Page 287 - gas transport in porous media

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Table 16.1. Description of input variables and base case values for these parameters
Base case values Definitions Units Rossabi
k r = 1.00E-12 Radial permeability m 2
µ g = 1.83E-5 Viscosity kg/m sec
ϕ = 0.35 Porosity unitless
S g = 0.25 Gas phase saturation unitless
P avg = 100000 Average pressure Pa
r w = 0.0254 Well radius m
b = 10 Zone thickness m
S wb = P diff = 100 Pressure differential Pa

Table 16.2. Sensitivity analysis of factors affecting flow through well
Sensitivity analysis
Radial permeability Pressure differential Zone thickness
2
k r (m ) Q(cfm) Variance(%) P diff (Pa) Q(cfm) Var. (%) b(m) Q(cfm) Var. (%)
1E-13 0.015 88% 50 0.059 50% 1 0.012 90%
5E-13 0.063 47% 100 0.118 0% 2 0.024 80%
1E-12 0.118 0% 200 0.237 100% 5 0.059 50%
5E-12 0.523 342% 300 0.355 200% 10 0.118 0%
1E-11 0.997 742% 400 0.473 300% 20 0.237 100%
5E-11 4.489 3693% 500 0.592 400% 30 0.355 200%
1E-10 8.610 7174% 600 0.710 500%
700 0.829 600%

Porosity Gas phase saturation Average pressure Well radius
ϕ Q(cfm) Var.(%) S g Q(cfm) Var.(%) P avg (kPa) Q(cfm) Var.(%) r w (cm) Q(cfm) Var.(%)

0.25 0.115 3% 0.1 0.110 7% 98.5 0.119 0.12% 1.25 0.106 10%
0.30 0.117 1% 0.2 0.116 2% 99.0 0.118 0.08% 2.54 0.118 0%
0.35 0.118 0% 0.3 0.120 2% 99.5 0.118 0.04% 3.79 0.127 7%
0.40 0.120 1% 0.4 0.123 4% 100.0 0.118 0% 5.08 0.133 13%
0.45 0.121 2% 0.5 0.125 6% 100.5 0.118 0.04%
0.50 0.122 3% 0.6 0.127 8% 101.0 0.118 0.08%
0.55 0.123 4% 0.7 0.129 9% 101.5 0.118 0.12%
0.8 0.131 10% 102.0 0.118 0.16%

permeability are the most important factors in determining the flow. If differential
pressure is known (either by field measurements or by using one of the analytical
solutions to pressure and surface pressure data), and permeability is known, and as
long as estimates of the other parameters are reasonable, the flow through the well can
be predicted accurately. It is important to remember that in this derivation, the radial
permeability is assumed to have a single value and is independent of changes that