Shale gas production in nanoscale fractures with real gas effect

Real Gas Effect and Bulk Diffusion Characteristics of Shale Mixed Gas Transport in Microscale Fractures

“…In this paper, the z -factor, viscosity, and density of gas mixture equations are calculated on the basis of previous studies. − ,,,,,,,,,,,− In the future, this model will be further validated with experimental data.…”

“…The compressibility factor is widely used in the petroleum industry and can be expressed as eqs –. , In addition, the viscosity, average molecular free path, Knudsen number, fracture geometry, and other parameters of mixed gas in shale reservoir need to be characterized. The relevant analytical expressions are shown below. − Z i = 1 + P normalr normali 10.24 T normalr normali [ 2.16 1 T r i true( 1 T normalr normali + 1 true) − 1 ] P normalr normali = P P normalc normali T normalr normali = T T normalc normali Z normalm normali normalx normalt normalu normalr normale = m 1 Z 1 + …”

“…The compressibility factor is widely used in the petroleum industry and can be expressed as eqs –. , In addition, the viscosity, average molecular free path, Knudsen number, fracture geometry, and other parameters of mixed gas in shale reservoir need to be characterized. The relevant analytical expressions are shown below. − where Z i is the compressibility factor of i th gas under the condition of high temperature and pressure, dimensionless; P ri and T ri are contrastive pressure and temperature, Pa & K, respectively; P ci and T ci are critical pressure and temperature, Pa & K, respectively; Z mixture is the compressibility factor of shale mixed gas under the condition of high temperature and pressure, dimensionless; μ real, i is the gas viscosity under the condition of high temperature and pressure, Pa·s; μ real,mixture represents the gas mixture viscosity under the condition of high temperature and pressure, Pa·s; λ real, i represents an average molecular free path of i th gas under the condition of high temperature and pressure, m ; λ real,mixture is an average molecular free path of gas mixture under the condition of high temperature and pressure, m ; Kn real, i is the Knudsen number under the condition of high temperature and pressure, dimensionless; Kn real,mixture is the Knudsen number of gas mixture under the condition of high temperature and pressure, dimensionless; and r equivalent is an equivalent radius, m . Based on the basic equations above, the modified slip flow can be modeled as Conductivity Due to the gravitational attraction of methane and other gases on the shale wall, some gases are adsorbed on the shale surface. The transport of these adsorbed gases to shale gas cannot be ignored.…”