# Numerical Analysis of the Groundwater Flow System and Heat Transport for Sustainable Water Management in a Regional Semi-Arid Basin in Central Mexico

## Abstract

**:**

^{3}/s of water are extracted from regional aquifers mainly for agro-export activities, causing declines in the water table of up to 10 m/a, increased temperature and dissolved elements that are harmful to health and the environment. Regional groundwater coupled flow and heat transport under current conditions were studied on a basin-wide scale (7000 km

^{2}) using a three-dimensional finite-element model under steady-state conditions to provide support for water management decisions and transient modeling. Isothermal, forced and free thermal convection under existing hydrological conditions prior to pumping are analyzed. The results show that the interaction of topography-driven groundwater flow and buoyancy-driven free thermal convection are consistent with historical hydrological records, the characteristics of the water table, and thermal anomalies observed in the basin. The simulated groundwater recharge is near 7 ± 0.25 m

^{3}/s, a balance broken since the 1980s by extensive pumping. The results show the importance of considering the groundwater temperature, its transient response in the evolution of groundwater extraction, and the upward migration of a thermal front through the fractured aquifer that has increased risks for health and sustainability.

## 1. Introduction

#### Description of the Study Basin

^{2}, the IB is in the state of Guanajuato in the semi-arid region of Mexico (Figure 1). It forms part of the continental watershed that separates the Lerma-Chapala basin, which drains towards the Pacific Ocean, from the Pánuco basin that drains into the Gulf of Mexico. Seven important municipalities exist in the IB: Dolores Hidalgo, San Felipe, San Diego de la Unión, San Luis de la Paz, Dr. Mora, San José Iturbide, and San Miguel de Allende (Figure 1). They have a combined population of over 500,000 inhabitants who depend almost exclusively on groundwater for human consumption, agriculture, and industry. Around 30 m

^{3}/s are currently being extracted from two aquifers, one granular and the other fractured. Around 80% is for agro-export industries. Various thermal anomalies are observable in springs and wells in the basin [2].

## 2. Hydrogeology of the Basin

#### 2.1. Geology

#### 2.2. Hydrostratigraphy

#### 2.3. Natural Manifestations of Groundwater Conditions

#### 2.4. Historical and Current Manifestations of Groundwater Conditions

#### 2.5. Preliminary Water Budget

^{6}m

^{3}/a in 1971 (three years after construction of the Allende dam at the exit of the basin) to about 100 × 10

^{6}m

^{3}/a in 2000; this can be explained by the effects of groundwater extraction. Minimum baseflow represented 20 × 10

^{6}m

^{3}/a (5%) to 34 × 10

^{6}m

^{3}/a (13%) of total streamflow in the 1970s [18]. These baseflow values may be underestimated because they were considered as the minimum streamflow rates and were not calculated by separation of the unitary hydrographs.

^{6}m

^{3}/a to 412 × 10

^{6}m

^{3}/a in 1980, with significant regional declines in the water table, which signal that the safe yield was exceeded and that over extraction from the aquifer had begun (Figure 3).

#### 2.6. Previous Modeling

## 3. Materials and Methods

#### 3.1. Conceptual Model of Flow

#### 3.2. Modeling of the Flow System and Heat Transport

#### 3.2.1. Description of the Numerical Model

^{®}6.2, which solves the equations governing flow, mass, and heat transport in porous and fractured media using a multidimensional, finite-element method for complex geometric and parametric situations, including variable fluid density, variable saturation, free surface(s), multispecies reaction kinetics, and non-isothermal flow effects. This model satisfied the assumptions described above and directly solved potentials and heat transport, with details of the theory by [38].

_{h}is for heat sinks or sources; ρ

_{w}c

_{w}is the heat energy transfer by the movement of the fluid mass through the porous medium;

**k**is the solid’s permeability;

**K**is thermal conductivity.

_{T}^{2}; b = 6.764771 × 10

^{−2}; c = −8.993699 × 10

^{−3}; d = 9.143518 × 10

^{−5}; e = −8.90073913 × 10

^{−7}; f = 5.291959 × 10

^{−9}; g = −1.359813 × 10

^{−11}.

_{o}is the dynamic water viscosity.

#### 3.2.2. Boundary Conditions

^{®}.

#### 3.2.3. Modeling Strategy

## 4. Results

_{xx}= 1 m/d) and fractured (K

_{xx}= 0.1 m/d) aquifers. Anisotropy is 0.1 for K

_{yy}and 0.01 for K

_{zz}.

^{−5}m/d at 1800 masl to 1.35 × 10

^{−5}m/d at 3000 masl, an increase of 6.67 × 10

^{−7}m/d for every 100 m of elevation. In this procedure, we considered equal elevation curves every 10 m. These infiltration rates generated annual balances that were similar in all three scenarios, in the range of 219 × 10

^{6}m

^{3}/a ± 8 × 10

^{6}.

^{−05}m/d to 6 × 10

^{−04}m/d, while around the discharge zones this increases to 5 × 10

^{−03}m/d, and near the La Laja River it reaches 1.5 × 10

^{−1}m/d, and occasionally 4.4 × 10

^{1}m/d. In scenario III, this relationship is doubled in the recharge and discharge zones (Figure 6c).

^{−4}m/d with a descending vertical component in the first 10 km. This later increases to a horizontal movement for 40–50 km with a Darcy flow of 1 × 10

^{−4}m/d to 1 × 10

^{−3}m/d, before finally discharging in an upwards movement towards the La Laja River with a Darcy flux as high as 4 × 10

^{−2}m/d (Figure 7a,b). In scenario III, the equipotential lines are reduced by as much as 300 m with respect to the two previous cases, and vary along the section from 2300 m in the S-G to 1950 at the La Laja River. In scenario III, these flow rates are doubled (Figure 7c).

## 5. Discussion

^{6}m

^{3}/a ± 8 × 10

^{6}(7 ± 0.25 m

^{3}/s), which contrasts with the extraction volume estimated in 2020 at 1000 × 10

^{6}m

^{3}/a (32 m

^{3}/s), which is over four times higher. This situation explains (i) many of the negative impacts reported in the basin over the past two decades [2,51,52,53] due to the lowering of the water table by 2–10 m/a caused by the concentration of pumping (Figure 3); (ii) the progressive temperature increase of water in the wells; and (iii) the occurrence and progressive increase of chemical elements that are harmful to health and the environment.

## 6. Conclusions

^{6}± 8 × 10

^{6}m

^{3}/a (7 ± 0.25 m

^{3}/s).

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of the Independence Basin and its divide in the state of Guanajuato, central Mexico. The municipalities that comprise the IB are San Felipe, San Diego de la Unión, San Luis de la Paz, Dolores Hidalgo, San Miguel Allende, Dr. Mora, and San José Iturbide. Small fractions of the municipalities of Guanajuato (G), León (L) and Ocampo (O) also belong to the IB.

**Figure 2.**Domain of the Independence Basin showing the elevation of mountain massifs and the course of the La Laja River that runs northwest-to-south. Several features of the flow system are shown, including the main discharge area in the central part of the basin (blue circle) associated with saline soils, phreatophytes, and thermal springs. Boundary conditions for flow (blue) and heat (red) are indicated. The sites of two ancient lakes, Juagué Nandé and Curi Nitz, appear in cyan. The main sierras that delimit the IB are Guanajuato (S-G), Santa Bárbara (S-SB), San Diego de la Unión (S-SDU), San Luis de la Paz-Mineral de Pozos (S-SLP-MP), Dr. Mora (S-DMR), San José Iturbide (S-SJI), Picachos-Támbula (S-PT), and Codornices (S-C). Two important mining districts are circled in red: Guanajuato (MD-G) and Mineral de Pozos (MD-MP). Vertical exaggeration of the scale is 5:1.

**Figure 3.**Evolution of groundwater extraction and annual decline of the water table at different places in the IB. Data are based on several hydrogeological studies conducted since the 1970s [2]. Blue circles represent the evolution, of groundwater extraction over time with an approximately exponential trend; the squares, triangles, and rhombuses show the decline of the water table at several locations in the aquifer. The zones with historically shallow water tables are visible near the ancient lakes and discharge areas (red squares).

**Figure 4.**Geometry of the granular (red) and fractured media (dark magenta), the hydraulic conductivity distribution and anisotropy used for the modeling analysis is presented Table 2. The IB is about 100 km long by 70 km wide. Vertical exaggeration of the scale is 5:1.

**Figure 5.**Hydraulic head distribution in the 3D domain: (

**a**) topography-driven groundwater flow isothermic, scenario I; (

**b**) Convective 1, scenario II; and (

**c**) Convective 2, scenario III, see Table 1. Vertical exaggeration of the scale is 5:1.

**Figure 6.**Nodal Darcy flux (m/d) in plan view, represented by bullets (relative length 8:1): (

**a**) isothermal, scenario I; (

**b**) convective 1, scenario II; and (

**c**) convective 2, scenario III, see Table 1. Vertical exaggeration of the scale is 5:1.

**Figure 7.**Cross-sections of W-Laja. Distribution of Darcy flow equipotential lines for: (

**a**) isothermal, scenario I; (

**b**) convective 1, scenario II; and (

**c**) convective 2, scenario III, see Table 1. Vertical exaggeration of the scale is 5:1 and 8:1 for the bullets in Darcy flux.

**Figure 8.**Cross-sections of Laja-E. Distribution of Darcy flux and equipotential lines for: (

**a**) scenario for isothermal conditions, scenario I; (

**b**) Convective 1, scenario II; and (

**c**) Convective 2, scenario III (Table 1). Vertical exaggeration of the scale is 5:1 and 8:1 for the bullets in Darcy flux.

**Figure 9.**Cross-sections of W-Laja. Distribution of temperature and equipotential lines for: (

**a**) scenario II (convective 1); and (

**b**) scenario III (convective 2) (Table 1).

**Figure 10.**Cross-sections of Laja-E. Distribution of temperature and equipotential lines for: (

**a**) scenario II (convective 1); and (

**b**) scenario III (convective 2) (Table 1).

**Figure 11.**Hydraulic head and temperature distribution for (

**a**) interaction of topography-driven groundwater flow and Convective 1, scenario II; and (

**b**) interaction of topography-driven groundwater flow and Convective 2, scenario III. Vertical exaggeration of the scale is 5:1.

Scenario | Density | Viscosity |
---|---|---|

I. Isothermal | Constant | Constant |

II. Convective 1 | Linear dependency on T ^{1} | Constant |

III. Convective 2 | Nonlinear dependency on T | Variable-dependent on T |

^{1}T: temperature.

Definition | Symbol | Value | Unit |
---|---|---|---|

Hydraulic conductivity Granular Porosity | K_{xx} | 1 | m/d |

K_{yy} | 0.1 | m/d | |

K_{zz} | 0.01 | m/d | |

ε | 0.3 | Vol/vol | |

Hydraulic conductivity Fractured Porosity | K_{xx} | 0.1 | m/d |

K_{yy} | 0.01 | m/d | |

K_{zz} | 0.001 | m/d | |

ε | 0.1 | Vol/vol | |

Hydraulic-head BC Fluid-flux BC | Elevation Laja River | m | |

Infiltration rate with elevation | m/d | ||

Surface temperature BC Bottom temperature BC Porosity Volumetric head capacity of fluid Volumetric head capacity of solid Thermal conductivity of fluid Thermal conductivity of solid Anisotropy of solid thermal conductivity Longitudinal dispersivity Transverse dispersivity | T Tb ε ρ ^{s} c^{s}ρ _{c}Λ Λ ^{s}βd βd | 20 100 0.1 4.2 2.56 0.65 3 1 5 0.5 | Celsius Celsius Vol/vol MJ/m ^{3}/KMJ/m ^{3}/KJ/m/s/K J/m/s/K m m |

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**MDPI and ACS Style**

Ortega Guerrero, M.A.
Numerical Analysis of the Groundwater Flow System and Heat Transport for Sustainable Water Management in a Regional Semi-Arid Basin in Central Mexico. *Water* **2022**, *14*, 1377.
https://doi.org/10.3390/w14091377

**AMA Style**

Ortega Guerrero MA.
Numerical Analysis of the Groundwater Flow System and Heat Transport for Sustainable Water Management in a Regional Semi-Arid Basin in Central Mexico. *Water*. 2022; 14(9):1377.
https://doi.org/10.3390/w14091377

**Chicago/Turabian Style**

Ortega Guerrero, Marcos Adrián.
2022. "Numerical Analysis of the Groundwater Flow System and Heat Transport for Sustainable Water Management in a Regional Semi-Arid Basin in Central Mexico" *Water* 14, no. 9: 1377.
https://doi.org/10.3390/w14091377