Transient Flow Model Research Articles

Effect of Initial Loading Position on the Propellant Particles Distribution in Two-module Charge

The propellant particles distribution in the ignition process of the modular charge has a significant effect on the interior ballistic stability. Thereinto, the particles final distribution is determined by the particles motion process. Based on the CFD-DEM method, a 3D transient gas-solid flow model is constructed to investigate the motion process and the dispersion of propellant particles. Moreover, the cold state test of the ignition process of modular charge is accomplished based on a visual ignition test platform. The simulated data are consistent with the test one. Furthermore, the effect of the initial loading position on the propellant particles distribution of two-module charge is predicted by the numerical simulation. All of two-module cases show that the distributions of particles are made up of a gentle-downhill, a horizontal, and a steep-uphill accumulation. As the initial loading position of modules moves to the right, the slope angle of the uphill is decreased first and then increased, with the minimum slope angle of 20.5°. When the initial loading position of modules is 40mm, the spatial distribution gradient of particles gets the minimum in the uphill accumulation area, and the particles axial-distribution is the most uniform.

Transient Coupled Flow Model for Matrix-Fracture in High-Pressure Gas Reservoirs Opened by Gas Drilling

Gas drilling technology is an effective method to protect low permeability tight sandstone reservoirs from damage. However, using this technology to drill high-pressure fractured reservoirs, the fluid flow characteristics are extremely complex, leading to drilling safety challenges. Therefore, based on the conservation equations of mass, momentum, and energy, a new transient coupled flow model in matrix-fracture is established for high-pressure gas reservoirs opened by gas drilling, considering convection term and energy equation, to research the pressure and flow velocity transient behaviors. This model is solved by Shaher Momani’s algorithm and CyabJiBe format, and the type curves of the pressure and flow velocity are plotted. The three flow stages are developed, and the impact of parameters and equation terms on the transient flow behavior is analyzed and discussed, such as the energy equation, the matrix permeability ( k ), the fracture aperture ( L f ), and the fracture outlet pressure. It is found that the energy equation term of the model has a great influence on the transient characteristics such as velocity and pressure, which cannot be ignored. In the first flow stage, the flow velocity characteristics are not affected by the matrix parameters being extremely unstable, but in the second and third stages, the influence of the gas supplied to fracture cannot be ignored. The proposed transient coupled flow model provides a new understanding of the transient flow behavior in matrix-fracture for high-pressure reservoirs during gas drilling, which can be used to interpret the characteristics of pressure and velocity more realistically, to provide support for safe drilling of gas drilling.

High-precision nonisothermal transient wellbore drift flow model suitable for the full flow pattern domain and full dip range

A reliable multiphase flow simulator is an important tool to improve wellbore integrity and production decision-making. To develop a multiphase flow model with high adaptability and high accuracy, we first build a multiphase flow database with 3561 groups of data and developed a drift closure relationship with stable continuity and high adaptability. Second, a high-order numerical scheme with strong fault capture ability is constructed by effectively combining MUSCL technology, van Albada slope limiter and AUSMV numerical scheme. Finally, the energy equation is coupled into the AUSMV numerical scheme of the drift flow model in the form of finite difference. A transient non-isothermal wellbore multiphase flow model with wide applicability is formed by integrating the three technologies, and the effects of various factors on the calculation accuracy are studied. The accuracy of the simulator is verified by comparing the measurement results with the blowout experiment of a full-scale experimental well.

Assessing the impact of groundwater abstractions on aquifer depletion in the Cauvery Delta, India

Many of the world’s deltas are highly productive areas for agriculture as well as important places of socio-economic development but are currently under stress. This study assesses the impacts of stresses on groundwater pumping, changing cropping patterns, and saltwater intrusion on groundwater resources in the Cauvery Delta in Tamil Nadu, India. A transient groundwater flow model of the delta was constructed for this assessment. The historical changes in groundwater resources in response to decreasing irrigation canal flows and increasing groundwater abstractions were assessed for the past 30 years. Furthermore, the model was used to formulate and analyze future sustainable groundwater development scenarios. Farmers’ narratives about a drying delta, as they experience water scarcity and quality issues most closely, were ascertained in the research. Farmers have abandoned many shallow wells in their fields. The model simulation shows groundwater levels are decreasing and aquifer storage depleting. Furthermore, salinization has increased, with continuous declining groundwater levels in the deep aquifer from 1990 to 2019. A more robust hydro-chemical assessment and further modeling of seawater intrusion are needed to better assess the sources and distribution of groundwater salinity. The pathway for future sustainability requires enhancing groundwater recharge in the shallow aquifer and controlling groundwater abstraction in the deep aquifers.

Transient flow characteristics analysis on the step-up process of control rod hydraulic drive system

Control rod hydraulic drive system (CRHDS) has been invented for 200 MW nuclear heating reactor (NHR-200). Water hammer occurs and adversely affects the operation of CRHDS. The step-up transient flow model was built, and the mechanism of the flow process was analyzed. The transient flow performance experiments were performed and verified the theoretical model. Next, the model was applied to high temperature working conditions. The findings suggest that there are three water hammer phenomena in the step-up process, and the corresponding pressures decay quickly. The peak pressure of the second water hammer is the largest. In addition, the hydraulic cylinder acts as both a water hammer source and a fluid energy damper in the transient flow process. What’s more, the variation laws of key parameters under different driving pressure conditions were obtained and studied. The research results provide a basis for the vibration reduction design and operation monitoring of CRHDS.

Seasonal biodegradation of the artificial sweetener acesulfame enhances its use as a transient wastewater tracer

The persistence of the artificial sweetener acesulfame potassium (ACE) during wastewater treatment and subsequently in the aquatic environment has made it a widely used tracer of wastewater inputs to both surface water and groundwater. However, the recently observed biodegradation of ACE during wastewater treatment has questioned the validity of this application. In this study, we assessed the use of ACE not only as a marker of wastewater, but also as a transient wastewater tracer that allows both the calculation of mixing ratios and travel times through the aquifer as well as the calibration of transient groundwater flow and mass transport models. Our analysis was based on data obtained in a nearly 8-year river water and groundwater sampling campaign along a confirmed wastewater-receiving riverbank filtration site located close to a drinking water supply system. We provide evidence that temperature controls ACE concentration and thus its seasonal oscillation. River water data showed that ACE loads decreased from 1.5–4 mg·s−1 in the cold season (December to June; T<10 °C) to 0–0.5 mg·s−1 in the warm season (July to November; T>10 °C). This seasonal variability of >600% was detectable in the aquifer and preserved >3 km, with ACE concentrations oscillating between <LOQ in the warm season up to 1 μg·L−1 in the cold season. The large seasonal variation in ACE concentrations during wastewater treatment, compared to the other sweeteners (sucralose, cyclamate, and saccharin) and chloride enables its use as a transient tracer of wastewater inflows and riverbank filtration. In addition, the arrival time of the ACE concentration peak can be used to estimate groundwater flow velocity and mixing ratios, thereby demonstrating its potential in the calibration of groundwater numerical models.

Numerical Simulation on Air-Liquid Transient Flow and Regression Model on Air-Liquid Ratio of Air Induction Nozzle

Air induction nozzle (AIN) has a special Venturi structure that has been widely used in the field of reducing the probability of drift of pesticide droplets and realizing precise application. The present research mainly adopts the method of comparative test and analyzes the difference between AIN and standard fan nozzle. However, the research on internal flow characteristics and air–liquid ratio (ALR) of AIN is very limited. In order to detect the air-liquid transient flow distribution and the influence of the geometric parameter structure of Venturi on the air–liquid ratio in the air induction nozzle, numerical simulation and air-liquid ratio prediction model of AIN combined with TD (Turbo Drop series) type Venturi tubes and ST110 (standard nozzle series) type fan nozzles are used. Based on the VOF (volume of fluid) model and Realizable k-ε turbulence control method, the TD-ST combined AIN is simulated numerically using open input and exit boundary conditions. The results show that the transient flow characteristic of the combined AIN is determined by the geometric structure of the Venturi tube, and the internal velocity and pressure change significantly at the Venturi angle. Under the same ST110 fan nozzle, the size of the larger TD Venturi tube will decrease the air phase content in the air–liquid flow. TD03-ST06 combined AIN has a maximum volume flow of 0.0092 (L/min) under 0.6 MPa. The air–liquid ratio regression model is established by designing the intake volume measurement system. According to this model, the influence law of tube size and spray parameters on the air–liquid ratio can be clarified. After variance analysis, it is proved that this model is suitable for air–liquid ratio prediction of TD-ST combined AIN. This study clarifies the air–liquid coupling law inside AIN and provides some reference for the quantitative analysis of the relationship between the geometric parameters, spray parameters, and the air–liquid ratio.

A HYBRID NUMERICAL/ANALYTICAL MODEL OF TRANSIENT SEEPAGE FOR VERTICAL FRACTURED WELL IN TIGHT GAS RESERVOIR BY USE OF FRACTAL THEORY AND CONFORMAL MAPPING METHOD

Insufficient consideration of the complex morphology of hydraulic fractures (HF) and heterogeneous physical properties of fractured reservoirs in seepage models can result in unreliable well testing analyses. The fractal porosity and permeability (FPP) model provides an effective method for characterizing reservoir heterogeneity in the near-wellbore zone. However, its application to scenarios involving irregularly-shaped hydraulic fracture networks and multiple fracture clusters is challenging due to the lack of spatial symmetry. To address this issue, this paper proposes a combined approach of FPP and conformal mapping (FPP-CM) to transform the region of fractured formation into the exterior of the unit disk domain using numerical conformal mapping. The transient seepage flow model of the vertical fracture well (VFW) is then established by coupling it with the FPP model. The typical curve of pressure transient behavior with the division of flow stages was plotted, and the model verification and sensitivity analysis of parameters were conducted. The results indicate that the fractal dimension primarily affects the formation linear flow stage and its subsequent flow stages; with a decrease in fractal dimension resulting in an increase in the position of the typical curve. For VFW with multiple HF wings, a decrease in the included angle of fracture wings causes an increase in the heterogeneity distribution of microfracture physical properties, resulting in an increase in the position of the pseudo-pressure derivative curve during the late flow stage.

Study on the Influence of Tripping Operation on Annular Transient Surge-Swab Pressure of Herschel–Bulkley Fluid

Abstract The accurate prediction of transient surge-swab pressure, during the tripping operation under a narrow pressure window, is an important premise to ensure the safety of tripping operation and drilling. Different rheological modes of drilling fluid will have a great influence on the surge-swab pressure in wellbore, while the Herschel–Bulkley mode can simulate the rheological characteristics of actual drilling fluid in a better way. Therefore, the influence of drilling fluid flow friction under different rheological modes was mainly considered according to the transient flow model. Meanwhile, the influence of pumpage on transient surge-swab pressure during tripping operation was also considered with Herschel–Bulkley fluid-based tripping operation bottomhole transient surge-swab pressure calculation model established and model verification carried out. The following research results were obtained. First, compared with the Herschel–Bulkley mode, the power-law mode and Bingham mode will overestimate the flow friction of drilling fluid. Second, the surge-swab pressure peak values of different mud systems are water-based mud &amp;gt; polymer mud &amp;gt; oil-based mud. Third, the peak value of bottomhole transient surge-swab pressure increases with the increase of drilling fluid yield value, consistency coefficient, and flow behavior index, and the influence law is similar. Fourth, the tripping velocity and pumpage will directly affect the peak value and variation rule of bottomhole transient surge-swab pressure. Herschel–Bulkley fluid-based tripping operation bottomhole transient surge-swab pressure study helps control the surge-swab pressure during tripping operations and it is of great significance for lean, safe, and efficient drilling in narrow pressure window formations.

Simulation study on multiphase flow considered seawater salinity in wellbore for deep-water bearing hydrate formation drilling

The gas-liquid-solid multiphase flow caused by decomposition of hydrate cuttings is a new problem facing the drilling of marine hydrate formations. In this paper, a gas-liquid-solid non-isothermal transient flow model is proposed considering the coupling relationships between hydrate decomposition, and heat and mass transfer in multiphase flow. The accuracy of the model in predicting gas void fraction, friction pressure and wellbore temperature is verified by using indoor experimental data and field measured data. Using this model, the influence of seawater salinity on the gas-liquid-solid flow behaviors is investigated. Numerical simulation results show that the decomposition area and decomposition rate of hydrate in the wellbore gradually increase with the increase of seawater salinity. Moreover, the higher the salinity of seawater, the greater the reduction in bottomhole pressure and the higher the decomposed gas void fraction reaching the wellhead. Increasing wellhead backpressure and lowering inlet temperature of seawater can effectively control the amount of hydrate decomposed in the wellbore. To ensure wellhead safety and reduce the rate of hydrate decomposition, the wellhead backpressure should be greater than 3.5 MPa. Compared with the wellhead backpressure of 2 MPa, the gas void fraction at the wellhead decreases 1.75 times when the wellhead backpressure is 5 MPa. When the seawater inlet temperature is in the range of 15 °C–30 °C, the seawater salinity control in the range of 8‰∼19‰ can manage the maximum gas phase volume fraction at the wellhead within 10%. Compared with the inlet temperature of 15 °C, the hydrate decomposition rate at the wellhead is 1.6 times higher when the inlet temperature is 30 °C.

Resin infusion in porous preform in the presence of HPM considering complex geometry and gravity: Flow simulation and experimental validation

Present work demonstrates the complete numerical modeling and experimental validation of transient incompressible two-phase flow during vacuum infusion (VI) in the presence and absence of high permeability media (HPM) considering gravity effects. Coupled flow modeling based on continuity equations, Darcy’s law for porous media flow, including gravity effects with level set front tracking algorithm, has been developed on the multiblock-structured grid with higher-order finite-difference framework to predict the spatio-temporal preform saturation during infusion with/without HPM on the complex mold configurations. The model-predicted instantaneous change in pressure, thickness elevation, fill time, flow front positions, and influence of gravity have been validated with experiments for horizontal and vertical flat plates using pressure sensors and digital cameras. For the first time, the complete modeling and experimentation of transient VI in the presence or absence of HPM, including gravity, shows the ability to predict realistic preform saturation during VI in different mold geometry.

A high-resolution upwind numerical scheme for solving transient multiphase flow in wellbore

The identification of gas-liquid interface is the basis for accurate calculation of wellbore flow parameters after gas invasion, which plays an important role in the safety and reliability of drilling engineering. At present, most petroleum engineering uses a simple difference algorithm to calculate the wellbore multiphase flow, this scheme can not capture the gas-liquid interface accurately, and the numerical accuracy is low. Therefore, this paper proposes a mathematical and numerical calculation model for transient multiphase flow in wellbore during gas invasion. Using second-order Runge-Kutta method and OMUSCL2 method, a high-precision and high-resolution upwind AUSMV numerical scheme is constructed to capture the gas-liquid interface. The research shows that the high-precision and high-resolution upwind AUSMV scheme can accurately capture the gas-liquid interface, and thus accurately solve the multiphase flow parameters in wellbore during the gas invasion.

Transient simulation of slag entrapment in a tundish

A transient multiphase flow model is established by solving the heterogeneous dynamic equation to simulate the process of the slag entrapment in the tundish, which can provide data for the trial production to reduce the tundish residue on the premise of ensuring no slag entrapment. A numerical simulation of critical slag entrapment height of 60 t tundish under different steel throughputs is analyzed, and the following conclusions are obtained: when the steel throughput is 3.5 t/min, 4.5 t/min, 5.5 t/min, and 6.4 t/min, the critical time of the risk of slag entrapment are 1042 s, 691 s, 561 s, and 476 s after casting end, respectively. The heights of slag entrapment are 186.9 mm, 202.9 mm, 220.5 mm, and 222.5 mm, and the heights without slag entrapment are 202.4 mm, 214.6 mm, 236.1 mm, and 238.0 mm with the throughput of 3.5 t/min, 4.5 t/min, 5.5 t/min, and 6.4 t/min.

Influence of the spatial configuration of available data on hydraulic conductivity estimates for a geostatistical-Kalman filter method

Abstract Accurate hydraulic conductivity estimates are vital for groundwater evaluation. Usually, interpolations of hydraulic conductivity data are needed to obtain spatial estimates over larger areas, but the results present a high uncertainty which can be reduced by adding a secondary variable in the estimation. In this paper, the influence of the number and spatial configuration of hydraulic conductivity (K) and hydraulic head (HH) data on the estimation of K is evaluated using univariate and bivariate geostatistical-Kalman filter approaches (similar to kriging and cokriging, respectively). A synthetic case based on a transient groundwater flow model is used to generate different numbers, spatial arrays, and data. With these data, variogram models for the univariate and bivariate cases were fitted and used to calculate the corresponding covariance matrices for the Kalman filter. The results show that K estimates are more reliable when HH data is added than when only K is used, independently of the number and distribution of the data, since there is a better agreement between the calculated errors and estimate error variances. HH data provides valuable information only where K is not sampled. This evaluation could support the design of optimal sampling strategies to obtain reliable K estimates.

An analytical and meshless model for 3D transient flow in a confined aquifer with nonuniform thickness: Application to stream depletion due to groundwater extraction

This study proposes an analytical and meshless model for three-dimensional transient flow induced by multiple wells in a stream-confined aquifer system with arbitrary nonuniform aquifer thickness. The model involves allocating external image wells near the aquifer boundary. The aquifer drawdown is defined as Theis’ solution plus a simple series expanded by complementary error functions reflecting the boundary effects of the stream and impervious stratum. The solution for stream depletion rate (SDR) can be derived based on the drawdown solution. Results suggest the Dupuit assumption of no vertical flow is valid to estimate SDRs affected by the landward exponentially decreasing thickness. The SDR induced by multiple wells is the same as that by a single well if the total well discharge rate and stream-well distances in the multiple well case are identical to those in the single well case. The present solution outperforms a finite difference solution in computational efficiency.

Response of hydrogeological processes in a regional groundwater system to environmental changes: A modeling study of Yinchuan Basin, China

The sustainable development of groundwater resources in arid and semi-arid regions is a challenging task hindered by climate change and human activities. The rational utilization and management of groundwater resources is, therefore, dependent on an understanding of the influences of human and climatic factors on the spatial distribution of groundwater resources and their change over time. The thick Quaternary aquifers in the Yinchuan Basin, China were used herein as an example of how to quantitatively assess spatial and temporal trends in groundwater resources in response to human activities and climate change. A 3D transient groundwater flow model was constructed and used to simulate the evolution and spatial variability of hydrogeological processes from 1990 to 2020. By subsequently applying regime shift detection and correlation analysis to the simulation results, we found that: 1) groundwater storage was continuously depleted over the 30-year period, reaching a cumulative depletion of 1.89×109 m3; 2) human activities were mainly responsible for variations in regional hydrogeological processes for a period of up to 30 years. Climate only affected short-term interannual fluctuations in groundwater storage; 3) human activities (e.g., river water diversion and groundwater abstractions) were the decisive factors causing a continuous reduction of groundwater resources. A policy-driven reduction in water diversion from the Yellow River directly led to a significant drop in groundwater storage, which had a consequent effect on surface water and groundwater interactions and altered agricultural irrigation patterns (crop patterns and irrigation methods); 4) the amount of groundwater recharge from the Yellow River and local lakes increased from 1990 to 2020, whereas the discharge of groundwater to the Yellow River and lakes decreased.

PTSNet: A Parallel Transient Simulator for Water Transport Networks based on vectorization and distributed computing

Modeling transient flow in water transport networks (WTNs) is characterized by hyperbolic partial differential equations. Existing commercial and open-source software for transient modeling in WTNs have limitations, such as lack of scalability and compatibility with high-performance computers, difficulty to systematically execute simulations and analyze results. This work proposes a novel open-source Python package that relies on vectorization and distributed computing to overcome the limitations of existing software. The proposed library, the Parallel Transient Simulator for Water Networks (PTSNet), surpasses in computational performance existing modeling tools and incorporates novel analytics functionalities. PTSNet has been tested on WTNs composed of tens, hundreds, and thousands of hydraulic elements using a personal and a supercomputer, running from tens to hundreds of processors. We show through rigorous analyses that PTSNet is scalable, accurate, and significantly speeds up simulations with sufficiently dense numerical grids.

Stochastic multi-fidelity joint hydrogeophysical inversion of consistent geological models

In Quaternary deposits, the characterization of subsurface heterogeneity and its associated uncertainty is critical when dealing with groundwater resource management. The combination of different data types through joint inversion has proven to be an effective way to reduce final model uncertainty. Moreover, it allows the final model to be in agreement with a wider spectrum of data available on site. However, integrating them stochastically through an inversion is very time-consuming and resource expensive, due to the important number of physical simulations needed. The use of multi-fidelity models, by combining low-fidelity inexpensive and less accurate models with high-fidelity expensive and accurate models, allows one to reduce the time needed for inversion to converge. This multiscale logic can be applied for the generation of Quaternary models. Most Quaternary sedimentological models can be considered as geological units (large scale), populated with facies (medium scale), and finally completed by physical parameters (small scale). In this paper, both approaches are combined. A simple and fast time-domain EM 1D geophysical direct problem is used to first constrain a simplified stochastic geologically consistent model, where each stratigraphic unit is considered homogeneous in terms of facies and parameters. The ensemble smoother with multiple data assimilation (ES-MDA) algorithm allows generating an ensemble of plausible subsurface realizations. Fast identification of the large-scale structures is the main point of this step. Once plausible unit models are generated, high-fidelity transient groundwater flow models are incorporated. The low-fidelity models are populated stochastically with heterogeneous facies and their associated parameter distribution. ES-MDA is also used for this task by directly inferring the property values (hydraulic conductivity and resistivity) from the generated model. To preserve consistency, geophysical and hydrogeological data are inverted jointly. This workflow ensures that the models are geologically consistent and are therefore less subject to artifacts due to localized poor-quality data. It is able to robustly estimate the associated uncertainty with the final model. Finally, due to the simplification of both the direct problem and the geology during the low-fidelity part of the inversion, it greatly reduces the time required to converge to an ensemble of complex models while preserving consistency.

Modeling and computation of nanofluid for thermo-dynamical analysis between vertical plates

It is well fact that the computational complexity of unsteady and viscoelastic nanofluid can be measured by mathematical modeling that allows the suitable performance for variations from specific to particular rheological parameters. This manuscript addresses the fractionalized mathematical modeling of an unsteady incompressible Maxwell transient free convection flow of nanofluids in the existence of radiation as well as damped thermal flux by using the Caputo time-fractional derivative. The integral transform technique is invoked on the fractionalized governing equations to find the exact solution. The numerical solution to the problem is also attained by utilizing Stehfest and Tzou algorithms. Finally, for the sake of graphical illustration, the comparative analysis for validating both algorithms on velocity and temperature profiles is performed numerically. The temperature and velocity curves are reduced by growing α for small time, and behavior is contrary for large time. By growing values of [Formula: see text] declines the velocity profiles. Velocity is linearly proportional to relaxation time λ, and the boundary layer difference is decreased by increasing the time. Our achieved solutions via two different numerical methods, that is, Stehfest and Tzou are equal.

Spatio-temporal variations of shallow seismic velocity changes in Salton Sea Geothermal Field, California in response to large regional earthquakes and long-term geothermal activities

We measure spatio-temporal variations of seismic velocity changes in Salton Sea Geothermal Field, California based on cross correlations of daily seismic traces recorded by a borehole seismic network from December 2007 to January 2014. We find clear co-seismic velocity reductions during the 2010 M 7.2 ​El Mayor–Cucapah, Mexico earthquake at ∼100 ​km further south, followed by long-term recoveries. The co-seismic reductions are larger with longer post-seismic recoveries in higher frequency bands, indicating that material damage and healing process mostly occurred in the shallow depth. In addition, the co-seismic velocity reductions are larger for ray paths outside the active fluid injection/extraction regions. The ray paths inside injection/extraction regions are associated with smaller co-seismic reductions, but subtle long-term velocity increases. We also build 3D transient water flow models based on monthly injection/extraction rates, and find correlations between several water flow parameters and co-seismic velocity reductions. We interpret the relative lack of co-seismic velocity changes within the geothermal region as unclogging of fracture network due to persistent fluid flows of geothermal production. The long-term velocity increase is likely associated with the ground water depletion and subsidence due to net production.