Real-Gas Effects and Phase Separation in Underexpanded Jets at Engine-Relevant Conditions

A numerical framework implemented in the open-source tool OpenFOAM is presented in this work combining a hybrid, pressure-based solver with a vapor-liquid equilibrium model based on the cubic equation of state. This framework is used in the present work to investigate underexpanded jets at engine-relevant conditions where real-gas effects and mixture induced phase separation are probable to occur. A thorough validation and discussion of the applied vapor-liquid equilibrium model is conducted by means of general thermodynamic relations and measurement data available in the literature. Engine-relevant simulation cases for two different fuels were defined. Analyses of the flow field show that the used fuel has a first order effect on the occurrence of phase separation. In the case of phase separation two different effects could be revealed causing the single-phase instability, namely the strong expansion and the mixing of the fuel with the chamber gas. A comparison of single-phase and two-phase jets disclosed that the phase separation leads to a completely different penetration depth in contrast to single-phase injection and therefore commonly used analytical approaches fail to predict the penetration depth.Comment: Preprint submitted to AIAA Scitech 2018, Kissimmee, Florid

The SILCC (SImulating the LifeCycle of molecular Clouds) project: I. Chemical evolution of the supernova-driven ISM

The SILCC project (SImulating the Life-Cycle of molecular Clouds) aims at a more self-consistent understanding of the interstellar medium (ISM) on small scales and its link to galaxy evolution. We simulate the evolution of the multi-phase ISM in a 500 pc x 500 pc x 10 kpc region of a galactic disc, with a gas surface density of $\Sigma_{_{\rm GAS}} = 10 \;{\rm M}_\odot/{\rm pc}^2$. The Flash 4.1 simulations include an external potential, self-gravity, magnetic fields, heating and radiative cooling, time-dependent chemistry of H$_2$ and CO considering (self-) shielding, and supernova (SN) feedback. We explore SN explosions at different (fixed) rates in high-density regions (peak), in random locations (random), in a combination of both (mixed), or clustered in space and time (clustered). Only random or clustered models with self-gravity (which evolve similarly) are in agreement with observations. Molecular hydrogen forms in dense filaments and clumps and contributes 20% - 40% to the total mass, whereas most of the mass (55% - 75%) is in atomic hydrogen. The ionised gas contributes <10%. For high SN rates (0.5 dex above Kennicutt-Schmidt) as well as for peak and mixed driving the formation of H$_2$ is strongly suppressed. Also without self-gravity the H$_2$ fraction is significantly lower ($\sim$ 5%). Most of the volume is filled with hot gas ($\sim$90% within $\pm$2 kpc). Only for random or clustered driving, a vertically expanding warm component of atomic hydrogen indicates a fountain flow. Magnetic fields have little impact on the final disc structure. However, they affect dense gas ($n\gtrsim 10\;{\rm cm}^{-3}$) and delay H$_2$ formation. We highlight that individual chemical species, in particular atomic hydrogen, populate different ISM phases and cannot be accurately accounted for by simple temperature-/density-based phase cut-offs.Comment: 30 pages, 23 figures, submitted to MNRAS. Comments welcome! For movies of the simulations and download of selected Flash data see the SILCC website: http://www.astro.uni-koeln.de/silc

Non-equilibrium of Ionization and the Detection of Hot Plasma in Nanoflare-heated Coronal Loops

Impulsive nanoflares are expected to transiently heat the plasma confined in coronal loops to temperatures of the order of 10 MK. Such hot plasma is hardly detected in quiet and active regions, outside flares. During rapid and short heat pulses in rarified loops the plasma can be highly out of equilibrium of ionization. Here we investigate the effects of the non-equilibrium of ionization (NEI) on the detection of hot plasma in coronal loops. Time-dependent loop hydrodynamic simulations are specifically devoted to this task, including saturated thermal conduction, and coupled to the detailed solution of the equations of ionization rate for several abundant elements. In our simulations, initially cool and rarified magnetic flux tubes are heated to 10 MK by nanoflares deposited either at the footpoints or at the loop apex. We test for different pulse durations, and find that, due to NEI effects, the loop plasma may never be detected at temperatures above ~5 MK for heat pulses shorter than about 1 min. We discuss some implications in the framework of multi-stranded nanoflare-heated coronal loops.Comment: 22 pages, 7 figures, accepted for publicatio

Convex hull method for the determination of vapour-liquid equilibria (VLE) phase diagrams for binary and ternary systems

Amieibibama Joseph wishes to thank Petroleum Technology Development Fund (PTDF) for their financial support which has made this research possible.Peer reviewedPostprin

A 6M digital twin for modeling and simulation in subsurface reservoirs

   Modeling and simulation of flow, transport and geomechanics in the subsurface porous media is an effective approach to help make decisions associated with the management of subsurface oil and gas reservoirs, as well as in other wide application areas including groundwater contamination and carbon sequestration. Accurate modeling and efficient, robust simulation have always been the main purposes of reservoir researches, and a 6M digital twin (multi-scale, multi-domain, multi-physics and multi-numerics numerical modeling and simulation of multi-component and multi-phase fluid flow in porous media) is designed, equipped with the following six pronounced features, to better digitally model and simulate the engineering processes and procedures in physical reality and further control and optimize such processes and procedures: 1. Efficient and reliable flash calculation: An accurate estimation on the phase equilibrium conditions is essentially needed prior to multi-phase flow and transport simulation for multi-component fluid mixtures in complex porous geometry and thermodynamic conditions. A remarkable progress was recognized in 2018, when a thermodynamically stable multi-phase equilibrium calculation algorithm of hydrocarbon mix- tures based on realistic equation of state (e.g., Peng-Robinson Equation of State) at specified moles, volume and temperature (NVT-flash) was generated and proposed (Kou and Sun, 2018a, 2018b; Sun, 2019). Robustness of this algorithm is preserved by proved consistency with the first and second laws of thermodynamics and capillarity can be incorporated in this algorithm to extend the application into unconventional reservoirs (e.g., shale gas reservoirs and tight oil reservoirs) and carbon dioxide sequestration (with cubic-plus-association type of equation of states) (Zhang et al., 2019a, 2019b; Li et al., 2020). Sparse grids method and parallel computing techniques have been involved in further studies to accelerate the phase equilibrium estimation  on parallel computers (Wu et al., 2015a). Recently, deep learning algorithms have been successfully developed to significantly speed up the multi-component flash calculations in complex thermodynamic conditions at the same time of ensuring stability and self-adaptivity (Li et al., 2019a, 2019b; Zhang et al., 2019c, 2020a).2. Advanced phase interface modeling: In multiphase flow simulation in porous media, modeling of the thin interface, usually in nanoscale thickness, is recognized as the key issue in order to simulate macroscale  fluid  behaviors  containing the formation and motion of interphase. The multi-component multi-phase flow can be investigated using a diffuse interface model based on realistic equations of state (typically Peng-Robinson equation of state), and bulk phase properties as well as interfacial properties could be modeled accurately and efficiently, where partial immiscibility can be considered to cover more engineering applications like carbon dioxide in oil (Qiao and Sun, 2014; Kou et al., 2018). Based on that, a new momentum balance equation was proposed in Kou and Sun (2018c) to identify the correlation associating the gradients of temperature and chemical potential and the pressure gradient, which further indicates that the gradient of the temperature and chemical potential has been found as the primary driving force of the macroscale fluid motions. Later, phase field modeling was incorporated with the moving contact line method to study the motion of soluble surfactants using two Chan-Hilliard type of equations, which are designed to govern the surfactant concentration and interface evolution respectively (Zhu et al., 2019). Recently, a semi-implicit scheme was proposed in Kou et al. (2020) to generate for the first time a scheme  that inherits the original energy dissipation law, using a delicate novel energy factorization (EF) approach to factorize an energy function into a product of several factors. Application of phase field modeling has been extended to a wider range in the whole process of petroleum engineering. An exploratory phase-field model was presented in Zhang et al. (2020b) to simulate the multiphase flow in  injection  pipeline  investigating  the  effect of injection salinity on pipeline scaling.3. Fully conservative bound-preserving Darcys scale flow simulation: Fully mass-conservative (both globally and locally, for wetting phase and non-wetting phase) IMPES (IMplicit Pressure Explicit Saturation) schemes for the simulation of incompressible and immiscible two-phase flow in porous media were generated in (Chen et al., 2019), which deserves a merit that a new treatment of capillarity was introduced and the unbiased and the bound-preserving property can provide a much larger time step choice. Furthermore, a nonlinear complementarity problem was reformulated and the resultant non-smooth nonlinear system of equations arising at  each time step  are  solved  fully  implicitly  by  a  parallel,  scalable, and nonlinearly preconditioned semi-smooth Newton algorithm (Yang et al., 2019a). Later, a new scheme containing up to three continuity equations were generated in Yang et al. (2020) so that mass conservation holds for all present phases. By using a variational inequality formulation with box inequality constraints, boundedness requirement on pressure and saturations can be preserved well and then the problem is solved using a well-designed nonlinear solver consisting of the nonlinear elimination preconditioning technique and active-set reduced-space  method.4. Reactive flow and transport in porous media: Reactive dissolution of carbonates by the action of the injected acid, also known as wormhole propagation, is a widely practiced technique in the product enhancement of petroleum industry. A semi-analytic scheme was proposed with a reconstruction of analytical porosity functions to analyze the time error of the porosity, and a coupled analysis approach was employed to achieve the estimates of pressure, velocity and solute concentration on the basis of porosity error estimation (Wu et al., 2015b; Kou et al., 2019). Meanwhile, various primal discontinuous Galerkin schemes, including NIPG, SIPG and IIPG have been investigated deeply for solving multi-component reactive transport and coupled with multiphase flow simulation in porous media (Sun and Wheeler, 2005, 2006).5. Molecular simulation of microscopic mechanisms: As an effective approach to investigate the microscopic mechanisms affecting macroscopic flow and transport behaviors as well as to obtain the value of key parameters in numerical modeling, molecular simulation has attracted increasing attentions. The diffusion and sorption behaviors of carbon dioxide and methane as well as the structural features were studied using molecular dynamics and hybrid Monte Carlo approaches (Kadoura et al., 2017; Yang et al., 2017a, 2019b). The intercalation behavior of carbon dioxide in various brines were studied using grand canonical Monte Carlo methods to study the molecular mechanisms indicating that the intercalation of carbon dioxide strongly depends on the relative humidity (Li et al., 2019c).6. High-performance computation based on fully-Implicit and bound-preserving algorithms: Bound-preserving discretization and solvers for subsurface flow models based on a fully implicit framework is the future of parallel reservoir simulation (Yang et al., 2019a, 2020). A family of mixed finite element methods have been used to discretize various model equations in porous media flow for the spatial terms, and the implicit backward Euler scheme with adaptive time stepping for the temporal integration. The resultant nonlinear system arising at each time step was  then  solved  in  a  monolithic way by using a Newton–Krylov type method, where the resultant nonlinear system was solved by a generalized Newton method, i.e., active-set reduced-space method, and then the ill-conditioned linear Jacobian systems were solved with an effective preconditioned Krylov subspace method. The used nonlinear preconditioner was built by applying overlapping additive Schwarz type domain decomposition and nonlinear elimination. Numerical results on parallel computers indicated that the nonlinear solver overcomes the severe limits on the time step associated with conventional methods, and it results in superior convergence performance, often reducing the total computing time by more than one order of magnitude (Yang et al., 2016, 2017b, 2018).Cited as: Sun, S., Zhang, T. A 6M digital twin for modeling and simulation in subsurface reservoirs. Advances in Geo-Energy Research, 2020, 4(4): 349-351, doi: 10.46690/ager.2020.04.0