Horizontal well refracturing is one of the major technologies in unconventional oil and gas development, which can achieve greater utilization of single well reserves and further enhance recovery (Brown and Economides, 1992; Dou and Zhou, 2003). Due to the failure of fracture initiation, sand filling failure and other problems in the production of primary fractured horizontal Wells, fractures may lose their conductivity. Therefore, refracturing is required to restore or improve the production capacity of horizontal wells (Giger, 1985; Vincent, 2011; Ren et al., 2015; Wan et al., 2019). At present, a large number of wells in the early development stage have been refractured (Siebrits et al., 2000; French et al., 2014; Fu et al., 2017; Athavale et al., 2019; Garza et al., 2019), and considerable results have been achieved. The research on related technology types and operation schemes have gradually attracted the attention of scholars and experts around the wold. A large number of studies have been carried out at home and abroad on repeated fracturing well selection methods, production increase potential, and production increase measures (Yang et al., 2016; Aniemena and Kohshour, 2017; Xia et al., 2017; Wang, 2018; Ibáñez et al., 2020; Kong et al., 2020; Lu et al., 2020; Kong et al., 2021; Zhang and Sun, 2021), However, relatively few studies have been conducted on the refracturing timing and the modification method of refracturing. At the same time, many scholars have carried out research on reservoir capacity characterization and dynamic prediction (Lee et al., 2003; Williams et al., 2004; Blasingame and Rushing, 2005; Cheng et al., 2009), There are mainly four methods:type-curve analysis,flow-regime analysis, numerical simulation and empir-ical methods. Despite the diversity of models, they always require knowledge of the reservoir that may not be known, originally, such as the shape of the drainage volume.Moghanloo and Yuan (Moghanloo et al., 2015) put forward the concept of dynamic drainage volume (DDV) for the first time. Although the model is not suitable for any reservoir, such as a fractured reservoir, but the data required by the model is easy to obtain. DDV refers to a continuously expanding oil drainage volume formed when the pressure fluctuation begins to spread in the whole reservoir when the production well is produced. With the progress of production, the boundary of DDV expands outward. Using DDV to evaluate the productivity of fractured horizontal wells does not need any prior knowledge of complex reservoir characteristics, and considering the advantages of dynamic change process. Therefore, the results are more in line with reality (Yuan et al., 2016; Zheng et al., 2017).

Based on the material balance theory, we deduce the calculation formulas of the DDV of horizontal wells. Using the diffusion law of DDV, the stimulation potential of wells is calculated, and the relationship between stimulation potential and refracturing timing is established. Moreover, the charts of refracturing timing with different initial pressure scales are drawn. Finally, the reconstruction mode of horizontal well refracturing is optimized by numerical simulation.

When the horizontal wells are exhausted in the initial stage of production, it depends on the natural energy of the reservoir for production. The oil drainage volume in the reservoir reconstruction area directly reflects the productivity of the horizontal wells. Therefore, based on the material balance equation, the equations of DDV is established, the DDV is evaluated by using the pressure and production data, and the relationship between the refracturing timing and scale is established.

Because it is difficult to obtain a large number of production data of fractured horizontal wells, this paper set different fracture parameters and established the numerical simulation model of multi-stage fractured horizontal wells under depletion development mode. Based on the reservoir physical parameters and production data under different initial pressure modes, the variation law of DDV is obtained by using the numerical simulation model. The relationship between initial pressure scale and refracturing timing is also analyzed. The numerical simulation model of a typical ultra-low permeability reservoir in Changqing Oilfield is established: the number of grids is 81 × 131×3. The grid unit size is 20 m, the average porosity is 11%, and the average permeability is 0.5 × 10^–3 μm². The fluid physical parameters are listed in Table 1, the relative permeability curve is shown in Figure 2 and the initial fracturing parameters are listed in Table 2.

There are 27 fracturing parameter combinations in Table 2, which are shown in Table 3.

The cumulative oil production and cumulative water production under different development modes are calculated and brought into the material balance equation. The production is normalized by considering the physical properties of the reservoir, and finally the variation value of the DDV with time is obtained. Figure 3 shows the variation of DDV with time when the interval of fracturing section is 40 m, the half length of fracture is 100 m, and the conductivity of initial fracturing fracture is 20 × 10^–3 μm² m. Figure 4 shows the change rate of DDV growth rate. The trend of drainage pore volume shows an asymptotic features, which is consistent with the previous studies (Yin et al., 2015).Due to the limitation of reservoir pressure, the DDV finally tends to a limit value.

See Figure 5 for the flow chart of determining the refracturing timing by using the DDV method. According to the cumulative water production and cumulative oil production under different initial fracture distribution, the DDV change law curve with time is obtained by using Eq. 12 respectively. The curve slope is then used to calculate the growth rate and change rate of the growth rate of DDV. When the change rate of the growth rate of DDV is less than 10%, the dynamic drainage boundary propagates slowly, the reservoir is in the development state of low production and low efficiency, and the output of the initially fractured oil well has not reached the expected effect. However, at this time, a large amount of residual oil still exists in the reservoir and between fractures. The horizontal well needs to be refractured to restore the oil well productivity. Through this method, we can obtain the refracturing timing of different initial fracturing scales under 27 groups of schemes, as shown in Figure 6.

The refracturing timing under different initial pressure scales is classified, and the chart shown in Figure 7. The horizontal axis represents the interval and the vertical axis represents the half length of the fracture. There are 9 grids in the chart and each grid is divided into 3 layers according to the fracture conductivity. The fracture conductivity from bottom to top is 20 × 10^–3 μm²·m, 120 × 10^–3 μm²·m and 240 × 10^–3 μm²·m, the chart is divided into 27 grids, representing 27 different schemes. We divided the grids into four categories: Class I is horizontal wells with poor initial development effect, which are production wells with low conductivity and large interval. It is recommended to carry out repeated fracturing in the first 20 months of the initial stage of production; Class II and III are horizontal wells with good development effect at the initial stage of production and low production after a period of time due to insufficient fracture length. It is recommended to extend the fracture length by half; Class IV is horizontal wells with good fracture length and conductivity and less influence of interval spacing. It is recommended to carry out refracturing finally. In conclusion, it is suggested that the sequence of refracturing for horizontal wells with different initial pressure scales should be followed: first, refracturing for horizontal wells of class I to restore the conductivity of fractures and add new fractures; Secondly, horizontal wells of class II and III are refractured to prolong the fracture length and restore the fracture conductivity; Finally, horizontal wells of class IV are refractured.

In the process of reservoir reconstruction, two types of refracturing are usually used: original fracture refracturing and new fracture refracturing. The main ways of refracturing the original fracture are: prolonging the old fracture, turning the old fracture and restoring the conductivity of the original fracture. There are mainly two ways to refracture new fractures: retaining the original fracture and sealing the original fracture. Choosing different refracturing reconstruction methods will lead to great changes in the seepage law and stimulation mechanism of horizontal wells after refracturing.

One horizontal well in a typical ultra-low permeability reservoir in Changqing Oilfield was put into operation in October 2012. After 6 years of initial fracturing production, it was refractured, 19 old fractures were blocked, and 23 new fractures were refractured between the old fractures. After the measures, the daily oil production is 15.9 t and the daily oil increase is 13.3 t, as shown in Figure 16. At present, it has been produced for nearly one year, with a daily oil production of 14.29 t, a daily oil increase of 11.61 t, a cumulative oil increase of 3442 t and a cumulative oil production of 4407 t.

In this paper, by introducing the calculation method and process of DDV, the discrimination model of refracturing timing is established. The refracturing timing chart under different initial pressure scale is formed, and the different reconstruction methods of refracturing are optimized and designed by numerical simulation method. The results show that.

1) With the depletion of the reservoir, the reservoir pressure continues to spread outward, and the boundary of the reservoir drainage volume continues to expand. However, the drainage volume finally tends to the extreme value under the limitation of the pressure range. The increase rate of DDV of horizontal wells shows a trend of first fast and then slow. When the change rate of growth rate is less than 10%, it can not meet the expected production requirements and needs to be refractured.