# Research Status of and Trends in 3D Geological Property Modeling Methods: A Review
## 4 Discussions  
Considering the model grid generation aspect, orthogonal hexahedral grids are still popular for three reasons: first, the number of connected surfaces of a hexahedral grid is smaller than that of a polyhedral or PEBI grid, and thus fewer fluid simulation equations need to be solved, implying an increase in computational efficiency; second, the orthogonality of hexahedra ensures the stability of the numerical simulation results; third, most commercial fluid simulation software still supports only hexahedral grids. At present, there are few studies on other grids besides pillar grids and PEBI grids in terms of generation methods.  
Most geological phenomena are nonstationary, while the current geostatistics methods always hold the stational assumptions. In two-point statistics, a second-order stationarity or intrinsic assumption is required; that is, the covariance or variogram is independent of the specific location in the space but is related to the vector distance. Similarly, in multiplepoint geostatistics, the training image is required to be stationary; that is, the geometric configuration and shape of the object in the training image are basically unchanged in the whole area without significant trend or local variability.  
Every approach to multiple-point geostatistics methods has certain limitations. The core idea of both the probability-based methods and the iterative multiple-point geostatistical methods is to create a new model describing the subsurface spatial structure from the original spatial model (training image). The two types of methods have obvious drawbacks. First, to successfully implement the statistical model with valid assumptions, some data that do not meet the requirements must be artificially discarded, but these data may be very important. In addition, some parameters must be set, and the implementation of the algorithm and the correctness of the model depend on the setting of the parameters. As mentioned above, certain parameters, such as convergence criteria and iteration-stopping positions, defy objective definition. In the pattern-based methods, simpat is computationally complex and has a rigid pattern comparison that lacks cognition, while filtersim still relies on parameters for pattern classification despite the method's improvement over the drawbacks of simpat. Distance-based multiple-point statistics is a new method proposed in recent years. This method uses the principle of pattern recognition in computer image processing to classify patterns based on distance but has not yet been studied in depth.  
Multiple-point geostatistics still face multiscale problems. The simulation results of multiple-point geostatistics have been less satisfactory for large-scale spatial patterns. To simulate spatial continuity on a large scale, the multiple-grid method is widely used; the main idea of this method is to perform multiple simulations by using sparse and gradually expanding data templates. However, this method is only an optimization of the results with no theoretical support. In addition, the method's simulation results may contain unassigned grid points.  
Deep-learning methods are new trends in 3D geological modeling. Among them, the reservoir facies modeling method based on the GAN network has the ability to build a continuous spatial structure and non-stationary geological model. The relevant research is in the stage of rapid development, and there are still many problems worthy of study: first, the effect of current method in the well point hard data constraint is unstable, so the model training method and hard data constraint method need to be optimized; the second is the lack of application in oilfield actual data; third, the method of generating the GAN network requires detailed information. The relevant reports of foreign commercial modeling software institutions lack relevant details, which is not conducive to the application and related software development in China; thus, independent exploration is needed.