摘要：Deviated wells are used to improve the performance of carbonate reservoirs with multiple heterogeneous layers and penetrate the “sweet spot” of each layer, which is full of fractures and vugs. It is difficult to consider in-layer and inter-layer heterogeneities simultaneously, and predict the production performance for these wells accurately. Therefore, a semi-analytical model to analyze the production performance of deviated wells in a multilayer heterogeneous stress-sensitive carbonate gas reservoir is proposed. For each layer, the inner region is a fractured-vuggy porous medium, while the outer region is merely a tight formation with matrix and formation properties, and penetrated inclination angles may be distinct. Pseudo-time/pressure factors are introduced to consider fracture stress sensitivity. Through the application of Laplace transformation, Fourier transform and inverse, Duhamel convolution, and Stehfest numerical inversion, the presented model is solved. The validity of this model is verified through comparison with single-layer composite formation with different porous mediums and vertical well in a multilayer carbonate gas reservoir. Moreover, by matching bottom-hole pressure data collected from a slanted well in the Anyue gas field, the applicability of this model is validated. A synthetic case, which has two composite formations, the first (upper) layer is more permeable than the second (lower) layer, is used to study the variations of inner region radius, fracture/matrix permeability, and inclination angles on production behaviors. The results show the properties of the first layer determine well bottom-hole pressure, whereas the rise of permeability, inner region radius and penetrated angle for the second layer can improve the gas recovery of this layer. In practice, to maintain well bottom-hole pressure with a relatively high level and enhance gas recovery of the tight layer, the inclination angle should be larger than 60° for each layer, and be increased to as large as possible. The findings of this study can help for a better understanding of the production behaviors of deviated wells in multilayer heterogenous reservoirs and could provide some guidance for the design of well trajectory.
