Mass Transfer Between Phases in a Porous Medium: A Study of Equilibrium

1965 ◽  
Vol 5 (01) ◽  
pp. 51-59 ◽  
Author(s):  
P. Raimondi ◽  
M.A. Torcaso
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Partition Coefficient ◽  
Oil Recovery ◽  
Carrier Phase ◽  
Peak Height ◽  
Lower Velocity ◽  
Immobile Phase ◽  
Two Phases ◽  
Gas Drive

Abstract To study mass transport in systems simulating oil recovery processes, different porous media were saturated with a mobile (carrier phase) and a stationary phase. Slugs of carrier phase containing a small amount of solute were displaced with pure carrier phase. By analogy to the chromatographic processes, the velocity of the solute can be predicted from a knowledge of the partition coefficient and the saturation provided that equilibrium between the two phases exists. Equilibrium was found to exist for different porous media, solutes and rates. The conditions were varied over the range normally encountered in the laboratory and in the field. The longitudinal dispersion of a solute undergoing interphase mass transfer was also investigated. Introduction The production of hydrocarbons by gas cycling, enriched gas drive and CO2 or alcohol displacement involves, among other factors, relative motion between two phases and compounds, hereafter called solute, which are soluble in both phases. The solute is carried forward by the faster flowing phase at a lower velocity than the average velocity of that phase. Retardation of the solute is caused by chromatographic absorption and desorption in the slower flowing phase and by the degree of departure from equilibrium. At equilibrium the concentration of solute in the two phases can be related by the equation* (1) where Csw and Cso are the concentration of solute in the aqueous and oleic phases respectively and K is the equilibrium ratio, or partition coefficient. Displacement theories must contain an explicit assumption with regard to equilibrium, i.e., whether the compositions can be related by Eq. 1. The existance of equilibrium depends, in general on the relative velocity between the phases. Unfortunately, other factors such as gravity segregation and viscous fingering, also depend on velocity. For this reason, whenever effects of rate on displacement were observed, it was practically impossible to discern what caused them - lack of equilibrium or the factors mentioned above. Equilibrium between phases has been the subject of extensive studies in fields such as extraction or chromatography. It has received only small attention in flow through the type of porous media encountered in oil production. For this reason a method was developed which makes it possible to study the movement of a solute as it is affected by rate, type of porous media, partition coefficient and carrier phase, but in the absence of segregation or fingering. The information obtained enables one to determine when the assumption of equilibrium can be made. Briefly, the method consists of (1) saturating the core with a mobile and an immobile phase, (2) injecting a slug made up of the same fluid as the mobile phase and a small concentration of mutually soluble solute, (3) measuring the lag and the peak height of the slug at arrival and (4) correlating these variables with fluid properties such as partition coefficient and mixing constants of the medium. PROPOSED MECHANISM The principles of chromatography are combined with the equation of longitudinal mixing to predict the velocity of a solute slug compared to the bulk velocity and the peak height of a slug. The equation so obtained is valid under equilibrium conditions only. Therefore, a comparison between experimental and predicted results will give a measure of departure from equilibrium. This work was done with either the oleic or the aqueous phase being immobile. For simplicity, the following development is based on the case where the oleic phase is immobile. However, the treatment is the same in either case. SPEC P. 51ˆ

An Overview: Analysis of Heat and Mass Transfer in Fractal Media by Fractal Geometry and Technique

2010 ◽  
Author(s):  
Boming Yu
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Porous Media ◽  
Heat And Mass Transfer ◽  
Oil Recovery ◽  
Fractal Geometry ◽  
Boiling Heat Transfer ◽  
Nucleate Boiling ◽  
Fractal Media ◽  
Nucleate Boiling Heat Transfer

In the past three decades, fractal geometry and technique have received considerable attention due to its wide applications in sciences and technologies such as in physics, mathematics, geophysics, oil recovery, material science and engineering, flow and heat and mass transfer in porous media etc. The fractal geometry and technique may become particularly powerful when they are applied to deal with random and disordered media such as porous media, nanofluids, nucleate boiling heat transfer. In this paper, a summary of recent advances is presented in the areas of heat and mass transfer in fractal media by fractal geometry technique. The present overview includes a brief summary of the fractal geometry technique applied in the areas of heat and mass transfer; thermal conductivities of porous media and nanofluids; nucleate boiling heat transfer. A few comments are made with respect to the theoretical studies that should be made in the future.

Hysteresis in Flow in Porous Media With Phase Transitions

1999 ◽  
Author(s):  
Pavel Bedrikovetsky ◽  
Dan Marchesin ◽  
Paulo Roberto Ballin
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Initial Boundary ◽  
Oil Reservoirs ◽  
Flow In Porous Media ◽  
Fractional Flow ◽  
Two Phase ◽  
Initial Boundary Problem ◽  
Gas Drive

Abstract Two-phase flow with hysteresis in porous media is described by the Buckley-Leverett model with three types of fractional flow functions: imbibition, drainage and scanning. The mathematical theory for the Riemann problem and for non-self-similar initial-boundary problem is developed. The structure of the solutions is presented and the physical interpretation of the phenomena is discussed. We obtain the analytical solution for the injection of water slug with gas drive into oil reservoirs. The solutions show that the effect of hysteresis is to decrease gas flux (in the case where the drainage relative permeability lies below the imbibition relative permeability). This effect increases oil recovery for Water-Alternate-Gas injection in oil reservoirs.

A Numerical Study of Diphasic Multicomponent Flow

1972 ◽  
Vol 12 (02) ◽  
pp. 171-184 ◽  
Author(s):  
N. Van-Quy ◽  
P. Simandoux ◽  
J. Corteville
Keyword(s):  
Mass Transfer ◽  
Oil Recovery ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Simple Fluids ◽  
Oil Saturation ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Gas Drive

Abstract This paper describes a general multicomponent two-phase flow model, taking into account convection, diffusion and thermodynamic exchange between phases. The main assumptions are: isothermal one-dimensional flow; two-phase flow (gas and liquid); each phase may be represented by a mixture of three components or groups of components. Actually, a great many recovery problems cannot be pictured by usual models because the oil and, in many cases, the injected fluid are not simple fluids and may bring about exchanges of components that considerably modify their characteristics. This is why efforts are now being made to develop "compositional" or "multicomponent" models capable of solving such situations. Generalization of the model to more complex systems can be considered. Cases treated may be any type of single- and two-phase flow, in particular any miscible process (e. g., high-pressure gas drive, condensing gas drive, slug displacement) and any diphasic processes with high mass exchange (e.g., displacement by carbon dioxide or flue gas). This model is working and has been successfully checked by experiments. Introduction Many investigations, broth experimental and theoretical, have been made on the recovery of oil from reservoirs. With regard to mathematical models, most of those conceived up to now have dealt with oil recovery by the injection of a fluid that is miscible or immiscible with the oil. For miscible drives, single-phase flow with a binary mixture and miscibility in all proportions is involved. In such an ideal situation oil recovery is theoretically total. For immiscible displacements flow is diphasic. Capillary pressure and relative permeability play a preponderant role. Since irreducible oil saturation preponderant role. Since irreducible oil saturation is inevitable, oil recovery can never be total. Actually, a great many recovery problems cannot be pictured by such models because the oil and, in many cases, the injected fluid are not simple fluids and may bring about exchanges of components that considerably modify their characteristics. This is why efforts are now being made to develop "compositional" or "multicomponent" models capable of solving such situations. Such a model is described here. It is designed to handle the most general case of the displacement of one fluid by another. This model offers the following possibilities.The fluids may be made up of more than two components.Flow may be entirely monophasic, entirely diphasic, or partially monophasic and diphasic.Miscibility may be partial or total.The material exchange between phases may take place under specific thermodynamic conditions. A model that is much closer to reality should provide more thorough knowledge of mass transfer provide more thorough knowledge of mass transfer mechanisms in a complex mixture as well as better oil recovery forecasting with the injection of a second fluid. DESCRIPTION OF THE MODEL In a porous formation, we will consider the displacement of a liquid hydrocarbon complex in place by another fluid that is injected into the place by another fluid that is injected into the formation. The injected fluid may be a gas or a liquid, containing or not containing hydrocarbons. We assume that the mass transfer in the transition zone between the displacing fluid and the displaced fluid occurs according to three mechanism: convection, diffusion and thermodynamic exchange between phases. We propose to study the flow thus described. The main assumptions are:flow is isothermal and one-dimensional;the porous medium is homogeneous and isotropic;there is no effect of gravity;there is a two-phase flow, i.e., oil and gaseach phase may be represented by a mixture of three components or three groups of components (e.g., C1, C2-6, C7+); SPEJ P. 171

Study on Alkaline Mass Transfer Regularity with Dissolution in Porous Media

2012 ◽  
Vol 516-517 ◽  
pp. 790-796
Author(s):  
Huai Jun Yang ◽  
Wei Dong Liu ◽  
Hui Hui Kou
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Oil Recovery ◽  
Alkaline Solution ◽  
Concentration Distribution ◽  
Reaction Dynamics ◽  
Solution Concentration ◽  
Reaction Series ◽  
One Dimensional ◽  
Solution Regularity

Inducting dissolution speed constant and multistage reaction series to the alkaline solution transmission equation, this article established the alkaline solution transmission equation with multistage reaction dynamics in the porous media of stratum mineral and calculated one-dimensional alkaline solution concentration distribution. Experimental results verified the correctness of transmission equation, moreover, it further analyzed the alkaline solution regularity in the porous media. The model will be used to predict alkali loss, optimize alkaline solution concentration and slug size, thereby alkaline waterflooding or combination drive can obtain better displacement characteristics and improve the oil recovery.

Experimental and Numerical Studies of Gas/Oil Multicontact Miscible Displacements in Homogeneous and Crossbedded Porous Media

SPE Journal ◽  
2007 ◽  
Vol 12 (01) ◽  
pp. 62-76 ◽  
Author(s):  
Yahya Mansoor Al-Wahaibi ◽  
Ann Helen Muggeridge ◽  
Carlos Atilio Grattoni
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Oil Recovery ◽  
Flow Direction ◽  
Gas Injection ◽  
Flow Simulation ◽  
Capillary Forces ◽  
Petroleum Engineering ◽  
Small Scale ◽  
First Contact

Summary We investigate oil recovery from multicontact miscible (MCM) gas injection into homogeneous and crossbedded porous media, using a combination of well-characterized laboratory experiments and detailed compositional flow simulation. All simulator input data, including most EOS parameters, were determined experimentally or from the literature produced fluids in all experiments were found not to be in compositional equilibrium. This was not predicted by the simulator, giving a poor match between experimental and simulated oil recoveries. The match was significantly improved for the cross-bedded displacements by using alpha factors derived from the MCM displacements in the homogeneous pack. Introduction The recovery of oil by miscible gas injection has been a subject of interest and research in petroleum engineering for more than 40 years (Stalkup 1983). In a first-contact, miscible (FCM) displacement, the gas and oil mix instantly in all proportions. No capillary forces exist, so, in principle, residual oil saturation is zero, and 100% oil recovery should be achieved. In practice, many phenomena conspire to limit the efficiency of the miscible flooding process, including viscous fingering, gravity override, and permeability heterogeneity. Moreover, it is often not economical, and sometimes not technically feasible, to inject a gas that is first-contact miscible with the oil. Instead, the injected gas is designed to develop miscibility with the oil by mass transfer during the displacement. This is a so-called MCM gas injection. If the bulk of the mass transfer is from the gas to the oil, then the displacement is termed a condensing drive. If most of the mass transfer is from the oil to the gas, then it is termed a vaporizing drive. In most cases, however, because of the multicomponent nature of oil and gas, the mass transfer is actually a mixture of both these cases, and the displacement is termed a condensing-vaporizing drive. Small-scale heterogeneities can have a significant impact on recovery efficiency (Jones et al. 1995; Jones et al. 1994; Kjonsvik et al. 1994), yet they cannot be modeled explicitly in field-scale simulations. Some of the most common small-scale heterogeneities found in sandstone reservoirs are laminations. However, because laminations have a small size and are generally at an angle to the principal flow direction, their influence onfluid flow is one of the most difficult features to predict numerically. There is a significant amount of literature describing systematic investigations of first-contact miscible and immiscible displacement processes in laminated sandstones (Huang et al. 1995, 1996; Ringrose et al. 1993; Kortekaas 1985; Honarpour et al. 1994; Hartkamp-Bakker 1991, 1993; McDougall and Sorbie 1993; Marcelle-DeSilva and Dawe 2003; Borresen and Graue 1996; Roti and Dawe 1993; Dawe et al. 1992; Caruana and Dawe 1996; Caruana 1997). Both experimental and simulation studies show that significant volumes of oil can be trapped by capillary forces during immiscible displacements (Huang et al. 1995, 1996; Ringrose et al. 1993; Kortekaas 1985; Honarpour et al. 1994; Hartkamp-Bakker 1991, 1993; McDougall and Sorbie 1993; Marcelle-DeSilva and Dawe 2003; Borresen and Graue 1996; Roti and Dawe 1993; Dawe et al. 1992; Caruana and Dawe 1996; Caruana 1997). However, the influence of these heterogeneities on MCM displacements, during which capillary forces change from being very significant when gas is first injected to negligible once miscibility has developed, has not yet been investigated. Indeed, the only comparisons of well-characterized MCM displacement experiments and detailed simulations reported in anywhere in the literature are those of Burger and colleagues (Burger and Mohanty 1997; Burger et al. 1996; Burger et al. 1994).

scholarly journals Microfluidic Study of Drainage and Imbibition in Porous Media: Definition of Amott Indices

2011 ◽  
Author(s):  
Emilie Dressaire ◽  
Howard A. Stone
Keyword(s):  
Porous Media ◽  
Oil Recovery ◽  
Pressure Difference ◽  
Flow Behavior ◽  
Critical Role ◽  
Rock Surface ◽  
Repeat Units ◽  
Fluid Saturation ◽  
Two Phases ◽  
Wetting Fluid

The wettability of reservoir rocks plays a critical role in oil recovery operations. This property is traditionally defined in terms of the contact angle between the fluid-fluid interface and the solid surface. In natural porous media, it has been preferred to characterize the wettability and its effects on fluid flow behavior in terms of Amott indices, through the capillary pressure-fluid saturation relationship. This “bulk” definition is based on the steady states reached by the two phases, the wetting one and the non-wetting one, upon drainage (removal of the wetting fluid) and imbibition (removal of the non-wetting fluid). These indices provide some indirect indication of the rock surface chemistry and porosity structure. Previous studies on Amott indices have mostly focused on numerical modeling of rocks. In this paper, we present an experimental study on two phase flow in regular lattices of glass microchannels. A wet etching technique is used to fabricate 2D networks composed of hundreds of repeat units. The repeat units are square, hexagonal, or triangular, with a lattice parameter of about 100 micrometers. Controlling and varying the microchannel wettability, network geometry, and fluid properties allow correlating the physical chemistry of the system and the characteristics of the multiphase flow. We perform drainage-imbibition cycles by controlling the pressure difference across the device. For each pressure difference, we record and characterize the distribution of the two phases at equilibrium. Our results capture the dependance of the Amott index on both fluid and network properties. The values obtained are consistent with previous studies on wetting phenomena at the pore level. The drainage-imbibition cycles also provide information on the patterns of invasion. We show that the study of the cycles can further predictability of Amott indices.

Analysis of the Physical Mechanisms in Surfactant Flooding

1978 ◽  
Vol 18 (01) ◽  
pp. 42-58 ◽  
Author(s):  
R.G. Larson
Keyword(s):  
Mass Transfer ◽  
Oil Recovery ◽  
Surfactant Flooding ◽  
Constant Composition ◽  
Phase Boundaries ◽  
One Dimensional ◽  
Mobile Phases ◽  
Immobile Phase ◽  
Oil Water ◽  
Core Flood

Abstract A model was developed to represent the physical displacement mechanism of tertiary oil recovery in an aqueous-phase surfactant flood. The chemical aspects were not modeled. In particular, the residual oil saturation in the presence of surfactant must be specified to use the model. This model was used to investigate the relationship between the system parameters (mobility ratio, partition coefficient, parameters (mobility ratio, partition coefficient, adsorption) and the performance variables (oil cut, chemical breakthrough, recovery efficiency at breakthrough). The model is an extension of Buckley-Leverett analysis and applies to the flow of two fluids in a system in which composition and saturation are variables. This model assumes a homogeneous one-dimensional system, the absence of dispersion, equilibrium mass transfer, and constant composition injection (infinite slug). Analysis applies to systems of two mobile phases (oil and water) and one immobile phase (reservoir rock) where three components (oil, water, and chemical) transfer between mobile phases. and chemical transfers to the rock. The model predicts that oil recovery and surfactant breakthrough may be retarded in low-tension surfactant floods where the surfactant partitions preferentially into the oil phase. This partitions preferentially into the oil phase. This prediction is confirmed by experimental core-flood prediction is confirmed by experimental core-flood results. Introduction In designing and optimizing a surfactant-flooding process, one is confronted with many mechanisms process, one is confronted with many mechanisms and corresponding physicochemical properties of the rock and fluid interactions that affect performance of a surfactant flood. Important properties are relative permeabilities, viscosities, interfacial tensions, dispersion coefficients, and adsorption isotherms. Laboratory investigation of these mechanisms is hampered by the high degree of coupling among mechanisms, which makes it difficult to analyze process sensitivity to each property. property. Therefore, a simple mathematical model was developed to interpret results of core-flooding experiments and to apply in cases in which surfactant is injected continuously (infinite slug). A sensitivity study of the effect of 14 model parameters on oil recovery revealed that recovery parameters on oil recovery revealed that recovery is affected strongly by pore-to-pore displacement efficiency (governed by interfacial tension) and fluid mobilities, and by interphase mass transfer of chemical (surfactant), oil, and water. The effect of this transfer phenomenon on surfactant-flood oil recovery previously has received little attention. ASSUMPTIONS OF THE MODEL SYSTEM The system is one-dimensional with uniform properties. properties. Two mobile fluid phases, an aqueous displacing phase, and an oleic displaced phase are considered, as well as one immobile phase (rock). Three mobile components (oil, water, and chemical) are considered. Each is assumed to behave as if it was a pure component. Mass transfer of chemical, water, and oil between the mobile phases and transfer of chemical to the immobile phase is allowed. The mass transfer rates are assumed sufficiently fast compared with fluid flow that chemical equilibrium exists across phase boundaries everywhere in the reservoir. phase boundaries everywhere in the reservoir. Initially, the reservoir contains pure oil at its waterflood residual oleic-phase saturation (Sorw), and the rest of the pore space contains pure water. The injected fluid is a single aqueous phase at constant composition (infinite slug injection). This injected composition lies on the two-phase envelope of a ternary diagram (that is, no phase extraction). The system is self-sharpening in that only the injected and the initial compositions exist in the composition profile. (Sufficient valid conditions for this assumption are derived in Appendix B.) There are no chemical reactions. In each phase, each component occupies the volume it would have in its pure state (VE = O, the excess volume of mixing is zero). SPEJ p. 42

The Study of Coupled Transfer of Heat, Moisture and Air in Reservoir Porous Media

2012 ◽  
Vol 271-272 ◽  
pp. 1195-1200
Author(s):  
Yong Ying Jia ◽  
Zhi Guo Wang
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Temperature Field ◽  
Heat And Mass Transfer ◽  
Oil Recovery ◽  
Theoretical Basis ◽  
Process Analysis ◽  
Black Box ◽  
Box Model ◽  
Mass Transfer Mechanism

This paper studied on heat and mass transfer mechanism of steam in reservoir porous media, built coupled mathematical models for heat and mass transfer in reservoir porous media. “Black box model” and “white box model” are first proposed in heat and mass process analysis of reservoir porous media. Temperature field has been simulated by CMG-STARS software. Our work will give theoretical basis and technical support for enhanced oil recovery technology.

scholarly journals Pore-Scale Modelling of Solvent-Based Recovery Processes

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1405
Author(s):  
Bita Bayestehparvin ◽  
S.M. Farouq Ali ◽  
Mohammad Kariznovi ◽  
Jalal Abedi
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Oil Recovery ◽  
Equilibrium Phase ◽  
Viscosity Reduction ◽  
Experimental Investigations ◽  
Small Scale ◽  
Pore Scale ◽  
Two Phase ◽  
Recovery Processes

A need for a reduction in energy intensity and greenhouse gas emissions of bitumen and heavy oil recovery processes has led to the invention of several methods where mass-transfer-based recovery processes in terms of cold or heated solvent injection are used to reduce bitumen viscosity rather than steam injection. Despite the extensive numerical and experimental investigations, the field results are not always aligned to what is predicted unless several history matches are done. These discrepancies can be explained by investigating the mechanisms involved in mass transfer and corresponding viscosity reduction at the pore level. A two-phase multicomponent pore-scale simulator is developed to be used for realistic porous media simulation. The simulator developed predicts the chamber front velocity and chamber propagation in agreement with 2D experimental data in the literature. The simulator is specifically used for vapor extraction (VAPEX) modelling in a 2D porous medium. It was found that the solvent cannot reach its equilibrium value everywhere in the oleic phase confirming the non-equilibrium phase behavior in VAPEX. The equilibrium assumption is found to be invalid for VAPEX processes even at a small scale. The model developed can be used for further investigation of mass transfer-based processes in porous media.

Theory of Multicomponent, Multiphase Displacement in Porous Media

1981 ◽  
Vol 21 (01) ◽  
pp. 51-62 ◽  
Author(s):  
Friedrich G. Helfferich
Keyword(s):  
Porous Media ◽  
Phase Equilibria ◽  
Oil Recovery ◽  
Arbitrary Number ◽  
Mobile Phase ◽  
Fluid Dynamic ◽  
Flow Behavior ◽  
Pressure Effects ◽  
Number Of Components ◽  
Two Phases

Abstract The basis of a general theory of multicomponent, multiphase displacement in porous media is presented. The theory is applicable to an arbitrary number of phases, an arbitrary number of components partitioning between the phases, and variable initial and injection conditions. Only the effects of propagation are considered; phase equilibria and dependence of fractional flows on phase compositions and saturations are required as input, but any type of equilibrium and flow behavior can be accommodated. The principal simplifying assumptions are the restriction to one dimension, local phase equilibria, volume additivity on partitioning, idealized fluid dynamic behavior, and absence of temperature and pressure effects. The theory is an extension of that of multicomponent chromatography and has taken from it the concept of "coherence" and, for practical application, the tools of composition routes and distance/time diagrams. The application of the theory to a surfactant flood is illustrated in a companion paper.1 Introduction A key problem in modern methods of enhanced oil recovery is that of multicomponent, multiphase displacement in porous media. This term means the induced flow of any number of simultaneous, not fully miscible fluid phases consisting of any number of components. The components may partition between the phases; moreover, the physical properties of the phases (densities, viscosities, interfacial tensions, etc.) depend on composition and, therefore, on partitioning of the components. Multicomponent, multiphase displacement may be viewed as a generalization and combination of two different and independent approaches. The first of these is the highly developed theory of multicomponent chromatrography,2 which allows for any number of components affecting one canother's distribution behavior but admits only one mobile and one stationary phase. This theory has to be extended to more than one mobile phase. The second is the fluid dynamic theory of immiscible displacement in porous media, allowing for more than one mobile phase but not for partitioning of components. This theory was developed in the 1940's for two mobile phases3 and so far has not been stated in general form for more than two phases. It has to be extended to include partitioning of the components between the phases and its effects on phase properties. A summary of the start of the art, including recent work on systems with up to three components and two phases, has been given by Pope.4 This paper describes the extension of the theory to multicomponent, multiphase displacement with partitioning and for arbitrary initial and boundary conditions. The theory concerns itself only with transport behavior. Phase equilibrium and flow properties of the phases (relative permeabilities) as a function of composition are considered as given. Application of the theory, therefore, requires as input either empirical correlations of experimental data on phase equilibria and properties or theories predicting these. Morever, the theory concentrates exclusively on multicomponent, multiphase effects and does not attempt to account for the complex fluid dynamic situation in real, three-dimensional, and nonuniform reservoirs.

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