Model-Based Decision Analysis of Production Strategy for Heavy-Oil Field Development and Management Under Uncertainty: Waterflooding, Polymer Flooding, and Intelligent Wells

Abstract

The decision-making procedure to develop and manage a production strategy is challenging because it requires a high investment and is performed under uncertainty. Heavy-oil reservoirs present low mobility and a high production of water under waterflooding. However, intelligent wells with ICVs (inflow control valves) and polymer flooding can improve the field’s performance. This work proposes a decision analysis to select the best strategy for the development of a heavy-oil field, evaluating and comparing the feasibility of waterflooding, polymers, and ICVs. We complement the nominal optimization accomplished for the base case in previous works by considering a probabilistic procedure with uncertainties, which includes the following: the generation of uncertain scenarios, the initial risk evaluation, the optimization of production strategies, a risk curve analysis, and the selection of the best strategy. A model-based reservoir simulation is used to perform the procedure, with the Expected Monetary Value (EMV) quantifying the economic returns. The case study is a sandstone heavy-oil reservoir (13° API) that represents a real Brazilian offshore field. Based on the EMV, we selected the polymer flooding strategy for this case study. However, since better water management was achieved with small differences to the polymer strategy, the option of using the ICVs in combination with polymer could be attractive depending on the various objectives of an oil field.

1. Introduction

The decision-making procedure to select a production strategy for the development and management of an oil field is very complex. Strategy implementation requires high-investment and high-risk decisions that affect the decades-long operations usually seen in oil production [1,2]. Life cycle optimization is used to help in the selection of production strategies, but the process is complex because it involves several optimization variables that can impact the objective function (OF) [3,4,5,6].

The available data to plan the development and management of an oil reservoir is generally limited, and new information is only collected after the field comes into operation. Thus, the selection of a production strategy is conducted under considerable uncertainty [7]. Typically, the combination of a reservoir, operational, and economic uncertainties generates uncertain scenarios (represented by simulation models) that an oil field project must consider [8,9]. Reservoir uncertainties involve reserves and fluid characteristics in the porous medium, operational uncertainties refer to system availability, and economic uncertainties relate to market variables, capital expenditure (CAPEX), and operational expenditure (OPEX). Moreover, poor or risky decisions may lead to significant losses if a production strategy is not flexible and adaptable enough when facing unexpected models and new data achievements [10,11,12].

Oil displacement by water injection and other reservoir stimulation techniques are key areas of research in reservoir science and production management, which play an important role in facing the challenges in the world’s energy supply security [13,14]. However, to address this issue, field development under risky conditions must be carried out while considering effective oil production by reducing the operation and energy requirements related to water management.

Heavy-oil reservoirs are characterized by low oil recovery factors (ORFs) because of low mobility [15,16,17,18]. This condition causes problems in the reservoir when an oil recovery technique such as waterflooding is applied. Poor sweep efficiency, a high water–oil mobility ratio, early breakthrough, and a high production of water are mostly presented under this technique [19,20,21].

More advanced EOR methods and field management operations are then necessary to improve the performance of a heavy-oil field. Polymer flooding and the use of intelligent wells equipped with inflow control valves (ICVs) are suitable alternatives to increase the oil recovery and deal with the problems faced under waterflooding.

Adding soluble polymer renders more viscous injection water, reducing the water–oil mobility ratio and the water fractional flow, thus increasing oil recovery and improving sweep efficiency [22,23]. Recent studies have indicated that the oil recovery increase is achieved by the mixture of viscous fingering and mainly viscous crossflow effects (VX) [24,25,26,27]. Intelligent wells have downhole devices installed, such as inflow control valves (ICVs), that allow for the remote monitoring and control of completed intervals without well interventions. The ICVs can control multiple production or injection zones, thereby accelerating oil production and managing the reservoir pressure, as well as reducing the production and injection of water [28,29,30,31,32].

The implementation of polymer flooding or intelligent wells is challenging because more complexity to the optimization problem is added by studying further decision variables. Generally, the extra variables are polymer concentration and slug sizes for polymer strategies [33,34], and the number, location, and controls of the ICVs in the strategies with intelligent wells [35,36,37,38,39,40,41]. There are also some physical phenomena/effects present in polymer flooding caused by the polymer-rocks properties and the non-Newtonian behavior. Retention, rheology (viscosity and polymer concentration), degradation, inaccessible pore volume (IPV), salinity, and permeability reduction are some of the effects that impact the response of this technique. The evaluation of these effects is essential because the polymer injection usually requires higher field investments for the testing, implementation, and management of the operation [42,43,44,45,46].

Very few works in the literature combine waterflooding, polymers, and ICVs with similarities to the model in this work [47,48,49]. These studies suggest that polymers improve oil recovery with better water management compared to water injection. Furthermore, ICVs help to reduce injected and produced water, as well as polymers, and they mitigate poor performance caused by incorrect well positioning.

Model-based reservoir simulation is a powerful, cost-effective, and time-efficient tool used in decision analysis to find suitable solutions to the problem of production strategy selection. Indeed, model-based nominal optimization for the selection of production strategies evaluated in this case study was concluded for a base case [50,51,52]. The previous research on the base case showed that the strategy of polymer flooding with ICVs (PF + ICV) was the best over waterflooding (WF), waterflooding with ICVs (WF + ICV), and polymer flooding (PF). The highest net present value (NPV) and ORF with the lowest production and injection of water, and an efficient reservoir pressure management were responsible for this result. Nevertheless, the differences in terms of NPV between PF and PF + ICV were not significant compared to WF against WF + ICV, indicating that the ICVs are more useful when injecting only water instead of polymers. Consequently, one must evaluate the strategies’ performance under uncertainties to support the selection of the best strategy through a decision analysis.

Model-based decision analysis has been applied to support the development and management of production strategy selection under uncertainty [47,53,54,55]. In this way, a production strategy response is evaluated across several uncertain models, supporting a decision-maker in the selection by identifying the potential gains and risks. Thus, the goal of the decision analysis is to complete the selection of a production strategy that is flexible and adaptable enough for uncertain models, therefore maximizing economic returns and reducing risks.

This work is based on the knowledge of a model-based field development and management procedure that has 12 steps divided into colors [56]. Our research study can be located in the blue steps where the development and management of an oil field is achieved through life cycle production optimization under uncertainty. However, we made some practical modifications from some of the blue steps, specifically described in the methodology section of this study.

In a general overview, our decision analysis involves the generation of uncertain models [57], the initial risk evaluation of the optimized strategies for the base case WF, WF + ICV, PF and PF + ICV, production strategy optimization for an optimistic case (P10) and pessimistic case (P90) [11,58], and the final decision to select the production strategy.

We also use the Expected Monetary Value (EMV) to select the strategies under uncertainty, and the NPV as the OF for optimization procedures considering long-term approaches. The optimization variables are categorized into G1 and G2L [59]. G1 refers to project or design variables that represent infrastructure, such as well number and platform capacities, before the start of field development. G2L are control variables used in the management of the equipment over time, such as operational specifications of well flow rates or ICV controls.

Objective

The objective of this work is to present a methodology to guide the selection of production strategy, complementing a decision analysis under uncertainty for the development and management of a heavy-oil reservoir, considering waterflooding (WF), waterflooding with ICVs (WF + ICV), polymer flooding (PF), and polymer flooding with ICVs (WF + ICV), and using model-based reservoir simulation under uncertain geological, operational, and economic conditions to evaluate the usefulness of polymers and intelligent wells.

2. Materials and Methods

The base of this work started at step 6 [56] where the production strategies were nominally optimized for the base case only. Details of the nominal optimization for the base case can be consulted in previous works [50,51,52]. This research completes the decision analysis by studying the uncertainties, covering the application from step 7 onwards, but we did not strictly apply each step from [56]. As this is the first analysis of the case study, some simplifications were applied to the steps to assess whether our approach can accomplish our hypothesis or whether more representative models with robust optimization are needed. Figure 1 illustrates the workflow of the methodology used in this research.

Figure 1. Workflow of the decision analysis under uncertainty.

2.1. Initial Risk Analysis

We applied the Discrete Latin Hypercube with Geostatistics (DLHG) sampling method to generate 100 scenarios (models) combining the geological, operational, and economic uncertainties through probability distributions [57]. More details of the uncertain attributes used to generate the models are shown in the application section of this work. The nominal optimized strategies for the base case (WF, WF + ICV, PF, and PF + ICV) were evaluated in the initial risk analysis. EMV values, risk curves of NPV, oil production (Np), ORF, water production (Wp), and water injection (Wi) were generated by simulating each strategy on the 100 uncertain models.

2.2. Selection of the Best Strategies

Two strategies were selected from the initial risk analysis. The selection was based on the EMV values and their behavior under the uncertain models in terms of NPV and field indicators, exposing the field risks, potential gains, and operationality.

2.3. Selection of a P10 and a P90 Models

One optimistic model (closest to P10) and another pessimistic one (near P90) were selected from the NPV risk curve for the selected strategies in the previous stage [11,58]. We selected these extreme models to evaluate possible notable differences in the behavior of the selected strategies in the uncertain analysis, using as a reference their uncertain assessment when the strategies were optimized from the base case. The selection of these models is a simplification since this research is one of the pioneering studies done in this particular case study. However, potential biases may affect the results if these extreme models do not capture the full uncertainty spectrum. Thus, we also evaluated the need for more representative models or robust optimization if the results of the decision analysis are inconsistent, or the possibility of evaluating different results.

2.4. G2L Optimization

We only optimized the G2L variables because the G1, which results from the nominal optimization, were quite similar among the strategies, particularly in the type and number of wells, well-opening schedule, and small changes in the well position [51]. The G2L optimization has the NPV as an OF and hierarchically follows the optimization of variables, which include the following: well flow rates, well water cut limit value, polymer concentration, water and polymer slug number and sizes, ICV controls, and apportionment method. The variables are optimized via assisted processes applied either manually or automatically using our standard algorithm (which is analogous to the idea of EDA—Estimation of Distribution Algorithm). Sensitivity analysis, knowledge of reservoir-production engineering, and simulation analysis are used in the manual procedure. The Iterative Discrete Latin Hypercube (IDLHC) [60] algorithm was selected for the automatic application running guided processes of about 100 simulations (sample size: 10, cut-off (%): 80, number of iterations: 10, and termination criterion: number of iterations). G2L optimization took around 800 to 1000 simulation runs, spending 130 to 180 h, respectively. More details about the optimization process are described in previous works [50,51,52].

2.5. Crossed Simulation

We performed crossed simulations of the selected strategies that were optimized from the P10, base, and P90 models. The process involves simulating each strategy in the models in which they were not optimized, thus obtaining quantitative results of NPV values. In this way, we evaluate if the optimization process achieved an acceptable result for the strategy in the model that was optimized by comparing its NPV value with its crossed-simulations.

2.6. Final Risk Curves and Decision Analysis

The optimized strategies from the P10 and P90 models were simulated on the 100 uncertain models. EMV values and risk curves with NPV and field indicators are shown together for the selected strategies optimized from the P10, base, and P90 models. Finally, we evaluated the response of the optimized strategies in the uncertain models and selected the best strategy based on the EMV.

2.7. Application

2.7.1. Description and Conditions of the Case

The case study of this research is named EPIC001. The base case was built from real data to represent part of a sandstone heavy-oil reservoir with 13° API of an offshore Brazilian field. Before obtaining the research results for this study, we validated our study case. In the validation, we performed a reservoir simulation analysis in which we approved the physical and computational time-consuming responses of the model for our research purposes. Thus, it is not computationally very time-consuming for optimization studies, and, yet, it showed good behavior to represent a real heavy-oil reservoir. As this is a new case without real history production data, the response model can be improved (in the future) for real production processes by updating new data and incorporating the uncertainty. Water phase has high salinity (100,000 ppm) and presents 0.43 cP of viscosity, and 1067.9 kg/m³ of density. More general information about the base case is listed in Table 1.

Table 1. Main parameters of the base case (data from [50]).

Parameter	Value	Unit
Total Oil Volume	8.97 × 107	m3
Average Permeability	3498	mD
Average Porosity	24	%
Depth	1933 to 2322	m
Average Depth	2138	m
Temperature	82	°C
Pressure	22,120	kPa (abs)

2.7.2. Simulation Model of the Base Case

The grid type of the model is the corner point, composed of 30 × 53 × 59 cells with 30,694 active blocks of 100 × 100 m length and varied thickness (avg 1.94 m). The reservoir has three facies (types of rock) distributed along the model. Moreover, there is no presence of aquifer or fractures. Due to the facies distribution, the model is highly heterogeneous with rock “packages” of high permeability (over 1000 mD) and porosity, and with others that have very low permeability and porosity, as illustrated in Figure 2.

Figure 2. Permeability X (mD); 3-D view for the base case.

2.7.3. Medium Scenario (Most-likely) for Polymer Flooding Strategies

A medium scenario was created to make the study more alike the strategies with polymer injection [52]. Viscosity and adsorption functions, permeability reduction, IPV, and correction in well injectivity were added to capture the effects and phenomena for the modeling of polymers in the black-oil simulator (E100). The synthetic polymer used in this study is of the HPAM type with 18 MDa molecular weight and a hydrolysis degree of about 30%. We show the input parameters of the medium scenario for the polymer modeling in the Table 2. We decided not to include the shear rate effects since it increased the simulation time by about 30 times longer without significantly impacting the results, making optimization procedures impractical. The salinity phenomenon was not studied as the ionic composition of production and formation water was unknown; however, polymer injection cost was slightly augmented to compensate for minor salinity effects in case of high polymer concentration requirements. Similarly, temperature effects were disregarded as larger temperature gradients between injectors and producers were not expected, and reservoir temperature (82 °C) is lower than the synthetic polymer tolerance of around 90 °C.

Table 2. Input parameters of the medium scenario to model the polymers in the E100 simulator.

Keyword	Description	Value	Source
PLYVISC	Polymer solution viscosity function	0 ppm (0.43 cP)−4000 ppm (81.91 cP)	Lab experimental data
PLYADS	Polymer adsorption functions	Figure 3	Lab experimental data
PLYROCK	Dead pore space	0.2	Lab experimental data
	Residual resistance factor	1.2	Lab experimental data
	Mass density	2560 (kg/m3)	Average of four sandstone samples with permeability range from 4 to 7D [61]
	Adsorption index	2	If a value of 2 is selected, then no polymer desorption may occur
	Maximum polymer adsorption	20 × 10−6 kg/kg	Lab experimental data
PLMIXPAR	Polymer Todd–Longstaff mixing parameter	1	Mixing parameter for the viscosity calculation in each polymer mixing region
PLYMAX	Polymer/salt concentrations for mixing calculations	914 ppm	Reservoir simulation analysis
WPOLYMER	Sets polymer/salt concentrations for injection wells	914 ppm (5 cP)	Reservoir simulation analysis
COMPDAT	Injectivity correction by adjusting the skin factor for polymer concentrations greater than 1200 ppm	−10	Reservoir simulation analysis [62]

Table 2. Input parameters of the medium scenario to model the polymers in the E100 simulator.

Keyword	Description	Value	Source
PLYVISC	Polymer solution viscosity function	0 ppm (0.43 cP)−4000 ppm (81.91 cP)	Lab experimental data
PLYADS	Polymer adsorption functions	Figure 3	Lab experimental data
PLYROCK	Dead pore space	0.2	Lab experimental data
	Residual resistance factor	1.2	Lab experimental data
	Mass density	2560 (kg/m3)	Average of four sandstone samples with permeability range from 4 to 7D [61]
	Adsorption index	2	If a value of 2 is selected, then no polymer desorption may occur
	Maximum polymer adsorption	20 × 10−6 kg/kg	Lab experimental data
PLMIXPAR	Polymer Todd–Longstaff mixing parameter	1	Mixing parameter for the viscosity calculation in each polymer mixing region
PLYMAX	Polymer/salt concentrations for mixing calculations	914 ppm	Reservoir simulation analysis
WPOLYMER	Sets polymer/salt concentrations for injection wells	914 ppm (5 cP)	Reservoir simulation analysis
COMPDAT	Injectivity correction by adjusting the skin factor for polymer concentrations greater than 1200 ppm	−10	Reservoir simulation analysis [62]

It is known that polymer adsorption functions reach a plateau value (maximum polymer adsorption value) regardless of polymer concentration increases [63]. At this point, all available adsorption sites on the surface are occupied without receiving any additional polymer molecules; therefore, no significant effect on the amount of polymer adsorbed is observed (polymer adsorption is measured in kg polymer per kg rock).

Figure 3. Adsorption vs. concentration for the applied polymer (data from [52]).

Figure 3. Adsorption vs. concentration for the applied polymer (data from [52]).

2.7.4. Well and Platform Operational Conditions

Table 3, Table 4 and Table 5 provide data about the well and platform conditions, including their operational efficiency.

Table 3. Well operational conditions (data from [50]).

Type	Producer	Injector
Max water rate (m3/d)		3000
Max oil rate (m3/d)	2500
Max liquid rate (m3/d)	2500
BHP (kPa-abs)	Min.: 12,500	Max.: 22,000

Table 4. Well data (data from [50]).

Type	Producer	Injector
rw (m)	0.108	0.108
Skin	5	5
Direction in which the well penetrates the grid block	I	I, J
Efficiency factor	1.0	1.0

Table 5. Maximum dimensions allowed for each platform applied as group operational conditions (data from [50]).

Type	Platform Production	Platform Injection
Max water rate (m3/d)	13,116	13,116
Max liquid rate (m3/d)	13,116
Max oil rate (m3/d)	7870
Well slots	7	12
Efficiency factor	1.0	1.0

2.7.5. Economic Scenario (Most-likely)

We use Equations (1) and (2) to calculate the net present value (NPV) and the net cash flow (NCF), respectively:

$$NPV= {\sum }_{j=1}^{N_t}{\displaystyle \frac{{NCF}_j}{{(1+i)}^{t_j}}}$$

(1)

where:

NCFj: net cash flow at period j;

Nt: total number of time periods;

i: discount rate;

tj: time period j (average time of the period) related to the date of analysis.

The NCF for each period is calculated considering the Brazilian R&T fiscal regime:

$$NCF= \left[(R-Roy-ST-OC)\times (1-T)\right]-Inv-AC$$

(2)

where:

R: gross revenues from oil and gas sales;

Roy: total amount paid in royalties (charged over gross revenue);

ST: total amount paid in Social Taxes (special taxes on gross revenues);

OC: operational production costs (associated with the oil and water/polymer production and water/polymer injection);

T: corporate tax rate;

Inv: investments in equipment and facilities (platform, production and injection wells, network systems, pipelines, etc.);

AC: abandonment cost.

The Expected Monetary Value (EMV) is computed by applying Equation (3), defined as the NPV sum of each uncertain model multiplied by its respective probability of occurrence:

$$EMV= {\sum }_{i=1}^n{P}_i\times {NPV}_i$$

(3)

The platform investments are calculated using Equation (4). Some parameters were incorporated in this equation, modifying the first version from [64,65]:

$${Inv}_{plat}=417+3.15\times C_{Pl}+12.2\times C_{Po}+3.15\times C_{Pw}+3.15\times C_{iw}+0.1\times C_{nw}$$

(4)

where:

Inv_plat: investment on platform (10⁶ USD);

C_Pl: liquid processing capacity (10³ m³/d);

C_Po: oil processing capacity (10³ m³/d);

C_Pw: water processing capacity (10³ m³/d);

C_iw: water injection capacity (10³ m³/d);

C_nw: number of wells capacity.

Term 417 in Equation (4) represents fixed costs.

The fiscal assumptions and economic scenario to compute the NPV are listed in Table 6 and Table 7. The costs related to the polymers include the logistics and investments required in the platform.

Table 6. Fiscal assumptions (data from [50]).

Variable	Value	Unit
Corporate tax rate	34	%
Social tax rate—charged over gross revenue	9.25
Royalties rate—charged over gross revenue	10

Table 7. Economic scenario (most-likely) (data from [51]).

Variable/Parameter	Value	Unit
Discount rate	9	%
Oil price	314.5	USD/m3
Operational fixed cost	1	106 USD/month
Oil production cost	62.9	USD/m3
Polymer mixture production cost	4	USD/kg
Polymer powder production cost	3	USD/kg
Water production cost	6.29	USD/m3
Water injection cost	6.29	USD/m3
Polymer injection cost	6	USD/kg
Drilling and completion of horizontal well (fixed cost)	60	106 USD
Connection of well (well–platform)	13.3	106 USD
Drilling and completion of vertical well	14	106 USD
Recompletion of horizontal well	3	106 USD
Recompletion of vertical well	3	106 USD
Well conversion	3	106 USD
1st inflow control valve (ICV) for each well	10	103 USD/joint
2nd or more ICV for each well	8	103 USD/ICV
Platform	Equation (4)	106 USD
Abandonment cost (% of investment on drilling and completion)	10%	106 USD

2.7.6. Dates and Important Events

Table 8 and Table 9 describe the main dates and events of this study. These correspond to the life cycle period with a duration of 22 years until the end of the concession contract by 2042. The strategy selection of this decision analysis considers this information to calculate Equations (1)–(3).

Table 8. Timeline events—field production (data from [50]).

Time (Day)	Date (MM/DD/YYYY)	Event-Field Timeline Description
0	FEB/27/2020	1. Simulation initial date
0	FEB/27/2020	2. Starting time of production forecast
0	FEB/27/2020	3. Beginning of well drilling operation
29	MAR/27/2020	4. Beginning of well completion operation
731	FEB/27/2022	5. End of production system installation
731	FEB/27/2022	6. 1st well connection (well–platform)
731	FEB/27/2022	7. Production starting time
7979	JAN/01/2042	8. Simulation final time
7979	JAN/01/2042	9. Maximum date for field abandonment

Table 9. Timeline events—cash flow (data from [50]).

Time (Day)	Date (MM/DD/YYYY)	Cash Flow Timeline Description
0	FEB/27/2020	1. Reference date for analysis (updating cash flow) REFERENCE (present date)
0	FEB/27/2020	2. Investments on platforms and facilities
0	FEB/27/2020	3. Investments on 1st well drilling
29	MAR/27/2020	4. Investments on 1st well completion
731	FEB/27/2022	5. Investments on 1st well connection (well–platform)
7979	JAN/01/2042	6. Maximum incidence date—field abandonment cost

2.8. Selected Uncertainties

The optimized strategies’ performance must be evaluated using the probabilistic approach in uncertain models. These equiprobable scenarios or models were created by the combination of uncertain reservoir, operational, and economic attributes. In the next sections, we describe these attributes in tables and show their levels, values, and probability of occurrence.

2.8.1. Reservoir Uncertainties

We selected some static and dynamic properties and polymer parameters as reservoir uncertainties. Regarding the static properties, 100 equiprobable geostatistical realizations (images) were generated by conducting uncertain modeling through geostatistical software Petrel (version 2023.2.0). We used the base case to generate the images based on the distributions of facies, porosity, and permeability. The dynamic uncertainties were the relative permeability, capillary pressure, oil viscosity and PVT, and rock compressibility. In the case of polymer parameters, we evaluated the viscosity, adsorption, IPV, RRF, and polymer injectivity correction by adjusting the well skin factor, since the simulator may present some injectivity issues under polymer injection [62]. Table 10 and Table 11 include data about the reservoir attributes that are considered uncertain.

Table 10. Uncertainty levels and probabilities of static and dynamic properties of the reservoir.

Attribute	Levels (Probability)
	−1	0	1
Images	100 petrophysical images (equiprobable)
Relative permeability	kr-1 (0.3)	kr0 (0.4)	Kr1 (0.3)
Capillary pressure	Pc-1 (0.3)	Pc0 (0.4)	Pc1 (0.3)
Oil viscosity and PVT	PVT-1 (0.3)	PVT0 (0.4)	PVT1 (0.3)
Rock compressibility (×10−6 1/psia)	Value	Probability	Type of distribution
	10% higher	5%	Normal
	5% higher	22.5%
	637 to 0.69 (varies with pressure)	45%
	5% lower	22.5%
	10% lower	5%

Table 11. Uncertainty levels and probabilities of polymer parameters in the reservoir.

Keyword	Description	Levels (Probability)			Comments
		−1 (0.33)	0 (0.34)	1 (0.33)
		Min	Medium Scenario	Max
PLYVISC	Polymer solution viscosity function	−0.5 cP	0.43–81.91 cP	+0.5 cP	The polymer solutions are expected to vary naturally with +/− 0.5 cP.
PLYADS	Polymer adsorption functions	10 × 10−6 kg/kg	Figure 3	40 × 10−6 kg/kg	The curve shape is assumed to have negligible uncertainty. The max value has a relatively large measurement uncertainty and depends on factors such as permeability and wettability.
PLYROCK	Dead pore space	0.15	0.2	0.25	Measurement uncertainty.
	Residual resistance factor	1.1	1.2	1.4	Measurement uncertainty.
	Maximum polymer adsorption	10 × 10−6 kg/kg	20 × 10−6 kg/kg	40 × 10−6 kg/kg	The curve shape is assumed to have negligible uncertainty. The max value has a relatively large measurement uncertainty and depends on factors such as permeability and wettability.
COMPDAT	Skin factor for injectivity correction under polymers	−3	5	13	Simulators tend to drastically reduce the injection under polymer flooding (at high polymer concentration). Moreover, observation from some field applications showed injectivity increases under polymer injection [62,66,67].

2.8.2. Operational Uncertainties

Uncertainties for operational attributes were also considered, as shown in Table 12 and Table 13. The system availability (SA) considers the operational efficiency of platform, groups, and wells. Uncertainties related to well productivity and injectivity use the well index multiplier to represent variations in the well proximity caused by formation damage, and chemical dissolution, among others.

Table 12. Uncertainty levels and probabilities for operational attributes.

Attribute	Type	Keyword	Levels (Probability)
			−1 (0.33)	1 (0.33)	0 (0.34)
System availability (SA)	Platform	GEFAC	0.88	0.95	1.0
	Group
	Producer	WEFAC	0.85	0.95	1.0
	Injector

Table 13. Uncertainty levels and probabilities for well productivity and injectivity attributes.

Attribute	Type	Keyword	Levels (Probability)
			−1 (0.33)	0 (0.34)	1 (0.33)
Well productivity	Producer	WPIMUL	0.95	1.0	1.05
Well injectivity	Injector

2.8.3. Economic Uncertainties

We also defined an optimistic and a pessimistic economic scenario with regard to the most-likely economic scenario from Section 2.7.5 of this work. The terms optimistic and pessimistic refer to the price of oil, since the investments and operational costs generally increase under optimistic oil prices; on the other hand, they decrease under pessimistic prices. The values and probability of occurrence for the economic scenarios are presented in Table 14.

Table 14. Pessimistic, most-likely, and optimistic economic scenarios for the uncertain analysis.

Variable/Parameter	Probability of Occurrence			Unit
	0.25	0.5	0.25
	Pessimistic	Most-likely	Optimistic
Discount rate	9	9	9	%
Oil price	220.14	314.5	440.28	USD/m3
Operational fixed cost	0.9	1	1.1	106 USD/month
Oil production cost	45.0	62.9	88.0	USD/m3
Polymer mixture production cost	2.8	4	5.6	USD/kg
Polymer powder production cost	2.0	3	4.0	USD/kg
Water production cost	4.5	6.29	8.80	USD/m3
Water injection cost	4.5	6.29	8.80	USD/m3
Polymer injection cost	4.3	6	8.4	USD/kg
Drilling and completion of horizontal well (fixed cost)	36	60	90	106 USD
Connection of well (well–platform)	7.8	13.3	21.6	106 USD
Drilling and completion of vertical well	8.23	14	22.4	106 USD
Recompletion of horizontal well	1.7	3	4.8	106 USD
Recompletion of vertical well	1.7	3	4.8	106 USD
Well conversion	1.7	3	4.8	106 USD
1st inflow control valve (ICV) for each well	6	10	16	103 USD/joint
2nd or more ICV for each well	5.6	8	12.8	103 USD/ICV
Platform	0.8 × (Equation (4))	1.0 × (Equation (4))	1.25 × (Equation (4))	106 USD
Abandonment cost (% of investment on drilling and completion)	10%	10%	10%	106 USD

2.8.4. Software Used

The simulation runs were done in ECLIPSE (E100) (version 2021.2) [68] through one processor in serial simulations. We used the ResInsight (version 2021.06.0) [69] for the visualization of the simulation outputs. The uncertain geostatistical modeling of the reservoir was conducted in Petrel (version 2023.2.0) [70]. The MERO software (version 2022.10.1) [71] from our UNISIM group (Simulation and Reservoir Group Management) was coupled with E100 to integrate the workflow of the evaluation process, executing both pre-simulation and pos-processing.

3. Results and Discussion

First, we show the main result of the nominal optimization for all the optimized strategies from the base case (step 6 from [56] because it is the basis of this risk analysis [51]). Through figures, tables, and analysis along each stage of the decision analysis workflow under uncertainties, we present the results to assess our methodology and support the implementation of the best strategy for the case study.

3.1. Summary of the Nominal Optimization for the Base Case

Previous nominal optimization found that the PF + ICV strategy was the best for the base case. It obtained a 50%, 26%, and 4% higher NPV than WF, WF + ICV, and PF, respectively. PF + ICV also produced more oil with a lower production and injection of water among the optimized strategies (see Table 15). However, the differences in the field indicators between PF + ICV and PF were small for NPV and oil production, rendering the ICV controls for the water management responsible for the low gain in the OF. However, the ICVs were more efficient under waterflooding strategies because a more considerable difference in the field indicators was observed for WF + ICV against WF. Table 15 presents the water management costs with polymers included for PF and PF + ICV. Supporting previous results, the PF + ICV strategy had the lowest costs due to the combined operation of polymers with ICV for more efficient water management. In general, conventional completion strategies, such as WF and PF, had higher costs than the ICV strategies WF + ICV and PF + ICV, respectively. Similarly, the efficiency of the ICVs is underscored in waterflooding strategies since the difference in costs between WF and WF + ICV is greater than in PF and PF + ICV.

Table 15. Field indicators of the optimized strategies from the base case.

Field Indicators	WF	WF + ICV	PF	PF + ICV
NPV (106 USD)	315.0	373.7	453.4	470.1
ORF	0.269	0.277	0.315	0.316
Np (106 m3)	24.2	24.9	28.3	28.4
Wp (106 m3)	34.8	27.4	14.5	11.6
Wi (106 m3)	58.5	52.9	43.9	41.1
Water management costs (106 USD)	589	507	511	475

3.2. Initial Risk Analysis

Once the uncertainties were combined, the optimized strategies from the base case were simulated in the 100 uncertain equiprobable models, generating the initial risk curves presented in Figure 4. From the NPV risk curves, the polymer strategies had a small difference in NPV, but they obtained potentially higher economic returns while the waterflooding strategies showed lower gains with the risk of providing negative returns. The field indicators showed that the polymer strategies produce more oil with better water management. In the case of the strategies with ICVs, they were more efficient in producing and injecting less water when injecting either water or polymers. However, the strategies under waterflooding presented a higher difference in NPV values than the polymers, which proves that ICVs are more useful for waterflooding.

Figure 4. Initial risk evaluation of the optimized strategies from the base case in the uncertain models: (a) net present value (NPV), (b) Np (oil production), (c) ORF (oil recovery factor), (d) Wp (production of water, and (e) Wi (injection of water). WF strategy in blue, WF + ICV strategy in gray, PF strategy in pink, and PF + ICV in green. Orange rhombus: values of WF in the base case; yellow rhombus: values of WF + ICV in the base case; light blue rhombus: values of PF in the base case, and black rhombus: values of PF + ICV in the base case.

These initial results under uncertainties confirm the findings from the nominal optimization since the polymer strategies were better than the waterflooding ones. Nevertheless, the difference in the NPV values between PF and PF + ICV was small, so more studies are needed to select the best strategy.

3.3. Selection of the Best Strategies

The EMV values for the optimized strategies from the base case are shown in Table 16. Contrary to the finding of nominal optimization for the base case, PF + ICV was not the best strategy; instead, PF was initially the best strategy under uncertainties since it obtained the highest EMV value. However, its difference with the PF + ICV strategy was again marginal in terms of EMV, making the intelligent completion advantageous due to the better water management when considering an energy efficiency point of view.

Table 16. EMV values for the optimized strategies from the base case.

Strategy	EMV (106 USD)
WF	168
WF + ICV	235
PF	405
PF + ICV	396

The superior EMV values for PF and PF + ICV also demonstrated that it is better for the case to inject polymers over simply waterflooding. Additionally, the ICV’s efficiency proves that it is advantageous for waterflooding because of the higher EMV difference between WF and WF + ICV.

Based on the small difference in EMV values, the oil production and water management, and the exposed potential gains, risks, and operability, we selected the PF and PF + ICV strategies as the best strategies for further studies in this decision analysis.

3.4. Selection of a P10 and a P90 Model

Figure 5 shows the selected P10 (optimistic) and P90 (pessimistic) models from the NPV risk curves for the selected strategies.

Figure 5. Selected P10 and P90 models for the selected strategies. NPV values of the PF strategy in pink, and PF + ICV in light green. The light blue circle represents the NVP value of PF in the base case, and the black triangle for PF + ICV. Dark green circle NVP value of PF in P10, and dark green triangle for PF + ICV. Red circle NVP value of PF in P90, and red triangle for PF + ICV.

3.5. G2L Optimization

Table 17 includes the optimization results of the G2L variables for the selected strategies in the P10 and P90 models, and their values obtained in the base case as a reference. The following findings about the optimized variables were achieved among the optimized strategies:

Table 17. Optimized G2L variables for PF and PF + ICV in the P10 and P90 models, and base case as reference.

Item Description		Base Case		P10		P90
		PF	PF + ICV	PF	PF + ICV	PF	PF + ICV
Well production flow rate (m3/d)	3P21	Max 2500	Max 2500	Max 2500	Max 2500	2400	Max 2500
	3P23	Max 2500			2200	Max 2500
	EP01	2300			1500		2200
	EP03	2400			2200	2200	2300
Well injection flow rate (m3/d)	3W9	Max 3000	Max 3000	Max 3000	2800	Max 3000	2900
	EI04						Max 3000
	EI05				2700		2800
Water cut limit (%)	3P21	100	100	100	100	100	100
	3P23					88
	EP01	70	64			100
	EP03	100	100				85
Polymer specification (ppm)	Concentration	600	900	1200	1300	1100	1200
Polymer slug (after starting production)	Number	1	1	1	1	1	1
	Start year	0	0	0	0	0	0
	Duration	11	8	13	12	10	9
Water slug (after starting production)	Number	1	1	1	1	1	1
	Start year	11	8	13	12	10	9
	Duration	9	12	7	8	10	11
ICV controls water cut limit (%)	3P21: ICV1, ICV2, ICV3		100, 48, 77	N/A	32, 100, 30		65, 100, 66
	3P23: ICV1, ICV2		78, 100		40, 100		70, 100
	EP01: ICV1, ICV2, ICV3		61, 50, 100		60, 60, 100		65, 30, 100
	EP03: ICV1, ICV2		100, 87		100, 22		100, 85
Apportionment method		W_grc_o	W_grc_o	WP	WP	WP	WP
		W_grc_w	W_grc_w

• More well flow rate controls were necessary for the producers in the PF + ICV strategies, and most of the production wells in the PF strategies operated at maximum capacity. Regarding the injection wells, they operated at maximum capacity in the three models for the PF strategies, thus confirming that it is better to inject as much as possible.
• It was not necessary to shut in wells due to the high water cut in the P10 (optimistic) model for the selected strategies. Thus, the production wells under polymer injection must operate during the entire life cycle in the optimistic case.
• The same behavior in the polymer concentration, number, and duration of the polymer slug size was found for the selected strategies in the three models. Only two slugs were needed, starting the injection with polymers, and then one slug of water. PF + ICV strategies inject the polymer at higher concentrations for shorter periods, while PF strategies inject at lower concentrations for a longer time.
• The ICVs were efficient in water management, especially for the base case and pessimistic case (P90), since the ICV controls (based on the water cut) were activated at greater values due to a faster and larger water production through the wells. As the optimistic case did not present severe problems with water production, the ICV controls were activated mainly to manage the reservoir pressure using lower water cut values.
• Regarding the apportionment method, the well potential (WP) method was selected for the strategies in the P10 and P90 models, which differs from the best method of the base case. The well guide rate control operated better in the base case because the operational efficiency of the platform and wells was considered to be 100%. Accordingly, the WP method operates better under a lower operational efficiency of either the platform or wells.

Table 18 lists the field indicators of the selected strategies optimized in the base case, before and after the optimization process of the G2L variables for the P10 and P90 models. Overall, the PF + ICV strategies had better performance after conducting the optimization. However, it is necessary to evaluate their response in all the uncertain models because the differences with PF strategies were still small for these specific models (base case, P10, and P90). Before optimization, the PF + ICV strategy presented better field indicators in the P90; in the same way, the PF strategy was better in the P10. Considering the increase in the NPV after the G2L optimization, they had an opposite result: the PF + ICV had a higher increase (14.3%) than PF (4.4%) in the P10. In the P90, PF was better obtaining a 5.9% NPV increase compared to 3.8% from PF + ICV. As a result, once optimized, the PF strategies could respond better to the uncertain models when optimized from a pessimistic case; on the other hand, the PF + ICV may present good results when optimized from an optimistic case. According to water management costs, strategies that combine polymers with IVCs showed consistently lower costs than those that inject polymers alone. This result was especially evident in the most optimistic scenario, P10, which showed the greatest difference.

Table 18. G2L optimization results for PF and PF + ICV in P10, P90, and base case as reference.

Field Indicators	Base Case		P10						P90
	Optimized		Before Optimization		After Optimization		∆ Increase in NPV (%)		Before Optimization		After Optimization		∆ Increase in NPV (%)
	PF	PF + ICV	PF	PF + ICV	PF	PF + ICV	PF	PF + ICV	PF	PF + ICV	PF	PF + ICV	PF	PF + ICV
NPV (106 USD)	453	470	705	670	736	766	4.4	14.3	118	156	125	162	5.9	3.8
ORF	0.315	0.316	0.288	0.278	0.319	0.324			0.259	0.268	0.280	0.285
Np (106 m3)	28.3	28.4	26.8	25.9	29.7	30.1			22.3	23.1	24.1	24.5
Wp (106 m3)	14.5	11.6	16.3	9.8	13.1	9.6			21.9	16.6	20.3	16.4
Wi (106 m3)	43.9	41.1	41.9	34.7	40.9	38.3			45.1	40.7	45.4	42.0
Water management costs (106 USD)	511	475			891	788					479	434

To better visualize the performance of the PF and PF + ICV strategies in the P90, base, and P10 scenarios with optimized G2L, Figure 6 displays fluid (water and oil) saturation maps. As the scenarios progress from pessimistic to base to optimistic, the sweep efficiency increases; however, the strategies with intelligent completion exhibit a more controlled sweep and, therefore, greater oil drainage.

Figure 6. Fluid saturation maps (SWAT: water saturation, and SOIL: oil saturation), on layer 20 on 1st Jan 2030, of the G2L optimized strategies PF and PF + ICV in the P90, base, and P10 cases: (a) PF in P90, (b) PF + ICV in P90, (c) PF in base case, (d) PF + ICV in base case, (e) PF in P90, and (f) PF + ICV in P90.

3.6. Crossed Simulation

We ran a crossed simulation considering the optimized strategies and the models used for their optimization procedures, following the nomenclature:

• PF opt: PF strategy optimized from P10;
• PF + ICV opt: PF + ICV strategy optimized from P10;
• PF bc: PF strategy optimized from the base case;
• PF + ICV bc: PF + ICV strategy optimized from the base case;
• PF pes: PF strategy optimized from P90;
• PF + ICV pes: PF + ICV strategy optimized from P90.

To indicate if the optimization process had acceptable results for the strategies in the applied models, we expect that the optimized strategies present the highest NPV values in the models in which they were optimized. As shown by Table 19, the NPV values of the crossed simulation found the expected results for the strategies above (see the NPV values in bold).

Table 19. Crossed simulation of the optimized strategies in the P10, base case, and P90 models.

Strategy	NPV (106 USD)
	P10	Base Case	P90
PF opt	736	361	110
PF + ICV opt	766	369	139
PF bc	705	453	118
PF + ICV bc	670	470	156
PF pes	710	400	125
PF + ICV pes	758	424	162

3.7. Final Risk Curves and Decision Analysis

The final risk curves of the NPV and field indicators for the optimized strategies from P10, base case, and P90 are illustrated in Figure 7. The optimized strategies provided similar results to the initial risk analysis, indicating that it is not necessary to select more representative models for the production strategy optimization in the decision analysis, as recommended in the original methodology proposed by [56]. The PF and PF + ICV again presented smaller differences in the NPV risk curves; however, some differences in the oil production and water management can be observed from the risk curves of the field indicators. Like previous studies [47,48,49], the PF strategies produced more oil while the PF + ICV strategies produced and injected less water, making the ICV completion attractive for the water management (lower operation and water management costs).

Figure 7. Final risk curves of the optimized strategies from the P10, base case, and P90 in the uncertain models: (a) net present value (NPV), (b) Np (oil production), (c) ORF (oil recovery factor), (d) Wp (production of water), and (e) Wi (injection of water). PF opt in black squares, PF + ICV in blue squares, PF bc in pink squares, PF + ICV bc in green squares, PF pes in red squares, and PF + ICV pes in yellow squares. Light blue rhombus: values of PF in the base case, and black rhombus: values of PF + ICV in the base case.

However, based on our proposed methodology, the best strategy is selected based on the EMV. Table 20 lists the EMV values of the optimized strategies from the optimistic case P10 (suffix opt), base case (suffix bc), and pessimistic case P90 (suffix pes). Like previous studies from the G2L optimization for the P10 and P90 of the selected strategies, the PF + ICV is potentially better when improved for the optimistic case, but PF provided higher economic returns when optimized for the pessimistic case. Consequently, we finally selected the PF strategy as the best for the case since it presented the highest EMV values when optimized from the base case and pessimistic case, overcoming the polymer strategies with the use of intelligent wells. However, the decision to use intelligent completion can be made according to the objectives of each decision-maker since PF EMV values also showed a marginal difference with the ICV strategies, which were more flexible for water management even though they produced slightly less oil.

Table 20. EMV values for the optimized strategies from the P10, base case, and P90.

Strategy	EMV (106 USD)
PF opt	403
PF + ICV opt	406
PF bc	405
PF + ICV bc	396
PF pes	403
PF + ICV pes	395

4. Conclusions

We presented a methodology to complement the decision analysis for the selection of production strategies under uncertainty for the development and management of a sandstone heavy-oil reservoir using model-based reservoir simulation, and combining waterflooding, polymers, and intelligent wells, considering a probabilistic approach and uncertain scenarios. The main idea was to present an efficient and practical procedure that could be applied to similar cases.

For this particular case (EPIC001), based on the EMV, we found it more viable to implement the PF strategy, reaching our main decision by evaluating the polymers and the use of intelligent wells among all the studied strategies.

ICVs are more recommended when comparing waterflooding strategies since significant differences in EMV and NPV values were observed between WF + ICV and WF. Instead, small differences in these indicators were present for PF against PF + ICV.

The PF + ICV strategy showed better results than PF in the management of water, and NPV values after optimization processes (specific models). Thus, the decision to use the ICVs depends on a project target (principal OF, secondary OFs, additional investments, ORF, water management, ICVs, and polymer failures).