Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH4, CO2 and N2) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation.

Spatial distribution of aerosol black carbon over India during pre-monsoon season

Aerosol black carbon (BC) mass concentrations ([BC]), measured continuously during a multi-platform field experiment, Integrated Campaign for Aerosols gases and Radiation Budget (ICARB, March-May 2006), from a network of eight observatories spread over geographically distinct environments of India, (which included five mainland stations, one highland station, and two island stations (one each ill Arabian Sea and Bay of Bengal)) are examined for their spatio-temporal characteristics. During the period of study, [BC] showed large variations across the country, with values ranging from 27 mu g m(3) over industrial/urban locations to as low as 0.065 mu g m(-3) over the Arabian Sea. For all mainland stations, [BC] remained high compared to highland as well as island stations. Among the island stations, Port Blair (PBR) had higher concentration of BC, compared to Minicoy (MCY), implying more absorbing nature of Bay of Bengal aerosols than Arabian Sea. The highland station Nainital (NTL), in the central Himalayas, showed low values of [BC], comparable or even lower than that of the island station PBR, indicating the prevalence of cleaner environment over there. An examination of the changes in the mean temporal features, as the season advances from winter (December-February) to pre-monsoon (March-May), revealed that: (a) Diurnal variations were pronounced over all the mainland stations, with all afternoon low and a nighttime high: (b) At the islands, the diurnal variations, though resembled those over the mainlands, were less pronounced; and (c) In contrast to this, highland station showed an opposite pattern with an afternoon high and a late night or early morning low. The diurnal variations at all stations are mainly caused by the dynamics of local Atmospheric Boundary Layer (ABL), At the entire mainland as well as island stations (except HYD and DEL), [BC] showed a decreasing trend from January to May, This is attributed to the increased convective mixing and to the resulting enhanced vertical dispersal of species in the ABL. In addition, large short-period modulations were observed at DEL and HYD, which appeared to be episodic, An examination of this in the light of the MODIS-derived fire count data over India along with the back-trajectory analysis revealed that advection of BC from extensive forest fires and biomass-burning regions upwind were largely responsible for this episodic enhancement in BC at HYD and DEL.

Vertical structure and horizontal gradients of aerosol extinction coefficients over coastal India inferred from airborne lidar measurements during the Integrated Campaign for Aerosol, Gases and Radiation Budget (ICARB) field campaign

Quantitative estimates of the vertical structure and the spatial gradients of aerosol extinction coefficients have been made from airborne lidar measurements across the coastline into offshore oceanic regions along the east and west coasts of India. The vertical structure revealed the presence of strong, elevated aerosol layers in the altitude region of similar to 2-4 km, well above the atmospheric boundary layer (ABL). Horizontal gradients also showed a vertical structure, being sharp with the e(-1) scaling distance (D-0H) as small as similar to 150 km in the well-mixed regions mostly under the influence of local source effects. Above the ABL, where local effects are subdued, the gradients were much shallower (similar to 600-800 km); nevertheless, they were steep compared to the value of similar to 1500-2500 km reported for columnar AOD during winter. The gradients of these elevated layers were steeper over the east coast of India than over the west coast. Near-simultaneous radio sonde (Vaisala, Inc., Finland) ascents made over the northern Bay of Bengal showed the presence of convectively unstable regions, first from surface to similar to 750-1000 m and the other extending from 1750 to 3000 m separated by a stable region in between. These can act as a conduit for the advection of aerosols and favor the transport of continental aerosols in the higher levels (> 2 km) into the oceans without entering the marine boundary layer below. Large spatial gradient in aerosol optical and hence radiative impacts between the coastal landmass and the adjacent oceans within a short distance of < 300 km (even at an altitude of 3 km) during summer and the premonsoon is of significance to the regional climate.

Implicit and multigrid procedures for steady-state computations with upwind algorithms

A computational study for the convergence acceleration of Euler and Navier-Stokes computations with upwind schemes has been conducted in a unified framework. It involves the flux-vector splitting algorithms due to Steger-Warming and Van Leer, the flux-difference splitting algorithms due to Roe and Osher and the hybrid algorithms, AUSM (Advection Upstream Splitting Method) and HUS (Hybrid Upwind Splitting). Implicit time integration with line Gauss-Seidel relaxation and multigrid are among the procedures which have been systematically investigated on an individual as well as cumulative basis. The upwind schemes have been tested in various implicit-explicit operator combinations such that the optimal among them can be determined based on extensive computations for two-dimensional flows in subsonic, transonic, supersonic and hypersonic flow regimes. In this study, the performance of these implicit time-integration procedures has been systematically compared with those corresponding to a multigrid accelerated explicit Runge-Kutta method. It has been demonstrated that a multigrid method employed in conjunction with an implicit time-integration scheme yields distinctly superior convergence as compared to those associated with either of the acceleration procedures provided that effective smoothers, which have been identified in this investigation, are prescribed in the implicit operator.

Oxygen transport in a three-dimensional microvascular network incorporated with early tumour growth and preexisting vessel cooption: Numerical simulation study

We propose a dynamic mathematical model of tissue oxygen transport by a preexisting three-dimensional microvascular network which provides nutrients for an in situ cancer at the very early stage of primary microtumour growth. The expanding tumour consumes oxygen during its invasion to the surrounding tissues and cooption of host vessels. The preexisting vessel cooption, remodelling and collapse are modelled by the changes of haemodynamic conditions due to the growing tumour. A detailed computational model of oxygen transport in tumour tissue is developed by considering (a) the time-varying oxygen advection diffusion equation within the microvessel segments, (b) the oxygen flux across the vessel walls, and (c) the oxygen diffusion and consumption with in the tumour and surrounding healthy tissue. The results show the oxygen concentration distribution at different time points of early tumour growth. In addition, the influence of preexisting vessel density on the oxygen transport has been discussed. The proposed model not only provides a quantitative approach for investigating the interactions between tumour growth and oxygen delivery, but also is extendable to model other molecules or chemotherapeutic drug transport in the future study.

Satellite evidence of harmful algal blooms and related oceanographic features in the Bohai Sea during autumn 1998

Harmful algal blooms (HABs) are truly global marine phenomena of increasing significance. Some HAB occurrences are different to observe because of their high spatial and temporal variability and their advection, once formed, by surface currents. A serious HAB occurred in the Bohai Sea during autumn 1998, causing the largest fisheries economic loss. The present study analyzes the formation, distribution, and advection of HAB using satellite SeaWiFS ocean color data and other oceanographic data. The results show that the bloom originated in the western coastal waters of the Bohai Sea in early September, and developed southeastward when sea surface temperature (SST) increased to 25-26 °C. The bloom with a high Chl-a concentration (6.5 mg m-3) in center portion covered an area of 60 × 65 km2. At the end of September, the bloom decayed when SST decreased to 22-23 °C. The HAB may have been initiated by a combination of the river discharge nutrients in the west coastal waters and the increase of SST; afterwards it may have been transported eastward by the local circulation that was enhanced by northwesterly winds in late September and early October.

Indian Ocean sea surface salinity variations in a coupled model

The variability of the sea surface salinity (SSS) in the Indian Ocean is studied using a 100-year control simulation of the Community Climate System Model (CCSM 2.0). The monsoon-driven seasonal SSS pattern in the Indian Ocean, marked by low salinity in the east and high salinity in the west, is captured by the model. The model overestimates runoff int the Bay of Bengal due to higher rainfall over the Himalayan-Tibetan regions which drain into the Bay of Bengal through Ganga-Brahmaputra rivers. The outflow of low-salinity water from the Bay of Bengal is to strong in the model. Consequently, the model Indian Ocean SSS is about 1 less than that seen in the climatology. The seasonal Indian Ocean salt balance obtained from the model is consistent with the analysis from climatological data sets. During summer, the large freshwater input into the Bay of Bengal and its redistribution decide the spatial pattern of salinity tendency. During winter, horizontal advection is the dominant contributor to the tendency term. The interannual variability of the SSS in the Indian Ocean is about five times larger than that in coupled model simulations of the North Atlantic Ocean. Regions of large interannual standard deviations are located near river mouths in the Bay of Bengal and in the eastern equatorial Indian Ocean. Both freshwater input into the ocean and advection of this anomalous flux are responsible for the generation of these anomalies. The model simulates 20 significant Indian Ocean Dipole (IOD) events and during IOD years large salinity anomalies appear in the equatorial Indian Ocean. The anomalies exist as two zonal bands: negative salinity anomalies to the north of the equator and positive to the south. The SSS anomalies for the years in which IOD is not present and for ENSO years are much weaker than during IOD years. Significant interannual SSS anomalies appear in the Indian Ocean only during IOD years.

Analytical model of reactive transport processes with spatially variable coefficients

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Statistical properties of turbulence: An overview

We present an introductory overview of several challenging problems in the statistical characterization of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer additives.

Wind drift of snowfall between the radar volume and ground

This study evaluates how the advection of precipitation, or wind drift, between the radar volume and ground affects radar measurements of precipitation. Normally precipitation is assumed to fall vertically to the ground from the contributing volume, and thus the radar measurement represents the geographical location immediately below. In this study radar measurements are corrected using hydrometeor trajectories calculated from measured and forecasted winds, and the effect of trajectory-correction on the radar measurements is evaluated. Wind drift statistics for Finland are compiled using sounding data from two weather stations spanning two years. For each sounding, the hydrometeor phase at ground level is estimated and drift distance calculated using different originating level heights. This way the drift statistics are constructed as a function of range from radar and elevation angle. On average, wind drift of 1 km was exceeded at approximately 60 km distance, while drift of 10 km was exceeded at 100 km distance. Trajectories were calculated using model winds in order to produce a trajectory-corrected ground field from radar PPI images. It was found that at the upwind side from the radar the effective measuring area was reduced as some trajectories exited the radar volume scan. In the downwind side areas near the edge of the radar measuring area experience improved precipitation detection. The effect of trajectory-correction is most prominent in instant measurements and diminishes when accumulating over longer time periods. Furthermore, measurements of intensive and small scale precipitation patterns benefit most from wind drift correction. The contribution of wind drift on the uncertainty of estimated Ze (S) - relationship was studied by simulating the effect of different error sources to the uncertainty in the relationship coefficients a and b. The overall uncertainty was assumed to consist of systematic errors of both the radar and the gauge, as well as errors by turbulence at the gauge orifice and by wind drift of precipitation. The focus of the analysis is error associated with wind drift, which was determined by describing the spatial structure of the reflectivity field using spatial autocovariance (or variogram). This spatial structure was then used with calculated drift distances to estimate the variance in radar measurement produced by precipitation drift, relative to the other error sources. It was found that error by wind drift was of similar magnitude with error by turbulence at gauge orifice at all ranges from radar, with systematic errors of the instruments being a minor issue. The correction method presented in the study could be used in radar nowcasting products to improve the estimation of visibility and local precipitation intensities. The method however only considers pure snow, and for operational purposes some improvements are desirable, such as melting layer detection, VPR correction and taking solid state hydrometeor type into account, which would improve the estimation of vertical velocities of the hydrometeors.

Optical and Physical Properties of Atmospheric Aerosols over the Bay of Bengal during ICARB

Simultaneous and collocated measurements of total and hemispherical backscattering coefficients (σ and β, respectively) at three wavelengths, mass size distributions, and columnar spectral aerosol optical depth (AOD) were made onboard an extensive cruise experiment covering, for the first time, the entire Bay of Bengal (BoB) and northern Indian Ocean. The results are synthesized to understand the optical properties of aerosols in the marine atmospheric boundary layer and their dependence on the size distribution. The observations revealed distinct spatial and spectral variations of all the aerosol parameters over the BoB and the presence of strong latitudinal gradients. The size distributions varied spatially, with the majority of accumulation modes decreasing from north to south. The scattering coefficient decreased from very high values (resembling those reported for continental/urban locations) in the northern BoB to very low values seen over near-pristine environments in the southeastern BoB. The average mass scattering efficiency of BoB aerosols was found to be 2.66 ± 0.1 m2 g−1 at 550 nm. The spectral dependence of columnar AOD deviated significantly from that of the scattering coefficients in the northern BoB, implying vertical heterogeneity in the aerosol type in that region. However, a more homogeneous scenario was observed in the southern BoB. Simultaneous lidar and in situ measurements onboard an aircraft over the ocean revealed the presence of elevated aerosol layers of enhanced extinction at altitudes of 1 to 3 km with an offshore extent of a few hundred kilometers. Back-trajectory analyses showed these layers to be associated with advection from west Asia and western India. The large spatial variations and vertical heterogeneity in aerosol properties, revealed by the present study, need to be included in the regional radiative forcing over the Bay of Bengal.

Flow field and traverse times for fan forced injection of fumigant via circular or annular inlet into stored grain

Fan forced injection of phosphine gas fumigant into stored grain is a common method to treat infestation by insects. For low injection velocities the transport of fumigant can be modelled as Darcy flow in a porous medium where the gas pressure satisfies Laplace's equation. Using this approach, a closed form series solution is derived for the pressure, velocity and streamlines in a cylindrically stored grain bed with either a circular or annular inlet, from which traverse times are numerically computed. A leading order closed form expression for the traverse time is also obtained and found to be reasonable for inlet configurations close to the central axis of the grain storage. Results are interpreted for the case of a representative 6m high farm wheat store, where the time to advect the phosphine to almost the entire grain bed is found to be approximately one hour.

The role of phosphorus as a regulator of bloom-forming diazotrophic cyanobacteria in the Baltic Sea

Eutrophication favours harmful algal blooms worldwide. The blooms cause toxic outbreaks and deteriorated recreational and aesthetic values, causing both economic loss and illness or death of humans and animals. The Baltic Sea is the world s only large brackish water habitat with recurrent blooms of toxic cyanobacteria capable of biological fixation of atmospheric nitrogen gas. Phosphorus is assumed to be the main limiting factor, along with temperature and light, for the growth of these cyanobacteria. This thesis evaluated the role of phosphorus nutrition as a regulating factor for the occurrence of nitrogen-fixing cyanobacteria blooms in the Baltic Sea, utilising experimental laboratory and field studies and surveys on varying spatial scales. Cellular phosphorus sources were found to be able to support substantial growth of the two main bloom forming species Aphanizomenon sp. and Nodularia spumigena. However, N. spumigena growth seemed independent of phosphorus source, whereas, Aphanizomenon sp. grew best in a phosphate enriched environment. Apparent discrepancies with field observations and experiments are explained by the typical seasonal temperature dependent development of Aphanizomenon sp. and N. spumigena biomass allowing the two species to store ambient pre-bloom excess phosphorus in different ways. Field experiments revealed natural cyanobacteria bloom communities to be predominantly phosphorus deficient during blooms. Phosphate additions were found to increase the accumulation of phosphorus relatively most in the planktonic size fraction dominated by the nitrogen-fixing cyanobacteria. Aphanizomenon sp. responded to phosphate additions whereas the phosphorus nutritive status of N. spumigena seemed independent of phosphate addition. The seasonal development of phosphorus deficiency is different for the two species with N. spumigena showing indications of phosphorus deficiency during a longer time period in the open sea. Coastal upwelling introduces phosphorus to the surface layer during nutrient deficient conditions in summer. The species-specific ability of Aphanizomenon sp. and N. spumigena to utilise phosphate enrichment of the surface layer caused by coastal upwelling was clarified. Typical bloom time vertical distributions of biomass maxima were found to render N. spumigena more susceptible to advection by surface currents caused by coastal upwellings. Aphanizomenon sp. populations residing in the seasonal thermocline were observed to be able to utilise the phosphate enrichment and a bloom was produced with a two to three week time lag subsequent to the relaxation of upwelling. Consistent high concentrations of dissolved inorganic phosphorus, caused by persistent internal loading of phosphorus, was found to be the main source of phosphorus for large-scale pelagic blooms. External loads were estimated to contribute with only a fraction of available phosphorus for open sea blooms. Remineralization of organic forms of phosphorus along with vertical mixing to the permanent halocline during winter set the level of available phosphorus for the next growth season. Events such as upwelling are important in replenishing phosphate concentrations during the nutrient deplete growth season. Autecological characteristics of the two main bloom forming species favour Aphanizomenon sp. populations in utilising the abundant excess phosphate concentrations and phosphate pulses mediated through upwelling. Whilst, N. spumigena displays predominant phosphorus limited growth mode and relies on more scarce cellular phosphorus stores and presumably dissolved organic phosphorus compounds for growth. The Baltic Sea is hypothesised to be in an inhibited state of recovery due to the extensive historical external nutrient loading, extensive internal phosphorus loading and the substantial nitrogen load caused by cyanobacteria nitrogen fixation. This state of the sea is characterised as a vicious circle .

Two-temperature accretion around rotating black holes: a description of the general advective flow paradigm in the presence of various cooling processes to explain low to high luminous sources

We investigate viscous two-temperature accretion disc flows around rotating black holes. We describe the global solution of accretion flows with a sub-Keplerian angular momentum profile, by solving the underlying conservation equations including explicit cooling processes self-consistently. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. We focus on the set of solutions for sub-Eddington, Eddington and super-Eddington mass accretion rates around Schwarzschild and Kerr black holes with a Kerr parameter of 0.998. It is found that the flow, during its infall from the Keplerian to sub-Kepleria transition region to the black hole event horizon, passes through various phases of advection: the general advective paradigm to the radiatively inefficient phase, and vice versa. Hence, the flow governs a much lower electron temperature similar to 10(8)-10(9.5) K, in the range of accretion rate in Eddington units 0.01 less than or similar to (M) over dot less than or similar to 100, compared to the hot protons of temperature similar to 10(10.2)-10(11.8) K. Therefore, the solution may potentially explain the hard X-rays and gamma-rays emitted from active galactic nuclei (AGNs) and X-ray binaries. We then compare the solutions for two different regimes of viscosity. We conclude that a weakly viscous flow is expected to be cooling dominated, particularly at the inner region of the disc, compared to its highly viscous counterpart, which is radiatively inefficient. With all the solutions in hand, we finally reproduce the observed luminosities of the underfed AGNs and quasars (e. g. Sgr A*) to ultraluminous X-ray sources (e. g. SS433), at different combinations of input parameters, such as the mass accretion rate and the ratio of specific heats. The set of solutions also predicts appropriately the luminosity observed in highly luminous AGNs and ultraluminous quasars (e. g. PKS 0743-67).