Numerical pressure transient analysis for unfilled-caved carbonate reservoirs based on Stokes-Darcy coupled theory

Abstract

Caved carbonate reservoirs are very special because of the strong heterogeneity. The pressure transient behavior of the caved carbonate reservoirs is quite different from the conventional homogeneous or dual medium reservoirs because of the presence of large-scale cavities. There are two types of cavities: filled and unfilled, which dominated the production of the reservoirs. Fluid flow in the unfilled cavity should be described by Stokes' equation rather than Darcy's law. It is needed to better understand the role of the unfilled cavities plays in the pressure transient analysis. The objective of this work is to analyze the pressure transient behavior of the unfilled cavities. A coupled Stokes-Darcy pressure transient model is developed and the finite element method is applied in the solutions of the mathematical models. Then, the numerical pressure transient model is used in the analysis of two typical cases: a well drilled into the unfilled cavity (WIC) and a well not drilled into the unfilled cavity (WOC). The type curves of the WIC model indicate that flow in the unfilled cavity is an oscillated pressure-drop rather than a radial flow. The unfilled cavity that the well drilled into would be considered as an enlarged wellbore which is equivalent to a negative skin factor, as a consequence the wellbore storage coefficient will increase. Main characteristics of type curves for WOC model are the valley on the pressure derivative. A cavity with a larger size and smaller distance from the wellbore would give rise to a deeper valley. Comparative results indicate that unfilled cavities described by the Stokes' equation are not the limit of the filled cavities with extremely large mobility, which was predicted by previous work.