Karst cavities and caves are often present along fractures in limestone reservoirs and are of significance for oil and gas exploration. Understanding the formation and evolution of caves in fractured carbonate rocks will enhance oil and gas exploration and development. Herein, a reactive transport model was established considering both the matrix and fractures. Different factors affecting the dissolution along fractures were considered in the simulation of matrix–fracture carbonate rocks, including the magnitude and characteristic length of the matrix porosity heterogeneity, intersecting fractures, and complex fracture network. The results show that a strong heterogeneity of the matrix porosity significantly affects the cave formation along the fracture and the existence of fractures increases the heterogeneity due to the high permeability as well as the dissolution area. The characteristic length of the matrix porosity heterogeneity affects the cave location and shape. The larger permeability of intersecting fractures or the matrix greatly increases the cave size, leading to the formation of large, connected cave areas. A complex fracture network leads to more developed karst dissolution caves. The topology of the fracture network and preferential flow dominate the distribution of caves and alleviate the effect of the matrix heterogeneity.

Multi-fractured horizontal wells (MFHW) is one of the most effective technologies to develop tight gas reservoirs. The gas seepage from tight formations in MFHW can be divided into three stages: early stage with high productivity, transitional stage with declined productivity, and final stage with stable productivity. Considering the characteristics and mechanisms of porous flows in different regions and at different stages, we derive three coupled equations, namely the equations of porous flow from matrix to fracture, from fracture to near wellbore region, and from new wellbore region to wellbore then an unstable productivity prediction model for a MFHW in a tight gas reservoir is well established. Then, the reliability of this new model, which considers the multi-fracture interference, is verified using a commercial simulator (CMG). Finally, using this transient productivity prediction model, the sensitivity of horizontal well's productivity to several relevant factors is analyzed. The results illustrate that threshold pressure gradient has the most significant influence on well productivity, followed by stress sensitivity, turbulence flow, and slippage flow. To summarize, the proposed model has demonstrated a potential practical usage to predict the productivity of multi-stage fractured horizontal wells and to analyze the effects of certain factors on gas production in tight gas reservoirs.