# The Influence of Sorption Pressure on Gas Diffusion in Coal Particles: An Experimental Study

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{ae}of the BD model, three samples display a decreasing trend with increasing gas pressure while the other sample shows a V-type trend. The slow diffusion coefficient D

_{ie}of BD model increases with gas pressure for all samples, while the ratio β is an intrinsic character of coal and remains constant. For the DD model, the characteristic rate parameter k

_{Φ}does not change sharply and the stretching parameter α increases with gas pressure. Both D

_{ae}and D

_{ie}are in proportion to k

_{Φ}, which reflect the diffusion rate of gas in the coal. The impacts of pore characteristic on gas diffusion were also analyzed. Although pore size distributions and specific surface areas are different in the four coal samples, correlations are not apparent between pore characteristic and diffusion coefficients.

## 1. Introduction

_{4}and CO

_{2}to conduct the adsorption kinetics experiments when the pressure is equal to 0.1 MPa and 5 MPa respectively. They found that the diffusion coefficient increases with gas pressure. Pan et al. [3] performed CH

_{4}adsorption/desorption diffusion test within 0~4 MPa pressures range, and results show a direct ratio between diffusion coefficient and gas pressure. Jian et al. [13] carried out the desorption experiments within 0~4.68 MPa pressure range and the conclusion remains the same. However, some scholars reckon that the diffusion coefficient decreases with the increase in pressure. Cui et al. [8] found that the diffusion coefficient of CO

_{2}reduces when gas pressure is smaller than 3.6 MPa. Staib et al. [4] conducted the adsorption kinetics experiments and analyzed the results using the BD model. It was found that the diffusion coefficient D

_{a}lowers when the pressure increases. Shi et al. [14] tested the influence of CO

_{2}injection on microporous diffusion coefficient after the adsorption of CH

_{4}was balanced. Findings show that the increasing injection pressure of CO

_{2}would cause the reduction of micropore diffusion coefficient. There are also a few scholars who concluded that gas pressure has small effects on the diffusion coefficient. Nandi et al. [15] conducted CH

_{4}adsorption/desorption experiments on bituminous and anthracite coals and they did not find an apparent relationship between pressure and gas sorption rate. To summarize, the research outcomes are listed in Table 1.

## 2. The Diffusion Models

#### 2.1. The Unipore Diffusion Model

_{t}in the equation refers to the total gas adsorption/desorption quantity at time t, m

_{∞}is the total quantity after the gas adsorption/desorption is balanced, r represents the radius of spherical coal particle, D refers to the diffusion coefficient (m

^{2}/s) and the value of $\frac{D}{{r}^{2}}$ is defined as the effective diffusion coefficient D

_{e}(1/s).

#### 2.2. The Bidisperse Diffusion Model

_{a}and D

_{i}respectively. The gas diffusion under the two systems are driven by the concentration gradients between exterior and interior of the coal particle. The BD model is illustrated in Figure 2. The simplified BD model includes the fast macropore diffusion stage and the slow micropore diffusion stage [5,22].

_{a}in the equation refers to the total gas adsorption/desorption quantity at time t in the macropore, r

_{a}and D

_{a}represent the radius of macropore spherical coal particle and macropore diffusion coefficient (m

^{2}/s), respectively. The value of $\frac{{D}_{a}}{{r}_{a}^{2}}$ is defined as the effective diffusion coefficient D

_{ae}(1/s).

_{i}in the equation refers to the total gas adsorption/desorption quantity in the micropore at time t, r

_{i}and D

_{i}represent the radius of micropore spherical coal particle and micropore diffusion coefficient (m

^{2}/s), respectively. The value of $\frac{{D}_{i}}{{r}_{i}^{2}}$ is defined as the effective diffusion coefficient D

_{ie}(1/s).

#### 2.3. The Dispersive Diffusion Model

_{t}in the equation refers to the total gas adsorption/desorption quantity, m

_{∞}is the total quantity after the gas adsorption/desorption is balanced, k

_{Φ}is the characteristic rate parameter, α is the stretching parameter (0 < α < 1). The research of Staib et al. [23] shows that α is an intrinsic property of coal and is greatly influenced by the coal pore characteristic.

## 3. Diffusion Experiments

_{m}

_{1}; (b) gas pressure in the reference tank after the gas is injected into the coal samples tank, P

_{m}

_{2}; (c) gas pressure in the coal samples tank before the reference tank gas is injected, P

_{c}

_{1}; (d) gas pressure in the coal samples tank after the reference tank gas is injected, P

_{c}

_{2}. P

_{m}

_{1}, P

_{m}

_{2}and P

_{c}

_{1}are constant while P

_{c}

_{2}is flexible.

_{4}and the correlation R

^{2}is listed in Table 3. It can be seen that the adsorption and desorption characteristics of CH

_{4}are represented well by the Langmuir model. The adsorption characteristic parameters are calculated in Table 3.

## 4. Analysis and Discussion

#### 4.1. Model Applicability Analysis

#### 4.2. Analysis of Pressure’s Effect on the Gas Diffusion

_{ae}, slow effective diffusion coefficient D

_{ie}and the ratio of macropore adsorption/desorption to the total adsorption/desorption β. Using Equation (4) to calculate the BD characteristic parameters and analyze the impact of pressure on D

_{ae}(Figure 6) and quadratic polynomial is to fit the results, the fitting goodness and calculated coefficient are shown in Table 4. As can be seen from Figure 6, the macropore diffusion coefficient D

_{ae}decreases with the increase in pressure in three out of four sample coals (i.e, HC, XM and QS). Concerning the HD, D

_{ae}shows a V-shape trend, which first decreases and then increases as the increases in pressure. Figure 6 also shows that the impact law of pressure on D

_{ae}is better illustrated by the quadratic polynomial. When comparing the values of D

_{ae}, in both the adsorption and desorption processes, D

_{ae}(HC) > D

_{ae}(XM) > D

_{ae}(QS) > D

_{ae}(HD). The difference of D

_{ae}in the absorption versus the desorption process becomes larger from HC to QS. No significant increasing trend of HC, XM and QS is found when the pressure increases, It is suspected that the set maximum pressure is not in the threshold level.

_{ie}is analyzed and is shown in Figure 7. Linear regression is used to fit the results and, results of the fitting goodness and calculated coefficient are given in Table 5. It can be clearly seen that the slow efficient diffusion coefficient D

_{ie}increases with the increase in pressure for all four samples. The impact law of pressure on D

_{ie}is better explained by the linear regression. When comparing the values of D

_{ie}, the order is D

_{ie}(HC) > D

_{ie}(XM) > D

_{ie}(QS) > D

_{ie}(HD) in the adsorption process and D

_{ie}(HC) > D

_{ie}(QS) > D

_{ie}(XM) > D

_{ie}(HD) in the desorption process.

_{Φ}and the stretching parameter α. The influencing law of pressure on the k

_{Φ}and α are re-analyzed, and calculated based on the gas diffusion experimental results and Equation (5). The results are shown in Figure 8 and Figure 9, respectively.

_{Φ}decreases with the increase in pressure which ranges from 0~3 MPa in their studies. In terms of the vitrinite-rich coal samples, α increases with gas pressure while for the inertinite-rich coal samples, no significant changing trend is found for α. Figure 8 shows that in our study, k

_{Φ}keeps unchanged in the pressure fluctuation process. Concerning XM and QS, k

_{Φ}slightly decreases with the increase in pressure when the pressure is less than P

_{0}, but it keeps constant while the pressure is larger than P

_{0}.

_{ae}, D

_{ie}and k

_{Φ}are the largest for HC, in the middle for XM and QS, and the smallest for HD. The linear regression results of k

_{Φ}on D

_{ae}and k

_{Φ}on D

_{ie}are shown in Figure 10 and Figure 11, respectively.

_{ae}, D

_{ie}and k

_{Φ}in our experimental results, and the goodness of fit is the best for D

_{ae}and k

_{Φ}. It suggests that both the diffusion coefficients D

_{ae}and D

_{ie}and characteristic rate parameter k

_{Φ}are suitable for describing the coal gas diffusion rate. The analysis above suggests that the fast diffusion coefficient D

_{ae}decreases with the increase in pressure while the slow diffusion coefficient D

_{ie}increases with the increase in pressure. k

_{Φ}keeps fixed and thus may be considered as a combined effect of D

_{ae}and D

_{ie}.

#### 4.3. Analysis of the Relationship between Pore Structure Characteristics and Gas Diffusion

_{4}diffusion under different pressures, we found the diversity of gas diffusion coefficients in both absorption and desorption process for different coal samples. Because the coal pore structures might directly affect the diffusion process of gas [28], experiments on the low temperature nitrogen absorption and mercury penetration were conducted to test the characteristics of coal pore structure.

_{ae}, D

_{ie}and k

_{Φ}on pore volume. As shown in Figure 12, the correlation between the pore volume and the diffusion coefficients is, largest for k

_{Φ}(R

^{2}= 0.912), middle for D

_{ae}(R

^{2}= 0.793) and smallest for D

_{ie}(R

^{2}= 0.722).

_{ae}, D

_{ie}and k

_{Φ}of CH

_{4}is the largest in HC, suggesting the porosity development level is correlated with the diffusion rate. However, Figure 13a shows that D

_{ae}of HD, QS and XM significantly increases when D

_{ae}is smaller than 1.6 × 10

^{−11}while the specific surface area keeps unchanged. Figure 13b,c show that the impact of specific surface area on D

_{ie}and k

_{Φ}is small in all coal samples excluding HC. It is worth to mention that our experimental results can only be considered as reference due to the small number of coal samples. The impact of coal structure on the diffusion parameters requires further study. In conclusion, the fluctuation of diffusion coefficients with respect to the gas pressure is correlated to the variation of pore characteristics, but the reason is still mysterious due to lack of evidence.

#### 4.4. Discussion on the Influence of Inconstant Diffusion Coefficients on CBM Recovery

_{ae}but a decrease of slow diffusion coefficient D

_{ie}during the drop of coal seam pressure. The increase or decrease of diffusion coefficient will certainly accelerate or hinder gas flow, but these two effects might be compromised for the BD model and the ultimate effect depends on the net value of these two effects. For the DD model, k

_{Φ}keeps at a stable level, this phenomenon proves the above speculation as k

_{Φ}can be seen as a combination of D

_{ae}and D

_{ie}. However, the stretching parameter α decreases during pressure dropping, which indicates the CBM recovery rate will be reduced due to the change of diffusion coefficient.

## 5. Conclusions

- (1)
- Compared with the UD model, the BD and DD models are more accurate in describing the whole gas adsorption/desorption process.
- (2)
- The fast efficient diffusion coefficient D
_{ae}decreases with the increase in pressure for three out of four coal samples (i.e, HC, XM and QS) while it shows a V-shape with the increasing pressure for HD. The slow efficient diffusion coefficient D_{ie}is positively correlated with the pressure for all coal samples. The diffusion characteristic parameter β keeps constant in the adsorption and desorption process for all coal samples. - (3)
- k
_{Φ}keeps fixed when the pressure changes and the stretching parameter α increases with the increase in pressure. - (4)
- Both the effective diffusion coefficient D
_{ae}and D_{ie}and the characteristic rate parameter k_{Φ}can be used to describe the gas diffusion rate. The impact of pore volume on D_{ae}, D_{ie}and k_{Φ}differs in the four coal samples while D_{ae}, D_{ie}and k_{Φ}are slightly affected by the specific surface area. The influence of pore structure characteristics on gas diffusion ability still requires further study.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, Y.; Xing, W.L.; Liu, S.Y.; Liu, Y.; Yang, M.J.; Zhao, J.F.; Song, Y.C. Pure methane, carbon dioxide, and nitrogen adsorption on anthracite from China over a wide range of pressures and temperatures: Experiments and modeling. RSC Adv.
**2015**, 5, 52612–52623. [Google Scholar] [CrossRef] - Charrière, D.; Pokryszka, D.; Behra, P. Effect of pressure and temperature on diffusion of CO
_{2}and CH_{4}into coal from the Lorraine basin (France). Int. J. Coal Geol.**2010**, 81, 373–380. [Google Scholar] [CrossRef] - Pan, Z.J.; Connell, L.D.; Camilleri, M.; Connelly, L. Effects of matrix moisture on gas diffusion and flow in coal. Fuel
**2010**, 89, 3207–3217. [Google Scholar] [CrossRef] - Staib, G.; Richard, S.; Gray, E.M.A. A pressure and concentration dependence of CO
_{2}diffusion in two Australian bituminous coals. Int. J. Coal Geol.**2013**, 116, 106–116. [Google Scholar] [CrossRef] - Clarkson, C.R.; Bustin, R.M. The effect of pore structure and gas pressure upon the transport properties of coal: A laboratory and modelling study. 2. Adsorption rate modelling. Fuel
**1999**, 78, 1345–1362. [Google Scholar] [CrossRef] - Han, F.S.; Busch, A.; Krooss, B.M.; Liu, Z.Y.; Yang, J.L. CH
_{4}and CO_{2}sorption isotherms and kinetics for different size fractions of two coals. Fuel**2013**, 108, 137–142. [Google Scholar] [CrossRef] - Li, D.Y.; Liu, Q.F.; Weniger, P.; Gensterblum, Y.; Busch, A.; Krooss, B.M. High-pressure sorption isotherms and sorption kinetics of CH
_{4}and CO_{2}on coals. Fuel**2010**, 89, 569–580. [Google Scholar] [CrossRef] - Cui, X.J.; Bustin, R.M.; Dipple, G. Selective transport of CO
_{2}, CH_{4}, and N_{2}in coals: Insights from modeling of experimental gas adsorption data. Fuel**2004**, 83, 293–303. [Google Scholar] [CrossRef] - Busch, A.; Gensterblum, Y.; Krooss, B.M.; Littke, R. Methane and carbon dioxide adsorption–diffusion experiments on coal: Upscaling and modelling. Int. J. Coal Geol.
**2004**, 60, 151–168. [Google Scholar] [CrossRef] - Zhang, J. Experimental study and modeling for CO
_{2}diffusion in coals with different particle sizes: Based on gas absorption (imbibition) and pore structure. Energy Fuels**2016**, 30, 531–543. [Google Scholar] [CrossRef] - Karacan, C.Ö. Heterogeneous sorption and swelling in a confined and stressed coal during CO
_{2}injection. Energy Fuels**2003**, 17, 1595–1608. [Google Scholar] [CrossRef] - Crosdale, P.J.; Beamish, B.B.; Valix, M. Coalbed methane sorption related to coal composition. Int. J. Coal Geol.
**1998**, 35, 147–158. [Google Scholar] [CrossRef] - Jian, X.; Guan, P.; Zhang, W. Carbon dioxide sorption and diffusion in coals: Experimental investigation and modeling. Sci. China Earth Sci.
**2012**, 55, 633–643. [Google Scholar] [CrossRef] - Shi, J.Q.; Durucan, S. A bidisperse pore diffusion model for methane displacement desorption in coal by CO
_{2}injection. Fuel**2003**, 82, 1219–1229. [Google Scholar] [CrossRef] - Nandi, S.P.; Walker, P.L. Activated diffusion of methane from coals at elevated pressures. Fuel
**1975**, 54, 81–86. [Google Scholar] [CrossRef] - Švábová, M.; Weishauptová, Z.; Prˇibyl, O. The effect of moisture on the sorption process of CO
_{2}on coal. Fuel**2012**, 92, 187–196. [Google Scholar] [CrossRef] - Pone, J.D.N.; Halleck, P.M.; Mathews, J.P. Sorption capacity and sorption kinetic measurements of CO
_{2}and CH_{4}in confined and unconfined bituminous coal. Energy Fuels**2009**, 23, 4688–4695. [Google Scholar] [CrossRef] - Crank, J. The Mathematics of Diffusion, 2nd ed.; Oxford University Press: New York, NY, USA, 1975; ISBN 0198533446. [Google Scholar]
- Wang, G.D.; Ren, T.; Qi, Q.X.; Lin, J.; Liu, Q.Q.; Zhang, J. Determining the diffusion coefficient of gas diffusion in coal: Development of numerical solution. Fuel
**2017**, 196, 47–58. [Google Scholar] [CrossRef] - Siemons, N.; Wolf, K.H.A.A.; Bruining, J. Interpretation of carbon dioxide diffusion behavior in coals. Int. J. Coal Geol.
**2007**, 72, 315–324. [Google Scholar] [CrossRef] - Wang, G.D.; Ren, T.; Qi, Q.X.; Zhang, L.; Liu, Q.Q. Prediction of Coalbed Methane (CBM) Production Considering Bidisperse Diffusion: Model Development, Experimental Test, and Numerical Simulation. Energy Fuels
**2017**, 31, 5785–5797. [Google Scholar] [CrossRef] - Ruckenstein, E.; Vaidyanathan, A.S.; Youngquist, G.R. Sorption by solids with bidisperse pore structures. Chem. Eng. Sci.
**1971**, 26, 1305–1318. [Google Scholar] [CrossRef] - Staib, G.; Sakurovs, R.; Gray, E.M.A. Dispersive diffusion of gases in coals. Part I: Model development. Fuel
**2015**, 143, 612–619. [Google Scholar] [CrossRef] - Busch, A.; Gensterblum, Y. CBM and CO
_{2}-ECBM related sorption processes in coal: A review. Int. J. Coal Geol.**2011**, 87, 49–71. [Google Scholar] [CrossRef] - Goodman, A.L.; Busch, A.; Duffy, G.J.; Fitzgerald, J.E.; Gasem, K.A.M.; Gensterblum, Y.; Krooss, B.M.; Levy, J.; Ozdemir, E.; Pan, Z.; et al. An Inter-laboratory comparison of CO
_{2}isotherms measured on Argonne Premium Coal samples. Energy Fuels**2004**, 18, 1175–1182. [Google Scholar] [CrossRef] - Wang, G.D. Adsorption and Desorption Hysteresis of Coal Seam Gas and Its Influence on Gas Permeability [D]; China University of Mining and Technology: Beijing, China, 2015. (In Chinese) [Google Scholar]
- Staib, G.; Sakurovs, R.; Gray, E.M.A. Dispersive diffusion of gases in coals. Part II: An assessment of previously proposed physical mechanisms of diffusion in coal. Fuel
**2015**, 143, 620–629. [Google Scholar] [CrossRef] - Liu, H.H.; Mou, J.H.; Cheng, Y.P. Impact of pore structure on gas adsorption and diffusion dynamics for long-flame coal. Nat. Gas Sci. Eng.
**2015**, 22, 203–221. [Google Scholar] [CrossRef]

**Figure 1.**Concepts of gas diffusion under unipore diffusion (UD) Model [19].

**Figure 2.**Concepts of gas diffusion under bidisperse diffusion (BD) Model [19].

Author | Coal Sample | Gas Category | Diffusion Model | Pressure Range | Diffusion Coefficient Changing Trend |
---|---|---|---|---|---|

Delphine Charrière | Bituminous coal | CO_{2} | UD model | 0.1 MPa, 5 MPa | Increase |

Pan Zhejun | Bituminous coal | CH_{4}, CO_{2} | BD model | 0~4 MPa | CH_{4} increases and CO_{2} remains unchanged |

Jian Xin | Bituminous coal | CO_{2} | UD model | 0~4.68 MPa | Increase |

Cui X.J | Bituminous coal | CH_{4}, CO_{2}, N_{2} | UD model | <3.6 MPa | Decrease |

Shi JQ | CH_{4}-CO_{2} | UD model | 4.2 MPa | D_{i} decreases | |

Gregory Staib | Bituminous coal | CO_{2} | UD model, BD model, FDR model | 0~4.5 MPa | D_{a} decreases and small impact on D_{i} |

Satyendra P. Nandi | Bituminous coal and anthracite coal | CH_{4} | UD model | 0~2.76 MPa | Small impact |

Coal Sample | M_{ad} (%) | A_{d} (%) | V_{daf} (%) | F_{c} (%) |
---|---|---|---|---|

HC | 8.40 | 32.47 | 47.40 | 11.73 |

HD | 0.25 | 5.32 | 23.52 | 70.91 |

XM | 2.65 | 7.83 | 17.25 | 72.27 |

QS | 0.73 | 18.53 | 15.80 | 64.94 |

Coal Sample | R^{2} | a/(mL/g) | b/MPa |
---|---|---|---|

HC | 0.9935 | 24.81 | 2.62 |

HD | 0.9891 | 19.33 | 1.04 |

XM | 0.9930 | 21.37 | 0.88 |

GH | 0.9933 | 25.46 | 0.67 |

Coal Sample | R^{2} | D_{ae} | ||
---|---|---|---|---|

Adsorption | Desorption | Adsorption | Desorption | |

HC | 0.950 | 0.977 | 2.58 × 10^{−3} | 2.50 × 10^{−3} |

HD | 0.991 | 0.948 | 5.49 × 10^{−5} | 5.29 × 10^{−5} |

XM | 0.764 | 0.906 | 9.53 × 10^{−4} | 1.11 × 10^{−3} |

QS | 0.873 | 0.961 | 2.75 × 10^{−4} | 2.07 × 10^{−4} |

Coal Sample | R^{2} | D_{ie} | ||
---|---|---|---|---|

Adsorption | Desorption | Adsorption | Desorption | |

HC | 0.747 | 0.886 | 6.79 × 10^{−5} | 5.27 × 10^{−5} |

HD | 0.968 | 0.967 | 8.92 × 10^{−6} | 9.44 × 10^{−6} |

XM | 0.875 | 0.824 | 3.22 × 10^{−5} | 3.03 × 10^{−5} |

QS | 0.955 | 0.828 | 2.88 × 10^{−5} | 4.79 × 10^{−5} |

Coal Sample | Adsorption | Desorption | R^{2} |
---|---|---|---|

HC | 0.355 | 0.356 | 0.876 |

HD | 0.510 | 0.506 | 0.825 |

XM | 0.376 | 0.353 | 0.908 |

QS | 0.473 | 0.560 | 0.898 |

Coal Sample | D_{ae} (s^{−1}) | D_{ie} (s^{−1}) | k_{Φ} (s^{−1}) | α | β |
---|---|---|---|---|---|

HC | 2.54 × 10^{−3} | 5.94 × 10^{−5} | 1.78 × 10^{−2} | 0.36 | 0.75 |

HD | 5.38 × 10^{−5} | 9.21 × 10^{−6} | 4.73 × 10^{−4} | 0.51 | 0.59 |

XM | 1.05 × 10^{−3} | 3.11 × 10^{−5} | 4.69 × 10^{−3} | 0.35 | 0.68 |

QS | 2.51 × 10^{−4} | 3.56 × 10^{−5} | 2.16 × 10^{−3} | 0.51 | 0.70 |

Coal Sample | Pore Size/nm | (0~25) |
---|---|---|

HC | Specific surface area/(m^{2}/g) | 11 |

HD | 0.234 | |

XM | 0.380 | |

QS | 0.177 |

Coal Sample | Pore Size Ranges/nm | (0~10) | (10~100) | (100~1000) | (>1000) | Total |
---|---|---|---|---|---|---|

HC | Pore volume/(mL/g) | 1.21 × 10^{−2} | 8.10 × 10^{−3} | 2.50 × 10^{−3} | 5.00 × 10^{−4} | 2.32 × 10^{−2} |

HD | 3.89 × 10^{−4} | 4.52 × 10^{−3} | 2.50 × 10^{−3} | 1.30 × 10^{−3} | 8.71 × 10^{−3} | |

XM | 7.55 × 10^{−4} | 3.27 × 10^{−3} | 2.60 × 10^{−3} | 1.50 × 10^{−3} | 8.13 × 10^{−3} | |

QS | 3.14 × 10^{−4} | 6.25 × 10^{−3} | 2.60 × 10^{−3} | 1.00 × 10^{−3} | 1.02 × 10^{−2} |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yang, X.; Wang, G.; Zhang, J.; Ren, T.
The Influence of Sorption Pressure on Gas Diffusion in Coal Particles: An Experimental Study. *Processes* **2019**, *7*, 219.
https://doi.org/10.3390/pr7040219

**AMA Style**

Yang X, Wang G, Zhang J, Ren T.
The Influence of Sorption Pressure on Gas Diffusion in Coal Particles: An Experimental Study. *Processes*. 2019; 7(4):219.
https://doi.org/10.3390/pr7040219

**Chicago/Turabian Style**

Yang, Xin, Gongda Wang, Junying Zhang, and Ting Ren.
2019. "The Influence of Sorption Pressure on Gas Diffusion in Coal Particles: An Experimental Study" *Processes* 7, no. 4: 219.
https://doi.org/10.3390/pr7040219