Analytical solutions for transient temperature distribution in a geothermal reservoir due to cold water injection

An analytical solution to describe the transient temperature distribution in a geothermal reservoir in response to injection of cold water is presented. The reservoir is composed of a confined aquifer, sandwiched between rocks of different thermo-geological properties. The heat transport processes considered are advection, longitudinal conduction in the geothermal aquifer, and the conductive heat transfer to the underlying and overlying rocks of different geological properties. The one-dimensional heat transfer equation has been solved using the Laplace transform with the assumption of constant density and thermal properties of both rock and fluid. Two simple solutions are derived afterwards, first neglecting the longitudinal conductive heat transport and then heat transport to confining rocks. Results show that heat loss to the confining rock layers plays a vital role in slowing down the cooling of the reservoir. The influence of some parameters, e.g. the volumetric injection rate, the longitudinal thermal conductivity and the porosity of the porous media, on the transient heat transport phenomenon is judged by observing the variation of the transient temperature distribution with different values of the parameters. The effects of injection rate and thermal conductivity have been found to be profound on the results.

A modeling study of the processes of surface salinity seasonal cycle in the Bay of Bengal

In response to the Indian Monsoon freshwater forcing, the Bay of Bengal exhibits a very strong seasonal cycle in sea surface salinity (SSS), especially near the mouths of the Ganges-Brahmaputra and along the east coast of India. In this paper, we use an eddy-permitting (similar to 25 km resolution) regional ocean general circulation model simulation to quantify the processes responsible for this SSS seasonal cycle. Despite the absence of relaxation toward observations, the model reproduces the main features of the observed SSS seasonal cycle, with freshest water in the northeastern Bay, particularly during and after the monsoon. The model also displays an intense and shallow freshening signal in a narrow (similar to 100 km wide) strip that hugs the east coast of India, from September to January, in good agreement with high-resolution measurements along two ships of opportunity lines. The mixed layer salt budget confirms that the strong freshening in the northern Bay during the monsoon results from the Ganges-Brahmaputra river discharge and from precipitation over the ocean. From September onward, the East India Coastal Current transports this freshwater southward along the east coast of India, reaching the southern tip of India in November. The surface freshening results in an enhanced vertical salinity gradient that increases salinity of the surface layer by vertical processes. Our results reveal that the erosion of the freshwater tongue along the east coast of India is not driven by northward horizontal advection, but by vertical processes that eventually overcome the freshening by southward advection and restore SSS to its premonsoon values. The salinity-stratified barrier layer hence only acts as a ``barrier'' for vertical heat fluxes, but is associated with intense vertical salt fluxes in the Bay of Bengal.

Virus-sized colloid transport in a single pore: Model development and sensitivity analysis

A mathematical model is developed to simulate the transport and deposition of virus-sized colloids in a cylindrical pore throat considering various processes such as advection, diffusion, colloid-collector surface interactions and hydrodynamic wall effects. The pore space is divided into three different regions, namely, bulk, diffusion and potential regions, based on the dominant processes acting in each of these regions. In the bulk region, colloid transport is governed by advection and diffusion whereas in the diffusion region, colloid mobility due to diffusion is retarded by hydrodynamic wall effects. Colloid-collector interaction forces dominate the transport in the potential region where colloid deposition occurs. The governing equations are non-dimensionalized and solved numerically. A sensitivity analysis indicates that the virus-sized colloid transport and deposition is significantly affected by various pore-scale parameters such as the surface potentials on colloid and collector, ionic strength of the solution, flow velocity, pore size and colloid size. The adsorbed concentration and hence, the favorability of the surface for adsorption increases with: (i) decreasing magnitude and ratio of surface potentials on colloid and collector, (ii) increasing ionic strength and (iii) increasing pore radius. The adsorbed concentration increases with increasing Pe, reaching a maximum value at Pe = 0.1 and then decreases thereafter. Also, the colloid size significantly affects particle deposition with the adsorbed concentration increasing with increasing particle radius, reaching a maximum value at a particle radius of 100 nm and then decreasing with increasing radius. System hydrodynamics is found to have a greater effect on larger particles than on smaller ones. The secondary minimum contribution to particle deposition has been found to increase as the favorability of the surface for adsorption decreases. The sensitivity of the model to a given parameter will be high if the conditions are favorable for adsorption. The results agree qualitatively with the column-scale experimental observations available in the literature. The current model forms the building block in upscaling colloid transport from pore scale to Darcy scale using Pore-Network Modeling. (C) 2014 Elsevier By. All rights reserved.

Interpreting the upper level structure of the Madden-Julian oscillation

The nonlinear response of a spherical shallow water model to an imposed heat source in the presence of realistic zonal mean zonal winds is investigated numerically. The solutions exhibit elongated, meridionally tilted ridges and troughs indicative of a poleward dispersion of wave activity. As the speed of the jets is increased, the equatorial Kelvin wave is unaffected but the global Rossby wave train coalesces to form a compact, amplified quadrupole structure that bears a striking resemblance to the observed upper level structure of the Madden-Julian oscillation. In the presence of strong subtropical westerly jets, the advection of planetary vorticity by the meridional flow and relative vorticity by the zonally averaged background flow conspire to create the distinctive quadrupole configuration of flanking Rossby waves.

Cryogenian magmatism and crustal reworking in the Southern Granulite Terrane, India

Understanding Neoproterozoic crustal evolution is fundamental to reconstructing the Gondwana supercontinent, which was assembled at this time. Here we report evidence of Cryogenian crustal reworking in the Madurai Block of the Southern Granulite Terrane of India. The study focuses on a garnet-bearing granite-charnockite suite, where the granite shows in situ dehydration into patches and veins of incipient charnockite along the contact with charnockite. The granite also carries dismembered layers of Mg-Al-rich granulite. Micro-textural evidence for dehydration of granite in the presence of CO2-rich fluids includes the formation of orthopyroxene by the breakdown of biotite, neoblastic zircon growth in the dehydration zone, at around 870 degrees C and 8kbar. The zircon U-Pb ages suggest formation of the granite, charnockite, and incipient charnockite at 836 +/- 73, 831 +/- 31, and 772 +/- 49Ma, respectively. Negative zircon epsilon Hf (t) (-5 to -20) values suggest that these rocks were derived from a reworked Palaeoproterozoic crustal source. Zircon grains in the Mg-Al-rich granulite record a spectrum of ages from ca. 2300 to ca. 500Ma, suggesting multiple provenances ranging from Palaeoproterozoic to mid-Neoproterozoic, with neoblastic zircon growth during high-temperature metamorphism in the Cambrian. We propose that the garnet-bearing granite and charnockite reflect the crustal reworking of aluminous crustal material indicated by the presence of biotite+quartz+aluminosilicate inclusions in the garnet within the granite. This crustal source can be the Mg-Al-rich layers carried by the granite itself, which later experienced high-temperature regional metamorphism at ca. 550Ma. Our model also envisages that the CO2 which dehydrated the garnet-bearing granite generating incipient charnockite was sourced from the proximal massive charnockite through advection. These Cryogenian crustal reworking events are related to prolonged tectonic activities prior to the final assembly of the Gondwana supercontinent.

REDUCED ORDER MODELLING OF COMBUSTION INSTABILITY IN A BACKWARD FACING STEP COMBUSTOR

This paper develops a fully coupled time domain Reduced Order Modelling (ROM) approach to model unsteady combustion dynamics in a backward facing step combustor The acoustic field equations are projected onto the canonical acoustic eigenmodes of the systems to obtain a coupled system of modal evolution equations. The heat release response of the flame is modelled using the G-equation approach. Vortical velocity fluctuations that arise due to shear layer rollup downstream of the step are modelled using a simplified 1D-advection equation whose phase speed is determined from a linear, local, temporal stability analysis of the shear layer just downstream of the step. The hydrodynamic stability analysis reveals a abrupt change in the value of disturbance phase speed from unity for Re < Re-crit to 0.5 for Re > Re-crit, where Remit for the present geometry was found to be approximate to 10425. The results for self-excited flame response show highly wrinkled flame shapes that are qualitatively similar to those seen in prior experiments of acoustically forced flames. The effect of constructive and destructive interference between the two contributions to flame surface wrinkling results in high amplitude wrinkles for the case when K-c -> 1.

Correlation equations for average deposition rate coefficients of nanoparticles in a cylindrical pore

Nanoparticle deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, the effect of various pore-scale parameters on nanoparticle deposition can be understood by studying nanoparticle transport at pore scale and upscaling the results to the Darcy scale. In this work, correlation equations for the deposition rate coefficients of nanoparticles in a cylindrical pore are developed as a function of nine pore-scale parameters: the pore radius, nanoparticle radius, mean flow velocity, solution ionic strength, viscosity, temperature, solution dielectric constant, and nanoparticle and collector surface potentials. Based on dominant processes, the pore space is divided into three different regions, namely, bulk, diffusion, and potential regions. Advection-diffusion equations for nanoparticle transport are prescribed for the bulk and diffusion regions, while the interaction between the diffusion and potential regions is included as a boundary condition. This interaction is modeled as a first-order reversible kinetic adsorption. The expressions for the mass transfer rate coefficients between the diffusion and the potential regions are derived in terms of the interaction energy profile. Among other effects, we account for nanoparticle-collector interaction forces on nanoparticle deposition. The resulting equations are solved numerically for a range of values of pore-scale parameters. The nanoparticle concentration profile obtained for the cylindrical pore is averaged over a moving averaging volume within the pore in order to get the 1-D concentration field. The latter is fitted to the 1-D advection-dispersion equation with an equilibrium or kinetic adsorption model to determine the values of the average deposition rate coefficients. In this study, pore-scale simulations are performed for three values of Peclet number, Pe = 0.05, 5, and 50. We find that under unfavorable conditions, the nanoparticle deposition at pore scale is best described by an equilibrium model at low Peclet numbers (Pe = 0.05) and by a kinetic model at high Peclet numbers (Pe = 50). But, at an intermediate Pe (e.g., near Pe = 5), both equilibrium and kinetic models fit the 1-D concentration field. Correlation equations for the pore-averaged nanoparticle deposition rate coefficients under unfavorable conditions are derived by performing a multiple-linear regression analysis between the estimated deposition rate coefficients for a single pore and various pore-scale parameters. The correlation equations, which follow a power law relation with nine pore-scale parameters, are found to be consistent with the column-scale and pore-scale experimental results, and qualitatively agree with the colloid filtration theory. These equations can be incorporated into pore network models to study the effect of pore-scale parameters on nanoparticle deposition at larger length scales such as Darcy scale.

A Lagrangian lattice Boltzmann method for Euler equations

A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution function consists of macroscopic Lagrangian variables at time steps n and n + 1. It is different from the standard lattice Boltzmann method. In this method the element, instead of each particle, is required to satisfy the basic law. The element is considered as one large particle, which results in simpler version than the corresponding Eulerian one, because the advection term disappears here. Our numerical examples successfully reproduce the classical results.

Simulations of oil spread on a water surface

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called sigma transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

A Multimoment Finite-Volume Shallow-Water Model On The Yin-Yang Overset Spherical Grid

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average ( VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

Shallow Water Model On Cubed-Sphere By Multi-Moment Finite Volume Method

A global numerical model for shallow water flows on the cubed-sphere grid is proposed in this paper. The model is constructed by using the constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM). Two kinds of moments, i.e. the point value (PV) and the volume-integrated average (VIA) are defined and independently updated in the present model by different numerical formulations. The Lax-Friedrichs upwind splitting is used to update the PV moment in terms of a derivative Riemann problem, and a finite volume formulation derived by integrating the governing equations over each mesh element is used to predict the VIA moment. The cubed-sphere grid is applied to get around the polar singularity and to obtain uniform grid spacing for a spherical geometry. Highly localized reconstruction in CIP/MM FVM is well suited for the cubed-sphere grid, especially in dealing with the discontinuity in the coordinates between different patches. The mass conservation is completely achieved over the whole globe. The numerical model has been verified by Williamson's standard test set for shallow water equation model on sphere. The results reveal that the present model is competitive to most existing ones. (C) 2008 Elsevier Inc. All rights reserved.

Seasonal cycles of phytoplankton in relation to the hydrography of Monterey Bay

Annual cycles of relative abundance are described for phytoplankton species collected from Monterey Bay, California, from July 1974 to June 1976, and the population dynamics related to the annual hydrographic cycle. Neritic diatom species dominated the population during the Upwelling and Oceanic periods, with dinoflagellate species becoming numerically more important during the Davidson period. Recurrent species groups identified using Fager's regroup analysis revealed the presence of a large neritic group of overwhelming numerical importance. This group is composed of indigenous species and is present in the bay during most of the year. Conspicuous changes in the phytoplankton population occurred predominantly among species within this group. During the Davidson period, the advection of southern waters into the bay may temporarily displace the endemic species with dinoflagellates becoming numerically more important. A red tide bloom of Gonyaulax polyedra occurred during this period in 1974, which dominated the phytoplankton population for a period of six weeks. The population dynamics of two hydrographically different stations were compared. A station located over the deep waters of the submarine canyon exhibited much lower phytoplankton standing stocks than a station located over the shelf area in the south of the bay, but seasonal changes in relative abundance and species composition were similar. Physical and chemical differences observed between the two stations appear to be the result of the presence of more recently upwelled water in the canyon area, and higher biological utilization in the south of the bay. A close correlation of species diversity with the depth of the mixed layer was observed, with diversity rising with the shoaling of the thermocline. It is suggested that this may reflect the introduction of new species from below the thermocline into the mixed layer as a result of upwelling activity. It is also suggested that this may be an artifact due to sampling problems associated with internal waves. (Document contains 100 pages.)

A Synoptic View of a Coastal Plain Estuary.

During October, 1972 the Patuxent River Estuary was monitored intensively and synoptically over two tidal cycles to determine the spatial and temporal patterns of various hydrodynamic, chemical and biological features. Forty-one depths at eleven stations along nine transects were sampled simultaneously at hourly intervals for salinity, temperature, dissolved oxygen, chlorohyll a, particulate nitrogen, nitrate, nitrite, total kjeldahl nitrogen, ammonia, particulate carbohydrate, dissolved organic carbon, total hydrolizable phosphorous, dissolved inorganic phosphorous, suspended sediment, particle size distribution, and zooplankton. Tidal velocity was continuously monitored at each depth by recording current meters. Riverine input and meteorological conditions were relatively stable for two weeks preceeding the deployment. This communication describes the calculation of the intrinsic rates of change of the observed variables from their measured distributions in the Estuary. The steady-state, one-dimensional equation of species continuity is employed to separate the advection and tidal dispersion of a hydrodynamically passive substance frbm its intrinsic rate of change at point. A new spatial transform is introduced for the purpose of interpolation and extrapolation of data.The intrinsic rate of change profiles reveal a region of heavy bloom activity in the upper estuary and a secondary bloom near the point in the River that most of the suspended material settles out. The changes in ammonia and nitrates are highly correlated to the productivity patterns. Phosphorous rates are less closely correlated to productivity. The perturbations that the Chalk Point steam electric power plant have on the heat and oxygen balances are easily discernible.

A Hybrid Scheme Based on Finite Element/Volume Methods for Two Immiscible Fluid Flows

We have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

Effects of particle size ratio on single particle motion in colloidal dispersions

The motion of a single Brownian particle of arbitrary size through a dilute colloidal dispersion of neutrally buoyant bath spheres of another characteristic size in a Newtonian solvent is examined in two contexts. First, the particle in question, the probe particle, is subject to a constant applied external force drawing it through the suspension as a simple model for active and nonlinear microrheology. The strength of the applied external force, normalized by the restoring forces of Brownian motion, is the Péclet number, Pe. This dimensionless quantity describes how strongly the probe is upsetting the equilibrium distribution of the bath particles. The mean motion and fluctuations in the probe position are related to interpreted quantities of an effective viscosity of the suspension. These interpreted quantities are calculated to first order in the volume fraction of bath particles and are intimately tied to the spatial distribution, or microstructure, of bath particles relative to the probe. For weak Pe, the disturbance to the equilibrium microstructure is dipolar in nature, with accumulation and depletion regions on the front and rear faces of the probe, respectively. With increasing applied force, the accumulation region compresses to form a thin boundary layer whose thickness scales with the inverse of Pe. The depletion region lengthens to form a trailing wake. The magnitude of the microstructural disturbance is found to grow with increasing bath particle size -- small bath particles in the solvent resemble a continuum with effective microviscosity given by Einstein's viscosity correction for a dilute dispersion of spheres. Large bath particles readily advect toward the minimum approach distance possible between the probe and bath particle, and the probe and bath particle pair rotating as a doublet is the primary mechanism by which the probe particle is able to move past; this is a process that slows the motion of the probe by a factor of the size ratio. The intrinsic microviscosity is found to force thin at low Péclet number due to decreasing contributions from Brownian motion, and force thicken at high Péclet number due to the increasing influence of the configuration-averaged reduction in the probe's hydrodynamic self mobility. Nonmonotonicity at finite sizes is evident in the limiting high-Pe intrinsic microviscosity plateau as a function of bath-to-probe particle size ratio. The intrinsic microviscosity is found to grow with the size ratio for very small probes even at large-but-finite Péclet numbers. However, even a small repulsive interparticle potential, that excludes lubrication interactions, can reduce this intrinsic microviscosity back to an order one quantity. The results of this active microrheology study are compared to previous theoretical studies of falling-ball and towed-ball rheometry and sedimentation and diffusion in polydisperse suspensions, and the singular limit of full hydrodynamic interactions is noted.

Second, the probe particle in question is no longer subject to a constant applied external force. Rather, the particle is considered to be a catalytically-active motor, consuming the bath reactant particles on its reactive face while passively colliding with reactant particles on its inert face. By creating an asymmetric distribution of reactant about its surface, the motor is able to diffusiophoretically propel itself with some mean velocity. The effects of finite size of the solute are examined on the leading order diffusive microstructure of reactant about the motor. Brownian and interparticle contributions to the motor velocity are computed for several interparticle interaction potential lengths and finite reactant-to-motor particle size ratios, with the dimensionless motor velocity increasing with decreasing motor size. A discussion on Brownian rotation frames the context in which these results could be applicable, and future directions are proposed which properly incorporate reactant advection at high motor velocities.