# Modeling of Characteristics of Complex Microstructure and Heterogeneity at the Core Scale
## 3 Results  
The experimental data of five carbonate rock samples reported by [PERSON] [62] (2020) are considered to illustrate the proposed model. The samples are from the Dengying Formation dolomite in the Sichuan Basin and the Ordovician limestone in the Tarim Basin, Xinjiang. According to thin section and scanning electron microscopy results and physics data for five rock samples obtained by [PERSON] [62], intergranular pores, intercrystalline pores, dissolved pores, and dissolved cracks are the main pore types. As detailed in Figures 5-8, the thin section and scanning electron microscopy results for the core sample reveal different kinds of pores [62]. Figure 5: Thin section of limestone sample 24: dissolution pores and dissolution fissures. Figure 6: Thin section of limestone sample 25: dissolution fissures and dissolution pores. [PERSON] and [PERSON] [63] (1970) classified carbonate pores into 15 basic types, providing detailed geological characteristics of almost all types of porosity in sedimentary carbonates. The flat and thin pores deform easily, so the seismic velocity of rocks containing such holes is low. In contrast, circular pores and holes are difficult to deform, so the seismic velocities are correspondingly high, even when the porosity may be high. Experiments on 52 carbonate rock samples have shown that the stiffness of samples containing large pores is high, while the stiffness of samples containing micropores or cracks is relatively low [64]. The porosity-velocity relationship varies for rocks containing different pore types, such as rocks with micropores, rocks with moldic pores, rocks with interparticle pores, rocks with intraparticle porosity, and densely cemented rocks [65]. In this study, to simulate the easily deformable, closed cracks and the less deformable large pores in the assumptions of the squirt flow model, circular pores are selected to represent stiff pores, and long and narrow elliptical pores are selected to represent compliant microcracks. The sizes, numbers, and number ratios of the two types of pores and the aspect ratios of the elliptical pores of the model were obtained from the description of the cores and the pore morphology of several thin sections in the literature. The model of sample 26 is shown in Figure 9, based on the pore morphology shown in the description and thin sections of the core and the heterogeneity of the matrix. The green circles in Figure 9 represent saturated water pores and microfractures, while the blue stripes in the matrix are tilted 45 degrees to the left, simulating the many heterogeneous black, left-leaning striped bodies in the matrix in Figure 7. The length of the stripes is about five times the size of the circles, reflecting the size ratio of the heterogeneous body to the pores in Figure 7. The specific parameter settings are as follows: The radius of the circular pore is 0.4 mm, the long axis length of the crack is 0.3 mm, the aspect ratio is 0.01, the autocorrelation lengths are a = 2 mm and b = 0.5 mm, the rounding coefficient n = 1, and the angle \(\theta\) = 135\({}^{\circ}\). Figure 8: Thin section and scanning electron microscopy image of dolomite sample 132: intercrystalline pores. Figure 7: Thin section of limestone sample 26: dissolution fissures and dissolution pores. The petrophysical parameters of the cores used in this study were obtained from ultrasonic tests performed on limestone cores and dolomite cores, as shown in Table 1. To verify the accuracy and practicality of the modified model in this study, we analysed and discussed the model parameters using the bulk and shear moduli measured for the dry carbonate core samples and information from thin section characterisation. Finally, the results were compared with the velocities obtained from ultrasonic saturated carbonate rock core experiments and predictions calculated by other models.