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Coordinate System
Finite Difference Method
Gas Flow
Natural Gas
Numerical Solution
Porous Media
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Applicability of the Linearized Governing Equation of Gas Flow in Porous Media
Applicability of the Linearized Governing Equation of Gas Flow in Porous Media,10.1007/s1124201197202,Transport in Porous Media,Jian Li,Hongbin Zha
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Applicability of the Linearized Governing Equation of Gas Flow in Porous Media
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Jian Li
,
Hongbin Zhan
,
Guanhua Huang
In order to make the nonlinear
gas flow
Equation tractable, the linearization treatment has been commonly applied in many subsurface
gas flow
problems such as
natural gas
production, soil vapor extraction, barometric, and pneumatic pumping. In this study, the accuracies of two representative linearization methods denoted as the conventional and the Wu solutions (Wu et al. Transp.
Porous Media
32(1):117–137, 1998), are investigated quantitatively based on a numerical solution. The conventional solution uses a linearized constant gas diffusivity, while the Wu solution employs a spatially averaged but timedependent gas diffusivity. The
numerical solution
is obtained by implementing the stiff solver ODE15s in MATLAB to deal with the time derivative and using the finitedifference method to approximate the spatial derivative in the nonlinear
gas flow
equation. Two scenarios, the onedimensional
gas flow
with constant pressure difference between two boundaries and the onedimensional radial
gas flow
with constant mass injection rate at the origin of the coordinate system, are considered. The percentage error, defined as the ratio of difference between the
numerical solution
and the linearization solution to the ambient pressure, is calculated. It is founded that the Wu solution generally provides more accurate pressure evaluation than the conventional solution. The conventional solution always underestimates the pressure, while the Wu solution generally underestimates the pressure near the higher pressure boundary and overestimates the pressure near the lower pressure boundary. The maximal percentage error of the conventional solution is insensitive to time. This observation can be explained through the property of the complementary error function involved in the convention solution. For the onedimensional flow example, the maximal percentage error of the conventional solution is 1.7, 25.5, and 90% when the pressure at one boundary suddenly rises above the ambient pressure by 50, 200, and 400%, respectively. While for the same example, the maximal percentage error of the Wu solution is 1.1, 14, and 44%, respectively.
Journal:
Transport in Porous Media  TRANS POROUS MEDIA
, vol. 87, no. 3, pp. 815834, 2011
DOI:
10.1007/s1124201197202
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