Chevron U.s.a. Inc.

Wen Hsiung Chen

Pallav Sarma

John R Wallis

Alexandre Castellini

Choongyong Han

Xian-Huan Wen

Yifan Zhou

Gary K Li

Mark Schrader

Herve Gross

Jincong He

A method, system and processor readable medium containing computer readable software instructions for selecting representative models from a large ensemble of models is disclosed. An ensemble of reservoir models that define an input uncertainty space is provided. A target number of representative models and one or more target percentiles of output variables that the representative models are to approximate are input. The representative models from the ensemble of reservoir models that match the one or more target percentiles of output variables are selected while maximizing the spread between the selected representative models in the input uncertainty space.

Model selection from a large ensemble of models

A computer-implemented method, system, and computer program product are disclosed for updating simulation models of a subterranean reservoir. An ensemble of reservoir models representing a subterranean reservoir having non-Gaussian characteristics is provided and the ensemble of reservoir models is updated using a subspace ensemble Kalman filter. Kemal principle component analysis parameterization or K-L expansion parameterization can be used to update the ensemble of reservoir models.

System and method for use in simulating a subterranean reservoir

A computer-implemented reservoir prediction system, method, and software are provided for updating simulation models of a subterranean reservoir. An ensemble of reservoir models representing a subterranean reservoir having non-Gaussian characteristics is provided, along with reservoir data from the subterranean reservoir used to condition the ensemble of reservoir models. For each of the reservoir models in the ensemble of reservoir models, a constrained optimization with equality constraints and inequality constraints are solved using a constrained Kernel Ensemble Kalman Filter to obtain a constrained optimal solution. The constrained optimal solutions are assembled to update the ensemble of reservoir models. The updated ensemble of reservoir models are consistent with the reservoir data provided from the subterranean reservoir and the non-Gaussian characteristics of the subterranean reservoir are preserved.

System and method for modeling a subterranean reservoir

A reservoir prediction system is disclosed that uses a kernel-based ensemble Kalman filter (EnKF) capable of representing non-Gaussian random fields characterized by multi-point geostatistics. The EnKF uses only the covariance and cross-covariance between the random fields (to be updated) and observations, thereby only preserving two-point statistics. The kernel-based EnKF allows the creation of nonlinear generalizations of linear algorithms that can be exclusively written in terms of dot products. By deriving the EnKF in a high-dimensional feature space implicitly defined using kernels, both the Kalman gain and update equations are nonlinearized, thus providing a completely general nonlinear set of EnKF equations, the nonlinearity being controlled by the kernel. By choosing high order polynomial kernels, multi-point statistics and therefore geological realism of the updated random fields can be preserved.

System and method for predicting fluid flow in subterranean reservoirs

A method, system and computer program product is disclosed for utilizing proxy models to evaluate a subterranean reservoir. The method includes constructing a proxy model from a set of sampling points to approximate simulation outputs of a reservoir model. The set of sampling points is updated by adding at least one new sampling point that is selected from a location associated with surface non-linearities such as gradients, curvature, and bending energy. Response surface values at new sampling points and distances to existing sampling points can also be used to evaluate new sampling points. Proxy models are refined with the updated set of sampling points until the proxy model satisfies a predetermined stopping criterion, such as when a predetermined number of iterations are reached or when changes to the response surface are below a predetermined threshold.

Iterative method and system to construct robust proxy models for reservoir simulation

A method, system and computer program product is disclosed for using a constrained pressure residual (CPR) preconditioner to solve adjoint models. A linear system of fluid flow equations comprising a plurality of variables that represent fluid flow properties in a geological formation of a subterranean reservoir is provided. Matrix (&#xc3;), which comprises a transpose of a Jacobian matrix associated with the linear system of fluid flow equations, is constructed. A constrained pressure residual preconditioner Mis constructed responsive to the matrix (&#xc3;). Matrix equation (&#xc3;)y=d is then solved using the constrained pressure residual preconditioner M.

Constrained pressure residual preconditioner for efficient solution of the adjoint equation

The disclosed methods, systems, and software are described for optimizing well placement in a reservoir field. A geological model of a reservoir field, a grid defining a plurality of cells, one or more wells to be located within the plurality of cells, and an objective function are all provided. The geological model is associated with the grid defining the plurality of cells. The locations of the wells are represented by continuous well location variables associated with a continuous spatial domain. A gradient of the objective function is calculated responsive to the continuous well location variables. The locations of the wells are then adjusted responsive to the calculated gradient of the objective function. Iterative calculation of the gradient and adjustment of the wells continue until the well locations are optimized. A visual representation of the reservoir field can be generated based on the optimized well placements.

System and method for efficient well placement optimization

A method, system and apparatus for real-time reservoir model updating using ensemble Kalman filters is described. The method includes a conforming step for bring bringing static and dynamic state variables into conformance with one another during a time step of the updating. Also, an iterative damping method is used in conjunction with the conformance step to account for nonGaussian and nonlinear features in a system. Also, a re-sampling method is described which reduces the ensemble size of reservoir models which are to be updated.

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Danville, CA, United States of America

Wen Hsiung Chen