SPE 153636

Integrated Risk Analysis of Uncertainties in Geological Model and Dynamic

Flow Properties for the Development of Oil Fields
Genilson A. da Silva, André M. de Oliveira Guimarães, Gislene A. da Silva, Marcos Aurélio Lucas, PETROBRAS

Copyright 2012, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Mexico City, Mexico, 16–18 April 2012.

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

Abstract

Given the high degree of uncertainty in the oil industry present production development projects, the use of probabilistic models
is of considerable interest as a means to support decision making. Besides that, there is a constant pursuit to optimize oil
drainage, to maximize reserves as well as the financial outcome of the project. A robust study, characterizing the uncertainty of
the various critical parameters, such as number of wells, maximum water injection rates, relative permeabilities and rock and
PVT data, is of paramount importance to assure that the impact of all uncertain parameters have been accounted for.
The present risk curve construction methodology takes into consideration uncertainties in the geological model and in the
dynamic properties in an integrated manner. Six geologic scenarios with distinct permo-porous distributions were generated. A
study was conducted to obtain PVT correlations of the produced fluids.
A sensitivity analysis was performed to eliminate non-significant parameters. The relevant ones were well adjusted to the
production data in all geologic scenarios. Optimum exploitation configurations were obtained for each model, using the net
present value (NPV) as an objective function. Each configuration was applied to all scenarios and the estimated monetary
values (EMV) of each configuration were calculated. The maximum EMV was used as optimum criteria. The final product
obtained was a development strategy risk curve, showing the viability of the proposed methodology.

Introduction
The high degree of risk and economic/technological uncertainties commonly associated with production development projects in
the Exploration and Production segment of the oil industry has a big influence in the future production forecast of reservoirs,
which forms the basis for decision making in the industry. In order to obtain greater reliability in the production forecast curves,
the detailed description of the porous media properties, such as porosity and permeability, becomes of great importance
(Deutsch, 2002).
These properties are inherently heterogeneous however, and exhibit a high degree of spatial variability. Significant spatial
heterogeneity and the sparse nature of the available data contribute to the rise of uncertainties in the characterization of these
properties and, consequently, to the uncertainties in the reservoir’s future behavior prediction (Zhang and Lu, 2006). Zhang and
Lu (2002) stress that it is indispensable that all uncertainties inherent to the project be considered in the face of the scarcity of
rock, fluid and pressure data of the reservoir, and that the impact of these uncertainties be quantified in the production forecast
of the area.
The present work proposes a methodology to evaluate the impact of geologic and dynamic properties’ uncertainties in an
integrated manner, aiming the creation of a development project risk curve in a scenario where there is scarcity of information.
A characterization of the model’s dynamic properties was made through the treatment of the reservoir’s rock and fluid data. In
the methodology, several geologic scenarios with associated occurrence probabilities are utilized. A sensitivity analysis of the
model to the considered parameters is performed, and the selected ones are adjusted to the production history. Following the
given adjustments, an optimization concerning the allocation of a well pair producer-injector and maximum injection rate is
performed, using the EMV as objective function.
The methodology employed in this work made it possible to determine the optimum exploitation strategy for the area and the
construction of a risk curve which incorporated uncertainties of several natures. This work involved several techniques among
Reservoir Engineering.

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 2 SPE 153636

Literature Review
In projects developed under conditions of uncertainty, as is the reality in the oil industry, scenarios are utilized with associated
occurrence probabilities, which should be appropriately treated. The deterministic treatment is not the best option, being
necessary a probabilistic treatment. The inherent project uncertainties can be quantified using statistical techniques so that the
project can be developed consistently, or even altered in the face of inadequate situations. The stochastic approach is the most
adequate in scenarios under conditions of uncertainty, in which there are scenarios associated with probability distributions.
Dynamic flow simulations demand greater computational effort, and are commonly handle with the use of parallel computing
techniques, for example.
Starting in the 80’s, numerical flow simulators have been used for oil production forecasts with stochastic approaches (Neto,
2003). The optimization of the production strategy of oil fields should consider different types of uncertainties. A robust
methodology for this should incorporate uncertainties to the forecast with a stochastic approach. Broader methodologies for the
production strategy optimization under uncertainty conditions have been developed.
Nogueira (2009) proposed a methodology for the optimization of the production strategy taking into consideration uncertainties
in the geologic model and the economic scenario. According to Reis, many works have been published concerning the themes
History Matching and Risk Analysis. However, only a few consider both of them together. The use of methodologies for the
optimization of production strategy maturally requires the use of statistical techniques, such as sensitivity analysis, history
matching and optimization.
The sensitivity analysis is a step of crucial importance; a wrong choice of parameters for adjustment and the decrease of the
total process time depend on its good accomplishment (Schiozer, 2003). As Leitão and Schiozer (1998) the success during
optimization depends strongly on the time spent in the sensitivity analysis. Among optimization algorithms, there exists two
main studied classes, the first one does not employ gradients of the objective function (direct search method) and the second
one bases itself in the use of such gradients. Some examples of the first class algorithms are the Genetic Algorithm, Simulated
Annealing, hybrid Methods, Polytope Method, Multivariate interpolation techniques, Tabu Search, Scatter Search and
Evolutionary algorithm employed in various papers (Beckner and Song, 1995; Fuji and Horne, 1995; Bittencourt and Horne,
1997; Pan and Horne, 1998). Some examples of the second class algorithms are the Quasi-Newton family algorithms and the
gradient method.
Using software to aid in the treatment of data is indispensable. In this work, the software CMOST (Computer Assisted History
Matching, Optimization, and Uncertainty Assessment Tool) from the Computer Modeling Group Ltd. (CMG) was used. It
possesses the capability of performing sensitivity analyses, history matching, optimization and uncertainty analysis. Basically, in
each of these tasks it uses an objective function to quantify the difference between measured and simulated data. It is through
the objective function that the whole optimization process occurs, as the problem will consist of minimizing or maximizing this
function. Objective functions are employed in the optimization techniques, where they quantify the relative difference between
measured and simulated data. According to each problem, local objective functions can be applied to each well i (Qi), taking
into consideration the quality and importance of the data. In CMOST, the equation used to measure the Qi is Eq. 1 (Yang et al.,
2007).

∑ (Y )
T (i , j )
2
s
i , j ,t − Yi ,mj ,t
t =1
N (i )
1 T (i, j )
Qi = N (i ) ∑ ∆Yi ,mj + 4 ⋅ Merri , j
⋅100% ⋅ wi , j (1)
∑ wi , j
j =1
j =1

The function Qi is of the relative percentage type. Given this definition, it is possible to calculate a global objective function
(Qglobal) using a weighted average of the local objective functions (Eq. 2) according to Yang et al. (2007).

1 NW
 N (i )

Q global = NW N ( i ) ∑ Q ∑ w i i, j 
 
∑∑w
i =1 j =1
i, j
i =1 j =1 (2)

The sensitivity analysis consists of a methodology for the reduction of complexities, in the sense that it identifies parameters
that influence the model the most and it allows the elimination of the non-significative ones. The non-significative parameter
identification is of great relevance for the subsequent steps of the study, given the time spent on the simulations performed in
the history matching, optimization and sensitivity analysis phases. The estimation of the effect of alterations in a given
parameter indicates relatively how much the response obtained by the objective function will be altered.
The sensitivity analysis is based, among other techniques on Experimental Design, which uses a response surface (RS), which
are polynomials obtained to reduce the computational effort with simulations for the acquisition of data, Eq. 3 shows an
equation for a RS.

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 SPE 153636 3

n n n n
y = a0 + ∑ai xi + ∑∑aij xi x j + ∑aii xi2
i=1 i=1 i=1 i=1 (3)
j>1

In this equation the coefficient values (ak) are related to the effects of the variables. The bigger their value, the larger will be
their influence in the objective function value. The effects’ values used in the construction of the response surface, which
approximates the reservoir simulation model, may be dimensionless and vary from -1 to 1. After the effect quantification, they
are converted to their original dimensions and presented on a Tornado Diagram.
The history matching process represents the integration of the reservoir characterization activities and the production forecast,
and because of that presents complexities that arise from uncertainties of the involved parameters and, a lot of times, of the
high number of involved variables. This problem is characterized by its inverse nature, that is, by the large number of solutions
among the possible combinations of the adjusted parameters. It consists in the application of optimization techniques to
minimize objective functions that quantify the difference between observed and simulated data.
The uncertainty analysis is normally used to determine the probable variation in the simulation results due to the uncertainties in
the model parameters. As the information available for the reservoir characterization step is limited and sometimes conflicting,
uncertainties are always present in this process, and therefore decisions are made under risk. In offshore oil fields, the risk is
even greater due to high information acquisition costs and little operational flexibility. Even with a good geological
characterization, the forecast models generated have limitations and simplifications in aspects that include grid, modeling scale,
fluid treatment, well modeling, among others. The uncertainty analysis consists of the realization of simulations that build a
response surface for each objective function and the realization of a Monte Carlo simulation by the selection of tens of
thousands of variable values combinations for the determination of each one’s objective function’s value, using the surface
response. Finally, density and cumulative probability functions are obtained for each objective function.
There are many optimization algorithms available, including DECE (designed exploration and controlled evolution) from CMG,
particle swarm optimization, random search, brute force search, and latin hypercube sampling.
The DECE optimization is an iterative method that consists of the steps projected exploration and controlled evolution. The first
step aims to collect as much information as possible employing experimental design techniques and Tabu search to choose
among values of parameters and create representative simulations. The second step aims to reduce the sampling space using
statistical tests and a parameter influence matrix (Yang et al., 2009).
The particle swarm optimization is a stochastic method based on the behavior of societies. Starting from a random population,
in each iteration particles follow the direction towards the particle where the best individual value was found and towards the
direction where the best value in the neighborhood of each particle was found, including its present value. The random search
method is of stochastic nature, each iteration does not depend on the previous one and is only viable when the dimension of the
search space is small and the numerical simulation is fast. The brute force search method consists of an exhaustive exploration
of the solution space, being viable only when the dimension of the search space is small. The optimization by means of
hypercube sampling consists in the division of the probability distributions in intervals and the use of random parameter
selection among the preselected intervals according to their probabilities, with the number of selections proportional to the
probability of each interval, in a way that the distribution of the picks among each interval occurs in a uniform manner (Maschio
et al., 2009).

Objectives
The objective of this work is to access the impact of geologic and dynamic flow properties uncertainties in an integrated manner
for the development of an oil field. The proposed methodology aims to create a risk curve for the development project in a
scenario where there is scarcity of good quality information. The work has the following specific objectives: characterize the
model’s dynamic properties through the treatment of rock and fluid data; perform history matching on the flow model using a
numerical simulator; perform uncertainty analysis for the quantification of risks; and determine the best development strategy for
the secondary recovery project under uncertainty conditions on the model’s static and dynamic properties.

Methodology
The present work consisted of the steps rock data treatment, fluid data treatment, sensitivity analysis, history matching,
optimization and uncertainty analysis, described in the following.

Step 1: Rock Data Treatment

The geologic models (scenarios) were constructed. Scenario deterministic was obtained in the preprocessing software Builder,
from CMG, using a petrophysical correlation between porosity and permeability of an analogous field of the Sergipe-Alagoas
basin. On the geological modeling software Petrel Facies Modeling®, from Schlumberger, another five other scenarios were
constructed, according to the oil in place volumes P10, P30, P50, P70 and P90, using geostatistical simulations with varying
variogram parameters.

Step 2: Available Fluid Data Treatment using analogous reservoirs

Correlations were obtained through non-linear regression of the available PVT data, for the determination of oil properties (Rs,

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 4 SPE 153636

Bo, µo, Co) using Luvizotto’s correlations (Luvizotto, 1993). Gas properties (Pc, Tc, Z, Bg, µg) were determined by the use of the
oil industry’s classic correlations Standing-Katz, 1942, and Dean-Stiel, 1965. Due to the shortage of information on the
properties of the reservoir and its fluids, correlations were used with the known data from other wells in the field and in an
analogous field and the API specific gravity of the oil to obtain the dead oil viscosity (µod), saturation pressure (Psat) and dead oil
density (Dod). The reservoir temperature was obtained through the average temperature gradient of the area. The average
specific gravity of the liberated gas (dg) was obtained using the solution gas-oil ratio data from differential liberation (obtained
through a correlation with pressure) and the initial liberated gas specific gravity.

Step 3: Sensitivity Analysis

In the sensitivity analysis, the selected parameters were pore volume multiplier (Volmod), in order to consider the uncertainty in
the reservoir volume, the oil, water and gas relative permeability curves’ exponents, the relative permeabilities of the gas on the
connate liquid saturation, the relative permeability of the oil on the initial gas saturation and the critical gas saturation. The value
-6 2 -1
adopted for the formation compressibility was 300x10 (kgf/cm ) . Table 1 presents the studied uncertain parameters in this
analysis. As local objective functions, were utilized the GOR (Gas Oil Ratio) and the reservoir pressure. The sensitivity analysis
module of the software CMOST was used in the adjustment of the response surface.

Table 1 – Parameters studied on the sensitivity analysis.

Parameter Description

EXP1 Exponent of the relative permeability to water power law curve on a given water saturation
EXP2 Exponent of the relative permeability to oil power law curve on a given water saturation
EXP3 Exponent of the relative permeability to gas power law curve on a given liquid saturation
EXP4 Exponent of the relative permeability to oil power law curve on the presence of gas and connate water at a
given liquid saturation
KRGCL Relative permeability to gas on the connate liquid saturation
KROGCG Relative permeability to oil on the connate gas saturation
SGCRIT Critical gas saturation
PORFORM Formation compressibility
VMOD Pore volume multiplier

Step 4: History Matching

Using the production historic record, a history match was performed using the software CMOST. The adjusted parameters were
considered significant in the sensitivity analysis step, as shown on Table 2. The production data were adjusted to the six
geologic scenarios, in order to specify the static (formation compressibility, gas critical saturation) and dynamic properties (gas
relative permeability curve parameters). The local objective functions used were the cumulative oil production (Cum_Oil) and
the reservoir pressure (reservoir_pressure).

Table 2 – Uncertain parameters.

Parameter Study Levels

EXP3 1.5 – 6.0

EXP4 1.5 – 6.0
KRGCL 0.70 – 0.95
KROGCG 0.70 – 0.95
SGCRIT 0.005 – 0.030
PORFORM 1.10-4 – 5.10-4
VMOD 1.2 – 3.0

Step 5: Optimization
The optimization had the objective of determining the injector (I1) and producer (P1) well locations, and the maximum injection
flow rate. The NPV was used as objective function, with the terms of the function the oil flow rate (qo), the water injection rate
(qwi), the produced water flow rate (qw) and the produced gas flow rate (qg). In the calculation of the objective function, a
simplified economic modeling was used which considers only revenues from oil and gas production and costs of water injection.
Table 3 presents the parameters to be optimized, the locations of the injector and producer wells and the maximum water
injection flow rate, as well as the value ranges that these parameters can assume during the optimization process. The
employed optimization method was DECE in the software CMOST.

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 SPE 153636 5

Table 3 – Uncertain parameters.

Parameter Description Study levels

Injx X coordinate of the injector well 24 - 32

Injy Y coordinate of the injector well 62 - 78

Prodx X coordinate of the producer well 11 - 14

Prody Y coordinate of the producer well 65 - 71

Qwi Maximum injection flow rate 300 - 650

Step 6: Uncertainties Analysis, Quantification of Risks and Determination of the Best Development Strategy
In order to take into consideration the uncertainties present in the producer and injector wells locations and in the injection flow
rate, and improve the strategy determination decision making process taking into account the different optimized scenarios,
each of the obtained configurations is applied to the different scenarios. Assuming that these scenarios are equiprobable, it is
possible to determine the expected monetary value (EMV) for each configuration. The configuration correspondent to the
optimized strategy is the one that presents the greatest EMV. Using the NPV values for each scenario, a risk curve was built.

Application
In order to demonstrate the practical viability of the methodology to problems with realistic characteristics and dimensions, a
three phase black-oil 3D model was used, adapted from a numerical simulation model of the Dourado Field, a Petrobras
concession. , This field was discovered in the 70’s and has always produced under primary recovery, it is located on the
continental shelf off the state of Sergipe – Brazil, in a region of shallow waters, and is considered nowadays a mature oil field
and because of that it is a candidate for a secondary recovery project. Although the field has a long production record it is
scarce of rock and fluid data, being necessary the use of analogies and parameter adjusts to the production record.
The presented methodology was tested performing the construction of a risk curve of a secondary recovery Project using water
injection in only one of the fields’ reservoirs. Differently from the model used in the field management, which contemplates a
single realization of the permeabilities field, the model used in this work considers a set of equiprobable realizations obtained
using the SGSIM algorithm of the software Petrel, which represent situations ranging from pessimistic to optimistic.
The problem involves water injection through an injector well (I1) and production through a producer well (P1). The model has a
49x94x3 grid. In each of the geologic scenarios created, history matching was performed and the best adjusted case was used
in an optimization algorithm using as parameters the maximum injection flow rate and the locations of the producer (P1) and
injector (I1) wells, using as an objective function the net present value (NPV) of the project. Six configurations were obtained
(the combination of injection flow rate and locations of the producer and injector wells) which maximized the NPV for each of the
scenarios. Next, each of the six configurations was applied to each scenario, generating six NPV’s for each scenario and,
assuming that the scenarios are equiprobable, the expected monetary value for each one was calculated, using it as the criteria
for the best configuration of the production area determination, and an associated risk curve was obtained.

Presentation of Results

Rock Data Treatment

Figure 1 presents the geostatistical realizations of the permeabilities field associated with the percentages P10, P30, P50, P70
and P90 and the deterministic scenario, related to the oil in place volume, which do not represent the real reservoir volumes,
what adds uncertainty about the reservoir’s volume for the methodology’s test.

7DO22D
7DO22D 7DO22D
7DO22D 7DO22D
7DO22D 7DO22D
7DO22D 7DO22D
7DO22D
7DO22D
7DO22D
7DO37 7DO37 7DO37 7DO37 7DO37
7DO37 7DO37 7DO37 7DO37 7DO37 7DO37
7DO37
8DO38
8DO38 8DO38
8DO38 8DO38
8DO38 8DO38
8DO38 8DO38
8DO38
8DO38
8DO38

Figure 1 – Permeability maps of the representative geologic models.

Comparing the original fluid in place volumes, it was verified that the deterministic scenario had a volume similar to the P50
scenario.

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Available Fluid Data Treatment

The new correlations obtained through non-linear regression of the available PVT data for the reservoir fluids are presented as
Eq.s 4, 5, 6, 7, 8 and 9.

(−0.1349× R 0.1386
×γ gi
0.3711
)
 p
si

γ gd = γ gi ×   (4)
 pb 

(0 .4316 γ − 2 . 9161 ×10 − 4 T +1 . 9811 ×10 − 2 γ oAPI )

R s = 4 . 9474 × 10 − 2 p 0 . 9759 ⋅ 10 gd
(5)

 γ gd 
B o = 1 . 0234 + 8 . 0489 × 10 − 4 R s + 1 . 3712 × 10 − 3 R s   + 3 . 2251 × 10 − 4 T (6)
 γo 

C o = [− 285 . 5 + 232 . 1 × B ob − 67 . 2 × log( p b ) ] × 10 − 6 (7)

µ o = µ ob + 5 . 2415 × 10 − 4 × µ ob
1 . 7474
× (p − pb ) (8)

µ od0 . 3096 T 3 . 0649

µ ob = 2 . 1596 × 10 − 4 × (9)
R si0 .9204 p b0 .6206

2
The original reservoir pressure is 126,0 kgf/cm , the temperature 63,8 ºC, the dead oil viscosity (µod) 1,60 cp and the saturation
2 3 3
pressure (Psat) 119,9 kgf/cm . The solution gas-oil ratio (Rs) is 83,53 m /m , obtained using Eq. 5, and the oil formation volume
3 3
factor (Bo) at Psat is 1,251 m /m calculated using Eq. 6. The Figures 2 and 3 present the oil and gas PVT properties obtained
using the equations above.

90.00 1.700 0.08000 0.0200

80.00 0.0180
1.600 0.07000

0.0160
70.00 Rs, vol/vol
Bo, vol/vol
1.500 0.06000
Bg, vol/vol
B o(m 3/m 3 ), Visco(cP)

Visco, cP 0.0140
60.00 Viscg, cP
1.400 0.05000
0.0120
R s(m 3 /m 3)

Bg(m /m3)

Viscg(cP)
50.00
1.300
3

0.04000 0.0100
40.00
1.200 0.0080
0.03000
30.00
0.0060
1.100 0.02000
20.00
0.0040
10.00 1.000
0.01000
0.0020

0.00 0.900
0.00000 0.0000
0.0 50.0 100.0 150.0 200.0 250.0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0
2 2
P(kgf/cm ) P(kgf/cm )

Figure 3 – PVT Properties of the oil. Figure 3 – PVT Properties of the gas.

Sensitivity Analysis
Evaluating Figures 4 and 5, it is possible to observe that the response surfaces (RS) represent in an acceptable manner the
simulation results within a confidence interval of 95%.
Figure 4 presents the GOR objective function values within a 95% confidence interval. On the vertical axis are the simulated
values and on the horizontal axis the surface response predicted values.
Figure 5 presents the well block pressure objective function values, on the vertical axis are the simulated values and on the
horizontal axis the surface response predicted values. It is desired that the points on the graph lie over a 45° straight line,
showing that simulated data can be well represented by the fitted response surface.

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Figure 4 – GOR function calculation: RS x simulator. Figure 5 – Reservoir pressure function calculation: RS x
simulator.

The Tornado diagrams on Figures 6 e 7 present the results of the sensitivity analysis obtained using the linear model for the
nine uncertain parameters studied. Through the analysis of the Tornado diagrams, it can be noted that the parameter with the
greatest influence over both the GOR and the reservoir_pressure functions is the power law exponent of the gas relative
permeability curve at a given saturation (EXP3), followed by the pore volume multiplication factor (VMOD), critical gas
saturation (SGCRIT), formation compressibility (PORFORM), gas relative permeability at connate liquid saturation (KRGCL), oil
relative permeability at connate gas saturation (KROGCG) and the power law exponent of the oil relative permeability curve at a
given saturation (EXP4).

Figure 6 – Tornado Diagram of the GOR function. Figure 7 – Tornado Diagram of the reservoir pressure
function.

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History Matching
The best results, as well as the parameters that minimized the local and global objective functions for each of the geologic
scenarios are shown on Table 4.

Table 4 – History Matching Data.

Scenario GlobalObj Cum_Oil Reservoir EXP3 EXP4 KRGCL KROGCG PORFORM SGCRIT VMOD
pressure

deterministic 0.65790 1.2664 0.04937 4.5 5.5 0.95 0.75 0.000260 0.020 1.2

P10 0.55790 1.0266 0.08916 4.5 5.5 0.75 0.80 0.000260 0.030 1.2

P30 0.79133 1.2202 0.36249 4.0 5.5 0.85 0.75 0.000180 0.005 1.6

P50 0.75665 1.0348 0.47849 4.5 6.0 0.85 0.70 0.000260 0.020 1.2

P70 0.54661 1.0326 0.06058 4.0 5.0 0.90 0.75 0.000420 0.010 1.4

P90 1.11470 2.2114 0.01795 2.5 2.5 0.80 0.75 0.000260 0.020 1.8

Optimization

The results are presented on Table 5. Besides the parameters is also presented the NPV value obtained with each geologic
scenario under the optimized configuration (injector and producer well locations and maximum injection flow rate) obtained.

Table 5 – Optimization Data.

Scenario Configuration GlObj (x103) Injx Injy Prodx Prody Qwi

deterministic 1 226.8 25 76 11 66 370

P10 2 239.1 24 76 11 65 580

P30 3 262.2 25 76 11 69 650

P50 4 244.5 28 74 11 65 370

P70 5 265.59 25 76 11 69 650

P90 6 268.9 25 76 11 65 650

Determination of the Best Development Strategy under Uncertain Conditions

Table 6 presents the performance of each production strategy, with each line displaying the NPV obtained for a given geologic
scenario altering the configurations of the production area. On the last line, the EMV is calculated assuming the occurrence of
each scenario is equiprobable, as there are no major indications that a given scenario is more likely to occur than others.

Table 6 – EMV Calculations.

NPV of the Configuration (Mil US$)
Scenario
1 2 3 4 5 6

deterministic 227.020 247.130 249.770 244.870 240.580 252.220

P10 222.280 239.150 234.930 237.100 224.610 257.820

P30 215.830 226.420 262.240 214.820 250.720 235.070

P50 231.150 252.390 257.310 244.930 249.050 275.540

P70 241.610 253.180 281.200 253.970 265.590 233.170

P90 218.620 249.000 248.460 227.570 240.190 268.920

VME 226.085 244.545 255.652 237.210 245.123 253.790

The optimized production strategy resulted in an EMV of US$ 255.652 mil. This strategy consisted of the employment of the

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 SPE 153636 9

production configuration 3, that is, the producer well (P1) located at position (11,69), the injector well (I1) located at position
3
(25,76) and an injection flow rate of 650 m /d, as shown on Table 5. The new well locations can be observed on Figure 8, which
presents a map displaying the depths of the Top of the reservoir. Figure 9 displays the risk curve of the secondary recovery
project considering geologic and dynamic flow properties uncertainties. It represents a decreasing cumulative probability
distribution, commonly used in reserves/reservoir studies. The highlighted with dots mark the P10, P50 and P90 percentage
values.

1.00
0.90
0.80
0.70

Probabilidade
0.60
0.50
0.40
0.30
0.20
0.10
0.00
200.00 220.00 240.00 260.00 280.00 300.00
VPL (M US$)

Figure 8 – Area’s Reservoir Top Map. Figure 9 – Risk Curve.

It should be noted that in this kind of curve the P10 percentage representative model corresponds to an optimistic scenario, the
P50 to a reference scenario and the P90 to a pessimistic scenario. Table 7 presents the NPV values obtained at the P10, P50
and P90 percentages. Also worthwhile to mention is that the inclusion of the injection flow rate in this analysis takes into
consideration possible operational problems that could cause a reduction in the injected water flow rate.
Table 7 – NPV of the P10, P50 and P90 percentages.
Scenario

P10 P50 P90

NPV (Mil US$) 272.308 250.769 227.692

Figure 10 presents the production and cumulative production obtained by the simulation runs corresponding to the P10, P50
and P90 percentages.

Figure 10 – Cumulative production and Oil Flow Rate of P10, P50 and P90.

Conclusions
In this work, a methodology was proposed for the quantification of uncertainties in the geological and dynamic properties of the
model. To test the method, a 3D model with real dimensions was used, for which a characterization of rock and fluid data was
performed. In order to improve the quality of the available data, the fluid PVT data were adjusted to reservoir conditions using
empiric correlations obtained by Luvizotto (1993) and data from analogous reservoir’s when needed. The agreement between
the measured available data and the correlation was very good.
Of the nine analyzed parameters in the sensitivity analysis, seven of them demonstrated to be representative. The elimination of

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 10 SPE 153636

non-significative parameters reduced the computational effort on the following steps of the work. Given the high number of
simulations demanded, this step was essential to reduce the computational effort and the time spent by the engineer on this
work. A good adjustment of the significative parameters was obtained for all the studied scenarios. The adjustment of the
parameters to the historic production record on the different scenarios studied shows clearly the inverse problem characteristic
of this step. Having been considered the uncertainties and having been performed the optimization, the ideal configuration for
the production development of the area was determined, with estimates of the locations of the producer-injector well pairs to be
constructed and the water injection flow rate to be employed.
The proposed methodology showed itself to be adequate for the quantification of uncertainties and associated risks of the
optimized production strategy. It is of very practical application, despite the high computational effort demanded, as well as the
many hours of engineering work. The multidisciplinar character of methods utilized should be pointed out, as in the
development of a project the adjusted parameter values should be geologically coherent. This gives a very big importance to
the joint work of engineers, geologists and geophysicists. This methodology aimed to bring greater reliability to the production
curve forecasts through the quantification of the associated risks.

Nomenclature

ak Coefficients of the linear modeled surface response equation

Bg Gas Formation Volume Factor
Bo Oil Formation Volume Factor
Co Oil Compressibility
EMV Expected Monetary Value
i, j, t Well, data series type and time, respectively
k Number of variables studied in the sensitivity analysis
m Measured data
Merri,j Measurement Error
N(i) Total number of the types of production data series for well i
NPV Net Present Value
T(i,j) Total number of time steps with measured data s
NW Total number of wells
p Pressure
Pb Bubble Pressure
Psat Saturation Pressure
PVT Pressure-Volume-Temperature laboratory experiment
qg Produced gas flow rate
Qi Local objective function for well i
qo Oil flow rate
qw Produced water flow rate
qwi Injected water flow rate
Rs Solution Gas-Oil Ratio
Rsi Initial Solution Gas-Oil Ratio
s Simulated data
SR Response Surface
TR Reservoir Temperature
wi,j Data series weight
xk Variables of the equation of the linear response surface model

γgd Dissolved gas density

γgi Initial gas density

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 SPE 153636 11

γºAPI Oil density in ºAPI

µo Oil Viscosity
µob Oil Viscosity at the bubble point
µod Dead oil viscosity

∆Yi ,mj Maximum change for the well i and production data j

Acknowledgments
To PETROBRAS, in special UO-SEAL, for making the present work possible, as well as the colleagues from ATM-SM/RES for
the help on the execution of it, specially to the engineer Marcelo Ramalho.

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