Using sensitivities and vertical-equilibrium models for parameter estimation of CO2 injection models with application to Sleipner data

Abstract

A key part of planning CO2 storage sites is to devise a monitoring strategy with proper modelling support. Herein, we show how a simulation framework that incorporates adjoint-based sensitivities can be combined with time-lapse seismics to update forecast models of the migrating plume, investigate the measurability of model parameters, and assess the effect of acquiring new measurements (value of information). In particular, we show how the sensitivities in measured quantities with respect to parameters can guide the choice of whether additional data should be obtained or not. To this end, we us singular value decomposition to find determine the model parameters that are best constrained with respect to the measured data, or, viewed alternatively, the parameters that has the largest influence on the mismatch between measured and simulated quantities. Other measurements like uplift data and gravitational data can also be used in our inversion algorithm. We apply the methodology to the Sleipner benchmark model. A large number of researchers have used plume data to better understand the flow physics and challenge assumptions made previously regarding the model properties. In particular, the parameters for the flow model are uncertain and have been topic of discussion in the literature. Using a vertical-equilibrium simulator, we show that Darcy flow adequately describes the physics of the CO2 injection and migration. Adjoint-based sensitivities are used to efficiently minimize the mismatch between observations and simulations in an optimization loop giving plausible changes in topography, permeability, CO2 density, porosity, and injection rates. However, since the minimization of the misfit is not unique, we investigate the Hessian of the misfit function for a reduced set of parameters. By considering the eigenvalue decomposition of this Hessian, we are able to identify its (approximate) null space, i.e., the combinations of parameter perturbations that do not affect plume migration. Similarly, by considering the complementary subspace, we identify the reduced set of parameter combinations that are sufficient to obtain a match. As a result, we obtain a parametrized family of (locally) optimal solutions to the minimization problem, i.e., a family of models that all match the observed data. We also investigate the effect of observation frequency on our model matching methodology, and conclude that for the model considered, frequent seismic measurements are not required to obtain adequate matched models however it give more accurate estimates of the top surface.