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Journal of Natural Gas Science and Engineering 27 (2015) 686e691

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Journal of Natural Gas Science and Engineering

journal homepage: www.elsevier .com/locate/ jngse

Numerical study of the gas-fluid displacement invasion behavior in afractured carbonate reservoir

Zhengguo Zhao a, *, Xiaolin Pu a, Gui Wang a, Zhijun Li b, Liqun Chen c, Cheng Cao a

a State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan, 610500, PR Chinab State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, Sichuan, 610059, PR Chinac Research Institute of Exploration and Development, Tarim Oilfield Company, Petro China, Korla, Xinjiang, 841000, PR China

a r t i c l e i n f o

Article history:Received 5 May 2015Received in revised form31 August 2015Accepted 3 September 2015Available online 8 September 2015

Keywords:Gas reservoirFractureGas-fluid displacementCFD simulation

* Corresponding author.E-mail address: zhengguo_mcd@163.com (Z. Zhao

http://dx.doi.org/10.1016/j.jngse.2015.09.0051875-5100/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

Gas-fluid displacement (GFD) invasion occurs frequently when drilling in fractured carbonate gas res-ervoirs. GFD invasion is a type of gas cut that is difficult to discover and is not widely known. In thisstudy, the GFD invasion behavior was simulated based on the volume of fluid (VOF) method using amultidimensional two-phase flow model under different conditions and Fluent 6.3 software. The causesand process of GFD invasion were also explored. The effects of fracture width, drilling fluid viscosity andpressure difference were studied. The results show that the gas pressure increases because drilling fluidinvades the fracture. Finally, GFD invasion occurs when the gas pressure is greater than the downholepressure. A fracture width between 0.2 mm and 0.5 mm causes GFD invasion to obviously occur, and asthe width increases, GFD invasion occurs more easily. Increasing the drilling fluid viscosity can postponethe GFD invasion to some degree. A small positive pressure difference between the wellbore and thefracture causes a more obvious GFD invasion. These results are also helpful for preventing and correctingGFD invasion.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Carbonate reservoirs are important hydrocarbon resources.They hold approximately 60% of the world's oil reserves (Akbaret al., 2000; Yuan et al., 2015). Generally, carbonate reservoirshave many fractures and caves in their reservoir spaces. Thesefractures cause a series of potential safety hazards for drilling en-gineering. Gas cuts occur frequently (Zhuo et al., 2012); however,one type of gas cut, gas-fluid displacement (GFD) invasion, is noteasily discovered (Zhang, 2008; Shu et al., 2011). Moreover, thedangers associated with this gas cut are concealed, thus, difficult toavoid. Therefore, GFD invasion must be studied and remedied.

In the past, it has been generally accepted that gas cuts occurwhen the formation pressure is higher than the wellbore pressure.However, during drilling, GFD invasion occurs when the bottomhole is under a positive differential pressure condition. Studies onGFD invasion have been lacking (Sui et al., 2004). Zhang (2008)verified the existence of GFD invasion using a simulator manufac-tured with transparent organic glass in the laboratory. The

).

experimental results indicated that GFD invasion was difficult toobserve. Shu et al. (2011) studied the conditions under which GFDinvasion occurs, as well as the flowing characteristics of drillingfluid and gas when drilling a single fracture. Dupriest (2011) notedthat the wellbore pressure was controlled by the formation pres-sure when severe cases of lost circulation occurred while drilling adeep-water carbonate gas reservoir. The negative pressure differ-ence peaked at the top of the fracture. The gas gradually displacesthe drilling fluid and then invades the wellbore. Zhang et al. (2014,2015) assumed that GFD invasion occurred in the bottom hole. Agas invasion rate was assigned. The process by which GFD invasionchanged into an underbalance gas cut was studied. In all of theresearch, one key issue has not been mentioned: GFD invasionoccurs when the bottom hole is under a condition of positivepressure difference. Only by clearly understanding the reason forGFD invasion can it be prevented and remedied.

GFD invasion is a typical gaseliquid two-phase flow that is verycomplicated. Software based on computational fluid dynamics(CFD) provides an economical and effective platform for complexflow problems. Moreover, laboratory experiments can be reducedand even displaced through simulation experiments. This approachcan reduce costs and risk and can save time. The solution method

Fig. 1. 3D model of wellbore-fracture.

Z. Zhao et al. / Journal of Natural Gas Science and Engineering 27 (2015) 686e691 687

for CFD models is to subdivide the model into a large number ofcontrol volumes. Then, partial differential equations are convertedinto algebraic equivalents and integrated over control-volumes. Thefield distributions of dependent variables can be obtained bysolving algebraic equations through iterative methods based on theboundary conditions, such as velocity and pressure distributions(Zambrano Meza et al., 2014). Fluent software, which is based onCFD, is widely used in the simulation of gaseliquid two-phase flows(Gruber et al., 2014; Saad et al., 2014; Lu et al., 2008).

In this study, a numerical simulation is performed using theFluent 6.3 software. The 3D geometry model and the fluid modelare established. GFD invasion behavior is investigated based on thevolume fraction equation and the momentum equation. Based onthe simulations, the causes and process of GFD invasion areobserved. The effects of fracture width, drilling fluid viscosity andpressure difference on GFD invasion are also discussed. The simu-lation is useful for increasing the knowledge and comprehension ofGFD invasion.

2. Basic equations

Selecting the appropriate multiphase flow model is veryimportant for the simulation results. In this study, the VOFmodel isselected. The flow characteristics and interface position could beprecisely calculated (Hirt and Nichols, 1981). In the VOF model,phases are completely independent, and there is no interpenetra-tion between them. The sum of the volume fraction for each phaseis 1 in every control-volume. Therefore, if the volume fraction of theq phase is denoted by aq, then aq ¼ 0 represents a case in whichthere is no q phase in the control-volume; aq ¼ 1 indicates that thecell is filled with q; and 0<aq <1 indicates that the q phase and oneor more of the other phases are contained in the control-volume.

2.1. The volume fraction equation

In the VOF model, the interface trace between phases is ob-tained by solving the continuity equation. For the q phase, thisequation is as follows:

vaqvt

þ vq,aq ¼ 0 (1)

where aq and vq are the volume fraction and the velocity of the qphase, respectively. The volume fraction of the q phase is calculatedbased on the following constraint:

Xn

q¼1

aq ¼ 1 (2)

2.2. Properties

The properties appearing in the transport equation are deter-mined by the phases that exist in the control-volume. In a two-phase system, the phases are distinguished by subscripts 1 and 2.If the volume fraction of the second phase is tracked, then thedensity of each cell is given by the following formula:

r ¼ a2r2 þ ð1� a2Þr1 (3)

Generally, for a systemwith n phases, the average density of thecontrol-volume is given by the following equation:

r ¼X

anrn (4)

Other properties, such as viscosity, are calculated in the samemanner.

2.3. Momentum equation

The single momentum equation for the entire area is firstsolved. The velocity field, which is derived as a result of the mo-mentum equation, is then shared by every phase. The momentumequation is as follows:

vðr v!Þvt

þ V,ðr v! v!Þ ¼ �VP þ V,hm�V v!þ V v!T

�iþ r g!þ F

!

(5)

where F!

is a continuum surface force and m is the viscosity ofthe mixture.

3. Model

There are many fractures and caves in carbonate reservoirs thatprovide large storage spaces for gas and oil. In the process ofgeological evolution, they could be filled with minerals or damagedby tectonic movement. The fracture connectivity might degenerate,and isolated fractures may appear (Chen et al., 2002; Xu, 2010).When drilling into these fractures, there is an increasing risk forGFD invasion.

In this study, we assume that one fracture with definite space isdrilled. Then, five 3D wellbore-fracture models with differentfracture widths are established and meshed by the structured gridgeneration method in Gambit 2.4.6. One of the models is shown inFig. 1. Their geometric parameters are shown in Table 1. The detailsof the computational domain are shown in Table 2.

In Fig.1, the original point of themodel is located at the center ofthe wellbore bottom. The cuboid on the right side of the fracture isused to represent an extension of the fracture and shows that it stillhas some space. The upper end face of the wellbore is set as thepressure inlet boundary, and the rest are set as wall boundaries.

In Table 1, “Length of Fracture” refers to the length between thewellbore and the cuboid. “Equivalent Length of Fracture” is the sumof two parts; one is the Length of Fracture, and the other is obtainedby converting the cuboid to a fracture with the same volume.

The simulations are operated using different models withdifferent fluids and inlet pressures. The phenomenon of GFD in-vasion could be observed. Before running a simulation, the well-bore is filled with the liquid phase, and the fracture is filled withgas. The input parameters are shown in Table 3.

Table 1Geometric parameters of the model.

Parameter Value (mm) Parameter Value (mm)

Outside diameter of wellbore 216 Length of fracture 1000Inside diameter of wellbore 127 Height of fracture 800Height of wellbore 1000 Width of fracture 0.2e2Size of the cuboid on the right side of the model 80 � 80 � 800 Equivalent length of fracture 33,000e3300

Table 2Details of computational domain.

Model Fracture width (mm) Total cells Minimum mesh size (mm)

1 0.2 146,760 0.052 0.4 141,360 0.13 0.6 121,360 0.154 1 129,040 0.255 2 112,040 0.5

Z. Zhao et al. / Journal of Natural Gas Science and Engineering 27 (2015) 686e691688

4. Results and discussion

4.1. Process of gas-fluid displacement invasion

The result of example number 5 is used to show the process ofGFD invasion, which is illustrated in Fig. 2. During simulation, thespread range of GFD invasion is only near the joint of the fractureand wellbore. Thus, to clearly show GFD invasion, only a portion ofthe wellbore is shown. The blue (in web version) area representsthe liquid phase, and the red (in web version) area represents thegas phase.

Fig. 2 shows that the drilling fluid quickly invades and occupiesthe fracture. At the top of the fracture, gas gradually enters thewellbore. The gas has already invaded the wellbore by 1.6 s, whichis shown in Fig. 2(c). In Fig. 2(d), the discontinuous gas can beobserved in the wellbore.

The pressures at point (84, 795, 0), which is in the wellbore, andpoint (280, 795, 0), which is in the fracture, are recorded. Thepressure curves are shown in Fig. 3. The straight line represents thehydrostatic pressure curve at point (84, 795, 0).

Fig. 3 shows that the pressure in the fracture increases rapidlyand exceeds the pressure in the wellbore. The pressure differenceincreases continuously to a maximum until the gas invades thewellbore. The pressure in the fracture decreases and then it in-creases again as the drilling fluid enters the fracture with a sus-tained flow. This process repeats endlessly. GFD invasion alsooccurs intermittently with pressure fluctuations in the fracture.This behavior agrees with the phenomenon observed in Fig. 2(d).

Table 3Input parameters of the simulation.

Examplenumber

Fluid viscosity(mPa s)

Fluid density(kg/m3)

Gas viscosity(mPa s)

1 1 1000 0.010872 18 1200 0.010873 26 1200 0.010874 34 1200 0.010875 42 1200 0.010876 50 1200 0.010877 66 1200 0.010878 34 1200 0.010879 34 1200 0.0108710 34 1200 0.0108711 34 1200 0.0108712 34 1200 0.0108713 34 1200 0.0108714 34 1200 0.0108715 34 1200 0.01087

Based on the simulation, when the bottom hole is under thecondition of a positive pressure difference, drilling fluid invades thefracture and occupies its space. The pressure in the fracture thenincreases. At the top of the interface between the fracture and thewellbore, the gas pressure initially equals the wellbore pressure.Then, the hydrostatic pressure of the drilling fluid, which corre-sponds to the vertical height of the fracture, causes the continuousinvasion of the drilling fluid. Finally, the gas pressure exceeds thewellbore pressure, and the gas invades the wellbore; this is the GFDinvasion process. As the gas invades the wellbore, the pressure inthe fracture is reduced briefly. Then, it increases again with thecontinuously invading drilling fluid; this process is cyclical.

4.2. Factors affecting the gas-fluid displacement invasion

According to the previous analysis, the drilling fluid invades thefracture and increases the gas pressure, which results in GFD in-vasion. Therefore, the invading speed of the drilling fluid affects theGFD invasion. The invading speed is influenced by the fractureshape, drilling fluid properties and pressure in the bottom hole.Thus, it was necessary to analyze these factors to better understandGFD invasion.

4.2.1. Effect of fracture widthThere are many fractures in a carbonate formation, and the

range of fracture widths changes with size. Morita et al. (1990)noted that drilling fluid could be lost into the formation when thefracture width reaches 0.01 inches (approximately 0.254 mm). Thesolid phase in the drilling fluid could plug microfractures andprevent drilling fluid loss. Thus, simulations were preformed usingdifferent models in which the fracture widths were 0.2 mm,0.4 mm, 0.6 mm, 1 mm, and 2 mm. The time required by GFD in-vasion from the beginning of the calculation is shown in Fig. 4.

Fig. 4 shows that the required time for GFD invasion decreasesexponentially with increasing width. The required time is 22.84 swhen the fracture width is 0.2 mm, which is approximately 18times higher than that at a fracture width of 0.6 mm. This findingindicates that the fracture width has a great effect on GFD invasion.

Inlet pressure(MPa)

Initial pressure in fracture(MPa)

Fracture width(mm)

36.6 36 0.636.6 36 0.636.6 36 0.636.6 36 0.636.6 36 0.636.6 36 0.636.6 36 0.636.1 36 0.636.3 36 0.637 36 0.637.5 36 0.636.6 36 0.236.6 36 0.436.6 36 136.6 36 2

Fig. 2. Gas-fluid flow regime at different time.

Z. Zhao et al. / Journal of Natural Gas Science and Engineering 27 (2015) 686e691 689

The flow resistance of the drilling fluid in the fracture increaseswith decreasing width. Thus, in a narrow fracture, more time isrequired to increase the gas pressure.

The cumulative invasion volume of gas in the wellbore is illus-trated in Fig. 5. As the width decreases, the quantity and rate of gasinvasion decrease rapidly. The cumulative volume of gas is

Fig. 3. Pressure change with time in the fracture and wellbore.

25.6� 10�3 cm3 after 1 s at a fracture width of 0.2mm. This is muchless than 640.5 � 10�3 cm3 when the fracture width is 2 mm. Thisresult also indicates that the GFD invasion is more difficult tomonitor when the fracture width is reduced.

During drilling, the severity of the lost circulation is closelyrelated to the fracture width. Generally, when the fracture widthexceeds 0.5 mm, the lost circulation is serious. Moreover, the

22.84

7.575

1.280.18 0.03

0.0

5.0

10.0

15.0

20.0

25.0

0.0 0.5 1.0 1.5 2.0 2.5

Requ

ired

tim

e for

GFD

inva

sion

(s)

Width of fracture (mm)

Fig. 4. Required time for GFD invasion at different fracture widths.

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Inva

sion

vol

ume

of g

as (1

0-3cm

3 )

Time after invasion (s)

2.0 mm

1.0 mm

0.6 mm

0.4 mm

0.2 mm

Fig. 5. Cumulative invasion volume of gas at different fracture widths.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Inva

sion

vol

ume

of g

as (1

0-3cm

3 )

Time after invasion (s)

26 mPa•s

34 mPa•s

42 mPa•s

50 mPa•s

66 mPa•s

Fig. 7. Cumulative invasion volume of gas at different viscosities.

Z. Zhao et al. / Journal of Natural Gas Science and Engineering 27 (2015) 686e691690

phenomenon of GFD invasion might not occur easily. Therefore, itcan be concluded that fracture widths between 0.2 mm and 0.5 mmlead to GFD invasion based on the simulation results.

4.2.2. Effect of drilling fluid viscosityThe time required for GFD invasion for different drilling fluids is

shown in Fig. 6. The required time for GFD invasion increases withincreasing viscosity of drilling fluid. In the fracture, the flow resis-tance of the drilling fluid increases as the viscosity increases. Then,the invading rate of the drilling fluid also decelerates. Finally, GFDinvasion is postponed.

In Fig. 7, the cumulative volume curves of gas in a wellbore areshown for different fluid viscosities. As the viscosity increases, theinvasion rate of the gas decreases, and the quantity of invading gasalso decreases. This finding indicates that a high fluid viscositycould simultaneously reduce the invasion speed of gas and theinvasion volume. However, exorbitant viscosity would lead to otherproblems in drillingdfor example, reducing the drilling speed orincreasing the load on the mud pumps. Therefore, an appropriatefluid viscosity to delay and weaken the GFD invasion must beselected while considering the actual drilling requirement.

4.2.3. Effect of the pressure differenceDuring the drilling, a positive pressure difference in the bottom

hole is necessary to prevent the gas cut. However, this pressure

0.05

0.88 0.931.28

1.54

1.91

3.17

0.0

1.0

2.0

3.0

4.0

0.0 20.0 40.0 60.0 80.0

Requ

ired

tim

e for

GFD

inva

sion

(s)

Viscosity (mPa·s)

Fig. 6. Required time for GFD invasion for different fluid viscosities.

difference is also the force that causes the drilling fluid to invadethe fracture and induce GFD invasion. The required time for GFDinvasion to occur at different pressure differences is shown in Fig. 8.

Fig. 8 shows that the required time for GFD invasion rapidlyincreases with increasing pressure differences. For GFD invasion,this indicates that the prevention effect of the pressure difference ismore obvious than the promoting effect. The GFD invasion could beobservably delayed by increasing the pressure difference betweenthe wellbore and the fracture.

Fig. 9 shows the cumulative invasion volume of gas at differentpressure differences. The rate and quantity of GFD invasiondecrease with an increasing positive pressure difference in thebottom hole. Therefore, the proper pressure difference in the bot-tom hole is beneficial for controlling GFD invasion.

The wellbore pressure is limited by the geological conditionsand drilling technology and cannot increase without restrictions.For the carbonate fractured formation, the narrow mud densitywindow causes frequent fluid loss. Currently, managed pressuredrilling is widely used to drill fractured carbonate reservoirs. Thewellbore pressure is controlled at a low value, which is alwayslarger than the formation pressure to simultaneously reduce fluidloss and avoid overflow. However, a small positive pressure dif-ference facilitates the GFD invasion processes. Based on the simu-lation results, the wellbore pressure changes only slightly when asingle GFD invasion occurs, which is difficult to monitor. Withincreasing time, more gas accumulates in the wellbore. When the

0.050.445

1.28

3.01

6.785

0.0

2.0

4.0

6.0

8.0

0.0 0.5 1.0 1.5 2.0

Requ

ired

tim

e for

GFD

inva

sion

(s)

Pressure difference (MPa)

Fig. 8. Required time for GFD invasion at different pressure differences.

0.0

20.0

40.0

60.0

80.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Inva

sion

vol

ume

of g

as (1

0-3cm

3 )

Time after invasion (s)

0.1 MPa

0.3 MPa

0.6 MPa

1.0 MPa

1.5 MPa

Fig. 9. Cumulative invasion volume of gas at different pressure differences.

Z. Zhao et al. / Journal of Natural Gas Science and Engineering 27 (2015) 686e691 691

gas invasion is monitored, more time is required to address it. Moreimportantly, this phenomenon would constantly occur in succes-sive drilling, which seriously affects the drilling rate and increasesthe costs.

5. Conclusions

(1) GFD invasion may occur when the wellbore pressure ishigher than the formation pressure. The drilling fluid invadesthe fracture and increases the gas pressure, which results inGFD invasion.

(2) GFD invasion occurs with an intermittent impulse. In asingle-pass invasion, the invading gas volume is very small,which changes the wellbore pressure so slightly that GFDinvasion is difficult to observe. The invasion could continue ifno measures are taken to prevent it.

(3) The occurrence of GFD invasion depends on the fracturewidth. It clearly occurs when the fracture width is between0.2 mm and 0.5 mm, and it occurs most easily as the widthincreases in this range. High drilling fluid viscosity andpressure difference are beneficial for preventing GFDinvasion.

Acknowledgments

We gratefully acknowledge the financial support of the OpenFund (PLN1310) of the State Key Laboratory of Oil and Gas ReservoirGeology and Exploitation (Southwest Petroleum University) andthe National High Technology Research and Development Programof China (2012AA091502).

Nomenclature

v velocity [m/s]

F!

continuum surface forceP pressure [Pa]g gravitational acceleration [m/s2]T temperature [K]

Greek symbolsa phase volume fractionm viscosity [Pa s]r density

AbbreviationsGFD gas-fluid displacementCFD computational fluid dynamicsVOF volume of fluid

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