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Multiphase Flows

# Highly Compressible Porous Media Flow near a Wellbore: Effect of Gas Acceleration

[+] Author and Article Information
Yan Jin

College of Petroleum Engineering, China University of Petroleum (Beijing), Beijing 102200, P. R. C.

Kang Ping Chen1

College of Petroleum Engineering, China University of Petroleum (Beijing), Beijing 102200, China;  School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, 85287-6106, USAk.p.chen@asu.edu

Mian Chen

College of Petroleum Engineering, China University of Petroleum (Beijing), Beijing 102200, China

1

Corresponding author.

J. Fluids Eng 134(1), 011301 (Feb 24, 2012) (6 pages) doi:10.1115/1.4005680 History: Received April 20, 2011; Revised December 01, 2011; Published February 23, 2012; Online February 24, 2012

## Abstract

A fundamental study on porous medium flow of a highly compressible gas near a wellbore is carried out. The effect of gas acceleration is assessed quantitatively. It is shown that gas acceleration induced by the converging flow introduces a quadratic drag on the flow; acceleration due to volumetric-expansion causes the pressure curve to steepen near the wellbore and the flow to become choked at high flow-rates. When the flow is choked, the pressure gradient at the wellbore wall becomes unbounded. It is also shown that for any given mass flow-rate, the well pressure predicted from the model considering acceleration effect is significantly below that calculated from the Darcy-Forchheimer model. Implications of these results to petroleum engineering are discussed.

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## Figures

Figure 1

The radial flow configuration. The wellbore radius is Rw*, and the outer boundary radius is Re*. Gas moves radially inward towards the wellbore.

Figure 2

Mach number as a function of radial distance to the wellbore. re = 1000,  σ = 10,  Y = 20, m = 3.7. The Mach number increases from 0.000185 at re = 1000 to 0.5877 for the acceleration model and to 0.4148 for the Darcy-Forchheimer model at the wellbore r = 1.

Figure 3

Variation of dimensionless mass flow-rate m with dimensionless well pressure S. re = 1000,  σ = 10,  Y = 20. The Darcy model gives significantly larger mass flow-rate. The acceleration model predicts choked flow at Sch = 0.2137, with a maximum mass flow-rate mmax = 3.7478.

Figure 4

Critical well pressure for choking versus Y for re = 1000,  σ = 10. For the same mass flow-rate, the Darcy-Forchheimer model over-predicts well pressure by nearly 100%.

Figure 5

Maximum mass flow-rate mmax versus Y for re = 1000,  σ = 10. The acceleration model and the Darcy-Forchheimer model both predict linear dependence of mmax on Y, while the Darcy model predicts a quadratic dependence.

Figure 6

Maximum mass flow-rate mmax versusthe Forchheimer parameter σ for re = 100,1000,  Y = 80. mmax is sensitive to changes in the Forchheimer parameter σ, but insensitive to changes in the outer radius re as long as re is large.

Figure 7

Critical well pressure for choking Sch versusthe Forchheimer parameter σ for re = 100,1000,  Y = 80. Sch is sensitive to changes in the Forchheimer parameter σ, but insensitive to changes in the outer radius re as long as re is large.

Figure 8

Pressure distributions as a function of radial distance to the wellbore. re = 1000,  σ = 10,  Y = 20, m = 3.7.

Figure 9

Pressure profile steepening with increasing mass flow-rate. re = 1000,  σ = 10,  Y = 20, m = 1.0, 2.0, 3.0, 3.5, 3.6, 3.7478. The flow becomes choked when m = 3.7478, and the pressure profile has a vertical tangent at the wellbore r = 1 at this choking condition.

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