Coupled Time‐Lapse Full‐Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation

Abstract

We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time‐lapse observed seismic data by coupling full‐waveform inversion (FWI), subsurface flow processes, and rock physics models. For the inverse modeling, we handle the back propagation of gradients by an intrusive automatic differentiation strategy that offers three levels of user control: (1) At the wave physics level, we adopted the discrete adjoint method in order to use our existing high‐performance FWI code; (2) at the rock physics level, we used built‐in automatic differentiation operators from the TensorFlow backend; (3) at the flow physics level, we implemented customized partial differential equation (PDE) operators for the multiphase flow equations. The three‐level coupled inversion strategy strikes a good balance between computational efficiency and programming efforts, and when the gradients are chained together, it constitutes a coupled inverse system. Our numerical experiments demonstrate that the three‐level coupled inverse problem is superior in terms of accuracy to a traditional decoupled inversion strategy. Additionally, our method is able to simultaneously invert for parameters in empirical relationships such as the rock physics models. Our proposed inverted model can be used for reservoir performance prediction and reservoir management/optimization purposes.

Accelerating innovation with software abstractions for scalable computational geophysics

“…Finally, we show that we can easily build a framework for seismic monitoring of geological carbon storage that integrates PDE solvers, deep learning models and physical constraints. These monitoring problems rely on three different types of physics [40]: fluid-flow physics, rock physics and wave physics. Given time-lapse seismic data collected over multiple years, we jointly invert for the rocks intrinsic permeability which can be used to recover the CO 2 concentration.…”

Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models

“…We excited waves from each source and recorded travel time at the receiver array, which constituted the observed data. We solved the eikonal equation using the fast sweeping method [63] and computed the gradient using the discrete adjoint-state method [33].…”

Learned coupled inversion for carbon sequestration monitoring and forecasting with Fourier neural operators

“…Given physical properties of the two fluids (brine and supercritical CO 2 ) and the spatial porosity and permeability distributions, these fluid-flow equations are capable of predicting CO 2 concentration snapshots during and after CO 2 injection. By coupling these fluid-flow equations, via a rock physics model (the patchy saturation model [Avseth et al, 2010]), to the wave equation, Li et al [2020a] proposed an end-to-end inversion framework where time-lapse seismic surveys are jointly inverted to yield estimates for the spatial permeability distribution. Compared to the sequential inversion [Hatab and MacBeth, 2021b,a] and history matching workflows [Oliver et al, 2021], estimates of the CO 2 concentration in the coupled inversion are regularized by fluid-flow physics.…”

“…Compared to the sequential inversion [Hatab and MacBeth, 2021b,a] and history matching workflows [Oliver et al, 2021], estimates of the CO 2 concentration in the coupled inversion are regularized by fluid-flow physics. Because coupled inversion [Li et al, 2020a] makes use of the fluid-flow equations, it offers a framework capable of producing direct estimates for the permeability. The latter can be used to generate improved predictions for the behavior of CO 2 plumes.…”

“…The latter can be used to generate improved predictions for the behavior of CO 2 plumes. Despite the initially promising results by Li et al [2020a] on synthetic experiments, the downside of their proposed coupled framework is the increased complexity that comes with including partial differential equations (PDEs) for the fluid-flow as constraints. Aside from the need to compute sensitivities of solutions of the fluid-flow equations, solving these PDE can be computationally expensive [Settgast et al, 2018, Rasmussen et al, 2021.…”