# The Principle and Downhole Testing of Water Injection Exploration in Depleted Reservoirs
## 1 Introduction
### Analysis and Discussion of Water Injection Results
#### 3.4.2 The Permeability Patterns at Different Distances from the Old Goaf  
When the injection point is at different distances from the old goaf, not only does the maximum injection pressure vary, but the permeability coefficient also shows differences. According to the injection test data, the permeability coefficient of the rock mass can be calculated using Formula (5) provided in the \"Technical Code for Drilling Water Pressure Test of Water Conservancy and Hydropower Engineering\" (NB/T35113-2018) issued by the Ministry of Water Resources [25].  
\[K=\frac{Q}{2\pi HL}\ln\frac{L}{r_{0}} \tag{5}\]  
In the formula, \(K\) represents the permeability coefficient of the rock mass, expressed in m/d; \(Q\) denotes the injection flow rate, measured in m\({}^{3}\)/d; \(H\) stands for the head of the test water (which can be converted from water pressure), expressed in meters; \(L\) represents the length of the test section, measured in meters; and \(r_{0}\) denotes the radius of the borehole, measured in meters.  
Based on the calculated permeability coefficients, the flow rate and pressure curves for injections at different locations of the three boreholes were plotted separately (refer to Figures 8-10).  
Figure 8: Box plot of permeability coefficient at different positions of borehole 151.  
Figure 9: Box plot of permeability coefficient at different positions of borehole 153.  
From Figure 8, it can be observed that the permeability coefficient exhibits a 2-3 times increase as the distance changes from the section 24-20 m from the old goat to the section 20-16 m from the old goat, and further to the section 16-12 m from the old goat. The permeability coefficient overall tends to be greater in the section 12-8 m from the old goat compared to the section 16-12 m from the old goat. The permeability coefficient of borehole 151 demonstrates that the closer it is to the old goat, the higher the permeability coefficient.  
From Figure 9, it can be observed that the permeability coefficient significantly increases from the section 38-34 m from the old goat to the section 34-30 m from the old goat. However, in the sections 30-26 m and 26-22 m from the old goat, the permeability coefficient decreases before rising again. In the section 22-18 m from the old goat, the permeability coefficient experiences a significant increase by orders of magnitude, reaching below 0.01 m/d. It is seen that, similar to the abnormal water pressure, in the section 30-22 m from the old goat, the injection of grouting after the injection from 34 to 30 m caused the grout to spread to the section 30-22 m from the old goat, resulting in an abnormal permeability coefficient for injection, but, overall, borehole 153 also exhibits the characteristic that the closer it is to the old goat, the higher the permeability coefficient.  
From Figure 10, it can be seen that the permeability coefficient of borehole 156 does not undergo significant numerical changes, but overall, it also demonstrates the characteristic that the closer it is to borehole 155, the higher the permeability coefficient.