Simultaneous Flow Of Gas Research Articles

Monte Carlo simulation of simultaneous gas flow and diffusion in an asymmetric distal pulmonary airway model.

In order to evaluate the effect of anatomic asymmetries on the gas concentration distribution in the pulmonary airways, a Monte Carlo simulation of combined bulk flow and molecular diffusion was carried out in a realistic distal airway model (Parkeret al., 1971). This airway model, composed of branches distal to the 0.5-ram diameter airways, contained an upper symmetric segment consisting of four generations of conducting airways and a lower asymmetric segment of alveolar ducts and sacs arranged in five transport paths of varying lengths. In accounting for the volume increases of these ducts and sacs occurring during normal respiration, uniform alveolar filling rates and a fixed length-to-diameter ratio of all airways were assumed. For a pulse injection of inert tracer gas, the simulation was employed to determine the longitudinal concentration profiles in the conducting airways. In the alveolated airways, not only were the longitudinal profiles determined along each path, but radial transport from the core to the periphery of the airways was considered.

Characterization of lung geometry from the single-breath nitrogen washout test

A previously developed transport analysis was used to simulate two sets of single-breath nitrogen washout data from each of four normal subjects. The analysis treats simultaneous gas flow and longitudinal diffusion and incorporates a modified form of Weibel's anatomical model “A” to describe the airway geometry. For each data set, four geometric parameters of the analysis were varied in a computer simulation until it matched the instantaneous expiratory concentration curve; particular emphasis was placed on matching the data in the concentration transition. Monitored values of functional residual capacity and instantaneous respiratory flow were supplied as inputs to each simulation. For each subject, a reasonable computer simulation could be obtained using a single set of lower airway geometric parameters, even though the average respiratory flow rate varied by as much as 53% from test to test; this result is due to the ability of the transport analysis to directly account for gas mixing during normal respiration. Under the same conditions the anatomic dead space varied by as much as 24%.

Simultaneous gas flow and diffusion in a symmetric airway system: A mathematical model

Finite difference solutions of the differential diffusion equation, incorporating simultaneous longitudinal diffusion and exponentially time varying flow, served as simulations of single-breath nitrogen washout. Using Weibel's anatomic model “A” for the conducting airways and assuming a well-mixed alveolar region, an anatomic dead space 70% larger than commonly measured values was predicted. This is due in part to the Weibel parameter values which overestimate conducting airway volume when inspiration is initiated at FRC. Moreover, the existence of additional mixing processes in the real lung would lead to a smaller dead' space than predicted by longitudinal diffusion alone. To test the reasonableness of the model, simulations with varying respiratory conditions were performed. The predicted dead space decrease for an increase in inspiration time, for a decrease in inspiratory volume and for an increase in diffusion coefficient were in agreement with experimental data. Decreases in dead space by breath-holding and increased expiratory times followed the experimental trends only qualitatively. A major point of interest in this work was the effect of variations in conducting airway geometry upon the washout data. The upper airways were found to behave as pure dead space because of the small role that diffusion plays in the overall transport occurring therein. For example, a 40-ml increase in conducting airway volume brought out by increasing the length or cross-section of the first four airway generations caused an equal volume change in the anatomic dead space. However, the same airway volume increase brought about by lengthening the 4th to 17th generation airways increased dead space by only 20 ml. If brought about by increasing the summed crosssection of these airways, the dead space increased by only 5–10 ml and the washout curve was only slightly changed. Thus, the washout test is especially insensitive to cross-sectional alterations in the lower airways because of the compensating effects of diffusion.

Morphology of distal airways in the human lung.

ArticleMorphology of distal airways in the human lung.H Parker, K Horsfield, and G CummingH Parker, K Horsfield, and G CummingPublished Online:01 Sep 1971https://doi.org/10.1152/jappl.1971.31.3.386MoreSectionsPDF (1 MB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInWeChat Previous Back to Top Next Download PDF FiguresReferencesRelatedInformation Cited ByDevelopment of anatomically based structure for human acinus by Lindenmayer system: accurate model for gas exchange in human lung15 August 2021 | The European Physical Journal Plus, Vol. 136, No. 8Development and Functional Anatomy of the Respiratory System21 February 2020N 2 gas egress from patients’ airways during LN 2 spray cryotherapyMedical Engineering & Physics, Vol. 44Alveolarization into AdulthoodCurrent Inhalers Deliver Very Small Doses to the Lower Tracheobronchial Airways: Assessment of Healthy and Constricted LungsJournal of Pharmaceutical Sciences, Vol. 105, No. 1Architecture of the Tracheobronchial TreeArchitecture of the Gas Exchange Region of the LungsModeling Deposition of Inhaled Particles25 July 2012Transport of Gases between the Environment and Alveoli—Theoretical Foundations1 July 2011Gas Mixing in the Airways and Airspaces1 April 2011Gas and aerosol mixing in the acinusRespiratory Physiology & Neurobiology, Vol. 163, No. 1-3Finite element 3D reconstruction of the pulmonary acinus imaged by synchrotron X-ray tomographyA. Tsuda, N. Filipovic, D. Haberthür, R. Dickie, Y. Matsui, M. Stampanoni, and J. C. Schittny1 September 2008 | Journal of Applied Physiology, Vol. 105, No. 3Expiration rate drives human airway designJournal of Theoretical Biology, Vol. 253, No. 2Bronchial AbnormalitiesAnthropometry of fetal vasculature in the chorionic plateJournal of Anatomy, Vol. 211, No. 6An anatomically realistic lung model for Monte Carlo‐based dose calculations22 February 2007 | Medical Physics, Vol. 34, No. 3Fetal Blood Flow in Branching Models of the Chorionic Arterial Vasculature15 February 2007 | Annals of the New York Academy of Sciences, Vol. 1101, No. 1Modeling deposition of inhaled particles15 December 2009Analysis of the conducting airway system in the lung: A new method combining morphometry with mathematical modeling for airway classification10 December 2001 | The Anatomical Record, Vol. 266, No. 1A three-dimensional model of the human pulmonary acinusHiroko Kitaoka, Shinichi Tamura, and Ryuji Takaki1 June 2000 | Journal of Applied Physiology, Vol. 88, No. 6Determinants of Gas Exchange and Acid–Base Balance During Exercise1 January 2011Physiology of the AirwaysStructure of a human pulmonary acinus.Thorax, Vol. 46, No. 2The fractal lung: Universal and species-related scaling patternsExperientia, Vol. 46, No. 3Modeling of lung morphogenesis using fractal geometriesIEEE Transactions on Medical Imaging, Vol. 7, No. 4Morphometry of the human pulmonary acinusThe Anatomical Record, Vol. 220, No. 4Diffusion and Convection in Intrapulmonary Gas Mixing1 January 2011Morphometry of Airways1 January 2011Dynamic Distribution of Gas Flow1 January 2011The Xiphosurida: Archetypes of Bradytely?Structure of the human respiratory acinusAmerican Journal of Anatomy, Vol. 162, No. 3Further considerations in a theoretical description of gas transport in lung airwaysBulletin of Mathematical Biology, Vol. 43, No. 5The anatomical basis for the sloping N2 plateauRespiration Physiology, Vol. 44, No. 3The Myogenic Response1 January 2011A statistical description of the human tracheobronchial tree geometryRespiration Physiology, Vol. 37, No. 2AtemphysiologieUneven perfusion and ventilation within lung regions studied with nitrogen-13Respiration Physiology, Vol. 34, No. 1Tree structures: Deducing the principle of mechanical designJournal of Theoretical Biology, Vol. 59, No. 2Monte Carlo simulation of simultaneous gas flow and diffusion in an asymmetric distal pulmonary airway modelBulletin of Mathematical Biology, Vol. 38, No. 2Use of a heat transfer analogy for a mathematical model of respiratory tract depositionBulletin of Mathematical Biology, Vol. 36, No. 2Casting the lungsin-situThe Anatomical Record, Vol. 177, No. 2Morphometry of the Human Pulmonary Arterial TreeCirculation Research, Vol. 33, No. 2Developmental Aspects of the Human LungPediatric Clinics of North America, Vol. 20, No. 2Comparative histology of the respiratory apparatus of three desert rodents and the albino rat a view on morphological adaptationsComparative Biochemistry and Physiology Part A: Physiology, Vol. 44, No. 2 More from this issue > Volume 31Issue 3September 1971Pages 386-91 https://doi.org/10.1152/jappl.1971.31.3.386PubMed4939280History Published online 1 September 1971 Published in print 1 September 1971 Metrics

Better Investment Planning of Gas-Producing Operations By Computer Simulation

Abstract Depending on the degree of selectivity possible and the degree of variation in the character of the reserves, an optimum solution to planning investments for multiple-reservoir gas operations can be very complex. A gas sales simulation computer program has been developed to assist in making investment decisions leading to maximum profits. The simulation permits an integrated case study calculation of the reservoir depletion process, well deliverability, gas liquid recovery and economics for a predetermined plan of operation. The factors simulated, data requirements and program logic are described in this article and applications to various field problems are discussed. The case study simulation technique has been used successfully in operations and investment planning for gas sales from a producing complex. It is considered to be a valuable tool both for detailing short-term investments and for forecasting long-range investment requirements and deliverability. Introduction From the standpoint of operations planning, a gas-producing property will be complex when a large number of investment alternatives exist. For most properties, the basic alternative will be between well development and amount of compression. There are unique situations, however, where several reservoirs will underlie a single-interest lease or unitized tract (only one operator and only one royalty owner), and equitable lease participation is not a factor in the producing operations. The investment alternatives for this type of property are far greater than usual since selection may be exercised in the depletion of individual reservoirs. The program to be discussed was developed for operations and investment planning for a complex property where all reservoirs have only one operator and one royalty owner. It is recognized that before this type of program can be generally applied, it is mandatory that the problem of equitable lease participation be solved. Because the reserves in a typical complex property may have wide variations in reservoir size, well deliverability, gas value and development cost, a judicious selection and timing of investments is necessary for maximum profits. However, an optimum solution to investment planning can be very difficult. The calculation of an optimum can be made using linear programming techniques if the sale involves only a very few reservoirs. For a large number of reservoirs, the excessive number of equations required for linear programming makes this calculation technique (and thus true optimization) impractical. This article describes a computer program which has been used to evaluate investment decisions by simulating complex gas-producing operations. Basically, the program computes the 20-year deliverability and economics for a complex system according to data which have been supplied to it. In other words, it permits a case study approach to evaluating a predetermined plan of operation. From an evaluation of several potentially attractive plans, a near-optimum solution can be selected. Simulation Structure The gas producing process simulated is illustrated schematically in Fig. 1. It may be described as the calculation of simultaneous gas flow from a group of reservoirs, interconnected at field separation stations and through gathering system network, to a single delivery point. JPT P. 157ˆ

The Effect of Entrained Liquid on the Measurement of Gas by an Orifice Meter

Abstract One of the simplest and most widely used devices for flow measurement is the orifice meter, Its use in industry is at present limited to measuring homogeneous fluids. This investigation was conducted to study orifice measurement of a two-phase flow system, to determine the magnitude of error induced in the measurements of gas by a liquid phase and to develop correlations which may be useful in predicting and compensating these errors. Introduction The successful operation of modern, large-scale continuous processes requires accurate and reliable measurement of flowing fluids. In most cases, sufficient accuracy can be obtained by measuring a single-phase fluid with one of several devices that are available. One of the simplest and most widely used devices for flow measurement is the flat-plate, square-edged orifice. It is relatively simple to obtain flow rates with an orifice meter for homogeneous fluids such as air, natural gas, various industrial gases, steam. water, oil and all liquids whose physical properties are known. However, serious errors in measurement result when this simple device is used where two or more fluid phases comprise the flowing stream. In many applications, homogeneity is difficult to achieve because of condensation. In others, the presence of more than one phase is unknown or ignored. Regardless, measurement of multiphase flow is complex and very little information is available for determining flow rate of such a system accurately. A standard method for measuring gas flow rates is reported in Orifice Metering of Natural Gas, a report prepared by the AGA. However, this is applicable only to homogeneous gas-flow measurement. A similar method for measuring the flow of liquids is not applicable to multi-phase flow systems. It was the purpose of this investigation to study orifice measurement of a two-phase flow system, to determine the magnitude of error induced by a liquid phase and to develop correlations which may be useful in predicting and compensating these errors. To study flow patterns and behavior in a visual system, this investigation was confined to an air-water system operating at pressures ranging from 0 to 15 psig at ambient temperature, using both horizontal and vertical meter runs. The results obtained are compared to and correlated with data obtained by R.A. Schuster and J.R. Wright in similar studies at different operating conditions. Review of Literature The behavior of compressible and non-compressible fluids in flow channels is well understood, and the pressure drop of a single-phase fluid due to friction in a pipe can be calculated quite accurately. Similarly, the flow rate of single-phase fluids can be calculated from the data obtained with flow-restricting devices such as the orifice meter. Any attempt to combine the equations describing the flow of a homogeneous gas or liquid in a circular duct results in a fundamental discrepancy in the assumptions inherent in deriving the separate equations. The following conditions occur in the simultaneous flow of gas and liquid in a horizontal pipe:1. A reduction in flow area available to the gas phase in a pipe due to liquid accumulation;2. A considerable loss of energy due to the roughness of the liquid surface which forms in waves and ridges; and3. A loss of energy by the gas phase which accelerates and transports the liquid along the length of the pipe, noting that the relative velocity of the gas is the greater of the two. So larger pressure drops are observed in horizontal two- phase flow than are found in the single-phase flow of either phase. Empirical attempts to relate the pressure drops of the individual phases to two-phase pressure drop have been made by several investigators. A study of the literature on two-phase vertical systems reveals the complexity of the flow characteristics, and it is not yet possible to predict the pressure drop due to a flow-restricting device, such its an orifice meter, from these data. JPT P. 657ˆ

Effect of Foam on Permeability of Porous Media to Gas

Abstract Laboratory experiments were conducted to determine the effect of foam on gas flow in porous media. Previous studies have indicated that foam may be applicable as a restrictive agent in influencing underground gas flow. Foam was found to be exceedingly effective in reducing the permeability of porous media to gas. Consolidated and unconsolidated sands with specific permeabilities of 100 to 146,000 md had, in the presence of foam, gas permeabilities that were less than 1 per cent of the specific permeability; in many cases the gas permeability was practically zero. Foam reduced the gas permeability of loose sand to a much greater degree than that of a tight sand. For example, the permeability of a 125,000-md sand was reduced to 3 md while the permeability of a 4,000-md sand was reduced to 7 md. This effect should cause, to some degree, a selective plugging of high permeability channels in various oil displacement processes. The presence of oil in a porous medium decreased the effectiveness of foam in reducing gas permeability; apparently oil acts as a foam depressant. However, it was found that certain foaming agents were very effective in reducing permeability even in the presence of oil. Also, continuous injection of other foaming agents increased their effectiveness, when oil was present. The effect of foam on permeability of porous media to gas was studied as a function of foaming agent concentration and injection rate, absolute permeability, total pressure, pressure gradient, length of porous system, brine concentration and time. Introduction The use of surface active agents in flood water to increase the recovery of oil has been studied in the laboratory and in the field for decades, with rather limited success. In recent years a new approach to the problem was proposed. Instead of using an aqueous solution of surfactant as an oil recovery agent, Bond and Holbrook proposed that the oil recovery agent he a mixture of surfactant solution and gas. In their method, a water-soluble surface active agent with foam-producing characteristics is injected into an underground formation as an aqueous slug. This slug is followed by gas to produce a foam within the rock. Foams are defined as "agglomerations of gas bubbles separated from each other by thin liquid films." A foam is fundamentally an unstable system. The foam process for oil recovery has since been studied by other investigators. Fried has shown that foam can displace from porous structures oil that normally is unrecoverable by conventional water or gas drives. This superior oil displacing action is believed to be the result of several factors: foam introduces into the reservoir many resilient interfaces of various sizes and curvatures, which increase the probability that a proper combination of forces for oil displacement will be created; foam has appreciable viscosity which improves mobility ratio and contact efficiency; foam accentuates the trapped gas effect because high gag saturations are possible without producing high gas/oil ratios. Deming studied the effect of various foam properties on the displacement of liquid. He found that high foaming ability favors high displacement efficiency; high foam stability is not necessary for high displacement efficiency; displacement efficiency decreases with increase in plasticity of foam and displacement efficiency is unaffected by surface tension of foaming agent solution. One of the important aspects of this oil recovery process is the effect of foam on gas permeability. The simultaneous flow of gas and liquid in porous media has been studied by numerous investigators and a large amount of literature exists on the subject. In this previous work, gas and liquid have generally been considered as essentially independent phases, whose flow characteristics are related through the saturation parameter. Foam, however, is a material with properties that are considerably different from those of its components; for example, the viscosity of a foam is greater than either of its components. SPEJ P. 267ˆ

Simultaneous Flow of Gas and Liquid As Encountered in Well Tubing

Abstract The paper deals with pressure gradients occurring in flowing and gas-lift wells, a knowledge of which can be applied to the determination of optimum flow-string dimensions and to the design of gas-lift installations. The study is based on a pressure-balance equation for the pressure gradient. It appears that a pressure-gradient correlation of general validity must essentially consist of two parts-one part being a correlation for liquid hold-up and the other part being one for wall friction. Dimensional analysis indicates that both liquid hold-up and wall friction are related to nine dimensionless groups. It is shown that in the field of interest only four groups are really important. On the basis of these four groups a restricted experimental program could be selected that nevertheless covered practically all conditions encountered in oil wells. This experimental program has been carried out in a laboratory installation. Three essentially different flow regimes were found. The pressure gradients in these regions are presented in the form of a set of correlations. Comparison of these correlations with a few available oilfield data showed excellent agreement. Introduction Prediction of the pressure drop in the flow string of a well is a widely known problem in oilfield practice. Accurate data on the pressure gradient of a simultaneous flow of gas and liquid in a vertical pipe are especially useful for the determination of optimum flowstring dimensions. It is well known that with moderate gas and liquid flows such a vertical string acts as a "negative restriction". The pressure drop decreaseswhen the throughput through a given pipe increases, andwhen at a given throughput the cross-sectional area is decreased. The reason is that, with increasing velocities, the flow becomes more agitated so that the gas slips relatively more slowly through the liquid. With the resulting increase in gas content in the string, the static head decreases. When the area becomes very small, however, the high velocities entail great wall friction, which causes an increase in pressure drop. For a given flow, therefore, minimal pressure drop is obtained by using a certain cross section. This means that, in principle, each well can be provided with an optimum flow string for minimum pressure drop and, hence, maximum possible production rate. The procedure for the selection of the optimum string has been discussed by Gilbert. A necessary tool in the procedure, however, is accurate knowledge of the pressure gradient to be expected for various values of the governing variables. Another application of pressure-gradient data lies in the field of gas-lift practice: they provide a means of determining the optimum gas-injection rate, optimum injection pressure and optimum injection depth. Much work has already been done in the study of the pressure gradient of vertical gas-liquid flow. Poettmann and Carpenter presented a pressure-gradient correlation based on measurements in wells. This correlation has been found to provide accurate predictions in high-pressure wells and in high-production wells for flow through both tubing and annuli. However, when their method is checked on low pressure-low production wells or on wells with viscous crudes, serious discrepancies are found. As we shall see in the next section, this is due to the fact that their correlation factor, representing all irreversible energy losses, is given as a function of only one correlation group. Some important variables, such as gas-liquid ratio and liquid viscosity, are not incorporated in this group so that their specific effects are not accounted for. To study also the mechanism of vertical gas-liquid flow outside the ranges covered by the Poettmann-Carpenter publication and extensions, a laboratory investigation has been carried out. This study is founded on a pressure-gradient equation that is based on a pressure balance. To reduce the number of test runs required, a dimensional analysis has been carried out, followed by a selection of relevant dimensionless groups. These groups guided a subsequent experimental study, and with their aid the experimental program could be minimized while still covering the majority of the situations encountered in oilfield practice. In this paper the choice of a formula for the pressure gradient is discussed first. This is followed by a brief description of the experimental setup. Subsequently, the dimensional analysis is discussed and the relevant dimensionless groups are selected, resulting in the experimental program required.

An analysis of critical simultaneous gas/liquid flow through a restriction and its application to flowmetering

A theoretical analysis is presented of the mechanism of simultaneous flow of gas and liquid through a restriction at critical speed. The study shows that a relationship exists between the mass flows of gas and liquid, restriction size and upstream pressure. Comparison of this relationship with measurements showed a reasonable agreement. It has therefore been concluded that a restriction can be used as a gas/liquid flowmeter with reasonably high accuracy, provided that the flow is a critical one. Further increase of accuracy seems possible by using a restriction especially designed for the purpose.

On a problem of diffusion and simultaneous gas flow

A diffusion problem of spherical symmetry, involving gas flow, has been treated quantitatively.