# Natural Hydrocarbon Samples Classification by Topological Analysis Method
## 4 Discussion  
The results show that the proposed algorithm is working well on studied samples: it classifies samples in all metrics and the most effective one is based on Heat Kernel. Calculation time is rather low: on average all the mentioned steps and calculations take less than an hour on a regular personal computer, which allows for quick calculations. Robustness and stability combined with a possibility to work in automated mode allow for a quick division of the samples into groups for further analysis or to find a sample that can be counted as a close structure analog to propose some a priori properties of the sample (if specific study procedure or sample preparation is needed). Compared to conventional methods, this approach can win when quick estimation is needed and time-consuming flow calculations are not suitable, or when classical statistical distribution classification is not working well. That case might happen when studied samples have complex or combined distributions or in the case of highly anisotropic samples. In that case, samples with quite formal distributions can have completely different properties due to the statistically rare microstructure objects that define integral sample properties. Taking into account topology allows using such objects for correct classification. Another application is multiscale analysis, when samples have more than one distribution of microstructure objects such as pores or pore channels in one or different scales. In  
Figure 14: Comparison of 2 classes of C (**CH, CL**) samples with T samples (**T**) in Heat Kernel metric in \(H_{0}\)–\(H_{1}\) and \(H_{1}\)–\(H_{2}\) coordinates. Figure 15: Comparison of 2 classes of C (**CH, CL**) samples with T samples (**T**) in Sliced Wasserstein metric in \(H_{0}\)–\(H_{1}\) and \(H_{1}\)–\(H_{2}\) coordinates. that case, it is quite hard to differentiate one from another just using statistics or cross-plots because distributions can interfere and peaks can be smoothed and hard to separate. As it happens, the proposed method also shows the possibility to separate distributions (as it was shown for subsamples of sample C) or even to separate scales with the use of threshold or resolution variations and make a multiscale classification in one automated calculation run. This might be useful to find dominating scale, find separate analogs for different scales of the same sample, or to check the possibility of some secondary formation processes that occurred with samples and thus generated some new distribution. In addition, usage of the proposed method can somewhat elucidate the physical and chemical processes that happened during sample (porous media) formation and evolution because genesis processes are not completely random and microstructure is connected to the genesis process and thus that process can be partially reconstructed with the use of sample microstructure objects topology. This approach is widely used in lithology and facial geological analysis and the proposed method can be used as an instrument for such type of workflow. However, the exact correlation of topological properties with physical and chemical processes yet needs to be studied in further research with more samples with different genesis. This methodology can be applied to many other complex structures with different scales. Due to the specifics and volume of the data we have accumulated in our work, we have chosen samples of hydrocarbon reservoirs for verification since they have been well studied using other methods, and many results have been accumulated on them. Obtained results show four main methodology limitations:  
* Calculation limitation: current maximum image size processed by the proposed workflow is \(500\times 500\times 500\), but it can be improved further by software and hardware optimization;
* High-quality images are required for adequate and precise calculations;
* Samples studied in this paper have quite different geometrical structures.