Continuous Point Source Research Articles

Similarity solution for one-dimensional heat equation in spherical coordinates and its applications

A similarity type of general solution for the one-dimensional heat equation in spherical coordinates is developed, and the solution is expressed by the Kummer functions. After introducing some useful properties of the general solution, the solution is then applied to establish analytical solutions of finite line source problems and moving boundary problems. For the finite line source problems, a continuous point source problem with a power-type source intensity is solved first, and then analytical solutions for a vertical finite line source problem and an inclined finite line source problem are established using the mirror image method and the solution of the continuous point source problem. For the moving boundary problems, a one-phase Stefan problem with power-type latent heat in spherical coordinates and a nonlinear heat conduction problem induced by a continuous point source are investigated, and analytical solutions are developed using the general solution. Computational examples are presented. For the finite line source problems, computational error caused by neglecting vertical heat transfer under the situation of a time-varying source intensity is investigated. For the moving boundary problems, an illustrative example of the one-phase Stefan problem is presented, and the computational results can be used to calibrate numerical solutions of Stefan problems.

The efficacy of aerosol–cloud radiative perturbations from near-surface emissions in deep open-cell stratocumuli

Abstract. Aerosol–cloud radiative effects are determined and quantified in simulations of deep open-cell stratocumuli observed during the VAMOS Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS-REx) campaign off the west coast of Chile. The cloud deck forms in a boundary layer 1.5 km deep, with cell sizes reaching 50 km in diameter. Global databases of ship tracks suggest that these linear structures are seldom found in boundary layers this deep. Here, we quantify the changes in cloud radiative properties to a continuous aerosol point source moving along a fixed emission line releasing 1017 particles per second. We show that a spatially coherent cloud perturbation is not evident along the emission line. Yet our model simulates an increase in domain-mean all-sky albedo of 0.05, corresponding to a diurnally averaged cloud radiative effect of 20 W m−2, given the annual mean solar insolation at the VOCALS-REx site. Therefore, marked changes in cloud radiative properties in precipitating deep open cells may be driven by anthropogenic near-surface aerosol perturbations, such as those generated by ships. Furthermore, we demonstrate that these changes in cloud radiative properties are masked by the naturally occurring variability within the organised cloud field. A clear detection and attribution of cloud radiative effects to a perturbation in aerosol concentrations becomes possible when sub-filtering of the cloud field is applied, using the spatio-temporal distribution of the aerosol perturbation. Therefore, this work has implications for the detection and attribution of effective cloud radiative forcing in marine stratocumuli, which constitutes one of the major physical uncertainties within the climate system. Our results suggest that ships may sometimes have a substantial radiative effect on marine clouds and albedo, even when ship tracks are not readily visible.

Solute transport with periodic input point source in one-dimensional heterogeneous porous media

In the present study, we presented analytical solutions for solute transport in a semi-infinite heterogeneous adsorbing porous media with time-varying boundary condition. Initially, solute concentration in the domain is function of the space variable. Continuous periodic point source is injected in the domain through left boundary, i.e. x = 0. Due to heterogeneity of the medium, dispersion parameter is considered proportional to (z +1) th power of linear function of space variable. The groundwater flow velocity is considered proportional to multiple of temporal function and z th power of linear function of space. First-order decay and zero-order production are also considered space as well as time dependent while retardation factor is a space dependent function. Laplace Transformation Technique is employed to get the solution of the proposed problem. Certain new transformations are introduced to convert the variable coefficient into constant coefficient. Comparison with analytical and pdepe MATLAB solution of the transport equation are illustrated graphically and found to be in excellent agreement.Keywords: Advection; Dispersion; Aquifer; Porous Medium ; Retardation; Laplace Transformation.

Analytical solution of two-dimensional advection–dispersion equation with spatio-temporal coefficients for point sources in an infinite medium using Green’s function method

In the present study analytical solutions of a two-dimensional advection–dispersion equation (ADE) with spatially and temporally dependent longitudinal and lateral components of the dispersion coefficient and velocity are obtained using Green’s Function Method (GFM). These solutions describe solute transport in infinite horizontal groundwater flow, assimilating the spatio-temporal dependence of transport properties, dependence of dispersion coefficient on velocity, and the particulate heterogeneity of the aquifer. The solution is obtained in the general form of temporal dependence and the source term, from which solutions for instantaneous and continuous point sources are derived. The spatial dependence of groundwater velocity is considered non-homogeneous linear, whereas the dispersion coefficient is considered proportional to the square of spatial dependence of velocity. An asymptotically increasing temporal function is considered to illustrate the proposed solutions. The solutions are validated with the existing solutions derived from the proposed solutions in three special cases. The effect of spatially/temporally dependent heterogeneity on the solute transport is also demonstrated. To use the GFM, the ADE with spatio-temporally dependent coefficients is reduced to a dispersion equation with constant coefficients in terms of new position variables introduced through properly developed coordinate transformation equations. Also, a new time variable is introduced through a known transformation.

Experimental determination of the dispersion of ions from a point source in the environment

ABSTRACTThe dispersion of ions from a point source has been extensively modelled but there have been very few attempts to experimentally verify the theoretical findings. The main reason for this has been the difficulty of discriminating between cluster ion and charged particle concentrations in the air. In this paper, we describe a novel technique for the experimental determination of the dispersion of ions from a point source in air. Laboratory experiments showed that the lifetime of cluster ions in an aerosol cloud was of the order of minutes. However, once they attached to aerosols, the particles retained the charge for at least 30 min, suggesting that they may be carried long distances in natural winds. A negative air ionizer was used to produce ions and charged particles in an open field in the presence of a steady horizontal wind. A neutral cluster and air ion spectrometer was used to measure cluster ion and charged particle concentrations as a function of downwind distance from the source. The results are broadly consistent with the Gaussian dispersion model for a continuous point source. We estimate that cluster ions can be carried up to a distance of several hundred metres before they fully attach to particles which can then be carried as far as 3–4 km. Therefore, these observations have important bearing on exposure to cluster ions and charged particles downwind of ion sources such as high voltage power lines and busy roads.

A new skin factor model for partially penetrated directionally-drilled wells in anisotropic reservoirs

To study the stimulation effect of partially penetrated directionally-drilled wells, the skin factor model for partially penetrated directionally-drilled wells needs to be figured out. Based on the solution of a continuous point source in a laterally infinite reservoir, the solution of partially penetrated directionally-drilled wells in an infinite slab reservoir is obtained by using integral along the directional well. Then by the approximation treatment of large-time pressure solution, a new simplified skin factor model for partially penetrated directionally-drilled wells is obtained. The good agreements with classical result and numerical simulation result validate the solution in this work. According to the new skin factor model, curves of skin factor in terms of several influencing factors, such as inclination angle, well length, formation thickness and reservoir anisotropy factor are presented. Analysis shows that with the increase of inclination angle and relative well length, the skin factor will decrease, but the increase of anisotropy factor causes the skin factor to increase. Besides, the application of how skin factor is used to analyze the stimulation ratio of WPI (well productivity index) is presented. It can be concluded that for a certain reservoir, partially penetrated directionally-drilled wells with large inclination angle and relative well length will have good stimulation effect. Moreover, large vertical permeability is beneficial to the production of partially penetrated directionally-drilled wells.

Dispersion of a Passive Scalar Within and Above an Urban Street Network

The transport of a passive scalar from a continuous point-source release in an urban street network is studied using direct numerical simulation (DNS). Dispersion through the network is characterized by evaluating horizontal fluxes of scalar within and above the urban canopy and vertical exchange fluxes through the canopy top. The relative magnitude and balance of these fluxes are used to distinguish three different regions relative to the source location: a near-field region, a transition region and a far-field region. The partitioning of each of these fluxes into mean and turbulent parts is computed. It is shown that within the canopy the horizontal turbulent flux in the street network is small, whereas above the canopy it comprises a significant fraction of the total flux. Vertical fluxes through the canopy top are predominantly turbulent. The mean and turbulent fluxes are respectively parametrized in terms of an advection velocity and a detrainment velocity and the parametrization incorporated into a simple box-network model. The model treats the coupled dispersion problem within and above the street network in a unified way and predictions of mean concentrations compare well with the DNS data. This demonstrates the usefulness of the box-network approach for process studies and interpretation of results from more detailed numerical simulations.

Oil Based Drilling Fluid Waste: An Overview on Environmentally Persistent Pollutants

Operational discharges of spent drilling fluid, produced water, and accumulated drill cuttings from oil and gas industry are a continuous point source of environmental pollution. To meet the strict environmental standard for waste disposal, oil and gas industry is facing a numerous challenges in technological development to ensure a clean and safe environment. Oil and gas industry generates a large amount of spent drilling fluid, produced water, and drill cuttings, which are very different in every drilling operation in terms of composition and characterisation. This review article highlights the knowledge gap in identifying the different sources of waste streams in combined drilling waste. This paper also emphasises how different chemicals turn into environmentally significant pollutants after serving great performance in oil and gas drilling operations. For instance, oil based drilling fluid performs excellent in deeper drilling and drilling in the harsh geological conditions, but ended with (produces) a significant amount of persistent toxic pollutants in the environment. This review paper provides an overview on the basic concepts of drilling fluids and their functions, sources and characterisation of drilling wastes, and highlights some environmentally significant elements including different minerals present in drilling waste stream.

Analytical solutions for solute transport in groundwater and riverine flow using Green’s Function Method and pertinent coordinate transformation method

In this study, analytical solutions of one-dimensional pollutant transport originating from instantaneous and continuous point sources were developed in groundwater and riverine flow using both Green’s Function Method (GFM) and pertinent coordinate transformation method. Dispersion coefficient and flow velocity are considered spatially and temporally dependent. The spatial dependence of the velocity is linear, non-homogeneous and that of dispersion coefficient is square of that of velocity, while the temporal dependence is considered linear, exponentially and asymptotically decelerating and accelerating.Our proposed analytical solutions are derived for three different situations depending on variations of dispersion coefficient and velocity, respectively which can represent real physical processes occurring in groundwater and riverine systems. First case refers to steady solute transport situation in steady flow in which dispersion coefficient and velocity are only spatially dependent. The second case represents transient solute transport in steady flow in which dispersion coefficient is spatially and temporally dependent while the velocity is spatially dependent. Finally, the third case indicates transient solute transport in unsteady flow in which both dispersion coefficient and velocity are spatially and temporally dependent. The present paper demonstrates the concentration distribution behavior from a point source in realistically occurring flow domains of hydrological systems including groundwater and riverine water in which the dispersivity of pollutant’s mass is affected by heterogeneity of the medium as well as by other factors like velocity fluctuations, while velocity is influenced by water table slope and recharge rate. Such capabilities give the proposed method’s superiority about application of various hydrological problems to be solved over other previously existing analytical solutions. Especially, to author’s knowledge, any other solution doesn’t exist for both spatially and temporally variations of dispersion coefficient and velocity.In this study, the existing analytical solutions from previous widely known studies are used for comparison as validation tools to verify the proposed analytical solution as well as the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) code and the developed 1D finite difference code (FDM). All such solutions show perfect match with the respective proposed solutions.

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Some analytical solutions of one-dimensional advection–diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green’s function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant’s mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.

Microscopic numerical modeling of Thermo-Hydro-Mechanical mechanisms in fluid injection process in unconsolidated formation

The temperature difference between injected fluid and surrounding rock can play an important role in the initiation and propagation of fractures in completion and simulation operations. In this work, the thermal effect is investigated using DEM-based micromechanics model implemented in Particle Flow Code (PFC). The rock mass is represented by an assembly of discrete particles that are bonded at contacts. In the developed thermo-hydro-mechanical (THM) module, heat conduction across the solids in the rock matrix and heat convection between the injected fluid and solid particles are coupled. The evolution of the system is driven by a continuous point source of heat. Simulation results show that more cracks tend to be generated in anisotropic thermal conductivity, and the thermal induced stress, temperature distribution and pore pressure predicted by this model are consistent with laboratory observations and simulation results from conventional continuum mechanics models. Furthermore, the Fracability Index is introduced for evaluating the fracturing performance, in the comparison between hydro-injection and hydro-thermal injection (heating and cooling). This study indicates that thermal stresses can greatly affect initiation and propagation of fractures and assist the communication between injection pressure and pore pressure in the rock formation; thermal fracturing can be considered as an effective method to connect fracture network, enhance weak zones and create more fractures.

An urban scale inverse modelling for retrieving unknown elevated emissions with building-resolving simulations

This study illustrates an atmospheric source reconstruction methodology for identification of an unknown continuous point release in the geometrically complex urban environments. The methodology is based on the renormalization inversion theory coupled with a building resolving Computational Fluid Dynamics (CFD) modelling approach which estimates the release height along with the projected location on the ground surface and the intensity of an unknown continuous point source in an urban area. An estimation of the release height in a three-dimensional urban environment is relatively more difficult from both technical and computational point of view. Thus, a salient feature of the methodology is to address the problem of vertical structure (i.e. height of a source) in atmospheric source reconstruction in three-dimensional space of an urban region. The inversion methodology presents a way to utilize a CFD model fluidyn-PANACHE in source reconstruction in the urban regions. The described methodology is evaluated with 20 trials of the Mock Urban Field Setting Test (MUST) field experiment in various atmospheric stability conditions varying from neutral to stable and very stable conditions. The retrieved source parameters in all the 20 trials are estimated close to their true source. The source height is retrieved within a factor of two and four in 55% and 75% of the MUST trials, respectively. The averaged location error for all 20 trials is obtained 14.54 m with a minimum of 3.58 m and maximum of 34.55 m. The averaged estimated release rate for all trials is overpredicted within a factor of 1.48 of the true source intensity and in 85% of the trials, it is retrieved within in factor of two. In source reconstruction with non-zero measurements, it was observed that the use of all concentration measurements instead of only non-zero essentially makes only the small differences in quality of the source reconstruction and gives a little additional information for better constraining the source parameters. A posteriori uncertainty analysis in the retrieved source parameters is also performed by adding a controlled noise in the concentration measurements and the source reconstruction results were also compared with an earlier study based on the stochastic Bayesian approach for identical 14 MUST trials. The study is useful for emergency regulators to detect an unknown accidental or deliberated continuous point releases in urban regions.

Prediction of the upper tail of concentration distributions of a continuous point source release in urban environments

The peak values observed in a measured concentration time series of a dispersing gaseous pollutant released continuously from a point source in urban environments, and the hazard level associated with them, demonstrate the necessity of predicting the upper tail of concentration distributions. For the prediction of concentration distributions statistical models are preferably employed which provide information about the probability of occurrence. In this paper a concentration database pertaining to a field experiment is used for the selection of the statistical distribution. The inverses of the gamma cumulative distribution function (cdf) for 75th–99th percentiles of concentration are found to be more consistent with the experimental data than those of the log-normal distribution. The experimental values have been derived from measured high frequency time series by sorting first the concentrations and then finding the concentration which corresponds to each probability. Then the concentration mean and variance that are predicted with Computational Fluid Dynamics-Reynolds Averaged Navier–Stokes (RANS) methodology are used to construct the gamma distribution. The proposed model (“RANS-gamma”) is included in the framework of a computational code (ADREA-HF) suitable for simulating the dispersion of airborne pollutants over complex geometries. The methodology is validated by comparing the inverses of the model cdfs with the observed ones from two wind tunnel experiments. The evaluation is performed in the form of validation metrics such as the fractional bias, the normalized mean square error and the factor-of-two percentage. From the above comparisons it is concluded that the overall model performance for the present cases is satisfactory.

Capabilities of IceCube's gamma-ray, optical and X-ray follow-up programs

The IceCube neutrino observatory is a 1 km3 detector for Cherenkov light in the ice at the South Pole. Although the presence of a diffuse astrophysical neutrino flux has been confirmed, its origin has yet to be resolved. Given the current constraints on continuous point source searches, transient and variable objects emerge as promising, detectable source candidates. IceCube boosts the sensitivity to these types of sources by alerting third-party observatories of neutrino events clustered in direction and time. This paper will showcase several neutrino-triggered multi-messenger programs in IceCube along with their results and prospects.

CFD simulation of short-range plume dispersion from a point release in an urban like environment

Abstract An accurate simulation of the short-range plume dispersion of a hazardous pollutant in a geometrically complex urban region is a prerequisite in emergency preparedness and to assist regulators for developing effective policies. This study critically examines the real predictive capability of a three-dimensional Computational Fluid Dynamics (CFD) model, Fluidyn-PANACHE, to apply it in emergency contexts of an accidental or deliberate airborne release in urban regions. The model is evaluated with the Mock Urban Setting Test (MUST) field experiment of a continuous point source release in an idealized urban geometry of a regular array of shipping containers in various atmospheric stability varying from neutral to stable, and very stable conditions. The simulations are performed using three combinations (cases 1, 2, & 3) of inflow boundary conditions for wind and turbulence profiles. A detailed analysis with statistical measures shows that the performance of the Fluidyn-PANACHE against MUST experiment with all the three cases of the inflow boundary conditions is well achieved within the acceptable standards for air quality applications. The model with three cases 1, 2, & 3 predicts respectively 52.8%, 59.9%, and 67.9% of the total concentrations within a factor of two and shows an overall under-prediction. The sampling line maximum concentrations are better simulated by the CFD model with case-3 (95% within a factor of two) in comparison to other cases 1 & 2. A comparative statistical analysis is also performed with other evaluation studies in the literature for the averaged and sampling line maximum concentrations. The present evaluation of the Fluidyn-PANACHE strengthen the evidence that it is capable of dealing properly with the dispersion phenomena in geometrically complex urban environments.

Modelling Short-Term Maximum Individual Exposure from Airborne Hazardous Releases in Urban Environments. Part ΙI: Validation of a Deterministic Model with Wind Tunnel Experimental Data.

The capability to predict short-term maximum individual exposure is very important for several applications including, for example, deliberate/accidental release of hazardous substances, odour fluctuations or material flammability level exceedance. Recently, authors have proposed a simple approach relating maximum individual exposure to parameters such as the fluctuation intensity and the concentration integral time scale. In the first part of this study (Part I), the methodology was validated against field measurements, which are governed by the natural variability of atmospheric boundary conditions. In Part II of this study, an in-depth validation of the approach is performed using reference data recorded under truly stationary and well documented flow conditions. For this reason, a boundary-layer wind-tunnel experiment was used. The experimental dataset includes 196 time-resolved concentration measurements which detect the dispersion from a continuous point source within an urban model of semi-idealized complexity. The data analysis allowed the improvement of an important model parameter. The model performed very well in predicting the maximum individual exposure, presenting a factor of two of observations equal to 95%. For large time intervals, an exponential correction term has been introduced in the model based on the experimental observations. The new model is capable of predicting all time intervals giving an overall factor of two of observations equal to 100%.

Dispersion of particles released at the leading edge of a crop canopy

A large-eddy simulation (LES) approach was used to investigate the flow characteristics at a canopy leading edge and their impact on the dispersion of particles released from point sources inside the canopy. Comparison of results from these LES simulations with those for a canopy that is infinite and uniform in both streamwise and spanwise directions reveals important insights about the adjustment lengths for mean flow, turbulent kinetic energy (TKE), and canopy-shear-layer vortices. Two critical locations were identified in the flow adjustment at the leading edge: (1) the location at which canopy-shear-layer vortices begin to develop and (2) the location at which the flow is fully developed. Simulations were conducted for particles released from continuous point sources at four streamwise locations downwind from the leading edge and three heights within the canopy. The four streamwise source locations corresponded to the canopy leading edge, the location at which canopy-shear-layer vortices began to develop, the transition region, and the fully developed region. The adjustment of flow near the leading edge has a profound impact on the dispersion of particles close to the source, which is where most particle escape from the canopy takes place. Particles released close to the canopy leading edge have much higher maximum escape fractions than particles released in the fully developed region. The adjustment length for particle escape is greater than that for the flow. Away from the source (approximately sixteen canopy heights for the present dense canopy), the geometries of the mean plume become similar for particles released from different regions. Within a few tens of canopy heights from the leading edge, the growth rates of converged mean plume height and depth are lower than those for the case of an infinite canopy.

The Radionuclide Pollutant Dispersion Simulation in Nuclear Accident of Liaoning Hongyanhe Nuclear Power Plant

In order to simulate the nuclear proliferation model of power plant accident, the objective factors of the nuclide dry deposition, wet deposition and radioactive decay are considered and studied based on Gauss diffusion model. With the model modified, the nuclear proliferation simulation of power plant accident is implemented. The simulation system of radionuclide nuclear proliferation is designed and realized with the application of information technology such as GIS and so on. In light of variations in such things as geography, climate and working, the nuclear proliferation of power plant accident emergency is simulated. The results showed that the system can effectively realize the simulation of radionuclide nuclear proliferation including the instantaneous point source, continuous point source, which provides decision support for nuclear accident emergency treatment.

Transient pressure analysis of fractured well in bi-zonal gas reservoirs

For hydraulic fractured well, how to evaluate the properties of fracture and formation are always tough jobs and it is very complex to use the conventional method to do that, especially for partially penetrating fractured well. Although the source function is a very powerful tool to analyze the transient pressure for complex structure well, the corresponding reports on gas reservoir are rare. In this paper, the continuous point source functions in anisotropic reservoirs are derived on the basis of source function theory, Laplace transform method and Duhamel principle. Application of construction method, the continuous point source functions in bi-zonal gas reservoir with closed upper and lower boundaries are obtained. Sequentially, the physical models and transient pressure solutions are developed for fully and partially penetrating fractured vertical wells in this reservoir. Type curves of dimensionless pseudo-pressure and its derivative as function of dimensionless time are plotted as well by numerical inversion algorithm, and the flow periods and sensitive factors are also analyzed. The source functions and solutions of fractured well have both theoretical and practical application in well test interpretation for such gas reservoirs, especial for the well with stimulated reservoir volume around the well in unconventional gas reservoir by massive hydraulic fracturing which always can be described with the composite model.

Turbulent Dispersion of a Passive Scalar in a Staggered Array of Cubes

In this article, we report a numerical and experimental study of turbulent dispersion of a passive scalar released from a continuous ground-level point source in a staggered array of 16 × 16 cubical obstacles. Experimental measurements of the flow and dispersion were obtained in a boundary-layer water channel using laser-induced fluorescence (for concentration) and laser Doppler velocimetry (for velocity). Numerical simulations of the flow and scalar fields for this experimental configuration were performed using two in-house computer codes based on the Reynolds-averaged Navier-Stokes (RANS) method. Results of a detailed comparison between water-channel measurements and model predictions of the mean flow, turbulence kinetic energy, mean concentration, and concentration variance are presented. An advanced model for the concentration variance dissipation rate is validated in the new context of plume dispersion within and above a staggered array of cubical obstacles.