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

Well Placement Optimization under Uncertainty with CMA-ES Using the Neighborhood

In the well placement problem, as well as in other field development optimization problems, geological uncertainty is a key source of risk affecting the viability of field development projects. Well placement problems under geological uncertainty are formulated as optimization problems in which the objective function is evaluated using a reservoir simulator on a number of possible geological realizations. In this paper, we present a new approach to handle geological uncertainty for the well placement problem with a reduced number of reservoir simulations. The proposed approach uses already simulated well configurations in the neighborhood of each well configuration for the objective function evaluation. We use thus only one single reservoir simulation performed on a randomly chosen realization together with the neighborhood to estimate the objective function instead of using multiple simulations on multiple realizations. This approach is combined with the stochastic optimizer CMA-ES. The proposed approach is shown on the benchmark reservoir case PUNQ-S3 to be able to capture the geological uncertainty using a smaller number of reservoir simulations. This approach is compared to the reference approach using all the possible realizations for each well configuration, and shown to be able to reduce significantly the number of reservoir simulations (around 80%)

A decision support system for multi-target geosteering

Geosteering is a sequential decision process under uncertainty. The goal of geosteering is to maximize the expected value of the well, which should be defined by an objective value-function for each operation. In this paper we present a real-time decision support system (DSS) for geosteering that aims to approximate the uncertainty in the geological interpretation with an ensemble of geomodel realizations. As the drilling operation progresses, the ensemble Kalman filter is used to sequentially update the realizations using the measurements from real-time logging while drilling. At every decision point a discrete dynamic programming algorithm computes all potential well trajectories for the entire drilling operation and the corresponding value of the well for each realization. Then, the DSS considers all immediate alternatives (continue/steer/stop) and chooses the one that gives the best predicted value across the realizations. This approach works for a variety of objectives and constraints and suggests reproducible decisions under uncertainty. Moreover, it has real-time performance. The system is tested on synthetic cases in a layer-cake geological environment where the target layer should be selected dynamically based on the prior (pre-drill) model and the electromagnetic observations received while drilling. The numerical closed-loop simulation experiments demonstrate the ability of the DSS to perform successful geosteering and landing of a well for different geological configurations of drilling targets. Furthermore, the DSS allows to adjust and re-weight the objectives, making the DSS useful before fully-automated geosteering becomes reality.publishedVersio

Implications of Spatially Variable Costs and Habitat Conversion Risk in Landscape-Scale Conservation Planning

‘‘Strategic habitat conservation’’ refers to a process used by the U.S. Fish and Wildlife Service to develop cost-efficient strategies for conserving wildlife populations and their habitats. Strategic habitat conservation focuses on resolving uncertainties surrounding habitat conservation to meet specific wildlife population objectives (i.e., targets) and developing tools to guide where conservation actions should be focused on the landscape. Although there are examples of using optimization models to highlight where conservation should be delivered, such methods often do not explicitly account for spatial variation in the costs of conservation actions. Furthermore, many planning approaches assume that habitat protection is a preferred option, but they do not assess its value relative to other actions, such as restoration. We developed a case study to assess the implications of accounting for and ignoring spatial variation in conservation costs in optimizing conservation targets. We included assumptions about habitat loss to determine the extent to which protection or restoration would be necessary to meet an established population target. Our case study focused on optimal placement of grassland protection or restoration actions to influence bobolink Dolichonyx oryzivorus populations in the tallgrass prairie ecoregion of the north central United States. Our results show that not accounting for spatially variable costs doubled or tripled the cost of meeting the population target. Furthermore, our results suggest that one should not assume that protecting existing habitat is always a preferred option. Rather, our results show that the balance between protection and restoration can be influenced by a combination of desired targets, assumptions about habitat loss, and the relative cost of the two actions. Our analysis also points out how difficult it may be to reach targets, given the expense to meet them. We suggest that a full accounting of expected costs and benefits will help to guide development of viable management actions and meaningful conservation plans