## 3 Results and Discussion
### Permeability Damage Mechanisms  
Permeability damage was high in all cases regardless of the pH value. Investigation of the causes revealed the following conclusions:  
Figure 7: Differential pressure between the core’s inlet and outlet during LSW injection and nanofluid injection steps. 1. Although the nanofluid was stable in the low-pH case, some sedimentation of nanoparticles occurred, but not as much as in the other experiments in which sedimentation was high. In all experiments, sedimentation contributed to the retention of nanoparticles inside the cores. 2. While the nanoparticles had an average diameter of 50 nm in powder form, they tended to form larger clusters after adding them to the nanofluid. The cluster size ranged between 100 and 1000 nm. The average cluster size of the nanoparticles at a pH of 4.5 was approximately 250 nm, and at a pH of 2.8, the average cluster size was 290 nm. The pH of the nanofluid during ball milling and beads to nanofluid weight ratio are two factors that greatly affected the average cluster size. For example, a pH of 6.5 or a beads to nanofluid weight ratio of 1 resulted in an average cluster size of around 500 nm. The smallest size was 250 \(\pm\) 10 nm and was consistently achieved using the ball milling method. Adding 30 min of an ultrasonic bath after ball milling did not lower the cluster size. The 250 nm size was not sufficiently small to not cause permeability damage. The pore size distribution of a limestone core similar to the cores used in the experiments and a size distribution of the nanoparticles were used to obtain an approximate difference between the pore size and the nanoparticles' size. As depicted in Figure 8, approximately 20% of the pores were too small for the smallest nanoparticles, and another 5% of the pores were too small for 25% of the nanoparticles. This case excluded the agglomeration occurring inside the core during the injection process, which rendered the retention through straining more impactful on permeability. 3. The roughness of the pore surface considerably influences the retention of nanoparticles inside the pores. The nanoparticles tend to accumulate in the dents of the rough surface because of the Brownian motion or repulsion between them. However, the repulsion between the nanoparticles and pore surface is only effective at a short distance, as displayed in Figure 6b, and that distance is shorter than the depth of the rough surface's dents. The surface roughness was investigated using SEM images, and the resulting images of the pores' surfaces are displayed in Figure 9. The images revealed that the surface of the pores was rough in general, but it had some smooth surfaces. Some pore channels were rough on one side and smooth on the other side. Figure 8: Size distributions of limestone pores and \(\alpha\)-Al\({}_{2}\)O\({}_{3}\) nanoparticles in the nanofluid at a pH value of 4.5. The pores' surface was mostly covered with irregular bumps and dents, which hindered the flow of nanoparticles and resulted in higher retention and permeability damage to the core. This phenomenon was confirmed by obtaining SEM pictures and EDX analysis of a thin section from the inlet area of the IDLS_2 core after the core flooding experiment. Montmorillonite, which constituted around 3% of the core composition, contains aluminum among its constituents. However, the EDX analysis of the material on the pore surface showed a large concentration of aluminum higher than that in montmorillonite, which confirmed that it was Al\({}_{2}\)O\({}_{3}\) nanoparticles, the only other source of aluminum inside the core. Several points were analyzed, and the aluminum concentration ranged between 70 and 90 wt% in each of them. Figure 10a displays the EDX analysis that confirmed the nanoparticles' retention in Figure 10b, and Figure 10c shows another example of retention within the rough dents of the limestone surface. In addition to sedimentation, the forms of the physical entrapment of nanoparticles are a major cause of permeability damage.