Uncertainty inversion method of fracture network in shale gas reservoir based on MCMC

Horizontal well combined with volume fracturing technics is an effective means to achieve the economic development of shale gas. Hydraulic fracturing can form a three-dimensional complex fracture network and improve the flow environment of shale gas reservoirs. However, due to the complexity of shale gas reservoir’s basic characteristics, especially the porosity-permeability conditions, formation temperature-pressure system and nonlinear flow mechanism in porous media make the inversion of shale gas pressure fracture network more uncertain, which makes it difficult to accurately evaluate the fracturing effect of shale gas reservoirs. Firstly, based on the dimensionless production solution of shale gas under constant-pressure production conditions, this paper obtained the local solutions of linear flow and boundary control flow in shale gas production process, introduces the mass balance pseudo-time and normalized pseudo-pressure to construct a deterministic inversion method of shale gas fracture network parameters combining the linear analysis method and the chart fitting method, and analysed the uncertainty of basic parameters required for fracture network inversion. The quantitative characterization formulas of uncertain parameters, which include reservoir parameters such as shale porosity and shale permeability et al, the characterization parameters of shale gas nonlinear flow and adsorption-desorption mechanism and the basic parameters required for inversion, were given respectively in this paper. Moreover, a fracture network uncertain inversion method of shale gas reservoir based on Markov Chain Monte Carlo method (MCMC) was proposed. MCMC sampling method was used to obtain the probability distribution of reservoir parameters, adsorption-desorption and flow parameters, and basic parameters of fracture network. By combining linear flow analysis method and chart fitting method, typical flow stages were identified and fitted to obtain the probability distribution of each inversion parameter. By randomly generating the sample set of basic parameters, the key parameters of fracture network under different sample sets were interpreted by deterministic method, and the key fracture network parameters such as artificial fracture length, conductivity, permeability and fracture width of reconstruction area and their probability distribution were quickly obtained. Finally, by analyzing the production performance of a volume fracturing horizontal well in a shale gas block in Southwest China, the uncertainty ranking of the four key parameters of the fracturing network was clarified, and the key parameter values and the probability results of P10, P50 and P90 were given. The uncertainty of artificial fracture half-length and artificial fracture conductivity was strong, the uncertainty of permeability in the reconstruction area was ordinary, and the uncertainty of width in the reconstruction area was weak. The research results provide a more comprehensive practical guidance for the evaluation of shale gas reservoir fracturing effect and the formulation of reasonable development strategy.