Transient well-test model of a slanted well in a heterogeneous multi-zonal reservoir

Abstract

To enhance the comprehension of flow characteristics and enrich the well-test theory of slanted wells, this study established a well-test model for a slanted well in a heterogeneous multi-zonal reservoir. The model considered closed boundaries at both the top and bottom, as well as an external boundary with infinite, closed, or constant pressure on the horizontal plane. We took the bi-zonal composite model as an example to carry out concrete analysis. Various contemporary mathematical techniques, including Laplace integral transformation, separation of variables, and eigenfunction methods, were employed to solve the model. The pressure solution in real space was obtained through Duhamel's principle and Stehfest numerical inversion, then analytical curves created, and flow stages were defined for a slanted well in a bi-zonal composite reservoir. In addition, we performed a sensitivity analysis on some parameters affecting the curves. For a tri-zonal composite model, we also plotted the well-test curves and categorized them. Finally, we validated the model through the interpretation of an example well. The results show that the fluid flow of a slanted well in a bi-zonal composite reservoir can be divided into seven main stages, including wellbore storage effect (WSE) stage, skin effect (SE) stage, linear flow (LF) stage, radial flow (RF) stage of the 1st zone, transitional flow (TF) stage from the 1st to the 2nd zone, RF stage of the 2nd zone, and the external boundary response stage. The position of the pressure curve at the SE stage and LF stage decreases as the length and inclination angle increase. Correspondingly, the pressure curve at the RF stage of the 2nd zone and external boundary response stage decreases with increasing mobility ratio. Furthermore, as the radius of the 1st zone increases, the pressure curve at the RF stage of the 1st zone and the TF stage shifts towards the right. The established model and plotted curves provide a theoretical basis for further studies on the flow behavior of slanted wells in composite reservoirs.