## 5 Establishment of 3D Geological Model
### Reservoir Parameter Model  
The culmination of geological reservoir modeling is the creation of a physical property parameter model that encapsulates the characteristics of the reservoir, including but not limited to porosity, permeability, and saturation. The spatial distribution of lithofacies within the reservoir is a pivotal attribute, fundamentally influencing the distribution and flow dynamics of fluids within the reservoir. Building upon the previously established lithofacies model, stochastic modeling is executed utilizing phase-controlled attribute parameters. The stochastic simulation of the lake basin structure in the southern Heshui region predominantly employs the sequential Gaussian stochastic simulation method [46]. This method, grounded in Gaussian probability theory and sequential simulation algorithms, generates the spatial distribution of continuous variables. The simulation proceeds pixel by pixel, constructing a local cumulative conditional probability function (ccdf) by taking the simulated data into account. Such simulation data generation not only includes the original conditional data but also takes into account the existing simulation data. This method is widely used in practice, and the input parameters mainly include statistical parameters of the model. Figure 11: Probability-surface-constrained rock’s relative ratio profile. variables (mean value, standard deviation), variable function parameters (bullion effect, variable range, etc. ), and conditional data. Firstly, experimental fitting of the variation function is conducted using data from single-well analyses, which is then followed by random simulation of the reservoir's physical property parameters. The 3D spatial model of the reservoir's physical properties in the study area is finally established by using permeability-phase-controlled Gaussian stochastic simulation, sequential Gaussian stochastic simulation, and porosity collaborative stochastic simulation. Sequential Gaussian simulation is a kind of algorithm for continuous variables, which is mature and widely used. The simulation results can reflect the continuous changes in physical parameters in the reservoir and are consistent with the sedimentary microfacies model. By adjusting the filtering parameters, the difference functions of each material property at various levels and phases, along with the results of Gaussian transformation, are recorded. The reservoir in the study area is characterized by typically low porosity and permeability. Based on the well-point discretization data as the basic constraint conditions, and the lithofacies model constrained by the probability plane as the trend constraint control, the sequential Gaussian simulation method is used to build a 3D geological reservoir attribute model (Figure 12). Comparative results demonstrate that the lithofacies phase-controlled constraint modeling method significantly enhances the modeling accuracy. According to the statistical analysis of reservoir attributes, the porosity of sandstone shale oil reservoirs in the Chang 7 member ranges from 1.27% to 15.04%, with an average of 8.47%. The normal distribution features are obvious, and the majority of ultra-low pores account for more than 88%. The permeability was mainly distributed in the range of 0.001-1 mD, with an average of 0.74 mD, and the correlation between porosity and permeability in the same layer was good. Among them, the porosity of the Chang 7 member was 70% below 8 m\({}^{3}\), and the porosity of 6-12 m\({}^{3}\) was 30%. It can be considered that the Chang 7\({}_{1}\)\({}^{1}\), Chang 7\({}_{1}\)\({}^{2}\), Chang 7\({}_{2}\)\({}^{1}\), Chang 7\({}_{2}\)\({}^{2}\), and Chang 7\({}_{3}\) shale reservoirs in the study area are extremely low-porosity reservoirs. According to the observation of the numerical porosity model (Figure 12a), the porosity is mainly distributed from northeast to southwest along the extension direction of the sandstone in the lithofacies model.