Energy Conservation Equations Research Articles

Functional and financial analysis of an inclined step solar desalination using phase change nanomaterials

ABSTRACT Recent decades have seen a shortage of water, which has led scientists to concentrate on solar desalination technologies. The present study examines the solar water desalination system with inclined steps, while considering various phase change materials (PCMs). The findings suggest that the incorporation of PCM generally enhances the productivity of the solar desalination system. Additionally, the combination of nanoparticles has been used to PCM, which is a popular technique utilized nowadays to improve the efficiency of these systems. The current investigation involves the transient modeling of a solar water desalination system, utilizing energy conservation equations. The equations were solved using the Runge–Kutta technique of the ODE23s order. The temperatures of the salt water, the absorbent plate of the glass cover, and the PCM were calculated at each time. Without a phase changer, the rate at which fresh water is produced is around 5.15 kg/m2·h. The corresponding mass flow rates of paraffin, n-PCM I, n-PCM III, n-PCM II, and stearic acid are 22.9, 28.9, 5.9, 11.9, and 73 kg/m2·h. PCMs, with the exception of stearic acid, exhibit similar energy efficiency up to an ambient temperature of around 29°. However, at temperatures over 29°, n-PCM II outperforms other PCM.

Dark energy nature of logarithmic f(R,Lm)-gravity models with observational constraints

This work explores the dark energy nature of logarithmic [Formula: see text]-gravity models with observational constraints, where [Formula: see text] represents the matter Lagrangian for perfect fluid and R is the Ricci-scalar curvature. With a matter Lagrangian [Formula: see text], a flat FLRW space–time metric and an arbitrary function [Formula: see text], where [Formula: see text] is a positive model parameter, we have derived the field equations of this model. By using the Hubble function, we have been able to solve the energy conservation equation and create a relationship between [Formula: see text], [Formula: see text] and [Formula: see text]. Using the most recent two observational datasets as 32 [Formula: see text] and 1048 Pantheon SNe Ia datasets, we conducted MCMC analysis. We have obtained best fit values of model parameters with [Formula: see text] errors and using these values, we have explored the cosmological properties of the model. We have performed om diagnostic analysis for the model and estimated the present age of the universe. Thus our derived model presents a transit phase decelerating to accelerating model without dark energy term [Formula: see text]. We found that the effective equation of state parameter is in the range [Formula: see text] over [Formula: see text] with present value [Formula: see text].

Sensitivity analysis of MHD nanofluid flow in a composite permeable square enclosure with the corrugated wall using Response surface methodology-central composite design

This work aims to conduct a numerical study on the magnetohydrodynamic (MHD) natural convection of nanofluid within a porous cavity corrugated hot and cold walls. The system comprises an external magnetic field. The study employs a finite element approach to solve the governing equations for momentum and energy conservation, while systematically varying influential parameters such as the Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), and the magnetic parameter (M). The fluctuations in these parameters allow for the analysis of their effects on the Nusselt number, flow patterns and thermal performance. A notable innovation of this research lies in the incorporation of a Response Surface Methodology (RSM)-based sensitivity analysis. This approach yields valuable insights for optimizing thermal management and enhancing energy efficiency in advanced Magnetohydrodynamics (MHD) systems. According to conclusive data, employing a permeable partition instead of a solid partition leads to a notable enhancement in the mean Nusselt value. Specifically, at Ra = 100, the improvement is recorded at 26.28%. Furthermore, at Ra = 104, this enhancement reaches its peak, with a substantial increase of 56.5%.

A first‐order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non‐linear solid dynamics

SummaryThe paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first‐order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first‐order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex‐based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi‐discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.

A dynamic mathematical model used for controller design of a supercritical once-through boiler-turbine unit in all load conditions

Recently, widespread adoption of renewable energy significantly impacts the security and stability of power grid. Utilizing coal-fired units in real-time load figuration remains a primary method to ensure grid stability. Therefore, supercritical Once-Through Boiler-Turbine (OTBT) units continuously enhance flexibility to meet the evolving needs of the grid. To broaden the load boundary and achieve fully automated control from unit start-up to rated load, establishing a dynamic mathematical model used for controller design of OTBT units in all load conditions is a necessary prerequisite. This model should accurately predict model outputs in both once-through mode (OTM) and recirculation mode (RCM) while also reflecting the dynamic transition processes between modes. In this study, we first conducted a detailed analysis of the characteristics of recirculation system. Mass and energy conservation equations are established separately for economizer-waterwall system and superheater system, including a level model for storage tank in RCM. Subsequently, through reasonable assumptions and analysis of the transition process, the modified steam dryness is identified as a crucial indicator to distinguish between RCM and OTM. This approach unified the model structures in RCM and OTM, avoiding issues related to model switching during mode transitions. Following this, model parameters were identified based on an improved dynamic search fireworks algorithm. Finally, multiple sets of comparative simulation experiments demonstrated that the established model exhibits high accuracy throughout the unit operation. Results from open-loop simulations indicated that this model can serve as a foundation for controller design of coordinated control system in all load conditions.

Conserved energy–momentum tensor for real-time lattice simulations

We derive an expression for the energy–momentum tensor in the discrete lattice formulation of pure glue QCD. The resulting expression satisfies the continuity equation for energy conservation up to numerical errors with a symmetric procedure for the time discretization. In the case of the momentum conservation equation, we obtain an expression that is of higher accuracy in lattice spacing (O(a2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(a^2)$$\\end{document}) than the naive discretization where fields in the continuum expressions are replaced by discretized counterparts. The improvements are verified by performing numerical tests on the derived expressions using classical real-time lattice gauge theory simulations. We demonstrate substantial reductions in relative error of one to several orders of magnitude compared to a naive discretization for both energy and momentum conservation equations. We expect our formulation to have applications in the area of pre-equilibrium dynamics in ultrarelativistic heavy ion collisions, in particular for the extraction of transport coefficients such as shear viscosity.

Experimental and Numerical Evaluations of Dynamic Transfer Matrix for a Three-Dimensional Centrifugal Impeller Based on Unsteady Energy Conservation

Abstract Under unsteady operating conditions in turbomachinery, the performance is unable to respond rapidly enough to follow characteristic curves for the steady condition. To design a reliable turbomachinery under unexpected unsteady conditions, we evaluated the dynamic transfer matrix of a three-dimensional centrifugal impeller. The working fluid is incompressible air. To make the current results more applicable in a broader sense such as pumps, all parameters and results were normalized. The experimental results showed a more significant negative slope in the unsteady performance curve compared to that in the steady performance curve. This was mainly caused by the phase delay of the pressure rise to the pulsating flowrate. We clarified the changes in gain and phase delay under unsteady conditions by conducting numerical simulations. The numerical results showed that the unsteady pressure rise was primarily generated by inertia and power terms in the unsteady energy conservation equation. The power term was predominantly influenced by the angular momentum flowrate difference and the change rate of angular momentum. Each term was quantitatively evaluated, and its contribution to the unsteady pressure rise was discussed. Within the range of frequencies tested in this study, the transfer matrix for the three-dimensional centrifugal impeller could be effectively approximated through a first-order lag approximation considering a series-connected derivative system. We believe that our findings can be extended to centrifugal pumps when disregarding the compressibility effects such as cavitation.

Numerical Analysis of Altered Parallel Flow Heat Exchanger with Promoted Geometry at Multifarious Baffle Prolongs

This study investigated the influence of BFFSP on the thermohydraulic performance of a SATHEC(s) using a novel computational approach. The novelty lies in the detailed exploration of the interplay between BFFSP, MFRT, and key performance parameters. Unlike prior studies, which often focus on a limited range of operating conditions, this work employs a comprehensive parametric analysis encompassing two BFFSPs (95 mm and 125 mm) and four MFRTs (0.1, 0.3, 0.5, and 0.7 kg/h). This extensive analysis provides a deeper understanding of the trade-off between the HTRFR enhancement and PDP associated with the BFFSP across a wider range of operating conditions. This investigation leverages the power of computational fluid dynamics (CFD) simulations for high-fidelity analysis. ANSYS Fluent, a widely recognized commercial CFD software package, was used as a computational platform. A three-dimensional steady-state model of HEXR geometry was established. The cold fluid was modeled as water, and the hot fluid was modeled as water. The selection of appropriate turbulence models is crucial for accurate flow simulations within the complex geometry of HEXR. This study incorporates a well-established two-equation turbulence model to effectively capture turbulent flow behavior. The governing equations for mass, momentum, and energy conservation were solved numerically within the CFD framework. Convergence criteria were meticulously established to ensure the accuracy and reliability of the simulation results. BFFs are crucial components in HEXRs as they promote fluid mixing and turbulence on the HTRFR surface, thereby enhancing HTRFR. This study explores the interplay between BFFSP and HTRFR effectiveness. It is hypothesized that a larger BFFSP (125 mm) might lead to a higher HTC owing to the increased fluid mixing. However, the potential drawbacks of the increased PDP due to the flow restriction also need to be considered. The PDP across the HEXR is a critical parameter that affects pumping costs and overall system yield. This study investigates the impact of BFFSP on the PDP. It is expected that a larger BFFSP (125 mm) will result in a higher PDP, owing to the increased resistance to fluid flow. Here, we aim to quantify the trade-off between enhanced HTRFR and increased PDP associated with different BFFSPs. The optimal design of an HEXR seeks a balance between achieving a high HTRFR rate and minimizing pressure losses. HTRPD, a metric combining both HTC and PDP, was employed to evaluate the thermohydraulic performance. We hypothesized that a specific BFFSP might offer a superior HTRPD, indicating an optimal balance between HTRFR effectiveness and PDP for the investigated HEXR geometry and operating conditions. CFD simulations were conducted using ANSYS Fluent to analyze the effects of BFFSP and MFRT on the HTC, PDP, and HTRPD. The simulations employed a commercially available HEXR geometry with water as the cold and hot fluid. The results are presented and discussed to elucidate the relationships between the BFFSP, MFRT, and key performance parameters of the HEXR. This study provides valuable insights into the influence of BFFSP on the thermohydraulic performance of HEXRs. The findings can aid in optimizing the HEXR design by identifying the BFFSP that offers the best compromise between HTRFR enhancement and PDP for specific operating conditions. The results contribute to the knowledge base of HEXR design and optimization, potentially leading to improved yield in various industrial applications. The results indicate that a larger BFFSP (125 mm) leads to higher outlet temperatures but also results in a higher PDP compared to the 95 mm design. Conversely, the 95 mm BFFSP exhibits a lower PDP but achieves a lower HTC. In terms of thermohydraulic performance, as indicated by HTRPD, the 95 mm BFFSP with the lowest MFRT (0.1 kg/h) achieved the highest value, surpassing the 125 mm design by 19.81%. This suggests that a 95 mm BFFSP offers a better trade-off between HTRFR effectiveness and pressure loss, potentially improving the overall HEXR performance.

Lumped‐element equivalent circuit modelling of district heating pipe in electromagnetic transients program

AbstractElectromagnetic transients program (EMTP) is widely used to analyze transients in power systems. With the increased interest in integrated energy systems (IESs), it would be beneficial to extend the application of EMTP to multi‐physics transients in integrated electrical and heating networks. In this paper, an accurate and efficient lumped‐element circuit model of the heating district pipe is developed in EMTP. The pipe is split into segments using spatial discretization. The application of the numerical discretization to the energy conservation equation gives the discretized pipe equation which is expressed in the form of a companion model of EMTP. In order to reduce the computational effort, the time‐varying terms in the admittance matrix of the companion model of pipe are eliminated. The modification of the admittance matrix is avoided. Furthermore, the internal nodes resulting from spatial discretization are eliminated, resulting in a lumped‐element circuit model with only two external nodes. Case studies are carried out to validate the proposed model in terms of accuracy and efficiency. The 2‐norm error of the proposed model is 0.0153%. With a pipe length of 100 m, the computational speed of the proposed model is increased by a factor of 2.94 compared with the existing distributed‐element circuit model. The implementation of the proposed pipe model in the EMTP‐type simulator enables the analysis of multi‐physics transients in a multi‐carrier energy system.

Математическая модель процесса СВЧ и конвективной выпечки хлеба из сбивного теста

Whipped yeast-free bakery products require effective energy supply to dough in order to optimize energy consumption, baking time, and quality. This article introduces a verified mathematical model of microwave and convective baking for whipped bread based on heat and mass exchange equations.
 A full-scale experiment to verify the calculations involved dough samples with a humidity of 56 ± 1%. The samples underwent microwave and convective processing until the temperature in the crumb center reached 98 ± 1°C.
 The mathematical model was formalized as energy and mass conservation equations, which made it possible to consider baking as a non-stationary process of heat and mass transfer of moisture in an isotropic incompressible continuous medium in the diffusion approximation. The equation took into account the unstable phase transition boundary. The practical verification showed the mean error for microwave baking as 14.5% in temperature and 18.2% in moisture content. For convective baking, the results included 12.6% in temperature and 9.7% in moisture content. The mathematical model proved adequate to the real processes of heat and mass transfer. The error in calculating the temperature and moisture content fields was sufficient tooptimize the process.
 The physical and mathematical model of the baking process made it possible to evaluate the effect of technological variables on the temperature and moisture concentration fields in the dough samples. The mathematical model and the computational experiment can be used to identify static and dynamic characteristics of baking as an object of automatic control, i.e., to identify optimal control channels and actions, as well as to adjust the automatic control system to specific quality indicators.

Offering a channel for cooling three lithium-ion battery packs with water/Cu nanofluid: An exergoeconomic analysis

This study focused on addressing the heat generation issue in Lithium-Ion battery packs (LIBPs). By simulating three LIBPs arranged in series within a duct, the momentum and energy conservation equations were solved using Computational Fluid Dynamics (CFD) to investigate cooling performance on the LIBPs' temperature. To enhance cooling, copper oxide nanoparticles were added to pure water to improve the thermal conductivity of the working fluid. Various cases were simulated to examine the effects of Reynolds number at inlet and volume fraction of copper oxide nanoparticles on flow parameters (streamlines, vortices, pressure drop) and heat transfer parameters (temperature distribution, maximum and average temperature of each LIBP) within the duct. Also, this study analyzed exergoeconomics by considering exergies and initial investment. The results demonstrate that increasing the volume fraction from 0 to 4 % at Re = 60 reduced the maximum temperature of LIBP 1, 2, and 3 by 2.19 °C, 2.26 °C, and 2.64 °C, respectively, while it had no remarkable impact on the maximum temperature of LIBPs for bigger Reynolds numbers.

Investigating micro-cutting mechanism of glow discharge polymer based on material properties and removal behaviors analysis

Glow discharge polymer (GDP) is the unique artificial material for the target balls in Inertial Confinement Fusion tests, while its practical micromachining such as the fabrication of microstructure on material surfaces keeps challenging due to its unclear micro-cutting mechanism. Hence, this paper seeks to investigate the micro-cutting mechanism of GDP from the perspective of the material flow and cutting energy. To achieve it, the energy conservation equation of three cutting modes triggered by different ratios of uncut chip thickness to the tool cutting edge radius (RTS) was established based on cutting deformation behaviors. Meanwhile, the diamond cutting tests and the FEM simulation at different RTS were developed. The experimental observation of cutting forces and specific cutting forces verified the evolution of three cutting modes, including shearing, shearing-ploughing and ploughing in the micro-cutting of GDP with the decrease of RTS. Next, from the change of the node displacement vector observed from the simulated results, it can be seen that the real-time material flow behavior during micro-cutting of GDP varies obviously with the evolution of cutting modes. Besides, the fracture toughness Gc, and the energy dissipation of different cutting modes were analyzed. The proportion of the energy spent on material fracture (Gc=9.95 N/mm) is the largest one in shearing and shearing-ploughing modes, while in ploughing mode, the material plastic deformation consumed the most energy. The above results reveal the specific material properties and removal behaviors of GDP and contribute to optimizing the machining strategies for the practical micromachining of microstructures on material surfaces.

Validation of a statistical-dynamic framework for predicting energy consumption: A study on vehicle energy conservation equation

Predictive models for vehicle energy consumption are crucial for sustainable development in urban road traffic systems. This paper comprehensively reviews classic predictive models and develops a novel statistical-dynamical energy consumption prediction framework called Vehicle Energy Conservation Equation (VECE). VECE is constructed based on the principles of vehicle energy flow and regression analysis, employing a continuous and concise mathematical formulation. Its coefficients possess clear physical interpretations, allowing for application in various vehicle categories. To validate VECE, this study collected energy consumption data from 28 vehicles, including 9 diesel vehicles, 16 gasoline vehicles, 1 ethanol gasoline vehicle, and 2 battery electric vehicles. A rigorous data processing procedure was designed. Data analysis revealed that the VECE coefficients are correlated with vehicle type, speed, and acceleration. VECE's predictive performance is minimally impacted by the number of vehicle categories, effectively modeling energy consumption for vehicles of the same fuel type or size category. Comparative analysis with E-EcoGest, VT-Micro, PERE, and CMEM demonstrates the moderate accuracy of VECE in predicting instantaneous vehicle energy consumption while excelling in predicting cumulative energy consumption. The minimum relative percentage error for the cumulative predicted values is 4.2%. Overall, VECE demonstrates outstanding performance in computational simplicity, coefficient interpretability, adaptability, and extensibility, making it a crucial tool for achieving energy-efficient road transport systems.

Magnetohydrodynamics thermosolutal convection of hybrid MWCNT-Fe[formula omitted]O[formula omitted]-water nanofluid along a vertical wavy surface with wall heat and mass flux

This numerical analysis investigates the behavior of magnetohydrodynamics (MHD) thermosolutal convection in a hybrid nanofluid made up of multi-wall carbon nanotube (MWCNT)-Fe3O4 and water along a vertical wavy surface with wall heat and mass flux conditions. The mathematical model is developed using the conservation equations of mass, momentum, energy, and energy. The governing equations are converted into a non-dimensional form using the appropriate transformation, and the implicit finite difference technique is used to solve them. The effects of various parameters, such as the Schmidt number (Sc), nanoparticles volume fraction (ϕ), wavy amplitude (a), magnetic parameter (M), buoyancy ratio (Br), on the velocity, temperature, concentration distribution (Φ), streamlines, isotherms, local skin friction coefficient (Cf), local Nusselt (Nu) number, local Sherwood number (Sh) are investigated. Results show that higher amplitude and the addition of hybrid nanofluids volume fraction slow down the heat and mass transport rate, as indicated by declining local Nusselt and Sherwood numbers. However, enhancing the buoyancy ratio increases the fluid flow’s skin friction, heat, and mass transport. The velocity, temperature, concentration distribution, skin friction, and convective heat transport within the wavy surface is weakened by the addition of the magnetic parameter M.

MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: Electromagnetic therapy simulation

The ureter typically experiences a frequency of one to five peristaltic contractions per minute. However, it is important to note that these contractions can be disrupted by various physical and mechanical irritants. Ionic contents in the urine make it electrically conducting and responsive to electromagnetic body forces. MHD can be deployed in bio magnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system. This article therefore focuses on the hydromagnetic effects on flow patterns of urine with debris (monoliths). The mechanism of urine flow is largely coordinated by the kidneys. The flow inside the ureter is interrupted by microliths, which are generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted, comprising the electromagnetic urological viscous fluid phase and the particulate phase for solid grains. The peristaltic propulsion of two-phase liquid in the ureter is simulated as a sinusoidal wave propagation of incompressible non-Newtonian fluid. The Williamson viscoelastic model is deployed for the rheology. Heat transfer is also included with Soret thermo-diffusion and viscous heating effects. Long wave and low Reynolds number approximations are employed based on lubrication theory. The mass, momentum, energy and concentration conservation equations with associated boundary conditions are rendered non-dimensional via appropriate scaling transformations. A numerical solution is achieved via BVP4C MATLAB quadrature. Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter ( ζ ), Hartmann number (M), Prandtl number (Pr), Weissenburg number (We), particle volume fraction (C), Eckert number (Ec), Soret number (Sr), Schmidt number (Sc). The novelty of the present work is therefore the simultaneous consideration of a generalized two-phase model, wall slip, non-Newtonian characteristics, cross diffusion, viscous dissipation, mass diffusion, magnetic body force and curvature effects in peristaltic urological transport, which has not been undertaken previously. The detailed simulations reveal that the flow velocity is reduced due to the presence of solid particles and the channel curvature, in comparison to the flow in an unobstructed channel devoid of solid particles. Enhancing the hydrodynamic slip parameter speeds up the movement of particles and fluid near the channel walls, boosts wall skin friction, raises pressure difference in the pumping area, and amplifies bolus magnitudes.The rise in peristaltic pumping results in a reduction in solid particle concentration, which is significant phenomena.This theoretical approach may aid in treating conditions such as Urinary Tract Infections (UTIs). The computations effectively demonstrate that significant manipulation of urological pumping characteristics can be achieved with an electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted as relevant to magnetic therapy techniques, which may be beneficial to clinicians.

Buoyancy and Velocity Field Synergy Principle in Convective Heat Transfer and Its Role in Thermo-Hydraulic Performance Improvement

Abstract This study proposes the buoyancy and velocity field synergy principle and aims to enhance thermo-hydraulic performance in convective heat transfer. A mechanical energy conservation equation concerning synergy between buoyancy and velocity was derived, which describes the mechanical energy transport and dissipation in convective heat transfer. Two new field synergy numbers, FsU,g and FsU,∇p, were proposed to characterize the degree of synergy between velocity and buoyancy, and the degree of synergy between velocity and pressure gradient over the fluid domain, respectively. The pressure drop of a channel subjected to convective heat transfer is related to not only Gr/Re2 but also FsU,g. Under a same Gr/Re2, a larger |FsU,g| leads to a smaller |FsU,∇p|, and thus the pressure drop is decreased. Furthermore, the multifield synergetic relationships among buoyancy, velocity, temperature gradient and pressure gradient were analyzed for convective heat transfer in channels. The correlation between FsU,∇p and (Gr/Re2)FsU,g, and the correlation between FsU,g and a traditional field synergy number characterizing convective heat transfer capability, Fc, were derived, which reveals the coupled mechanisms of mechanical energy dissipation and thermal energy transport in convective heat transfer. The proposed principle was applied in typical channel flows subjected to convective heat transfer, and its benefits were demonstrated. It is noted that both pressure drop reduction and convective heat transfer enhancement can be achieved in convective heat transfer using the proposed principle. This paper provides a new insight for improving thermo-hydraulic performance of heat exchangers.

A hydro-thermo-damage-mechanical fully coupled cohesive phase-field model for fracking in quasi-brittle thermo-poroelastic media

A hydro-thermo-damage-mechanical fully coupled cohesive phase-field method is developed for modelling of fracking in quasi-brittle thermo-poroelastic media. A new sigmoid interpolation function is proposed to characterize the transitional behaviour from porous media to cracks for permeability, specific heat capacity, and thermal conductivity. A fluid continuity equation with the Darcy-Poiseuille law and an energy conservation equation with the Fourier’s law are then used to simulate fluid flow and heat transfer in cracking porous media, respectively. The fluid pressure and temperature of fluids and solids are fully incorporated into the governing equation of the phase-field regularized cohesive zone model to efficiently simulate complicated quasi-brittle hydro-thermal fracking, without the need of remeshing, crack tracking or auxiliary fields. The resultant displacement–pressure-temperature-damage coupled multiphysics system of equations is solved using a staggered Newton–Raphson iterative algorithm within the finite element framework. The method is first validated by five two-dimensional thermally or hydro-thermally induced fracture examples with analytical solutions, experimental data, and published numerical solutions. Three-dimensional fracking and fluid circulation problems in a vertical five-spot wellbore system with complex natural fracture networks, are then simulated as an application to energy harvesting in enhanced geothermal systems (EGS). It is found that the present method is capable of accurately and robustly modelling complicated hydraulic fracture propagation and fluid circulation problems and has the potential to be used for fracking design and optimization of EGS.

Extended gravitational vortex without dark matter

This paper analyzes, within the extended gravitoelectromagnetic (GEM) formulation, the equilibrium of a large scale gravitational system formed by rotating dust. The force balance equation gives the rotation velocity in terms of the GEM fields. Boundary conditions for the fields are introduced using Helmholtz’s decomposition and the virtual casing principle. Hydro-gravitomagnetic Cauchy invariance is implemented to relate the fluid and gravitomagnetic field vorticities. An energy conservation equation gives the rotation velocity in terms of the gravitational field and respective boundary values. A detailed solution is calculated for the case of rotating oblate spheroids. The equilibrium is in the form of a sheared rotational vortex, without introducing dark matter. The results are consistent with the Tully–Fisher relation and the Virginia Trimble correlations.

Modeling of high-speed, methane–air, turbulent combustion, Part I: One-dimensional turbulence modeling with comparison to DNS

The ability of the one-dimensional turbulence (ODT) model to serve as a surrogate direct numerical simulation (DNS) is assessed for highly turbulent flames. The ODT model is applied to freely propagating premixed methane–air flames at Karlovitz numbers 10, 102, 103, and 104, and results are compared with DNS. The ODT model solves the conservation equations for momentum, energy, and species on a one-dimensional domain, which corresponds to a streamwise line of sight spanning the DNS domain. The effects of turbulent advection are modeled via a stochastic process, in which the Kolmogorov and reactive length and time scales are explicitly resolved. Molecular transport and chemical kinetics are concurrently advanced in time. Both the ODT and DNS simulations use a 21-species skeletal chemical model for methane combustion. The accuracy of the ODT model is assessed by comparing its predictions of several key characteristics of the flames for each Karlovitz number tested, including the turbulent flame speed and width and the joint probability density functions (jPDFs) of major and selected minor species as well as the heat release rate conditioned on temperature with the results of DNS under comparable conditions. The ODT model is shown to yield qualitative and quantitative agreement with the DNS data for most of the above flame characteristics. Discrepancies are observed primarily for the jPDFs of several minor species examined. Overall, the ODT approach is shown to be an effective surrogate of DNS, potentially useful for guiding chemical reaction model reduction and for assessing the sensitivities of the flame structure and the burning rate to chemistry under highly turbulent conditions.Novelty and Significance:The direct numerical simulations (DNS) of premixed turbulent methane–air flames presented in this work span a uniquely wide range of turbulent intensities, from relatively modest corresponding to Karlovitz number Ka=10 to ultra-high intensities at Ka=104. This represents virtually the entire range of turbulent intensities that could be encountered in any realistic situation. This is also the first time that such a wide range of conditions is probed for methane in high-fidelity, fully resolved simulations, which use a fully compressible set of flow equations. The one-dimensional turbulence (ODT) model utilizes the same forcing that is present in the DNS enabling a direct comparison between the ODT and DNS. The results show that ODT captures the key features of the DNS results. ODT is shown to be an effective surrogate for DNS and may be useful in guiding chemical reaction model reduction, where many simulations are required.

Prediction of Production-Inflow Profile of a Well Producing Single-Phase Flow of Slightly Compressible Fluid from Multilayer Systems by Temperature and/or Pressure Transient Data

Summary This study focuses on the prediction of the production-inflow profile of a well producing a single-phase flow of slightly compressible fluid (water or oil flow) in a multilayered system using the layer permeability and skin values estimated by history matching spatial and temporal temperature and/or pressure data sets along the completion interval. Such data may be acquired by wireline formation testing, production-logging-tool (PLT), or distributed temperature sensing (DTS) fiber-optic cables. We use an in-house thermal, transient coupled reservoir/wellbore simulator developed during this study. It solves transient mass, momentum, and energy conservation equations simultaneously for both reservoir and wellbore. The effects of the Joule-Thomson (J-T), adiabatic expansion, conduction, and convection are all included for predicting the flow profiles across the wellbore. The results from our in-house simulator are verified with the results from a commercial simulator for the single-phase fluid flow of a vertical well producing geothermal brine and oil in a two-zone multilayer system. We also compare the results from our rigorous transient coupled wellbore/reservoir model with the results from a model assuming steady-state thermal wellbore model used in the previous studies. We find that the steady-state thermal wellbore model used in the previous studies that ignore accumulation terms in mass, momentum, and thermal energy balances is a reasonably accurate model for predicting wellbore pressures and temperatures when it is coupled with a nonisothermal reservoir model for slightly compressible fluid because the transient effect in the wellbore is less important with the slightly compressible fluid. We investigate the nonlinear parameter estimation problem based on the use of single or multiple observed temperature and/or pressure (if available) profiles recorded spatially inside the wellbore and at the sandface. The purpose is to identify if the wellbore or sandface data profiles are more useful to accurately estimate the permeability and skin information and predict a production-inflow profile of the well depending on the representation of an actual multilayer system by a reduced-layered or fine-layered model. We show that using an upscaled-layered model (e.g., representing each heterogeneous layer with a lumped single layer with uniform permeability and skin) provides estimates that are more toward the thickness-average permeability and skin factors of the layers and may not provide a good prediction of the well’s production-inflow profile. We show that including the sandface temperature data in regression worsens, while the use of wellbore temperature data sets improves the quality of parameter estimation if an upscaled multilayered model is used. We also show that regressing on multiple temperature profiles, preferably at the sandface, alone could be used to predict the production-inflow profile accurately if a “fine” multilayered heterogeneous model is used. We also investigate if including or excluding the temperature and/or pressure measurements at the nonperforated sections along the completion interval could help enhance the parameter estimation problem. The results show that when multiple profiles of temperatures including the data at nonperforated zones at different production rates are regressed, reliable estimates of the individual layer properties that predict the production-inflow profile accurately can be obtained, though layer permeability and skin factors may often exhibit wide 95% confidence intervals and high correlations among them. Adding sandface or wellbore pressure data, if available, into observed data sets in history matching always improves the quality of parameter estimation.