Production Behavior Evaluation on Inclined Well in Commingled Carbonate Gas Reservoir With Multiple Heterogeneous Layers Without Crossflow

To estimate production behaviors of inclined well in multilayer heterogeneous carbonate gas reservoir, two semi-analytical models for different formation distribution patterns are proposed, which are named as model I and model II. For model I, the inner region of each layer is fractured-vuggy porous medium, while the outer region only contains matrix. For model II, the inner and outer regions are consisted of matrix and fractured-vuggy porous mediums, respectively. To solve the model, Laplace transformation, Fourier transformation and inversion, Duhamel convolution, and Stehfest numerical inverse are applied. The validities of these models are verified through the comparisons with the published datum, which include well bottom-hole pressure (BHP) and gas production rate of individual layer for vertical and inclined wells in multilayer homogenous gas reservoir. Furthermore, by matching the well BHP data collected from a field case, the applicability of model is validated. The influences of prevailing factors, such as the radius ratio between inner and outer regions, horizontal–vertical permeability ratio, and inclination angle, on production behaviors are analyzed. The results show that influenced by the diverse formation distribution patterns, the variation of radius ratio between inner and outer regions has opposite effect on the well BHP for models I and II. Formation anisotropy and inclination angle have minimal effects on the well BHP of model I, but have significant impacts on model II. To keep the well BHP with a relatively high value, for model I and model II, the penetrate inclination angles should be greater than 50 deg and 55 deg, respectively.