F. Pereira

F. Furtado, F. Pereira, S. Ribeiro

We compare the Kurganov-Tadmor (KT) two-dimensional second order semi-discrete central scheme in dimension by dimension formulation with a new two-dimensional approach introduced here and applied in numerical simulations for two-phase, two-dimensional flows in heterogeneous formations. This semi-discrete central scheme is based on the ideas of Rusanov's method using a more precise information about the local speeds of wave propagation computed at each Riemann Problem in two-space dimensions. We find the KT dimension by dimension has a much simpler mathematical description than the genuinely two-dimensional one with a little more numerical diffusion, particularly in the presence of viscous fingers. Unfortunately, as one can see, the KT with the dimension by dimension approach might produce incorrect boundary behavior in a typical geometry used in the study of porous media flows: the quarter of a five spot. This problem has been corrected by the authors with the new semi-discrete scheme proposed here. We conclude with numerical examples of two-dimensional, two-phase flow associated with two distinct flooding problems: a two-dimensional flow in a rectangular heterogeneous reservoir (called slab geometry) and a two-dimensional flow in a 5-spot geometry homogeneous reservoir.

S. Van Cranenburgh, S. Wang, A. Vij et al.

Since its inception, the choice modelling field has been dominated by theory-driven modelling approaches. Machine learning offers an alternative data-driven approach for modelling choice behaviour and is increasingly drawing interest in our field. Cross-pollination of machine learning models, techniques and practices could help overcome problems and limitations encountered in the current theory-driven modelling paradigm, such as subjective labour-intensive search processes for model selection, and the inability to work with text and image data. However, despite the potential benefits of using the advances of machine learning to improve choice modelling practices, the choice modelling field has been hesitant to embrace machine learning. This discussion paper aims to consolidate knowledge on the use of machine learning models, techniques and practices for choice modelling, and discuss their potential. Thereby, we hope not only to make the case that further integration of machine learning in choice modelling is beneficial, but also to further facilitate it. To this end, we clarify the similarities and differences between the two modelling paradigms; we review the use of machine learning for choice modelling; and we explore areas of opportunities for embracing machine learning models and techniques to improve our practices. To conclude this discussion paper, we put forward a set of research questions which must be addressed to better understand if and how machine learning can benefit choice modelling.

E. Abreu, F. Pereira, S. Ribeiro

We are concerned with central differencing schemes for solving scalar hyperbolic conservation laws arising in the simulation of multiphase flows in heterogeneous porous media. We compare the Kurganov-Tadmor, 2000 semi-discrete central scheme with the Nessyahu-Tadmor, 1990 central scheme. The KT scheme uses more precise information about the local speeds of propagation together with integration over nonuniform control volumes, which contain the Riemann fans. These methods can accurately resolve sharp fronts in the fluid saturations without introducing spurious oscillations or excessive numerical diffusion. We first discuss the coupling of these methods with velocity fields approximated by mixed finite elements. Then, numerical simulations are presented for two-phase, two-dimensional flow problems in multi-scale heterogeneous petroleum reservoirs. We find the KT scheme to be considerably less diffusive, particularly in the presence of high permeability flow channels, which lead to strong restrictions on the time step selection; however, the KT scheme may produce incorrect boundary behavior.