Model for Predicting Horizontal Well Transient Productivity in the Bottom-Water Reservoir with Finite Water Bodies

To better understand the horizontal well transient productivity in the bottom-water reservoir with finite water bodies, the horizontal well transient productivity model for the bottom-water reservoir with finite water-body multiple was developed using Green’s function and potential superposition method. Laplace transforms, Fourier transforms, superposition of point source, and Duhamel principle were used to obtain the transient productivity of the horizontal well, and the transient productivity of the horizontal well in real space was obtained by the Stehfest numerical inversion method. The typical pressure response curve and dimensionless productivity curves were plotted. The effects of the water-body multiple, the distance between the horizontal well and oil–water contact, and the skin factor, were analyzed. Six main flowing stages were divided for horizontal wells in the bottom-water reservoir with finite water bodies. When the water body multiples are zero or tend to infinity, the results obtained from the model are consistent with the calculations by the conventional top-bottom closed reservoir model or infinite rigid bottom-water reservoir model, respectively, and the pressure dynamic for the finite water body falls in between both. With the increase in the water body multiples and the decrease in distance between the horizontal well and the oil–water contact, and the horizontal well productivity decreases slowly. With the increase in the skin factor, the initial productivity decreases; moreover, the skin factor has a great influence on the initial productivity of the horizontal well, while the later influence gradually decreases. Accurate horizontal well productivity prediction in the bottom-water reservoir with finite water bodies provides a strong basis for horizontal well deployment, design optimization, and formulation of development policy.