DC181747 DOI: 10.2118/181747-PA Date: 17-May-16
Stage:
Page: 134
Total Pages: 11
A Review on Fracture-Initiation and
-Propagation Pressures for Lost Circulation
and Wellbore Strengthening
Yongcun Feng, University of Texas at Austin; John F. Jones, Marathon Oil Corporation; and
K. E. Gray, University of Texas at Austin
Summary
Fracture-initiation pressure (FIP) and fracture-propagation pressure (FPP) are both important considerations for preventing and
mitigating lost circulation. For significant fluid loss to occur, a
fracture must initiate on an intact wellbore or reopen on a wellbore with pre-existing fractures, and then propagate into the farfield region. Wellbore-strengthening operations are designed to
increase one or both of these two pressures to combat lost circulation. Currently, some theoretical models assume that FIPs and
FPPs are only functions of in-situ stress and rock-mechanical
properties. However, as demonstrated by numerous field and laboratory observations, they are also highly related to drilling-fluid
properties and to interactions between the drilling fluid and formation rock.
This paper discusses the mechanisms of lost circulation and
wellbore strengthening, with an emphasis on factors that can
affect FIP and FPP. These factors include microfractures on the
wellbore wall, in-situ-stress anisotropy, pore pressure, fracture
toughness, filter-cake development, fracture bridging/plugging,
bridge location, fluid leakoff, rock permeability, pore size of rock,
mud type, mud solid concentration, and critical capillary pressure.
The conclusions of this paper include information seldom considered in lost-circulation studies, such as the effect of microfractures on FIP and the effect of capillary forces on FPP. Research
results described in this paper may be useful for lost-circulation
mitigation and wellbore-strengthening design, as well as hydraulic-fracturing design and leakoff-test (LOT) interpretation.
Introduction
Lost circulation is the partial or complete loss of whole drilling
fluid into the formation rock while drilling a well. It is among the
major nonproductive-time (NPT) events in the drilling industry.
In addition to the high cost associated with lost drilling fluids,
other negative consequences may include stuck pipe, induced
kicks, unplanned casing, reduced drilling rates, and even the loss
of the entire well or wellbore. Published data show that more than
12% of NPT in the Gulf of Mexico (GOM) is caused by lost circulation (Wang et al. 2007), and 10 to 20% of the drilling cost of
high-temperature and high-pressure wells is related to lost circulation (Cook et al. 2011).
Most lost-circulation events occur when the hydraulic pressure
in the wellbore exceeds the FIP and FPP of the formation rock.
Lost circulation is common in wellbores with a narrow drilling
mud-weight window, which is the difference between the maximum mud weight before the occurrence of lost circulation and the
minimum mud weight to balance formation pore pressures or to
avoid excessive wellbore failure. Typical scenarios include drilling within depleted reservoirs, drilling highly inclined wellbores
in which increased fluid densities are required for hole stability,
and drilling highly overpressured formations, in which the margin
between formation pore pressure and the overburden pressure is
reduced (Feng and Gray 2016a). Commonly encountered pressure
C 2016 Society of Petroleum Engineers
Copyright V
Original SPE manuscript received for review 1 December 2014. Revised manuscript
received for review 25 February 2016. Paper (SPE 181747) peer approved 12 April 2016.
134
ramps and pressure regressions may also lead to significant reductions in the drilling mud-weight window. It is well-known that carbonate formations (limestone/dolomite) are usually characterized
by the presence of natural fractures, vugs, and cavities, and consequently lost circulation occurs frequently (Wang et al. 2010; Masi
et al. 2011). However, lost circulation in carbonate formations is
outside the scope of this work, and the discussion in this paper is
mainly for clastic formations such as sandstones and shales.
The reduction in pore pressure in depleted reservoirs results in
a corresponding, though smaller, reduction in fracture gradient
(Hubbert and Willis 1957; Matthews and Kelley 1967). Conversely, bounding and interbedded shale layers, as well as any isolated and undrained sands, will maintain their original pore
pressure and fracture gradient. Therefore, as shown in Fig. 1a, it
may be difficult or impossible to reduce the drilling-fluid density
sufficiently to maintain equivalent circulating densities (ECDs)
below the depleted-zone fracture gradient. ECD is defined as the
effective density of the circulating fluid in the wellbore, resulting
from the sum of the hydrostatic pressure imposed by the staticfluid column and the friction pressure (American Petroleum Institute 2010). In deepwater formations, the total vertical stress is
relatively low because seawater does not provide as much overburden loading as sediment and rock. A reduction in total vertical
stress also results in a lower lateral stress and fracture gradient. If
abnormal pressures are also present, the mud-weight window may
be very narrow, as shown in Fig. 1b. Under these circumstances,
it may be challenging to avoid hydraulic fracturing while tripping
caused by surge/swab effects and while circulating caused by
high annular-friction losses and ECDs.
FIP and FPP are two important considerations for preventing
and mitigating lost circulation. Only after a fracture initiates on
an intact wellbore or reopens on a wellbore with pre-existing fractures, and then propagates into the far-field region, can significant
fluid loss occur. Therefore, accurate predrill estimates of these
two pressure values are critical for reducing lost-circulation
events. A common theoretical method to estimate FIP for a vertical well compares a simple tensile-failure criterion to the hoop
stress defined by the Kirsch equation (Fjar et al. 2008). FIP predicted by this approach is related to formation rock strength, insitu stresses, and the formation-fluid pressure, and it is assumed
that the fracture initiates at the wellbore wall. However, the
Kirsch equation assumes zero leakoff (i.e., impermeable rock or
perfect mudcake).
In theory, FPP can be determined from injectivity tests,
extended leakoff tests (XLOTs), analysis of fluid losses while drilling, or from fracture-mechanics modeling. In field practice, FPP
is often estimated from LOTs performed at casing or liner shoes.
However, these tests are generally insufficient for this analysis,
which may lead to significant error (Ziegler and Jones 2014).
It is worth noting that FIPs and FPPs are commonly taken as
properties of the formation rock, dependent on the in-situ stresses,
mechanical properties of the rock, and inclination and orientation
of deviated wells. However, field experience suggests that they
may also be influenced by other parameters related to the drilling
fluid (e.g., mud type, fluid leakoff, solid particles within the
fluid, and temperature), as well as other properties of the rock
(e.g., lithology, permeability, wettability, and capillary effect).
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Stage:
Pore-pressure
gradient
Depth
Depth
Fracture
gradient
Mud
weight
Total Pages: 11
Pressure Gradient
Pressure Gradient
Pore-pressure
gradient
Page: 135
Fracture
gradient
ECD
Mud
weight
ECD
Depleted zone
(a)
Abnormally
pressured zone
(b)
Fig. 1—(a) Pore-pressure and fracture-gradient plot in depleted zone. Pore-pressure decrease leads to a decrease in fracture gradient. (b) Pore-pressure and fracture-gradient plot in deepwater formation with abnormally high pressure. There is a reduced mudweight window.
A detailed study of these factors’ effects on fracture-initiation
and/or -propagation pressures is therefore needed for better understanding of lost circulation.
To drill through problematic zones with a high risk of lost circulation, various drilling technologies may be useful, including
managed-pressure drilling, dual-gradient drilling, and casing/liner
drilling. Alternatively, “wellbore strengthening” is a different
approach that seeks to artificially increase the pressure that the
wellbore can sustain and hence widen the mud-weight window.
Rather than actually increase the strength of the wellbore rock, as
its name implies, this methodology is believed to work by bridging/plugging/sealing fractures.
There are two main types of wellbore-strengthening methods
currently used in the petroleum industry—the hoop-stress
enhancement method (e.g., stress cage) (Alberty and McLean
2004) and the fracture-resistance enhancement method (e.g., fracture-propagation resistance) (Morita et al. 1990; Fuh et al. 1992;
van Oort et al. 2011). The first method is based on inducing and
plugging a fracture to increase the local hoop stress, thus raising
fracture-reopening resistance. The authors of this paper have conducted detailed numerical studies and found that theoretically, at
least, hoop stress can be increased significantly if the fracture can
be plugged effectively (Feng et al. 2015, 2016b). Although theoretical studies show that there is large potential in hoop-stress
increase (Alberty and McLean 2004; Wang et al. 2009), and
numerous successes are reported for the stress-cage method
(Aston et al. 2004; Song and Rojas 2006; Whitfill et al. 2006;
Aston et al. 2007), lost-circulation problems are still commonly
encountered with an ECD much lower than the hoop stress around
the wellbore. Therefore, numerous doubts still persist, including
the following: (1) Is hoop stress a good indicator of lost circulation and the evaluation of wellbore-strengthening success? and (2)
When wellbore strengthening works, is it actually caused by an
increase in hoop stress? This paper will discuss these questions in
detail.
For this discussion, fracture-propagation resistance theory is
based jointly on experimental and field observations, including
the DEA 13 (Morita et al. 1990; Fuh et al. 1992) and GPRI
2000 (van Oort et al. 2011) laboratory studies. Both theory and
experience indicate that fracture-propagation resistance can be
effectively enhanced with appropriate wellbore-strengthening
methods. Although several models (Fuh et al. 2007; van Oort
et al. 2011; van Oort and Razavi 2014) have been introduced to
explain how fracture-propagation resistance may be increased,
there remains a lack of understanding of the precise role that a list
of influencing factors may play. These factors include in-situ
stresses, wellbore pressure, fracture geometry and size, mud type
and properties, rock lithology and properties, lost-circulation-material (LCM) locations and properties, fluid leakoff, mudcake,
and capillary force. Therefore, significant disagreement about
the fundamental physics of wellbore strengthening still exists in
the industry.
The purpose of this paper is to analyze the mechanisms of lost
circulation and wellbore strengthening by investigating the factors
that may affect both fracture initiation and fracture propagation.
In view of the existing disagreement about the fundamentals of
lost circulation and wellbore strengthening, a critical and detailed
analysis of these two pressure thresholds is conducted. It should
be noted that wellbore strengthening discussed in this paper is
physical or mechanical strengthening of the wellbore by development of filter cake caused by fluid leakoff in relatively permeable
formation. In impermeable shales with very low leakoff, chemical
strategies are commonly used to strengthen the wellbore, either
by changing chemical composition of the formation (Growcock
et al. 2009) or by forming chemical sealants in the fracture (Aston
et al. 2007). The chemical wellbore-strengthening technique is
outside the scope of this paper. It should also be noted that most
of the discussions in this paper are based on the case of a vertical
well, but the principles and perspectives are also applicable to
deviated and horizontal drilling.
Lost-Circulation “Thresholds”
For significant fluid loss to occur through either a drilling-induced
or closed pre-existing natural fracture, the wellbore pressure must
overcome both the fracture-initiation/reopening pressure and the
FPP. These two pressure limits may be regarded as “thresholds”
to lost circulation, which are critical for well construction and
drilling-fluid design.
In theory, FIP is usually greater than FPP, if the wellbore is an
intact cylinder. However, when the stress anisotropy is relatively
high and/or there are pre-existing fractures, fracture-propagation
pressure may be equal to or greater than the calculated fractureinitiation pressure. In general, this condition should not cause significant concern.
There are four general conditions related to lost circulation,
depending on the relative magnitudes of ECD, fracture-initiation
gradient, and fracture-propagation gradient. (1) When ECD is
lower than both fracture-initiation gradient and fracture-propagation gradient, fluid loss will not occur. (2) When ECD is higher
than fracture-initiation gradient but lower than fracture-propagation gradient, only very small fractures will generate near the
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1.4
Stage:
1
1
1.1
Shmin
1.25
1.5
0.8
1.75
0.6
0.6
0.7
η
0.75
PIini /Shmin
1.2
PIini /Shmin
Total Pages: 11
1.2
SHmax
0.4
0.5
Page: 136
1
0.5
0.9
0.25
0.8
0.8
0.9
0.7
0.5
pi /Shmin
0.6
0.7
0.8
0.9
pi /Shmin
(a) η = 0.5
(b) SHmax/Shmin = 1.3
Fig. 2—FIP of a vertical well: (a) with different horizontal stress anisotropies and pore pressure (eta 5 0.5); (b) with different g and
pore pressure (SHmax/Shmin 5 1.3).
wellbore wall and no significant fluid loss will occur. (3) When
ECD is larger than fracture-propagation gradient but lower than
fracture-initiation gradient, the situation is less stable. No fluid
loss will occur as long as the wellbore remains intact, and the farfield stress region of each formation is isolated from the pressure
in the wellbore. However, lack of wellbore isolation may result
from inadequate filter-cake development in permeable formations
or where pre-existing natural or mechanically induced fractures
are present in any type of formation. (4) When ECD is above both
fracture-initiation gradient and fracture-propagation gradient,
fluid loss is expected to occur. In this case, remedial actions must
include some form of ECD reduction and/or wellbore-strengthening operation.
Fracture-Initiation Pressure
Conventional interpretation theories for FIP generally assume a
perfectly intact wellbore. Fracture initiation is predicted when the
tangential stress (also called hoop stress) at the wellbore wall
equals the tensile strength of the rock. It is widely accepted that
FIP depends much more on in-situ stresses, which determine the
hoop stress around the wellbore, than on the tensile strength of the
rock, which is comparatively very small. In reality, the assumption
of a perfectly intact wellbore is rarely true. The most likely imperfect wellbore condition is a wellbore with microfractures (Morita
et al. 1990). Microfractures may develop naturally from tectonic
movement, rapid sediment compaction, and/or thermal-fluid
expansion, as well as from destructive drilling operations. In the
case of pre-existing, hydraulically conductive microfractures at
the wellbore wall, the aforementioned method to predict FIP is no
longer valid. In this case, the wellbore pressure that begins to fail
the formation rock is the propagation pressure for the microfractures, rather than the initiation pressure for any new fractures.
However, for the purposes of this paper, microfracture-propagation pressure is considered as FIP, because the fracture size is very
small and the assumption of a perfect wellbore is seldom satisfied.
Fracture Initiation in a Perfect Wellbore. FIP for an intact cylindrical wellbore may be easily determined from continuum
mechanics (Kirsch equations). However, FIP may be very different for permeable and impermeable formations. For an impermeable formation with negligible tensile strength, FIP of a vertical
wellbore can be estimated by the Hubbert-Willis equation (Hubbert and Willis 1957; Jin et al. 2013):
pini ¼ 3Shmin SHmax pp ; . . . . . . . . . . . . . . . . . . . . ð1Þ
where pini is fracture-initiation pressure; Shmin and SHmax are the
minimum and maximum horizontal stresses, respectively; and pp
is the pore pressure.
However, FIP for a permeable rock may be significantly
affected by an additional induced-stress term, related to fluid pen136
etration from the wellbore to the formation. For a permeable rock,
FIP can be estimated by the Haimson-Fairhurst equation (Haimson and Fairhurst 1967):
3Shmin SHmax gpp
. . . . . . . . . . . . . . . . . . . ð2Þ
2g
1 2
g ¼ ap
; . . . . . . . . . . . . . . . . . . . . . . . . . . ð3Þ
1
pini ¼
where g is a poroelastic parameter of the rock, which determines
the magnitude of the stress induced by fluid penetration, and
varies in the range [0, 1], from zero fluid penetration to unimpeded fluid penetration, respectively; ap is Biot’s coefficient; and
v is Poisson’s ratio.
Fig. 2a shows the relationship between FIP, horizontal stress
anisotropy, and pore pressure for a vertical well with a constant
poroelastic parameter, g ¼ 0:5. It is clear that FIP decreases with
an increase in stress anisotropy. It is also clear that for a given
Shmin and SHmax, FIP also decreases with an increase in pore pressure. However, this observation must be viewed in proper context,
because Shmin and SHmax are generally a function of pore pressure
and overburden stress (Hubbert and Willis 1957; Matthews and
Kelley 1967) and increase with increasing pore pressure, if the
overburden is held constant or increases. With horizontal stress
ratio SHmax =Shmin ¼ 1:3, Fig. 2b shows a very interesting observation for the effect of g on FIP for a vertical well. That is, FIP
increases with the increase of g when the pore pressure is lower
than a certain value but decreases when pore pressure is higher
than that value. In this case, the crossover point is 0.85Shmin.
However, with the decrease of horizontal stress ratio, the crossover point will move to the right. The crossover point in Fig. 2b
will no longer exist on the x-axis scale when the horizontal stress
ratio is smaller than 1.2.
Fracture-Initiation Pressure of a Wellbore With Microfractures. As mentioned previously, when hydraulically conductive drilling-induced microfractures or pre-existing natural microfractures exist on the wellbore wall, the wellbore pressure that
begins to fail the formation rock is the propagation pressure for
the microfractures rather than the initiation pressure for any new
fractures. Therefore, the continuum-mechanics method with the
Kirsch equation to determine FIP is no longer valid. Instead, a
fracture-mechanics approach should be used to determine FIP (or
microfracture-propagation pressure).
Seeking to interpret LOTs for estimating horizontal stress, Lee
et al. (2004) analytically studied the propagation pressure of a
fracture extending from a wellbore in the direction of maximum
horizontal stress. This analysis is based on the Barenblatt condition, which dictates a balance between the tensile stress-intensity
factor produced by fluid pressure in the fracture and the negative
stress-intensity factor caused by the compressive in-situ stress
(Lee et al. 2004; Yew and Weng 2014). According to their study,
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1.3
SHmax
1.2
Shmin
1.0
1.1
1.2
1
1.4
Pini /Shmin
0.9
1.6
0.8
1.8
0.7
2.0
0.6
0.5
0.4
0.05
0.1
0.15
0.2
0.25
0.3
0.35
KIc/(Shmin*a0.5)
Fig. 3—FIP (microfracture-propagation pressure) decreases
dramatically with an increase in horizontal-stress anisotropy,
and increases moderately with an increase in fracture toughness; it can be much smaller than the minimum horizontal
stress with high stress anisotropy and low fracture toughness.
the FIP of a wellbore with microfractures (or microfracture propagation pressure) should be
pini ¼
3Shmin SHmax
KIc
þ pffiffiffiffiffiffi ; . . . . . . . . . . . . . . . . . ð4Þ
2
p 2L
where KIC and L are the fracture toughness of the formation and
the length of the microfracture, respectively. On the basis of Eq.
4, FIP is not only related to horizontal stress but is also a function
of fracture toughness KIC of the rock and microfracture length L.
By dimensionally normalizing the pressure and stress terms with
minimum horizontal stress Shmin , fracture length with wellbore
radius a, and fracture toughness with the product of minimum
pffiffiffi
horizontal stress and the square root of wellbore radius Shmin a,
Eq. 4 can be transformed to
p0ini ¼
3R
K0
ffiffiffiffiffiffiffi ; . . . . . . . . . . . . . . . . . . . . . . ð5Þ
þ pIc
2
p 2L0
0
, L0 , and R are dimensionless FIP, dimensionless
where p0ini , KIc
fracture toughness, dimensionless fracture length, and horizontal
stress anisotropy, respectively. Note that Eq. 5 has a mathematic
singularity signature, because the normalized FIP goes to infinitely high with a normalized fracture length approaching zero.
Dimensional analysis shows that with reasonable values for R and
0
, Eq. 5 is not suitable for a fracture length less than 0.01 in. In
KIc
fact, the wellbore can be considered intact, with a fracture as short
as 0.01 in.
Leakoff
pressure
Stage:
Page: 137
The fracture toughness of sedimentary rocks varies approximately in the range of 500 to 2,000 psi-in.0.5 (Senseny and Pfeifle
1984; Wang 2007), and horizontal stress anisotropy under most
geologic settings ranges from 1 to 2 on the basis of the authors’
experience. Assuming Shmin ¼ 3; 000 psi, wellbore radius
a ¼ 4:25 in:, and microfracture length L ¼ 0:5 in:, Fig. 3 shows
the FIP of a vertical well under various sets of horizontal stress
anisotropy and fracture-toughness conditions. It indicates that FIP
(1) is very sensitive to and decreases dramatically with an
increase in horizontal stress anisotropy, (2) increases moderately
with an increase in fracture toughness, and (3) can be much
smaller than the minimum horizontal stress with a relatively high
stress anisotropy and low fracture toughness.
From this analysis, it is critical to highlight the influence of
microfractures on FIP. For instance, in impermeable rocks, the
continuum-mechanics (Kirsch) equation predicts a FIP equal to
the minimum horizontal stress when stress anisotropy is 2.0.
However, with the same stress anisotropy, Fig. 3 shows FIP will
be far below the minimum horizontal stress, with a fracture length
of only approximately 10% of the wellbore radius.
Fracture-Initiation Pressure vs. Leakoff Pressure. In conventional field practice, LOTs are often used to estimate FIP, which
is taken as the pressure value at the first inflection point where the
pressure-ramp-up curve deviates from linearity before formation
breakdown. A typical pressure-volume/time response of an LOT
is shown in Fig. 4b.
Although it is commonly accepted that the leakoff point indicates the start of a fracture and should be identical to the FIP, a
careful analysis indicates they are not necessarily the same, especially when “dirty” mud (drilling fluid with high solids content) is
used for an LOT in a permeable formation.
For an intact wellbore with solids-free fluid or clean mud, fracture initiation is largely dominated by in-situ stresses. For a wellbore with microfractures and clean mud, fracture initiation is
controlled by the fluid-pressure distribution inside the fracture
(this will be analyzed in detail in a separate paper). The leakoff
pressure in these two cases should be approximately equal to FIP.
However, for a drilling fluid with high solids content (e.g., containing LCM), the mud properties may affect the observed leakoff
behavior and lead to a leakoff pressure very different from FIP.
This can be explained as follows.
When a short hydraulically conductive microfracture is created
during an LOT, in theory it should be easily extended with sufficient wellbore pressure. In reality, the microfracture may be
quickly sealed by mud solids, forming a filter cake within the
fracture. This “internal” filter cake can then isolate the fracture
from the wellbore, and not enough fluid pressure will reach the
fracture face to extend it. This “opening and healing” or
Formation-breakdown
pressure
Formation-breakdown
pressure
Formation-breakdown
pressure
Total Pages: 11
Time/Volume
(a)
Pressure
No clear leakoff
response at fracture
initiation
Pressure
Pressure
Leakoff
pressure
Time/Volume
(b)
Multiple leakoff points
Time/Volume
(c)
Fig. 4—Schematic pressure-volume/time curves in LOTs. (a) no visible leakoff response at fracture initiation, the leakoff pressure
is very close to formation breakdown pressure; (b) a clear leakoff point before formation breakdown; (c) multiple leakoff points
before formation breakdown.
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“fracturing and packing” behavior within the fracture can theoretically restore the pressure-containment capability of the wellbore,
and perhaps increase it to a higher value than the ideal case in
which no fracture exists.
This phenomenon is similar to wellbore strengthening. However, the “opening and healing” of such small fractures is not
likely detectable in a field LOT or even in a laboratory test (Guo
et al. 2014). In many field LOTs, it is difficult to identify a clear
leakoff response at the fracture-initiation point, and the leakoff
pressure can be very close to the breakdown pressure, as shown in
Fig. 4a. Therefore, the lack of a visible leakoff response reasonably below the formation-breakdown pressure does not necessarily mean a small fracture has not been generated.
Numerous elements may influence the signature of an LOT,
including the compressibility and elasticity of the mud, casing,
cement, and formation rock; fluid seepage from the wellbore wall;
and fluid leakoff into fractures. Among these factors, only the
effect of leakoff into fractures is observably nonlinear (Fu 2014).
Therefore, when there is a clear leakoff response, as shown in Fig.
4b, a relatively large fracture is likely to have been created, and
the leakoff pressure, commonly considered to be fracture initiation, is actually microfracture propagation. Undetectable microfracture generation has already occurred before this leakoff point,
so leakoff pressure is somewhat higher than FIP.
It is also possible to observe multiple leakoff points on the
pressure-volume/time curve. Fig. 4c shows a case in which there
are two inflection points. This signature is more common for
LOTs conducted in permeable formations, with a low pump rate
and high solids-content fluid. These observations may be
explained by a filter-cake break within the fracture, where wellbore pressure breaks the filter cake, leading to additional fracture
extension. The fracture will be quickly sealed again by solids in
the mud, and the wellbore pressure will continue to build. If the
subsequent wellbore pressure increases enough, the filter cake
may fail again, and the process is repeated. This repeated fracturing and healing behavior might continue until formation breakdown. It should be emphasized that a clear slope change in the
pressure-volume/time response during an LOT is usually after
fracture initiation. This response is most likely a filter-cake break
in a fracture larger than a microfracture, but still in the vicinity
and under the influence of the near-wellbore stress concentration.
Laboratory tests show that fractures can grow significantly without any clear leakoff signature (Guo et al. 2014).
It may not be possible to accurately predict FIP from an LOT
with a high-solids-content fluid. A slope-change point may be
undetectable before formation breakdown, or if detected, it may
indicate filter-cake breakdown rather than fracture initiation.
Fracture Propagation
After initiation, a fracture will tend to propagate from the wellbore
wall to the far field, under sufficient wellbore-fluid pressure. Typically, this fracture propagation consists of both a stable and an
unstable stage. During an LOT, the stable fracture-propagation
stage begins at fracture initiation or leakoff and ends roughly at formation breakdown. Initially, the fracture grows very slowly, and its
volume increases at a rate lower than the pump rate. Therefore, the
wellbore pressure continues to rise before formation breakdown,
which is the upper pressure limit for stable fracture growth.
The unstable fracture-propagation stage begins immediately
after formation breakdown. During a very short time period, the
fracture volume expands at a much greater rate than the pump
rate, and the wellbore experiences a sudden pressure drop. Ultimately, the wellbore pressure stabilizes as fracture propagation
continues, with a rate of fracture-volume increase roughly equal
to the pump rate. From a theoretical viewpoint, the FPP with clean
injection fluid will gradually decrease with the continued increase
in fracture length, as will be shown later in this paper. However,
from a practical viewpoint, the FPP can either increase or
decrease with fracture growth, likely caused by the high friction
pressure in a relatively large fracture and the complex nature of
formation rock.
138
Stage:
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Total Pages: 11
FPP is a very important parameter for well construction and
drilling-fluid design, especially for lost-circulation prevention. In
challenging areas with severe lost-circulation problems, XLOTs
are recommended to obtain reliable estimates of FPP.
Formation-Breakdown Pressure. With a clean fluid, the pressure required to initiate a fracture on the wellbore wall is usually
greater than that required to propagate the fracture into the formation. Furthermore, formation breakdown is often assumed to occur
when the hoop stress at the wellbore wall equals the tensile
strength of the rock (Hubbert and Willis 1957).
By use of a fluid with a high solids content, numerous laboratory and field tests (Morita et al. 1990; Aadnøy and Belayneh
2004; Liberman 2012; Guo et al. 2014) have shown that formation-breakdown pressure is often significantly higher than
that predicted by conventional continuum-mechanics theories.
This phenomenon may be elegantly explained by the filter-cake
sealing effect.
Before formation breakdown, the fracture size (length)
remains small, and fracture propagation is determined by fracture
toughness. When the fracture length is small, the toughness term
in Eq. 5 can be much larger than the stress term. According to linear elastic fracture mechanics, a tensile fracture will start to
extend when the stress-intensity factor KI reaches fracture toughness KIC ; that is,
KI ¼ KIC : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð6Þ
The stress-intensity factor KI is a function of fracture size and
geometry, as well as load condition. Fracture toughness KIC is a
material constant representing the strength of the material. For a
short fracture on the wellbore wall (as shown in Fig. 5a), on the
basis of linear elastic fracture-mechanics theory, the stress-intensity factor can be estimated by (Gray and Feng 2014)
pffiffiffiffiffiffi
KI ¼ 1:12ðPf Shh Þ pL; . . . . . . . . . . . . . . . . . . . . . ð7Þ
where Pf is the pressure inside the fracture and Shh is the average
normal stress (closure stress) acting on the fracture face and can
be roughly calculated by the Kirsch equation (neglecting the presence of the fracture). Hence, for a given fracture, Shh is only a
function of the wellbore pressure and the far-field stresses. In
most geologic settings, Shh is a compressive (positive) stress,
unless a very-high horizontal stress anisotropy (larger than 3)
exists. In order for KI to reach KIC to propagate the fracture, Pf
must be large enough to overcome the closure stress Shh . Therefore, for a given fracture, wellbore pressure, and horizontal
stresses, Pf acting on the fracture face should dominantly control
fracture propagation.
When the fracturing fluid is clean, wellbore fluid can easily
flow into the fracture and apply pressure to the fracture face,
approximately the same magnitude as wellbore pressure. Thus, a
stress-intensity factor higher than the fracture toughness is more
easily achieved, and the fracture will propagate. However, when
the fluid contains solids, the following mechanisms will significantly reduce or eliminate the pressure acting on the fracture face,
preventing fracture propagation:
• Solids are transported with fluid flow into the fracture,
resulting in a high solids density and fluid viscosity in the
fracture. The fracture may also be plugged/sealed by a filter
cake, as shown in Fig. 5b. A high solids density and/or fluid
viscosity will significantly increase the fracture-pressure
drop from fracture inlet to tip, leading to a much lower Pf
and smaller KI . Filter-cake sealing inside the fracture can
decrease further Pf as well as KI .
• Because of the small aperture of the fracture, it is very likely
to be bridged and sealed quickly by the filter cake, before
solids can enter the fracture, as shown in Fig. 5c. The low
permeability of the filter cake will restrict further fluid flow
into the fracture, and finally lead to Pf in the fracture equal
to pore pressure, caused by pressure bleedoff into porous
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Shmin
Total Pages: 11
Shmin
Pf
Shmin
Pf
Pw
Wellbore
Page: 139
Pf
Pw
Sθθ
Pw
Wellbore
Sθθ
L
Wellbore
Sθθ
L
(a)
(b)
L
(c)
Fig. 5—A small fracture on the wellbore wall before formation breakdown: (a) no filter-cake plugging with clean fluid; (b) high solids concentration or filter cake inside the fracture; (c) fracture is plugged at the inlet on wellbore wall.
rock. The excess pressure ðPf Shh Þ will then decrease or
become negative under most conditions. Therefore, the
stress-intensity factor will not reach the fracture-toughness
magnitude, unless the wellbore pressure builds high enough
to break the filter cake at the fracture mouth. As mentioned
previously, the “fracturing and healing” process can be
repeated several times before formation breakdown, and,
therefore, the formation-breakdown pressure may be significantly higher than the theoretically predicted FIP.
Fracture-Propagation Pressure. Theoretical Prediction. At
formation breakdown, the filter cake in the microfracture breaks
completely, allowing fluid to enter the fracture. The fracture then
grows quickly in both width and length, extending to the far-field
region. The wellbore pressure drops to the FPP. A great number of
field and laboratory hydraulic-fracturing tests have indicated that
FPP decreases with the increase in fracture length. This phenomenon might be partly caused by the minimal excess pressure
required to maintain fracture propagation with a large fracture
face, and partly caused by the high accessibility of a weak point,
with a large fracture circumference (Økland et al. 2002). However,
this phenomenon can be interpreted more elegantly with a coupled
fluid-mechanics and solid (fracture) -mechanics approach.
After the fracture has propagated a significant distance, the
influence of the wellbore on fracture-propagation behavior is
greatly diminished (Zheltov 1955). Fig. 6 shows a hydraulic fracShmin
Fracture
Well location
Q
2L
Shmin
Fig. 6—A large hydraulic fracture (wellbore at the fracture center is neglected).
ture with a neglected wellbore in the fracture center. Consider a
fracture with a length of 2L, perpendicular to the minimum horizontal stress Shmin , as shown in Fig. 6. The formation rock is
considered isotropic, homogeneous, linearly elastic, and impermeable. The fluid is assumed to be incompressible, nonviscous Newtonian fluid. It is injected through the well at the fracture center at
a constant rate Q. The pressure everywhere inside the fracture is
the same as wellbore pressure. With a coupled fluid- and solidmechanics method, similar to that of Detournay (2004), both the
fracture half-length and pressure during fracture propagation can
be determined as functions of time:
0
E Qðt t0 Þ 2=3
/ t2=3 . . . . . . . . . . . . . . . . . ð8Þ
aðtÞ ¼
2p1=2 KIC
pðtÞ ¼
E0 Qðt t0 Þ
/ t1=3 ; . . . . . . . . . . . . . . . . . . . . ð9Þ
2pa2
where t is injection time; aðtÞ is the fracture half-length at time t;
E
is the
pðtÞ is the pressure inside the fracture at time t; E0 ¼
1 v2
plane-strain modulus, which is a function of Young’s modulus E
and Poisson’s ratio v; and t0 is the start time of fracture propagation.
The pressure behavior theoretically predicted by Eq. 9 is schematically shown in Fig. 7a. Before t0 , the pressure builds up linearly inside the fracture without fracture propagation. At t0 , the
stress-intensity factor of the fracture reaches fracture toughness,
triggering sudden fracture propagation. Following t0 , the pressure
drops nonlinearly and proportional to t1=3 . Fig. 7b is the FPP
when water-based mud (WBM) was used as the fracturing fluid in
a laboratory test of the DEA-13 project (Morita et al. 1990; Fuh
et al. 1992). Apart from the fluctuating signature, a fitted curve
shows the pressure decreases proportionally to t0:305 , which is
reasonably close to the predicted result.
The previous model is established under the assumptions of an
ideal condition: The rock is impermeable, and the fluid is clean
with zero viscosity. Eq. 9 shows that FPP for the model depends
only on injection rate, injection time, and fracture toughness. In
reality, FPP also depends on a list of other factors including insitu stress, pore pressure, solids plugging, base-fluid leakoff, lithology, permeability, aqueous/nonaqueous fluid, rock wettability,
capillary force, and others. Most of these factors’ effects are not
independent, but related to others. Several of these factors’ effects
on FPP are discussed here.
In-Situ Stress, Pore Pressure, and Solids Plugging. Consider
a fracture similar to that in Fig. 6, which is perpendicular to the
minimum horizontal stress, but now the fracture is in a formation
with pore pressure pp , and is effectively plugged by solid particles
in the fracturing fluid at some location inside the fracture, as
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Pressure in Fracture ∝ t –1/3
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9
Pressure (1,000 psi)
Pressure in Fracture
8
6
5
4
3
t0
P ∝ t 0.305
7
0
100
200
300
Injection Time
Time (seconds)
(a)
(b)
400
Fig. 7—Pressure response during fracture propagation: (a) theoretical result (b) DEA-13 (Morita et al. 1990; Fuh et al. 1992) laboratory-test result.
shown in Fig. 8. Assume the plug is perfect without permeability;
thus, it completely stops fluid penetration. The fracture domain
behind the plug, from the wellbore to the plug, is wetted by fluid,
and its pressure is the same as wellbore pressure. The pressure in
the fracture section ahead of the plug (nonpenetrated zone) is
equal to pore pressure, caused by fracture pressure bleedoff into
porous rock. This model was first solved analytically by Abe et al.
(1976). On the basis of their work, the FPP for a large fracture can
be given roughly by the following equation:
pprop ¼
1
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
Lnw 2
1 1 1
L
2
3
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ffi
L
nw
5;
4Shmin pp 1 1 L
ð10Þ
where pprop is the FPP and Lnw is the fracture length of the nonpenetrated zone. Note that Eq. 10 is only valid for a fracture with a
length much larger than the wellbore radius. Therefore, the effect
of the wellbore can be ignored. Another limitation of this equation
is that it should not be used when the plug location is close to the
wellbore, because the detailed stress-concentration in the wellbore
vicinity is neglected. Eq. 10 also neglects the effect of fracture
toughness caused by its unimportant role when the fracture is
large. This is one of the major differences between large fracture
and microfracture propagation: The influence of fracture tough-
ness might be the dominant factor for microfractures, but it is trivial for large fractures.
It is indicated by Eq. 10 (also see Fig. 9) that FPP after plugging is primarily determined by the minimum horizontal stress,
pore pressure, and the nonpenetrated-zone length or the location
of the plug. As shown in Fig. 9, for a given minimum horizontal
stress Shmin , with an increase in pore pressure pp , FPP decreases.
Another important observation from Fig. 9 is that for low values
of pp =Shmin , corresponding to formations with hydrostatic or
abnormally low pressure, the FPP is very sensitive to nonpenetrated-zone size: the larger the nonpenetrated-zone size, the higher
the FPP. This confirms the statement in the stress-cage concept
(Alberty and McLean 2004; Feng et al. 2015) that the best place
to plug a fracture for wellbore strengthening is the fracture inlet
or mouth, and also the statement in the fracture-propagation resistance concept (van Oort et al. 2011) that plugging the fracture
to isolate its tip from wellbore pressure can significantly enhance
the fracture-propagation resistance (pressure). FPP in low-pressure formations, as shown in Fig. 9, can be increased several times
higher than the minimum horizontal stress. However, the influence of plugging is smaller for high values of pp =Shmin (e.g., formations with abnormally high pressure). Therefore, from the
pore-pressure point of view only, wellbore-strengthening methods
based on plugging the fracture might be more effective for
depleted reservoirs with larger differences between pp and Shmin
than for high-pressure formations with relatively small differences
between pp and Shmin .
4.0
Shmin
3.5
Pp /Shmin
Pf
Plug
Well location
Lnw
2L
Pp
Pprop /Shmin
3.0
0
2.5
0.2
0.4
2.0
0.6
1.5
0.8
1.0
1.0
0.00
0.20
0.10
0.30
Lnw /L
Shmin
Fig. 8—A fracture plugged by solid particles.
140
Fig. 9—FPP with nonpenetration-zone length, pore pressure,
and minimum horizontal stress.
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Shmin
Pf
Pp
2L
Shmin
Fig. 10—A stationary fracture model.
Fluid Leakoff Through Fracture Face. To investigate the
effect of fluid leakoff on fracture-propagation behavior, a stationary fracture model, as shown in Fig. 10, is used. In a hypothetical
fracture extending perpendicular to the minimum-horizontalstress direction, in a poroelastic rock with initial pore pressure pp
and time t ¼ 0, a fluid pressure Pf (greater than pp ) is applied
inside the fracture. The fracture fluid and pore fluid have identical
properties. Therefore, after applying fluid pressure, the normal
traction on the fracture face changes from Shmin to Pf (here, tension is positive) whereas the pore pressure on the fracture face
changes from pp to Pf . Detournay and Cheng (1991) indicated
that this problem may be examined by decomposing it into two
separate problems: (1) applying normal traction (fluid pressure) to
the fracture face while keeping pore pressure unchanged and (2)
applying pore pressure while keeping the traction constant. The
solutions of each problem are then superposed to obtain the full
solution of the original problem. In this case, only Problem 2 is of
interest (the effect of pore-pressure increase on fracture behavior,
caused by fluid leakoff through the fracture face). According to
the analysis results reported by Detournay and Cheng (1991), a
pore-pressure increase in this case will lead to a negative change
in both fracture volume and stress-intensity factor. As schematically shown in Fig. 11, the instantaneous fracture volume VC0 at
t ¼ 0 decreases to the long-term volume VC1 , when pore pressure
reaches Pf . The instantaneous stress-intensity factor KI0 also
drops to the long-term value KI1 . The decrease of fracture volume and stress-intensity factor reveals the fact that a pore-pressure increase as a result of fluid leakoff tends to close the fracture
and inhibit fracture growth.
Permeability. The previous analyses of fracture propagation
indicate that both solids-plugging- and fluid-leakoff-induced porepressure increases can contribute to preventing fracture propagation
or enhancing fracture-propagation resistance. Fluid leakoff, how-
Stage:
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ever, is well-recognized as a critical prerequisite for creating an
effective filter plug (Aston et al. 2007). Therefore, any factors affecting filter-plug formation and/or fluid leakoff can influence fracture
propagation and, hence, lost circulation and wellbore strengthening.
Permeability attracts much attention in lost-circulation and
wellbore-strengthening analysis, because it is generally believed
that only in permeable formations (i.e., sandstone) can an effective filter plug be formed. Conversely, in impermeable rocks (i.e.,
shale), it is generally believed that wellbore strengthening is not
likely to be successful, although several successful cases in shale
are reported with specific pre-engineered drilling fluids and LCM
(Aston et al. 2007). When permeability is low, as depicted in
Fig. 12a, the base fluid (or filtrate) leakoff rate is too low to allow
mud solids or LCM to aggregate in the fracture, and, therefore, an
effective filter plug is not formed. Low leakoff rates also mean
that very limited fracture pressure/energy is released into the formation. Therefore, pressure is trapped inside the fracture, facilitating fracture growth. On the contrary, in permeable formations, as
depicted in Fig. 12b, filtrate leakoff rate is high enough to form an
effective filter plug, and the pore-pressure increase caused by fluid
leakoff inhibits fracture growth, as previously discussed. In addition, fracture pressure/energy is easily released into the formation;
hence, less pressure/energy acts toward extending the fracture.
Capillary-Entry Pressure. In addition, if the wellbore fluid
(filtrate) and pore fluid are immiscible, capillary-entry pressure
Pce , also known as threshold capillary pressure, is an important
consideration for analyzing fluid leakoff behavior, especially if
pore-throat openings or capillaries are relatively small (Nelson
2009). Unfortunately, this parameter is often neglected for lost-circulation mitigation and wellbore-strengthening design. High Pce
can significantly inhibit fluid leakoff, filter-cake/plug development,
and pore-pressure increase. Pce , usually estimated by the YoungLaplace equation (Peters 2012), depends highly on the largest
pore-opening (throat) size, wettability (contact angle), and miscibility [interfacial tension (IFT)] of the drilling and pore fluids:
1
Pce ¼ 2cf ;m cosh; . . . . . . . . . . . . . . . . . . . . . . . . . ð11Þ
r
where Pce is the capillary-entry pressure, cf ;m is the IFT between
the wellbore fluid and pore fluid, r is the largest pore-opening radius, and h is the wetting (contact) angle.
It is clear from Eq. 11 that Pce increases as pore-opening size
decreases. When the difference between wellbore pressure and
pore pressure exceeds Pce , wellbore fluid (filtrate) will be pushed
(leakoff) into the formation and displace the pore fluid. The typical pore-opening size for sandstone is from several to dozens of
microns, but is much smaller for shale, in the range of several to
dozens of nanometers (Nelson 2009). In sandstone, Pce for hydrocarbons and brine is approximately 10 to 50 psi, and for shale it is
approximately 200 to 800 psi in the deepwater GOM, according
to the study by Dawson and Almon (2006). Because sandstone
has significantly lower Pce than shale, it is easier for the wellbore
fluid to leak off into sandstone, facilitating filter-plug development and pore-pressure elevation. In contrast, this is less likely to
+
Vco
Time
Vc∞
–
Stress-Intensity Factor
+
Fracture Volume
Page: 141
KI0
Time
KI∞
–
Fig. 11—Fracture volume and stress-intensity factor change with applying pore pressure to the fracture face only, while keeping
the traction on the fracture face constant.
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Permeable
Impermeable
Solid particles (LCM)
Solid particles (LCM)
Pf
Pf
Pp
Pp
(a)
Solid plug
(b)
Fig. 12—Hydraulic fractures in impermeable and permeable formations with high-solids-content fluid.
Water
Pore size
Shale
Sandstone
Solid particles
OBM/SBM
Fracture faces
Fig. 13—Fluid leakoff and filter-plug development controlled by capillary pressure for water-wet sandstone with larger pore size
and shale with smaller pore size. Formation fluid is water, whereas fracture fluid is OSM/SBM.
happen in shale because of its high Pce . Fig. 13 schematically
shows the fluid leakoff and the corresponding filter-cake/plug development controlled by capillary pressure for water-wet sandstone and shale when the fracture and pore fluids are oil-/
synthetic-based mud (OBM/SBM) and water (brine), respectively.
In addition to pore-opening size, rock wettability and fluid
immiscibility also control Pce and, therefore, fluid leakoff and filter-plug formation. It is also important to note that for extremely
low-permeability shale, fluid leakoff may be very restricted
regardless of fluid type. For brine-saturated, water-wet rocks with
relatively small pore-opening size, if the fluid is OBM/SBM, it
cannot easily enter the pore openings because of high IFT
between immiscible fluids, and therefore, there is little, if any,
fluid leakoff or filter-cake/plug development (Fig. 14). In contrast,
if the fluid is WBM, the water in the mud may readily invade the
pore openings, leaving the solid particles behind and thereby
forming a filter-cake/plug.
Brine
Solid particles
OBM/SBM
The preceding capillary-entry-pressure analysis may further
explain the following field observations:
• Lost circulation in fractured and silty shale formations occurs
much more frequently (Ziegler and Jones 2014; Wang 2007)
with OBM/SBM than with WBM, and it is often more difficult to cure fluid losses with OBM/SBM. Because of high
capillary-entry pressures, OBM/SBM cannot easily invade
the pores of water-wet shale and silty shale (most shale is
water-wet), and, therefore, all the fluid pressure acts toward
propagating the fracture tip. No effective filter plug is developed to isolate wellbore pressure and to increase fracturepropagation resistance.
• Wellbore “breathing” is a phenomenon that occurs when
formations take drilling fluid when the pumps are on and
give the fluid back when the pumps are off, because of the
opening and closing of drilling-induced fractures. This phenomenon is usually observed in water-wet shale (especially,
Fracture faces
WBM
Fig. 14—Fluid leakoff and filter-cake development controlled by fluid immiscibility and capillary pressure.
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silty-shale) formations, while drilling with OBM/SBM. One
plausible explanation is that OBM/SBM will often flow
back to the wellbore rather than leak off into the formation,
caused by very-high capillary-entry pressures (Ziegler
and Jones 2014). Conversely, WBM will leak off readily
into these same formations, rather than flow back to
the wellbore.
Conclusions
• FIP of a perfectly cylindrical wellbore can be determined by
continuum-mechanics methods (Kirsch equations). However,
for a wellbore with microfractures, fracture-mechanics methods
should be used to predict FIP.
• FIP of a wellbore with microfractures is controlled not only by
pore pressure and in-situ stresses, but also by fracture length
and fracture toughness of the formation rock. It can be much
lower than that of a perfect wellbore.
• Leakoff pressure from an LOT may not be equivalent to the FIP
when a high-solids-content “dirty” mud is used. Because of the
continuous sealing effect of dirty mud, the observable “leakoff”
pressure may instead be the filter-cake breakdown pressure
(i.e., propagation pressure) of a relatively larger sealed fracture,
rather than FIP of an intact wellbore wall.
• Formation-breakdown pressure is the upper pressure limit for
the stable fracture-propagation stage. During this stage, the
fracture size remains small, and a fracture-mechanics method
can be used to determine formation-breakdown pressure, which
is controlled to a very large extent by fracture toughness. A
high solids concentration in the drilling fluid, a filter cake inside
the fracture, and/or a filter plug at the fracture mouth can significantly increase formation-breakdown pressure.
• FPP is the fracture pressure during the unstable propagation
stage. A coupled fluid- and solids-mechanics method predicts a
decrease in FPP with an increase in fracture length.
• Plugging a fracture can significantly increase its propagation
pressure, especially in formations with large differences between pore pressure Pp and minimum horizontal stress Shmin .
Therefore, wellbore-strengthening methods that are based on
plugging the fracture should be more effective in depleted reservoirs with large differences between Pp and Shmin than in
deepwater overpressured formations with relatively small differences between Pp and Shmin .
• Fluid leakoff through the fracture face hinders fracture growth
by facilitating filter-cake development and reducing the fluid
energy available to propagate the fracture.
• Capillary-entry pressure Pce is an important and often neglected
consideration for lost-circulation mitigation and wellbore
strengthening. High capillary-entry pressures, associated with
small pore openings and immiscible fluids, can significantly
restrict fluid leakoff and filter-cake/plug development. Field
observations indicate that lost circulation in fractured and siltyshale formations occurs more frequently with OBM/SBM than
with WBM. In addition, the observation that wellbore breathing
typically occurs in water-wet formations drilled with OBM/
SBM may be elegantly explained by capillary theory.
Nomenclature
a ¼ wellbore radius, in.
aðtÞ ¼ fracture half-length at time t, in.
E ¼ Young’s modulus, psi
E0 ¼ plane-strain modulus, psi
KI ¼ stress-intensity factor, psi-in.0.5
KIC ¼ fracture toughness, psi-in.0.5
0
KIC
¼ dimensionless fracture toughness, dimensionless
L ¼ fracture length, in.
L0 ¼ dimensionless fracture length, dimensionless
Lnw ¼ length of the nonpenetrated zone, in.
Pce ¼ capillary-entry pressure, psi
Pf ¼ pressure inside the fracture, psi
pini ¼ fracture-initiation pressure, psi
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p0ini ¼ dimensionless fracture-initiation pressure, dimensionless
pp ¼ pore pressure, psi
pprop ¼ fracture-propagation pressure, psi
pðtÞ ¼ fracture pressure at time t, psi
Pw ¼ wellbore-fluid pressure, psi
Q ¼ injection rate, gal/s
r ¼ largest pore-opening radius, in.
R ¼ horizontal-stress anisotropy, dimensionless
Shmin ¼ minimum horizontal stress, psi
SHmax ¼ maximum horizontal stress, psi
Shh ¼ average closure stress on fracture faces, psi
t ¼ injection time, s
t0 ¼ start time of fracture propagation, s
ap ¼ Biot coefficient, dimensionless
cf ;m ¼ IFT between the wellbore fluid and pore fluid, lbf/in.
g ¼ poroelastic parameter, dimensionless
h ¼ contact angle, degree
v ¼ Poisson’s ratio, dimensionless
Acknowledgments
The authors wish to thank the Wider Windows Industrial Affiliate
Program, the University of Texas at Austin, for financial and
logistical support of this work. Project support and technical discussions with industrial colleagues from Wider Windows sponsors BHP Billiton, British Petroleum, Chevron, ConocoPhillips,
Halliburton, Marathon, National Oilwell Varco, Occidental Oil
and Gas, and Shell are gratefully acknowledged.
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Yongcun Feng is a PhD degree student in the Department of
Petroleum and Geosystems Engineering at the University of
Texas at Austin, where he performs research in lost circulation
and wellbore strengthening. Feng holds an MS degree in drilling engineering and a BS degree in petroleum engineering,
both from China University of Petroleum, Beijing. He is a member of SPE.
John F. Jones is a Senior Staff Drilling Engineer for Marathon Oil
Company in Houston. He currently specializes in wellbore stability and geopressure analysis for operations worldwide,
including seal capacity and column-height estimation for the
international and GOM exploration groups. During his 28 years
in the industry, Jones has also worked as a logging and petroleum software-development engineer and in various capacities as a rigsite supervisor, office drilling engineer, and drilling
superintendent for US and international drilling-and-completion operations. He holds a BS degree in petroleum engineering from the University of Texas at Austin.
K. E. Gray is a professor of petroleum engineering at the University of Texas at Austin. He teaches advanced drilling and
conducts research in drilling, rock mechanics, wellbore stability, and geomechanics applications to managed-pressure
drilling. Gray is a Senior Member, Life Member, Distinguished
Member, and Legion of Honor Member of SPE. He holds two
drilling patents, served twice as an SPE Distinguished Lecturer,
and has received the SPE North America Drilling Engineering
Award and the SPE International Drilling Engineering Award.
Gray holds BS and MS degrees from the University of Tulsa and
a PhD degree from the University of Texas at Austin, all in petroleum engineering.
June 2016 SPE Drilling & Completion
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