## 1 Introduction  
In recent years, given the newly added geological reserves in China, low-permeability and very-low-permeability geological reserves have increased yearly [1, 2]. Based on previous statistical results, the porosity of low-permeability reservoirs is less than 15% and their permeability is less than 20 mD [3]. Many fine pore throat structures exist in low-permeability reservoirs [4]. Owing to the existence of microcapillary forces, the solid-liquid interface and the electrochemistry effect, a start-up pressure difference exists in low-permeability reservoirs [5, 6]. Moreover, the clay in the formation is easy to expand [7, 8], which leads to the high pressure of the water injection well. So, it directly affects the efficiency of water injection, increases the burden of the water injection system and causes high energy consumption. In addition, a casing rupture will occur when the water injection system is under a long-term high-pressure condition, which would result in a reduction in sweep efficiency and oil recovery efficiency [9]. Therefore, the development of high-efficiency pressure-reducing and injection-enhancing agents is key to the exploitation of low-permeability reservoirs. The pressure-decreasing and augmented injection in low-permeability reservoirs have been extensively studied. At present, the technology of pressure-decreasing and augmented injection has two main methods: reservoir modification and surface modification [10]. Reservoir reconstruction technology is used to expand the effective diameter of rock pores by acidizing plugging removal and hydraulic fracturing [11; 12] to reduce injection resistance to achieve the result of reduced pressure and increased injection [13; 14; 15]. In the process of hydraulic fracturing and acidification, it is easy for the reservoir to be injured by the intrusion of external fluids, resulting in a serious decline in the exploitation degree [16; 17; 18]. Therefore, how to reduce the damage to the reservoir and the equipment during the use of reservoir reconstruction technology is also a main problem that needs to be solved urgently. Surface modification technology is utilized to change the rock surface properties of pores [19] and prevent clay from swelling by injecting modifiers into rock pores [20], so as to achieve the effect of reducing pressure and increasing injection [21; 22; 23; 24]. Hydrophobically modified nano-SiO\({}_{2}\), as a modifier to reduce pressure and increase injection, is a newly developing technology. The hydrophobic nano-SiO\({}_{2}\) dispersion is injected into the formation to achieve the pressure-decreasing and augmented injection of the reservoir. The surface of the modified nano-SiO\({}_{2}\) particles has unsaturated bonds and strong adsorption capacity. After entering the formation, the nano-SiO\({}_{2}\) adsorbs onto the surface of the rock pores, replacing the existing hydration film and forming a new adsorption layer, making the rock pores hydrophobic. It reduces the flow resistance and the contact between the water and the rock pores, achieving the effect of the pressure-decreasing and augmented injection [25; 26]. [PERSON] [27] synthesized an environmentally responsive modified nano-SiO\({}_{2}\), which was covalently modified by organic compounds containing hydrophobic groups and double bonds. The chemical adsorption method was used to cover a layer of hydrophilic organic matter on the surface of the modified nano-SiO\({}_{2}\) to ensure its good dispersibility in water. Owing to the change in the environment (temperature, pH and salinity), the nano-SiO\({}_{2}\) would be released from the dispersion and adsorbed onto the rock pores when the nano-SiO\({}_{2}\) enters the injection well from the normal environment, thereby achieving the effect of reduced pressure and increased injection. [PERSON] [28] used dimethyldichlorosilane to modify nano-SiO\({}_{2}\).