Equations of state (EoS) are essential in the modeling of a wide range of industrial and natural processes. Desired qualities of EoS are accuracy, consistency, computational speed, robustness, and predictive ability outside of the domain where they have been fitted. In this work, we review present challenges associated with established models, and give suggestions on how to overcome them in the future. The most accurate EoS available, multiparameter EoS, have a second artificial Maxwell loop in the two-phase region that gives problems in phase-equilibrium calculations and excludes them from important applications such as treatment of interfacial phenomena with mass-based density functional theory. Suggestions are provided on how this can be improved. Cubic EoS are among the most computationally efficient EoS, but they often lack sufficient accuracy. We show that extended corresponding state EoS are capable of providing significantly more accurate single-phase predictions than cubic EoS with only a doubling of the computational time. In comparison, the computational time of multiparameter EoS can be orders of magnitude larger. For mixtures in the two-phase region, however, the accuracy of extended corresponding state EoS has a large potential for improvement. The molecular-based SAFT family of EoS is preferred when predictive ability is important, for example, for systems with strongly associating fluids or polymers where few experimental data are available. We discuss some of their benefits and present challenges. A discussion is presented on why predictive thermodynamic models for reactive mixtures such as CO2–NH3 and CO2–H2O–H2S must be developed in close combination with phase- and reaction equilibrium theory, regardless of the choice of EoS. After overcoming present challenges, a next-generation thermodynamic modeling framework holds the potential to improve the accuracy and predictive ability in a wide range of applications such as process optimization, computational fluid dynamics, treatment of interfacial phenomena, and processes with reactive mixtures.

Flow of CO 2 in wells is associated with substantial variations in thermophysical properties downhole, due to the coupled transient processes involved: complex flow patterns, density changes, phase transitions, and heat transfer to and from surroundings. Large temperature variations can lead to thermal stresses and subsequent loss of well integrity, and it is therefore crucial to employ models that can predict this accurately. In this work, we present a model for vertical well flow that includes both two-phase flow and heat conduction. The flow is described by a two-fluid model, where mass transfer between the phases is modelled by relaxation source terms that drive the phases towards thermodynamic equilibrium. We suggest a new formulation of the mass transfer process that satisfies the second law of thermodynamics, and that is also continuous in the single-phase limit. This provides a more robust transition from two-phase to single-phase flow than the previous formulation. The model predicts which flow regimes are present downhole, and calculates friction and heat transfer depending on this. Moreover, the flow model is coupled with a heat conduction model for the layers that comprise the well, including tubing, packer fluid, casing, cement or drilling mud, and rock formation. This enables prediction of the temperature in the well fluid and in each layer of the well. The model is applied to sudden shut-in and blowout cases of a CO 2 injection well, where we employ the highly accurate Span-Wagner reference equation-of-state to describe the thermodynamics of CO 2. We predict pressure, temperature and flow regimes during these cases and discuss implications for well integrity.

Bernaise (Binary Electrohydrodynamic Solver) is a flexible high-level finite element solver of two-phase electrohydrodynamic flow in complex geometries. Two-phase flow with electrolytes is relevant across a broad range of systems and scales, from 'lab-on-a-chip' devices for medical diagnostics to enhanced oil recovery at the reservoir scale. For the strongly coupled multi-physics problem, we employ a recently developed thermodynamically consistent model which combines a generalized Nernst-Planck equation for ion transport, the Poisson equation for electrostatics, the Cahn-Hilliard equation for the phase field (describing the interface separating the phases), and the Navier-Stokes equations for fluid flow. As an efficient alternative to solving the coupled system of partial differential equations in a monolithic manner, we present a linear, decoupled numerical scheme which sequentially solves the three sets of equations. The scheme is validated by comparison to limiting cases where analytical solutions are available, benchmark cases, and by the method of manufactured solution. The solver operates on unstructured meshes and is therefore well suited to handle arbitrarily shaped domains and problem set-ups where, e.g., very different resolutions are required in different parts of the domain. Bernaise is implemented in Python via the FEniCS framework, which effectively utilizes MPI and domain decomposition, and should therefore be suitable for large-scale/high-performance computing. Further, new solvers and problem set-ups can be specified and added with ease to the Bernaise framework by experienced Python users. * linga@nbi.dk arXiv:1805.11642v1 [physics.comp-ph] 29 May 2018 Two-phase flow with electrolytes is encountered in many natural and industrial settings. Although Lippmann already in the 19th century [1, 2] made the observation that an applied electric field changes the wetting behaviour of electrolyte solutions, the phenomenon of electrowetting has remained elusive. Recent decades have seen an increased theoretical and experimental interest in understanding the basic mechanisms of electrokinetic or electrohydrodynamic flow [3,4]. Progress in micro-and nanofluidics [5,6] has enabled the use electrowetting to control small amounts of fluid with very high precision (see e.g. the comprehensive reviews by Mugele and coworkers [2,7] and Nelson and Kim [8] and references therein). This yields potential applications in, e.g., "lab-on-chip" biomedical devices or microelectromechanical systems [9][10][11], membranes for harnessing blue energy [12], energy storage in fluid capacitors, and electronic displays [13][14][15][16].It is known that electrohydrodynamic phenomena affects transport properties and energy dissipation in geological systems, as a fluid moving in a fluid-saturated porous medium sets up an electric field that counteracts the fluid motion [17][18][19]. Electrowetting may also be an important factor in enhanced oil recovery [20,21]. Here, the injection of water of a particular salinity, or "smart water" ...