Influencing Factors Analysis and Optimization of Hydraulic Fracturing in Multi-Layered and Thin Tight Sandstone Gas Reservoir

Abstract

With the deepening of exploration and development of tight sandstone gas reservoirs, the remaining recoverable reservoirs gradually become thinner with the vertical stratigraphic structure. The geomechanical properties become complex, and development based on conventional hydraulic fracturing methods often leads to serious problems, such as difficult control of fracture height, penetrating interlayers, too short fracture length, and inadequate proppant filling. In view of the above problems, we conducted a numerical investigation on a hydraulic fracturing scheme in a multi-layered and thin tight sandstone gas reservoir. According to the dataset from wells in a real gas reservoir in China’s Ordos Basin, the relevant geomechanical characteristics of the gas layers, together with the interlayers in the main production interval, were obtained, based on which, a fine numerical model was developed. By using the PL3D fracture propagation algorithm, a 3D hydraulic fracture propagation model was produced, and then using microseismic monitoring and production data matching, a high-precision hydraulic fracture model of the multi-layered and thin tight sandstone gas reservoir was obtained. On this basis, the influence of different geomechanical parameters and fracturing operational parameters on hydraulic fracture propagation was analyzed. Finally, an optimized hydraulic fracturing scheme that fitted the characteristics of the multi-layered and thin tight sandstone gas reservoir was proposed. Using a typical reservoir example, the optimized scheme enabled control of the fracture height in thin layers and the creation of long fractures with better proppant filling, so that the productivity of the fracture was significantly improved.

1. Introduction

Tight sandstone gas is a type of unconventional hydrocarbon resource that is stored in tight sandstone formations with low permeability (<1 mD), low porosity (<10%), and low gas saturation (<60%). It is widely distributed and includes huge reserves, which account for nearly 40% of the total natural gas reserves that have been confirmed [1,2,3], indicating huge potential for development. However, with low permeability and porosity, poor mobility, and weak natural energy, tight gas reservoirs cannot achieve commercial exploitation without hydraulic fracturing [4,5,6,7].

Numerical simulation has proven to be a highly effective approach for investigating the propagation of hydraulic fractures, thereby aiding in the optimization of fracturing strategies. This method of study is grounded in the principles of the Khristianovic–Geertsma–de Klerk (KGD) model [8] and the Perkins–Kern–Nordgren (PKN) model [9], both of which have been the subject of extensive research by scholars over several decades. This research has led to the development of three primary categories of models: the finite element model (FEM) [10], the boundary element model (BEM) [11], and the discrete element model (DEM) [12]. Among these, the BEM stands out for its speed and flexibility, outperforming both the FEM and DEM in these respects. It is capable of simulating intricate fracture networks, although it is generally less precise than the other two models. To simulate the vertical propagation of hydraulic fractures in complex geological formations, researchers have developed three-dimensional (3D) and pseudo-three-dimensional models [13]. In recent years, volume fracturing methods [14,15,16] have seen a surge in application, facilitating the creation of the stimulated reservoir volume (SRV). The continuous evolution and application of these models and methods underscore the importance of numerical simulation in the study and optimization of hydraulic fracture propagation.

Many numerical approaches have been developed to improve hydraulic fracturing in tight sandstone gas reservoirs. Parvizi et al. (2015) [17] evaluated the hydraulic fracturing performance in tight sandstone gas reservoirs with high perm streaks and natural fractures and optimized the fracture design parameters and well spacing. Gao et al. (2018) [18] developed a 3D numerical model for the investigation of the hydraulic fracture configuration in multi-layered tight sandstone gas reservoirs and compared the effects of general fracturing and separate layer fracturing on the fracture geometry and production performance. Wang et al. (2020) [19] presented a thermal-hydraulic-mechanical numerical simulator for the simulation of hydraulic fracturing operations in tight sandstone reservoirs and applied it to a field case in China. Zhang et al. (2020) [20] studied hydraulic fracturing in transversely isotropic tight sandstone reservoirs using a bonded-particle model approach and analyzed the influence of bedding planes on fracture initiation and propagation. Zhang et al. (2023) [21] proposed a numerical simulation to simulate the hydraulic fracturing process in tight sandstone gas reservoirs and analyzed the effects of the injection rate, fluid viscosity, and stress contrast on fracture geometry and complexity.

With decades of exploration and development, thick tight sandstone gas reservoirs gradually became exhausted, and the remaining recoverable formations gradually became thinner and presented a multi-layered geological structure. Mudstone, coal seam, dry layer, and water layers were overlapped between the gas layers, changing the vertical lithology and geomechanical properties drastically. Scholars named this kind of reservoir a multi-layered and thin tight sandstone gas reservoir. Due to the particularity of the geological structure of this type of gas reservoir, inappropriate hydraulic fracturing schemes usually lead to too large a fracture height and a short fracture length, causing problems such as low gas production or water production in gas wells. Given this serious situation, this paper reports a numerical study on hydraulic fracturing in this type of gas reservoir. The principal objectives of this paper include the following: I - to precisely describe the geological structure condition and fractured well production status of this type of gas reservoir based on the data of wells in the real reservoir; II - to establish a high-precision 3D hydraulic fracture propagation numerical model based on this kind of gas reservoir using the PL3D fracture propagation algorithm and assessment using microseismic monitoring and production data matching; III - to study the geomechanical and fracturing operational parameters’ influences on hydraulic fracture propagation in this type of gas reservoir by numerical simulation. IV - to propose an optimized fracturing scheme for low-production wells based on the numerical model and influencing factors’ analysis, providing a theoretical basis and examples for subsequent hydraulic fracturing development in this type of gas reservoir.

2. Description of Fractured Well Production Status in Multi-Layered and Thin Tight Sandstone Gas Reservoirs

2.1. Geological Condition of Multi-Layered and Thin Tight Sandstone Gas Reservoirs

The multi-layered and thin tight sandstone gas reservoir is a new concept that is derived from recent tight sandstone gas reservoir development. There is no strict classification standard for this kind of gas reservoir; commonly, based on field development experience, tight sandstone gas reservoirs with gas layers thinner than 5 m and with more than two overlapping sandstone layers are regarded as multi-layered and thin tight sandstone gas reservoirs. Due to inappropriate hydraulic fracturing schemes, it is hard to obtain good fractures in this kind of gas reservoir and this usually leads to a set of problems, such as low gas production.

The geological conditions of hydraulic fracturing wells in a real tight sandstone gas reservoir in the Ordos Basin in China are illustrated in Figure 1 and Figure 2. The predicted and observed absolute open flow rates (AOFs) of tens of wells are compared in Figure 1. The predicted AOFs are calculated based on the geological parameters of these wells and the observed AOFs are obtained from well tests. The difference between the predicted and observed AOFs reflects the effects of hydraulic fracturing. These wells are classified based on the AOFs. Taking account of the existence of error, wells with an observed AOF lower than 50% of the predicted AOF are classified as low-production wells, while those with an observed AOF higher than 150% of the predicted AOF are classified as high-production wells. The remaining wells are normal production wells. The statistical results in Figure 2 show that about 21% of wells suffer from low production after hydraulic fracturing.

Since the hydraulic fracturing schemes for all the wells in this reservoir are similar, the main cause of the production difference is the geological structure of the formation. As shown in Figure 3, a comparison between the high and low-production wells after fracturing intuitively indicates that the low-production wells generally have more layers with both thinner sandstone layers and inter-layers (mudstone and coal seam). The comparative results clearly illustrate the problems encountered in a multi-layered and thin tight sandstone gas reservoir—more layer numbers and thinner inter-layers significantly hinder the control of fracture height during hydraulic fracturing, and the fractures easily propagate into the adjacent water layers, dry sandstone layers, or other unproductive layers, resulting in wastage of substantial fracturing fluid. Additionally, the out-of-control fracture height also affects the fracture length, as the majority of fracture lengths do not surpass 150 m, with some being even shorter than 100 m. Even worse, the effective propped fracture length falls considerably short of the total length generated, so that gas reserves in the formation cannot be effectively produced.

2.2. Statistics for the Geomechanical Parameters of Multi-Layered and Thin Tight Sandstone Gas Reservoirs

Although complex in geological structure, the formation layers of multi-layered and thin tight sandstone gas reservoirs can be classified into four types according to their lithologies: tight sandstone layer, mudstone layer, coal seam layer, and marl layer, as shown in

Table 1. Different types of formation layers in this type of gas reservoir.

Type of Layer	Layer Type Description
Layer type 1	Tight sandstone layer
Layer type 2	Mudstone layer
Layer type 3	Coal seam layer
Layer type 4	Marl layer

. The production sandstone layers are usually thin and overlap with dry or water sandstone layers, divided by mudstone or coal seam interlayers, while the marl layers are usually distributed at the bottom of the entire formation.

The statistical results for the geological and geo-mechanical parameters for different types of formation layers of low-production wells are displayed in Figure 4, including the layer thickness, principal geo-stress, elastic modulus, and Poisson’s ratio. Their mean values and variation ranges are shown in

Table 2. The variation ranges and mean values of the geo-mechanical data for different layer types.

	Thickness (m)			Geo-Stress (MPa)			Elastic Modulus (GPa)			Poisson’s Ratio
	Mean	Max	Min	Mean	Max	Min	Mean	Max	Min	Mean	Max	Min
Layer type 1	6.0	1.6	3.8	31.0	25.5	28.0	59.6	42.1	50.5	0.3	0.2	0.2
Layer type 2	7.9	2.2	4.7	37.9	29.7	34.0	50.8	28.2	38.2	0.3	0.3	0.3
Layer type 3	3.2	1.0	2.2	35.2	31.4	33.4	9.7	4.9	7.0	0.4	0.4	0.4
Layer type 4	12.2	5.3	8.3	36.6	29.5	33.6	79.8	62.8	73.1	0.3	0.3	0.3

. As can be seen, the thickness of the coal seam is relatively low and uniform (1–3.2 m), and that of sandstone is slightly greater (1.6–6 m). The thickness distributions of the mudstone and marl layers cover a large range, but the mean values are larger than those of the coal seam and sandstone layers. The geo-stress of the sandstone is relatively the least, being around 25–31 MPa, while that of the mudstone is the largest, ranging from 29–38 MPa, while the values for the coal seam and marl are in the middle. The elastic modulus values of the marl layers are the largest (62–80 GPa), while the coal seam presents the smallest values (5–10 GPa), with a greater than ten-fold difference. The Poisson’s ratio distribution is similar to that of geo-stress but is more concentrated.

3. Construction of a 3D Hydraulic Fracture Propagation Numerical Model in Multi-Layered Reservoirs

There are several kinds of commonly used hydraulic fracturing numerical simulation models which are described in the introduction section for this study. A planar 3D model (PL3D) [22] is adopted to simulate the hydraulic fracturing in multi-layered and thin tight stone gas reservoirs. The PL3D model is a numerical tool that simulates the hydraulic fracturing process in a simplified way. It assumes that the fracture propagates in a plane perpendicular to the minimum principal stress and that the fluid flow is governed by Poiseuille’s law. The model can capture the effects of the formation rock toughness, fluid viscosity, injection rate, pressure, and geo-stress for different formation layers varying in fracture geometry. In the PL3D model, the fracture is divided into a series of discrete frac-meshes during simulation, with two kinds of meshes being commonly used, which are the moving mesh system [23] and the fixed mesh system [24] (Figure 5). In this study, the fixed mesh system PL3D model is adopted, and the following are the main functions of this model.

The first is the fluid flow function. In the PL3D model, Poiseuille’s law is applied to calculate the fluid flow within the fracture. Since there is two-dimensional flow when simulating 3D fracture propagation, the fluid flow function is calculated along the x- and y-directions:

$$\frac{\partial p}{\partial x}+{\left[k\left(2+\frac{1}{n}\right)\frac{2\left(n+1\right)}{n}\right]}^{1/n}{\left(\frac{\left|q\right|}{w^2}\right)}^{n-1}\frac{q_x}{w^3}=0$$

(1)

$$\frac{\partial p}{\partial y}+{\left[k\left(2+\frac{1}{n}\right)\frac{2\left(n+1\right)}{n}\right]}^{1/n}{\left(\frac{\left|q\right|}{w^2}\right)}^{n-1}\frac{q_y}{w^3}={\rho }_f{g}_y$$

(2)

where $p$ is the fluid pressure on the fracture surface, $\mathrm{Pa}$; $q$ is the overall flow rate, and $q_x$ $q_y$ are the divert flow rate along the x- and y-directions, ${\mathrm{m}}^3/\mathrm{s}$; $w$ is the fracture width, $\mathrm{m}$; $g_y$ is the gravitational acceleration along the y-direction, $\mathrm{N}/\mathrm{kg}$; ${\rho }_f$ is the fracturing fluid density, $\mathrm{kg}/{\mathrm{m}}^3$; and $k$ and $n$ are the fracturing fluid rheological parameters, dimensionless.

To solve the fluid flow function, the fracture width $w$ is required. Based on geo-mechanical theory, the width of the fracture is controlled by the combined effect of the fluid pressure and the principal geo-stress, so it can be obtained by solving the following 2D elastic integral function:

$$p-{\sigma }_0=\frac{G}{4\pi \left(1-v\right)}\int \int \left(\frac{\partial }{\partial y^{\prime }}\left(\frac{1}{R}\right)\frac{\partial w}{\partial y^{\prime }}+\frac{\partial }{\partial x^{\prime }}\left(\frac{1}{R}\right)\frac{\partial w}{\partial x^{\prime }}\right)d{x}^{\prime }d{y}^{\prime }$$

(3)

where ${\sigma }_0$ stands for the minimum principal stress, $\mathrm{Pa}$; $G$ is the shear modulus, $\mathrm{Pa}$; $v$ is the Poisson’s ratio, dimensionless; $R$ is the distance between the point $\left(x,y\right)$ where the pressure acts and the point $\left(x^{\prime },y^{\prime }\right)$ where the width is calculated, $\mathrm{m}$.

The fluid flow function and the elastic function are combined by the fluid continuity function:

$$\frac{\partial q_x}{\partial x}+\frac{\partial q_y}{\partial y}+q_L=-\frac{\partial w}{\partial t}$$

(4)

where $q_L$ is the fracturing fluid leak off of the formation, ${\mathrm{m}}^2/\mathrm{s}$.

When simulating the fracture propagation, LEFM theory [25] is used to calculate the critical width; when the frac-element width on the edge of the fracture is above the critical width, the fracture could break the formation rock and propagate.

The PL3D model simulates the fracture propagation using the following steps: (1) Assign a new frac-element at the edge of the fracture, which will be the initial frac-element if it is the first time step. Set the fluid pressure $p$ for the existing frac-element and define a proper simulation time step $\Delta t$. (2) Obtain the fracture width $w$ by solving the coupled fluid flow function and fluid continuity function based on the given parameters. (3) Solve the elastic function using the obtained $w$ to obtain a new fluid pressure $p$ of the frac-element. If the new fluid pressure converges with the initial one, go to the next step; if not, update the fluid pressure and return to step (2) to repeat the calculation until convergence. (4) After finishing one simulation time step, compare the width of the edge frac-element with the critical fracture width to check if the fracture could propagate; if yes, return to step (1) and repeat the overall simulation procedure until the fracturing injection operation is completed. (5) If the simulation time step is finished, output the parameters of the final fracture. The entire workflow of the hydraulic fracture propagation based on the PL3D model is visualized in Figure 6. To obtain a more detailed statement of the PL3D fracture model, these articles [24,26,27] are recommended.

4. Geological and Fracturing Operational Parameters Influencing Analysis

4.1. Theoretical Numerical Model for Sensitivity Analysis

In our previous study [21], some geological and fracturing operational parameters’ influence on hydraulic fracture propagation were analyzed. The geological parameters included the geo-stress, the elastic modulus, and the Poisson’s ratio of the gas layer. The fracturing operational parameters included the viscosity, the total volume, the injection rate of the fracturing fluid, and also the proppant density. In this research, we expand the sensitivity analysis study by considering the geological characteristics of a multi-layered and thin tight sandstone gas reservoir. Based on the PL3D model in Section 3, and the geomechanical parameters from the real reservoir described in Section 2, a theoretical numerical model for sensitivity analysis is constructed, which is a three-layered thin tight sandstone gas reservoir, with a gas layer in the middle and two dry layers around. The inter-layers are considered to be mudstones. The thicknesses and corresponding parameters are shown in

Table 3. The thickness and geo-mechanical parameters of each layer.

Lithology	Top Depth (m)	Bottom Depth (m)	Thickness (m)	Geo-Stress (MPa)	Elastic Modulus (104 MPa)	Poisson’s Ratio	Sg (%)
Mudstone	1950	1990	40	34	3.9	0.3	0
Dry sandstone	1990	1995	5	27	5.1	0.2	0
Mudstone	1995	2000	5	34	3.9	0.3	0
Gas sandstone	2000	2005	5	27	5.1	0.2	54
Mudstone	2005	2010	5	34	3.9	0.3	0
Dry sandstone	2010	2015	5	27	5.1	0.2	0
Mudstone	2015	2055	40	34	3.9	0.3	0

. The perforation zone is in the middle of the gas layer from 2001.5–2003.5 m, with a perforating density of 16 holes/m, and a diameter of 9.6 mm per hole. The hydraulic fracturing scheme is derived from a real field fracturing operation, which is shown in

Table 4. The hydraulic fracturing scheme at every injection stage.

Fracturing Injection Stage	Injection Volume (m3)	Proppant Concentration (kg/m3)	Injection Rate (m3/min)	Single-Stage Injection Time (min)	Total Injection Time (min)	Fluid Type	Proppant Type
1	40	0	3.5	11.4	11.4	Base fluid	/
2	20	73	3.5	5.8	17.3	Base fluid	40/70 mesh
3	35	0	3.5	10.0	27.3	Base fluid	/
4	15	102	3.5	4.5	31.7	Gel	30/50 mesh
5	23	203	3.5	7.0	38.7	Gel	30/50 mesh
6	30	290	3.5	9.5	48.2	Gel	30/50 mesh
7	45	363	3.5	14.6	62.8	Gel	30/50 mesh
8	35	435	3.5	11.6	74.4	Gel	30/50 mesh
9	20	508	3.5	6.8	81.1	Gel	30/50 mesh

. The fracturing fluid consists of a base fluid (24 mPa.s) and a gel (160 mPa.s). Two types of ceramic proppant with mesh sizes of 40/70 and 30/50 are used.

4.2. Sensitivity Analysis of the Gas Layer and Inter-Layer Thicknesses

According to the thickness distribution range of each layer type from the real reservoir (shown in Figure 4 and Table 2), the thickness of the formation layers in the theoretical numerical model is adjusted and the fracture propagation parameters under different layer thicknesses are simulated and compared, as shown in Figure 7, where the fracture height ratio means the ratio of the three sandstone layers’ total thickness to the fracture height.

Table 5. The inter-layer thickness that can control the fracture height under different gas layer thicknesses.

		Gas Layer Thickness
		1 m	2 m	5 m	8 m	10 m	12 m	15 m
Inter-layer thickness	1 m	No	No	No	No	No	No	No
	2 m	No	No	No	No	No	No	No
	5 m	No	No	No	No	No	No	Yes
	8 m	No	No	No	No	No	Yes	Yes
	10 m	No	No	No	No	Yes	Yes	Yes
	12 m	No	No	No	Yes	Yes	Yes	Yes
	15 m	No	No	Yes	Yes	Yes	Yes	Yes

shows if the corresponding inter-layer thickness can control the fracture height growth under different gas layer thicknesses, and Figure 8 displays some fracture simulation results under different gas layer and inter-layer thicknesses.

As can be observed from the figures and tables, the hydraulic fracture in the thin multi-layered reservoir is notably affected by the thickness of the gas layer and the inter-layers. When the gas layer is too thin (1–2 m), any inter-layer thickness cannot control the fracture height, since there is no obvious variation in the fracture parameters. When the gas layer thickness is above 5 m, the fracture height faces reduction and the fracture height ratio increases significantly as the inter-layer thickness increases, which means the fracture height is controlled by the increasing inter-layer thickness. Furthermore, this variation trend occurs towards a thinner inter-layer thickness when the gas layer thickness increases, which means that the fracture height can be controlled by a thinner inter-layer thickness at a larger gas layer thickness. Similar results can be seen in Table 5, which also indicates that when the inter-layer thickness is larger than 15 m, it can control the fracture height for most of the gas layer thicknesses.

4.3. Sensitivity Analysis of the Geo-Stress Difference between the Gas Layer and the Inter-Layers

As well as the layer thickness, the geo-stress difference between the gas layer and the inter-layer is another factor that affects fracture propagation. According to the geo-stress distribution range for each layer type shown in Figure 4 and Table 2, the geo-stress difference is adjusted for a range of 3–15 MPa with a step of 3 MPa. The fracture propagation is simulated under different geo-stress differences, and the corresponding results are compared in Figure 9. In these models, the gas layer thickness is fixed as 5 m, and the inter-layer thicknesses are varied from 1 to 15 m.

Table 6. The geo-stress difference that can control the fracture height under different inter-layer thickness.

		Geo-Stress Difference
		3 Mpa	6 Mpa	9 Mpa	12 Mpa	15 Mpa
Inter-layer thickness	1 m	No	No	No	No	No
	2 m	No	No	No	No	No
	5 m	No	No	No	No	Yes
	8 m	No	No	No	Yes	Yes
	10 m	No	No	Yes	Yes	Yes
	12 m	No	Yes	Yes	Yes	Yes
	15 m	No	Yes	Yes	Yes	Yes

shows if the corresponding geo-stress differences can control the fracture height growth under different inter-layer thicknesses.

As is clearly visible in the figure, the effect of the geo-stress difference is not obvious when it is lower than 3 Mpa, but an increase in the geo-stress difference results in a decrease in the fracture height, and an increase in the fracture half-length. This signifies that a higher geo-stress difference makes it harder for the fracture to penetrate the interlayer, thereby promoting lateral fracture propagation within the formation. Moreover, the curves and Table 6 both indicate that the fracture height reduces as the inter-layer thickness increases, which indicates that the fracture height is easier to control with a thinner inter-layer. As the geo-stress difference increases, the inter-layer thickness that can control the fracture height tends to a lower value.

4.4. Sensitivity Analysis of the Prepad Fluid and Sand-Carrying Fluid Volume Percentage

Fracture propagation is influenced not only by the geological parameters but also by the fracturing operational parameters. Studies have found that the prepad fluid injection stage mainly affects the shape of the fracture, while the sand-carrying fluid injection stage mainly affects the proppant filling and fracture conductivity [21]. In this section, different volume percentages of the prepad fluid and the sand-carrying fluid are analyzed to examine their influence on fracture propagation. In Table 4, the fluid injection stages 1–3 are the prepad fluid and 4–9 are the sand-carrying fluid; the volume percentages of these two fluid types are changed and the total fluid volume is kept unchanged. The corresponding fracture parameters under different fluid volume percentages are illustrated in Figure 10, where the effective propped fracture length ratio means the ratio of the effective propped fracture length to the total generated fracture length.

As is illustrated in these figures, the morphology of hydraulic fractures is influenced by the volume percentages of the prepad fluid and the sand-carrying fluid. With prepad fluid percentage increase, the fracture height exhibits a decreasing trend and the fracture length exhibits an increasing trend under the same inter-layer thickness, since the prepad fluid is of low viscosity, which is better for fracture height control. In addition, the sand-carrying fluid percentage decreases as the prepad fluid percentage increases, resulting in a decrease in the effective propped fracture length ratio and a significant reduction in the fracture width. However, when the fracture height is controlled by the inter-layer, the effective propped fracture length ratio increases, which means that the proppant is carried deeper into the fracture in the gas layer. These findings suggest that the fluid volume percentages should be carefully selected to achieve the optimal fracture geometry.

4.5. Sensitivity Analysis of Multi-Slug Sand Filling and Secondary Sand Filling Fracturing Schemes

Some sand filling methods can help to control the fracture height in hydraulic fracturings, such as the slug sand filling and secondary sand filling fracturing schemes. The slug sand filling divides the sand filling into several slugs with fracturing fluid without sand between them and keeps the pump running for the entire fracturing procedure. The secondary sand filling method involves the sand filling two times—when the first filling is over, the pump is stopped to let the sand settle to the bottom of the fracture, and then the second filling is started. However, which of these is superior in a multi-layered and thin tight gas reservoir has not been fully studied. In this section, the original fracturing scheme in Table 4 is modified in the multi-slug sand filling and secondary sand filling fracturing schemes, while the total fluid and sand volume are unchanged. The fracture parameters under the different fracturing schemes are compared in Figure 11.

The figure shows that both the multi-slug sand filling and the secondary sand filling methods can improve the control of the fracture height to a certain extent when compared to the original fracturing scheme when the inter-layer thickness is larger than 10 m. However, the secondary sand filling method does not perform well in increasing the fracture length—the fracture closes when the pumping stops, and during the second pumping, the sand cannot be transported to the deeper part of the fracture, resulting in a shorter propped fracture length. By comparison, the multi-slug sand filling method does not need to stop the pump, allowing the sand to be transported further into the fracture—with the fracturing fluid pumping, the sand slug gradually settles, forming an additional inter-layer that helps prevent fractures from penetrating the thin interlayers. This results in both longer fracture lengths and effective propped fracture lengths. Among the various sand slug numbers, the two-slug sand filling method demonstrates the best performance.

5. Example: The Hydraulic Fracturing Simulation of a Low-Production Well in the Multi-Layered and Thin Tight Sandstone Gas Reservoir and the Fracturing Scheme Optimization

5.1. Geological Condition of a Low-Production Well and the Hydraulic Fracturing Simulation Result

In this section, we select a specific well in the Ordos Basin, named Well X-1, which is a low-production well after hydraulic fracturing. This well was selected as an example to investigate the optimization scheme for hydraulic fracturing in the multi-layered thin tight sandstone gas reservoir. Well X-1 is a vertical well that experiences low production issues after fracturing, with its actual AOF measured at 1.13 × 10⁴ m³/d, significantly lower than the estimated AOF of 3.36 × 10⁴ m³/d. For visual reference, please refer to Figure 12 for the logging curves of this well. As obtained from the well logging interpretation,

Table 7. Layer division and the corresponding lithologies and geological parameters of Well X-1.

Lithology	Top Depth (m)	Bottom Depth (m)	Thickness (m)	Geo-Stress (MPa)	Elastic Modulus (104 MPa)	Poisson’s Ratio	Sg (%)	Poro (%)	Perm (mD)
Coal	2072.9	2074.1	1.2	30.2	1.57	0.22	0	0	0.01
Mudstone	2074.1	2075.4	1.3	36.7	2.29	0.33	0	0	0.01
Coal	2075.4	2086.9	11.5	33.2	0.89	0.27	0	0	0.01
Mudstone	2086.9	2095.6	8.7	35.3	3.35	0.3	0	0	0.01
Gas sandstone	2095.6	2098.3	2.7	27.7	4.68	0.17	54	9	0.83
Gas sandstone	2098.3	2101.3	3	30.7	4.6	0.23	56	9	0.76
Mudstone	2101.3	2102.3	1	36.8	4.4	0.32	0	1	0.02
Coal	2102.3	2104.7	2.4	36	4.9	0.31	0	3	0.12
Mudstone	2104.7	2105.4	0.7	37.6	3.09	0.33	0	2	0.16
Dry sandstone	2105.4	2108.3	2.9	33.1	4.86	0.27	0	8	0.29
Mudstone	2108.3	2109.4	1.1	33	4.76	0.27	0	0	0.56
Dry sandstone	2109.4	2117.4	8	31.2	5.18	0.23	0	7	0.22
Mudstone	2117.4	2118.2	0.8	36.9	5.89	0.32	0	0	0.01
Marl	2118.2	2120.1	1.9	39.8	5.26	0.36	0	0	0.01
Mudstone	2120.1	2120.9	0.8	35.8	4.14	0.31	0	0	0.01
Marl	2120.9	2124.5	3.6	37.5	5.91	0.33	0	0	0.01
Mudstone	2124.5	2124.6	0.1	36.3	6.07	0.31	0	0	0.01
Dry sandstone	2124.6	2128	3.4	33.4	5.31	0.27	0	8	0.26
Marl	2128	2134.3	6.3	32.9	4.33	0.26	0	0	0.01

displays the lithologies and the geological parameters of each layer.

As is shown in the above well logging curve and the table, this formation is a stratum formed by thin and overlapping mudstone, sandstone, coal seam, and marl. Although complex in its geological structure, this formation can be approximately categorized into two sections: the upper and the lower portions, divided by a thin barrier layer in the middle. The upper part consists of gas sandstone with a thickness of 5.7 m, while the lower part also contains sandstones of a total of 14.3 m but with no gas. Between these two parts, the fragile interlayer made by a coal seam and mudstone is less than 5 m, and the capacity to control the fracture from penetration is doubtful. The reservoir numerical model is then built according to the geo-mechanics parameters of Well X-1 and numerical simulation of hydraulic fracturing is conducted based on the real field fracturing scheme, as shown in

Table 8. The hydraulic fracturing scheme of Well X-1.

Fracturing Injection Stage	Injection Volume (m3)	Proppant Concentration (kg/m3)	Injection Rate (m3/min)	Single-Stage Injection Time (min)	Total Injection Time (min)	Fluid Type	Proppant Type
1	27.1	/	3.6	7.6	7.6	Base fluid	/
2	34.2	75.5	3	13.7	21.3	Base fluid	40/70 mesh
3	19.8	/	3	7.9	29.2	Base fluid	/
4	40.1	106.6	3	12.9	42.1	Gel	30/50 mesh
5	34.2	213.3	3.0	11.4	53.5	Gel	30/50 mesh
6	32.5	304.4	3.4	9.5	63.0	Gel	30/50 mesh
7	33.6	304.4	3.4	1.9	65.0	Gel	30/50 mesh
8	33.4	379.9	3.4	9.8	74.8	Gel	30/50 mesh
9	34.3	456.5	3.7	9.3	84.1	Gel	30/50 mesh
10	18.4	304.4	3.7	5.0	91.0	Gel	30/50 mesh
11	14.8	379.9	3.7	4.0	95.0	Gel	30/50 mesh
12	10.0	456.5	3.7	2.7	97.7	Gel	30/50 mesh

. The properties of the fracturing fluid are the same as those used for the sensitivity analysis in Section 4. The perforation interval is located at a depth of 2095.6–2001.3 m, the middle of the gas layer, with a perforating density of 16 holes/m, and a diameter of 9.6 mm per hole.

The hydraulic fracturing simulation results according to the geological parameters and the field fracturing scheme are shown in Figure 13. The fracture’s horizontal and vertical distribution in the multi-layered formation, as well as the fracture’s cross-section, are displayed in Figure 13a, while the conductivity along the fracture length is displayed in Figure 13b. As can be seen, in the horizontal direction, the half-length of the fracture is around 145 m, but the effective propped length is not as long, being about 60 m, as analyzed from the fracture distribution map and the conductivity curve. The accuracy of the simulation result is examined using the micro-seismic data and the production data of this well. The formation rock broken area from the micro-seismic data is shown in Figure 14. The micro-seismic data show that the fracture half-length is 160 m, which is quite close to the simulated result, with an error of 9.3%. The production data of Well X-1 are shown in Figure 15. The gas rate, together with the wellhead pressure, is transformed by Blasingame type curve [28] matching. The matching result in Figure 16 shows that the effective fracture half-length is 65.2 m, which is close to the effective propped length from the simulation, with an error of 7.5%. The comparison results with the micro-seismic and production data confirm the accuracy of the simulation results.

An analysis of the reason for low production from the simulation result is provided. First, as can be seen in the horizontal direction in Figure 13a, the effective propped length of the fracture is not as long as the generated length—the proppant can only reach the middle of the fracture. The fracture conductivity along with the fracture shown in Figure 13b also indicate that the proppant presents an uneven distribution, which drastically decreases along the fracture length. Most of the proppant is deposited near the wellbore and there is nearly no proppant from the middle to the top along the fracture length. Furthermore, the fracture height is about 40 m, which is not effectively controlled by the thin interlayer below the gas layer. The fracture penetrates the inter-layer of the mudstone and the coal seam and opens the dry sandstone layers that have no gas content. A large amount of fracturing fluid and proppant is wasted, which also inhibits the fracture length, together with the proppant, from growing further into the gas layer. Third, the large fracture height provides space for proppant settlement. The fracture cross-section in Figure 13a shows that most of the proppant settles to the fracture bottom in the dry sandstone layer, which reduces the proppant density and the conductivity in the production layer. The combination of the above factors leads to the low production of this well after fracturing.

5.2. Optimization Study on the Hydraulic Fracturing Scheme of Well X-1

The main factor contributing to the low production is the ineffective control of the fracture height in the multi-layered thin formation. The fracture length is too short, and there is uneven distribution of the proppant within the fracture, which is mainly caused by the inappropriate hydraulic fracturing scheme. To optimize the fracturing scheme, we should focus on three main goals: (1) Effectively controlling the fracture height to prevent it from penetrating the thin interlayer; (2) Making a longer fracture length to let the fracture go further into the gas layer; (3) Making the proppant move deeper into the fracture to extend the effective propped length.

Based on these three main goals, a hydraulic fracturing scheme optimization for Well X-1 is proposed. Taking account of the sensitivity analysis in Section 4 and in our previous study [21], the utilization of a low-viscosity fracturing fluid is more effective in fracture height control in thin reservoirs with weak barrier layers, but an overly low-viscosity fluid is not good at carrying the proppant. Thus, three kinds of fracturing fluid are used: slickwater (1 mPa.s) is added to the first stage of the prepad fluid to help control the fracture height, and the base fluid and the gel are kept to carry the proppant. Furthermore, according to the sensitivity analysis, the multi-stage sanding method is better at carrying the proppant deeper into the fracture and can help to control the fracture height as well, so two slugs of sand are added before the main sand carrying injection stage. Thirdly, a lower injection rate helps to control the fracture height, and a higher injection rate helps to prevent the proppant from settling, so a varying injection rate is adopted. The rate at the beginning of the injection is kept at a low value and gradually increases along with the injection. Based on the above optimization principles, and after many simulations and improvements, an optimized hydraulic fracturing scheme is derived for Well X-1, which is shown in

Table 9. The optimized hydraulic fracturing injection pumping procedure of Well X-1.

Fracturing Injection Stage	Injection Volume (m3)	Proppant Concentration (kg/m3)	Injection Rate (m3/min)	Single-Stage Injection Time (min)	Total Injection Time (min)	Fluid Type	Proppant Type
1	15.0	/	2.0	7.5	7.5	Slick water	/
2	25.0	76	2.5	10.0	17.5	Base-fluid	40/70 mesh
3	15.0	/	2.5	6.0	23.5	Base-fluid	/
4	25.0	95	2.5	10.0	33.5	Base-fluid	40/70 mesh
5	15.0	/	3.5	4.3	37.7	Base-fluid	/
6	30.1	136	4.0	7.5	45.2	Gel	30/50 mesh
7	34.2	253	5.0	6.8	52.1	Gel	30/50 mesh
8	35.5	355	5.0	6.5	58.6	Gel	30/50 mesh
9	36.6	409	6.0	6.1	64.7	Gel	30/50 mesh
10	33.0	486	6.0	5.5	70.2	Gel	30/50 mesh
11	23.0	559	6.0	3.8	74.0	Gel	30/50 mesh

and compared more intuitively with the original hydraulic fracturing scheme in Figure 17.

Figure 18 illustrates the hydraulic fracture resulting from the optimized fracturing scheme. The corresponding fracture parameters are compared in Figure 19. By comparing the optimized hydraulic fracture with the original one in Figure 13, we can see that the hydraulic fracturing effect is comprehensively improved. First, the fracture height obtains effective control within the thin layer; it decreases from 42 m to around 20 m, except for the near wellbore region. The major part of the fracture is stopped by the thin barrier layer below the gas layer, not by opening the dry sandstone layer. We can also see in Figure 18b the proppant density map in the fracture shows an obvious high-density strip at the bottom. This is caused by the settlement of the two proppant slugs in the injection stages 2–4 shown in Table 9. This proppant strip acts as an additional barrier layer to help control the hydraulic fracture height. Second, the half-length of the fracture increases from 145 m to 256 m, exceeding 76% of the original length, penetrating deeper into the gas layer, which indicates that when the fracture height obtains effective control, the fracturing fluid can be used more to create a longer fracture length. Figure 18c indicates that the proppant is filled deeper inside the fracture and shows a more even distribution, and the effective propped length increases from 70 m to 220 m—more than three times the original length. This demonstrates that the multi-stage sand addition method, together with a high sand-carrying fluid injection rate, can bring the proppant deeper into the fracture, creating a longer effective fracture-length and higher fracture productivity.

5.3. Application of the Optimized Hydraulic Fracturing Scheme for Other Low-Production Wells

As illustrated in the previous Section 5.2, the optimized hydraulic fracturing scheme used in the multi-layered and thin tight sandstone reservoir is based on the following criteria: (1) Use of a low-viscosity fracturing fluid as the prepad fluid to create fractures. A low-viscosity fracturing fluid can effectively avoid excessive fracture height growth and reduce the interference with adjacent layers. Moreover, the low-viscosity fracturing fluid helps improve the fracture horizontal propagation efficiency; (2) Use of a high-viscosity fracturing fluid as the sand-carrying fluid, as it enhances the capacity of sand carrying and improves the proppant placement within the fracture. It can also reduce the proppant settlement and maintain high fracture conductivity. (3) Maintaining a low injection rate in the prepad fracturing fluid stage as this can help to avoid breaking through the interlayer when creating the fracture. Then, gradually increasing the injection rate to help to carry the proppant faster into the desired location and to reduce proppant settlement. (4) Adopting a multi-stage sanding filling method. This can help carry the proppant further into the generated fractures and create additional barriers to avoid the fracture penetrating the thin interlayer, which is beneficial to fracture height control. Applying the above criteria, we conducted numerical simulations of optimized hydraulic fracturing for the other 11 low-production wells in this gas field. The simulation results for the original and optimized fracturing schemes are compared in Figure 20.

The simulation results for multiple low-production wells indicate that the application of hydraulic fracturing optimization schemes in multi-layered and thin tight gas reservoirs results in a remarkable improvement. Compared with the original fractures, the average fracture height obtained by the optimized hydraulic fracturing scheme decreases by about 51%, more effectively avoiding break-through of the thin interlayers and communication with the ineffective layers. Additionally, the fracture length obtained by the optimized hydraulic fracturing method generally reaches more than 200 m and increases by about 90% in the average length. Overall, comparison of the results from Well X-1 and the other low-production wells demonstrates the effectiveness and feasibility of the proposed optimized hydraulic fracturing scheme in this research. It achieves the goals of controlling the fracture height, creating longer fractures, increasing the effectively propped fractures, and improving the fracture conductivity, in the multi-layered and thin tight gas reservoir in the Ordos Basin, and provides guidance for the fracturing development of the same type of reservoirs in other areas.

6. Conclusions

This study utilized the data from a real multi-layered and thin tight sandstone gas reservoir of China’s Ordos Basin and adopted a numerical method to analyze the geomechanical and fracturing operational parameters’ influences on the hydraulic fracturings in this kind of reservoir and optimized the hydraulic fracturing schemes. Summing up the entire study, the following conclusions can be drawn:

(1)

In contrast to common gas reservoirs, multi-layered and thin tight sandstone gas reservoirs have a complex and overlapping vertical structure. The thickness of gas layers in this type of reservoir is usually less than 5 m, while the inter-layers are also typically thin and fragile. Improper fracturing schemes make it hard to control the fracture height in this kind of reservoir and can easily result in bad fracture shape and low production.

(2)

The geo-stress difference and the thickness difference between the gas layers and the interlayers have significant impacts on fracture propagation; a thinner gas layer needs thicker interlayers and higher geo-stress differences to control the fracture height.

(3)

Fracture propagation primarily takes place during the injection of the prepad fluid. A higher volume percentage of prepad fluid helps to create a longer fracture length; low fracturing fluid viscosity at a low injection rate is better for fracture height control in thin formations with weak interlayers.

(4)

The multi-slug sand filling method performs better than the secondary sand filling method. It carries the proppant further into the generated fractures to create a longer propped length and creates an additional barrier at the bottom of the fracture to avoid the fracture penetrating a thin interlayer, while the two-slug sand filling method shows the best performance.

In conclusion, this study demonstrates that low-viscosity prepad fluid, high-viscosity sand carrying fluid, gradually increasing the injection rate, and multi-stage sand filling are the core concepts underpinning an optimal hydraulic fracturing scheme, which can adapt to the geological characteristics of multi-layered and thin tight sandstone gas reservoirs and can effectively improve the fracturing effect.