International Journal of Environmental Research University of Tehran ISSN: 1735-6865 EISSN: 2008-2304 Vol. 4, Num. 3, 2010, pp. 395-406

International Journal of Environmental Research, Vol. 4, No. 3, July-September, 2010, pp. 395-406

Article

Modelling thermal stratification and artificial de-stratification using DYRESM; Case study: 15-Khordad reservoir

Etemad - Shahidi, A . ^1* , Faghihi, M . ¹ and Imberger, J . ²

¹ Enviro-Hydroinformatics COE School of Civil Eng., Iran University of Science and Technology, Tehran, Iran
² CWR, University of Western Australia, Nedlands, 6907, Australia

Correspondence Address: *Enviro-Hydroinformatics COE School of Civil Eng., Iran University of Science and Technology, Tehran, Iran
etemad@iust.ac.ir

Date of Submission: 25-Jan-2009
Date of Decision: 15-Mar-2010
Date of Acceptance: 25-Mar-2010

Code Number: er10043

Abstract

Keywords: Modelling, De-stratification, Plume, Diffuser, Mixer, DYRESM, Simulation, Reservoir

Introduction

Thermal stratification is a natural phenomenon in lakes and reservoirs during summer. Solar radiation is absorbed by surface water and a well-mixed layer with low density and high temperature (epilimnion) is formed. The epilimnion is well mixed due to exposure to wind. The bottom layer (hypolimnion) remains dense and cold due to the extinction of solar radiation through the water column. Between these two layers, a strong thermal gradient zone (thermocline or metalimnion) in-hibits vertical mixing. The thermocline acts as a barrier preventing active exchange of temperature, dissolved oxygen (DO), and dissolved nutrients between the res-ervoir surface and bottom layers (Sahoo & Luketina, 2006). Because of biological and biochemical oxygen consumption in the hypolimnion, dissolved oxygen decreases. As the replenishment of DO is restrained by the thermocline, the bottom layer faces anaerobic con-ditions. This condition in the hypolimnion leads to sig-nificant increase in the release of undesirable sub-stances and deterioration of water quality.

In order to inhibit this deterioration, the rate of verti-cal transfer should be increased. Artificial destratification of the water column is a common mean for this purpose. Air bubbling, a continuous release of pumped air through diffusers in the bottom of lakes (Moshfeghi et al., 2005), is the most popular artificial destratification method (Sahoo and Luketina, 2006). The rising bubbles entrain the ambient water. When the upwards buoyancy flux due to the air bubbles is equal to the downward force (due to the gravity) on the entrained water, the bubble plume sheds the en-trained water. In this way, the heavy bottom water is lifted up and mixed with the lighter water in the top layer. The bubble plume then begins to entrain the ambient water again, until it reaches the surface where any entrained water is shed. Continuation of this pro-cess mixes the water column thoroughly.

The application of surface mechanical mixer is an-other artificial destratification system. This system consists of a large impeller mounted at the surface of the water body which points vertically downwards. The impeller is surrounded by a non-permeable cur-tain (a draft tube), through which water is impelled until escaping at the end of the draft tube. Once reach-ing the end of the draft tube, the water rises, enters the ambient water and mixes the water column.

The aim of this study is to simulate the perfor-mance of different destratification systems in the 15-Khordad reservoir using DYRESM. The DYRESM (DYnamic REservoir Simulation Model) (Schladow and Hamilton, 1997) is a calibration-free, process-based, one-dimensional hydrodynamic model for the simula-tion of vertical distribution of temperature, salinity and density in lakes and reservoirs. This model is also ca-pable of simulating artificial destratification systems.

15-Khordad Reservoir is located at 34 ^o 102 N and 50 ^o 302 E, in Qom, Iran. The dam is constructed on the brackish river, Qomrood, to supply the drinking water for Qom. The capacity of the reservoir is 200 MCM and it is designed to provide an average supply of 37.4 MCM per year for drinking and 28.3 MCM per year for agriculture purposes. The surface area of the reservoir is 13.5 km² and the length is 12 km. The average flow rate of the river is 5.61 m ³ /s varying from 1 m ³ /s in summer to 14.5 m ³ /s in spring. The average salinity of the inflowing river is 1525 mg/L varying from 1235 to 2219 mg/L, entering 266000 tons of salt into the reser-voir each year. Considering the high salinity of the inflowing river and the dominant stratification, the study of the influence of the stratification and destratification on the dynamics of this water body is vital.

Materials & Methods

15-Khordad Reservoir is located at 34 ^o 102 N and 50 ^o 302 E, in Qom, Iran. The dam is constructed on the brackish river, Qomrood, to supply the drinking water for Qom. The capacity of the reservoir is 200 MCM and it is designed to provide an average supply of 37.4 MCM per year for drinking and 28.3 MCM per year for agriculture purposes. The surface area of the reservoir is 13.5 km² and the length is 12 km. The average flow rate of the river is 5.61 m ³ /s varying from 1 m ³ /s in summer to 14.5 m ³ /s in spring. The average salinity of the inflowing river is 1525 mg/L varying from 1235 to 2219 mg/L, entering 266000 tons of salt into the reser-voir each year. Considering the high salinity of the inflowing river and the dominant stratification, the study of the influence of the stratification and destratification on the dynamics of this water body is vital. The DYRESM was developed in the Water Re-search Centre of the University of Western Australia. An extensive description of the model has been given in the Imberger and Patterson (1981), Hocking et al. (1988) and Hocking and Patterson (1991) studies. In brief, it is a one-dimensional model, which simulates the vertical distribution of temperature and salinity in lakes and reservoirs. The model assumes horizontal homogeneity, which is based on the density stratifica-tion usually found in reservoirs. Density stratification inhibits the vertical motions while the horizontal varia-tions in density are quickly relaxed by the horizontal advection and convection.

The one dimensional assumption is valid when L _N >>1,L _N,I >>1, F _O<<1 and R>>1; where L _N is the ratio between restoring force and distributing force intro-duced by the wind (Imberger and Paterson, 1990), L _N,I is the ratio between restoring force and distributing force introduced by plunging inflow, F _O is the ratio between outflow distributing force and restoring force and R is the ratio between Rossby radius of deforma-tion and lake dimensions.

The physics of the DYRESM is based on the fol-lowing processes: (1) surface heat and mass transfer; (2) energetics of the surface layer; (3) vertical diffu-sion in the hypolimnion; (4) inflow and outflow dy-namics; (5) air bubble plume dynamics; and (6) water plume dynamics. The model is based on the Lagrangian layer scheme (i.e., the layers are adjusted to stay within user-defined limits; a fixed grid approach would be an Eulerian scheme), in which the lake is modelled by a series of horizontal layers of uniform property but vari-able thickness. These layers can expand, contract, amalgamate, divide and move up and down as they are affected by the inflow, outflow, evaporation and rain-fall or according to the physical processes represented in the model.

The main advantage of the DYRESM, compared to the other models, is its ability to simulate destratification systems. In modelling the air bubbler destratification, the model uses the simple buoyant plume equations, and assumes the plumes are circular and non-interacting. The bubbler is initialized by first computing the upwards buoyancy flux due to the air (Fischer et al., 1979):

B_air = gQ_diff       (1)

Q _diff is the air flow rate of the diffuser at its level. Once the value of Q_diff  is passed into the model, it is divided by the number of ports (or clusters) to deter-mine the flow rate per port. All the subsequent calcula-tions are done on a per port basis, and then outcomes are multiplied by the total number of ports to get the total effect of the destratification system. The flow rate of entrained water is computed as (Fischer et al. 1979):

where B is the buoyancy flux [m ⁴ /s ³ ], z is the bottom layer thickness [m], b ₁ is a constant (4.7 according to Fischer et al., 1979), L _R is the plume aspect ratio (plume radius to plume length, assumed to be a constant of 0.1) and a is an entrainment coefficient. As the bubbles rise upward, they expand adiabatically due to the de-crease of the pressure. The new flow rate of bubbles is calculated according to Wallace and Hobbs (1977):

where P is the pressure and i-1 refers to the layer be-low. The combined buoyancy flux of the air bubbles and entrained water is calculated as:

where P_i is the density of the current layer, and Q _P is the flow rate of the entrained volume. The second term is the reduction in buoyancy flux due to the entrained water which the plume is dragging. The flow rate of the entrained volume in the layer i is calculated as:

When the combined buoyancy flux becomes zero or negative, the entrained water detrains from the air plume. It is then routed to its neutrally buoyant level instantaneously. The plume characteristics are then reset, and the air continues to rise and begins entrain-ing the water again.

In modelling the surface mechanical mixers, the model assumes that water acts as a buoyant plume when exiting from the draft tube. The plume is mod-elled as a line plume, wrapped around the circumfer-ence of the circular draft tube. The plume is initialized by computing the upwards buoyancy flux due to the difference in density between the water in the draft tube (assumed to have the same properties as the sur-face layer water) and the water at the base of the draft tube (Fischer et al., 1979):

where Q _P is the daily average impeller flow rate (m ³ s ^-1 ), and D is the draft tube diameter in meter. The unit of B is (m ³ s ^-3 ), which describes the buoyancy flux per unit length for a line plume (Fischer et al., 1979). The new flow rate due to the entrained water is computed as (Fischer et al., 1979):

where ∆z _j . is the starting layer thickness (the layer thickness at the base of the draft tube), and  is an entrainment coefficient, found experimentally to be 0.1024 (Fischer et al., 1979). This number has been halved for this application, as the ambient water is only being entrained along one side of the plume due to the vertical barrier of the draft tube. When the plume reaches the neutral buoyancy, the buoyancy flux be-comes zero and the plume is instantaneously inserted. As the plume is single phase, there is no re-initializa-tion after detrainment, as occurs for the bubble plumes. The simulations were conducted over a 12-month pe-riod between April 1997 and April 1998. Daily averaged inflow volume and temperature and outflow volume were available in the simulation period, but the inflow salinity was only measured once or twice in a month in normal conditions, and the results were considered as monthly average. All the required meteorological data were obtained from a nearby weather station located at 34 ^o 422 N and 50 ^o 512 E. The monthly measured tem-perature and salinity profiles in the deepest part of the reservoir were used for model calibration. The light extinction coefficient, was not measured so its value was calibrated to obtain the best fit between measured and simulated temperatures.

As difference existed between observed and simu-lated surface water temperatures, a sensitivity analy-sis was conducted to reveal the most important param-eters affecting the epilimnion temperature. Short and long wave radiation, air temperature, wind speed, vapour pressure, inflow temperature and light extinc-tion coefficient were selected as the parameters to be investigated. Finally, in order to evaluate the applica-tion of a destratifying system to the reservoir, firstly, two destratification systems were modelled and com-pared to each other. The characteristics of each sys-tem which affect its efficiency were also evaluated.

Results & Discussion

The simulation results showed that the reservoir was stratified approximately 210 days in the simula-tion year, and was warm monomictic because it was mixed once in a year, and the water temperature did not drop below 4°C [Figure - 1]. The Comparison of the simu-lated surface elevation with the measured one showed that the conservation of mass is correct in the model as the computed absolute mean error was 1.30%.

DYRESM assumes that the light extinction coefficient of water remains constant during the simulation pe-riod. While changing this coefficient for the model cali-bration, it was revealed that higher values of the light extinction coefficient cause the surface layer to be-come warmer, the hypolimnion to become cooler and the thermocline to rise up nearer to the surface. Reduc-ing this coefficient had the opposite effect. In the 15-Khordad Reservoir the best fit of the simulation re-sults to the field measurements was obtained with the light extinction coefficient of 0.15 m ^-1 . Using this value, the absolute mean error of the simulation was 5% (0.66 to 6.94%). As shown in [Figure - 2] in the stratified period, the hypolimnion and metalimnion temperatures were simulated close to the measured profiles, but the epil-imnion temperature was overestimated.The observed error could be caused by the inaccuracy in input data. The existing difference between the real values of me-teorological data in the reservoir and the measured values in the nearby station is the most important point. In order to define the most affective parameters on the epilimnion temperature, a sensitivity analysis was con-ducted as follows:

Long wave radiation : This parameter is given to the model as the fraction of sky covered with clouds. The DYRESM calculates the net long wave radiation con-sidering the reflection from the clouds. Higher cloud cover causes more long wave radiation emitted to the reservoir. Long wave radiation is mostly absorbed or emitted from the surface layer, so it directly affects the surface layer and makes it warm. However, in the study area, the sky is almost clear through out the year. The mean coverage of the sky (clouds) during the simula-tion period is only 2%. Hence, the long wave radiation is always at its lowest level, and the high surface tem-perature cannot be due to the overestimation of this parameter.

Short wave radiation : The wavelengths between 280 nm and 2800 nm were measured directly. The model divides the short wave radiation into penetrative and non-penetrative. Radiation shorter than 700 nm (Pho-tosynthetically Active Radiation, or PAR) is consid-ered to be penetrative and is distributed through the water column. This has been found experimentally to be approximately 45% of incoming solar radiation (Gates, 1966; Jellison and Melack, 1993). The DYRESM therefore assumes that 55% of the incoming solar ra-diation is non-penetrative and it is absorbed or emit-ted from the surface layer.

In order to evaluate the effect of uncertainty in this parameter on the simulation results, 20% increase and 20% decrease in the incoming short wave radia-tion were adopted. Results showed that in the strati-fied period, 20% increase in short wave radiation causes 6% (1°C) increase in the surface layer tempera-ture and 2% (0.3°C) increase in the bottom layer tem-perature. When the reservoir is mixed, this increase caused 20% (1.10°C) increase in the water column tem-perature. With 20% decrease, the results were exactly opposite. Hence, the accuracy in measuring short wave radiation has a considerable effect on the simu-lation results.

Vapour pressure: Using the measured values of dry bulb air temperature and relative humidity of the air, this parameter was calculated using equation C2 of TVA (1972). Vapour pressure affects evaporation from the surface layer, and as the evaporation is a mecha-nism through which water looses energy, the vapour pressure affects the surface layer temperature. For evaluation of this effect, a simulation was conducted considering ±20% change to this parameter. Results showed that 20% increase in the vapour pressure, in the stratified period, caused the epilimnion tempera-ture to increase 1.40% (0.35°C), but the hypolimnion remained unchanged. In the mixed period, this in-creased the water column temperature by approximately 10% (0.50°C). For 20% decrease in the vapour pres-sure, the results were vice versa.

Wind speed : Similar to the vapour pressure, by alter-ing evaporation from the surface layer, wind speed af-fects the epilimnion temperature. Simulations' results indicated that, in the stratified period, 25% increase in the wind speed caused 5% (1.20°C) decrease in the epilimnion temperature while the hypolimnion tempera-ture remained unchanged. In the mixed period, this in-crease caused 10% decrease in the water column tem-perature. Reducing the wind speed by 25% increased the epilimnion temperature by 1.10% (0.3°C) and did not affect the hypolimnion. In the mixed period, the water column temperature increased 13% (0.65° C) due to 25% decrease in the wind speed.

Thus, increasing the wind speed increases the evapo-ration from the surface layer and decreases its tem-perature. Vice versa, increasing the wind speed de-creases the epilimnion temperature. In addition, it could be concluded that increasing the wind velocity had a stronger impact on the epilimnion temperature than decreasing it.

Air temperature : Thermal interactions between wa-ter and air are considerable. Air temperature varies sig-nificantly in different areas, so the difference between real values in the reservoir location and the measured values in the station might be considerable. The simu-lation showed that increase in air temperature signifi-cantly increases the epilimnion temperature without changing the hypolimnion temperature, and vice versa decreasing the air temperature decreases the surface water temperature. Under the case of 20% decrease in the air temperature, the simulated results matched the measured profiles very well. As the ±20% change in the air temperature caused ±12.3% change in the sur-face water temperature, the air temperature was recog-nized as the most affecting parameter. In [Table - 1] the outcomes of this analysis are given briefly.

As the air temperature and short wave radiation were found to be the most important parameters af-fecting the surface water temperature, the effect of applying daily averages values of these parameters was evaluated by running the model with hourly values. The model was run for one month with hourly values of these two parameters while the other param-eters were set to be constant through out each day. Simulation results showed that the only parameter which varied in different hours of a day was the sur-face layer temperature, and this variation was about 0.77°C. The lowest surface water temperature occurred at 9:00 and the highest one at 18:00 [Figure - 3]. Conse-quently, the application of daily average of parameters did not significantly decrease the model's accuracy.

Bubble plume destratification : In the DYRESM, the characteristics of bubble diffusers are the number of diffusers, height of diffuser above the lake bottom, num-ber of ports of the diffuser, air flow rate of diffuser and the type and length of operation. Three types of opera-tion for artificial destratification can be modelled in the DYRESM: daytime operation, night-time operation and continuous operation. First, one diffuser with 100 ports and air flow rate of 0.1 m ³ /s, which was located 4 meters above the reservoir bottom and operated continuously during the reservoir stratification (200 days), was mod-elled. Results of simulation showed that after approxi-mately 3 weeks of operation, the reservoir destratified [Figure - 4]. In addition, increasing the air flow rate of dif-fuser increased the rate of destratification [Figure - 5]. and decreasing the number of ports had the same effect. It is due to the fact that the reduction of the number of ports increases the air flow rate from each port. Slip velocity and the size of bubbles increase when the air flow rate increases. It should be mentioned that the rate of destratification is a function of these two parameters and increases with their increase.

In [Figure - 6] a diffuser located 4 meter above the bottom destratifies the reservoir, but locating a diffuser 10 meter above the bottom just deepens the thermocline and the stratification remains unchanged. Hence, the diffuser should be located as near as possible to the bottom of reservoir, and the only consideration needed is the avoidance of sediment resuspension.plume in-teraction. In order to evaluate the effect of the number of diffusers on the destratification rate, two diffusers with air flow rate of 0.1 m ³ /s were modelled. As seen in [Figure - 7] compared to [Figure - 4] and [Figure - 5], results indicated that the operation of two diffusers simultaneously was more effective on destratification rate. Consequently, the most effective parameters on bubbler destratification rate were number of diffusers, air flow rate, number of ports and diffuser height, respectively.

Surface mechanical mixer : As the difference be-tween the surface and bottom water densities, com-pared to the difference between density of water and air, is very low and the formed plume in this case is single phase; it is predicted that the efficiency of the surface mechanical mixers in destratifying the reser-voir will be less than that of bubble diffusers.Characteristics of this destratifying system are: the length and diameter of draft tube, flow rate of water, number of destratification devices, and type and length of operation. A continuous operating surface mechanical mixer during the stratified period of the res-ervoir (200 days) with flow rate of 1 m ³ /s was modelled. The diameter of the draft tube and its lengths were selected 2 and 35 meters, respectively. [Figure - 8] shows the performance of this mixer in destratifying the reservoir. As seen, this mixer is not capable of destratifying the reservoir although the water flow rate of 1 m ³ /s is very high. The effect of increasing the flow rate to 3m ³ /s is shown in [Figure - 9]. Increasing the diameter of draft tube is also effective in increasing the destratification rate. [Figure - 10] shows the results of simu-lated mechanical mixer with 1 meter increase in draft tube diameter. Considering the equations 6 and 7 and comparing [Figure - 10] with [Figure - 9], it can be concluded that the diameter of draft tube was more effective in destratification rate than the water flow rate. Same as diffusers, the number of destratifying devices was the most effective parameter in mixers, and the length of draft tube, like the diffuser height, only affected the thermocline depth and is not important in destratification rate. In order to gain a destratification rate close to that of a diffuser, the number of mixers, diameter of draft tube and water flow rate were in-creased. The result is shown in [Figure - 11]. As observed, the efficiency of three mixers with flow rate of 3 m ³ /s and diameter of 5 meter was approximately close to that of a diffuser with air flow rate of 0.1 m ³ /s and 100 ports [Figure - 4]. Consequently, the bubble diffuser effi-ciency in destratification compared with mechanical mixers is very high and the use of mechanical mixers is not recommended.

Conclusion

This study showed that the DYRESM can accu-rately describe physical processes in reservoirs if the input data are accurately given. In the 15-Khordad Res-ervoir the air temperature, short wave radiation, wind speed and vapour pressure mainly control the thermal structure. Therefore, it is strongly recommended that these parameters, specifically air temperature and short wave radiation, to be measured in situ. Also, accurate measurements of light extinction coefficient are recom-mended to be carried out because this coefficient af-fects the thermocline position. Modelling the destratification devices shows that in diffusers, the num-ber of diffusers, air flow rate and number of ports; and in mechanical mixers, the number of mixers, diameter of the draft tube and water flow rate, are respectively impor-tant in the destratification rate. Height of the diffuser above the bottom of the lake and the length of the draft tube only control the thermocline depth and do not af-fect the destratification rate. Considering these devices efficiencies, application of bubble diffusers rather than mechanical mixers is recommended for artificial destratification in this reservoir.

Acknowledgements

This work was partly supported by the deputy of research, Iran University of Science and Technology. The first author would like to acknowledge CWR, Uni-versity of Western Australia for receiving the Gledden senior visitor fellowship. The authors also have their special appreciation to Dr. Matthew Hipsey, whose helps led to substantial improvement of this study.^[18]

References

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