Flow mechanism of Forchheimer's cubic equation in high-velocity radial gas flow through porous media. [High-velocity, high-pressure gas flow through porous media near the wellbore]
Until recently, the visco-inertial flow equation, which is an adaptation of Forchheimer's quadratic equation, has been used to describe gas flow behavior at higher flow rates and pressures. The inability of this equation, in some cases, to fully describe high-velocity, high-pressure gas flow behavior, especially around the well bore, led to the consideration of other empirical equations. In this paper, formal derivation of Forchheimer's cubic equation is made by considering the kinetic energy equation of mean flow and dimensional relations for one-dimensional, linear, incompressible fluid flow. By the addition of the cubic term, this equation is regarded as a modified Forchheimer's quadratic equation which accounts for the flow rates obtained beyond the laminar flow condition. The cubic equation spans a wide range of flow rates and regimes, i.e. Darcy type, inertial type, and turbulent. For suitable use in gas flow studies, this equation has been adapted, modified, and corrected for the gas slippage effect. The physical basis of the cubic term has been established by using boundary layer theory to explain the high-velocity, high-pressure flow behavior through a porous path. Gamma, the main parameter in the cubic term, is directly related to a characteristic, dimensionless shape factor which is significant at higher flow rates. It is inversely related to viscosity, but has no dependence on the gas slippage coefficient in the higher flow regime.
- Research Organization:
- Nigerian Agip Oil Co., Ltd.
- OSTI ID:
- 5452088
- Report Number(s):
- CONF-820927-
- Journal Information:
- Soc. Pet. Eng. AIME, Pap.; (United States), Vol. SPE 10979; Conference: 57. AIME Society of Petroleum Engineers annual technical conference and exhibition, New Orleans, LA, USA, 26 Sep 1982
- Country of Publication:
- United States
- Language:
- English
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GAS FLOW
FLOW MODELS
NATURAL GAS
INCOMPRESSIBLE FLOW
NATURAL GAS WELLS
POROUS MATERIALS
RESERVOIR ROCK
POROSITY
CALCULATION METHODS
DARCY LAW
EQUATIONS OF STATE
FLOW RATE
KINETIC ENERGY
KINETIC EQUATIONS
RESERVOIR FLUIDS
ROCK-FLUID INTERACTIONS
ENERGY
ENERGY SOURCES
EQUATIONS
FLUID FLOW
FLUIDS
FOSSIL FUELS
FUEL GAS
FUELS
GAS FUELS
GASES
MATERIALS
MATHEMATICAL MODELS
WELLS
030300* - Natural Gas- Drilling
Production
& Processing