Gas Flow Equations Research Articles

Thermochemical reduction modeling in a high-temperature moving-bed reactor for energy storage: 1D model

The design of robust and efficient high-temperature thermochemical reactors and determination of operating conditions are critical steps toward enabling high-efficiency long-duration solar energy storage. This work presents a computational model for the thermal reduction of a metal oxide material (Mg-Mn-O) up to 1450 °C and the coupled complex transport phenomena in a novel tubular thermal reactor design that features the capability for a high extent-of-reduction (high energy storage density) and inherent heat recuperation. A one-dimensional model coupling counter-current gas–solid flow, two-phase heat transfer, thermochemical redox reactions, and species transport in a moving-bed reactor is developed. Simplified versions of the model are validated with published results in the literature for packed beds with both inert and reactive particles; the fully coupled model is also validated with experimental measurements of a moving-bed reactor in terms of local temperatures and oxygen release at the exit. Detailed comparisons on the effects of different boundary conditions in the reaction zone (prescribed wall temperature vs. heat flux conditions) and formulations based on a simple uniform flow assumption vs. plug flow using Ergun equation for gas flow are investigated. The results are compared with experimental measurements, and for all cases, the energy flow components in the reactor system and the thermal to chemical conversion efficiency and overall system efficiency are computed. The predicted high thermal-to-chemical efficiency ∼95% and system efficiency ∼30% agree with experimental measurements.

Determining reservoir parameters with nonisothermal real gas flow

Creation and developing methods of determining gas reservoir properties are one of the most important gas hydrodynamics tasks as production project efficiency and reservoir exploitation depend upon layer properties knowledge. Nonstationary gas hydrodynamics investigations are one of the base well and layer researching methods. Results of these investigations are interpreted based on solving of linear isothermal gas flow equation. The current investigation describes the nonstationary gas hydrodynamic survey results interpretation algorithm, which is based on nonlinear equations system solving. The system consists of nonlinear nonisothermal real gas flow and energy equations accounting well influence, Joule-Thompson and adiabatic expansion effects. Integro-interpolation and iteration finite methods were used for creating their own numerical algorithm. Numerical programs allow solving as direct as inverse gas flow tasks in the cylindrical layer. For verification of inverse task solution, the survey interpretation results from the real gas field were paralleled with currently methods results and showed sufficient accuracy. The described method allows to interpret survey gas hydrodynamic results accounting real gas and porous matrix properties, and well influence to enhance integrity and precision reservoir properties estimation.

Goaf Gas Control Improvement by Optimizing the Adjacent Roadway Large-Diameter Boreholes

This study introduced gas control technology in goaf using adjacent roadway large-diameter (550 mm) boreholes to control gas accumulation in the upper corner of a fully mechanized working face in high-gas coal seams. The gas control process in the upper corner and gas interception in goaf by large-diameter boreholes was analyzed using the CFD model of the gas flow in goaf. The latter considered the control equation of gas flow, the established permeability model of goaf, and the gas emission law in goaf. Using the 2-105 working face of the Tenghui Coal Mine, Shanxi Province, China, as a case study, the distribution patterns of gas concentration and flow field in the goaf for various extraction flow parameters and different positions of boreholes were numerically simulated. The dependences between various locations, drainage flows, and the gas concentration in the upper corner were determined and fitted by engineering equations. The evolution pattern of the spontaneous combustion zone in the goaf under the drainage conditions was also analyzed. The optimal borehole configuration parameters ensuring the extraction flow rate exceeding 3 m·s−1 and the effective gas control in the upper corner of the working face at a distance of 5 m–15 m behind the working face were identified. The engineering practice proved the feasibility of gas control in the goaf using the adjacent roadway large-diameter borehole. The gas concentrations in the return airflow and the upper corner of the working face were kept below 0.65 and 0.8%, respectively, to ensure production safety and improve the gas utilization efficiency.

Distributionally robust day-ahead operation of power systems with two-stage gas contracting

Due to stronger interactions between power and gas systems promoted by the deployment of fast-response gas-fired power plants and the advanced technology of power-to-gas facilities, secure and optimal energy management becomes highly challenging. In industrial practice, the two systems are operated by different regulatory authorities, which is commonly neglected in the existing studies, therefore, information exchange is limited, and bilateral energy transactions are vital. This paper revisits the day-ahead operation of the coupled power and gas system with large-scale wind power generation integration, where a two-stage gas contracting mechanism is proposed to incorporate cost-effective day-ahead and rarely-event real-time gas contracts. To balance the robustness and the conservativeness of the operation strategy, a distributionally robust optimization (DRO) based decision-making framework is derived, which effectively handles the proposed mechanism. The intractable DRO model is reformulated to be solved by the nested column and constraint generation algorithm. The nonconvex gas flow equations are approximated as convex ones, which are solved by a difference-of-convex programming-based procedure to find feasible solutions. Simulation results demonstrate the benefits of the DRO and two-stage contract modeling.

New exact solutions for microscale gas flows

We present a number of exact solutions to the linearised Grad equations for non-equilibrium rarefied gas flows and heat flows. The solutions include the flow and pressure fields associated to a point force placed in a rarefied gas flow close to a no-slip boundary and the temperature field for a point heat source placed in a heat flow close to a temperature jump boundary. We also derive the solution of the unsteady Grad equations in one dimension with a time-dependent point heat source term and the Grad analogue of the rotlet, a well-known singularity of Stokes flow which corresponds to a point torque.

The phenomena of concentration and cavitation in the Riemann solution for the isentropic zero-pressure dusty gasdynamics

The aim of the present paper is to investigate the concentration and cavitation phenomenon in the solution of the Riemann problem (RP) to the pressureless isentropic Euler equations for the dusty gas flow by using the two parameter flux approximation. The similar solution of the RP for dusty gas flow is obtained. The formation of δ-shock and vacuum state in the flow field is discussed. Also, it is shown that the solution, containing two shock waves, of the RP to the isentropic Euler equations for dusty gas converges to the δ-shock wave solution of the transport equations and the solution, containing two rarefaction waves, of the RP converges to the vacuum state solution of the transport equations.

The Partial Transformational Decomposition Method for a Hybrid Analytical/Numerical Solution of the 3D Gas-Flow Problem in a Hydraulically Fractured Ultralow-Permeability Reservoir

SummaryThe analysis of gas production from fractured ultralow-permeability (ULP) reservoirs is most often accomplished using numerical simulation, which requires large 3D grids, many inputs, and typically long execution times. We propose a new hybrid analytical/numerical method that reduces the 3D equation of gas flow into either a simple ordinary-differential equation (ODE) in time or a 1D partial-differential equation (PDE) in space and time without compromising the strong nonlinearity of the gas-flow relation, thus vastly decreasing the size of the simulation problem and the execution time.We first expand the concept of pseudopressure of Al-Hussainy et al. (1966) to account for the pressure dependence of permeability and Klinkenberg effects, and we also expand the corresponding gas-flow equation to account for Langmuir sorption. In the proposed hybrid partial transformational decomposition method (TDM) (PTDM), successive finite cosine transforms (FCTs) are applied to the expanded, pseudopressure-based 3D diffusivity equation of gas flow, leading to the elimination of the corresponding physical dimensions. For production under a constant- or time-variable rate (q) regime, three levels of FCTs yield a first-order ODE in time. For production under a constant- or time-variable pressure (pwf) regime, two levels of FCTs lead to a 1D second-order PDE in space and time. The fully implicit numerical solutions for the FCT-based equations in the multitransformed spaces are inverted, providing solutions that are analytical in 2D or 3D and account for the nonlinearity of gas flow.The PTDM solution was coded in a FORTRAN95 program that used the Laplace-transform (LT) analytical solution for the q-problem and a finite-difference method for the pwf problem in their respective multitransformed spaces. Using a 3D stencil (the minimum repeatable element in the horizontal well and hydraulically fractured system), solutions over an extended production time and a substantial pressure drop were obtained for a range of isotropic and anisotropic matrix and fracture properties, constant and time-variable Q and pwf production schemes, combinations of stimulated-reservoir-volume (SRV) and non-SRV subdomains, sorbing and nonsorbing gases of different compositions and at different temperatures, Klinkenberg effects, and the dependence of matrix permeability on porosity. The limits of applicability of PTDM were also explored. The results were compared with the numerical solutions from a widely used, fully implicit 3D simulator that involved a finely discretized (high-definition) 3D domain involving 220,000 elements and show that the PTDM solutions can provide accurate results for long times for large well drawdowns even under challenging conditions.Of the two versions of PTDM, the PTD-1D was by far the better option and its solutions were shown to be in very good agreement with the full numerical solutions, while requiring a fraction of the memory and orders-of-magnitude lower execution times because these solutions require discretization of only the time domain and a single axis (instead of three). The PTD-0D method was slower than PTD-1D (but still much faster than the numerical solution), and although its solutions were accurate for t < 6 months, these solutions deteriorated beyond that point.The PTDM is an entirely new approach to the analysis of gas flow in hydraulically fractured ULP reservoirs. The PTDM solutions preserve the strong nonlinearity of the gas-flow equation and are analytical in 2D or 3D. This being a semianalytical approach, it needs very limited input data and requires computer storage and computational times that are orders-of-magnitude smaller than those in conventional (numerical) simulators because its discretization is limited to time and (possibly) a single spatial dimension.

Multi-objective transient peak shaving optimization of a gas pipeline system under demand uncertainty

It is the primary responsibility of a gas pipeline company to satisfy the gas demand of customers and ensure the economical operation of its pipelines. This paper presents a stochastic multi-objective transient peak shaving optimization model that considers uncertainty in gas demand while optimizing operational schemes of compressors and peak shaving measures of underground gas storages. The model is a rigorous multi-objective non-linear program (NLP) constrained by governing gas flow equations, operating envelopes of centrifugal compressors, and thermodynamic equations that model natural gas properties. The proposed multi-objective model aims to minimize the operational costs (the sum of the electricity cost of compressor stations and the gas withdrawal cost of underground gas storage) and maximize the line pack at the end of the time horizon subject to multiple legal and physical constraints. The model was tested on a real gas pipeline system, and a set of Pareto optimal solutions are obtained. The optimal operational schemes and peak shaving measures under three typical Pareto optimal solutions are analyzed in detail, and numerical results are presented following stochastic and robust optimization approaches.

A data-driven approach towards fast economic dispatch in electricity–gas coupled systems based on artificial neural network

The optimization of electricity–gas coupled systems is typically complicated by the nonconvex relationships such as gas flow equations. Piecewise linearization, despite being one of the few solutions that guarantee exactness and optimality, is often discarded for an exceptionally long computational time. In this paper, we present a novel data-driven approach based on artificial neural networks, to enable fast economic dispatch in electricity–gas coupled systems, by utilizing simulation data from the piecewise-linearization-based model-driven method. Load profiles at each electric bus and gas node are fed into the artificial neural network as input neurons; optimal economic dispatch results are set as output neurons, where the dispatch results can be either continuous (e.g. power and gas output) or binary (e.g. scenario feasibility). In generating power and gas outputs, the slack generator method is proposed to further eliminate load mismatch. Case studies on an integrated Belgium 20-node gas/IEEE 24-bus power system show that, after the artificial neural network is properly trained, the data-driven economic dispatch method is 104∼105 times faster than model-driven piecewise linearization. It even outperforms second-order cone programming, a well-known convex relaxation technique to model natural gas systems, in terms of both the coupled system’s state recovery accuracy and computational efficiency. Furthermore, the data-driven method is applied to a multi-period dispatch problem to demonstrate its scalability.

Effect of Radiative Filling Gas in Compound Parabolic Solar Energy Collectors

In the present paper, the use of radiating gas instead of air inside the cavity of compound parabolic collectors (CPSs) is suggested and verified by numerical analysis. The collector under study has a simple cone shape with flat absorber which is filled with a participating gas such as carbon dioxide instead of air for the purpose of increasing the thermal performance. In numerical simulation, the continuity, momentum and energy equations for the steady natural convection laminar gas flow in the CPC’s cavity and the conduction equation for glass cover and absorber plate were solved by the finite element method (FEM) using the COMSOL multi-physics. Because of the radiative term in the gas energy equation, the intensity of radiation in participating gas flow should be computed. Toward this end, the radiative transfer equation (RTE) was solved by the discrete ordinate method (DOM), considering both diffuse and collimated radiations. The approximation was employed in calculation of the diffuse part of radiation. It was observed that the gas radiation causes high temperature with more uniform distribution inside the cavity of collector. Also, numerical results reveal more than 3% increase in the rate of heat transfer from absorber surface into working fluid and hence a desired performance for the collector because of the gas radiation effect. Comparison between the present numerical results with theoretical and experimental data reported in the literature showed good consistency.

High‑Order Bicompact Schemes for Numerical Modeling of Multispecies Multi-Reaction Gas Flows

Euler equations for multidimensional inviscid gas flows with multispecies and multi‑reaction are considered. By using the Marchuk–Strang splitting method, an implicit numerical scheme for this system is constructed. Its convection part is computed using the bicompact scheme SDIRK3B4 of fourth order in space and third order in time, while its chemical part is computed using the L-stable Runge–Kutta method of second order. The SDIRK3B4 scheme is compared with the WENO5/SR scheme in the case of one- and two-dimensional flows with detonation waves. It is shown that the SDIRK3B4 scheme has the same actual accuracy as the WENO5/SR, but the former needs fewer time steps by a factor of 20–40 and does not require any special algorithms to suppress the nonphysical breakdown of detonation waves on relatively coarse meshes.

Енергоефективність заправки автомобільного транспорту стиснутим природним газом при використанні газогідратного акумулятора

The article briefly describes the processes carried out during the operation of the gas hydrate accumulator (GHA) at the automobile gas-filling compressor station (AGCS): formation of natural gas hydrates, their accumulation and storage, and melting with the release of natural gas at high-pressure р = 25MPa, sufficient for full refueling gas cylinders. The circuit-constructive solution of filling with compressed natural gas in AGCS-GHA is offered, and the principle of its work is described in a good example. It is shown that during AGCS-GHA operation with four compression stages and ACG compressed gas accumulators, the gas from GHA to ASG moves in the connecting pipeline at adiabatic conditions at subcritical speed, i.e., below the speed of sound, because the pressure ratio рASG / рGHA coefficient is more critical. Calculations performed for these conditions by thermodynamic equations of gas flow in the subcritical mode of motion, without losses, showed that the velocity in a pipe with a diameter of d = 15 mm has a value of w = 793 m / s. This will ensure a specific gas supply from GHA to ASG at the level of m = 0.178 kg / s. It is proposed to use the coefficient efficiency of refueling to characterize the energy efficiency of refueling vehicles with compressed natural gas in AGCS-GHA. According to the results of calculations, it is evident that the energy efficiency of refueling vehicles with compressed natural gas in AGCS-GHA is 6% higher than in traditional AGCS at the same conditions: the corresponding values of coefficient refueling efficiency = 0.47 and = 0.41. The article also illustrates that in the process of melting gas hydrates in GHA at a temperature of t = 26-28 0C, one can get compressed natural gas at a pressure of р = 30-35 MPa, which will use AGCS-GHA without additional compressor equipment for refueling mobile gas stations (PAGZ), in which the optimal values of the maximum pressure are in the range of 32-35 MPa.

Multiscale simulation of molecular gas flows by the general synthetic iterative scheme

The in-depth knowledge of rarefied gas dynamics is crucial to address challenges in a wide range of engineering problems, where gas flows are usually multiscale, i.e., covering a wide range of Knudsen numbers. As the traditional Navier–Stokes equations fail, gas kinetic equations are required to model the flows. So far, very few numerical methods are designed to efficiently solve the multiscale gas dynamics and reveal the role of internal degrees of freedom of gas molecules. In this work, a general synthetic iterative scheme (GSIS) is proposed to find steady-state solutions of the gas kinetic equations for molecular gas flows accurately and efficiently, where the gas kinetic equations are solved together with the macroscopic synthetic equations that expedite solutions towards the steady state. In the macroscopic synthetic equations, while the momentum equation is the same as that used in the GSIS for monatomic gas, two energy equations are introduced here for polyatomic gases: one is for the translational energy and the other for the internal energy; these equations are derived exactly from the gas kinetic equations hence no approximation is made in final solutions. The Fourier stability analysis is performed to show that the GSIS permits fast convergence to steady-state solutions in the entire flow regime; meanwhile the asymptotic analysis shows that the GSIS recovers the Navier–Stokes equations when the Knudsen number is small, even on the spatial grid with cell size much larger than the molecular mean free path. With all these unique features, several challenging numerical examples are given to show that the proposed GSIS is a promising tool to simulate multiscale molecular gas flows and investigate the effects of internal degrees of freedom.

Оценка концентрации оксидов азота на выходе из камеры сгорания модельной газовой турбины

The study applies a new technique for evaluating the NOx concentration when burning syngas in the gas turbine combustion chamber. The technique allows correlating the complete detailed mechanism of the Grimech 3.0 array of parallel reactions with the computer hydrodynamics equations (motion, heat and mass transfer, turbulence, and molecular diffusion equations for an ideal gas flow). Selectivity diagrams of the NOx formation process including eleven key reactions are built based on the specific reaction rates for lean and rich fuel mixtures. Verification calculations have been performed based on a model gas turbine combustion chamber within a fuel-air equivalence ratio of 0.5–2. The new technique has been applied for determining the NOx emissions and the maximum temperature of the industrial combustion chamber fire tube wall. The GE gas composition showed the best NOx emission result. The most problematic is Polk Power and Texaco syngas (oxygen process). When burning LCV gases in the primary air suction area, a recirculation zone is observed; due to the high heat release in this area, the maximum wall temperature is about 500 °С.

N-k interdiction modeling for natural gas networks

Although electricity transmission systems are typically very robust, the impacts that arise when they are disrupted motivate methods for analyzing outage risk. For example, N-k interdiction models were developed to characterize disruptions by identifying the sets of k power system components whose failure results in “worst case” outages. While such models have advanced considerably, they generally neglect how failures outside the power system can cause large-scale outages. Specifically, failures in natural gas pipeline networks that provide fuel for gas-fired generators can affect the function of the power grid. In this study, we extend N-k interdiction modeling to gas pipeline networks. We use recently developed convex relaxations for natural gas flow equations to yield tractable formulations for identifying sets of k components whose failure can cause curtailment of natural gas delivery. We then present a novel cutting-plane algorithm to solve these problems. Finally, we use test instances to analyze the performance of the approach in conjunction with simulations of outage effects on electrical power grids.

An experimentally verified three-dimensional non-stationary fluid model of unloaded atmospheric pressure inductively coupled plasmas

A three-dimensional non-stationary numerical model of spectrochemical and technological inductively coupled plasma (ICP) systems is presented in the paper. The model considers the ICP as a gaseous media (with temperature-dependent electric conductivity) interacting with electromagnetic field generated by inductive coil. The model is based on simultaneous solution of the Maxwell’s and gas flow equations together with the energy equation coupled-together by corresponding source terms and material properties to take into account inductive current forming within the carrier gas and subsequent Joule heating, the Lorentz force and how does it affect the gas flow pattern. It allows calculation of temporal evolution of three-dimensional distributions of electromagnetic fields, pressure, gas velocity and temperature within a plasma torch and a condensation chamber used for powder processing. The model is applicable for simulation of atmospheric pressure electrodeless plasmas under local thermodynamic equilibrium that consist of pure gases and their mixtures. Such operating conditions are typical for ICPs that are used for elemental analysis and technological powder processing. Special attention is paid to experimental verification of the model. The simulation results are cross-verified for both types of ICPs (spectrochemical and technological one) using high-speed optical and schlieren visualization of gas flows. The discrepancy between calculations and experimental data does not exceed 10%.

Affine Policies for Flexibility Provision by Natural Gas Networks to Power Systems

Using flexibility from the coordination of power and natural gas systems helps with the integration of variable renewable energy in power systems. To include this flexibility into the operational decision-making problem, we propose a distributionally robust chance-constrained co-optimization of power and natural gas systems considering flexibility from short-term gas storage in pipelines, i.e., linepack. Recourse actions in both systems, based on linear decision rules, allow adjustments to the dispatch and operating set-points during real-time operation when the uncertainty in wind power production is revealed. We convexify the non-linear and non-convex power and gas flow equations using DC power flow approximation and second-order cone relaxation, respectively. Our coordination approach enables a study of the mitigation of short-term uncertainty propagated from the power system to the gas side. We analyze the results of the proposed approach on a case study and evaluate the solution quality via out-of-sample simulations performed ex-ante.

Invariant subspaces and exact solutions for some types of scalar and coupled time-space fractional diffusion equations

We explain how the invariant subspace method can be extended to a scalar and coupled system of time-space fractional partial differential equations. The effectiveness and applicability of the method have been illustrated through time-space (i) fractional diffusion-convection equation, (ii) fractional reaction-diffusion equation, (iii) fractional diffusion equation with source term, (iv) two-coupled system of the fractional diffusion equation, (v) two-coupled system of fractional stationary transonic plane-parallel gas flow equation and (vi) three-coupled system of fractional Hirota-Satsuma KdV equation. Also, we explicitly presented how to derive more than one exact solution of the equations as mentioned above using the invariant subspace method.

Modeling and Simulation of Pigging for a Gas Pipeline Using a Bypass Pig

The pipeline inspection gauge (PIG, lowercase pig is commonly used) with a bypass valve is widely used in pipeline inspection because it operates at a low speed without reducing the flow rate. Understanding the dynamics of a bypass pig in a gas pipeline would contribute to the design of the pig and the control of pig speed. This paper deals with the dynamic model for the process of a bypass pig travelling through a hilly gas pipeline. The method of characteristics (MOC) is used to solve the equations of unsteady gas flow. The backward flow of the gas in the bypass valve and pipe is shown by a simulation of pigging for a hilly gas pipeline. Parametric sensitivity analysis of pigging in the horizontal gas pipe using a bypass pig is then carried out. The results indicate that the speed of a bypass pig is most sensitive to the gas speed in the pipe followed by the bypass area and the friction of the pig. A formula, obtained from the results of the simulations using response surface methodology (RSM), is presented to predict the steady speed of a bypass pig in the horizontal gas pipeline.

Computational study of plasma-induced flow instabilities in power modulated atmospheric-pressure microwave plasma jet

This work presents a combined experimental and simulation-based investigation of gas flow perturbations caused by atmospheric-pressure microwave plasma jet with modulated power. These plasma-induced flow instabilities are observed experimentally by schlieren imaging and the mechanism of their formation is explained using a numerical model. The model offers a time-resolved self-consistent solution of plasma dynamics, gas flow, and heat transfer equations. The simulation results are in good agreement with the experimental observations and we conclude that the key mechanism behind the flow perturbations is rapid gas heating at the end of the discharge tube.