Adjoint method acceleration protocols for model maturation to update static models with time-lapse reservoir surveillance data

We develop an ensemble model-maturation method that is based on the Randomized Maximum Likelihood (RML) technique and adjoint-based computation of objective function gradients. The new approach is especially relevant for rich data sets with time-lapse information content. The inversion method that solves the model-maturation problem takes advantage of the adjoint-based computation of objective function gradients for a very large number of model parameters at the cost of a forward and a backward (adjoint) simulation. The inversion algorithm calibrates model parameters to arbitrary types of production data including time-lapse reservoir-pressure traces by use of a weighted and regularized objective function. We have also developed a new and effective multigrid preconditioning protocol for accelerated iterative linear solutions of the adjoint-simulation step for models with multiple levels of local grid refinement. The protocol is based on a geometric multigrid (GMG) preconditioning technique. Within the model-maturation workflow, a deep-learning technique is applied to establish links between the mesh-based inversion results (e.g., permeability-multiplier fields) and geologic modeling parameters inside a static model (e.g., object dimensions, etc.). Our workflow integrates the learnings from inversion back into the static model, and thereby, ensures the geologic consistency of the static model while improving the quality of the ensuing dynamic model in terms of honoring production and time-lapse data, and reducing forecast uncertainty. This use of deep learning (DL) to post-process the model-maturation outcome effectively converts the conventional continuous-parameter history-matching result into a discrete tomographic inversion result constrained to geological rules encoded in training images.