On-The-Fly History Matching of Simulation Models Using Generative Diffusive Learning (SimGDL)

History matching is an inverse problem in which a geological model needs to be calibrated under uncertainty in order to produce a representative reservoir simulation model. While there are many methods for computer-assisted history matching, most of them require substantial computational power and manifest slow convergence for large-scale simulation models. To tackle these challenges, we propose a new technique for history matching reservoir simulation models using generative diffusive learning (SimGDL) [1]. Our work consisted of several steps based on conditional denoising diffusion probabilistic models. First, we generated several thousands of geologic realizations covering a wide range of spatial subsurface uncertainties. Secondly, we added various amounts of gaussian noise to these realizations and trained a U-Net to predict the added noise based on the corresponding production response. When history matching, a certain amount of noise is added to one of the geologic realizations and then the trained U-Net, guided by the targeted production response, is used to iteratively remove the noise until it converges to a newly generated, dynamically calibrated geologic realization. To test the potential of this new approach, we created a synthetic simulation model. Several thousands of permeability realizations were prepared and used to train the diffusion U-Net. The simulation model combines a single water injector and an oil producer, where oil rate, water cut, and bottom-hole pressure were designated as production responses. Dynamically calibrated permeability realizations were generated by adding noise to some of the existing realizations and then passing them through our diffusion U-Net, conditioned by the selected target production data. The simulated dynamic responses using the generated geologic realizations showed great improvements in matching the target production data. In addition, the posterior realizations were able to retain main feature signatures from the prior distribution and the areas to be updated. Furthermore, the generated models incorporate the quantification of uncertainty, as captured with multiple geologic realizations that were used in training. This paper presents a new method for data-driven dynamic calibration of reservoir simulation models utilizing Generative Diffusive Learning. It incorporates a robust uncertainty quantification using an ensemble of representative subsurface reservoir models. By adding further complexity to conditioning parameters, this innovative method could be further extended and scaled-up to history match simulation models with diverse structural layouts and production profiles.