*2.1. Sample Preparation and Experimental Apparatus*

In this study, fluvial facies sandstone outcrop from Guantao formation was used in this study. We can clearly see that the sample has developed plate-like cross-beds, which are at an angle of 30 degrees with the ground (Figure 1). We define the bedding direction as the x direction, the y direction orthogonal to x, and the z direction perpendicular to the xy plane. The water permeability in the three directions of x, y, and z is 37.87 mD, 20.83 mD and 18.94 mD, respectively, and the porosity is 15.98%. The testing oil is a mixture of crude oil and diesel with a viscosity of 10 mPa·s at 20 ◦C. The salinity and viscosity of the testing water are 4000 mg/L and 1.0 mPa·s, respectively. The testing fluids are based on the actual reservoir oil and water properties in the Shengli Oilfield.

**Figure 1.** Cores used in our experiment (**a**–**e**) are the 4 side and top photos of the cubic core, (**f**) is the full-view photo of the cubic core.

The experimental apparatus consists of five different parts: injection control system, temperature and pressure control system, core holding system, outlet back pressure control system, and data acquisition system. The schematic representation of the experimental apparatus is shown in Figure 2.

(<sup>1</sup> —anisotropic cubic core holder; <sup>2</sup> —pressure sensor; <sup>3</sup> —six-way value; <sup>4</sup> - oil– water separator; <sup>5</sup> —Monitoring camera system; <sup>6</sup> —value; <sup>7</sup> —output liquid collector; <sup>8</sup> —backpressure regulator (BPR); <sup>9</sup> —confining pressure system; <sup>ŀ</sup>—water flooding system; ᬏ—oil flooding system; ᬐ—filter; ᬑ—control system).

**Figure 2.** Schematic representation of the experimental apparatus of the anisotropic relative permeability measurement.
