Inverting The Parameters in Shale Gas Reservoirs with the Bottom Hole Pressure

Abstract

The adsorption relationship of shale gas and single well controlled reserves are the most important parameters in shale gas development. In this paper, according to the multi-fractured horizontal well technique generally used in shale gas reservoirs, the flow equations of the formation and fractures are established. It is calculated the flow rate of each fracture with solving the Fredholm integral equations in the Laplace space. Considering the stress sensitivity as well as the physical properties of mixed gas in shale gas formations, normalized pressure is defined to linearize the flow equations, and the gas adsorption and diffusion can be considered with Laplace transform. The theoretical type curves for the bottom hole pressure inversion (or production analysis) are provided by solving the flow rate in fractures and the normalized pressure equations together, then the parameters of the formation can be inverted with curve fitting. A case study of one shale gas well in China is also presented; in this case, it is gotten the adsorption relationship and single well controlled reserves.