We consider numerical solutions of the Darcy and Buckley-Leverett equations for ow in porous media. These solutions depend on the geology of the porous media, which is given here as a realization of a random eld to describe the reservoir permeability. We measure the solution error as the diierence between the oil production rates (oil cut) for ne grid and upscaled coarse grid solutions of the e...

Neglecting capillary pressure effects in two-phase flow models for porous media may lead to non-physical solutions: indeed, the physical solution is obtained as limit of the parabolic model with small but non-zero capillarity. In this paper, we propose and compare several numerical strategies designed specifically for approximating physically relevant solutions of the hyperbolic model with negl...

Unsteady-state (USS) core flood experiments provide data for deriving twophase relative permeability and capillary pressure functions. The experimental data is uncertain due to measurement errors, and the accuracy of the derived flow functions is limited by both data and modeling errors. History matching provides a reasonable means of deriving in-phase flow functions from uncertain unsteady-sta...

In part I the authors reported on the design of a robust and versatile gradientweighted moving finite element (GWMFE) code in one dimension and on its application to a variety of PDEs and PDE systems. This companion paper does the same for the two-dimensional (2D) case. These moving node methods are especially suited to problems which develop sharp moving fronts, especially problems where one n...

Field tests indicate that temporary well shut-ins may enhance oil recovery from a shale reservoir; however, there is currently no systematic research to specifically guide such detailed operations in the field, especially for design of shut-in scheme and multiple rounds shut-ins. In this study, applicability reservoirs studied, numerical model built using finite element method. order simulate p...

Capillary pressure/saturation data are often difficult and time consuming to measure, particularly for non-water-wetting porous media. Few capillary pressure/saturation predictive models, however, have been developed or verified for the range of wettability conditions that may be encountered in the natural subsurface. This work presents a new two-phase capillary pressure/saturation model for ap...

Machine learning (ML) techniques have drawn much attention in the engineering community due to recent advances computational and an enabling environment. However, often they are treated as black-box tools, which should be examined for their robustness range of validity/applicability. This research presents evaluation application flow/transport porous media, where exact solutions (obtained from ...

Abstract A time-continuous (tc-)embedding method is first proposed for solving nonlinear scalar hyperbolic conservation laws with discontinuous solutions (shocks and rarefaction waves) on codimension 1, connected, smooth, closed manifolds (surface PDEs or SPDEs in $${\mathbb {R}}^2$$ R <...

The first paper, entitled Françoise, a fifteen year follow-up, from Jean Rondal and his colleagues M. Elbouz, M. Ylieff, and L. Docquier, at the University of Liège in Belgium presents an individual case study that describes in detail the changes in language and memory function of Françoise, a 47 year old lady with Down syndrome. Françoise will already be well known to many in this field as she...