Influencing Factors of Drainage and Production and Quantitative Evaluation in Shale Gas Reservoirs

Abstract

As a transitional energy source, natural gas plays a crucial role in the energy transition. In the efficient development of shale gas, the drainage and production process, as an important link between hydraulic fracturing and production, determines the recovery rate of individual wells. To clarify the main controlling factors of shale gas drainage and production, provide strategies for classification, and improve the recovery rates of individual wells, a numerical simulation method was proposed to analyze the factors affecting drainage and production, and the VIKOR method was used for quantitative evaluation of the drainage and production effects. The research results showed that: (1) The study identified nine main controlling factors affecting drainage and production performance, including gas saturation, permeability, stress difference, burial depth, formation pressure, cumulative fracture volume, final fracture loss rate, average final diversion ability, and wellbore liquid loading. (2) A workflow for quantitatively evaluating the drainage and production effectiveness of shallow shale gas wells and selecting wells with potential for optimized drainage and production was proposed. The correlation between the evaluation results and EUR fitting had an R² value of 0.71, indicating a good level of credibility. (3) The evaluation results for the target gas field indicated that out of the 16 representative wells, 12 wells have optimization potential, with 5 wells showing significant optimization potential. Studying the rules of shale gas drainage and production and evaluating the drainage and production effects can help us to propose refined drainage and production strategies, which are essential for improving the estimated ultimate recovery (EUR).

1. Introduction

Modern energy development has reached a crucial moment of transition from fossil fuels to renewable energy sources, and natural gas plays a transitional role in this conversion [1,2,3,4]. It serves as a major driving force for achieving sustainable development. In recent years, China has made significant breakthroughs in the efficient development of shallow shale gas [5,6,7,8]. From the hydraulic fracturing experience of shale gas, it can be observed that the drainage and production plan implemented after fracturing can have a significant impact on the fracturing effectiveness [9]. Compared to the low flowback rates and high production of deep shale gas [10,11], shallow shale gas reservoirs commonly exhibit low pressure, low initial production, and high flowback rates [12]. Within the same block, wells with similar geological conditions can exhibit significant differences in flowback rates and production capacities. Therefore, studying the drainage and production patterns of shallow shale gas and evaluating the drainage and production effectiveness are helpful in formulating refined drainage and production strategies based on different categories, which plays an important role in improving the estimated ultimate recovery (EUR).

In the past, numerous scholars have conducted extensive research on factors influencing flowback in drainage and production. In the 1980s, scholars had already begun studying the influence of properties such as capillary force and relative permeability on flowback. The results showed that the flowback process is significantly affected by permeability, pressure drop, and capillary pressure [13]. After years of research, scholars have found that the impact of factors such as relative permeability, capillary pressure, stress-sensitive fracture conductivity, invasion-zone permeability damage, skin factors, fracture complexity, matrix and fracture permeability, and drawdown on the flowback efficiency should not be overlooked [14,15,16,17,18]. During the drainage and production processes, wellbore liquid loading can also increase the difficulty of gas production. Nari et al. pointed out that when wellbore liquid loading is severe, it can lead to a displacement in liquid production until the liquid phase decreases and the flow regime changes, resulting in the resumption of gas production in the wellbore [19]. Despite numerous studies by scholars on the factors affecting flowback and production, there has been a lack of comprehensive consideration of the factors affecting the matrix–fracture–wellbore system. A systematic investigation is advantageous in clarifying the primary controlling factors influencing flowback and gas production processes, ultimately leading to increased production.

Numerical simulation is an important method for obtaining hydraulic fracture parameters and simulating the drainage and production effectiveness. Alkouh et al. [20,21] first established a single-medium model based on the equivalent porous media theory, which designed high-conductivity fractures using local grid refinement method. This model can simulate field conditions by setting pore-permeability characteristics in the local grid to represent the actual situation. However, due to its simplicity, this model cannot simulate capillary forces, post-fracture saturation fields, and other conditions. The flowback model developed by Zhang et al. [22] considers stress sensitivity factors and incorporates multiple natural fractures to account for their influence on flowback. They subsequently proposed a boundary-controlled flow model for analyzing water and gas flowback data. This model can be used to calculate fracture half-length, permeability, and elastic modulus. Wang et al. [23] proposed a simple iterative method to address the non-linear characteristics of hydraulic fracturing problems. Xu et al. [24,25] developed the Closed-tank model, which considers gas and water expansion as well as fracture closure, based on the material balance method. They also introduced the Open-tank model as an extension to the Closed-tank model, which additionally accounts for matrix water and gas production. Previous studies have focused extensively on establishing equivalent fractures and conducting production capacity simulations. However, they have overlooked the significance of combining pre-fracturing prediction and post-fracturing production parameters to better obtain hydraulic fracture parameters for more accurate production capacity simulations. Therefore, it is necessary to conduct relevant research in this area.

The strategies for shale gas drainage and production mainly focus on three aspects: well shut-in, pressure control production, and reduction of wellbore liquid. Lan et al. [26] conducted extensive spontaneous imbibition experiments to address the phenomenon of low flowback rates observed in the field. They found that spontaneous imbibition can reduce the flowback rate. Subsequently, Bertoncello et al. [27] simulated the injection and flowback processes of hydraulic fracturing fluids. The study revealed that extending the shut-in time after fracturing significantly increases the initial gas production rate and reduces the flowback rate of the fracturing fluid. In 1988, Robinson et al. [28] proposed that the closure pressure of fractures is mainly influenced by the nozzle size and presented a low-flowback model focusing on controlling the flowback rate. Subsequently, based on the model’s characteristic of reducing fracture closure stress, the theory of “early low-flowback” was developed [28]. Coleman et al. [29] suggested that low-pressure gas wells do not require a 20% flowrate correction like high-pressure gas wells and proposed a spherical droplet model. Scholars such as Nosseir et al. [30] found that the Reynolds number has a certain influence on the critical liquid carrying velocity in gas wells and proposed models within different Reynolds number ranges. Li et al. [31] observed that droplets in high-speed gas flows are elliptical in shape, leading to the development of an elliptical droplet model. Scholars have conducted numerous studies on drainage and production strategies, but there has been limited research on quantitative evaluation of drainage and production effects. Since quantitative evaluation of drainage and production effects is conducive to guiding the implementation of drainage and production strategies, research in this area is of considerable importance.

This paper is based on the geological exploration, reservoir transformation, and initial gas production data from different structurally producing wells in the T gas field’s shallow shale gas reservoir. It considers the matrix–fracture–wellbore system and relies on an integrated geological engineering numerical simulation platform, with the optimization objectives of unit pressure drop production and initial gas flowback rate. This paper studies the drainage and production patterns of different fabrics and depths, analyzes the influence of multiple parameters on the shallow shale gas drainage and production patterns, and quantitively judges the drainage and production effectiveness of the targeted well, aiming to provide suggestions for production approaches.

2. Background

2.1. Geological Settings

The T Gas Field has a complex geological structure, consisting of two east–west trending anticlines and three synclines. Faults and microfractures are well developed, and the reservoir characteristics mainly include shallow burial, low pressure, thin target bodies, and good quality [7]. This gas field has favorable accumulation conditions and reservoir space (with an average porosity of 4% and a target layer total organic carbon (TOC) greater than 2 wt.%) [32]. It has a high gas content (with an average greater than 2.5 cm³/g) and exhibits good brittleness and compressibility [33,34].

The target wells are mainly distributed within anticline A, syncline B, and anticline C, at depths ranging from 500 m to 2000 m. The block exhibits well-developed and well-sealed faults, and the target layers are generally well-preserved. The overall thickness of the reservoir ranges from 32 m to 45 m, with a slightly lower thickness of 35 m in anticline C. The dominant formation has a porosity of 3.5 wt.% to 5.1 wt.% and a gas content ranging from 1.1 m³/t to 5.1 m³/t. The TOC content ranges from 3.1% to 4.3%. Based on on-site gas field data, the reservoir in this area is primarily categorized as Type I, with fewer Type II and Type III reservoirs. The reservoir quality is generally good, with the thickness of Type I + II reservoirs following the order of anticline A > anticline C > syncline B. The formation pressure, stress, and stress difference show significant variations with depth.

2.2. Drainage and Production Characteristics

Compared to deep shale gas, shallow shale gas exhibits the following characteristics: longer average gas indication time by 99%, lower gas indication pressure by 24%, lower trial gas production by 54%, and higher gas flowback rate by 114%. Therefore, shallow shale gas in the T field demonstrates the features of low pressure, low gas production, and high flowback. A comparison of the drainage and production characteristics of both is shown in Figure 1.

Reservoir energy is a geological attribute that characterizes the drainage and gas production capacity, including the natural energy of the formation and the energy added by hydraulic fracturing. It is represented by the gas production per unit of pressure drop.

We conducted a statistical analysis of the unit pressure drop production of 28 wells in the T field and 36 wells in a deep shale gas reservoir. The results showed that the unit pressure drop production in the T field ranged within 120 m³/MPa, while for the latter, it ranged from 29 to 249 m³/MPa. Due to the shallow burial depth, shallow shale gas exhibits low reservoir energy and low wellhead pressure.

The flowback rate during the drainage and production process is one of the key parameters that reflects the effectiveness of the drainage and production. The flowback rate in the first 15 days can indicate the speed of flowback. In the typical wells of T Gas Field’s shallow shale gas reservoir, 67% of the wells have higher flowback rates in the first 15 days compared to the deep shale gas wells, indicating a faster flowback speed. An analysis of flowback speeds was conducted on 16 shallow shale gas wells, revealing that 4 wells exhibited fast flowback rates, sand production, and shorter fracture lengths. During the early stage of flowback, excessively high flowback speeds can result in a significant production pressure difference near the fractures, causing rapid fluid flow within the fractures and leading to sand production. As a result of sand production, there is a loss of effective fractures, so compared to normal fractures, the half-length of effective fractures in wells with sand production is relatively shorter, ultimately indicating the occurrence of sand production and fracture closure in shallow shale gas reservoirs.

Due to the lower reservoir energy and poor liquid drainage capacity in shallow shale gas formations, there is a possibility of inadequate gas-phase flow velocity in the wellbore, leading to the inability to carry liquids. The continuous liquid carry formula for gas wells [35] is used to assess the liquid accumulation in the wellbore. When the actual production rate falls below the critical liquid carry rate, liquid accumulation occurs. The calculation results for 16 typical wells in the T Gas Field indicate that 6 wells experienced wellbore liquid accumulation issues. Wellbore liquid accumulation occurs when the initial stable production rate is too low to reach the critical liquid carry rate, and this liquid accumulation phenomenon in turn negatively impacts the production rate.

3. Numerical Simulation Methods

In order to address the challenges of low reservoir energy, proppant flowback, easily closed fractures, and liquid accumulation in the drainage and production process of shallow shale gas in the T Field, a numerical simulation method was proposed to analyze the controlling factors of drainage and production. This method mainly involves two processes: model establishment and analysis of influencing factors. The key steps in the numerical simulation include: (1) Establishing a heterogeneous geological model based on well logging interpretations, fault information, and other data; (2) predicting hydraulic fracture propagation by field fracturing parameters and correcting fracture properties using fracturing construction curves; (3) generating unstructured grid and building models of relatively permeability, adsorption gas, stress sensitivity, and fitting production capacity, as well as correcting the geological properties by using production data, finally achieving a geological model building which can truly reflect the targeted block properties; and (4) analyzing the influencing factors based on the above situations.

Due to the hydraulic fracture propagation and productivity simulation being based on the Petrel platform, the numerical simulation process needs to adhere to the relevant assumptions of the UFM model and productivity simulation: ① All fractures in the model are assumed to be vertical fractures; ② the fracturing fluid is assumed to exhibit laminar flow behavior as a power-law fluid within the planar (fracture) structure; ③ the model assumes that the non-stimulated area consists of a single matrix pore, while the volume-stimulated area is composed of a matrix system and a fracture system; ④ it is assumed that during the initial flowback period, the fractures contain single-phase liquid flow.

3.1. Establishing a Three-Dimensional Geological Model

A heterogeneous reservoir quality and geomechanical model was established based on basic information of the wells and the interpretation results of well logs in the gas field. The geological model, as shown in Figure 2, incorporated information on natural fractures. The grid precision was set at 50 m× 50 m, with a vertical grid precision of 1 m. Based on the field logging data of the gas field, a geological model was established. The basic information range of this model is presented in

Table 1. Average properties of the target formation.

Property	Range	Property	Range
formation thickness, m	32~45	Young’s modulus, GPa	23.6–37.4
Porosity, %	1.8–7.3	Poisson’s ratio	0.1–0.2
permeability, mD	0.0001–0.05	maximum horizontal principal stress, MPa	7.9–27.8
gas saturation, %	28.7–82	stress difference	2–11.3
gas content, m3/t	0.7–6.4	pressure coefficient	1.1–1.5

.

3.2. Hydraulic Fracturing Simulation

Due to the challenge of accurately acquiring fracture attributes, it is necessary to comprehensively analyze them using methods such as deep learning [36] or numerical simulation [22,37]. Here, numerical simulation methods are employed for the study of hydraulic fractures. A three-dimensional geological model is established based on the Petrel platform. The hydraulic fracturing data, microseismic data, and fracturing construction curves used in the numerical simulation were all derived from the design, construction, and measurement data of the target well. The complex fracture distribution was simulated using the field fracturing plan, and the fracture and geological parameters were corrected using microseismical data, fracturing construction curves, and closed-tank models. By considering parameters such as capillary forces, stress sensitivity, and relative permeability of the matrix, the reservoir properties were calibrated by fitting them with the production history of corresponding wells, thereby establishing a calibrated three-dimensional geomechanical model. The calibrated model was then used to study the impact of different hydraulic fracture attributes on drainage and production, and the influencing factors were analyzed and characterized using the Pearson correlation coefficient method.

Accurate simulation of post-fracturing hydraulic fracture distribution is the basis for studying drainage and production effectiveness, and determines the reliability of numerical simulations. Due to the development of natural fractures in shale reservoirs, simulating the interaction between natural fractures and hydraulic fractures is essential for accurately obtaining the post-fracture morphology. Compared to other propagation models such as discrete fracture network models, the unified fracture model (UFM) takes into account factors such as fluid–solid coupling, interactions between hydraulic and natural fractures, and stress interference, which more reliably reflects the post-fracture morphology [38,39]. This study establishes a method for simulating post-fracture fracture distribution based on the UFM combined with the fracturing construction curve and the closed-tank model. The UFM model was used to predict the post-fracture fracture morphology, while the fracturing construction curve was employed to correct stress, Young’s modulus, and frictional resistance during the fracturing process. The closed-tank model, based on production data, was utilized to correct fracture attributes. Compared to microseismical monitoring, this method does not require additional time and cost, making it more practical and applicable.

The closed-tank model [24,25] is based on the mass balance equation and assumes the initial dynamics of drainage and production as a closed system. This model assumes that the initial drainage and gas production come from fracture closure, as well as the expansion of water and gas, without water and gas from the matrix entering the fractures. Since this process primarily occurs in the early stages of drainage and production, the data for this model are relatively easier to obtain.

Taking well Y7 as an example, the horizontal section of the well was 516 m long, divided into seven segments with three to nine clusters per segment. Through the application of this model, the final average fracture length was calculated to be 269 m, with an average fracture height of 43 m. A comparison with on-site microseismical detection data showed that using the traditional UFM model combined with the fracturing construction curve resulted in an average deviation of 50.89 m for fracture length and an average deviation of 4.6 m for fracture height. After fitting with the closed-tank model, the average deviation for fracture length was 24.89 m, and the average deviation for fracture height was 2.29 m. Compared to the microseismical detection results, this method demonstrates a higher level of accuracy, as shown in Figure 3.

3.3. Establishing a Drainage and Production Model

In a reservoir numerical simulation, it is necessary to characterize hydraulic fractures. The unstructured grid auto-generation technique proposed by Cipolla et al. [40] was used to divide the output results of complex fractures generated by the UFM model into grids. This method not only achieves the characterization of complex fractures, but also inherits the non-uniform distribution of fracture conductivity. At the same time, the local refinement method was employed to reduce the disparity in grid sizes near the fractures. This approach simultaneously reduces the number of grids, guarantee the flow characteristics in the vicinity of fractures, and ensures numerical convergence. We adopted a model segmentation approach to control the number of grids. The number of grid cells for a single well ranged between 100,000 to 200,000, and the generated locally refined unstructured grids are shown in Figure 4.

Due to the existing numerical models, the distribution of fracturing fluid in the fractures and matrix is not accurately depicted; therefore, the phenomenon of early high-water production during flowback cannot be effectively simulated. Thus, it is necessary to establish a stress-sensitive model for the fractures and matrix which simulates the distribution of the fracturing fluid and pressure field in the fractures and matrix after the completion of hydraulic fracturing by simulating the injection process of fracturing fluid. Additionally, the model needs to consider properties such as PVT (pressure–volume–temperature) behavior, relative permeability, capillary forces, and gas adsorption [41]. Due to the secondary development capabilities of the numerical simulation platform, we only need to input the established PVT and stress-sensitive models to achieve the optimization of numerical simulations.

In natural gas production, the reservoir properties undergo changes due to the decline in reservoir pressure, which adversely affects the productivity. Scholars have extensively studied the stress sensitivity of permeability in shale through laboratory experiments or productivity simulations. The stress sensitivity of shale is calculated using the expression for stress-sensitive matrix permeability [22,42,43], as shown in Equation (1).

$$k_m=k_{mo}\ast e^{-b\mathsf{\Delta }P}$$

(1)

In the formula, $k_m$ is the matrix permeability; $k_{mo}$ is the initial matrix permeability; $\mathsf{\Delta }P$ is the pressure difference; and $b$ is the stress sensitivity constant of the matrix, with a value of 0.066 MPa⁻¹. The calculation results are shown in Figure 5.

The stress sensitivity of hydraulic fractures differs from that of the matrix and mainly includes stress sensitivity during the fracturing and closure stages. During the fracturing fluid injection stage, as the fluid pressure is transmitted to the reservoir with the injection of fracturing fluid, artificial fractures begin to form when the fluid pressure exceeds the fracturing pressure. Currently, the pore-permeability characteristics of the fractures change with the net pressure difference. When the net pressure difference is positive, the fracture aperture increases, and the pore-permeability characteristics improve. During the shut-in and flowback stages, as the fracturing fluid is lost and flows back, the net pressure within the fractures decreases. Once it falls below the closure pressure, fractures start to close. Due to factors such as fracture proppant embedment, the fractures maintain a certain aperture, and the pore-permeability characteristics cannot fully recover to their initial state. This phenomenon is even more pronounced in the presence of proppant, as shown in Figure 6a.

Combining the field data from the T gas field, the changes in porosity and permeability during the fracture initiation stage were calculated using empirical formulas (2) and (3) [34]. The calculated results were then normalized, with the maximum value representing the porosity and permeability when the fracture initiation degree was at its maximum. The computed results are shown in Figure 6b.

$$\frac{{\varphi }_f}{{\varphi }_{f0}}=e^{C_{fi}P}$$

(2)

$$\frac{K_f}{K_{f0}}={10}^{m_{i}P}$$

(3)

In the formula, ${\varphi }_f$ represents porosity; ${\varphi }_{f0}$ represents initial porosity; $P$ represents pore pressure; $C_{fi}$ represents the compressibility factor during the fracture propagation stage; $K_f$ represents permeability; $K_{f0}$ represents initial permeability; and $m_i$ represents the permeability variation coefficient, which is taken as 6.67 × 10⁻² MPa [43].

Prior to flowback prediction, it is necessary to simulate the fracturing injection process on the reservoir model to reflect the saturation and pressure distribution prior to flowback. Based on the previously established stress sensitivity model for fractures, this module can be further developed to simulate the opening of complex hydraulic fracture networks and the closure of the fracture system in subsequent shut-in and flowback processes.

Based on the established base reservoir model, the entire process of fracturing fluid injection, well shut-in, and flowback was simulated. By continuously adjusting the stress sensitivity curves of fractures, the numerical simulation results were matched with historical data. As shown in Figure 7, the fitting results were favorable.

4. Analysis of Key Factors Controlling Drainage and Production Effectiveness

Studies by researchers [13,14,15,16] have shown that the factors influencing the drainage and production effectiveness of shale gas can be categorized into three main aspects: (1) Matrix factors: capillary pressure, relative permeability, permeability, pressure, stress sensitivity; (2) fracture factors: fracture complexity, fracture permeability, pressure drop; and (3) wellbore factors: wellbore liquid accumulation, etc. This paper analyzes the influencing factors of drainage and production from three perspectives: reservoir quality and geomechanics, hydraulic fracture properties, and wellbore fluid drainage.

4.1. Reservoir Quality and Geomechanics

4.1.1. Simulation Plan

The drainage and production process includes two stages: water drainage and gas production, which are represented by the gas indication flowback rate (GIFR) and gas production per unit of pressure drop (GUPD), respectively. We based our study on field logging data to construct a three-dimensional geological model. We extracted reservoir quality and geomechanical information from the model. Production and drainage data were collected from field gas well output statistics. The Pearson correlation coefficient method was used to compare the correlation between the mean values of target layer attributes and the two flowback parameters in order to assess the impact of each attribute on the flowback effectiveness.

Reservoir-related attributes include burial depth, gas content, organic matter content, gas saturation, permeability, and porosity. Geomechanical attributes include maximum principal stress, minimum principal stress, stress difference, Young’s modulus, Poisson’s ratio, and formation pressure. Due to strong correlations among multiple attributes, the evaluation results may be redundant, affecting the quantitative calculations of the evaluation method. After screening, nine parameters, including burial depth, porosity, permeability, gas saturation, maximum principal stress, stress difference, Young’s modulus, Poisson’s ratio, and formation pressure, were selected for analysis.

4.1.2. Results Analysis

The analysis results are shown in Figure 8. Taking into account the correlation with the gas indication flowback rate and the water production per unit of pressure drop, the ranking of influencing factors was as follows: gas saturation > permeability > stress difference > burial depth > formation pressure > in-situ stress > Young’s modulus > porosity > Poisson’s ratio. Wells with high gas saturation had a better imbibing displacement effect during the shut-in period, resulting in early gas indication and a lower flowback rate. Wells with high permeability had good flow channels for fluid flow and strong liquid absorption capacity, resulting in lower water production during flowback. Therefore, gas saturation, permeability, stress difference, burial depth, and formation pressure were identified as the main controlling factors.

4.2. Fracture Factors

The impact of hydraulic fracturing effectiveness in shale gas horizontal wells on production and recovery is crucial. The quality of fracture distribution directly affects the flowback performance and the ultimate estimated ultimate recovery (EUR). Fractures can be classified into hydraulic fractures and natural fractures, with the focus of this study mainly on the influence of hydraulic fracture properties on production and recovery. The key properties of hydraulic fractures include fracture length, width, height, volume, average conductivity, and ultimate fracture loss rate.

The T Gas Field has a complex geological structure with developed folds and faults, and a maximum burial depth difference of over 1000 m. The formation dip angle in the working area is complex and varies greatly, ranging from 0° to 40°. There is a significant variation in gas content, ranging from 0.67 m³/t to 6.35 m³/t. Traditional fracture estimation methods cannot accurately calculate the properties of artificial fractures. Therefore, numerical simulation methods will be used for hydraulic fracturing to establish fractures with different attributes. Firstly, a refined geological model will be established to capture the complex geological features of the T Gas Field. Subsequently, different fracture properties will be simulated to determine the impact of hydraulic fracture attributes on drainage and production. Then, the influence of the hydraulic fracture properties on the drainage and production will be determined.

4.2.1. Simulation Plan

Based on the integrated geological and engineering simulation process mentioned above, we devised various construction scenarios. The corresponding fracture parameters for each scenario are presented in

Table 2. Crack simulation scheme.

Case	Average Fracture Length/m	Average Fracture Height/m	Cumulative Fracture Volume/m3	Average Conductivity/mD·m	Fracture Loss Rate/%
1	125.51	26.91	3750.09	84.30	0.56
2	113.85	27.30	1764.12	103.42	0.52
3	144.47	25.15	2247.19	100.74	0.54
4	119.41	26.46	2583.40	89.47	0.58
5	163.34	24.37	3957.63	78.98	0.54
6	106.34	30.67	4219.11	150.08	0.51
7	169.60	26.68	4848.84	66.10	0.44
8	110.88	27.77	3300.00	121.17	0.62
9	101.52	27.16	2942.36	106.21	0.66
10	111.11	30.41	2613.04	117.38	0.47
11	109.28	29.85	3350.92	86.24	0.61
12	136.72	25.89	3904.56	94.52	0.55

. The fracture parameters in the simulation results of fracture propagation are represented using the following methods: (1) the average fracture length was the arithmetic mean of the lengths of fractures in each cluster of a single well; (2) the cumulative fracture volume was the sum of the volumes of fractures in each cluster of a single well; (3) the average fracture height and average conductivity were the weighted averages of the heights and conductivity of fractures in each cluster of a single well; and (4) the fracture loss rate was the volume of the closed part of the fracture divided by the initial fracture volume. The average fracture length in the simulation results for each scheme ranged from 101.52 m to 169.6 m; the average fracture height ranged from 24.37 m to 30.67 m; the cumulative fracture volume ranged from 1764.12 m² to 4848.84 m²; the average final conductivity ranged from 66.1 mD·m to 150.08 mD·m; and the final fracture loss rate ranged from 0.44 to 0.66.

Based on the simulation results of the 180-day production capacity for each scenario, it can be observed that there was not a strong correlation between cumulative gas production and cumulative water production, as shown in Figure 9. Case 1 had a higher water production than Case 12, but the latter had a higher gas production than the former. Meanwhile, Case 2 and Case 10 exhibited much lower water and gas production compared to other cases. Due to the complex correlation between the cases, direct analysis of their correlation was not feasible. Therefore, the Pearson correlation coefficient method needed to be employed to analyze the degree of influence of various factors on the drainage and production effectiveness.

4.2.2. Results Analysis

Using the Pearson correlation coefficient methods, the correlations between various factors and the optimization objectives of unit pressure drop production and gas indication flowback rate were calculated. The results, as shown in Figure 10, indicate the degree of impact of each factor on the drainage and production performance: cumulative fracture volume > fracture loss rate > conductivity > average fracture height > average fracture length. The cumulative fracture volume could, to some extent, reflect the parameters of fracture height and fracture length. The fracture loss rate affected the effective fracture volume after closure, and conductivity influenced the efficiency of gas–liquid flow within the fractures. Therefore, the main controlling factors selected were the cumulative fracture volume, final fracture loss rate, and conductivity due to their higher degree of impact.

4.3. Wellbore Liquid Loading

After injecting a certain volume of fracturing fluid into shale gas reservoirs, the permeability will be reduced to some extent. The presence of liquid accumulation in the wellbore causes an increased pressure gradient, leading to declining production and significantly impacting the single-well EUR. The phenomenon of wellbore liquid loading during the drainage and production process occurs when the gas flow rate in the wellbore falls below the critical liquid carrying rate, preventing effective fluid flowback and resulting in liquid accumulation. Nari et al. pointed out that the process of wellbore liquid loading includes the following stages: ① When the reservoir energy is low, the gas flow rate in the wellbore is below the critical liquid carrying rate, leading to liquid accumulation in the low bottomhole pressure areas; ② as the liquid accumulation in the wellbore increases, it starts to affect gas production, eventually leading to liquid production only; ③ wellbore liquid loading has a severe shut-in effect, causing an increase in bottomhole pressure; ④ when the wellbore pressure reaches the gas lift pressure, liquid is produced from the wellbore, and as the liquid accumulation decreases, gas breakthrough occurs, and gas production resumes; ⑤ continuous production leads to insufficient gas flow rate, and the above steps are repeated [19].

The VFP table can reflect the correlation between production rate, water–gas ratio, wellhead pressure, and bottomhole flowing pressure. Under the same production rate and bottomhole flowing pressure, a higher water content in the wellbore leads to lower wellhead pressure, as shown in Figure 11a. When the flow rate is constant, wellbore liquid loading results in increased water content, higher pressure gradient in the wellbore, and lower wellhead pressure, as depicted in Figure 11b. Therefore, the degree of wellbore liquid loading is one of the key controlling factors affecting drainage and production. Closing the well helps to increase the wellhead pressure, allowing for higher flow rates and improved liquid-carrying capacity. Hence, adopting intermittent production methods contributes to enhancing the liquid drainage capability and reducing wellbore liquid loading.

5. Field Evaluation Methods for Drainage and Production Effectiveness

To address the issues in the production and drainage of shallow shale gas, combining the results of the parameters’ correlation, a systematic process for quantitatively evaluating the effectiveness of gas well production and drainage was proposed. By quantifying the various influencing factors and representing them numerically, an evaluation was conducted to assess the performance and categorize the production and drainage effectiveness of each well.

5.1. Drainage and Production Effect Evaluation Process

In order to identify the main influencing factors in an individual well and to quantitatively evaluate the production and drainage effectiveness of the T Gas Field, a comprehensive evaluation process for production and drainage effectiveness was proposed based on the analysis of the key controlling factors discussed earlier (see Figure 12). This evaluation process aimed to assess and classify the target wells in the field and provide targeted optimization solutions for production and drainage.

The process began with the input parameters for the model, including the reservoir’s geological parameters, well parameters, and gas testing data. These parameters were used to establish a three-dimensional geological model, simulate fracture propagation, and predict productivity. The Pearson correlation coefficient method was applied to analyze the correlation among various factors in the model’s calculation results. Finally, the VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method was used for compromise calculations to obtain comprehensive and individual index analysis results for each well. The VIKOR method was used for decision-making problems involving multiple criteria. It assisted in finding the optimal compromise solution under the influence of multiple factors.

5.2. Parameter Calculation Data Analysis

5.2.1. Parameter Acquisition

Due to the heterogeneity of the reservoir, it was unable to input complete geological information into the model for calculation. Therefore, certain techniques needed to be employed to express the varying attribute information of various well locations in order to obtain characteristic values of the corresponding attributes near the well locations. Firstly, heterogeneous geological modeling was performed, and then the average values of the corresponding well locations and main layers were taken to obtain a more reasonable representation of the geological properties. The established heterogeneous geological model is shown in Figure 2. The basic reservoir quality parameters of 16 shale gas wells in the T Gas Field were obtained.

Obtaining accurate information regarding the actual distribution of hydraulic fractures is challenging. Therefore, a three-dimensional geological model was established, and the fracture properties were calculated by combining the construction curves, closed-tank model, and microseismical data. The fracture volume was obtained by summing up the cumulative hydraulic fracture volume of the horizontal wells. The calculation results varied significantly due to the different lengths of the horizontal sections and the clustering results of each well, ranging, approximately, from 7020.4 m³ to 25514.60 m³. The conductivity was calculated as the average conductivity, considering the cases in which some clusters may not have been fully open, resulting in relatively lower average values. The average conductivity ranged from 70.24 mD·m to 150.35 mD·m. The fracture loss rate represented the initial loss rate during flowback, ranging from 35.20% to 71.65%.

The calculation of the wellbore liquid loading degree was based on the minimum critical liquid carrying rate formula established by Pan et al. [44]. This formula considers the droplet diameter, droplet deformation, and their impact on surface free energy. Compared to the Turner model, it provides a smaller critical liquid carrying velocity and is closer to the actual situation. The calculation method for the minimum critical liquid carrying velocity is shown in Equation (4).

$$v=\frac{6.89K}{(K^3+2)\sqrt{C_D}}{[\frac{\sigma ({\rho }_L-{\rho }_g)}{{\rho }_g^2}]}^{0.25}$$

(4)

In the equation, v represents the fluid velocity, $K$ is the droplet deformation parameter, $C_D$ is the droplet drag coefficient, σ is the interfacial tension between gas and liquid, ${\rho }_L$ is the fluid density, and ${\rho }_g$ is the gas density.

The formula for calculating the minimum critical liquid carrying rate is shown in Equation (5).

$$q_{sc}=2.5\times {10}^8\frac{Apv}{ZT}$$

(5)

In the formula, $q_{sc}$ is the minimum critical liquid carrying rate, $A$ is the cross-sectional area of the wellbore, $p$ is the pressure, $Z$ is the deviation factor, and $T$ is the wellhead temperature.

Since the T gas field adopts precise pressure control methods to prevent sand production during initial liquid production, there was no need to consider wellbore liquid loading issues in the early pure liquid phase. After reaching the gas breakthrough state, the risk of fracture sanding is reduced, and high-rate production methods should be employed to prevent fracture water blockage and wellbore liquid loading. Therefore, by subtracting the actual wellhead flow rate from the minimum critical liquid carrying rate, the difference serves as a quantitative indicator of wellhead liquid loading. A negative difference indicates the presence of liquid loading, while a positive difference indicates the absence of a liquid loading phenomenon.

5.2.2. Drainage and Production Evaluation

The VIKOR decision-making method was used for compromise calculation, and the target wells were ranked based on maximizing group utility and minimizing individual regret. The specific steps were as follows: firstly, the main controlling factors of the drainage and production evaluation, analyzed earlier, were listed to form a matrix. Then, the influencing factors were standardized to eliminate the influence of dimensions on the results. Finally, the compromise evaluation index value was calculated using the following normalization methods shown in Equations (6) and (7).

$$b_{ij}=(x_{ij}-x_{ij}^{-})/(x_{ij}^{*}-x_{ij}^{-})$$

(6)

$$b_{ij}=(x_{ij}^{*}-x_{ij})/(x_{ij}^{*}-x_{ij}^{-})$$

(7)

In the formula, $b_{ij}$ is the normalized result, $x_{ij}^{*}$ is the maximum value, and $x_{ij}^{-}$ is the minimum value.

The group utility $S_i$ and individual regret values $R_i$ were calculated using formulae (8) and (9).

$$S_i={\displaystyle \sum _{i=1}^n{\omega }_j(b_j^{*}-b_{ij})}/(b_j^{*}-b_j^{-})$$

(8)

$$R_i=\underset{1\le j\le n}{\max }\left[{\omega }_j\left(b_j^{\ast }-b_{ij}\right)/\left(b_j^{\ast }-b_j^{-}\right)\right]$$

(9)

In the formulae, $b_j^{*}$ represents the maximum value in the column where the influencing factor is located; $b_j^{-}$ represents the minimum value; and ${\omega }_j$ represents the coefficient, which is expressed in terms of correlation.

The method for calculating the compromise evaluation indicator Q is shown in Equation (10).

$$Q=\frac{v\left(S_i-S^{-}\right)}{S^{*}-S^{-}}+\frac{(1-v)\left(R_i-R^{-}\right)}{R^{*}-R^{-}}$$

(10)

In the formulae, $v$ represents the compromise coefficient, $S^{*}$ and $S^{-}$ represent the maximum and minimum group utility values, and $R^{*}$ and $R^{-}$ represent the maximum and minimum individual regret values.

The larger the decision indicator obtained using this method, the greater the potential for optimization through drainage and production. The group utility value was used to assess the optimization potential of individual factors in each well, thereby prioritizing the optimization efforts. Taking into account the overall optimization requirements and production conditions, the target wells were categorized into three groups based on their scores. Good wells had compromise decision indicator values less than or equal to 0.3. Moderate wells had compromise decision indicator values between 0.3 and 0.7, requiring optimization of two or more indicators. Poor wells had compromise decision indicator values greater than 0.7, requiring focused optimization of three or more indicators.

5.3. Field Application

5.3.1. Evaluation Results

The main controlling factors affecting the drainage and production effectiveness in the T gas field can be divided into three parts: (1) Reservoir indices: gas saturation, permeability, stress difference, burial depth, and formation pressure; (2) fracture indices: cumulative fracture volume, fracture loss rate, and fracture conductivity; (3) wellbore index: wellbore liquid loading. Among them, the fracture loss rate belongs to the cost-type index, while the other factors belong to the benefit-type indices.

The group utility index was used as a reference for the degree of influence of each attribute. The reservoir quality index included permeability, gas saturation, stress difference, and formation pressure, with a comprehensive range of 0.099 to 0.28. The fracture index consisted of the fracture volume index and the support efficiency index. The fracture volume index had a significant impact on drainage and production and required targeted construction measures. It was listed separately, with a range of 0 to 0.25. The support efficiency index included fracture loss rate and fracture conductivity, which could be optimized through drainage and production measures, ranging from 0 to 0.26. The wellbore liquid loading was addressed by adjusting drainage and production strategies and using drainage assistance methods, with a range of 0 to 0.15. The individual well evaluation indicators are shown in

Table 3. Evaluation indices of single gas well drainage and production.

Well	Reservoir Quality Index	Fracture Volume Index	Support Efficiency Index	Wellbore Liquid Accumulation Index
Y1	0.14	0.21	0.26	0.02
Y2	0.12	0.22	0.23	0.03
Y3	0.15	0.21	0.19	0.07
Y4	0.13	0.00	0.19	0.06
Y5	0.18	0.12	0.25	0.08
Y6	0.14	0.03	0.15	0.05
Y7	0.24	0.25	0.20	0.08
Y8	0.19	0.21	0.18	0.04
Y9	0.28	0.19	0.12	0.08
Y10	0.17	0.12	0.00	0.00
Y11	0.15	0.12	0.15	0.02
Y12	0.15	0.18	0.21	0.02
Y13	0.10	0.15	0.19	0.15
Y14	0.12	0.19	0.14	0.09
Y15	0.14	0.16	0.15	0.07
Y16	0.09	0.17	0.20	0.06

.

With the VIKOR method as the core, the evaluation indices for the 16 wells in the T Gas Field were calculated, and the evaluation results were classified as shown in Figure 13. There were four wells classified as “good”, seven as “moderate”, and five as “poor”. A higher evaluation index indicates a greater potential for improving drainage and production effectiveness through drainage and production measures. It can be observed that well Y7 had excessively high geological and fracture indices, accompanied by a certain degree of wellbore liquid accumulation. Well Y12 had a relatively high fracture efficiency index and a large reservoir quality index, indicating high optimization potential.

The goal of evaluating shallow shale gas wells is to increase individual well production. The evaluation results should not only be beneficial for selecting wells with optimization potential for drainage and production, but should also ensure that the wells with optimization potential are the target wells for increasing EUR. Therefore, it is necessary to compare and validate the evaluation results with on-site EUR data. The evaluation results are shown in Figure 14. The results indicate that with the increase in evaluation indicators, the EUR decreased. The fitting result shows an R2 value of 0.71, indicating the good reliability of the evaluation results.

5.3.2. Drainage and Production Strategies

By calculating the group utility values, optimization of the drainage and production techniques was conducted for the shallow well Y7. The obtained indices for this well were as follows: reservoir quality index of 0.24, cumulative fracture volume index of 0.25, support efficiency index of 0.20, and wellbore liquid accumulation index of 0.08. The following optimizations were proposed for this well: (1) The high fracture index was due to the design limitation of a relatively short horizontal section of 516 m, resulting in a smaller cumulative fracture volume. (2) The low support efficiency index after hydraulic fracturing was attributed to the shallow burial depth, which delayed the closure of fractures under low closure stress. Therefore, it was necessary to control the critical flow rate of proppant flowback to restrict the fluid flow rate during the pure liquid stage. (3) The well had a high reservoir quality index and a high wellbore liquid accumulation index. Due to the low formation pressure, the original reservoir energy was insufficient for effective fluid return, resulting in wellbore liquid accumulation. To mitigate this issue, a timely fluid drainage strategy should be implemented to prevent inefficient fluid removal caused by low formation energy, thereby avoiding water blockage and wellbore liquid accumulation.

By calculating the group utility value, the well Y12, with a greater depth, was selected for production and extraction process optimization. The results indicate that the reservoir quality index of the well was 0.15, the cumulative fracture volume index was 0.18, the support efficiency index was 0.21, and the wellbore liquid accumulation index was 0.02. Overall, the well demonstrated the following characteristics: (1) The reservoir quality index of the well was moderate, and the reservoir energy could be enhanced through the method of wellbore shut-in. (2) The cumulative fracture volume index was relatively high. Despite having high three-dimensional stresses and stress differentials, the actual volumes of the fractures were small (horizontal section length of 1500 m). Therefore, it is necessary to improve the fracturing conditions by increasing the viscosity of the fracturing fluid, and by using other methods to enhance the effectiveness of hydraulic fracturing. (3) The support efficiency index was relatively high. Therefore, it is necessary to control the rate of fluid production to reduce the possibility of sand production. (4) The wellbore liquid accumulation index was relatively low. This is due to the high formation pressure of the well and its strong liquid production capability, resulting in favorable wellbore liquid conditions.

6. Discussion

6.1. Analysis of Factors Influencing Drainage and Production Effects

Through the study of factors influencing drainage and production effects, it was found that these factors can be categorized into three groups: reservoir factors, fracture-related factors, and wellbore factors. In investigating reservoir factors, we primarily employed well logging data and drainage and production parameters for analysis. The results indicate that the major controlling factors include gas saturation, permeability, stress difference, burial depth, and reservoir pressure. For the analysis of the impact of fracture parameters and wellbore factors on drainage and production effects, numerical simulation was the main approach. The outcomes revealed that significant controlling factors encompass cumulative fracture volume, ultimate fracture loss rate, average final conductivity, and wellbore liquid loading.

The research findings are generally consistent with factors previously proposed by scholars, such as permeability, pressure drop, fracture conductivity, fracture complexity, and wellbore liquid loading [13,14,15,16,17,18,19]. In addition, we considered factors such as gas saturation, stress difference, and burial depth, which were found to have a significant impact on drainage and production effects. This was due to our study encompassing both flowback and gas production processes, wherein gas saturation plays a prominent role in drainage and production effects, while stress difference influences the efficiency of hydraulic fracturing, thereby affecting the overall drainage and production outcomes. As fracture complexity cannot be adequately captured by a single parameter, we divided it into fracture length, width, volume, conductivity, and fracture loss rate for analysis. The results revealed that fracture volume, fracture loss rate, and fracture conductivity have substantial impacts on drainage and production effects. An increase in wellbore liquid loading leads to a reduction in gas production, aligning with previous research on its influence on drainage and production effects.

The research results not only validate the findings of scholars regarding drainage and production effects, but also comprehensively consider the influencing factors at various stages of the matrix–fracture–wellbore system. This provides a basis for future quantitative evaluations of drainage and production effects.

6.2. Analysis of Evaluation Results

Based on the primary controlling factors affecting drainage and production effects, this paper proposes a workflow for quantitatively evaluating drainage and production effects. Using this workflow, an analysis was conducted on 16 wells in the field. A comparative assessment of the results with field estimated ultimate recovery (EUR) data revealed an inverse relationship between optimization potential and EUR. The coefficient of determination between the two was 0.71, indicating a strong correlation. The reason for the correlation not reaching 1 is that this assessment result only represents the optimization potential of drainage and production. There are many ways to increase EUR, and drainage and production is just one of them. Therefore, such a phenomenon can occur.

7. Conclusions

In response to the shale gas reservoir drainage and production issues in the T Oilfield, a combination of on-site data analysis and numerical simulation methods was employed to analyze the influencing factors and quantitatively assess the drainage and production effects. The following conclusions were drawn:

(1)

A method was established to study the influencing factors of drainage and production in shallow shale gas reservoirs through numerical simulation. It proposes a hydraulic fracturing simulation method that combines the UFM, construction curves, and closed-tank models. This approach demonstrates a relatively high level of accuracy.

(2)

The nine main controlling factors affecting drainage and production were identified as follows: gas saturation, permeability, stress difference, burial depth, formation pressure, cumulative fracture volume, final fracture loss rate, average final conductivity, and wellbore liquid loading degree.

(3)

A workflow for quantitatively evaluating the drainage and production effectiveness of shallow shale gas wells and selecting wells with potential for optimized drainage and production was proposed. This workflow yielded both comprehensive and individual indices. The determination coefficient (R²) of the evaluation results fitted with EUR was 0.71, indicating a good level of reliability.

(4)

A quantitative evaluation of the drainage and production effect was conducted for the T gas field, and a classification was performed. The results show that among the typical wells in this gas field, 12 wells had optimization potential, with 5 of them having significant potential for optimization.

(5)

For shallow wells with low pressure and low closure stress, it is recommended to limit the fluid flow rate during the pure liquid phase by using the critical flowback rate of proppants, and to promptly implement assisted drainage measures. As for deep wells, more aggressive fracturing measures can be employed, and the reservoir energy can be enhanced through the method of well shut-in to increase the formation energy.