This study analyzes the effects of anisotropies on production performance during waterflooding under fracturing conditions. Reservoir simulations were conducted with varying permeability anisotropy and oil types. The results show: 1) Higher permeability anisotropy led to lower sweep efficiency, as indicated by decline indexes less than 1 for most production parameters. 2) Introducing fracturing generally improved sweep efficiency over cases without fracturing, as recovery indexes were mostly greater than 1. 3) Different oil types affected sweep efficiency, necessitating analysis of their combination with permeability anisotropy.

1. SPE 107846
Study of Sweep Efficiency of Water Injection under Fracturing Conditions Process
Eduin O. Muñoz Mazo, SPE, UNICAMP/CEPETRO/DEP/UNISIM, Juan M. Montoya Moreno and Denis J. Schiozer, SPE,
UNICAMP/FEM/DEP
Copyright 2007, Society of Petroleum Engineers
The results show the applicability of water injection under
This paper was prepared for presentation at the 2007 SPE Latin American and Caribbean fracturing conditions in different scenarios. In addition, this
Petroleum Engineering Conference held in Buenos Aires, Argentina, 15–18 April 2007.
work shows the importance of the reservoir parameters into
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, as
the injectivity loss and fracture propagation models, the
presented, have not been reviewed by the Society of Petroleum Engineers and are subject to significance of the FR and NPV in the quantification of these
correction by the author(s). The material, as presented, does not necessarily reflect any
position of the Society of Petroleum Engineers, its officers, or members. Papers presented at effects. Finally, the relation between the heterogeneity degree
SPE meetings are subject to publication review by Editorial Committees of the Society of
Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper
and production parameters is presented.
for commercial purposes 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 Introduction
acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.
Box 833836, Richardson, Texas 75083-3836 U.S.A., fax 01-972-952-9435.
Water injection is the most common method for oil
recovery and pressure maintenance. Injectivity loss is the
Abstract principal problem associated with water injection. Altoé et. al.1
Water injection performance depends on the petrophysical describe that it is caused, mainly, when seawater, produced
reservoir properties and fluid-flow characteristics. Reservoir water or any other poor quality water is injected into reservoir.
simulation models should include rock properties variation and Solid and liquid dispersed particles from the injection water
rock-fluid interactions and, when it is necessary, are deposited in the porous media; it can turn inefficient the
geomechanical phenomena. injection process with time. Palson et. al.2 comments about
When water Injection above Fracture Propagation Pressure different solutions that can be applied to improve the injection
(IFPP) is used, its effects over the reservoir model process: (i) treatment of the water injection for removal
performance, and specially, on waterflooding sweep suspended particles, bacteria and oil droplets, (ii) well
efficiency, become a critical point to be assessed. workovers for removal the damage, using mechanical and
Quantification of these effects using parameters such as the chemical treatments. As mentioned by Souza et. al.3, any of
Recovery Factor (FR) and Net Present Value (NPV) is these solutions can be expensive, some in CAPEX, others in
important for the water injection project dimensioning and to OPEX.
determine the feasibility and usefulness of the injection Actually, there is other option to attack the injectivity
process to be implemented. decline and it is know as water injection above the formation
Water injection under fracturing conditions is an important parting pressure. This option reestablishes the well injectivity
method to overcome the production decline caused by the creating high conductivity channels and avoids complex
injectivity loss in reservoirs with water injection. Also, the systems of water treatment. However, the apprehension to use
modeling of injectivity loss and fracturing processes are water injection above formation parting pressure is associated
subject of several studies, which aim to understand these to the canalization of the injected water towards producing
processes in order to enhance the results to be used for the wells leading to negative results for the production
reservoir development strategy proposal. performance. Even though, this technique is applied in North
The objective of this work is to quantify, using Sweep Sea and Alaska (Ovens et. al.4, Ali et. al.5).
Efficiency and NPV as study parameters, the effects of Due to complexity and number of variables, involve in
anisotropies on the production performance during a water injection above formation parting pressure, recent
waterflooding under fracturing conditions. The methodology studies are focused in different aspects as fracture
proposed considers the simulation of scenarios in which the mechanisms, modeling and fracture’s effects in the reservoir
injectivity loss is represented by an analytical decline model, performance (Van den Hoek6, Gadde et. al.7).
and the fracture is represented using a virtual horizontal well. To model those effects, the fracture behavior must be
This proposal is implemented in order to show the effect of the reproduced in the flow simulator and its effects in the behavior
water injection – injectivity loss – fracturing process on the of the production during the process of injection of water. It
reservoir behavior. Three different fluid models were used to also necessary study tools that allows model the injectivity
illustrate their effect in some production parameters and loss. In this way, it can couple the process injection with loss
usefulness of fracturing process in several scenarios. of injectivity and fracturing in a more complete and coherent
way for refined and coarse simulation grids.

2. 2 SPE 107846
This work seeks mainly to study the effects of anisotropies fluid injection properties and water injection parameters
on the production performance (sweep efficiency) during a (Devloo et. al.10). This program predicts formation parting
waterflooding under fracturing conditions. In addition, it aims pressure, vertical penetration, pressure propagation, width and
to show the modeling of the injectivity loss and its coupling length fracture.
with models of fracture propagation in commercial flow
simulators. Effect of directional permeability anisotropy in
sweep efficiency analysis
Fracture modeling in commercial simulators.
Simulation models and methodology analysis
Injectivity loss modeling
Injectivity loss modeling consists in an analytical model to The simulation models used to obtain the results reported
represent the absolute permeability variation near to the in this work and to accomplish the analysis consist in a
injector well or formation damage region (Figure 1). The synthetic reservoir, represented by a Cartesian grid, with
analytical model is represented by a hyperbolic decline of the 51x51x10 active cells. Each cell has 30 x 30 x 4 m. The
permeability and this variation is incorporated in the flow production strategy is represented by a five spot arrangement,
simulator to represent the injectivity loss in the injector well as is shown in Figure 3.
(Montoya et. al.8).
Virtual horizontal injector well
Formation damage Well
Region
Original region
Virtual multilateral injector well
Figure 1. Injector well and damage region
The information generated by the analytic model is used in
the model of Well Index, WI, through the modification of the
damage factor (s), the permeability of the simulation block (kb)
or the combination of both parameters as shown in Equation 1.
Other variables from the Equation 1 are defined in the
nomenclature:
Figure 2. Fracture propagation using virtual wells
2πhkb
WI = (1)
r 
ln e  + s
r 
 w
Once obtained the values of WI, the data are introduced
automatically in the simulation file for each time step, until the
well bottom pressure reach the formation pressure fracture.
Fracture propagation model.
Nowadays, some commercial simulators do not present
options to model induced fractures by water injection, and Producer Injector
some artifices, as transmissibility modifiers, local refinements Figure 3. Well arrangement in the simulation grid
and equivalent well radius, are used to represent it. Souza et.
al.9 altered the block transmissibility to model the fracture Other salient parameters for this study are:
induced by water injection. On the other hand, geomechanical • Porosity (φ): 25%;
simulators are the best option but these simulators are under • Vertical permeability (kz): 200 mD (except for the
development or are time consumption and this makes more case with kx = ky = 100 mD, where kz = 40 mD);
difficult their use under realistic full field simulation. • Matrix compressibility (cf): 4.5x10-7.
In this work, the fracture’s propagation is modeled using a
virtual horizontal well (or multilateral wells) as is showed in The goal of the tests is to analyze the behavior of the
the Figure 2, where the perforations are open in agreement production under anisotropic horizontal permeability. For that,
with the fracture’s propagation profile. Information about the they were defined some sets of horizontal permeability with
fracture is obtained from an in-house program for simulation different anisotropies. It is important to take into account that
of hydraulic fracturing process, which based on the rock and the model only has anisotropy in the horizontal permeability

3. SPE 107846 3
and for this reason is not considered the condition of models. Equations 2 and 3 present the definition of parameter
heterogeneous to define the model, since the permeability DAC:
value in a certain direction (x or y) is constant for all the
blocks of the simulation grid. Table 1 shows the sets of
directional Permeability used in the tests. k y − k mean
DAC = (2)
ky
Table 1. Directional permeability sets
k mean − k x
Set number kx (mD) ky (mD) DAC = (3)
1 2000 2000 k mean
2 500 2000
DAC is an adaptation of the Coefficient of Heterogeneity
3 50 2000 of Dykstra–Parsons, which is based on the accumulated
4 500 500 probability that a heterogeneous system has that its equivalent
5 100 500 permeability, has a determined value between the minimum
6 50 500 permeability and the maximum permeability of the system
(Maschio et. al.12). Due to that, the cases tested in this work
7 100 100
did not present heterogeneities and, in any direction the
probability of the permeability to have a certain value is 1
It can be noticed that the permeability value in the y (anisotropy in permeability is constant in x and y directions),
direction is larger or, at most, the same to the permeability in the coefficient of Dykstra-Parsons was not used. This is a
the x direction. This is due to the y direction is the axis of reason to introduce the parameter DAC to determine the
propagation of the fracture, and consequently, according to the reservoir anisotropy degree (Muñoz Mazo et. al.13).
pointed by Ji et. al.11, it is the direction of the maximum DAC has values between 0 and 1, where the value zero
horizontal stress and the largest permeability in the case of indicates a total isotropy in the directional permeability, and
heterogeneous or anisotropic systems. the value of one it indicates an elevated degree of this
The simulations are made in three stages: initially a base condition. Besides, for the cases here shown, the value of
model is simulated without injectivity loss and without DAC calculated by the Equations (2) and (3) it is the same, in
fracturing presence (NLNF for No Loss – No Fracture). such a way that will only be reported an only value of DAC in
Afterwards, the injectivity loss is introduced into the the analysis of the results.
simulation model, reproducing the effect of the formation The Decline Index (DECLI) is the ratio between the values
damage, but maintaining the pressure of the reservoir below obtained from the simulation of the cases that involve the
the value of the fracture pressure (WLNF, for With Loss – No injectivity loss due to the formation damage (WLNF) and the
Fracture) with the purpose of establishing the effect of the cases with the original model (NLNF). In this way, if DECLI
formation damage on the original model. values are smaller than 1, it will indicate that due, to the
Finally the fracture is introduced when the well bottom injectivity loss, there was a decrease in the control indicators
hole pressure reaches the fracturing pressure. Fracture used for the analysis. Values of DECLI equal to the unit is
propagation was represented using an horizontal virtual well indicative that the process of injectivity loss did not affect the
(WLWF, for With Loss – With Fracture). reservoir performance, and values larger than 1 will indicate
To analyze the results, it was introduced some parameters that even with injectivity loss the productive behavior of the
to quantify the degree of anisotropy of the sets and for allow system was improved.
establish the degree of decline or recovery of the production In the other hand, the Recovery Index (RECOVI) is the
conditions of the used models. In the case of the tests ratio between the obtained values of the simulation of the
accomplished for the elaboration of this work were used the cases that involve the fracture presence (WLWF) and the
parameters that are listed following in the Table 2. obtained values of the other two cases: the original case
(NLNF) and the case that takes into account the injectivity loss
Table 2. Parameters used in the directional (WLNF). For the Recovery Index (inverse DECLI), values
permeability anisotropy effects analysis. smaller than 1 will indicate that the presence of the fracture
did not improve the behavior of the system, considering, or
Parameter Definition not, the injectivity loss. Otherwise, values equals or larger than
kmean Mean Permeability 1 will show that the fracture got, at least, to equal the
DAC Directional Anisotropy Coefficient indicators of the cases to the which it is compared, showing
DECLI Decline Index (Reservoir performance) improvement indicators of behavior of the reservoir when the
RECOVI Recovery Index (Reservoir Performance)
values of the index are larger than 1.
Besides the Factor of Recovery in terms of the mobile oil
(FRMO) and of the Net Present Value (NPV) as control
The kmean corresponds to the geometric mean of the
parameters, they will be used the Accumulated Production of
permeabilities in the directions x and y. The DAC parameter
Water (Wp) and the Accumulated Injection of Water (Wi). To
aims to establish the degree of anisotropy of the simulation
accomplish a global analysis, it was used an economic

4. 4 SPE 107846
scenario for the calculation of NPV. Economic parameters are Table 4. Quantification of the degree of directional
shown in the Table 3. anisotropy.
Effect of oil type on the sweep efficiency of the
kx ky kmean DAC
waterflooding under fracturing conditions process
2000 2000 2000.0 0.00
Additional to the sets of horizontal directional
500 2000 1000.0 0.50
permeability, three oil types were used. These tests have the
500 500 500.0 0.00
purpose of also examining the behavior of the combination of
directional permeability anisotropy with different motilities 50 2000 316.2 0.84
and its effects in the sweep efficiency of the process. 100 500 223.6 0.55
50 500 158.1 0.68
Table 3. Economic scenario for the simulations. 100 100 100.0 0.00
Taxes Table 5. Decline indexes for the used control
Discount rate (%) 10 parameters.
Royalties (%) 10
Other 0.3665 ID
kx ky kmean CAD
Price
FR Wp Wi VPL
Oil price (US$/bbl) 35 2000 2000 2000.0 0.00 1.12 0.92 0.98 1.10
Oil price (US$/m³) 500 2000 1000.0 0.50 1.00 0.97 0.99 1.00
220.15
500 500 500.0 0.00 0.87 0.18 0.82 0.91
Gas price (US$/m³) 0.09
50 2000 316.2 0.84 0.68 0.43 0.52 0.80
Investments
100 500 223.6 0.55 0.54 0.01 0.36 0.58
Platform (US$) 10000000
50 500 158.1 0.68 0.55 0.00 0.16 0.61
Producer well (US$) 2000000
100 100 100.0 0.00 0.40 0.00 0.23 0.35
Injector well (US$) 2000000
Costs The effect of the mean permeability on the Decline Index
Oil production (US$/m³) 37.74 (DECLI) of the control parameters is shown in the Figure 4.
Water production (US$/m³) 4.03
Gas production (US$/m³) 0.002
1,2
Water injection (US$/m³) 4.03
Gas injection (US$/m³) 0.002 1,0
Results and Discussions 0,8
This analysis of the obtained results is based on the tests
DECLI
FR
for an intermediate fluid. 0,6 Wp
Wi
Quantification of the degree of directional anisotropy 0,4 NPV
Table 4 shows the values of the indexes used to quantify 0,2
the degree of directional anisotropy (kmean and DAC) for the
tested cases, using the Equations 2 and 3. 0,0
0 500 1000 1500 2000
Analysis of the effect of the directional permeability
anisotropy and the injectivity loss on sweep efficiency k mean
Figure 4. Effect of kmean on the Decline Index of the control
In this section, the results of the comparison of the original parameters.
model (NLNF) and the case with injectivity loss (WLNF) are
analyzed. For the achievement of this analysis, the Decline It can be observed from Figure 4 that DECLI for the
Index (DECLI) is used and it will be examined his impact on control parameters does not follow a specific trend in relation
the indicators of directional anisotropy kmean and DAC). to the variation of the mean permeability. The Figure 4 also
Table 5 presents the results of the comparison of the cases shows that for the model with kmean = 2000 mD, FR and NPV
for the control parameters proposed for the analysis of the increase instead of decreasing, what can be interpreted as,
production performance. eventually, the injectivity loss improved the acting of a
probably over-rated water injection for the conditions of the
system. It is evident that the injection rates should be observed

5. SPE 107846 5
with attention for high permeability systems, and that makes Table 8. DECLI vs. DAC for anisotropic models with
necessary several studies to establish an efficient injection rate ky = 500 mD.
for the model within established limits by the geomechanical
simulation. This guarantee fracturing and propagation of the DECLI
fracture once the fracture pressure is reached around the kx ky DAC
FR Wp Wi NPV
injector well. 500 500 0.00 0.87 0.18 0.82 0.91
The analysis using the mean permeability is shown much
100 500 0.55 0.54 0.01 0.36 0.58
more useful for the results obtained from isotropic cases (DAC
50 500 0.68 0.55 0.00 0.16 0.61
= 0) reported in the Table 6 and the effect on DECLI for the
control parameters is illustrated in the Figure 5.
From the information contained in the Tables 7 and 8 it can
Table 6. DECLI vs. kmean for the isotropic cases. be observed that as well for the anisotropies with ky = 2000
mD as for the with ky = 500 mD, DECLI for the control
DECLI parameters decreases in function of the increase in DAC. Of
kx ky kmean course, this evidences that when the anisotropy increases, the
FR Wp Wi NPV
effect of the injectivity loss also increases, making that the
2000 2000 2000 1.12 0.92 0.98 1.10 productive behavior of the reservoir gets worse if compared as
500 500 500 0.87 0.18 0.82 0.91 well with the original model (NLNF) as with an isotropic
100 100 100 0.40 0.00 0.23 0.35 model (DAC = 0). The behavior of the models with
anisotropies with ky = 2000 mD and with ky = 500 mD are
shown in the Figures 6 and 7.
Isotropic Models
1,2
Anisotropy with ky = 2000 mD.
1,2
1,0
1,0
0,8
DECLI
0,8
0,6
DECLI
FR
0,6
0,4 Wp
FR
Wi 0,4
0,2 Wp
NPV
0,2 Wi
0,0 NPV
0,0
2000 500 100
0,00 0,50 0,84
k mean
DAC
Figure 5. Effect of kmean on DECLI for the isotropic models
Figure 6. DECLI vs. DAC for anisotropic models, ky = 2000 mD.
Figure 5 illustrates the effect of the permeability for
isotropic cases where. It is observed a decreasing tendency in
the indicators as the permeability decreases. It is also possible Anisotropy with ky 500 = mD.
notice that the decline, caused by the injectivity loss, is higher 1,0
for lower permeabilities.
For the analysis using DAC, the tests were organized in 0,8
two groups according to the permeability in the axis y, as
shown in Table 7 and Table 8. 0,6 FR
DECLI
Wp
Table 7. DECLI vs. DAC for anisotropic models with 0,4 Wi
ky = 2000 mD. NPV
0,2
DECLI
kx ky DAC
FR Wp Wi NPV 0,0
2000 2000 0.00 1.12 0.92 0.98 1.10 0,00 0,55 0,68
500 2000 0.50 1.00 0.97 0.99 1.00 DAC
50 2000 0.84 0.68 0.43 0.52 0.80 Figure 7. DECLI vs. DAC for anisotropic models, ky = 500 mD.

6. 6 SPE 107846
Analysis of the effects of the anisotropy on directional In Figures 9 and 10 the effect of the anisotropy,
permeability and the fracture presence on the sweep represented by DAC, on RECOVI is shown for the cases with
efficiency of reservoirs with injectivity loss problems ky = 2000 mD and ky = 500 mD.
In this section, the results of the comparison of the model
with injectivity loss (WLNF) and the case with injectivity loss Isotropic Models
and with fracture (WLWF) are analyzed. In this analysis, the 3,5
Index of Recovery (RECOVI) is used to observe the effects of
the directional anisotropy in the behavior of the indicators of FR
3,0
Wi
tested models (kmean and DAC).
NPV
RECOVI
The comparisons among the cases are shown as a function 2,5
of RECOVI in the Table 9. It is observed that for permeability
of 2000 mD there are not values of RECOVI for the control 2,0
parameters. This is because the process of injectivity loss,
1,5
although it has leaded to an increase in the injector bottom-
hole pressure, it did not do that in the well bottom the fracture 1,0
pressure was reached. That condition confirms the illustrated
2000 500 100
in the previous section regarding the injection rates for k mean
reservoirs with high permeabilities.
Figure 8. Effect of kmean on the Recovery Index of thr isotropic
The analysis of the isotropic cases using the mean cases.
permeability is illustrated in the Table 10 and in the Figure 8.
Table 9. Recovery indexes (RECOVI) for the used Anisotropy with ky = 2000 mD.
control parameters.
2,3
RECOVI 2,1 FR
kx ky kmean DAC Wp
FR Wp Wi NPV
RECOVI
1,9
Wi
2000 2000 2000.0 0.00 - - - - 1,7 NPV
500 2000 1000.0 0.50 0.99 1.05 1.00 0.99 1,5
500 500 500.0 0.00 1.13 5.08 1.20 1.08 1,3
50 2000 316.2 0.84 1.45 2.19 1.85 1.25 1,1
100 500 223.6 0.55 0.94 0.94 0.94 0.90
0,9
100 500 223.6 0.55 1.69 108.24 2.59 1.53
0,00 0,50 0,84
50 500 158.1 0.68 1.55 187.96 2.88 1.39 DAC
100 100 100.0 0.00 2.04 ** 3.38 1.91
Figure 9. RECOVI vs. DAC for anisotropic models, ky = 2000 mD.
Table 10. RECOVI vs. kmean for the isotropic cases.
Anisotropy with ky = 500 mD.
RECOVI
kx ky kmean 200
FR Wp Wi NPV
FR
2000 2000 2000 - - - - 160 Wp
500 500 500 1.13 5.08 1.20 1.08 Wi
RECOVI
120 NPV
100 100 100 2.04 ** 3.38 1.91
80
In Table 10, it can be observed that the values of the
control parameters increase as well mean permeability 40
decreases. In the model with kmean = 100 mD. RECOVI Wp
0
grows infinitely due to the production of water, which in the
case with injectivity loss was shown nonexistent, begins to 0,00 0,55 0,68
appear as consequence of the presence of the fracture. In DAC
general, it is observed that for all the control parameters the Figure 10. RECOVI vs. DAC for anisotropic models, ky = 500 mD.
effect of the fracture was favorable. These parameter increases
in a more pronounced way when the mean permeability For the models with anisotropy in directional permeability,
decreases, showing the usefulness of the process of injection Figures 9 and 10, show that RECOVI grows as the anisotropy
of water with pressures above the fracture pressure to increases, being much more expressive for high coefficients of
reestablish the well productivity. anisotropy. It is observed that the cumulative production of
water is the control parameter that more increment presents.

7. SPE 107846 7
This evidences the water canalization owed to the combination Observing the Figure 11, it can be seen that RECOVI for
of the anisotropy presence with the induced fracture, the control parameters, that in the previous section it was
increasing the flow of water into the direction of the producing ascending, now decreases with the fall of the medium
wells parallel to the axis of propagation of the fracture, fact permeability, and for lower permeabilities the difficulty that
that is more evident for high coefficients of anisotropy. the fracturing has to return to the conditions of the original
It is observed that for all the cases, although a considerable system is larger.
increase is shown in the water production, that fact is not
negative for NPV, which shows larger for the cases with
fracture presence when compared with cases only with Isotropic Models
injectivity loss, independent of the degree of anisotropy of the 1,0
models. In general the favorable result of the fracture presence FR
is observed, which gets to improve the productive behavior of 0,8 Wp
the reservoir, remedying the current effects of the injectivity Wi
RECOVI
loss. 0,6 NPV
0,4
Analysis of the effects of the directional permeability
anisotropy and the fracture presence on the sweep 0,2
efficiency of reservoirs, comparison with the case without
injectivity loss and without fracture. 0,0
2000 500 100
In this section, the results of the comparison of the model k mean
without injectivity loss and without fracture (NLNF) and the Figure 11. Effect of kmean on the Recovery Index of the isotropic
case with injectivity loss and with fracture (WLWF) are cases.
analyzed. In this analysis, the Recovery Index (RECOVI) is That same difficulty that the fracture has is also evident in
used to observe the effects of the indicators of directional the models with anisotropy, where the trend to the fall of
anisotropy (kmean and DAC) on the behavior of the tested RECOVI is more evident for the models with permeability of
models. The objective of this comparison of cases is to 500 mD in the y axis, as it is shown in the Figures 12 and 13.
illustrate to what extent the fracture presence can elevate the
value of the control parameters in relation to the models
without injectivity loss. Table 11 shows the results of the Anisotropy with ky = 2000 mD.
comparison of the cases WLWF and NLNF in terms of 1,04
RECOVI. FR
1,02 Wp
Table 11. Recovery indexes (RECOVI) for the used 1,00 Wi
RECOVI
control parameters. NPV
0,98
RECOVI 0,96
kx ky kmean CAD
FR Wp Wi NPV 0,94
2000 2000 2000.0 0.00
0,92
500 2000 1000.0 0.50 0.99 1.00 0.99 0.99
0,00 0,50 0,84
500 500 500.0 0.00 0.99 0.90 0.99 0.98 DAC
50 2000 316.2 0.84 0.98 0.94 0.97 1.00 Figure 12. RECOVI vs. DAC for anisotropic models, ky = 500 mD.
100 500 223.6 0.55 0.92 1.00 0.94 0.89
50 500 158.1 0.68 0.36 0.00 0.21 0.39
Anisotropy with ky = 500 mD.
50 500 158.1 0.68 0.85 0.50 0.45 0.85 1,1
100 100 100.0 0.00 0.81 0.00 0.78 0.68 1,0
0,9
The results reported in Table 11 show that the difference of
RECOVI
0,8
the comparison among the models with injectivity loss without
fracture, and injectivity loss with fracture of the previous 0,7
FR
section. Although the fracture improves the behavior of 0,6 Wp
systems under the effect of the injectivity loss, it does not get Wi
0,5 NPV
to improve the conditions of the system with loss and without
fracture until the conditions of the original model (without 0,4
injectivity loss and without fracture). Figure 11 shows the 0,00 0,55 0,68
behavior of RECOVI between the cases WLWF and NLNF for DAC
the isotropic models tested in function of the mean Figure 13. RECOVI vs. DAC for anisotropic models, ky = 500 mD.
permeability.

8. 8 SPE 107846
To better illustrate the comparison procedure shown in the In Figure 15, the effect of the different fluids on the
previous sections, in the Figure 14 the behavior of the behavior of FR (and the sweep efficiency) is shown for the
recovery Factor is shown for the three cases of comparison indexes proposed for the model above mentioned.
(NLNF vs. WLNF; WLNF vs. WLWF and WLWF vs. NLNF)
and the effect of DAC on this behavior.
Effect of Fluid type on the behavior of FR
1,9
DECLI and RECOVI behavior for FR
1,7
1,8 1,5
DECLI (RECOVI)
1,6
DECLI (RECOVI)
1,3
1,4 WLNF vs. NLNF (DECLI)
1,2 WLNF vs. WLWF (RECOVI) 1,1
WLWF vs. NLNF (RECOVI)
1,0 0,9
0,8 FR Light Oil
0,7 FR Intermediate Oil
0,6 FR Heavy Oil
0,4 0,5
0,00 0,55 0,68 WLNF vs. NLNF WLNF vs. WLWF WLWF vs. NLNF
DAC Figure 15. Behavior of DECLI and RECOVI for the FR of the three
Figure 14. Behavior of DECLI and RECOVI with DAC for the FR of fluid types.
anisotropic models.
From Figure 15, it can be observed that the effect of the
Figure 14 illustrates clearly the decreasing behavior of fluid difference is larger on the recovery of FR among the
DECLI with the increase of DAC for FR (and consequently cases with injectivity loss without fracture and with injectivity
for sweep efficiency). It can be seen that the effect of the loss with fracture. It can be noticed that for these cases
injectivity loss is more notorious as the system becomes more RECOVI increases in a more expressive way as the density of
anisotropic (blue line). For the comparison of cases where the the fluid decreases, showing a more favorable effect of the
fracture is opened once the system with injectivity loss reaches fracture on the sweep efficiency of the process for lighter
the fracture pressure, the ascending trend of RECOVI (line fluids. The comparison among the cases with loss and
magenta) can be observed and is more accentuated with the fractures, and without loss and without fracture shows that the
increase of the anisotropy degree. These two previous more dense the fluid of the reservoir, the larger the difficulty
comparisons indicate that the injection with pressure above the that the fracture has to reestablish the productive conditions of
fracture pressure shows a more favorable effect in systems the original model.
with high anisotropy degree or in systems with a very
expressive loss of injectivity. In these cases, the productive Conclusions
behavior of those systems presents a significant improvement Effect of injection pressure above the fracture pressure on
in comparison to its behavior under the effect of the injectivity sweep efficiency and NPV were studied in cases with
loss. permeability anisotropy. In order to compare the results, some
It is observed that the fracture presence, even improving performance indexes were created.
the indicators of systems with injectivity loss, it does not get to It can be inferred that the mean permeability does not get
elevate those indicators at the level of the original case to reflect a specific tendency on the results for cases with
(NLNF). It is Noticed that the difficulty to get back to the level anisotropy, doing necessary the calculation and use the new
of the original case is more evident for models with larger performance indexes as the Index of Decline (DECLI) and the
degree of anisotropy (yellow line), what shows that the Index of Recovery (RECOVI). These parameters are used to
influence of the damage is larger and needs a more careful quantify the effects on the control parameters and to describe
treatment for models with high anisotropy degree. the behavior of anisotropic systems in the injection of water
above the fracture pressure.
Analysis of the effect of the fluid on the performance of the To quantify the level of anisotropy, it was introduced the
simulation models. Directional Anisotropy Coefficient (DAC). This parameter
was used to analyze the behavior of models and measure the
In this section, the effect of the different fluids in the degree of anisotropy of the models with different permeability
performance of the injection process with pressure above the sets used in the simulations.
fracture pressure is evaluated. For that is only taken a With those indexes, it is possible to establish different
simulation model with a DAC 0.84 (kx = 50 mD, ky = 2000 relations to study water injection above fracture propagation
mD) and the effect of the three fluids proposed in the behavior pressure. Some relations are: (i) relationship between the
of the performance indexes proposed for the analysis of the decrease of the sweep efficiency with the increase of the
models and cases simulated (DECLI and RECOVI). anisotropy level; (ii) capacity that the water injection above

9. SPE 107846 9
formation pressure has to resolve the well impairment in presented at the 2005 Offshore Technology Conference,
anisotropic models; and (iii) relations to establish the capacity Houston, May 2-5.
that the fracture presence has to improve the productive 4. Ovens, J. E. V. et al.: “Making Sense of Water Injection
conditions of the models with respect of cases where there are Fractures in the Dan Field,” SPERE Vol 1 (December
1998), 556.
injectivity loss not fracture propagation. 5. Ali, N. et al.: “Injection Above Parting Pressure
Three different fluid types were tested to establish their Waterflood Pilot, Valhall Field, Norway,” SPERE, Vol. 9,
influences in the sweep efficiency of the process. That analysis (February 1994) 22.
also took into consideration the different anisotropy levels and 6. Van den Hoek, P. J.: “Impact of Induced Fractures on
the performance indicators implemented for the analysis. Sweep and Reservoir Management in Pattern Floods,”
It can be observed that the fracture propagation gets to paper SPE 90968 presented at the 2004 SPE Annual
improve the behavior and the sweep efficiency in reservoirs Technical Conference and Exhibition. Houston, Sept. 26-
that present injectivity loss, and that capacity of improvement 29, 2004.
of the productive conditions is more significant in systems that 7. Gadde, P. B. et al.: “Growing Injection Well Fractures and
Their Impact on Waterflood Performance,” paper SPE
present high degrees of anisotropy. 71614 presented at the 2001 SPE Annual Technical
In a similar way, the fracturing process, however it gets to Conference and Exhibition, New Orleans, Sept. 30 – Oct. 3.
improve the performance indicators, it does not get, in most of 8. Montoya Moreno, J. M. et al.: “Well Impairment Upscaling
the cases, to recover the production conditions of the models at Applied to Water Injection Above Fracture Pressure
the level of the cases hat do not have injectivity loss nor Simulation,” paper CIL28-502 presented at the 2006 XXVII
fracture propagation. It was also observed that the difficulty in CILAMCE - Iberian Latin American Congress on
recuperating the performance levels increases in function of Computational Methods in Engineering, Belém, Sept. 3-6.
the index of anisotropy of the tested models. 9. Souza, A. L. S. et al.: “The Impact of Injection with
Finally, the influence of the oil type can be observed in the Fracture Propagation During Waterflooding Process,”
paper 94704 presented at the 2005 SPE Latin American and
behavior of the performance indexes. For lighter fluids, the Caribbean Petroleum Engineering Conference, Rio de
effect of the fracture in relation to the improvement of the Janeiro, Jun. 20-23.
conditions of productivity of the models is much more 10. Devloo, P. R. B. et al.: “Modelagem Numérica de
expressive, and it decreases as the density of the fluid Fraturamento Hidráulico,” paper presented at the 2001
increases. In the case of heavy fluids, with a higher difficulty XXII CILAMCE - Iberian Latim Americam Congress on
in recovering the production conditions with respect to models Computational Methods in Engineering, Campinas, Nov. 7-
without loss not fractures, this difficulty decreases as the 9.
density of the fluid increases. 11. Ji, L. et al.: “Methods for Modeling Dynamic Fractures in
Coupled and Geomechanis Simulation,” paper 90874
presented at the 2004 SPE Annual Technical Conference
Acknowledgements and Exhibition, Houston, Sept. 26 – 29.
The authors would like to thank the Petroleum Engineering 12. Maschio, C. et al.: “A New Upscaling Technique Based on
Department of the State University of Campinas (UNICAMP), Dykstra-Parsons Coefficient: Evaluation with Streamline
the Center for Petroleum Studies (CEPETRO), PETROBRAS, Reservoir Simulation,” JPSE Vol 40, (October 2003) 27.
FINEP and CNPq for their technical and economic support. 13. Muñoz Mazo, Eduin O. et al.: “Efeito do Acoplamento da
Geomecânica à Simulação Numérica de Reservatórios com
Nomenclature Injeção de Água a Pressão Acima da Pressão de Fratura,”
Letters paper IBP1581-06 presented at the 2006 Rio Oil & Gas
CAPEX : Capital expenditure Exposition and Conference 2006, Rio de Janeiro, Sept.11-
14.
DAC : Directional permeability coefficient
DECLI : Decline index
h : Formation thickness
k : Permeability
OPEX : Operational expenditure
re : Equivalent radius
rw : Well radius
RECOVI : Recovery index
s : Formation damage
References
1. Altoé, J. E. et al.: “Effects of Oil-Water Mobility on
Injectivity Impairment due to Suspended Particles”, paper
SPE 88501 presented at the 2004 SPE Asia Pacific Oil and
Gas Conference, Perth, October 18-20.
2. Palsson, B. et al.: “A Holistic Review of the Water Injection
Process,” paper SPE 82224 presented at the 2003 SPE
European Formation Damage Conference, The Hague, May
13-14.
3. Souza, A. L. S. et al.: “Water Management in Petrobras:
Developments and Challenges,” paper OTC 17258