Abstract
Natural gas exists in considerable quantities in tight reservoirs. Tight formations are rocks with very tiny or poorly connected pors that make flow through them very difficult, i.e., the permeability is very low. The mixed finite element method (MFEM), which is locally conservative, is suitable to simulate the flow in porous media. This paper is devoted to developing a mixed finite element (MFE) technique to simulate the gas transport in low permeability reservoirs. The mathematical model, which describes gas transport in low permeability formations, contains slippage effect, as well as adsorption and diffusion mechanisms. The apparent permeability is employed to represent the slippage effect in low-permeability formations. The gas adsorption on the pore surface has been described by Langmuir isotherm model, while the Peng-Robinson equation of state is used in the thermodynamic calculations. Important compatibility conditions must hold to guarantee the stability of the mixed method by adding additional constraints to the numerical discretization. The stability conditions of the MFE scheme has been provided. A theorem and three lemmas on the stability analysis of the mixed finite element method (MFEM) have been established and proven. A semi-implicit scheme is developed to solve the governing equations. Numerical experiments are carried out under various values of the physical parameters.
Highlights
Natural gas was formed in tight formations over millions of years, when organic material was buried under high heat and pressure and slowly converted to natural gas
Due to the gas slippage effect, the permeability of a sample to a gas varies with the molecular weight of the gas and the applied pressure, which was first proposed by Klinkenberg [1], i.e., the so-called
Some preliminaries have presented about the finite element spaces that used in the mixed finite element method (MFEM) analysis
Summary
Natural gas was formed in tight formations over millions of years, when organic material was buried under high heat and pressure and slowly converted to natural gas. Energies 2018, 11, 208 analyzing steady-state and transient gas flow through porous media including Klinkenberg effects Other popular approaches such as those by Pazos et al [5], and Esmaili and Mohaghegh [6] consider the determination of the shale gas permeability. Shabro et al [10] have presented numerical simulation of shale-gas production including pore-scale modeling of slip-flow, Knudsen diffusion, and Langmuir desorption and reservoir modeling of compressible fluid. El-Amin et al [18,19] have presented analytical solutions using the power-series method for the apparent permeability and fractional derivative gas-transport equation in porous media. This paper presents a model to simulate the transport of gas in tight permeability formations considering slippage, adsorption, and diffusion effects.
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