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INTERNATIONAL JOURNAL OF MODELING AND SIMULATION FOR THE PETROLEUM INDUSTRY, VOL. 9, NO. 1, APRIL 2015 21
UNISIM-I: Synthetic Model for Reservoir
Development and Management Applications
Avansi, Guilherme D. 1 and Schiozer, Denis J.
1
[email protected] , [email protected]
1Petroleum Engineering Department, Faculty of Mechanical Engineering, State University of Campinas, Campinas, Brazil
Abstract. Several methodologies related to reservoir management
applications were created recently. Many times, it is difficult to
know the applicability of these methodologies when applied in real
reservoirs that are unknown. In order to test them, a synthetic
model was created (UNISIM-I-R) where the real reservoir is
substituted by a reference model with known properties, so
methodologies can be tested and compared. The reference model
was built in a high resolution geocellular model, using public data
from Namorado Field, Campos Basin, Brazil. The level of details
is high to ensure that geological model is reliable in order to
guarantee derivative suitable models for simulations that honor the
used data. In addition, a simulation model with uncertainties
(UNISIM-I-D) was created in a medium numerical grid resolution
after the upscaling of a geomodel realization with some
information of the reference model. The reference and simulation
models were then submitted to production and injection scheme to
compare the results. The focus of the application was an initial
stage of the field management. The comparison between reference
and simulation model was done to check the consistency and
highlight the differences, using a base production strategy to
ensure the quality and reliability of the UNISIM-I-R. The main
result of this work is then a model which can be used for future
comparative project solutions.
Index Terms – Reservoir Characterization; Reservoir Simulation;
Reservoir Management; Uncertainty Quantification.
1 INTRODUCTION
Simulation of petroleum reservoirs refers to the construction
and operation of numerical models whose objective is field
performance estimation, i.e., oil recovery, under producing
schemes. Petroleum fields can produce only once at high
expenses and long period of time while a model can run
many times at low cost and low computational time, being
the most powerful predictive tool for reservoir engineering
(Ertekin et al., 2001).
The general idea of reservoir simulation studies is based
on defining the objectives, collecting and analyzing data,
approach selection, reservoir description and model design,
matching the simulation model, running prediction cases
and reporting. Usually, these steps can be more complex,
mainly in real reservoirs. In an initial stage of a field man-
agement, it is necessary to quantify the impact of uncertain-
ties to mitigate risk (Hayashi et al., 2010).
Methodologies to mitigate risk and optimize production
are then proposed considering the results of numerical simu-
lation models and the production prediction (Suslick and
Schiozer, 2004). In order to test new methodologies, post-
mortem studies could be conducted but this is not an usual
procedure. A possible alternative is to test these methodolo-
gies in synthetic models with characteristics of real reser-
voirs.
As a result of this, the proposed work focuses on gener-
ating the UNISIM-I-R model, working as a real reservoir
with known answer, to test and compare reservoir manage-
ment applications with realistic problems by various re-
search centers and, a simulation model with uncertainties,
UNISIM-I-D, in an initial field management phase. It is
applied a production strategy to UNISIM-I-D, in a natural
working progress of reservoir studies to introduce the UNI-
SIM-I-R through this application. In addition, differences
between UNISIM-I-R and UNISIM-I-D models are high-
lighted in order to check the consistency and reliability of
the created models.
2 MODEL DATA
The UNISIM-I-R and UNISIM-I-D models are based on the
geomodel of Namorado Field, located in Campos Basin in
Brazil. Some judgment is involved during the reservoir
modeling because there are seldom enough data and gener-
ally uncertainties, mainly in the UNISIM-I-D model due to
its initial phase of field management.
2.1 Well Data
Core descriptions and well logs of Namorado Field (public
data released by the Brazilian National Petroleum Agency,
ANP) were used to build UNISIM-I-R. The dataset contains
well log information of 56 wells drilled through the upper
Macaé formation (Meneses and Adams, 1990), a limited
number of 18 wells have the Sonic data and the other 19
have the core description. This field is one of the main res-
ervoirs in the Campos Basin, corresponding mostly to sand-
stones of turbiditic origin (Guardado et al., 1989a; Guardado
et al., 1989b; Guardado et al., 2000). This package contains,
essentially, an assembly of five well logs: Gamma Ray
(GR), Density (RHOB), Neutron (NPHI), Sonic (DT) and
Resistivity (ILD) that describe physical property variations
through the formation at the surroundings of correspondent
wells, allowing the identification of the oil-bearing Namo-
rado sandstone reservoir. Initial discrete data from electro-
facies were informed by Petrobras, added to the available
dataset.
Manuscript received Oct. 16, 2013. Corresponding Author: Guilherme
Daniel Avansi (E-mail: [email protected] ).
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AVANSI & SCHIOZER: UNISIM-I: SYNTHETIC MODEL FOR RESERVOIR DEVELOPMENT AND MANAGEMENT APPLICATIONS 22
2.1.1 Grouped Facies Estimation
The initial electrofacies description with eight types was
analyzed and regrouped into four facies groups as in Figure
1.
Figure 1. Illustration of the regrouped facies.
Electrofacies 1, 2, 3 and 4 illustrate a signature of sand-
stone units that are medium, massive, grained and conglom-
eratic (GR1 ≤ 70 and RHOB
2 ≤ 2.3); electrofacies 5 and 8
nearly indicate attributes of shaly sandstone composed of
alternating fine-grained, contorted and interbedded sand-
stone and shale (GR ≤ 70 and 2.3 < RHOB < 2.5); charac-
teristics of electrofacies 6 are near shale with alternating and
interbedded siltstone and shale (GR > 70); and electrofacies
7 practically reflects on carbonate composed of interbedded
shaly siltstone and marl and conglomeratic carbonate (GR ≤
70 and RHOB ≥ 2.5). This regrouped facies is designed as
facies 0, 1, 2 and 3 respectively, following the probabilities
calculated from well data and user-defined input (Galli and
Beucher, 1997). Figure 2 highlights the initial electrofacies
and the regrouped facies estimation histogram.
Figure 2. UNISIM-I-R – well logs: initial electrofacies and regrouped
facies distribution.
The class 0 is defined as reservoir facies with good res-
ervoir properties (porosity), classes 1 and 2 are possible
reservoir facies with medium reservoir properties and class
3 is non-reservoir facies with very low porosity magnitude.
1Recorded in API (American Petroleum Institute) units. 2Recorded in g/cm³.
2.1.2 Shaliness Estimation
In well logging, the commonest natural radioactivity (by
volume) is found in shales (clays), i.e., a high gamma ray
value frequently means shale. In this case, Atlas (1982)
apud Rider (1996) presented an empirical formula of Vsh
estimation based on relationship changes between younger
(unconsolidated) and older (consolidated) rocks. Taking into
account that the Namorado sandstone is dated as Albian-
Cenomanian Age (Winter et al., 2007), i.e., the sediments
are then older rocks, it is applied Dresser Atlas’ equation for
shaliness estimation expressed as
𝑉𝑠ℎ = 0.33 × [2(2×𝐼𝐺𝑅) − 1]
where IGR is gamma ray index (Brock, 1986; Hilchie, 1982)
and it is calculated through Equation (2).
𝐼𝐺𝑅 =𝐺𝑅𝑙𝑜𝑔 − 𝐺𝑅𝑚𝑖𝑛
𝐺𝑅𝑚𝑎𝑥 − 𝐺𝑅𝑚𝑖𝑛
where GRlog is gamma ray well log reading; GRmax is the
maximum value of gamma ray well log for shale facies;
GRmin is the minimum value of gamma ray well log for
sandstone facies. It is assumed GRmin ≈ 22 API units and
GRmax ≈ 125 API units for the sedimentary interval, corre-
sponding to the Namorado Formation.
2.1.3 Effective Porosity Estimation
In addition to the discrete information of facies, effective
porosity values related to pure sandstone (Øeff,0), i.e., facies
0, are calculated following the Equation (3) (Rider, 1996).
∅𝑒𝑓𝑓,0 = 𝜌𝑚𝑎 − 𝜌𝑏
𝜌𝑚𝑎 − 𝜌𝑓
The parameter ρb represents a reading in the density log; the
Namorado Formation has quartz matrix, then the matrix
density (ρma) is defined as 2.65 g/cm³; and the fluid density
(ρf) is assumed 1.10 g/cm³ (Rider, 1996).
In case of effective porosity estimation with some
shale in its structure (Øeff,1,2), i.e., effective porosity with
shale for facies 1 and 2, it is essential to correct the total
porosity with shaliness, considering a shale volume (Vsh) as
a correction factor in the succeeding equation, as follows in
Equation (4):
∅𝑒𝑓𝑓,1,2 = [(𝜌𝑚𝑎 − 𝜌𝑏
𝜌𝑚𝑎 − 𝜌𝑓
) − 𝑉𝑠ℎ × (𝜌𝑚𝑎 − 𝜌𝑠ℎ
𝜌𝑚𝑎 − 𝜌𝑓
)]
where ρsh is density well log in shale facies. Dewan (1983)
showed that a way of assessing the density at the shale point
ρsh is to take the difference between the neutron log and the
total porosity log at its maximum, i.e., max(Øni-Øti), where
Øni and Øti correspond to the ith
sample of the neutron and
the total porosity logs, respectively. In this study, the densi-
ty at the shale point is nearly of 2.65 g/cm³. The porosity of
3132.0 6 2
3132.2 6 2
3132.4 5 1
3132.6 1 0
3132.8 5 1
3133.0 5 1
3133.2 7 3
3133.4 7 3
3133.6 7 3
3133.8 5 1
3134.0 5 1
3134.2 2 0
3134.4 3 0
3134.6 3 0
3134.8 3 0
3135.0 3 0
3135.2 3 0
3135.4 3 0
3135.6 4 0
3135.8 4 0
3136.0 4 0
3136.2 4 0
3136.4 2 0
3136.6 1 0
3136.8 5 1
3137.0 5 1
3137.2 5 1
3137.4 5 1
3137.6 8 1
TVD
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6 7 8
Rela
tive F
req
uen
cy,
%
Electrofacies
Initial Electrofacies Distribution
0
5
10
15
20
25
30
35
0 1 2 3
Re
lati
ve
Fre
qu
en
cy,
%
Facies
Grouped Facies Distribution
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INTERNATIONAL JOURNAL OF MODELING AND SIMULATION FOR THE PETROLEUM INDUSTRY, VOL. 9, NO. 1, APRIL 2015 23
facies 3 was not computed because it is assumed a non-
reservoir facies.
2.2 3D Seismic and Horizons
The 3D seismic volume and 2D seismic lines are presented
in the public dataset from ANP. These data are used to de-
rive structural (reservoir boundary limit; top, bottom, se-
quences and faults) and sedimentological (zones and hori-
zons) information to reservoir characterization. Extra infor-
mation is added into this dataset, such as well markers,
being measured along the wells and giving a true vertical
depth at the well intersections with surface layer in time
units. In Figure 3, it is possible to observe the top, three
depositional sequences (Ponte and Asmus, 1978) and the
bottom that are estimated for the 3D seismic and converted
to depth units. Top and base had already identified in previ-
ous works such as Johann (1997) and Souza Jr. (1997). The
reference surface is defined as the reservoir top to represent
the orientation at the deposition time.
Figure 3. UNISIM-I-R – horizon modeling: top; sequences 3, 2 and 1; and
bottom.
The uncertainties associated with the structural model
can increase significantly, depending on the volume of
available data. For this reason, it is assumed no uncertainties
for the UNISIM-I-R model and some ones for the UNISIM-
I-D. This takes into account uncertainties in fault location
and mapping due to the initial stage of the field develop-
ment plan and the quality of the seismic acquisition. So, it is
supposed that the 3D seismic acquisition is able to map only
the main fault during this initial period because of his high
slip tendency. The UNISIM-I-R and UNISIM-I-D fault
models are shown in the Figure 4. The faults presented in
the reservoir area of each model are used to construct the
structural model.
(a) (b)
Figure 4. Fault modeling and reservoir boundary limit: (a) UNISIM-I-R
and (b) UNISIM-I-D.
3 UNISIM-I-R
The UNISIM-I-R is constructed based on structural, facies
and petrophysical model, using the available data presented
for Namorado Field. The structural part, including top, bot-
tom, reservoir limit and faults, was previously defined. In
this case, it is desirable to construct a synthetic reservoir
model, with known answer in a high resolution grid, to be
used in numerical simulation and management integrated
studies of petroleum reservoir, being possible to test and
compare methodologies by research groups.
On account of predicting reservoir performance by
small-scale heterogeneities, a grid cell resolution was de-
fined as 25x25x1 m (Figure 5), discretized into a corner
point grid with 326 x 234 x 157 cells (3,408,633 active total
cells). The regrouped facies log is scaled up to the grid reso-
lution previously defined without loss of heterogeneity.
(a) (b)
Figure 5. UNISIM-I-R: (a) Structural model and (b) Grid cell resolution.
Facies modeling is defined using a Sequential Indicator
Simulation (SIS) with vertical trend (Ravenne et al., 2002),
providing 3D realistic images of the reservoir heterogenei-
ties and being useful for controlling fluid flow and assessing
final uncertainties on the production (Seifert and Jensen,
1999). Facies simulations are constrained by regularized
well facies information (facies 0, 1, 2 and 3), calculated on
probabilities of each well and vertical proportion curve. SIS
is not strongly constrained in terms of geological bodies. On
the other hand, this is solved for using variogram models.
Omni-directional variograms are developed for each facies
from blocked well data and worked as a constraint during
the facies modeling. The applied variogram values are illus-
trated in Table 1.
In this type of variogram, it is assumed the equivalent
parameters in facies 0, 1 and 2 because they nearly have
similar classification in terms of reservoir and possible res-
ervoir facies. In another way, different values are used for
facies 3 (non-reservoir facies). The modeled facies outline is
shown in Figure 6.
25 m
1 m
25 m
TABLE 1. UNISIM-I-R – SPHERICAL VARIOGRAM: FACIES MODELING.
Facies Range
Azimuth Parallel Normal Vertical
0 1000 600 9 135
1 1000 600 9 135
2 1000 600 9 135
3 2000 1000 9 135
FC
Top
Bottom
reservoir
boundary
FD
FC
FB
FA
reservoir
boundary
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AVANSI & SCHIOZER: UNISIM-I: SYNTHETIC MODEL FOR RESERVOIR DEVELOPMENT AND MANAGEMENT APPLICATIONS 24
(a) (b)
Figure 6. UNISIM-I-R – facies modeling: (a) Top and (b) Bottom of the reservoir.
Facies modeling must honor all geological information
of the reservoir, including body form, dimensions and spa-
tial trends. Thus, it is made a statistical analysis (histogram)
to check the quality of the results during the facies modeling
process. It can be seen in Figure 7, a comparison among
well logs, regularized well logs (upscaled) and the distribu-
tion of facies property in the entire reservoir.
Figure 7. UNISIM-I-R: histogram of facies for well logs, upscaled cells
and model.
From this analysis, it is possible to observe that the faci-
es modeling was well done, honoring the upscaled cells
previous determined from well logs measurements.
For more realistic reservoir model, it is important to link
simulated facies and petrophysics, such as porosity and
permeability, taking into account facies distribution for
constraining the simulations in the interwell areas.
Porosity and permeability distribution are a necessary
prerequisite to model flow behavior under both steady and
unsteady state conditions. Porosity data from well logs is
scaled up to grid resolution without loss of heterogeneity
and checked for depth trends. A 3D stochastic modeling,
Sequential Gaussian Simulation (SGS), is used to perform
the petrophysical modeling, combining well logs, omni-
directional variogram (Table 2) and 3D facies model to
control and condition the porosity distribution (Dubrule,
1998; Kelkar et al., 2002).
The assumed spherical variogram, used during the
petrophysical modeling of porosity, is based on the upscaled
well logs, mean and standard deviation from well log meas-
urements. The porosity modeling is illustrated in Figure 8.
(a) (b)
Figure 8. UNISIM-I-R – petrophysical modeling of porosity: (a) Top and (b) Bottom of the reservoir.
The petrophysical modeling was done, although an extra
step is necessary to check the quality of the modeling re-
sults. Therefore, it is made a histogram of porosity for well
logs, the regularized well logs (upscaled) and the modeled
porosity distribution in the entire reservoir as it can be seen
in Figure 9.
Figure 9. UNISIM-I-R: histogram of porosity for well logs, upscaled cells
and model.
In general, there is a smooth difference among the up-
scaled cells and the modeled property qualitatively. Howev-
er, it is important to focus on a quantitative analysis in order
to complete the other one, as illustrated in Table 3.
36.5
25.4 24.1
14.0
37.8
23.9 24.9
13.5
36.5
24.3 25.3
13.9
0
5
10
15
20
25
30
35
40
0 1 2 3
Rela
tive F
req
uen
cy, %
Facies
UNISIM-I-R: Histogram of Facies
Well Logs
Upscaled
Model
0
4
8
12
16
20
24
28
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34
Rela
tiv
e F
req
ue
ncy, %
Porosity, %
UNISIM-I-R: Histogram of Porosity
Well Logs
Upscaled
Model
TABLE 2. UNISIM-I-R – SPHERICAL VARIOGRAM: PETROPHYSICAL MOD-
ELING.
Property Range
Azimuth Parallel Normal Vertical
Porosity 1000 700 9.5 135
Bottom Top
Bottom Top
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INTERNATIONAL JOURNAL OF MODELING AND SIMULATION FOR THE PETROLEUM INDUSTRY, VOL. 9, NO. 1, APRIL 2015 25
In this table, it can be seen an insignificant increase and
decrease in the mean and standard deviation respectively in
the entire reservoir model. In short, the petrophysical mod-
eling of porosity is performed satisfactory, maintaining
almost the same distribution pattern from the upscaled well
logs.
Porosity can be measured reliably by logging, but not by
permeability. So, it is necessary to estimate permeability
using the porosity determined from the core analysis data
(Boyer, 1985), giving an important contribution to reservoir
characterization at this stage. Relationship of porosity to
permeability is shown from analysis of the available core
description, being possible to observe in Figure 10.
Figure 10. Core analysis data: porosity versus permeability.
In this case, it is assumed a linear dependence of perme-
ability (logarithm scale) and porosity in the core description
data. So, a linear regression is used in order to obtain a
mathematical equation to represent the permeability distri-
bution as a function of porosity in the entire reservoir mod-
el. The curve fitting (red line) and the equation are illustrat-
ed in the Figure 10. The calculated R square value is 0.89
and reflected in a good fitting, attesting the consistency for
indirect measurements of permeability (porosity) from core.
Thus, it is possible to manipulate the fitting function that it
is highlighted in Figure 10 in order to obtain the Equation
(5).
𝐾ℎ = 10[(0.1346×∅ℎ)−0.9794]
where kh is horizontal absolute permeability and Øh horizon-
tal absolute porosity. In
Figure 11, it is possible to see the permeability distribution
of the UNISIM-I-R after this estimation and applied for the
full reservoir.
(a) (b)
Figure 11. UNISIM-I-R – permeability estimation from cores: (a) Top and
(b) Bottom of the reservoir.
Interval facies cut-off is used to calculate net-to-gross
ratio (NTG) of each area for the model, as illustrated in
Table 4.
The facies type was associated with porosity and this
was the criteria used to set up reservoir NTG. It can be seen
in
Figure 12, NTG estimation based on the distribution
analysis of facies 0, 1, 2 and 3 obtained from the well data
regularization.
(a) (b)
Figure 12. UNISIM-I-R – NTG estimation: (a) Top and (b) Bottom of the reservoir.
The NTG aims to preserve the facies trend during a flow
simulation, accounting for facies proportion and the vario-
gram used in geostatistical simulation. The idea is to use the
UNISIM-I-R in the numerical simulator to create the history
production and map distribution.
Following the idea of modeling important properties to
be used in the reservoir simulation, it can be seen in Table 5
a correlation analysis of these ones.
log10Kh = 0.1346øh - 0.9794
R² = 0.89-2
-1
0
1
2
3
4
0 5 10 15 20 25 30 35
Lo
g1
0(K
h),
mD
Øh, %
Core Description: Porosity vs Permeabilitiy
TABLE 3. UNISIM-I-R: QUALITY CONTROL OF PETROPHYSICAL MODEL-
ING.
Zones
Mean Standard Deviation
Well
Logs Upscaled Porosity
Well
Logs Upscaled Porosity
All 13.7 13.8 14.0 10.4 9.9 9.7
1 15.8 15.8 15.2 10.8 10.4 10.2
2 16.0 16.0 17.3 10.4 9.8 9.5
3 13.5 13.6 14.0 10.6 10.0 9.9
4 10.9 11.1 10.6 9.2 8.7 8.3
Note: 1st and 4th zones are the top and base of the reservoir respectively.
TABLE 4. FACIES CUT-OFF.
Facies NTG
0 1.0
1 0.8
2 0.6
3 0.0
Bottom Top
Bottom Top
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AVANSI & SCHIOZER: UNISIM-I: SYNTHETIC MODEL FOR RESERVOIR DEVELOPMENT AND MANAGEMENT APPLICATIONS 26
In this table, it is possible to observe that porosity and
horizontal permeability have the same correlation factor that
means they have the same behavior in the entire reservoir.
In fact, this is right, because the permeability is directly
generated as a function of the porosity.
4 UNCERTAINTY VARIABLES
Scenarios around facies, porosity, NTG, permeability, east
structural model, water relative permeability (Krw), Black-
Oil pressure, volume and temperature dependencies (PVT),
water oil contact depth (WOC), rock compressibility (Cpor)
and vertical permeability multiplier (Kz) are considered
during the UNISIM-I-D reservoir modeling. The uncertain-
ties are quantified on purpose to create a comparison project
during a field management. Table 6 summarizes the uncer-
tainty data and scenarios used to construct the UNISIM-I-D.
.
Uncertainties in porosity, NTG (as a function of facies),
fluid contacts and structural model affect the fluid volumes
in the model; and PVT, permeability (as a function of poros-
ity), rock compressibility, vertical permeability multiplier
and water relative permeability are related to the fluid flow
and also as reservoir energy source.
Facies and porosity scenarios are generated using a ran-
dom seed during the facies and petrophysical modeling.
NTG and permeability distribution are then calculated as a
function of facies and porosity respectively. Water relative
permeability tables are included to uncertainty models,
assuming a range of Corey exponents (water wet). PVT
tables are added to reflect the uncertainty around oil density
and gas in solution. Structural model uncertainties are de-
fined to reproduce a possible geological region in the reser-
voir model that is not covered by the initial well develop-
ment planning. In addition, uncertainties in vertical continu-
ity and rock compressibility are presented during the initial
development planning.
5 UNISIM-I-D
The UNISIM-I-D was created for a project developed in the
data t1 (05-31-2017), i.e., an initial stage of field manage-
ment plan under uncertainties, including 4 years of produc-
tion data (2013-2017) considering the available information
of four production wells. There is a well log measurement, a
core description and a seismic data that are used to build the
structural, facies and petrophysical model based on the
previous steps of UNISIM-I-R.
The geomodel used to build the UNISIM-I-D in terms of
resolution is identical and followed the same steps of the
UNISIM-I-R, based on structural, facies and petrophysical
modeling. Therefore, Figure 13 presents facies, porosity,
permeability and NTG distribution of the top of the geo-
model.
(a) (b)
(c) (d)
Figure 13. Top of UNISIM-I-D at geological grid: (a) Facies, (b) Porosity,
(c) Horizontal permeability and (d) NTG distributions.
Using the four conditioning wells, the initial porosity
distribution is obtained by petrophysical modeling (Figure
13b), conditioned by variogram analysis and well log meas-
urement.
The porosity-permeability correlation is corresponded to
the same law of UNISIM-I-R and it is applied for compu-
TABLE 5. UNISIM-I-R: CORRELATION ANALYSIS AMONG POROSITY, HORIZONTAL PERMEABILITY AND NET GROSS.
Property Porosity Horizontal
Permeability
Net Gross
Porosity 1.00 1.00 0.49
Horizontal
Permeability 1.00 1.00 0.49
Net Gross 0.49 0.49 1.00
TABLE 6. UNISIM-I-D: UNCERTAINTY ATTRIBUTES.
Attribute Uncertainty
Type Levels/PDF*
Facies discrete
(scenario)
500 equiprobable realizations
Porosity discrete
(scenario)
NTG, fraction correlated
with facies
Permeability,
md
correlated with porosity
East structural
model, unitless
discrete
(scenario)
presence (0.7);
absence (0.3)
Krw, unitless discrete
(scenario)
Krw0 (0.2); Krw1 (0.2);
Krw2 (0.2); Krw3 (0.2);
Krw4 (0.2)
PVT discrete
(scenario) PVT0 (0.34); PVT1 (0.33);
PVT2 (0.33)
WOC, m continuous (triangular)
0, x<3024
(x-3024)/22500, 3074≤x≤3174 (3324-x)/22500, 3174≤x≤3324
0, x>3324
Cpor,
(106 kgf/cm²)-1
continuous (triangular)
0, y<10
(y-10)/1849, 10≤y≤53 (96-y)/1849, 53≤y≤96
0, y>96
Kz multiplier,
unitless
continuous
(triangular)
0, z<0 2z/4.5, 0≤z≤1,5
( 6-2z)/4,5, 1,5≤z≤3
0, z>3
*Probability Density Function.
Top Top Top
Top Top
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INTERNATIONAL JOURNAL OF MODELING AND SIMULATION FOR THE PETROLEUM INDUSTRY, VOL. 9, NO. 1, APRIL 2015 27
ting the permeability fields (Equation (5)), as follows in
Figure 13c.
Finally, NTG distribution calculation is conditioned by
facies of each interval for the UNISIM-I-D (Figure 13d),
being represented in the numerical simulation model after
the upscaling procedure.
On the other hand, an upscaling procedure is necessary
to reduce the dimension of the reservoir grid cell in terms of
manageable level of flow simulation.
5.1 Upscaling of UNISIM-I-D
Based on the UNISIM-I-D at high resolution grid, an up-
scaling procedure to a medium reservoir scale is necessary
to decrease the computational effort as a result of the num-
ber of simulation generated during a reservoir management.
The cell scale of the simulation model is defined to reflect
reservoir behavior properly, i.e., the heterogeneities. Thus, it
is assumed a simulation grid cell resolution of 100 x 100 x 8
m (Figure 14), discretized into a corner point grid (81 x 58 x
20 cells, with 36,739 active total cells).
(a) (b)
Figure 14. UNISIM-I-D: (a) Structural model and (b) Grid resolution, highlighting the UNISIM-I-R block size.
Porosity is upscaled by simply using an arithmetic vol-
ume weighted method to ensure that the hydrocarbon pore
volume remains constant when upscaling (additive property
characteristics). Figure 15 highlights the original scale and
upscaled porosity map, i.e., an upscaling procedure of the
geological to the flow simulation model.
(a) (b)
Figure 15. UNISIM-I-D – porosity distribution at: (a) Geological and (b) Flow simulation scale after the upscaling procedure.
Permeability is upscaled using a flow-based upscaling
technique. This one produces effective permeability to rep-
licate the fine scale behavior in overall flow rate by using a
single-phase pressure solver, FLOWSIM (Deutsch, 1989).
When an isotropic permeability is upscaled, the effective
results become anisotropic; three effective permeabilities in
all directions (i, j and k) are then obtained for the upscaled
reservoir (UNISIM-I-D). Figure 16 shows the results of the
upscaling procedure of the original scale permeability to
effective permeability Ki, Kj and Kk.
(a) (b)
(c) (d)
Figure 16. UNISIM-I-D –permeability distribution at: (a) Geological scale,
and (b) Effective Ki, (c) Effective Kj and (d) Effective Kk at flow simulation
scale after the upscaling procedure.
NTG is upscaled using the same procedure as porosity
because it is an additive property and it is directly related to
maintain constant the hydrocarbon volume during this ap-
plication. It can be seen in Figure 17, the original scale and
upscaled values of NTG.
(a) (b)
Figure 17. UNISIM-I-D – NTG distribution at: (a) Geological and (b)
Flow simulation scale after the upscaling process.
Table 7 is generated to illustrate the correlation among
the reservoir properties of the UNISIM-I-D.
In this table, porosity and horizontal permeability do not
have the same correlation factor like the UNISIM-I-D at the
geologic grid because of the upscaling procedure used to
8 m
100 m
100 m
TABLE 7. UNISIM-I-D: CORRELATION ANALYSIS AMONG POROSITY, HORIZONTAL PERMEABILITY AND NET GROSS.
Property Porosity Ki Kj Kk NTG
Porosity 1.00 0.90 0.89 0.96 0.45
Ki 0.90 1.00 0.99 0.80 0.36
Kj 0.89 0.99 1.00 0.80 0.35
Kk 0.96 0.80 0.81 1.00 0.44
NTG 0.45 0.36 0.35 0.44 1.00
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AVANSI & SCHIOZER: UNISIM-I: SYNTHETIC MODEL FOR RESERVOIR DEVELOPMENT AND MANAGEMENT APPLICATIONS 28
transfer from the geological to simulation model, losing
resolution in vertical and horizontal direction.
6 BASE PRODUCTION STRATEGY
The idea of this application is to have a production strategy
to compare the UNISIM-I-R and UNISIM-I-D models. The
original volume of oil of UNISIM-I-D model is 130 million
m3, the oil density is 28º API and the fluid model is the
Black Oil.
The production strategy is selected based on a manual
process proposed by Botechia et al. (2013) with some modi-
fications. The idea is to observe well behavior and perfor-
mance to improve the production strategy, discarding wells
with low performance and changing the configuration of
production system, aiming to maximize an economic indica-
tor, such as Net Present Value (NPV). The use of this meth-
odology on the base production strategy definition relies on
the following assumptions:
History production period of 1461 days (t1) is availa-
ble;
Four vertical wells are presented during the history
production time. So, they cannot be removed from
the strategy because they had already been drilled
and they were already used to build the UNISIM-I-
D;
Waterflooding was chosen as a secondary oil recov-
ery method;
The NPV is used as the main indicator to select the
production strategy. The behavior of wells is ob-
served in order to have a good strategy.
Some of the main fiscal and economic assumptions are
outlined in Table 8. These are mean values used for the
deterministic base production strategy optimization using a
numerical reservoir simulation. The investments in platform
were in the function of its production capacity (Hayashi,
2006).
Thus, a base production strategy is defined by which
presented the maximum economic return based on NPV. In
Figure 18, it can be seen the reservoir simulation outline
with the defined strategy. Due to a matter of visibility, hori-
zontal wells are not included and well names are omitted on
the left and right reservoir model respectively.
(a) (b)
Figure 18. UNISIM-I-D - base production strategy definition: (a) Wells are
in the same visualization level (second layer) and (b) 3D visualization.
The strategy is defined with 25 wells (4 original vertical
producers, 10 horizontal producers and 11 injectors). The
results show a recovery factor of 47 % and a NPV of 1.77
billion dollars, calculated from the economic parameter
defined previously. It is possible to check more alternatives
than the previous found, maximizing the NPV or Recovery
Factor (RF). In addition, a consistency check for the de-
fined exploitation scheme and the geology information of
the initial perforated vertical wells can be carried out, espe-
cially in an initial phase of the field development because of
the high level of uncertainties and risks followed by changes
in alternatives less optimized. Although they are not the
focus of this work.
In reservoir management, several models under uncer-
tainties can be generated using reservoir characterization. In
order to check the consistency of the UNISIM-I-D based on
the production strategy definition and available uncertain-
ties, the uncertainty curves for cumulative oil production
(Np), cumulative water production (Wp) and NPV are cre-
ated as shown in Figure 19.
(a) (b)
(c)
Figure 19. UNISIM-I-D – uncertainty curves: (a) Np, (b) Wp and (c) NPV.
In this uncertainty analysis, it is possible to conclude that
the UNISIM-I-D is among the possible reservoir models and
it can be used in future works.
7 RESULTS
The main goal of this project is to create different models: a
reference with known properties and a simulation with low
available information.
0.0
0.2
0.4
0.6
0.8
1.0
30 40 50 60 70 80 90
Pe
rce
nti
les
Np, MM m³
UNISIM-I-D: Uncertainty Curves
UNISIM-I-D
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60 80 100
Pe
rce
nti
les
Wp, MM m³
UNISIM-I-D: Uncertainty Curves
UNISIM-I-D
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 0.0 1.0 2.0 3.0
Pe
rce
nti
les
NPV, USD Billions
UNISIM-I-D: uncertainty Curves
UNISIM-I-D
TABLE 8. UNISIM-I-D: ECONOMIC PARAMETERS FOR SIMULATION MODEL.
UNISIM-I-D Model
Market
Values
Oil price (USD/bbl) 50 Discount rate (%) 9
Taxes
Royalties (%) 10
Special Taxes on G. Revenue (%) 9.25 Corporate Taxes (%) 34
Costs
Oil production (USS/bbl) 10
Water production (USS/bbl) 1
Water injection (USS/bbl) 1 Abandonment (USD Millions) 7.4
Investments
Initial Investment (USD Millions) 768.9
Wells (USD Millions) 13.3
Platform (USD Millions) 786.3
Page 9
INTERNATIONAL JOURNAL OF MODELING AND SIMULATION FOR THE PETROLEUM INDUSTRY, VOL. 9, NO. 1, APRIL 2015 29
The previous stage presented a base production strategy
on UNISIM-I-D. This model is built after 4 years from the
onset of its oil production. The strategy is applied in UNI-
SIM-I-R in order to obtain production curves to be com-
pared with UNISIM-I-D checking the differences between
them. The idea is to illustrate how much they are different,
focusing on production curves, saturation and pressure dis-
tribution maps, highlighting the importance of having a
known “real” reservoir.
Figure 20 illustrates a comparison between oil and water
curves in a production history (HIST) and prediction of
UNISIM-I-D and UNISIM-I-R models.
Figure 20. UNISIM-I-R (REF) and UNISIM-I-D (SIM): oil and water
production curves.
From the oil and water production curve, it is possible to
observe that the productivity of the UNISIM-I-R is lower
than UNISIM-I-D. This decline production occurs due to
the differences of available geological information that is
used to build the UNISIM-I-D, following an initial man-
agement phase.
Figure 21 shows the average reservoir pressure (ARP)
and the oil recovery factor (ORF) in a production history
and prediction of both models.
Figure 21. UNISIM-I-R (REF) and UNISIM-I-D (SIM): ARP and ORF.
It can be noticed, from Figure 21, that the productivity is
related directly to the reservoir pressure, besides the reser-
voir drive mechanism (waterflooding). From these produc-
tion curves, it is possible to affirm the significance of char-
acterizing the reservoir model with uncertainties in order to
get better results during a field management plan.
This analysis can be linked to the oil and water distribu-
tion presented in the reservoir (Figure 22).
(a) (b)
Figure 22. UNISIM-I-R and UNISIM-I-D: ternary distribution of a layer at
2021.
In Figure 22, it is possible to observe the differences in
the movement of the water front, where there are regions
which contained more water than others. This mistake is
affected by the initial management phase that the reservoir
characterization was performed, showing a deviation from
the “real” property to the modeled one. Other differences
can be obtained from the simulation of both models.
As a result, the main objective of creating different
models is completed, creating and comparing UNISIM-I-R
and UNISIM-I-D models considering that little information
was available during the initial field development phase.
8 CONCLUSIONS
The main contribution of this work is to build a reliable
reservoir model (UNISIM-I-R) to be used for future com-
parative projects solutions, bringing options to create, test
and compare new approaches related to reservoir develop-
ment and management by several research centers.
The UNISIM-I-R was used in a related study of petrole-
um reservoir simulation and management, guiding and prov-
ing some information to the UNISIM-I-D after an upscaling
procedure. The results showed the importance of condition-
ing the simulation model to used data and representing the
uncertainties, mainly in an initial stage of a field manage-
ment plan where a small amount of information was availa-
ble.
A base production strategy was defined during the reser-
voir studies, aiming to validate the UNISIM-I-D and intro-
duce the UNISIM-I-R, guiding the choice of one alternative
of production plan with the best exploitation scheme. An
approximate number of wells are defined during this stage,
considering the geological uncertainties. This application
allowed comparison of UNISIM-I-R and UNISIM-I-D
models to check the consistency and reliability of the UNI-
SIM-I case.
ACKNOWLEDGMENT
The authors are grateful to the support of the Center of Pe-
troleum Studies (Cepetro-Unicamp/Brazil), Department of
Petroleum Engineering (DEP-FEM), Petrobras S/A, Brazil-
ian National Agency of Petroleum, Natural Gas and Biofu-
els (ANP) and CGG Geoscience Company for the financial
0
2
4
6
8
10
12
14
16
18
20
0 2000 4000 6000 8000 10000 12000Oil/W
ate
r P
rod
ucti
on
Rate
, 10
3m
³/d
ay
Time, days
UNISIM-I-R and UNISIM-I-D
Oil - REF Oil - SIM Water - REF Water - SIM
HIST PREDICTION
0
67
134
201
268
335
402
0
10
20
30
40
50
60
0 2000 4000 6000 8000 10000 12000
Oil
Re
co
ve
ry F
ac
tor,
%
Time, days
UNISIM-I-R and UNISIM-I-D
ORF - REF ORF - SIM ARP - REF ARP - SIM
HIST PREDICTION
Page 10
AVANSI & SCHIOZER: UNISIM-I: SYNTHETIC MODEL FOR RESERVOIR DEVELOPMENT AND MANAGEMENT APPLICATIONS 30
support for this research. In addition, special thanks to
UNISIM and Petroleum Engineering Department (DEP-
FEM-Unicamp/Brazil).
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