Shale formation is featured in nanopores and much gas adsorptions. Gas flow in the shale matrix is not a singular viscous flow, but a combination of multiple mechanisms. Much work has been carried out to analyze apparent permeability of shale, but little attention has been paid to the effect of unique gas behavior in nanopores at high pressure and adsorbed layer on apparent permeability. This work presents a new model considering multiple transport mechanisms including viscous flow (without slip), slip flow, Knudsen diffusion, and surface diffusion in the adsorption layer. Pore diameter and mean free path of gas molecules are corrected by considering the adsorption layer and dense gas effect, respectively. Then the effects of desorption layer, surface diffusion, and gas behavior on gas apparent permeability in nanopores of shale are analyzed. The results show that surface diffusion is the dominant flow mechanism in pores with small diameter at low pressure and that the effect of adsorbed layer and dense gas on apparent permeability is strongly affected by pressure and pore diameter. From the analysis results, the permeability value calculated with the new apparent permeability model is lower than in the other model under high pressure and higher than in the other model under high pressure, so the gas production calculated using the new permeability model will be lower than using the other model at early stage and higher than using the other model at late stage.

Two-phase flow behavior in fractured carbonate reservoirs was investigated due to the importance for geothermal and petroleum resource recovery, such as in this study the phase change of volatile oil. This paper presents a semi-analytical method for accurately modeling two-phase flow behavior and quickly predicting the production performance. The fractured carbonate reservoir was modeled with a dual-porosity model, and the phase change and two-phase flow were modeled using the black oil model. The production of the oil phase was obtained through linearizing and solving the mathematical model. The gas phase production was forecast using the producing gas-oil ratio (GOR), calculated using flowing material balance equations. By comparing the semi-analytical solution to the solution of the commercial numerical simulator and applying it to a field case, the accuracy and practicability of the proposed semi-analytical method could be validated. Based on the semi-analytical model, the influences of several critical parameters on production performance were also analyzed. The proposed model was shown to be efficient in evaluating two-phase production performance of horizontal volatile oil wells. Furthermore, the new technique is able to serve as a useful tool for analyzing two-phase production data and making forecasts for volatile oil wells in fractured carbonate reservoirs.