Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named generalised latent assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional (CFD) application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.
Downhole monitoring of streaming potential, using electrodes mounted on the outside of insulated casing, is a promising new technology for monitoring water encroachment towards an intelligent well. However, there are still significant uncertainties associated with the interpretation of the measurements, particularly concerning the streaming potential coupling coefficient. This is a key petrophysical property which dictates the magnitude of the streaming potential for a given fluid potential. The coupling coefficient can be measured experimentally, but previous studies have obtained data for sandstone cores saturated with relatively low salinity brine (less than seawater). Formation and injected brine in hydrocarbon reservoirs is typically more saline than this. Extrapolating data obtained at low salinity into the high salinity domain suggests that the coupling coefficient falls to zero at approximately seawater salinity. If this is the case, then streaming potential signals will be very small in most hydrocarbon reservoirs.We present the first measured values of streaming potential coupling coefficient in sandstone cores saturated with brine at higher than seawater salinity. We find that the coupling coefficient is small, but still measureable, even when the brine salinity approaches the saturated concentration limit. Consistent results are obtained from two independent experimental setups, using specially designed electrodes and paired pumping experiments to eliminate spurious electrical potentials. We apply the new experimental data in a numerical model to predict the streaming potential signal which would be measured at a well during production. The results suggest that measured signals should be resolvable above background noise in most hydrocarbon reservoirs, and that water encroaching on a well could be monitored while it is several tens to hundreds of metres away.
Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional computational fluid dynamics (CFD) application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.