Unit Pressure Drop Research Articles

CFD SIMULATION OF FLOW THROUGH AN OPEN CELL FOAM

A sample of an open-celled plastic foam has been examined using a combination of experimental, microscopic and computational methods. The aim was to use image-based meshing techniques to generate for the first time geometrically faithful models of the microstructure of the foam, and to use Computational Fluid Dynamics (CFD) to compute flow properties and pressure drops across the sample. The microstructure of the foam was also investigated experimentally and using SEM to provide further information for the computational analysis. A comparison was made with existing experimental data on flows through foams, and the unit pressure drop was found to correlate with the flow speed in the appropriate manner.

An Experimental Study of Shell-and-Tube Heat Exchangers With Continuous Helical Baffles

Two shell-and-tube heat exchangers (STHXs) using continuous helical baffles instead of segmental baffles used in conventional STHXs were proposed, designed, and tested in this study. The two proposed STHXs have the same tube bundle but different shell configurations. The flow pattern in the shell side of the heat exchanger with continuous helical baffles was forced to be rotational and helical due to the geometry of the continuous helical baffles, which results in a significant increase in heat transfer coefficient per unit pressure drop in the heat exchanger. Properly designed continuous helical baffles can reduce fouling in the shell side and prevent the flow-induced vibration as well. The performance of the proposed STHXs was studied experimentally in this work. The heat transfer coefficient and pressure drop in the new STHXs were compared with those in the STHX with segmental baffles. The results indicate that the use of continuous helical baffles results in nearly 10% increase in heat transfer coefficient compared with that of conventional segmental baffles for the same shell-side pressure drop. Based on the experimental data, the nondimensional correlations for heat transfer coefficient and pressure drop were developed for the proposed continuous helical baffle heat exchangers with different shell configurations, which might be useful for industrial applications and further study of continuous helical baffle heat exchangers. This paper also presents a simple and feasible method to fabricate continuous helical baffles used for STHXs.

On the Reproducibility of Chromolith� RP Columns

Monolithic columns are of growing importance in routine analysis. As all of these columns are solitaires, the reproducibility has been studied for the commercially available RP Chromolith column. The chromatographic test revealed that in respect of efficiency this column is equivalent a column (of identical length: 5 cm) packed with particles around 4 μm, however, the pressure drop corresponds to a column packed with particles around 10 μm. Per unit pressure drop about 6 times the plates are generated. Four Chromolith columns from different batches were compared in respect of efficiency and retention times. The plate numbers were 5330 with a RSD of 5%. The retention times varied less than 1.6%, corresponding to good batch to batch reproducibility as achieved in the preparation of bulk reversed phases. Because of the short column length and the relatively high linear velocities, data acquisition time has to be increased at least to 25 Hz to be able to fully exploid the potential efficiencies these columns are able to generate.

Heat transfer characterization of support structures for catalytic combustion

Convective heat transfer and pressure drop characteristics within metal foil catalyst structures are determined with a unique experimental procedure. Various honeycomb-type structures with 100, 150, 160 and 200 cpsi (cells per square inch) are investigated at empty tube air velocities ranging from 0.5 to 10 m/s at atmospheric pressure. Both commercially available and novel structures, designed and manufactured by the authors, are compared. The convective heat transfer between fluid and substrate can be well described by the correlation Nu=¢Re mPr 1/3 . The experimental method to obtain values of ¢ and m is described in detail and is based on unsteady state cooling of the hot structures in an air stream. The data are discussed in view of application of the structures as catalyst supports and are compared with a 400 cpsi conventional, parallel-channel, Cordierite honeycomb. Results show that the novel structures offer greater heat transfer per unit volume but at the cost of higher pressure drop and thus lower heat transfer per unit pressure drop, relative to the 400 cpsi, parallel-channel honeycomb.

An analysis of variations in isentropic melt productivity

The amount of melt generated per unit pressure drop during adiabatic upwelling, the isentropic melt productivity, cannot be determined directly from experiments and is commonly assumed to be constant or to decrease as melting progresses. From analysis of one– and two–component systems and from calculations based on a thermodynamic model of peridotite partial melting, we show that productivity for reversible adiabatic (i.e. isentropic) depressurization melting is never constant; rather, productivity tends to increase as melting proceeds. Even in a one–component system with a univariant solid–liquid boundary, the 1/T dependence of (∂S/∂T)_P and the downward curvature of the solidus (due to greater compressibility of liquids relative to minerals) lead to increased productivity with increasing melt fraction during batch fusion (and even for fractional fusion in some cases). Similarly, for multicomponent systems, downward curvature of contours of equal melt fraction between the solidus and the liquidus contributes to an increase in productivity as melting proceeds. In multicomponent systems, there is also a lever–rule relationship between productivity and the compositions of coexisting liquid and residue such that productivity is inversely related to the compositional distance between coexisting bulk solid and liquid. For most geologically relevant cases, this quantity decreases during progressive melting, again contributing to an increase in productivity with increasing melting. These results all suggest that the increases in productivity with increasing melt fraction (punctuated by drops in productivity upon exhaustion of each phase from the residue) predicted by thermodynamic modelling of melting of typical mantle peridotites using MELTS are neither artifacts nor unique properties of the model, but rather general consequences of adiabatic melting of upwelling mantle.

Studies on a recirculating fluidized‐bed incinerator—cold model

Cold model studies are widely carried out to predict, analyse and improve performance details and operating conditions of the actual unit and to train operators. Cold model experiments carried out to visualize and investigate the operation of recirculating fluidized-bed incinerator are reported. Some of the details of operation which are difficult to measure on an actual unit, such as solid circulation rate, particle velocity, residence time, voidage etc., are measured on the cold model. Effects of various parameters such as jet diameter, clearance between perforated plate and draft tube bottom, draft tube superficial air velocity and solid inventory on these details are discussed. The combinations of various parameters which give higher kinetic energy transfer from gas to solids per unit pressure drop across the draft tube are identified.

Studies on a recirculating fluidized-bed incinerator—cold model

Cold model studies are widely carried out to predict, analyse and improve performance details and operating conditions of the actual unit and to train operators. Cold model experiments carried out to visualize and investigate the operation of recirculating fluidized-bed incinerator are reported. Some of the details of operation which are difficult to measure on an actual unit, such as solid circulation rate, particle velocity, residence time, voidage etc., are measured on the cold model. Effects of various parameters such as jet diameter, clearance between perforated plate and draft tube bottom, draft tube superficial air velocity and solid inventory on these details are discussed. The combinations of various parameters which give higher kinetic energy transfer from gas to solids per unit pressure drop across the draft tube are identified.

Simulation of laminar confined flow past a circular cylinder with integral wake splitter involving heat transfer

A finite element method is used to study the effect of flow past a circular cylinder with an integral wake splitter. A fractional step algorithm is employed to solve the Navier‐Stokes and Energy equations with a Galerkin weighted residual formulation. The vortex shedding process is simulated and the effect of splitter addition on the time period of shedding is studied at a Reynolds number of 200 and a blockage ratio of 0.25. The effect of splitter and the Strouhal number and heat transfer augmentation per unit pressure drop has been investigated.

Osteoblast hydraulic conductivity is regulated by calcitonin and parathyroid hormone

It is our hypothesis that osteoblasts play a major role in regulating bone (re)modeling by regulating interstitial fluid (ISF) flow through individual bone compartments. We hypothesize that osteoblasts of the blood-bone membrane lining the bone surfaces are capable of regulating transosseous fluid flow. This regulatory function of the osteoblasts was tested in vitro by culturing a layer of rat calvarial osteoblasts on porous membranes. Such a layer of osteoblasts subjected to 7.3 mm Hg of hydrostatic pressure posed a significant resistance to fluid flow across the cell layer similar in magnitude to the resistance posed by endothelial monolayers in vitro. The hydraulic conductivity, the volumetric fluid flux per unit pressure drop, of the osteoblast layer was altered in response to certain hormones. Hydraulic conductivity decreased approximately 40% in response to 33 nM parathyroid hormone, while it exhibited biphasic behavior in response to calcitonin: increased 40% in response to 100 nM calcitonin and decreased 40% in response to 1000 nM calcitonin. Further, activation of adenylate cyclase by forskolin dramatically increased the hydraulic conductivity, while elevation of intracellular calcium, [Ca2+]i, by the calcium ionophore A23187 initially decreased the hydraulic conductivity at 5 minutes before increasing conductivity by 30 minutes. These results suggest that cyclic adenosine monophosphate (cAMP) and [Ca2+]i may mediate changes in the osteoblast hydraulic conductivity. The increase in hydraulic conductivity in response to 100 nM calcitonin and the decrease in response to PTH suggest that the stimulatory and inhibitory effects on bone formation of calcitonin and parathyroid hormone, respectively, may be due in part to alterations in bone fluid flow.

Screening of Crude Oils for Asphalt Precipitation: Theory, Practice, and the Selection of Inhibitors

Summary This paper describes a simple method to screen crude oils for their tendency to precipitate asphalt, which may cause problems during production. The method is based on a thermodynamic model of asphalt solubility, derived earlier by Flory and Huggins. The most important parameters in this model are the Hildebrand solubility parameters for oil and asphaltene, and their molar volumes. The oil parameters can all be correlated with the in-situ density of the crude. The relative change in asphalt solubility in the crude per unit pressure drop is shown to be highest for light crudes that are undersatu-rated with gas, which usually contain only a small amount of asphaltenes. Hence, the chance that asphalt will precipitate will be greatest for these light crudes. For pressures below the bubblepoint, depres-surising of the crude will cause a rapid increase in asphalt solubility, due to changes in liquid composition. It is shown that heavy crudes usually will give fewer problems with asphalt precipitation, despite their higher asphaltene content, certainly if the reservoir pressure is close to bubblepoint pressure. Consequently, the tendency for asphalt precipitation is mainly determined by three parameters: the extent to which the crude is under-saturated with gas, the density of the crude at reservoir conditions, and its saturation with asphalt at downhole conditions. Apart from the simple screening method, more elaborate methods are described to assess the potential for asphalt precipitation more accurately; asphaltene analysis on produced reservoir fluid and tank oil; n-heptane titration of the tank oil; visual inspection of a bottom-hole sample in a high-pressure cell during pressure reduction; and dynamic flow tests on tank oil after η-heptane addition. An ultrasonic back scattering technique is described for monitoring the influence of different asphalt precipitation inhibitors. Using above techniques asphalt precipitation inhibitors have been identified that can be applied in the field.

Vortex Generator Induced Heat Transfer Augmentation Past a Rib in a Heated Duct Air Flow

The present investigation represents the initial phase of a comprehensive experimental program designed to study the potential for increasing the heat transfer per unit pressure drop in a ribbed duct by positioning vortex generators at key locations in the flow. In particular, the present investigation consists of a rib positioned at the inlet to a rectangular test section with uniform heating at its bottom wall. Local and average Nusselt number results are obtained for a circular rod positioned either immediately above or just downstream of the rib.

Transient Behaviour Of Nonhomogeneous Linear Aquifers

Abstract This paper presents new analytical solutions for the dimensionless pressure drop or cumulative influx for nonhomogeneous aquifers whose thickness, permeability-viscosity ratio. or porosity-compressibility vary linearly with distance. These solutions apply to one-dimensional linear flow conditions with finite aquifer size. The inner boundary condition may be either constant rare or constant pressure. The outer boundary may be either dosed, or at constant pressure. The solutions presented; n this paper contain homogeneous aquifer solutions as limiting cases. Thus, this study extends the state-of-the-art of analytical aquifer modeling. Based on this study, a nonhomogeneous aquifer behaves as a homogeneous aquifer at early times. At late times, pseudosteady or steady-state behaviour is observed, depending on the outer boundary condition. But the dimensionless time to late-time state is dependent on the type and severity of the property variation. Limiting solutions at early and late times are presented for each case. Introduction Most hydrocarbon reservoirs are at least partly bounded by water bearing rocks called aquifers. The aquifer size may appear infinite or finite compared to the reservoirs they adjoin. In performing material balance calculations as proposed by van Everdingen and Hurst(1), and Hurst(2), the dimensionless aquifer response to a unit pressure drop or a unit fluid-withdrawal rate is needed. Also, aquifers are frequently represented in reservoir simulators using analytical response functions. Past studies have considered linear, radial, and spherical flow in the aquifers, Several studies of water influx have been described by Craft and Hawkins(3). Schilthius(4) first proposed a steady-state water influx model. A significant advance was made by the van Everdingen and Hurst(l) unsteady-state water influx model that used the response of a dimensionless aquifer v..ith time. They Considered the aquifer to be homogeneous and infinite in extent. Later, Hurst(2) presented a simplified solution of a material balance equation which used the response for linear and radial homogeneous, infinite aquifers. Miller(5), and Nabor and Barham(6) presented analytical solutions for linear, homogeneous aquifers. Nabor and Barham(6) considered both constant rate and constant pressure inner boundary conditions. They also considered the outer boundary to be infinite, closed or at a constant pressure. Mueller(7) used finite-difference techniques to compute dimensionless pressure drop or cumulative influx for few cases of a non-homogeneous aquifer. This paper presents analytical solutions for the transient behaviour of nonhomogeneous linear aquifers. Mathematical Model for Linear Aquifers A partial differential equation describing the flow of a slightly compressible fluid in porous media is: Equation 1 (available in full paper) In writing equation (1), we assume a horizontal formation, no gravity forces, isotropic properties, a single fluid of small but constant compressibility, etc. For a linear one-dimensional medium, equation (l) can be written as: Equation 2 (available in full paper) As indicated by Mueller(7), kh/ µ and Φc,h are two groups of variables which can be functions of the space variable. Thickness, appears in both groups. So one may study cases wherein either k/ µ (or k), h or Φc is a function of the space variable. Let us identify these as different cases:

Optimal Fin-Side Design of Compact Tube-in-Fin Heat Exchangers with Rippled Fins

The optimal design of rippled fins found in the common compact heat exchanger is addressed to maximize the heat transferred per unit pressure drop (pumping power). Ripples are common for structural integrity and to facilitate handling and manufacture. Typical designs operate at Reynolds numbers below about 1200. Because a complex flow with heat transfer-process is involved, the optimal design synthesis approach—modeling, objective function definition and optimization—coupled with the desire to efficiently verify the results leads to a highly effective hybrid design technique and substantially less experimentation than might be expected. The model uses a finite difference marching procedure and variable fluid properties. General results for ripple designs and spacings are obtained and corroborated experimentally. In general a short ripple of about 25 deg and height/fin spacing of 0.25 are optimum. Distance between ripples is shown to be a simple function of Reynolds numbers. The final discussion addresses aspects of this approach, its strengths and limitations.

Mass transfer in ideal and geometrically deformed open tubes : II. Potential application of ideal and coiled open tubes in liquid chromatography

It has been shown experimentally in Part I that the peak broadening in an open tube with a liquid mobile phase can be described solely by the C m u term of the Golay equation, if the inner diameter is small (< 100 μm) and the linear velocity is not extremely high (< 1 m/sec). With this assumption optimal values achievable in capillary columns are calculated for the number of theoretical and effective plates, the speed of analysis, the number of plates per unit pressure drop and the peak volume. These parameters yield results which are hardly, if at all, better than those generated in packed columns in routine liquid chromatography. Even if the instrumental problems, including the coating of the open tube, are neglected, capillary columns will be of interest in liquid chromatography only is secondary flow can be generated within the open tubes.

The Use of Integral Equations in the Numerical Solution of Complex Reservoir Engineering Problems

Abstract Quite a number of problems that cannot be bandied economically with the methods usually applied in reservoir engineering can be solved by the theory of integral equations. The main purpose of this paper is to draw attention once more to the usefulness of integral equations. Their benefit is shown by considering a typical example; namely, the behavior of a horizontal multilayered system of oil reservoirs bounded by aquifers. Introduction A number of reservoir engineering problems involving the flow of compressible fluids in porous media are so complex that they cannot be solved analytically, yet the usual numerical techniques require excessive computer time. An example of such a problem is simultaneous production from a horizontal multilayered system of production from a horizontal multilayered system of separate oil reservoirs, each reservoir being bounded by its own aquifer but sharing production wells with the other reservoirs. The difficulties in obtaining an analytical solution to this problem are insuperable; consequently, Tempelaar-Lietz and Lefkovits et al have restricted their studies to particular aspects under simplified conditions. The modern approach is to simulate the flow problem numerically. This implies that the differential equations that describe the problem are approximated by finite-difference equations, problem are approximated by finite-difference equations, which are subsequently solved by a computer. As both the aquifers and the reservoirs must be simulated, the numerical calculations require considerable computer time and storage capacity. In this paper it is shown that problems involving the influx of fluids (e.g., fluid influx from pay zones into wellbores, or water influx from aquifers into reservoirs) can often be described by a system of intergral equations that require much less computer time for solution. These integral equations can be derived only if the motion of the inflowing fluids can be described by linear and homogeneous differential equations, so that the superposition principle applies. The fluid influx can then be principle applies. The fluid influx can then be calculated from integral expressions that contain standard functions, This obviates the need for numerical simulation of those parts of the reservoir from which the influx originates. The standard functions are the cumulative influx as a function of time for a unit pressure drop at the influx boundary, and the pressure drop at the influx boundary as a function of time for a unit influx rate. These functions are interrelated so that if one is known the other can be calculated. For homogeneous and isotropic flow regions of linear or radial geometry, the standard functions have been evaluated in dimensionless form by van Everdingen and Hurst. For other flow regions, they can be evaluated with an auxiliary computer program. The integral equations presented here are by no means new. They are special cases of Duhamel's theorem (see also Carslaw and Jaeger, p. 30), and one of them is explicitly formulated by Samara in his analysis of pressure decline.

Rarefied Gas Flow through Passages with Static Boundaries

A resume of the current state-of-knowledge concerning rarefied gas flow through passages with static boundaries is presented. A brief development of the theoretical gas flow models which have been used for long tubes and annuli is included. These theoretical models have been developed to cover the flow regime extending from laminar continuum flow to free molecular flow. The analysis required to use these models is simple and straightforward. Experimental data are presented for the flow of argon through a long tube and for the flow of argon and xenon through annuli. The experimental values of mass flow rate per unit pressure drop as a function of Knudsen number are graphically presented for a long tube and for two annuli. Also presented on the same figures are the values predicted by the theoretical models. The agreement between theory and experiment for the complete regime between continuum and free molecular flow is very good. Presented at the ASLE Annual Meeting in Cleveland, May 6–9, 1968.

Transient Response of Nonhomogeneous Aquifers

Abstract Many investigators have used the response of the "dimensionless aquifer" to a unit pressure drop or a unit fluid-withdrawal volume to calculate the performance of an aquifer in supplying water influx to an oil reservoir. In the past, these response functions have been calculated with the aid of the Laplace transform. With the advent of ultra high-speed digital computers, it becomes practical to solve for the response functions with finite-difference techniques. The computer method also permits extension of the dimensionless-aquifer concept to include the nonhomogeneous aquifer wherein the permeability and other properties vary as a function of the space co-ordinates. This paper gives results of calculating the response functions for a series of nonhomogeneous aquifers. Response functions are presented for both linear and radial aquifers whose thickness, permeability-viscosity ratio and porosity-compressibility vary. These functions are new and should prove useful to the petroleum engineer in analyzing the behavior of nonhomogeneous aquifers. Results are presented in the form of charts that can be easily used by the field engineer. Introduction Aquifers which surround many oil and gas reservoirs have the ability to supply water influx to such reservoirs as oil and gas are withdrawn. This water influx, called natural water drive, provides one of the most effective driving mechanisms for the production of oil and gas. In producing a reservoir, therefore, it behooves one to make the maximum use of natural water drive. To achieve the maximum use, the reservoir engineer must be able to predict the performance of an aquifer under a variety of production schemes that may be proposed for the reservoir. Unfortunately, the physical properties which dictate aquifer behavior often are known only within limits. Seldom do wells penetrate the porous strata of the aquifer.

The upward vertical flow of air‐water mixtures: III. Effect of gas phase density on flow pattern, holdup and pressure drop

AbstractResults of measurements of pressure drop and holdup are reported over a range of air and water rates for the upward vertical flow of air‐water mixtures in a 1.50 inch I.D. tube with average air densities ranging from 0.092 to 0.552 lb./ft.3 Superficial water velocities were between 0.0695 and 7.35 ft./sec.The data are analyzed by the method first suggested by Govier, Radford and Dunn and later used by Govier and Short. This involves the division of the flow range into four regimes on the basis of the pressure drop curves (to aid correlation of flow pattern and holdup data) and the separation of the unit pressure drop into hydrostatic and irreversible components. A superficial friction factor is calculated from the irreversible component of the unit pressure drop.The average density of the gas phase has a more or less marked effect on all three regime transitions. The transitions all shift similarly to lower air‐water discharge volume ratios with increasing gas phase density. While the flow patterns were not directly observed in the investigation here reported, the flow pattern transitions would be expected to behave similarly.Over the range investigated, the gas phase density has little or no effect on the superficial friction factor. The holdup ratio is unaffected by the gas phase density in Regimes I and II but is significantly affected in Regimes III and IV.

Production Potential Changes During Sweep-Out in a Five-Spot System

Abstract In predicting the performance of a pattern injection operation, the engineer needs to know both the amount of oil to be recovered and the rate at which the recovery will take place. This paper describes fluid flow model studies on the effect of mobility ratio on the rate of oil recovery in a five-spot. The results show the change in fluid conductivity (total flow rate/ pressure drop) as the sweep-out pattern increases for mobility ratios between 0.1 and 10. These data, when combined with a knowledge of reservoir permeabilities and sweepout pattern efficiencies, can be used to predict the cumulative oil production as a function of time for homogeneous five-spot injection systems. Introduction The flow potential in a pattern flood element is a function of the mobility ratio and how far the injected flood front has gone. For a waterflood project having a mobility ratio of one, the conductance - which is the flow rate per unit pressure drop (q/ ?p) - will remain the same throughout the life of the flood. If the mobility ratio is favorable &amp;lt; 1), the conductance of the project will drop continuously throughout the operation. If, on the other hand, the mobility ratio is unfavorable, the conductance ratio will increase continuously. Therefore, if the reservoir engineer wishes to predict either the rate at a specified pressure or the pressure at some rate for a secondary recovery project, he must know how the conductance will vary during the flood. Other investigators have studied this problem using potentiometric models or analytical solution. The method described in this paper uses fluid flow models to study the variation in conductance with mobility ratio and flood front advance. Fluid flow models are more directly analogous to the reservoir and the resulting data can be directly applied to secondary recovery projects. This method was developed to yield reservoir engineering data which can be applied directly from graphs to the reservoir problem.

The upward vertical flow of air‐water mixtures: II. Effect of tubing diameter on flow‐pattern, holdup and pressure drop

AbstractResults of visual observations and measurements of holdup and pressure drop are reported over a range of air‐water ratios for the upwards vertical flow of air‐water mixtures in four tubes with diameters ranging from 0.630 in. to 2.50 in. Tests were conducted under conditions of constant air density corresponding with an average pressure of 36 psia and at 10 constant superficial water velocities ranging from 0.0695 to 7.35 ft./sec.The data are analyzed by the method previously suggested by Govier, Radford and Dunn involving the separation of the unit pressure drop curves into four regimes to aid in flow pattern description and the separation of the unit pressure drop itself into two components to facilitate correlation.Tubing diameter is found to have little or no effect on the border between Regimes I and II or on the transition from the bubble to the slug flow pattern. The borders between Regimes II and III and between Regimes III and IV are markedly affected by tubing diameter as by consequence are the transitions from slug to froth and from froth to ripple flow.Tubing diameter is found to have an important effect on the superficial friction factor and the holdup. The pressure drop data for each of the diameters have been successfully brought together in a single friction factor‐Reynolds number correlation. The holdup data are separately correlated for pressure drop Regimes I and II and for Regime III and Regime IV.