Multi-scale uncertainty quantification in geostatistical seismic inversion

Geostatistical seismic inversion is commonly used to infer the spatial distribution of the subsurface petro-elastic properties by perturbing the model parameter space through iterative stochastic sequential simulations/co-simulations. The spatial uncertainty of the inferred petro-elastic properties is represented with the updated a posteriori variance from an ensemble of the simulated realizations. Within this setting, the large-scale geological (metaparameters) used to generate the petro-elastic realizations, such as the spatial correlation model and the global a priori distribution of the properties of interest, are assumed to be known and stationary for the entire inversion domain. This assumption leads to underestimation of the uncertainty associated with the inverted models. We propose a practical framework to quantify uncertainty of the large-scale geological parameters in seismic inversion. The framework couples geostatistical seismic inversion with a stochastic adaptive sampling and Bayesian inference of the metaparameters to provide a more accurate and realistic prediction of uncertainty not restricted by heavy assumptions on large-scale geological parameters. The proposed framework is illustrated with both synthetic and real case studies. The results show the ability retrieve more reliable acoustic impedance models with a more adequate uncertainty spread when compared with conventional geostatistical seismic inversion techniques. The proposed approach separately account for geological uncertainty at large-scale (metaparameters) and local scale (trace-by-trace inversion)

Quick Review: Uncertainty of Optimization Techniques in Petroleum Reservoir Management

The notable increase in petroleum demand, together with a decline in discovery rates, has highlighted the desire for efficient production of existing oil wells worldwide. Mainly, the productivity of the existing large oil fields makes us consider the principles of managing reservoirs to make the most of extraction. At the same time, many different uncertainties in the course of the developing oil field, including geological, operational, and economic uncertainties, have a detrimental impact on the reservoir\u27s effective production, which is why dealing with uncertainty is crucial for maximizing output. There is a broad variety of studies on managing oil reservoirs under uncertainty information in the literature. In this study a short review of earlier works has been done on optimization strategies and management of uncertainty in reservoir production

Modelling discrepancy in Bayesian calibration of reservoir models

Simulation models of physical systems such as oil field reservoirs are subject to numerous uncertainties such as observation errors and inaccurate initial and boundary conditions. However, after accounting for these uncertainties, it is usually observed that the mismatch between the simulator output and the observations remains and the model is still inadequate. This incapability of computer models to reproduce the real-life processes is referred to as model inadequacy. This thesis presents a comprehensive framework for modelling discrepancy in the Bayesian calibration and probabilistic forecasting of reservoir models. The framework efficiently implements data-driven approaches to handle uncertainty caused by ignoring the modelling discrepancy in reservoir predictions using two major hierarchical strategies, parametric and non-parametric hierarchical models. The central focus of this thesis is on an appropriate way of modelling discrepancy and the importance of the model selection in controlling overfitting rather than different solutions to different noise models. The thesis employs a model selection code to obtain the best candidate solutions to the form of non-parametric error models. This enables us to, first, interpolate the error in history period and, second, propagate it towards unseen data (i.e. error generalisation). The error models constructed by inferring parameters of selected models can predict the response variable (e.g. oil rate) at any point in input space (e.g. time) with corresponding generalisation uncertainty. In the real field applications, the error models reliably track down the uncertainty regardless of the type of the sampling method and achieve a better model prediction score compared to the models that ignore discrepancy. All the case studies confirm the enhancement of field variables prediction when the discrepancy is modelled. As for the model parameters, hierarchical error models render less global bias concerning the reference case. However, in the considered case studies, the evidence for better prediction of each of the model parameters by error modelling is inconclusive

Impact of Stratigraphic Heterogeneity on Hydrocarbon Recovery in Carbonate Reservoirs: Effects of the Continuity of Cemented Sequence Boundaries

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Developing a workflow to represent fractured carbonate reservoirs for simulation models under uncertainties based on flow unit concept

International audienceDescription of fractured reservoir rock under uncertainties in a 3D model and integration with reservoir simulation is still a challenging topic. In particular, mapping the potential zones with a reservoir quality can be very useful for making decisions and support development planning. This mapping can be done through the concept of flow units. In this paper, an integrated approach including a Hierarchical Cluster Analysis (HCA), geostatistical modeling and uncertainty analysis is developed and applied to a fractured carbonate in order to integrate on numerical simulation. The workflow begins with different HCA methods, performed to well-logs in three wells, to identify flow units and rock types. Geostatistical techniques are then applied to extend the flow units, petrophysical properties and fractures into the inter-well area. Finally, uncertainty analysis is applied to combine different types of uncertainties for generating ensemble reservoir simulation models. The obtained clusters from different HCA methods are evaluated by the cophenetic coefficient, correlation coefficient, and variation coefficient, and the most appropriate clustering method is used to identify flow units for geostatistical modeling. We subsequently define uncertainties for static and dynamic properties such as permeability, porosity, net-to-gross, fracture, water-relative permeability, fluid properties, and rock compressibility. Discretized Latin Hypercube with Geostatistical (DLHG) method is applied to combine the defined uncertainties and create an ensemble of 200 simulation models which can span the uncertainty space. Eventually, a base production strategy is defined under operational conditions to check the consistency and reliability of the models created with UNISIM-II-R (reference model) as a real reservoir with known results. Results represent the compatibility of the methodology to characterize fractured reservoirs since those models are consistent with the reference model (used to generate the simulation models). The proposed workflow provides an efficient and useful means of supporting development planning under uncertainty

Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario

A variety of methods is available to quantify uncertainties arising with\-in the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods' advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond

Understanding the Impact of Open-Framework Conglomerates on Water-Oil Displacements: Victor Interval of the Ivishak Reservoir, Prudhoe Bay Field, Alaska

The Victor Unit of the Ivishak Formation in the Prudhoe Bay Oilfield is characterized by high net-to-gross fluvial sandstones and conglomerates. The highest permeability is found within sets of cross-strata of open-framework conglomerate (OFC). They are preserved within unit bar deposits and assemblages of unit bar deposits within compound (braid) bar deposits. They are thief zones limiting enhanced oil recovery. We incorporate recent research that has quantified important attributes of their sedimentary architecture within preserved deposits. We use high-resolution models to demonstrate the fundamental aspects of their control on oil production rate, water breakthrough time, and spatial and temporal distribution of residual oil saturation. We found that when the pressure gradient is oriented perpendicular to the paleoflow direction, the total oil production and the water breakthrough time are larger, and remaining oil saturation is smaller, than when it is oriented parallel to paleoflow. The pressure difference between production and injection wells does not affect sweep efficiency, although the spatial distribution of oil remaining in the reservoir critically depends on this value. Oil sweep efficiency decreases slightly with increase in the proportion of OFC cross-strata. Whether or not clusters of connected OFC span the domain does not visibly affect sweep efficiency.Comment: 27 pages including 14 figure

Population-based algorithms for improved history matching and uncertainty quantification of Petroleum reservoirs

In modern field management practices, there are two important steps that shed light on a multimillion dollar investment. The first step is history matching where the simulation model is calibrated to reproduce the historical observations from the field. In this inverse problem, different geological and petrophysical properties may provide equally good history matches. Such diverse models are likely to show different production behaviors in future. This ties the history matching with the second step, uncertainty quantification of predictions. Multiple history matched models are essential for a realistic uncertainty estimate of the future field behavior. These two steps facilitate decision making and have a direct impact on technical and financial performance of oil and gas companies. Population-based optimization algorithms have been recently enjoyed growing popularity for solving engineering problems. Population-based systems work with a group of individuals that cooperate and communicate to accomplish a task that is normally beyond the capabilities of each individual. These individuals are deployed with the aim to solve the problem with maximum efficiency. This thesis introduces the application of two novel population-based algorithms for history matching and uncertainty quantification of petroleum reservoir models. Ant colony optimization and differential evolution algorithms are used to search the space of parameters to find multiple history matched models and, using a Bayesian framework, the posterior probability of the models are evaluated for prediction of reservoir performance. It is demonstrated that by bringing latest developments in computer science such as ant colony, differential evolution and multiobjective optimization, we can improve the history matching and uncertainty quantification frameworks. This thesis provides insights into performance of these algorithms in history matching and prediction and develops an understanding of their tuning parameters. The research also brings a comparative study of these methods with a benchmark technique called Neighbourhood Algorithms. This comparison reveals the superiority of the proposed methodologies in various areas such as computational efficiency and match quality

An application of AHP and fuzzy entropy-TOPSIS methods to optimize upstream petroleum investment in representative African basins.

The growing demand of China for petroleum heightens the complexities and prospects in worldwide investments, necessitating refined and strategic investment approaches. Evaluating the potential of different hydrocarbon-potential areas needs more comprehensive scientific evaluation models. This study aims to establish a Comprehensive Investment Potential of Petroleum (CIPP) framework for targeted sedimentary basins by using an integrated approach that combines the Analytic Hierarchy Process (AHP) and the Entropy-Weighted Fuzzy TOPSIS models. We focus particularly on representative African basins to inform strategic decision-making for the Chinese overseas petroleum enterprises. We firstly interpret the geological condition of these petroleum basins by researching multiple databases and proprietary research data. Then, we use a combined approach of ranking-classification-correlation analysis to evaluate 17 representative basins, taking into account both overall and individual key performance indicators. Our findings suggest the Illizi Basin and the Offshore Côte d'Ivoire Basin could be the most favorable for investment and development. Those like Southwest African Basin warrant cautious consideration. The new evaluation model and computational workflow offer an effective workflow for assessing multiple petroleum basins. This work provides not just practical investment strategies for companies aiming for African petroleum basins, but also a transferable methodology for optimizing investment decisions. [Abstract copyright: © 2024. The Author(s).