Showing papers on "Pressure drop published in 1997"

High-Pressure Trickle-Bed Reactors: A Review

Abstract: A concise review of relevant experimental observations and modeling of high-pressure trickle-bed reactors, based on recent studies, is presented. The following topics are considered: flow regime transitions, pressure drop, liquid holdup, gas−liquid interfacial area and mass-transfer coefficient, catalyst wetting efficiency, catalyst dilution with inert fines, and evaluation of trickle-bed models for liquid-limited and gas-limited reactions. The effects of high-pressure operation, which is of industrial relevance, on the physicochemical and fluid dynamic parameters are discussed. Empirical and theoretical models developed to account for the effect of high pressure on the various parameters and phenomena pertinent to the topics discussed are briefly described.

Moderate Reynolds number flows through periodic and random arrays of aligned cylinders

Abstract: The effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders is investigated. Numerical simulations using a lattice-Boltzmann formulation are performed for Reynolds numbers up to about 180.The magnitude of the drag per unit length on cylinders in a square array at moderate Reynolds number is strongly dependent on the orientation of the drag (or pressure gradient) with respect to the axes of the array; this contrasts with Stokes flow through a square array, which is characterized by an isotropic permeability. Transitions to time-oscillatory and chaotically varying flows are observed at critical Reynolds numbers that depend on the orientation of the pressure gradient and the volume fraction.In the limit Re[Lt ]1, the mean drag per unit length, F, in both periodic and random arrays, is given by F/(μU) =k1+k2Re2, where μ is the fluid viscosity, U is the mean velocity in the bed, and k1 and k2 are functions of the solid volume fraction ϕ. Theoretical analyses based on point-particle and lubrication approximations are used to determine these coefficients in the limits of small and large concentration, respectively.In random arrays, the drag makes a transition from a quadratic to a linear Re-dependence at Reynolds numbers of between 2 and 5. Thus, the empirical Ergun formula, F/(μU) =c1+c2Re, is applicable for Re>5. We determine the constants c1 and c2 over a wide range of ϕ. The relative importance of inertia becomes smaller as the volume fraction approaches close packing, because the largest contribution to the dissipation in this limit comes from the viscous lubrication flow in the small gaps between the cylinders.

Devolatilization‐generated fluid pressure and deformation‐propagated fluid flow during prograde regional metamorphism

Abstract: The obstruction to fluid flow formed by the rocks overlying a metamorphic devolatilization front causes the fluid pressure gradient in the reacting rocks to diverge from lithostatic. This drives deformation in tandem with the fluid pressure anomaly generated by the volume change of the reaction. Numerical simulations show that once the vertical extent of the reacted rocks is comparable to the compaction length, compaction processes caused by the difference between confining and fluid pressure gradients generate a positive fluid pressure anomaly (effective pressure < 0) above the reaction front, irrespective of the reaction volume change. Consequent dilational deformation propagates the anomaly upward, leading to underpressuring and densification at the reaction front and detachment of a wave of anomalous fluid pressure and porosity. Creep is a viable mechanism for such wave propagation for crustal viscosities < 10 15 MPa s. Continuous upward strengthening of the crust increases the wavelength and amplitude of the fluid pressure waves and thereby the likelihood of hydrofracture. Order of magnitude strength contrasts are adequate to arrest wave propagation, forming water sills that become increasingly stable in the absence of deviatoric stress. Although the fluid pressure gradient within a wave may be near hydrostatic, Rayleigh convection is unlikely. Thus, in the absence of lateral perturbations, fluid flow is upward and episodic, despite continuity of devolatilization. Porosity waves provide a mechanism for temporal focusing of metamorphic fluid fluxes with the potential to increase the efficacy of heat and mass transport.

Pt resistor thermometry and pressure calibration in a clamped pressure cell with the medium, Daphne 7373

Abstract: Calibration of a Pt resistance thermometer (Netsushin) in magnetic fields and under pressure in the range of 1.5–300 K and below 1.5 GPa is presented. With the pressure medium, olefin olygomers, Daphne 7373, the pressure is continuous at its solidification and the pressure drop from 300 to 4.2 K by 0.15–0.17 GPa is constant, irrespective of the initial clamped pressure at 300 K. The applicability of the thermometer and the medium for precise study in field and pressure at low temperature is discussed.

Drop formation in viscous flows at a vertical capillary tube

Abstract: Drop formation at the tip of a vertical, circular capillary tube immersed in a second immiscible fluid is studied numerically for low-Reynolds-number flows using the boundary integral method. The evolution and breakup of the drop fluid is considered to assess the influences of the viscosity ratio λ, the Bond number B, and the capillary number C for 10−2⩽λ⩽10, 10−2⩽C⩽1, and 0.1⩽B⩽5. For very small λ, breakup occurs at shorter times, there is no detectable thread between the detaching drop and the remaining pendant fluid column, and thus no large satellite drops are formed. The distance to detachment increases monotonically with λ and changes substantially for λ>1, but the volume of the primary drop varies only slightly with λ. An additional application of the numerical investigation is to consider the effect of imposing a uniform flow in the ambient fluid [e.g., Oguz and Prosperetti, J. Fluid Mech. 257, 111 (1993)], which is shown to lead to a smaller primary drop volume and a longer detachment length, as ...

Two-phase flow in microchannels

Abstract: : The purpose of this study was to investigate fluid mechanic and heat transfer characteristics of two-phase two-component flow in rectangular microchannels Experiments were conducted using rectangular aluminum channels with hydraulic diameters ranging between 56 micrometers and 256 micrometers and aspect ratios which varied from 05 to 15 Both single- and two-phase tests were conducted using water and gaseous argon, helium, and nitrogen as the working fluids The Reynolds number for both types of experiments ranged from approximately 50 to nearly 10,000 The Nusselt number ranged between 00002 and 70 The single- and two-phase experimental data were empirically correlated, using parameters derived from a dimensional analysis Experimental data were also used to correlate the unknown variables in derived analytical expressions Both single- and two-phase tests yielded excellent correlations of the friction factor For Nusselt number, the correlations were fair to poor Reynolds number and the combination of Reynolds number and Prandtl number were the dominant parameters in the prediction of pressure drop and heat transfer rate, respectively, in both single- and two-phase flows The pressure drop predictions based on the semi-empirical relations by Martinelli for two-phase flows were shown to substantially over-predict the pressure drop measured in these experiments

A note on the lift force on a spherical bubble or drop in a low-Reynolds-number shear flow

Abstract: The analytical solution giving the lift force on a spherical drop of arbitrary viscosity moving in a low-Reynolds-number linear shear flow is derived through a matched asymptotic expansion procedure. This solution extends the result established by Saffman in the particular case of a solid sphere [J. Fluid Mech. 22, 385 (1965)]. It appears that, to leading order, the lift force is proportional to the square of the vorticity present at the surface of the drop. As a consequence the lift force decreases with the viscosity of the drop and the ratio of the forces experienced by an inviscid bubble and a solid sphere is equal to (2/3)2.

Two Types of Nonlinear Pressure-Drop Versus Flow-Rate Relation Observed for Saturated Porous Media

Abstract: Previous reports of experiments performed with water (Fand et al., and Kececioglu and Jiang) indicated that beyond the Forchheimer regime the rate of change of the hydrostatic pressure gradient along a porous medium suddenly decreases. This abnormal behavior has been termed transition to turbulence in a porous medium. We investigate the relationship between the hydrostatic pressure gradient of a fluid (air) through a porous medium and the average seepage fluid velocity. Our experimental results, reported here, indicate an increase in the hydrostatic pressure rate beyond a certain transition speed, not a decrease. Physical arguments based on a consideration of internal versus extemal incompressible viscous flow are used to justify this distinct behavior, a consequence of the competition between a form dominated transition and a viscous dominated transition. We establish a criterion for the viscous dominated transition from consideration of the results of three porous media with distinct hydraulic characteristics. A theoretical analysis based on the semivariance model validation principle indicates that the pressure gradient versus fluid speed relation indeed departs from the quadratic Forchheimer-extended Darcy flow model, and can be correlated by a cubic function of fluid speed for the velocity range of our experiments.

Stokes flow in collapsible tubes: computation and experiment

Abstract: This paper is concerned with the problem of viscous flow in an elastic tube. Elastic tubes collapse (buckle non-axisymmetrically) when the transmural pressure (internal minus external pressure) falls below a critical value. The tube's large deformation during the buckling leads to a strong interaction between the fluid and solid mechanics.In this study, the steady three-dimensional Stokes equations are used to analyse the slow viscous flow in such a tube whose deformation is described by geometrically nonlinear shell theory. Finite element methods are used to solve the large-displacement fluid–structure interaction problem. Typical wall deformations and flow fields in the strongly collapsed tube are shown. Extensive parameter studies illustrate the tube's flow characteristics (e.g. volume flux as a function of the applied pressure drop through the tube) for boundary conditions corresponding to the four fundamental experimental setups. It is shown that lubrication theory provides an excellent approximation of the fluid traction while being computationally much less expensive than the solution of the full Stokes equations. Finally, the computational predictions for the flow characteristics and the wall deformation are compared to the results obtained from an experiment.

Flow regime determination and flow measurement in multiphase flow pipelines

Abstract: A predetermined multiphase flow anomaly, for example, a plug, a slug, or a pseudo-slug, in a pipeline may be identified by identifying an analysis pipe section containing a multiphase fluid flow, measuring a first differential pressure at a first pair of pressure measuring points positioned along the analysis pipe section, measuring a second differential pressure at a second pair of pressure measuring points positioned along the analysis pipe section, identifying a primary drop in the first differential pressure and a secondary drop in the second differential pressure, measuring a time delay between initiation of the primary pressure drop and initiation of the secondary pressure drop, and determining as a function of the time delay whether the primary pressure drop corresponds to a predetermined multiphase flow anomaly moving through the pipe analysis section.

Gas-Liquid Stratified-Wavy Flow in Horizontal Pipelines

Abstract: Gas-liquid stratified-wavy flow with low liquid loading is common in natural gas transmission pipelines and offshore gas pipelines. This specific case of two-phase pipe flow has been studied experimentally and theoretically in the present paper. The interfacial behavior during air-kerosene stratified-wavy flow in a 77.9-mm-dia 420-m-long pipeline was observed carefully. The gas-liquid interface usually exhibits a concave downward curved configuration. The liquid film-wetted wall fraction, liquid holdup, and pressure drop were also measured. A mechanistic double-circle model and a correlation for interfacial friction factor, required as a closure relationship in the model, have been developed. The new model gives significantly improved predictions for both liquid holdup and pressure drop during gas-liquid stratified-wavy flow in horizontal pipelines.

Microchannels for applications in liquid dosing and flow-rate measurement

Abstract: To investigate the performance of microengineered fluid channels in liquid dosing applications, flow-rate measurements have been performed with various channel geometries in a range from 0.01 to 1000 μl min -1 . An optical flow-measurement technique has been developed to enhance the measurement range into the desired low flow range (10 -3 to 1 μl min -1 ), and is compared to a standard gravimetric method, which is preferably used for flow rates above 1 μl min -1 . In addition, influences of the temperture-dependent viscosity and effects arising from fluidmechanical characteristics are studied. These influences are also calculated from laminar flow theory and semi-emprical models to obtain a theoretical model. It is found that the theoretical model is able to describe the measurement results well in the whole flow range. The model is implemented on a PC-based system, which measures the pressure drop across the microchannel and the fluid temperature and calculates the flow. In a temperature range from 20 to 50°C excellent agreement is found.

Modelling and Control of a Riser Type Fluid Catalytic Cracking (FCC) Unit

Abstract: A model for a fluid catalytic cracking (FCC) unit which describes the dynamic behaviour of the riser, particle separator vessel, and the regenerator is developed. The model consists of coupled ordinary differential equations. This facilitates the solution of the equations and makes the model particularly suitable for control studies. A sensitivity study is carried out to determine the interactions between the three controlled and manipulated variables and the elements of the Bristol 1 relative gain array matrix. The relative gain array analysis suggested that the temperature at the top of the riser, the pressure drop between the particle separator vessel and the regenerator, and the catalyst holdup in the particle separator vessel should be controlled by manipulation of the flow rates of the regenerated catalyst, flue gas from the regenerator, and the spent catalyst leaving the particle separator vessel, respectively. Three Pi-controllers were used to achieve reasonable control of the process.

Influence of elastic properties on drop deformation in elongational flow

Abstract: We report experimental results on the deformation of a single drop suspended in a medium under uniaxial elongational flow along the central axis of a converging conical channel made of Plexiglas. Both the drop and the continuous phases consist of constant viscosity elastic fluids, so-called Boger fluids. This study reveals several interesting features about the role played by both the drop and matrix elasticities on the drop deformability. In a given matrix fluid, the drop deformation decreases as its elasticity increases. For a given drop fluid, the matrix elasticity has the opposite effect: the drop deformation increases with increasing matrix elasticity. An empirical relation between the drop and matrix deformations is established as a function of the drop and matrix characteristic elastic times.

Mechanistic pressure drop model for columns containing structured packings

Abstract: A mechanistic model was developed to predict pressure drop and flooding in packed columns equipped with corrugated packing of the regular type. It was developed after considerating the interaction of falling liquid film with the gas phase, based on mass-and momentum-conservation equations. Among the most common structured packings, the behavior of the Mellapak and BX types was analyzed. The aim of this work is to demonstrate how mechanistic models, developed for simple geometry, can also be used to compute pressure drops in cases where the geometry is more complex, as with a structured packing. This approach, based on the geometric characteristics of the packing and measurable parameters such as liquid holdup, enables the development of a basic model by limiting the number of adjustable parameters, which are numerous in all the available models. Because of its nature, this model is extremely easy to extend to different types of structured packings.

Bypass type coriolis effect flowmeter

Abstract: A bypass flowmeter for measuring the material flow in a conduit. An optimum pressure drop is developed across the flowmeter by coupling the material outlet of the flowmeter to the throat of a venturi positioned within the conduit. This increased pressure drop improves the material flow rate through the flowmeter. This enhances flowmeter accuracy and sensitivity and the flowmeter's ability to measure mass flow rates for low density materials such as gas. The ratio of the material flow within the flowmeter to that of the conduit is derived with improved precision over prior arrangements which assume a constant ratio of material flow between the flowmeter and the conduit. The material flow information for the conduit is obtained for materials having a varying viscosity by the use of a differential pressure sensor which measures the pressure drop across the flowmeter and transmits this information to instrumentation which uses it to derive material flow information for the conduit with improved precision. An alternative embodiment not having a venturi operates in the same manner to derive the material flow ratio between the flowmeter and the conduit and, in turn, the total material flow in the conduit.