Individual Mass Transfer Coefficients Research Articles

Evaluation of the Sublimation Process of Some Purine Derivatives: Sublimation Rate, Activation Energy, Mass Transfer Coefficients and Phenomenological Models.

Caffeine and theophylline are compounds with important applications in the pharmaceutical industry and other fields of the chemical industry. These purine derivatives have simple chemical structures, therefore, the evaluation of their sublimation process contributes to the development of mass transfer analysis methods that can later be applied to other compounds with more complex structures. With the help of thermogravimetric analysis in isothermal conditions, the kinetic study of the sublimation of caffeine and theophylline, along with the evaluation of kinetic parameters (activation energy and the pre-exponential factor), was carried out. Global mass transfer coefficients were determined, which vary for caffeine between 53 × 10−8 and 631 × 10−8 mol/s·m2·Pa, and for theophylline between 68 × 10−8 and 441 × 10−8 mol/s·m2·Pa. The dimensionless equations of the form: have been proposed, which allow the determination of individual mass transfer coefficients at temperatures between 130 and 160 °C for caffeine and between 170 and 200 °C for theophylline.

Extractive desulfurization using ethylene glycol and glycerol-based deep eutectic solvents: engineering aspects and intensification using ultrasound

In the present study, three deep eutectic solvents (DESs), namely TBAB:2EG, TPAB:3EG, and TPAB:2G, were synthesized by using hydrogen-bond acceptors (HBAs) (tetrabutylammonium bromide (TBAB), tetrapropylammonium bromide (TPAB)), and hydrogen-bond donors (HBDs) (ethylene glycol (EG), glycerol (G)). These DESs formed eutectic points at HBA:HBD molar ratios of 1:2, 1:3, and 1:2, respectively. The prepared DESs were analyzed by FTIR, and their structures were confirmed through 1H-NMR. The performance of the prepared DES was evaluated in terms of distribution coefficient, selectivity, performance index, and capacity of solvents for extractive desulfurization. Maximum extraction efficiencies of 81%, 77%, and 72% were obtained with TBAB:2EG, TPAB:3EG, and TPAB:2G, respectively, with optimized parameters but without the use of ultrasound. The extractive desulfurization was intensified using ultrasound that enhanced the mass transfer between the two phases. Individual and overall mass transfer coefficients in the fuel and solvent phases with and without ultrasound have been determined. The intensified extraction indicates the positive effect of the US on the DBT extraction by DES. The decrease in efficiency due to prolonged use of the DES was regained after regeneration. The thermodynamic parameters of the sulfur extraction process have also been calculated.

Mass transfer characteristics of a continuously operated hollow-fiber membrane contactor and stripper unit for CO2 capture

Mass transfer performance of a polypropylene hollow-fiber membrane contactor as part of a continuously operated CO2 capture unit with amino acid salt (potassium glycinate) absorbent and vacuum solvent regeneration was studied. The effects of key operating parameters on the absorption mass transfer characteristics were explored. Without vacuum stripping, absorption rate was found to be limited by low CO2 desorption efficiency from the loaded absorbent solution in the stripping unit, resulting in high solvent CO2 loadings and limited chemical absorption rates. Introduction of vacuum stripping greatly improved desorption performance, resulting in improved steady-state absorption performance. The overall mass transfer coefficient increased at higher stripping temperatures and lower vacuum pressures in the range of 60−80 °C and 300−800 mbar (abs). The overall mass transfer coefficient increased with increasing liquid flow rate, and the highest value reached was 1.8 ∙ 10−4 m s-1. The individual mass transfer coefficients in absorption were calculated based on mass transfer correlations and experimental data, including estimation of the enhancement factor for chemical absorption. The overall mass transfer resistance was found to be dominated by the liquid-side resistance, at almost 90 % of the total resistance. The estimated membrane mass transfer coefficient was low compared to a theoretical value assuming non-wetted operation, suggesting potential partial wetting of the membrane. Stable performance of the unit and the membrane contactor was demonstrated during a stability test with over 30 h of operation.

Mass and heat transfer from the surface of a gas sparged pool of liquid to an immiscible liquid under swirl flow and potential applications

Rates of mass and heat transfer (by analogy) between a gas sparged mercury pool and a swirling aqueous solution were studied by the electrochemical technique. Variables studied were superficial gas velocity, physical properties of the solution, and swirl flow velocity. The data were correlated by the equation:Sh=0.011Sc0.33Reg0.31Ren0.23The overall mass transfer coefficient due to the combined gas sparging and swirl flow k can be calculated in terms of the individual gas sparging mass transfer coefficient kg and swirl flow mass transfer coefficient ks from the equation:k=[kg3+ks3]0.33Application of the present results in the recovery of heat from low melting point liquid metal pools [such as mercury, gallium, indium and tin] in the production stage by direct cooling with water or high boiling point liquids was pointed out. Implication of the present results for the rational design of high space–time yield batch recycle electrochemical reactor with a mercury pool cathode suitable for conducting diffusion controlled electroorganic synthesis was highlighted.Liquid–liquid extraction processes involving surface active organic solutes which form stable emulsions between the dispersed phase and the continuous phase can be benefited from the present results in the design of a high productivity extractor.

Analogy of absorption and distillation processes. Wetted-wall column study

This article is the second one from a pair focusing on the mass transfer fundaments and the analogy between the processes of absorption and distillation. The wetted wall column, a device with known interfacial area, was built for this purpose enabling evaluation of the mass-transfer coefficients instead of the volumetric mass-transfer coefficients usually provided by experiments in the packed columns. The analogy of the processes has been assessed by comparison of the mass-transfer characteristics (HETP, individual mass-transfer coefficients kL and kG) evaluated on the basis of the absorption experiments with those found under the distillation conditions. In the prior paper the results of the absorption experiments performed under distillation-like conditions have been published in the form of dimensionless correlations ShL=0.33ReL−0.12ScL0.47 and ShG=0.012ReLG0.90ScG0.61.In this paper we present results of the distillation experiments in the form of the HETP data and mass-transfer coefficients evaluated by the profile method. The experimental data are compared with those predicted on the basis of the absorption experiments results. The experimental HETP data acquired on the methanol-n-propanol and ethanol-n-propanol systems agree within 10–20% with the data predicted. The distillation mass-transfer coefficients evaluated by the profile method were correlated in the dimensionless form ShL=0.25ReL−0.12ScL0.47 and ShG=2.3⋅10−3ReLG1.07ScG0.61. The distillation kL values have been found to be 24% lower and the kG values 13% lower than the ones predicted according to absorption correlations. The gas-phase mass-transfer coefficient, kG, exhibits higher dependence on the vapor velocity than it was found in standard absorption measurements. Similar difference was found also for packed columns in previous works. Apparently, there is at least one unaccounted phenomenon which affects differently the mass-transfer performance of absorption and distillation packed columns. Poor results of the present diffusion models have been noticed in this work preventing deeper study of these differences. Improvement of these models is found to be inevitable for the further research in this area as well as for the reliable rate-based modeling of the industrial absorption and distillation columns.

CO2 absorption into N-methyldiethanolamine aqueous-organic solvents

The present work studied the CO2 absorption into N-methyldiethanolamine hybrid (chemical and physical) solutions, using pure water, pure methanol and water+methanol mixtures as solvents. The variables considered were amine concentration (0%, 5%, 15% and 30% in mass), methanol ratio in the solvent according to molar fractions (0, 0.4, 0.7 and 1) and temperature (283.15, 293.15, 303.15 and 313.15K). Experiments were carried out at atmospheric pressure in a batch-operated stirred reactor, and the direct measurement of the CO2 absorbed was performed in a calibrated bubble meter.The absorbed CO2 per unit area, Q (kmolm−2), and CO2 flow density, NA (kmolm−2s−1), were determined for each experimental series. The ratio between the CO2 flow density in MDEA aqueous solutions, Nw, and the value in aqueous organic solutions, Nw+m, was also analyzed. Individual mass transfer coefficients in the liquid phase, kL (ms−1), were determined from physical absorption experiments, as well as data on the CO2 solubility. Both CO2 diffusivity, DCO2 (m2s−1), and N-methyldiethanolamine, D0MDEA (m2s−1), diffusivity values in the liquid phase were also provided.The CO2 absorption experiments were significantly influenced by the effect of temperature, amine concentration and water/methanol ratio. The performance of CO2 absorption into aqueous MDEA solutions was compared to that into hybrid MDEA solutions. It was concluded that MDEA aqueous solutions demonstrated lower performance than amine solutions using pure methanol or water–methanol mixtures as solvents, even at high temperatures and amine concentrations. Results showed that at high temperatures, amine concentration and chemical absorption had no relevant influence on the process. The methanol effect was noticed to improve the diffusivity and solubility in the process, by means of physical absorption.

OpenFOAM Computational Fluid Dynamic Simulations of Two-Phase Flow and Mass Transfer in an Advanced-Flow Reactor

Advanced-flow reactor (AFR) technology is an alternative to scale-up continuous flow chemistries from micro to milli scales, while retaining mass and heat transfer performance. Here we conduct two-phase computational fluid dynamic (CFD) simulations using the open source software OpenFOAM in order to predict hydrodynamic parameters in the AFR for different operating conditions. After modification and validation of the interFoam solver based on the volume-of-fluid method to account for mass transfer across immiscible interfaces, it is applied to the AFR to predict specific interfacial areas (a) and individual mass transfer coefficients (kL) to yield overall mass transfer coefficients (kLa). The results are in good agreement with semiempirical values and the surface renewal theory of Danckwerts, except at the largest flow rates for which numerical coalescence is observed. A study of the influence of fluid properties yields the following conclusions. The contact angle is the variable that affects the flow pat...

Reactive mass transfer in a membrane-based microcontactor

The extraction kinetics of Zn(II) from sulfate solutions with di-(2-ethylhexyl) phosphoric acid (D2EHPA) in isododecane was studied in a flat-sheet, membrane-based microcontactor. The potential of process intensification due to microstructured length scales, a dispersion-free contacting, laminar flow and the constant interfacial area allow a detailed view in reactive extraction kinetics, where the rate-determining step can be diffusion- or reaction-limited (or both in a mixed regime). The individual mass transfer coefficients can be manipulated by the experimental conditions, consequently, the chemical reaction resistance is negligible at high pH and high extractant concentrations and the extraction process is mainly governed by aqueous boundary layer resistance (>95%). Therefore, the developed diffusion model accounts for the overall mass transfer coefficient. In the next step, the reaction resistance is quantified at lower pH. The relative reaction resistance reaches up to 78% at pH 1.33.

Assessment of mass transfer correlations in rate-based modeling of a large-scale CO2 capture with MEA

A Rate-based simulation model was utilized for assessing the effect of correlations for mass transfer coefficients (kg, k1) and effective interfacial area (ae) on the performance of absorber for large-scale CO2 capture from a gas-fired power plant with a chemical solvent. The mass transfer and interfacial area correlations available in the literature are applied in the RateSep model to demonstrate the uncertainty associated with using these correlations in a large-scale CO2 capture plant. Selecting the best correlations for such a CO2 capture process is outside the scope of this work due to a lack of large-scale data for model validation. The absorption performance is expressed in terms of pressure drop per height of packing, gas and liquid phase temperature and concentration profiles, enhancement factor and necessary packing height. Variations in individual mass transfer coefficients, effective interfacial area, and overall mass transfer coefficient are also shown. The study showed that there is substantial uncertainty associated with applying the proposed correlations for determining the required absorber height. The variation in results, given as packing height needed for 90% CO2 removal, was very high, ranging from 6 to 24m. These are clearly too large discrepancies to be acceptable. The reason can, at least partly, be explained by the relationship between transport parameters, kinetics, mass transfer coefficients and effective interfacial area. Most packing mass transfer correlations available in the literature were developed and tested for specific packing types, specific chemical systems and mainly for distillation where the resistance lies mostly in the vapor phase. The best way to judge the correctness of these correlations for application in a large-scale CO2 capture processes with chemical solvents is to see how well the correlations predict reality, and validating the correlation's performance with pilot, or full scale data from CO2 capture with the same chemical solvent.

Effects of baffles on separation of aqueous ethanol solution with hollow fibers

The effects of baffles on the operation and mass-transfer characteristics in novel hollow fiber membrane contactor used in distillation were investigated. Hollow fiber membranes, coated with a 7 μm polydimethyl-siloxane, were operated as structural packing in the separation of ethanol-water solutions. The parallel flow mode was chosen for separation due to the stronger driving force of the concentration difference, in which liquid flows through the lumens of the fibers and vapor flows countercurrent-wise outside the fibers. Two baffles were installed on the shell side of the membrane contactors to enhance separation, which had a round shape with a semi-lunar hole. The results show that both baffled and unbaffled membrane contactors gave better, more productive separations than traditional packing in distillation, such as the excellent Sulzer Gauze BX structured packing. The baffled membrane contactors performed better than unbaffled ones, especially at high vapor velocities. The minimal HTU of membrane contactor with baffles could reach as low as 4.5 cm, and almost all the contactors could work well above the limit where flooding normally occurs in conventional cases. Theoretical analysis predicted that baffles helped membrane module to obtain a higher masstransfer coefficient and a smaller mass-transfer resistance. Finally, theoretical mass-transfer coefficient and experimental value were compared as well as the contribution of each individual mass-transfer coefficients among liquid, gas and membrane.

Scrubbing of CO2 Greenhouse Gases, Accompanied by Precipitation in a Continuous Bubble-Column Scrubber

A continuous bubble-column scrubber that absorbs carbon dioxide (CO2) gas using an alkaline solution under a pH-stat condition was used to explore the effects of the pH of the solution, gas concentration, gas-superficial velocity, and liquid-flow rate on the absorption rate and volumetric mass-transfer coefficient of CO2. When the scrubbing factor was evaluated, this scrubber outperformed other scrubbers. Correlations of local volumetric mass-transfer coefficients with process variables are presented here and the gas−liquid interfacial area and individual mass-transfer coefficient are discussed to provide insight into the mass-transfer mechanism. Investigation of the liquid-side mass transfer coefficient revealed that the kL/[OH−]0.5 value was a constant, thus demonstrating that the system obeyed second-order kinetics. Evidence also shows that liquid-side resistances are within the range of 27%−99%, indicating that gas-side mass-transfer resistance cannot be neglected in some cases. This implies that the absorption mechanism is flexible and can be shifted by adjusting the process parameters.

Model Assessment for the Prediction of Mass Transfer Coefficients in Liquid‐Liquid Extraction Columns

AbstractA large number of theories are reported in the literature for the calculation of individual mass transfer coefficients and each has a well defined application range, which depends on the nature of the continuous and the dispersed phases. Each theory is also based on a different transfer mode, e.g., the dispersed phase depends essentially on the drop behavior, which is directly related to the drop size. However, an accurate determination of the overall mass transfer coefficient depends upon the choice of the combination of theories to be used for the calculation of the individual mass transfer coefficients, i.e., for the continuous and dispersed phases. In the present work, different combinations for the calculation of the overall mass transfer coefficient have been tested for the commonly recommended Acetone/Toluene/Water system, which is characterized by relatively large drop sizes.

Prediction of the concentration polarization in the nanofiltration/reverse osmosis of dilute multi-ionic solutions

The aim of this work was to develop a simple and accurate model for predicting the concentration polarization index in the nanofiltration (NF)/reverse osmosis (RO) of dilute multi-ionic solutions. On the grounds of this model, the total flux of the ion i at the feed-solution/membrane interface consists of the sum of the diffusion, convection and migration fluxes, the former of which is determined by conventional mass-transfer correlations duly corrected to take into account the permeation through the membrane (suction effect). The coupling of the ionic fluxes is enforced by the electroneutrality requirement at the feed-solution/membrane interface. The model developed dispenses with the arbitrary assumption of the thickness of a film layer in the vicinity of the membrane surface. Assessing the accuracy/validity of this model with multi-ionic solutions would be rather harsh, thus the model accuracy and ranges of validity were ascertained for a benchmark case: NF/RO of single salt solutions. The model predicts approximate concentration polarization indexes of the salts A +B −, A + 2B 2− and A + 3B 3− (or A 2B − 2 and A 3+B − 3) with positive deviations lower than 10% with respect to the benchmark concentration polarization index, for ions diffusivities ratios, D 1/ D 2 (or D 2/ D 1), in the range 0.16–5.5 and ϕ ≡ J v / k c < 3 , where J v is the permeation flux and k c is the mass-transfer coefficient of the salt for vanishing mass-transfer rates at impermeable walls. The main assumption of the model – the individual mass-transfer coefficients of the ions are independent of each other – appears to hold in a broad range of conditions, for single salt solutions. The model developed was expeditely applied to predict the concentration polarization in the nanofiltration of solutions containing Na +, Cl − and a dye 3− (experimental data of Bowen and Mohammad [AIChE J. 44 (8) (1998) 1799–1812]), and its predictions are in fair agreement with the predictions of the extended Nernst–Planck equations in the film layer of the “slowest” ion.

Mass Transfer Modeling with and Without Evaporation for Iodine Chemistry in the Case of a Severe Accident

Iodine is a fission product of major importance in a severe reactor accident because volatile species exist under reactor containment conditions. Radiolytic oxidation of iodide ions is an important source of volatile iodine species. The SISYPHE tests provide an experimental database of prime importance for the study of the mass transfer between the sump and the atmosphere of a containment building under natural convection and in an evaporating flow regime. This phenomenon greatly impacts the airborne iodine concentrations. The two main effects of evaporating conditions are to increase the kinetics of transfer from the liquid to the gaseous phase and to change the steady-state iodine concentrations. The well-known two-film model has been modified to extend to these types of conditions. The agreement between the experimental results and modeling is satisfactory. However, when applied to typical reactor conditions, the impact of this improved modeling on gaseous iodine concentration is not as strong as other phenomena; for example, uncertainties remain concerning organic iodide production mechanisms. Correlations enabling the calculation of individual mass transfer coefficients for the liquid and the gas phases are proposed. The values resulting from these correlations agree well with those obtained from the test interpretations.

Mass transfer in extractive ultrafiltration of α-phenylglycine with TOMACl in a hollow fiber contactor

Extractive ultrafiltration of α-phenylglycine from sodium hydroxide solutions with the ion-exchange extractant trialkylmethylammonium chloride (TOMACl) dissolved in toluene using a microporous polypropylene hollow fiber contactor has been studied. The effect of the hydrodynamic conditions on the mass-transfer rates was determined. The overall mass-transfer coefficients were calculated by two different methods, i.e. assuming a constant distribution coefficient and using an equilibrium model. Individual mass-transfer coefficients were estimated by two alternative methods: Wilson-plot two-step calculation, and a more accurate one-step calculation. It is shown that a correct equilibrium model is required for the estimation of the mass-transfer coefficients. The influence of feed concentration, flow pattern and the composition of the stripping solution on the extractive ultrafiltration performance is also reported.

Water and solute transport in pervaporation hydrophilic membranes to reclaim contaminated water for micro-irrigation

The suitability of a homogeneous hydrophilic dense membrane for reusing brackish and/or contaminated waters was investigated. Its performance was evaluated in terms of water permeate flux and membrane enrichment factors using borate, selenate, sodium chloride and glucose as model contaminants. A series of experiments were conducted using a sweeping air pervaporation unit to examine the effects of membrane configuration (hollow fiber membranes (HFM) and corrugated sheet membranes (CSM)), sweeping air velocity, feed temperature, pressure and contaminant concentration. The collected data were then modelled to determine the individual mass transfer coefficients. The results showed that water fluxes ranged from 2.9 to 4.4 and 2.0 to 3.7 kg/(m 2 day) for HFM and CSM, respectively. Air velocity and feed pressure were identified as the controlling factors for water flux. In all the cases, the average enrichment factors for glucose, selenate, borate and sodium chloride were 0.18, 0.08, 0.20 and 0.23, respectively. Thus, it was concluded that this membrane has the promise to provide an innovative treatment alternative for reusing brackish groundwater and residential wastewater in agriculture micro-irrigation.

Dense gas extraction using a hollow fiber membrane contactor: experimental results versus model predictions

Hollow fiber membrane contactors offer a number of advantages over dispersed phase contactors for mass transfer operations such as extraction of aqueous feeds. In addition, dense gases provide benefits that traditional extraction solvents do not. A mathematical model of a membrane contactor was developed that predicts the steady state fluid velocities and solute concentrations by solving the applicable conservation equations. The gravitational force term was included because the low kinematic viscosity of dense gases can render buoyancy-induced flow significant. A method of calculating the individual and overall mass transfer coefficients from the model results is also presented. The model was validated by comparing predicted Sherwood versus Graetz numbers for tube flow to those obtained from the classical equations that have been repeatedly confirmed by experiment. The three boundary conditions examined were constant wall concentration, constant flux, and linear variation of wall concentration with length. For all three cases the model predictions were in close agreement with those of the classical equations over a wide range of Graetz numbers, except for the constant flux condition at Graetz numbers greater than about 1000. This exception reflects a limit on the mass transfer rate imposed by the constant flux boundary condition. Graetz numbers greater than 1000 (found with short tubes or very high velocities) are not usually encountered in practical applications. Model results are compared to experimental data for the extraction of isopropanol or acetone from water into dense CO 2, obtained over a range of flow rates using modules of different packing densities. Overall the model predicted the data reasonably well, proving the model to be a useful tool for evaluating potential new applications of the technology. For the isopropanol extractions the average absolute errors in the predicted mass transfer coefficients and yields were 29% and 31%, respectively, while for the acetone work the average absolute errors were 39% and 11%. In both cases the predicted mass transfer coefficients were lower than the observed values at the highest aqueous flow rates studied; usually the error became less negative (then increasingly positive in some instances) with decreasing flow rate. This trend is partly attributable to flow maldistribution (leading to reduced efficiency) caused by unavoidable non-uniform fiber spacing and variation in fiber diameter. Other possible sources of modeling error are discussed as well. With acetone, most of the resistance to mass transfer was in the aqueous phase boundary layer, as expected for a solute with a relatively high partition coefficient ( m A). On the other hand, for isopropanol (a lower m A compound) a greater portion of the resistance was attributable to the solvent-filled pore and the solvent phase boundary layer, although the aqueous resistance was still significant. Mass transfer coefficients and yields were higher for acetone than for isopropanol, and aqueous boundary layer penetration was more rapid; both results were a consequence of the higher m A of acetone. For both solutes, usually the mass transfer coefficient increased with increasing aqueous phase Graetz number, as expected when the aqueous phase mass transfer resistance is important. Moreover, yield generally increased with increasing solvent/feed ratio as anticipated.

Cyanide removal from industrial wastewaters using gas membranes

Results are presented for the removal of cyanide from four industrial wastewaters using hollow fiber gas membranes in a pilot plant. The plant was operated in batch mode using 1000 L of feed solution. The plant contained 10 hollow fiber modules with total membrane surface area of 180 m 2. The strip stream consisted of 10% NaOH. The overall mass transfer coefficient for cyanide has been determined experimentally and found to agree well with predictions using empirical correlations. Both the feed and membrane mass transfer coefficients contribute to the overall mass transfer coefficient. The strip side mass transfer coefficient may be ignored. Real wastewaters often contain other volatile species. These volatile species will also transfer to the strip solution. If the volatile species does not react with the strip stream, all three individual mass transfer coefficients contribute to the overall mass transfer coefficient. Good agreement between the experientially determined overall mass transfer coefficient and the predicted values is obtained for other volatile species. The osmolarity of a wastewater may be different to that of the strip solution. Consequently, water vapor transport due to osmotic distillation will occur from the lower to higher osmolarity solution. The effects of osmotic distillation should be considered when sizing the feed and strip tanks.

Liquid-Side Mass-Transfer Resistance of Structured Packings

Stripping of oxygen from water using air was performed in four different structured packings. Because the transfer of oxygen to air is easy, the resistance to mass transfer lies on the liquid side. From these experiments, the measured global volumetric mass-transfer coefficient (KLae) is equal to the individual mass-transfer coefficient of the liquid phase (kLae). The value of the interfacial area ae is estimated using a model proposed in 1992, and the individual mass-transfer coefficient of the liquid is deduced and compared to one based on the penetration theory used in the first model proposed for structured packing in distillation columns published in 1985. It was found that the correction factor CE used to equate both coefficients is close to unity.

Modeling of mass transfer characteristics of bubble column reactor with surfactant present.

Danckwert's method was used to determine the specific interfacial area, a, and the individual mass transfer coefficient, k(L), during absorption of CO(2) in a bubble column with an anionic surfactant in the carbonate-bicarbonate buffer solution and NaAsO(2) as catalyst, the presence of which decreases the specific interfacial area and the individual mass transfer coefficient. The specific interfacial area and the individual mass transfer coefficient increase with increasing superficial gas velocity. The specific interfacial area decreases whereas the individual mass transfer coefficient increases with increasing temperature. The results of experiments were used to determine the dependence of a, k(L), and k(L)a on the surface tension, the temperature of the absorption phase, and the superficial velocity of the gas. The calculated results from the correlation were found to be within 10% deviation from the actual experimental results.