Real Gas Effects Research Articles

Numerical Investigation and Experimental Comparison of the Gas Dynamics in a Highly Underexpanded Confined Real Gas Jet

A numerical study for a supersonic underexpanded argon gas jet driven by a pressure ratio of 120 is described in this work, and the results are compared to experiments. A single phase large-eddy simulation (LES) employing a fully-coupled pressure-based finite volume solver framework is carried out. The numerical results are validated against experimental Schlieren and particle-image-velocimetry (PIV) measurements taken under the same conditions. Due to the high pressure conditions imposed on the gas, real gas effects are taken into account via the Peng-Robinson equation of state. This approach enables the accurate prediction of the gas properties throughout all pressure conditions encountered within this study. Flow velocity data obtained from numerical simulations and experiments are presented, leading to valuable insights into the features of the flow. Comparisons between experimental and numerical Schlieren images show a very good agreement for the location and shape of the main shock structure in the near nozzle exit region. The predicted velocity field further downstream, at a stream-wise distance over 100 nozzle diameters from the nozzle exit, is reasonably close to the PIV data, with less than 25% difference between the root-mean-square (RMS) simulated and experimental velocity field. The agreement obtained in this study is remarkable in light of the challenging flow configuration involving a vast range of flow speeds and time scales. There are also discrepancies, predominantly for the near-throat velocity profiles obtained from PIV measurements and numerical simulations: in the immediate post-shock region the simulation results predict a major converging throat of low, subsonic fluid velocity surrounded by the supersonic shear layer, which is not observed in the experiment.

Estimation of Shale Apparent Permeability for Multimechanistic, Multicomponent Gas Production Using Rate Transient Analysis

Gas-producing shale and ultratight reservoirs are playing a key role in the energy industry and the global gas market. Compositional simulation of gas production from shale media in the presence of different mechanisms such as viscous flow, slip flow (Klinkenberg effect), Knudsen diffusion, sorption, pore radius variation, and real gas effect is a computational challenge. In this work, we present a model that takes into account all of the noted mechanisms of gas transport in shale media. It is shown that the compositional effect of gas in shale media can be lumped into a single component by introducing an apparent gas permeability, which can be estimated from the conventional rate transient analysis. The main contribution of this study is a workflow incorporating the relevant physics into a single term (apparent permeability) that will substitute the Darcy permeability. This procedure reduces the simulation runtime substantially and will find applications in reservoir characterization and simulation of pr...

A New Unified Gas-Transport Model for Gas Flow in Nanoscale Porous Media

SummaryA new unified gas-transport model has been developed to characterize single-component real-gas flow in nanoscale organic and inorganic porous media by modifying the Bravo (2007) model. More specifically, a straight capillary tube is characterized by a conceptual layered model consisting of a viscous-flow zone, a Knudsen-diffusion zone, and a surface-diffusion zone. To specify the contributions of the viscous flow and the Knudsen diffusion to the gas transport, the virtual boundary between the viscous-flow and Knudsen-diffusion zones is first determined using an analytical molecular-kinetics approach. As such, the new unified gas-transport model is derived by integrating the weighted viscous flow and Knudsen diffusion, and coupling surface diffusion. The model is also comprehensively scaled up to the bundles-of-tubes model considering the roughness, rarefaction, and real-gas effect. Nonlinear programming methods have been used to optimize the empirical parameters in the newly proposed gas-transport model. Consequently, the newly proposed gas-transport model yields the most accurate molar fluxes compared with the Bravo (2007) model and four other analytical models. One of the advantages of the new unified gas-transport model is its great flexibility, because the Knudsen number is included as an independent variable, which also endows the newly proposed model with the capability to cover the full-flow regimes. In addition, the apparent permeability has been mathematically derived from the new unified gas-transport model. A series of simulations has been implemented using methane gas. It is found through sensitivity analysis that apparent permeability is strongly dependent on pore size, porosity, and tortuosity, and weakly dependent on the surface-diffusivity coefficient and pore-surface roughness. The increased viscosity can reduce the total molar flux in the inorganic pores up to 66.0% under the typical shale-gas-reservoir conditions. The viscous-flow mechanism cannot be neglected at any pore sizes under reservoir conditions, whereas the Knudsen diffusion is found to be important when pore size is smaller than 2 nm and pressure is less than 35.0 MPa. The contribution of surface diffusion cannot be ignored when the pore size is smaller than 10 nm and the pressure is less than 15.0 MPa.

Numerical Modeling of Evaporation and Combustion of Isolated Liquid Fuel Droplets: a Review

Understanding the transport processes during evaporation and combustion of isolated liquid fuel droplet is highly important in several applications involving sprays. Comprehensive numerical models assist in carrying out simulations involving interlinked transport processes in liquid and gas phases using proper interface coupling conditions. The predictions from such numerical models reveal flow, temperature and species fields, with which the evaporation, as well as combustion characteristics, can be thoroughly analyzed. In this article, a detailed review of numerical models used to simulate evaporation of isolated droplets under several operating conditions is presented. This includes evaporation in high-pressure conditions, where real gas effects and solubility of ambient gas into the liquid droplet, come into play. Subsequently, a review of droplet combustion models, which are comprehensive enough to reveal the burning characteristics of an isolated droplet, is presented. Importance of liquid phase motion on evaporation and combustion behavior and water absorption in the case of alcohol droplets are reported. This review also includes modeling concepts applied to multi-component droplets.

Analysis of production prediction in shale reservoirs: Influence of water film in inorganic matter

To commercially develop shale gas reservoirs, multi-fractured horizontal wells are widely employed in the industry. A number of analytical models have been proposed to evaluate and forecast production from fractured horizontal wells. However, the water film adsorbed in inorganic pores of shale matrix is often neglected and its effect on gas production has never been focused on. Moreover, the effect on gas production caused by the characteristic of a well not located in the center of drainage area has not been drawn much attention. In this work, on a basis of enhanced-fracture-region (EFR) model, a new model is put forward to conduct production prediction of multi-fractured horizontal wells from shale gas reservoirs. This novel approach incorporates critical gas transport mechanisms in shale, and considers the characteristic of a well not located in the center of drainage area. Specifically, this model takes the bulk-gas transport regimes, water film effect, stress dependence and real gas effect into account, which matches well with the real shale reservoirs. The analytical solution of the proposed model is deduced by employing the Laplace transformation approach, and then introducing the numerical algorithm put forward by Stehfest to invert to the real time domain. This presented model is verified by both numerical simulation cases and actual field applications. In addition, a sensitivity study is performed to illustrate various parameters on flow-regime and production curves. Results illustrate that both the size of stimulated zone and distance from the well to the outer boundary contribute to the well performance. A larger size of the stimulated zone increases the duration of the first linear flow period, whereas will shorten the duration of the third boundary dominated flow period. A larger distance from the well to the outer boundary leads to stronger gas production. The real gas has non-obvious effect on gas production. Both the stress dependence and humidity have negative effects on production curves, which are induced by the decrease of the effective pore radius. Specifically, compared with the gas production without considering water film effect, when the humidity value is 0.1, gas production can achieve an average decrease of 18.57%. When the humidity value is 0.3, gas production can reach an average decrease of 26.10%.

Transport behaviors of real gas mixture through nanopores of shale reservoir

Abstract The modeling of shale gas transport through nanopores is the basis for shale gas production simulation. The real shale gas always consists of a series of gases, including ethane, propane and hydrogen sulfide etc. Previous models neglected the multi-component effect on the shale gas transport mechanisms. In this paper, a novel model is presented for simulating the real gas mixture transport through nanopores of shale formation. Firstly, a model is presented for ideal shale gas transport through nanopores considering the multi-component effect, then, the real gas effect is coupled into the model. Simulation results show that: (a) When it is under low pressure level condition, the conductivities of slippage flow and Knudsen diffusion increase with decreasing methane fraction. (b) When it is under medium pressure level condition, the conductivities of slippage flow and Knudsen diffusion increase with decreasing methane fraction. (c) Under high pressure condition, the conductivities of different flow patterns increase with decreasing methane fraction.

High-Enthalpy Effects on Hypersonic Boundary-Layer Transition

In the present study, three boundary-layer stability codes are compared based on hypersonic high-enthalpy boundary-layer flows around a blunted 7 deg half-angle cone. The code-to-code comparison is conducted between the following codes: the Nonlocal Transition analysis code of the DLR, German Aerospace Center (DLR); the Stability and Transition Analysis for hypersonic Boundary Layers code of VirtusAero LLC; and the VKI Extensible Stability and Transition Analysis code of the von Kármán Institute for Fluid Dynamics. The comparison focuses on the role of real-gas effects on the second-mode instability, in particular the disturbance frequency, and deals with the question on how far not accounting for real-gas effects compromises the stability analysis. The experimental test cases for the comparison are provided by the DLR High Enthalpy Shock Tunnel Göttingen and the Japan Aerospace Exploration Agency High Enthalpy Shock Tunnel. The focus of the comparison between the stability results and the measurements is, besides real-gas effects, the influence of uncertainties in the mean flow on the stability analysis.

A NEW FRACTAL TRANSPORT MODEL OF SHALE GAS RESERVOIRS CONSIDERING MULTIPLE GAS TRANSPORT MECHANISMS, MULTI-SCALE AND HETEROGENEITY

Duo to different transport mechanisms and gas storage in organic and inorganic systems, a new triple-continuum model coupling Discrete Fracture Model (DFM) was established to investigate gas flow in shale gas reservoir. Considering the multi-scale and heterogeneity of shale matrix, fractal theory was used to calculate the apparent permeability of organic and inorganic systems while multiple gas transport mechanisms such as viscous flow, Knudsen diffusion, surface diffusion, gas absorption/desorption effect and real gas effect were incorporated. This coupled mathematical model was solved by Finite Element Method (FEM) and the presented fractal apparent permeability model was validated with the experimental data. The results show that fractal characteristics of shale matrix have great impact on gas reservoir performance. The model without considering the influence of fractal characteristics could lead to underestimate gas production by approximately 17%. Viscous flow is the dominate transport mechanisms of shale gas and Knudsen diffusion has an impact on gas flow when the pressure declines. Surface diffusion should be only considered in organic systems and can be ignored. Then the results of sensitivity analysis show that the characteristic parameters of inorganic matter have a greater impact than those of organic matter and establishing a triple-continuum model with considering comprehensive effect of organic and inorganic matter is necessary. In addition, gas production would decrease as the pore fractal dimension and tortuosity fractal dimension increase, which results from the increasing number of small pores and more tortuous path for gas flow.

Condensation characteristics of natural gas in the supersonic liquefaction process

The real gas effect was not taken into account in the current nucleation models, which will cause relatively big errors in the simulation of condensation process, and the supersonic condensation characteristics in the nozzle are still not clear now. Therefore, the fugacity is introduced into the model to increase the calculation accuracy of nucleation rate. Based on the modified model, the supersonic condensation process of the methane-ethane binary mixture was studied to clarify the nucleation and droplet growth process. Then the condensation characteristics of natural gas with different operation parameters were analyzed. The results show that in the condensation process of methane-ethane binary mixture, the ethane vapor first reaches critical radius and breaks through the free energy barrier and serve as the condensation nuclei for methane and ethane gas. The latent heat of condensation plays a dominant role in the change of the droplet growth rate of the binary mixture. Higher pressure or lower temperature or higher ethane content will result in greater nucleation rate and humidity.

On the dynamic modeling of Brayton cycle power conversion systems with the CATHARE-3 code

As the share of intermittent energy sources is increasing, the dynamic modeling of thermal power plants including their power conversion system gets researchers' attention. Recent applications require transient simulations of high-pressure nitrogen closed Brayton cycle for which the ideal gas assumption is no longer verified. In this work, the REFPROP real gas equation of state and pressure drop correlations suitable for high Reynolds numbers have been implemented in the CATHARE-3 code. Moreover, new real gas turbomachinery and sonic flow models have been developed and integrated in the code. Relative errors obtained for the nominal state of a high-pressure nitrogen closed Brayton cycle are in the range −3%/+0.8%. A detailed analysis of real gas effects is carried out on the heat exchangers heat flux and the piping pressure losses. The new sonic flow computed during a loss of coolant accident is in the best possible agreement with literature experimental results. With regard to the turbomachinery, the new real gas model creates a pressure dependence that brings compressors closer to the choke region when the pressure drops in the cycle. This work is expected to provide an efficient and reliable simulation tool for transient analysis of real gas closed Brayton cycles.

Modeling of interaction of long-wave disturbances with a shock wave on a flat plate with allowance for real gas effects

The problem of the long-wave disturbance interaction with a shock wave on a wedge at an angle of attack is considered. Numerical simulations are performed by solving two-dimensional unsteady Navier–Stokes equations with the module addition created by the user and allowing taking into account the vibrational nonequilibrium of carbon dioxide molecules within the two-temperature model of relaxation flows. A parametric study on the effect of Mach numbers, Reynolds numbers and angles of attack on the disturbance transformation coefficients is carried out for the following gases: equilibrium air, equilibrium vibrationally excited CO2, and nonequilibrium CO2. The calculation results on the pressure pulsations on the model surface were compared with the data obtained for long-wave disturbance from the general solution of the inviscid problem of the disturbance interaction with a shock wave on a wedge [1]. It is shown that the obtained long wavelength disturbance transformation coefficients are practically the same as for the inviscid case in the studied range of Mach numbers (M∞=4.5÷8.9).

Gas permeability calculation of tight rocks based on laboratory measurements with non-ideal gas slippage and poroelastic effects considered

Permeability measurements on low-permeable rocks in the laboratory require much higher pressure gradients than those in real reservoirs to produce detectable flow rates in finite laboratory time. This may result in a high effective stress gradient that can cause non-uniform deformation of the pore system. To better understand the measured laboratory data, a theoretical model has been developed for calculating gas permeability of tight rock from laboratory measurements, which couples the effect of poroelastic deformation with the gas non-ideality and slippage effects. The proposed characteristic pressure model considers the poroelastic deformation and the real gas effects in the permeability calculation, which improves the accuracy of calculated permeability from laboratory measurements of tight rocks under large pressure gradients. The new model is validated by independent multiscale simulations, in which the poroelastic deformation and slippage effects are captured on the pore scale while the real gas behavior is captured on the core scale. The numerical results also indicate that the poroelastic deformation mainly affects the high-pressure region while the variation of gas properties dominates the low-pressure region. The new model is then applied to the calculation of gas permeability based on the laboratory measurements on coal and shale samples with non-ideal gas slippage and poroelastic effects considered. The poroelastic deformation and the real gas effect can be important as well as the slippage effect and the calculated apparent permeability will be overestimated if these two effects are neglected.

Concentration-Dependent Diffusion Coefficients of Binary Gas Mixtures Using a Loschmidt Cell with Holographic Interferometry

A model-based experimental approach is presented to measure concentration-dependent diffusion coefficients of binary gases from a single experimental run. The diffusion experiments are performed with a Loschmidt cell combined with holographic interferometry that has been improved in Part I of this paper (Wolff et al. in Int. J. Thermophys. 2018, https://doi.org/10.1007/s10765-018-2450-8 ). Measurements are taken with the system helium–krypton. Besides highly accurate measurements, a highly accurate diffusion model is required to retrieve the weak concentration dependence of the diffusion coefficient. We derive a consistent diffusion model considering real gas effects and the concentration dependence of the diffusion coefficient. The model describes the experimental fringe data with deviations of less than 0.2 interference fringe orders, which corresponds to a relative deviation of 0.17 % indicating high quality of both the experimental data and the employed model. Therefore, the concentration dependence of the helium–krypton diffusion coefficient could be successfully retrieved from a single experiment of mixing pure gases. Thus, the presented approach allows for the efficient characterization of diffusion in gases.

Investigation of a highly underexpanded jet with real gas effects confined in a channel: flow field measurements

This article describes experiments to investigate the fluid-to-wall interaction downstream of a highly underexpanded jet, with a pressure ratio of 120, confined in a channel. Heat transfer induced by Joule-Thomson cooling, which is a real gas effect in such a configuration, has critical implications on the safety of pressurised gas components. This phenomenon is challenging to model numerically due to the requirement to implement a real gas equation of state, the large range of (subsonic and supersonic) velocities, the high turbulence levels and the near-wall behaviour. An experimental setup with simple geometry and boundary conditions, and with a wide optical access was designed and implemented. It consisted of a high-pressure gas reservoir at controlled temperature and pressure, discharging argon through a nozzle into a square channel. This facility was designed to allow for a steady-state expansion from over 120 bar to atmospheric pressure for over 1 min. The choice of fluid, pressure and temperature regulation system, and the implementation of a high pressure particle seeding system are discussed. The gas dynamics of this flow was then investigated by two separate optical techniques. Schlieren measurements were used to locate the position of the Mach disk, and planar particle image velocimetry (PIV) was used to measure the turbulent velocity field in the regions of lower velocity downstream. Mie scattering images also indicated the presence of a condensed argon phase in the supersonic region as expected from previous studies on nucleation. The observed location of the sharp interface at the Mach disk was found to be in excellent agreement with the Crist correlation. Rapid statistics were derived from the PIV measurements at 3 kHz. The recirculation zone was found to extend about 4 channel heights downstream, and in the region between 2 and 3 channel heights downstream, a continuous deceleration on the centerline velocity was observed in line with the narrowing of the recirculation zone. The first and second velocity moments as well as Reynold stresses were quantified, including pdf distributions. In addition, a sensitivity and repeatability analysis, an evaluation of the PIV random uncertainty, as well as an estimation of errors induced by particle inertia were performed to allow for a full quantitative comparison with numerical simulations.

Thermal analysis of Stirling thermocompressor and its prospect to drive refrigerator by using natural working fluid

The Stirling thermocompressor (STCP), usually working at low frequency (<5 Hz), is a novel Stirling-type external-combustion machine. It utilizes the temperature difference between the heating temperature and ambient temperature to generate the thermoacoustic power and pressure wave for refrigerators. In order to explore the characteristics of STCP, a detailed thermal analysis based on the third order 1-D finite volume model considering the real gas effect and variable physical properties was proceeded. Three natural fluids, helium, nitrogen and hydrogen are chosen as the working fluids and compared with each other. The parameter effects of pressure fluctuation under no-load operation were studied. To understand the output capacities for refrigerator with using different working fluids, the RC load method is adopt to analysis the STCP’s capacity and efficiency of the conversion from heat energy to acoustic energy, also the loss characteristics under different working gas. When the working pressure, frequency and heating temperature are 4 MPa, 4 Hz and 800 K respectively, the STCP using helium as the working fluid could output about 380 W acoustic power for the RC load and relative Carnot efficiency is about 33%.

A methodology for the preliminary design and performance prediction of high-pressure ratio radial-inflow turbines

Modern power generation technologies, such as organic Rankine cycle power systems, require turboexpanders operating with high-efficiency and high power density. These features often lead to high-pressure ratios machines, characterised by the presence of choking and supersonic flow conditions. This paper proposes a comprehensive methodology for the preliminary design and performance prediction of radial-inflow turbines operating at high-pressure ratios. A steady-state, mean-line model of a radial-inflow turbine is developed including real-gas effects and a detailed modelling strategy for the treatment of choking flow conditions. In addition, a set of loss models tailored to high-pressure ratio radial-inflow turbines is developed. After a global sensitivity analysis, the model is calibrated by means of a multi-objective optimisation with a Genetic Algorithm and using the data of six high-pressure ratio turbines with total-to-total pressure ratios up to 5.8. The calibration method allows a significant reduction in the overall predicted deviation of the turbine isentropic efficiency and mass flow rate. The design model yields predicted deviations in isentropic efficiency within ± 3 %-points and the off-design model within 5%. The methodology and the results are intended to be used as a benchmark for the future development of radial-inflow turbines in high-pressure ratio applications.

Aerodynamic Design of a Laval Nozzle for Real Gas Using Hodograph Method

We propose an approach for the design of the subsonic part of plane and axisymmetric Laval nozzles for real gases. The proposed approach is based on the hodograph method and allows one to solve the inverse design problem directly. Real gas effects are taken into consideration using the chemical equilibrium model. We present nozzle contours computed with the proposed method for a stoichiometric methane-air mixture. Results confirm that real gas effects have a strong influence on the nozzle shape. The described method can be used in the design of nozzles for rocket engines and for high-enthalpy wind tunnels.

Fractal-based real gas flow model in shales: An interplay of nano-pore and nano-fracture networks

Characterizing fluid flow in shale is challenging due to the existence of small-sized pores, variable wettability conditions, and different pore fluid occupancies. Majority of the sub-irreducible water saturation is stored inside the hydrophilic inorganic material (iOM) nanopores in the form of bound water film or capillary water at initial reservoir condition. During production, gas is transported through nano-pores and nano-fractures where a water film covers iOM’s walls and crevices. That gives rise to the existence of multiphase fluid occupancies in pores and fractures. In this paper, we present an improved gas permeability model by taking into account the impacts of nanoscale (i.e., slippage effect, Knudsen diffusion) and sub-irreducible water saturations. To do so, the gas flow is modeled in hydrophilic iOM consisting of two types of pore networks (i.e., porous matrix and fracture network). We expand gas transport equations for nano-capillaries and nano-slits by taking into account pore size distribution (PSD) and fracture aperture distribution (FAD) using fractal theory. The proposed model is compared against the relevant experimental data and other analytical models available from the literature. The results show that by neglecting the nanoscale effect, the existence of water film could lead to an underestimation of flow capacity while ignoring the PSD/FAD would overestimate the calculated gas conductance. At higher pressures (>10 MPa), the gas apparent permeability rises as we increase the percentage of nano-capillary pores in the pore space. This trend reverses at lower pressures. For all pressures lower than 10 MPa, the apparent permeability decreases with increasing contribution of nano-capillary pores in the pore space. Real gas effect can significantly enhance gas flow capacity in nano-capillaries and nano-slits at higher pressures and lower temperatures. This effect is particularly significant in small pore sizes.

An analytical model for shale gas transport in circular tube pores

An analytical model for gas transport in shale media is proposed on the basis of the weighted superposition of slip flow, bulk diffusion and Knudsen diffusion. The model takes account of slip effect and real gas effect, and is successfully validated by experimental data and Lattice Boltzmann simulation results. The contribution of each transport mechanism to the total flow is investigated. The effect of porosity, diameter and pressure on the apparent permeability is studied and a sensitivity analysis is performed to evaluate the significance of the parameters for gas transport. The results show: (1) the present model can reasonably describe the process of the mass transform of all different gas transport mechanisms; (2) As pressure and pore diameter decrease, the number of molecule-wall collisions gradually predominates over the number of intermolecular collisions, Knudsen diffusion contributes more to the total flow; and (3) the apparent permeability increases with porosity, pore diameter, and decreases with pressure. It is more sensitive to pressure in rarefied gas flow regime, and pore diameter has a significant impact under high pressure. The present model can provide some theoretical support in numerical simulation of shale gas production.

An Assessment of Shock-Disturbances Interaction Considering Real Gas Effects

In this study, a theoretical analysis is performed to assess the interaction of freestream disturbances with a plane normal shock considering real gas effects. Such effects are important in a field with high velocities and high temperatures. To perform the theoretical analysis, the downstream disturbances field is expressed as a mathematical function of the upstream one by incorporating real gas effects in the formulation. Here, the linearized one-dimensional perturbed unsteady Euler equations are used for the classification of the downstream/upstream disturbances field and the linearized one-dimensional perturbed Rankine–Hugoniot equations are applied to provide a relationship between the disturbances field of two sides of the shock. To incorporate real gas effects in the formulation, real gas relations and equilibrium air curve-fits are used in the resulting system of equations. The general formulation presented here may be simplified to derive Morkovin's formulation by the perfect gas assumption. The magnitudes of downstream disturbances field resulting from different types of upstream disturbances field (entropy wave and fast/slow acoustic waves) with the shock are expressed by appropriate analytical relations. Results for different disturbance variables are presented for a wide range of upstream Mach number considering real gas effects and compared with those of the perfect gas and some conclusions are made. The effects of the presence of body are also studied theoretically and the analytical relations for the magnitude of the pressure disturbance at the body for different types of upstream disturbances field considering real gas effects are provided and their results are presented and discussed.