## 3 Results and Discussion  
### Change in Pore Space Due to Rock Dissolution  
Before building a 3D model of the samples, images of their slices were analyzed for the presence of any features (Figures 5 and 6). Figure 5 shows the original and segmented images of the inlet, middle, and outlet slices of sample #2 before (Figure 5a) and after (Figure 5b) the injection of HCl solutions. As shown in Figure 5, sample #2 has three natural vertical fractures, which are indicated by red lines. As can be seen from Figure 5a, there is only one fracture present on each slice of the sample, which indicates their short length along the length of the sample. Figure 4: Simulations of liquid flow at different pressure drops for randomly selected sub-volumes of each sample before (**left**) and after (**right**) the injection of HCl solutions. Figure 5: Original and segmented images of the inlet (**upper**), middle (**middle**), and outlet (**lower**) slices of sample #2 before (**a**) and after (**b**) injection of HCl solution. Red and orange lines indicate natural fractures and vugs, respectively. Yellow and green lines indicate secondary and main wormholes, respectively. To remove noises from the original images obtained using X-ray microcomputed tomography, a median filter was used [36]. It can be seen from Figures 5 and 6 that there is a good visual match of the processed images with the original images of sample slices. Figure 5 also indicates that, unlike the other samples (Figure 6), sample #2 also has vugs of different sizes (Figure 5a), which are marked with orange lines. Note that the pore spaces on the original and segmented images are marked in black and blue, respectively. The presence of fractures and vugs in the inlet slice of sample #2 caused the formation of secondary wormholes (yellow lines, Figure 5b), along with a main wormhole (green line, Figure 5b) that broke through in the outlet slice of the sample (Figure 7). Due to the presence of natural fractures in sample #2, it will be considered separately from the other samples. Thus, samples #1, #3, and #4 will be considered as heterogeneous samples, and sample #2 will be considered as naturally fractured. The built 3D models of the samples before and after the injection of HCl solutions are shown in Figure 7. The injection of solutions was carried out from the bottom up. As shown in Figure 7, as a result of the dissolution of the carbonate rock, conical wormholes were formed, which led to a several-times increase in the permeability of the samples over the initial values (see Table 3). Samples #1 and #4 show face dissolution near the inlet slice at low injection rates. Pore volumes of HCl solutions of 2.4 to 4.4 were required for breakthrough (see Table 3). The largest increases in permeability (8.81 and 9.11 times) were observed in samples #2 and #4 at solution injection rates of 8 and 4 mL/min, respectively. As shown above, a total of 408 sub-volumes were extracted from all the considered cylindrical samples. To provide a more detailed visual evaluation of the effect of rock  
Figure 6: Original and segmented images of inlet slices of samples #1 (**a**), #3 (**b**), and #4 (**c**) before (**upper**) and after (**lower**) injection of HCl solution. Figure 7: Three-dimensional digital models of samples #1-#4 before and after injection of HCl solutions. dissolution on the pore structure, Figure 8 illustrates the pore space of three randomly selected sub-volumes extracted from each cylindrical sample before and after HCl solutions were injected. Note that Figure 8 shows only interconnected pores, which play a key role in fluid flow and the formation of permeability. As shown in Figure 8, noticeable changes in the pore space due to rock dissolution occurred in samples #2-#4, which led to relatively large increases in their permeability (see Table 3). From Figure 8, we also note that in the sub-volumes extracted from samples #2 and #3, a significant increase in the number of interconnected pores is observed as a result of the injection of HCl solutions.