Study On Fractal Model Of Shale Gas

Shale gas is an important unconventional resources, which has different microstructures migration laws with conventional gas reservoir. The microstructures migration laws of shale gas include desorption, diffusion, slippage and seepage. Traditional double media models of shale are mostly based on Euclidean geometry, and did not consider the diffusion process of desorbed gas from pore wall surface to matrix pore. This paper based on fractal geometry to build shale gas fractal dual media model, and consider these four microscopic transport processes, then establish a non-steady-state flow model and consider the multi-stage fractured horizontal wells. Finally, get the shale gas reservoirs fractal dual media multistage fractured horizontal well production decline model by solving the model in different boundary conditions.In this paper, in-depth analysis of shale gas in four microscopic transport mechanism. Then establish a fractal dual media unsteady flow model based on the fractal theory. By solving the multi-stage fractured horizontal wells mathematical model to obtain the following results and understanding:(1) The results indicate that shale gas adsorption-desorption process can be fit for Langmuir isotherm equation. The diffusion process of desorbed gas from the pore wall surface to matrix pores belongs Knudsen diffusion. The free gas diffusion of matrix pores is free diffusion (diffusion). The gas flow in the matrix porosity are slipping flow. And the gas flow in the natural fractures are Darcy flow.(2) Shale was established by applying the fractal theory. The matrix-fracture fractal double medium model, and the model of porosity fractal characterization based on fractal circuity capillary bundle model, then obtained the fractal apparent permeability of integrated diffusion-slip transport process of matrix. Binary tree model based on fractal theory and use Hagen-Poisenille equation to get the natural fracture system Darcy seepage fractal apparent permeability.(3) Using fractal binary tree model simulation of shale natural fracture system must satisfy two implicit relation. The implicit relation is about the fracture fractal binary tree model bifurcation angle2θ to the capillary length coefficient β and the branch number n to capillary diameter coefficient α. The parameter2θ, β, n and α are not random values. They must satisfy two implicit equation respectively.(4) Considering four microscopic shale gas migration process, on the basis of shale gas reservoir is established fractal dual porosity multi-stage fracturing of horizontal seepage model, according to different boundary conditions, using the superposition principle of point source solution Duhamel principle methods of Laplace transform, solve the production decline model.(5) Shale gas reservoir fractal dual porosity multi-stage fracturing horizontal well production decline curve sensitive factor analysis showed that the adsorption coefficient, the greater the interporosity flow stage of the production of the higher, the longer the life of production wells. Dimensionless diffusion coefficient is smaller, interporosity flow phase appeared earlier. Matrix pore fractal dimension, the greater the matrix porosity up to natural fracture flow of gas in the faster, the stage of production is higher. The natural fracture fractal dimension, the greater the single well production is higher, interporosity flow stage in the later. The greater the interporosity flow coefficient, formation of linear flow and the higher the interporosity flow stage production, and the longer the late stage of channeling duration. The skin factor, the greater the near wellbore zone pollution level, the greater the single well production is smaller. The longer the artificial fracture, the higher the production. Fractures of the increase in the number, the single well production increases, when the artificial fracture number after reaching a certain number of article, basic no effect for the entire decline stage of single well production.(6) In order to verify the dependability and practicability of the shale gas fractal percolation model, this article analyze the shale gas production decline of a single well to obtain reservoir parameters.