Production from Natural Gas Reservoirs:
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Properties of natural gas
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Correlations and calculations for natural gas
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Approximations of the gas well deliverability
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Gas well deliverability for non-Darcy flow
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Transient flow of a gas well
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Horizontal well IPR in a gas reservoir
The development of flow equations for compressible gases is more complicated than for
nearly incompressible liquids (ex.oil). In particular, the following effects are important
with the flow of gases:
 gas volumetric flowrate varies with pressure. Inertial effects, which result from the
expansion of gas caused by a reduction in pressure, are not addressed in the
incompressible liquid equations discussed earlier.
 gas viscosity is a strong function of pressure (along with temperature) which is not
included in the earlier equations. This can have a significant effect on pressure drop.
 In addition, lower gas viscosity, combined with higher volumetric flow rates, result in
higher Reynolds numbers. It is possible for the flow regime to be turbulent (not
laminar as assumed in the earlier equation) requiring a more sophisticated approach to
calculations.
Equations of State:
For an ideal gas:
PV = nRT
For a real gas we introduce the parameter, Z, which is called the compressibility factor or
gas deviation factor. This factor compensates for non-ideal behavior of a gas:
PV = ZnRT
One method of evaluating Z is to use the chart (see handout) which was specifically
developed for hydrocarbon mixtures. To use the chart, the pseudo-reduced pressure, Ppr
(=Pr), and pseudo reduced temperature Tpr (=Tr), must be evaluated based on the pseudocritical pressure and temperature of the mixture, Ppc and Tpc respectively.
Ppr = _P_
Ppc
Tpr = _T_
Tpc
As temperature increases and pressure decreases Z  1 and the mixture approaches
ideal gas behaviour.
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Given:
composition of gas: name of components and mole fraction (yi)
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Data (from handbooks):
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molecular weight (Mwi), critical temperature (Tci), critical pressure (Pci) for each
component
Calculate:
gas gravity
Pseudo critical T of gas mixture
Pseudo critical P of gas mixture
Pseudo reduced T of gas mixture:
Pseudo reduced P of gas mixture:
read Z from appropriate graph
Use PV=ZnRT
Note: T and P are absolute values
T(°R)=T(°F)+460
Gas formation volume factor
Bg  0.0283
ZT
( Pe  Pwf ) / 2
resft 3 / SCF
Gas well deliverability
Steady State:
r
141.2qB
pe  pwf 
[ln( e )  s ]
Take steady state equation for laminar flow of oil:
hk
rw
ZT
3
Replace Bg  0.0283
resft / SCF
( Pe  Pwf ) / 2
Modify for flow rate. Instead of STB/d of oil, use MSCF/d of gas (M1000)
Z and μ are found at average of Pe and Pwf
Similarly for pseudo steady state:
P 2  Pwf2 
r
1424qZ T
(ln 0.472 e  s)
kh
rw
Turbulent (non-Darcy) Dry Gas Flow from a Natural Gas Reservoir:
Turbulence in high gas flow is considered in Forchheimer (rather than Darcy) flow
equation.
Aronofsky and Jenkins solved differential eq of stabilized gas flow in porous media by
adding turbulence skin effect Dq
qMSCF / d  
kh( p 2  pwf2 )
1424 Z T [ln( rd / rw )  s  Dq ]
D: Non-Darcy coefficient
rd: Aronofsky and Jenkins effective drainage radius
rd is time dependent until rd=0.472re
Otherwise
rd
 1.5 t D
rw
where t D 
0.000264kt
ct rw2
D is in the order of 10-3
To find D
Rearrange
qMSCF / d  
kh( p 2  pwf2 )
1424 Z T [ln( rd / rw )  s  Dq ]
0.472re
1424Z T
1424Z TD 2
(ln
 s)q 
q
kh
rw
kh
On the RHS, the 1st term represents Darcy effect and
p 2  pwf2 
To the form:
the 2nd term represents non-Darcy effects.
Above equation can be plotted as a straight line
( p 2  pwf2 )
q
a
 a  bq
0.472re
1424Z T
(ln
 s)
kh
rw
Using test data plot
b
1424Z TD
kh
( p 2  pwf2 )
versus q
q
For the straight line, slope is “b” and intercept is “a”. D is found.
In the absence of field data an empirical relationship is used
6  10 5 k s0.1h
D
2
rw h perf
: gas gravity (-)
Ks: near-wellbore permeability (md)
h, hperf: net and perforated thickness (ft)
μ: gas viscosity at the flowing bottomhole pressure(cp)
Real Gas Pseudo-Pressure:
Al-Hussainy and Ramey (1966) developed a different approach for addressing non-ideal
gas behaviour, which can be applied to the steady state, transient (line source) and
pseudo-steady state equations. This approach is more accurate compared to the previous
approach which used Z in situations where there are significant changes in pressure.
The real gas pseudo-pressure is substituted for pressure squared in the flow equations to
compensate for the non-ideal gas behaviour. For example the pseudo-steady state
equation becomes:
The same approach is taken for the steady state and transient equations as shown on the
handout.
Approximations for the integral can be made for the following two cases:
pi
m( p )  2 
Low pressure:
p wf
pi2  pwf2
p
dp 
Z
Z
pi
High pressure (pi, pwf >3000 psi):
m( p )  2 
p wf
p
p
dp  2
( pi  pwf )
Z
Z
The real gas pseudo-pressure is substituted for pressure squared in the flow
equations to compensate for the non-ideal gas behavior.
For example, steady state gas2 well2 deliverability equation
qMSCF / d  
kh( p  pwf )
1424 Z T [ln( 0.472re / rw )  s  Dq ]
becomes:
qMSCF / d  
kh[m( p )  m( pwf )]
1424T [ln( 0.472re / rw )  s  Dq ]
HORIZONTAL GAS WELLS:
An approach similar to that used for vertical gas wells can be applied to horizontal gas
wells. Horizontal wells have large surface area and local gas velocities are much less
than those in vertical wells. As a result Reynold’s number are much lower.
Turbulent effects are normally negligible; therefore the Dqv term is not required. The
equations for horizontal gas wells are provided on the handout.
When the horizontal well is only partially open to flow, turbulent effects may become
significant due to the higher gas velocities.