Gas Transfer Model Research Articles

Carbon dioxide stripping in aquaculture – Part II: Development of gas transfer models

The basic mass transfer equation for gases such as oxygen and carbon dioxide can be derived from integration of the driving force equation. Because of the physical characteristics of the gas transfer processes, slightly different models are used for aerators tested under the non steady-state procedures, than for packed columns, or weirs. It is suggested that the standard condition for carbon dioxide should be 20°C, 1atm, CCO2=20 mg/kg, and XCO2=0.000285. The selection of the standard condition for carbon dioxide based on a fixed mole fraction ensures that standardized carbon dioxide transfer rates will be comparable even though the value of CCO2* in the atmosphere is increasing with time. The computation of mass transfer for carbon dioxide is complicated by the impact of water depth and gas phase enrichment on the saturation concentration within the unit, although the importance of either factor depends strongly on the specific type of aerator. For some types of aerators, the most accurate gas phase model remains to be determined for carbon dioxide. The assumption that carbon dioxide can be treated as a non-reactive gas in packed columns may apply for cold acidic waters but not for warm alkaline waters.

Simulation of phosphine flow in vertical grain storage: a preliminary numerical study

To fumigate grain stored in a silo, phosphine gas is distributed by a combination of diffusion and fan-forced advection. This initial study of the problem mainly focuses on the advection, numerically modelled as fluid flow in a porous medium. We find satisfactory agreement between the flow predictions of two Computational Fluid Dynamics packages, Comsol and Fluent. The flow predictions demonstrate that the highest velocity ($>0.1$\,m/s) occurs less than $0.2$\,m from the inlet and reduces drastically over one metre of silo height, with the flow elsewhere less than $0.002$\,m/s or $1$\% of the velocity injection. The flow predictions are examined to identify silo regions where phosphine dosage levels are likely to be too low for effective grain fumigation. References K. Bullen, Insect control in stored grain, Technical report , DPIandF, Plant Science, Toowoomba, Queensland, 2007. http://www.dpi.qld.gov.au/26_6263.htm J. Canchun, D. W. Sun, and C. Cao, Computer simulation of temperature changes in a wheat storage bin, Journal of Stored Products Research , 37 , 165--177, 2001. doi:10.1016/S0022-474X(00)00017-5 P. J. Collins, G. J. Daglish, M. K. Nayak, P. R. Ebert, D. Schlipalius, W. Chen, H. Pavic, T. M. Lambkin, R. Kopittke, and B. W. Bridgeman, Combating resistance to phosphine in Australia, Proc. Int. Conf. Controlled Atmosphere and Fumigation in Stored Products , Executive Printing Services, 593--607, 2001. http://www.ftic.info/CAFSITE/CAFPDF/60.pdf Comsol (2008). Comsol multiphysics user's guide. http://www.comsol.com P. W. Flinn and C. Reed, Effects of outside air temperature on movement of phosphine gas in concrete elevator bins, Proceedings of the International Conference on Controlled Atmosphere and Fumigation in Stored Products , 704--706, 2008. Fluent, Ansys inc. http://www.ansys.com A. K. Singh and G. R. Thorpe, A solution procedure for three-dimensional free convective flow in peaked bulks of grain, Journal of Stored Products Research , 29 , 221--235, 1993. doi:10.1016/0022-474X(93)90004-N E. A. Smith, D. S. Jayas, and A. D. Ville, Modelling the flow of carbon dioxide through beds of cereal grains, Transport in Porous Media , 44 , 123--144, 2001. doi:10.1023/A:1010760508392 E. A. Smith and D. S. Jayas, Modeling the movement of fumigant gas within grain beds, American Society of Agricultural Engineers , 44(3) , 661--667, 2001. http://asae.frymulti.com S. Xu, D. S. Jayas, N. D. G. White, and W. E. Muir, Momentum-diffusive model for gas transfer in granular media, Journal of Stored Products Research , 38 , 455--462, 2002. doi:10.1016/S0022-474X(01)00048-0

A Lagrangian Model to Predict the Modification of Near-Surface Scalar Mixing Ratios and Air–Water Exchange Fluxes in Offshore Flow

A model was developed to predict the modification with fetch in offshore flow of mixing ratio, air–water exchange flux, and near-surface vertical gradients in mixing ratio of a scalar due to air–water exchange. The model was developed for planning and interpretation of air–water exchange flux measurements in the coastal zone. The Lagrangian model applies a mass balance over the internal boundary layer (IBL) using the integral depth scale approach, previously applied to development of the nocturnal boundary layer overland. Surface fluxes and vertical profiles in the surface layer were calculated using the NOAA COARE bulk algorithm and gas transfer model (e.g., Blomquist et al. 2006, Geophys Res Lett 33:1–4). IBL height was assumed proportional to the square root of fetch, and estimates of the IBL growth rate coefficient, α, were obtained by three methods: (1) calibration of the model to a large dataset of air temperature and humidity modification over Lake Ontario in 1973, (2) atmospheric soundings from the 2004 New England Air Quality Study and (3) solution of a simplified diffusion equation and an estimate of eddy diffusivity from Monin–Obukhov similarity theory (MOST). Reasonable agreement was obtained between the calibrated and MOST values of α for stable, neutral, and unstable conditions, and estimates of α agreed with previously published parametrizations that were valid for the stable IBL only. The parametrization of α provides estimates of IBL height, and the model estimates modification of scalar mixing ratio, fluxes, and near-surface gradients, under conditions of coastal offshore flow (0–50 km) over a wide range in stability.

Determination of CO2 sensitivity of micro-organisms in shaken bioreactors. II. Novel online monitoring method

In the present study, a new online monitoring method for the determination of the CO₂ sensitivity of micro-organisms, based on the values of the respiration factors [OTR (oxygen transfer rate) and CTR (carbon dioxide transfer rate)], obtained by using the RAMOS (respiratory activity monitoring system) device considering a variety of aeration rates in the measuring flask, is investigated. Based on the data of the OTR, obtained by RAMOS under a variety of specific aeration rates, the proposed new method was developed as an online monitoring method for CO₂ sensitivity of micro-organisms in shaken bioreactors. A maximum accumulated CO₂ concentration of 12% was derived in applied methods, provided that the cultivation system is carried out under optimal conditions. Additionally, to predict these conditions, an unsteady-state gas transfer model in shaken bioreactors would be very advantageous. The data of OTR obtained using the RAMOS device were analysed and recalculated by a programme considering the calibration factor (Cf). The major advantage of the new method is the possibility to determine the metabolic activity, regardless of manual sampling.

Development of an unsteady‐state model for a biological system in miniaturized bioreactors

In the present study, the special shake flasks, so-called ventilation flasks, are equipped with oxygen sensors and then an unsteady-state gas transfer model for shake flasks was developed and experimentally investigated for a wide range of gas transfer resistances (kplug). For the validation of our unsteady-state model to simulate the gas transfer in a biological system in the ventilation flasks, a strain of Corenobacterium glutamicum DM1730 was used as a model organism. For further easy processing, the resulting total mass-transfer resistance (kplug) is described as a function of the mass flow through the sterile plug (OTRplug) by an empirical equation. This equation is introduced into a simulation model that calculates the gas partial pressures in the headspace of the flask. Additionally, the gas transfer rates through the sterile closure and gas/liquid interface inside the flask are provided. This unsteady-state model would be a very useful method for scaling up from a shake flask to a fermentor; comparing the results of the gas concentration in the gas phase, there is good agreement between the introduced unsteady-state model and experimental results for the biological system.

Open ocean DMS air/sea fluxes over the eastern South Pacific Ocean

Abstract. Air/sea fluxes of dimethylsulfide (DMS) were measured by eddy correlation over the Eastern South Pacific Ocean during January 2006. The cruise track extended from Manzanillo, Mexico, along 110° W, to Punta Arenas, Chile. Bulk air and surface ocean DMS levels were also measured and gas transfer coefficients (kDMS) were computed. Air and seawater DMS measurements were made using chemical ionization mass spectrometry (API-CIMS) and a gas/liquid membrane equilibrator. Mean surface seawater DMS concentrations were 3.8±2.2 nM and atmospheric mixing ratios were 340±370 ppt. The air/sea flux of DMS was uniformly out of the ocean, with an average value of 12±15 μmol m−2 d−1. Sea surface concentration and flux were highest around 15° S, in a region influenced by shelf waters and lowest around 25° S, in low chlorophyll gyre waters. The DMS gas transfer coefficient exhibited a linear wind speed-dependence over the wind speed range of 1 to 9 m s−1. This relationship is compared with previously measured estimates of k from DMS, CO2, and dual tracer data from the Atlantic and Pacific Ocean, and with the NOAA/COARE gas transfer model. The model generated slope of k vs. wind speed is at the low end of those observed in previous DMS field studies.

Gas transfer under breaking waves: experiments and an improved vorticity-based model

Abstract. In the present paper a modified vorticity-based model for gas transfer under breaking waves in the absence of significant wind forcing is presented. A theoretically valid and practically applicable mathematical expression is suggested for the assessment of the oxygen transfer coefficient in the area of wave-breaking. The proposed model is based on the theory of surface renewal that expresses the oxygen transfer coefficient as a function of both the wave vorticity and the Reynolds wave number for breaking waves. Experimental data were collected in wave flumes of various scales: a) small-scale experiments were carried out using both a sloping beach and a rubble-mound breakwater in the wave flume of the Laboratory of Harbor Works, NTUA, Greece; b) large-scale experiments were carried out with a sloping beach in the wind-wave flume of Delft Hydraulics, the Netherlands, and with a three-layer rubble mound breakwater in the Schneideberg Wave Flume of the Franzius Institute, University of Hannover, Germany. The experimental data acquired from both the small- and large-scale experiments were in good agreement with the proposed model. Although the apparent transfer coefficients from the large-scale experiments were lower than those determined from the small-scale experiments, the actual oxygen transfer coefficients, as calculated using a discretized form of the transport equation, are in the same order of magnitude for both the small- and large-scale experiments. The validity of the proposed model is compared to experimental results from other researchers. Although the results are encouraging, additional research is needed, to incorporate the influence of bubble mediated gas exchange, before these results are used for an environmental friendly design of harbor works, or for projects involving waste disposal at sea.

CO 2 transfer in an aqueous potassium carbonate liquid membrane module with dense polymeric supporting layers: Influence of concentration, circulation flow rate and temperature

Gas–liquid separation systems have already received considerable attention in a great number of situations of industrial interest. The attention paid to membrane contactors and immobilized liquid membranes have recently increased due to their separation performances. For the sake of simplicity, most experiments are usually performed at room temperature. It is, however, obvious that increasing the temperature would increase the reaction rate and thereby also possibly enhance the system's productivity. This work presents a systematic study of CO 2 and H 2 transport in a novel flowing liquid membrane (FLM) module with dense membranes separating layers and aqueous potassium carbonate (concentration 0.1–3 kmol/m 3) solutions in the temperature range 295–353 K. A model of CO 2 transport with reversible chemical reactions through the FLM was developed and compared to a series of experimental data. It was found that increasing the concentration of potassium carbonate as well as the temperature led to large increases in both the CO 2 productivity and the CO 2/H 2 selectivity. The industrial implications of these observations were discussed. Unsteady state transport of CO 2 was also investigated and a simple model of gas transfer in the FLM with physical absorption in the liquid phase was developed.

Gas permeability of combined membrane systems with mobile liquid carrier

Gas transfer in a membrane system called a selective membrane valve (SMV) is studied. The SMV is a system consisting of two mobile gas phases, one mobile liquid phase, and two membranes acting as interfaces between gas and liquid. Such a membrane system has supplementary variable parameters and is designated for the separation of multicomponent gas mixtures. System permeability for individual gases (CO2, O2, and H2) and its dependence on a flow rate of a liquid phase are studied. Time dependences of the non-steady state transfer of CO2 through the immobile layer of chemisorbent (aqueous K2CO3 solution) at its different concentrations are studied for the first time. Two theoretical models are developed: the model of gas transfer through a selective membrane valve system with a mobile liquid absorbent (in the absence of chemical interaction) and the model of a non-steady-state transfer of CO2 through the immobile layer of aqueous potassium carbonate solution. The first model makes it possible to determine gas-to-liquid diffusion coefficients; the second model permits us to plot kinetic permeability curves and to calculate system permeability with allowance for the CO2 transfer accompanied by reversible chemical reaction with the carrier. The model dependences agree well with the experimental data.

DMS sea‐air transfer velocity: Direct measurements by eddy covariance and parameterization based on the NOAA/COARE gas transfer model

Estimates of the DMS sea‐air transfer velocity (kDMS) derived from direct flux measurements are poorly modeled by parameterizations based solely on wind speed and Schmidt number. DMS and CO2 flux measurements show to be a stronger function of wind speed than kDMS. The NOAA/COARE gas flux parameterization, incorporating the bubble‐mediated gas transfer theory of Woolf (1997), appears to do a better job reproducing the observations for both gases, illustrating the importance of trace gas solubility in sea‐air exchange. The development of gas transfer parameterizations based on physical principles is still in its infancy, but recent advances in direct flux measurement methods provide an opportunity to evaluate the success of various modeling approaches for this critical geophysical process.

PREDICTION OF OXYGENATION, HEMOLYSIS AND THROMBOSIS IN BLOOD MEMBRANE OXYGENATORS USING COMPUTATIONAL FLUID DYNAMICS

The fundamental engineering problems to develop a functional and biocompatible blood oxygenating device involve optimizing the flow path to efficiently transfer gas between blood and gas phases, to reduce pressure drop, and to minimize flow-induced blood trauma and thrombosis. All of them are closely related to the local fluid dynamics. It is difficult to experimentally investigate the effects of fiber buddle and device structure on localized blood flow, gas transfer and biocompatibility due to their complex structure of contemporary hollow fiber membrane oxygenators. To obviate these difficulties, we developed computational fluid dynamics (CFD) based mathematical models to predict gas transfer, shear-induced hemolysis and thrombosis in hollow fiber membrane blood oxygenators. The gas transfer model includes transport between blood and gas phases, oxygen binding to hemoglobin and reaction with blood. The hemolysis model is based on an Eulerian approach to consider both the shear stress and exposure time as the primary factors. These models were tested by comparing computationally predicted results with experimentally measured data. They are in excellent agreement. Our on-going activities will be including flow-induced platelet activation and deposition modeling. The advantage of CFD modeling is the ability to optimize the expended design to avoid the time-consuming and costly process of trial and error. By incorporating gas transport, blood damage, and thrombosis models, it will be a very attractive design paradigm to optimize the design of blood contacting devices.

An estimate of the global distribution of radon emissions from the ocean

There is a need for improved estimates of the radon (222Rn) flux density from the ocean for use in the modeling and interpretation of atmospheric radon in global climate and air pollution studies. We use a modification of a frequently used model of gas transfer to generate global predictions of ocean radon flux density for each month of the year (climate averaged) on a 192 by 94 global grid. Compared with the often‐used approximation of a constant radon flux from the ocean, the model's predictions indicate large variations over regions of the ocean (a factor of ten is not uncommon). For example, latitude bands near the equator and Southern Ocean are predicted to emit relatively high average radon flux compared with other latitude bands. The predicted annually‐averaged flux density from the ocean is 0.0382 mBq m−2 s−1 (0.00182 atoms cm−2 s−1), smaller than some commonly‐used estimates.

Mercury dynamics in a small Northern Minnesota lake: water to air exchange and photoreactions of mercury

Mercury speciation at a small seepage lake in Northern Minnesota was shown to be influenced by photoreduction and photooxidation. Fluxes of Hg 0 from water to air were greatest in the warmer, sunnier months in 2001 to 2002; however, correlation with solar radiation was weak. The daytime evasional loss was generally from water to air and was estimated at 5.3 pmol m −2 h −1 for 2001 and 6.2 pmol m −2 h −1 for 2002 using a two-layer gas transfer model. Losses of Hg 0 (aq) in the dark over 10 days were observed in lake water (0.02 h −1), Milli-Q™ water, and HPLC grade water (0.002 h −1) and agreed with reported pseudo-first-order loss rates in the dark in other freshwaters. Using a mercury arc lamp, the pseudo-first-order loss rate of Hg 0 in water from Spring Lake was found to range from 0.39 to 0.76 h −1. Other sinks for Hg 0 exist through reaction with ozone, hydroxyl radical, and possibly singlet oxygen. A second-order reaction rate constant for Hg 0 (aq) and OH of 1.0×10 9 M −1 s −1 was estimated based on data from experiments and the literature. Although less reactive, there is a higher steady state concentration of ozone in lake water compared to hydroxyl radical. Consequently, loss of Hg 0 (aq) by ozone may predominate. Potential oxidation of Hg 0 (aq) by singlet oxygen using rose bengal as a sensitizer could not distinguish between oxidation by rose bengal and by singlet oxygen itself. Chloride enhanced the oxidation of Hg 0 (aq) and should be considered in the mercury cycle in the ocean.

Estimation of Surface Flow and Net Heat Flux from Infrared Image Sequences

The study of dynamical processes at the sea surface interface using infrared image sequence analysis has gained tremendous popularity in recent years. Heat is transferred by similar transport mechanisms as gases relevant to global climatic changes. These similarities lead to the use of infrared cameras to remotely visualize and quantitatively estimate parameters of the underlying processes. Relevant parameters that provide important evidence about the models of air-sea gas transfer are the temperature difference across the thermal sub layer, the probability density function of surface renewal and the flow field at the surface. Being a driving force in air sea interactions, it is of equal importance to measure heat fluxes. In this paper we will present algorithms to measure the above parameters of air-sea gas transfer during night-time and show how to combine physical modeling and quantitative digital image processing algorithms to identify transport models. The image processing routines rely on an extension of optical flow computations to incorporate brightness changes in a total least squares (TLS) framework. Statistical methods are employed to support a model of gas transfer and estimate its parameters. Measurements in a laboratory environment were conducted and results verified with ground truth data gained from traditional measurement techniques.

CHARACTERISTICS OF SURFACE-RENEWAL TURBULENCE AT AN AIR-WATER INTERFACE

A mathematical model of gas transfer velocity was formulated by considering the divergence of horizontal velocities at an air-water interface. Characteristics of surface-renewal turbulence were investigated experimentally to examine the validity of the model. The experiments were performed in grid-generated turbulent flows with shallow water depth. The velocity fields at the water surface were measured using a particle image velocimetry (PIV). Statistical quantities such as the turbulent energy and the dissipation rate were obtained from the measurements. The experimental data support that the surface velocity divergence increases in proportion to √eS/ν, where eS is the dissipation rate and ν the kinematic viscosity. This indicates that the gas transfer model is found to depend on a Reynolds number to the power of-1/4.

A biological model of tamponade gases following pneumatic retinopexy

Purpose. Predict the persistence and expansion of intraocular tamponade gases used in retinal detachment surgery. Quantify factors that contribute to elevations in the intraocular pressure. Methods. We developed a non-equilibrium physiological model of intraocular gas transfer in vitreoretinal surgery. The model was calibrated using published volumetric decay measurements for four perfluorocarbon gases (CF 4, C 2 F 6, C 3 F 8, C 4 F 10) injected into the New Zealand red rabbit. We validated the model by comparing predicted and experimental results at different conditions in the rabbit. Using the rabbit results, the model was scaled up to humans. Results. Predictions of gas expansion, half-life, and intraocular pressure in humans were found to correlate very well with clinical results. Gas transfer in the eye was controlled by diffusion through plasma and membranes. Although intraocular pressure depended on several complicating factors such as the physiological condition of the eye as well as the medications being used, prediction of conditions that favor elevations in intraocular pressure were identified based on the transport and thermodynamic properties of the gases. Conclusions. The biological model accurately predicted the dynamics of intraocular gases in the human eye. The major factor affecting the intraocular pressure was the aqueous humor dynamics, which is highly dependent on the physiological conditions in the eye. However, for long duration gases such as perfluoropropane, elevations in intraocular pressure are possible following an increase in volume and/or purity of the injected gas. By injecting a mixture of air with an expansive gas, it is possible to reduce elevations in intraocular pressure in patients with the trade off of a reduced longevity of the gas bubble. For gases that diffuse faster than perfluoropropane, there are minimal effects on intraocular pressure due to these changes.

Gas transfer experiment on a lake (Kerguelen Islands) using 3He and SF6

Gas transfer velocities of SF6 and 3He were determined in a Kerguelen Islands lake at wind speeds in the range 0–10 m/s by injecting the two tracers into the water and measuring their concentrations over 40 days. Two methods are investigated for the determination of the relationship linking the gas transfer velocity K to the wind speed W. The first method postulates a power law relationship K = βWα. This leads to the same exponent α = 1.5±0.2 for both gases. The second method is the classic determination of the gas transfer velocity Kij between two tracer measurements at times ti and tj using the well‐mixed reservoir assumption. This method proves to be less favorable owing to its nonlinearity bias and also because it induces much scatter in the gas transfer coefficient/wind speed relationship. This dispersion is shown to arise from the experimental scatter of the data and, above all, from the high sensitivity of the method to even small heterogeneities in the tracer vertical distribution. In the present experiment, the Liss and Merlivat correlation [Liss and Merlivat, 1986] is shown to underestimate the actual mean gas exchange rate by about 40%. Our results agree with the recent dual‐tracer experiment by Wanninkhof et al. [1993] and are also consistent with CO2 transfer coefficient data derived from the study of 14C oceanic inventories. As expected from gas transfer theories and various experimental observations, the Schmidt number exponent in the comparison of 3He and SF6 transfer velocities is found to vary substantially with the transfer regime. However, its variation is found to be greater than that forecast by current gas transfer models, with values as high as n = −0.2 for intermediate to strong winds. This again raises the question of the validity of the normalization method for KCO2 calculation from gas transfer experiments, especially in high‐wind regimes.

Variabilities in the fluxes and annual emissions of nitrous oxide from the Arabian Sea

Extensive measurements of nitrous oxide (N2O) have been made during April–May 1994 (intermonsoon), February–March 1995 (northeast monsoon), July–August 1995 and August 1996 (southwest monsoon) in the Arabian Sea. Low N2O supersaturations in the surface waters are observed during intermonsoon compared to those in northeast and southwest monsoons. Spatial distributions of supersaturations manifest the effects of larger mixing during winter cooling and wind‐driven upwelling during monsoon period off the Indian west coast. A net positive flux is observable during all the seasons, with no discernible differences from the open ocean to coastal regions. The average ocean‐to‐atmosphere fluxes of N2O are estimated, using wind speed dependent gas transfer velocity, to be of the order of 0.26, 0.003, and 0.51, and 0.78 pg (pico grams) cm−2 s−1 during northeast monsoon, intermonsoon, and southwest monsoon in 1995 and 1996, respectively. The lower range of annual emission of N2O is estimated to be 0.56–0.76 Tg N2O per year which constitutes 13–17% of the net global oceanic source. However, N2O emission from the Arabian Sea can be as high as 1.0 Tg N2O per year using different gas transfer models.

Branchial gas transfer models.

Gas transfer in fish gills is simulated by a simple counter-current model, with ventilation, water-blood transfer and blood flow characterized by conductances. The ventilation and perfusion conductances are products of flow rate and effective solubility. The diffusion conductance of water-blood transfer (diffusing capacity) is considered to depend on diffusion properties of both the water-blood tissue barrier and of interlamellar water. In the gills of the dogfish Scyliorhinus stellaris, more than half of the total resistance to O2 diffusion was located into interlamellar water. Complicating factors like water shunt, blood shunt, ventilation-perfusion maldistribution, pulsatile flow, diffusion in blood and reaction of O2 with hemoglobin may reduce the O2 transfer efficacy predicted by the simple model. In S. stellaris, the effect of such complicating factors appeared to be minor in most conditions, but in other species and/or conditions, more complex models might be required.

Enantiomers of α-Hexachlorocyclohexane as Tracers of Air−Water Gas Exchange in Lake Ontario

The technique of chiral phase capillary gas chromatography was applied to investigate the degradation and transport of the persistent chiral pesticide α-hexachlorocyclohexane (α-HCH) in the Lake Ontario environment. Chiral analysis gave the enantiomeric ratios (ERs) of α-HCH in samples taken May−October 1993 from the lake and its atmosphere. ERs of (+)α-HCH/(−)α-HCH for Lake Ontario surface and deep water samples were similar and averaged 0.85 ± 0.02 as compared with a value of 1.00 for the α-HCH standard. Higher ERs were observed in water samples from the Niagara River (0.91 ± 0.02) and from precipitation (1.00 ± 0.01). Air samples of α-HCH measured at 10 m above the lake show a seasonal variability with values near 1.00 in spring and fall and minimum values in individual samples near 0.90 in summer. A simple air−water gas transfer model demonstrates that enantiomeric ratios <1.0 in air are derived from equilibration of the air with the water during transport of the air mass over the lake. Based on the m...