SPE-174370-MS

Integrated Model Based Decision Analysis in Twelve Steps Applied to Petroleum Fields Development and Management Denis José Schiozer, Antonio Alberto Souza Santos, Paulo Soares Drumond (State University of Campinas)

Copyright 2015, Society of Petroleum Engineers This paper was prepared for presentation at the EUROPEC 2015 held in Madrid, Spain, 1–4 June 2015. 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 This work describes a new methodology based on 12 steps for integrated decision analysis related to

petroleum fields development and management considering reservoir simulation, risk analysis, history

matching, uncertainty reduction techniques, representative models and selection of production strategy

under uncertainty. The example of application is the field UNISIM-I-D which is a benchmark case based

on Namorado field, Campos Basin, in Brazil. The main focus of the results is to show that the method can

be used in practical applications, i.e., complex reservoirs in different field stages (development and

management) because it allows the integration of static (geostatistical images generated by reservoir

information) and dynamic data (well production and pressure) to reduce uncertainties allowing risk

analysis integrating geological, economic and other uncertainties yielding a decision analysis based on

risk-return techniques. In this methodology, no proxy model is used so reservoir simulation is used

directly to reproduce field performance. We also show that the methodology is efficient and easy to use,

even in complex cases where the computational time is an important concern and in real time operations.

Introduction The decision analysis related to the development and management of petroleum fields involves risk due

to several uncertainties, mainly in reservoir and fluid parameters, economic model, and operational

availability. The effect of all these uncertainties must be combined to estimate the risk involved in the

decisions.

This process is not simple to model due to the type of decisions (long time projects) and complexity of

the problem (petroleum reservoir, production facilities, economic evaluation and statistics techniques).

The process can also be very time consuming when high fidelity models and specific statistical

techniques are used. Therefore, some simplifications are often used to enable the analysis but some of

these simplifications can yield wrong results so it is important to be very careful due to the importance of

the decisions related to the development of petroleum fields.

In order to enable a methodology with reliable results, some important steps must be guaranteed:

The models used to simulate the problem must honor all dynamic data;

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The reservoir simulation model must be complete but fast enough to generate a reliable result of

each scenario;

The statistical analysis must be carefully chosen in order to avoid a high number of evaluations

for the problem (which is very time consuming);

The decision (selection of the production strategy) must reflect, in the models, the most accurately

as possible the effects on the real problem; in this particular problem, there is a high influence of

the production strategy in the performance of the project, and consequently in the risk evaluation;

The economic evaluation must be integrated with the technical evaluation because the decisions

are influenced by the economic return of the project;

Many solutions presented in the literature and used in some companies address some of these points

but may have some drawback in other points which may be crucial to complex cases. Therefore, we are

presenting a methodology that was a result of several study cases and that we believe that contains the

main parts of the decision analysis that are necessary to a good decision making process.

The first important point is that we try to preserve a high fidelity model for the physical simulation of

the problem (using an accurate reservoir simulation model) because of the complex integration between

the decision (production strategy) and the performance of the system. As a consequence of that, we had to

develop a simplified statistical technique (Schiozer et al, 2015) that was exhaustive tested in several

examples with good performance considering the precision of the results and computational time. We

also have developed a methodology to reduce the number of scenarios to be used to select production

strategies using a reduced number of representative models. The methodology has low computation cost

and it is simple enough to be applied in a day-to-day basis in the companies.

The methodology was applied here in the UNISIM-I-D case which is a benchmark case based on the

Namorado Field, Campos Basin, in Brazil (http://www.unisim.cepetro.unicamp.br/unisim-i).

Objective The objective of this work is to propose a methodology based on 12 steps to be applied in the decision

analysis processes related to petroleum fields development and management integrating reservoir

simulation, risk analysis, history matching, uncertainty reduction techniques, representative models and

selection of production strategy under uncertainty.

The methodology is developed to be used in practical applications (complex reservoirs) and it has the

flexibility to be applied to reservoirs in different field stages (before and after reservoir development),

once this methodology can be applied partially (a subset of the 12 steps).

Methodology The steps of the methodology are described below:

1. Reservoir characterization under uncertainties (to build models, develop scenarios and estimate

probabilities). This is a crucial step and a multidisciplinary approach must be applied to consider

all possible important uncertainties which for this problem are mainly: reservoir, fluid, economic

and operational parameters.

2. Build and calibrate simulation model: in order to have accurate risk quantification, it is necessary

to trust in the response of the model for each scenario created; therefore, it is necessary to

calibrate the simulation model to have a fast response but robust enough to avoid bias evaluation.

We believe that a high fidelity model is necessary here because the interaction between the

reservoir model and the production strategy so we haven´t use low fidelity models (proxies,

emulators, for instance). The calibration is normally done with a Base Case (called Base0 in this

work).

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3. Verify inconsistencies of the Base Case with well dynamics data: scenarios correction and

uncertainty. This step is normally simplified in the risk quantification methodologies but it is a

very crucial step because, in many times, it may avoid inconsistency between the model and the

data from the fields. A typical history matching procedure can be used in this step (Maschio and

Schiozer, 2008).

4. Scenarios generation considering all possible scenarios (Schiozer et al, 2015).

5. Reduction of scenarios with dynamic data: the Base Case and uncertainties in reservoir and fluid

properties are used to generate probabilistic scenarios (Schiozer et al, 2015). Several techniques

(Armstrong M. et al., 2012; Maschio and Schiozer, 2015) can be used to reduce the number of

possible scenarios that represent the case depending on the complexity of the case and amount of

data. With the selected models, a base case must be selected to be used in the next step (Base1).

The usual recommendation is to use a model that is close to P50 in all main indicators for the

initial strategy. The step of selecting a new Base Case that represents an intermediate case (Base1)

may be necessary if the Base0 does not honor the dynamic data or becomes an optimistic or

pessimistic case.

6. Selection of deterministic production strategy for Base Case. The decision (production strategy)

and the risk quantification have mutual influence so it is important to use an iterative technique to

select the production strategy. The first production strategy (called here E1) is selected using an

optimization procedure and the Base1 Model (Ravagnani, et al, 2011).

7. First estimative of risk curve, considering E1 with all possible scenarios from Step 5, has to be

done. In many cases presented in the literature, this risk curve is used in the projects but we show

in this paper that the final risk curve can be very different from this option.

8. Selection of Representative Models (RM) (Schiozer, 2004; Costa, A.P. et al., 2008) based on all

objective functions and input variables.

9. Selection of production strategy for each RM repeating Step 6 for each RM.

10. Selection of production strategy under uncertainty including economic and other uncertainties,

using a risk-return analysis combining all possible strategies and all possible scenarios. If the

number of scenarios combined with the simulation time of each scenario is too time consuming

the RM can be used to represent the uncertainties.

11. Identification of potential for change in the production strategy to improve chance of success

based on the value of information, value of flexibility and robustness of the production strategy,

implying in possible modifications and final strategy.

12. Final risk curve and decision analysis.

Application The 12 steps methodology is applied in a case presented by Avansi and Schiozer (2015a) which is based

on data from Namorado field in Brazil. A synthetic field, named UNISIM-I-R (reference model), was

built in order to have a benchmark. A simulation model (UNISIM-I-D) was built to represent the field for

a project developed on the date (05-31-2013), i.e., in an initial stage of field management plan under

uncertainties, including 4 years of production data (2013-2017) and considering the information of 4

production wells (from the reference case). The grid block was defined as 100x100x8 m discretized into a

corner point grid with 81x58x20 cells with a total of 36,739 active cells.

Results Step 1

The uncertainties of the model were composed by (summarized in Table 1):

Geostatistical realizations of facies, porosity, NTG, permeability and east structural model:

facies and porosity scenarios are generated using a random seed during the facies and

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petrophysical modeling. NTG and permeability distribution are then calculated as a function of

facies and porosity respectively.

Attributes: water relative permeability (krw), PVT, water oil contact depth (WOC), rock

compressibility (CPOR) and vertical permeability multiplier (kz) are considered during the

reservoir modeling.

Economic uncertainties are presented in Table 2.

Technical (operational) uncertainty attributes include system availability (SA) and well index

multiplier (dWI) (Table 3).

The full explanation of the simulation model, economic model and uncertainties was done by Avansi

and Schiozer (2015a). The models and files to reproduce the results are in the benchmark case description

(http://www.unisim.cepetro.unicamp.br/unisim-i).

Table 1. Uncertainties parameters for the simulation model (Avansi and Schiozer, 2015a).

Attribute Uncertainty Type Levels (Probability - %)

Facies discrete (realization)

500 (equi-probable realizations) Porosity discrete (realization)

NTG, fraction correlated with facies

Permeability correlated with porosity

East structural model discrete presence (0.7); absence (0.3)

krw discrete krw0 (0.2); krw1 (0.2); krw2 (0.2); krw3 (0.2); krw4 (0.2)

PVT discrete PVT0 (0.34); PVT1 (0.33); PVT2 (0.33)

WOC, CPOR, Kz continuous Triangular distribution

Table 2. Economic Parameters and Uncertainties (Schiozer et al, 2015).

Parameter Description Base Economic

Scenario 1

Economic

Scenario 2

Market

Values

Oil price (USD/bbl) 50 70 40

Discount rate (%) 9 9 9

Royalties (%) 10 10 10

Taxes

Special Taxes on G. Revenue (%) 9.25 9.25 9.25

Corporate Taxes (%) 34 34 34

Oil production (USS/bbl) 10 13 8

Costs

Water production (USS/bbl) 1 1.3 0.8

Water injection (USS/bbl) 1 1.3 0.8

Abandonment (USD Millions) (% well investments) 7.4 9.2 6.5

Initial Investment (USD Millions) 768.9 961.1 678.8

Investments Wells (USD Millions) 13.3 16.7 11.7

Platform (USD Millions) 786.3 982.5 628.8

Probability (%) 50 25 25

Table 3. Uncertainty Levels for Discrete Technical Parameters (Schiozer et al, 2015).

Parameter Type Levels

0 1 2

System availability

Platform 0.95 1.00 0.90

Group 0.96 1.00 0.91

Producer 0.96 1.00 0.91

Injector 0.98 1.00 0.92

Well index multiplier dWI 1.00 1.40 0.70

Probability (%)

33 34 33

Steps 2 and 3 Step 2 was done to guarantee that the simulation run is robust enough to represent the reservoir and fast

enough to be included in a methodology that demands thousands of simulation runs. In our case, the

simulation time was around 5 minutes running in parallel in a cluster. This methodology is applicable to

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cases with simulation time of hours. If more complex reservoir models are required, some simplifications

may be necessary depending on the time and scope of the project.

Step 3 was done to guarantee that the model was compatible with the initial response of the model

(material balance, pressure and initial production).

Step 4 In Step 4, scenarios were generated to start the process. In several cases, the risk curve is generated

directly from these scenarios but, in general, the companies have the dynamic data that have to be

honored. In Figure 1, we show the risk curve for 500 and 100 scenarios.

Figure 1: Risk curve for 100 and 500 scenarios (Step4); risk curve for 214 filtered scenarios (Step 5) and

Base model (Base0).

Step 5 In Step 5, as the case has initial production from 4 wells, a matching indicator was used to filter the

scenarios. The indicator was normalized for each well and each objective function (Qo, Qw, Qg and BHP).

Values between -1 and 1 were considered acceptable. Figure 2 shows that 214 from the 500 initial models

were selected. Figure 3 shows the water production curves for the 4 wells as an example. Figure 1 shows

the risk curve with the 214 selected models. The index NQDS represents a normalized quadratic

deviation with sign (Avansi and Schiozer, 2015b; Bertolini et al, 2015); in this work, values between -1

and +1 represent low deviation with history data and, therefore, models are accepted to be used in the

sequence of the work.

With the selected model, an initial strategy (E0) must be used to select a base case. This initial strategy

is not critical because it will be improved in the next steps; it is just used to select the Base1 case. The

most usual approach to choose the Base1 case is to select the deterministic case (using all attributes in the

most probable value – level 0). As in this work this model was not selected among the 214 models then

we use the initial strategy (E0), which is composed of 14 producers and 11 injectors, yielding results of

Figure 4, to select the Base1 case (an intermediate case).

Step 6 After choosing an intermediate case (Base1) the selection of a deterministic production strategy takes

place. In order to optimize the Base1 production strategy, it was considered as optimization parameters

the decision (G1) and operation (G2) variables related to UNISIM-I-D definition (Gaspar et al, 2014).

The G1 variables were: number, type (vertical or horizontal), location and schedule of wells and

capacities constraints (liquid, oil and water production and water injection) of platform. The G2 variables

were: maximum water-cut, maximum liquid production and water injection of wells.

The optimization procedure was divided in the following phases: (1) number and type of wells and

capacities constraints; (2) schedule of wells; (3) location of wells and capacities constraints (fine tune);

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(4) schedule of wells; (5) water-cut, maximum liquid production and water injection of wells; (6) fine

tune.

Phases 1, 3 and 5 were done using software from CMG©, where the optimizer method used was

DECE (Yang et al, 2007). The objective function used was NPV, based on UNISIM-I-D proposal and

calculated with software UNIPAR (UNISIM internal development).

A summary of NPV evolution (Figure 5), for some intermediate phases, are shown below.

The selected strategy configuration (adopted as final and named E1) is:

Number and type of wells: 18 total, 10 horizontal and 2 vertical producers, 6 horizontal injectors

(all conventional wells);

Capacities constraints: 16275 m3/day (liquid/oil production), 9068 m

3/day (water production) and

23328 m3/day (water injection).

At the 10957 days the strategy indicators are: USD 2.236E9 (NPV), 6.498E7 m3 (Np), 5.046E7 m

3

(Wp), 6.892E9 m3 (Gp), 1.380E8 m

3 (Wi), 0.561 (ORF). The oil per unit area (total) map at 1461 (Figure

6a) and 10957 days (Figure 6b), with the location of the drilled wells are depicted in Figure 6.

Step 7 In this step, the first estimative of Risk Curve considering the strategy E1 with all possible scenarios from

Step 5 (Figure 7) was carried out. In many cases presented in the literature, this risk curves is used in the

projects but we show in this paper that the final risk curve can be very different from this option; this is

not the actual risk curve because production strategy was not optimized under uncertainty.

Figure 2: Normalized quadratic deviation with sign (NQDS) for 214 selected models (286 not selected

models in gray).

Step 8 The strategy E1 was optimized to Base1 model so it is necessary to verify the quality of this decision

considering uncertainties. Therefore, it is necessary to verify other possibilities, especially for scenarios

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that are different from Base1. We then recommend selecting some representative models (RM) (Schiozer

et al, 2004) and check other strategies that are good for other scenarios.

In this work, we select 9 RM based on Figure 8 (main output variables) but we also guarantee that all

input variables are well represented (including all levels of the attributes, except the geostatistical

realizations that has 500 levels and only 9 were used). The Base1 case was forced to be one of the RM

(Base1=RM1) because the strategy E1 was already select for this model so it saves time in the next steps.

One interesting point to highlight here and that is normally neglect in many approaches is the

relationship of the uncertainties and the production strategy. The RM1 that was intermediate case for E0

became an optimist case for E1 and this behavior happened in all our cases tested. Once a strategy is

optimized for a particular model, it becomes more optimistic considering the output parameters optimized

(NPV for instance).

Figure 3: Water production for the 4 initial wells with history data (500 initial models and 214 selected

models).

Figure 4: Np, Wp, NPV and ORF for the 214 models and selection of an intermediate case (Base1) using the

strategy E0.

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Figure 5: Intermediate phases of the optimization procedure: (a) Phase 3 and (b) Phase 5.

Figure 6: Oil per unit area map at (a) 1461 and (b) 10957 days, including wells locations.

Figure 7: Risk curve with strategy obtained in Step 6 (E1) (a) NPV with and without economic uncertainties;

(b) Np.

Step 9 After selecting the RM, the production strategy of each RM has to be defined. In this step we repeat

the optimization procedure described in Step 6 for each RM obtained the set of optimized strategies [E2,

E3, …E9], where Ei is the optimized strategy defined for RMi.

For each RM, the underlined NPV (Table 4) identifies the best strategy. As it shows, the strategy

optimized for each RM is the best strategy among all other strategies applied to that RM (best results in a

row).

One of the uncertainties considered in this study is the “east structural model”. The presence or

absence of this uncertainty associated with the fact that there is not connectivity between “west and east

structural blocks” (due a sealed fault) plays a big role in the selection of production strategy, once it may

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affect considerably the total amount and the drain of oil in the field and consequently the definition of the

production strategy.

The representative models RM3, RM6 and RM7 (Figure 9a shows RM7 with E7) don’t have the “east

block”, differently of the other models. Figure 9b shows RM9 where it’s possible to see the “east block”

and the production strategy selected (E9).

The absence of the “east block” also has a main impact in the risk curves, as it can be seen in Step 10,

due the fact that optimized strategies for RM3, RM6 and RM7 don’t have wells drilled in that area and

then the oil is not drained.

Figure 8: Np, Wp, NPV and ORF for the 214 models and selection of an intermediate case (Base1) using the

strategy E1; selection of 9 representative models (RM).

Table 4. Strategies applied to all RM (NPV in USD millions).

NPV

E1 E2 E3 E4 E5 E6 E7 E8 E9

RM1 2.236 1.912 0.790 1.331 1.419 0.961 1.482 1.319 1.717

RM2 1.635 2.302 0.778 1.836 2.007 0.870 1.539 1.773 1.672

RM3 0.804 1.039 1.636 0.974 0.651 1.142 1.057 1.054 0.569

RM4 1.999 1.609 1.100 2.500 1.991 1.240 1.183 2.187 2.007

RM5 1.360 1.703 0.821 1.680 2.413 0.865 1.305 1.552 1.723

RM6 1.101 1.065 0.9.31 0.512 0.390 1.908 0.905 0.712 1.038

RM7 0.617 0.737 0.260 0.617 0.596 0.530 1.481 0.542 0.395

RM8 1.745 1.819 1.245 1.821 1.950 1.225 1.254 2.506 1.690

RM9 2.274 2.178 1.077 1.667 2.068 1.558 1.244 2.129 2.972

Step 10 Considering all 9 strategies optimized in Step 9, there are several ways to select the best alternative. The

usual approach is to consider typical values that represent the return of the project considering

uncertainties and the risk. For the return the expected monetary value, EMV, is the most usual indicator.

Several risk indicators are used to estimate risk (standard deviation, P10-P90, probability to have a NPV

below a tolerance and others). In our example here, we have considered only the EMV to select the best

strategy (Figure 10). In both cases, Figure 10 (a) and (b), E9 was the selected strategy. It is important to

observe the difference of the risk curve as the steps are performed.

Steps 11 Step 11 is dedicated to a detailed analysis of the strategy select in the previous step (E9 in our case). This

step is necessary because there are several improvements that can be made to the strategy considering the

uncertainties and the risk aversion of the companies. The most common studies that must be included in

this step are: information, flexibility and robustness that can reduce risk or improve the EMV of the

projects but they have some associated investments and costs; therefore, it is important to have

quantitative methodologies to estimate the benefits of these 3 approaches. Ligero et al (2005) show a

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typical way to estimate the Value of Information (VoI). Marques et al (2013) show a methodology to

estimate the value of flexibility. The robustness (Narahara et al, 2004; Moczydlower, B. et al, 2012;

Salomão, M.C., 2007) can be associated to NPV or oil production and it is a function of the risk aversion

of the companies; for a robust project related to NPV, lower investments can be done to avoid negative or

lower NPV values for the pessimistic scenarios; for a robust project related to oil production, higher

investments can be done to be prepared to produce higher rates from optimistic scenarios, for instance.

These 3 concepts were not included in this paper because they are complex analysis and therefore they

will be treated in future works.

Figure 9: Oil per unit area map (a) RM7 including (E7) and (b) RM9 including (E9).

Figure 10: Risk curve considering the 9 strategies (a) without and (b) with economic uncertainties.

Step 12 and Discussions After passing through all steps detailed, above, we believe we have a robust process to be used in the

decision analysis yielding a strategy that is appropriate to the case honoring the history data and

considering all uncertainties mapped for each particular case.

The 12 steps procedure has to be repeated whenever new important information is obtained and,

therefore, it is a continuous process that must be used by the company. The most critical time is, of

course, the moment to prepare the development plan, select the production facilities. The number of wells

and well placement is also an important consequence of such analysis but the procedure can be useful

also in later times for reservoir management as will be shown in future work (real time reservoir

management).

Conclusions We have presented a methodology bases on 12 steps to be used in a decision analysis related to petroleum

reservoir development and management under uncertainties.

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Many times, several steps are not performed by companies to speedup projects but we believe that

with the simplification presented here the methodology can be applicable to real cases even with complex

cases with long simulation time.

It is very important to observe that further simplification can yield suboptimal decisions. The level of

detail of each step is a function of the importance of the study and complexity of the case. The most time

consuming part is the optimization of the production strategy and the results are a function of the quality

of this process; therefore, it is important to use robust optimization processes. The results and time

consumption is also a consequence of the number of representative models; for the tests done so far, a

minimum of 9 models is necessary to represent all uncertainties and output parameters; if more RM can

be used better results are expected.

The methodology is flexible enough to be applicable to reservoir in different life stages. We have

presented a case in a development phase but it can be used in other stages. It is also simple enough to be

used in practical application because it does not required proxy models, or complex tools to be applied.

Acknowledgments The authors would like to thank UNISIM, DE-FEM, CEPETRO and PETROBRAS for supporting this

work. We also thank CMG and Schlumberger for software licenses.

Nomenclature BHP bottom-hole pressure

Gp cumulative gas production

NQDS normalized quadratic deviation with sign

Np cumulative oil production

NPV net present value

ORF oil recovery factor

Qg gas rate

Qo oil rate

Qw water rate

RM representative models

VoI value of information

VoF value of flexibility

Wi cumulative water injection

Wp cumulative water production

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