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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.