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ACS Omega
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American Chemical Society

10.1021/acsomega.4c05973
Article
Productivity Prediction Model for Horizontal Wells of Shale under Cyclic Conflagration Compression Fracturing Percussion
https://orcid.org/0000-0002-3603-0338
Liu Jing *†‡
Zeng Zhixing †‡
Xia Lei §
Wang Qian ∥⊥
Dong Hong ∥
Wu Feipeng †‡
† School of Petroleum Engineering, China University of Petroleum, Qingdao, Shandong 266580, China
‡ State Key Laboratory of Deep Oil and Gas, China University of Petroleum(East China), Qingdao 266580, China
§ Daqing Oilfield Production Technology Institute, Daqing, Heilongjiang 163000, China
∥ Exploration and Development Research Institute of PetroChina Xinjiang Oilfield Company, Karamay, Xinjiang 834000, China
⊥ Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
* E-mail: liujing4522009@163.com.
30 08 2024
17 09 2024
9 37 3914639158
28 06 2024
21 08 2024
17 08 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

A multiscale complex fracture and matrix damage coupled productivity prediction model under cyclic percussion of horizontal wells is established, according to the evolution of matrix permeability and the characteristics of complex fracture seepage after cyclic conflagration compression fracturing. The effects of the conflagration loading rate, cyclic percussion times, horizontal in situ stress difference, seepage interference, and wellbore pressure drop on horizontal well productivity are analyzed. The results show that the loading rate and percussion times are positively correlated with the production growth rate, but the growth through percussion has a threshold. Besides that, the length of the branch fracture is closer to that of the main fracture when there is a small stress difference, which results in a higher initial productivity and recovery degree of the gas well. Additionally, section spacing can affect the distribution of the pressure field and flow field around the well. An excessive spacing can lead to bending of flow field around the well, while a too small value is able to aggravate interjoint interference. Therefore, the critical section spacing, which can establish pressure communication between sections, is taken as the optimal section spacing. According to our work, when the fracture half-length is 5, 7, and 9 m, the optimum section spacing is 15, 25, and 30 m, respectively. Under this condition, when the horizontal length exceeds 800, 700, and 500 m, the influence of the wellbore pressure drop on the productivity of horizontal wells should be considered.

National Key Research and Development Program of China 10.13039/501100012166 2020YFA0711800 document-id-old-9ao4c05973
document-id-new-14ao4c05973
ccc-price
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pmc1 Introduction

With the continuous development of oil resources and the continuous development of human industrial technology, the increase of conventional oil and gas resources is difficult to meet the growing social needs, while the development of unconventional oil and gas can effectively alleviate the energy shortage, among which shale gas resources are unconventional oil and gas resources with huge oil and gas reserves and great potential.1 Due to the typical ultralow porosity and low permeability of the shale gas reservoir, its collection state, seepage characteristics, development mode, and evaluation method are fundamentally different from the development of conventional oil and gas resources. Whether it is developed by a vertical well or horizontal well, large-area fracturing transformation is a necessary means to crack the reservoir, expand the shale gas seepage channel and achieve a production increase.2,3

In the past ten years, with the in-depth understanding of the properties of shale reservoirs, breakthroughs have been made in synchronous fracturing technology, supercritical CO2 fracturing of tight reservoirs, hydraulic volumetric fracturing technology, and ultralong horizontal section cutting technology.4−6 These technologies can effectively improve the formation probability of shear fractures in shallow fractured, brittle, and dense formations, resulting in the formation of a fracture network, which means shale gas development has entered a stage of rapid development.7,8 However, the traditional fracturing technology with fracturing fluid as the main body has some problems, such as a long construction period, a large consumption of resources, difficulty in controlling filtration loss and wellbore collapse; in addition, for the reservoirs with deep burial, high in situ stress, and high clay content, there are some technical problems like high fracture pressure, reservoir fracturing failure, small fracture net scale, low fracture distribution complexity, narrow effective support range, rapid production decline, and so on.9,10 Therefore, conflagration compression fracturing technology has received widespread attention as a feasible solution.

The study shows that reservoir fracturing transformation through conflagration fracturing is mainly realized by mechanical action, hydraulic oscillation, high temperature thermal effect, and chemical action. Different from hydraulic fracturing, conflagration fracturing does not require a large amount of fracturing fluid, proppant, and fracturing equipment, which greatly reduces the operation cost. What’s more, instantaneous gas impact can produce a higher and faster peak loading rate, so that fracture propagation is not affected by in situ stress, which is conducive to efficient fracturing of reservoirs with a deep burial, high in situ stress, and large horizontal stress difference, so as to achieve the effect of increasing production.11−13 Conflagration compression fracturing originated in the 1860s. This fracturing technology was first developed after the deep transformation of explosive fracturing and the replacement of the gunpowder. The technology was outdated at the time, making it difficult for conflagration compression fracturing to spread to the mines. Until the 1970s, researchers in various countries have renewed their research on conflagration compression fracturing to increase production, and this technology has made a further breakthrough. Nowadays, this technology has been relatively mature, and some oil fields have also carried out a series of on-site production applications for this technology.14,15

Conflagration compression fracturing technology is mainly studied in depth at two levels, namely, the kinetic properties of rocks and the mechanism of multifracture expansion under impact load. Researchers have carried out a lot of research work with the help of experiments and tests, and have achieved a lot of results in the research on the kinetic properties of rocks, the research on multiple fractures under impact load and the research on the mechanism of fracture expansion of explosive gas.16−18 With the help of the research mechanism of hydraulic fracturing, experts and scholars have studied the influence of the fracture expansion pattern and slip factor on the microscopic seepage scale of shale gas reservoirs in the process of high-energy gas fracturing; Schatz, Paine, and David et al. investigated fracture extension modeling and simulated fracturing processes for combustion–explosion fracturing;19−21 Wu Feipeng et al. established a rock impact damage calculation model based on the Von Mise criterion, revealing the rock damage mechanism and crack extension mechanism;22 In terms of production capacity research, Zhu based it on the production capacity model of multistage fractured horizontal wells under the consideration of shale gas slip, diffusion, and adsorption desorption conditions. Liu investigated a cross-scale coupled seepage capacity model for straight well zoning under conflagration compression fracturing conditions.23−26 Generally speaking, the technical research on explosion fracturing has been more mature, but there are few studies about the fluid coupling percolation mechanism in the multifracture system and wellbore in repeated explosion impact shale gas horizontal wells, and it is difficult to predict production dynamics under repeated cycle damage and a complex fracture network, which restricts the development of this technology in the shale fracturing field.

Based on the above research status of cyclic-conflagration fracturing percussion, the author subdivides the fracturing zone of the shale reservoir into the main fracture, the branch fracture, the broken damage area, the microfracture, and the interfracture matrix zone and considers the multifield coupling seepage characteristics of shale gas in the fracturing zone, matrix damage zone, seepage interference zone, and wellbore pressure drop zone. To study the effects of the horizontal geo-stress difference on fracture extension and cyclic shock on the evolution of permeability around wells, a zonal cross-scale complex fracture coupled with a matrix damage production capacity prediction model under cyclic shock in horizontal wells after presetting the number of fracture bars was innovatively established. The influences and sensitivities of multiple factors, such as loading rate, cyclic impact times, in situ stress conditions, intersegment interference, and wellbore pressure drop, on the production capacity of horizontal wells with conflagration compression fracturing were analyzed, which provides an important theoretical basis for the design of horizontal wells with cyclic-conflagration fracturing percussion in shale reservoirs and the accurate prediction of the production capacity after compression.

2 Establishment and Solution of the Model

2.1 Physical Model and Assumptions

Under the same wellbore explosion pressure condition, the more cyclic shocks, the worse the accumulation of shale damage near the wellbore, the better the porosity and permeability reconstruction effect, and the greater the effective transformation distance of rock porosity and permeability around the wellbore. Therefore, the shock wave generated by the explosion and the number of cyclic loading times can jointly improve the pore permeability of shale and affect the productivity of horizontal wells in combustion and explosive fracturing. The impact effect is represented by the change in matrix permeability Ka. The difference of geo-stress will affect the expansion of the crack in the process of fire and explosion fracturing. The high stress condition will inhibit the expansion of fire and explosion fracture, and the high stress difference will narrow the range of fire and explosion fracture and inhibit the expansion of fire and explosion fracture. Therefore, different geo-stress differences are significantly different in the range and propagation patterns of blasting fractures, and there are also significant differences in the transformation effects, thus affecting the productivity of horizontal wells with blasting fracturing.27,28

To set the model and simplify the calculation, the assumptions are made as follows:(1) With multistage fracturing of a horizontal well in a shale reservoir with equal thickness and isotropy of gas reservoir, the production of shale gas satisfies the law of conservation of mass and the method of material balance.

(2) The reservoir is divided into a modified zone, a percolation interference zone, and a wellbore pressure drop zone, as shown in Figure 1, according to the rock damage degree and the cross-scale seepage characteristics of fluid after fracturing.

(3) By considering the impact of the horizontal geo-stress difference on fracture propagation morphology under blasting and utilizing the method of analyzing the number and length of prestored cracks, the fracturing zone can be categorized into main fractures, branch fractures, fracture damage zones, microfractures, and interfracture matrix zones.

(4) The original formation pressure of the reservoir is Pe, and the pressure at the junction of the main fracture and the unmodified area is Pc, while the edge pressure of the fracture damage zone is Pa. Assuming that there is no seepage resistance in the fracture and that the pressure in the fracture is equal to the pressure at the edge of the damage zone, the bottom hole pressure of the k-cluster fracture is assumed to be Pwk.

(5) The fluid flow in the stimulation zone can be regarded as the radial flow in the interfracture matrix and the linear flow from the matrix to the main fractures and branch fractures. The interstitial matrix permeability can be regarded as the weighted average of the microfracture permeability and its surrounding matrix permeability.

(6) The effect of cyclic blasting impact on the improvement of cyclic permeability in a fractured shale matrix is considered.

(7) The adsorption and desorption, mass transfer and diffusion of shale gas, friction pressure drop in wellbore, acceleration pressure drop, and intersegment interference on a horizontal well are considered, while the capillary force and gravity are ignored.

Figure 1 Fracture network of a horizontal well under cyclic conflagration impact.

2.2 Mathematical Model

2.2.1 Stimulation Zone

Multiple fractures expand in the shale reservoir under the action of conflagration impact loads, forming a large range of dominant seepage channels around the wellbore, shale gas flowing along the unmodified area sequentially into the fracture-matrix, main fracture, branch fracture, broken damage zone, and finally into the wellbore. The above seepage zone is defined as a unit of the fracturing stimulation zone.(1) Seepage model in unmodified area.

The unmodified area is not affected by the impact wave after conflagration compression fracturing. The reservoir in this region shows low porosity and low permeability, and the gas flows into the interfracture matrix area in the form of sliding diffusion. The supply radius of the unmodified area is re, m, and the inner boundary radius is rc, m, while the reservoir thickness is h, m. Considering the change of flow state and mass transfer and diffusion of shale gas, the mass flow formula of free gas in the unmodified area is as follows:1

The formula of shale gas desorption in the unmodified area is shown below.2

Therefore, the total mass flow rate in the unmodified area is obtained.3

where Km1 is the matrix permeability in the unmodified area, m2, and Ta represents temperature of shale gas, K, while T means the absolute temperature of shale gas, K. Za is the compression factor for shale gas, while Z represents the compression factor of gas. ρa is the gas density under standard conditions, kg/m3. Pe is the initial formation pressure, MPa, and Pc represents the pressure at the edge of the crack, MPa. Pa is the edge pressure of the crushing damage area, in MPa. a is the flow correction coefficient. φ is the porosity, and μ represents the gas viscosity, mPa·s; Dk is the diffusion coefficient, m2/s, while ρc represents the rock density, g/cm3. VL is the Langmuir volume, m3/kg. PL is the Langmuir pressure, MPa. Pe is the original formation pressure, MPa, and p is the current average pressure of the gas reservoir, MPa.(2) Seepage model in fracturing modified area.

The influence of repeated impact and variations in horizontal geo-stress on the fracture growth morphology during blasting is being taken into account. In order to facilitate calculation, the number of cracks after prefabricated repeated impact and the two cracks expanding along the direction of the maximum horizontal principal stress were defined as the main fractures, and the other cracks appearing symmetrically in the artificial direction were defined as fracturing branch fractures. The fracture lengths were represented by Lf2 and Lf1, respectively. And the length ratio of Lf2 and Lf1 will change with different stress difference.28 It is assumed that there are two main fracture fractures and two m-2 branch fractures. In order to facilitate the subsequent calculation, the part between the main fracture boundary rc and the branch fracture boundary rk is defined as the I zone, and the part between the branch fracture boundary rk and the fracture zone ra is defined as the II zone, as shown in Figure 2.

Figure 2 Seepage model in the stimulation area.

There are n-arc grids along the length of the main fracture. Due to the symmetrical appearance of the fracture, the fluid will flow symmetrically from the central axis between the two fractures to the two fractures, and the flow direction to the fracture is equivalent to the direction of flow to the fracture damage zone boundary, and the pressure Pa at the edge of the fracture damage zone is the same as the pressure inside the fracture. Among them, part of the fluid in area I is a radial flow from the center of the grid to area II, and the other part is regarded as a linear flow from the center of the grid to the main fracture. Therefore, according to the seepage characteristics of shale gas in zone I and the principle of hydroelectric similarity, the radial percolation formula and linear percolation formula of free gas in the fracture circle of area I are obtained.4

Part of the fluid in area II is a radial flow from the center of the grid to the broken damage zone, and its seepage formula is consistent with the radial seepage formula in eq 4. The other part is regarded as the linear flow from the center of the grid to the main fracture and branch fracture, and the linear flow formulas of them are shown below.5

6

where Km2 is the permeability of the interfracture matrix area, which can be regarded as the weighted average of the permeability of the microfracture area and the permeability of the surrounding matrix, m2. Pi is the pressure corresponding to the center of the ith grid in the fracture circle, MPa. n is to divide the crack length Lf2 into n equal parts. Pa is the boundary pressure of the broken damage area, MPa. Lf2 is the length of the main fracture, while Lf1 represents the length of the branch fracture, m. Li is the crack length in the ith grid, m, Lf is the total length of the crack in the corresponding area, m, and ra is the radius of broken damage area, m.(3) Fracturing reconstruction damage area.29

The explosion compression shock wave acts on the rock wall around the horizontal well shaft to form a fracture damage area. The Ka repeated circulation impact has a great influence on the fracture extension and permeability change around the well shaft. Based on the Hopkinson pressure bar experiment and nuclear magnetic resonance experiment, as well as the propagation attenuation law of shock wave, the influence laws of five factors including impact loading rate, impact frequency, impact peak value, peak strain, and location away from wellbore on wellbore permeability can be obtained. Taking Longmaxi Shale as an example and taking a certain confining pressure and initial loading rate of 1067090 MPa·s–1 (peak detonation impact force 100 MPa) as an example, the permeability expression of the core after repeated impact damage is as follows:7

where the Ka100 loading rate is the wellbore permeability of loading rate 1067090 MPa·s–1 (peak explosive impact force 100 MPa), and X1 is the loading rate of the shock wave (MPa·s–1). X2 is the position away from the wellbore, m; X3 is the number of shocks, times; X4 is the peak stress, MPa; and X5 is the peak strain, decimal.

The conflagration compression impact wave acts on the rock wall around the wellbore, forming a broken damage zone of the wellbore with a permeability of Ka. Shale gas flows into the fracture zone through the main fractures and interfracture matrix and then reenters the wellbore in a radial flow. Based on the plane radial steady flow model of the fluid, the mass flow formula in this region is shown in the equation.8

According to the Langmuir isotherm adsorption equation, the shale gas desorption equation is derived as follows:9

Combining eqs 4, 5, and 6 and 7, 8, and 9, and based on the coupled seepage relationship in different fracturing areas and the mass conservation law of shale gas, the fluid mass change equation in each fracture circular grid can be obtained.10

The Newton iterative method is used to solve eq 10, and the single cluster fracture productivity formula of the horizontal well multifracture system considering shale gas adsorption and desorption, mass transfer and diffusion, and multiscale seepage can be obtained.11

2.2.2 Seepage Interference Zone

Multistage conflagration fracturing along the horizontal wellbore is helpful in expanding the fracturing volume and improving the conductivity of the shale reservoir. However, with the expansion of the flow at the end of the fracture, the pressure sweep range generated by each cluster of fractures is approximately circular, and when the pressure wave further expands, the seepage field overlaps in the adjacent fracturing reconstruction area, thus affecting the development effect of the shale reservoir. Therefore, based on the principle of superposition of seepage flow, a mathematical model with consideration of seepage interference was established to further study the impact of seepage interference on productivity of horizontal well with multifracture network, so as to optimize the multistage conflagration fracturing design of horizontal wells.

Generally speaking, the seepage control area formed by hydraulic fracturing is elliptical, and the long and short semiaxes are ak and bk. The intersection area of two adjacent ovals also representing the seepage interference area can be obtained by integrating, Sk.12

It can be seen from Figure 2 that the seepage control area formed by conflagration fracturing is approximately circular. By integration, the seepage interference area Sk of two adjacent fracturing regions can be obtained.13

Therefore, the productivity formula of the horizontal wells under cyclic conflagration impact considering seepage interference is as follows:14

where ak is the length of the semimajor axis, m; bk is the length of the semiminor axis, m; lk indicates the cluster distance, m; rk is the radius of the branch fracture, m; qk is the volume flow rate of the kth cluster of fractures.

2.2.3 Wellbore Pressure Drop Zone

On the one hand, the fluid in the horizontal wellbore flowing along the axis of the wellbore under cyclic impact will disturb the boundary layer of the wall and then change the frictional resistance of the wall surface determined by the velocity distribution, resulting in frictional pressure drop. On the other hand, the process of the flow of fluid from the fracture into the wellbore interferes with the normal flow of the fluid inside the wellbore, resulting in changes in the flow velocity at the upstream and downstream ends of the fracture, resulting in an acceleration pressure drop. It can be seen from the above that it is necessary to comprehensively consider the influence of flow coupling between reservoir fluid and the horizontal wellbore on the productivity prediction of horizontal wells.

The horizontal wells are divided into n clusters according to the number of fracturing clusters, and each cluster of fractures is an independent circular seepage zone. In the gas flow process, the wellbore between the kth inlet and the k + 1 inlet is taken as the research object (as shown in Figure 3). According to the principle of conservation of momentum, the formula is obtained.15

Figure 3 Diagram of horizontal wellbore pipe flow.

Equivalent to16

(1) Frictional pressure drop.

The frictional pressure drop from the kth cluster of cracks to the k + 1 cluster of cracks is shown as formular.1717

Equation 15 is written in a differential form and simplified by integration.18

In the calculation process, the friction coefficient of the wellbore wall involved is calculated as shown in eq 19.19

where τ is the shear stress of the wellbore wall, MPa; v is the gas flow rate, m·s–1; λ is the friction coefficient of the pipe wall, decimal; d is the inner diameter of the wellbore, m; Re is the Reynolds number, decimal; ε is the relative roughness of the pipe wall, decimal.(2) Acceleration pressure drop.

Acceleration pressure drop caused by kinetic energy change can be calculated by formular.2020

Since the gas in the horizontal wellbore totally flows from artificial fractures, the accelerated pressure drop only occurs at artificial fractures, and the above formula can be rewritten as formular.2121

The fluid flow process is regarded as the flow in the elbow when the fracture is located at the end of the horizontal wellbore; therefore, there is no accelerated pressure drop caused by the mass increase.22

Among them, the pressure value of the kth cluster fracture takes the average value of the pressure at the inlet and outlet.23

According to the flow continuity, the main flow of the Kth cluster fracture, the main flow rate of the kth cluster, is Qk, while the main flow rate of the k – 1 cluster of fractures is Qk–1, and the inflow qk of the kth cluster of fractures satisfies the following relationship.24

2.3 Model Solving

2.3.1 Solution of the Horizontal Well Productivity

Combining the single-cluster fracture productivity formula, seepage interference formula, friction pressure drop formula, and acceleration pressure drop formula, the multifactor coupling equations of the productivity model are obtained.25

There are no new variables in the combined equations, and three sets of unknowns are to be obtained. They are the gas production rate qk of the kth cluster of fractures, the pressure at the entrance of the kth cluster of fractures Pk,1, and the pressure at the exit of k-cluster fractures, Pk,2. Among them, the gas production rate Q1 of the first cluster at the toe end is calculated by the cross-scale coupled productivity model for vertical well,26 while the influence of cyclic impact on matrix permeability evolution is added.29 Furthermore, the production of each cluster of fractures and the pressure distribution in the horizontal wellbore can be obtained by using the Newton iterative method, and the total gas production Q of the shale gas well is the sum of each cluster production.

2.3.2 Prediction of Production Dynamics

On the study of the steady flow law of a multifracture system in a shale reservoir, the volume method is introduced to determine the original geological reserves of the shale gas reservoir.26

According to the material balance method of the gas reservoir, the production performance of shale gas under the steady productivity equation is forecasted. Assuming that the gas reservoir has no water drive, the material balance equation of the gas reservoir during development is as follows.27

Where,28

29

30

31

32

where G is the total surface reserves, m3. is the average formation pressure at time t, MPa. Gp is the cumulative ground production, m3. Zt* represents the visual deviation factor. Ppc is the critical pressure of gas, Mpa. Tpc indicates the critical temperature of gas, K. Sg is gas saturation, and ρpr is the dimensionless contrast density.

2.3.3 Computational Solution

Calculation steps are as follows:a. Calculate Ppr and Tpr with known reservoir physical parameters.

b. Assign the initial value Zt0 = 1, then calculate ρpr from eq 30, and then substitute ρpr into eq 29 to calculate Zt1.

c. Substitute Zt1 into eq 30 for the calculation of ρpr, and then substitute ρpr into eq 29 to calculate Zt2.

d. Repeat step c until |Ztk+1 – Ztk| < 0.0001, thereby the values of Zt and Zt* are determined.

e. Calculate the surface reserves of shale gas with eq 26 and assign the initial value Gp = 0.

f. Assuming that the production cycle of the shale gas well is t days and set the time step △t = 1 d.

g. The daily gas production of the horizontal wells and the cumulative surface production, Gp, can be obtained by solving eqs 12, 15, 19, 22, and 23.

h. The bottomhole flow pressure is kept constant, and the average formation pressure and boundary pressure Pet of the shale reservoir after gas production are calculated according to eqs 27 and 32.

i. Determine whether the production time is satisfied, and if it is established, the calculation ends. Otherwise, repeat steps a–d and f–h.

The calculation process is shown in Figure 4.

Figure 4 Flowchart for the calculation process.

2.4 Model Validation

In order to verify the accuracy of the productivity prediction model, this model can be simplified as retaining only two main fractures in the fracturing modified area, ignoring the broken zone and repeated cycle damage for the matrix formed by conflagration compression fracturing. So, Lf1 = 0 m, ra = rw, pa = pw. As a result, a simplified productivity model of the flat-like double-wing fracture with hydraulic fracturing characteristics is obtained. Fracturing data for staged fractured horizontal wells for shale gas were used in the references,30 model calculation is carried out under the condition that the basic data such as half-length of fractures, number of fractures, cluster spacing, segment spacing and reservoir parameters are consistent. It is shown in Figure 5 that the shale gas productivity decline law obtained by the simplified model is basically consistent with the law in the literature model, thus verifying the accuracy and reliability of the model.

Figure 5 Results comparison between simplified model simulation and reference.

3 Results and Discussion

Based on the formula derived above and combined with on-site data, the influence of parameters like impact loading rate, repeated impact times, seepage interference, wellbore pressure drop, and production time on the production capacity of horizontal wells is discussed, which provides guidance for the design of shale reservoir conflagration fracturing.

3.1 Parameter Setup

As a new high energy gas fracturing technology, in situ combustion and explosion fracturing technology of the shale reservoir methane has carried out key link tests and implementation process design in the aspects of compressibility analysis, fracture prediction, effect evaluation, and process optimization. The current test range includes a theoretical numerical simulation, an indoor test, and an outdoor small combustion and explosion test. In terms of productivity evaluation research, since the peak pressure of detonation that can be formed in the current laboratory test research is not more than 100 MPa, the simulation study of crack propagation can be seen that it is difficult to form effective cracks. Based on theoretical simulation, the crack length and number of cracks are less than 5 m and less than 6 under the peak load of 300 MPa. One of the research focuses of this paper is the influence of damaged rock permeability on productivity under different cyclic impact energies and impact times.

In order to better simulate the production capacity of horizontal wells under the coupling of the cyclic complex fracture network and matrix damage, the cyclic impact and matrix damage are separately considered before physical coupling solution. It is possible to couple and simulate the horizontal well productivity under complex fracture network conditions and cyclic matrix damage based on the matrix damage law and permeability evolution model under different cyclic impact conditions in the early stage,27,28 and considering pre-existing 6 cracks with a length of 5 m.

Combined with the basic parameters of a shale gas reservoir in the Changning area, Sichuan Province, China, MATLAB numerical simulation software is used to program the conflagration fracturing productivity. Basic parameters of shale gas reservoir simulation are shown in Table 1.

Table 1 Basic Parameters for Shale Gas Reservoir Simulation

data type	value	data type	value	
thickness of gas reservoir (m)	30	radius of wellbore (m)	0.1	
rock density (g·cm–3)	2.6	vertical well supply radius (m)	400	
bottomhole pressure (MPa)	5	diffusion coefficient (m2·s–1)	8.4067 × 10–7	
gas compressibility factor	0.89	initial permeability of matrix (m2)	0.5 × 10–16	
original formation pressure (MPa)	20	gas viscosity (mPa·s)	0.017	
gas density under standard conditions (kg·m–3)	0.717	avg pore diameter (nm)	20	
absolute temperature of shale gas (K)	366	porosity (%)	8.7	
Langmuir pressure (MPa)	2.5	Langmuir volume (m3·kg–1)	0.00285	
fracture length (m)	5	the number of fractures	6	

3.2 Analysis of Factors Affecting the Production Capacity of Horizontal Wells

3.2.1 Influence of Cyclic Impact on the Productivity of Horizontal Wells

Based on the optimization of the number and length of multiple fractures in a single section of a horizontal well and the number and length of explosive fractures in a vertical well,29 the fractures are prepositioned in a single section of a horizontal well fracture model. The effects of the cyclic impact loading rate and cyclic impact frequency on the daily and cumulative production capacity of a single section of horizontal wells are simulated, and the results are shown in Figures 6 and 7.

Figure 6 Daily shale gas production change with peak loading pressure and percussion times: (a) Peak loading pressure, 50 MPa; (b) Peak loading pressure, 75 MPa; (c) Peak loading pressure, 100 MPa.

Figure 7 Cumulative shale gas production change with peak loading pressure and percussion times: (a) Peak loading pressure, 50 MPa; (b) Peak loading pressure, 75 MPa; (c) Peak loading pressure, 100 MPa.

As shown in Figures 6a and 7a, 0 impact indicates that under the pre-existing fracture conditions, there is no rock impact damage and the initial production capacity and cumulative gas production are lower than those under the consideration of cyclic impact, which indicates that the simulation can be more accurate with the consideration of the influence of cyclic impact on the matrix.

When the pulse width is constant, different loading rates correspond to different loading peaks. Figures 6 and 7 show the shale gas daily production and cumulative production under peak loading pressures of 50 MPa (corresponding loading rate 533546 MPa·s–1), 75 MPa (corresponding to loading rate 800318 MPa·s–1), and 100 MPa (corresponding to loading rate 1067090 MPa·s–1). The peak loading pressure and percussion frequency have a significant impact on the initial production capacity of a single section and have a more significant impact on production decline. With other factors unchanged, the initial production increases with the peak loading pressure and the number of percussions. This is because the high-energy shock wave and the number of cyclic loadings can improve the permeability of the rocks around the wellbore and the effective transformation distance, thus improving the initial productivity of shale gas wells through this synergy. At the same time, since the model adopts a constant pressure production method, under the condition of a certain gas content in the reservoir, the initial production increases as the peak loading pressure and the number of shocks grow, which in turn leads to a greater production decline rate and earlier entering the pseudosteady-state coupled seepage stage. Under the peak loading pressure of 50 MPa, during the first 4 impacts, the number of impacts and the cumulative production capacity are positively correlated, and the fifth impact has little effect on the increase in cumulative production capacity. Under the peak loading pressures of 75 and 100 MPa, the effect of the last three percussions on the cumulative productivity is not obvious, because the permeability of shale near the wellbore is significantly improved under the initial medium and high energy percussion. Although subsequent cyclic percussion process can improve shale permeability, the improvement is little, which reflects in the cumulative capacity curve is that the cumulative capacity is similar during the 600-day production process.

In order to quantify the cumulative gas production of horizontal wells under different combinations of peak loading rates and cycle impact times, the cumulative production under different cyclic loads is summarized and compared with the productivity under the condition of not considering matrix damage permeability, so the contribution rate of damage permeability to productivity under different cyclic loads is obtained, as shown in Figure 8. It is shown that the loading rate, the number of shocks, and the cumulative production growth rate are positively correlated. At the same time, with the increase of the number of shocks, the growth rate of production capacity slows, indicating that the effect of the number of shocks on reservoir permeability has reached a threshold value. Therefore, peak loading is preferred 100 MPa (loading rate is 1067090 MPa·s–1), and the number of cycle impacts is 4 times.

Figure 8 Growth rate of single-stage gas production in fractured horizontal wells under different cyclic impact loads.

3.2.2 Influence of Horizontal In Situ Stress Difference on Horizontal Well Productivity

According to the existing research, different in situ stress conditions can affect the fracture growth pattern of conflagration fracturing.27,28 When there is no stress difference, fractures expand uniformly in all directions. While with the increase of the stress difference, fractures form a dominant expansion in the direction of the maximum horizontal stress, which is the main fracture defined in this paper. Moreover, the range of explosion cracks is also getting narrow. Therefore, in order to facilitate data analysis and comparison, the main fracture length Lf2 is preset to be 5 m, and the length of the branch fractures in the fracturing modified area is changed to analyze effect of the uneven expansion of fractures caused by different in situ stress conditions on gas well productivity. As shown in Figure 9, with other factors remaining unchanged, the initial productivity and recovery degree of the gas well are much higher when the branch fracture length is close to that of the main fracture. Therefore, fully considering the influence of in situ stress difference on the fracture propagation form has great importance to controlling the degree of fracturing and then more accurately completing the productivity prediction of horizontal wells.

Figure 9 Influence of uneven fracture propagation and time on productivity.

3.2.3 Influence of Intersection Interference on the Productivity of Horizontal Wells

The half-length of horizontal well fractures is closely related to the control range of the gas well productivity. A reasonable design of fracturing interval spacing is beneficial for reducing seepage interference and obtaining higher fracturing productivity according to the different fractures half-length.

Figure 10 shows the production capacity variation curve of a methane conflagration compression fracturing horizontal well with a horizontal section length of 750 m, 25 fracturing sections, a reservoir pressure of 20 MPa, and a bottom hole pressure of 5 MPa. From Figure 11 it can be seen that daily production grows with the spacing between adjacent crack segments in the early production stage. As the production time prolongs, the daily production gradually decreases and tends to stabilize at different intervals. The total gas production increases with the increase of the spacing, while the increasing production rate slows down as the overlapping area of seepage decreases. Therefore, under the conditions of this study, when the half-length of cracks is 5, 7, and 9 m, the optimal segment spacing is 15, 25, and 30 m, respectively.

Figure 10 Effect of different fracture half-lengths and segment spacing on productivity (from top to bottom: fracture half-length is 5, 7, and 9 m).

Figure 11 Reservoir pressure distribution of multifracture system at different times: (a) Reservoir pressure distribution when spacing is 10 m; (b) Reservoir pressure distribution when spacing is 15 m; (c) Reservoir pressure distribution when spacing is 20 m.

In order to further explain the impact of intersegment interference on the productivity of horizontal wells, taking a fracture with a half-length of 5 m as an example, the distribution of reservoir pressure at different time periods and different fracture spacing was obtained during constant pressure production.

It is clearly shown in Figure 11 that the spacing between the conflagration and compression fracturing sections in a horizontal well will affect the pressure field and flow field distribution around the well. When the spacing is 20 m, excessive spacing will cause the flow field around the well to bend and increase the seepage resistance. When the spacing is 10 m, too small an interval will exacerbate the interference between joints and increase construction costs. Therefore, the spacing that can establish pressure communication between segments is the critical value, and when the half-length is 5 m, the optimal spacing is 15 m.

3.2.4 Influence of Wellbore Pressure Drop on Horizontal Well Productivity

The influence of the wellbore pressure drop on the productivity of horizontal wells is discussed based on the parameters selected above. As shown in Figure 12, when shale gas flows from toe end to root end along the wellbore, the pressure drop caused by gas-wall friction and radial confluence is small at the initial stage, and the change range of bottom hole flow pressure and flow rate is small. But the pressure drops fast when it is close to the root, and the gas production reduction is more obvious as well. This is because there is also a continuous influx of gas into the wellbore during the process of gas flowing from the toe to the heel, so the flow rate inside the wellbore continues to increase, leading to a gradual increase in the frictional pressure drop caused by the friction between the fluid and the wellbore wall as well as the acceleration pressure drop caused by the influx of gas, resulting in a decrease in the gas production rate of a single fracture along the way. Therefore, for gas wells with long horizontal sections and high production capacity, it is necessary to consider the influence of the wellbore pressure drop on production capacity and optimize the development plan reasonably. In our study, when the half length of the fracture is 5, 7, and 9 m and the optimal interval between segments is 15, 25, and 30 m, respectively, and when the horizontal segment length exceeds 800, 700, and 500 m, it is necessary to consider the impact of wellbore pressure drop on the production capacity of horizontal wells.

Figure 12 Influence of wellbore pressure drop on productivity: (a) Fracture half-length is 5 m; (b) Fracture half-length is 7 m; (c) Fracture half-length is 9 m.

4 Conclusion

(1) The productivity prediction model of the horizontal wells considering matrix damage is established. The effects of blasting loading rate, cyclic impact times, horizontal in situ stress difference, seepage interference, and wellbore pressure drop on horizontal well productivity are analyzed.

(2) Loading rate and impact times are positively correlated with the production growth rate. However, the increase in the production growth rate slows down with the increase in the loading rate and impact times, and the loading rate and cyclic impact times are selected to be 1067090 MPa·s–1 and 4 times, respectively, for comprehensive consideration.

(3) The smaller the horizontal geo-stress difference is, the closer the length of the main and branch seams are to each other, and the higher the initial production capacity and recovery rate are in order to minimize the seepage interference between seams, the simulation conditions when the length of the fracture is 5, 7, and 9 m, the optimal segment spacing is 15, 25, and 30 m, respectively; with this fracture half-length and optimal segment spacing, when the horizontal segment length exceeds 800, 700, and 500 m, respectively, the impact of the borehole pressure drop on the production capacity of the horizontal wells needs to be considered.

(4) The research provides an important theoretical basis for the design of multistage cycle conflagration compression fracturing and the productivity prediction of horizontal wells in shale reservoirs.

Author Contributions

J.L.: Methodology, research, writing, thought guidance. Z.Z.: Formal analysis, resources, writing. L.X.: Software, funding acquisition, supervision, validation. Q.W.: Data processing and verification. H.D.: Data processing and verification. F.W.: Project administration, writing–review and editing.

The authors declare no competing financial interest.

Acknowledgments

This work is supported by the National Key R&D Program of China (Project Number: 2020YFA0711800).
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