... initial condition permeability field algorithm loss function equation machine learning partial differential equation deep learning resolution iteration saturation architecture Introduction Earth systems predictions largely rely upon the modeling of complex fluid dynamics in the porous...

... flow architecture permeability field society of petroleum engineers reduced-order model multiphase flow dynamic Introduction Reservoir management is a complex process to be performed given the multidisciplinary nature of all of the steps involved in combining proper reservoir modeling...

... and the liquid phase pressure. The algorithm is sequential and controls the nonlinearity with a subiteration scheme. Robustness of the method is shown on reservoirs with different heterogeneities: random permeability field, reservoir with barriers and layered reservoir. The algorithm easily handles phase...

... Modeling & Simulation Fluid Dynamics locality algorithm complexity reservoir simulation conservative estimate vector saturation Solution Method permeability Newton iteration Newton update residual vector equation permeability field Introduction Implicit methods are a main staple...

... Implementation solver scaling method solution stage multigrid algorithm scalability Multigrid solver convergence history gpu architecture setup stage bbmg permeability field architecture Upstream Oil & Gas multi-core architecture multi-gpu architecture gmres-accelerated cycling operator...

.... Building on the work of Afra and Gildin (2013) ; Afra et.al. (2014) ; Afra and Gildin (2016) , permeability fields of multiple model realizations are collected in a tensor form which is subsequently decomposed to derive a low-dimensional representation of the dominant spatial structures in the models...

... numbers of components and highly heterogeneous permeability fields. The K-value based coarse-scale operator produces results that are in good agreement with the fine-scale solutions for the quantities of interest, including the component overall compositions and saturation distributions. scaling...

... space finite element space upscaled system equation finite element discretization construction society of petroleum engineers amge preconditioner permeability field Upstream Oil & Gas upscaled problem freedom solver preconditioner computational cost Introduction Numerical...

... than EnKF. However, if ES-MDA (or EnKF) is applied to update the rock-property fields where the underlying geological model is a facies model, then the boundaries between facies are not preserved. Here, we couple an ES-MDA update of the permeability field with an update of the distribution of facies...

... estimation permeability field permeability input-output relation Introduction Estimating reservoir parameters from measured data is an ill-posed inverse problem due to the large number of parameters and the limited available data ( Shah et al., 1978 ; Oliver et al., 2008 ). Consequently...

... polynomial chaos proxy random variable permeability field expansion algorithm Introduction History matching and uncertainty quantification is an indispensible element of closed-loop reservoir modelling and management. It entails the adjustment of unknown reservoir properties, such as permeability...

... reservoir simulation finite-volume method neighborhood permeability field gradient ml scheme grid equation peclet number viscous flux permeability tensor Introduction Many industrial applications in the area of chemical, geothermal, petroleum and metallurgical engineering require...

... geostatistics. The procedure is demonstrated on two examples, one with a multi-Gaussian permeability field, one with a channel sand, and is shown to prevent ensemble collapse while also honoring geostatistical properties much better compared to the standard EnKF/EnS. Reservoir Characterization Upstream...

... permeability field OMP algorithm Artificial Intelligence different ensemble size sparse calibration algorithm ensemble size orthogonal matrix equation Introduction Subsurface flow models relies on many parameters that cannot be measured directly. Instead, a sparse set of measurements may exist...

...) provides a highly attractive technique for history matching production data. In this work, we apply EnKF with a recently proposed method of covariance localization to history-match production data from a real field to generate multiple realizations of the permeability field. A single manually history...

... function principal component production data reduction spe 141913 parameter estimation principal component analysis permeability field avo gradient permeability Introduction Because of geological uncertainties, reservoir models are usually only very crude approximations of the reality...

... Abstract We present a method for history matching and uncertainty quantification for channelized reservoir models using Level Set Method and Markov Chain Monte Carlo. Our objective is to efficiently sample realizations of the channelized permeability fields conditioned to the production data...

... Abstract We present the development and field application of a workflow for multiscale reservoir model calibration that seamlessly integrates production data into reservoir description from the facies to the grid-cell scale. To start with, the permeability field is parameterized using a novel...

... Abstract In this work, an approach for estimating non-Gaussian permeability field is developed, through a probabilistic collocation based Kalman filter (PCKF). In this approach, the polynomial chaos expansion is used to parameterize the non-Gaussian permeability field. The state variables...

... matching prediction procedure ensemble markov chain water production reynolds relative freq permeability field cumulative freq model parameter enkf covariance localization probability localization vector algorithm matrix posterior pdf Introduction In a reservoir simulation study...