In this paper, Shell's in-house reservoir simulator MoReS is applied to a recently introduced CO 2 sequestration benchmark problem entitled "Estimation of the CO 2 Storage Capacity of a Geological Formation" (Class et al. 2008). The principal objective of this benchmark is the simulation of CO 2 distribution within a modeling region, and leakage of CO 2 outside of it, for a period of 50 years. This study goes beyond the benchmarking exercise to investigate additional factors with direct relevance to CO 2 storage capacity estimations: water and gas relative permeabilities, permeability anisotropy, presence of sub-seismic features (conductive fractures, thin shale layers), regional hydrodynamic gradient, CO 2 -enriched brine convection (due to brine density differences), and injection rates. The effects of hydrodynamic gradients and gravitationally induced convection only become significant over 100 s of years. This study has thus extended simulation time to 1,000 years. It is shown that grid resolution significantly impacts results. Vertical-grid refinement results in larger and thinner CO 2 plumes. Lateral-grid refinement delays leakage out of the model domain and reduces injection pressure for a given injection rate. Sub-seismic geological features such as fractures/faults and shale layers are demonstrated to have impact on

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The ability to accurately simulate and optimize fully integrated oil and gas fields is of critical importance in the development and operation of an asset. To this end, a novel and comprehensive framework for simulating fields comprised of connected reservoirs, wells, and production facilities is presented. Individual field components may be connected to each other through physical equipment such as pipes, and operations may be subject to field-wide constraints, such as limits on total production of green house gases. The proposed framework allows for simulation of the evolution of such a field, optimization of the field under various constraint choices, and planning and scheduling of the entire field operations. The framework is founded on representing each component using appropriate sets of Models, Equations and Variables (MEV) combined with a common Physical Property Manager that ensures a consistent calculation methodology, and uses grid-level partitioning to support parallelism. The MEV system operates in concert with customized nonlinear and linear equation solvers to generate updated values for variables in all the different sub-systems, regardless of their originating component. Optimizers in the system manipulate the same variables employed in the MEV solution process to assemble objective functions, act on decision variables, and satisfy constraints. These variables may also be parameterized to support uncertainty analysis or design possibilities. The componentized nature of the equation set allows the ability to plug in alternate custom technologies to replace or augment capabilities. The framework supports multiple fidelities for modelling the components, and enables the use of different coupling styles between them. Choices range from using simple proxy models for certain components, to explicit one- and two-way coupling of more rigorous models, up to solving a fully coupled, detailed field representation. It will be demonstrated that this approach allows for efficient simulation of the combined systems under different constraints.

The limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method performs very efficiently for large-scale problems. A trust region search method generally performs more efficiently and robustly than a line search method, especially when the gradient of the objective function cannot be accurately evaluated. The computational cost of an L-BFGS trust region subproblem (TRS) solver depend mainly on the number of unknown variables (n) and the number of variable shift vectors and gradient change vectors (m) used for Hessian updating, with m << n for large-scale problems. In this paper, we analyze the performances of different methods to solve the L-BFGS TRS. The first method is the direct method using the Newton-Raphson (DNR) method and Cholesky factorization of a dense n × n matrix, the second one is the direct method based on an inverse quadratic (DIQ) interpolation, and the third one is a new method that combines the matrix inversion lemma (MIL) with an approach to update associated matrices and vectors. The MIL approach is applied to reduce the dimension of the original problem with n variables to a new problem with m variables. Instead of directly using expensive matrix-matrix and matrix-vector multiplications to solve the L-BFGS TRS, a more efficient approach is employed to update matrices and vectors iteratively. The L-BFGS TRS solver using the MIL method performs more efficiently than using the DNR method or DIQ method. Testing on a representative suite of problems indicates that the new method can converge to optimal solutions comparable to those obtained using the DNR or DIQ method. Its computational cost represents only a modest overhead over the well-known L-BFGS line-search method but delivers improved stability in the presence of inaccurate gradients. When compared to the solver using the DNR or DIQ method, the new TRS solver can reduce computational cost by a factor proportional to n2/m for large-scale problems.

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