Abstract
Accurate determination of unsteady bottom hole pressure helps to monitor and predict well production in real-time. On the premise of fully considering the seepage characteristics of carbonate rock, a new source function suitable for the seepage of carbonate rock is established. It enlarges the application scope of source function theory and lays a theoretical foundation for solving the seepage problem of carbonate rock. This paper presents the process of solving bottom hole pressure step by step. Step 1: Based on the triple media model, the Pedrosa permeability calculation formula is applied to establish the seepage model of the triple media reservoir considering the formation stress sensitivity. Step 2: By perturbation transform and Laplace transform, the point source function considering stress sensitivity in carbonate reservoir is obtained in Laplace space. The point source function in the infinite plate reservoir is obtained by the principle of mirror image and superposition. Step 3: The method of solving the horizontal well pressure under the constant pressure boundary is established. Through literature comparison and numerical simulation, the rationality of the proposed method is verified. Simultaneously, the sensitivity analysis of pressure and pressure derivative is carried out, and the influences of fracture number, fracture angle, fracture half-length, skin factor, horizontal well segment length, and horizontal well segment spacing on pressure and pressure derivative are analyzed in detail. Considering fracture orientation and stress sensitivity, we divide the triple media fracture-vuggy reservoir fluid flow into five stages. The number of fractures and fracture direction mainly affect stage C. In contrast, the length of horizontal subsection and skin factor mainly affect stage B. Stage D is more obvious when the fracture half-length and the horizontal sublevel interval of the horizontal well are small.
New Method for Calculating Bottom Hole Pressure of Horizontal Well in Fracture-cavity Reservoir Based on Point Source Function