We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical mod- els contain uncertain parameters because of geological uncertainties. In that case, ‘robust optimization’ is performed by optimizing the expected value of the objective function over an ensemble of geological mod- els. In earlier publications, based on the pioneering work of Chen et al. (2009), it has been suggested that a straightforward one-to-one combination of random control vectors and random geological models is capa- ble of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca et al. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as ‘modified robust EnOpt’) and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoreti- cal arguments to show why StoSAG is superior to EnOpt @en

Conflicting objectives are frequently encountered in most real-world problems. When dealing with conflicting objectives, decision makers prefer to obtain a range of possible optimal solutions from which to choose. In theory, methods exists that can produce a range of possible solutions, some of which are “Pareto Optimal”. The application of these methods to solve bi-objective production optimization problems is increasing. A recent paper introduced a method to find points on the boundary of the objective function space by solving a constrained optimization problem using adjoint gradients. In this work, we investigate the applicability of using ensemble optimization (EnOpt) (which relies on approximate ensemble gradients instead of exact adjoint-based gradients) to generate points along a “Pareto” front with acceptable computational effort.. Moreover, we investigate the applicability of this approximate gradient technique to solve constrained optimization problems using the augmented Lagrangian method. Finally, we compare the performance of this bi-objective optimization method to a traditional weighted sum method for bi-objective water flooding optimization of two different synthetic reservoir models. The two objectives used in this work are, undiscounted (0%) net present value (NPV), representing long-term targets and highly discounted (25%) NPV, representing short-term operational targets. The controls are inflow control valve (ICV) settings over time for one model and water injection rate controls for the other. The effect of different starting points and the computational efficiency of the constrained optimization method are also investigated.@en

The binary neutron star merger event GW170817 was detected through both electromagnetic radiation and gravitational waves. Its afterglow emission may have been produced by either a narrow relativistic jet or an isotropic outflow. High-spatial-resolution measurements of the source size and displacement can discriminate between these scenarios. We present very-long-baseline interferometry observations, performed 207.4 days after the merger by using a global network of 32 radio telescopes. The apparent source size is constrained to be smaller than 2.5 milli-arc seconds at the 90% confidence level. This excludes the isotropic outflow scenario, which would have produced a larger apparent size, indicating that GW170817 produced a structured relativistic jet. Our rate calculations show that at least 10% of neutron star mergers produce such a jet.@en

The binary neutron star merger event GW170817 was detected through both electromagnetic radiation and gravitational waves. Its afterglow emission may have been produced by either a narrow relativistic jet or an isotropic outflow. High-spatial-resolution measurements of the source size and displacement can discriminate between these scenarios. We present very-long-baseline interferometry observations, performed 207.4 days after the merger by using a global network of 32 radio telescopes. The apparent source size is constrained to be smaller than 2.5 milli-arc seconds at the 90% confidence level. This excludes the isotropic outflow scenario, which would have produced a larger apparent size, indicating that GW170817 produced a structured relativistic jet. Our rate calculations show that at least 10% of neutron star mergers produce such a jet.@en

The binary neutron star merger event GW170817 was detected through both electromagnetic radiation and gravitational waves. Its afterglow emission may have been produced by either a narrow relativistic jet or an isotropic outflow. High-spatial-resolution measurements of the source size and displacement can discriminate between these scenarios. We present very-long-baseline interferometry observations, performed 207.4 days after the merger by using a global network of 32 radio telescopes. The apparent source size is constrained to be smaller than 2.5 milli-arc seconds at the 90% confidence level. This excludes the isotropic outflow scenario, which would have produced a larger apparent size, indicating that GW170817 produced a structured relativistic jet. Our rate calculations show that at least 10% of neutron star mergers produce such a jet.@en

The binary neutron star merger event GW170817 was detected through both electromagnetic radiation and gravitational waves. Its afterglow emission may have been produced by either a narrow relativistic jet or an isotropic outflow. High-spatial-resolution measurements of the source size and displacement can discriminate between these scenarios. We present very-long-baseline interferometry observations, performed 207.4 days after the merger by using a global network of 32 radio telescopes. The apparent source size is constrained to be smaller than 2.5 milli-arc seconds at the 90% confidence level. This excludes the isotropic outflow scenario, which would have produced a larger apparent size, indicating that GW170817 produced a structured relativistic jet. Our rate calculations show that at least 10% of neutron star mergers produce such a jet.@en

The binary neutron star merger event GW170817 was detected through both electromagnetic radiation and gravitational waves. Its afterglow emission may have been produced by either a narrow relativistic jet or an isotropic outflow. High-spatial-resolution measurements of the source size and displacement can discriminate between these scenarios. We present very-long-baseline interferometry observations, performed 207.4 days after the merger by using a global network of 32 radio telescopes. The apparent source size is constrained to be smaller than 2.5 milli-arc seconds at the 90% confidence level. This excludes the isotropic outflow scenario, which would have produced a larger apparent size, indicating that GW170817 produced a structured relativistic jet. Our rate calculations show that at least 10% of neutron star mergers produce such a jet.@en