Study On Pressure Performance Of Fractured Horizontal Wells In Fractal Tight Gas Reservoirs

Tight gas reservoirs are characterized by dense matrix and highly-developed fractures,and usually developed by horizontal wells with hydraulic fracturing stimulation.Traditional flowing model for multi-fractured horizontal wells in tight gas reservoirs are mostly based on classical Euclidean geometry.However,the structure of real tight gas reservoirs are highly heterogeneous and of multiscale,and the fractal theory provides a powerful method to describe the disorder,heterogeneity,uncertainty and complexity of the complex and disordered systems.As the diffusion process in complex and disordered systems is history dependent,while the classical integer-order diffusion equation cannot fully take account for the characteristic of anomalous diffusion in complex and disordered systems.In this paper,three different fractally fractional diffusion models(FFDMs)for multi-fractured horizontal wells(MFHWs),MFHWs with multiple finite conductivity fractures and MFHWs with stimulated reservoir volume(SRV)in fractal tight gas reservoirs is established based on fractal theory and fractional calculus.Particularly,fractal theory is used to describe the complex,disordered and heterogeneous fracture network,with consideration of anomalous behavior of diffusion process in tight gas reservoirs by employing the fractional calculus.The Laplace transformation,line source function,dispersion method,and superposition principle are used to solve the three new model.The type curves of pressure performance of three different fractally fractional diffusion models for fractured horizontal wells in fractal tight gas reservoirs are obtained with Stehfest numerical inversion algorithms,and the pressure performance are then studied in depth.The proposed FFDM provides a new understanding of the performance of fractured horizontal wells in tight gas reservoirs,which can be applied to a more accurate and appropriate interpretation of the real pressure data in field.