Calculation analysis of sustained casing pressure in gas wells
Calculation analysis of sustained casing pressure in gas wells
Zhu Hongjun 1
Lin Yuanhua 1
Zeng Dezhi 0
Zhang Deping 0
Wang Feng 0
0 Jilin Field Company , PetroChina, Songyuan, Jilin 138000 , China
1 State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University , Chengdu, Sichuan 610500 , China
Sustained casing pressure (SCP) in gas wells brings a serious threat to worker safety and environmental protection. According to geological conditions, wellbore structure and cement data of gas wells in the Sichuan-Chongqing region, China, the position, time, environmental condition and the value of SCP have been analyzed. On this basis, the shape of the pressure bleed-down plot and pressure buildup plot were diagnosed and the mechanism of SCP has been claried. Based on generalized annular Darcy percolation theory and gas-liquid two-phase uid dynamics theory, a coupled mathematical model of gas migration in a cemented annulus with a mud column above the cement has been developed. The volume of gas migrated in the annulus and the value of SCP changing with time in a gas well in Sichuan have been calculated by this model. Calculation results coincided well with the actual eld data, which provide some reference for the following security evaluation and solution measures of SCP.
Sustained casing pressure; gas migration; coupled mathematic model; gas well
After well completion, pressure in all of the casing strings
should be zero if the well is owing at steady state conditions,
but due to initial thermal expansion effects a small volume of
uids has to be bled through a needle valve in order for the
casing pressure to fall to atmospheric pressure
et al, 1999)
. If the casing pressure builds up when the needle
valve is closed, the casing is said to exhibit sustained casing
Well cement problems such as small cracks or channels
can result in gas migration and lead to SCP at casing heads
(Dusseault et al, 2000; Kinik and Wojtanowicz, 2011)
some cases, the casing pressure can reach dangerously high
values. SCP in acid gas wells brings a serious threat to worker
safety and environmental protection. Therefore, we need
to better understand the reason for gas migration and the
mechanism of SCP.
11,498 casing strings in 8,122 wells in the Gulf of
Mexico (GOM) have been reported with SCP
et al, 1998)
. Studies funded by the MMS (US Minerals
Management Service) have been done by some investigators
(Wojtanowicz et al, 2001; Xu, 2002; Xu and Wojtanowicz,
. Based on previous research, MMS regulations
(30 CFR 250.517) require elimination of SCP and grant
departures permitting operation of wells with small SCP
problems. However, wells with approved departure must be
frequently tested in order to monitor and control the severity
of SCP. These tests include pressure bleed-down and pressure
The diagnostic test calls for bleeding the pressure to
zero through a 0.5-in needle valve and recording the casing
pressure. Then the value of initial pressure bled down during
the test can be obtained from the recorded data. Recorded
pressures from other annuli would indicate whether there
is communication between different casings in the well.
However, no analytical method has been developed for
quantitatively analyzing these tests. The needle valve is
closed to initiate pressure buildup and the pressure recorded
for 24 hours. The rate of pressure buildup could provide
additional information about the size and possibly the location
of the leak. But there is still no method for interpreting the
test. Furthermore, testing of SCP is mostly qualitative and
limited to arbitrary criteria. Such information is insuf cient
for operators to quantitatively analyze SCP problems. Thus
there is a need for improved analysis that could provide more
The work presented here focuses on the mechanism of
SCP and a coupled mathematical model of gas migration in
a cemented annulus with a mud column in a gas well, which
provide some reference for the following security evaluation
and solution measures of SCP.
2 Field data analysis
SCP is a universal problem occurred in gas wells in
China. The field data are casing pressure records provided
by various operators from 13 gas wells, which mainly come
from the Longgang, Luojiazhai, Puguang, Zhongba and Moxi
gas elds in Sichuan-Chongqing region in China.
2.1 Statistical analysis of SCP data
Of the 13 gas wells, 12 show SCP problems (shown in
Table 1) and all the production casing strings exhibit SCP.
The percentage of SCP presenting in intermediate casing
strings, surface casing strings and conductor casing strings
are 90%, 83.3% and 7.7%, respectively.
Fig. 1 shows the frequency of SCP for different casings.
Production casings and intermediate casings present more
serious SCP. Fifty percent of the production casings and 56
percent of the intermediate casings have SCP of less than 10
MPa. And 80 percent of the surface casings have SCP of less
than 5 MPa. The SCP magnitude in conductor strings is the
lowest, all have SCP of less than 5 MPa.
For instance, the productive reservoir of A gas field is
in the Feixianguan Formation. After well completion, the
gas production rate of the A1 well reached 114×104 m3/d.
However, the casing pressure in the production casing string
is 43.5 MPa, which indicates serious gas migration in the
annulus. The location of the mud surface in the annulus is at
a depth about 200 m. The possible reasons leading to SCP
are a poor cementing job, pressure fluctuation, and tubing
leak. In some cases, the tubing leak even presents above the
mud surface. The production casing pressure in the A2 well
is 23 MPa, and the intermediate casing pressure is 8.4 MPa.
Intermediate casing pressure in the A3 well is 12 MPa. A
major cause of the SCP problem in the two wells, besides
poor quality of cement, is casing leakage.
Notes: Y-SCP problem; N-no SCP problem; NA-data not available.
Production casing Intermediate casing Surface casing
2.2 SCP typical patterns
Five typical response patterns
(Xu, 2002; Milanovic and
could be concluded from the eld data of 13 gas
wells, which include two SCP bleed-down patterns and three
SCP buildup patterns:
Instant bleed-down pattern
Long bleed-down pattern
Normal buildup pattern
S-shape buildup pattern
Incomplete buildup pattern
The bleed-down pattern depends on the opening of the
needle valve controlled by operators and the amount of uids
bled from the casing annulus. If the needle valve is opened
wide to bleed a small amount of gas and liquid from the
casing annulus, the casing pressure would drop to 0 in a very
short time, named as instant bleed-down pattern. On the other
hand, if operators manipulate the needle valve to minimize
the removal of fluids, the duration of bleed-down would be
prolonged by the operation, so the casing pressure may not
decrease to 0 over the duration of the bleed-down test. It is
the other pattern, the long bleed-down pattern. The two
bleeddown patterns are shown in Figs. 2 and 3.
Removed 0.15 m3
1.21 g/cm3 fluid
As shown in Figs. 4, 5 and 6, we can see three buildup
patterns, which depend on operating conditions such as the
magnitude of gas migration, the duration of bleed-down,
and the mud weight. After the bleed-down, a normal buildup
pattern is observed when a quick initial pressure increase
is followed with a transition period of gradual increase
until it comes to pressure stabilization. The stabilized
casing pressure depends on the mud weight and gas-source
formation pressure. The transition period is determined by the
magnitude of gas migration in the cement and mud column.
If there is almost no gas left in the mud column after
bleeddown, there would be no obvious increase in the casing
pressure until the rst pulse of gas reaches the casing head.
Then the casing pressure will increase gradually and nally
stabilize. This is the S-shape buildup pattern. An incomplete
buildup pattern is noted where no late-time stabilization is
apparent in the testing interval (usually 24 hours) and the
initial casing pressure increase in the early time is relatively
Fig. 4 Normal buildup pattern
Gas wells are composed of many layers of casing strings,
which constitute several annuli. According to the location, the
annulus from inside to outside can be named “A” annulus, “B”
annulus, “C” annulus, and so forth
(Anders et al, 2006)
shown in Fig. 7, “A” annulus represents the annulus between
the tube and production casing. “B” annulus represents the
annulus between production casing and adjacent intermediate
casing. The rest can be obtained by analogy.
As shown in Fig. 8, two possible configurations of the
cement column in the annulus are common: cemented to the
surface or a mud column above the cement. A gas cap may
be present above the mud column. In wells cemented to the
surface, gas migration can be considered as a one-dimensional
flow through a medium of some conductivity
. After bleed-down, the buildup behavior is controlled
by cement properties, such as permeability and porosity, and
by the gas formation pressure. While in wells with a mud
Fig. 11 Possible faults leading to SCP in the B or C annulus
Corrosion leak Connector leak
where p is the pressure in the cement, MPa; z is the distance
from the gas-source formation, m; t is time, s; k is the cement
permeability, m2; Lc is the length of the cement column,
m; g is the gas viscosity, Pa·s; is the cement porosity,
dimensionless; and cg is the gas compressibility; Pa-1.
The boundary and initial conditions may be stated as
a) p=pc at t=0 for z (0<z<Lc)
b) p=pf at z=0 for all t
c) g g for t>0
z z Lc kA
where pc is the pressure on the top of the cement, MPa; pf is
the reservoir pressure, MPa; qg is the gas ow rate, m 3/s; and
A is the wellbore area, m .
4.2 Gas migration in the stagnant mud
Gas migration in the stagnant mud can be modeled as
dispersed two-phase flow that can be described by a
(Xu and Wojtanowicz, 2003)
. Basic assumptions
are a concentric annulus, equal phase pressure, uniform phase
pressure in the cement can be obtained as:
if p 15MPa and z Lc
15MPa and z Lc
densities normal to the ow direction, constant temperature
pro le, and thermodynamic equilibrium. Due to slow phase
segregation after the bleed-down, it is assumed that the
relative velocity term is negligible. Under the assumptions,
the one-dimensional two-equation drift-flux model is
summarized in the following
(Santos and Azar, 1997; Xu,
Continuity equations for the continuous (mud) and the
dispersed phase (gas) are:
where is the void fraction; g and L are the gas and liquid
density, kg/m3; and vg and vL are the gas and liquid velocity,
And mixture momentum equation is:
qL ) / A
where m and vm are the mixture density (kg/m3) and
velocity (m/s), respectively; f is the friction factor; C0 is the
distribution factor; dh is the hydraulic diameter of the annulus,
m; di and do are the diameter of the inner string and the outer
string, respectively, m; vs is the gas slip velocity, m/s; vsg and
vsL are the supercial velocity of gas and liquid, respectively,
m/s; and qL is the liquid ow rate, m 3/s.
In order to complete the model, the slip velocity (vs) and
the fluid fraction factor (f) must be algebraically specified.
Based on analysis of the SCP field data, it can be safely
assumed that the ow pattern in annulus is either bubble or
slug ow. According to the Hasan and Kabir method
and Kabir, 1993)
, the value of the distribution factor C0 for
bubble ow can be described as:
where m is the mixture viscosity, m/s; and Rem is the
Reynolds number of two-phase ow.
The mixture viscosity for two-phase ow is:
where L is the mud viscosity, Pa·s; L is the liquid holdup,
dimensionless; and Ag and AL are the ow areas occupied by
gas and liquid respectively, m .
For turbulent ow (Reynolds number is usually less than
105 due to the high viscosity of mud), the friction factor is:
Obtaining an analytical solution is generally not possible
for most practical problems in two-phase flow. Numerical
methods based on finite-difference concepts provide
an alternate and powerful solution approach. The three
equations, (3), (4) and (5) have been solved using the nite
difference method with computational cells shown in Fig. 13,
the semi-implicit pattern of which is as follows
) L i
) L i 1/2 (vL )in 11/2
) L i
) L i 1/2 (vL )in 11/2
n n 1
g )i 1/2 (vg )i 1/2
n n 1
g )i 1/2 (vg )i 1/2
4.3 Gas unloading and accumulation at the wellhead
At the wellhead, gas is released from the top when the
needle valve is open. While in SCP buildup, gas accumulates
at the top with the closed needle valve. Thus, two different
upper boundary conditions are considered.
Gas or gas-liquid flowing through the needle valve to
the atmosphere can be considered as single-phase gas or
multiphase flow through a choke
bleed-down, gas usually ows at choked velocity and its ow
rate is easy to record. If the gas ow rate cannot be measured
directly, it can be computed from the following iterative
a) Initial guess that the critical pressure ratio yc*=0.5,
then calculate the pressure ratio y=p2/p1, where p2 is the
downstream pressure (atmospheric pressure), and p1 is the
b) If y<yc*, critical ow exists. Calculate the gas ow rate
using the following equation
where dch is the diameter of the choke, m; and qLm is the
liquid ow rate (m 3/s) which can be calculated by the volume
of liquid collected and the bleed-down time recorded in SCP
If not, sub-critical ow exists. The gas ow rate is:
where m1 is the mixture density at p1, kg/m3.
c) Calculate the gas/liquid ratio R1
(Ashford and Pierce,
and yc, which is obtained from the following equation.
where is the ratio of specic heats, dimensionless.
Then set yc*= yc.
d) Repeat step b) to c) until there is no change in the ow
The gas chamber in the wellhead is treated separately
from all other cells, which are completely filled with gas.
When the needle valve is closed, it does not lose gas to any
other cell but receives gas from the cell immediately below
it. The volume of this gas chamber changes with time, at n+1
time step, which is related to the n-th step volume
in the following manner:
where N is the number of equal-size cells in the well; Vwh is
the volume of gas chamber, m3; Vg and VL are the volumes of
gas and liquid respectively, m3; and qgm is the gas flow rate
from the choke, m3/s.
The second term on the right side of the equation is the
volume of gas accumulated in the remaining mud column.
The following term is the volume increase caused by
increased liquid column pressure during this time step. The
second to last term is the volume reduction due to gas ow
from the cement below the liquid column. The last term
indicates the increased volume caused by gas ow out from
the annulus during the bleed-down, which is zero during
casing pressure buildup.
The wellhead pressure at n+1 time step is:
pwnh n'n 1Vwnh Z n 1
n'nVwnh 1Z n
where pwh is the wellhead pressure, MPa; Z is gas-law
deviation factor, and n is the moles of gas.
Once the volume of the gas chamber is estimated by Eq.
(24), the wellhead pressure can be calculated from Eq. (25).
This step, in turn, allows calculation of interface pressure
from the wellhead pressure from Eq. (20).
4.4 Coupled gas ows in cement and mud
The most important problem for coupling gas flow in
the cement and the mud is calculating the interface pressure.
The calculation procedure is iterative, which involves a
simultaneous solution of the mass and momentum equations
for pressure and velocity in all cells in the mud column except
for the gas chamber.
The coupling procedure is shown in Fig. 14 (Xu and
244.5 mm intermediate casing was bled for 12 minutes before
the needle valve was closed and the following casing buildup
measurement lasted 24 hours. As shown from Fig. 16, the
calculation result coincides well with the actual data, which
presents a long bleed-down and normal buildup pattern.
Five patterns of SCP bleed-down and buildup were
summarized from the field data. The possible mechanisms
leading to SCP have been analyzed, which include thermal
expansion, tubular mechanical failures, and gas migration.
Then possible reasons for SCP in different annulus have also
been indicated. On this basis, a coupled mathematical model
of gas migration in a cemented annulus with a mud column
has been developed based on annular percolation and
gasliquid two-phase flow theories. Finally, the mathematical
model was verified with selected data from one actual gas
Research work was co-financed by the China National
Natural Science Foundation and Shanghai Baosteel Group
Corporation (No. 51074135), Program for New Century
Excellent Talents in University (No. NCET-08-0907) and
Jilin Oilfield Company Project (No. JS10-W-14-JZ-32-51).
Without their support, this work would not have been
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