Risk Analysis Applied to Field Developments

5/21/2018 Risk Analysis Applied to Field Developments

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RISK ANALYSIS APPLIED TO PETROLEUM FIELD DEVELOPMENT:

AUTOMATED METHODOLOGY AND PARALLELCOMPUTING TO SPEEDUP THE PROCESS

E.L. Ligero and D.J. Schiozer

Departamento de Engenharia de Petrleo, Faculdade de Engenharia Mecnica UNICAMP.P.O.Box 6122, Zip Code 13081-970, Campinas, So Paulo, Brasil.

([email protected])

1. INTRODUCTION

The petroleum field life cycle has the following stages: exploration, appraisal,

development, production and abandonment. The appraisal phase is strongly related touncertainties, high investment and field development decisions. There are three main

types of decisions involved in this phase: abandonment of the discovered field (lowprofit, low stock tank oil originally in place (STOIP), high oil viscosity, etc.),continuation of the appraisal phase (risk mitigation) and development of the field.

A petroleum field development requires large investments and any improvementin the process can represent significant additional profit. However, in the 80s, it wasusual production forecast based in a deterministic reservoir simulation model. In this

way, production forecast had a deterministic approach. In most of cases, productionforecast was optimistic. Thus, economical viability of the project of oil and gas fields

was guaranteed by high prices practiced in the market.The current tendency is production forecast obtained by a probabilistic approach.

This approach is based in numeric flow simulation of several models representing

uncertainties of a petroleum reservoir and allows the evaluation of the uncertaintyperformance, like cumulative productions and oil rates, in any simulated time.

Important advances in hardware development allow increasing accuracy inproduction prediction in the decision processes. Furthermore, for complex reservoirsand large fields, probabilistic approach is possible and highly necessary in the

production strategy definition.The application of a probabilistic approach requires the definition of a

methodology, which must have the following characteristics: easy to use, flexible, andapplicable to a large range of cases. However, special attention must be given to reduceexcessive computation effort and to minimize the total time of the process. In order to

achieve this, it is necessary to make some simplifications to improve performancewithout losses in precision.

The objective of this paper is to show some advantages of having an automatedmethodology to perform risk analysis in Exploration and Production Project, during theappraisal phase, using reservoir simulation. Parallel computing can be used to reduce

total processing time. As an example, the methodology is applied to a syntheticreservoir model.

During the appraisal phase, the use of reservoir simulation is necessary to obtainmore accurate results of several economic and technical parameters. However, the useof numerical simulation increases substantially the computational effort. Therefore,

automated procedures are necessary to make the process viable.


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Base Model

Attribute1-P

Attribute1-M

Attribute1-O

Attribute2-M

Attribute2-P

Attribute2-O

Attribute2-M

Attribute2-P

Attribute2-O

Attribute2-M

Attribute2-P

Attribute2-O

Prob(1P_2P)

Prob(1P_2M)

Prob(1P_2O)

Prob(1M_2P)

Prob(1M_2M)

Prob(1M_2O)

Prob(1M_2P)

Prob(1M_2M)

Prob(1M_2O)

2. METHODOLOGY

The risk analysis methodology used here was first developed by Loschiavo et al.

(2000) and implemented by Steagall and Schiozer (2001). It is based on the simulation

of several flow models that represent the possible scenarios of the reservoir, through thecombination of the uncertain attributes. The simulation models are built through the

derivative tree, as in Figure 1. Each final branch of the derivative tree corresponds to acomplete simulation model. The probability of each resulting model is equivalent to the

multiplication of the probability of attributes that composes it. The sum of probabilitiesfor the models represented by branches in the tree must be equal to 1.

For a simple example as illustrated in Figure 1, the total number of models to be

simulated is equal to 9 (32). The inclusion of two more attributes, with three uncertainlevels each one, it would increase the number of models for 81 simulations. To reduce

the number of models to be simulated, a sensitivity analysis is applied to uncertainattributes in order to select the critical ones. This is one important simplification that

reduces the total time for the risk analysis process.Examples of usual uncertain attributes are the structural model, horizontal and

vertical permeability, relative permeability, pore volume, rock compressibility, PVT

curve, etc. The sensitivity analysis is done changing the attributes one by one in the basemodel. The base model is equivalent to the deterministic model and is generated bycombination of medium or probable values for all attributes. This analysis can be made

in one or more simulation times considering different production or economicalparameters such as Cumulative Oil, Gas and Water Production or Net Present Value

(NPV).

Figure 1: Example of Derivative Tree with Two Attributes and Three Levels

(P - Pessimistic, M Medium and O - Optimistic) (Schiozer et al., 2002)


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The generated models are simulated and the results are compared each one with

the base model. Thus, it is possible to choose the critical attributes. Once criticalattributes are chosen, it is possible to elaborate the derivative tree. It is important to

have in mind that only the branches, which are constituted by critical attributes, are

submitted to simulation runs.

3. AUTOMATED PROCESS AND PARALLEL COMPUTING

In automated process, reservoir simulation models covering the sensitivityanalysis are automatically generated and sent to a commercial Black-Oil simulator.These models are submitted to flow simulation with parallel computation in a network

of workstations. After all simulation processes during sensitivity analysis, results arestored in order to avoid their unnecessary simulation later.

The sensitivity analysis is obtained in a graphic interface where the criticalattributes can be selected. Flow models, resulting from the combination of the critical

attributes, are built automatically through the derivative tree technique. An importantaspect is that only models that have not been simulated in the sensitivity analysis aresubmitted to the flow simulation.

After simulation of the derivative tree models, a statistic treatment is done toobtain a risk curve, or an expectation curve, of the production forecast. The final resultsare individual results of each model and cumulated percentiles of all simulated models.

The percentiles, usually, calculated are P90, pessimistic, P50 medium or most probableand P10, optimistic.

This automated procedure and parallel computing used here are illustrated inFigure 2. Building process of simulation models, simulation runs and statistical analysisof the results are executed automatically, thus providing a great reduction in time.

Reservoir

Parameter

Uncertainty

Studies

Sensibility

Analysis

Flow Models

Decision Tree

Building

(uncertainty

representatives)

Parallel

Computing

Simulation

Statistical

Treatment

Uncertainty

Production Forecasts

P10, P50, P90, Models

Risk Curves

Reservoir

Parameter

Uncertainty

Studies

Sensibility

Analysis

Flow Models

Decision Tree

Building

(uncertainty

representatives)

Parallel

Computing

Simulation

Statistical

Treatment

Uncertainty

Production Forecasts

P10, P50, P90, Models

Risk Curves

Figure 2: Automated Process of Risk Analysis in Exploration andProduction Projects (Steagall and Schiozer, 2001)

The automated process must be flexible. Some possible alternatives that dont

require additional simulations are: changing the occurrence probability of criticalattributes and modifying the economic data model. These modifications can be done


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very fast, since they dont change the simulation results, which are stored to avoid

unnecessary simulation runs.It is highly recommendable to execute a sensitivity analysis regarding

uncertainty in economical parameters, which permit having a range of possible

economical scenario with no extra simulations.The application of the derivative tree methodology may increase the

computational effort, but in general, the time required for the whole process decreases ifthe computational tool is used in a correctly.

Parallel computing is responsible for the speedup of the process. Though thisspeedup can be observed, it is difficult to be measured. Figure 3 shows the speedupcaused by parallel computing. The process can be executed 5 to 10 times faster, if a

typical network of 10 to 15 workstations is correctly implemented.

Speedup

1

2

3

4

5

6

7

8

9

10

1 3 5 7 9

processors

ideal

het. measured

hom. measured

het. trend

hom. trend

Figure 3: Speedup Measured and Trend for Homogeneous and

Heterogeneous Network. (Schiozer et al., 2002)

4. APPLICATION

4.1. Description

The global reservoir has 20x44x17 cells (14,496 cells) and it was obtainedthrough an upscaling procedure from the Model 2 presented by Christie and Blunt

(2001). The coarse grid is described on a regular Cartesian grid and its dimensions are183 x 152 x 3 m. A fixed five-spot production strategy was adopted. An importantreservoir characteristic is the absence of gas, in other words, the fluids contained in the

reservoir are only oil and water.Considered uncertain attributes were structural model, porosity, horizontal

permeability, vertical permeability, relative permeability and water-oil contact. Theseuncertainties and their respective values and occurrence probabilities are illustrated onTable 1.

Since the structural model is an uncertain attribute, area0 denotes the globalstructural model (20x44x17) and area1 represents another possible model with

15x44x17 (11,220 cells). Excluding structural model and water-oil contact, that have 2levels of uncertainty, all attributes have three levels of uncertainty, a probable or amedium (level 0), an optimistic and another pessimistic.


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If all attributes on Table 1 were combined, the total number of possible reservoir

simulation model would be equal to 324 (22 * 34). The simulation of this high modelnumber is sometimes not feasible. The reduction of the number of simulations is

possible through the sensitivity analysis, whose main purpose is to exclude the attributes

with little influence on a specific function.

Table 1: Uncertain Attributes for the Studied Case

Attribute Level Probability

area0 0.50StructuralModel area1 0.50

por0 0.50por1 = por0 * 1.2 0.25Porosity

por2 = por0 * 0.8 0.25

kx0 0.50

kx1 = kx0 *1.5 0.25HorizontalPermeability

kx2 = kx0 * 0.6 0.25ky0 0.50

ky1 = ky0 * 2.0 0.25VerticalPermeability

ky2 = ky0 * 0.5 0.25

kr0 0.50

kr1 0.25RelativePermeability

kr2 0.25

dwoc0 0.50Water-OilContact dwoc1 0.50

4.2. Sensitivity Analysis

In most cases of derivative tree application, such as in the studied case, criticalattributes are not known at the beginning. In the sensitivity analysis it is necessary to

choose one or more functions and simulation times in order to determinate the criticalattributes. The main functions to be chosen are: Cumulative Oil Production (Np),Cumulative Gas Production (Gp), Cumulative Water Production (Wp), Net Present

Value (NPV), Internal Rate of Return (IRR) and Return over Investment(NPV/Investment).

Three functions, in the studied case, were selected to illustrate the sensitivityanalysis procedure. Two of them are directly related to production, Cumulative OilProduction and Cumulative Water Production and the third one is an economical

function, Net Present Value. On the other hand, only two simulation times werespecified in order to calculate the values of these functions, 3650 days (10 years) and

7300 days (20 years).The number of reservoir simulation models generated in sensitivity analysis is,

in this case, 11, comprising 1 corresponding to base model, 8 models (4 attributes with

2 extra levels each) and 2 models (2 attributes with 1 extra level each). The Figure 4shows the sensitivity analysis results. Figures 4(a) to (f) show that sensitivity analysis

depends on the function (VPL, Np or Wp) and simulation time (10 or 20 years).


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(a) (b)

(c) (d)

(e) (f)

Figure 4: Influence of Function and Time in Sensitivity Analysis

(a),(b) Net Present Value, (c),(d) Cumulative Oleo Production,and (e),(f) Cumulative Water Production.


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The sensitivity analysis by itself is a simplification and two important decisions

can be taken after it: reduction of the number of uncertain attributes and reduction ofnumber of levels of each critical attribute. A very important characteristic of the

automated procedure is the addition, progressively, of critical attributes and/or levels

until there are no more significant modifications in the values for analyzed function. Itis important to emphasize if levels are added or subtracted, the probabilities of each

level must be recalculated based on the characteristic of attribute.

4.3. Critical Attributes and Risk Curve

Once critical attributes are chosen, it is possible to build the derivative tree and

estimate the production risk. The automated methodology is capable of building thederivative tree from the specified critical attributes. The models were simulated in

sensitivity analysis are not simulated anymore. In this way, it is possible to reduce therequired time to simulate all branches of the tree.

In order to illustrate the results obtained from the statistical treatment ofsimulation models that constitute derivative tree, only one function and one time werechosen from Figure 4. Then the sensitivity analysis and risk were made for Net Present

Value (NPV) for 20 years of production, Figure 4(b).The influence of critical attribute number was evaluated considering two groups

of attributes: Group 1 with four attributes, dwoc (level 0 and 1), area (level 0 and 1), por

(level 0, 1 and 2) and kr (level 0 and 1) and Group 2 with five attributes, dwoc, area,por, kr (level 0 and 1) and kz (level 0, 1 and 2). In both groups, kr had one uncertain

level excluded by the sensitivity analysis then its probabilities were recalculated to 50%to Kr0 and 50% to Kr1.

Figure 5 shows the percentiles P10, P50 and P90 considering the two groups of

critical attributes. It is possible to observe that the base case is very close to theoptimistic model (P10). A very small difference between the estimated P10, P50e P90to

four and five critical attributes is shown. The consideration of five critical attributesincreases the simulation number from 18 to 46. It was unnecessary to consider fivecritical attributes, since only four could represent the reservoir uncertainty with almost

the same precision. Therefore, it would be not necessary to add kz as critical attribute,since additional simulations could be avoided.

The uncertainty is quantified by risk curve. The risk curve depends on thenumber of attributes and their values, the number of levels and their associated

probabilities. The comparison between risk curves considering four and five critical

attributes are considered. The estimated Net Present Value for 20 years, considering thedefined critical attributes on Group 1 and 2, is on Figure 6. The risk of Cumulative Oil

Production forecast for 20 years, with the same critical attributes like in NPV, isillustrated on Figure 7. In both figures, Net Present Value and Cumulative OilProduction risk curves are practically coincident and they are in concordance with the

results on Figure 5.The results of the simulated models that constitute the derivative tree can be

plotted as shown in Figures 8 and 9, which represent the typical uncertainty inCumulative Oil Production and Cumulative Water Production, respectively.


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Figure 5: Net Present Value for 20 years 4 and 5 Attributes

Figure 6: Net Present Value Risk Curve

Figure 7: Risk Curve of Cumulative Oil Production

-20

0

20

40

60

80

100

P10

P50

P90

BASE

NPV(MMUS

$)

4 Attributes

5 Attributes

0

10

20

30

40

50

60

70

80

90

100

-25 0 25 50 75 100 125 150

NPV (MM US$)

Cu

mulativeProbability(%)

4 Attributes

5 Attributes

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80

Np (MM m3)

CumulativeProbability(%)

4Attributes

5 Attributes


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Figure 8: Uncertainty in Cumulative Oil Production

Figure 9: Uncertainty in Cumulative Water Production.

4.4. Discussion

The most common simplification in the automated risk analysis process is thesensitivity analysis, which is directly related to the critical attribute number and their

levels.In addition to the sensibility analysis, other simplifications can be performed in

order to decrease the computational effort. Examples of these simplifications can beseen in Ligero and Schiozer (2001) who used upscalled grid with a fewer number of

0

10000000

20000000

30000000

40000000

50000000

60000000

70000000

80000000

0 730 1460 2190 2920 3650 4380 5110 5840 6570 7300

Time (days)

Np(m3)

Structural Model 1 (area0)


0

10000000

20000000

30000000

40000000

50000000

60000000

70000000

80000000

90000000

0 730 1460 2190 2920 3650 4380 5110 5840 6570 7300

Time (days)

Wp(m3)




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blocks and in Costa and Schiozer (2002) who considered fewer levels of uncertainties

for attributes that were considered not critical and aggregated several attributes in thesensitivity analysis.

Other typical and usual simplifications are the use of production strategies as

function only of the structural models, aggregation of variables, etc. In such cases,representative models (Steagall and Schozer, 2001) can also be very useful in the

integration of geological and economical uncertainties.Representative models for the studied case are shown in Figure 10, which

presents the relationships between Net Present Value and Recovery Factor of Oil of themodels with uncertainties. Representative P10, P50and P90models are indicated throughcircles. It is possible to observe two groups of models, each group representing different

values of dwoc. The distribution of points of this example if different of all otherexamples tested here because of the low number of simulations and high sensitivity of

the water-oil contactThese representative models can be used for several applications, for instance, to

perform an economic sensitivity analysis. It is not necessary to use all simulationmodels to make this analysis. In addition, changing only economic models do notrequire extra simulations, since reservoir parameters do not depend on economic

factors. The NPV variation caused by changing oil price is on Table 2.Santos and Schiozer (2003) have shown that different production strategies can

be incorporated in the procedure in an automated way. Schiozer, Maschio and Ligero

(2003) and Christie et al. (2002) used streamline simulation to reduce the computationaltime of each simulation run performed for the prediction the uncertainties in petroleum

reservoirs.Many other simplifications are possible but the procedures will not be used if

they are not automated because of the excessive amount of work involved.

Figure 10: Representative Models P10, P50and P90of NPV

-20000000

0

20000000

40000000

60000000

80000000

100000000

120000000

10 15 20 25 30 35 40 45 50

Recovery Factor of Oil (%)

N

PV(

US$)



dwoc0

dwoc1

P10

P50

P90


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Table 2: Economical Sensitivity Analysis Representative Models

NPV (MM US$)Representative

Models Oil Price(Base)

Oil Price(Optimistic)

Oil Price(Pessimistic)

1 86 164 9

2 84 160 8P10

4 77 143 11

P50 5 27 71 -18

6 -0.6 40 -41

7 -3 29 -35

8 -6 32 -44P90

9 -11 17 -40

5. CONCLUSIONS

In the 80s, production forecast used to be performed deterministically.Nowadays, the use of a suitable methodology, such as derivative tree, associated with

numerical simulation flow, allows probabilistic predictions.The presented automated methodology to quantify exploration and production

risk can be easily applied to most type of petroleum reservoir, from simple to complex

models. It has the advantage to store simulation results, avoiding unnecessarysimulation runs. In addition, parallel computing speedup the process, which may be fast

until to complex reservoirs.In order to simplify the process, sensitivity analysis must be performed, which

reduces the number and/or level of uncertain attributes. So the derivative tree is built,only, with critical attributes, reducing the model number and the global process time.

Normally, the ideal number of critical attributes varies from 4 to 7, and they are

included in the tree one by one. The process is interrupted when the required precisionis reached. If critical attributes are more than 7, other simplifications are necessary toreduce the computational time and computational effort.

Automated process permits to determinate representative models, allowingoptimizing reservoir development plan for probable, optimistic and pessimist models

with different geological characteristics.

6. REREFENCES

Christie, M., Subbey, S., Sambridge, M., Thiele, M., 2002. Quantifying Prediction

Uncertainty in Reservoir Modelling Using Streamline Simulation, 15th ASCEEngineering Mechanics Conference, June, New York, USA

Christie, M.A. and Blunt, M.J., 2001, Tenth SPE Comparative Solution Project: AComparison of Upscaling Techniques, SPE Reservoir Simulation Symposium,

February, Texas, USA, SPE 66599

Costa, A.P.A. and Schiozer, D.J., 2002, Escolha de Atributos na Anlise de Risco em

Campos de Petrleo na Fase de Desenvolvimento, 9th Brazilian Congress ofThermal Engineering and Sciences (ENCIT), October, Caxambu, Brasil.


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Ligero, E.L. and Schiozer, D.J., 2001, Importncia da Escala do Modelo de Simulaode Reservatrios de Petrleo na Anlise de Incertezas em Projetos de Explorao e

Produo, I Congresso Brasileiro de P&D em Petrleo e Gs, November, Natal,

Brasil.

Loschiavo, R., Steagal D., and Schiozer D.J., 2000. Estudo do Impacto de Incertezasno Desempenho de Reservatrios de Petrleo, 8th Brazilian Congress of Thermal

Engineering and Sciences (ENCIT), Porto Alegre, Brasil.

Santos, J.A.M., Schiozer, D.J., 2003, Quantifying Production Strategy Impact in Risk

Analysis of an E&P Project Using Reservoir Simulation, 17th Reservoir SimulationSymposium, February, Houston, USA (to be published).

Schiozer, D.J., Maschio, C., Ligero, E.L. 2003, Quantifying the Impact of Grid size,

Upscaling and Streamline Simulation in the Risk Analysis Applied to Petroleum FieldDevelopment, 17th Reservoir Simulation Symposium, February, Houston, USA (tobe published).

Schiozer, D.J., Ligero, E.L., Costa, A. P.A., Santos, J.A.M, 2002. Risk Assessment forReservoir Development under Uncertainty, Journal of Petroleum Science and

Engineering(to be published).

Steagall, D.E. and Schiozer, D.J., 2001. Uncertainty Analysis in Reservoir ProductionForecast during the Appraisal and Pilot Production Phases, SPE Reservoir SimulationSymposium, February, Dallas, USA, SPE 66399.

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Risk Analysis Applied to Field Developments