Three-dimensional Simulation Model Research Articles

Numerical simulation and intelligent prediction of a 500 t/d municipal solid waste incinerator

After classifying municipal solid waste (MSW), understanding how changes in its characteristics affect the incineration process becomes essential. Optimizing and adjusting operating parameters is crucial to ensure the smooth operation of MSW incinerators. In this study, we developed a three-dimensional numerical simulation model for a 500 t/d MSW incinerator, based on a two-fluid model that accounts for grate motion. We examined the effects of load and moisture on the combustion process. Using the results from the numerical simulation and on-site operational data, we established a machine learning model to predict incinerator conditions based on load, waste particle size, and moisture content. The average relative errors for the training and test sets were approximately 0.33 % and 0.44 %, respectively. Finally, we compared the influence of different operating parameters on flue gas temperature. Our numerical simulation model and intelligent prediction method offer valuable guidance for optimizing existing MSW incinerators and designing new ones.

Equivalent Simulation Study of Delta-Rotor Engine

The mechanical structure, movement mode, and combustion process of a triangular rotor engine differ from those of a conventional engine with a crank connecting rod mechanism as the core. This makes it impossible to directly use existing simulation software to simulate the performance of the entire engine, rendering it difficult to conduct structural evaluation and performance prediction during the engine development stage. Therefore, using existing performance simulation software to establish a performance-equivalent model for a triangular rotor engine is crucial. To solve the above problems, this study proposes a performance-equivalent simulation modelling method for a triangular rotor engine based on a three-dimensional simulation model and the operating principles of the triangular rotor and four-stroke engines. Compared to various performance indicators obtained from the three-dimensional simulation model, the results show that the equivalent model established in this study has sufficient accuracy for key indicators such as the cylinder pressure, cylinder temperature, and in-cylinder quality under various working conditions. This can satisfy the requirements of the complete machine-performance simulation of a triangular rotor engine.

Rapid simulation of knitted fabrics based on a ribbon yarn model

In the study, an innovative three-dimensional ribbon-based yarn model simulation technique is introduced, aimed at significantly enhancing the realism and speed of knitted fabric simulation through efficient model construction and rendering processes. The method successfully overcomes the limitations of traditional two-dimensional loop models and tubular yarn models, accurately capturing the textural details of knitted fabrics with a vivid three-dimensional representation. Experimental results demonstrate the outstanding performance of this simulation system in simulating the fuzz effects of yarn and in processing speed. This technology offers significant potential in textile design and production, notably in boosting design efficiency and accelerating new product development. By employing low-cost image capture methods, the study effectively reduces technical and financial barriers in knitted fabric simulation, enhancing its practical and industrial applicability.

Research on the Dynamic Leaking and Diffusion Law of Hydrogen-Blended Natural Gas under the Soil–Atmosphere Coupled Model

With the breakthrough in mixing hydrogen into natural gas pipelines for urban use, the widespread application of hydrogen-blended natural gas (HBNG) in energy delivery is imminent. However, this development also introduces significant safety concerns due to notable disparities in the physical and chemical properties between methane and hydrogen, heightening the risks associated with gas leaks. Current models that simulate the diffusion of leaked HBNG from buried pipelines into the atmosphere often employ fixed average leakage rates, which do not accurately represent the dynamic nature of gas leakage and diffusion. This study uses computational fluid dynamics (CFD) 2024R1 software to build a three-dimensional simulation model under a soil–atmosphere coupling model for HBNG leakage and diffusion. The findings reveal that, in the soil–atmosphere coupling model, the gas diffusion range under a fixed leakage rate is smaller than that under a dynamic leakage rate. Under the same influencing factors in calm wind conditions, the gas primarily diffuses in the vertical direction, whereas under the same influencing factors in windy conditions, the gas mainly diffuses in the horizontal direction.

Noise reduction design of new residential buildings along urban roads-taking a residential district in Foshan as an example

Taking a residential district in Foshan along the city road as an example, the impact of urban road traffic noise on it is studied. Firstly, the data is monitored in the noise field, then three-dimensional simulation models of residential buildings and road distribution are established in Cadna/A software, and noise simulation prediction is carried out according to the actual situation and relevant norms and standards. The predicted noise values of the exterior surface of residential buildings are obtained, which has exceeded the permissible interior noise level for residential buildings. By comparing the application effects of noise reduction measures in buildings, the noise reduction design scheme of new residential buildings along urban roads is finally proposed: the sound insulation doors and windows that meet the requirements are adopted. After the completion of the house, the indoor background noise and the sound insulation performance of the doors and windows are measured. The measured results show that the selection of sound insulation doors and windows is suitable and the indoor noise environment meets the design requirements of noise reduction. The results are helpful to provide technical reference for the noise reduction design and renovation of other residential buildings along urban roads.

Using three turbulence simulation methods for modeling the flying of high-speed railway tunnel lining blocks under piston airflow

The detached tunnel lining concrete blocks poses a serious threat to the safety of moving high-speed train. Understanding the flight characteristics of detached blocks from the tunnel soffit under train piston airflow is essential for devising appropriate measures to mitigate such risks during train operation. Computational Fluid Dynamics (CFD) simulation methods, known for their high efficiency and good repeatability, are effective approaches to study this subject. Large Eddy Simulation (LES), Improved Delayed Detached Eddy Simulation (IDDES), and Unsteady Reynolds-Averaged Navier-Stokes (URANS) are three commonly used turbulence simulation methods in the CFD simulation of train/tunnel aerodynamics. In this study, a three-dimensional CFD simulation model based on the three turbulence simulation methods is established for the airflow-tunnel-train-detached block system, and an experiment is conducted for validating the CFD model. Using the established models, the influence of different turbulence simulation methods on the flight trajectory and aerodynamic coefficients of detached lining blocks under train-induced airflows is compared. By visualizing the macroscopic flow field inside the tunnel and the local flow field near the detached block, the flow mechanisms of detached blocks under different turbulence simulation method conditions are revealed. The results showed that in the 1st stage (BTT stage), the flight of the detached block is influenced by the airflow near the train body, while in the 2nd stage (ATT stage), it is mainly affected by the train wake vortex. Compared with experimental results, the errors of LES and IDDES in simulating the longitudinal direction displacement of the block are only 2.3% and 5.5%, respectively, while the error of URANS is 10.6%. The simulation error of URANS for the longitudinal direction flight speed reached 8.8% in the ATT stage. In the BTT stage, LES and IDDES predicates more and larger leeward side vortex structures of the detached block, while URANS predicates fewer and smaller vortex structures. Compared with URANS method, the dissipation rate of the vortex structures simulated by LES and IDDES in the ATT stage is slower. These are the main reasons explaining why the flight characteristics of detached lining blocks obtained by URANS method are different from the LES and IDDES methods.

Design of innovative phase-change cold storage refrigerator and simulation analysis of discharging progress

At present, the field of cold chain logistics experiences significant growth, with refrigerator playing a pivotal role in cold chain transportation. An innovative compartmentalized phase-change cold storage refrigerator has been proposed in this study, designed to address the increasing demand for efficient and energy-saving solutions in the cold chain transportation industry. A conceptual module prototype is designed and built in this study, with an analysis of the system's charging and discharging processes under varying conditions. The cold storage refrigerator exhibits favorable matching characteristics, the charging process requires approximately 270 min, and the cooling effect sustains for about 23 h. A three-dimensional simulation model of the cold storage refrigerator is developed, enabling a comprehensive evaluation of the cooling effect and further optimization of the cold storage plate layout. The results indicate that the layout of the three-sided type cold plate significantly reduces the pre-cooling time. It is determined through simulation calculations in this study that setting the loading capacity to 50 % can strike a balance between efficient cooling and transportation efficiency. Additionally, under high-temperature conditions, the cold storage refrigerator maintains a low temperature for up to 10 h at a filling rate of 50 %.

Thermodynamic performance and compression characteristics analysis of low GWP refrigerant in compressors: Experimental investigation and 0-D/3-D simulation

The utilization of low global warming potential (GWP) refrigerants is crucial for reducing greenhouse gas emissions. Among these alternatives for hydrofluorocarbons (HFCs), R290 stands out as a natural refrigerant with a low GWP value of 3. Therefore, it is beneficial to promote its widespread adoption and enhance the efficiency of compressors and their systems that utilize R290 to mitigate the greenhouse effect. The present study investigates and compares the thermodynamic performance and compression characteristics of a high-speed compressor employing R290 as a refrigerant with those of an R32 compressor. In contrast to previous studies, this paper presents a novel approach by developing validated the zero-dimensional (0-D) and three-dimensional (3-D) simulation model, along with experiments, to investigate the distribution of performance loss and suction-compression characteristics in high-speed R290 compressors. The results demonstrate that the R290 compressor exhibits superior volumetric efficiency, while excessive compression at high speeds leads to a noticeable reduction in indicated power. The combination of increased over-compression loss and motor loss at high speeds resulted in a 11.7% rise in input power, leading to an 8.4% decline in thermodynamic performance for the R290 compressor under standard heating compared to the R32 compressor.

A meshless model for three-dimensional direct numerical simulation of local scour around cylinder bridge foundation

A meshless local scour model for cylinder bridge foundation based on the smoothed particle hydrodynamics (SPH) method is proposed in this paper. Differing from the traditional Eulerian mesh model used for monopile local scour, it overcomes the high requirements of mesh quality and density for capturing large deformations at the fluid interface. Unlike the transient sediment erosion SPH model used for dam-break, sediment flushing, and water jet, the meshless approach is innovatively applied to the continuous simulation of bridge local scour under steady flow conditions. The present SPH model is established based on the SPH multi-phase fluid model, integrating a classical fluid model combined with numerical stabilization algorithms to govern water particle motion and a sediment model from Zhang et al. (2024) to govern sediment evolution, and tests a new scheme for boundary treatment in the model based on DualSPHysics. Furthermore, a novel scour visualization method that aims at extracting both visible and actual bed surfaces from discrete particles is proposed. The model is validated through comparison with rigid bed and live bed experiments, demonstrating favorable agreement in terms of flow and scour simulation. Importantly, the model results reveal a discrepancy between the elevation of the post-scour visible bed surface derived from the conventional Eulerian mesh model and experimental data, compared to the actual bed surface unaffected by water flow erosion. This indicates the necessity for incorporating a safety margin in foundation design when utilizing experimental results to determine the maximum scour depth.

Identification and Application of Wave Field Characteristics of Channel Waves in Extra-Thick Coal Seams

Channel wave seismic activity often occurs with thin and medium-thick coal seams being the main target layer. To address the problem of channel wave applicability detection in extremely thick coal seams, the propagation and identification characteristics of channel waves remain the focus of research. Therefore, this paper takes the in-seam wave exploration of a 27 m extremely thick coal seam as an example and uses the staggered mesh finite difference method to construct a three-dimensional medium model for numerical simulation. An analysis of the physical parameters of coal and rock, along with the dispersion characteristics of channel waves in extra-thick coal seams, is utilized, through the Zoeppritz equation and the total reflection propagation method, to calculate the imaging. We found the following: (1) The dispersion areas and weak dispersion areas along the detection direction are extremely thick coal seams. (2) There are apparent channel waves in extra-thick coal seams, with a waveform similar to body waves; the length of the wave train is shorter than that of the conventional channel wave, and the arrival time can be estimated accurately. The amplitude of the apparent channel wave is affected by the degree of dispersion, with lower attenuation and higher resolution. The characteristic of total reflection in extremely thick coal seams is that the incident angle is equal to the critical angle, and the dispersion characteristics are weak. (3) The channel waves with weak dispersion characteristics in extra-thick coal seams are mainly Love-type waves.

Large-Scale Physical Simulation Experiment of Water Invasion Law for Multi-Well Development in Sandstone Gas Reservoirs with Strong Water Drive

In order to clarify the water invasion law and residual gas distribution characteristics in edge and bottom water gas reservoirs with multi-well development, a large-scale three-dimensional physical simulation model was developed and a physical simulation experiment method for the water invasion law of multi-well development in sandstone gas reservoirs with strong water drives was established. Water invasion physical simulation experiments of multi-well development under the conditions of different water body multiples and production systems were conducted. The results show the following: (1) Gas wells near fractures and high-permeability zones experience the earliest water breakthrough. The larger the water body multiple, the faster the rate of water invasion, the earlier the water breakthrough time of gas wells, the more severe the degree of water invasion in gas reservoirs, and the lower the ultimate recovery rate. (2) Shutting in low-position gas wells immediately after water breakthrough reduces the overall water production of the gas reservoir and extends the overall water-free gas production period. However, the ultimate recovery rate is lower than when the wells are not shut in. (3) The residual gas in the fracture model is mainly distributed around the fracture and the edge of the gas reservoir, with the ultimate recovery rate ranging from 38.5% to 58.2%. The residual gas in the fracture–high-permeability zone model is mainly distributed around the fracture–high-permeability zone and the edge of the gas reservoir, with the ultimate recovery rate ranging from 28.32% to 41.8%. The experimental results have important guiding significance for the economical and efficient development of similar gas reservoirs.

Study of the Impact of Surface Topography on Wear Resistance

The surface texture parameter is a real reflection of the surface topography, which is closely related to the tribological properties of the surface, and the study of the correlation between the surface texture parameter and wear resistance is of great significance in revealing the tribological influence mechanism of the surface and realising the functional manufacturing of the surface. This paper takes the ball-end milling surface as the research object, establishes the three-dimensional simulation model of the surface topography, and analyses the surface topography and the surface texture parameter change rule. Based on the improved correlation analysis model, the correlation characteristics between the surface texture parameters, and between the surface texture parameters and the relative wear rate of per unit sliding distance KV, were investigated, and the prediction model of KV was established based on the surface texture parameters Sku, Sa, Sxp, Sp, and Ssk, and the correctness of the model was verified by experiments. The study in this paper provides a new idea to further reveal the relationship between surface topographical features and wear resistance and to guide the functional manufacturing of surfaces.

Gas Fire Coupling Control of Goaf Based on Numerical Simulation

ABSTRACT In response to the problem that traditional gas control methods such as water injection and inert gas fire extinguishing are not effective and have a high level of risk in goaf, this study uses COMSOL software to establish a three-dimensional numerical simulation model of goaf, and combines air leakage intensity, oxygen concentration, and floating coal thickness to calculate the gas fire hazard area, in order to achieve effective control. The results show that the deviation between the data obtained from the numerical simulation and the actual measurement value is about 7 m, which proves that the given solution is reliable. The gas concentration of the wind lane and the upper corner is controlled below 1%, which proves that this method ensures the safety of the working environment. The above results show that the design method realizes the effective control of gas fire in the goaf, and provides reference for mine safety management and gas disaster control.

A LiDAR-driven three-dimensional simulation model for far-red solar-induced chlorophyll fluorescence in forests

Solar-induced chlorophyll fluorescence (SIF) is a subtle but informative probe of plant photosynthesis. Quantifying the three-dimensional (3D) distribution of SIF benefits a better understanding of photosynthesis variations over heterogeneous canopies. Although radiative transfer models (RTMs) provide a solid theoretical basis for simulating the 3D SIF distribution, most RTMs use virtual scenes with complex reconstruction processes. This study aims to develop a 3D SIF simulation model (FluorLiDAR) directly driven by terrestrial light detection and ranging (LiDAR) data using leaf and canopy RTMs, including a 3D PAR (photosynthetically active radiation) simulation model, the Fluspect model, the atmosphere radiative transfer module in SCOPE, and the multiple scattering coefficients of sunlit and shaded leaves from the 4-scale model. The results show that (1) the simulated and measured SIF patterns were consistent, with R2 (RMSE) values of 0.73 (0.17 mW/nm/m2/sr) and 0.76 (0.12 mW/nm/m2/sr) for 1-min sampling and 10-min averages, respectively. Moreover, the R2 between FluorLiDAR and the DART simulation reached 0.94. The R2 of FluorLiDAR and DART were both higher than 1D mSCOPE using every 10-min sampling data. (2) Point density, denoted by average NPD (nearest point distance), influenced the performance of our model mainly when it was smaller than 0.1 m. Chlorophyll content had less influence on the model accuracy (R2 and rRMSE), and the bias between simulation and measurement decreased as chlorophyll content increased. (3) The simulated 3D SIF distribution pattern closely resembled PAR within the canopy. Besides, FluorLiDAR can simulate the hot spot effect like DART and mSCOPE though the effect was not as obvious as the other two models. This study highlights the potential of a LiDAR-driven SIF model for 3D SIF simulation over a heterogeneous canopy, which may benefit the understanding of the structural impacts on forest photosynthesis in real forest scenes.

Numerical investigations on electrolytic performance of proton exchange membrane electrolysis cell with parallel flow field

In this study, a three-dimensional simulation model of PEMEC with parallel flow field was established, the heat and mass transfer, electrochemical reactions were described to investigate the electrolytic performance. The distribution characteristics of temperature, liquid water and gas products in the electrolysis cell were obtained. The results show that during the operation of PEMEC system, the liquid water content decreases sequentially along the flow channel direction, while there is a significant temperature gradient in the flow direction of the electrolysis cell. The increase of the initial temperature can increase the current density of the electrolytic cell when the temperature increases from 60 ℃ to 80 ℃, the current density can be increases by 7.86 %, but it can also lead to the dehydration of PEMEC, resulting in thermal degradation of PEMEC, and further the reactivity and proton transfer performance were decreased. It is also found that the increase of liquid water inlet flow not only increased the reactant concentration, accelerated the chemical reaction rate, but also took away more heat generated by ohmic polarization as a coolant, which was conducive to the improvement of electrolytic performance. As the inlet flow rate increased from 1 mL/s to 3 mL/s, the current density at 2.4 V and 1.4 V can be increased by 3.66 % and 1.77 %, respectively, and the maximum temperature can be reduced by 7.4 K.

Optimizing Mid-Temperature Sodium Iodine Batteries for Sustainable Large-Scale Energy Storage: A Comprehensive Modeling Approach and Experimental Validation

The need for safe, eco-friendly, low-cost batteries for large scale implementation rises in the presence of the expansions of renewable energy sources. High-temperature liquid sodium batteries (e.g. sodium-sulfur) are a well-established technology for large-scale grid storage. Combining the molten sodium anode with an aqueous iodine cathode overcomes the problems of thermal loses and sealing by reducing the operating temperature to about 100°C. This leads to higher cost efficiency, energy density and a simplified cell design.Here we present a novel modelling approach for complex carbon-based cathode structures and its limits and abilities on enhancing the utilizable capacity. Due to their sustainability and high efficiency, which is comparable to Li-Ion –batteries, mid-temperature sodium-iodine batteries are a promising candidate for stationary energy storage applications. With a high specific energy of around 200 Wh kg-1, sodium-iodine batteries have the ability to meet the growing demand of short-term energy storage caused by the integration of renewable energy sources into the power grid. Up to this day, the detailed processes inside the battery are not well-understood. Quantities like initial species concentrations, C-rate, cell design and cathode geometry have large impacts on the overall battery performance. A deeper understanding of these processes is inevitable for enhancing the battery performance by choosing the optimal abovementioned quantities. We set up a fully resolved 3D Simulation model to gain insight into microstructural processes inside the battery, as experimental studies are limited to macroscopic quantities like electronic current and potential. The methodology is based on continuum hypothesis by using an open-source CFD software, which is rewritten accordingly. The proposed spatially resolved three-dimensional simulation model takes charge and mass transport, heterogeneous and homogeneous reactions as well as the electrochemical processes into account. Results show that transport limitations confine the utilizable capacity of the battery [1].This contribution focuses on enhancing the battery energy density and efficiency by including open-pored glassy carbon foam structures in the cathode half-cell [2, 3]. We state simulation predicted, optimal morphology properties of such a structure. Furthermore, we describe the evaluation of improved thermodynamic data of the aqueous iodine solution by refitting simulation results to polarization curves. We utilize a novel impedance spectroscopy simulation method for sodium iodine batteries to improve parameterization of the underlying electrochemical model by comparing the results with experimental data. References Gerbig, F., Cernak, S., Nirschl, H. (2021). 3D Simulation of Cell Design Influences on Sodium–Iodine Battery Performance. Energy Technology, vol. 9, no. 6, p. 2000857Gerbig, F., Cernak, S. and Nirschl H. (2021), Towards a Novel Sodium-Iodine Battery with an Aqueous Catholyte: Numerical Investigations of Complex Cathode Structures, ECS Trans., vol. 104, no. 1, pp. 123–130Gerbig, M. Holzapfel, and H. Nirschl, Simulating the Impact of Glassy Carbon Foam Electrodes on the Performance of Sodium Iodine Batteries, J. Electrochem. Soc., vol. 170, no. 4, p. 40517, 2023, doi: 10.1149/1945-7111/accab7. Figure 1

Performance Prediction of GFRP-Reinforced Concrete Deep Beams Containing a Web Opening in the Shear Span

This study aimed to investigate the nonlinear structural behavior of concrete deep beams internally reinforced with glass fiber-reinforced polymer (GFRP) reinforcing bars and containing a web opening of various sizes and locations within the shear span. Three-dimensional (3D) numerical simulation models were developed for large-scale GFRP-reinforced concrete deep beams (300 mm × 1200 mm × 5000 mm) with a shear span-to-depth ratio (a/h) of 1.04. Predictions of the numerical models were validated against published experimental data. A parametric study was conducted to examine the effect of varying the opening size and location on the shear response. Results of the numerical analysis indicated that the strength of the deep beam models with an opening in the middle of the shear span decreased with an increase in either the opening width or height. The rate of the strength reduction caused by increasing the opening height was, however, more significant than that produced by increasing the opening width. Placing a web opening in the compression zone close to the load plate was very detrimental to the beam strength. Conversely, a negligible strength reduction was recorded when the web opening was placed in the tension side above the flexural reinforcement and away from the natural load path. Data of the parametric study were utilized to introduce simplified analytical formulas capable of predicting the shear capacity of GFRP-reinforced concrete deep beams with a web opening in the shear span.

Research on reliable coverage planning of substation based on equipment service level

Abstract 5G network can meet the multi-type service access needs of substations and promote the intelligent upgrade and transformation of power grids. The layout of buildings and electrical equipment in substations, as well as electromagnetic interference, will have a greater impact on 5G signal coverage. In this paper, a three-dimensional simulation model of the substation is first established, and basic parameters of base station planning are determined. Then, a safety function considering equipment service level and an electromagnetic interference calculation method are defined. Finally, a coverage planning algorithm based on electrical equipment service level and received power quality is proposed to improve the reliability of service access and ensure the safe and stable operation of the system. Simulation results show that the algorithm is effective and reliable.

The Influence of Pre-Chamber Parameters on the Performance of a Two-Stroke Marine Dual-Fuel Low-Speed Engine

With increasing environmental pollution from ship exhaust emissions and increasingly stringent International Maritime Organization carbon regulations, there is a growing demand for cleaner and lower-carbon fuels and near-zero-emission marine engines worldwide. Liquefied natural gas is a low-carbon fuel, and when liquefied natural gas (LNG) is used on ships, dual-fuel methods are often used. The pre-chamber plays a key role in the working process of dual-fuel engines. In this paper, an effective three-dimensional simulation model based on the actual operating conditions and structural characteristics of a marine low-pressure dual-fuel engine is established. In addition, the effects of changing the Precombustion chamber (PCC) volume ratio and the PCC orifice diameter ratio on the mixture composition, engine combustion performance, and pollutant generation were thoroughly investigated. It was found that a small PPC volume ratio resulted in a higher flame jet velocity, a shorter stagnation period, and an acceleration of the combustion process in the main combustion chamber. When the PCC volume was large, the Nitrogen oxygen (NOx) ratio emission was elevated. Moreover, the angle of the PCC orifice affected the flame propagation direction of the pilot fuel. Optimizing the angle of the PCC orifice can improve combustion efficiency and reduce the generation of NOx. Furthermore, reasonable arrangement of the PCC structure can improve the stability of ignition performance and accelerate the flame jet velocity.

A Study on Three-Dimensional Multi-Cluster Fracturing Simulation under the Influence of Natural Fractures

Multi-cluster fracturing has emerged as an effective technique for enhancing the productivity of deep shale reservoirs. The presence of natural bedding planes in these reservoirs plays a significant role in shaping the evolution and development of multi-cluster hydraulic fractures. Therefore, conducting detailed research on the propagation mechanisms of multi-cluster hydraulic fractures in deep shale formations is crucial for optimizing reservoir transformation efficiency and achieving effective development outcomes. This study employs the finite discrete element method (FDEM) to construct a comprehensive three-dimensional simulation model of multi-cluster fracturing, considering the number of natural fractures present and the geo-mechanical characteristics of a target block. The propagation of hydraulic fractures is investigated in response to the number of natural fractures and the design of the multi-cluster fracturing operations. The simulation results show that, consistent with previous research on fracturing in shale oil and gas reservoirs, an increase in the number of fracturing clusters and natural fractures leads to a larger total area covered by artificial fractures and the development of more intricate fracture patterns. Furthermore, the present study highlights that an escalation in the number of fracturing clusters results in a notable reduction in the balanced expansion of the double wings of the main fracture within the reservoir. Instead, the effects of natural fractures, geo-stress, and other factors contribute to enhanced phenomena such as single-wing expansion, bifurcation, and the bending of different main fractures, facilitating the creation of complex artificial fracture networks. It is important to note that the presence of natural fractures can also significantly alter the failure mode of artificial fractures, potentially resulting in the formation of small opening shear fractures that necessitate careful evaluation of the overall renovation impact. Moreover, this study demonstrates that even in comparison to single-cluster fracturing, the presence of 40 natural main fractures in the region can lead to the development of multiple branching main fractures. This finding underscores the importance of considering natural fractures in deep reservoir fracturing operations. In conclusion, the findings of this study offer valuable insights for optimizing deep reservoir fracturing processes in scenarios where natural fractures play a vital role in shaping fracture development.