## Abstract

Studying the effect of boiler water released in rivers on some water properties such as density, viscosity was done in this research. Equations of momentum, conversation, turbulence and energy were used with the relation between the temperature and water properties to describe those properties along the study reach. Simplifying of partial equation was done to obtain system of linear equation. Verification of numerical model by conducting comparison of observed data from Euphrates River at Mussaib Thermal Power Station with those computed by the model. The comparison results of density and viscosity show an agreement with using statistical tests such as Chi square and RMSE. The results of the study showed that increasing the bed roughness from 0.04 m to 0.12 m causes a longitudinal retardation of the values of density and viscosity values about (26 and 22%) respectively and vertical advance of these values about (14 and 12% ) respectively. Increasing the water surface slope from (6 cm/km to 12 cm/km) causes a longitudinal advance of density and viscosity values about (19 and 12%) respectively and vertical retardation of these values about (16 and 13%) respectively.

## HIGHLIGHTS

Effects of boiler water on water river properties such as water density and water viscosity were studied.

Significance and degree of freedom between observed data from the river and predicted data from the model were studied.

The effects of hydraulic river properties such as bed height and water surface slope on distribution of the values of these water river properties were explored.

## LIST OF SYMBOLS

*X*,*Z*Horizontal and vertical coordinates respectively (m)

*P*Pressure (N/m

^{2})*g*Acceleration due to gravity (m/s

^{2})*H*Heat exchange across the water surface kg. °K/(m

^{2}.s)*C*_{p}Specific heat w.s/(kg. °K)

*T*Heated water temperature (°C)

*T*_{r}River water temperature (°C)

*K*Turbulent kinetic energy (kg/s)

*G*Rate of production of turbulence kinetic energy

*C*1,*C*2Constants in kinetic energy turbulence model

*C*_{p}Heating capacity (j/kg.K)

*V*Velocity (m/s)

*h*Water depth measured at Z-axis (m)

*S*Slope of the water surface (cm/km)

*n*Roughness height (m)

*U*Longitudinal velocity components (m/s)

*R*Hydraulic radius (m)

*G*Acceleration due to gravity (m/s

^{2})*U*_{f}Friction velocity (m/s)

**Greek symbols**

## INTRODUCTION

Discharging boiler water into rivers or any bodies of water causes thermal pollution, which leads to several important effects. River water temperature increases more than normal levels when hydropower discharges boiler water, causing harms to animals and plants living in the water. Physical water properties such as density, viscosity, etc., are affected by temperature change (Babartutsi & Chu 1998). The abnormal process causes thermal pollution and changes the temperature of the surrounding water. Hydropower plants use water for cooling factory elements and the resulting hot water to streams. High water temperatures may be disastrous to the environment by affecting aquatic life such as fish (APHA 2011; Kalinowska & Rowinski 2012). An Environmental Impact Assessment (EIA) is crucially required for establishing such facilities. Among many EIA aspects, the prediction of a potential water temperature rise with the source of artificial heat is of great importance. Using numerical models, the predictions are usually made. Choosing an appropriate model, as well as collecting data to be used as model inputs, are often challenging tasks (APHA 2011). In principle, the predictive calculations should be carried out in dangerous situations from an environmental point of view (Kalinowska & Rowinski 2015; Abidalla *et al.* 2022). The rising river temperatures are an environmental concern so heat pollution is regulated by the Clean Water Act (CWA), which prohibits industrial facilities without permits from raising river temperatures above permissible limits. While previous studies of electricity generation focused on impacts on water resources and climate changes, assessments of thermal pollution had a unifying effect in focusing on the determining of temperature rise in the receiving water (EPA 2001; Macknick *et al*. 2016). The importance of incorporating a higher resolution for an accurate assessment of thermal pollution has also not yet been addressed. Assessments of susceptibility to thermal pollution and electricity generation are typically performed across large fields. Studies using coarse spatial resolution may miscalculate the extent of thermal pollution because they force the placement of multiple plants within a single grid cell and fail to capture subtle differences in the river discharge, temperature and the rates of thermal equilibrium. The rate of thermal equilibrium plays a main role in the river temperature modeling because they determine the natural warming cooling of the river and the longevity of thermal pollution as it moves downstream (Behrens *et al.* 2017; Nasir *et al.* 2022).

Nasir *et al.* (2013) applied a numerical model for studying the distribution of some other water properties caused by discharging of boiler water in rivers. The results showed an increase in the bed roughness and the slope of the water surface, which causes changes in the dissolved oxygen distribution. Miaral *et al.* (2018) evaluated the impact of warming in the Mississippi River as a result of power plant waste. The results showed that the use of coarse river network decisions may lead to a significant exaggeration in estimating the size and length of the weak river tributaries, and therefore necessitates the use of recycled cooling techniques that can reduce thermal pollution, but at the expense of the electric power generation capacity. This study aims to use two-dimensional numerical models to simulate the behavior of water properties, such as density and viscosity, due to released boiler water in the Euphrates River and the effects of the hydraulic conditions in river, such as the bed roughness and slope of watersurface, on the behavior of these properties.

## MATERIAL AND METHODS

### The study area

### Numerical modelling

The numerical model of the behavior of the water properties is a set of partial differential equations. These properties will be sited to obtain algebraical equations which can be solved by use of numerical solutions. Equations must be set with a proper of boundary conditions. The equations that formulate problems of the behavior of the water properties in water bodies according to Roberson & Crowe (1997), Babartutsi & Chu (1998) and Nasir *et al.* (2013) are shown below.

#### Momentum conservation equations

#### Thermal energy equation

#### Turbulence kinetic equation

#### Dissipation rate equation

#### Temperature–density distribution

#### Temperature–viscosity distribution

### Numerical model solution

#### Numerical solution

The finite difference technique was used to solve partial differential equations. Some assumptions were used in transforming those equations, from the non-linear to the linear equations (Smith 1985; Vincenzo & Gauss 1998). Formulation and simplification of these equations in a two-dimensional numerical model were achieved by using the Alternative Direction Implicit-Explicit method (ADI) with up winding technique. The resulting linear equations were solved using the Gauss-elimination method. Fortran language was the computer program used.

#### Input data

The input data needed to operate the model and run the computer program are the long reach of the river, depth, hydraulic river properties (such as slope and roughness), time interval and the total time of the study, as well as the temperature of the boiler water, which were obtained from (ECSDIP 2010).

#### Boundary conditions

The conditions are:

*u*= upper value (at the river surface)*u*= zero (at river bottom)*w*= zero (at all points in the horizontal and vertical plane)

*μ*) and the rate of dissipation (

*ε*) in the river were obtained from the equations below (Vincenzo & Gauss 1998):

Using initial conditions of (μ) and (*ε*) as calculated from Equations (8) and (10), the initial conditions for the turbulence kinetic energy (K) in the river can be obtained from Equation (8).

The boundary conditions used in the computer program are:

- 1.
In the upstream boundary:

at *X* = 0, 0 < *Z* < *D* in which (*W, U, T, K*, *ε*) are constants, and *D* is the depth of the river.

- 2.
In the downstream boundary:

### Field works and validation of the model

## RESULTS AND DISCUSSION

The effect of the hydraulics river parameters along the longitudinal and vertical distribution of water properties, such as density and viscosity, were studied. The results were taken at boiler water temperature equal to 48 °C at the outfall stream, and at the downstream water temperature equal to 30 °C at 500 m length reach of Euphrates river.

### Statistical analysis

### Prediction of water density values in the study area

*n*= 0.04 m, while it has reached 300 m distance from the outfall in the case of

*n*= 0.12 m. This is because increasing the roughness height causes the advance of water density depletion toward the bottom below the outfall. For example, at a depth of 3 m the density reached 999.5 kg/m

^{3}when

*n*= 0.04 m, while at the same depth, the density reached 994.5 kg/m

^{3}when

*n*= 0.12 m.

^{3}in length in the case of

*S*= 6 cm/km, while at the same length, it had reached 995 kg/m

^{3}in the case of

*S*= 12 cm/km. For example, at a depth of 3 m the water density reached 994.5 kg/m

^{3}at

*S*= 6 cm/km, and at the same depth, it reached 996 kg/m

^{3}at

*S*= 12 cm/km. This can be attributed to the effect of buoyancy force which increases vertical diffusion with the increase in water surface slope.

### Prediction of water viscosity values in the study area

*n*= 0.04 m, while it has reached 300 m. The distance from the outfall in the case of

*n*= 0.12 m, on the other hand, increasing the roughness height causes the advance of viscosity depletion toward the bottom below the outfall. For example, at a depth of 3 m the viscosity values had reached 0.7513 mm

^{2}/s when

*n*= 0.04 m, while at the same depth, the density had reached 0.7223 mm

^{2}/s when

*n*= 0.12 m.

^{2}/s in length in the case of

*S*= 6 cm/km, while at the same length, it had reached 0.705 mm

^{2}/s in the case of

*S*= 12 cm/km. Increasing the water surface slope causes vertical retardation in viscosity values below the outfall. For example, at a depth of 3 m, the water viscosity reached 0.710 mm

^{2}/s at

*S*= 6 cm/km. For the same depth, it reached 0.752 mm

^{2}/s at

*S*= 12 cm/km.

## CONCLUSIONS

The numerical model was verified by the agreement of the model results for density and viscosity with those observed from the Euphrates River according to statistical tests such as Chi-square with the degree of freedom = 3 to both properities above, RMSE was found to be 6.55496 × 10^{−6} and 0.007895422 for density and viscosity respectively where they are close to zero and another test *p*-value was found to be 95%.

The height of roughness of the river bed has an impact on the behavior of the water properties distribution as density and viscosity in the rivers, which increases the height of roughness from 0.04 to 0.12 m, causing the longitudinal retardations of density and viscosity depletion of about 26 and 22% and vertical advance of about 14 and 12% respectively

The water surface slope has an impact on the behavior of water properties distribution (such as density and viscosity) of the river. The increasing in slope from 6 to 12 cm/km causes vertical retardation of density and viscosity of about 16 and 13% and the longitudinal advance of depletion of about 19 and 12% respectively.

## ACKNOWLEDGEMENTS

The authors are grateful to the Al-Furat Al-Awsat Technical University, Southern Technical University and Al-Mussaib power station, Iraq for their support.

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.

## CONFLICT OF INTEREST

The authors declare there is no conflict.