O objetivo desta dissertação é desenvolver estimadores não paramétricos para a função de covariância de dados funcionais agregados, que consistem em combinações lineares de dados funcionais que não podem ser observados separadamente. Estes métodos devem ser capazes de produzir estimativas que separem a covariância típica de cada uma das subpopulações que geram os dados, e que sejam funções não negativas definidas. Sob estas restrições, foi definida uma classe de funções de covariância não estacionarias, à qual resultados da teoria de estimação de covariância de processos estacionários podem ser estendidos. Os métodos desenvolvidos foram ilustrados com a aplicação em dois problemas reais: a estimação do perfil de consumidores de energia elétrica, em função do tempo, e a estimação da transmitância de substâncias puras em espectroscopia de infravermelho, através da inspeção de misturas, em função do espectro da luz.
Autor: João Lucas Braga Da Silva
A Procedure to Parameterize High Permeability Zones in Naturally Fractured Reservoir
This paper presents a novel-methodology to compensate for the poor characterization of high-permeability structures (excess-K: vugs, karsts and super-K features), and non-fault-related-fractures, in naturally fractured Brazilian Pre-Salt carbonate reservoirs. These heterogeneities are often undetectable in well logs and seismic data, but significantly impact well performance. The methodology aims to enhance the representation of such features within dynamic simulation models, improving reservoir characterization and supporting more reliable data-assimilation and forecasting processes. The methodology involves: (1) upscaling high-fidelity fine-grid models to coarser-grids while preserving dynamic behavior, (2) identifying wells with productivity/injectivity mismatches due to a poor excess-K characterization, (3) applying a data assimilation (DA) process to minimize the mismatch between modeled and measured wells production and injection rates by updating the absolute permeability of the matrix. The novelty of the process is that the permeability field is updated by creating a mask (3D property) built by kriging permeability increments estimated from the well cells with productivity/injectivity issues. Therefore, the DA aims to find the least increments of permeability needed for each well such that when this mask is summed with the matrix permeability field all wells present good productivity/injectivity matching with history data. The methodology was applied to a dual-porosity/dual-permeability (DP/DK) compositional reservoir model. Two distinct well behaviors were observed: (1) wells located within fracture zone (12 of 33) showed good productivity/injectivity alignment with historical data and (2) the remaining 21 wells, located away from fracture zone, exhibited significantly poorer productivity/injectivity. This mismatch was attributed to the absence of excess-K features in the original matrix permeability model (Km-field). The optimization process was applied to these 21 wells. For each well a specific Ki-value was settled, defining input-points for kriging. The resulting kriged permeability correction volume (mask) was summed with the Km-field to generate an updated-permeability model. This process was repeated until all wells presented good productivity/injectivity matching with historical data. The process not only corrected the simulated dynamic responses, but also revealed key spatial permeability patterns that had not been captured in the static model. The results served as feedback to the geologists and enabled iterative improvement of the geological model, supporting a more integrated and realistic characterization. Overall, the results validate the methodology as a robust tool for incorporating unresolved high-permeability features in reservoir simulation and improving the quality of data assimilation. This study introduces an automated, iterative probabilistic data-assimilation framework that directly integrates geostatistical kriging with permeability adjustments for excess-Kstructures. The approach provides bidirectional feedback to geological modeling and allows the generation of realistic ensembles for data assimilation workflows. By combining geo-statistics within an uncertainty reduction scheme, the method addresses key modeling gaps encountered when modelling a Brazilian Pre-Salt carbonate.
A probabilistic approach for selection of well opening schedule in pre-salt reservoirs using WAG-CO2
The development of petroleum reservoirs is essential to maximize the chances of efficient oil and gas production and to meet global energy demands. In previous work, we proposed a simple procedure for fast decision-making considering a deterministic problem if there is no time to perform an optimization process. In this work, we also propose a fast procedure, but focusing on the probabilistic situation, while also estimating the impact of making a bad decision to this problem. Using representative models (RMs) of the UNISIM-II-D-BO benchmark case and a well positioning configuration proposed in the reference approach, with 21 wells, we propose a fast procedure based on the process developed for the deterministic problem. After the application of the fast procedure, we run a robust optimization on the same RMs to have a reference expected monetary value (EMV) for comparisons. At the end, we verified that there is a range of differences between 2.2% and 4.3% between the best value from the robust optimization and values of the proposed approach, depending on the RM considered. We found that a suboptimal choice of well opening schedule could lead to an EMV up to 12% lower than the best value obtained from robust optimization. Therefore, if there is enough time and computational resources, we recommend that decision makers perform the robust optimization. However, we suggest using the proposed faster procedure as an option for cases with time constraints.
7th EPIC Conference
A edição de 2025 da Epic Conference apresentou um formato um pouco diferente em relação aos anos anteriores. A segunda-feira, 1º de dezembro, foi dedicada a reuniões internas das linhas de pesquisa, realizadas em conjunto com membros do International Advisory Board do EPIC — Dr. Mike King e Prof. Robert Goldstein. No segundo dia, 2 de dezembro, o evento (fechado ao público geral e exclusivo para membros do EPIC) contou com apresentações dos responsáveis técnicos pelas quatro linhas de pesquisa: Vinicius Botechia, Vanessa Guersoni, Guilherme Chinelatto e Daniel Rojas. Os responsáveis técnicos apresentaram um panorama geral de cada linha, abordando os temas de pesquisa atuais, os principais resultados alcançados e os próximos passos previstos. O programa incluiu ainda duas sessões de pôsteres, totalizando 45 trabalhos expostos. Nas sessões de pôster, os pesquisadores do EPIC tiveram a oportunidade de apresentar suas pesquisas para seus colegas, promovendo troca de conhecimento e discussão dos resultados. A palestra de abertura foi ministrada pelo Prof. Denis Schiozer, diretor do EPIC, e contou com a participação de Juliana Bueno e Fernanda Hoerlle, coordenadoras do projeto junto à Equinor.
Para mais informações, consulte o Programa da Conferência, disponível em:
Model-based production strategy optimization for an offshore heavy oil reservoir considering polymer flooding and intelligent wells
Heavy oil reservoirs are known for their low recovery factors. Additional energy consumption, special operations, and enhanced oil recovery (EOR) techniques are required for production due to high viscosities. Also, unfavorable water-oil mobility ratio is a serious problem when waterflooding (WF) is implemented, usually causing early breakthrough and higher water cut. Developing and managing a production strategy through a comprehensive decision-making procedure is also complex due to the high number of variables, uncertainties, and physical phenomena involved. Polymer flooding (PF) is an EOR method that can be applied to heavy oil reservoirs to improve field performance by producing more oil and reducing water production. This improvement is achieved through the increase in water viscosity caused by the injection of polymers, thus reducing water-oil mobility ratio, and obtaining better oil displacement efficiency. In the case of intelligent wells (IW) equipped with Inflow Control Valves (ICVs), the WF limitations can be mitigated by controlling multiple production/injection zones, increasing oil production, and maintaining the reservoir pressure. This work aims to perform a nominal production strategy optimization to develop and manage a heavy oil reservoir considering PF as a production strategy (using conventional wells only) and comparing it to waterflooding with ICVs (WF+ICV) for the same case. A complete methodology to optimize the design and control variables is applied to the strategies by using model-based reservoir simulation. The objective function (OF) is the Net Present Value (NPV), this study case is named EPIC001, which has a 13° API heavy oil reservoir that represents part of a Brazilian offshore field. We have applied a specific methodology to optimize the PF strategy for a heavy oil reservoir of a nominal case which is practical and clear in the selection and comparison of strategies for similar cases. The results found PF strategy is the more suitable for the case, obtaining an NPV that is 21% higher than WF+ICV. Injecting polymers in the earlier stages of the life cycle at lower polymer concentration rendered PF with greater oil recovery (+13%) with a better efficiency in management of water and polymers, therefore surpassing the good ICV management from WF+ICV.
High-pressure PVT properties of synthetic oil/gas systems for EOR: The effect of CH4 and a CO2-rich gas on a heptane/toluene mixture
Understanding the flow and phase behavior properties of reservoir fluid–injected gas systems is essential for optimizing oil production strategies and designing gas injection-based Enhanced Oil Recovery (EOR) techniques. In the absence of live oil data, synthetic model mixtures with similar characteristics can provide reliable input for reservoir simulation. This study investigates the bubble point pressures (BPP) and the volumetric behavior of two synthetic systems: (n-heptane + toluene + methane) and (n-heptane + toluene + carbon dioxide + methane). BPP values were measured for mixtures with varying CH4 or (CO2 + CH4) content over the (304.7–363.2) K range. The two experimental techniques used, a stepwise and a visual method, showed excellent agreement with each other (RMSD = 0.01 MPa). Liquid phase densities were determined across wide temperature (293.2–363.2) K and pressure (5–90) MPa ranges.
The Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) equations of state (EoS) were applied to model the saturation pressures, achieving average relative deviations (ARDs) of 5.8% and 6.0%, respectively. The experimental density data were correlated using the Tammann-Tait equation, yielding low ARDs of 0.09% (ternary system) and 0.03% (quaternary system). Isothermal compressibility and the isobaric thermal expansivity were subsequently derived from the fitted Tammann-Tait equation parameters. Finally, liquid densities were predicted using the original and volume-translated (VT) forms of the SRK and PR EoS. The volume-translated correction significantly improved predictive accuracy, reducing the global ARD from 11.2% (SRK) to 2.1% (SRK-VT) and from 2.0% (PR) to 1.4% (PR-VT).
Optimizing Gas Export Flexibility for Complex Offshore Reservoirs: A Brazilian Case
Oil and gas reservoir management is associated with uncertainties and risks that can significantly impact performance and economic outcomes. The objective of this work is to present how flexibility can be used to manage risk and uncertainty, as well as evaluate the potential flexibility to export and commercialize natural gas as an alternative to water-alternating-gas (WAG) in Brazilian pre-salt fields, identifying favorable and unfavorable scenarios for its implementation. This work presents a case study that addresses the challenges and opportunities of the expected value of the flexibility associated with natural gas export.
The methodology developed presents a structured technique to assess and select optimal strategies under subsurface uncertainties and possible market fluctuations, combining asset portfolio management with reservoir simulation. One of the main advantages of this methodology is that the chance of success is determined through an automated procedure that can be obtained using the production optimization of representative scenarios. Additionally, to illustrate the applicability, we present an application case study to design flexible facilities that allow future expansion for natural gas commercialization, thus capturing possible upsides considering variations in oil and gas selling prices. We also present how these variations impact the overall design to reduce risks and enhance asset value using a simulation model designed to replicate the Brazilian pre-salt fields and forecasting the value of the natural gas in the country.
The results show that this integrated analysis addresses immediate challenges and highlights future advancement potentials through strategic flexibility in Brazil’s natural gas industry, demonstrating that well-planned flexibility can significantly mitigate risks and enhance the resilience of petroleum management strategies. By aligning sustainable petroleum production with CO2 fraction reinjection, we argue that it is more lucrative to produce the natural gas fraction at lower oil prices and that there is a balance point of WAG miscibility to gas price, coupled with enhanced flexibility. We demonstrate how it is possible to increase asset value and mitigate risks, therefore addressing a major concern for stakeholders.
Investigation of Biases Caused by Model-Based Optimization Processes for Reservoir Management
In reservoir management, many decisions are made considering model-based production forecasts and optimization processes. These approaches can generate biases and the actual production and economic return may be overestimated. One of the reasons for these biases is the optimization process itself (procedure bias). Thus, the objective of this work is to investigate biases caused by model-based optimization processes using synthetic benchmark cases, analyzing the magnitude and the impact on future decisions.
We use synthetic benchmarks composed of: (1) an ensemble of data-assimilated simulation models; (2) a subset of this ensemble, named Representative Models (RMs); (3) a reference case, used as the real response of the reservoir (ground truth). Two case studies are analyzed: one focused on design variables (development phase), and the other on control variables (management phase). We demonstrate how specialized and robust strategies (resulting from nominal and robust optimizations, respectively) behave in relation to the ensemble of models and in relation to the reference case, using Net Present Value (NPV) and Expected Monetary Value (EMV) as objective functions.
The results confirm the presence of bias and overestimated forecasts caused by optimization processes. In Case Study 1 (development phase), the robust strategy showed an expected return improvement of 45% due to optimization, while the actual gain was only 6%. Specialized strategies presented differences between expected and actual economic gains ranging from 38% to 179% (with an average of 79%). In Case Study 2 (management phase), the robust strategy yielded a 4.1% expected increase in economic return compared to a 2.5% actual gain, with specialized strategies showing an average overestimation of 38% for the specialized strategies. The bias was stronger in Case Study 1 due to the greater impact of development variables on reservoir performance. Risk curve and boxplot analyses showed that strategies tend to become overly specialized to the model in which they were optimized, may leading to suboptimal decisions when applied to the real field.
By employing synthetic benchmarks with known reference cases, this work quantifies the overestimation introduced by optimization processes, providing valuable insights to help practitioners recognize and account for procedure bias, reducing the risk of overconfident model-based decisions in real-field applications.
Fast Objective Function Estimator Based on Parametric Dynamic Mode Decomposition for Wag-Co2 Injection in Carbonate Reservoirs
Objective/Scope
Fast-objective function estimators (FOFE) are often used to speed up reservoir management. This work presents a FOFE constructed with the parametric Dynamic Mode Decomposition (DMDp) method for a carbonate reservoir with WAG-CO2 injection. The FOFE results are then compared to simulation results to analyze the FOFE’s efficiency.
Method/Procedure/Process
We present an example of how changes in the production strategy can affect reservoir behavior. The FOFE utilizes snapshots of gas and water saturation of numerical simulation runs with different sizes of WAG-CO2 cycles to predict the snapshots and fluid rates of a production strategy with a desired WAG-CO2 cycle size. The FOFE utilizes the DMDp method to calculate the saturation snapshots and material balance equations to calculate oil, water, and gas rates. Unlike the standard where snapshots are stacked up for multiple parameters, leading to increased computational costs, here we perform interpolation directly on the reduced Koopman operator. This leads to enhanced performance as the time eigenvalues are no longer shared between all parameters. The case study is the public access benchmark UNΊSFM-ΓV-2022, a carbonate reservoir model with characteristics of the Brazilian pre-salt. This model represents a developed reservoir with a WAG-CO2 recovery method for a compositional simulator with historical data.
Results/Observations/Conclusions
For this work, the FOFE utilizes snapshots of two reservoir simulations, one with a WAG-CO2 cycle size of 6 months and the other with 18 months, to predict the states of a production strategy with 12 months of WAG-CO2 cycle. The FOFE results of gas, oil, and water are compared to a simulation result with the same production strategy. The comparisons for fluid dynamics are shown for reservoir conditions, and their curves with relative differences are provided. The FOFE can predict the states of a different field scenario, dispensing the necessity of extra numerical simulation runs. This result is promising for production optimization problems which require a significant amount of simulation runs to incorporate the many reservoir uncertainties, as it is observed in highly heterogeneous carbonate reservoirs.
Novel/Additive Information
The innovation of this work is the utilization of the DMDp in a highly heterogeneous reservoir with three-phase flow and WAG-CO2 injection utilizing commercial software. This FOFE can be utilized to reduce the time and computational effort necessary for the decision-making process involving the control variable of WAG-CO2 cycle size.