Productivity Model Study of Water-Bearing Tight Gas Reservoirs Considering Micro- to Nano-Scale Effects

Tight sandstone is rich in micron- and nano-scale pores, making the two-phase flow of gas and water complex. Establishing reliable relative permeability and productivity models is an urgent issue. In this study, we first used a slip model to correct the gas phase's no-slip Hagen-Poiseuille equation for nano- and micropores. Then, combined with the fractal theory of porous media and the tortuous capillary bundle model, we established two-phase relative permeability models for nanopores and micropores. These relative permeability models comprehensively consider the gas slippage effect, the initiation pressure gradient, the pores' fractal characteristics, and water film mechanisms. Based on these models, we developed a three-region coupling productivity model for water-bearing tight gas reservoirs with multi-stage fractured horizontal wells. This productivity model considered the micro- and nano-scale effects and the heterogeneity of fracture networks. Then, the model was solved and validated with a field case. The results indicated that the three-region composite unsteady productivity model for water-bearing tight gas reservoirs, which incorporated micro- and nano-scale effects (with consideration of micro-scale and nano-scale phenomena in the fluid flow), could accurately predict a gas well's productivity. An analysis of the factors influencing productivity showed that ignoring the micro- and nano-scale effects in water-bearing tight gas reservoirs will underestimate the reservoir's productivity. The initial water saturation, the two-phase flow's initiation pressure gradient, and capillary force are all negatively correlated with the productivity of gas wells, while the conductivity of the fractures is positively correlated with gas well productivity.