SPE 115526

Fracture Ballooning in Naturally Fractured Formations: Mechanism and Controlling Factors R. Majidi, SPE, S.Z. Miska, SPE, M. Yu, SPE, and L.G. Thompson, SPE, University of Tulsa

Copyright 2008, Society of Petroleum Engineers This paper was prepared for presentation at the 2008 SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 2124 September 2008. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Fracture ballooning observed while drilling naturally fractured formations has often been mistakenly interpreted as influx of formation fluid or the loss of drilling fluids. This misinterpretation leads to costly well control procedures that may make the situation even worse. The main mechanisms and factors controlling the ballooning phenomenon must be well understood to avoid confusing this phenomenon with conventional losses or formation kick. Amongst several mechanisms that are quoted for borehole ballooning, the opening/ closing of natural fractures plays a major role in naturally fractured formations.

In this work, a mathematical model describing the fracture ballooning process is developed and solved numerically using finite difference approximation. The governing equation is derived using principles of conservation of mass and linear momentum for transient radial flow in a single fracture. The effects of fracture parameters (aperture, extension and deformability) have been studied as well as fluid properties and operational conditions. Describing drilling fluid rheology with Yield-Power-Law (Herschel-Bulkley/YPL) allows for the investigation of the effect of drilling fluid rheology on borehole ballooning.

Results show how the rheological properties of drilling fluid such as yield stress and shear-thinning/thickening effect, influence ballooning or mud losses in fractured formations. We conclude that the fluid loss in the fractures could be stopped either because of high yield stress of drilling fluid or limited extension of the fracture. The proposed model is also helpful for detecting and treating ballooning as well as evaluating fracture characteristics. The field potential application of the model is described. Introduction Fracture deformation, or ballooning observed while drilling fractured formations is the result of loss/gain due to fractures being opened and closed. Fracture opening/closing is caused by the annular pressure fluctuation at the wellbore resulting from the change in circulation rate. Mud losses take place when drilling fluid at the well flows into the fracture because the fracture is pressurized and opened. However, when the pumps are turned off such as during a connection the pressure at the well will fall and the mud in the fracture will return to the well due to fracture closing. Usually any flow during drilling is interpreted as an influx of the formation fluid and the common cure is to increase the mud weight and ensure an adequate overbalance. But if the mud weight is increased and the influx is only mud return, the situation will get progressively worse with a rise in equivalent circulating density (ECD). Mud losses will continue and the fracture propagation pressure may even be exceeded, resulting in total losses. Therefore, it is very crucial to understand the major mechanisms and factors controlling the ballooning phenomenon to avoid confusion with conventional losses or formation kick. Ward et al.1 suggested that diagnosis of downhole pressure response with a real-time PWD tool is very helpful to distinguish an influx from mud return.

Several examples of ballooning modeling are found in the literature. Lavrov and Tronvoll2-5 considered mud loss into a deformable fracture of finite length. Two different flow geometries, linear and radial flow were modeled separately. Possible leakoff through the fracture wall caused by the pressure difference between the incoming mud and the formation fluid was accounted for in the linear system. They also justified and used a linear fracture deformation. According to the theory of Lavrov and Tronvoll, the eventual stop of mud losses is due to finite fracture extension. They later studied the incorporation of non-Newtonian mud rheology, ballooning and associated mud loss into a single deformable, horizontal and circular fracture intercepted by a borehole at its center. The effect of different types of fluid rheology, i.e. Newtonian, Power-Law and bi-viscous fluid and various formation properties and operational conditions e.g., formation pressure, borehole pressure and fracture dimensions, were discussed.

2 SPE 115526

Ozdemirtas et al.6 has recently developed a two-dimensional flow model with an emphasis on the effect of fracture roughness. They also performed experiments on several artificially fractured rock samples to study this effect. From the results of experimental observations and numerical models they reported that there are critical situations in which the roughness can cause the losses to diminish.

We have developed a model for fracture ballooning of YPL type of drilling fluids as a general rheological behavior case. Mathematical Modeling A horizontal disk-shaped fracture of outer radius re located in an impermeable rock is considered in this study. Initially, the fracture is fully saturated with liquid under the static formation pressure pi. Drilling fluid propagates into the fracture because of the overbalance pressure at the well. All properties of the drilling fluid are assumed to be identical to the fluid that is already in the fracture. Cylindrical coordinate r denotes the distance from the borehole axis in the fracture plane. Fluid rheology The fluid rheology is described by Yield-Power-Law. For YPL fluids, the shear stress is related to shear rate as,

my k )(

. += Eq.1 where y is the yield stress, k and m are the consistency factor and flow behavior index of the fluid, respectively. Describing drilling fluid rheology, (as described by the Yield-Power-Law model), allows for investigation of the effect of drilling fluid rheological properties such as yield stress and shear-thinning on ballooning. Fracture deformation The major mechanism under which fracture ballooning takes place is the fracture deformation. Therefore, the model behavior is critically dependent on the way that the fracture deformation is described. Hydro-mechanical models for fracture deformation as a function of fluid pressure and mechanical stresses are beyond the scope of this work. A linear relationship between fracture aperture and the fluid pressure inside the fracture is considered as

n

ii K

ppww

+= Eq.2 where w is the width of the fracture Kn is the normal fracture deformation modulus or fracture stiffness, and wi is the initial fracture aperture at initial pressure pi before it is intercepted by the well. The assumed local linear relation between fluid pressure and fracture aperture is a large simplification. For further development of the model, more realistic nonlinear deformation laws such as the exponential law should be used for describing fracture deformation. Governing equation Conservation of mass for radial flow of an incompressible fluid in a variable width fracture is given by

01)( =++

twvw

rrvw Eq.3

where v is the average radial velocity of the fluid in the fracture which varies with position and time. Fluid flow inside the fracture can be described locally by momentum conservation; the average radial velocity for a YPL fluid at a distance r from the borehole axis can be expressed as7:

my

mm

m

wmm

drdp

k

wmmv

1

111

11

)2

)(112(1

2)

12(

+++= +

+ Eq.4

Substituting the average velocity from Eq.4 into Eq.3 we have

0)2

)(112

(1

2

1)

12()

2)(

112

(2

1)

12(

11

2

111

11

2

111

=+

++++

++

+

+

+

+

+ tw

wmm

drdp

rw

kmm

wmm

drdpw

rk

mm mym

mm

mym

mm

Eq.5

Although the considered fracture deformation law is quite simple, Eq.5 is still nonlinear and needs to be solved numerically. The resulting second order Partial Differential Equation (Eq.5) requires an initial condition and two boundary conditions to be solved. Initially, the pressure within the fracture is uniform and equal to formation pressure. At time t=0, a vertical borehole of radius rw intersects the fracture at its center. After being penetrated by the borehole, fluid pressure at borehole suddenly increases from initial pressure pi to pw and stays constant. The fracture tip is assumed to act like a no-flow boundary (dp/dr=0 at r=re).

Equation 5 was solved implicitly using Newtons method with a variable fracture grid size and time-step (Appendix A). The general solutions of Eq.5 in dimensionless coordinates are presented in the form of mud loss curves for the ballooning process. These curves express the dimensionless volume or rate of losses/gains as a function of time for various fracture and fluid properties.

SPE 115526 3

Results Figure1 demonstrates the dimensionless pressure profile in the fracture at various times after it is intercepted by the wellbore. When the fracture is encountered, a pressure disturbance is applied to the fracture from the wellbore. The pressure disturbance propagates throughout the fracture until it reaches the tip of the fracture. As long as the pressure disturbance has not reached the fracture tip the behavior of ballooning for various fracture extensions remains the same. However, when the pressure disturbance reaches the fracture tip the incoming fluid pressurizes the fracture until the pressure throughout the fracture becomes identical to the borehole pressure and as a result the flow stops. The eventual stop of losses depends upon the extension of the fracture re, fracture stiffness and the amount of overbalance pressure applied at the well. In the equilibrium state the fracture aperture increases by (pw-pi)/kn. The ultimate volume of loss/gain can be calculated in terms of fracture extension as

( )

=

n

iwwu K

PPrrVe

22

Eq.6

( )nD

eDuD k

rV2

12 = Eq.7 where Vu and VuD are the ultimate volume of losses in real and dimensionless coordinates respectively. The ultimate volume of losses is directly proportional to the pressure difference at the well and inversely proportional to the fracture stiffness. This is the result of the linear relationship assumed to describe the fracture deformation. The ultimate volume of losses also quadratically changes with the extension of the fracture. Figure 2 shows the dimensionless volume of loss/gain due to fracture deformation of various fracture extensions. The smaller the fracture the sooner the mud losses will stop.

Effect of drilling fluid rheology In addition to fracture properties such as fracture extension and fracture stiffness, drilling fluid properties also influence the rate and volume of losses. Figure 3 shows the effect of yield stress of drilling fluid on fracture ballooning. Dimensionless mud invasion factor is a measure of the yield stress of the drilling fluid. Fluid flow may stop merely because of high yield stress of the fluid before it could be stopped due to the limited length of the fracture or even before the pressure disturbance could be felt at the fracture tip. The higher the yield stress the sooner the losses will stop. It seems that the high yield stress fluid flow in the fracture may act like a limited extension fracture. However, the cessation of mud losses due to the high yield stress of the fluid is not as dramatic as it is due to limited fracture extension. Depending upon the relative value of fracture and fluid parameters one may precede the other.

A typical example in real coordinates is given to investigate shear-thinning effect. It seems misleading to judge about the shear-thinning effect of the fluid directly from the dimensionless type-curves since the dimensionless time tD is a function of flow behavior index m. Figure 4 demonstrates the effect of shear-thinning of the drilling fluid on mud losses due to ballooning. In this example, we used Power-Law fluids (y=0 or =0) with consistency factor k=0.5 pas.sm. A 1000 overpressure is considered across a fracture with stiffness of 8.9103 MPa/m and aperture of 1 mm. According to Fig. 4, the rate of losses for shear-thinning fluids is much greater than for thick fluids. The ultimate volume of fluid losses is still controlled by facture extension (reD=1000) in this case (no yield stress). We know that in general the losses could stop either due to yield stress of the fluid or limited fracture extension.

Effect of fracture properties Figures 5 and 6 show the effect of fracture stiffness (deformability) on ballooning process. The rate of loss/gain due to ballooning declines when the fracture stiffness increases. The ultimate volume of losses is proportional to the reciprocal of fracture stiffness. Knowing the effect of fracture stiffness, the effect of overbalance pressure could be investigated in the same manner. According to the definition of dimensionless fracture stiffness (A-10) the higher overbalance pressure increases the volume of losses exactly in the same manner that the fracture stiffness decreases. The rate and volume of losses for various pressure differences at the well are shown in Figs. 7 and 8. The rate and volume of fluid losses for a YPL fluid with m=0.8, k=0.5 lb/100ft2.sm and y =16 lb/100ft2 in a very long (reD=10,000) fracture of 1 mm aperture and stiffness of 3.45104 MPa/m is considered. Losses highly depend upon the applied pressure difference at the well. The ultimate volume of losses linearly increases with increasing the overbalance pressure.

Figures 9 and 10 demonstrate how the fracture aperture influences the losses. The model predicts much higher losses in wider fractures. According to Fig. 10 fracture aperture can change the ultimate volume of losses in situations that the losses are controlled by yield stress of the fluid. However, if the fracture is of limited extension or the yield stress of the fluid is not high enough to stop the losses before the disturbance reaches the fracture tip, the width of the fracture can not influence the ultimate volume of losses. In this case, the ultimate loss volume is controlled by fracture extension while the fracture aperture only influence initial rate of losses.

4 SPE 115526

Conclusions Flow of a non-Newtonian drilling fluid from a borehole into a non-propagating fracture was modeled under the

assumptions of linear fracture deformation and Yield-Power-Law fluid rheology.

The presented model is very helpful for understanding the major mechanisms and factors controlling fracture ballooning and to distinguish between this phenomenon and conventional losses or formation kick. This can avoid unnecessary expensive well control procedures.

The presented model helps to investigate the effect of fracture parameters (extension, aperture and deformability)

and fluid properties such as yield stress and shear-thinning/thickening effect as well as operational condition (overbalance pressure).

The volume of the fluid loss or gain due to ballooning into/out of the fracture is shown to be an almost linearly

decreasing function of the fracture stiffness. Shear-thinning effect of drilling fluids influence the rate of losses particularly at the initial stages of losses, whereas, the ultimate volume of losses is controlled by fracture extension and/or yield stress of the fluid. Mud losses may stop either because of limited extension of the fracture or high yield stress of drilling fluid.

The model can be used to optimize the drilling regime in naturally fractured formations. It can also provide an aid

when using mud loss data for fracture characterization purposes when the ballooning is the major mechanism. Acknowledgment The authors wish to thank Tulsa University Drilling Research Projects (TUDRP) member companies for supporting this work. SI Metric Conversion Factors bbl x 1.589 8 E01 = m3 bpm x 2.649 667 E03 = m3 s-1 lb/100ft2 x 0.478 803 E 00 = Pa psi x 6.894 757 E+03 = Pa Nomenclature drD = dimensionless radius differential dtD = dimensionless time differential m = flow behavior index k = consistency factor, Pa.secm pw = wellbore pressure, Pa pi = initial formation pressure, Pa qD= dimensionless mud loss flow rate rD= dimensionless radius rw= wellbore radius, m t = time, s tD = dimensionless time v = radial velocity, ms-1 VD= dimensionless mud loss volume Vu= ultimate mud loss volume, m3 VuD= dimensionless ultimate mud loss volume w = fracture aperture, m = dimensionless mud invasion coefficient = time factor, s-1

. =shear rate, s-1 p = drilling overpressure, Pa p = drilling mud plastic viscosity, Pa.s = shear stress, Pa y = drilling mud yield stress, Pa

SPE 115526 5

References [1] Ward, C., Clark, R., Anatomy of ballooning borehole using PWDTM tool Presented at The Overpressure in Petroleum

Exploration workshop, Pau, France, 7-8 April , 1998. [2] Lavrov, A., and Tronvoll, J.: Mud loss into a single fracture during drilling of petroleum wells: Modeling approach, in

Proceedings of the 6th International Conference on Analysis of Discontinuous Deformation, October 2003, 189. [3] Lavrov, A., and Tronvoll, J., Modeling Mud Loss in Fractured Formations, Paper SPE 88700 presented at the 11th Abu

Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, U.A.E., 1013 October, 2004. [4] Lavrov, A., and Tronvoll, J., Mechanics of Borehole Ballooning in NaturallyFractured Formations Paper SPE 93747

presented at the 14th SPE Middle East Oil & Gas Show and Conference, Bahrain, 1215 Murch, 2005. [5] Lavrov, Modeling Flow of a Biviscous Fluid from Borehole into Rock Fracture. SINTEF Petroleum Research, Journal of

Applied Mechanics, Vol.73 Jan-2006. [6] Ozdemirtas M., Babadagli T., and Kuru E., "Experimental and Numerical Modeling of Borehole Ballooning - Effect of

Fractures Roughness" Paper SPE 110121 presented at the 2000 SPE Annual Technical Conference and Exhibition, Anaheim, California, 11-14 November 2007.

[7] R. Majidi, S.Z. Miska, M. Yu, and L.G. Thompson, Quantitative Analysis of Mud Losses in Naturally Fractured Reservoirs: The Effect of Rheology, SPE 114130 the 2008 SPE Western Regional and Pacific Section AAPG Joint Meeting held in Bakersfield, California, U.S.A., 31 March2 April 2008.

[8] Litard O., Unwin T., Guillot D., and Hodder M. H.: Fracture Width Logging While Drilling and Drilling Mud / Loss-Circulation-Material Selection Guidelines in Naturally Fractured Reservoirs, SPEDC (December 2002) 237

Appendix A Mathematical Modeling To obtain a general solution for Eq.5 we use the following dimensionless variables. Dimension distance from borehole axis:

wD r

rr =

(A-1)

Dimensionless width of the fracture:

iD w

ww =

(A-2)

where wi is the initial fracture width. Dimensionless pressure is defined as the pressure difference at any point in the fracture divided by the total pressure difference at the well (over/under balance pressure).

iw

iD pp

ppp

=

(A-3)

Therefore, the dimensionless form of the inner boundary condition at the well will be PD=1 at rD=1 and the outer boundary condition will be

0=

= eDD rrDD

rp (A-4)

The dimensionless mud invasion factor is defined as:

pwr

mm y

i

w

++= 2)112(

(A-5)

where is a measure of the ratio of the yield stress of the drilling fluid to the applied overbalance pressure. It represents the relative value of the resistance to flow due to yield stress of drilling fluid to the driving force (overpressure). Dimensionless time factor is defined as:

mm

w

i

mkp

rw

mm

111

11)

12(

2

1

+=+

+

(A-6)

So dimensionless time is calculated as:

ttD = (A-7)

6 SPE 115526

Using the dimensionless variables defined from Eq.A-1 to A-7 the dimensionless form of Eq.5 obtained as:

0

112112 =+

+

++

D

Dm

DD

D

D

mD

m

DD

DmD

D tw

wrp

rw

wrpw

r

(A-8)

where the dimensionless fracture aperture is a function of dimensionless pressure as shown below:

nD

DD K

pw +=1

(A-9)

pKwK ninD =

(A-10)

KnD is the dimensionless fracture stiffness. Substituting wD from Eq.A-9 into Eq.A-7

01

1

1

11

1121

12

=+

+

+

+

+

+

+

+

D

D

nD

m

nD

DD

D

D

m

nD

Dm

nD

DD

Dm

nD

D

D tp

KKpr

pr

Kp

Kpr

pKp

r

(A-11)

The dimensionless flow rate is obtained as

m

DD

DD

mDD wr

prwq

112

= +

(A-12)

where the dimensionless and actual flow rate are related as below.

qp

kwr

mm

rwq

mm

i

w

wi

m

D

111

2

11

)12(22

+=

++

(A-13)

Dimensionless flow rate at the wellbore is

m

rDD

DmDDw

Dwr

pwq

1

1

12

=

+

=

(A-14)

Dimensionless volume of losses is obtained from cumulative rate of losses at the well as shown below.

== Dt

DDwwi

D dtqrwVV

022

(A-15)

In order to numerically solve the resulting Partial Differential Equation (eq.A-7), one may discretise the fracture into a number of intervals and solve implicitly in time. The discritised form of the Eq.A-7 is

( )0

12

1 11

11

11

1211

1

12

21

111

11

2

21

1

=+

++

++

+++

+

++

++

+D

nDj

nDj

nD

m

DDm

nDj

nDj

Dj

mDj

DDb

nDj

nDj

m

Dj

m

DDf

nDj

nDj

m

DjD t

ppKwr

ppr

wwr

ppw

wrpp

wr

m (A-16)

where

nD

DjDjDiDj K

ppww

21

21

++

++=

(A-17)

nD

DjDjDiDj K

ppww

211

21

++=

(A-18)

Equation A-16 leads to a system of nonlinear equations that requires an iterative method to solve for pressure profile. nn

f fPJ D =+ )( 1 (A-19) where J denotes the Jacobean matrix of pressure distribution vector and f is the pressure function from Eq.A.16 which is

( )0

11

11

1211

1

12

21

111

11

2

21

1

1

=

+=

++

+

+++

+

++

++

++ n

DjDDm

nDj

nDj

Dj

mDj

DDb

nDj

nDj

m

Dj

m

DDf

nDj

nDj

m

DjD

nDnDjj pwr

ppr

wwr

ppw

wrpp

wr

tKpf

m

(A-20)

Solving the system of nonlinear equations by Newtons method, the pressure profile at any time can be obtained. Having pressure profile, we can calculate mud flow rate at the well and also volume of fluid losses from eq.A-14 and eq.A-15.

SPE 115526 7

0

0.2

0.4

0.6

0.8

1

0 2000 4000 6000 8000 10000

rD

PD

tD=10^6

tD=5*10^6tD=10^7

tD=2*10^7

reD=10,000

Figure 1Pressure Profile in the fracture

1.E+0

1.E+1

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

1.E+7

1.E+8

1.E+0 1.E+1 1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7 1.E+8 1.E+9

tD

VD

reD=104

reD=103

reD=102

reD=10

Figure 2Volume of losses due to ballooning for various fracture extensions

1.E+0

1.E+1

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

1.E+7

1.E+8

1.E+0 1.E+1 1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7 1.E+8 1.E+9

tD

VD

=0 =0.0001

=0.01

=0.001

Figure 3Volume of losses due to ballooning for various fluid yield stress

8 SPE 115526

reD=1000

1

10

100

1000

0.1 1.0 10.0 100.0 1000.0

time (min)

Volu

me

of lo

sses

(bbl

)

m=0.6

m=1

m=0.8

Figure 4Shear-thinning effect on mud losses

1.E+0

1.E+2

1.E+4

1.E+6

1.E+8

1.E+0 1.E+2 1.E+4 1.E+6 1.E+8

tD

VDknD=0.5knD=1

knD=2

reD=10,000

Figure 5 The effect of fracture stiffness on volume losses

0

1

2

3

4

5

6

7

1.E+0 1.E+2 1.E+4 1.E+6 1.E+8

tD

qD

reD=10,000KnD=0.5

KnD=0.5

KnD=1

Figure 6Effect of fracture stiffness on rate losses

SPE 115526 9

reD=10,000

0.001

0.01

0.1

1

10

100

0.0 100.0 200.0 300.0 400.0 500.0 600.0

time (min)

loss

rat

e (b

bl/m

in)

Dp=2000 psi

Dp=1000 psi

Dp=500 psi

Figure 7Rate of losses for various pressure difference

reD=10,000

1

10

100

1000

10000

0.1 1.0 10.0 100.0 1000.0

time (min)

Volu

me

of lo

sses

(bbl

)

Dp=2000 psi

Dp=1000 psi

Dp=500 psi

Figure 8Volume of losses for various pressure difference

reD=10,000

1

10

100

1000

0.1 1.0 10.0 100.0 1000.0

time (min)

Volu

me

of lo

sses

(bbl

)

w =0.5

w =1

w =2

Figure 9Rate of losses for various fracture apertures

reD=10,000

0.01

0.1

1

10

100

0.0 100.0 200.0 300.0 400.0 500.0 600.0

time (min)

loss

rat

e (b

bl/m

in)

w =2

w =0.5

w =1

Figure 10Volume of losses for various fracture apertures