Estimation of River Tigris Dispersivities Using a Steady-State Numerical Model

A recent study, published in Applied Water Science, investigated the dispersion of pollutants in the Tigris and Diyala Rivers, proposing a simple approach for simulation using computational fluid dynamics (CFD).

Illustration of Tigris–Diyala Rivers confluence with CFD-based pollutant dispersion simulation for BOD and TDS using FlexPDE.

The research employed the FlexPDE code to solve the two-dimensional advection-dispersion equation, aiming to predict the concentrations of biochemical oxygen demand (BOD) and total dissolved solids (TDS) at the confluence of the Diyala with the Tigris Rivers.

The study utilized two sets of data for calibration and validation processes. Various values of longitudinal and transverse dispersion coefficients were adopted in the model to determine the most suitable values through a trial-and-error method.

The results indicated that the best agreement between simulated and measured values for both BOD and TDS was observed when the longitudinal dispersion coefficient ( $ϵ_{x}$ ) was approximately $10 m^{2} / s$ and the transverse dispersion coefficient ( $ϵ_{y}$ ) was approximately $5 m^{2} / s$ .

The model demonstrated higher suitability for predicting TDS concentrations, which is a conservative pollutant. The estimated relative errors for TDS ranged from 0.56% to 1.00% during the calibration process and from 1.69% to 3.96% during validation.

In contrast, for BOD, a non-conservative pollutant, the estimated relative errors were significantly higher, ranging from 4.34% to 18.40% for calibration and 1.63% to 25.73% for validation. This discrepancy for BOD is likely due to the complex biological transformations (e.g., oxidation of carbonaceous BOD, oxidation of nitrogenous BOD, and sediment oxygen demand "SOD") that need to be accurately represented in the model, and the fact that organic matter is not always uniformly dispersed in the water mass.

The methodology employed in this study presents a simpler, more effortless, time-saving, and inexpensive approach compared to conventional experimental and field tracer studies for estimating dispersion coefficients.

The model primarily requires river flow velocity and water quality data as input. However, it is important to note that this model is applicable only for steady-state and uniform flow conditions, and it does not account for the effect of side inflow velocities from the Diyala River.

Despite some errors, particularly with reactive pollutants like BOD, the results for non-reactive pollutants (TDS) were deemed acceptable and provided a realistic initial impression of the river's water quality status.

Study Area and Data Collection

The study area focused on the confluence region of the Diyala River with the Tigris River, located southeast of Baghdad, Iraq. The Diyala River is a major tributary of the Tigris, originating in the Zagros Mountains in Iran and entering Iraq from the eastern part. The lower Diyala region is identified as the most polluted area due to various drains and effluents discharging into the river.

Water quality data and river hydraulic characteristics were essential for the simulation process. Grab water samples were collected at nine points (30 cm depth) in June 2016 and February 2017. Samples for TDS analysis were analyzed using the temperature-controlled oven method, while BOD samples were measured using the standard Winkler method.

Water temperature was measured in situ with a mercury thermometer. River deoxygenation rates ( $k_{d}$ ) were estimated through long-term BOD analysis using the Thomas method. Mean velocities in two directions were obtained using the floating method at the same sampling points, with surface velocities approximated by $v e l oc i t y_{M e an} \approx 0.85 \times v e l oc i t y_{S u r f a ce}$ .

Numerical Algorithm and Model Calibration

The numerical solution of the advection-dispersion equations (Equations 3 and 4 in the original paper) was achieved by developing a customized program using the FlexPDE code. FlexPDE is a software based on the finite element method, capable of solving nonlinear partial differential equations and offering automatic grid refinement.

Model calibration was performed using data from June 2016, with longitudinal ( $ϵ_{x}$ ) and transverse ( $ϵ_{y}$ ) dispersion coefficients adjusted by the trial-and-error method until simulated outputs reasonably agreed with observed data. The model was then validated using data from February 2017 without further adjustment of the calibrated coefficients.

Neumann boundary conditions (zero flux of BOD and TDS) were applied to the entire section, and various scenarios with different dispersion coefficient values were examined based on existing literature.

Author Background and Research Contributions

Asst Prof Muntair Shareef and Prof Dr Alhassan H. Ismail are faculty members at Middle Technical University, Iraq, with extensive expertise in hydrochemistry, pollutant dispersion modeling, and water quality assessment. Their research covers both groundwater and surface water systems, with a focus on the Tigris and Diyala Rivers, and has resulted in multiple joint publications on environmental modeling and hydrochemical analysis.

Together, they have contributed to regional and international studies, including work on the Danube and Euphrates Rivers. Their recent publications (2023–2025) explore topics ranging from multivariate water analysis to the environmental impacts of agricultural treatments. Their collaborative efforts continue to support sustainable water management in Iraq and beyond.

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Estimation of River Tigris Dispersivities Using a Steady-State Numerical Model