# Assessment of Groundwater Flow Dynamics Using MODFLOW in Shallow Aquifer System of Mahanadi Delta (East Coast), India

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## Abstract

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## 1. Introduction

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^{3}) as it is fresh and readily available [5,6]. However, the groundwater of coastal regions is more susceptible to deterioration due to several factors, such as rapid urbanization, intensified agricultural development, economic development, climate change, sea-level rise, and lack of sufficient surface water resources [7,8,9]. The effect of groundwater withdrawal on coastal aquifer systems with the smallest topographic gradient is more pronounced than the impact of sea-level rise and variation in groundwater recharge due to the dynamic nature of surface water–groundwater interaction [3]. Consequently, the coastal aquifer will become more saline due to saltwater intrusion and make this precious water resource unfit for consumption without any sophisticated treatment [10]. Therefore, it is essential to set up a diligent monitoring system, e.g., using numerical models for evaluating the maximum viable pumping rates to protect from seawater intrusion in the coastal aquifers [11].

## 2. Study Area

^{2}and nearly 1.1 million population residing in these regions [35]. Geographically, the Jagatsinghpur area is located between longitude 86°03′ to 86°45′ E and latitude 19°53′ to 20°23′ N (Figure 1). This coastal region is a part of the Mahanadi delta, surrounded by two rivers i.e., the Mahanadi River (flowing from west to east) and the Devi River (flowing from north-northwest to south-southeast) forming the northern boundary, and the southern and western boundary of the district, respectively, and Bay of Bengal in the eastern part [36]. The study area comprises the central and middle part of the Mahanadi delta with a thick deposition of quaternary sediments. As it belongs to the coastal region, possible vulnerabilities, e.g., sea-level rise, saltwater intrusion, and frequent climate variations, may affect the study region. The average annual rainfall in this region is 1436 mm and is received mainly from the southwest monsoon. As the study area is a part of a deltaic region, it mainly consists of thick sediments supplied by the rivers, such as Mahanadi, Birupa, Kathjodi, Devi, and Kuakhai. Moreover, it has a gentle slope towards the Bay of Bengal [37,38].

## 3. Hydrogeology

## 4. Methodology

_{x}, K

_{y}, and K

_{z}refer to hydraulic conductivity in three different directions; S

_{s}, h, and R represent specific storage, hydraulic head, and sink or source, respectively. Visual MODFLOW is based on the finite-difference mathematical equation (Equation (2)) with assumptions of constant density and viscosity of groundwater flow under transient state conditions [44].

#### 4.1. Development of the Model

#### 4.1.1. Discretization of the Study Area

^{2}and is gridded into 9394 cells with 77 rows (I = 77) and 122 columns (J = 122) and each cell consists of 600 m × 600 m blocks (Figure 2). The modeled layer thickness varies approximately from 30 to 50 m in the study area. The layer elevation and ground elevation data are imported in Visual MODFLOW through an ASCII file.

#### 4.1.2. Hydraulic Head Data

#### 4.1.3. Boundary Conditions

_{r}= hydraulic conductivity of the river bed (m/day), L = length of the reach/grid size (m) W

_{r}= width of the river (m), and B = thickness of the river bed (m). The river bed conductance of two rivers is approximately the same, i.e., 30,000–35,000 m

^{2}/day [35].

#### 4.2. Hydrological Parameters

_{h}) are 40 m/day, 42 m/day, and 45 m/day for ZONE I, ZONE II, and ZONE III, respectively, whereas the corresponding vertical conductivity (K

_{v}) of the three zones is 4, 4.2, and 4.5 m/day. The different specific yield values of 0.05, 0.06, and 0.07 for three respective zones I–III were taken during the calibration of the groundwater model (Table 2). As the water table is very close to the ground surface, some groundwater is extracted through the evapotranspiration process. Hence the evapotranspiration data have been taken into consideration for the groundwater simulation model. Further, the study area has been divided into eleven different recharge zones, in which monthly rainfall recharge values have been assigned.

#### 4.3. Calibration and Validation of Model

_{o}refers to the observed head value, h

_{c}the calculated head value, and n the total number of observed data. A statistical analysis of calibrated model under steady-state conditions has been given (Figure 3). Under transient state conditions, the calibrated and validated model indicates a good correlation between the observed head and calculated head in the study area (Figure 4a,b). The correlation coefficient values for calibrated and validated models are 0.994 and 0.988 respectively.

#### 4.4. Parameter Estimation (PEST) Model

## 5. Results and Discussion

#### 5.1. Interaction between Aquifer and River

#### 5.2. Fluctuation in Groundwater Level

#### 5.3. Groundwater Recharge Estimation

#### 5.4. Groundwater Outflow to the Bay of Bengal

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Steady-state condition: calculated head versus observed head during calibration (2004–2005) of the model.

**Figure 4.**Transient state condition (

**a**) calculated head versus observed head during calibration of the model (

**b**) calculated head versus observed head during validation of the model.

**Figure 6.**Interaction between river and aquifer (

**a**) River inflow/outflow into/from the aquifer system in 2006 (

**b**) River inflow/outflow into/from the aquifer system in 2007 (

**c**) Graph showing the influence of groundwater abstraction on the river systems in seasons.

**Figure 7.**A correlation Graph between the river stage and groundwater flux (

**a**) the river stage vs. inflow from the river boundary (

**b**) the river stage vs. outflow the river boundary.

**Figure 10.**Estimated net recharge in the study area in different time periods for the year 2006–2007.

**Figure 11.**Groundwater outflow from the constant head in different time periods for the year 2006–2007.

Sl No. | Parameters | Inputs |
---|---|---|

1. | Cell | |

1.1 | Active | White Cells (600 m × 600 m) |

1.2 | Inactive | Green Cells (600 m × 600 m) |

2. | Model Boundaries | |

2.1 | Constant Head | Head = 0 m (Bay of Bengal-SW to NE) |

2.2 | Recharge | Variable |

2.3 | Evapotranspiration | Rate = 1400 mm/year |

Extinction Depth = 3.0 m | ||

3. | Layer | |

3.1 | Layer No. | 1 |

3.2 | Layer Type | Unconfined |

4. | Aquifer Parameters | |

4.1 | Hydraulic Conductivity (K) | K_{x} = K_{y} = 40 to 45 m/d |

K_{z} = 4 to 4.5 m/d | ||

Specific Yield (S_{y}) | 0.05 to 0.07 | |

5. | Wells | |

5.1 | Observation Wells | 11 nos. |

6. | Aquifer Stresses | Data for individual pumping wells is not available, the same has been included in net recharge |

7. | Simulation Period | |

7.1 | Steady State | 1 January 2004 (1 day) |

7.2 | Transient State | 2004 to 2009 |

Zones | Horizontal Hydraulic Conductivity (K_{h}) in m/Day | Vertical Hydraulic Conductivity (K_{v}) in m/Day | Specific Yield |
---|---|---|---|

I | 40 | 4 | 0.05 |

II | 42 | 4.2 | 0.06 |

III | 45 | 4.5 | 0.07 |

Zones | Initial Hydraulic Parameters | PEST Estimated Parameters | ||
---|---|---|---|---|

Hydraulic Conductivity in m/Day | Specific Yield | Hydraulic Conductivity in m/Day | Specific Yield | |

I | 40 | 0.05 | 36.85 | 0.058 |

II | 42 | 0.06 | 44.39 | 0.075 |

III | 45 | 0.07 | 44.01 | 0.053 |

Zones | Hydraulic Conductivity (K) in m/Day | Specific Yield (S_{y}) |
---|---|---|

I | 30.746 < K < 44.18 | 0.046 < S_{y} < 0.074 |

II | 40.81 < K < 48.30 | 0.048 < S_{y} < 0.116 |

III | 39.70 < K < 48.78 | 0.043 < S_{y} < 0.067 |

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**MDPI and ACS Style**

Behera, A.K.; Pradhan, R.M.; Kumar, S.; Chakrapani, G.J.; Kumar, P.
Assessment of Groundwater Flow Dynamics Using MODFLOW in Shallow Aquifer System of Mahanadi Delta (East Coast), India. *Water* **2022**, *14*, 611.
https://doi.org/10.3390/w14040611

**AMA Style**

Behera AK, Pradhan RM, Kumar S, Chakrapani GJ, Kumar P.
Assessment of Groundwater Flow Dynamics Using MODFLOW in Shallow Aquifer System of Mahanadi Delta (East Coast), India. *Water*. 2022; 14(4):611.
https://doi.org/10.3390/w14040611

**Chicago/Turabian Style**

Behera, Ajit Kumar, Rudra Mohan Pradhan, Sudhir Kumar, Govind Joseph Chakrapani, and Pankaj Kumar.
2022. "Assessment of Groundwater Flow Dynamics Using MODFLOW in Shallow Aquifer System of Mahanadi Delta (East Coast), India" *Water* 14, no. 4: 611.
https://doi.org/10.3390/w14040611