Productivity Analysis and Evaluation of Fault-Fracture Zones Controlled by Complex Fracture Networks in Tight Reservoirs: A Case Study of Xujiahe Formation

: The development of tight gas reservoirs presents a signiﬁcant challenge for sustainable development, as it requires specialized techniques that can have adverse environmental and social impacts. To address these challenges, efﬁcient development technologies, such as multistage hydraulic fracturing, have been adopted to enable access to previously inaccessible natural gas resources, increase energy efﬁciency and security, and minimizing environmental impacts. This paper proposes a novel evaluation method to analyze the post fracturing productivity controlled by complex fault fracture zones in tight reservoirs. In this article, a systematic method to evaluate stimulated reservoir volume (SRV) and fault-fracture zone complexity after stimulation was established, along with the analysis and prediction of productivity through coupled fall-off and well-test analyses. Focusing on the Xujiahe formation in the Tongnanba anticline of northeastern Sichuan Basin, a 3D geological model was developed to analyze planar heterogeneity. The fall-off analytical model, coupled with rock mechanical parameters and fracturing parameters such as injection rates, fracturing ﬂuid viscosity, and the number of clusters within a single stage, was established to investigate the fracture geometric parameters and complexities of each stage. The trilinear ﬂow model was used to solve the well-test analysis model of multi-stage fractured horizontal wells in tight sandstone gas reservoirs, and well-test curves of the heterogeneous tight sandstone gas fracture network model were obtained. The results show that hydraulic fractures connect the natural fractures in fault-fracture zones. An analysis of the relationship between the fracture geometric outcomes of each segment and the net pressure reveals that as the net pressure in the fracture increases, the area ratio of natural fractures to main fractures increases notably, whereas the half length of the main fracture exhibits a decreasing trend. The overall area of natural fractures following stimulation is 7.64 times greater than that of the main fractures and is mainly a result of the extensive development of natural fractures in the target interval. As the opening ratio of natural fractures increases, the length of the main fractures decreases accordingly. Therefore, increasing net pressure within fractures will signiﬁcantly enhance the complexity of fracturing fractures in shale gas reservoirs. Furthermore, the initial production of Well X1–10, which is largely controlled by fault-fracture zones, and the cumulative gas production after one year, are estimated. The systematic evaluation method in this study proposed a new way to accurately measure fracturing in tight reservoirs, which is a critical and helpful component of sustainable development in the natural gas industry.


Introduction
Tight sandstone gas exploration and development spans almost a century, with the United States and Canada spearheading the research in the 1960s.The world's tight sandstone gas resources are vast, with nearly 70 basins worldwide being discovered or speculated to contain 603.5 trillion cubic meters of resources according to the United States Energy Information Administration (EIA) of January 2021 [1].China's technically recoverable resources have been assessed to be 3.0109 trillion cubic meters by 2010 [2].Tight sandstone gas accounts for roughly 30% of annual natural gas production in countries such as the United States and China, underscoring its indispensable position in the respective energy structures [3,4].Efficient development technologies can be vital and good for sustainability, as they enable the extraction of natural gas resources with reduced environmental impact while supporting broader sustainable development objectives such as climate change mitigation, energy security, and increasing access to affordable energy.Efficient technologies such as multistage fracturing optimization in tight reservoirs can help minimize the environmental footprint of gas development while ensuring proper engagement and consultation with local communities are emphasized.
The natural gas resources of the Xujiahe Formation in the Sinopec exploration area are 4.05 trillion cubic meters, and the cumulative natural gas tertiary reserves are 1.52 trillion cubic meters [5].The proven reserves of the Xujiahe Formation in the northeast of the Sichuan Basin total 738.182 billion cubic meters [6], of which the proven natural gas reserves of the Xujiahe Formation in the Tongnanba block cover an area of 156.42 km 2 and reserves of 51.523 billion cubic meters [7].The block is bounded by the Micangshan structural belt in the north and the Dabashan thrust nappe belt in the east.It mainly contains a NEE-SWWtrending "strip-type" Tongnanba anticline, which is one of the important gas-producing areas in northeast Sichuan.The main gas-bearing layer system is the Upper Triassic Xujiahe Formation, of which the main source rock are subaqueous sandstone deposits of the braided river delta front sub-facies.The reservoir porosity is mainly distributed between 1% and 5%, and the permeability is mainly distributed in (0.01~1) × 10 −3 µm 2 , belonging to ultra-low porosity and ultra-low permeability tight sandstone reservoirs [8].
The sandstone reservoirs of the Xujiahe formation in the Tongnanba block of the tight northern Sichuan basin are tight, where complex faults and fractures are developed.After stimulation, hydraulic fractures could connect the complex multiple fractures formed by the "faulted fracture zone" [9], which are the main factors for high production after fracturing.However, the mechanisms of productivity of fault-fracture zones in tight reservoirs after fracturing have not been analyzed deeply, and it is difficult to predict the production contribution of the complex fractured zones.The technology needs to be further improved.The main problems and technical difficulties include the following aspects: (1) the reservoir is dense, with faults and complex network of natural fractures developed, making it difficult to characterize; (2) complex fractures are formed in the fault-fracture zone after fracturing stimulation, and it is difficult to predict the Stimulated Reservoir Volume (SRV) and fracture geometry; (3) the simulation and evaluation technology for productivity contributions of fault-fracture zone needs further research.

Mathematical Methods of Hydraulic Fracturing Effect Evaluation
Accurately evaluating fracturing measurements can optimize the production of natural gas from the reservoir.By determining how much of the reservoir is effectively stimulated, reservoirs can be developed with greater precision, thereby minimizing the surface footprint and reducing the impact on the surrounding environment.There are many factors affecting the fracturing effect, and each factor will have an impact on the fracturing effect to a certain extent and range.If only the fitting regression of the traditional mathematical method is used, there will be great limitations in evaluating the relationship between the fracturing effect and the influencing factors.For the case where multiple influencing factors act on the fracturing effect comprehensively, the fracturing effect has a nonlinear relationship with a single factor.If these data are fitted, there will often be a large error between the predicted value and the actual value of the sample.Therefore, methods such as gray relational analysis theory, fuzzy neural network system, fuzzy comprehensive evaluation, and gray topology prediction are often used in the evaluation of post-fracturing effects.These methods can determine the primary and secondary relationships of factors affecting fracturing effects.Oberwinkler et al. [10] used data mining technology to discover the relationship between influencing factors and fracturing effects and found out the factors that had the greatest impact on fracturing effects from multiple influencing factors to guide fracturing construction.Shelley et al. [11] used the artificial neural network method to optimize refractured wells.The selected influencing factors included current well production, original reservoir fracturing and current formation pressure, perforation parameters, and well completion parameters.Based on the optimized results, the network predicted the well with the largest difference between the post-fracturing production and the current production is the target of refracturing.Mohaghegh et al. [12] studied the method of selecting fracturing wells by the virtual intelligent system.Well selection parameters mainly include general information, reservoir parameters, fracturing parameters, production parameters, etc., using the neural network model system, genetic algorithm, and fuzzy expert scoring system.The method is to optimize the fractured wells.In terms of applying mathematical analysis methods to evaluate fracturing effects, Chen Shanshan et al. [13] used gray relational analysis methods to establish a mathematical model for the analysis of factors affecting fracturing effects in Hujianshan oilfield, sorted the factors affecting fracturing effects, and determined each influencing factor primary and secondary relationship.Qu Zhanqing et al. [14] divided the factors affecting the fracturing effect into parameters such as permeability, reservoir thickness, formation pressure, and sand addition amount, and determined the priority order and degree of influence of the factors affecting the fracturing effect through the gray correlation analysis method.Shi Shanzhi et al. [15] used the gray correlation analysis method to obtain the influencing factors affecting the cumulative oil production after fracturing, and then introduced the parameter α representing the fracture shape parameters to establish a BP neural network prediction model between the cumulative oil production and the influencing factors.

Evaluation Method of Artificial Fracture after Fracturing
According to different stages of the stimulation and production process, the indicators that can be monitored by the post-fracture evaluation technology include fracture orientation and shape, fracture geometric parameters, and fracturing fluid loss coefficient.Technologies such as wellbore logging, unstable well testing, net pressure fitting, and pressure drop curve analysis can be used in the process of shutting in wells and flowback period; during the production process, methods such as production dynamic analysis, unstable well testing, and radioactive technology get used.According to the principles and characteristics of fracture monitoring technology, post-fracture evaluation technology can be divided into pressure analysis, wellbore testing, large field monitoring, and other special methods.The pressure analysis method can better give the fracture conductivity, fracture length, and width.It can better predict the propagation of fracture height, and the large ground field monitoring technology can achieve the fracture azimuth and dip angle more accurately.Ma Jianjun et.[16][17][18] proposed a new model for the analysis of saturated fractured porous media, which integrates complex geological features, including rock heterogeneity, anisotropy, and fractures, into the numerical simulations.The proposed model provides a promising new tool for the analysis and prediction of fluid flow and deformation in geological systems and engineering applications.Compared with the fracturing net pressure fitting technology and micro-seismic imaging method, the comprehensive evaluation index of surface potential method is the highest.Zhang Zhiyong [19] and others from the China Petroleum Exploration and Development Research Institute took two typical wells in the Xujiahe Formation in central Sichuan as research objects and analyzed the pressure drop curve, "G function", net pressure, fracture shape, and proppant distribution.The fracturing curve characteristics and post-fracture effects of Xujiahe low-permeability sandstone gas reservoirs were analyzed and evaluated.Zhang et al. [20] presents the results of laboratory experiments and numerical simulations investigating the behavior of hydraulic fractures in the presence of multiple closed cemented natural fractures (CCNFs) in a tight sandstone reservoir.Wang Fei and others [21] from the China University of Petroleum (Beijing) summarized three methods suitable for evaluation of post-fracture effects of multi-stage fracturing horizontal wells in tight reservoirs, which were micro-seismic monitoring imaging, net pressure fitting analysis, and pseudo-pressure production dynamic analysis.

Research on Productivity Analysis Methods of Tight Oil and Gas
For tight oil and gas reservoirs, due to the existence of the stimulated volume, the composite flow model has been proposed and widely used.Ozkan et al. [22] proposed and used trilinear flow to study the flow discipline of tight gas, obtained a typical pressure response curve, and accurately described the SRV of tight gas reservoirs after fracturing.Xiang, Huizhu, et al. [23] used trilinear flow to study the influence of microfractures in the matrix on productivity.Ketineni [24] established an elliptical composite reservoir flow model for tight oil reservoirs, characterized SRV with an inner elliptical area, obtained pressure instability response results and production decline curves, and enriched the model described by SRV.Since then, Zhao et al. [25] have established a circular composite reservoir flow model, obtained the unstable change law of production and pressure, and further improved the production prediction model of tight oil and gas after fracturing stimulation.Methods such as point source solution, pull space transformation, Green's function, and numerical inversion have been widely used to solve analytical and semi-analytical models and obtain the productivity of fractured wells.Luo and Tang et al. [26] established an unsteady pressure response model of a multi-fracture system in a vertical well using pull-space transformation and numerical methods and analyzed the influence of limited conductivity fractures.Qanbari and Clarkson [27] used the early linear flow idea to study the productivity analysis method of tight oil and gas two-phase flow.In terms of numerical simulation, Mayerhofer et al. [28] combined micro-seismic observation data with numerical simulation to study the productivity of tight oil and gas after fracturing and analyzed the influence of fractures of different scales on productivity.Weng et al. [29] used the network model to carry out numerical simulation of reservoirs by dividing unstructured grids, realizing the productivity prediction and production optimization analysis of tight oil and gas.
The Xujiahe Formation in the Tonnanba block is known for the presence of faultfracture zones, yet there is currently no established and comprehensive method for assessing the post-fracturing effects and accurately predicting productivity of these fractured bodies.This paper focuses on investigating the tight sandstone gas reservoirs in the Xujiahe Formation in the Tonnanba block of the northern Sichuan Basin.The primary goal is to develop a post-fracturing complex fracture parameter and stimulated reservoir volume (SRV) evaluation method for fault-fracture zones in the Tonnanba block.Furthermore, a post-fracturing complex fracture production analysis method is proposed to facilitate theoretical research and effect evaluation, and ultimately to improve fracturing effect, and optimize the production of tight natural gas and minimize environmental impacts, leading to greater economic and environmental sustainability.

Regional Characteristics 2.1. Regional Structure Features
The Malubei structural belt in the Tongnanba block is in the northeast section of the northeast Sichuan fold belt in the Sichuan Basin (Figure 1), the structural superimposition of the Micangshan thrust structural belt and the Dabashan arc-shaped thrust structural belt.The Malubei anticline structural belt has strong structural deformation and developed faults, and it is generally a large northeast-trending anticline structural belt.The anticline belt can be divided into three secondary structural units from southwest to northeast: Nanyangchang faulted anticline structure, Malubei structure, and Heichiliang faulted anticline structure.The tight sandstone of the Xujiahe Formation in the Malubei-Tongjian subjected to the compression transformation of the Micangshan-Dabashan Yanshan-Xiashan period, controlled by faults and folds, where faults, fold-asso tures, and superimposed matrix pores are developed.Large-scale network fra seepage storage body, that is, fault-fracture zone (Figure 2), is the key to oil a richment and high production with high-efficiency dual-source charging.

Regional Sedimentary Characteristics
Braided river delta deposits are developed in the Malubei area, along the d material transport, transitioning from the braided river delta plain sub-fa braided river delta front sub-facies, with small changes in facies and sub-facies large lateral rapid changes in microfacies types, and the poor lateral contrast of ies.Affected by provenance, the sandstone grain size in Upper sub-member of t formation gradually became finer from Micangshan to the basin, and the sedim The tight sandstone of the Xujiahe Formation in the Malubei-Tongjiang area was subjected to the compression transformation of the Micangshan-Dabashan in the late Yanshan-Xiashan period, controlled by faults and folds, where faults, fold-associated fractures, and superimposed matrix pores are developed.Large-scale network fracturepore seepage storage body, that is, fault-fracture zone (Figure 2), is the key to oil and gas enrichment and high production with high-efficiency dual-source charging.
northeast: Nanyangchang faulted anticline structure, Malubei structure, and H faulted anticline structure.The tight sandstone of the Xujiahe Formation in the Malubei-Tongjiang subjected to the compression transformation of the Micangshan-Dabashan Yanshan-Xiashan period, controlled by faults and folds, where faults, fold-asso tures, and superimposed matrix pores are developed.Large-scale network fra seepage storage body, that is, fault-fracture zone (Figure 2), is the key to oil a richment and high production with high-efficiency dual-source charging.

Regional Sedimentary Characteristics
Braided river delta deposits are developed in the Malubei area, along the d material transport, transitioning from the braided river delta plain sub-fa braided river delta front sub-facies, with small changes in facies and sub-facies large lateral rapid changes in microfacies types, and the poor lateral contrast of ies.Affected by provenance, the sandstone grain size in Upper sub-member of t formation gradually became finer from Micangshan to the basin, and the sedim cies gradually transitioned from the braided river delta plain sub-facies from south.

Regional Sedimentary Characteristics
Braided river delta deposits are developed in the Malubei area, along the direction of material transport, transitioning from the braided river delta plain sub-facies to the braided river delta front sub-facies, with small changes in facies and sub-facies types, but large lateral rapid changes in microfacies types, and the poor lateral contrast of sand bodies.Affected by provenance, the sandstone grain size in Upper sub-member of the Xujiahe formation gradually became finer from Micangshan to the basin, and the sedimentary facies gradually transitioned from the braided river delta plain sub-facies from north to south.
According to the imaging logging interpretation results of Well X1-10, the lithology in Xujiahe formation (2840-3046 m) is mainly sandstone and mudstone interbedded with unequal thickness, where seven high conductivity fractures, five filling fractures and sixtytwo stress relief fractures are distributed.Natural fractures were more developed in upper Xujiahe formation (3160-3700 m), where seventy high conductivity fractures are collected, and fault-fracture zones are existed.The imaging logging result of the production well section is shown in Figure 3.The 3D geological model of the Xujiahe formation in Well X1-10 area was built (Figure 4), and rock properties parameters could be obtained both in vertical and horizontal directions for the fracture evaluation.

Models
Two evaluation models were established in this part: (1) pressure fall-off model is built to analyze the fracture geometric parameters and complexity of fractures in different stages; (2) differential facture dynamic fitting model is used to calculate the effective SRV.

Pressure Fall-Off Model
Menouar et al. [30] proposed a method to accurately determine the instantaneous shut-in pressure based on the Liu-Economides model [31], through which the friction loss during the pumping process can be determined.Generally speaking, the stage where fric-

Models
Two evaluation models were established in this part: (1) pressure fall-off model is built to analyze the fracture geometric parameters and complexity of fractures in different stages; (2) differential facture dynamic fitting model is used to calculate the effective SRV.

Pressure Fall-Off Model
Menouar et al. [30] proposed a method to accurately determine the instantaneous shutin pressure based on the Liu-Economides model [31], through which the friction loss during the pumping process can be determined.Generally speaking, the stage where friction loss plays a leading role is mainly from 0.5 to 5 min after stopping the pump, and after a period of time, the crack closure characteristic will appear.The pump stop analysis begins at the moment of instantaneous pump stop, the first part with a slope of 1 on the logarithmic graph and the subsequent "hump".This stage mainly reflects the storage effect of the wellbore and can be used to estimate the friction losses and determine the instantaneous shut-in pressure (ISIP).Afterwards, the "hump" ends about 3 min after shutting in the well.The pressure difference at this time can be considered as the total friction loss at the moment of shutting in the well, and the bottomhole pressure at this time can be regarded as ISIP.After a period of transition (tip extension, etc.), the second trend segment with a slope of 1 represents the fracture closure phase, which begins approximately 20 min after shut-in.Therefore, when inverting fracture parameters after fracturing, the main focus is on the analysis of the fracture closure trend line.
Liu and Ehlig-Economides [31] deduced a series of analytical calculation models that can explain complex fracture and formation characteristics, including pressure-dependent fluid loss, fracture tip expansion, variable flexibility, and fracture height considering the opening and closing of natural fractures.In formations with well-developed natural fractures, pressure-related fluid loss due to the opening and closing of natural fractures is likely to occur.This model pointed out that under a high net pressure state, the hydraulic fractures and the natural fractures where connection occurs are both open, and the fluid loss at this time takes place on all the fracture surfaces that are in contact with the liquid (Figure 5.) Since the pressure decrease at this time is mainly caused by fluid loss, the pressure decrease can reflect the characteristics of fracture closure.Therefore, by applying the pressure-dependent fluid loss model in the model with the analysis of the main fracturing pump stop pressure decline, the parameters of natural fractures and hydraulic fractures can be obtained.effect of the wellbore and can be used to estimate the friction losses and determine the instantaneous shut-in pressure (ISIP).Afterwards, the "hump" ends about 3 min after shutting in the well.The pressure difference at this time can be considered as the total friction loss at the moment of shutting in the well, and the bottomhole pressure at this time can be regarded as ISIP.After a period of transition (tip extension, etc.), the second trend segment with a slope of 1 represents the fracture closure phase, which begins approximately 20 min after shut-in.Therefore, when inverting fracture parameters after fracturing, the main focus is on the analysis of the fracture closure trend line.
Liu and Ehlig-Economides [31] deduced a series of analytical calculation models that can explain complex fracture and formation characteristics, including pressure-dependent fluid loss, fracture tip expansion, variable flexibility, and fracture height considering the opening and closing of natural fractures.In formations with well-developed natural fractures, pressure-related fluid loss due to the opening and closing of natural fractures is likely to occur.This model pointed out that under a high net pressure state, the hydraulic fractures and the natural fractures where connection occurs are both open, and the fluid loss at this time takes place on all the fracture surfaces that are in contact with the liquid (Figure 5.) Since the pressure decrease at this time is mainly caused by fluid loss, the pressure decrease can reflect the characteristics of fracture closure.Therefore, by applying the pressure-dependent fluid loss model in the model with the analysis of the main fracturing pump stop pressure decline, the parameters of natural fractures and hydraulic fractures can be obtained.Before fracture closure, after shutting in, the bottom wellbore pressure could be achieved as Which could be re-written as, In which pw is bottom wellbore pressure, MPa; ∆t is time after shut in, s; rp is the ratio of fluid loss fracture area and total fracture area; tp is total pumping time, s; Afm and Afn are hydraulic fracture area and natural fracture area, m 2 ; cfm is fracture flexibility; G(∆tD,α) is G function; α is index of fracture area, and its value equals to 4/5 (PKN model) and 2/3 (KGD model); p1 * is the value of dp/dG in G function within the fracture closure period.
According to the material balance equation, that is, after shutting in the well, the total injected material volume is equal to the sum of fracture volume and fluid loss volume, which could be written as follows [31]: In which pc is the fracture closure pressure, MPa; Vp is total fracturing fluid volume in the stage, m 3 ; nc is the total perforation number; g0 is constant, as shown in Table 1.
Table 1.Flexibility expressions in three 2D fracture models.Before fracture closure, after shutting in, the bottom wellbore pressure could be achieved as Which could be re-written as, In which p w is bottom wellbore pressure, MPa; ∆t is time after shut in, s; r p is the ratio of fluid loss fracture area and total fracture area; t p is total pumping time, s; A fm and A fn are hydraulic fracture area and natural fracture area, m 2 ; c fm is fracture flexibility; G(∆t D ,α) is G function; α is index of fracture area, and its value equals to 4/5 (PKN model) and 2/3 (KGD model); p 1 * is the value of dp/dG in G function within the fracture closure period.According to the material balance equation, that is, after shutting in the well, the total injected material volume is equal to the sum of fracture volume and fluid loss volume, which could be written as follows [31]: In which p c is the fracture closure pressure, MPa; V p is total fracturing fluid volume in the stage, m 3 ; n c is the total perforation number; g 0 is constant, as shown in Table 1.If we combine Equations ( 2) and (3), we can obtain the fracture half length, hydraulic fracture area, and natural fracture area with equation below.
In which x fm is fracture half length, m; E is Young's plane modulus, MPa; h f is fracture height, m.

Differential Facture Dynamic Fitting Model
After the horizontal well undergoes fracturing, fractures are generated in the nearwellbore area, and the fractures communicate with each other to form a complex fracture network.Therefore, the model not only considers the main fractures, but also considers the formation of complex fracture networks and high-permeability areas after formation fracturing, that is, the model includes: the main fractures of the fracture, the complex fracture network stimulation area near the wellbore, the affected area of secondary fractures far from the wellbore, and the original reservoir, as shown in Figure 6.The fluid in the affected area flows linearly into the stimulated area, and the fluid in the matrix block in the stimulated area flows into the secondary fracture network, flows linearly to the primary fracture through the secondary fracture network, and flows into the wellbore through the primary fracture, as shown in Figure 6.
In which xfm is fracture half length, m; E′ is Young's plane modulus, MPa; hf is fracture height, m.

Differential Facture Dynamic Fitting Model
After the horizontal well undergoes fracturing, fractures are generated in the nearwellbore area, and the fractures communicate with each other to form a complex fracture network.Therefore, the model not only considers the main fractures, but also considers the formation of complex fracture networks and high-permeability areas after formation fracturing, that is, the model includes: the main fractures of the fracture, the complex fracture network stimulation area near the wellbore, the affected area of secondary fractures far from the wellbore, and the original reservoir, as shown in Figure 6.The fluid in the affected area flows linearly into the stimulated area, and the fluid in the matrix block in the stimulated area flows into the secondary fracture network, flows linearly to the primary fracture through the secondary fracture network, and flows into the wellbore through the primary fracture, as shown in Figure 6.The chart fitting analysis method is relatively intuitive, but because the theoretical well test curve charts of complex fracture network wells in low-permeability oil and gas reservoirs are relatively complex, and the establishment of well test curve charts requires a lot of work, so it is not suitable in multi-stage fractured analysis.
In this paper, bottomhole pressure in real space could be solved with Stehfest method and Laplace transformation (see in Appendix A.), considering wellbore storage and flow in primary and secondary fractures: The chart fitting analysis method is relatively intuitive, but because the theoretical well test curve charts of complex fracture network wells in low-permeability oil and gas reservoirs are relatively complex, and the establishment of well test curve charts requires a lot of work, so it is not suitable in multi-stage fractured analysis.
In this paper, bottomhole pressure in real space could be solved with Stehfest method and Laplace transformation (see in Appendix A.), considering wellbore storage and flow in primary and secondary fractures: where p wD is the dimensionless bottomhole pressure; s is the Laplace space variable; S is the skin factor; C D is the dimensionless wellbore storage coefficient.
The dynamic production fitting method is used in the coupled production and pressure dynamic model (see in Appendix A.), and wellbore and fracture parameters can be achieved.Additionally, the specific steps include: Step 1. Collect and sort geological and engineering parameters.
Step 2. Specify the input and output parameters of the identification method, analyze the data according to the credibility of the data, and clarify its input and output parameters.
Step 3. Apply well test dynamic model, and use well test curve fitting to perform effective fracture network parameter calculation.
Step 4. Apply production pressure coupling dynamic inversion parameters, use production pressure coupling curve fitting to perform effective fracture network parameter calculation of SRV and productivity on production dynamic data.
In the first step, the geological engineering parameters are collected and organized, including gas reservoir, fluid and wellbore parameters, fracturing construction parameters, microseismic monitoring data, well-test data, and production performance data.Analyze the data according to the feasibility of the data, and clarify their input and output parameters.Well X1-10 in Tongnanba block was stimulated with 11 stages, which is shown in Table 2. Fracturing fluid used in each stage is from 1706.5 m 3 to 2484.1 m 3 .With the log-log plot of fall-off pressure after shut-in of different stages of Well X1-10 (Figures 7-10), the fracture closure characteristic appeared with a segment of slope 1.Additionally, the ISIP (instantaneous shut-in pressure) and bottom wellbore pressure could be achieved.p 1 * (the value of dp/dG in G function) could be obtained with G-function analysis at the fracture closure time determined by characteristic period in log-log plot.The 1-7th stages of Well X1-10 are distributed in the fault-fracture zone (3160-3700 m).

Results and Discussion
With the log-log plot of fall-off pressure after shut-in of different stages of Well X1-10 (Figures 7-10), the fracture closure characteristic appeared with a segment of slope 1.Additionally, the ISIP (instantaneous shut-in pressure) and bottom wellbore pressure could be achieved.p1 * (the value of dp/dG in G function) could be obtained with G-function analysis at the fracture closure time determined by characteristic period in log-log plot.The 1-7th stages of Well X1-10 are distributed in the fault-fracture zone (3160-3700 m).G-function and log-log plot of fall-off pressure after shut-in indicate that pressure falls off much faster in fault-fracture zone than that of other stages.With the pressure fall-off model, the fracture geometrical parameters and the fracture complexity (ratio of natural fracture area to hydraulic fracture area) could be obtained, which is shown in Table 3.There were 11 stages analyzed and the average fracture height is 28.4m.The fracture half lengths vary from 113.99 to 161.18m, and average fracture half length is 139.3m.The area of primary fracture area per stage is from 30,946.6m 2 to 65,091.5m 2 , and the fracture complexity per stage is from 3.88-12.63.Additionally, fracture complexity in the 3rd stage (fault-fracture zones) reaches its highest value, which means plenty of natural fractures are activated during the stimulation process.

Influential Factors of Fracture Complexity
The results in Figure 11 show that the ratio of the area of the natural fracture to the main fracture decreases with fracture length.When fracture half length increases from 110-125 m to 155-160 m, the fracture complexity drops down 31.0%, from 9.78 to 6.75.The ratio of the area of the natural fractures to that of the main fracture decreases with the increase in the main fracture's length, as the natural fractures become less influential, and the main fracture takes over as the dominant pathway for fluid flow.The natural fractures are typically shorter and more irregular than the main fracture, and therefore they intersect the main fracture less frequently as its length increases.The main fracture is typically created during hydraulic fracturing, and it forms the primary pathway for fluids such as oil, gas, or water to flow through the rock.As the main fracture propagates, it intersects and incorporates natural fractures, which provide additional pathways for the fluids to flow.The natural fractures, however, are often irregularly distributed and discontinuous, and their orientation and spacing can vary widely.As the main fracture propagates and extends, it encounters fewer intersections with the shorter and less prominent natural fractures, and as a result, the ratio of their area to the area of the main fracture decreases.Moreover, the main fracture tends to grow in length faster than the natural fractures due to the higher injection pressure that is applied to it during hydraulic fracturing.This causes the main fracture to dominate the hydraulic conductivity of the formation, and with the increasing length of the main fracture, the ratio of the area of the natural fractures to the main fracture area becomes less significant.The results in Figure 12 indicate that the increase in net pressure is related to the formation of a complex fracture network.When net pressure within the fracture increases from 2-4 MPa to more than 10 MPa, the fracture complexity increases by 58.3%, from 5.71 to 9.04.As the net pressure within the fracture increases, the hydraulic pressure pushes outwards on the walls of the fracture, increasing the chances of the formation of new secondary fracture and the propagation of existing ones.In a tight sandstone gas reservoir such as Xujiahe, the rock is usually low permeability, which means that the flow of gas is obstructed.To improve the flow of gas, the rock is fractured using hydraulic fracturing.However, when the net pressure within the fracture increases, the fractures become more complex and can link with each other, forming a network.This is because the pressure is strong enough to create new fractures, and also to reopen previously closed fractures, leading to a more intricate web of fractures that can enhance the gas flow by providing more pathways for the gas to migrate.Therefore, increasing the net pressure within a fracture can lead to the propagation of a complex fracture network, which is beneficial for improving the production of gas from tight sandstone gas reservoirs.The results in Figure 12 indicate that the increase in net pressure is related to the formation of a complex fracture network.When net pressure within the fracture increases from 2-4 MPa to more than 10 MPa, the fracture complexity increases by 58.3%, from 5.71 to 9.04.As the net pressure within the fracture increases, the hydraulic pressure pushes outwards on the walls of the fracture, increasing the chances of the formation of new secondary fracture and the propagation of existing ones.In a tight sandstone gas reservoir such as Xujiahe, the rock is usually low permeability, which means that the flow of gas is obstructed.To improve the flow of gas, the rock is fractured using hydraulic fracturing.However, when the net pressure within the fracture increases, the fractures become more complex and can link with each other, forming a network.This is because the pressure is strong enough to create new fractures, and also to reopen previously closed fractures, leading to a more intricate web of fractures that can enhance the gas flow by providing more pathways for the gas to migrate.Therefore, increasing the net pressure within a fracture can lead to the propagation of a complex fracture network, which is beneficial for improving the production of gas from tight sandstone gas reservoirs.

Fracture Dynamic Fitting
Based on the fracture geometric results from the pressure fall-off model (Table 3.), a multistage fractured horizontal wellbore model was built as shown in Figure 13.Compared to traditional equal-length fracture model in well-test analysis, the differential fracturing model for horizontal wells integrates the differences in the effectiveness of fractures across different segments, providing a more accurate description of the fractures and avoiding the issue of uniform fracture size associated with the homogenized model.This enables more precise analysis and prediction of productivity control by different levels of fractures through methods such as production profile testing.
However, when the net pressure within the fracture increases, the fractures become more complex and can link with each other, forming a network.This is because the pressure is strong enough to create new fractures, and also to reopen previously closed fractures, leading to a more intricate web of fractures that can enhance the gas flow by providing more pathways for the gas to migrate.Therefore, increasing the net pressure within a fracture can lead to the propagation of a complex fracture network, which is beneficial for improving the production of gas from tight sandstone gas reservoirs.

Fracture Dynamic Fitting
Based on the fracture geometric results from the pressure fall-off model (Table 3.), a multistage fractured horizontal wellbore model was built as shown in Figure 13.Compared to traditional equal-length fracture model in well-test analysis, the differential fracturing model for horizontal wells integrates the differences in the effectiveness of fractures across different segments, providing a more accurate description of the fractures and avoiding the issue of uniform fracture size associated with the homogenized model.This enables more precise analysis and prediction of productivity control by different levels of fractures through methods such as production profile testing.Based on the 3D geological model with fractures and flow model (Appendix) in tight reservoir, a detailed production-pressure dynamic fitting was investigated to obtain the SRV of different clusters with real in situ production data.The fitting results are shown in Figure 14.Results in Table 4 show that the conductivity of primary fracture in stimulated zones is 18.4 md•m, which means effective flow channels are built within the fractured area.Additionally, the permeability of the stimulated zone is 0.13 md, which is 3.2 times of that in matrix and indicates hydraulic fracturing increases the gas flow potential in matrix.Based on the 3D geological model with fractures and flow model (Appendix) in tight reservoir, a detailed production-pressure dynamic fitting was investigated to obtain the SRV of different clusters with real in situ production data.The fitting results are shown in Figure 14.Results in Table 4 show that the conductivity of primary fracture in stimulated zones is 18.4 md•m, which means effective flow channels are built within the fractured area.Additionally, the permeability of the stimulated zone is 0.13 md, which is 3.2 times of that in matrix and indicates hydraulic fracturing increases the gas flow potential in matrix.Results in Table 4 show that the conductivity of primary fracture in stimulated zones is 18.4 md•m, which means effective flow channels are built within the fractured area.Additionally, the permeability of the stimulated zone is 0.13 md, which is 3.2 times of that in matrix and indicates hydraulic fracturing increases the gas flow potential in matrix.The results of effective SRV of each cluster are obtained with dynamic fitting model, as shown in Table 5.Average effective length of SRV per cluster in the fault-fracture zone is 227.4 m (Table 6.), which is 10.2m less than that in the natural fracture undeveloped zone.Meanwhile the average width per cluster of the stimulated zone in fault-fracture zone could reach 8.4m, which increased by 20% compared with that in other parts.Additionally, average stimulated reservoir volume per cluster increased by 7.3% to 52,360.7 m 3 , which is shown in Table 6.In the fault-fracture zone where natural fractures are more developed, more natural fractures are activated during fracturing and fracture complexity tends to be higher, which leads to wilder and relatively shorter stimulated volume in reservoir.
Based on the effective SRV per cluster and fracture geometric parameters obtained, the numerical production model of Well X1-10 in Xujiahe formation were adjusted with 3D geological model, and the production rate and productivity could be estimated, which is shown in Table 6.After 1 year, the gas production rate of Well X1-10 could be 22,300 m 3 /d, and the accumulative gas production could reach 9.087 million m 3 , which is shown in Figure 15.

Conclusions
1.By combining the pressure fall-off analysis and differential facture dynamic fitting model, a new systematic evaluation method is developed to investigate the fracture complexity and productivity in the fracture-fault zone of tight reservoirs controlled by complex fractures networks, which is useful to optimizing the production of tight natural gas and minimizing environmental impacts, leading to greater economic and environmental sustainability.2. The well-based evaluation method is successfully used in the field case of Xujiahe formation in northeast Sichuan basin, which shows that the ratio of natural fracture area to main fracture area in tight reservoirs is between 3.88-12.63,indicating that hydraulic fractures are connecting the natural fractures in fault-fracture zones.As the net pressure in the fracture increases, the area ratio of natural fractures to main fractures increases notably, whereas the half length of the main fracture exhibits a decreasing trend.3.In the fault-fracture zone where natural fractures are more developed, more natural fractures are activated during fracturing and fracture complexity tends to be higher, which leads to wilder and relatively shorter stimulated volume in reservoir.4. The evaluation method offers a new way to evaluate the effectiveness of hydraulic fracturing measures in unconventional reservoirs, especially where natural fractures exist.

1.
By combining the pressure fall-off analysis and differential facture dynamic fitting model, a new systematic evaluation method is developed to investigate the fracture complexity and productivity in the fracture-fault zone of tight reservoirs controlled by complex fractures networks, which is useful to optimizing the production of tight natural gas and minimizing environmental impacts, leading to greater economic and environmental sustainability.

2.
The well-based evaluation method is successfully used in the field case of Xujiahe formation in northeast Sichuan basin, which shows that the ratio of natural fracture area to main fracture area in tight reservoirs is between 3.88-12.63,indicating that hydraulic fractures are connecting the natural fractures in fault-fracture zones.As the net pressure in the fracture increases, the area ratio of natural fractures to main fractures increases notably, whereas the half length of the main fracture exhibits a decreasing trend.3.
In the fault-fracture zone where natural fractures are more developed, more natural fractures are activated during fracturing and fracture complexity tends to be higher, which leads to wilder and relatively shorter stimulated volume in reservoir.

4.
The evaluation method offers a new way to evaluate the effectiveness of hydraulic fracturing measures in unconventional reservoirs, especially where natural fractures exist.
Appendix A.1.3.Wellbore Model The fracture flow rate normalization equation can be solved based on the above equation to obtain the corresponding solution ψ wD in Laplace space for the bottomhole pressure, considering the wellbore storage effect and skin effect.
where ψ wCD is the dimensionless perturbation solution for the bottomhole pressure including wellbore storage and skin effects; C D is the dimensionless wellbore storage coefficient; S is the skin factor, also dimensionless.By using the Stehfest numerical inversion method, the perturbation solution for the bottomhole pressure including wellbore storage and skin effects can be obtained.In order to facilitate computation, the trilinear flow method is used for solving, and by simplifying the model with dimensionless variables, the following is obtained: (1) Equation of hydraulic fracturing in Stimulated zone Using the Laplace transform method to solve the linearized well testing mathematical model, the bottomhole pressure solution is obtained by combining the model:

Figure 1 .
Figure 1.Map showing the location of Tongnanba area in northern Sichuan Basin.

Figure 1 .
Figure 1.Map showing the location of Tongnanba area in northern Sichuan Basin.

Figure 1 .
Figure 1.Map showing the location of Tongnanba area in northern Sichuan Basin.

Sustainability 2023 ,
15,  x FOR PEER REVIEW 6 of 22 unequal thickness, where seven high conductivity fractures, five filling fractures and sixty-two stress relief fractures are distributed.Natural fractures were more developed in upper Xujiahe formation (3160-3700 m), where seventy high conductivity fractures are collected, and fault-fracture zones are existed.The imaging logging result of the production well section is shown in Figure3.

Figure 3 .Figure 3 .
Figure 3. Imaging logging map of Well X1-10 in Tongnanba area.The 3D geological model of the Xujiahe formation in Well X1-10 area was built (Figure4), and rock properties parameters could be obtained both in vertical and horizontal directions for the fracture evaluation.

Figure 5 .
Figure 5. Schematic of hydraulic fracture and natural fractures.

Figure 5 .
Figure 5. Schematic of hydraulic fracture and natural fractures.

Figure 6 .
Figure 6.Schematic of complex fractured networks of multistage fracturing.

Figure 6 .
Figure 6.Schematic of complex fractured networks of multistage fracturing.

Figure 7 .
Figure 7. log-log plot of fall-off pressure after shut-in in fault-fracture zone (3rd stage of Well X1-10).Figure 7. log-log plot of fall-off pressure after shut-in in fault-fracture zone (3rd stage of Well X1-10).

Figure 9 .
Figure 9. log-log plot of fall-off pressure after shut-in in fracture-underdeveloped area (10th stage of Well X1-10).

Figure 9 .
Figure 9. log-log plot of fall-off pressure after shut-in in fracture-underdeveloped area (10th stage of Well X1-10).

Figure 9 .
Figure 9. log-log plot of fall-off pressure after shut-in in fracture-underdeveloped area (10th stage of Well X1-10).

Figure 9 .
Figure 9. log-log plot of fall-off pressure after shut-in in fracture-underdeveloped area (10th stage of Well X1-10).

Figure 11 .
Figure 11.Relationship between fracture complexity and fracture half-length in different stages of Well X1-10.

Figure 12 .
Figure 12.Relationship between fracture complexity and net pressure in different stages of Well X1-10.

Figure 11 .
Figure 11.Relationship between fracture complexity and fracture half-length in different stages of Well X1-10.

Figure 12 .
Figure 12.Relationship between fracture complexity and net pressure in different stages of Well X1-10.

Figure 12 . 22 Figure 13 .
Figure 12.Relationship between fracture complexity and net pressure in different stages of Well X1-10.Sustainability 2023, 15, x FOR PEER REVIEW 16 of 22

Figure 14 .
Figure 14.Plot of variable flow and pressure fitting in Well X1-10.

Figure 13 .
Figure 13.Schematic of differential fractures distribution in Well X1-10.Based on the 3D geological model with fractures and flow model (Appendix A) in tight reservoir, a detailed production-pressure dynamic fitting was investigated to obtain the SRV of different clusters with real in situ production data.The fitting results are shown in Figure 14.

Figure 14 .
Figure 14.Plot of variable flow and pressure fitting in Well X1-10.

Figure 14 .
Figure 14.Plot of variable flow and pressure fitting in Well X1-10.

Table 1 .
Flexibility expressions in three 2D fracture models.

Table 2 .
Basic parameters for each stage of Well X1-10.

Table 3 .
Fracture geometric parameters and areas in different stages of Well X1-10.

Table 4 .
Results of dynamic flow and pressure analysis after stimulation.

Table 4 .
Results of dynamic flow and pressure analysis after stimulation.

Table 4 .
Results of dynamic flow and pressure analysis after stimulation.

Table 5 .
Effective SRV of each cluster in Well X1-10.
Funding: Institutional Review Board Statement: Not applicable Informed Consent Statement: Not applicable Data Availability Statement: Not applicable Conflicts of Interest: The authors declare no conflicts of interest.
Then, bottomhole pressure in Laplace space could be achieved considering wellbore storage and skin effect:p wD (s, S, C D ) = S + sp wD s + C D s 2 (sp wD + S) (A16)