Establishment And Application Of Seepage Mathematical Model For Fractured Horizontal Wells In Tight Gas Reservoirs

The seepage mathematical model of fractured horizontal wells based on traditional Euclidean method is only suitable for characterizing homogeneous reservoirs,and it is difficult to describe the heterogeneity of actual fractured fracture distribution.Therefore,in order to accurately describe the complex distribution and connectivity characteristics of fractures in reservoirs,it is necessary to establish a new seepage mathematical model of fractured horizontal wells in tight gas reservoirs.Firstly,fractal theory and anomalous diffusion theory are introduced to establish the fracturing horizontal trilinear seepage mathematical model of tight gas reservoir considering natural fracturing fractal and artificial fracturing fractal respectively.Then,the mathematical method is used to solve the equation,and the functional expression of production is obtained,which is compared with Brown model data,and it is found that the fractal model can be very good.Good fitting;finally,based on the results of the fractal seepage mathematical model,draw the curve.The fractal dimension of mass and anomalous diffusion coefficient were changed to analyze the sensitivity of parameters.The results show that the smaller the fractal dimension of mass,the upward change of pseudo-pressure curve and the faster the yield curve decreases,the greater the influence of the fractal dimension change of natural micro-fracture mass;the greater the abnormal diffusion index,the more difficult the gas diffusion in fractal body,the upward movement of pseudo-pressure curve,the faster the yield curve decreases,and the corresponding seepage stage will appear later.Using the model established in this paper,the production expression is properly processed,and the slope of the seepage characteristic section in three different seepage stages is combined to solve the expression of the length of the fracture reconstruction zone.The model is applied to a fractured horizontal well in a gas field.The calculated results are in good agreement with those obtained by microseismic measurements.It can be used to calculate the length of the fracture reconstruction zone of actual gas wells through the production data of gas wells,which has certain guiding significance for the design of fracturing schemes and the evaluation of fracturing effects.