Experimental Investigation and Mathematical Modeling of Gas

Article pubs.acs.org/IECR

Cite This: Ind. Eng. Chem. Res. 2019, 58, 12392−12400

Experimental Investigation and Mathematical Modeling of Gas Diffusivity by Carbon Dioxide and Methane Kinetic Adsorption Afshin Davarpanah* and Behnam Mirshekari

Downloaded via BUFFALO STATE on July 28, 2019 at 14:53:54 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Department of Petroleum Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran ABSTRACT: Gas transportation is of significance, especially in carbon dioxide sequestration and successful performances of enhanced methane recovery from shale layers. Among the three primary transportation mechanisms for the gas phase in shale layers, diffusion is considered as the most important phenomenon. The main objective of this comprehensive study is to propose a mathematical model of unipore diffusion and modified unipore diffusion to consider the kinetic adsorption of methane and carbon dioxide for two different shale samples at different pressure ranges. To validate the accuracy of this model, experimental investigations such as methane kinetic adsorption at pressure ranges of 3.2−9.3 MPa and carbon dioxide kinetic adsorption at pressure ranges of 2.5−6.5 were performed to compare with the results of the proposed model. The kinetics adsorption analysis for methane indicated that the required time for the completion of fractional uptake process is about 4−13 min, whereas for the adsorption of carbon dioxide it takes approximately 5−17 min to reach 70% fractional uptake for both shale samples. Subsequently, the modified unipore diffusion model provides a good agreement for both carbon dioxide and methane kinetic adsorption from gas shale layers.

1. INTRODUCTION One of the main challenges of petroleum industries is concerned about carbon dioxide emissions, which is produced from numerous operational performances from the atmosphere to reduce the pollution problem.1−5 Carbon sequestration is widely utilized in production operations to reinject the produced gas in the reservoirs to enhance the oil recovery factor and virtually eliminate the vast expenditures of gas supply. Saline aquifers, depleted reservoirs, and gas hydrate reservoirs are considered as the potential reservoirs to carbon sequestration performances.6−11 Gas transportation in shale layers is defined by the dual porosity or the triple porosity that needed to be numerically modeled to simulate the reservoir characteristics.10,12−16 Although, previous models have considered the primary and secondary porosity in the dual porosity of the shale layers, which indicated that micropores had contained the primary porosity in the shale layers, macropores have consisted of natural fractures and cracks.17−19 The issue of enhanced gas recovery from unconventional reservoirs like shale reservoirs would be essentially vital to optimize the procedure of carbon dioxide and methane production. Gas transportation in shale layers has utterly depended to the primary three mechanisms which control the fluid flow in the rock matrixes.7−9,20,21 These mechanisms are diffusion, viscous flow, and desorption that are depended to the reservoir characteristics and the type of gas phase. Nurturing the concept of gas transportation in shale layers has provided a successful carbon dioxide sequestration and methane recovery performances.20,22−25 Gas transportation in shale layers has divided into two different stages. The first stage © 2019 American Chemical Society

is related to the faster diffusion of the gas phase in macropores that are controlled by Fickian diffusion. In the second stage, there was slower diffusion regarding the Knudsen diffusion in the dominance of pore wall-molecular collision.26−29 Due to the single process of micropores diffusivity, it is the mixture of three kinds of diffusion such as surface diffusion, Knudsen diffusion, and bulk diffusion.30−32 Therefore, the diffusivity phenomenon is expressed as the controlling agent of the gas flow rate from the micropores to the macropores.33−35 The unipore diffusion model for predicting the fractional uptake and gas flow in the coals was reported by Sevenster, which were based on the second Fick’s law to model the diffusion phenomenon.36 According to the Smith and Williams, unipore diffusion model has witnessed an excellent matching with the experimental investigation, especially in the initial times of fractional uptake. Cui et al.investigated the kinetic adsorption of carbon dioxide, methane, and nitrogen by the administration of bidisperse model. According to the results of their investigation, the diffusion rate in micropores had the highest rate for carbon dioxide rather than nitrogen and methane due to the small kinetic diameter of carbon dioxide (0.33 nm) than methane (0.38 nm) and nitrogen (0.36 nm). Moreover, they proposed that regarding the swelling of coal matrixes, which was a cause of gas adsorption, apparent diffusivity was decreased with the pressure increase.23,24,37 Received: Revised: Accepted: Published: 12392

April 20, 2019 June 5, 2019 June 13, 2019 June 13, 2019 DOI: 10.1021/acs.iecr.9b01920 Ind. Eng. Chem. Res. 2019, 58, 12392−12400

Article

Industrial & Engineering Chemistry Research

Figure 1. Schematic of the experimental setup.

provided better fitting with the experimental data for both shale samples.

Mianowski and Marecka (2008) reported that unipore diffusion model was not a good candidate model in the whole time of adsorption processes for methane and carbon dioxide. They concluded that the modified diffusion model, which will be described in the next section, would be a good fitting with experimental data.37 Hildenbrand et al. (2012) provided different mechanisms such as sorption, viscous flow, desorption, and diffusion, which considerably influenced the gas transportation phenomenon in the unconventional oil reservoirs.38 According to their findings, the diffusion phenomenon is primarily controlled the gas transportation in shale gas layers. The existence of carbon dioxide or methane would be considered as the influential parameter of the flow that is called sorption. Moreover, regarding the previous numerical and analytical modeling of the gas transportation in the porous media of shale layers, Knudsen diffusion mechanism would consider as the dominant mechanism in the gas flow rate of shale matrixes.39,40 Yuan et al. (2014) were experimentally evaluated the profound impact of particle size on the gas diffusion and adsorption. Hence, it was concluded that Knudsen and Fickian diffusion were the dominated phenomena on the gas transportation of shale gas layers. Furthermore, gas diffusion is a time-dependent and particle size independent.3 Although, there are numerous studies have been reported in literature to illustrate the importance of gas diffusivity phenomenon in coal layers, in this extensive study, a mathematical model which are based on the Fick’s second law for the diffusion issue was proposed to consider kinetic adsorption of carbon dioxide and methane for two different shale samples regarding the similar behavior of shale layers to coals. To validate the proposed model and quantify them as the more appropriate model, some experimental investigations were taken into consideration at different pressure ranges to compare the gas diffusivity for carbon dioxide and methane. Subsequently, the modified unipore diffusion model has

2. PORE DIFFUSION MODELING 2.1. Unipore Diffusion Model. According to the second law of Fick for spherical fluid flow, the unipore diffusion model is defined as the following equation;

D ∂ ij 2 ∂C yz ∂C jjr zz = (1) ∂t r 2 ∂r k ∂r { Where D is the diffusion coefficient, r is the core radius, t is the time, and C is the concentration adsorbate. In this model, it is assumed that adsorption isotherm is considered as linear flow, and the size of the pores are the same. By solving eq 1 at the constant surface, the diffusing species is defined as the following equation;

ji Dn2π 2t zyz 1 zz expjjjj− 2 j n rp2 zz (2) n=1 k { Where M is the total mass for the diffusing species in the time of t and infinite (∞) respectively and rp is the length of the diffusion path. By the consideration of surface concentration sequential alteration, the gas fraction is defined as the following equation when the fractional uptake was assumed less than 0.5. Mt 6 =1− 2 M∞ π

∞

∑

0.5 Vt P − Pt iDty = 6jjj e zzz = 0 V∞ P π k { 0 − P∞

Where

Vt V∞

(3)

is the fractional uptake, V is the total volume of

adsorbed gas in the time of t and infinite (∞) respectively, De is the effective diffusivity defined as D2 , P0 is the initial pressure rp

drop, and Pt and P∞ are the pressures at time t and infinite (∞), respectively. One of the main consequences of this model is the unclear value of rp when the length of the diffusion path is not equivalent to the spherical radius, and it is validated just 12393

DOI: 10.1021/acs.iecr.9b01920 Ind. Eng. Chem. Res. 2019, 58, 12392−12400

Article


from two layers in this oilfield at the temperature of 313 K. Thereby, the adsorbed volume for shale A and B was calculated at experimental equilibrated pressure and plotted in Figure 2 and 3.

for lower fractional uptake ratios. Furthermore, regarding the previous research investigation in coal beds, it is evident that because of the heterogeneous nature for the coal pores and repulsive force increase with the rise of surface coverage, this model has not provided a proper agreement in the coal beds. 2.2. Modified Unipore Diffusion Model. According to the second law of Fick for spherical fluid flow, the modified unipore diffusion model is defined to estimate the kinetics data for several pressure steps as the following equation: Vt 6 =1− 2 V∞ π

∞

∑ n=1

1 exp( −n2Ct ) 2 n

(4)

Where r is the radius of grain and C is the kinetic parameter 2 that is accounted the gas diffusivity as π 2D . r

According to the Terzyk and Gauden estimations for the calculation of Ct in different ranges, the following equations apply: Ct =

π 2Dt = 0.286·8.151yy1.453 0.0025 ≤ y ≤ 0.8 2 r

(5)

Ct =

0.285 − 0.284y π 2Dt = 0.8 < y ≤ 0.9 2 r 1 − 1.927y + 0.927y 2

(6)

Where y =

Vt V∞

Figure 2. Carbon and methane adsorption for shale A.

is the fractional uptake.

3. MATERIALS AND METHODS To perform the experimental diffusion evaluations, we utilized an experimental setup that is drawn schematically in Figure 1 and is based on the volumetric technique. This experiment was performed beyond the temperature of 313 K for shale samples from Pazanan oilfield in the southwest of Iran. Two types of shale samples were collected from two geological sections of this oilfield to provide a comparison with them. To simulate the process of gas molecules diffusion in the sale matrixes, we took experimental diffusion setup by the administration of powered shale samples into consideration. The core shale samples were crushed and sieved in the size of 160−450 μm with the approximate weight of 50 g. The more detailed process of adsorption and diffusion experimental evaluations as it was performed in this paper according to the volumetric techniques were widely reported in the literature. Diffusion experimental evaluations were performed in five pressure drops for both carbon dioxide (2.5−6.5 MPa) and methane (3.2−9.3 MPa). First of all, the provided gas, which consisted of carbon dioxide and methane, was injected into the reference tank to give the equilibrium pressure. Since then, the equilibrated gas was conducted to the core sample for about 20 h, and the records of the experiment were reported in the data collection system. In this experimental evaluation, the initial time of the core sample was considered the maximum pressure value after the valve between the core sample and the reference tank was opened. Therefore, the initial pressure was measured in this step, and other parameters such as the diffusion coefficient and the kinetic parameter were estimated by the unipore diffusion and modified unipore diffusion model.

Figure 3. Carbon and methane adsorption for shale B.

As is evident in Figures 2 and 3, the adsorption isotherm behavior has followed the type I behavior for carbon dioxide and methane. Furthermore, for shale B, there is good repeatability of 6.5% of adsorbed volume for methane adsorption. 4.2. Methane Kinetic Adsorption. The kinetic adsorption of methane was conducted experimentally for both shale samples at five different pressures of 3.2, 4.8, 6.1, 7.6, and 9.3 MPa sequentially to compare each pressure on the fractional uptake. The value of fractional uptake versus time for different five pressure points was plotted in Figures 4 and 5. As can be seen in Figures 4 and 5, the methane kinetic adsorption rate has witnessed a linear rise in the first periods and in the next time increases, it has reached a plateau for each pressure. As it is evident in both shale sample, the plotted curves are approximately the same as the kinetic sorption graphs that were reported in previous literature. According to Figures 4 and 5, the sorption rate for several pressure drops is not differentiated enough. The adsorption kinetics rate is calculated precisely with the linear slope of the adsorption kinetics graphs, and they are expressed statistically in Table 1. The range of adsorption kinetic slope is approximately same for both shales; it is 0.0417−0.0456 for

4. RESULTS AND DISCUSSION 4.1. Adsorption of Carbon Dioxide and Methane. The procedure of carbon dioxide and methane adsorption were explained in more detail in section 3 for two different shales 12394


Article


Table 2. Fractional Uptake Time of Methane Adsorption (sec) for Shale A Vt/V∞

3.2 MPa

4.8 MPa

6.1 MPa

7.6 MPa

9.3 MPa

10 30 50 70 85

11 180 490 670 1080

23 115 234 367 512

19 122 264 405 823

21 142 270 394 784

17 128 176 253 416

Table 3. Fractional uptake time of methane adsorption (sec) for shale B

Figure 4. Methane kinetics adsorption for shale A.

Vt/V∞

3.2 MPa

4.8 MPa

6.1 MPa

7.6 MPa

9.3 MPa

10 30 50 70 85

12 95 160 240 310

14 86 153 267 403

17 73 152 243 374

18 101 172 221 335

21 82 134 197 286

perform as the function of adsorption vacant site and the high concentration of driving forces, which is considered to be an available mass transfer agent to transfer gas molecules to the vacant places.41 4.3. Carbon Dioxide Kinetic Adsorption. The kinetic adsorption of carbon dioxide was conducted experimentally for both shale samples at five different pressures of 2.5, 3.5, 4.5, 5.5, and 6.5 MPa sequentially to compare each pressure on the fractional uptake. The value of fractional uptake versus time for different five pressure points was plotted in Figures 6 and 7. As

Figure 5. Methane kinetics adsorption for shale B.

Table 1. Methane Kinetic Adsorption Slope for Shale A and B pressure (MPa)

ma for shale A

m for shale B

3.2 4.8 6.1 7.6 9.3

0.0456 0.04443 0.0435 0.0422 0.0417

0.0440 0.0432 0.0429 0.0426 0.0406

Figure 6. Carbon dioxide kinetics adsorption for shale A.

a

m is the slope of adsorption kinetic graph.

shale A and 0.0406−0.0440 for shale B. Furthermore, the slope of the adsorption kinetic graph is decreased gradually with the increase of pressure drop. Hence, pressure drop would play a substantial role in the diffusion of gas shale layers, and it has a negative relation between pressure and r2, which was observed in refs 3, 23, and 24. The fractional uptake for both shale samples are measured at different pressure drops, and they are expressed in Tables 2 and 3. As is evident in Table 2 and 3, approximately 70% of fractional uptake was completed in a short time of 4−13 min. However, the rest of the adsorption (30%) was taken a long time. Therefore, it indicated that gas molecules uptake in the primary stages of contact is fast enough, and to reach the equilibrium point, it becomes slower in the next steps. The reason for this phenomenon might be related to the presence of numerous active surface sites that are adsorbed fast to

Figure 7. Carbon Dioxide kinetics adsorption for shale B. 12395


Article


range of adsorption kinetic slope is approximately the same for both shales; it is 0.0213−0.0392 for both shales. Furthermore, the slope of the adsorption kinetic graph has the highest value at the pressure drop of 2.5 MPa. Hence, pressure drop would play a substantial role in the diffusion of gas shale layers and provide faster rates at a lower pressure which has decreased with the pressure rise, and it has a negative relation between pressure and r2 that was observed by Cui et al. (2009) and Bhowmik and Dutta (2013).3,23 To provide a comparison between the adsorption kinetics for carbon dioxide and methane, Tables 2−5 are compared together separately for each shale sample. As is evident, for shale A, 70% of fractional uptake for methane is 253−670 s, which is lower than carbon dioxide fractional uptake (302− 1095 s). Also, for shale B, 70% of fractional uptake for methane is 197−240 s, which is lower than carbon dioxide fractional uptake (286−617 s). Thereby, the methane adsorption rate was faster than carbon dioxide adsorption rate, which might be related to the smaller methane molecular mass (16.04 g/mol) rather than 44 g/mol for carbon dioxide. Because of Graham’s diffusion law, the gas diffusion rate has a different proportion to the molecular mass square root. Hence, methane has a smaller molecular mass than carbon dioxide and a faster diffusion rate according to Graham’s diffusion law. Subsequently, because of the faster methane sorption rate than carbon dioxide, it would be a significant issue during the enhanced gas recovery processes and the gas breakthrough occurred at earlier times for methane, which was previously reported in the literature.6,8,9,24,42 4.4. Validation of Proposed Models with Experimental Data for Methane. Equation 3 was used to model the adsorption rate of methane for both shale samples. To do this, we drew the fractional uptake versus time; the adsorption kinetic plots are linear at the beginning stages, and it has reached a plateau after the critical time. To calculate the diffusion coefficient (D) and effective diffusivity (De), we used the slope of the linear section in unipore diffusion model. Then, fractional uptake was calculated again by the consideration of diffusion coefficient, and the results were compared with the experimental investigation in previous sections. The modified unipore diffusion model was derived from eq 4 to model the methane adsorption kinetics at different pressure drops. First of all, C is estimated according to the previous studies correlations, and then fractional uptake was calculated. The adsorption kinetic plots are linear at the beginning stages, and it has reached a plateau after the critical time. Diffusion parameters that were used in unipore diffusion model and modified unipore diffusion model were expressed statistically in Tables 7 and 8. As it is evident from Tables 7 and 8, the diffusion coefficient decrease due to the pressure increase is related to the matrix swelling of shale that was caused by adsorption. As the swelling issue has reduced the permeability, shale micropores were blocked, and the channel

can be seen in Figures 6 and 7, the carbon dioxide kinetic adsorption rate witnessed a linear rise in the first periods, and in the next time increases it reached a plateau for each pressure. As is evident in both shale samples, the plotted curves are approximately the same as the kinetic sorption graphs that were reported in previous literature. The fractional uptake for both shale samples is measured at different pressure drops, and they are expressed in Table 4 and Table 4. Fractional Uptake Time of Methane Adsorption (s) for Shale A Vt/V∞

2.5 MPa

3.5 MPa

4.5 MPa

5.5 MPa

6.5 MPa

10 30 50 70 85

12 144 234 302 514

14 170 251 785 2056

19 153 241 642 1478

24 124 203 584 1246

16 302 412 1095 19658

Table 5. Fractional Uptake Time of Methane Adsorption (s) for Shale B Vt/V∞

2.5 MPa

3.5 MPa

4.5 MPa

5.5 MPa

6.5 MPa

10 30 50 70 85

8 137 164 286 582

19 174 210 531 1013

14 117 221 702 2458

16 128 230 592 3679

17 146 254 617 12415

5. As is evident in Table 4 and 5, approximately 70% of fractional uptake for shale A was completed in 5−17 min, and for shale, B was completed in 5−10 min. However, the rest of adsorption (30%) was taken a long time regarding the pressure increase. Therefore, it indicated that gas molecules uptake in the primary stages of contact is fast enough, and to reach the equilibrium point; it becomes slower in the next steps. The carbon dioxide adsorption kinetics rate is calculated precisely with the linear slope of the adsorption kinetics graphs, and they are expressed statistically in Table 6. The Table 6. Carbon Dioxide Kinetic Adsorption Slope for Shale A and B pressure (MPa)

ma for shale A

m for shale B

2.5 3.5 4.5 5.5 6.5

0.0392 0.0362 0.0337 0.0286 0.0267

0.0325 0.0268 0.0241 0.0228 0.0213

a

m is the slope of adsorption kinetic graph.

Table 7. Diffusion Parameters of Methane for Shale A and B pressure (MPa) 3.2 4.8 6.1 7.6 9.3

D (cm2/s) for shale A 3.6514 3.5314 3.1514 2.9714 2.7464

× × × × ×

−8

10 10−8 10−8 10−8 10−8

C (s−1) for shale A 1.7543 2.6840 1.2156 3.4813 2.5716

× × × × ×

−3

10 10−3 10−3 10−3 10−3

12396

D (cm2/s) for shale B 3.7325 3.5271 3.4462 3.1876 3.0297

× × × × ×

−8

10 10−8 10−8 10−8 10−8

C (s−1) for shale B 5.1354 3.0341 2.8634 4.3261 3.2583

× × × × ×

10−3 10−3 10−3 10−3 10−3


Article

Industrial & Engineering Chemistry Research Table 8. Diffusion Parameters of Carbon Dioxide for Shale A and B pressure (MPa) 2.5 3.5 4.5 5.5 6.5

D (cm2/s) for shale A 2.7621 2.2534 1.9317 1.5624 1.2168

× × × × ×

−8

10 10−8 10−8 10−8 10−8

C (s−1) for shale A 3.146 8.698 8.217 5.425 4.967

× × × × ×

−3

10 10−3 10−3 10−3 10−3

D (cm2/s) for shale B 2.0126 1.9878 1.6217 1.3622 1.1426

× × × × ×

−8

10 10−8 10−8 10−8 10−8

C (s−1) for shale B 2.012 1.875 6.145 7.416 4.698

× × × × ×

10−3 10−3 10−3 10−3 10−3

was narrowed, which caused it to resist the movement of gas molecules . Another reason for this decrease might be related to the repulsive forces, which are happened between the adsorbed molecules and the surface coverages.19,24 The comparison of the proposed model with an experimental investigation for shale A is plotted in Figure 8−12. As can be seen in Figure 8−12, unipore diffusion model

Figure 11. Validity of unipore diffusion model and modified unipore diffusion model with experimental data for shale A at P = 7.6 MPa.




Figure 13. Validity of unipore diffusion model and modified unipore diffusion model with experimental data for shale B at P = 3.2 MPa.


has provideda good agreement with experimental data in the initial times for all pressure stages. At longer stages, modified unipore diffusion model has matched with the experimental data for shale A. Furthermore, the comparison of the proposed model with the experimental investigation for shale B is plotted in Figure 13−17. As can be seen in Figures 13−17, unipore diffusion model has provided a good agreement with experimental data in the initial times for all pressure stages.


At longer stages, the modified unipore diffusion model matches with the experimental data for shale B. 4.5. Validation of Proposed Models with Experimental Data for Carbon Dioxide. The comparison of the 12397


Article






Figure 17. Validity of unipore diffusion model and modified unipore diffusion model with experimental data for shale B at P = 9.3 MPa. Figure 21. Validity of unipore diffusion model and modified unipore diffusion model with experimental data for shale A at P = 5.5 MPa.

proposed model with an experimental investigation for shale A is plotted in Figure 18−22. As can be seen in Figure 18−22,

Figure 18. Validity of unipore diffusion model and modified unipore diffusion model with experimental data for shale A at P = 2.5 MPa. Figure 22. Validity of unipore diffusion model and modified unipore diffusion model with experimental data for shale A at P = 6.5 MPa

unipore diffusion model has provided a good agreement with experimental data in the initial times for all pressure stages. At longer stages, modified unipore diffusion model has matched with the experimental data for shale A. Furthermore, the comparison of the proposed model with an experimental investigation for shale B is plotted in Figure 23−27. As can be seen in Figure 23−27, unipore diffusion model has provided a good agreement with experimental data in the initial times for all pressure stages. At longer stages, the modified unipore

diffusion model has matched with the experimental data for shale B.

5. CONCLUSION Production from unconventional reservoirs like gas shale layers has considered as one of the principal concerns of petroleum industries which should be taken into consideration to 12398


Article


Figure 23. Validity of unipore diffusion model and modified unipore diffusion model with experimental data for shale B at P = 2.5 MPa. Figure 27. Validity of unipore diffusion model and modified unipore diffusion model with experimental data for shale B at P = 6.5 MPa.

min, whereas for the adsorption of carbon dioxide it is approximately 5−17 min to reach the 70% of fractional uptake for both shale samples. Because of the smaller molecular mass for the methane (16.04 g/mol) than the carbon dioxide (44 g/ mol) has witnessed faster adsorption rate, and this phenomenon is obeyed as Graham’s diffusion law. Moreover, a diffusivity decrease with the increase in pressure would imply the dominant influence of molecular diffusion and molecule− molecule collision of the gas phase. Unipore diffusion model and modified unipore diffusion model were modeled analytically for both shales in the presence of carbon dioxide and methane adsorption and to validate the accuracy of each model, they were compared with the experimental data for both shale samples at different pressure drops. According to the results of this comprehensive study, modified unipore diffusion model has provided better matching with the experimental data in the whole pressure ranging period. Consequently, the modified unipore diffusion model has recommended for the production of gas from shale layers by the presentation of carbon dioxide and methane in the enhanced gas recovery performances.


■


AUTHOR INFORMATION

Corresponding Author

*Email: [email protected]. ORCID

Afshin Davarpanah: 0000-0002-3697-1808 Notes

The authors declare no competing financial interest.

■

NOMENCLATURE D = diffusion coefficient r = core radius t = time C = concentration of adsorbate M = total mass rp = length of the diffusion path Vt = fractional uptake


emphasize the concept of gas transportation in the porous medium. Kinetic adsorption of carbon dioxide and methane were analytically modeled for both shale samples, and they were experimentally investigated to compare the validity of propose models. The proposed models were included unipore diffusion model and modified unipore diffusion model to select the more appropriate and compatible technique regarding the provided experimental data. The kinetics adsorption analysis for methane indicated that the required time for the completion 70% of fractional uptake process is about 4−13

V∞

Vt = total volume of adsorbed gas in the time of t V∞ = total volume of adsorbed gas in the time of ∞ De = effective diffusivity Pt = pressure at time t P∞ = pressure at time ∞ C = Kinetic parameter y = Fractional uptake 12399


Article


■

(21) Davarpanah, A. A feasible visual investigation for associative foam > \ polymer injectivity performances in the oil recovery enhancement. Eur. Polym. J. 2018, 105, 405−411. (22) Connell, L. D.; Lu, M. A dual-porosity model for gas reservoir flow incorporating adsorption behaviourPart II. Numerical algorithm and example applications. Transp. Porous Media 2007, 69 (2), 139−158. (23) Cui, X.; Bustin, A.; Bustin, R. M. Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications. Geofluids 2009, 9 (3), 208−223. (24) Cui, X.; Bustin, R. M.; Dipple, G. Selective transport of CO2, CH4, and N2 in coals: insights from modeling of experimental gas adsorption data. Fuel 2004, 83 (3), 293−303. (25) Eliebid, M.; et al. Effect of CO2 adsorption on enhanced natural gas recovery and sequestration in carbonate reservoirs. J. Nat. Gas Sci. Eng. 2018, 55, 575−584. (26) Gan, H.; Nandi, S.; Walker, P., Jr Nature of the porosity in American coals. Fuel 1972, 51 (4), 272−277. (27) Harpalani, S.; Prusty, B. K.; Dutta, P. Methane/CO2 sorption modeling for coalbed methane production and CO2 sequestration. Energy Fuels 2006, 20 (4), 1591−1599. (28) Honari, A.; et al. Enhanced gas recovery with CO2 sequestration: The effect of medium heterogeneity on the dispersion of supercritical CO2−CH4. Int. J. Greenhouse Gas Control 2015, 39, 39−50. (29) Dunn, C. A.; Shi, Z.; Zhou, R.; Gin, D. L.; Noble, R. D. (CrossLinked Poly (Ionic Liquid)−Ionic Liquid−Zeolite) Mixed-Matrix Membranes for CO2/CH4 Gas Separations Based on Curable Ionic Liquid Prepolymers. Ind. Eng. Chem. Res. 2019, 58, 4704. (30) Song, W.; et al. Methane surface diffusion capacity in carbonbased capillary with application to organic-rich shale gas reservoir. Chem. Eng. J. 2018, 352, 644−654. (31) An, Y.; et al. Nuclear magnetic resonance measurement of methane diffusion in organic-rich shales. Fuel 2019, 247, 160−163. (32) Wu, K.; et al. Model for surface diffusion of adsorbed gas in nanopores of shale gas reservoirs. Ind. Eng. Chem. Res. 2015, 54 (12), 3225−3236. (33) Shi, J.; Durucan, S. Methane Displacement Desorption in Coal by CO2 Injection: Numerical Modelling of Multi-Component Gas Diffusion in Coal Matrix. In Greenhouse Gas Control Technologies 6th International Conference; Elsevier, 2003. (34) Davarpanah, A.; Mirshekari, B. A simulation study to control the oil production rate of oil-rim reservoir under different injectivity scenarios. Energy Reports 2018, 4, 664−670. (35) Roy Moulik, S.; et al. Evidence of Isotope Selective Diffusion of Ambient CO2 Gas in WO3 Nanostructures. J. Phys. Chem. C 2019, 123 (4), 2573−2578. (36) Sevenster, P. Diffusion of gases through coal. Fuel 1959, 38 (4), 403−418. (37) Mianowski, A.; Marecka, A. The isokinetic effect as related to the activation energy for the gases diffusion in coal at ambient temperatures: part I. Fick’s diffusion parameter estimated from kinetic curves. J. Therm. Anal. Calorim. 2009, 95 (1), 285−292. (38) Amann-Hildenbrand, A.; Ghanizadeh, A.; Krooss, B. M. Transport properties of unconventional gas systems. Mar. Pet. Geol. 2012, 31 (1), 90−99. (39) Darabi, H.; et al. Gas flow in ultra-tight shale strata. J. Fluid Mech. 2012, 710, 641−658. (40) Jin, J.; Wang, Y.; Nguyen, T. A. H.; Bai, B.; Ding, W.; Bao, M. The morphology and surface-chemistry of gas-wetting nanoparticles and its effect on the liquid menisci in porous media. Ind. Eng. Chem. Res. 2019, 58, 6747. (41) Mall, I. D.; Srivastava, V. C.; Agarwal, N. K. Removal of Orange-G and Methyl Violet dyes by adsorption onto bagasse fly ashkinetic study and equilibrium isotherm analyses. Dyes Pigm. 2006, 69 (3), 210−223. (42) Jessen, K.; Tang, G.-Q.; Kovscek, A. R. Laboratory and simulation investigation of enhanced coalbed methane recovery by gas injection. Transp. Porous Media 2008, 73 (2), 141−159.

REFERENCES

(1) Alshehry, A. S.; Belloumi, M. Energy consumption, carbon dioxide emissions and economic growth: The case of Saudi Arabia. Renewable Sustainable Energy Rev. 2015, 41, 237−247. (2) Balcombe, P.; Brandon, N.; Hawkes, A. Characterising the distribution of methane and carbon dioxide emissions from the natural gas supply chain. J. Cleaner Prod. 2018, 172, 2019−2032. (3) Bhowmik, S.; Dutta, P. Adsorption rate characteristics of methane and CO2 in coal samples from Raniganj and Jharia coalfields of India. Int. J. Coal Geol. 2013, 113, 50−59. (4) Davarpanah, A., Shirmohammadi, R.; Mirshekari, B. Experimental evaluation of polymer-enhanced foam transportation on the foam stabilization in the porous media. Int. J. Environ. Sci. Technol. 2019, DOI: 10.1007/s13762-019-02280-z (5) Ebadati, A.; Akbari, E.; Davarpanah, A. An experimental study of alternative hot water alternating gas injection in a fractured model. Energy Exploration & Exploitation 2019, 37, 945. (6) Busch, A.; et al. Methane and carbon dioxide adsorption− diffusion experiments on coal: upscaling and modeling. Int. J. Coal Geol. 2004, 60 (2−4), 151−168. (7) Charlet, L.; et al. Diffusive transport and reaction in clay rocks: A storage (nuclear waste, CO2, H2), energy (shale gas) and water quality issue. Adv. Water Resour. 2017, 106, 39−59. (8) Charrière, D.; Pokryszka, Z.; Behra, P. Effect of pressure and temperature on diffusion of CO2 and CH4 into coal from the Lorraine basin (France). Int. J. Coal Geol. 2010, 81 (4), 373−380. (9) Clarkson, C.; Bustin, R. The effect of pore structure and gas pressure upon the transport properties of coal: a laboratory and modeling study. 1. Isotherms and pore volume distributions. Fuel 1999, 78 (11), 1333−1344. (10) Davarpanah, A.; Mirshekari, B. Mathematical modeling of injectivity damage with oil droplets in the waste produced water reinjection of the linear flow. European Physical Journal Plus 2019, 134 (4), 180. (11) Davarpanah, A.; et al. Integrated production logging tools approach for convenient experimental individual layer permeability measurements in a multi-layered fractured reservoir. J. Pet. Explor. Prod. Technol. 2018, 8 (3), 743−751. (12) Wei, Z.; Zhang, D. Coupled fluid-flow and geomechanics for triple-porosity/dual-permeability modeling of coalbed methane recovery. International Journal of Rock Mechanics and Mining Sciences 2010, 47 (8), 1242−1253. (13) King, G. R. Material balance techniques for coal seam and Devonian shale gas reservoirs. In SPE Annual Technical Conference and Exhibition; Society of Petroleum Engineers, 1990. (14) Davarpanah, A.; Mazarei, M.; Mirshekari, B. A simulation study to enhance the gas production rate by nitrogen replacement in the underground gas storage performance. Energy Reports 2019, 5, 431− 435. (15) Mazarei, M.; et al. The feasibility analysis of underground gas storage during an integration of improved condensate recovery processes. J. Pet. Explor. Prod. Technol. 2019, 9 (1), 397−408. (16) Davarpanah, A. Feasible analysis of reusing flowback produced water in the operational performances of oil reservoirs. Environ. Sci. Pollut. Res. 2018, 25 (35), 35387−35395. (17) Perera, M. S. A.; et al. Numerical simulation of gas flow through porous sandstone and its experimental validation. Fuel 2011, 90 (2), 547−554. (18) Davarpanah, A.; Mirshekari, B. Experimental study and field application of appropriate selective calculation methods in gas lift design. Petroleum Research 2018, 3 (3), 239−247. (19) Ebadati, A.; Davarpanah, A.; Mirshekari, B. Stimulated-based characterization recovery enhancement feedback of oil-rim reservoirs. Energy Sources, Part A 2018, 40 (21), 2528−2541. (20) Dong, C.; et al. What is the probability of achieving the carbon dioxide emission targets of the Paris Agreement? Evidence from the top ten emitters. Sci. Total Environ. 2018, 622, 1294−1303. 12400


Experimental Investigation and Mathematical Modeling of Gas

Recommend Documents