Numerical Reservoir Simulation Research Articles

Phase Behavior and Rational Development Mode of a Fractured Gas Condensate Reservoir with High Pressure and Temperature: A Case Study of the Bozi 3 Block

The Bozi 3 reservoir is an ultra-deep condensate reservoir (−7800 m) with a high temperature (138.24 °C) and high pressure (104.78 MPa), leading to complex phase behaviors. Few PVT studies could be referred in the literature to meet such high temperature and pressure conditions. Furthermore, it is questionable regarding the applicability of existing condensate production techniques to such a high temperature and pressure reservoir. This study first characterized the phase behavior via PVT experiments and EOS tuning. The operating conditions were then optimized through reservoir numerical simulation. Results showed that: (1) the critical condensate temperature and pressure of Bozi 3 condensate gas were 326.24 °C and 43.83 MPa, respectively; (2) four gases (methane, recycled dry gas, carbon dioxide, and nitrogen) were analyzed, and methane was identified as the optimal injection gas; (3) gas injection started when the production began to fall and achieved higher recovery than gas injection started when the pressure fell below the dew-point pressure; (4) simultaneous injection of methane at both the upper and lower parts of the reservoir can effectively produce condensate oil over the entire block. This scheme achieved 8690.43 m3 more oil production and 2.75% higher recovery factor in comparison with depletion production.

A novel model for low-permeability reservoir numerical simulation considering dynamic capillary force

ABSTRACT Capillary force is not only affected by water saturation but also affected by fluid flow velocity, which is necessary to modify the prior numerical simulation methods. First, a dynamic capillary force testing device was developed, then, an experimental procedure was adopted to measure the dynamic capillary force curve. Three dynamic capillary force curves were obtained under different displacement velocity conditions. Finally, the dynamic capillary force was introduced into the flow equation of low-permeability reservoir numerical simulation. The oil-phase equation and water-phase equation were discretized in three-dimensional space, and the IMPES method was used to solve the water saturation and pressure difference. The calculation results between the traditional numerical simulation method and the novel method under heterogeneous and inhomogeneous conditions were analyzed. The results reveal that the difference in water cut is mainly reflected in the rapid rise of water cut. In the early stage of rapid increase, the water cut calculated by the new method is slightly higher than traditional method. When the water cut is more than 65%, the water cut calculated by the new method is slightly lower than the traditional method.

Comparative Study on Artificial Fracture Modeling Schemes in Tight Reservoirs—For Enhancing the Production Efficiency of Tight Oil and Gas

In order to improve the reliability of the deployment of production schemes after artificial fracturing in tight reservoirs, it is urgent to carry out research on the description of fractures after artificial fracturing. In this study, taking the Chang 61 oil formation group in the Wangyao South area of Ordos Basin as an example, three different fracture modeling schemes are used to establish the geological model of fractured reservoirs, and the fitting ratios of the respective reservoir models are calculated by using the method of reservoir numerical simulation of the initial fitting, and the optimal fractured reservoir modeling scheme is screened in the end. The research area adopts three types of fracture prediction results based on FMI fracture interpretation data, seismic fracture prediction data, and rock mechanics artificial fracturing simulation data. On this basis, geological models of fractured reservoirs are established, respectively. The initial fitting of reservoir values of each geological model are compared, and the highest initial fitting rate of reservoir values is 88.44%, which is based on rock mechanics artificial fracturing simulation data. However, the initial fitting rate of the reservoir model was the lowest at 75.76%, which was established based on the fracture random modeling results of FMl fracture interpretation data. Under the constraints of seismic geostress prediction results and microseismic monitoring data, the simulation results of rock mechanics artificial fracturing fracture are used as the basis, on which the geological model of artificially fractured reservoirs is thus established, and this scheme can more realistically characterize the characteristics of fractured reservoirs after artificial fracturing in the study area.

Numerical simulation of shale gas reservoir based on ILU-GMRES method

ABSTRACT The numerical simulation of shale gas reservoirs requires transforming mathematical models into large linear equation systems, and solving large linear equation systems requires a lot of time. A novel ILU-GMRES method for solving large linear equations is presented, which treats the sub matrix discretized at nodes as the basic elements of the coefficient matrix. By combining the incomplete LU decomposition method (ILU) with the generalized minimum residue method (GMRES), the discretized large linear equations are iteratively solved. A comparison was made between the new method and other methods for calculating the actual shale gas reservoir model. The results reveal that the new method has a faster calculation speed in solving linear equation systems. The calculation time of the novel ILU-GMRES method is 1029s, the calculation time of the generalized minimum residual method (GMRES) method is 2709s, the calculation time of the Gauss–Seidel method (GS) is 3786s, and the calculation time of the successive over relaxation method (SOR) method is 3386s, the calculation time of the preprocessing conjugate gradient method (PCG) is 3115s. The calculation speed of the novel method is almost 2.6 times faster than the GMRES method, the novel method is more effective in the numerical simulation of shale gas.

Modeling unobserved geothermal structures using a physics-informed neural network with transfer learning of prior knowledge

Deep learning has gained attention as a potentially powerful technique for modeling natural-state geothermal systems; however, its physical validity and prediction inaccuracy at extrapolation ranges are limiting. This study proposes the use of transfer learning in physics-informed neural networks to leverage prior expert knowledge at the target site and satisfy conservation laws for predicting natural-state quantities such as temperature, pressure, and permeability. A neural network pre-trained with multiple numerical datasets of natural-state geothermal systems was generated using numerical reservoir simulations based on uncertainties of the permeabilities, sizes, and locations of geological units. Observed well logs were then used for tuning by transfer learning of the network. Two synthetic datasets were examined using the proposed framework. Our results demonstrate that the use of transfer learning significantly improves the prediction accuracy in extrapolation regions with no observed wells.

A novel meshless method for numerical simulation of fractured-vuggy reservoirs

This paper proposes a novel meshless numerical simulation method for fractured-vuggy reservoirs. Initially, model discretization involves extracting fracture and vug feature nodes along the contours of the reservoir bodies and in alignment with fracture orientations, tailored to the characteristics of the fractured-vuggy oil deposit. Subsequently, a connection element model is established within the influence domain. Based on the seepage equations of the connection system, a computational method for the parameters of the connection elements (connection transmissibility and connection volume) is defined. In addition, a sequential method is employed to solve for the pressure and saturation, achieving rapid prediction of the reservoir's production dynamics. On this basis, an automatic history matching algorithm is utilized for real-time fitting of oil–water dynamic indicators, inverting the characteristic parameters of the connection element model, and quantitatively characterizing the injection–production connection elements. The research findings indicate that the method is capable of rapidly fitting and predicting the dynamics of oil reservoir production. Furthermore, conceptual model examples have substantiated that it achieves comparable computational efficiency and superior computational accuracy when compared to the traditional finite difference (volume) method under the same nodal conditions. Additionally, the node arrangement for fractures and vugs is comparatively flexible, and it can ensure the integrity of the flow paths with a limited number of nodes to enhance predictive accuracy. Therefore, this method can effectively meet the rapid prediction requirements for fractured-vuggy reservoirs and also provides a novel meshless computational approach for the numerical simulation of such reservoirs.

A geothermal doublet in a single well: application of the recirculation well concept to reuse wells to be abandoned

The depletion of oil and gas reservoirs leaves many deep and expensive wells with no option but to be abandoned. However, these wells could have a second chance to extend their life as a source of geothermal energy, especially if they are located next to urban or industrial areas in need of heating. This article shows a technical analysis of the well recirculation or geothermal doublet in a single well approach as a strategy to reuse wells that cross aquifers. Different aspects of this strategy are highlighted, including the technical conditions required for the application, the well completion, and the geothermal performance. The latest is assessed via numerical reservoir simulations using geological data from an existing well. The results show that vertical petrophysical heterogeneities play an important role in the performance and feasibility of this approach.

The Time-Varying Characteristics of Relative Permeability in Oil Reservoirs with Gas Injection

Relative permeability is a critical parameter in reservoir numerical simulation and production prediction, intimately associated with reservoir architecture and fluid property. During gas injection development, substantial alterations in reservoir properties and fluid phase behavior induce dynamic changes in relative permeability. Clearly characterizing the time-varying features of relative permeability is very useful for an understanding of how gas injection influences fluid mobility within the reservoir and enhances recovery rates. In this paper, core displacement experiments are firstly conducted to obtain the characteristics of the relative permeability of oil and gas under various development stages and displacement conditions, further delineating the comprehensive shifts in reservoir properties at different gas injection stages. Subsequently, a novel reservoir numerical simulation method is proposed that considers the spatial and temporal segmentation of relative permeability curves in the reservoir simulation. Finally, a practical application is presented to clarify the effects of injection and production parameters on the development performance of gas flooding oil reservoirs. The results show the following: (i) Significant time-varying characteristics of relative permeability occur throughout gas injection development, in the early stages of gas injection, where most of the reservoir is at the gas injection front, and a rightward shift in relative oil and gas permeability indicates that gas injection promotes oil mobility. Conversely, in the later stages of gas injection, as the reservoir reaches the trailing edge of gas injection, the change trend in relative oil and gas permeability reverses, shifting leftward, thereby exacerbating the gas breakout phenomena. (ii) Increasing the rate of gas injection causes relative oil and gas permeability to move leftward, effectively enhancing the gas volume sweep coefficient and microscopic oil displacement efficiency at lower injection speeds while reducing development performance at higher injection speeds. (iii) An increase in gas injection pressure causes relative oil and gas permeability to shift rightward, and although it reduces residual oil saturation and enhances microscopic oil displacement efficiency, it also intensifies gas breakout phenomena and lowers the gas volume sweep coefficient. This paper provides theoretical guidance and technical support for the design of gas injection strategies, optimization of injection and production parameters, and production forecasting.

Inverse Problem of Permeability Field under Multi-Well Conditions Using TgCNN-Based Surrogate Model

Under the condition of multiple wells, the inverse problem of two-phase flow typically requires hundreds of forward runs of the simulator to achieve meaningful coverage, leading to a substantial computational workload in reservoir numerical simulations. To tackle this challenge, we propose an innovative approach leveraging a surrogate model named TgCNN (Theory-guided Convolutional Neural Network). This method integrates deep learning with computational fluid dynamics simulations to predict the behavior of two-phase flow. The model is not solely data-driven but also incorporates scientific theory. It comprises a coupled permeability module, a pressure module, and a water saturation module. The accuracy of the surrogate model was comprehensively tested from multiple perspectives in this study. Subsequently, efforts were made to address the permeability-field inverse problem under multi-well conditions by combining the surrogate model with the Ensemble Random Maximum Likelihood (EnRML) algorithm. The research findings indicate that modifying the network structure allows for improved integration of the outputs, resulting in prediction accuracy and computational efficiency. The TgCNN surrogate model demonstrated outstanding predictive performance and computational efficiency in two-phase flow. By combining the surrogate model with the EnRML algorithm, the inversion results closely aligned with those from the commercial simulation software, significantly improving the computational efficiency.

Combined mechanistic and machine learning method for construction of oil reservoir permeability map consistent with well test measurements

We introduce a novel method for estimating the spatial distribution of absolute permeability in oil reservoirs, consistent with well logging and well test measurements. The primary objective is to create a permeability map, incorporating the well test interpretation results and achieving hydrodynamic similarity to the actual permeability distribution around each well. This enhancement aims to improve the accuracy of reservoir modeling outcomes in reproducing real data. We utilize Nadaraya-Watson kernel regression to parameterize the two-dimensional spatial distribution of rock permeability. The kernel regression parameters are optimized by minimizing the discrepancies between actual and predicted values of permeability at well locations, the integral permeability of the reservoir domain around each well, and skin factors. This inverse optimization problem is addressed by repeatedly solving forward problems, where an artificial neural network (ANN) predicts the integral permeability of the formation surrounding a well and skin factor. The ANN is trained on a physics-based dataset generated through a synthetic well test procedure, which includes the numerical modeling of the bottomhole pressure decline curve in a reservoir simulator and its interpretation using a semi-analytical reservoir model. The proposed method is tested on the “Egg Model”, a synthetic reservoir with significant heterogeneity due to highly permeable channels. The permeability map created by our approach demonstrates hydrodynamic similarity to the original map. Numerical reservoir simulations, corresponding to the constructed and original permeability maps, yield comparable pore pressure and water saturation distributions at the end of the simulation period. Additionally, we observe a notable match in flow rates and total volumes of produced oil, water, and injected water between simulations. The developed approach outperforms kriging in terms of numerical reservoir modeling outcomes. This research advances existing geostatistical interpolation techniques by fusing well logging and well test data to build the reservoir permeability map through an optimization framework coupled with machine learning. Unlike traditional variogram-based geostatistical simulation algorithms, our method provides a permeability distribution that is hydrodynamically similar to the actual one, enhancing initial guess in the history matching process. The novel incorporation of well test interpretation results into the permeability map represents a significant improvement over existing methods, offering an innovative approach that can benefit the petroleum industry. We also provide recommendations for further development of the proposed algorithm to account for geological realism.

Research on the water flooding front based on dynamic and static data inversion – a case study

To clarify the movement of the water flooding front in fluvial reservoirs, this research takes the BZ oilfield as an example. By considering the equivalent flow resistance theory for oil–water two-phase flow, the horizontal micro-element equivalent method and the strong heterogeneity of fluvial facies reservoir comprehensively, a calculation model for a non-piston water flooding front in a horizontal well pattern was established. First, five horizontal injection–production well groups in the BZ oilfield were taken as examples to calculate the water breakthrough time for the oil wells. The calculation results are in good agreement with the actual production performance. In detail, the advancing speed of the water flooding front in the high-permeability strip was 0.8–1.6 m/day, and the speed in the low-permeability strip was 0.12–0.35 m/day. When water is seen in the oil well, the advancing speed in the low-permeability strip is reduced, resulting in uneven displacement and the formation of non-dominant potential areas. In addition, the water flooding front advancing distance was simulated to be 300–450 m by establishing a reservoir numerical simulation model, which is close to the result of the proposed model, indicating that the calculation method is reliable. This research is of great significance for predicting the water breakthrough time of horizontal production wells, judging the weak affected area on the mainstream line, and optimizing water injection and tapping reservoir potential in good time.

Research on CO2-WAG in Thick Reservoirs: Geological Influencing Factors and Random Forest Importance Evaluation.

In the development process of thick reservoirs, the impact of various geological factors on the effectiveness of the CO2 water alternating gas (CO2-WAG) flooding technology remains unclear. This paper establishes multiple CO2-WAG flooding models for thick reservoirs to study the effects of sedimentary rhythm, dip angle, matrix permeability, high-permeability streaks (HPS), and barrier layers on the effectiveness of CO2-WAG flooding and then uses the random forest algorithm to rank the importance of these geological factors. The results show that different geological factors have varying degrees of impact on the distribution of water and gas migration and recovery rates during the CO2-WAG flooding process. The ranking of the importance of various factors obtained by reservoir numerical simulations and the random forest algorithm is HPS, sedimentary rhythm, dip angle, matrix permeability, and barrier layers. These research findings will provide effective guidance and a reference for the optimal selection of CO2-WAG flooding schemes for similar thick reservoirs under different geological conditions.

Research on Geological-Engineering Integration Numerical Simulation Based on EUR Maximization Objective

Shale gas reservoirs, as representative reservoirs in the Sichuan Basin, have attracted widespread attention regarding development. Using gas reservoir numerical simulation to assist development has greatly improved the work efficiency of workers. However, traditional gas reservoir numerical simulation is widely criticized for its inability to effectively integrate with geological and engineering factors. In this study, we proposed a geological engineering integration method that considers pre-fracturing parameters. We further applied it to a typical well (N03) in a certain block of the Sichuan Basin. The reliability of the method was determined through historical fitting. Based on the N03 geological model, the optimization range of fracturing construction parameters in adjacent areas was determined with the goal of maximizing EUR. Recommended values for widely distributed construction parameter combinations of Class II reservoirs were provided through orthogonal analysis. The influence order of fracturing construction parameters is (1) sand addition strength, (2) cluster spacing, (3) construction displacement, (4) fracture fluid strength, and (5) horizontal segment length. Finally, we compared the simulated data with the actual case. The results showed that an integrated numerical simulation method including geological and engineering factors can comprehensively and accurately assist in reservoir development.

Novel THAI well arrangements for improving heavy oil recovery rate in comparison to that achievable in the conventional THAI in situ combustion technology

The toe-to-heel air injection (THAI) method is an environmentally friendly process for in situ upgrading of heavy oils and bitumen via in situ combustion (ISC). Unlike the conventional ISC that uses a vertical producer, the THAI process uses a horizontal producer (HP) well to produce the upgraded oil to the surface. Recent field data has shown that the THAI process is a relatively low-oil-production-rate technology. These considerations call for innovative solutions so that the oil production rate is improved, whilst propagating a stable, efficient, and safe combustion front. Consequently, this work has provided those solutions. Through numerical reservoir simulations, using CMG STARS, five completely new THAI well configurations, which have been labeled A01, A02, A03, A04, and A05, have been developed and studied, and their performances are compared against that of the conventional THAI process which has wells arranged in a classic SLD pattern (i.e. the best-performing conventional THAI process) and against each other. The THAI arrangements A02-A04, however, assume a horizontal air injection well, which currently is not used in field practice but may be developed in the future. In field practice, THAI is applied in a line drive configuration starting up-dip and going down on the structure whilst taking advantage of the contribution provided by the drainage due to gravity; the expansion is made one way only (by drilling new patterns in one direction only). For this reason, the classic SLD pattern refers to the case where the dip of the reservoir is significant (>2–3°). However, when the dip of the reservoir is not significant (“flat” reservoirs) there is a possibility to expand the process in both opposing directions. This is the case dealt with in this work. All configurations A01-A05 assume expansion of the THAI commercial operation in both directions. Selection criteria have been developed and used to determine the two best performing processes. For example, in terms of long-term stability, safety, and efficiency of the combustion process, a process named model A01 is the best, as it achieved 99.8% oxygen utilisation when compared with any other model. It also achieves oil recovery, due to two years of combustion only, of 30.78% OOIP, which is greater than that in the base case model. Overall, based on the weighted selection criteria, which are developed from the deepest analyses of the quantitative 1-dimensional time-dependent parameters and from thorough analyses of the qualitative 2-dimensional profiles of temperature, the combustion zone in the form of oxygen mole fraction, and the oil-flow dynamics inside the reservoir in the form of oil saturation, then model A01 is the best and is followed by model A03. The overall performance of each of these two novel methods outweighs that of the conventional THAI process. However, model A03 uses a horizontal well for injection, which is not current field practice. Therefore, future developmental work should concentrate on the novel method A01 for upgrading and recovery of heavy oils and bitumen, especially since this is low-carbon, efficient, wastewater-free, and provides upgrading inside the reservoir and hence it has a low surface footprint.

On the Feasibility of Deep Geothermal Wells Using Numerical Reservoir Simulation

This study examines the geothermal energy extraction potential from the basement rock within the Denver–Julesburg Basin, focusing on the flow performance and heat extraction efficiency of different geothermal well configurations. It specifically compares U-shaped, V-shaped, inclined V-shaped, and pipe-in-pipe configurations against enhanced geothermal system setups. Through numerical modeling, we evaluated the thermal behavior of these systems under various operational scenarios and fracture conditions. The results suggest that while closed-loop systems offer moderate temperature increases, Enhanced geothermal system configurations show substantial potential for high-temperature extraction. This underscores the importance of evaluating well configurations in complex geological settings. The insights from this study aid in strategic geothermal energy planning and development, marking significant advancements in geothermal technology and setting a foundation for future explorations and optimizations.

A dual-porosity flow-net model for simulating water-flooding in low-permeability fractured reservoirs

The physics-based data-driven flow-network models with high computational efficiency have received great attention as the promising surrogate models for reservoir numerical simulation. However, the existing flow-network models developed for water-flooding reservoirs fail to consider different seepage characteristics of matrix and fractures and cannot be straightly applied to simulate the water-flooding process in low-permeability fractured reservoirs. In this study, we combine the flow-network model with the dual-porosity model to propose a new physics-based data-driven surrogate model, namely the Dual-Porosity Flow-Network Model (Flow-Net-DP), which can consider the non-Darcy flow in tight matrix and the stress-sensitive effects and preferential flow characteristic in fractures. Specifically, we refer to the dual-porosity model and use two channels to represent the connections between wells: one indicates the fracture system, the other represents the matrix system, and the fluid exchange between these two systems is considered by using a transfer function. Besides, each channel is discretized into one-dimensional grids, and a fully implicit scheme with Newton iteration is used to calculate pressure and saturation. Moreover, we establish an automated history matching method by using the Ensemble Smoother with Multiple Data Assimilation (ESMDA) algorithm to calibrate model parameters of Flow-Net-DP, and develop a production optimization method by using the Differential Evolution (DE) algorithm. Finally, the numerical simulation, history matching, and production optimization are conducted on different numerical examples to validate the capability of Flow-Net-DP. The results indicate that the Flow-Net-DP can provide a better description of water flooding process in low-permeability fractured reservoirs compared with the existing flow-network model, especially the rapid water breakthrough caused by the preferential flow characteristic in fractures. Furthermore, both history matching and production optimization based on the Flow-Net-DP yield satisfactory outcomes. For instance, when the optimization results are similar to the full-order simulation model, the optimization speed of Flow-Net-DP is increased by more than five times.

A novel model for oil reservoirs considering stress sensitivity and dynamic relative permeability

ABSTRACT Stress sensitivity and dynamic relative permeability are undeniable phenomenon in oil reservoir numerical simulation. In this paper, a complex two-phase flow model was established considering the deformation of porous media and relative permeability dynamic changes during water injection. A sensitivity analysis on this new model is carried out. The results reveal that stress sensitivity is a key factor that cannot be ignored when using reservoir numerical simulation to calculate water saturation. When the stress-sensitivity coefficient is not considered, the average water saturation of the model is 51.59%. When the stress-sensitivity coefficient is 0.12MPa−1, the average water saturation of the model is 48.45%. After considering stress sensitivity, the average water saturation of the model decreases by 6.1%. The water saturation difference between the new model and the traditional model is mainly reflected in the vicinity of the water injection well. Additionally, the influence of the range of changes in reservoir permeability on the calculation of water saturation by the new model cannot be ignored.

A Novel Method to Calculate Water Influx Parameters and Geologic Reserves for Fractured-Vuggy Reservoirs with Bottom/Edge Water

In practical oilfield production, the phenomenon of water influx typically shortens the water-free recovery period of wells, leading to water flooding and causing a sharp decline in the production well yields, bringing great harm to production. Water invasion usually occurs as a result of the elastic expansion of the water as well as the compaction of the aquifer pore space. However, it can be due to the special characteristics of fractured-vuggy reservoirs such as non-homogeneity and the discrete distribution of the pore spaces. It is challenging to use traditional seepage flow theories to analyze the characteristics of water influx. Also, reservoir numerical simulation methods require numerous parameters which are difficult to obtain, which significantly reduces the accuracy of the results. In this study, considering the driving energy for water influx, a water influx characteristic model was obtained by fitting a graph plate. Subsequently, an iterative calculation method was used to simultaneously obtain water influx volume and OOIP. The aquifer to hydrocarbon ratio was determined by fitting the water influx curve with the graphic plate. Results show that the calculation method is sensitive to the values of reservoir pressure and the crude oil formation volume factor. After applying the method to one field case, it was discovered that water influx performance can be characterized into two types, i.e., linear water influx and logarithmic water influx. In the early stages, the water influx rate of logarithmic water influx is greater compared to linear water influx. However, the volume and energy of waterbody are limited, and the water invasion phenomenon occurs almost exclusively within a short period after the invasion. On the other hand, the volume of waterbody invaded by linear water influx is larger, and it can maintain a stable rate of water influx. The results of the study can provide theoretical support for the waterbody energy evaluation and dynamic analysis of water influx, as well as the control and management of water in these types of reservoirs.

Optimizing cluster spacing in multistage hydraulically fractured shale gas wells: balancing fracture interference and stress shadow impact

Horizontal drilling and multistage hydraulic fracturing have seen widespread application in shale formations during the past decade, leading to significant economic productivity gains through the creation of extensive fracture surfaces. The determination of the ideal cluster spacing in shale gas wells is contingent upon the unique geological and formation characteristics. Generally, reducing the spacing between clusters has the potential to augment gas recovery, albeit at the expense of higher drilling and completion costs, as well as the influence of stress shadows on fracture propagation. This study introduces an integrated methodology designed to explore the impact of cluster interference on well performance. Commencing with a fracture propagation model accommodating stress shadow effects for an equivalent slurry volume injection, analytical rate transient analysis (RTA) was amalgamated with reservoir numerical simulation to compute the effective fracture surface area (Aca.) for hydrocarbon production. The correlation between the effective fracture surface area determined by RTA and the actual stimulated fracture area (Aca.) derived from numerical simulations was established in relation to cluster spacing. The findings of this research reveal that wells featuring a greater number of stages and tighter cluster spacing tend to exhibit elevated cluster interference, resulting in a lower effective-to-actual fracture surface area ratio and heightened stress shadow effects impeding fracture propagation. A cluster spacing of 33 feet with six clusters per stage emerges as the optimal choice at formation permeability of 0.00005 md that decreased to 18 ft at formation permeability of 0.00001 md. ACe either stabilizes or decreases above the optimal value, suggesting that more clusters would not have a major impact on increasing the effective stimulated area. Allowing 20% interference, regardless of the permeability of the formation, maximized cumulative production while preventing thief zones and excessive cluster interference. The insights gained from this study will serve as a valuable resource for completion and reservoir engineers, enabling them to fine-tune cluster spacing to maximize well revenue in the dynamic landscape of shale gas extraction.

Complex fracture description and quasi-elastic energy development mathematical model for shale oil reservoirs

Reservoir numerical simulation is an important tool and method for the reasonable and efficient development of shale reservoirs. Accurate description of three-dimensional fractures in shale reservoir development is a necessary and sufficient condition to improve the accuracy and robustness of shale reservoir numerical simulation. This paper achieves precise characterization of complex fracture shapes and oil, gas and water flow by establishing an embedded discrete fracture model based on a non-structural network, which has advantages in the fine characterization of complex morphological fractures in the reservoir and the grid division of the reservoir. In the large matrix solution method, the Newton-Raphson method is used to linearize the nonlinear equations, the Jacobian matrix is ​​constructed, the ILU method is used for preprocessing, the conjugate gradient method is used to solve the linear equations, and the shale oil quasi-elasticity is established A fully implicit solution method for mathematical models of energy development.