**1. Introduction**

The development of oil and gas reservoirs generally goes through three stages. The first stage is the increased production period. The second is the constant production stage, and the third is characterized by declining production. As the reservoir enters its production decline period, there are several EOR methods available to help the field achieve maximum recovery [1,2]. Increasing the waterflooding PVs is an economical and straightforward technique, considering the economic cost. In the process of actual reservoir water flooding development, which is affected by reservoir heterogeneity, water is injected into the planes and longitudinal high-permeability bands, the water–oil ratio rises sharply, and the waterflooding PVs can reach hundreds or thousands of times in the mainline or near the well area [3,4]. The uneven distribution of waterflooding PVs in the reservoir leads to the invalid circulation of injected water. It has been found that the method of flow diagnosis that has been applied to profile control and water plugging measures, by defining the relationship of the connectivity volume, flux, distribution factors of injection flow, production wells in the reservoir, and Lorentz coefficient, can semi-quantitatively judge the waterflooding PVs in the reservoir and provide well reference for profile control and water plugging [5–9]. The traditional relative permeability test is usually performed

**Citation:** Qi, G.; Zhao, J.; He, H.; Sun, E.; Yuan, X.; Wang, S. A New Relative Permeability Characterization Method Considering High Waterflooding Pore Volume. *Energies* **2022**, *15*, 3868. https://doi.org/ 10.3390/en15113868

Academic Editors: Riyaz Kharrat and Mofazzal Hossain

Received: 31 March 2022 Accepted: 19 May 2022 Published: 24 May 2022

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under the conditions of 30–50 PV displacement multiple and 50–60% oil displacement efficiency. Laboratory tests in the Shengli oilfield show that the oil recovery efficiency can reach 70–80% by increasing waterflooding PVs and displacement pressure gradient. The oil recovery efficiency of the Daqing oilfield is nearly 100% when the waterflooding PVs are 26,331 PVs [10,11]. After long-term waterflooding, the pore throat structure of loose sandstone reservoirs will change [12]. It is suggested that the formation is formed in large water channels. In the stage of high water cut and high recovery of China's Bohai SZ oilfield, the coring data of new drilling wells shows that the microscopic pore throat characteristics of the reservoir went through significant changes after long-term waterflooding. The south China sea offshore oil field laboratory experimental study shows that the oil displacement efficiency can be increased from 60.67% in the case of waterflooding (100 PVs) to 71.27% in the case of extra high waterflooding (2000 PVs), and the residual oil saturation can be reduced from 29.56% to 21.72%, indicating that high water-cut oil fields still have grea<sup>t</sup> exploitation potential [13–15]. Similar characteristics are also found in the Daqing Lasaxing oilfield and some foreign oilfields in the North Sea. The remaining oil saturation of the strongly water washed oil layer is lower than the laboratory experiment results [16–18]. A large number of field practice and laboratory physical simulation experiments prove that increasing the waterflooding PVs can effectively improve the oilfield development effect.

However, there are several understandings of the mechanism of high waterflooding PVs in EOR. First, long-term waterflooding can cause a change in the reservoir; the essence of high waterflooding PVs is the long-term reconstruction of underground reservoir conditions. If the sandstone is poorly cemented, long-term waterflooding will cause the migration of particles and clay swelling, even sanding, which can cause physical parameters such as reservoir porosity, permeability, and reservoir microscopic pore structure changes. This affects fluid percolation characteristics in the reservoir [19–24]. Second, in the whole process of waterflooding development, the residual oil saturation is not a constant, and the oil displacement efficiency measured in the laboratory at the early stage of development does not represent the ultimate recovery efficiency. High waterflooding PVs will reduce the critical capillary number of the reservoir, thus improving the oil displacement efficiency [17,25]. Third, increasing waterflooding PVs can improve the wettability of reservoir and oil recovery [26]. Either of the above mechanisms or the combination of two or more mechanisms will result in significant changes in the relative permeability curves that describe the characteristics of oil–water two-phase seepage.

Fang Yue et al. [27] conducted water–oil displacement experiments with high waterflooding PVs. They found that under high waterflooding PVs, oil-phase permeability decreased slowly while water-phase permeability increased significantly, and the waterflooding characteristic curve showed an upward "inflection point". After the "inflection point", water consumption increased sharply. The higher the permeability, the higher the displacement efficiency, and increasing injection speed can improve oil displacement efficiency. Hong-min Yu [28] found that high water waterflooding PVs relative permeability curve has the characteristic of semi-logarithmic piecewise linear bounded by the turning point of water cut, the relative permeability of oil and water does not change before the turning point, the residual oil saturation decreases after the turning point, and the relative permeability of oil and water extends to the limit. Zhang Wei et al. [13] found that the isotonic point of the relative permeability curve shifts to the right after the high waterflooding PVs, indicating that the water wettability is enhanced, which is beneficial to water flooding. Microscopic remaining oil flow patterns are classified and studied by Chun lei Yu [29] through the micro-glass etching model experiment and computer image recognition processing technology. The results show that the remaining oil flow patterns can be divided into clusters of flow, porous flow, columnar, membrane, and flows in dropwise flow. In five classes considering oil-water and the contact relation between the pore throat, cluster flow accounts for the largest proportion. With the increase in water saturation, the cluster flow gradually transformed into porous flow, columnar flow, membrane flow, and droplet flow. At the same time, the reason for the nonlinear relative permeability curve and the mobility

law of oil and water in the ultra-high water cut period is explained from the microscopic point of view.

From the above research results, it can be clearly seen that the physical simulation of waterflooding with high PVs is relatively mature. However, different types of reservoirs with different properties also have significant differences in their production systems [30–35]. Therefore, the performance of oil displacement efficiency and relative permeability is also quite different for the high waterflooding PVs treatment. Moreover, the application of the understanding of high waterflooding PVs' relative permeability in numerical simulation is still unclear. In other words, there are bottlenecks when the in-house experimental results are applied to the field.

The relative permeability in the traditional numerical simulation model can not change automatically according to the actual production strategy and reservoir properties changes. Therefore, we took the natural core of Q oilfield in the Bohai Sea as the research object and carried out high waterflooding PVs experiments. According to the experimental results, the relationship between relative permeability and water saturation (Sw) and waterflooding PVs is established. The knowledge is coupled to the numerical simulator. The effectiveness of the simulator is verified by the latest logging interpretation results of the passing well and the fitting of the water cut in the well area.
