# Investigation on Interference Test for Wells Connected by a Large Fracture
## 5 Discussion  
The assumption that two wells are connected by a large fracture is usually too strong. Actually, they may be connected by the channel formed through several groups of intersected fractures. However, this does not influence the analysis process and results in this study. When one well connects with multiwells through several large fractures, it has little impact on the computation result of the pressure conductivity coefficient because the equation of the pressure conductivity coefficient derived by the extremum analysis is independent of the flow rate.  
To further understand its characteristics, the interference test of WsCLF, is compared with cases of homogeneous and double porosity medium reservoirs. The equation of pressure conductivity coefficient for homogeneous reservoirs is as follows [40]  
\[\eta=\frac{x^{2}t_{p}}{4t_{m}(t_{m}-t_{p})\ln\frac{t_{m}}{t_{m}-t_{p}}} \tag{42}\]  
From Equations (35) and (40), it can be seen that the pressure conductivity coefficient for WsCLF differs from that for homogeneous reservoirs by a factor 2. The distance used in Equation (35) is the distance along the fracture rather than the straight line distance. Although, the former is always longer than the latter, they are on the same order of magnitude. Actually, a large fracture and homogeneous reservoirs are respectively two extreme connection forms of two wells. This indicates that the pressure conductivity coefficient computed by the equation for homogeneous reservoirs is on the same order of magnitude of the actual value if the fundamental information is precise. It should be pointed out that according to the definition of the pressure conductivity coefficient, the permeability would be very different because of the huge diversity between their porosity and total compressibility.  
Different connection forms and boundary conditions also reflect their characters in the interference test type-curve. For two wells connected by a homogeneous reservoir, the dimensionless pressure derivative increases and then approaches a 0.5 horizontal line [38]. Therefore, the shapes of their dimensionless pressure derivative curves are highly different. The pressure derivative would appear between the 0.5 horizontal lines and the straight line with a slope of 0.5, when the difference between the conductivity of the large fracture and the matrix is not large enough to ignore the influence of the matrix. Considering the crossflow of the reservoir matrix to the large fracture, the pressure transient can be obtained through Laplace transformation and the Stehfest numerical inversion method. The details can be seen in the Appendix A. The interference test type-curve of WsCLF with a crossflow of reservoir matrix is shown in Figure 5. It can be seen that the pressure and pressure derivative curves approach parallel straight lines with a slope of 0.25. It can be found that \(F_{D}\) and \(C_{f}\) have a similar influence on the curves, and they cannot be distinguished. This can also be concluded from Equation (A19).  
The intensity of the fractures can affect the shape of the pressure derivative curves. The reservoir approximates a double porosity medium when there are intensive fractures, and the pressure derivative curve has a cavity compared with that of the homogeneous reservoir [41]. The storativity ratio \(\omega\) is related to the intensity of fractures and can be evaluated by the pressure derivative [38].  
Therefore, the appearance of the pressure and pressure derivative curves in the double logarithmic coordinate can be used to diagnose the form of connections. In addition, the fracture intensity can be qualitatively judged based on the deviation of the pressure derivative from that of a homogeneous reservoir and WsCLF.