Perpustakaan Digital ITB

A Mathematical model for total mass flow rate per unit area and total permeability of real gas flow in fractal porous media was proposed on the basis of fractal theory. Proposed models in this paper paid attention to the influence of real gas effect on gas, taking transition regime as the coupling of slip regime and Knudsen diffusion, considering multi-flow-regime coexist, multi-flow-regime is continuum flow regime, slip flow regime, transition flow regime and Knudsen diffusion regime., pore which pore diameter is ? mass flow rate per unit area multiply corresponding pore number dN obtain mass flow rate(dq). Integrate dq within corresponding diameter range and divide fractal porous media work out corresponding flow regime the mass flow rate per unit area. The total mass flow rate per unit area was then calculated through integrating over the mass flow rate deduced, where different flow regimes have been engaged, including continuum regime, slip regime, transition regime and Knudsen diffusion. Based on the Darcy theory, the total permeability was then calculated. In order to verify correctness of model, compare proposed model to Wang's model and Fan's model. Calculate correlation coefficient of proposed model and Wang's model, R2=0.9912; Calculate correlation coefficient of proposed model and Wang's model, R2=0.9997. Indicate that proposed model can fit well with Wang's model and Fan's model, proposed model can correctly predict total permeability. And calculate correlation coefficient of D.B.Bennion experiment data and three model. In the last part, the paper analyzed the influence factor of total mass flow rate per unit area and total permeabilities and mass flow rate per unit area and permeability of different flow regimes. The concludes as follow: (1) total mass flow rate per unit area, total permeability and each flow regime mass flow rate per unit area and permeability increase with fractal dimension(Dp) increasing and tortuous fractal dimension(Dt) decreasing. Variation of Dp and Dt has different influence on each flow regime. Dp and Dt has most influence on Knudsen diffusion flow regime, least influence on continuum flow regime. (2) Real gas effect affects the mass flow rate per unit area and permeability in different flow regime by affecting the mean free path of gas molecule. Whether consider real gas effect would cause great difference, maximum difference is 232.35%. (3) Flow regime that have the lowest Knudsen number play leading role in variation of total mass flow rate and total permeability. (4) The more maximum pore diameter of fractal porous media, the more significant influence of total mass flow rate per unit area and total permeability. Maximum pore diameter has different influence on each flow regime, has most influence on Knudsen diffusion flow regime, least influence on continuum flow regime.