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Sequential Slope and Intercept Method for Estimation of Gas Absorption and Diffusion Coefficients in Binary Gas–Liquid Systems
Abstract
A novel geometric method based on a sequential slope-intercept approach is derived for estimation of concentration dependent diffusion, gas absorption and gas dissolution concentration in gas-liquid binary systems. The gas absorption and diffusion are modeled using an inverse free boundary problem governed by Fick's second law of diffusion and Henry's absorption law. An unknown gas-liquid interface is governed by the Stefan's type boundary condition. Implementation of the estimation method involves piecewise linear approximation of the transformed concentration data and sequential application of the estimated slopes and intercepts from this approximation. Application and validation of the developed estimation method is given for synthetic concentration profiles, and for real concentration measurements for a dimethyl ether-bitumen binary system obtained using computer tomography. The developed estimation method overcomes the existing estimation methods derived based on polynomial approximations that significantly underestimate or overestimate the diffusion coefficients at very low dissolved gas concentrations.
The overall objective of this study was to perform a series of diffusion experiments between liquid hydrocarbons (e.g., propane, pentane, and toluene) and bitumen or heavy oil to observe and analyze mass transfer in the systems. Some difficulties, such as the complex behavior of the phases, the high viscosity, and the opacity of hydrocarbons, generate the need for different techniques to measure mass transfer coefficients in heavy crude oils. In this work, X-ray tomography was used for such measurements. The measurements are carried out in environments where the sedimentation of solids is encouraged. To achieve this, a novel setup was designed and assembled to measure the mass transfer in these systems based on the density profiles established over time in aluminum containers that contain fluids. The containers were regularly scanned to track the behavior of the density profiles over time. The data was collected and analyzed, obtaining interesting results, which will be important as a starting point for future research related to systems that integrate interactions between solvents and oils in the recovery processes. Due to the novel results obtained in the original test, 7 sets of experiments were carried out, all with unique characteristics, trying to analyze its results in detail.
One of the objectives is to analyze if the mass transfer is uniform and constant during long periods. This work shows results that were never published in the previous literature, such as partial miscibility when mixing n-propane and bitumen, oil swelling, oil shrinking, asphaltene precipitation and sedimentation, total miscibility, and the effect of adding pure asphaltenes and calcium carbonate to the mixture, among others. In addition, the impacts on the effectiveness of the proposed processes for the production and refining of these solvents are discussed.
A reliable and accurately estimated value of molecular diffusion coefficient is an essential input for modeling and performance prediction of solvent-aided recovery processes of heavy oil and bitumen reserves. Despite the importance of this crucial parameter, there is no method that is universally acceptable for its measurement, particularly for systems of low soluble gaseous solvents and bitumen. In this article, various experimental techniques developed for estimating the diffusivity of gaseous solvents in bitumen systems are critically reviewed, highlighting their strengths and weaknesses. The methodologies are divided into various categories, depending on their technique, test operating conditions, and the adopted technology. Despite the extensive research in the area of diffusivity estimation, further studies are required for developing more feasible, efficient, and reliable approaches.
Unit operations and processes abound with gas diffusion in liquids, which is a sophisticated phenomenon in which mass transfer is characterized by diffusion coefficient or diffusivity. Compared to diffusion in gas phase, the closely packed liquid molecules strongly influence diffusive mass transfer to the extent that it is impossible to have a general theory for a reasonably accurate estimation of diffusivity in liquids. This situation is further compounded by the fact that diffusivity cannot be measured directly but can only be estimated indirectly with the help of a number of observable properties (eg, mass, volume, pressure, etc). This fact gives rise to a myriad of experimental methods for the determination of gas diffusivity in liquids. These methods report gas diffusivities over widely varying ranges of temperature, pressure, and liquid composition. To provide a state‐of‐the‐art knowledge base for such methods is the objective of this work. The focus is on gas diffusion in binary gas‐liquid systems. Starting with necessary theoretical foundations, we provide a systematic categorization of these methods based on the property change utilized for diffusivity determination. The methods are then concisely described, and the diffusivity data are summarized for over 160 gas‐liquid systems at different temperature and pressure conditions. Empirical correlations are provided for different gas‐liquid systems, which could be used for interpolating gas diffusivity as a function of temperature, pressure, and composition.
Solvent based recovery processes have gained some advantage over thermal recovery processes under specific reservoir conditions. Solvent-bitumen mass transfer is a diffusion dominated process. The calculation of diffusion coefficients is fundamental for the design of solvent-based recovery processes as it allows to understand the performance of the process. In a recent work, Babak et al.¹ developed a new slopes and intercept method which was demonstrated to be very robust for the calculation of diffusion coefficients of binary systems. In this paper, the diffusion coefficients of dimethyl ether (DME), pentane and toluene into two different bitumen systems are calculated using this method as a function of concentration. X-ray Computed Tomography (CT) is used to obtain the concentration profiles of the bitumen-solvent systems. Furthermore, a new modification of Vignes’ equation is introduced to predict concentration dependant diffusion coefficients. This new modification includes the acceleration and deceleration parameter associated to the solvent and bitumen mass transfer behaviour. The developed equation successfully predicts the diffusion coefficients of the studied systems.
The effect of CO2 absorption on the aromaticity and hydrogen bonding in ionic liquids was investigated. Five different ionic liquids with choline based cations and aprotic N-heterocyclic anions were synthesized. Purity and structures of the synthesized ionic liquids were characterized by 1H and 13C NMR spectroscopy. CO2 capture performance was studied at 20°C and 40°C temperatures under three different pressures (1, 3, 6 bar). The IL [N1,1,6,2OH][4-Triz] showed highest CO2 capture capacity (28.6 wt.%, 1.57 mol of CO2/mol of IL, 6.48 mol of CO2 per kg of the ionic liquid) at 20 °C temperature and 1 bar pressure. The high CO2 capture capacity of the [N1,1,6,2OH][4-Triz] IL is due to the formation of carbonic acid (-OCO2H) together with carbamate by participation of –OH group of the [N1,1,6,2OH]+ cation during CO2 capture process. The adduct structure of CO2 reaction with the IL [N1,1,6,2OH][4-Triz] was probed by using IR, 13C NMR and 1H-13C HMBC NMR experiments utilizing 13C labeled CO2 gas. 1H and 13C PFG NMR studies were performed before and after CO2 absorption to explore the effect of cation-anion structures on the microscopic ion dynamics in the ILs. The ionic mobility was significantly increased after CO2 reaction due to lowering of aromaticity in the case of ILs with aromatic N-heterocyclic anions.
Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement by neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells (≃330 g.L⁻¹) corresponds to an optimum for oxygen transport for individuals under strong activity.
Flooding carbon dioxide into oil reservoirs is a promising technique for improving the pressure of a reservoir when it is depleted through primary and secondary production. In the context of global warming, it is a viable method for geological storage of CO2 emissions. Once CO2 is injected into a reservoir, it is forced to come into partial contact with formation water. To estimate the rate of CO2 transfer and the total amount of CO2 dissolved in the formation water, correct estimation of CO2 diffusivity is required. In this study, the rate of CO2 diffusion in water was experimentally determined in a PVT cell using the pressure depletion method at reservoir conditions (temperature: 50–75 °C and pressure: 17,450 kPa). As expected, the rate of CO2 diffusion in water increases with increasing temperatures. In addition, the impact of salinity of the water on the rate of CO2 diffusion was investigated. A significant decrease in the rate of CO2 diffusion was found with increasing salinity. Subsequently, a diffusion model describing the experiments was developed to predict the behavior of CO2 diffusivity under simulated conditions. Unique correlations between CO2 diffusion coefficients and water at different temperatures and salinities were obtained using the results of modeling.
We establish conditions for the existence and uniqueness of a smooth solution to the inverse problem for a two-dimensional diffusion equation with unknown time-dependent leading coefficient in a domain with free-boundary. The equation of unknown boundary is given in the form of the product of a known function of space variables and an unknown time-dependent function.
We consider an inverse problem for a one-dimensional parabolic equation with unknown time-dependent major coefficient in a domain whose unknown boundary weakly degenerates at the initial time moment. The conditions for existence and uniqueness of the classical solution of the problem are established.
Molecular diffusion has been considered to be an underlying mechanism for many of oil recovery processes like miscible and immiscible gas injection projects. Reliable estimation of the molecular diffusion coefficient as a transport property is therefore important in studying the performance of such systems. Interpretation of pressure-decay data has been traditionally used to estimate the molecular diffusion coefficient and usually to simplify the interpretation, its concentration dependency has been neglected. A pressure-decay model with concentration-dependent diffusion coefficient leads to a non-linear problem in which an analytical solution is difficult if not impossible to obtain. In this study, we used the Heat Integral Method (HIM) to solve the non-linear diffusion problem as a forward model. Using that forward model, we have developed a simple methodology for estimating the diffusion coefficient regardless of the form of function used for the concentration dependency of the molecular diffusion. Three different forms of functions for diffusion coefficient were considered. In its simplest form, the diffusion coefficient is set to be a constant value. In the two other forms, the diffusion coefficient was evaluated as a concentration-dependent two parameter equation using exponential and power-law functions, respectively. The proposed methodology is verified and tested using direct numerical solutions of the non-linear diffusion problem. Many numerical examples with a wide range of input parameters demonstrate the effectiveness of the proposed approach.
We establish conditions for the existence and uniqueness of a solution of the inverse problem for a one-dimensional heat equation with unknown time-dependent leading coefficient in the case where a part of the boundary of the domain is unknown.
To determine the diffusion coefficient of a gas in a liquid the usual procedure is to expose the liquid interface for a period of time, measure the amount of gas absorption, and from this infer the diffusion coefficient. The usual assumption to make at the liquid–gas interface is that equilibrium is established immediately upon exposure of the liquid to the gas. This assumption has led to the illogical consequence of the inferred diffusion coefficient depending upon the period of time for which the liquid interface is exposed to the gas. We use the Einstein expression for the probability of a transition in a system to derive an expression for the rate of gas absorption. When this derived rate is used to infer the diffusion coefficient, the same value is found from experimental techniques with extreme values of the exposure time. The accuracy of the predicted gas absorption rate supports the view that the Einstein relation is not limited to predicting fluctuations about an equilibrium state.
Semiparametric regression is concerned with the flexible incorporation of non-linear functional relationships in regression analyses. Any application area that benefits from regression analysis can also benefit from semiparametric regression. Assuming only a basic familiarity with ordinary parametric regression, this user-friendly book explains the techniques and benefits of semiparametric regression in a concise and modular fashion. The authors make liberal use of graphics and examples plus case studies taken from environmental, financial, and other applications. They include practical advice on implementation and pointers to relevant software. The 2003 book is suitable as a textbook for students with little background in regression as well as a reference book for statistically oriented scientists such as biostatisticians, econometricians, quantitative social scientists, epidemiologists, with a good working knowledge of regression and the desire to begin using more flexible semiparametric models. Even experts on semiparametric regression should find something new here.
The multifaceted process of gas absorption and diffusion of dissolved gases has several useful applications in engineering, medicine, pharmaceutics and science. A new systematic study for modeling of this process using an inverse problem for concentration dependent diffusion with free boundary at the gas-liquid interface is presented in this work. The study includes the model derivation based on the Fick's first law of diffusion, the Henry's absorption law, the Stefan's principles of free boundary problems, and the development of new techniques for estimation of concentration dependent diffusion coefficient and the gas absorption coefficient governing propagation of gas-liquid interface due to absorption. The developed estimation technique utilized the dissolved gas concentration profiles measured and different time moments and is applied to real x-ray CT measurement data for a binary gas liquid mixture containing dimethyl ether and bitumen.
Carbon dioxide (CO2) cryogenic desublimation separation has become an emerging carbon capture method in recent years due to its advantages of a contamination-free process and compactness. So far, there have been few research works on revealing the detailed desublimation characteristics of CO2 associated with the flow as well as mass and energy conservation in the practical cryogenic CO2 capture process. In this study, a transient model for analyzing the CO2 cryogenic desublimating in mixture gas is proposed. The model contains a tube-in-tube counter-flow heat exchanger including three control volumes, the nitrogen (or helium) coolant, the wall with the solid CO2 layer and the mixture. The deposition distribution, capture rate and energy consumption of the dynamic desublimation process under different operation conditions are investigated. The model is verified by some experiment results. Results show that an improved modeling accuracy is obtained by taking the solid CO2 layer into consideration. During the dynamic desublimation process, the deposition rate is the highest near the inlet of gas mixture due to the high mass diffusion there, and a low energy consumption will be obtained at high concentration and low flow velocity of CO2 supply. The theoretical method here provides better understanding of the CO2 desublimation features in annular tube, which will be helpful for conducting an efficient CO2 capture process.
A new geometrical method for diffusion estimation in binary liquids is derived and validated. It incorporates the slope and intercept approach into the integral representation for diffusion. The method significantly improves the existing slope and intercept methods for estimation of the concentration dependent diffusion coefficients. It produces much more accurate diffusion estimations for non-constant diffusion. The slope and intercepts are calculated using the derivative approximation for deterministic concentration data, or the spline linear regression for measurement data containing noise. The verification of the proposed method is performed either by comparing estimated and known diffusion coefficients, or measured and calculated concentration profiles. The sensitivity analysis conducted with respect to the Matano interface position showed that for incorrect Matano interface values the diffusion are significantly overestimated or underestimated. The proposed iterative slope and intercept (ISI) method is applied for the toluene-bitumen binary liquid system with concentration profiles obtained using X-ray Computer Assisted Tomography.
The diffusion coefficient (D) of gases in heavy oils is an important mass transfer parameter to model and design gas injection processes for oil recovery. The pressure-decay technique (PDT) is one of the widely used experimental methods available to infer this coefficient. PDT records the declining gas phase pressure resulting from the diffusion of gas into heavy oil inside a pressure/volume/temperature (PVT) cell. Commonly, the gas phase pressure decay is modelled by use of Fick's second law along with gas-phase mass balance equations and assuming a constant diffusion coefficient. In this work, we evaluate two concentration-dependent diffusion coefficient functions, power-law and exponential. A simple history matching technique is used to estimate the apparent diffusion coefficient (Do) and concentration dependency factor (ma) from pressure-decay data. Extensive application of our method to experimental pressure-decay tests shows that in addition to constant diffusion coefficients, both power-law and exponential functions are capable of predicting the experimental data. This implies that other experimental techniques are required to extract the functionality of diffusion coefficients with gas concentrations in heavy oil. This article is protected by copyright. All rights reserved
The pressure-decay technique is used to determine the diffusivity and solubility of methane and carbon dioxide in pure hydrocarbons and bitumen at temperatures of 0, 15, 20 and 25 °C and pressure of 3.5 MPa. An analytical-graphical technique is implemented to extract the related mass-transfer parameters, i.e., diffusion coefficient and Henry’s constant, from the pressure-decay data. The results reveal that the diffusion coefficient of methane and carbon dioxide in both, pure hydrocarbons and bitumen, decreases as the temperature decreases. On the basis of the estimated Henry’s constants, the effect of the temperature on the solubility of the gaseous solvents in bitumen and pure hydrocarbons is also determined. As expected, the solubility of both gases in the studied pure hydrocarbons increases as the temperature decreases. In addition to confirming the known trends, this study provides new experimental data for low temperature gas-hydrocarbon diffusion process.
Solvent-based processes are often used as potential recovery agents in bitumen systems, with and without the addition of heat to the solvent. Solvents can sometimes be applied as a liquid phase, during SAGD start-up operations or processes aimed at developing injectivity into the oil. Light hydrocarbon liquids are traditionally tested for this application. Solvent injection may also occur in a vapour state and its objective is to reduce oil viscosity and improve mobility of bitumen under low temperatures <100°C. In general, hydrocarbon solvents such as propane are often used for this application. The objective of this study is to conduct CT-based measurement of static mixing of bitumen and both liquid and vapour phase solvents, and to quantify some of the time-dependent changes that occur during solvent mixing with bitumen.
Diffusion experiments have been conducted with propane and DME (vapour phase) and with propane, DME, pentane and toluene (liquid phase) solvent systems. Solvents are mixed with medium viscosity Peace River bitumen and high viscosity Grosmont bitumen. The Tests are run under constant pressure and temperature, and Computer-Assisted Tomography (CT) is used to monitor mass transfer of solvent into oil as a function of time. The outcome of this study is measurements of mass transfer rates of solvent into oil, and the degree of oil phase swelling during the tests.
During solvent injection processes in the field, the rate of mixing is a key parameter that will help in deciding which solvent is optimal for different processes. This study focuses on the rate of solvent mixing with oil. In vapour phase solvent systems, the analysis of the CT images allows for an understanding of the impact of oil phase swelling on the effective rate of penetration of solvent into oil. Overall, the test data provided in this work demonstrates that DME mixes into oil faster than other solvents, and leads to more swelling in a vapour solvent-bitumen system. The analysis of CT data provides an understanding of concentration-dependent diffusion coefficients and limitations from predicting mass transfer using constant coefficients in liquid and vapour solvent systems.
A new graphical procedure is proposed to estimate the interface resistivity in terms of interface mass-transfer coefficient in gas-oil pressure decay experiments. We provide a time-domain closed-form analytical solution by the use of Integral Method (IM) to the equations governing the gas-phase-pressure decay with the improved time-dependent gas-oil interface boundary condition. A graphical technique, derived from this analytical solution, is proposed to extract the interface mass-transfer coefficient and Henry’s constant. Application of this method to synthetic and experimental pressure-decay data shows that the estimated parameters are in agreement with those reported in the literature. The proposed procedure, coupled with a graphical technique to estimate the diffusion coefficient, is an asset for a simple, quick, and reliable estimation of interface mass-transfer coefficient and Henry’s constant.
Mass diffusion relates to migration of one species in another and is a consequence of local heterogeneity of concentration distribution and energy. The present study describes an optical method based on the shadowgraph technique for measuring a binary mass diffusivity of a solute in a solvent using a collimated beam of light. The measurement technique exploits the principle that refraction of a light beam due to concentration gradient creates a sharp visible streak in an image. The streak is a bright, visible linear feature in a shadowgraph image and opens up a new method of diffusivity measurement. The movement of the streak with time is due to a finite mass diffusivity of a solute in a solvent. Experiments with glucose, salt and glycerin diffusion in water have been conducted within a time window obtained from the sensitivity analysis. The respective mass diffusivities are determined by the light streak as well as the linearized shadowgraph technique, and compared with the values reported in the literature. The proposed approach promises to yield a simple method of determining mass diffusivity in a variety of binary systems without explicit measurement of the species concentration.
CO2-enhanced oil recovery (CO2-EOR) has emerged as a major option for productively using CO2 emissions captured from electric power and other industrial facilities as part of carbon capture and storage (CCS) operations. Not only can depleting oil fields provide secure, well-characterized sites for storing CO2, such fields can also provide a source of revenues to offset the costs of capturing CO2 by producing incremental oil. This paper draws significantly on work by Advanced Resources International, Inc. (ARI), sponsored by the United States Department of Energy’s National Energy Technology Laboratory (U.S. DOE/NETL) [Advanced Resources International, Inc. (ARI). Improving Domestic Energy Security and Lowering CO2 Emissions with “Next Generation” CO2-Enhanced Oil Recovery; ARI: Arlington, VA, 2011; http://www.netl.doe.gov/energy-analyses/pubs/storing%20co2%20w%20eor_final.pdf] and the International Energy Agency Greenhouse Gas Research and Development Programme (IEAGHG) [Advanced Resources International, Inc. (ARI). CO2 Storage in Depleted Oilfields: Global Application Criteria for Carbon Dioxide Enhanced Oil Recovery; ARI: Arlington, VA, Dec 2009; IEAGHG Programme Technical Report Number 2009-12], that demonstrates that CO2-EOR offers large CO2 storage capacity potential and could accommodate a major portion of the CO2 captured from industrial facilities for the next 30 years. This work also demonstrates that CO2 can be effectively and permanently stored when deployed in association with CO2-EOR, with the amount stored depending upon the priority placed on maximizing storage. In addition to showing that CCS benefits from CO2-EOR by providing the revenues from sale of CO2, overcoming other barriers, while producing oil with a lower CO2 emissions “footprint”, the report demonstrates that CO2-EOR needs CCS, because large-scale future implementation of CO2-EOR will be dependent upon CO2 supplies from industrial sources.
An analytical method of calculating variable diffusion coefficients has been developed. The Boltzmann-Matano graphical method used up to now has certain disadvantages which restrict the acuracy of the evaluated diffusion coefficients. Due to these disadvantages, the accuracy of this method is restricted even more when diffusion coefficients are determined in an area of low concentration of the diffused species of atom. The reliability of the analytical expression obtained in the present investigation has been verified experimentally by comparing the results obtained with those of the graphical method. On the basis of this comparison the analytical method can claim an accuracy better than, or at least equal to, that of the graphical method.
The solubility of CO2 (carbon dioxide), SO2, CO, N2, O2, and H2 in ionic liquids (ILs) was studied. The results showed that the solubility data of gases except for CO 2 in ILs are still limited and should be complemented especially at low temperatures. Solubility data of mixed gases in ILs are also scarce, which can provide fundamental knowledge for developing the actual processes because one gas solubility may be significantly influenced by the presence of another gas. Predictive molecular thermodynamic models are still needed to be advanced so as to improve the prediction accuracy and thus reduce the amount of experimental work in measuring the solubility data due to numerous combinations of cations and anions and extreme operating conditions. The solubility of gases in ILs may be improved by combing the advantages of ILs with other new types of materials, such as metal-organic frameworks (MOFs), not limited to other commercially available ILs and organic solvents.
A mathematical model for the non-equilibrium combustion of droplets in rocket engines is developed. This model allows to determine the divergence of combustion rate for the equilibrium and non-equilibrium model. Criterion for droplet combustion deviation from equilibrium is introduced. It grows decreasing droplet radius, accommodation coefficient, temperature and decreases on decreasing diffusion coefficient. Also divergence from equilibrium increases on reduction of droplet radius.Droplet burning time essentially increases under non-equilibrium conditions. Comparison of theoretical and experimental data shows that to have adequate solution for small droplets it is necessary to use the non-equilibrium model.
An interferometric technique is described by which the absorption of carbon dioxide into quiescent water has been examined. There is no measurable resistance at the interface to solution of the gas into pure water, the rate of absorption into the liquid being governed by molecular diffusion. A measurable interfacial resistance is found when carbon dioxide is absorbed by solutions of surface-active agents.RésuméLes auteurs décrivent une méthode interférométrique qui permet d'étudier l'adsorption du CO2 dans l'eau au repos. La résistance à l'interface de la solution du gaz et de l'eau pure est trop faible pour être mesurable, la vitesse d'adsorption dans le liquide étant déterminée par la diffusion moléculaire. Les auteurs trouvent une résistance interfaciale mesurable quand le CO2 est absorbé par des solutions d'agents tensio-actifs.ZusammenfassungZur Bestimmung der Absorption von Kohlendioxyd durch ruhendes Wasser wird eine interferometrische Versuchstechnik beschrieben. Da bei der Lösung des Gases in reinem Wasser kein messbarer Grenzflächenwiderstand vorhanden ist, wird die Geschwindigkeit der Absorption in die Flüssigkeit durch die molekulare Diffusion bestimmt. Ein messbarer Grenzflächenwiderstand wird bei der Absorption von Kohlendioxyd durch Lösungen von oberflächenaktiven Stoffen gefunden.
Mathematical models are developed to describe the transport of dissolved CO2 in a liquid phase, and results of measurements of the diffusivity of CO2 in hydrocarbons and water at reservoir conditions are reported. The measurements were made with novel techniques based on the direct observation of the motion of an interface caused by the diffusion of CO2 through oil or oil shielded by water. Diffusion coefficients were determined by fitting the mathematical models to the observed motion of the interfaces. This method allows the measurement of diffusion coefficients without the need to determine phase compositions and is therefore suited to measurements at elevated pressures (reservoir conditions). Measured diffusion coefficients are reported for CO2 in pentane, decane, and hexadecane at 25°C [77°F] and pressures up to 6000 kPa [870 psia]). Limited measurements of CO2 diffusion in Maljamar crude oil are also described. In addition, results of measurements for the diffusion of CO2 in water are presented. These are the first such measurements at high pressures (up to 6000 kPa [870 psia]). Correlations of diffusion coefficients in liquids at atmospheric pressure are shown to give reasonable estimates of diffusion coefficients for CO2 in fluids at reservoir conditions. Finally, the measured diffusion coefficients and mathematical models are used to assess the impact of diffusive mixing on CO2 floods at various length scales to examine the relationship between laboratory-scale corefloods and field-scale displacements.
Traditional models for gas absorption have considered the gas-liquid interface to be instantaneously saturated with the gas, hence ignoring any interfa
A novel in-situ method for measuring molecular diffusion coefficients of CO2 and other solvent gases in consolidated porous media at high pressure has been developed and is described. This technique is unique because visual observations and measurements of composition are not required. Experimental diffusion coefficients are reported for CO2 in decane up to 850 psia [5.86 MPa], for CO2 in 0.25 N NaCl brine up to 850 psia [5.86 MPa], and for ethane in decane up to 600 psia [4.14 MPa]. All tests were conducted in Berea cores saturated with liquid phase at 100°F [311 K]. Cores were oriented both vertically and horizontally to assess the effects of gravity-induced convection on the observed mass transfer. The experimental diffusion coefficients obtained from this study have also been correlated, together with literature data for methane, ethane, and propane, as a function of liquid viscosity and thermophysical properties of the diffusing gases.
The Matano‐Boltzmann method of graphical calculation of diffusion coefficients in solutions is replaced by an analytical method in certain systems. This procedure enables accurate calculation of diffusion coefficients near the concentration extremes. An equation is derived for the diffusion coefficient D as a function of concentration c. The equation predicts a variation of D with c which is not exponential in metallic systems, contrary to the proposal of Wagner. Comparison of D values with those obtained graphically, for the system copper‐nickel, indicates that the graphical values may be appreciably in error at that extreme where the diffusion coefficient is greatest.
The method of computing differential diffusion coefficients in liquids from diaphragm cell data has been re-examined to allow for volume changes upon mixing. The diffusion coefficient upon which the new calculational method is based is of greater theoretical interest than the common Fick diffusivity. The difference between the two is usually small in diaphragm cell work, but deviations as large as 6% have been found for the ethanol-water system.
A modified pressure decay method has been designed and tested for more reliable measurements of molecular diffusion coefficients of gases into liquids. Unlike the conventional pressure decay method, the experimental setup has been designed such that the interface pressure and consequently the dissolved gas concentration at the interface are kept constant. This is accomplished by continuously injecting the required amount of gas into the gas cap from a secondary supply cell to maintain the pressure constant at the gas−liquid interface. The pressure decay is measured in the supply cell. The advantage of the new technique is that, assuming the diffusion coefficient to be constant, a simple analysis allows determination of the equilibrium concentration and diffusion coefficient.
Measurements of the liquid diffusion coefficients over the complete range of compositions of the ethanol-water system at 25°C. have been carried out using the porous diaphragm technique with a magnetically-stirred and modified cell. Both the integral and differential coefficients agree very closely with the values reported by Hammond and Stokes, although an improved method of calculating the differential coefficients has been used. The limiting values at 0 and 100% concentrations differ somewhat from those previously reported. By means of an experimental investigation the work of Smith and Storrow on the same system has been shown to be in error. Analytical errors in calibration have been reduced to a probable error of ± 0.1%, although there is an average deviation of ± 2% for all experimental points relative to the best line drawn through them. The diffusion coefficients based on concentration as a driving force, show a minimum at 25 mole % ethanol, corresponding to the minimum for the relative decrease in volume on mixing and the maximum for the viscosity-composition curve. For the dimensionless Schmidt number, a very sharp peaking to a value of 7500 occurs at the same composition.
The assumption of an intraparticle parabolic profile was investigated by parametrically comparing the approximate solutions and the exact solutions for two physical systems: a single particle response, and batch adsorbant behavior. An extension to a quartic profile was also attempted. The simple parabolic profile model for intraparticle composition is quite satisfactory for larger times tau greater than 0. 05 and leads to simplifications in model building, but for early time experiments using the approximate models is in error by around 10%. For a quartic profile assumption, the approximate solution is found to be valid when tau greater than 0. 015 but the advantage of simplicity is lost.
A new technique is developed to measure the diffusivity of gas in bitumen as a function of composition. Results are presented for a carbon dioxide-bitumen system, which is of considerable industrial relevance. The technique employs transient pressure data obtained from a nonintrusive pressure decay experiment at constant temperature and volume. The underlying theory is presented along with a computational algorithm to calculate diffusivity. Using experimental pressure decay data in the range 25-90 °C at 4 MPa, the diffusivity of carbon dioxide in bitumen is calculated. The results are compared with the limited data available in the literature. The approach is straightforward and can be easily applied to other nonvolatile liquid systems.
Diffusion plays a vital role in the “Vapex” process. In the present work the results of experiments on “Vapex” using a Hele-Shaw cell have been used to obtain empirical correlations for the diffusivities of propane and butane in Peace River bitumen. Additional data required for the estimation of diffusivities from these experiments are the solubilities of solvent in bitumen and a correlation for the viscosity of solvent bitumen mixture. Diffusivities are assumed to decline exponentially with viscosity. Computed values of diffusion coefficients fall within the range of the published data for similar systems. This simple experiment can be used to estimate the diffusivities of gaseous solvents in highly viscous fluids.
La diffusion joue un rǒle primordial dans le procédé Vapex. Dans le présent travail, on a utilisé les résultats d'expériences menées avec ce procédé dans une cellule de Hele-Shaw pour obtenir des corrélations empiriques des diffusivités du propane et du butane dans des bitumes de Peace River. Les autres données nécessaires à l'estimation de ces diffusivités sont les solubilités du solvant dans le bitume et une corrélation pour la viscosité du mélange de bitume et de solvant. On suppose que les diffusivités diminuent de manière exponentielle avec la viscosité. Les valeurs des coefficients de diffusion calculées par ordinateur sont dans la gamme des données publiées pour des systèmes similaires. Cette expérience simple peut servir à l'estimation des diffusivités de solvants gazeux dans des fluides hautement visqueux.
Experimental data for the diffusivity of carbon dioxide, methane, ethane and nitrogen in Athabasca bitumen are presented in the range 25–90°C at 4 and 8 MPa. The diffusivity of these gases has been determined as a function of gas concentration in bitumen using a non-intrusive experim̀ental method. The diffusivity of gas in general is found to increase with temperature and pressure, and is a unimodal function of concentration. A correlation is provided for the average diffusivity of these gases as a function of temperature.
On présente des données expérimentales pour la diffusivité du dioxyde de carbone, du méthane et de l'azote dans du bitume d'Athabasca dans la gamme de 25–90°C à 4 et 8 MPa. La diffusivité de ces gaz est déterminée en fonction de la concentration de gaz dans le bitume à l'aide d'une méthode expérimentale non intrusive. II ressort qu'en général la diffusivité du gaz augmente avec la température et la pression et qu'elle est une fonction unimodale de la concentration. On propose une corrélation pour la diffusivité moyenne de ces gaz en fonction de la température.
The effective diffusion coefficient of oxygen, IDe, was determined in different gel support materials (calcium alginate, -carrageenan, gellan gum, agar and agarose) which are generally used for immobilization of cells. The method used was based upon fitting Crank's model on the experimental data. The model describes the solute diffusion from a well-stirred solution into gel beads which are initially free of solute. The effect of the gel concentration on IDe of oxygen in the gel was investigated. The results showed a decreasing IDe for both agar and agarose at increasing gel concentration. In case of calcium alginate and gellan gum, a maximum in IDe at the intermediate gel concentration was observed. It is hypothesized that this phenomenon is due to a changing gelpore structure at increasing gel concentrations. The IDe of oxygen in calcium alginate, -carrageenan and gellan gum varied from 1.5*10–9 to 2.1*10–9 m2s–1 in the gel concentration range of 0.5 to 5% (w/v).
In a domain with free boundary, we establish conditions for the existence and uniqueness of a solution of the inverse problem
of finding the time-dependent coefficient of heat conductivity. We study the case of strong degeneration where the unknown
coefficient tends to zero as t → +0 as a power function t
β
, where β ≥ 1.
The accurate prediction of diffusion coefficients of methane in liquid hydrocarbons is one of the key parameters for improving the prediction of compositional oil reservoir simulators, for designing surface facilities, and for high pressure gas/liquid mass transfer operations. In this investigation, a precision high pressure and temperature diffusion cell apparatus has been used to measure diffusion coefficients of methane in dodecane and in a typical Iranian crude oil at high pressures and temperatures. The diffusion cell is modelled using a finite-domain moving boundary method. Extensive experimental results are presented at high pressures and temperatures, especially for regions where published data were insufficient. The mechanism of mass transfer during the incubation period is analysed by solving the equation of continuity for the diffusion cell numerically and considering that the diffusion coefficient is changing with time and concentration. The effects of pressure, liquid phase viscosity and operating temperature on the diffusion coefficient of the solute gas in the solution are discussed. The results indicate that uncertainties which generally exist in the physical and thermodynamic properties of the crude oils may have a significant effect on the diffusion coefficient of a solute gas in a complex mixture like crude oil.
A simple method is presented for determining diffusion coefficients of dense gases in liquids using a PVT cell. When a non-equilibrium gas is brought into contact with a liquid in a sealed container at a constant temperature, the final state is determined by thermodynamic equilibrium. However, the time which is required to reach the final state is determined from the diffusion process in each phase. At the gas-liquid interface, thermodynamic equilibrium exists between the two phases at all times, but the position of the interface as well as the pressure may change with time.The rate of change of pressure and the interface position as a function of time depends on the rate of diffusion in each phase and therefore on the diffusion coefficients. No compositional measurements are necessary for this method of measuring diffusion coefficients; hence, it is less expensive than conventional methods. Results obtained by this method for the binary system of methane and n-pentane at 311 K and 70 bar yielded diffusion coefficients within ± 5% of literature values. The technique can be easily applied to multicomponent systems for measurement of effective diffusion coefficients in reservoir fluids.