Well-Interference Characteristics of the Production of Shale Well Pads: A Case in the Southern Sichuan Basin

Abstract

With the development of shale gas horizontal well-filling technology, by drilling infill wells between wells, the well spacing is continuously reduced to make shale reservoir reconstruction more effective. However, in shale gas reservoirs in China, the problem of inter-well interference is becoming increasingly serious, which not only affects the production of well groups but also causes wellbore damage. Currently, the process of interference in the production process is unclear. This study addresses the inter-well interference issue in deep shale gas reservoirs. An integrated numerical simulation method combining the Discrete Fracture Network, Finite Element Method, and Finite Difference Method is proposed. A comprehensive reservoir numerical model considering the production process is proposed. According to the actual reservoir model parameters and operation parameters, a multi-factor analysis model under multiple production conditions was established. Cumulative gas production and inter-well interference were analyzed. Finally, a field model was established, and the history matching of formation pressure was carried out. According to the history-matching results, the pressure expansion range in the production stage was analyzed. These research results provide a scientific basis and practical suggestions for the effective management and mitigation of inter-well interference and are expected to play an important role in practical engineering applications.

1. Introduction

With the development of shale gas horizontal well infill technology, by drilling infill wells between wells, the well spacing is continuously reduced, which makes the shale reservoir reconstruction more effective [1,2,3,4]. Encryption technology is also applied in the drilling and fracturing technology [5,6]. In the fracturing process of infill wells, when well spacing is too small or adjacent wells are fractured too much, it is often observed that the pressure of existing wells suddenly increases, the production drops sharply, and it is difficult for new wells to maintain a high net pressure [7,8]. This indicates that there is communication between the mother and child well. This fracturing-induced inter-well interference is commonly known as Frac-Hit [9]. The problem of inter-well interference in shale gas reservoirs in China is becoming more and more serious. It is mainly reflected in the two stages of fracturing and post-fracturing production. The main manifestation is the disturbance of wellbore pressure. Severe inter-well interference can lead to wellhead damage, compromise well integrity, and even lead to well abandonment [10,11]. Among them, the most serious situation is the occurrence of inter-well interference response during fracturing and production. At present, there is a lack of research on inter-well interference, and the process of inter-well interference in post-pressure production is still unclear. Field practice has shown that inter-well interference caused by fracturing has become a major difficulty faced by the shale industry, which will have many negative impacts on platforms and adjacent platforms [12]. There is an urgent need for a set of effective methods to solve or mitigate the effects of inter-well interference to guide the operation of the field.

At present, the development of shale gas reservoirs is one of the main forces of natural gas exploration and development in China. Improving the recovery rate of shale gas reservoirs is an important goal and a difficult challenge in development. Due to strong heterogeneity, poor physical properties, and a high degree of natural fracture development, water lock damage is easily formed in the development process. As a result, the recovery rate of shale gas reservoirs is relatively low [13]. Global scholars mainly focus on well test analysis, field diagnosis, and prevention and control of inter-well interference [14]. In the aspect of numerical simulation analysis of inter-well interference, exploration and research have been carried out in the Sichuan shale gas block. Well spacing was optimized through productivity simulation combined with economic evaluation, and the mechanism of pressure diffusion between wells and fractures was studied [15,16,17,18]. In the process of fracturing, the main fracture is more likely to form in the area where the single-directional fracture develops. The reconstruction degree is relatively low, and it can easily lead to complex downhole phenomena such as inter-well pressure channeling and casing change [19]. Inter-well interference caused by fracturing may occur between adjacent fractured wells, or between fractured wells and adjacent producing wells [20]. The latter is more likely to affect gas well production [21]. According to statistics, inter-well interference in five shale oil and gas development blocks, including Woodford and Bakken, has caused both positive and negative impacts [22]. In the Woodford, Eagle Ford, and Niobrara blocks, in particular, the vast majority of parent and sub-wells were negatively impacted. Oil and gas production has fallen sharply and has been slow to recover. The first six months of production of the parent well was reduced by 30% to 60%, and the 20-year estimated ultimate recoverable reserves (EURs) of the sub-well were reduced by an average of 50%. More than half of the disturbances in the Bakken and Haynesville shales increased parent well production, but only for a few months or a year [23].

In order to investigate the influence of multiple factors on the inter-well interference and the output in the production process of deep shale reservoir. In this paper, the FDM-FEM numerical method is combined. A multi-factor analysis of the scope of reconstruction and the production model is carried out. The change in production and pressure is analyzed, and the optimal production model is finally determined. Finally, a numerical model of the field reservoir is established considering the production process. Based on the actual reservoir model parameters and construction parameters, the production system is established to carry out the history matching of formation pressure. According to the history matching results, the pressure spread range is analyzed. The results can provide a research direction for the study of inter-well interference in deep shale reservoirs and can effectively guide field production.

2. Theoretical Model

2.1. Fracture Model

The motion equation of gas in a fracture, known as the gas–water two-phase motion equation [24] is as follows:

$$\left\{\begin{array}{l}{v}_{gf}=-{\displaystyle \frac{k_{gf}}{{\mu }_g}}\left(\nabla p_{gf}-{\gamma }_g\nabla D\right)\\ v_{wf}=-{\displaystyle \frac{k_{wf}}{{\mu }_w}}\left(\nabla p_{wf}-{\gamma }_w\nabla D\right)\end{array}\right.$$

(1)

where $k_{gf}$ and $k_{wf}$ represent the permeability of gas and water in the fracture, respectively, with units in mD. $p$ represents the pressure in the fracture. g represents the gas phase. w stands for the water phase. f stands for the shale fracture system. γ is the volumetric weight, which is the product of the density and the gravitational acceleration. D stands for top depth, with units in m.

According to the law of conservation of mass, the fluid continuity equation of the fracture system is as follows [24]:

$$\left\{\begin{array}{l}-\nabla \left({\rho }_g{v}_{gf}\right)+{\rho }_g{q}_g+{\rho }_g{Q}_g={\displaystyle \frac{\partial \left({\varphi }_f{\rho }_g{S}_{gt}\right)}{\partial t}}\\ -\nabla \left({\rho }_w{v}_{wf}\right)+{\rho }_w{Q}_w={\displaystyle \frac{\partial \left({\varphi }_f{\rho }_w{S}_{wt}\right)}{\partial t}}\end{array}\right.$$

(2)

where, ${\rho }_g$ and ${\rho }_w$ represent the densities of the gas phase and the water phase, respectively. ${\varphi }_f$ represents the fracture porosity. $q_g$ represents gas crossflow term between fracture and matrix. Water crossflow between fracture and matrix is neglected, and only the gas phase, unit s⁻¹. Q_g and Q_w are the injection-production term of gas-water two-phases flow. Inflow is positive, Outflow is negative, unit s⁻¹. $S$ represents two-phase saturation, dimensionless.

Simultaneous saturation and capillary force auxiliary equation [24]:

$$\left\{\begin{array}{l}{S}_{gf}+S_{wf}=1\\ p_{gf}=p_{wf}+p_{cf}\end{array}\right.$$

(3)

where, $p_{cf}$ represents capillary force in the fracture system, unit Pa. Coupled state equations for gas-liquid two-phase flow [24]:

$$C_w={\displaystyle \frac{1}{{\rho }_w}}{\displaystyle \frac{d{\rho }_w}{dp}}$$

(4)

$${\rho }_w={\displaystyle \frac{T_{sc}{Z}_{sc}{\rho }_{sc}}{p_{sc}}}{\displaystyle \frac{p_f}{ZT}}$$

(5)

where, $C_w$ represents the water phase compression coefficient expressed in terms of density, unit MPa⁻¹. $p_{sc}$ means the pressure at standard conditions, unit MPa. $Z_{sc}$ represents deviation factor under standard conditions. ρ_sc means gas density in standard conditions, unit kg/m³. $T_{sc}$ stands for temperature at standard conditions, unit K.

Rock compressibility is defined as [24]:

$$C_f={\displaystyle \frac{d{V}_p}{V_f}}{\displaystyle \frac{1}{dp}}$$

(6)

where, V_p stands for pore volume, unit m³. V_f represents fracture volume, unit m³. Then the porosity expression is [24]:

$${\phi }_f={\phi }_{f0}+C_f\left(p-p_0\right)$$

(7)

where, ${\phi }_f$ represents the reference fracture porosity at reference pressure, dimensionless.

2.2. Matrix Model

The matrix mainly plays the role of storage, the fracture is the seepage channel, the matrix supplements the fluid to the fracture, considering the pressure change of the matrix.

As the gas in the matrix is discharged into the fracture and wellbore, the adsorbed gas in the matrix is desorbed. Because the pore water of shale matrix is small and mostly in the form of water film, it is difficult to participate in the flow, and the water phase channeling in the solid matrix is not considered.

Taking the gas equation as an example, the continuity equation is [24]:

$$-\nabla \left({\rho }_g{v}_{gm}\right)+{\rho }_g{q}_r-{\rho }_g{q}_g={\displaystyle \frac{\partial \left({\varphi }_m{\rho }_g{S}_{gm}\right)}{\partial t}}$$

(8)

where, $q_r$ represents the desorption term in the matrix, the free air volume of desorption in the matrix pores per unit volume, m³/(s·m³).

According to the Langmuir isothermal adsorption model adopted by the model, with the progress of time, the pressure of the matrix system decreases and the gas desorption is attached, satisfying the Langmuir law. The calculation expression is as follows [24]:

$$q_r=-B{\displaystyle \frac{\partial V_m}{\partial p_m}}\cdot {\displaystyle \frac{\partial p_m}{\partial t}}=B_g{V}_L{\displaystyle \frac{p_L}{{\left(p_L+p\right)}^2}}{\displaystyle \frac{\partial p_m}{\partial t}}$$

(9)

where, B represents the volume factor. V_m represents the amount of gas adsorbed per unit volume of shale matrix, $V_m={\displaystyle \frac{V_L{p}_L}{p_L+p}}$, unit m³/m³.

Gas flow velocity equation, considering knudsen diffusion and other forms [24]:

$$v_g=-{\displaystyle \frac{k_{gm}}{{\mu }_g}}\left({\displaystyle \frac{\partial p_{gm}}{\partial r}}-{\gamma }_g\nabla D\right)$$

(10)

where, ${\mu }_g$ represents the gas viscosity, unit cP. Simultaneous saturation and capillary force auxiliary equation [24]:

$$\left\{\begin{array}{l}{S}_{gm}+S_{wm}=1\\ p_{gm}=p_{wm}+p_{cm}\end{array}\right.$$

(11)

where, $p_{cm}$ represents the capillary force of the matrix system, unit Pa. Gas equation of state [24]:

$${\rho }_g={\displaystyle \frac{T_{sc}{Z}_{sc}{\rho }_{sc}}{p_{sc}}}{\displaystyle \frac{p_m}{ZT}}$$

(12)

$${\rho }_w={\rho }_{w0}\left[1+C_w\left(p_m-p_0\right)\right]$$

(13)

$${\phi }_m={\phi }_{m0}+C_m\left(p-p_0\right)$$

(14)

where, ${\phi }_m$ represents the porosity of the reference matrix system under the reference pressure. C_m represents the compressibility coefficient of matrix system rock volume, MPa⁻¹.

2.3. Matrix–Fracture System Channeling Equation

The production mainly depends on the seepage from fractures into the wellbore. Although the matrix has very low permeability, it is very important to calculate the cross-flow term of the matrix, which is the main fluid supply system.

Assume that there is no starting pressure gradient. The flow equation of shale gas channeling from matrix system to fracture system can be expressed as [24]:

$$q_g={\displaystyle \frac{\alpha k_m}{{\mu }_g}}\left(p_m-p_f\right)$$

(15)

where, α represents the shape factor of the matrix block system.

3. Geological Setting

3.1. Study Area

Well area Y is located in the northeast of Luzhou Block, which is the main production area of deep shale gas in southern Sichuan. The formation lithology of Wufeng Formation to Longmaxi Formation is mainly shale. Shale gas field in Luzhou Yang101 well area is buried 3600~4200 m. The structure of the area is wide and slow. High-quality continuous reservoir thickness of 35–40 m. The formation pressure coefficient is generally greater than 2.0. The lithology is mainly black shale and gray-black carbonaceous shale. The interpreted porosity is 4.5–5.9%, with an average of 4.9%. The organic carbon content is 2.5~5.7%, with an average of 3.5%. The total gas content is 4.8~8.1 m³/t, with an average of 6.7 m³/t. High gas saturation and gas content, good preservation conditions, large resource potential [25].

3.2. Model Building

In this paper, a numerical simulation model for fracturing and production of shale gas horizontal wells in deep reservoir is established. The influence mechanism of many factors on pressure breakthrough is analyzed. As shown in Figure 1. The model considers two wells with a bottom hole distance of 300 m within a model size of 1500 × 3000 m. The parameters used in the model are outlined in

Table 1. Model parameter table.

Parameter		Value
Number of cells (NX × NY × NZ)		300 × 600 × 10
Reservoir size (km) (LX × LY × LZ)		1.5 × 3 × 0.1
Cell size (m)	DX × DY	5 × 5
	DX × DY	10
Top depth (m)		3630
$\mathrm{Horizontal} \mathrm{Permeability} k_h$ (mD)		0.001
$\mathrm{Vertical} \mathrm{Permeability} k_v$ (mD)		0.0001
$\mathrm{Horizontal} \mathrm{Fracture} \mathrm{Permeability} k_{hf}$ (mD)		100
$\mathrm{Vertical} \mathrm{Fracture} \mathrm{Permeability} k_{vf}$ (mD)		10
$\phi$		0.05
$\rho$ (g/cm3)		2.6
Pressure at the 3580 m depth (MPa)		81

. The model simulates and examines the fracturing process, taking into account factors such as fracturing scale and the impact of different production model on inter-well interference. Through this analysis, a better understanding of the mechanisms and influencing factors of pressure breakthrough during the post-fracturing production of deep shale gas [26].

4. Results and Discussion

4.1. Fracturing Scale

In the field, due to the heterogeneity of the formation and the defects of the fracturing process, the fracture propagation is usually unbalanced after hydraulic fracturing. In order to investigate the influence of the expansion range of hydraulic fracture on production, we simulated the hydraulic fracturing process under three different conditions. Finally, three kinds of fracture propagation distances are obtained. This satisfies the current fracture propagation situation in most of the field. According to the fracture relationship between the two wells, they are divided into unconnected fractures, partially connected fractures and fully connected fractures. Unconnected fractures of the two wells can be considered as independent fractures without any connection. Partially connected fractures occur when some fractures in two wells have a connecting path between them, but not all fractures are connected. Fluid flow is limited. Fully connected fractures occur when fractures are fully connected through a through path, allowing fluid to flow freely in the fracture network. The connectivity between fractures is strong and usually shows high permeability.

Figure 2 shows the final gas production cumulative under the same production conditions for different fracture ranges. When two adjacent wells in the reservoir are completely fractured and then produced at the same time, the longer the hydraulic fracture length (effective reconstruction volume), the larger the space for reserve utilization, the more shale gas can be effectively exploited, and the final gas production cumulative will be larger.

A line across two wells was selected. The pressure was extracted along this line and the pressure interference between wells was observed. As can be seen from the Figure 3, the longer the fractures length, the more easily the fractures between wells intersect. Even if pressure channeling does not occur during the fracturing process, during the production process, due to the prolonged production, the pressure will propagate along the matrix, resulting in increased interference between the wells.

4.2. Production Model 1—Constant Pressure Production and Constant Rate Production

This section is identical to Section 4.1 except that the production system. When the scope of the reconstruction area is small, the influence of constant pressure production and constant rate production on the total output is very small, almost negligible. As shown in Figure 4, when the scope of the reconstruction zone gradually increases to partially connected fractures, the cumulative gas production of constant pressure production is higher than that of constant rate production. This is mainly because the larger the range, the greater the pressure relief radius of the formation. When there is a sufficient pressure difference, the yield can be increased.

As can be seen from the pressure curve of connected wells in Figure 5, there is little difference between constant pressure production and constant rate production on formation pressure, and they have similar shapes and sizes.

The interference between wells is very serious when fully fracture is connected, and many engineering problems are easy to occur during construction. This phenomenon should be avoided as much as possible in the project. Therefore, fully fracture connectivity will not be discussed in the following analysis.

4.3. Production Model 2—Simultaneous Production and Sequential Production

When the two wells are fully fractured and produced sequentially, as shown in Figure 6 and Figure 7. When the reconstruction area is small and the fracture zone is not connected. Due to the tightness of the shale reservoir, there is no inter-well pressure interference. Production sequence has little effect on gas production cumulative. However, with the increase of the reconstruction scope and the connection of fractures, sequential production will lead to the use of reserves in the new well reconstruction area during the production of old well. And with the more serious fracture communication, the more reserves of old well to be used in new well.

But the positive thing is that sequential production increased the production time and caused some recovery of formation pressure, as shown in Figure 8 and Figure 9. Sequential production can effectively solve the inter-well barrier of simultaneous production. The final gas production cumulative is greater than the simultaneous production.

When the gas production of each well is studied. The difference in ultimate recovery is small when the fracture is not connected. Whether it is constant pressure production, constant rate production or sequential production, the difference in final recovery efficiency is small and negligible.

When the fractures begin to connect and the connectivity becomes more and more serious, the gas production of the old well gradually increases, while the gas production of the new well gradually decreases. In other words, when there is more fracture connectivity, the gas production of new well will decrease. The more fractures are connected, the greater the impact on gas production of new well.

4.4. Production Model 3—Complete Fracturing and Sequential Fracturing

The gas production of the two wells has no influence on each other because of non-connected fractures. In the analysis of the effect of sequential fracture production on gas production cumulative. We only discuss the effect of partially connected fractures on gas production cumulative. Unlike Section 4.3, sequential production involves two wells being complete fracturing fractured and then sequentially produced. Sequential fracturing production involves fracturing a well first and then starting production. When the old well is produced, the new well is fractured and the new well is produced again. There is no fixed time between drilling and fracturing an infill well. A plateau period is set for infill well operations where the parent well may have new impacts due to formation energy.

When the production is produced after sequential fracturing, the effective range of production is limited to the hydraulic fracture range of old well. When the production is completed after fracturing, part of the production of the old well is within the scope of the fracture range of the new well. As shown in Figure 10 and Figure 11. As a result, sequential fracturing of older well is less productive than complete fracturing. However, the recovery rate of new well is increased. Even newer well are more productive than older well due to the recovery of formation energy after shut-in. The pressure in the reconstruction area of the old well is very low during the sequential fracturing. Sequential fracturing results in partial fracture closure, which affects the entire effective reconstruction range. As a result, the total gas production from the sequential fracturing was lower than the produced after the two wells were complete fractured.

As shown in Figure 12 and Figure 13, although sequential fracturing can reduce some of the inter-well interference, the impact on overall production can be significant. In the actual fracturing process, the change of ground stress should be considered in the sequential fracturing. It may lead to more serious pressure channeling during fracturing and serious engineering problems.

5. Figures Field Application

Firstly, the fracture inversion is carried out. The existing natural fracture model was modified using various parameters (spatial distribution function, density, occurrence, geometric size, etc.) to form the DFN model, as shown in Figure 14. The results show that high angle fractures and bedding fractures are opened at the same time. The fracture distribution is basically symmetrical on both sides of the wellbore, and the fracture initiation is uneven in some sections. The fracture network near the fracture zone is complicated, and some sections are affected by pressure channels. The average fracture length is about 300 m, the width is about 135 m, and the height is about 62 m. The accuracy of the model is verified by comparing the simulation results of fracture propagation with the field microseismic data.

Based on the fracture morphology verified by microseismic, the reservoir numerical simulation model of Yang101 well area is established, as shown in Figure 15. The production history is fitted on the multi-scale discrete fracture model, and the bottom-hole pressure is fitted with the fixed gas production.

Under the fixed daily gas production of each well, the fitted bottomhole pressure of a single well and the fitted gas production and bottomhole curve of the whole area are shown in Figure 4. Because of the pressure breakthrough behavior in the fracturing process of H4-6 well in the later period, the pressure surge of H4-5 well. The relative error of the fitting results of bottomhole pressure in the later period is high, but the fitting of the production dynamic of gas well in the gas reservoir has reached a high fitting accuracy. The pressure fitting of the whole gas reservoir is basically consistent with the existing understanding, as shown in Figure 16.

As shown in Figure 17, Figure 18 and Figure 19, when the production of well H4-5 was finished, the pressure around the well dropped by 38 MPa, and when the two wells were all finished, the pressure around the well H4-6 dropped by 30 MPa. Due to the connectivity effect of fracturing, the bottom pressure of well H4-5 rose rapidly, and the pressure connectivity between wells was formed. On the plane, at the interwell fracture connection between well H4-5 and H4-6, the pore pressure appears interwell communication. The circumferential interference is excessive, and the interference intensity decreases continuously. In the longitudinal direction, The range of production pressure disturbance after fracturing is limited by both hydraulic fracture and natural fracture zone and is slightly higher than that of hydraulic fracture. The inter-well connectivity range is greater than the fracturing height. The inter-well interference characteristics after fracturing in vertical and horizontal direction show local heterogeneity. The variation difference of inter-well interference pressure in the inter-well interference section is more than 5 MPa. The conduction characteristics of inter-well interference pressure caused by production are different between sections. Even if they are both pressure channeling sections, the degree of inter-well interference in production is also significantly different.

6. Conclusions

The results show that:

• When the fracturing range is small, inter-well interference can be reduced, but the total gas production is small. When the fracturing range is larger, the more fractures are connected, the inter-well interference problem will be aggravated, and engineering accidents will easily occur, resulting in greater economic losses.
• In the post-fracturing production process, the fracture zone should be as disconnected as possible or with little connectivity. Adjacent wells should be complete fractured and then sequential production to maximize cumulative gas production.
• Inter-well interference remains concentrated around fracture propagation channels, constrained by the ultra-low permeability of deep shale layers, and the pressure propagation range does not further expand during the production process.
• Fracture propagation causes communication between wells, leading to a surge in bottom-hole pressure in older well and a sudden drop in bottom-hole pressure in new well, ultimately resulting in a decline in productivity.

These research results provide scientific basis and practical suggestions for effective management and mitigation of inter-well interference, and are expected to play an important role in practical engineering applications.