Numerical models of brine dilution as design tools

Numerical models of brine dilution as design tools Authors: V. Hernández, A. Riaza & A. Buenaventura, Befesa CTA T. Soriano & E. Ortiz, Hidrogaia A. Moñino, A. Baquerizo & M. A. Losada, University of Granada Presenter: [A. Buenaventura, R&D Manager – Befesa CTA – Spain] Abstract Seawater desalination is already part of the solution to satisfy drinking water needs in many regions of the world. The objective is now to assure that desalination is a sustainable solution, and therefore a solution for the future. Sustainability of desalination depends on two main aspects: energy consumption and negative effects on marine communities due to brine discharge. Regarding the effects on marine communities, more R&D effort is required in order to better understand the phenomenon of brine dilution in the marine environment and the possible effects on its biological communities.

This paper presents the work that Befesa CTA, in collaboration with Hidrogaia and the University of Granada, is doing to develop a validated numerical hydrodynamic model which will be able to reproduce marine dynamics and the evolution of the brine transport spilled in the sea. This tool will be useful allowing the design of more effective brine discharge systems that assure the minimal impact on the marine environment.

Nowadays several numerical models exist to simulate marine dynamics and water discharges.

Nevertheless, the dilution phenomenon depends on many variables (bathymetry, tides, currents, turbulence…) and the simulation becomes very complex. Those simulations have a high content of variability and no much precision, so their utilization is mostly qualitative. Therefore validated numerical models of the discharge of a hypersaline solution into seawater are required.

The work presented in this paper allowed the comparison of different models in order to choose the most accurate and adapted to simulate desalination brine discharges into the sea. First of all, a preselection of the numerical models has been made within the set of the commercial softwares more widely used, recommended and validated at the present time. Then a comparative study of the softwares was done against an analytical case.

The comparison in 2D of the 3 preselected models against the analytical solution showed similar results and same order of deviations. Next step will be the comparison in 3D and the definitive selection of the most appropriate numerical model to be used.

Once selected the most appropriate simulation tool, the results of its simulation will be compared with measurements from a scaled physical model representing a desalination brine discharge. The results of this comparison will serve to validate the model and to define, experimentally, the driving parameters of the brine dilution phenomenon in general.

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I.

INTRODUCTION

Water is indispensable for life and human development. Nowadays more than 700 million people in 43 countries live below water-stress threshold [1]. It is clear that competition for water will intensify in the decades ahead. Population growth, urbanization, industrial development and the needs of agriculture are driving up demand for water resource.

When natural water resources are no more available or scarce, alternative sources of water are the only solution. Desalination is being accepted by many countries to solve their water problems. The objective is now to assure that desalination is a sustainable solution, and therefore a solution for the future.

Sustainability of desalination depends on two main aspects: energy consumption and negative effects on marine communities due to brine discharge. Regarding the RO technology, the most popular technology in recent projects, energy consumption has been the major problem since its development. In last years, Research and Development effort has led to the improvement of the process efficiency; hence, energy consumption for seawater desalination has been dramatically reduced. Regarding the effects on marine communities, more R&D effort is required in order to better understand the phenomenon of brine dilution in the marine environment and the possible effects on its biological communities. The most appropriate method to minimize the negative effects of increase in salinity is to assure a good dilution.

The mixing behavior of a submerged sea outfall is governed by the interplay of ambient conditions in the receiving water body (bathymetry, currents and stratification) and by the discharge characteristics. The discharge hydrodynamics into a receiving water body can be conceptualized as a mixing process occurring in two separate regions, usually called near and far field [2-3].

The near field dilution is called initial dilution and is dependent on initial jet characteristics (momentum flux, buoyancy, outfall geometry). These parameters influence the effluent trajectory and mixing resulting in better or worse dilution. In this region, outfall designers can usually affect the initial mixing characteristics through appropriate manipulation of design variables.

As the turbulent plume travels further away the source characteristics become less important and the far-field is attained. In this region ambient environmental conditions will control trajectory and dilution of the turbulent plume through buoyant spreading motions, passive diffusion due to ambient turbulence, and advection by the ambient, often time-varying, velocity field.

The mixing processes due to waste water discharges into the sea is well known leading its description by mathematical models, most of them are one and two-dimensional (1D, 2D) than threedimensional (3D). The main difference between the brine and waste discharges is the plume buoyancy behavior; the first one is negative and the second positive. Depending of the plume characteristics and mixing regions (near or far field) the model selection has to be appropriate selected. Nowadays it seems to be ignored the previous mentioned due to the lack of brine discharge models, Cormix model is a typically example reported in literature widely used for predicting brine dilution in many projects. In fact, there is not commercial software that allows near and far field simulation jointly.

It is very important to take into account that mixing processes in the marine ambient are related to a wide range of spatial and temporal scales doing impossible to develop a numerical model with high order of accuracy in solving the advective diffusion equation, therefore nowadays there are many 2D and 3D numerical models with limitations on their applications due to model assumptions.

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The work presented in this paper allowed the comparison of different models in order to choose the most accurate and adapted to simulate desalination brine discharges into the sea.

II

TRANSPORT EQUATIONS AND NUMERICAL MODELS

In coastal waters with complex bathymetries and current structures, numerical models must be used to solve this transport equation in order to predict spatial and temporal distribution of a substance concentration. Several numerical models exist to solve this problem.

The two dimensional differential equation that describes the temporal variation concentration of soluble non reactive substance spilled in a turbulent fluid, as coastal waters, is the following advection and diffusion transport equation (Fischer et al., 1979):  c c c   c    c u v  (D x )   (D y )  t x y x  x  y  y 

advection

(1)

diffusion

where: c

average concentration of soluble substance

u, v

average velocities in x, y directions respectively

Dx, Dy

longitudinal and transversal dispersion coefficients respectively (x and y directions)

t

time

Governing equation (1) comes from vertical integration of three dimensional differential transport equation, which assumes that turbulent dispersion is dominant with respect to molecular one.

In this paper, H2D-UNICAN (Cantabria University) [6], Delft 3D (Delft Hydraulics) [4] and Mike3 (DHI Water &Environment) [5] numerical models are analyzed in order to compare its precision degree by its application in a simple case which has analytical solution for transport equation (1).

Among numerical model differences are equations assumptions: discretization, type of turbulence model, etcetera. The main numerical models characteristics selected in this paper are resumed in table 1, with the particularity of belonging numerical models set more widely used, recommended and validated at the present time for hydrodynamics and transport coastal simulations.

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NUMERICAL MODEL Delft 3D

H2D-UNICAN

(Cantabria University)

(Delft Hydraulics) [4]

[6]

HYPOTHESIS EQUATION SPATIAL DISCRETIZATION TURBULENCE MODEL

- Uncompressible flow - Hydrostatic presion - Boussinesq - Eddy viscosity Finite differences, ADI technique; Arakawa C mesh - Constant Eddy - Algebraic equation

DISTRIBUTION

Public domain

- Uncompresible flow - Hydrostatic presion - Boussinesq - Eddy viscosity Finite differences, ADI technique; Arakawa C mesh - Constant Eddy - k-L model - k -  model Commercial

Mike3 (DHI Water &Environment) [5] - Artificial compressibility, - Boussinesq - Eddy viscosity Finite differences: ADI technique, Arakawa C mesh - Constant Eddy - Smagorinsky - k model - k -  model Commercial

Table 1.- Overview of the applied numerical models.

The study case consists on the punctual and continuous injection of a conservative substance into a rectangular channel showed at Figure 1 with a uniform distribution of velocity. Meanwhile, Figure 2 describes the parameters used for numerical simulations. Constant longitudinal and transversal dispersion coefficients were used. Analytical solution of equation (2) was obtained from literature [7, 8] and applied to compare with 2D numerical models results.

h

width = 66 m TRANSVERSAL VIEW

Central axis width = 66 m

y x

Length = 500 m PLAN VIEW

Figure 1.- Definition sketch of rectangular channel used for advection-dispersion analysis of a constant conservative substance injection.

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discharge

= 60 m3/s

water depth

= 0.61 m

flow velocity

= 1.5 m/s

longitudinal bed slope = 0.001 mass discharged

= 48 000.0 mg/s

longitudinal and transversal dispersion coefficients = 0.07 m2/s Inyection Inyection point point

y

Central Central (axial) (axial) axis axis

width= 66 m y = 33 m

Velocity x Length= 500 m

Figure 2.- Parameters used for advection-dispersion analysis of a constant conservative substance injection.

III

ANALYSIS AND RESULTS

According with the analytical equation and far field numerical models characteristics used for comparison, numerical simulations next to the injection zone has to be ignored as indicated in Figure 3.

Figure 3.- Delimitation of the area of comparison among 2D numerical models and analytical solution.

For the study case, non reactive substance transport by advection and dispersion, spatial distribution of the plume concentration resulting from the analytical (see Figure 4) and numerical solutions IDA World Congress-Maspalomas, Gran Canaria –Spain October 21-26, 2007 REF: IDAWC/MP07-169 -5-

distance x 2 (m)

obtained with H2D (Cantabria University) [6], Delft 3D (Delft Hydraulics) [4] and Mike3 (DHI Water &Environment) [5], see Figure 5 to Figure 7.

distance x 2 (m)

Figure 4. Isoconcentration curves (mg/l) from the analytical solution.

distance x 2 (m)

The isoconcentration curves obtained with H2D-Unican are showed in Figure 5 [9]. The maximum width of the plume has an approximate value of 8m (4 x 2 m in the y axis: transversal flow direction) and the maximum concentration furthest away (showed at 180 m, 90 x 2 m, along x axis) is 2 mg/l.

From Figure 8 and Figure 9 can be observed that H2D-UNICAN gives lower dilution (higher concentrations) of the non reactive substance in both longitudinal and transversal directions in comparison to the analytical solution.

distance x 2 (m)

Figure 5.- Isoconcentration curves (mg/l) calculated by H2D-UNICAN model (Cantabria University).

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Delft3D model plume is illustrated at Figure 6, where it can be observed that it shows slightly higher dilution than the H2D-UNICAN, with the maximum concentration furthest away (showed at 180 m, 90 x 2 m, in the x axis) of 1.8 mg/l. The maximum width of the plume is slightly wider than the obtained with H2D-UNICAN. Finally, in the Figure 7 are presented the results obtained with Mike3 model. It can be observed a good approximation with analytical solution isoconcentration curves, also the calculated plume has similar width and maximum concentration (1.7 mg/l) furthest away (showed at 180 m, 90 x 2 m, in the x axis) as Delft3D model.

Figure 6.- Isoconcentration curves (mg/l) calculated by Delft3D model (Delft Hydraulics).

Figure 7.- Isoconcentration curves (mg/l) calculated by Mike 3 model (DHI Water &Environment).

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Figure 8.- Longitudinal axes used for advection-dispersion analysis of a constant conservative substance injection.

Some longitudinal axes are defined as can see in Figure 8 to visualize the numerical differences. The longitudinal concentration distributions along two axes are represented in Figure 9 and Figure 10, where it can be observed that the numerical and analytical concentration converge to the same value when the distance in the x axis increase.

Figure 9.- Longitudinal concentration distribution in central axis.

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Figure 10.- Longitudinal concentration distribution in central axis.

As can see, Mike3 and Delft3D show better results compared to analytical solution than H2DUNICAN model. The quadratic error Mike3 and Delft3D models were 5.49% and 6.03% respectively, compared with 10.98% in the case of H2D-UNICAN. IV

CONCLUSIONS

Three numerical models are selected in order to determinate its precision degree by its application in a case with analytical solution for two dimensional transport equation. The application case consists on a punctual and continuous injection of a conservative substance into a rectangular channel.

The models used for this purpose are the numerical model sets more widely used, recommended and validated at the present time for hydrodynamics and transport coastal simulations: H2D-UNICAN (Cantabria University) [6], Delft 3D (Delft Hydraulics) [4] and Mike3 (DHI Water &Environment) [5], all of them were applied in 2D mode. The models differences are mainly due to equations assumptions, type of spatial discretization, turbulence model characteristics, etcetera, see table 1.

The numerical simulation comparisons among the models were carried out and it was presented their deviations from analytical solution, where Mike3 and Delft3D models accuracy of solving transport equation 2D are approximately the same, and H2D-UNICAN has the higher error of approximation to the analytical solution.

Nevertheless, in order to select the most appropriate numerical model in solving the mixing of brine discharge into the sea, it will be necessary an exhaustive analysis of models application in 3D mode which corresponds to the future research work. Final numerical model selection has to be justified also from a technical and practical point of view as the versatility in its application.

Once selected the most appropriate simulation tool, the results of its simulation will be compared with measurements from a scaled physical model representing a desalination brine discharge. The results of this comparison will serve to validate the model and to define, experimentally, the driving parameters of the brine dilution phenomenon in general.

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Acknowledgments This work has been partially financed by the Innovation, Science and Enterprise Council of the Andalusia Autonomous Government.

V

REFERENCES

1. PNUD (2006). Human Development Report. Beyond scarcity: Power, poverty and the global water crisis. United Nations Development Programme, New York, USA. 2. Jirka, G.H. and Lee, J.H.-W. (1994). Waste Disposal in the Ocean, in Water Quality and its Control, M. Hino (ed.), Balkema, Rotterdam.

3. Fischer H.B., List E.J., Koh R.C., Imberger J. y Brooks N.H. (1979) Mixing in inland and coastal waters. Academic Press, Inc., New York.

4. Delft Hydraulics, 2001. “Delft3D user interface. Capabilities and applications”, Delft Hydraulics, Delft, The Netherlands.

5. DHI, Danish Hydraulic Institute, 1995. Mike 3. User’s Guide and Reference Manual. Lingby, Denmark.

6. AQUALAB (2001). Manual del usuario. Grupo de Emisarios Submarinos y Saneamiento Litoral, y de la Ingeniería Oceanográfica y de Costas, Departamento de Ciencias y Técnicas del Agua y del Medio Ambiente. Universidad de Cantabria, Spain.

7. Sauty J.P., 1980. “An analysis of hydrodispersive transfer in aquifers”, Water Resources Research, vol.16, no.1, 1980, pp. 145-158.

8. Bonillo M.J.J., 2000. “Un modelo de transporte de sustancias solubles para flujos turbulentos en lámina libre”. Tesis Doctoral, Universidad de la Coruña, Departamento de Tecnología de la Construcción, La Coruña, Spain.

9. Soriano Pérez, T., 2002. “Modelado matemático de la evolución de contaminantes en sistemas fluviales”, Tesis Doctoral, Universidad de Cantabria, Departamento de Hidráulica y Medio Ambiente, Santander, Spain.

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