GANSim-surrogate: An integrated framework for stochastic conditional geomodelling

Stochastic conditional geomodelling requires effective integration of geological patterns and various types of data, which is crucial but challenging. To address this, we propose a deep-learning framework (GANSim-surrogate) for conditioning geomodels to static well facies data, facies probability maps, and non-spatial global features, as well as dynamic time-dependent pressure or flow rate data observed at wells. The framework consists of a Convolutional Neural Network (CNN) generator trained from GANSim (a Generative Adversarial Network-based geomodelling simulation approach), a CNN-based surrogate, and options for searching appropriate input latent vectors for the generator. The four search methods investigated are Markov Chain Monte Carlo, Iterative Ensemble Smoother, gradient descent, and gradual deformation. The framework is validated with channelized reservoirs. First, a generator is trained using GANSim to generate geological facies models; in addition, a flow simulation surrogate is trained using a physics-informed approach. Then, given well facies data, facies probability maps, global facies proportions, and dynamic bottomhole pressure data (BHP), the trained generator takes the first three static conditioning data and a latent vector as inputs and produces a random realistic facies model conditioned to the three static data. To condition to the dynamic data, the produced facies model is converted to permeability property and mapped to BHP data by the trained surrogate. Finally, the mismatch between the surrogate-produced and the observed BHP data is minimized to obtain appropriate input latent vectors which are further mapped into appropriate facies models through the generator. These facies models prove to be realistic and consistent with all of the conditioning data, and the framework is computationally efficient.