# Modeling of Evaporation-Driven Multiple Salt Precipitation in Porous Media with a Real Field Application

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## Abstract

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## 1. Introduction

## 2. Model Formulation

#### 2.1. Model Assumptions and Conceptualization

#### 2.2. Geochemical Modeling

#### 2.3. Mathematical Modeling

## 3. Description of the Study Area

#### 3.1. Location

#### 3.2. Climatic Conditions

- ${R}_{n}$ net radiation at the crop surface $\left[\mathrm{MJ}\phantom{\rule{4.pt}{0ex}}{\mathrm{m}}^{-2}{\mathrm{day}}^{-1}\right]$,
- G soil heat flux density $\left[\mathrm{MJ}\phantom{\rule{4.pt}{0ex}}{\mathrm{m}}^{-2}{\mathrm{day}}^{-1}\right]$,
- T mean daily air temperature at 2 m height [${}^{\circ}$C],
- ${u}_{2}$ wind speed at 2 m height $[\mathrm{m}\xb7{\mathrm{s}}^{-1}]$,
- ${e}_{s}$ saturation vapour pressure [KPa],
- ${e}_{a}$ actual vapour pressure [KPa],
- ${e}_{s}-{e}_{a}$ saturation vapour pressure deficit [KPa],
- $\delta $ slope vapour pressure curve $\left[{\mathrm{KPa}}^{\circ}{\mathrm{C}}^{-1}\right]$,
- $\gamma $ psychometric constant $\left[{\mathrm{KPa}}^{\circ}{\mathrm{C}}^{-1}\right]$.

#### 3.3. Chemical Composition

#### 3.4. Management of the Oasis of Segdoud

## 4. Modeling of Salt Precipitation Sequences under Evaporation of a Soil Profile Typical of the Oasis of Segdoud

#### 4.1. Problem Setup

#### 4.2. Simulation Results and Discussion

## 5. Summary and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Bonn, N.S.; Desarnaud, J.; Bertr, F.; Chateau, X.; Bonn, D. Damage in porous media due to salt crystallization. Phys. Rev. E
**2010**, 81, 066110. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bryant, R.G. Application of AVHRR to monitoring a climatically sensitive playa. Case study: Chott el Djerid, Southern Tunisia. Earth Surf. Process. Landforms
**1999**, 24, 283–302. [Google Scholar] [CrossRef] - Bryant, R.G.; Sellwood, B.W.; Millington, A.C.; Drake, N.A. Marine-like postash evaporite formation on a continental playa: Case study from Chott el Djerid, southern Tunisia. Sedimentory Geol.
**1994**, 90, 269–291. [Google Scholar] [CrossRef] - Nassar, I.N.; Horton, R. Salinity and compaction effects on soil water evaporation and water and solute distribution. Soil Sci. Soc. Am. J.
**1999**, 63, 752. [Google Scholar] [CrossRef] - Peyson, Y.; Bazin, B.; Magnier, C.; Kohler, E.; Youssef, S. Permeability alteration due to salt precipitation driven by drying in the context of CO
_{2}injection. Energy Procedia**2011**, 4, 4387–4394. [Google Scholar] [CrossRef][Green Version] - Eloukabi, H.; Sghaier, N.; Nasrallah, S.B.; Prat, M. Experimental study of the effect of sodium chloride on drying of porous media: The crusty-patchy efflorescence transition. Int. J. Heat Transf.
**2013**, 56, 80–93. [Google Scholar] [CrossRef][Green Version] - Hidri, F. Evaporation from a Porous Medium Containing a Dissolved Salt. Influence of Heterogeneities at Darcy’s Scale on the Distribution of Ions at the Evaporative Surface. Ph.D. Thesis, University of Toulouse, Toulouse, France, 2013. [Google Scholar]
- Veran-Tissoires, S.; Prat, M. Evaporation of a sodium chloride solution from a saturated porous medium with efflorescence formation. J. Fluid Mech. Camb. Univ. Press
**2014**, 749, 701–749. [Google Scholar] [CrossRef][Green Version] - Bernabé, Y.; Mok, U.; Evans, B. Permeability-porosity Relationships in Rocks Subjected to Various Evolution Processes. Pure Appl. Geophys.
**2003**, 160, 937–960. [Google Scholar] [CrossRef] - Fujimaki, H.; Shimano, T.; Inoue, M.; Nakane, K. Effect of a salt crust on evaporation from a bare saline soil. Vadose Zone J.
**2006**, 5, 1246–1256. [Google Scholar] [CrossRef][Green Version] - Le, D.; Hoang, H.; Mahadevan, J. Impact of Capillary-Driven Liquid Films on Salt Crystallization. Transp. Porous Media
**2009**, 80, 229–252. [Google Scholar] [CrossRef] - Nachshon, U.; Weisbrod, N.; Dragila, M.I.; Grader, A. Combined evaporation and salt precipitation in homogeneous and heterogeneous porous media. Water Resour. Res.
**2011**, 47. [Google Scholar] [CrossRef] - Shimojima, F.; Yoshioka, R.; Tamagawa, I. Salinization owing to evaporation from bare soil surfaces and its influences on the evaporation. J. Hydrol.
**1996**, 176, 109–136. [Google Scholar] [CrossRef] - Tsypkin, G.; Woods, A.W. Precipitate formation in a porous rock through evaporation of saline water. J. Fluid Mech.
**2005**, 537, 35–53. [Google Scholar] [CrossRef] - Battistelli, A.; Calore, C.; Pruess, K. Analysis of salt effects on the depletion of fractured reservoir blocks. In Proceedings of the World Geothermal Congress, Florence, Italy, 18–31 May 1995. [Google Scholar]
- Batzle, M.L.; Wang, Z. Seismic properties of pore fluids. Geophysics
**1992**, 57, 1396–1408. [Google Scholar] [CrossRef] - Brooks, R.H.; Corey, A.T. Hydraulic Properties of Porous Media; Hydrology Papers; Colorado State University: Fort Collins, CO, USA, 1964. [Google Scholar]
- Colon, F.; Oelkers, E.H.; Schott, J. Experimental investigation of the effect of dissolution on sandstone permeability, porosity and reactive surface area. Geomech. Cosmochim. Acta
**2004**, 68, 805–817. [Google Scholar] [CrossRef] - Espinosa-Marzal, R.M.; Scherer, G.W. Impact of in-pore salt crystallization on transport properties. Environ. Earth Sci.
**2013**, 69, 2657–2669. [Google Scholar] [CrossRef][Green Version] - Lai, K.H.; Chen, J.S.; Liu, C.W.; Yang, S.Y. Effect of permeability-porosity functions on simulated morphological evolution of a chemical dissolution front. Hydrol. Process.
**2012**. [Google Scholar] [CrossRef] - Laabidi, E.; Bouhlila, R. Impact of mixing induced calcite precipitation on the flow and transport. Carbonates Evaporites
**2017**, 32, 473–485. [Google Scholar] [CrossRef] - Pape, H.; Clauser, C.; Iffl, J. Permeability prediction based on fractal pore-space geometry. Geophysics
**1997**, 64, 1447–1460. [Google Scholar] [CrossRef] - Xu, T.; Ontoy, Y.; Molling, P.; Spycher, N.; Parini, M.; Pruess, K. Reactive transport modeling of injection well scaling and acidizing at Tiwi, Philippines. Geothermics
**2004**, 33, 447–491. [Google Scholar] [CrossRef] - Bechtold, M.; Haber-Pohlmeier, S.; Vanderborght, J.; Pohlmeier, A.; Ferre, T.P.A.; Vereecken, H. Near-Surface solute redistribution during evaporation. Geophys. Res. Lett.
**2011**, 38. [Google Scholar] [CrossRef][Green Version] - Van Dam, J.C.; Feddes, R.A. Numerical simulations of infiltration, evaporation and shallow groundwater levels with the Richards equation. J. Hydrol.
**2000**, 233, 72–85. [Google Scholar] [CrossRef] - Jambhekar, V.A.; Helmig, R.; Schröder, N.; Shokri, N. Free-flow-porous-media coupling for evaporation-driven transport and precipitation of salt. Transp. Porous Media
**2015**, 110, 251–280. [Google Scholar] [CrossRef] - Sghaier, N.; Prat, M. Effect of efflorescence formation on drying kinetics of porous media. Transp. Porous Media
**2009**, 80, 441–454. [Google Scholar] [CrossRef] - Shokri, N.; Lehman, P.; Or, D. Liquid-phase continuity and solute concentration dynamics during evaporation from porous media: Pore scale processes near vaporization surface. Phys. Rev. E
**2010**, 81 Pt 2, 046308. [Google Scholar] [CrossRef][Green Version] - Lehmann, P.; Or, D. Evaporation and capillary coupling across vertical textural contrasts in porous media. Phys. Rev. E
**2009**, 80, 046318. [Google Scholar] [CrossRef] - Nachshon, U.; Shahraeeni, E.; Or, D.; Dragila, M.; Weisbrod, N. Infrared thermography of evaporative fluxes and dynamics of salt deposition on heterogeneous porous surfaces. Water Resour. Res.
**2011**, 47. [Google Scholar] [CrossRef] - Veran-Tissoires, S.; Marcoux, M.; Prat, M. Salt crystallization at the surface of a heterogeneous porous medium. Letters
**2012**, 98, 34005. [Google Scholar] - Barbieri, R.; Stivaletta, N.; Marinangeli, L.; Ori, G.G. Microbial signatures in sabkha evaporite deposits of Chott el Gharsa (Tunisia) and their astrobiological implications. Planet. Space Sci.
**2006**, 54, 726–736. [Google Scholar] [CrossRef] - Askri, B.; Bouhlila, R. The water and salt budget of an irrigated plot in an oasis in southern Tunisia. Irrig. Water Resour. Manag.
**2001**, 272, 431–478. [Google Scholar] - Attia-Essaies, S.; Zayani, L.; Chehimi, D.B.; Adad, R.C.; Ariguib, N.K.; Trabelsi-Ayadi, M. Simulation of Crystallization sequence during the evaporation of Chott El Jerid brine (South Tunisia). Thermochim. Acta
**2010**, 503–504, 8–11. [Google Scholar] [CrossRef] - Shofield, R.; Thomas, D.S.G.; Kirkby, M.J. Causal processes of soil salinization in Tunisia, Spain and Hungary. Land Degrad. Dev.
**2001**, 12, 163–181. [Google Scholar] [CrossRef] - Askri, B.; Bouhlila, R.; Job, J.O. Development and application of a conceptual hydrologic model to predict soil salinity within modern Tunisian oases. J. Hydrol.
**2010**, 380, 45–61. [Google Scholar] [CrossRef] - Askri, B.; Bouhlila, R. Evolution de la salinité dans une oasis moderne de la Tunisie. Etude et Gestion des Sols
**2010**, 17, 197–212. [Google Scholar] - Askri, B.; Bouhlila, R.; Job, J.O. A conceptual hydrologic model for studies of salinisationa in Tunisian oases. Int. J. Water Resour. Arid. Environ.
**2011**, 6, 428–439. [Google Scholar] - Askri, B.; Ahmed, A.T.; Abichou, T.; Bouhlila, R. Effects of shallow water table, salinity and frenquency of irrigation water on the date palm water use. J. Hydrol.
**2014**, 513, 81–90. [Google Scholar] [CrossRef] - Bouhlila, R. Ecoulement, Transport et Réactions géOchimiques Couplés dans Les Milieux Poreux. Cas des sels et Des Saumures. Ph.D. Thesis, Université Tunis el Manar (ENIT), Tunis, Tunisia, 1999. [Google Scholar]
- Mejri, E.; Bouhlila, R.; Helmig, R. Heterogeneity Effects on Evaporation-Induced Halite and Gypsum Co-precipitation in Porous Media. Transp. Porous Media
**2017**, 118, 39–64. [Google Scholar] [CrossRef] - Askri, B. La Modélisation des Processus de Salinisation des sols Irrigués en Zones Arides: Cas de l’Oasis de Segdoud. Ph.D. Thesis, Ecole Nationale d’Ingénieurs de Tunis, Tunis, Tunisia, 2002. [Google Scholar]
- Parkhurst, D.; Appelo, C. Description of Input and Examples for Phreeqc Version 3-a Computer Program for Speciation, Batch-Reaction, One Dimentional Transport, and Inverse Geochemical Calculations; U.S. Geological Survey: Denver, CO, USA, 2013.
- Derluyn, H.; Saidov, T.; Espinosa-Maezar, R.; Pel, L.; Scherer, G. Sodium sulfate heptahydrate i: The growth of single crystals. J. Cryst. Growth
**2011**, 329, 44–51. [Google Scholar] [CrossRef] - Saidov, T.; Pel, L.; van der Heijden, G. Crystallization of sodium sulphate in porous media by drying at a constant temperature. Int. J. Heat Mass Transf.
**2015**, 83, 621–628. [Google Scholar] [CrossRef] - Steiger, M.; Asmussen, S. Crystallization of sodium sulfate phases in porous materials: The phase diagram Na
_{2}SO_{4}—H_{2}O and the generation of stress. Geochim. Cosmochim. Acta**2008**, 72, 4291–4306. [Google Scholar] [CrossRef] - Ben Chaaban, S.; Chermiti, I.; Kreiter, S. Oligonychus afrasiaticus and phytoseiid predators seasonal occurence on date palm Phoenix dactylifera (Deglet Noor cultivar) in Tunisian oases. Bull. Insectol.
**2011**, 64, 15–21. [Google Scholar] - Allen, R.; Pereira, L.S.; Raes, D.; Smith, M. Crop Evapotranspiration—Guidelines for Computing Crop Water Requirements; FAO Irrigation and Drainage Paper N°56; FAO: Rome, Italy, 1998. [Google Scholar]
- Wooding, R.A.; Scott, W.T.; White, I. Convection in groundwater below an evaporating salt lake: 1. Onset of instability. Water Resour. Res.
**1997**, 33, 1199–1217. [Google Scholar] [CrossRef] - Geng, X.; Boufadel, M.C. Numerical modeling of water flow and salt transport in bare saline soil subjected to evaporation. J. Hydrol.
**2015**, 524, 427–438. [Google Scholar] [CrossRef] - Geng, X.; Boufadel, M.C. The influence of evaporation and rainfall on supratidal groundwater dynamics and salinity structure in a sandy beach. Water Resour. Res.
**2017**, 53, 6218–6238. [Google Scholar] [CrossRef] - Jambhekar, V.A.; Mejri, E.; Schröder, N.; Helmig, R.; Shokri, N. Kinetic approach to model reactive transport and mixed salt precipitation in a coupled free-flow-porous-media system. Transp. Porous Media
**2016**, 114, 341–369. [Google Scholar] [CrossRef][Green Version]

**Figure 2.**Three-phase (solid, liquid and gas)—multiple components porous medium model. The liquid phase consists of dissolved air and ionic species ($N{a}^{+}-C{a}^{2+}-C{l}^{-}-S{O}_{4}^{2-}$). There is exchange of dissolved ions between liquid and solid phase through precipitation and formation of Gypsum (G), Halite (H) and Thenardite (T).

**Figure 7.**Hourly temperature in Segdoud during the month of July 2012 (National Institute of Meteorology).

**Figure 8.**Numerical results depicting the spatial distribution of water saturation in the sand column for different time intervals (

**a**) initially and after (

**b**) 3 days, (

**c**) 5 days, (

**d**) 10 days.

**Figure 9.**Mass fraction distribution of different ionic species (

**a**) Na${}^{+}$, (

**b**) Cl${}^{-}$, (

**c**) Ca${}^{2+}$ and (

**d**) SO${}_{4}^{2-}$ dissolved in the saline water. The concentration distributions are depicted along a vertical section in the top region of the porous medium domain and are plotted after several days for each ionic species.

**Figure 10.**Numerical results depicting the spatial distribution of gypsum solidity in the porous medium domain for different time intervals (

**a**) 0 days, (

**b**) 3 days, (

**c**) 5 days and (

**d**) 10 days.

**Figure 11.**Numerical results depicting the spatial distribution of thenardite solidity in the porous medium domain for different time intervals (

**a**) 0 days, (

**b**) 3 days, (

**c**) 5 days and (

**d**) 10 days.

**Figure 12.**Numerical results depicting the spatial distribution of halite solidity in the porous medium domain for different time intervals (

**a**) 0 days, (

**b**) 3 days, (

**c**) 5 days and (

**d**) 10 days.

**Figure 13.**Variation of the volume of the precipitated salts at the evaporating surface at the top of the porous medium.

**Figure 16.**Variations of the evaporation rate obtained from Dumux simulations and from ET0 calculator.

**Table 1.**Chemical composition (in mg/L) of Segdoud brine (March 1995) taken from [42].

${\mathit{Ca}}^{2+}$ | ${\mathit{Mg}}^{2+}$ | ${\mathit{Na}}^{+}$ | ${\mathit{K}}^{+}$ | ${\mathit{SO}}_{4}^{2-}$ | ${\mathit{Cl}}^{-}$ |
---|---|---|---|---|---|

620 | 86 | 2254 | 31 | 2822 | 3231 |

Minerals | Chemical Formula |
---|---|

Calcium Sulphate ($Gypsum$) | $CaS{O}_{4}\xb72{H}_{2}O$ |

Anhydrite | $CaS{O}_{4}$ |

Sodium Chloride ($Halite$) | $NaCl$ |

Glauberite | $N{a}_{2}Ca{\left(S{O}_{4}\right)}_{2}$ |

Mirabilite | $N{a}_{2}S{O}_{4}\xb72{H}_{2}O$ |

Sodium Sulphate (Thenardite) | $N{a}_{2}S{O}_{4}$ |

Component | Source/Sink Term |
---|---|

Water | ${q}^{w}=-2{r}_{precip,G}$ |

$N{a}^{+}$ | ${q}^{N{a}^{+}}=-2{r}_{precip,T}-{r}_{precip,H}$ |

$C{l}^{-}$ | ${q}^{C{l}^{-}}=-{r}_{precip,H}$ |

$C{a}^{2+}$ | ${q}^{C{a}^{2+}}=-{r}_{precip,G}$ |

$S{O}_{4}^{2-}$ | ${q}^{S{O}_{4}^{2-}}=-{r}_{precip,T}-{r}_{precip,G}$ |

Gypsum | ${q}^{G}={r}_{precip,G}$ |

Thenardite | ${q}^{T}={r}_{precip,T}$ |

Halite | ${q}^{H}={r}_{precip,H}$ |

**Table 4.**Chemical composition (in mg/L) of irrigation water (October 1995) taken from [42].

Well | $C{a}^{2+}$ | $M{g}^{2+}$ | $N{a}^{+}$ | ${K}^{+}$ | $S{O}_{4}^{2-}$ | $C{l}^{-}$ | $HC{O}^{3-}$ |
---|---|---|---|---|---|---|---|

CT2 | 450 | 238 | 598 | 21 | 1473 | 1943 | 193 |

CT3 | 360 | 144 | 391 | 16 | 826 | 1207 | 159 |

Properties | Value [Unit] | |
---|---|---|

Porosity ${\varphi}_{0}$ | 0.364 [-] | |

Permeability ${K}_{0}$ | 2 × 10${}^{-12}$ [m${}^{2}$] |

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**MDPI and ACS Style**

Mejri, E.; Helmig, R.; Bouhlila, R. Modeling of Evaporation-Driven Multiple Salt Precipitation in Porous Media with a Real Field Application. *Geosciences* **2020**, *10*, 395.
https://doi.org/10.3390/geosciences10100395

**AMA Style**

Mejri E, Helmig R, Bouhlila R. Modeling of Evaporation-Driven Multiple Salt Precipitation in Porous Media with a Real Field Application. *Geosciences*. 2020; 10(10):395.
https://doi.org/10.3390/geosciences10100395

**Chicago/Turabian Style**

Mejri, Emna, Rainer Helmig, and Rachida Bouhlila. 2020. "Modeling of Evaporation-Driven Multiple Salt Precipitation in Porous Media with a Real Field Application" *Geosciences* 10, no. 10: 395.
https://doi.org/10.3390/geosciences10100395