In reservoir engineering, history matching and calibration process yields nonunique plausible outcomes due to the inherited uncertainty of earth models. The process is carried on with the ultimate objectives of providing reliable predictive reservoir models with the highest possible quality at minimal computational overhead. This work capitalizes on the development of a tightly-coupled Surrogate AI model with Ensemble Iterative algorithm (Alturki et. al, 2024) to devise the relationships of uncertainty variables and physics model's responses with minimal full-physics simulations of the reservoir model.
Surrogate AI models are supervised machine learning models that are driven by physical model responses to the changes in uncertainty variables. They are widely used methods in different engineering disciplines when the outcomes are hard to be quantified, measured or computational expensive to carry on using full physics models. Models’ calibration and history matching process involves dealing with large volumes of data, exploring vast solution space, and quantification of uncertainty in modeling. Coupling of Surrogate AI models with the power of Ensemble iterative methods allows for proper quantification of uncertainties with much less computational requirements and minimal full-physics simulation runs. In this work, modified NORNE and BRUGGE benchmark models were used to demonstrate the efficiency of the developed hybrid model to the traditionally compute-intensive and time-consuming history matching process. An initial equally probable ensemble size of 50 and 60 for NORNE and BRUGGE models, respectively, were generated to capture the influential uncertain reservoir properties (e.g., permeability tensor, transmissibility tensor, etc.).
The efficiency of the tightly coupled Surrogate AI and Ensemble Iterative optimization algorithm is demonstrated by carrying on history matching on the modified NORNE and BRUGGE benchmark models. The objective function consists of a set of vectors (i.e., responses) as a result to the perturbations of the uncertainty variables (i.e., reservoir properties). The hybrid model starts with running the full-physics simulation runs for all the ensembles. The Surrogate AI model then, iteratively, evaluates the misfit and computes the responses as a result of updating uncertain reservoir parameters in searching for minima in the solution space to satisfy the minimization objective function. Once convergence is reached, full-physics simulations are run once for the ensembles to validate the updates. The results show faster convergence rate in just few iterations of the Surrogate AI model without the need for the intermediate full-physics simulation runs. This translates to eliminating about 60% of the full-physics simulation run that would normally be required by an iteration Ensemble algorithm. In addition, it is observed that the Surrogate AI convergence rate and solution quality is directly proportional to the representation of the uncertainty by the initial ensemble. As a sanity check, the history matched ensembles were run in prediction with full-physics simulation with "No Further Action" scenario to evaluate the models‘ predictive capabilities and ensure that uncertainty is well-represented in prediction.
Hybrid tightly-coupled Surrogate AI model with the iterative Ensemble algorithm, drastically, reduced the number of needed full-physics simulations. That is with a faster convergence rate, remarkable computational, good quality history match. The cumulative oil production from the prediction runs indicate splendid quantification of uncertainty, measure of history match quality, and predictive capabilities.
