© D.J. Schiozer et al., published by IFP Energies nouvelles, 2019

Nomenclature

AC: Abandonment Costs

B: Benchmark return

BHP: Bottom-Hole Pressure

CAPEX: Investments in equipment and facilities

CLRM: Closed-Loop Reservoir Management

CLFDM: Closed-Loop Field Development and Management

E: Expectation operator

Ei: Specialized production strategy optimized for RMi

EMR: Robust production strategy

EMV: Expected Monetary Value

EVoF: Expected Value of Flexibility

EVoI: Expected Value of Information

G_p : Cumulative gas production

NCF: Net Cash Flow

N_p : Cumulative oil production

NPV: Net Present Value

NQDS: Normalized Quadratic Deviation with Signal

OPEX: Operational Expenditure

ORF: Oil Recovery Factor

Q_g : Gas rate

Q_o : Oil rate

Q_w : Water rate

Q_wi : Water injection rate

R: Gross revenue

RM: Representative Model

S_B− : Lower semi-deviation from B

S_B+ : Upper semi-deviation from B

${\mathrm{S}}_{\mathrm{B}-}^2$ : Lower semi-variance from B

${\mathrm{S}}_{\mathrm{B}+}^2$ : Upper semi-variance from B

Roy: Amount paid in royalties

ST: Amount paid in social taxes

T : Corporate tax rate

W _i : Cumulative water injection

W _p : Cumulative water production

ε(NPV): Economic value of the production strategy adjusted to the decision maker’s attitude

τ _dr : Tolerance level to downside risk

τ _up : Tolerance level to upside potential

Subscript

wi: With information

woi: Without information

1 Introduction

Field development and management decisions involve risks due to several uncertainties, mainly (1) reservoir, associated with recoverable reserves and flow characteristics, (2) operational, related to production system availability, and (3) economic, such as oil price, capital expenditures, and operational expenditures. These uncertainties typically coexist because data is usually acquired indirectly and sparsely, and because developing a petroleum field is a long-term, capital-intensive project. Their combined effects must be assessed to estimate the risks involved in decisions.

Today, due to the challenges of new oil and gas discoveries, decision makers recognize the shortcomings of simplistic uncertainty assessments and the importance of integrated model-based decision analysis. In particular, current research focuses on improving the decision-making process in field development and management, making use of new information that arrives as new development wells are drilled and production begins. In this context, the Closed-Loop Reservoir Management (CLRM) was proposed (Chen et al., 2009; Jansen et al., 2005, 2009; Nævdal et al., 2006; Wang et al., 2009), which consists of a continuous update of the geological model accompanied by a continuous optimization of well-control for existing and future wells. Based on this concept, the Closed-Loop Field Development (CLFD) was generalized (Shirangi and Durlofsky, 2015) to include the continuous optimization of decision variables related to the production strategy configuration (e.g., type and position of future wells). This study is based on the CLFD concept.

However, many factors make this a complex, time-consuming process to model, namely (1) the coexistence of multiple endogenous and exogenous uncertainties, (2) the large search spaces, and that (3) flow simulation is time-consuming in itself. In addition, this is a multidisciplinary problem, integrating reservoir engineering, production engineering, economic evaluation, and statistical analyses. Thus, simplifications are often required in analyses that perform a high number of evaluations, such as uncertainty quantification, optimization procedures, and decision risk analysis. However, these simplifications may yield inaccurate results and so must be selected carefully.

Proxy models, which are used to bypass the flow simulator, are a common simplification in uncertainty quantification, history matching, and probabilistic forecasting (Douarche et al., 2014; Feraille, 2013; Feraille and Marrel, 2012; Imrie and Macrae, 2016; Osterloh, 2008; Panjalizadeh et al., 2014; Scheidt et al., 2007; Touzani and Busby, 2014). However, multiple factors affect prediction accuracy of the proxy, which is not physics-based: (1) the high nonlinearity between input variables (reservoir, operational, and economic uncertainties) and output variables (production, injection, and economic forecasts) complicates proxy modeling, and (2) assumptions and approximations when modeling the proxy may introduce non-negligible errors (Trehan et al., 2017).

Lower-fidelity models, another class of approximations, have also been applied in history matching (Lodoen and Omre, 2008; Subbey et al., 2004) and production strategy optimization (Aliyev and Durlofsky, 2015; Wilson and Durlofsky, 2013). Lower-fidelity models entail many simplifications to increase computational efficiency while respecting the physical processes governing the reservoir. In this approach, high-fidelity models are upscaled through numerical homogenization procedures, prior to flow simulation. This simplification is attractive because upscaling is relatively straightforward to implement (Trehan et al., 2017). However, its use is not straightforward because upscaling errors arise from neglecting subgrid heterogeneity effects (Durlofsky, 1997, 1998; Preux, 2016; Zabalza-Mezghani et al., 2004).

Computational efficiency can also be achieved through efficient sampling. The Monte Carlo method is often used in the petroleum industry. However, as the sampling is purely random, a very high number of samples is necessary to ensure reliable results (Mishra, 1998), frequently at unfeasible levels (Risso et al., 2011). This study uses a simplified statistical technique developed in a related work (Schiozer et al., 2017), the Discretized Latin Hypercube with Geostatistical realizations (DLHG). By incorporating the desirable features of random sampling and stratified sampling, the DLHG ensures minimum computational costs without requiring proxy models. We tested this technique in several examples, achieving a good balance of precision and computational time. This sampling technique was applied to uncertainty quantification (Schiozer et al., 2017), history matching (Maschio and Schiozer, 2016), and production strategy optimization (von Hohendorff Filho et al., 2016).

This study also increases the computational efficiency of the CLFD process by using representative models of the uncertain system. Techniques to select representative models were the focus of recent research (Jiang et al., 2016; Meira et al., 2016, 2017; Shirangi and Durlofsky, 2016). This work applies a method developed in related research (Meira et al., 2016, 2017) to reduce the number of scenarios for production strategy selection and optimization. The method combines a mathematical function that captures the representativeness of a set of models with a metaheuristic optimization algorithm, to ensure full representation of the variability of system inputs (uncertain attributes) and outputs (production and economic forecasts). Additional advantages include low computational cost and simplicity for day-to-day decision making because the method is software based. Production strategy optimization is computationally consuming because of the high number of evaluations required. This is particularly challenging for the Robust Optimization (van Essen et al., 2009; Yang et al., 2011; Yasari and Pishvaie, 2015), where multiple scenarios are evaluated simultaneously.

For the methodology to deliver reliable results, some conditions must be guaranteed:

• The performance of a high-fidelity model must be preserved using an accurate simulation model because of the complex integration between the production strategy and the system performance (production, injection, and economic forecasts) (Botechia et al., 2018a).

• The reservoir simulation model must honor all dynamic data and be fast enough to allow analyses of multiple scenarios.

• The statistical analysis must be carefully performed to ensure adequate uncertainty representation while avoiding a high number of evaluations (which is very time consuming).

• The procedure for production strategy selection must reflect the effects of both the uncertain models and the production strategy because both highly influence the performance of the project and, consequently, the risk evaluation.

• Production and economic evaluations must be integrated because both of them impact decisions.

This work presents a methodology that resulted from several case studies and was first outlined in Schiozer et al. (2015). The method comprises the key steps of decision analysis to ensure good decisions. We integrate key steps of reservoir characterization, data assimilation, and production optimization providing a core basis for specialized methodologies, as we demonstrate in the results section.

2 Objectives

Despite the growing concern for in-depth, model-based decision making, we observed that many solutions, presented in the literature and used in some companies, still entail many simplifications, which can be critical in complex cases. This is because industry professionals value fast, easy-to-apply techniques because of limited time and highly complex decisions.

The objective of this work is to improve the decision-making process in petroleum field development and management. We present a model-based methodology integrating reservoir simulation, risk analysis, history matching, uncertainty reduction, representative models, and production strategy selection under uncertainty.

This method aims to ensure good decisions while being practical for application in complex reservoirs and at different stages of the field lifetime, both before and after reservoir development. Specific objectives of this study include: (1) practical for day-to-day decisions and based on reliable production forecasts from numerical reservoir simulation, (2) probabilistic-based decision-making based on an adequate representation of uncertainty, and (3) quantitative and objective decision-making based on indicators and automated procedures.

The methodology was applied to UNISIM-I-D, a benchmark case based on the Namorado field in the Campos Basin, Brazil.

3 Methodology

The proposed method is based on the concept of Closed-Loop Field Development and Management, as an extension of the Closed-Loop Reservoir Management by Jansen et al. (2009) (Fig. 1). The main components of the process are divided into colors:

• Green: gathering of all data and uncertainties and model construction; multiple simulation models are used in the process so model fidelity (low, medium or high) is adapted to balance quality of the results and computational time.

• Blue: model-based, long-term decisions under uncertainties; the best alternative is implemented in the field (with operational noise due to delays, fails, etc.) generating measured dynamic data (production, pressure, 4D seismic, etc.).

• Red: data assimilation; all dynamic data must be within a tolerance range to select models that will be used in the blue part; data assimilation may directly change the simulation models or the high fidelity geologic models (big loop).

• Black: (1) implementation of long-term decisions (normally model-based) and short-term decisions (normally data-driven), (2) definition of study objective, and (3) selection of the type of study (past – data assimilation; or future – decision analysis).

The twelve steps of the methodology are described below:

3.1 Green steps

1. Reservoir characterization under uncertainties (to build models, develop scenarios, and estimate probabilities) (Correia et al., 2015, 2018a, 2018b; Mahjour et al., 2019). This crucial step requires a multidisciplinary approach to consider all possible uncertainties: reservoir, fluid, economic, and operational attributes.

2. Build and calibrate the simulation model: accurate risk quantification requires reliable responses; therefore, the simulation model must be calibrated to have a fast and yet robust response to avoid biased evaluations (Avansi et al., 2019). Decision makers define the degree of model precision according to the objective. We believe that a high-fidelity model should be preferred over low-fidelity or proxy models because of the high nonlinearity between the reservoir model and the production strategy performance. The calibration is normally done with a Base Case (in this work, called Base0).

3.2 Red steps

3. Verify inconsistencies in the Base Case and dynamic well data (fluid rates and BHP measurements) to be used in the data assimilation procedures. This step is often simplified or skipped but it is crucial as it can identify inconsistencies in the simulation model and the real data.

4. Generate scenarios considering reservoir uncertainties. In this work, a scenario is a particular combination of all possible uncertainties. Several sampling techniques are available in the literature, but we recommend the efficient DLHG (Schiozer et al., 2017).

5. Data assimilation: history match and reduce the number of scenarios with dynamic and seismic data. Several techniques are available (Avansi and Schiozer, 2015a; Bertolini et al., 2015; Costa et al., 2018; Davolio and Schiozer, 2018; Maschio and Schiozer, 2008, 2015, 2016; Oliveira et al., 2018) depending on the complexity of the case and the available data. From the accepted models, a Base Case is selected for the following steps (Base1). The usual recommendation is to use a model close to P50 in all indicators to optimize the initial production strategy, representing an intermediate case. A new Base Case must be selected only when Base0 fails to honor the dynamic data or is too optimistic or pessimistic.

3.3 Blue steps

6. Selection of a deterministic production strategy for the Base Case. As the production strategy selection strongly affects the risk quantification, an iterative technique is best to select the production strategy. The first production strategy is selected using an optimization procedure (Gaspar et al., 2014, 2016a; Ravagnani et al., 2011; von Hohendorff Filho et al., 2016).

7. Initial risk estimate of the first production strategy with all possible scenarios (from Step 5). This risk curve is often used in projects. Here, we propose additional analyses (Steps 8–12) to further improve decisions and reduce risk, showing that the final risk curve can be very different.

8. Selection of Representative Models (RMs) (Costa et al., 2008; Meira et al., 2016, 2017; Schiozer et al., 2004) based on multiple system inputs (probability distribution and range of uncertain attributes) and outputs (production, injection, and economic forecasts).

9. Selection of a specialized production strategy for each RM, as in Step 6, to provide different solutions for field development.

10. Production strategy selection under uncertainty including reservoir, economic, and other uncertainties. A Robust Optimization procedure (Silva et al., 2016) can be used, or a risk-return analysis (Santos et al., 2017a) to select the best strategy from the candidates obtained in Step 9. If the simulation runtime for the number of scenarios is unfeasible, the RMs can be used to represent them.

11. Identification of potential changes in the production strategy (obtained in Step 10) to manage uncertainty and improve the chance of success based on the value of information (Botechia et al., 2018b; Santos et al., 2017b) and value of flexibility analyses (Santos et al., 2018a; Silva et al., 2017), and integration with production facilities (von Hohendorff Filho and Schiozer, 2017, 2018). If the simulation runtime for the number of scenarios is unfeasible, the RMs can be used to represent them.

3.4 Black step

12. The black step is dedicated to the decision analysis. Technical and economic indicators support long-term, model-based decisions as well as short-term, data-driven decisions. The objective guides the process: model quality, need for further data assimilation (history matching), objective function selection, etc.

The literature provides several methods for each specific step of the comprehensive 12 steps of this study. We referenced methods for specific steps that we have conducted in related works. The discussion section explores the focus of our current research to address existing challenges.

4 Application

The 12-step methodology was applied to a benchmark case study based on the Namorado field in the Campos Basin, Brazil. A synthetic reservoir, UNISIM-I-R (Avansi and Schiozer, 2015b), was built to provide a reference model that represents the true reservoir. The uncertain simulation model UNISIM-I-D (Gaspar et al., 2015) is in the initial stages of field development and has four years of production data for four production wells (NA1A, NA2, NA3D, RJS19). The reservoir model is discretized into a corner point grid with 81 × 58 × 20 cells measuring 100 × 100 × 8 m with a total of 36 739 active cells.

We reference results from related studies in the results section. Note that our focus is not to compare the efficacy of each method, but to demonstrate that the 12-step decision-structure allows the development of different approaches.

5 Results

5.1 Step 1

The uncertainties of the model include:

• Reservoir attributes: geostatistical realizations of facies, porosity, net-to-gross ratio, and permeability; structural model (BL), water relative permeability (K _rw), fluid properties in the East block (PVT), depth of Water-Oil Contact in the East block (WOC), Rock Compressibility (CPOR), and vertical permeability multiplier (K _z) (Tab. 1).

• Economic attributes: oil price, operational expenditures, and capital expenditures (Tab. 2).

• Operational attributes: System Availability (SA) and Well Index Multiplier (dWI) (Tab. 3).

Details of the simulation model, economic model, and uncertainties can be found in Avansi and Schiozer (2015b) and in Gaspar et al. (2015), while open source files can be accessed at http://www.unisim.cepetro.unicamp.br/unisim-i.

5.2 Steps 2 and 3

Step 2 guarantees that the simulation model adequately represents the reservoir and is fast enough to be included in a methodology that demands thousands of simulation runs. In our case, the simulation runtime was around 7 min running in parallel while using four processors in a cluster. Although our methodology is applicable to cases with very high runtimes (hours), simplifications may be necessary depending on the time available and scope of the project.

Step 3 ensures compatibility of the initial response of the Base Case (Base0) (material balance, pressure, and initial production) with the existing data. Note that the Base0 case corresponds to the most likely value of each uncertain attribute.

5.3 Step 4

In Step 4, scenarios were generated to start the probabilistic process using the DLHG (Schiozer et al., 2017), which applies the efficient Latin Hypercube Sampling (LHS) and integrates all types of uncertainties in the sampling step, i.e., continuous attributes are discretized, and then combined with discrete attributes and geostatistical realizations. In LHS, the range of each variable (x _j ) is divided into n disjoint intervals of equal probability, then one value is selected at random from each interval. The n values obtained for x ₁ are randomly paired, not replaced, with the n values obtained for x ₂. This process is continued until a set of n nX-tuples is formed (Helton and Davis, 2003).

Each attribute is treated according to (1) sampling number, (2) number of discrete levels, and (3) probability of each discrete level. The sampling number, which is equal to the number of flow simulation runs, is set at the beginning of the process based on (1) simulation runtime, (2) importance of the study (i.e., the required precision), and (3) available work time (Schiozer et al., 2017). Note that all sampled scenarios are simulated using the flow simulator while no proxy models are used for production forecasts.

Santos et al. (2018b) showed that independence between the precision of the DLHG and the number of samples is achieved with a few samples (from 50 samples for UNISIM-I-D). Due to the short simulation runtime and the available computational resources, we used more samples to create smoother risk curves. Figure 2 shows risk curves for sampling numbers 500 and 100. It is possible to notice that the Base Case is no longer close to P50 in the risk curve.

5.4 Step 5

In Step 5, we applied a filtering technique to select the subset of scenarios (from the full set of sampled scenarios) that matched the four years of production data. We used the Normalized Quadratic Deviation with Signal (NQDS) (Avansi and Schiozer, 2015a; Bertolini et al., 2015) as the matching indicator, which is normalized for each well and each objective function (Q _o, Q _w, Q _g, and BHP). We considered NQDS values between −1 and +1 an acceptable misfit. Figure 3 shows the 214, out of the 500 initial scenarios, selected (with all objective functions within the tolerance range). Figure 4 shows water production curves for the four wells as an example.

As the Base Case, Base0, did not match the production data, we selected a new Base Case (Base1) as an intermediate case from the set of filtered models, using an initial production strategy (E0) (Fig. 5). Note that this initial strategy does not represent the final decision for field development and it is only used to select the Base1 case.

5.5 Step 6

The first important consideration is how to integrate production facilities with the field production forecast and modeling. Generally, when production facilities impose strong restrictions, integrated modeling is used in all of the blue steps. In other cases, and in this application, integrated modeling is used to establish approximate well boundary conditions in Step 6 and to confirm these conditions in Step 11.

We optimized deterministically a production strategy for Base1, considering design (G1) and operation (G2) variables. The G1 variables were: number, type (vertical or horizontal), placement, and opening-schedule of wells, and platform capacity constraints (liquid, oil and water production, and water injection). The G2 variables were constraints of maximum water-cut, maximum liquid production for producers, and water injection for injectors.

The optimization procedure was divided into phases: (1) number and type of wells, and platform capacity, (2) well placement and fine-tuning the platform capacity constraints, (3) well-opening schedule, (4) well operating and monitoring constraints, and (5) fine-tuning.

We performed phases 1, 2, and 4 on commercial software CMOST (CMG^©), which uses the optimizer method Designed Exploration Controlled Evolution (DECE) (Yang et al., 2007). We used the black-oil numerical reservoir simulator IMEX (CMG^©).

The objective function for optimization is the Net Present Value (NPV) (Fig. 6) and is calculated using the most likely economic scenario (Tab. 3) and a simplified net cash flow formula based on the Brazilian Royalty & Taxes fiscal regime (eq. (1)).$$\mathrm{NCF}=\left[\left(R-\mathrm{Roy}-\mathrm{ST}-\mathrm{OPEX}\right)\times \left(1-T\right)\right]-\mathrm{CAPEX}-\mathrm{AC},$$(1)where NCF is the net cash flow, R is the gross revenue, Roy is the amount paid in royalties, ST is the amount paid in social taxes, OPEX is the operational expenditure, T is the corporate tax rate, CAPEX is the investment in equipment and facilities, and AC are the abandonment costs.

The production strategy for Base1 is called E1 and consists of:

• Number and type of wells: 10 horizontal producers, two vertical producers (existing wells NA1A and NA3D), six horizontal water injectors, in a total of 18 conventional wells.

• Platform capacity constraints: 16 275 m³/day (liquid and oil production), 9068 m³/day (water production), and 23 328 m³/day (water injection).

At the end of the prediction period (10 957 days), E1 recorded: NPV of USD 2236 million, N _p of 65 million m³, W _p of 50 million m³, G _p of 6892 million m³, W _i of 138 million m³, and Oil Recovery Factor (ORF) of 56%. Figure 7 compares the map of total oil per unit area at the beginning and end of the prediction period, showing the well placement of E1.

5.6 Step 7

We conducted a first risk estimate using production strategy E1 and the 214 possible scenarios from Step 5 (Fig. 8). Risk curves are also referred to as descending or complementary cumulative distribution functions in the statistics literature, and we constructed them with the production forecasts of multiple scenarios from numerical reservoir simulation.

One interesting point to highlight here, which is normally neglected in many analyses, is the relationship between the uncertainties and the production strategy. Base1, the intermediate case for E0 (Fig. 5), became an optimistic case for E1 (Fig. 8). We observed this behavior in other cases. Once a strategy is optimized for a particular model, it becomes more optimistic considering the optimized output parameters (NPV for instance).

Note that these risk curves do not reflect the final risk assessment for this project, but provide input for Step 8.

5.7 Step 8

We applied the proposal by Meira et al. (2016) to select nine RMs from the 214 matched models using multiple risk curves and cross-plots for four objective functions: NPV, N _p, W _p, and ORF (examples in Figs. 9 and 10). Geostatistical realizations are particularly difficult to handle, and from the set of 214, we used only nine.

The proposal by Meira et al. (2016) ensures that the set of RMs represents both the probability distribution of the input variables (uncertain attributes), ensuring that not only attributes but also uncertain levels are represented, and the variability of the main output variables (production, injection, and economic forecasts). In addition, this method is applied using RMFinder software, improving ease-of-use.

As we already had production strategy E1, we took Base1 as one of the RMs (Base1 = RM1), saving time and computational costs.

5.8 Step 9

Because production strategy E1 was optimized specifically for Base1, we analyzed other possibilities for field development using the RMs obtained in Step 8. This follows the rationale that, if the set of RMs represents the uncertain system, their respective production strategies provide different field development possibilities, including number and placement of wells and platform processing capacities.

We repeated the optimization procedure (described in Step 6) for each RM, obtaining a set of specialized strategies: E2, E3, …, E9 (Tab. 4), where Ei is the strategy optimized for RMi.

A key uncertainty affecting production strategy selection is the structural model (Fig. 11). The presence of hydrocarbons in the, still undrilled, East block is uncertain because the connectivity of the fault separating the West and the East blocks is unknown. Of the set of representative models, RM3, RM6, and RM7 do not have hydrocarbons in the East block and their respective production strategies (E3, E6, E7) are solutions for such scenarios.

5.9 Step 10

In Step 10, we select the production strategy that performs best under uncertainty, before considering further actions to manage this uncertainty (addressed in Step 11).

A production strategy is said to be robust when is insensitive to uncertainty and ensures good performance across multiple scenarios without requiring system modifications after production has started (de Neufville, 2004). However, note that the definition of robustness also depends on the company and can be associated with NPV or oil production. For a robust project related to NPV, lower investments can help avoid negative or lower NPV values for pessimistic scenarios. For a robust project related to oil production, higher investments can be made to increase rates in optimistic scenarios, for instance.

In Step 9, we obtained a set of specialized production strategies. One possible approach for Step 10 is to select the strategy that performs best under uncertainty. The Robust Optimization, an automated optimization problem formulated under uncertainty, is another approach that has become increasingly preferred by practitioners. Alternatively, a robust strategy can be obtained by manually refining the best specialized strategy, improving the performance under uncertainty (to be addressed in Step 11).

Following the concept of Robust Optimization, Silva et al. (2016) obtained the robust production strategy for UNISIM-I-D, called EMR, optimized for nine RMs and three economic scenarios, simultaneously. Thus, the key difference between the optimization procedure is that Step 6 simulates each strategy configuration for one reservoir scenario (resulting in one NPV), while Silva et al. (2016) simulate strategy configuration for many scenarios (resulting in one Expected Monetary Value [EMV]).

The robust EMR consists of:

• Number and type of wells: 15 producers and nine water injectors.

• Platform capacity constraints: 20 150 m³/day (liquid and oil production), 13 950 m³/day (water production), and 29 295 m³/day (water injection).

The literature provides several techniques for risk-return analyses to select one of a set of alternatives. Santos et al. (2017a) followed on from the classic mean-variance model and proposed a mean-semivariance framework based on the premise that variance reflects only the overall uncertainty in returns, and not necessarily the risk of a project. The risk (referred to here as downside risk) is the chance of failure to achieve a targeted or benchmark return (B). Thus, variability above this target is not perceived as risk, but as potentially exploitable optimistic scenarios (referred to here as upside potential) (Fig. 12).

Santos et al. (2017a) combined the expected monetary value, downside risk, and upside potential (eq. (2)) to determine the economic value of a production strategy adjusted to the decision maker’s attitude, ε(NPV), while maintaining the same units and dimension as the NPV:$$\epsilon \left(\mathrm{NPV}\right)=\mathrm{EMV}-\frac{{\mathrm{S}}_{\mathrm{B}-}^2}{{\tau }_{\mathrm{dr}}}+\frac{{\mathrm{S}}_{\mathrm{B}+}^2}{{\tau }_{\mathrm{up}}},$$(2)where ε(NPV) is the economic value of the production strategy adjusted to the decision maker’s attitude (in USD); EMV is the expected monetary value, given by the sum of the NPV of each scenario weighted by its probability (in USD); ${\mathrm{S}}_{\mathrm{B}-}^2$ and ${\mathrm{S}}_{\mathrm{B}-}^2$ are the lower and upper semi-variance from benchmark B, respectively (in square USD); τ _dr and τ _up are the tolerance (or indifference) levels to downside risk and upside potential, respectively (in USD). Note that decisions based on EMV are a particular case of equation (2), where decision makers are neutral to downside risk and upside potential (i.e., τ _dr = τ _up → ∞).

Equation (2) uses lower semi-deviation from benchmark return B (eq. (3)) to quantify downside risk, and upper semi-deviation from B (eq. (4)) to quantify upside potential:$${\mathrm{S}}_{\mathrm{B}-}=\sqrt{{\mathrm{S}}_{\mathrm{B}-}^2}= \sqrt{\mathrm{E}\left\{\min {\left[\left(\mathrm{NPV}-\mathrm{B}\right),0\right]}^2\right\}},$$(3) $${\mathrm{S}}_{\mathrm{B}+}=\sqrt{{\mathrm{S}}_{\mathrm{B}+}^2}= \sqrt{\mathrm{E}\left\{\max {\left[\left(\mathrm{NPV}-\mathrm{B}\right),0\right]}^2\right\}},$$(4)where S_B− is the lower semi-deviation from benchmark B; ${\mathrm{S}}_{\mathrm{B}-}^2$ is the lower semi-variance from B; S_B+ is the upper semi-deviation from B; ${\mathrm{S}}_{\mathrm{B}+}^2$ is the upper semi-variance from B; E is the expectation operator; and NPV is the net present value.

The benchmark (B) is defined by the decision maker as it depends solely on his/her definition of loss and gain. However, note that all production strategies must use the same benchmark for impartiality. Here, we set the benchmark as the EMV of production strategy E1, optimized for the Base Case, and defined τ _dr and τ _up as a function of this value. For this synthetic case study, we considered a fictitious decision maker averse to downside risk and willing to exploit the upside potential (τ _dr = τ _up = 0.4 × B ≈ USD 700 million).

In Table 5 and Figure 13, we evaluate and compare the nine production strategies (E1–E9) and the robust strategy (EMR), with and without economic uncertainty. EMR is the best production strategy under uncertainty. From the set of nine alone, E9 is the best. Production strategies E3, E6, and E7, optimized for RMs without hydrocarbons in the East block, are the least attractive alternatives considering the 214 scenarios simultaneously.

5.10 Step 11

Step 11 consists of detailed analyses of the best strategy obtained in Step 10.

5.10.1 Managing uncertainty

The best strategy can be improved to better manage uncertainty, considering the company’s risk attitude. The most common actions are (1) acquiring information, to reduce reservoir uncertainty, (2) adding flexibility to the system, to allow system modifications as uncertainty unfolds over time, and (3) increasing robustness (an automated procedure was addressed in Step 10, here we discuss a manual procedure). Despite reducing risks and increasing the EMV, these approaches incur investment and costs and may delay production. Therefore, before making a decision, their benefits should be quantified using the Expected Value of Information (EVoI) and Expected Value of Flexibility (EVoF).

The petroleum literature provides many methods to estimate the EVoI and the EVoF. In related works (Santos et al., 2017b; Santos et al., 2018a), we showed how these can become fully automated procedures when integrated into the 12-step decision structure, as exemplified in Figure 14 for EVoI.

The automated EVoI and EVoF analyses use the following as input: (1) the set of uncertain scenarios that match production data (obtained in Step 5), (2) the set of specialized production strategies, optimized individually for each RM (obtained in Step 9), and (3) the robust production strategy, optimized probabilistically for all RMs simultaneously (obtained in Step 10).

The use of a robust production strategy is optional for EVoI, where we aim to learn the most-likely reservoir scenario so that we can implement a specialized production strategy. However, considering a robust production strategy is important for cases with high uncertainty, where a single source of information may be insufficient to reduce all uncertainties. In such cases, the use of a robust production strategy in the EVoF study is highly recommended to define the rigid attributes of the production strategy.

As the set of RMs represents the uncertain system, their respective strategies quantify the possibilities to develop the field, namely number and placement of wells, platform size, and fluid processing capacities. Thus, these strategies are indicators for the degree and type of flexibility required by the system. The flexible strategy is defined in an iterative procedure that combines features of the robust strategy (e.g., well placement) and flexible features from the differences between specialized strategies (e.g., available slots for connection of additional wells).

5.10.1.1 Determining the EVoI of an appraisal well

We considered drilling an appraisal well to gather information on the presence or absence of hydrocarbons in the East block (BL) and the Water-Oil Contact (WOC), simultaneously. We estimated EVoI for perfect information (100% reliable when interpreting BL and WOC) and imperfect information (95% reliable when interpreting BL, and 80% for WOC). Without further information, EMR is chosen (Tab. 5).

We determined the value of the project with information using equation (2) with the EMV of E1 as the benchmark, the same used in the case without information. We considered three economic scenarios.

Using equation (2) for project evaluation, EVoI is given by equation (5), where ε(NPV)_wi is the value of the project with information and ε(NPV)_woi is the value of the project without information. Because of the non-linearity of ε, the cost of information must be deduced to the NPV values stored in the database before estimating ε(NPV)_wi: $${\mathrm{EVoI}}_{\epsilon }={\epsilon \left(\mathrm{NPV}\right)}_{\mathrm{wi}}-{\epsilon \left(\mathrm{NPV}\right)}_{\mathrm{woi}}.$$(5)

We also calculate the EVoI as the expected increase in EMV (eq. (6)), which is a particular case of equation (5), where decision makers are neutral to downside risk and upside potential (τ _dr = τ _up → ∞):$${\mathrm{EVoI}}_{\mathrm{EMV}}={\mathrm{EMV}}_{ \mathrm{wi}}-{\mathrm{EMV}}_{\mathrm{woi}}.$$(6)

We determined the EVoI using the pre-existing set of 214 scenarios matching production data, with updated probabilities using Bayes Theorem. That is, the 214 equiprobable scenarios are used to estimate ε(NPV)_woi and the 214 scenarios with updated probabilities for BL and WOC are used to estimate ε(NPV)_wi.

In this application, we assumed that information could be acquired without delaying the development plan and that the appraisal well would be used for field development. Thus, the cost of this well is already included in the NPV values of most production strategies (E1, E2, E4, E5, E8, E9, those with wells planed for the East block). Aiming for a first assessment, we used the NPV values directly in the automated procedure, meaning that we only update the probability of occurrence of each scenario. This first approximate is not the true EVoI but provides an initial diagnosis. If it reveals that the information source has potential, a more precise EVoI calculation should be performed.

Table 6 shows EVoI calculated with equations (5) and (6). Note that equation (5) improved the EVoI estimate by accounting for all changes in the risk curve, not only the increased EMV but also the decreased downside risk and increased upside potential. Thus, equation (6) underestimated the EVoI.

Table 7 shows the best production strategy for each information outcome. We observed that the robust strategy EMR is the best decision for many information outcomes, meaning that strong uncertainty remains after information acquisition (other attributes besides BL and WOC). This conclusion is only possible because we used the 214 scenarios to determine the EVoI, meaning that we accounted for the effects of all mapped uncertainties, and not only BL and WOC.

5.10.1.2 Refining the best strategy for further improvements

For complex problems with a large search space, automatic procedures often yield local maxima. As Step 11 is manual, local minima can be avoided. We can check for misconceptions from previous automated steps, as shown by Santos et al. (2017c). The authors used several indicators to assess the performance of E9 over the 214 scenarios, aiming to increase its robustness. The remaining strategies E1 through E8 served as boundaries for the different variables, such as platform size and number of wells. Ultimately, the authors observed that many of the horizontal producers had been placed in a suboptimal layer of the reservoir, further improving the automated optimization procedure (production strategy R4) (Fig. 15).

5.10.2 Integration with production facilities

As mentioned in Step 6, the integration of reservoir and production systems can improve production forecasts. As the integration increases computation time, it is important to assess the need for this integration and to use a suitable methodology (in this application, we used approximate boundary conditions in Step 6 and applied the integration in Step 11 only).

von Hohendorff Filho and Schiozer (2017) analyzed the influence of this integration, evaluating its effects on the production strategy parameters. The integration was applied to E9 for RM9 as an integrated production development, resulting in a lower initial NPV.

We re-optimized E9 altering configurations related to platform position, pipe diameters, gas lift rates, platform capacities, and the number, schedule, placement and shut-in times of wells. Figure 16 shows how NPV and ORF were affected during the global optimization for the best integrated production strategy. The optimization shows that standalone E9 is not the optimal strategy for integrated RM9.

Comparing standalone and integrated production strategies, we observed important changes in number and placement of wells that indicate the need to integrate reservoir and production models. Specific variables from production systems such as pipe diameters and gas lift rates also had a great impact, indicating the need to couple reservoir and production system models to reach more robust results.

The optimized integrated systems resulted in significantly increased NPVs, maintaining the same oil recovery factor while requiring a lower initial investment. These results demonstrate the benefits of integrating reservoir and production systems to increase robustness for decision making.

5.11 Step 12 and discussions

Steps 1–11 deliver a robust process to be used in the decision analysis, yielding an appropriate strategy that honors the history data and considers all uncertainties. At the end of the twelve steps, decision makers have technical and economic indicators to support both long-term, model-based decisions and short-term, data-driven decisions. This flexible 12-step procedure is suitable for companies with different aims as the process is guided by the objective: model quality, the necessity for further data assimilation (history matching), objective function selection, etc.

The 12-step procedure must be repeated whenever new important information is obtained and, therefore, is a continuous and iterative process. The most critical time is, of course, when the development is prepared and the production facilities selected. The number and placement of wells are important outputs of this analysis but the procedure can also be useful at later stages for real-time reservoir management. Readers interested in the management phase are referred to the case study UNISIM-I-M (Gaspar et al., 2016b).

The Robust Optimization, the optimization problem formulated under uncertainty to maximize a probabilistic objective function, ensured the best performance under uncertainty, considering the EMV, downside risk, and upside potential. However strong in robustness, this single production strategy gives little information on the different possibilities of field development, such as number and placement of wells, and platform processing capacities. Conversely, these data can be retrieved from the production strategies optimized individually for each RM. This approach gives decision makers an objective assessment of how different (or similar) these alternatives are, which provides valuable insights for EVoI and EVoF studies. In addition, as extensive optimization procedures were unnecessary in this final step, the analyses were automated. This automation is particularly important for EVoI, as it facilitates the assessment of the value of perfect and imperfect information, for varying degrees of information reliability. Note that, although we aim to automate as many procedures as possible, we recognize that manual refinement procedures can be valuable to investigate possible misconceptions or avoid local maxima of optimization processes with large search spaces.

We showed that specialized (deterministic) optimization can be advantageous in decision and risk analyses, provided that it is part of a probabilistic process (i.e., it is not limited to the most likely scenario). However, note that an adequate RM selection must be guaranteed, representing system inputs (probability distribution of uncertain attributes) and outputs (variability in production, injection, and economic forecasts). Furthermore, we showed that robust and specialized optimizations are complementary approaches in the decision-analysis process, and our current recommendation is to perform both in a case study. As this can be computationally demanding, the decision to choose one type of optimization over the other depends on the company’s objectives. Future research is planned on methods to make conducting both approaches computationally feasible for day-to-day applications.

In our case study, we used the proposal by Meira et al. (2016) to select the RMs. The attractiveness of this proposal is that it ensures that the set of RMs represents uncertainty in both system inputs and outputs. Ease-of-use is guaranteed as the method is software based, RMFinder. At the time of this study, we applied the initial proposal of RMFinder (Meira et al., 2016), which had some simplifications, namely the set of RMs were assumed to be equiprobable and it only considered a maximum of four field indicators (e.g., NPV, N _p, W _p, ORF). Meira et al. (2017) improved RMFinder by assigning probabilities to each RM. Further improvements are still ongoing, such as increasing the number of objective functions (up to 50), including not only field indicators, but also well indicators (such as fluid rates and BHP).

From previous studies for different case studies, we observed that around nine RMs are sufficient for production strategy selection. Future research is currently being conducted on the optimal number of RMs and candidate production strategies applied to studies of information acquisition, robustness, and flexibility, and on the possible loss of precision that this simplification may cause.

Some probabilistic analyses of this study used the full set of hundreds of scenarios matching production data. Although ensuring the most accurate predictions possible, this approach is computationally demanding and potentially unfeasible for simulation models with a very high runtime. Thus, it is important to define an objective and the necessary precision in Step 2. We are currently conducting research on assessing the feasibility of performing all probabilistic-based analyses on a small subset of RMs, each characterized by a probability of occurrence.

Our case study was in an early development phase, meaning that model updating was conducted with limited production data (four years of production data for four production wells). However, the 12-step method is not limited to such cases and can be applied to fields with many years of production data from producers and injectors, as demonstrated by Soares et al. (2018).

Data-driven, short-term decisions were not included in this work because they are more appropriate to a field in the management phase.

6 Conclusion

We have presented a model-based, closed-loop methodology based on twelve steps to be used in decision analysis for petroleum reservoir development and management under uncertainties, covering both model updating and production optimization.

Companies often skip several steps to expedite projects but we believe that, with the simplification presented here, the methodology is applicable to real cases, including complex cases with long simulation runtimes, and still ensure reliable decisions. In such a case, it is possible to decrease the number of simulations in Steps 6, 7 and 9 and select a smaller number of representative models (Step 8).

Note that further simplifications can yield suboptimal decisions. The level of detail of each step is a function of the importance of the study, the complexity of the case, and the available resources and time. 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 computationally efficient optimization processes.

The methodology is flexible enough to be applied to reservoirs in different stages of their lifetime. We presented a case in the development phase but it can be used at other stages. It is also simple enough to be used in practical applications because it does not require proxy models or complex tools.

By providing a comprehensive decision structure that integrates reservoir characterization, data assimilation, and production optimization, our method works as the core basis for specialized methodologies for each of these domains, as our results have shown.

Acknowledgments

This work was conducted with the support of Energi Simulation and Petrobras within the ANP R&D tax as “commitment to research and development investments”. The authors are grateful for the support of the Center of Petroleum Studies (CEPETRO-UNICAMP/Brazil), the Department of Energy (DE-FEM-UNICAMP/Brazil) and the Research Group in Reservoir Simulation and Management (UNISIM-UNICAMP/Brazil). In addition, special thanks to CMG and Schlumberger for software licenses and technical support.

References

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