better reservoir management through improved waterinjection method with data analysis and deail fracture model reservoir

Copyright 2007, Society of Petroleum Engineers

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Abstract
The search for practical engineering tools to better manage
water injectors has been ongoing for many years. Simple
analytical solutions have proven inadequate, and most reser-
voir simulators do not explicitly model water injectors. This
paper proposes a methodology of using detailed and coupled
fracture and reservoir modeling to ensure proper injection
start-up procedures, and managing injection rates to avoid out-
of-zone injection. This is combined with simple rate-pressure
data to understand injection behavior, and from that control
the process.

Introduction

Water injection, in particular produced water injection, in most
cases creates a fracture. As is well established

[1], temperature
effects are important, because the cold injection fluid reduces
the temperature of the near well formations, leading to a
reduced minimum in situ stress. If the fracture remains within
the cooled region, the reduced stress may be a significant
factor in reducing fracture height growth, or in other words,
for the confinement of the fracture to a given formation. As a
result, simulations of water injection need to take fracturing
and the temperature effects on fracturing into account.
In this paper we briefly review some elementary aspects of
the response of a fractured injector. We proceed to show field
examples of fracture growth, with particular emphasize on its
episodic nature.
Next, we describe a new model for the simulation of water
injection, which includes thermal effects and plugging due to
dirty injection water.
The main part of the paper is a discussion of some
simulations, focusing in particular on how the rate schedule of
injection start-up may be used to influence the height growth
of the fracture. This is of central relevance for many field
cases, where it may be imperative to constrain fracture height
growth, e.g. to avoid growing into a thief zone.
In terms of reserve recovery, this is crucial. If the fracture
grows into high permeability layers, those layers begin to ac-
cept more injection. This causes preferential cooling in those
zones, reducing closure stress there. The fracture then migrates
there, further increasing injection into that zone, causing more

cooling, etc., etc. Ultimately, this causes early water break-
through and lost reserves!

Basic injector performance
With modern data acquisition systems, extensive datasets are
normally available for all or many of the injectors in a field.
Hence it is important to find an effective way of screening the
data, in order to single out the features for further study. A plot
of large amounts of data in a pressure versus rate plot may be
an effective method, in particular if color coding is used to
separate different time intervals.
Before showing real data, we briefly recap the main
features of injector response in the pressure versus rate
domain. Fig. 1 schematically shows the response of an injector
working both in the matrix and fracture regimes. The full line
describes an initial situation, in which the injector injects into
matrix up to a given pressure where the fracture opens, and an
increased injectivity results. The dashed line shows the change
resulting from a stress reduction due to reservoir cooling. To a
first approximation the slopes of the matrix and fracture
injection lines are unchanged, but the intercept takes place at a
lower pressure due to the reduced reservoir stress.
The dash-dot lines show the effect of pressure build-up
around the injector. This affects both the matrix injection and
the fracture injection. Note how the intercept occurs at a lower
injection rate. This is because the matrix injection responds
directly to the pressure, while the initiation of fracture
injection responds to the changes in the leakoff stress, which is
general smaller.
Fig. 2 shows the effects of changing the injector’s choke.

The curved full lines correspond to various choke settings,
while the straight lines represent two different values of
injectivity. If, for a fixed choke setting, the injectivity changes
for some reason, the response will stay on the fixed choke line.
Thus, the path in the p-q plot is fully determined by the choke
setting, and in itself cannot say anything about the mechanism
leading to the change in injectivity.


SPE 110329
Better Reservoir Management Through Improved Water
-Injection Methods With Data
Analysis and Detailed Fracture/Reservoir Modeling
Håvard Jøranson, SPE, Statoil; Henry H. Klein, SPE, H.K. Technologies; Arne M. Raaen, SPE, Statoil; and Michael B. Smith, SPE, NSI
2 SPE 110329
Analysis of injector data
In this section we will show some field examples of injector
response, focusing on effects of reservoir pressure build-up
around the injection well and on fracture growth incidents.

Reservoir Pressure Build-Up Effects
Although a steady injection is aimed for, an injector will in
practice be shut in and reopened at irregular intervals during
normal operation. It is generally attempted to close and reopen
an injector in a controlled manner, with a constant choke
closing/opening rate, but in certain situations a fast shut-in
may be necessary. Depending on the cause for the shut-in, the
length of the shut-in interval may vary from a few hours or
less up to several days. As a result, data from the daily ope-
ration of an injector may give information on local reservoir

pressure build-up.
The basics of the influence of reservoir pressure build-up
around injectors were discussed in conjunction with Fig. 1.
Fig. 3 shows a field example of pressure versus rate data for a
period of about two weeks. Prior to the period, the injector
was shut in for several days. This example demonstrates that
the simple principles outlined above are relevant for field data:
The 3 main groupings of data (emphasized by the pairs of
solid lines in the figure) result from injection being shut-in for
various periods of time. The data indicated by the rightmost
solid lines (red data points) is for the start-up after several
days of shut-in, while the leftmost data is a controlled shut-
down after some days of injection at full rate. The middle data
are from the start-up after a shorter shut-in period.
Note how the intercept of the matrix and fracture lines
occur at lower flow rate for the pressured-up cases, in accord-
ance with Fig. 1. The vertical separation of the matrix
injection lines is an indication of the change in near well
pressure, while the vertical separation of the fracture lines is a
response to the change in in situ stress seen by the fracture.
Hence, plots like Fig. 3 may be a quick method to determine
the reservoir stress path (Δσ
h
/Δp). However, much caution is
necessary, since temperature effects etc. may strongly in-
fluence the situation. Also, the measured stress path is relevant
for the situation around the injector, and not necessarily for the
field itself.
The data in Fig. 3 are particularly easy to interpret, since
the typical time for pressure build-up is long compared to the

time used for starting and stopping the injector. If the time
constants are more similar, the trends during start-up and shut-
down will deviate from straight lines.

Fracture growth episodes
As shown in Fig. 2 any pressure-rate change at constant choke
appears as a line with negative slope in the pressure versus
rate (p-q) plot. When reservoir pressure build-up around the
injection well is significant, such negative slope changes will
occur after any choke change. When the choke opening is
increased, the initial response is to move up-right along an
injectivity line. Increased injection rate may then locally
increase reservoir pressure/stress, causing the negative slope,
constant choke event (up-left). Similarly, closing (reducing)
the choke would first cause a reduced pressure/rate, a
movement down-left along the injectivity line. Reduced
injection rate then results in a reduction in near wellbore
reservoir pressure that might then cause a negative p-q slope
constant-choke event (down-right).
Sometimes, however, similar behavior is observed even if
the choke has been constant for a long time. In such cases, a
“negative slope event” is a signal of a change in injectivity not
related to reservoir pressure build-up. Often, one will see that
the increase in injectivity is only temporary, and in such cases
the “negative slope events” stand out clearly from the main
injector response.
Fig. 4 shows an example with several events that can not
be related to reservoir pressure build-up around the injection
well. The plot quickly identifies some events that may be can-
didates for further investigation.

Fig. 5 shows pressure and rate versus time for one of the
incidents in Fig. 4. The rate increases significantly over a few
hours, while the injection pressure drops correspondingly. We
emphasize that the choke was kept constant prior to, during
and after the incident. Then, the situation is more or less re-
stored over a few hours. We interpret this as a fracture growth
incident, which exposes fresh formation, possibly in a lower
pressure regime. Then injectivity reduces as the faces of the
new part of the fracture gradually plug, or reservoir pressure
builds up around the recently exposed fracture.
During the life of the injector, many such incidents occur,
indicating episodic fracture growth. The size of the episodes
may be very significant, as demonstrated in Fig. 5, or much
less pronounced, as seen in Fig. 6. This response is an indica-
tion of repeated small fracture growth incidents, resulting in a
net increase in injectivity.

A New Simulator
Clearly, as seen in the injection/time histories above, water
injection is complex. As opposed to “simple” hydraulic frac-
turing, changes in reservoir pressure/temperature have a strong
impact on fracturing and injectivity. Thus, the problem be-
comes highly “coupled”. Injection can alter the injection and
the fracture geometry, fluid loss from the fracture, reservoir
pressure/temperature/stress changes, etc. must all be consi-
dered simultaneously.
This complex behavior also forces the use of “Fully” 3D,
planar fracture geometry simulations. Since the exact path of
fracture growth cannot be predicted with any reasonable cer-
tainty (except maybe for very simple, single layer cases), sim-

pler “2D”/“Pseudo 3D” fracture growth models are not appli-
cable.
The numerical model (using a combination of finite ele-
ment/finite difference techniques) employed in the data analy-
sis here implicitly couples a planar, “Fully” 3-D, gridded frac-
ture propagation model to a 3-D single phase, multi-compo-
nent, variable temperature reservoir simulator. The coupled
model includes thermal and pore pressure modification of
stress, “filter cake” build-up and plugging on the fracture face
inhibiting leakoff. The simulator was used to study the long
term injection (> 1 year) on fracture evolution and water
placement in the reservoir and to identify the importance of
the each of the phenomena of permeability contrasts (vertical
and horizontal), stress contrasts, plugging, and injection rate.
The details of the model for fluid flow in the fracture and
fracture propagation are presented in [2], and the details of the
SPE 110329 3
coupled fracture-reservoir model are presented in [3]. An
overview is included in Appendix A.
In standard fracture models leakoff is determined analyti-
cally using the standard “Carter” leak-off coefficients. In the
present model fluid loss from the fracture face is directly
computed from flow into the reservoir.
Finally, as discussed in more detail below, a fluid “filter
cake” effect was used to simulate the effects of water quality
on fracture growth for injection above fracturing pressure.
This C
W
, i.e., filter cake, effect was based on laboratory core
data for a formation similar in character to the zones studied

here.

Some example results
Discussions below present results demonstrating the role of
thermally induced waterflood fracturing in vertical sweep con-
formance of injection wells. In highly variable reservoir qual-
ity sands, injection water tends to be injected into the best
zones. This promotes cooling, and the resulting thermally
induced fracturing further enhances injection into these zones.
This phenomenon has been thoroughly discussed previously
[4,5], and typical field experience is early water breakthrough
in the high permeability layers, leaving the other zones poorly
swept with poor reserve recovery.
While the example simulations below use data from actual
cases, the discussion is meant to be general. The reservoir se-
quence is shown in Fig. 7. Injection water has a downhole
temperature of 25 °C, and initial reservoir temperature is
80 °C. The reservoir rock is quite “soft”, a Young’s modulus
of, 2–6 GPa (about 0.3–0.9×10
6
psi).
Since thermally induced stress changes are related to the
modulus (and the coefficient of thermal expansion)
TE
T
Δ∝Δ
α
σ

it might be expected that cooling effects are not significant.

However, for injection above fracturing pressure, the low
modulus also leads to low net pressure (i.e., the injection pres-
sure above fracture closure pressure), and thus, relatively
small stress changes might be important. Only detailed,
rigorous simulations can address such questions.
The “pre-injection” in situ stresses are additional important
data, and the stress profile in the figure is based on differential
depletion measured prior to the start of injection. Initially, all
sands and shales in this reservoir have similar horizontal
stress. With depletion in the sands, a stress contrast between
sand/shale layers develops.

Reservoir Goals
For the example well in the figure, the injection goal is to
achieve maximum injection into the zones from 2482–2507 m.
Ideally, some fracture growth upwards would provide
injection and sweep into the zones from 2450 to 2482 m.
However, fracture growth into the high permeability zone with
its base at 2445 m must be avoided.

Effects of Injection Rate
All simulations use a constant injection rate in each step. We
first study the effect of rate, and want to find the maximum in-
jection rate that can be injected into the sands between 2482–
2507 m. Ideally we would like to see some fracture growth to
sweep the sands above, but fracture growth into the extremely
high permeability sand with base at 2445 m must be avoided.
Table 1 shows the injection history for the well during the
first 2 months of injection. Fig. 8 shows the fracture geometry
after this injection. What is seen is that the well is fractured,

but there is no need to extend the fracture more than what is
needed to bypass the plugged near wellbore area, i.e. there
seems little risk of fracture growth out-of-zone from this lim-
ited interval at this limited rate.
The simulations assume very dirty water is injected. The
“C
W
” of the model represents the lab data shown in Fig. 9,
where the sea water in this case had a particle (fines) content
of 0.00375. That is, 0.375 % by volume of the fluid was solid
particles. Injection water samples from the field have been tak-
en in a few wells. They show a particle content typically much
less than 1/10 of the lab data. In actual fact, the lab tests do
NOT show a physical filter cake, rather the apparent “C
W
”
effect is caused by formation damage a short distance into the
formation. Presumably this damage is related to the volume of
particulates, just as a physical filter cake is related to the
thickness of the filter cake (i.e., to the volume of fines). In that
case, C
W
is related to the particle concentration
fluidfines
cakecake
W
2
μ
C
pk

C
Δ
∝

where C
fines
is the volume fraction of particles. Thus, if the
actual particle concentration is 1/10 (0.000375), then C
W
is
increased by a factor of √10.
When simulating the dirtier water, the need for bigger frac-
tures is enhanced. The simulations should therefore represent a
conservative view on the effect of fracture growth. Simula-
tions with no particles in the water show no fracture is created.
Naturally, there would be substantial benefit from in-
creased injection rate. Fig. 10 shows the results of an injection
period of 200 days at 4000 m
3
/D. As seen, even this rate can
be injected without undesired height growth.
To demonstrate that “any rate” can be injected into this
moderately permeable sand, a simulation with 9000 m
3
/D was
run for an injection period of 200 days. Fig. 11 shows a frac-
ture half-length of about 120 m, but almost no height growth
outside the perforated interval.
Thus, a different problem, we need to perforate the sands
higher up to achieve vertical sweep, but we still must avoid in-

jection into the extremely high permeability sand at the top.
Simulations were then run to determine if a fracture starting
from the next sand up (2468–79 m) would sustain injection
without frac growth into the high permeability sand at the top.
The width profile after 200 days at 1500 m
3
/D is shown in
Fig. 12. The fracture has grown down into the lower, more
permeable sand, but still injects into newly perforated sand
and the sand above. There is no risk of fracturing into the
extremely permeable sand at the top. The figure also shows
the leakoff contours, showing most of the leakoff at the tip and
dominated by the permeability. However, while the highest
rates of injection are, of course, into the higher permeability
zone, overall this injection scenario slightly favors the poorer
quality rock as seen in Fig. 13. This appears to be a reasonable
possible injection plan, and further investigation of higher
rates would be required.
4 SPE 110329
Taking this one step further, i.e. perforating the next sand
up and injecting at 2000 m
3
/D will result in a fracture growing
into the top sand after 5–6 days. The width profile after
100 days of injection is shown in Fig. 14. Due to cooling
effects, the fracture is migrating near totally into the overlying
zone.
Since fracture propagation is strongly affected by injection
(increased reservoir pressure around the well and formation
cooling) it should be possible to control fracture height

growth. That is, cooling the formation by injecting at a low
rate will reduce stress; rate can then be gradually increased. In
this way one could force a fracture to be contained. Simula-
tions were conducted to design such an injection scheme for
this example case.
Assuming the same perforation interval as the case above
(where undesired, upward height growth occurred), injection
start-up used a relatively low rate of 1000 m
3
/D for 50 days,
1500 m
3
/D for 50 days and finally 2000 m
3
/D. The evolution
of the fracture is pictured in Fig. 15.
In the first picture (after about 1 day), contours show the
essentially instant response to injection pressure. Fracture clo-
sure pressure has increased by about 35 bar (at the wellbore) –
with no apparent cooling (stress reduction) effects yet appear-
ing. Then after about 1 week (second picture), one sees a re-
gion of “0” stress change near the wellbore. The poro- and
thermal effects cancel. Finally, the third picture shows the
stress change after about 50 days. This shows a stress reduc-
tion of about 15 bar in the injection zone. Note, however, that
the stress reduction in the shale at 2454 m is even greater
(−35 bar). Basically, the thermal effects are slower/larger in
the shale since the cooling is only by conduction (no convec-
tion from fluid flow through the rock). However, there is NO
poro-effect. Thus, the overall effect (for this case) is a greater

stress reduction in the shale than in the sand. Thus, eventually
fracture height growth may occur. However, even though
“breakthrough” may occur, the large fracture area open in the
deeper, lower permeability zones would continue to allow
those zones to dominate injectivity long after “breakthrough”.
For even better height confinement (for this case), a lower
initial rate would be required in order to let the formation
cooling move out into the formation faster than the fracture
length growth. This would then further reduce injection pres-
sure, and totally prevent any fracture height growth into the
shale. At that point, the shale cool down, stress reduction
would depend solely on vertical heat conduction, further de-
laying shale stress reduction and subsequent height growth.
The final picture shows the fluid loss (inflow into the for-
mation) distribution at the end of 200 days. Fracture growth
downward has contacted the lower sand, and upward height
growth is nearing the overlying, high permeability zone. The
major difference between upward/downward growth is that the
upper shale is slightly thicker, thus cooling by conduction
takes additional time. While not plotted here, eventually after
a year, the fracture did penetrate the high permeability zone.
However, even for months after “‘breakthrough”, the deeper,
lower permeability zones still dominated injectivity.


Conclusions
• As expected, and discussed many times in the literature,
reservoir cooling has a strong effect on fracturing. Even
for this low modulus formation, there is a strong tendency
to keep fractures well confined. However, even where

shale barriers exist, eventually cooling via conduction
may reduce the stress in the shale and allow vertical
fracture migration.
• Start-up procedures can be used to reduce or delay un-
wanted height growth. However, the exact procedure or
injection pattern will depend on the specific conditions of
permeability, fluid/formation temperatures, etc. In gene-
ral, however, cooling of shale layers via conduction will
eventually cause stress reduction and fracture height
growth may resume.
• Quite “dirty” water can be injected as long as fractures are
allowed to grow with no danger of fracturing into “forbid-
den” zones.
• The combination of detailed injection data, a simple “p-q”
plot, and rigorous coupled model (simultaneously
considering injection, fracture growth, temperature, pore
pressure, etc.) can provide a powerful engineering tool for
management of water injectors.

Nomenclature
A = Area
A
p
= Poroelastic constant
A
T
= Thermoelastic constant
B = Biot coefficient
C = Concentration
C

t
= Compressibility
E = Young’s modulus
K = Stiffness matrix
T = Temperature
V = Volume
k = permeability
p = Pressure
q = Flow rate
w = width

α
T
= Coefficient of thermal expansion
φ =
Displacement potential

σ
= stress

μ
= Viscosity
ν =
Poisson's number

References
1. Perkins, T.K. and Gonzalez, J.A., The effect of thermoelastic
stresses on injection well fracturing. Soc. Petr. Eng. J., 25, 78–
88, 1985.
2. M. B. Smith, A. B. Bale, L. K. Britt, H. H. Klein, E. Siebrits,

and X. Dang, “Layered Modulus Effects on Fracture
Propagation, Proppant Placement, and Fracture Modeling,”. SPE
71654, presented at the 2001 SPE Annual Technical Conference
and Exhibition. New Orleans, Louisiana, 30 September–3
October 2001.
3. Michael B. Smith, Michael Bose, Henry H. Klein, Brent R.
Ozenne, Ron S. Vandersypen, “High-Permeability Fracturing:
"Carter" Fluid Loss or Not”, SPE 86550 presented at the SPE
International Symposium and Exhibition on Formation Damage
Control held in Lafayette, Louisiana, 18–20 February 2004.
SPE 110329 5
4. Clifford, P.J., “Simulation of Waterflood Fracture Growth with
Coupled Fluid Flow, Temperature and Rock Elasticity,”
presented at the 2
nd
joint IMA/SPE European Conference on the
Mathematics of Oil Recovery, Cambridge, 25–27 July 1989.
5. Clifford, P.J., Berry, P.J., Hongren, G., “Modeling the Vertical
Confinement of Injection-Well Thermal Fractures”, SPEPE,
6(6), 377–383, 1991.
6. E. J. L. Konig, “Fractured Water Injection Wells – Analytic
Modelling of Fracture Propagation,” SPE 14684 (Unsolicited),
1985.


Appendix A
The fracture evolution is determined by volume conservation
of the fluid,

()

x
zpl
V
qq qq
t
∂
+Δ + = +
∂
(A-1)
where V is the local fracture volume = wA
y
, w is the fracture
width, A
y
is the area

of the fracture face,
x
q and
z
q are the
volumetric flow rates along the length and height of the
fracture respectively. These flow rates are functions of the
pressure gradient, the (non-Newtonian) viscosity, and the
width.
p
q is the pump rate and
l
q is the leakoff rate at the
fracture face

p
. The fracture width is related to the pressure
through the fracture stiffness,

[
]
[
]
[
]
Kw p
σ
=− (A-2)
K is the stiffness matrix, pre-calculated using the finite
element method for varying layer moduli or analytically for
uniform modulus using a boundary integral approach. p is the
pressure and  is the stress.
In the standard fracture models the leakoff is determined
using the standard “Carter” leak-off coefficients. In the present
model the fluid loss from the fracture face is directly from
flow into the reservoir. The leak-off rate is

()
y filtrate reservoir fracture
l
filtrate l
Ak p p
q
L
μ

−
=− (A-3)
where
f
iltrate
k
is the permeability inside the fracture-reservoir
face, and can include relative permeability effects;.
f
iltrate
μ
is
the viscosity of the fluid inside the fracture-reservoir face, and
it can include non-Newtonian and temperature effects.
reservoir
p is the pressure at the reservoir face, and
f
racture
p is
the pressure at the fracture face.
l
L is a length that includes
gel and solids filtercake buildup on the fracture face, the
distance of the invaded zone of the leak-off fluid, and the
compressibility of the reservoir fluid
The volume conservation in the reservoir is given by

0
y
x

z
t
k
k
k
pp p p
C
tx x y y z z
μμμ
⎛⎞
⎛⎞ ⎛⎞
∂∂ ∂ ∂ ∂ ∂ ∂
+− +− +− =
⎜⎟
⎜⎟ ⎜⎟
∂∂ ∂ ∂ ∂ ∂ ∂
⎝⎠ ⎝⎠
⎝⎠
(A-4)
t
C is the compressibility of the reservoir fluid;
x
k ,
y
k ,
z
k are the permeabilities in the three space dimentions;  is
the fluid viscosity.
Equations (A-1)–(A-4) are solved simultaneously for the
fracture width and the pressure in the fracture and reservoir.

Equations for the conservation of energy are solved to provide
the temperature in the fracture and reservoir.
As the injected fluid leaks off from the fracture the
reservoir pore pressure increases and the temperature increases
or decreases depending on the relative injected and reservoir
temperatures. The pressure and temperature changes have a
direct effect on the stresses confining the fracture. Following
Konig [6] the poro-thermo stress change is

1
ij p ij T ij
ij
E
Ap AT
vx x
σ
ϕδ δ
∂
∂
Δ= +Δ +Δ
+∂∂
(A-5)
 is the displacement potential which is a solution to the
Poisson Equation

2
11
pT
Ap AT
EE

ν
ν
φ
++
⎛⎞ ⎛⎞
∇=−Δ −Δ
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
(A-6)
Δp is the pressure change from the initial reservoir pressure,
and ΔT is the temperature change from the original reservoir
temperature.
p
A is the poro-elastic constant defined as

12
1
p
A
B
ν
ν
−
=
−
(A-7)
where B is Biot’s constant.
T
A is the thermo-elastic constant defined as

1
T
T
E
A
α
ν
=
−
(A-8)
where
T
α
is the thermal expansion coefficient.
Equations (A-5) and (A-6) are solved to give the change in
local fracture confining stress. The updated stresses are used in
Equation (A-2) to give the fracture response to the stress
changes.




6 SPE 110329

Figure 1 – Basic injector response. The full (black) line shows
the transition from matrix to fracture injection at the level
indicated by the dotted gray line. The dashed (blue) line shows
the effect of cooling. Similarly, the dash-dot line (red) shows
how reservoir pressure increases around the injector changes
both matrix and fracture injectivity. Note how the crossing

moves towards lower rate, as discussed in the text.

Figure 2 –Basic injector response. The dashed (blue) lines
correspond to two different injectivities, while the solid (black)
lines apply for different choke settings. If injectivity changes
with constant choke, the response will move along the choke
curves, as illustrated by the thick (red) line segments.

Figure 3 – Field example of reservoir pressure build-up around
an injector. The data points are colour coded with rainbow
colors, with early data being red and late date being blue. The
solid black lines indicate the matrix and fracture injection
regimes for three different levels of pressure build-up around
the injector, as dicussed in the text.

Figure 4 – Field example of fracture growth incidents. Most of
the data points gather around the fracture injection “line”, but
there are several “negative slope events” corresponding to
temporary increase in injectivity. One of the events is shown in
more detail in Fig. 5.
SPE 110329 7

Figure 5 – Flow rate (upper) and pressure (lower) versus time
for one of the fracture growth incidents in Fig. 4.


Figure 6 – Field example of a series of smaller fracture growth
incidents, leading to a net increase in injectivity. Note, however,
how the injectivity decreases following each event.
Heidrun A49 Lower Tilje Injection_LastSP
TVD (m)
240024202440246024802500
ShalesandSilt
GR API
0200100
RHOB g/cm3
1.95 2.952.45
Pcl
(Bar)
300 400

E
(MMpsi)
0.0 1.6
K
Ic
02000
S
Heidrun A49 Lower Tilje Injection_LastSP
TVD (m)
240024202440246024802500
ShalesandSilt
GR API
0200100
RHOB g/cm3
1.95 2.952.45
Pcl
(Bar)
300 400
E
(MMpsi)
0.0 1.6
K
Ic
02000
S
Drag logs onto
graphs as desired

Figure 7 – Geologic layering for example simulations
8 SPE 110329

Table 1 – Actual Startup Injection Rate History
Injection - (m
3
/D) Time - (Days)
950 4
1250 9
1550 4
0 21
2000 7

Fracture Penetration (m)
10 20 30
64145.82 min
2470

m
TVD
2480
2490
2500
2510
Stress (Bar)
350 375
sandsandsandShale
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
Width - Total in

Figure 8 – Fracture Geometry After Startup Injection


10 20 30 40 50 60 70
20
40
60
80

Pore Volumes Injected
Start Dirty Water
5 micron particles
Solids Fraction 0.00375
Consta nt Flowrate
Variable
Δ
p

5101520
20
40
60
80
√
Time (min)
Loss Volume (cc/cm )
2
C = 0.0164 X Slope
= 0.065 ft/
√
min
W

Figure 9 – “C
W
” for “Dirty” Injection Water
Fracture Penetration (m)
20 40 60 80
274305.16 min

2460
2480
m
TVD
2500
2520
2540
Stress (Bar)
320 360 400
sandsandShalesand
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
Width - Total in

Figure 10 – 4000 m
3
/D

Figure 11 – 9000 m
3
/D

SPE 110329 9















Fracture Penetration (m)
20 40
273328.97 min
2460
m
TVD
2480
2500
Stress (Bar)
320 360
sandsandsandShale
0.000
0.025
0.050

0.075
0.100
0.125
0.150
0.175
0.200
0.225
0.250
Width - Total in

Fracture Geometry after 200 Days
Fracture Penetration (m)
20 40
273328.97 min
2460
m
TVD
2480
2500
Stress (Bar)
320 360
sandsandsandShale
0.000
0.500
1.000
1.500
2.000
2.500
3.000
3.500

4.000
4.500
5.000
Leakoff M3/Day

Injection Distribution after 200 Days
Figure 12 – Injection of 1500 m
3
/D into “middle” zone (2468–
79m)
00.20.40.60.8
Fraction "kh"
Fraction Injection
2456-63m
2468-79m
2482-89m
2489-
2507m
Shale
Shale

Figure 13 – Cumulative Injection Distribution
(1500 m
3
/D for 200 Days)

Figure 14 – Injection into “Top” Zone at 2000 m
3
/D. The fracture
penetrates into the overlying, “forbidden” high permeability

zone in < 1 week.
10 SPE 110329








Fracture Penetration (m)
10 20 30 40 50 60 70 80
1494.05 min
2400
m
TVD
2410
2420
2430
2440
2450
2460
2470
2480
Stress (Bar)
320 360
sandsand
(50.000)
(40.000)
(30.000)

(20.000)
(10.000)
0.000
10.000
20.000
30.000
40.000
50.000
Stress Change Bar

Fracture Penetration (m)
10 20 30 40 50 60 70 80
10134.05 min
2400
m
TVD
2410
2420
2430
2440
2450
2460
2470
2480
Stress (Bar)
320 360
sandsand
(50.000)
(40.000)
(30.000)

(20.000)
(10.000)
0.000
10.000
20.000
30.000
40.000
50.000
Stress Change Bar

Fracture Penetration (m)
10 20 30 40 50 60 70 80
70614.05 min
2400
m
TVD
2410
2420
2430
2440
2450
2460
2470
2480
Stress (Bar)
320 360
sandsand
(50.000)
(40.000)
(30.000)

(20.000)
(10.000)
0.000
10.000
20.000
30.000
40.000
50.000
Stress Change Bar

Fracture Penetration (m)
10 20 30 40 50 60 70 80
305647.00 min
2400
m
TVD
2410
2420
2430
2440
2450
2460
2470
2480
Stress (Bar)
338 360 382
sandsand
0.000
1.000
2.000

3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
Leakoff M3/Day

Figure 15 – Effect of Injection Start-Up on Fracturing