The article analyzes the well-known methods for analytical solution of the problem of unsteady fluid flow to a directional well. The first method is based on dividing the perforated interval of the well into a set of discrete linear elements with a uniform flux. This approach allows to accurately calculate the changes in downhole pressure. However, the duration of the calculation is unacceptable for engineering practice. The second method describes a directional perforated section with a single linear source with a uniform flux. In this case, the result is achieved due to the appropriate selection of equivalent point at which the pressure response in a borehole is calculated. This approach has high computational efficiency, but its accuracy is inferior to the first method. The authors proposed a modification of the second method to make calculations both fast and accurate. An equation for determining the coordinates of the equivalent pressure point is obtained by the method of the best combination of bottom-hole pressure curves calculated using both solutions. The required dependencies were obtained for all types of borders on the roof and bottom. It is established that calculations based on the proposed modification significantly reduce the calculation time. At the same time, the accuracy is within the limits sufficient for practical calculations. Pressure calculations were performed for the maximum values of the angle of inclination corresponding to the vertical and horizontal location of the well. The results are in good agreement with the data published in the literature and calculated in third-party commercial software. The proposed model of directional well completely solves the problem of efficient and high-speed calculation of unsteady pressure. This model is implemented by employees of RN-BashNIPIneft LLC (a subsidiary of Rosneft Oil Company) in the corporate software package RN-VEGA, designed for the analysis and interpretation of well tests.
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