Flow In Such Systems Research Articles

The link between a heterogeneous model and its flow response: examples from fault damage zones highlighting issues in domain discretization and flow simulation

Abstract Natural fault damage zones (FDZs) are characterized by complex geometries and topologies, and by strongly-contrasting material properties. Accurate simulation of fluid flow in such systems is dependent on the method of discretization and the mathematical representation of the flow. In this paper, we focus on the conceptual and methodological issues that link a model of a heterogeneous system and its flow response. We study FDZs as our example, where each thin fault strand is a barrier to flow. We examine two contrasting discretization schemes and apply them to 2D FDZ models that contain a realistic array of linear fault traces. Both schemes produce results that are generally in good agreement, and agree with the results calculated by a more accurate (but computationally less efficient) reference scheme. However, differences occur when the discretization approach fails to maintain the fault connectivity (topology) of the input model. It is important to guide the modelling by identifying any continuous flow pathways in the matrix linking fluid inlets and outlets (Through-Going Regions, TGRs). We illustrate a new scheme that identifies all TGRs and determines a grid that is just fine enough to resolve them.

Nanofabrication of top-gated carbon nanotube-based transistors: Probing electron-electron interactions in one-dimensional systems

Carbon nanotubes are interesting for studying the remarkable electronic properties of one-dimensional (1D) quantum systems. Electron flow in such systems is not described by Fermi liquid theory—restricted dimensionality leads to the appearance of collective excitations—or Luttinger liquid behavior. Previous studies have probed Luttinger liquid behavior by tunneling into or between one-dimensional systems. We propose to extend these studies by using narrow top gates to introduce tunable tunnel barriers within nanotubes. We report on the scalable fabrication of carbon nanotube-based transistors with nanowire top gates. We have used electron-beam lithography (EBL) to create single-walled carbon nanotube (SWNT) transistors with source-drain spacings down to 200 nm and with sub-30 nm metal top gates for creating tunable tunnel barriers. The top metal gate is isolated from the nanotube by a thin aluminum oxide layer deposited by atomic layer deposition. We fabricated chips with 100 devices using multiple electron-beam lithography alignment steps and achieved overall placement better than 30 nm. The details of top-gated SWNT transistor fabrication are presented, and initial transport measurements on fabricated devices are discussed.

Size matters: extraordinary rodent abundance on an Australian tropical flood plain

Abstract: Published estimates of the total biomass of natural populations of mammalian herbivores generally have ignored small‐bodied taxa (especially, rodents). Including such taxa may dramatically change our understanding of total biomass and energy flow in such systems. Dusky rats (Rattus colletti) are small (up to 210 g) native Australian mammals, and our 5‐year mark‐recapture study on a tropical flood plain (Adelaide River, Northern Territory) revealed that rat biomass can reach extraordinary levels (up to 4.7 t km−2). Because their small body size results in high mass‐specific metabolic rates, a given biomass of rodents has a several‐fold higher total energy requirement than the same mass of large‐bodied herbivores. Accordingly, during some years dusky rat biomass can be double that estimated for large herbivores on the world's most productive savannas in eastern and southern Africa. The huge rodent biomass strongly suggests that the Adelaide River flood plain must be an incredibly productive habitat. Considering the immense biological importance of these productive ecosystems, flood plain conservation must be placed high on the priority list of habitats that require immediate protection.

Structure, Dynamics and Properties of Materials with Polymers Having Complex Architectures

AbstractVarious non‐linear highly branched polymers such as multiarm stars, block copolymer micelles and bottlebrush‐like polymers have been studied in order to analyze their intramolecular structure and effects of spatial ordering resulting from their specific macromolecular architecture. These polymers constitute a class of compact macromolecules which, due to the high intramolecular density, interact strongly, excluding each other in space. Investigations of the structure and dynamics in such systems, using various experimental methods as well as computer simulations, have been performed. Small angle X‐ray scattering is used to characterize the structure and mechanical spectroscopy is used for the detection of the dynamic behavior of the systems. Simulations have been performed using the cooperative motion algorithm with lattice polymers equivalent to the considered macromolecules. Results of both experiments and the simulation seem to support the concept of slow structural cooperative rearrangements controlling the flow in such systems. The effects are analogous to those related to flow in low molecular liquids but take place on another size scale. The new slow relaxation processes creates new super soft‐states which are characterized by shear modulus plateau lower than 104 Pa.

A note on pressure drop for the cross-flow of power-law liquids and air/power law liquid mixtures past a bundle of circular rods

The steady flow of non-Newtonian polymer solutions on their own and together with air transverse to a bundle of circular rods, has been studied experimentally. In particular, the frictional pressure drop has been measured as a function of non-Newtonian power-law constants, flow rates, voidage of bundles and the input fraction of air over wide ranges of conditions as: power-law flow behaviour index, 0.5 to 1; voidage values of 0.78 and 0.87–0.88; air velocity (superficial), 0.09 to 0.28 m/s and liquid velocity (superficial) 0.018 to 0.5 m/s. While the single phase flow results for power-law liquids are in excellent agreement with an existing equation, the two-phase pressure drop results are also in accordance with the form of the well-known Lockhart–Martinelli correlation. Based on these results, it is suggested that a value of 5–10 for the Reynolds number based on rod diameter marks the limit of the laminar flow in such systems.

Flow measurement in partially filled closed conduits

The measurement of free surface flows in closed conduits can present some interesting challenges to the flow measurement engineer and equipment designer. Regulatory pressures and the need for improved operational information is leading to increased interest from the water industry in measuring flow in such systems. A new ISO Technical Report has been drafted to update the existing document and combine its two parts into a single publication. The Technical Report presents the user with a summary of the various commercially available and near to market options available for measurement in partially filled conduits. Techniques covered include volumetric methods, tracer and dilution methods, use of gauging structures, ultrasonic Doppler and transit time, electromagnetic methods, slope-area methods and non-contact methods. It also summarises the operating constraints of such an environment.

Estimation of three-phase flow functions in porous media

Several important processes involve the flow of three immiscible fluids through porous media, such as the flow of oil, water and gas in petroleum reservoirs, or water, non-aqueous-phase liquid and air in underground aquifers. Multiphase flow functions (relative permeability and capillary pressure) are important to simulate the flow in such systems. Unfortunately, there are few, if any, reliable estimates of these flow properties from laboratory experiments. One of the main reasons for this is the use of unsupported simplifications in the procedures for determining property estimates from measured data. The authors present a method for simultaneous estimation of three-phase relative permeability and capillary pressure functions from laboratory experiments. The method is not limited by restrictions in the experimental design or assumptions regarding the saturation dependence or shape of the functions to be estimated. The method is demonstrated with simulated experiments. It is shown that with a suitable experimental design, regions of the functions represented by the measured data can be determined accurately.

Determination of gas transport coefficients in ceramic bodies during thermolysis of organic additives

In many ceramic processing routes organic additions are made which are later removed from the particle assembly before firing. These include residues from the manufacture of chemically derived powders, pressing aids or lubricants used in compaction processes, dispersants and binders added to casting suspensions, and organic vehicles which convey ceramic particles in plastic forming processes such as injection moulding. In many cases, large organic molecules are required to move in the pore structure of ultrafine powder assemblies so that a range of flow regimes, e.g. Knudsen, intermediate, molecular, and viscous, have to be considered. The quantitative evaluation of gas flow in such systems is used to evaluate the pressure that develops during ceramic processing and the viability of heating schedules. This review describes the procedures that can be used for the determination of transport coefficients in such systems and highlights the ways in which simplification can be achieved by judicious approximation. The effects of molecular dimensions and pore size are explored for typical ceramic processing situations.

Photoinduced energy and electron transfer in inorganic covalently linked systems

Photoinduced electron transfer and charge recombination can be studied in metal-polypyridine polynuclear complexes based on the (MebpyCH 2CH 2Mebpy) (Me, methyl; bpy,2,2′-bipyridine) bridging ligand. An example is provided by the binuclear complex [Ru(Me 2phen) 2(MebpyCH 2CH 2Mebpy)Rh(Me 2bpy) 2] 5+ (phen, 1,10-phenanthroline) (abbreviated as Ru(II)Rh(III)). In this system, photoinduced electron transfer processes originating from both local excited states (*Ru(II)Rh(III)→Ru(III)Rh(II) and Ru(II)*Rh(III)→Ru(III)Rh(II)), as well as charge recombination (Ru(III)Rh(II)→Ru(II)Rh(III)), have been resolved in the nanosecond and picosecond time domains using transient absorption and emission measurements. An energy transfer process (Ru(II)*Rh(III)→*Ru(II)Rh(III) can also be observed in rigid media, where the competing electron transfer process is suppressed. The factors affecting the kinetics of the various electron transfer steps can be discussed in terms of current transfer theories. Polychromophoric complexes suited for the study of intercomponent energy transfer can be designed using Re(I) and Ru(II) polypyridine units as molecular components and cyanide bridges as connectors. The energy flow in such systems is determined by the relative energy ordering of the metal-to-ligand charge transfer (MLCT) excited states of the various units, which can be controlled synthetically through the type of metal, the type of polypyridine ligand and the binding mode of the bridging cyanide(s). For example, in [NCRu(bpy) 2CNRu(bpy) 2CN] +, the flow is from the C-bonded to the N-bonded (to bridging cyanide) unit; in [(CO) 3Re(phen)NCRu(bpy) 2CN] +, the flow is from Re(I) to Ru(II); in [NCRu(bpy) 2 CNRu(bpy(COO) 2) 2NCRu(bpy) 2CN] 2−, the flow is from the bpy-containing units to the units containing dicarboxy—bpy. With regard to the identification of the lowest energy state in such systems, valuable information can be obtained using vibrational spectroscopies, such as time-resolved IR and resonance Raman. Compounds of this series behave in many respects as supramolecular antenna systems. Applications of the antenna effect to the spectral sensitization of semiconductors are discussed.

THE IMPORTANCE OF INTRAPARTICLE MASS TRANSFER AND PORE EXPANSION DURING THERMAL DECOMPOSITION REACTIONS

Abstract The importance of transient pore expansion and mass transfer (including diffusion and viscous flow) during isothermal decomposition of porous-solid particles is investigated theoretically. This model is demonstrated for the isothermal pyrolysis of oil shale parlicles. The results show that both the consideration of transient pore expansion and mass transfer are important when evaluating the rate of oil production. It is also shown that viscous flow in such systems is an important mass transfer mechanism, not only in the large pores (>1000A), where it dominates, but also in the small pores (<100A).

Generalized rheological characteristic of plastic disperse systems with polymeric and low-molecular dispersion media (matrices)

Analysis of literature data on the flow of polymeric and oligomeric compositions as well as on systems of low viscous dispersion media containing a high-disperse filler (carbon black, silica, high-disperse chalk) has been carried out. As the basic idea, a proposal is made that their viscosity anomaly is due not to the matrix viscosity anomaly, but to the gradual breakdown of the filler structural skeleton with increasing shear stressτ and shear rate\(\dot \gamma\). The viscosity anomaly of those compositions is determined by the zeroshear but not by the apparent matrix viscosity. A general relationship has been found to describe the flow of such systems depending on the zero-shear matrix viscosity values,η0, their yield stress,τy, and filler volume concentration\(\varphi :\tau = \tau _y + K\varphi \eta _o^n \dot \gamma ^n\), whereK=4.9 andn=0.69 are constants.

NOSCOW — A predictive model of the energy system of cows

Energy is a major currency and resource in ecological systems. It is essential that the energy flows in such systems are understood for effective control of the production of livestock. With growing, lactating or pregnant cattle the farmer is faced with the problem of feeding to give optimum results. He needs to be able to predict the effects of feed quality, quantity and its distribution in time. Central to this problem is the prediction of how energy is used by the cow, for the competing processes of growth, lactation and pregnancy. The purpose of this paper is to introduce a deterministic model, NOSCOW, of the bioenergetic system for lactating, and pregnant, cattle. The model uses the recommendations of ARC (1980) as a base but includes the key ideas of potentials for lactation and growth. Twelve input factors are required by the model. The output is a time series with a weekly time step.

The interaction of lakes with variably saturated porous media

Numerical simulation of variably saturated porous media indicates that groundwater recharge is variable in time and space, depending on the thickness of the unsaturated zone through which infiltrating water must move. The resulting complex, transient groundwater flow systems have significant impact on contiguous surface water. In very permeable media, small, local, closed groundwater flow systems can develop and dissipate within a few weeks to several months after major recharge. These have a direct effect on contiguous surface water by alternately causing seepage to and seepage from the surface water. The transient nature of these flow systems indicates that reversals of the direction of groundwater flow may be common. In less permeable media the same complex flow systems may occur, but the time for development and dissipation is much greater. For example, it is conceivable that small, local flow systems may exist for many months or years as a result of major recharge. Therefore directions of flow in such systems are more stable, and the effect on contiguous surface water also is more stable. The findings of this study indicate that wells and groundwater quality sampling sites need to be carefully located to define accurately water table configuration, groundwater recharge, direction of seepage through the beds of surface water bodies, and complex geochemical processes related to changing directions of groundwater flow.

Orifice Metering of Two-Phase Flow

Several correlations for two-phase flow through orifice meters are reviewed and verified experimentally, using air and oil mixtures in a 2-in. (5.08-cm) orifice meter. A simple, empirically determined relationship is shown to be valid for a limited range of oil/gas ratios when separator tests are possible. For predictive purposes, however, a more complex relationship is recommended. Introduction The flow of two-phase mixtures in a single pipeline is becoming more common. To determine the rates of flow in such systems, the phases are separated first, and the flow rate of each phase is measured individually.In many instances, we need to know the flow rates without having to separate the phases. A typical example would be when continuously (automatically) monitoring sour gas fields, where retrograde condensation occurs before measurement by an orifice meter. Sometimes existing installations, which were once producing dry gas, now are producing in two-phase flow, and satisfactory interpretation of these orifice meter readings is desired. Another application of interest is the determination of steam quality during the flow of wet steam when the total mass flow rate (boiler feed rate) is known.This study tries to obtain a relationship between the orifice-meter differential reading and the flow rates of the individual phases, using air and oil as the flowing fluids. Review of the Literature Most investigations into two-phase flow-rate measurement with orifices have been concerned with the flow of wet steam. Occasionally, air/water systems were studied. There are few papers relating to natural gas/oil flow. All correlations presented in the literature are based on the single-phase, orifice-meter equation, which may be written as (1) James, working with geothermal steam wells, used Eq. 1, but replaced the density with an effective two-phase mixture density. He obtained this density by raising the mass dryness fraction to the empirically determined power of 1.5.In another approach, Smith and Leang used a "blockage factor" to modify the coefficient of discharge, Kd, and expressed it as a function-of-dryness fraction.Smith and Leang and Smith et al., reviewed and evaluated several published correlations.Murdock, Bizon, and Chisholm and his coworkers took a different approach from those mentioned before. They related the two-phase pressure drop to that obtained by flowing the gas and liquid pressure drop to that obtained by flowing the gas and liquid separately. Murdock and Bizon assumed there was no interfacial shear between the gas and liquid phases (no slip model) and derived the relationship, (2) We show in the Appendix that / is proportional to the liquid-to-gas ratio. When there is no proportional to the liquid-to-gas ratio. When there is no liquid flowing, the liquid-to-gas ratio is zero, and must equal one. Eq. 2 then becomes equivalent to that reported by Wichert, (3) JPT P. 955

Viscous model study of groundwater flow in a wedge‐shaped aquifer

Groundwater flow in sands of nonuniform thickness is 2‐dimensional in nature, assuming, of course, that the flow has no significant component of velocity in the y‐direction, so that its pattern in all vertical (x‐z) planes is the same. Rigorous expressions for the hydraulic head distribution in several such flow systems are available but, in general, they are relatively complicated and formidable to use. Analytical studies have revealed, however, that these expressions can be simplified considerably if the actual 2‐dimensional flow in such systems is replaced with unidirectional flow, that is, flow in which the vertical component of velocity can be assumed to be negligible. Theoretical analyses have shown that such an assumption can be safely made if the slopes of the confining beds in such systems are less than 20%. These analyses assume, of course, that the aquifer is homogeneous and that the hydraulic properties of the formation remain uniform in space and time. The approximate solutions thus obtained yield results that are in close agreement with those obtained from their rigorously derived counterpart. Such conclusions are here tested experimentally, using a viscous‐flow model in which 2‐dimensional flow is simulated. In general, the experimental results confirm the theoretical conclusions. (Key words: Groundwater; drainage; model study)

Unsteady Spherical Flow in Petroleum Reservoirs

Abstract A description of the geometrical characteristics of spherical reservoir systems, a discussion of unsteady-state flow of such systems and examples of engineering applications are presented as background material. The fundamental differential equation, a description of average spherical permeability and the introduction of the Laplace transformation serve as theoretical foundations. Engineering concepts are investigated to indicate particular solutions of interest, which are analytically obtained with the aid of the Laplace transform. These are numerically evaluated by computer, and presented in tabular form. Introduction A tractable mathematical analysis of unsteady fluid flow through porous media generally requires incorporation of a geometrical symmetry. The simplest forms include the linear, cylindrical (radial) and spherical. Most analytical endeavors have concentrated on cylindrical symmetry because it occurs more often in petroleum reservoirs. Nevertheless, some reservoir systems do exist that are better approximated by spherical geometry. Review of technical literature revealed but a single reference to unsteady spherical flow in petroleum reservoirs. The motive and purpose of the present work was to remove this gap in technical information, and to provide the practicing engineer with some useful analytical tools. The mathematical details associated with the particular solutions of interest involved use of the Laplace transformation. Hurst and van Everdingen previously demonstrated the efficacy of this operational technique, and in many respects the present treatment was patterned after their earlier work. PRELIMINARY CONSIDERATIONS GEOMETRICAL CHARACTERISTICS Geometrically, a spherical reservoir system is defined at any instant of time by two concentric hemispheres whose physical properties of interest vary only with the radial distance. Every physical property is thus restricted to be a space function of only one variable: the distance along a radius vector emanating from the center. Such a system is composed of an outer region and an inner region, separated by a defined internal boundary. The inner region simply extends inward from this boundary, whereas the outer region extends outward from it to an external boundary. The position of the internal boundary is presumed fixed, so that the size of the inner region remains constant. On the other hand, the position of the external boundary at any given instant of time is determined by the distance into the system that a sensible pressure reaction has occurred. Thus, the external boundary may change position with time. It initially emerges from the inner region and advances outward to its ultimate position. When this ultimate position coincides with a geometric limit, the reservoir system is said to be limited. When it coincides with points subject to pressure gradients furthest removed from the internal boundary, yet short of a geometric limit, the system is said to be unlimited. In this investigation two different boundary conditions are imposed at the ultimate boundary of limited systems. The first requires that no fluid flow occur across this boundary; the second that the pressure remain fixed at this boundary. UNSTEADY-STATE FLOW In a strict sense virtually all flow phenomena associated with a reservoir system are unsteady-state. The transient behavior of these phenomena requires accounting, however, only when time must be introduced as an explicit variable. Otherwise, steady-state mechanics may be used. Analytically, steady-state conditions prevail in a reservoir system only over that portion of its history when this relation is satisfied: c p= 0 ...........................(1)k t SPEJ P. 102ˆ