An experimental approach for measuring carbon dioxide diffusion coefficient in water and oil under supercritical conditions

Mohammad Sadegh Sharafi,Mehdi Ghasemi,Mohammad Ahmadi,Alireza Kazemi

Department of Petroleum Engineering,Amirkabir University of Technology – Tehran Polytechnic,Iran

Keywords: Diffusion coefficient Modified pressure decay method Incubation period Solubility uncertainty

ABSTRACT Several direct or indirect approaches have been proposed to measure diffusion coefficient of gases into liquids.The main complexity of indirect techniques such as pressure decay method is interpreting early pressure–time data which strongly affected by incubation period effect or convective instability.In the current approach,accurate apparatus and precise experimental setup including a high pressure and temperature PVT cell,a high precision Sanchez pump,heating and recording sub-system are implemented and a novel data analysis procedure is applied to modify pressure decay method.The effect of incubation period is reduced remarkably and diffusion coefficient of carbon dioxide in water in wide range of pressures and temperatures is determined and the effects of temperature,pressure and carbon dioxide phase alteration from gas to supercritical are investigated and the value of uncertainty is estimated.Furthermore,diffusion coefficient of CO2 and methane in an oil sample from one of the Iranian southwest oil formations is determined precisely using the experimental approach while no incubation period is detected.The results showed that incubation period duration decreases with increasing diffusion coefficient.Additionally,when CO2 state is gas,rate of increasing diffusion coefficient with pressure is decreased with temperature and when CO2 state is supercritical,the rate of increasing diffusion coefficient with pressure is decreased significantly.

1.Introduction

The process of molecular diffusion is occurred when two phases are in close contact,while they are not thermodynamically in equilibrium.This leads transferring of components from one phase to another phase due to existent concentration gradient in the mixture.Accurate data for diffusion phenomenon in the mixtures such as carbon dioxide–water(CO2–Water)or carbon dioxide–oil(CO2–Oil) and sufficient knowledge of transfer phenomena and thermodynamic are of considerable importance for numerous industrial applications such as controlling global warming by capturing carbon dioxide which causes reducing greenhouse gas emission and injection of carbon dioxide as a tertiary stage of enhanced oil recovery [1–3].Owning to great miscibility potential of CO2with oil which leads to desired changes in heavy oilviaviscosity reduction,swelling effect of heavy oil and reduced interfacial tension(IFT)mechanisms,makes CO2as a preferential gas for gas injection process [4–6].Therefore,CO2diffusion coefficient in these mixtures is a crucial designing parameter which depends on the miscibility and solubility of CO2.

During the past decays,numerous researches have been performed to quantify diffusion coefficient of gases into a liquid phase.The applied methods for measuring the diffusion coefficient can be divided into two general categories including direct and indirect approaches.Direct methods determine the diffusion coefficient by measuring the concentration gradient of the diffused solute in the solution versus time.In addition,sampling analysis method,nuclear magnetic resonance (NMR) method and X-ray Computer-Assisted are known as direct methods[7–11].The main limitation of indirect methods under experimental condition of high pressure and elevated temperature relates to the difficulty system intrusive sampling and also the accuracy of measured gas concentration in the liquid.Moreover,some of the indirect techniques such as NMR are not cost-effective.Alternatively,indirect methods including pressure-decay method[12–14],Dynamic Pendant Drop Shape Analysis (DPDSA) [15–17]and dynamic volume analysis [18,19]are commonly used to overcome many of the direct method’s challenges.Among all mentioned methods,pressure decay is the most applicable indirect method for measuring diffusivity of gas in liquids.However,the analysis of data in this method suffers from some convective instability effects at early time such as incubation period effect [20].Atharet al.[21]measured propane diffusion coefficient in oil at various temperatures ranging from 353 to 403 K using this method.They concluded that propane diffuses at three stages called early,transition and late time regions.In addition,the experimental approach of semi-infinite volume method at temperatures of 303.15,313.15 and 323.15 K and the method of online FTIR measurement at temperature of 303.15 K were implemented to measure CO2diffusion coefficient in some ionic liquids[22,23].Moreover,Sheikhaet al.[24]used experimental data which were obtained by Upretti and Mehrotra [25,26]to develop a new graphical approach for calculation of the gas diffusion coefficient in bitumen and Henry’s constant was used for estimation of the solvent concentration at the interface with assumption of negligible volume expansion (swelling).The same work was published by Roman and Hejazi[27]and a new graphical approach based on integral method for estimation of diffusion coefficient and Henry’s constant by using late time data of the pressure decay experiment was introduced.Another experimental work was carried out by Yuet al.[28]and diffusion coefficient of CO2in poly(l-lactic acid) was measured using gravimetric method at elevated temperature and high pressure.Furthermore,some experimental studies were conducted by Etminanet al.[29–31]to measure the concentration-dependent diffusivity coefficient in the gas-heavy oil system.First,they modified the pressure decay technique by considering constant gas cap pressure in the diffusion cell.Indeed,they established a relationship between the pressure of gas cap and the boundary condition at the gas/liquid interface.In later works,they focused on the presence of resistance at the interface,the effect of oil expansion and Front-tracking moving boundary algorithm for prediction of the diffusion coefficient.Another interesting works were performed by Liet al.[32,33]in which they applied pressure decay method to measure CO2diffusion coefficient of supercritical CO2in oil Micro and Nano pores of porous media.They coupled Fick’s law with Peng-Robinson equation of state to consider interaction of CO2with oil.However,they ignored incubation period effect or convection stability.In this paper,the diffusion coefficient of CO2in water was determined in a wide range of pressures and temperatures using modified pressure decay method and an accurate apparatus and precise experimental approach were implemented.Moreover,a robust data analysis procedure was presented to interpret data and minimizing the incubation period effect.Initially,the effect of temperature,pressure and CO2phase alteration from gas to supercritical were investigated by consideration incubation period effect for each test.Afterward,the diffusion coefficient of CO2and Methane in an oil sample from one of oil formations of Iran were determined precisely using the current method and the effects of convective instabilities and incubation period effect were minimized.

2.Experimental

2.1.Materials

Dead oil sample which was used in this study was prepared from one of oil formations of southwest of Iran with temperature of 358.15 K and pressure of 26.2 MPa.After filtration of dead oil sample,to remove any sand particles,gas chromatography test was carried out to determine dead oil composition.The compositional analysis of the dead oil is presented in Table 1.Moreover,the CO2and methane with purity of 99.99%were supplied in this work.

Table 1Gas chromatography test results for cleaned dead oil sample

2.2.Experimental setup

All experimental tests have been carried out using Sanchez full visibility PVT cell.The schematic diagram of the experimentalsetup is depicted in Fig.1.The PVT cell has been equipped with data acquisition and processing system,high pressure valves,pipes and filters,calibrated pressure sensor,constant temperature control system and 6 MP digital video camera.The experimental setup includes four major parts as follows:

(1) A high pressure and temperature PVT cell which is a cylindrical space with a certain volume of 250 cm3and inner diameter of 6 cm that contains fluid.Maximum working pressure and temperature of the PVT cell are 150 MPa and 473.15 K.The cell is also equipped with a motorized piston which can change the pressure by moving upward and downward.As it moves downward,the pressure decreases and inversely as it moves upward,the pressure increases.Additionally,pressure,volume and temperature are measured precisely duo to existence of numerous sensors and detectors.Furthermore,a gas-oil interface detector mounted at the top of the cell enables a reliable detection of the dew point.

(2) Injection sub-system which is a highly precision Sanchez pump manufactured by Sanchez company that is applied for injecting of solvents continuously into PVT cell.This pump with volume of 500 cm3has been composed of a double screw pump.This equipment has been specially designed to control different parameters including pressure,volume,and flow rate.

(3) Heating sub-system including an oven which is used for preheating fluid samples and controlling temperature with accuracy of ±0.1 °C.

(4) Recording sub-system including a 6 MP digital video camera which is used for measuring the height of the liquid phase during performing experimental tests.Moreover,a high pressure stainless steel Jefri cell which can tolerate up to 70 MPa is used to maintain gas and liquid sample in the oven until they reach to experimental temperature and be prepared for diffusion tests.The injection of sample into the PVT cell is performed by using Sanchez pump which is connected to the bottom of the Jefri cell.

2.3.Experimental procedures

To conduct a typical diffusion test for measuring gas diffusion coefficient,both Jefri cells are cleaned and dried.Then,they are placed in the oven container and evacuated to remove air or any existing gas in the system.Afterward,both gas and liquid samples are injected into the cells.Then,the power of the heater is turned on and temperature of the system is allowed to rise gradually up to the desired experimental temperature for 24 hours.In the next step,PVT cell is completely cleaned and degassed.Afterward,the prepared heated gas is injected into the cell by using Sanchez pump until the pressure of the cell is reached to the desired experimental pressure.

Fig.1.Schematic of the experimental setup (1 psi=6.895 kPa).

The volume of the PVT cell is fixed to the desired gas volume of 97.5 cm3.Immediately,the inlet valve is closed and simultaneously to increase system temperature up to desired experimental temperature,the heating system of PVT cell is turned.

In the next step,a certain amount of heated liquid sample is pressurized in the Jefri cell to reach PVT cell condition.Next,the banned bottom valve of the PVT cell which is connected to the liquid contained Jefri cell is opened.No natural flow occurs due to the same pressure of Jefri cell and PVT cell.

Then,the liquid sample is injected into the PVT cell at constant pressure condition and simultaneously the PVT cell volume is allowed to increase up to the desired volume of 150 cm3.It is worth noting that due to the same rate of water injection and increasing the volume of PVT cell during process,the pressure of the system is remained almost constant.

After filling the cell with liquid,the inlet liquid valve is closed.Then,the PVT cell is maintained in isolation situation during diffusion process.After a period of time,the gas phase diffuses into the liquid phase,therefore decreasing the gas phase pressure is resulted.Meanwhile,the pressure–decay of gas phase system is recorded every 10 second for about 10 hours.

It should be mentioned that at the end of each experiment,the PVT cell is degassed and cleaned by toluene for preparation of the next experiment.This experimental procedure is repeated for different systems including CO2–water,CO2–dead oil and methane–dead oil systems.

3.Data Analysis Procedure

To measure carbon dioxide diffusion coefficient in liquids the pressure of gas phase in a closed and constant volume of a PVT cell in which gas and liquid are thermodynamically in equilibrium is recorded.The relationship between pressure of gas phasePA,and timet,when gas and liquid phases are thermodynamically in equilibrium,and pure diffusion is established,has been presented and derived using Fick’s second law by Zhanget al.[31]and Jamialahmadiet al.[20]as described in Eq.(1).The interaction of gas and liquid phases have been ignored in this equation.

At the beginning of dissolution,the measured pressure–time data are often affected by mixing and convection due to instabilities of surface tension and initial significant rate of mass transfer[20].The early period or ‘‘incubation period” extends as experimental pressure increases.Consequently,it is more reliable to use middle and late time data for determination of gas diffusion coefficients from the experimental data because pure diffusion and negligible convection occur.

Before starting diffusion process in the cell,the solute concentration or gas concentration in the liquid phase,CA0,is negligible and it is assumed to be zero.In addition,equilibrium pressure,,is the final pressure in each pressure decay experiment.In fact,when pressure change be less than 0.1 psi(1 psi=6.895 kPa).for 10 hours,the experiment is considered to be finished and the pressure is equal to equilibrium pressure.

The termˉzgis average CO2compressibility at experimental temperature and average pressure of PVT cell during recording pressure.This parameter can be easily determined from compressibility curve and is applied to consider non ideal gas behavior at high pressure and elevated temperature.In this paper,equilibrium solubility of CO2,,in water and oil was found at average pressure and experimental temperature,using a reliable thermodynamic software package,Computer Modeling Group(CMG) Winprop?2012 module.The validation of solubility data using (CMG) Winprop?has been confirmed in the literature [29].

Fig.2.The flowchart of data procedure analysis and fitting data to Eq.(1) in which the constants H,L,R,π and experimental temperature are known.

To determine the diffusion coefficient for each test,initially,the best diffusion coefficient was obtained based on curve fitting laboratory data to Eq.(1) using all data which leads to least error and maintains data trend.Afterward,the diffusion coefficient was determined again using all data without first five minutes’ data which is less than previous value.This procedure was repeated until diffusion coefficient change became negligible.In fact,by using this approach,pressure–time data start at the end of the incubation period and the effect of this instability effect will be minimized.In other words,to satisfy assumptions of Eq.(1),only pressure–time data that are after incubation period must be used to determine diffusion coefficient.The summary of data analysis procedure has been presented by a flowchart in Fig.2.

The accuracy of recorded pressures versus time and PVT cell temperature which refer to systematic measurement error and uncertainty in the solvent composition can lead to measured diffusion coefficient be uncertain.Since,the equilibrium solubility of CO2,,is dependent on pressure,temperature and solvent composition,therefore,it can be uncertain.In this study,a tolerance interval for equilibrium solubility based on possible fluctuations of input data in each test was obtained to estimate expected range of diffusion coefficient.Accordingly,the presented data procedure analysis was performed for an interval possible values of solubility to obtain uncertainty in diffusion coefficient.

4.Results and Discussions

4.1.Finding optimum total cell volume

To find optimum total volume of fluids,three tests at the same pressure and temperature conditions were conducted at different total cell volumes.The results of the tests have been presented in Table 2 and Figs.3 and 4.

Table 2Volume sensitivity test to find optimum total cell volume for water–CO2 system

Fig.3.Pressure versus time at 308.15°C(for total cell volume of 100 cm3 and initial pressure of 5.29 MPa).

Fig.3 shows pressure–time data for the water–CO2system at total cell volume of 100 cm3which has not been stabilized due to the insufficiency of total volume.In fact,due to considerable value of pressure and insufficient cell volume,gas will rapidly disperse into liquid and pressure decreases quickly and both convection and diffusion will occur.But,as gas dispersed in liquid,due to insufficient total cell volume,it reaches bottom of the cell and some fluctuations in pressure data are recorded.Therefore,this fluctuation is only due to insufficient cell volume and instability mixing effects.In such conditions,the Rayleigh number for the system would be more than minimum Rayleigh number for closed systems and convection will be occurred.Therefore,it can be concluded that total volume must be increased.Consequently,the experiment was carried out at the same pressure and temperature conditions but total volume of 150 cm3for about 7 hours until negligible pressure changes for about 3 hours.Data analysis and curve fitting proved that diffusion coefficient is equal to 5.99×10-9m2·s-1as presented in Fig.3.Finally,another experiment was performed at the same conditions but total volume of 235 cm3.Data analysis also demonstrated that the diffusion coefficient is equal to 6.00×10-9m2·s-1as presented in Fig.4 which is approximately equal to the previous value.Accordingly,the optimum total volume of the cell was selected to be 150cm3for all experiments in this paper.Moreover,the internal cross-sectionalarea of the cell has been designed such that the variation in the liquid height as a result of the dissolution of the gas could be ignored.Therefore,the height of each phase is supposed to be constant during each experiment.Furthermore,the liquid phase and gas phase should occupy 35% and 65% of the total volume,respectively [20].Therefore,cell length and liquid phase length were selected to be 5.308 cm and 1.858 cm respectively as presented in Fig.5.

Fig.4.Pressure versus time at 308.15 K (experimental and model results for total cell volumes of 150 cm3 and 235 cm3).

Fig.5.Schematic of cell dimension which is applied in all diffusion experiments.

4.2.Temperature effect on diffusion coefficient

To consider temperature effect on diffusion coefficient,several experiments were conducted at approximately same pressure conditions but different temperatures in water–CO2system.The results of the tests have been summarized in Table 3 and final match has been shown in Fig.6.

As described in Table 3,diffusion coefficient of CO2into water strongly depends on temperature.It increases with temperature due to enhancing molecular motions which lead to augmentation of kinetic energy of gas molecules and rate of mass transfer.Moreover,as presented in Table 3,equilibrium time increases with temperature which validates higher motion of gas molecules at higher temperature.Additionally,as represented in Table 3,the incubation period lasts shorter at the higher temperature.It means the convective process is gradually dominated by diffusion process which causes that incubation period be minimized.However,as shown in Fig.7 incubation period reaches its minimum value at the temperature about 333.15 K and incubation period is less sensitive to the temperature.

4.3.Pressure effect on diffusion coefficient

To investigate pressure effect on diffusion coefficient,12 experiments were conducted in the water-CO2system at constant temperature 298.15 K and 323.15 K and two different fluid states of CO2including gas and supercritical,in which,CO2exhibits properties of both gas and liquid.

4.3.1.Pressure effect at T=298.15K

To evaluate the pressure effect on the diffusion coefficient of CO2into the water at constant temperature of 298.15 K,four experiments were conducted.In these tests,temperature and pressure range is less than critical properties of CO2(Tc=304.2 K andPc=7.388 MPa) therefore,CO2remains in the gas phase.The results of the tests have been summarized in Table 4 and final match has been shown in Fig.8.

As presented in Table 4,diffusion coefficient of CO2into water increases gradually with pressure.In fact,increasing pressure,actsas a driving force for gas molecules to diffuse and penetrate faster and generally overcomes the effect of increasing CO2viscosity which prevents fast diffusing rate.Therefore,pressure effect on diffusion coefficient is rather small.Furthermore,with increasing pressure,the required time for the system to reach equilibrium or diffusion duration time decreases.Moreover,as demonstrated in Table 4,with incresing pressure the incubation period lasts shorter at constant temperature (298.15 K) and process is dominated by molecular diffusion.

Table 3Summary of experimental tests results,data analysis and curve fitting results for investigation of temperature effect on diffusion coefficient in water–CO2 system for total cell volume of 150 cm3

Fig.6.Pressure versus time at various temperature 298.15 K,308.15 K,323.15 K,338.15 K and 353.15 K and approximately same initial pressure (experimental and model results for total cell volumes of 150 cm3 in water–CO2 system).

Fig.7.The incubation period dependency on temperature.

4.3.2.Pressure effect at T=323.15K

To investigate pressure effect on the diffusion coefficient of the CO2into water at constant temperature 323.15 K which is more than the critical temperature of CO2,8 experiments were carried out in two different pressure ranges of lower and upper than the critical pressure of CO2.Therefore,the fluid state of CO2in the first four tests is gas and in the second four tests is supercritical.The results of all tests have been summarized in Tables 5 and 6 and final match results have been described in Figs.9 and 10.

Table 4Summary of experimental tests results,data analysis and curve fitting results for investigation of pressure effect on diffusion coefficient in water–CO2 system at 298.15 K for total cell volume of 150 cm3

Table 5Summary of experimental tests results,data analysis and curve fitting results for investigation of pressure effect on diffusion coefficient in water-CO2 system at 323.15 K in which fluid state of CO2 is gas for total cell volume of 150 cm3

Table 6Summary of experimental tests results,data analysis and curve fitting results for investigation of pressure effect on diffusion coefficient in water-CO2 system at 323.15 K in which fluid state of CO2 is supercritical for total cell volume of 150 cm3

As expected,increasing temperature causes increasing in diffusion coefficient.Additionally,at constant temperature,increasing pressure leads to slowly increasing diffusion coefficient.However,as presented in Fig.11 with increasing temperature,diffusion coefficient would be less sensitive to the pressure and the rate of increasing diffusion coefficient is less at higher temperature.This is due to the fact that gases viscosity increases with temperature therefore,effect of viscosity is intensified.

In addition,as represented in Fig.12 when CO2state is supercritical and pressure is more than the critical pressure,the rate of change of diffusion coefficient is significantly lower in comparison with when CO2state is gas due to higher sensitivity of supercritical viscosity to the pressure.Therefore,for supercritical state,the positive impact of pressure on diffusion coefficient will be neutralized by negative impact of viscosity growth.

4.4.CO2-heavy oil system and methane-heavy oil system

To determine the CO2diffusion coefficient in CO2–oil and Methane–oil systems,the same experimental set up was conducted and diffusion coefficient of CO2in oil at supercritical condition was measured.Figs.13 and 14 present the results of the experiments,data analysis and curve fitting results.In theseexperiments,due to the high accuracy of the experimental approach and equipment,no incubation period was detected and no initial data were removed.It means diffusion coefficients were determined using all data.As anticipated,the CO2diffusion coefficient in CO2–oil system is less than the diffusion coefficient in CO2–water system due to the increasing range of pressure and higher value of oil viscosity in comparison with water.Moreover,experimental results demonstrate that CO2diffusion coefficient in oil is higher than methane diffusion coefficient in oil at the same experimental conditions which represent real reservoir condition that oil sample has been prepared.Obtaining this information which is very effective in gas injection modeling industrial projects was the main purpose of this paper.

Fig.8.Pressure versus time at 298.15 K and various initial pressure 2.07,3.45,4.90 and 5.72 MPa(experimental and model results for total cell volumes of 150 cm3 in water–CO2 system).

Fig.9.Pressure versus time at 323.15 K and various initial pressures 2.11,3.40,4.82 and 5.83 MPa(experimental and model results for total cell volumes of 150 cm3 in water–CO2 system in which CO2 state is gas).

4.5.Results validation

To ensure that results are valid,most of experiments were conducted again and all data analysis procedure was repeated and same results were accomplished.Furthermore,the results were compared with previously experimental measurements or simulation studies.

An experimental approach for measuring methane and carbon dioxide diffusion coefficient in heavy oils was presented by Zhanget al.[34].The comparison of results with the current study have been presented in Table 7.However,in the current work the gas state is supercritical and pressure and temperature range are different and the oil composition may not be same but,logically the good agreement between results was achieved.As discussed in this paper,increasing both temperature and pressure lead to rising diffusion coefficient.

The results were also compared with another experimental works which has been performed by Jamialahmadiet al.[20]and Luet al.[35].They measured methane diffusion coefficient in dodecane (C12H26) and crude oil and also CO2diffusion coefficient in water at various pressure and temperature range.Another comparison was carried out with Cadoganet al.experimental work[36]in which diffusion coefficient of CO2in water was measured by Taylor dispersion apparatus.They concluded that pressure has negligible effect on the diffusion coefficient which confirms one of the conclusions in this study.The experimental temperature and pressure range in their study is close to the conditions of the current study and just the oil composition is different.Therefore,the comparison between results was performed and described in Table 8.Although the methodology or fluid composition may not be as same as each other,but acceptable consistency between results and same conclusions were attained.

Table 7Comparison results of diffusion coefficient measurement between current work and Zhang et al. [34]work

Table 8Comparison results of diffusion coefficient measurement between current work and previous published work by Jamialahmadi et al. [20],Lu et al. [35]and Cadogan et al. [36]

Fig.10.Pressure versus time at 323.15 K and various initial pressures 8.60,9.65,14.87 and 18.53 MPa(experimental and model results for total cell volumes of 150 cm3 in water–CO2 system in which CO2 state is supercritical).

Fig.11.Temperature effect on rate of increasing diffusion coefficient with pressure.

Moreover,a molecular dynamic simulation study to predict CO2diffusion coefficient in water-CO2system was carried out by Moultoset al.[37].From their work,it can be concluded that diffusion coefficient of CO2in water at temperature of 323.15K and pressure of 20 MPa is about 5×10-9m2·s-1which has less than 7%relative error in comparison with the current study at same condition.

Fig.12.Effect of phase alteration on CO2 diffusion coefficient dependency on initial pressure in water–CO2 system at 323.15 K (total cell volume of 150 cm3).

5.Conclusions

Fig.13.Pressure versus time at 358.15 K in CO2–oil system in which CO2 solubility in oil is 0.758986 mol·m-3 (total cell volume is 150 cm3 and initial pressure is 22.53 MPa).

Fig.14.Pressure versus time at 358.15 K in methane–oil system in which methane solubility in oil is 0.546856 mol·m-3 (total cell volume is 150 cm3 and initial pressure is 23.33 MPa).

At the beginning of each pressure-decay experiment,dissolution may be affected by convection due to high mass transfer rate and convection dominates on diffusion.The duration of this stage is called incubation period stage.The current experimental approach,minimizes this convective instability effect by using high accuracy experimental setup and precise approach of data analysis.The incubation period duration in all tests is less than 2600 seconds which is significantly lower than those values that have already been reported in the literature.In CO2–oil and methane–oil systems no incubation effect was detected in this study.Moreover,the results showed that incubation period time decreases with increasing diffusion coefficient.

The CO2diffusion coefficient is extremely sensitive to the temperature and it increases rapidly with temperature.Furthermore,the time that system reaches steady state or equilibrium time increases with temperature which validates higher average kinetic energy at higher temperature.However,pressure effect on diffusion coefficient is rather small due to viscosity effect.Pressure rise causes that CO2diffusion coefficient to be increased slowly.Moreover,the results of this paper showed that when CO2state is gas,rate of increasing diffusion coefficient with pressure is decreased with increasing temperature due to the gases viscosity effect at higher temperature.

Since,there is little published data on CO2diffusion coefficient at supercritical condition,in this paper,several diffusion tests were conducted using high accurate apparatus at different pressures more than CO2critical pressure.The results showed that when CO2state is supercritical,the rate of increasing diffusion coefficient with pressure is significantly lower in comparison with when CO2state is gas.

Nomenclature

Cconcentration,mol·m-3

C*solubility,mol·m-3

Ddiffusion coefficient,m2·s-1

Hcell height,m

Lcell length,m

Ppressure,MPa

P*equilibrium pressure,MPa

Runiversal gas constant is equal to 8.314 J·mol-1?K-1

Ttemperature,K

ttime,s

Subscripts

A solute component (In this paper is carbon dioxide,CO2)

g gas phase

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2020.08.034.