## 4 Reservoir Case Application and Comprehensive Evaluation  
The rock samples for research were taken from Kumkol South Oil Field. The field is located in the city of Kizilorda in central Kazakhstan, which geologically belongs to the South Turgai Basin. The field has been in production since 1995, and 681 wells have been drilled. The rock slices shown in Figure 17 are from well 40\(\mu\) and well 16\(\mu\) at a depth of 1070-1080 m. The area exhibits certain heterogeneity, so there are some differences in the micro pore-throat structure of the reservoir. Pores and throats are shown in blue, while the other colors are the rock skeleton. Sample I has a pore radius primarily ranging from 75 \(\mu\)m to 125 \(\mu\)m and a throat radius mainly between 1 \(\mu\)m and 15 \(\mu\)m, which is classified as a large pore-small throat type, with an average porosity of 26%. Sample II has a pore radius predominantly distributed between 50 \(\mu\)m and 110 \(\mu\)m, with the throat radius mainly in the range of 1 \(\mu\)m to 10 \(\mu\)m, classified as a medium pore-small throat type, with an average porosity of 30%. Figure 16: Heterogeneous pore-throat network model based on geological maps. (**a**) Sedimentary facies geological map, different colors have different permeability; (**b**) generated heterogeneous microcosmic pore-throat network according to (**a**). Figure 17: Rock slice image of Kumkol South Oil Field. (**a**) Sample I with 26% Porosity; (**b**) Sample II with 30% Porosity. After processing and analyzing the images and combining them with the oilfield geological data, the pore radius, throat radius, coordination number, and particle diameter distribution data of the two samples are shown in Figure 18.  
According to the porosity and statistical microscopic parameters of Sample I and Sample II, the new algorithm is used to automatically generate a microscopic pore network model with pore 2000 \(\times\) 2000 pixels, as shown in Figure 19. It can be seen that the pore, throat, and particle size in Figure 19a is larger than that in Figure 19b, which better represents the real microscopic pore-throat characteristics and differences between rock Sample I and Sample II. Figure 19: The pore throat network model is generated based on the parameters of Sample I and Sample II. (**a**) Pore-throat model based on the porosity and microscopic parameters of Sample I; (**b**) pore-throat model based on the porosity and microscopic parameters of Sample II. Figure 18: Pore structure parameters of Kumkol South reservoir samples. It is necessary to quantitatively evaluate the similarity of the generated models. The characteristic parameters can be divided into two types: numerical data and distributed data. The numerical data includes porosity, while the distributed data includes pore radius, throat radius, particle diameter, and pore coordination number. For numerical and distributed data, the similarity degree of each partition is calculated using Formula (9) and Formula (10), respectively. The total similarity degree of the model is the area-weighted average of the similarity degree of each partition to evaluate the similarity degree of the generated model and the real model. For numerical data, porosity and the similarity of each partition are calculated as follows:  
\[S=\frac{|\Phi_{0}-\Phi_{1}|}{\Phi_{0}}\times 100 \tag{8}\]  
where, \(\Phi_{0}\) is the porosity of the real model, and \(\Phi_{1}\) is the porosity of the generated model. For distributed data, the similarity of each partition is calculated as follows:  
\[S=\sum_{i=1}^{n}\min\left(x_{i},y_{i}\right)\times 100 \tag{9}\]  
where \(n\) is the total number of distribution intervals of the real model, \(x_{i}\) is the distribution frequency of the real model in the \(i\)-th interval, and \(y_{i}\) is the distribution frequency of the generated model in the \(i\)-th interval.