numerical models of brine dilution as design tools

IDA World Congress-Maspalomas, Gran Canaria –Spain October 21-26, 2007REF: IDAWC/MP07-169

-1-

Numerical models of brine dilution as design tools

Authors:V. Hernández, A. Riaza & A. Buenaventura, Befesa CTAT. Soriano & E. Ortiz, HidrogaiaA. 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 regionsof the world. The objective is now to assure that desalination is a sustainable solution, and therefore asolution for the future. Sustainability of desalination depends on two main aspects: energyconsumption and negative effects on marine communities due to brine discharge. Regarding theeffects on marine communities, more R&D effort is required in order to better understand thephenomenon of brine dilution in the marine environment and the possible effects on its biologicalcommunities.

This paper presents the work that Befesa CTA, in collaboration with Hidrogaia and the University ofGranada, is doing to develop a validated numerical hydrodynamic model which will be able toreproduce marine dynamics and the evolution of the brine transport spilled in the sea. This tool willbe useful allowing the design of more effective brine discharge systems that assure the minimalimpact 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 ofvariability and no much precision, so their utilization is mostly qualitative. Therefore validatednumerical 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 themost accurate and adapted to simulate desalination brine discharges into the sea. First of all, apreselection of the numerical models has been made within the set of the commercial softwares morewidely used, recommended and validated at the present time. Then a comparative study of thesoftwares was done against an analytical case.

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

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


-2-

I. INTRODUCTION

Water is indispensable for life and human development. Nowadays more than 700 million people in43 countries live below water-stress threshold [1]. It is clear that competition for water will intensifyin the decades ahead. Population growth, urbanization, industrial development and the needs ofagriculture are driving up demand for water resource.

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

Sustainability of desalination depends on two main aspects: energy consumption and negative effectson marine communities due to brine discharge. Regarding the RO technology, the most populartechnology in recent projects, energy consumption has been the major problem since itsdevelopment. In last years, Research and Development effort has led to the improvement of theprocess efficiency; hence, energy consumption for seawater desalination has been dramaticallyreduced. Regarding the effects on marine communities, more R&D effort is required in order tobetter understand the phenomenon of brine dilution in the marine environment and the possibleeffects on its biological communities. The most appropriate method to minimize the negative effectsof 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 inthe receiving water body (bathymetry, currents and stratification) and by the dischargecharacteristics. The discharge hydrodynamics into a receiving water body can be conceptualized as amixing 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 trajectoryand mixing resulting in better or worse dilution. In this region, outfall designers can usually affectthe initial mixing characteristics through appropriate manipulation of design variables.

As the turbulent plume travels further away the source characteristics become less important and thefar-field is attained. In this region ambient environmental conditions will control trajectory anddilution of the turbulent plume through buoyant spreading motions, passive diffusion due to ambientturbulence, 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 itsdescription by mathematical models, most of them are one and two-dimensional (1D, 2D) than three-dimensional (3D). The main difference between the brine and waste discharges is the plumebuoyancy behavior; the first one is negative and the second positive. Depending of the plumecharacteristics and mixing regions (near or far field) the model selection has to be appropriateselected. Nowadays it seems to be ignored the previous mentioned due to the lack of brine dischargemodels, Cormix model is a typically example reported in literature widely used for predicting brinedilution in many projects. In fact, there is not commercial software that allows near and far fieldsimulation jointly.

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


-3-

The work presented in this paper allowed the comparison of different models in order to choose themost 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 usedto solve this transport equation in order to predict spatial and temporal distribution of a substanceconcentration. Several numerical models exist to solve this problem.

The two dimensional differential equation that describes the temporal variation concentration ofsoluble non reactive substance spilled in a turbulent fluid, as coastal waters, is the followingadvection and diffusion transport equation (Fischer et al., 1979):

)D(yc

y)D(

xc

xyc

vxc

utc

yx (1)

advection 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 transportequation, 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 precisiondegree 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 turbulencemodel, etcetera. The main numerical models characteristics selected in this paper are resumed intable 1, with the particularity of belonging numerical models set more widely used, recommendedand validated at the present time for hydrodynamics and transport coastal simulations.


-4-

NUMERICAL MODELH2D-UNICAN

(Cantabria University)[6]

Delft 3D(Delft Hydraulics)

[4]

Mike3(DHI Water

&Environment)[5]

HYPOTHESIS

- Uncompressible flow- Hydrostatic presion- Boussinesq- Eddy viscosity

- Uncompresible flow- Hydrostatic presion- Boussinesq- Eddy viscosity

- Artificialcompressibility,

- Boussinesq- Eddy viscosity

EQUATIONSPATIAL

DISCRETIZATION

Finite differences, ADItechnique; Arakawa Cmesh

Finite differences, ADItechnique; Arakawa Cmesh

Finite differences: ADItechnique, Arakawa Cmesh

TURBULENCEMODEL

- Constant Eddy- Algebraic equation

- Constant Eddy- k-L model- k - model

- Constant Eddy- Smagorinsky- k model- k - model

DISTRIBUTION Public domain Commercial Commercial

Table 1.- Overview of the applied numerical models.

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

y

PLAN VIEW

x

Central axis

width = 66 m

Length = 500 m

TRANSVERSAL VIEW

h

width = 66 m

y

PLAN VIEW

x

Central axis

width = 66 m

Length = 500 m

TRANSVERSAL VIEW

h

width = 66 m

TRANSVERSAL VIEW

h

width = 66 m

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


-5-

Length= 500 m

width= 66 m

x

Central (axial)axis

Central (axial)axisInyection

pointInyectionpoint

y = 33 m

y

Velocity

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

Length= 500 m

width= 66 m

x

Central (axial)axis


pointInyectionpoint

y = 33 m

y

Velocity

Length= 500 m

width= 66 m

x

Central (axial)axis


pointInyectionpoint

y = 33 m

y

Velocity

y

Velocity

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

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 forcomparison, numerical simulations next to the injection zone has to be ignored as indicated in Figure3.

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 distributionof the plume concentration resulting from the analytical (see Figure 4) and numerical solutions


-6-

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

distance x 2 (m)

dis

tan

cex

2(m

)

distance x 2 (m)

dis

tan

cex

2(m

)

distance x 2 (m)

dis

tan

cex

2(m

)

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

The isoconcentration curves obtained with H2D-Unican are showed in Figure 5 [9]. The maximumwidth 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 (higherconcentrations) of the non reactive substance in both longitudinal and transversal directions incomparison to the analytical solution.

distance x 2 (m)

dis

tan

cex

2(m

)

distance x 2 (m)

dis

tan

cex

2(m

)

distance x 2 (m)

dis

tan

cex

2(m

)

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


-7-

Delft3D model plume is illustrated at Figure 6, where it can be observed that it shows slightly higherdilution 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 theobtained with H2D-UNICAN.

Finally, in the Figure 7 are presented the results obtained with Mike3 model. It can be observed agood approximation with analytical solution isoconcentration curves, also the calculated plume hassimilar width and maximum concentration (1.7 mg/l) furthest away (showed at 180 m, 90 x 2 m, inthe 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).


-8-

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. Thelongitudinal 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 valuewhen the distance in the x axis increase.

Figure 9.- Longitudinal concentration distribution in central axis.


-9-

Figure 10.- Longitudinal concentration distribution in central axis.

As can see, Mike3 and Delft3D show better results compared to analytical solution than H2D-UNICAN 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 ina case with analytical solution for two dimensional transport equation. The application case consistson 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 andvalidated 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 equationsassumptions, 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 theirdeviations from analytical solution, where Mike3 and Delft3D models accuracy of solving transportequation 2D are approximately the same, and H2D-UNICAN has the higher error of approximationto the analytical solution.

Nevertheless, in order to select the most appropriate numerical model in solving the mixing of brinedischarge into the sea, it will be necessary an exhaustive analysis of models application in 3D modewhich corresponds to the future research work. Final numerical model selection has to be justifiedalso 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 comparedwith measurements from a scaled physical model representing a desalination brine discharge. Theresults of this comparison will serve to validate the model and to define, experimentally, the drivingparameters of the brine dilution phenomenon in general.


-10-

Acknowledgments

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

V REFERENCES

1. PNUD (2006). Human Development Report. Beyond scarcity: Power, poverty and the globalwater 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 itsControl, 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 coastalwaters. 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 ydel 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 enlámina libre”. Tesis Doctoral, Universidad de la Coruña, Departamento de Tecnología de laConstrucción, La Coruña, Spain.

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