China has abundant unconventional oil and gas reserves, and under current economic and technological conditions, fractured tight sandstone reservoirs are gradually becoming a focus of exploration and development (Chen, 2024; Yan et al., 1997; Gang et al., 2023). The most representative fractured tight sandstone reservoirs in China are located in the Tarim Basin. As an important component of tight sandstone reservoirs, these fractured reservoirs are characterized by low porosity, low permeability, and low productivity. The development of natural fractures within these reservoirs is a key factor in enhancing production capacity (Zhimin et al., 2023; Liu et al., 2024; Qin et al., 2024; Jin et al., 2022). Currently, the conventional characterization methods for fracture parameters after hydraulic fracturing mainly include microseismic monitoring and wide-area electromagnetic monitoring techniques (Le Zhou et al., 2024; Zeng et al., 2023; Wu et al., 2024). However, both methods are easily influenced by natural fracture zones and various faults underground, making it difficult to provide effective guidance for actual production.

During the construction process, the fracturing construction curve provides a complete depiction of how injection pressure, injection rate, and proppant concentration change over time (Jinzhou et al., 2022; Wang et al., 2024). Therefore, deeply exploring the geological and engineering information revealed by the fracturing curves at different construction stages is of significant importance. Some scholars have studied the fracturing construction curves to indirectly characterize hydraulic fracture parameters. Notably, Nolte and Smith established the relationship between net pressure curves and fracture geometry under a double-logarithmic system, forming a classic fracturing diagnostic method, which subsequent research has built upon (Hong-Yan et al., 2023; Fuqiang et al., 2022; Xiaodong et al., 2022). Barree et al. developed a tangent method for analysis based on Nolte’s theory, determining fracture closure time and closure pressure by drawing a line through the origin that is tangent to the overlaid derivative GdP/dG curve. This method has been widely applied in the field (JeongWon et al., 2023; Gong and El-Monier, 2019). Yao (2018) characterized fracture complexity by analyzing fracture fluctuation states and improving the G-function. Wang et al. (2014) studied the pressure drop patterns of shale gas wells during small-scale fracturing tests using numerical simulation methods. Their findings indicated that the pressure drop process after stopping the pump involves four stages: fracture extension, elastic closure of fractures, pseudo-linear flow stage post-closure, and pseudo-radial flow stage. They estimated reservoir and fracture parameters using G-function, linear flow time function, and radial flow time function models. Xianshan et al. (2024) analyzed flow patterns in tight sandstone gas reservoirs using views of homogeneity, linear fractures, and complex fractures, identifying artificial fracture characteristics based on G-function theory and comprehensively evaluating the complexity of the hydraulic fracture network, validating results against microseismic monitoring data to enhance diagnostic accuracy.

The prerequisite for realising the full mobilisation of fractured tight sandstone reservoirs is whether the artificial fractures during hydraulic fracturing can interact with natural fractures to form a complex fracture network, and the study of the interaction mode between artificial fractures and natural fractures for hydraulic fracturing process is particularly important, e.g., Sang et al. (2023). obtained four kinds of natural fractures by establishing a coupled fluid-solid computational model of natural fracture extension in porous elastic strata, and examined the relevant influencing factors. Yu et al. (1997) and others carefully analysed the key factors affecting the interaction between hydraulic fracture extension and natural fractures, and focused on the formation mechanism and final structure of the fracture network, while Yueliang et al. (2022) and others investigated the influence of natural fractures on hydraulic fracture extension during hydraulic fracturing of tight reservoirs through indoor experiments, where the main influencing factors are the inclination angle of natural fractures and the relationship between natural fractures and wells. inclination angle and the distance between natural fractures and wellbore. Currently, there is still exploration space for the study of construction curves in fractured tight sandstone reservoirs, particularly a lack of detailed descriptions of post-fracture extension states and widely applicable field cases. This study focuses on various wells in the Bozi Block of the Tarim Basin. Based on real-time monitored construction data such as wellhead pressure, injection rate, and proppant concentration, we established a novel dynamic bottomhole net pressure conversion model. By simulating fracture extension scenarios on an integrated platform, we performed double-logarithmic processing of the net pressure curve and summarized the changes in curve slopes, identifying five distinct fracture extension modes to describe different fracture behaviors and corresponding mechanical conditions during the fracturing process. We propose a post-fracturing complex fracture network index and comprehensively establish a diagnostic recognition model for the construction pressure curves of fractured tight sandstone reservoirs, aiming to provide positive guidance for field operations.

In the Bozi Block, the ultra-deep reservoirs exhibit well-developed fractures, predominantly featuring high-angle structural fractures. The main type of fractures is shear fractures, followed by extensional fractures. Shear fractures typically develop at high angles, have flat fracture surfaces, extend over long distances, and exhibit small openings (0.1–0.3 mm). Most of these fractures are unfilled, while a small number of smaller fractures are filled with calcite or gypsum.

In contrast, extensional fractures account for a smaller proportion; they usually have rough fracture surfaces, shorter extensions, and larger openings (>2 mm), with the majority filled by calcite or gypsum. The general orientation of natural fractures in the Bozi Block is primarily near north-south and northwest-southeast, displaying a network-like distribution. Most fractures are in an unfilled or partially filled state, with the main fillings consisting of calcite, gypsum, and clay materials. The dip angle of these fractures is generally greater than 70°.

The development of natural fractures in various wells within the Bozi Block is summarized in Table 1 and illustrated in Figures 3A, B.

Table 2 presents the transformation process parameters obtained from the construction data of various wells in the Bozi Block. Most wells in this block utilize a cased perforation completion method, with a sand-based hydraulic fracturing technique being commonly employed. The overall transformation scale for the Bashijiqike Formation is relatively large, with an average transformation volume of 1,030 m³. The pre-treatment fluid volume typically ranges from 70 to 600 m³, while the average sand volume is 52.42 m³, with a sand-to-fluid ratio between 5% and 30%. The construction pressure varies from 87 to 122 MPa, and the pumping rate ranges from 1 to 6 m³/min.

In contrast, the transformation scale, pre-treatment fluid volume, and sand volume for the Baxi Formation are generally smaller than those of the Bashijiqike Formation, although the pressure range and average pumping rate are similar. Due to the development of natural fractures in the fractured sandstone reservoirs, there is significant fluid loss during fracturing. To ensure proper fracture initiation, extension, and sand addition, the study area typically employs stable high-rate construction (generally exceeding 4 m³/min). To control excessive vertical extension of the fractures, some wells utilize variable rate pumping techniques, with pumping rates generally ranging from 1 to 7 m³/min.

The activation process of natural fractures is often accompanied by changes in fluid pressure inside the fractures, and this increase and decrease in fluid pressure inside the fractures can provide insight into the fracturing of the formation and natural fracture communication, which can lead to the diagnosis of the overall fracture complexity after modification (Yan et al., 2024; Changgui et al., 2023). The key to the opening of natural fractures in fractured tight sandstone reservoirs lies in the net pressure, which is the difference between the pressure of the fluid in the fracture (bottom-of-well pressure) and the minimum principal stress (closure pressure) (Shen and Ji, 2024; Campos et al., 2024).

In the actual fracturing construction process, the fracturing fluid enters the fracture from the pumping machine through the surface pipeline, wellbore tubing column, and injection hole, and pressure loss occurs in each flow channel due to the friction, and along with the continuous change of the construction volume, sand concentration, etc., the column pressure and wellbore friction change accordingly, so the increment of the wellbore pressure changes dynamically, which makes the calculation of the wellbore pressure more complicated (Leonardo et al., 2023; Hongyang et al., 2023).

At present, the general practice of calculating the bottomhole pressure is to regard the whole wellbore as a whole, take the average value of the density of fracturing fluid in the wellbore, calculate the static wellbore column pressure without considering the change of well inclination angle, and calculate the wellbore resistance using the theoretical formula, which leads to a large deviation of the calculated value of the bottomhole pressure from the actual value (Liu et al., 2013; Haibo et al., 2021). In order to address the above problems, the author proposes a method of calculating dynamic bottomhole pressure based on specific fracturing construction data. By dividing the wellbore liquid into units, calculating the liquid volume and sand concentration of the liquid units at different moments by correction, and correcting the formula for calculation of moiré of indoor experiments by using on-site construction moiré, the results of calculation of bottomhole pressure can be more accurate, which can improve the accuracy of the subsequent analysis of the fracture extension situation. The accuracy of the subsequent analysis of the fracture extension is improved.

(1) Fluid Unit Hydrostatic Pressure:

In Equation 2, ρ i is: ρ i = 1 − c i ρ s r ρ l + c i (2) Where c i is the sand concentration in fluid unit i , in k g / m 3 ; ρ s r is the true density of the proppant, in k g / m 3 ; and ρ l is the base fluid density of the fracturing fluid, in k g / m 3 .

In Equation 1, h i is, if the wellbore is reduced to a cylinder model, the length of the wellbore is the height of the cylinder, as shown in Equation 3: h i = V i π r 2 (3) Where V i is the volume of fluid unit i , in m 3 ; and r is the radius of the wellbore, in meters.

(2) Fluid Unit Friction:

In practical application, the wellbore fracturing fluid friction is often calculated on the basis of clean water friction, because the value of clean water friction is the largest under the same conditions, as shown in Equation 4: P f 1 = σ P f 0 (4) Where P f 1 is the theoretical value of wellbore fracturing fluid friction at maximum flow rate, in MPa; σ is the friction reduction ratio (dimensionless); and P f 0 is the theoretical value of clear water friction at maximum flow rate in the wellbore, in MPa.

In Equation 5, σ is: σ = exp ⁡ − 2.14 − 1.1547 × 10 − 4 ⁢ d 2 Q max − 0.2842 × 10 − 4 ⁢ G d 2 Q max − 0.1639 ⁡ ln ⁢ G 0.11983 (5) Where d is the wellbore diameter, in mm; Q max is the maximum flow rate during the operation, in m 3 / ⁡ min ; and G is the concentration of the thickener, in k g / m 3 .

In Equation 6, P f 0 is: P f 0 = 1.3866 × 10 6 d − 4.8 Q max 1.8 H (6) Where H is the depth of the oil and gas well, in meters.

Actual value of fracturing fluid friction in fluid unit iii at flow rate Q t : P f r i = f ⋅ P f 1 i (7) The friction calculation formula mentioned above is the theoretical calculation value under the maximum displacement, and in the actual construction process, it is necessary to consider the influence of objective factors, so the actual friction calculation formula is shown in Equation 7.

Where P f r i is the actual value of fracturing fluid friction in fluid unit iii at flow rate Q t ​, in MPa; f is the friction correction coefficient (dimensionless); and P f 1 i is the theoretical value of fracturing fluid friction in fluid unit iii at flow rate Q t , in MPa.

In Equation 8, f is: f = P f r P f 1 (8) Where P f r is the actual value of wellbore fracturing fluid friction at maximum flow rate (calculated based on the instantaneous pressure drop during pump shutdown in field operations), in MPa.

In Equation 9, P f 1 i is: P f 1 i = σ i P f 0 i (9) Where σ i is the friction reduction ratio of fluid unit i ; and P f 0 i   is the theoretical value of clear water friction in fluid unit iii at flow rate Q t , in MPa.

In Equation 10, σ i is: σ i = exp ⁡ − 2.14 − 1.1547 × 10 − 4 ⁢ d 2 Q t − 0.2842 × 10 − 4 ⁢ G d 2 Q t − 0.1639 ⁡ ln ⁢ G 0.11983 − 2.3367 × 10 − 4 ⁢ c i ⁢ e 0.11983 G (10) Where   Q t is the flow rate at different times, in m³/min.

In Equation 9, P f 0 i   is: P f 0 i = 1.3866 × 10 6 d − 4.8 Q t 1.8 h i (11) As shown in Equation 11, the theoretical value of clean water friction of liquid unit i under displacement Q_t is calculated as

(3) Dynamic Bottom-Hole Pressure During Fracturing Operations. The bottom hole pressure at different times is shown in Equation 12:

In Equation 13, ∆ P i is: Δ P i = P h i − P f r i (13)

As shown in Equation 14, the final bottom-hole net pressure calculation formula is P = P t t + ∑ i = 1 n Δ P i − σ h m i n (14) Where P is the bottom-hole net pressure, in MPa; and σ h   min is the minimum horizontal principal stress, in MPa.

The analysis of fracture propagation is typically based on the classic Nolte-Smith (N&S) diagnostic theory. The classic N&S theory is established on traditional 2D fracture models and does not consider the extension of fractures in the vertical direction. It mainly includes PKN, KGD, and radial models, which categorize different ranges of double-logarithmic slopes of net pressure to derive various fracture propagation scenarios. However, in fractured tight sandstone reservoirs characterized by high geological complexity, well-developed natural fractures, and diverse modes of fracture propagation, the N&S theory is no longer applicable (Luo et al., 2020; Deng et al., 2024). Therefore, the author optimizes the N&S theory by simulating fracture propagation through an integrated platform, using the UFM model for complex fracture simulation and the planar 3D model PLANAR3D for simulating artificial primary fractures and vertical extension. This approach aims to address the shortcomings of the classic N&S theory while establishing a fracture propagation mode identification mechanism suitable for fractured reservoirs.

Currently, there is limited systematic research on the initiation and propagation of natural fractures in fractured tight sandstone reservoirs. Most studies focus on the changes in mechanical parameters related to the fracture of matrix rocks. For instance Zhao et al. (2021), discusses and explains the variations in the stress-strain curve, irreversible strain, elastic modulus, and Poisson’s ratio during the rock fracture process Zhou et al. (2019). investigates the influence of rock brittleness on fracture initiation, propagation, and merging processes, noting that variations in rock brittleness can directly affect fracture initiation modes. While these studies clarify the changes in mechanical parameters during fracture initiation, they do not address the propagation of artificial fractures when encountering natural fractures.

As shown in Table 3, based on the actual fracturing conditions of various wells in the work area, basic parameter settings for fracturing parameters, proppant parameters, and construction displacement parameters are established. Subsequently, under conditions of variable displacement (with a simulation range of 1–7 m³/min) and variable fluid (determined by the use of fracturing fluids over the past 5 years in the work area, resulting in four combinations of consistency and flow coefficients as shown in Table 4), the net pressure curve is processed logarithmically to determine the double-logarithmic slope ranges for various fracture propagation modes. This leads to the establishment of a fracture propagation identification mode specific to fractured sandstone reservoirs.

As shown in Figure 13, using the above-calibrated method for bottom-hole net pressure and the fracture extension mode identification mechanism for fractured reservoirs, an analysis was conducted on the fracture extension modes for 29 wells in the work area. It can be observed that none of the wells exhibit vertical fracture penetration. Based on the time proportions of fracture extension modes, two main categories emerge: (1) complex fracture extension and communication with natural fractures as the dominant mode; (2) extension impeded and communication with natural fractures as the leading mode. The overall modification effect in the work area is quite favorable, with wells primarily extending artificial fractures being in the minority; most wells achieve communication with natural fractures, yielding an average fracture network complexity index of 0.21.

Figure 14 illustrates the relationship between the time proportion of complex fracture extension for each well and the open flow capacity. A strong positive correlation is evident, with a correlation coefficient of 0.7. This suggests that after the modification operations, the time proportion of complex fracture extension (fracture network complexity index) can be used to predict the post-fracturing productivity of the reservoir.

In this study, well A in the western Tarim Basin was selected for the field application and analysis of a fracturing construction curve diagnosis method for fractured sandstone. The main modification section of well A is the Bashkichik Formation (vertical depth/measured depth 6,813.00–6,961.00 m), with a reservoir depth of 6,887 m and a thickness of 148 m. The horizontal minimum principal stress in the modification section is about 2.14 MPa/100 m, with vertical stress at approximately 2.4 MPa/100 m and maximum horizontal stress ranging from 2.5 MPa/100 m to 2.6 MPa/100 m. The stress state indicates a potential strike-slip type, with an average horizontal stress difference of about 25 MPa. The average compressive strength of the Bashkichik Formation rocks is 98 MPa, with a Young’s modulus of about 29 GPa and a Poisson’s ratio of about 0.25. Due to the large modification span and thin mudstone layers, artificial fractures can easily activate natural fractures, hence the use of a temporary plugging and directional fracturing technique for modification.

FMI imaging logging data shows that natural fractures are well developed in the Bashkichik Formation of well A, indicating high overall fracturability of the reservoir. Analysis of logging data reveals that a total of 58 natural fractures were identified in well A, predominantly oriented northwest and northeast with high angles (almost exceeding 80°). The principal stress direction forms a moderate angle (less than 45°) with the direction of the natural fractures.

Based on the previously established fracturing construction curve diagnosis method for fractured sandstone, a diagnostic analysis was performed on well A’s fracturing construction curve. By calibrating the bottom-hole pressure, the net pressure curve was obtained, and the fracture extension modes were identified, allowing for an assessment of the overall effectiveness of the fracturing operation. Using the actual field parameters from well A and the Bashkichik Formation construction curve as an example, as shown in Figures 15A–E, the fracture extension modes before and after the directional change were identified using the fracturing construction curve diagnosis method.

Before the directional change, the dominant fracture extension modes included complex fracture extension, impeded extension, and communication with natural fractures (increased fluid loss), with time proportions of 30.44%, 36.49%, and 32.75%, respectively. During the early stage of the pre-fill phase, the bottom-hole net pressure exhibited an upward trend with minor fluctuations, indicating complex fracture extension and successful activation of natural fractures. Subsequently, the net pressure curve decreased while the oil pressure curve rose (212–1135 s), due to the gradual opening of natural fractures leading to increased fluid loss. From 1,150 s to 3,100 s, the net pressure curve showed periodic fluctuations, with alternating modes of increased fluid loss and impeded extension, attributed to continuous activation of natural fractures, causing changes in fluid loss area and periodic net pressure fluctuations. After 3,100 s, the net pressure curve continued to rise, indicating impeded extension. The increase in net pressure facilitated further extension and communication with more natural fractures. At 42,68 s, the fracture extension mode shifted from impeded to complex extension, indicating that the net pressure had surpassed the critical value, successfully activating natural fractures. The complexity index before the directional change was 0.35.

After the directional change, the dominant fracture extension modes shifted to complex extension and communication with natural fractures (increased fluid loss), with time proportions of 45.48% and 35.42%, respectively. Prior to the segmental sand plug, the net pressure curve sharply decreased, indicating increased fluid loss, as human-induced and natural fractures intersected, opening the natural fractures. The net pressure then rose overall (235 s–1,620 s), transitioning from impeded extension to complex extension mode. In the following stage (1,620 s–3,000 s), a combination mode of increased fluid loss, impeded extension, and fracture network extension appeared alongside changes in the net pressure curve. From 3,000 s to 4,180 s, the net pressure further increased, showing a prolonged period of complex fracture extension. In the final section, while the net pressure slightly declined, the dominant modes remained increased fluid loss and complex extension, suggesting significant natural fractures were activated in this stage. The complexity index after the directional change was 0.56.

Through the analysis of the bottom-hole net pressure recalibration and identification of fracture extension modes before and after the directional change in well A, it can be concluded that the formation of complex fracture extensions is closely related to net pressure. An increase in net pressure within a certain range can effectively communicate with natural fractures, facilitating the formation of complex fractures. Given the characteristics of fractured sandstone reservoirs, periodic trends in the net pressure curve may lead to branching and directional extensions of natural fractures, resulting in more complex multi-level fractures that enhance the effectiveness of reservoir modification.

(1) Breaking through the conventional idea of calculating the net bottomhole pressure, a method of calculating the dynamic net bottomhole pressure of fracturing based on specific real-time fracturing construction data is established. Using the idea of “turning the whole into zero”, the net bottomhole pressure calculation results are more accurate by dividing the wellbore fluid into units, correcting the fluid volume and sand concentration of the fluid units at different moments, and correcting the formula of the indoor experimental fitted friction formula with the on-site construction friction, which is a more accurate calculation of the net bottomhole pressure.