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The calibration of a reservoir model with observed transient data of fluidpressures and rates is a key task in obtaining a predictive model of the flowand transport behaviour of the earth's subsurface. The model calibration task,commonly referred to as "history matching", can be formalised as an ill-posedinverse problem where we aim to find the underlying spatial distribution ofpetrophysical properties that explain the observed dynamic data. We use agenerative adversarial network pretrained on geostatistical object-based modelsto represent the distribution of rock properties for a synthetic model of ahydrocarbon reservoir. The dynamic behaviour of the reservoir fluids ismodelled using a transient two-phase incompressible Darcy formulation. Weinvert for the underlying reservoir properties by first modeling propertydistributions using the pre-trained generative model then using the adjointequations of the forward problem to perform gradient descent on the latentvariables that control the output of the generative model. In addition to thedynamic observation data, we include well rock-type constraints by introducingan additional objective function. Our contribution shows that for a synthetictest case, we are able to obtain solutions to the inverse problem by optimisingin the latent variable space of a deep generative model, given a set oftransient observations of a non-linear forward problem.

DeepFlow: History Matching in the Space of Deep Generative Models