Gradient-based inversion for subsurface porosity using the adjoint two-phase flow equations: A pseudo-transient approach

Abstract

<p>Porous flow is of major importance for reservoir-scale processes such as waste fluid sequestration or oil and gas <br>exploration. The motion of a low-viscous fluid through a high-viscous matrix (rock) can be described by the coupled <br>nonlinear hydro-mechanical equations. This two-phase flow may result in the initiation of porosity waves, triggering <br>high-porosity vertical pipes or chimneys. Such fluid escape features may lead to localized and fast vertical flow <br>pathways that may be problematic in the case of e.g. CO<sub>2</sub> sequestration. Determining the porosity in such environments <br>is a major challenge. Seismic imaging methods can localize the high-porosity chimneys very well in the inverted wave speed <br>field but the conversion to porosity is not straightforward. </p><p>Here, we develop an inversion framework that allows us to invert for the porosity using fluid velocities as observables <br>and investigate its behavior for simple examples. We introduce the adjoint framework for the two-phase flow equations, <br>which allows for efficient calculation of the pointwise gradients of the flow solution with respect to the porosity. <br>These gradients are then used in a gradient descent method to invert for the pointwise porosity. Technically, the forward <br>and adjoint equations are solved using a parallel iterative finite-difference pseudo-transient approach, which executes <br>optimally on latest manycore hardware accelerators such as GPUs. Numerical results show that an inversion for porosity is <br>feasible and that the porosity is very locally sensitive to the fluid velocity.</p>