The Similar Structure Of The Solution For The Dual Medium Model Of The Shale Gas Reservoir

Based on the solution of the similar structure theory,solving differential equation boundary value problem is gotten as a starting point.As fundamentals,the solution of the similar structure theory about second-order homogenous linear differential equations is revealed directly,using the boundary value problem of Laguerre equation and Gegenbauer equation for further explanation and demonstration of this theory.It is found that the solution for the two kind of equation can be expressed in the form of continued fraction and that the steps of the solution of the similar structure in this two kind of equation are given respectively.It further illustrates that the solution of similar structure theory is good for solving this kind of problem.The topic of this article is to solve the similar structure of the solution for the dual medium model of the shale gas reservoir.First,according to the shale gas seepage theory,it takes the dual medium model for shale gas reservoir as the research object.Aim for shale gas reservoir of complex seepage problems about adsorption & desorption,stress-sensitivity,gas diffusion,slippage effect,threshold pressure gradient and so on,it establishes three shale gas reservoir percolation models with the premise of adsorption & desorption.The three kinds of shale gas reservoir percolation models are respectively the dual porosity model in naturally fractured shale gas based on stress-sensitivity,considering start-up pressure gradient fractured shale gas reservoir model and the dual-permeability model of the shale gas reservoir.The dualpermeability models of the shale gas reservoir include the model considering slippage effect in matrix porosity,the model taking into account slippage effect and gas diffusion in micro-matrix porosity,and the model thinking about stress-sensitivity,slippage effect,gas diffusion in micro-matrix porosity.Second,the three kinds of shale gas seepage models are transformed into the boundary value problems of corresponding variant Bessel equation,by separately using mathematical methods about linearized processing,perturbation method,constant variation method and Laplace transformation.Then,the three kinds of models in Laplace space solution can be obtained.Finally,according to solutions in variant Bessel equation of the similar structure theory,it is found that solutions in the three kinds of shale gas seepage models have the similar structures for further research and analysis.This not only extends the application range of the solution of the similar structure theory,verifies the effectiveness of the solution of similar structure theory in the double medium model of shale gas,but also provides a new method for solving shale gas seepage model.It provides convenience for studying further shale gas model,too.