A novel pressure transient response model considering multiple migration mechanisms in shale gas reservoir

Since the shale gas production data predicted by traditional simulators is far below that of field test, reservoir volume parameters are often modified to meet the fitting demands. Most pressure transient models of reservoir, merely based on Darcy flow in the matrix and natural fractures, neglect the comprehensive influences of viscous flow, slip flow, transition flow and Knudsen flow, etc. In this paper, two gas apparent permeability models considering multiple migration mechanisms are established through theoretical derivation and fitting. The models are applicable to various flow states and will help to simplify percolation models of matrix and fracture system. To achieve a better understanding of the migration mechanisms of shale matrix, the effects of compressed gas in the matrix pores, adsorbed gas on the pore wall and the diffused gas from kerogen on transient pressure should all be taken into account. Based on the newly established gas apparent permeability models, a pseudo-triple-medium transient percolation mathematical model of multi-fractured horizontal well affected by multiple migration mechanisms is presented with the consideration of dissolved gas diffusion in kerogen and adsorbed gas desorption on matrix surface in the shale gas reservoir. Source function idea combined with Laplace transform, linear approximation and δ generalized function is used to get the point source solution of the mathematical model. By discretizing the artificial fractures, the pressure transient response of multi-fractured horizontal well in Laplace space is obtained on the basis of point source solution. Then pressure transient response type curves are plotted by computer programming, and pressure influence factors are also analyzed. Besides, isothermal adsorption experiment data of shale cores indicates that the organic carbon content (TOC) has obvious correlation with the adsorption coefficient defined in this paper, which gives a clue to link up the exploitation research with geological study, playing a guiding role in analyzing pressure response of the shale gas reservoir.