Abstract: Systems, methods, and computer-readable media for determining the production rate of oil produced from each of a plurality of oil-bearing geological layers in an oil field. In some embodiments, the method comprises allocating injected fluid into each layer of a plurality of oil-bearing geological layers to a plurality of paths from injection sites of injection wells to production wells in each layer by balancing the mass of fluid injected into and the total fluid recovered from each oil-bearing geological layer. In some embodiments, the method comprises calculating estimated geological properties for each path in the plurality of paths to match total oil and injection fluid recovered at each production well in the plurality of production wells. In some embodiments, the method comprises using the estimated geological properties, calculating an oil production rate for each path between an injector well and a production well in a geological layer.

Abstract: Systems, methods, and computer-readable media for determining the production rate of oil produced from each of a plurality of oil-bearing geological layers in an oil field. In some embodiments, the method comprises allocating injected fluid into each layer of a plurality of oil-bearing geological layers to a plurality of paths from injection sites of injection wells to production wells in each layer by balancing the mass of fluid injected into and the total fluid recovered from each oil-bearing geological layer. In some embodiments, the method comprises calculating estimated geological properties for each path in the plurality of paths to match total oil and injection fluid recovered at each production well in the plurality of production wells. In some embodiments, the method comprises using the estimated geological properties, calculating an oil production rate for each path between an injector well and a production well in a geological layer.

Abstract: A system and method for characterizing subsurface hydrocarbon reservoirs, such as through fault modeling in low order continuous scale simulation of real world subsurface hydrocarbon reservoirs having discontinuities and improving an accuracy and speed of the characterizations.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: A computer-implemented reservoir prediction system, method, and software are provided for quantifying uncertainty and evaluating production performance of a subterranean reservoir. A reservoir simulation model representing a subterranean reservoir and an associated distribution of input variables are provided. A plurality of polynomial chaos expansions is generated. Each polynomial chaos expansion is used to approximate a simulation output of the reservoir simulation model for the distribution of input variables. Deterministic coefficients of the polynomial chaos expansions are calculated using a sampling process, such as a quasi-Monte Carlo method using a low discrepancy sequence. An output variable, such as cumulative oil production, and associated output variable uncertainty are forecasted using the polynomial chaos expansions and the deterministic coefficients such that production performance of the subterranean reservoir can be evaluated.

Abstract: 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 (Ã)T, which comprises a transpose of a Jacobian matrix associated with the linear system of fluid flow equations, is constructed. A constrained pressure residual preconditioner MCPRA?1 is constructed responsive to the matrix (Ã)T. Matrix equation (Ã)Ty=d is then solved using the constrained pressure residual preconditioner MCPRA?1.

Abstract: 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.

Abstract: 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.

Abstract: A computer-implemented reservoir prediction system, method, and software are provided for quantifying uncertainty and evaluating production performance of a subterranean reservoir. A reservoir simulation model representing a subterranean reservoir and an associated distribution of input variables are provided. A plurality of polynomial chaos expansions is generated. Each polynomial chaos expansion is used to approximate a simulation output of the reservoir simulation model for the distribution of input variables. Deterministic coefficients of the polynomial chaos expansions are calculated using a sampling process, such as a quasi-Monte Carlo method using a low discrepancy sequence. An output variable, such as cumulative oil production, and associated output variable uncertainty are forecasted using the polynomial chaos expansions and the deterministic coefficients such that production performance of the subterranean reservoir can be evaluated.

Abstract: 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.

Abstract: 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 (Ã)T, which comprises a transpose of a Jacobian matrix associated with the linear system of fluid flow equations, is constructed. A constrained pressure residual preconditioner MCPRA?1 is constructed responsive to the matrix (Ã)T. Matrix equation (Ã)Ty=d is then solved using the constrained pressure residual preconditioner MCPRA?1.

Abstract: 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.

Abstract: A reservoir prediction system and method are provided that use generalized EnKF using kernels, capable of representing non-Gaussian random fields characterized by multi-point geostatistics. The main drawback of the standard EnKF is that the Kalman update essentially results in a linear combination of the forecasted ensemble, and the EnKF only uses the covariance and cross-covariance between the random fields (to be updated) and observations, thereby only preserving two-point statistics. Kernel methods allow 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.

Abstract: 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.