As shown in Figure 1 , if there are n point sources (sinks) at the same time, and they are respectively located at points a₁, a₂, a₃, ..., a_n on the complex plane Z, then the complex potential at any point M on the plane, The principle of superposition can be used to get [9] [10] :

$W\left(Z\right)={\displaystyle \underset{j=1}{\overset{n}{\sum }}\left[\pm \frac{q_{hj}}{2\text{π}}\ln \left(Z-a_j\right)+C_j\right]}$ (1)

At this point, the potential function is:

$\varphi ={\displaystyle \underset{j=1}{\overset{n}{\sum }}{\varphi }_j=}{\displaystyle \underset{j=1}{\overset{n}{\sum }}\left[\pm \frac{q_j}{2\text{π}}\ln \left(r_j\right)+C_{j1}\right]}$ (2)

The flow function is:

$\psi ={\displaystyle \underset{j=1}{\overset{n}{\sum }}{\psi }_j=}{\displaystyle \underset{j=1}{\overset{n}{\sum }}\left[\pm \frac{q_j}{2\text{π}}\ln \left({\theta }_j\right)+C_{j2}\right]}$ (3)

The flow function calculation in Equations (1)-(3) above is applicable to homogeneous isotropic models. Considering the heterogeneity of actual oil reservoirs, the streamline distribution calculated by homogeneous isotropy should be corrected. Given that there is a monotonic relationship between water cut, a certain position x on the streamline, and water saturation, a relationship between water cut and a certain position x can be established. This article uses a complex potential function to solve the streamline distribution of the entire oil reservoir under the assumption of homogeneity; Further derivation of the oil-water two-phase flow theory yields the corresponding relationship between water cut and the position within the flow line. By substituting the water cut, the sequential positions of each well point in the flow line are obtained, thereby correcting the distribution of the flow line under homogeneous conditions [11] [12] .

Based on the one -dimensional water -removing model, ignore the capacity and gravity of the capacity, and use the reciprocating function to solve the streamline distribution of the entire oil under the hypothesis; further derives the theory of two-phase infiltration theory of oil and water The corresponding relationship of the inner location, through the substitution of the water cut, obtains the sequence of each well in the streamline. Thus correcting the streamline distribution under homogeneous conditions. The water cut value adopted here is the measured dynamic water cut during production. The simplification process is as follows: For a given time and injection volume, the Buckley-Leverett equation provides the saturation profile. This profile is highly nonlinear. At each point on the saturation profile, there is a corresponding saturation. Substituting this saturation into the diversion equation allows the calculation of the instantaneous water cut at that point. Therefore, the relationship between water cut and position is a composite function.

The specific research process is as follows:

The formula for moving the isosaturation surface is:

$x-x_0=\frac{{f^{\prime }}_w\left(S_w\right)}{\varphi A}{\displaystyle {\int }_0^{t}Qdt}$ (4)

Establish the relationship between a certain position x in the streamline and the water cut at that position. You can calculate ${f^{\prime }}_w$ by giving x in Equation (4) [13] [14] , and then find the corresponding $S_{wf}$ from the diversion function and its derivative function graph. Since ${f^{\prime }}_w$ has two monotone intervals, $S_{wf}$ has a double solution. In applied mathematics, it is unique to use the starting point of the monotone function as the tangent line. For the monotonically increasing function $f_w$, use S_wi as the $f_w$ tangent line, and the tangent point is located on the right side of the peak value of the derivative curve, To determine the unique solution of $S_{wf}$, the corresponding relationship between water cut $f_w$ and a certain position x on the streamline can be obtained through the $f_w$ curve, where $f_w$ is monotonic with respect to x; The area where the current edge has not reached, $f_w$ = 0 ( Figure 2 , Figure 3 ).

Based on complex function and oil-water two-phase seepage theory, a new streamline model is established, and a new method of seepage channel identification is proposed. That is, by drawing a streamline diagram, the number of flow pipes in a unit area is counted. Taking the number of streamlines per unit area as the variable and using the quartile system for classification, this method is stable and practical. The seepage channel levels are divided according to the cumulative frequency distribution of 25% and 75%.

Through the new method of seepage channel identification, the dominant channels are divided into three levels: major dominant channels, secondary dominant channels, and non-dominant channels. Among them, there are 10 major dominant channels in the K Oilfield, 14 secondary dominant channels, and 7 non-dominant channels (as shown in Table 1 and Figure 4 ).

Explanation: Blue represents the water injection rate of the water injection well and the liquid production rate of the oil well. When substituted into the complex function, the water injection rate is a negative value, and the liquid production rate is a positive value.

According to the classification results of dominant channels, different governance methods are proposed for the three levels of dominant channels [15] . For the non-dominant passage area, the main well areas include the X14 and X26 wells in the W7 well area, the X15 well in the W9 well area, the X17 and X23 wells in the W11 well area, the X14 well in the W19 well area, and the X23 well in the W16 well area. The remaining oil is relatively rich. First, the flow of remaining oil is increased by oil well transfer, and second, the oil well is used to increase the liquid production and reduce the water cut of the oil well; for the main dominant passage area, The main well areas include the X1 and X8 wells in the W7 well area, the X2, X3 and X8 wells in the W9 well area, the X4 and X5 wells in the W11 well area, the X13 well in the W19 well area, the X15 and X20 wells in the W21 well area, and the X10 well in the W16 well area. The remaining oil is relatively small. Reduce the water injection rate of water injection wells, increase the water injection rate of adjacent water injection wells, and change the direction of the original streamline; for the secondary dominant seepage channel, The main well areas include the X2, X13 and X27 wells in the W7 well area, the X4, X10 and X14 wells in the W9 well area, the X24 well in the W18 well area, the X20 and X26 wells in the W19 well area, the X14 and X22 wells in the W21 well area, and the X15, X17 and X22 wells in the W16 well area. Increase the liquid production rate in the area with low streamline density, increase the streamline in the remaining oil-enriched area, Redistribute the streamlines in the well area.