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We propose a novel approach based on Deep Learning methods using a convolutional neural networks (CNNs) to compare observed four-dimensional (4-D) seismic data with reservoir simulation model results and select the simulation models with the best match. Our approach advantages are twofold: 1) it is not a pixel-based approach, as it learns spatial features through training examples and 2) it does not require the simulation model and 4-D seismic maps to be in the same domain, enabling a direct comparison of maps in the seismic domain with maps in the numerical simulation domain. Additionally, we present a new methodology to quantitatively assess the performance of each method relative to the expected results. For this purpose, we build an annotated dataset containing the maps that best match the 4-D seismic in different realistic scenarios while taking into account the specialists' knowledge. We apply our methodology to evaluate if a method is able to perform according to what specialists expect, considering the annotated data. We also propose an improvement to traditional methods using a statistical method to convert maps of different physical properties into a common property, which can be used as an alternative to avoid forward and/or inversion procedures commonly used to bring 4-D seismic and simulation data to the same domain. Finally, we present an extensive comparison, qualitative and quantitative, of our approaches with other methods in the literature, such as the traditional pixelwise strategy for maps in the same domain, and methods based on binarization of maps in different domains. The results show that our proposed methods are capable of more accurately identifying the best-matched models, according to the specialists' answers.

SummaryHistory matching (HM) is a complex process that aims to increase the reliability of reservoir-simulation models. HM is an inverse problem with multiple solutions that call for probabilistic approaches. When observed data are integrated with sampling methods, uncertainty can be reduced by updating the uncertainty distribution of the reservoir properties. This work presents a practical methodology to systematically reduce uncertainties in a multiobjective assisted HM while dealing with multiple scenarios and assimilating well and 4D-seismic (4DS) data quantitatively. The frequency-distribution update goes through an iterative process. The distribution of the current iteration is combined with the histogram generated using the best-matched simulation scenarios from the current iteration to generate the updated distribution. To evaluate the matching quality, multiple local objective functions (LOFs) are independently evaluated, enabling the identification of LOFs that expose the need for reparameterization. This quantitative process was applied in two phases: Phase 1, in which only well data were used to constrain the scenarios, and Phase 2, when 4DS data were added. The methodology was successfully validated against a synthetic benchmark case of medium complexity, with the production-history data generated at a fine scale (reference model). Each iteration increased the number of matched scenarios, demonstrating good convergence. Most of the reservoir properties had uncertainty reduced gradually while avoiding the premature reduction of the uncertainty range (minimizing convergence to an incorrect solution). Local probabilistic perturbations were conducted on the petrophysical realizations in the regions around the wells that manifested LOFs, which hindered the match. The method efficiently achieved multiple matched simulation scenarios, with all (87) LOFs evaluated within the defined tolerance range. The 4DS data were included regionally with an acceptable increase in computation time. In both phases, the matched simulation scenarios presented production forecasts similar to the reference model. The quantitative assimilation of 4DS data generated scenarios that forecast production with less variability than did scenarios generated without 4DS data. This was expected for this study because the 4DS data provided do not present noise or artifacts.

History matching (HM) is an inverse problem where uncertainties in attributes are reduced by comparison with observed dynamic data. Typically, normalized misfit summarizes dissimilarities between observed and simulation data. Especially for long-time series, objective functions (OFs) aggregate multiple events and tendencies relevant to field performance in a single indicator (e.g. water rate and breakthrough time). To capture the attributes influencing the reservoir behavior, we evaluate the assimilation of data series through additional OFs, obtained from splitting time-series data. In this study, two additional OF groups supplement the time-series misfits: Breakthrough Deviation (BD) indicating dissimilarities in water breakthrough time; Productivity Deviation (PD), representing mismatches of the well potential, mainly impacting the transition from history to forecast conditions. The Productivity Deviation (PD) is adapted from previous studies. Instead of simulating the last time of the historical period under forecast conditions, we propose keeping it under historical data. The change is the historical data used as target condition to the simulator: Bottom Hole Pressure (BHP) in place of liquid production and water injection rates; with this, we estimate a mismatch in well productivity, while avoiding the influence of other boundary conditions in the evaluation. Two applications (1 & 2), assimilating different OF quantities, highlight the influence of the additional groups. Application 1 only computes time-series misfit (64 OFs) whereas Application 2 includes the BD and PD (counting 128 OFs). The iterative HM method presents flexibility regarding OFs assimilated and incorporation of uncertain attributes. UNISIM-I-H case allows us to evaluate the HM considering history and forecast data. We examine differences between the 450 scenarios resulting of data assimilation for each application through four perspectives. Application 2 resulted in scenarios with better predictability of the field behavior and smoother transitions between field history and forecast periods. Field cumulative oil production of Application 2 is also forecasted closer to the reference data when compared to Application 1; all forecast periods (1, 5 and 19 years) emphasize this impact. Some wells presented breakthrough time closer to the reference for Application 2. The challenging achievement of exact BD matches leads to the third advantage of the additional indicators. These OFs supply supplementary information to the diagnosis of scenarios, identifying unnoticed problems in the traditional approach. Finally, even with an overall better performance, some of the well OFs presented poorer matches for Application 2. To explain this, we analyzed the relationship between attributes and the OFs used to update the attributes. In conclusion, the improved forecast of the simulation scenarios indicates that superior performance of the HM process is possible by splitting the available dynamic data in relevant additional OFs. This study presents a case application with 11 years of field history, in which additional OFs, derived from dynamic data, add value to the reservoir characterization. They allow the influence of uncertain attributes to be captured for relevant events in reservoir performance. We also show how the increased quantity of OFs assimilated makes the HM harder for some OFs.

Numerical simulations use past reservoir behavior to calibrate models used to predict future performance. Traditionally, this process is carried out deterministically through history matching and most current approaches focus on developing probabilistic procedures, called data assimilation, whereby reservoir simulation models are calibrated to reproduce plausible performance under different operating conditions. The output of different data-assimilation strategies can over-reduce the variability by having several highly-similar scenarios. Consequently, the need to ensure the variability of simulation models arises, to consider multiple possible solutions. In this vein, we introduce a visual analytics approach, based on phylogenetic trees, as a means to evaluate the variability of numerical reservoir simulation models throughout the probabilistic data assimilation process. Phylogenetic trees arrange simulation results based on similarity and visually convey match quality through color encoding. We applied our methodology to two scenarios: (i) a synthetic scenario to exemplify the properties of the phylogenetic tree for the analysis of simulation models; and (ii) two different ensembles of simulation models, each representing a data-assimilation iteration, from the UNISIM-I-H benchmark case based on the Namorado Field, Campos Basin, Brazil. Our strategy is intuitive and easy-to-use, allowing the user to assess the similarity of the numerical reservoir scenarios, ensemble variability, and match improvement during data assimilation iterations.

Data assimilation is an important and time-consuming process in petroleum reservoir numerical simulation. It produces a set of calibrated models used to forecast and optimize oil and gas production. The process focuses on reducing uncertainties related to reservoir properties, yielding numerical reservoir models that plausibly reproduce measured data from the field, such as well rates and pressure. Besides the traditional well-production data, 4D seismic data are increasingly being used to reduce the uncertainty of numerical reservoir models, by providing dynamic spatial data to be matched. Although 4D seismic data reveal essential information about the dynamic behavior of the reservoir, its integration in data assimilation procedures is challenging, especially in a quantitative way, because of their noisy and uncertain nature and their larger resolution when compared to the resolution of simulated data from numerical reservoir models. The development of metrics able to efficiently estimate the discrepancies between 4D seismic data and numerical reservoir model outputs is a current research interest for data assimilation, given the challenges of integrating these different types of data. We introduce the Momenta Tree. It uses orthogonal moments supporting a multi-level data representation, where features are organized in nodes related to different levels of region detail. It supports the comparison of simulated data from numerical reservoir models and observed 4D images of seismic data, images, using different resolutions and considering various domains. The similarity between data is calculated with the extended Jaccard distance and is represented by a phylogenetic tree; the simulated models are represented as circles in branches, and their similarity is captured by connections. We apply the Momenta Tree to a controlled case, introduced in this paper, to validate and compare the new metric with traditional metrics, and a more complex representative case based on real oil industry data. Our results show that the Momenta Tree metric retains the same sequential similarity in environments affected by noise. The highest-ranked models using the Momenta Tree relate to forecast behavior closer to the reference data than the highest-ranked models obtained with traditional methods. An additional advantage of the Momenta Tree is its ability to enable data comparison in various domains (P-impedance and Water Saturation) at different resolutions of seismic and simulation data.

The current work introduces an automatized process coupled with geological modeling to reduce uncertainty in reservoir properties. The method assimilates dynamic data of wells interactively, and applies the deviations to constrain uncertainties. The methodology deals with scalar (e.g. rock compressibility) and spatial (e.g. porosity) attributes at same time, employing specialized uncertainty reduction procedures. The procedure reduces the uncertainty of scalar attributes through Iterative Discrete Latin HyperCube method (IDLHC). To reduce uncertainties of spatial attributes, we worked on an extension of a regionalized co-simulation (co-DSS) method. The main contributions regard the proposition of update, at same time, both kinds of uncertainties (spatial and scalar); the definition of sequential rules, that simplify the process execution and avoiding subjectivities on the coupling of the geological modeling on data assimilation, as well as the automation of the process. The procedure was validated under a siliciclastic black-oil benchmark field (UNISIM-I-M), established based on Namorado Field, Campos Basin, Brazil. The procedure reduced the range of uncertainty of the scalar attributes, centralizing final PDFs with the values presented in the reference model, without collapse to a particular level, as well as preserved the geological consistency throughout data assimilation, obtaining porosity responses in agreement with the reference porosity distribution. The potential of the procedure is supported by the consistent production forecast observed in the outcomes.

This paper proposes new objective functions to assimilate dynamic data for history matching, and evaluates their influence on the uncertainty conditioning. Representative events are observed and evaluated separately for the available dynamic data. The proposed objective functions evaluate two specific events: (1) the production transition behavior between the historical and forecasting period, and (2) the water breakthrough time. To assess production transition behavior, the deviation between the latest available historical data is compared with the forecast value, at a specific moment, under forecasting conditions. To assess water breakthrough, the irruption time error is measured in addition to the water-rate objective function. The new objective functions are normalized using the Normalized Quadratic Deviation with Sign, for comparison with conventional objective functions (i.e. NQDS-oil production rate). These additional objective functions are included in a probabilistic and multi-objective history matching and applied to the UNISIM-I-M benchmark for validation. Two history-matching procedures evaluate the impact of the additional objective functions, based on the same parameterization, boundary conditions and number of iterations. The first procedure (Procedure A) includes objective functions traditionally used such as fluid rates and bottom-hole pressure, computed using all the historical data points. The second procedure (Procedure B) considers the same as for A as well as the two additional objective functions. The advantages of including the additional objective functions was the supplementary data used to constrain the uncertainties, improving attribute updates. Consequently, Procedure B generated better-matched models considering the historical period and more consistent forecasts for both field and well behavior when compared to available reference data. The addition of the breakthrough deviation improved the quality of the match for water rates because breakthrough deviation is sensitive to reservoir attributes different to those objective functions related to water rate. The production transition error assisted the identification of scenarios that under or overestimated well capacity. Production transition error also improved the transition of the models from the historical to the forecasting period, reducing fluctuations due to the changes in boundary conditions. Despite the increased number of objective functions to be matched, the improved reliability for forecasting is an incentive for further study. Other representative events, such as oil rate before and after the start of water production could be separated and evaluated, for example. The improved reliability for forecasting supports the inclusion of the proposed objective functions in history-matching procedures.

History matching (HM) is a complex process that aims to increase the reliability of reservoir simulation models. HM is an inverse problem with multiple solutions that calls for a probabilistic approach. When observed data are integrated with sampling methods, uncertainty can be reduced by updating the probability density function (pdf) of the attributes. This work presents a practical methodology to systematically reduce uncertainties in a multi-objective probabilistic assisted history matching, integrating well and 4D seismic data (4DS) quantitatively. The pdf update goes through an iterative process. The pdf of the current iteration is combined with the pdf generated using the best-matched models to generate the posterior pdf. The multiple local objective functions (OF) are evaluated independently, allowing the identification of OFs that indicate the requirement of re-parameterization. This quantitative process was applied in two phases: (I) using only well data to constrain the models; (II) adding 4DS data. The methodology was successfully validated against a benchmark case of medium complexity, with the history-production data generated at fine scale (reference model). The proposed methodology reduced uncertainties for the majority of attributes, achieving the highest probable levels similar to those of the reference values. The identification of objective functions that restricts the match allowed improving of the parameterization employed, by locally adding probabilistic perturbations to the petrophysical realizations. The method efficiently achieved multiple matched simulation models, with all (87) local objective functions within the defined tolerance range. Each iteration increased the number of matched models, demonstrating good convergence. The uncertainties were reduced gradually, avoiding premature level elimination (minimizing convergence at an incorrect solution). In both phases, the matched simulation models presented similar production forecasts to the reference model. The 4D seismic data were included regionally with an acceptable increase in computation time. The quantitative incorporation of 4D seismic data generated models that forecasted production with less variability than models generated without 4DS data. This was expected as for this study, 4D seismic data provided perfect information.

Orientadores: Denis José Schiozer, Alessandra Davolio Gomes Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências Resumo: A modelagem numérica de reservatórios petrolíferos envolve muitas incertezas, as quais podem resultar na construção de modelos com previsões de produção distintas das observadas na unidade de produção fazendo com que estes não representem adequadamente a dinâmica de produção do reservatório. Na indústria do petróleo, o procedimento aplicado para reduzir os desvios observados e consequentemente obter modelos que representem adequadamente a dinâmica de produção é conhecido como ajuste de histórico. Devido à relevância do processo de ajuste de histórico, este tem sido exaustivamente estudado e aperfeiçoado, mas ainda apresenta diversos desafios. Com o objetivo de aumentar a robustez do processo, existem três abordagens que tem despertado interesse. A primeira está ligada a aplicação de processos probabilísticos, que possibilitam uma melhor avaliação das incertezas, sendo uma abordagem mais consistente do que a abordagem determinística tradicional. A segunda se refere ao uso de múltiplas funções-objetivo locais para mensurar a qualidade do ajuste; trabalhos recentes demonstram que esta abordagem é mais indicada do que o uso da função-objetivo global tradicional. A terceira refere-se ao uso de outras fontes de dados, como a sísmica 4D, para o melhor condicionamento dos modelos numéricos de simulação. Neste contexto, Maschio et al. (2015) formalizaram uma metodologia que visa incorporar todos estes aspectos, porém com passos ainda subjetivos. Com isso, o presente trabalho propõe uma extensão a esta metodologia com o propósito de sistematizar alguns passos do processo. A principal inovação apresentada está ligada ao processo de redução de incertezas proposto, o qual consiste na atualização dos atributos incertos baseado nos modelos de simulação que apresentaram os melhores ajustes, através de um processo sistemático. Baseado em um reservatório de média complexidade, a metodologia foi validada em duas fases de aplicação. Na Fase I, foi desenvolvido o processo de calibração e redução de incertezas, utilizando somente dados de poço como fonte de dados para o condicionamento dos múltiplos modelos de simulação, enquanto que na Fase II, mapas de variação de pressão (?p) e de saturação de água (?Sw), oriundos da sísmica 4D, foram adicionados de forma quantitativa ao processo. Os resultados obtidos ilustraram a eficácia do processo proposto, o qual possibilitou uma redução acentuada das incertezas obtendo múltiplos modelos de simulação ajustados em um pequeno número de iterações Abstract: The numerical reservoir modelling is surrounded by uncertainties. These can lead to constructing numerical models which present production forecast different from observed production. In the petroleum industry, the procedure applied to reduce the observed differences, and consequently obtain adequate models, is known as history matching. Although this process has been exhaustively studied and improved, diverse challenges still exist. Aiming to improve the process robustness, three approaches have aroused: (1) application of probabilistic procedures that enables to better evaluate uncertainties, a more consistent approach than the traditional deterministic one; (2) the evaluation of multiple local objective functions to measure the quality of the match, more suitable than the traditional global objective function; (3) the additional incorporation of observed data as, for instance 4D seismic, to improve the conditioning of the numeric simulation models. In this context, Maschio et al. (2015) formalized a general methodology that aims to incorporate all these aspects, however, with subjective steps. The current work proposes an extension to this methodology with the target to systematize some of these steps. The main innovation is in the proposed uncertainty reduction process, which consists in updating the uncertain attributes based on the simulation models that presented the best matches. The validation of the proposed methodology is presented in two phases of application in a reservoir of medium complexity. In Phase I, the procedure of calibration and uncertain reduction is developed using only well data to condition the multiple models; while in Phase II, the maps of pressure changes (?p) and water saturation changes (?Sw) from 4D seismic data are integrated in a quantitative way as additional constraints. The obtained results showed the efficiency of the proposed methodology, which provided a clear reduction in the uncertainties, obtaining multiple matched models in less iterations Mestrado Reservatórios e Gestão Mestre em Ciências e Engenharia de Petróleo Brasil/MS

Assisted history matching procedures are usually implemented within an optimization procedure, where the goal is to minimize the object function, which is written in terms of the error between observed and simulated data. One of the problems of the process is that the objective function represented by a single value is not sufficient to express the complexity of the problem. The errors that are normally measured for each well and for all production rates and pressure are converted to a single value; usually the norm of all error vectors. If the problem is well behaved and the objective function quickly converges within a desired tolerance, this would not be a problem, but this is usually not the case for complex history matching processes, since it is very difficult to find a model (or a set of them) that matches with a reasonable tolerance the production profiles for every wells. This work proposes a new approach to deal simultaneously with several objective functions (for instance, well rates and pressure). The methodology follows a probabilistic approach where several simulation models are handled during the entire procedure. The initial step is to generate several simulation models by combining the most important uncertainties of the reservoir. Then, an iterative procedure is performed to iteratively change the reservoir attributes and filter the models that are closer to history data. This procedure encompass a re-characterization step, where the probability of the attributes are updated, global multipliers are applied and local changes are made around problematic wells in order to provide a set of model that yield production and pressure curves with better dispersion compared to history data for every well. The key point of the methodology is that for every iteration the errors of each model, well and objective function can be visualized in a very concise plot that is based on the normalized quadratic error of each curve. The plot clearly shows global and local problems of the set of simulation models, so it is a good indicator of the changes to be made in the next iteration. Another point to highlight is that the same type of iterative procedure is performed to integrate 4D seismic into the process. Thus, after selecting a set of models with a good representation of well history data the same iterative process is repeated to generate a new set of models that match 4D seismic data as well. Thus, the proposed methodology integrates 4D seismic and well history data to reduce uncertainties with a probabilistic approach. To validate the methodology an application is shown where it can be seen the gradual improvement achieved for the models along the iterations.