Prediction of sustained annular pressure for high pressure gas well

PETROLEUM EXPLORATION AND DEVELOPMENT Volume 42, Issue 4, August 2015

Online English edition of the Chinese language journal

Received date: 25 Nov. 2014; Revised date: 02 Jun. 2015. * Corresponding author. E-mail: guanzhch@https://www.sodocs.net/doc/d69179436.html,

Foundation item: Supported by the National Science and Technology Major Project (2011ZX05021-001); The Yangtze River Scholars and Innovation Team of Ministry of Education (IRT1086).

plastic and thermophysical properties of casings and cement stones. In addition, micro-fractures would also occur when the external load caused by operations (such as perforation) exceeds the strength of cement mantle.

(2) Effect of formation conditions. Poor formation condi-tions can lead to irregular wellbores, and in turn uneven dis-tribution of drilling mud; most hi-pressure gas reservoirs have complex pressure systems and big temperature difference between reservoir top and bottom, which could cause su-per-retarding of cement slurry in some well sections, and wa-ter loss and shrinkage of cement in other sections.

(3) Effect of annular fluid distribution. Long cement slurry column may lead to weight loss of the column in the process of solidification, and in turn occurrence of micro-fractures after solidification; if the cement slurry is contaminated by drilling mud due to low displacement efficiency, the quality of cement mantle will be affected; if the formation acid fluid invades into cement mantle, some particles of cement stone will be corroded.

According to random fracture theory[8], micro-fractures in cement mantle could connect into pathways for gas channel-ing. The gas channeling pathways can be divided into three kinds according to their structural form and distribution, per-forative microannulus, reticular fractures and combination of fractures and microannulus as shown in Fig. 1. The low den-sity and viscosity confer natural gas stronger pervasion ability, making gas easier to seep in fractures and reach the top of annulus, and resulting in sustained annular pressure.

2. Calculation model of sustained annular pressure

2.1. Calculation method of pressure in confined annulus containing liquid

The annular pressure caused by gas channeling depends on

Fig. 1. Sketch map of gas channeling pathways. the state and distribution of gas in annulus. One part of the gas

dissolves in the annular liquid while the other gathers at the

top of annulus and finally forms a gas column. According

to mass conservation law, the sum of the two parts equals to

the total gas entering into annulus through channeling path-

ways, which can be expressed as:

4

s l gan g

10R AH V V

?+= (1) Based on volume compatibility principle, the total annular

volume equals to the sum of gas column volume and liquid

column volume. Taking state equation of actual gas and the

compressibility of annular liquid into consideration, an equa-

tion can be got as following:

()

l

gan an an a4

an T an

an a a

101

V T Z p

AH p K V

p Z T

?

+?= (2)

Previous research[9] indicates that gas solubility R s in Equa-

tion (1) rises with the increase of annular pressure, and is im-

pacted by liquid density, salinity and solid content, so gas

solubility is usually tested through experiment. After R s is

obtained, the annular pressure can be acquired by solving the

equation group of Equations (1) and (2).

2.2. Analysis of gas seepage process

The micro-annulus has high permeability but low storage

ability while cement stone has low permeability and low

storage ability, and they form gas channeling pathways to-

gether. Since the cement stone has no big absorption and

conductivity for gas, cement mantle containing channeling

pathways is not a double porosity medium. According to the

above analysis, the gas channeling process can be regarded as

linear seepage, in which comprehensive permeability is used

to express the transport ability of cementing mantle, so gas

channeling process can be illustrated as the following equa-

tion:

()

e

C p

p p p p

x Z x K Z t

φμ

μμ

??

???

=

??

???

??

(3)

It can be seen that annular pressure changes with time, so

gas channeling is a one-dimensional unsteady seepage process. Consequently, Equation (3) becomes a second order nonlinear

partial differential equation, which doesn’t have an exact so-

lution. However the annular pressure can be regarded as un-

changed in a very short time t a, then the unsteady seepage

process becomes steady. So we can calculate the total gas

volume through superposition of the gas in every short time t a.

The solving method of steady seepage is given in reference

[10], and the solution is:

2

l

2

5e a a

e an1

an a

10

2

j j

K A T Z

Q p p p

L T Z p

μ

??

?

??

?

??

??

=?+

??

??

(4)

The total gas volume invading into the annulus is:

g a

1

m

j

j

V Q t

=

=∑ (5) The comprehensive permeability in Equations (3) and (4) is

the superposition of cement stone permeability and mi-

cro-fracture permeability. Theoretically the permeability of

micro-fractures can be calculated by smooth plate model and cubic law [11], however the parameters used in these two methods can hardly be obtained and the actual fracture is not smooth, so these two methods are impossible to use. Here we give a method by using the data of annular pressure at the early stage to obtain the comprehensive permeability:

(1) Record the time interval between pressure p an and p an +1 as t 1;

(2) Release the annular gas to reduce the pressure from p an +1 to p an again and record the gas volume as V 1;

(3) Let Q j =V 1/t 1 and p an j-1=p an +0.5, and then calculate comprehensive permeability by Equation (4).

3. Case study

A hi-pressure gas well has well depth of 4 127 m, reservoir pressure of 78.9 MPa, reservoir temperature of 137.05 °C. The natural gas produced has a viscosity of 0.035 mPa ?s, and compressibility factor of 0.89. Sustained annular pressure appeared in annulus

B between production casing and inter-mediate casing. Ultrasonic testing and theoretical derivation suggest annulus B has microannulus. The production casing and intermediate casing are 139.7 mm and 244.5 mm in di-ameter respectively. The cement top is 2 550 m and the length of annular liquid column is 1576 m. The annular liquid has an isothermal compressibility of 5.2×10?4 MPa ?1, and density of 1.62 g/cm 3. The comprehensive permeability of cement man-tle is 34.5×10?3 μm 2. The total volume of annulus is 50.20 m 3. The relationship between gas solubility R s and annular pres-sure is given by Equation (6) (The original gas solubility is 0.771 8 m 3/m 3).

242an 0.77188.769610 5.178510s an R p p ??=+×?× (6) Fig. 2 shows the change pattern of annular pressure and gas volume obtained from the model proposed in this paper. As shown in Fig. 2, the rising process of annular pressure can be divided into rapid rising stage and stable rising stage. At rapid rising stage, annular pressure and gas volume rise quickly as time goes on, and then the rising velocity declines gradually. At stable rising stage, both the rising velocity slows down, the annular pressure approximates a certain value infinitely, here we name this value maximum annular pressure. The maxi-mum annular pressure is equal to the pressure difference be-

tween reservoir pressure and annular liquid column

Fig. 2. Curves of annular pressure and gas volume with time.

pressure, so we can find where the gas comes from. In this hi-pressure gas well, the annular pressure reached 53.82 MPa 300 days after put into production, which exceeded the maximum acceptable annular pressure (42 MPa) and caused potential risk to the safety production of the well.

4. Analysis of factors influencing annular pressure and control measures

Rapid rise of annular pressure could threaten the safety of gas well production string badly [12], bringing about heavy routine maintenance and management workload. Therefore, in order to control the rapid rise of annular pressure and ensure the safety of gas well production string, it is necessary to ana-lyze various factors affecting annular pressure and work out reasonable measures for pressure control.

4.1. Gas solubility and compressibility of annular liquid and relevant control measures

Fig. 3 shows the curves of annular pressure with time at different initial gas solubilities and compressibilities. Com-pared with the baseline data (baseline data is from the case study in section 3, similarly hereinafter, with initial gas solu-bility of 0.771 8 m 3/m 3), the curve at the gas solubility of 3.0 m 3/m 3 only moves to the right a little while the change trend keeps unchanged. The rising velocity of annular pressure at the isothermal compressibility of 0.002 MPa ?1 is much lower than that at isothermal compressibility of 0, and the largest pressure difference at the same time can be as high as 26 MPa. Because the annular pressure approximates infinitely but can never reach the maximum annular pressure, 0.95 times of maximum annular pressure was taken as target pressure to calculate the required time and gas volume when pressure reached the target pressure. As shown in Fig. 4, the time and gas volume required to reach 0.95 times of maximum annular pressure have a linear relationship with isothermal compressi-bility.

It can be seen from the above analysis that the initial gas solubility of annular liquid has no impact on the rising process of annular pressure, but increasing the isothermal compressi-b i l i t y c a n e x t e n d t h e t i m e r e q u i r e d t o r e a c

h

Fig. 3. Curves of pressure with time under different initial gas solubilities and compressibilities.

Fig. 4. Curves of required time and gas volume to reach target annular pressure with the isothermal compressibility. specified pressure, in other words, the rising velocity of pres-sure becomes slower. So from the perspective of controlling the annular pressure, hi-pressure gas wells should have annu-lar liquid with high compressibility. But the isothermal com-pressibility should not be too big, otherwise the risk and dif-ficulty of gas bleed-off will increase too as the required gas volume ascends.

4.2. Effects of cement mantle parameters and relevant control measures

Fig. 5 shows the impact of cement top and comprehensive permeability on annular pressure. Comparison of the curves at different cement tops shows that the pressure rising velocity and maximum annular pressure increase as cement top as-cends. Comparison of the curves at different comprehensive permeabilities shows that the increase of permeability has a significant impact on rising process of annular pressure: the higher the permeability is, the quicker the rising velocity will be.

In order to seal the hi-pressure gas effectively, the cement in high pressure gas wells usually returns to wellhead. There-fore once the channeling pathways form in high pressure gas wells, the annular pressure produced will be much higher than the case with lower cement top. So for the wells with cement

Fig. 5. Curves of pressure with time at different cement tops and comprehensive permeability value. returning to well head, the cement quality must be taken seri-ously, and self-healing cement should be used to keep the comprehensive permeability of cement mantle at low level. After annular pressure occurs, it is necessary to repair the well or adopt chemical plugging to lower the comprehensive per-meability of the cement mantle, and thus prevent the annular pressure from rising too fast.

4.3. Effect of annular volume and relevant control measures

Annuli usually contain residue liquid left after cementing and channeling gas, so its volume has some impacts on annu-lar pressure. It can be seen from Fig. 6, the pressure with the annular volume of 52.85 m3 is smaller than the pressure with the annular volume of 49.85 m3 at the same moment. In Fig. 7, when the volume difference between annulus and annular liquid increases from 0 to 3.0 m3 (meanwhile the annular volume increases from 49.85 m3 to 52.85 m3), the time re-quired for annular pressure to reach the 0.95 times of maxi-mum annulus pressure increases in a linear trend.

The above analysis indicates that the required time can be prolonged through increasing the volume difference between annulus and annular liquid. But Fig. 7 also shows the required

gas volume increases at the same time as the volume differ- Fig. 6. Curves of pressure with time at different annular vol-

umes.

Fig. 7. Curves of required time and gas volume for annular pressure to reach target pressure with the difference between annular volume and annular liquid volume.

ence increases. Since too much gas may enhance the difficulty of bleed-off, annular volume cannot expand without limitation. To keep a balance between pressure control and pressure bleed-off, a reasonable annular volume should be determined by the following method:

(1) Working out the maximum annular pressure and gas volume acceptable for a specific well;

(2) Drawing curves like Fig. 7 with the prediction model built in section 2;

(3) Working out the volume difference according to the maximum gas volume the well allows;

(4) Finding out the rising pattern of annular pressure based on volume difference provided in step (3) to facilitate well maintenance and management.

5. Conclusions

(1) Influenced by changes in temperature and pressure, poor formation properties and fluid distribution in the well-bore, gas channeling pathways may generate in cement mantle of high pressure wells. According the structural form and dis-tribution features, channeling pathways can be classified into perforative microannulus, reticular fractures and combination of fractures and microannulus.

(2) The rising process of sustained annular pressure can be divided into rapid rising stage and stable rising stage and the maximum annular pressure equals to the pressure difference between reservoir pressure and liquid column pressure. At the rapid rising stage, the annular pressure rises quickly, posing threat to well safety.

(3) The factors affecting annular pressure include gas solu-bility and compressibility of annular liquid, cement top, com-prehensive permeability of cement mantle and annular volume. The rising velocity of annular pressure decreases as com-pressibility of annular liquid increases. The maximum annular pressure and rising velocity increase as cement top increases. The pressure rising velocity increases as the comprehensive permeability increases. The increase of annular volume can reduce pressure rising velocity.

(4) Based on the analysis of factors affecting annular pres-sure, the following measures are proposed to control sustained annular pressure: adopting proper annular liquid compressi-bility; improving cementation quality by using self-healing cement in the fully cemented gas wells; if necessary, taking some measures to reduce the cement mantle comprehensive permeability; increasing the annular volume and volume dif-ference between annulus and annular liquid reasonably.

Nomenclature

A—cross section area of cement mantle, cm2;

C(p)—isothermal gas compressibility coefficient, (105 Pa)?1;

H l—height of gas column, m;

K e—comprehensive permeability of cement mantle, μm2;

K T—isothermal compressibility of annular liquid, MPa?1;

L—length of cement mantle, cm;

m—number of iterations, dimensionless;

p—pressure, 105 Pa;

p a—gas pressure under standard conditions, MPa;

p an—annular pressure, MPa;

p e—gas reservoir pressure, MPa;

p l—annular liquid column pressure, MPa;

p an j-1—annular pressure in the iteration of (j-1)th time, MPa;

Q j—gas rate in the iteration of j, m3/s;

Rs—gas solubility of annular liquid, m3/m3;

t—time, s; t a—iteration size of time, s;

T a—gas temperature under standard conditions, K;

T an—annular temperature, K;

V an—annular volume, m3;

V gan—the volume of gas column, m3;

V g—total gas volume invading into annulus under standard condi-tions, m3;

x—coordinate along gas channeling direction, cm;

Z—gas compressibility factor, dimensionless;

Z a—gas compressibility factor under standard conditions, dimen-sionless;

Z an—gas compressibility factor in annulus, dimensionless;

Z—gas compressibility factor under average pressure difference, dimensionless;

μ—gas viscosity, mPa?s;

μ—gas viscosity under average pressure difference, mPa?s; Φ—porosity, f.

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