fluid properties. In addition, natural gamma ray and spontaneous potential curves are also often used to assist calculation. Natural gamma logging measures natural radioactivity in strata. Spontaneous potential logging is used to measure the variation of the potential naturally generated on the shaft with depth in an open hole so as to study the stratigraphic properties of the well profile. In the permeability prediction experiment, we split all the input logs into three different input log sets. Among them,


As shown in Figure 14, compared with Curve\_ Set1, the prediction error of the Curve\_Set2 experiment is significantly lower in MSE and RMSE. The results of MAE, MSE and RMSE of Curve\_Set3 are all optimal, but it performs significantly better than Curve\_Set1 and slightly lower than Curve\_Set2. The reason may be that Curve\_Set3 is very similar to the Curve\_Set2, except that Curve\_Set3 has several additional high-definition induction logging curves of different feet, which are very similar to the M2R10 logging curve in Curve\_Set2. In practical applications, it can be considered to reduce the cost of logging by removing the high-resolution array induction logs of different feet and retain only the M2R10.

**Figure 14.** Comparison of different logging input sets.

#### *4.5. Comparison of Methods*

For the purpose of estimating the effectiveness of the FTCN prediction method proposed in this paper, a series of comparative experiments are carried out to compare the proposed FTCN with LSTM, GRU and unimproved TCN. In our experiments, we employed the adaptive learning rate RMSProp algorithm to optimize the network. The initial learning rate was set to 0.001, and batch size the batch size was set to 32 to predict reservoir parameters such as porosity (POR), permeability (PERM) and water saturation (SW).

We used 20% of the logging data samples to test, and the results are shown in Table 1. The RMSE of the FTCN model in porosity prediction is 0.23, 0.19 and 0.13 lower than the LSTM, GRU and TCN models, respectively. For the purpose of estimating the effect of the FTCN prediction model on different reservoir parameters, the FTCN model is used to predict permeability and water saturation. The MAE, MSE and RMSE of the FTCN model reach 0.12, 0.06 and 0.24, respectively. The MAE, MSE and RMSE predicted by the FTCN model are 0.08, 0.03 and 0.16, respectively, and the RMSE is 0.25 and 0.2 lower than the LSTM and GRU model, respectively. The possible reason is that the FTCN model's fusional module considers the effects of different network layers and learns more accurate response relationships comprehensively. It can make better use of logging curves; thus, it achieves better performance than other methods. Compared with LSTM, GRU and TCN models, the FTCN model has a more accurate prediction effect and stable performance in the prediction of different reservoir parameters.

**Table 1.** Prediction performance of four models in three reservoir parameters.


Figures 15–17 show the experimental results of reservoir parameters predicted by the four models, respectively. It can be seen that the LSTM and GRU models can predict the parameter values at different depths of the reservoir roughly, but there is a prediction deviation in the detailed value of the curves. The prediction performance of TCN is better than the former, but the problem is still not solved. The FTCN model more accurately reflects the slight fluctuations in the curve, and its prediction results are more consistent with real reservoir conditions. This may be because of the design of the unique fusional module in FTCN, which makes it achieve better results than other methods. In addition, as shown in Figure 15, the lower parts of the well section are water-flooded layers, and the upper part is a mudstone section, which reflects the characteristics of this area.

**Figure 15.** Contrast of permeability prediction of distinct models.

**Figure 16.** Contrast of porosity prediction of distinct models.

**Figure 17.** Contrast of water saturation prediction of distinct models.

#### **5. Conclusions and Future Works**

Reservoir parameter prediction is exceedingly significant in petroleum exploration and development. Predicting reservoir parameters effectively can provide a reference for analyzing reservoir properties and assist interpreters in evaluating oil and gas reservoirs. In this paper, a reservoir parameter prediction method named FTCN is proposed. Firstly, a fusion module is designed to fully exploit the nonlinear mapping on curves by using data information of different network layers, which makes our method more sensitive to the relationship between logging curves and reservoir parameters. Secondly, we design the structure of the FTCN. Dilated causal convolution and residual connection are taken, which expands the receptive field of the network so that the effective information obtained is richer and the model is more stable. At last, experiments on real logging datasets show that the prediction results of FTCN are more consistent with the real formation conditions in reservoir parameter prediction, even if there are great changes in stratus. Therefore, our work can provide a reference for well interpreters to analyze reservoirs.

The reservoir parameter prediction effect may be improved by selecting representative and sensitive curves. In the future, we will conduct research in many different exploration areas, and further study the improved reservoir parameter prediction method by considering the curve quality improvement and the response curve selection strategy to improve the prediction effect under poor geological environments and imperfect well data. Additionally, we will explore whether considering the mixed application of multiple models for different strata can further enhance the anti-interference ability to improve the prediction effect.

**Author Contributions:** Conceptualization, H.Z. and K.F.; methodology, H.Z.; software, K.F.; validation, Z.L., Z.W. and J.S.; formal analysis, Z.L.; investigation, K.F.; resources, H.Z.; data curation, H.Y.; writing—original draft preparation, K.F.; writing—review and editing, H.Z., H.Y. and X.G.; visualization, Z.L.; supervision, Z.W.; project administration, J.S.; funding acquisition, H.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by The Major Scientific and Technological Projects of CNPC (No. ZD2019-183-004), The Fundamental Research Funds for the Central Universities (No. 20CX05019A) and Sponsored by CNPC Innovation Found (2021DQ02-0402).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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