Production performance analysis for slanted well in multilayer commingled carbonate gas reservoir

This paper proposes a semi-analytical model to evaluate the production performance for slanted wells in a multilayer commingled carbonate gas reservoir, in which the porous medium types and penetrated angles for each layer may be distinct. The triple-porosity/single-permeability and single porosity/permeability models are utilized to describe the fluids flow in natural fractured vuggy and tight formations, respectively. In addition, the stress sensitivity for different formations is considered in pseudo-time and pseudo-pressure. Laplace transformation, Fourier transform and inverse, Duhamel convolution, Stehfest inversion, and point source function are used to calculate the well bottom-hole pressure and production rate for each layer. After proper simplification on the proposed model, the calculated results match very well with the classical solutions in published papers. Furthermore, the accuracy of this model is validated by comparing the well bottom-hole pressure with the monitored data of a well in the Gaoshiti-Moxi carbonate gas reservoir. A synthetic case, which contains two layers that the upper one is naturally fractured vuggy formation and lower one is tight formation, is constructed to analyze the variation of horizontal-vertical permeability ratio and penetrated angles on production performance. The results show that the horizontal-vertical permeability ratio and the penetrated angle in naturally fractured vuggy formation determine the level of well bottom-hole pressure, while these two parameters have significant influences on production rate for tight formation. In practice, to enhance the gas recovery of tight formation, and to keep the well bottom-hole pressure a relatively high level, for tight and naturally fractured vuggy layers, the penetrated angles should be larger than 50° and 45°, respectively, and be increased as large as possible.