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3. Analysis of the current research status at home and abroad 3.1 Current status of stochastic modeling research for oil and gas reservoirs internationally Since its inception by Professor G. Matheron in France in the early 1960s, geostatistics has seen significant development in terms of its research topics and application areas (Matheron, 1971, 1976). His student, Professor A. Journel, published a monograph titled \"Geostatistics in Mining\" in English in 1978, which had a significant impact worldwide and played a major role in advancing the field of geostatistics. The basic principle of geostatistics is based on the study of the spatial correlations among various geological variables. On this basis, the observed values of a geological variable at certain spatial points are used to estimate or simulate the value of that variable at those points. Geostatistics consists of three main components: spatial correlation analysis of variables, Kriging estimation, and stochastic simulation. During its first twenty years, the application of geostatistics was mainly in the solid mineral industry. It was not until the 1980s, with the emergence of the technique of reservoir description, that the application of geostatistics in oil exploration and development began to develop **significantly. Stochastic simulation is based primarily on probability and statistics as its theoretical foundation. It is also known as the Monte Carlo method. Random simulation in geostatistics can be expressed as follows. Random simulation, as a sampling process, selects joint realizations of various possible random model components with equal probability. This series of realizations (usually expressed using networked data) represents L possible images of the spatial distribution of attribute values in region A. Each implementation, also known as Stochastic Imaging, reflects certain properties imposed on the stochastic model. In a paper published in 1974 (Journel, 1974), Journel, a professor at Stanford University in the United States, discussed the application of random simulation in mining. There, he referred to random simulation as conditional simulation. Subsequently, he discussed it in detail in Chapter 7, \"Simulation of Deposits,\" of his monograph \"Geostatistics in Mining\", published in 1978. The application of stochastic simulation in geostatistics to reservoir description has been referred to by colleagues around the world as stochastic modeling of oil and gas reservoirs. It began with the first paper on stochastic modeling of oil and gas reservoirs, published together in 1984 by Dr. H. Hatdorsen from Norway’s Hydro Oil Company and Prof. L. Lake from The University of Texas at Austin (Holdorsen and Lake, 1984), and has since gone through a fifteen-year development process. Currently, stochastic modeling of oil and gas reservoirs is in a period of rapid development, with three major schools of thought gradually emerging. The Stanford school at the University of Stanford in the United States, led by A. Journel and C. Deutsch, primarily uses sequential instruction simulation methods (Deutsch and Journel, 1992; Journel and Isaaks, 1984; Journel, 1986). The school of the French Center for Geostatistics, led by Professor Matheron in France and his students M. Armstrong and A. Galli, relies on truncated Gaussian simulation methods (Galli and Armstrong, 1996; Leloc’h and Galli, 1996; Matheron and others, 1987). The Norwegian school, led by H. Haldorsen and H. Omre, primarily relies on the indicator point process simulation method (Haldorsen and Damsleth, 1990; Haldorsen and Macdonald, 1987; Hjort and Omre, 1990). In recent years, reservoir stochastic modeling has continued to develop various methods focused on the distribution of reservoir sedimentary facies, while also seeing new advancements in the following two areas. Seismic data are incorporated into the set of observational data used for stochastic reservoir modeling, **thus expanding the scope of application of stochastic reservoir modeling. The nature and spatial distribution of faults and fractures have a significant impact on oil and gas production, making random modeling of them highly important. 3.2 Current status of domestic reservoir description and stochastic reservoir modeling research: Professor Qiu Yinan from the Beijing Institute of Petroleum Exploration and Development has been working in oilfield development geology for over forty years. He and his collaborators started with the development of the Daqing oil field, carrying out many pioneering works in the field of oil field development geology (Qiu Yinan et al., 1994, 1996) ； Qiu Yinan, 1996). The theory of oil sand bodies they proposed for China’s continental reservoirs has established a unique position on the international stage. Through the practice of developing the Daqing Oil Field, 9 geological characteristics related to development that must be clarified to identify an oil field were identified, and these remain the fundamental principles of development geology to this day. In recent years, they have carried out a great deal of valuable work in reservoir description, reservoir evaluation, and characterization. Their work has significantly contributed to oil and gas production as well as to the development of domestic oilfield technologies, representing China’s capabilities in reservoir description and reservoir evaluation. Since 1985, Professor-level Senior Engineers Liu Xingcai and Wang Jie from the Shengli Oilfield, as well as Professors Zhang Yiwei and Xiong Qihua from the China University of Petroleum, have done extensive work in the promotion and application of reservoir description technologies. During the Seventh and Eighth Five-Year Plans, China National Petroleum Corporation carried out research on \"national oil and gas reservoir evaluation\". As one of the outcomes of this project, \"Oil and Gas Reservoir Research Techniques\" (Chen Lihua et al., 2000) summarizes quantitative reservoir evaluation and computer simulation techniques, including random reservoir modeling methods, numerical simulation of lacustrine and deltaic sedimentation processes, quantitative simulation of reservoir fractures, and comprehensive evaluation of oil and gas reservoirs. It also covers new experimental techniques such as reservoir geochemistry, inclusion analysis, laser microsampling, and nuclear magnetic resonance. "\"Study on River-Delta Reservoirs in the Daqing Oil Field\" (Sui Jun et al., 2000) systematically summarizes the achievements in reservoir research in the Daqing Oil Field from the 1960s to the 1990s. Their research went through four stages: from the 1960s to the early 1970s, it was the stage of establishing thin-layer comparison ； From the mid-1970s to the mid-1980s, in order to combine static and dynamic approaches, understanding of reservoir stages was pursued from a genetic perspective ； In the mid-to-late 1980s, to gain a comprehensive understanding of reservoir stages ； Since the 1990s, it has been a period for detailed geological studies of reservoirs under dense well network conditions. The book is divided into three parts. The first paper provides an overview of the reservoir research work in the Daqing Oilfield, focusing on the depositional environment of the large river-delta sediments in the Daqing Changyuan area, the delta patterns, and the genetic types of sand bodies. The second paper mainly introduces the methods and techniques for detailed description of reservoirs under dense well networks, including methods and examples for the detailed description of channel sands, interchannel sands, and delta front sands using sedimentological approaches, as well as discussions on the prediction of inter-well reservoir parameters through quantitative characterization methods such as geostatistics. The third article focuses on the application of reservoir research in oil field development. Over the past decade or so, the Reservoir Description and Prediction Research Institute at China University of Petroleum (Beijing), represented by Professors Zhang Yiwei and Xiong Qihua, has continued to explore and innovate through practical production activities, gradually developing a set of theories, techniques, and methods for reservoir description that are suitable for the geological conditions in China (Zhang Yiwei, 1992, 1997) ； Wu Shenghe et al., 1998). The series titled \"Description and Prediction of Typical Oil and Gas Reservoirs in China\" that they wrote and published includes twelve volumes such as \"Modern Reservoir Description Techniques\" (Wang Zhizhang et al., 1999). This series of works systematically elaborates on the dynamic and static characteristics, as well as the geological models, of different reservoir types at various exploration and development stages in China’s continental oil fields. It presents new theories, perspectives, and concepts regarding the rock physics phases of continental and complex reservoirs, phase-controlled reservoir comparison, phase-controlled reservoir prediction, the composition of apparent standard layers, and the composition of apparent reservoir spaces. Furthermore, it develops and improves the associated technologies and methods for seismic reservoir prediction, multi-parameter identification of oil, gas, and water layers, mechanisms and prediction of remaining oil, evaluation of fractured reservoirs, and characterization of carbonate reservoirs. They have done considerable work on the application of geostatistics in reservoir description, as well as in the random modeling of reservoirs (Zhang Yiwei et al., 1992) ； Wu Shenghe et al., 1998; Wang Zhizhang et al., 1999). Wu Shenghe et al. (1999) discussed the purpose and significance of reservoir modeling, the types of reservoir models, the reservoir modeling process and strategies, and described and compared various modeling methods. In his early research on reservoir description, Zhang Jinliang, building on the existing limited data from paleontological, paleomagnetic, and spore-pollen studies of certain wells, and by combining waveform similarity analysis with seismic stratigraphy, resolved for the first time the long-debated issue of stratigraphic classification in the study area (1993). In their research on residual oil distribution, they combined reservoir sedimentology methods with reservoir engineering methods in a creative and distinctive way (1995). Lin Renzi and others summarized the recent advances in the study of continental reservoir sedimentology in China (1995) through research in six areas: reservoir geochemistry, lake sedimentary facies and reservoir sand bodies, sequence stratigraphy, sandstone diagenetic evolution patterns, reservoir geological modeling, and regional reservoir evaluation. At present, reservoir stochastic modeling technology has gradually been adopted by a large number of experts in reservoir geology in China. Mu Longxin et al. (2000) summarized the characteristics and contents of detailed reservoir studies, their theoretical foundations and methods, the characterization of reservoir heterogeneity and quantitative modeling, the use of outcrops and modern sedimentology for analogous reservoir geological modeling, and the application of results obtained from outcrop studies. They summarized various qualitative and quantitative geological knowledge bases on the study of sedimentary reservoirs such as rivers and deltas, both domestically and internationally, as well as the basic theories and applications of reservoir prediction methods, particularly stochastic modeling. Lü Xiaoguang et al. (2000) studied the significance of stochastic reservoir modeling and the main stochastic modeling methods currently in use. Mu Longxin et al. (1994) discussed a new set of research approaches and methods for establishing a series of quantitative geological conceptual models of reservoirs, pointing out that the close integration of geological principles with modern stochastic modeling techniques, computer technology, and their practical applications represents the trend toward quantification in reservoir modeling. Li Yuanjue (1994) applied the principles of reservoir modeling based on the pseudo-3D conditional simulation method, proposing random variable distribution functions to control the geometry of stratified constant-volume gas reservoirs and the spatial continuity of the reservoir and permeability media, as well as an algorithm for maintaining the overall structure. By simulating the distribution of sedimentary facies in each sub-layer, a numerical model of the Ma Wu I reservoir in the central area of the gas fields in the Shaanxi-Gansu-Ningxia Basin was developed. The reserve assessment and reservoir numerical simulation results conducted using this numerical model show that it provides more reasonable estimates of reservoir parameters between wells; this method can automatically delineate relatively accurate boundaries of the viable reservoir, and it offers a fairly precise quantitative description of the strong heterogeneity in this reservoir. A \"conditional simulation method reservoir modeling software\" with a Chinese interface in the \"Windows\" environment was also developed on a microcomputer, which can serve as an effective tool for reservoir modeling of stratified constant-volume gas reservoirs. Nie Changmou (1996), in the reservoir description of the Huzhuangji oilfield, applied the sequential indicator modeling method from stochastic modeling techniques to study the permeability of Oil Group 7 in the Sha3 middle member of the H12 fault block. The results showed that the sequential indicator modeling method can reflect changes in reservoir parameters more effectively than the commonly used interpolation methods, and it is also capable of describing the uncertainty in the model resulting from a lack of data. Du Qizhen et al. (1997) discussed the current research status of stochastic reservoir modeling methods at home and abroad, as well as their application in reservoir description. Zhang Yonggui et al. (1997) discussed the methods and steps for using the simulated annealing combined optimization algorithm in the stochastic fine-scale modeling of reservoirs, including issues such as the construction of the objective function, the selection of initial states, sampling and perturbation mechanisms, the choice of annealing strategy parameters, and how to integrate various types of data. They pointed out that using the simulated annealing optimization algorithm in reservoir modeling has two advantages, namely the ease of integrating various types of data ； It can objectively reproduce the spatial correlation structure of reservoir variables. Its main drawback is the large amount of computation, necessitating parallel processing. Wen Jian et al. (1998) studied the stochastic model of the reservoirs in the upper part of the Guantao Formation in the Chengdao Oil Field. Zhong Baorong et al. (1998) discussed the computer implementation of stochastic reservoir modeling and conditional simulation. Zhang Yonggui et al. (1998) comprehensively discussed the significance, methods, and techniques of stochastic reservoir geology simulation, as well as its applications in oil and gas exploration and development. Zhao Yongsheng (1998) pointed out the limitations of using results from stochastic modeling. Chen Xia et al. (1998) discussed two approaches to using stochastic modeling of reservoir geological properties in reservoir research. Li Longyan et al. proposed a method for predicting interwell sand bodies using geostatistics. Xu Ningyu (1999) identified the challenges and issues faced by stochastic simulation technology in petroleum geology research, and finally discussed the economic value and significance of using this technology for the geological study of continental reservoirs and reservoir characterization. Yu Qitai (1999) proposed a method and its results for synthesizing numerical abstract geological models of the planar permeability distribution in riverine and deltaic phases, by using plane equal-permeability maps of 5 representative sub-layers each from the riverine and deltaic phases. Wu Xiaoguang et al. (1999) studied the types of reservoir geological models, research contents, modeling steps, and modeling methods.