Pressure Gradient Method Research Articles

An improved pressure gradient method for viscous incompressible flows

The pressure gradient method solves the viscous incompressible flow with the pressure gradients, rather than the pressure, as unknown variables. Two variants of the pressure gradient method have been developed in the past but have not received much attention due to their unsatisfactory performance or implementation complexity. Based on the artificial compressibility concept, this study proposes an improved pressure gradient method. One distinct feature of this method is that it requires no pressure/pressure gradient boundary condition or special treatment on wall boundaries. An auxiliary variable is introduced to represent the velocity dilatation, greatly simplifying the spatial discretization and computational procedure. The mathematical formulations are elaborated and compared with the previous pressure gradient methods, followed by discussions of compatibility relationships, boundary condition setup, and an extension to a pressure Poisson-like equation. Four validation examples are performed for various flow scenarios, and the solutions and domain solenoidity are examined for each case. The study also compares associated computational methods, different pressure boundary conditions, and flow characteristics, demonstrating the benefits of the present method.

Lateral Heterostructures Fabricated via Artificial Pressure Gradient.

Hydrostatic conditions are generally pursued in high-pressure research, maintained to prevent the intrinsic pressure gradient on the culets of diamond anvil cells (DACs) from introducing heterogeneity to the structure and physical properties of the regulated materials. Here, a pioneering route to fabricate lateral heterostructures is proposed via artificial pressure gradients intentionally designed in DACs. Under the tailored pressure gradients, different structural phases emerge in distinct parts of the material, resulting in the formation of heterostructures. Harnessing the polymorphic transition nature of violet phosphorus under high pressure, violet/blue and violet/black phosphorus lateral heterostructures with different electrical properties have been successfully prepared by the pressure gradient method. This achievement highlights the potential of artificial pressure gradients as a portable and universal strategy for the fabrication of lateral heterostructures, shedding new light on the preparation and regulation of lateral heterostructures across a wider range of materials.

Research on Gas Drainage Pipeline Leakage Detection and Localization Based on the Pressure Gradient Method

Research on Gas Drainage Pipeline Leakage Detection and Localization Based on the Pressure Gradient Method

Activation of cGAS-STING signaling pathway promotes liver fibrosis and hepatic sinusoidal microthrombosis

Inflammation plays an essential role in the development liver fibrosis.The Cyclic guanosine monophosphate-adenosine monophosphate synthase (cGAS) is a central cytoplasmic DNA sensor which can recognize cytoplasmic DNA, known to trigger stimulator of interferon genes (STING) and downstream proinflammatory factors. Here, we investigated the role of cGAS-STING signaling pathway in the pathogenesis of liver fibrosis.Differentially expressed genes (DEGs) in human liver tissue were identified using RNA-Seq analysis. As models of liver fibrosis, chronic Carbon tetrachloride (CCl4) exposure were applied in cGAS-knockout mice. LX-2 cells were co-cultured with human liver sinusoidal endothelial cells (LSECs) to explore the underlying mechanisms of hepatic sinusoidal microthrombosis in an inflammatory microenvironment. The endoscopic ultrasound-guided portal vein pressure gradient (EUS-PPG) method was used to analyze the associations between hepatic sinusoidal microthrombosis and PPG in patients with liver fibrosis and portal hypertension (PTH). The RNA-seq analysis results showed that DEGs were enriched in inflammation and endothelial cell activation. The upregulation of the cGAS-STING signaling exacerbated liver fibrosis and intrahepatic inflammation. It also exacerbated LSECs impairment and increased the contribution of hepatic sinusoidal microthrombosis to liver fibrosis in vivo and in vitro. Prothrombotic mediators and proinflammatory factors were associated with PPG in patients with liver fibrosis and portal hypertension. Therefore, activating cGAS-STING signaling pathway promotes liver fibrosis and hepatic sinusoidal microthrombosis, which may lead to increased portal vein pressure.

Analysis of the internal flow features of a CO2 transonic nozzle and optimization of the nozzle shape profile

Two-phase flow Laval nozzles are simple and have promising applications, but the internal flow is intricate and encompasses physical phenomena like phase transition, transonic and Mach waves. Therefore, a 1D mathematical model for validating and designing a CO2 two-phase flow transonic nozzle was developed and validated based on experiments. The findings demonstrated that a grid density of 0.292 mm was appropriate and that the maximum error of the model was less than 6.0 %, with an average error of less than 2.5 %. Additionally, it was discovered that when a phase transition occurred at the nozzle throat, whether through condensation or evaporation, there was a minimum critical pressure ratio in the nozzle; when the phase transition took place in the nozzle diffusion chamber, there was a minimum total pressure ratio. Finally, the Laval nozzle was designed to utilize the isostatic pressure gradient method (IPG), which gave a more significant pressure drop than a conventional nozzle while eliminating the shock wave strings at the nozzle throat. Under the typical operating conditions of a transcritical CO2 heat pump system, the ejector performance was boosted by an average of 5.44 %.

Transition from nanobubble-induced-blockage to enhancing water flux

Gas bubbles often form and accumulate in microfluidic devices, which is a critical obstacle in microfluidic applications. Here, we report by molecular dynamics simulations that “nanobubbles” can form and hinder water flow through the carbon nanotubes which are core components of nanofluidic devices. It is exceedingly difficult to remove the “nanobubble” trapped in the nanotube by a conventional method of hydrostatic or osmotic pressure gradient. Ratchet-like mechanics is applied to resume water flow powered by mechanical resonance. Interestingly, the water flow is even faster as compared to the pure water system without nanobubbles. Our findings provide a new means for solving pore-blocking problems in nanochannels and have potential applications in the design of high-flux nanofluidic systems.

Performance analysis and enhancement of a PVDF-based P-P sound intensity probe

This study investigates the feasibility of a laminated polyvinylidene fluoride (PVDF) structure for realising a pressure–pressure (P-P) intensity probe, as well as the effects of various backing materials on the performance of the probe. The PVDF structure consists of two parallel PVDF films that serve roles as pressure sensors, and each of them is laminated between stiff plates. The sensitivity and directivity of these pressure sensors are examined numerically and experimentally. The physical properties and configuration of the PVDF sensing structure are optimised for the best sensing performance. For frequencies below 15 kHz, the averaged voltage outputs of the two PVDF films are proportional to the sound pressure of the incident plane sound wave. It has a flat frequency response and omni-directional directivity pattern. The difference between the outputs is proportional to the particle velocity of the incident sound, featured by a dipole directivity pattern and almost-linear dependence upon frequency. Such under-covered properties of the pressure- and velocity-generated voltages for the integrated sensing structure demonstrate its suitability for intensity estimation in the aforementioned frequency range. This study shows that the probe can determine the intensity of a plane wave field below an upper-frequency limit with pre-determined probe gains. The upper limit is determined by the finite-difference approximation error introduced by the pressure gradient method. Small errors exist in narrow frequency bands around resonances and are sensitive to the pressure-intensity index, which is the ratio of the mean square pressure to the sound intensity. These errors are caused by variations of probe gains due to the resonances and can be reduced by careful calibration around the resonance frequencies.

Hydrodynamic Properties Investigation of Ebullated Bed Reactor Using Non-Newtonian Liquid

The importance of using EBR has been renewed recently due to the sharp increase in heavy feedstocks sent to refineries and the hydrocracking process. Most of these feedstocks have a non-Newtonian behavior. The performance of this type of reactor using non-Newtonian liquid is complicated and has not been covered well yet. Hence, the present work is devoted to elucidating the effect of the non-Newtonian behavior of fluid on the hydrodynamic properties of a three-phase (gas-liquid-solid) reactor under operating conditions of different values ​​of gas velocity (2, 4, 6) cm/sec, liquid velocity (0.9, 1.39, 1.8, 2.3) cm/sec, and recycle ratio (1.5, 2, 2.5). The study observed the effect of non-Newtonian behavior using polymethyl Cellulose (PMC) at different concentrations (0.1, 0.2, 0.3, and 0.4) wt%. The pressure gradient method was used to elucidate the minimum liquid fluidization velocity and to estimate hold up, while the imaging method was used to measure the bubble's size. The results showed that the higher the gas velocity, the lower the minimum liquid fluidization velocity. As the intensity of the non-Newtonian behavior increased, gas velocity showed the opposite effect. The results also showed that increasing the velocity of liquid and gas and the intensity of the non-Newtonian increase the gas hold-up. The bubbles characteristics, represented by bubble size results, show that small bubbles appear at low gas velocities, and these bubbles collapse as gas and liquid velocities increase as well as liquid viscosity.

Experimental study on the diagnosis of operation state of gas extraction pipeline based on pressure gradient method

ABSTRACT The working state of the gas drainage pipe network is the key to the safe drainage of underground mine gas. In order to quickly and accurately determine whether the pipe network is working normally, the flow law of the gas in the pipeline is studied. A diagnosis method of gas extraction pipeline by pressure gradient method is established. A gas drainage pipe network experimental platform is constructed. And the blockage and leakage of single pipe are carried out. The influence of air leakage of main pipe on negative pressure of branch pipe is studied, as well as the influence of negative pressure change of temporary pumping station on parallel pipe is explored. The method of image photography is proposed to calculate the pipeline flow, and the error is 2.7% compared with the orifice flowmeter. The results show that when the abnormalities exist in the extraction pipeline, the slope of the pressure curve corresponding to the abnormalities increases rapidly, the slope of the downstream curve is slightly larger than the slope of the upstream curve when the pipeline is leaking, and the slope of the downstream curve returns to the same as the slope of the upstream curve when the pipeline is blocked. The closer the location of the vacuum pump is to the air leakage, the faster the negative pressure of the vacuum pump decreases, and the less it affects the negative pressure of the branch circuit. When the downhole temporary pumping station extraction system is connected in series with the permanent pumping station extraction system on the ground, the temporary pumping station’s negative pressure value needs to be set reasonably, seriously affecting the extraction effect of the adjacent extraction pipeline. Finally, monitoring the gas drainage pipeline in Yuwu mine by pressure gradient method, it is found that the pressure drop slope at measuring points 6–7 is abnormal (−3 × 104), and the pressure drop slope of measuring points 7–8 returned to normal (−7 × 105), so it is judged that the drainage pipeline is blocked at 1300–1500 m away from the pump station.

Study on unsaturated shapes of helium ballonet of rigid airship during ascent process

Airship has a good application prospect in tourism, material transportation, emergency rescue, communication relay, early warning, environmental protection and other fields. Airships can be classified into non-rigid types, semi-rigid types and rigid types. The rigid airship relies on the external skeleton to maintain its overall stiffness and shape, and the internal helium ballonet provides buoyancy. The helium ballonet is always in unsaturated state during ascent process, which will affect the center of gravity and buoyancy and the stress in wrinkle area, so it is great significance to study the unsaturated shape of the helium ballonet during ascent process. In this paper, the principal stress-principal strain principal is used to judge the stress state of the membrane. The modified constitutive matrix method and the pressure gradient method are used to obtain the shape of the helium ballonet under different saturation by the dynamic explicit FEM (Finite Element Method). When the pressure gradient method is used to apply the pressure difference internal and external of the ballonet, the change of unsaturated shape of the ballonet can be interpreted as the change of zero pressure level of the ballonet. The modified constitutive matrix method can effectively avoid the problem of non-convergence in the process of programming. The simulation results are in good agreement with the experimental results, which shows that the analysis method is reasonable and correct.

Quantification of carbon dioxide released from effervescent granules as a predictor of formulation quality using modified Chittick apparatus

Purpose: To develop a method for the measurement of carbon dioxide (CO2) released from effervescent formulations.
 Methods: Effervescent granules were prepared using sodium bicarbonate and citric acid by fusion and solvent-assisted granulation methods. The amount of CO2 released was determined from the maximum pressure of gas release, time profile of pressure gradient using modified Chittick apparatus and gravimetric changes following effervescence.
 Results: The amount of CO2 released from effervescent granules prepared by fusion method was 8.125, 8.763 and 7.98 mM/g measured by ideal gas equation, pressure gradient and gravimetric method, respectively. The formulation prepared by solvent-assisted granulation showed 5.525, 5.475 5.36 mM/g of carbon dioxide measured by the above three methods, respectively. The effervescent granules prepared by fusion method showed approximately 2 % loss in effervescence. However, approximately 39 % loss in effervescence was observed for the formulation prepared by solventassisted granulation. The commercial products showed a loss in effervescence in the range of 5 - 15%.
 Conclusion: Modified Chittick’s apparatus is a useful analytical tool for monitoring of the CO2 from effervescent granules as a function of method of preparation.

Validation and Diagnostic Performance of a CFD-Based Non-invasive Method for the Diagnosis of Aortic Coarctation.

Purpose: The clinical diagnosis of aorta coarctation (CoA) constitutes a challenge, which is usually tackled by applying the peak systolic pressure gradient (PSPG) method. Recent advances in computational fluid dynamics (CFD) have suggested that multi-detector computed tomography angiography (MDCTA)-based CFD can serve as a non-invasive PSPG measurement. The aim of this study was to validate a new CFD method that does not require any medical examination data other than MDCTA images for the diagnosis of CoA.Materials and methods: Our study included 65 pediatric patients (38 with CoA, and 27 without CoA). All patients underwent cardiac catheterization to confirm if they were suffering from CoA or any other congenital heart disease (CHD). A series of boundary conditions were specified and the simulated results were combined to obtain a stenosis pressure-flow curve. Subsequently, we built a prediction model and evaluated its predictive performance by considering the AUC of the ROC by 5-fold cross-validation.Results: The proposed MDCTA-based CFD method exhibited a good predictive performance in both the training and test sets (average AUC: 0.948 vs. 0.958; average accuracies: 0.881 vs. 0.877). It also had a higher predictive accuracy compared with the non-invasive criteria presented in the European Society of Cardiology (ESC) guidelines (average accuracies: 0.877 vs. 0.539).Conclusion: The new non-invasive CFD-based method presented in this work is a promising approach for the accurate diagnosis of CoA, and will likely benefit clinical decision-making.

Radial Permeability Measurements for Shale Using Variable Pressure Gradients

AbstractShale gas is becoming an important component of the global energy supply, with permeability a critical controlling factor for long‐term gas production. Obvious deviation may exist between helium permeability determined using small pressure gradient (SPG) methods and methane permeability obtained under actual field production with variable pressure gradients (VPG). In order to more accurately evaluate the matrix permeability of shale, a VPG method using real gas (rather than He) is established to render permeability measurements that are more representative of reservoir conditions and hence response. Dynamic methane production experiments were performed to measure permeability using the annular space in the shale cores. For each production stage, boundary pressure is maintained at a constant and the gas production with time is measured on the basis of volume change history in the measuring pump. A mathematical model explicitly accommodating gas desorption uses pseudo‐pressure and pseudo‐time to accommodate the effects of variations in pressure‐dependent PVT parameters. Analytical and semi‐analytical solutions to the model are obtained and discussed. These provide a convenient approach to estimate radial permeability in the core by nonlinear fitting to match the semi‐analytical solution with the recorded gas production data. Results indicate that the radial permeability of the shale determined using methane is in the range of 1×10−6 – 1×10−5 mD and decreases with a decrease in average pore pressure. This is contrary to the observed change in permeability estimated using helium. Bedding geometry has a significant influence on shale permeability with permeability in parallel bedding orientation larger than that in perpendicular bedding orientation. The superiority of the VPG method is confirmed by comparing permeability test results obtained from both VPG and SPG methods. Although several assumptions are used, the results obtained from the VPG method with reservoir gas are much closer to reality and may be directly used for actual gas production evaluation and prediction, through accommodating realistic pressure dependent impacts.

Hydrodynamic Study of an Ebullated-bed Reactor in the H-oil Process

The effectiveness and performance of industrial hydro-processing ebullated bed reactors (EBRs) are highly dependent on the bed hydrodynamics and operating conditions. Hydrodynamics of ebullated bed reactors was studied in a cold model experimental setup. The results of a dynamic similarity test showed that the experimental data could be applied in the study of a large scale unit (Refinery of Lukoil, Burgas, Bulgaria) within a reasonable accuracy. Air and magnesium sulfate 20 wt% (MgSO4 + H2O) solution and solid catalyst particles were used as the gas, liquid and solid phases, respectively. For the design of experiments in the lab-scale cold-flow column, factorial method was introduced to study the influence of operating variables on the individual holdups and bubble characteristics. Pressure gradient method was used to estimate the individual holdups and bed porosity along the column, while photographic method was utilized to obtain images of the moving gas bubble. The images were analyzed using Ai Adobe illustrator CC (64 Bit) software to determine the bubbles geometric characteristics. Large gas bubbles were broken to smaller ones due to the increased turbulent intensity and shear forces at higher liquid velocities, reducing mass transfer resistances. Empirical correlations were developed for prediction of phase holdups and bed porosity with high accuracy. The results showed that liquid internal reflux ratio, which characterized the ebullated bed reactors has a predominant effect on the individual holdups and bubble size. A good agreement was observed between the results and available data in the literature.

Experimental and analysis study on dispersion of phases in an Ebullated Bed Reactor

The effectiveness and performance of industrial hydro-processing Ebullated Bed Reactors (EBRs) are highly dependent on the bed hydrodynamics and operating conditions. In present work, hydrodynamics of EBRs was studied in a cold model experimental setup using air–water–solid particles system. Pressure gradient method and Residence Time Distribution (RTD) technique were used to estimate the individual holdups, and dispersion coefficients in the lab-scale ebullated bed column. System Hydraulic Efficiency (HEF) was also estimated. The results showed that liquid internal recycle ratio, which characterized the EBRs, has a predominant effect on the individual holdups and dispersion coefficients. Empirical correlations were developed for prediction of phase holdups, and dispersion coefficients with good accuracy.

Quantitative Characterization and Dynamic Law of Interlayer Interference for Multilayer Commingled Production in Heavy Oil Reservoirs by Numerical Simulation

This paper moves one step forward to build a numerical model to research quantitative characterization and dynamic law for interlayer interference factor (IIF) in the multilayer reservoir which was heavy oil reservoirs and produced by directional wells. There are mainly four contributions of this paper to the existing body of literature. Firstly, an equivalent simulation method of the pseudo start pressure gradient (PSPG) is developed to quantitatively predict the value of IIF under different geological reservoir conditions. Secondly, the interlayer interference is extended in time, and the time period of the study extends from a water cut stage to the whole process from the oil well open to produce a high water cut. Thirdly, besides the conventional productivity interlayer interference factor (PIIF), a new parameter, that is, the oil recovery interlayer interference factor (RIIF) is put forward. RIIF can be used to evaluate the technical indexes of stratified development and multilayer co-production effectively. Fourthly, the effectsof various geological reservoir parameters such as reservoir permeability and crude oil viscosity, etc. on the PIIF and RIIF’s type curves are discussed in detail and the typical plate is plotted. The research results provide a foundation for the effective development of multilayer heavy oil reservoirs.

The effects of contaminating noise on the calculation of active acoustic intensity for pressure gradient methods.

Bias errors for two-dimensional active acoustic intensity using multi-microphone probes have been previously calculated for both the traditional cross-spectral and the Phase and Amplitude Gradient Estimator (PAGE) methods [Whiting, Lawrence, Gee, Neilsen, and Sommerfeldt, J. Acoust. Soc. Am. 142, 2208-2218 (2017)]. Here, these calculations are expanded to include errors due to contaminating noise, as well as probe orientation. The noise can either be uncorrelated at each microphone location or self-correlated; the self-correlated noise is modeled as a plane-wave with a varying angle of incidence. The intensity errors in both magnitude and direction are dependent on the signal-to-noise ratio (SNR), frequency, source properties, incidence angles, probe configuration, and processing method. The PAGE method is generally found to give more accurate results, especially in direction; however, uncorrelated noise with a low SNR (below 10-15 dB) and low frequency (wavelengths more than 1/4 the microphone spacing) can yield larger errors in magnitude than the traditional method-though a correction for this is possible. Additionally, contaminating noise does not necessarily impact the possibility of using the PAGE method for broadband signals beyond a probe's spatial Nyquist frequency.

Transient sub-channel code development for lead-cooled fast reactor using the second-order upwind scheme

For its unique safety and economic advantages, the lead cooled fast reactor has become one of the most interesting candidate reactors for the Generation IV nuclear system. To study the thermal-hydraulics of the core under transient conditions, KMC-SUBtra--a sub-channel code for transient thermal-hydraulic analysis of lead cooled fast reactor has been developed. The code uses a modified pressure gradient method to solve the simultaneous equations of the fluid mass, momentum and energy containing cross flow and turbulent mixing, in which the axial pressure gradients are solved as pending variables of the simultaneous equations. A staggered mesh scheme is used for scalar and vector quantities and the second-order upwind scheme is adopted in the discretization of the convection term. The code was validated and verified by the experimental data and CFD simulation results on the steady and transient conditions so its capability for lead cooled reactors was confirmed. The transient flow and heat transfer in the fuel assembly with time-varying boundary conditions were studied, which revealed different transient thermal characteristics of the coolant and fuel rods. In addition, the results calculated using different order upwind schemes were compared and showed the second-order derivative of the axial flow is small.

Experimental study on the location of gas drainage pipeline leak using cellular automata

In recent years, researches on leak detection and location of oil and gas pipeline have attracted considerable attention. A variety of methods have been proposed, including a pipeline-model-based method that predicts pressure distribution along the pipeline and locates the leak through the pressure and flow rate signal on both ends of the pipeline. At present, the most widely used pipeline-model-based methods include the pressure gradient (PG) method and the average friction coefficient (AFC) method. Nevertheless, the pressure gradient PG method which ignores the influences of friction coefficient, temperature, pipe diameter and other factors on the pressure distribution along the pipeline considers the pressure to be linear. The average friction coefficient (AFC) method assumes the friction coefficient and pipe diameter to be constant, yet gas pipeline is nonlinear and complex. Additionally, other uncertain factors such as changes in medium components and working conditions increase the difficulty of accurately describing the pipeline. To solve this problem, this study proposed a cellular automata (CA) model to locate the leak of main gas drainage pipeline. In the cellular automata model, the friction coefficient and diameter change are discretely distributed along the pipeline. The pressure distribution along the pipeline is predicted using flow rate and pressure parameters at both ends of the pipeline. This method assumes a continuous change in the pipeline fluid over time and space, thus improving the location accuracy.

A dynamic-pulse pseudo-pressure method to determine shale matrix permeability at representative reservoir conditions

Matrix permeability is a key factor in determining long term gas production from shale reservoirs – requiring that it is determined under true reservoir conditions. We suggest a variable pressure gradient (VPG) protocol to measure shale matrix permeability using real reservoir fluids in powdered samples. The VPG method is described and a mathematical protocol for its analysis is developed. The first measures gas fractional production rate history under constant external pressure for each production stage and with a designated pressure gradient. The second establishes the mathematical protocol for analysis using pseudo-pressure to accommodate both the effect of gas pressure-dependent PVT parameters and desorption rate coefficient. The matrix permeability is determined by matching the solution of the model with the experimental data. The model fits the experimental data well when the fractional production is <0.75. Shale matrix permeability is calculated in the order of magnitude of 10−7–10−6 md. Methane permeability decreases with a decrease in both average pore pressure and particle size of the individual component grains. Permeability considerably more sensitive to changes in desorption rate coefficient than flow regimes. Compared with current small pressure gradient (SPG) methods, the VPG method is considerably more applicable to actual gas production and reduces to the SPG method under simplified boundary conditions. Although some approximate treatments are used for establishing the VPG method and some flow mechanisms are not considered, this study still provides an information-rich technique to determine shale matrix permeability at conditions close to reality.