The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

The unsteady flow of a weakly compressible fluid in a thin porous layer III: three-dimensional computations

We describe a novel method for determining the pressure and velocity fields for a weakly compressible fluid flowing in a thin three-dimensional layer composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Our approach uses the method of matched asymptotic expansions to derive expressions for all significant process quantities, the computation of which requires only the solution of linear, elliptic, two-dimensional boundary value and eigenvalue problems. In this article, we provide full implementation details and present numerical results demonstrating the efficiency and accuracy of our scheme.

Model estimation of cerebral hemodynamics between blood flow and volume changes: A data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.

Flow-aligned jets in the magnetospheric cusp: Results from the Geospace Environment Modeling Pilot Program

The extended flight of the Airborne Ionospheric Observatory during the Geospace Environment Modeling (GEM) Pilot program on January 16, 1990, allowed continuous all-sky monitoring of the two-dimensional ionospheric footprint of the northward interplanetary magnetic field (IMF) cusp in several wavelengths. Especially important in determining the locus of magnetosheath electron precipitation was the 630.0-nm red line emission. The most striking morphological change in the images was the transient appearance of zonally elongated regions of enhanced 630.0-nm emission which resembled “rays” emanating from the centroid of the precipitation. The appearance of these rays was strongly correlated with the Y component of the IMF: when the magnitude of By was large compared to Bz, the rays appeared; otherwise, the distribution was relatively unstructured. Late in the flight the field of view of the imager included the field of view of flow measurements from the European incoherent scatter radar (EISCAT). The rays visible in 630.0-nm emission exactly aligned with the position of strong flow jets observed by EISCAT. We attribute this correspondence to the requirement of quasi-neutrality; namely, the soft electrons have their largest precipitating fluxes where the bulk of the ions precipitate. The ions, in regions of strong convective flow, are spread out farther along the flow path than in regions of weaker flow. The occurrence and direction of these flow bursts are controlled by the IMF in a manner consistent with newly opened flux tubes; i.e., when |By| > |Bz|, tension in the reconnected field lines produce east-west flow regions downstream of the ionospheric projection of the x line. We interpret the optical rays (flow bursts), which typically last between 5 and 15 min, as evidence of periods of enhanced dayside (or lobe) reconnection when |By| > |Bz|. The length of the reconnection pulse is difficult to determine, however, since strong zonal flows would be expected to persist until the tension force in the field line has decayed, even if the duration of the enhanced reconnection was relatively short.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part I. Mathematical modeling

The conventional Newton and fast decoupled power flow (FDPF) methods have been considered inadequate to obtain the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. It is well known that the PV and Q-theta decoupling assumptions of the fast decoupled power flow formulation no longer hold in the vicinity of the critical point. Moreover, the Jacobian matrix of the Newton method becomes singular at this point. However, the maximum loading point can be efficiently computed through parameterization techniques of continuation methods. In this paper it is shown that by using either theta or V as a parameter, the new fast decoupled power flow versions (XB and BX) become adequate for the computation of the maximum loading point only with a few small modifications. The possible use of reactive power injection in a selected PV bus (Q(PV)) as continuation parameter (mu) for the computation of the maximum loading point is also shown. A trivial secant predictor, the modified zero-order polynomial which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used in predictor step. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approach for the IEEE test systems (14, 30, 57 and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that parameters can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. (C) 2003 Elsevier B.V. All rights reserved.

Mathematical modeling of the ester oil-refrigerant R134A mixture two-phase flow with foam formation through a small diameter tube

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An exact equation for the free surface of a fluid in a porous medium

We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a. at impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with new variable coefficients, the boundary conditions. We use a kernel of the Laplace equation which allows us to write the Dirichlet-to-Neumann operator, and in this way we are able to find an exact differential-integral equation for the evolution of the free surface in one space dimension. Although not amenable to direct analytical solutions, this equation turns out to allow an easy numerical implementation. We give an explicit illustrative case at the end of the article.

Supercritical fluid extraction from fennel (Foeniculum vulgare): global yield, composition and kinetic data

Supercritical fluid extraction (SFE) from solids has proven to be technically feasible for almost any system; nonetheless, its economical viability has been proven for a restricted number of systems. A common practice is to compare the cost of manufacturing of vegetable extracts by a variety of techniques without deeply considering the huge differences in composition and functional properties among the various types of extracts obtained; under this circumstance, the cost of manufacturing do not favor SFE. Additionally, the influence of external parameters such as the agronomic conditions and the SFE system geometry are not considered. In the present work, these factors were studied for the system fennel seeds + CO2. The effects of the harvesting season and the degree of maturation on the global yields for the system fennel seeds + CO2 were analyzed at 300 bar and 40 degrees C. The effects of the pressure on the global yields were determined for the temperatures of 30 and 40 degrees C. Kinetics experiments were done for various ratios of bed height to bed diameter. Fennel extracts were also obtained by hydrodistillation and low-pressure solvent extraction. The chemical composition of the fennel extracts were determined by gas chromatography. The SFE maximum global yield (12.5%, dry basis) was obtained with dry harvested fennel seeds. Anethole and fenchone were the major constituents of the extract; the following fat acids palmitic (C16H32O2), palmitoleic stearic (C18H36O2), oleic (C18H34O2), linoleic (C18H32O2) and linolenic (C18H30O2) were also detected in the extracts. A relation between amounts of feed and solvent, bed height and diameter, and solvent flow rate was proposed. The models of Sovova, Goto et al. and Tan and Lion were capable of describing the mass transfer kinetics. (c) 2005 Elsevier B.V. All rights reserved.

Study of alternative schemes for the parameterization step of the continuation power flow method based on physical parameters, part I: Mathematical modeling

The conventional power flow method is considered to be inadequate to obtain the maximum loading point because of the singularity of Jacobian matrix. Continuation methods are efficient tools for solving this kind of problem since different parameterization schemes can be used to avoid such ill-conditioning problems. This paper presents the details of new schemes for the parameterization step of the continuation power flow method. The new parameterization options are based on physical parameters, namely, the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, and transmission line power losses (real and reactive). The simulation results obtained with the new approach for the IEEE test systems (14, 30, 57, and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are not only preserved but also improved.

Distribution Transformer Modeling for Application in Three-Phase Power Flow Algorithm

In this paper, it is presented a methodology for three-phase distribution transformer modeling, considering several types of transformer configuration, to be used in algorithms of power flow in three-phase radial distribution networks. The paper provides a detailed discussion about the models and the results from an implementation of the power flow algorithm. The results, taken from three different networks, are presented for several transformer configurations and for voltage regulators as well.

Simulations of incompressible fluid flows by a least squares finite element method

In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using velocity-pressure-vorticity and velocity-pressure-stress formulations, named u-p-ω) and u-p-τ formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is convenient for implementation by LSFEM. The main purposes of this work are the numerical computation of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier-Stokes equations in u-p-ω and u-p-τ formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate the numerical code and the preliminary results are presented and compared with available results from the literature. Copyright © 2005 by ABCM.

Voltage regulator modeling for the three-phase power flow in distribution networks

In this paper a three-phase power flow for electrical distribution systems considering different models of voltage regulators is presented. A voltage regulator (VR) is an equipment that maintains the voltage level in a predefined value in a distribution line in spite of the load variations within its nominal power. Three different types of connections are analyzed: 1) wye-connected regulators, 2) open delta-connected regulators and 3) closed delta-connected regulators. To calculate the power flow, the three-phase backward/forward sweep algorithm is used. The methodology is tested on the IEEE 34 bus distribution system. ©2008 IEEE.

Energetic, ecologic and fluid-dynamic analysis of a fluidized bed gasifier operating with sugar cane bagasse

This work aims to study the thermodynamic, ecological and fluid-dynamic aspects of a circulating fluidized bed gasifier using sugar cane bagasse as biomass, in order to estimate a model of its normal operation. In the initial stage was analysed the composition of biomass selected (sugar cane bagasse) and its lower heating value (LHV) was calculated. The energy balance of the gasifier was done, being the volumetric flow of air, synthesis gas and biomass estimated. Also the power produced by this gasifier was theoretically estimated. Then the circulating fluidized bed gasifier was designed for operation with approximately 100 kg/h of processed biomass. Cross-sectional area of the reactor, feeder size, diameter of the exit zone of the gases and minimum height of the expanded bed were selected. Some bed gasifier hydrodynamic factors were also studied. The minimum fluidization velocity, fluidization terminal velocity, and average fluidizing velocity were calculated, in order to understand the fluid-dynamic behaviour of gasification of this fuel. It was obtained a theoretical model that can support a possible prototype of circulating fluidized bed gasifier biomass. Finally, there were studied the ecological aspects of the gasifier, through an overall methodology. Ecological efficiencies were estimated for two scenarios: first considering the carbon cycle and thereafter disregarding the carbon cycle. In both cases, it can be proved the ecological viability of the project. © 2013 Elsevier Ltd. All rights reserved.

A snapshot of suspended sediment and fluid mud occurrence in a mixed-energy embayment, Tijucas Bay, Brazil

Along the southern Brazilian coast, Tijucas Bay is known for its unique muddy tidal flats associated with chenier plains. Previous field observations pointed to very high suspended sediment concentrations (SSCs) in the inner parts of the bay, and in the estuary of the Tijucas River, suggesting the presence of fluid mud. In this study, the occurrences of suspended sediments and fluid mud were examined during a larger-scale, high-resolution 2-day field campaign on 1-2 May 2007, encompassing survey lines spanning nearly 80 km, 75 water sampling stations for near-bottom density estimates, and ten sediment sampling stations. Wave refraction modeling provided qualitative wave energy estimates as a function of different incidence directions. The results show that SSC increases toward the inner bay near the water surface, but seaward near the bottom. This suggests that suspended sediment is supplied by the local rivers, in particular the Tijucas. Near-surface SSCs were of the order of 50 mg l(-1) close to the shore, but exceeded 100 mg l(-1) near the bottom in the deeper parts of the bay. Fluid mud thickness and location given by densimetry and echo-sounding agreed in some places, although being mostly discordant. The best agreement was observed where wave energy was high during the campaign. The discrepancy between the two methods may be an indication for the existence of fluid mud, which is recorded by one method but not the other. Agreement is considered to be an indication of fluidization, whereas disagreement indicates more consolidation. Wave modeling suggests that waves from the ENE and SE are the most effective in supplying energy to the inner bay, which may induce the liquefaction of mud deposits to form fluid mud. Nearshore mud resuspension and weak horizontal currents result in sediment-laden offshore flow, which explains the higher SSCs measured in the deeper parts of the bay, besides providing a mechanism for fine-sediment export to the inner shelf.