All the marine conditions cannot be realistically recreated in laboratory glassware because the size of the laboratory testing equipment is limited and cannot simulate/mimic the infinite possibility of dilution which prevails in the open sea (Holder et al. 2015; Ross 2013). Also, it is challenging to carry out the sea trials (Merlin 2008). Thus, research teams developed mesoscale tests using medium-sized test facilities (e.g., tanks, canals, pools) in the lab or at the field under controlled conditions (Cui et al. 2020). Such tests could validate the bench-scale results and investigate the previously hard-to-access factors (e.g., wave, wind, etc.) in a more realistic manner. The key elements of the mesoscale testing facilities include their geometry, the agitation mode (e.g., wave generator), the control of temperatures (possibility of adjusting the ambient and water temperatures), the possibility of recreating the air circulation (wind), and the possibility of photo-oxidize the surface oil (solar light simulation). Other additional important points are the features in controlling and measuring the dispersion, the possibility of monitoring what occurs in the testing facility, and the possibility of dilution (changing the water content progressively by new sea water) (King et al. 2018).
In these facilities, almost the whole dispersion process can be reproduced, including oil release, application of the dispersant on the oil, dispersion of the oil under a steady agitation. To better target the dispersant application, the oil is often kept confined at the beginning of the test. Sometimes, the oil can be weathered in the facility prior to the test itself. Typically, a test consists in releasing the oil in the facility and applying the dispersant on the oil, starting the agitation, and then following the dispersion process. Usually, the dispersion is assessed and quantified by measuring the dispersion effectiveness (DE). This is a parameter used to determine the effectiveness of chemical dispersant in dispersing spilled oils and has been applied as the most important criteria in the dispersant screening and approval process. It is also an important parameter that needs to be closely monitored in the field, as it directly related to whether or not to use chemical dispersants, and when to terminate the operations. The oil droplet size distribution is another parameter that has been widely investigated (Yang et al. 2020). This information is of great importance on the transportation and fate of chemically dispersed oils (e.g., resurface, oil-mineral aggregation, emulsification and biodegradation, etc.). Finally, dispersed oil concentrations in the water column (quantification of the dispersion) and/or measuring the distribution of the dispersed oil droplet diameter and their composition are sometimes determined (Faksness et al. 2016) (the quality/stability of the dispersion). But a global assessment could also be done by measuring the residual floating oil left on the surface (undispersed oil) at the end of the test (Baszanowska et al. 2019; Duan et al. 2019).
Mesoscale tests may be expensive and messy, but when they are done carefully, they can bring greater realism compared to laboratory bench-scale tests (National Academies of Sciences and Medicine 2005). Because of its large scale, mesoscale experiments are considered to be more representative of the real sea conditions. Mesoscale testing can be used to tie the artificialities of laboratory studies to the operational realities of dispersant use in spill response. As such, mesoscale testing should be judged primarily on the basis of the additional realism—over laboratory studies—that is incorporated into their test design while remaining sufficient controls to allow the replication and the collection of quantitative data (National Academies of Sciences and Medicine 2005).
Different types of mesoscale test tanks have been designed around the world; they have been used to investigate the chemical dispersion in the context of surface oil/ surface dispersant application. The main types of mesoscale testing facilities include the straight flume tanks (linear canals), the circulating flume tanks (loop canals) and the testing pools. There is an additional type of mesoscale testing facility which can be deployed at sea or in a large natural water body, the floating cells. Each facility has its advantages and disadvantages and is more adapted/efficient to carry out certain investigations than others.
The straight flume tanks
The straight flume tanks are linear canals (or straight canals) around 10 to 30 m long, 0.5 to 1.2 m wide (relatively narrow), and 1 to 2 m deep. The water capacity of these mesoscale facilities is typically around 10 to 20 m3. They can be indoors or outdoors for the larger ones. They are equipped with a wave generator. To get a well-controlled wave agitation, the wave generator at one end of the canal may be designed to generate specific waves (specific frequency and height) while the other end of the canal is equipped with a device for avoiding wave reflection (waves damper). In these wave tanks, by modulating the wave generated at one end of the canal, it is possible to get repeatable breaking waves at specific spots of the canal (Li et al. 2017).
At the beginning of a test, the oil is released and kept confined at a specific spot of the canal, then treated before the containment is removed and agitation is started; the dispersion process starts and can be monitored. If the canal is equipped with a flow-through system, the dispersed plume is progressively moved forward with the water. The dispersant is added by a regular sprayer which allows a realistic contact condition between the dispersant and the oil, but a part of the sprayed dispersant may be lost aside the oil slick and on the walls of the tank, which may lead to the uncertainty of dispersant to oil ratio (DOR).
These facilities are suitable to carry out dispersion with a controlled and repeatable mixing energy level. A few studies have been conducted to quantify the level of mixing energy provided by those facilities (Venosa et al. 2005; Li et al. 2017). However, its comparison with real sea states is difficult and empirical as the quantification of the level of mixing energy at sea remains uncertain concerns, especially at the local scale. However, wave tanks are closed systems (except it is equipped with a flow-through system), which have the limitation on fully reproducing the open sea environment. Their limited dilution capacity may lead to enhanced coalescence of dispersed oil droplets. Limiting the oil quantities used for the tests is a way to counteract this problem (i.e., keeping the oil amount negligible compared to the volume of water). It is worth mentioning that these facilities are not suitable for oil weathering. If necessary, weathered oil needs to be prepared and weathered separately. This can be done artificially in the laboratory or in another tank, in which the oil is let to evaporate and emulsify naturally. Also, due to the narrowness of the strait flume tanks, some oil can be trapped on the walls of the tank, particularly when testing sticky oils (weathered emulsified oil), which may skew the test itself.
There are several straight flume tanks in the world, but usually, it is not allowed to release oil inside as they are devoted to hydrodynamic issues. DFO Canada and S.L. Ross operate specialized wave tanks devoted to oil pollution issues. Additionally, there are straight canals that are not equipped with wave generators. In the context of oil spill response, they can be used for studying sub-sea release, or completing ecotoxicity experiments.
Testing pools are generally large water bodies designed to implement testing activities. These are often equipped with a large wave generator designed to produce well controlled surface mixing (round and breaking waves). Sometimes they can be equipped with a specific feature to generate a controlled stream of water. When placed indoors, experiments can be performed with temperature control (such as in Norway, -SFT or Sintef). However, a lot of these facilities are devoted to studies other scientific activities (i.e., hydrodynamics) and oil release inside is not allowed. Those which are designed for oil pollution activities are not necessarily opened to testing dispersion. One reason is that dispersion tests would produce large volumes of polluted water that would have to be filtered/cleaned before disposal.
The testing pools are appropriate to investigate the actual relationship between dispersant penetration and oil characteristics because these systems are large enough to use realistic dispersant application systems (e.g., spray booms with typical nozzles) and they can be designed well enough to characterize the fraction of dispersant droplets that encounter floating oil (National Academies of Sciences & Medicine 2005).
The largest testing pool is the Ohmsett facility (Oil and Hazardous Materials Simulated Environmental Test Tank), which was originally designed for testing mechanical oil recovery equipment. Now, it has been adapted with a filtration system to implement testing with dispersed oil. This facility is more than 200 m long and equipped with movable bridges which can browse the pool at a controlled speed. The pool contains nearly 10,000 m3 of water, which can be chilled if necessary.
A test usually involves releasing oil into an area (≈ 900 m2) surrounded by a floating boom. Then the wave generator is activated to complete the dispersion process. The entire volume of the tank is available for the dilution of the dispersed oil plume. The dispersion can be monitored through oil concentration and mean droplet diameter measurements. Confining the oil in an area allows weathering the oil in natural conditions ahead of the dispersant test, and it offers the advantage to better target the slick when applying the dispersant. Conversely, confining the slick presents the inconvenience of biasing the oil natural spreading, and according to the wind, the oil distribution in the confining device may be heterogeneous (oil accumulates downwind). In order to avoid these inconveniences, another way to proceed is using the movable bridge at a controlled speed to spill the oil and to treat it in the same run, in such a case the slick is no longer confined. The large size of the Ohmsett pool offers the possibility of investigating certain aspects of operational effectiveness (e.g., the dispersant application equipment can produce dispersant droplets with realistic size distributions) and hydrodynamic effectiveness (e.g., the facility allows dispersed oil to diffuse in a relatively large volume of water). It also allows effective studies under specialized conditions (e.g., in broken ice). The huge-sized pool provided by Ohmsett best simulates the real marine environment and thus allows for the full-scale validation of laboratory work, especially the laboratory testing methods (Holder et al. 2015; Ross 2013). However, the large size of the tank also presents several difficulties. The primary one is the high operational cost (e.g., the cost of chilling 9700 m3 of seawater is considerable). This financial constraint may lead to the lack of sufficient replication of the experimental designs to support the statistical analysis of the results. In addition, once the oil is released, the slick could rapidly drift from one side of the tank to the other, particularly with strong wind. Therefore, the dispersants need to be immediately applied after the oil release in the mesoscale test. In addition, the tank is too large to allow the water to be replaced after each test to avoid possible biases caused by residual oil and/or dispersant on the following tests. The maximum dispersant concentration that can be present in the water without affecting the validity of subsequent effectiveness tests is 400 ppm, and to date, this concentration has not been exceeded in sequential tests (Ross 2013). However, the 400 ppm oil concentration considered by the operators represents one, possibly two, orders of magnitude the actual concentration measured at sea. It is doubtful such a high concentration could not bring perturbation by promoting oil droplets coalescence. The presence of dispersant may lead to a more acute problem disturbing the oil spreading (Gomaa 2013; Nedwed et al. 2011).
Many studies have been conducted in straight flume tanks in the recent five years. At the Ohmsett facility, Steffek et al. (2017) conducted large-scale comparative testing regarding the effectiveness of five different dispersants and found that Finasol and Corexit have the best performance. Boufadel et al. (2017) studied the chemical properties of the Ohmsett tank water and found that the hardness of water was below the value in oceans, it could enhance oil dispersion compared with in oceans. Brandvik et al. (2021) investigated oil droplet size distribution under various conditions, they generated an extensive data set on oil droplet sizes from subsea releases and found that the data set could well fit modified Weber scaling for predicting oil droplet sizes. Zhao et al. (2016) conducted a large-scale experiment of underwater oil release at Ohmsett, and measured the plume trajectory, velocity, oil droplet size distribution, and oil holdup during underwater oil release to validating the models JETLAG and VDROP-J. In addition, Fisheries and Oceans Canada (DFO) Centre for Offshore Oil, Gas and Energy Research (COOGER) wave tank was well used in different studies. King et al. (2018) studied the DE of four oil products by natural and chemical dispersion in different seasons and found the dispersant increased the DE by order of magnitude compared with natural dispersion and the DE of dilbit was highly dependent on the season. O’Laughlin et al. (2017) explored the formation of dilbit-derived oil-mineral aggregates (OMAs) in COOGER wave tank, and they found that in cold water (< 10 °C) and at a low sediment concentration, the in-situ formation of OMAs in the wave tank was unsuccessful. Zhao et al. (2017) adopted a horizontal release of oil without and with dispersant at COOGER wave tank and developed a new conceptual module VDROP‐J to capture the tip streaming observed.
The circulating flume tanks
The circulating flumes form loop canals. Usually, their total length is approximately 10 m for a volume of 5 to 10 m3, in which the water is circulated during the duration of the test. These canals are designed to recreate sea conditions. Generally, they are located in a temperature-controlled room, and equipped with a wave generator, a fan to recreate the wind, and a ultraviolet (UV) lamp to mimic sunlight (Fig. 1). This facility allows oil weathering in realistic conditions, which involves all the different phenomena (evaporation, emulsification, photo-oxidation, dispersion) simultaneously (Delacroix et al. 2016).
The circulating flumes are mainly used to assess the dispersibility of oils according to its weathering stage. These are used to determine the possible place (role) of the chemical dispersion when implementing oil spill contingency plan; forecast the evolution of an oil and to test the different combatting techniques; and assess alternative combatting techniques regarding specific oil in specific environments. Accordingly, there are two ways to process the tests. For the first one, the oil is weathered gradually and turn in the loop under the waves and the wind. When the oil is sufficiently weathered, the dispersant is applied on the oil and then the dispersion of the oil can be observed and monitored. Such tests could estimate oil dispersibility at a certain weathering degree. The second one, the oil is weathered gradually in the tank, and oil samples are collected, characterized and tested regularly in bench scale to assess their dispersibility. The changes of oil dispersibility with its viscosity evolution can be determined and the feasibility of dispersant application thus could be predicted. The advantage of the circulating flumes is the possibility to study the whole evolution of oil, including the weathering process, especially when performing aside the measures on oil samples taken in the flume tank. When dispersing the oil directly in the loop tank, the plume of dispersed oil can be monitored while it turns in the loop and progressively dilutes into the whole volume of the loop. At the end of such a test, an oil balance sheet can be performed between the dispersed and non-dispersed oil fractions. The dispersant can be applied in a realistic way (using a sprayer), but, as in wave tanks, some dispersant can be lost in the water or on the flume tank walls. All characteristics of a specific environment can be recreated and well controlled (i.e., agitation, wind, solar exposition). The level of mixing energy can be adjusted in the tank (easily by adjusting the frequency of the wave beater). However, the experimental conditions created in the wave tanks still cannot represent the real marine environment. Moreover, the agitation created in the circulating flume tank is less controlled than the ones in the straight wave tanks, thanks to the overlapped waves generated in the loop. In addition, as the pollutant circulates in the loop during the test, it regularly passes the vicinity of the wave generator. In addition, care should be taken to avoid the close even direct contact with wave generator, through which a high agitation could be created and adversely affect the oil behaviours.
Although field tanks mimic the environmental conditions of the sea, the weathering processes at sea and in a canal may differ. Test tools designed to simulate sea conditions manage to reproduce the extent of oil weathering processes and the oil dispersibility but fail to reproduce the kinetics of these changes. Therefore, at sea trials remain essential for the development of predictive models, particularly to clarify evolutionary kinetics. Till now, there are four flume tanks located in Sintef-Norway, Cedre-France (Polludrome), S.L. Ross-Canada, and Environment Canada. After the construction of SINTEF flume tank in Norway (0.5 m × 0.4 m × 4 m W × H × L, with 1.75 m3 of seawater), a set of other flume tanks have been developed, on the grounds of the design presented by SINTEF. The Polludrome flume tank was developed by Cedre-France had a much larger size (0.6 m × 1.4 m × 12 m W × H × L, with 10.5 m3 of seawater). A large storage tank was equipped with the tank, allowing the pumping of water and generation of tides. Instead of using UV lamps in SINTEF tank to simulate the photooxidation process, Polludrome adopts a solar radiation simulation system for such a process. Also, a laser particle size analyzer was equipped for Polludrome to evaluate the oil droplet size distributions. The flume tanks at S.L. Ross-Canada and Environment Canada were developed based on the existing flume tanks located at Sintef-Norway and Cedre-France. It worth mentioning, the tank constructed by Environment and Climate Change Canada is intended for long term evaluation of chemical spills in aquatic environments (freshwater and marine environment) under temperate and Arctic conditions (National Academies of Sciences and Medicine 2020).
Several studies have been conducted in circulating flume tanks recently. Faksness et al. (2017) summarized results of approximately 70 tests performed in the recirculating flumes at Sintef and S.L. Ross, they found that the oil dispersant effectiveness varied with both oil and dispersant type, and dispersants could be considered as a response option for spills in ice. Jézéquel et al. (2018) assessed the ability of clays to create oil-mineral aggregates and dispersed oil under arctic conditions in Cedre’s flume tank and found that high mixing energy was required to initiate OMA formation and low energy was necessary to prevent the OMAs from resurfacing. Guyomarch et al. (2012) simulated various oil weathering processes in the Cedre’s circulating flume then measured different parameters including density, viscosity, chemical composition, flash point, chemical dispersibility, etc. Cyr et al. (2019) tested the applicability of an ocean glider-compatible fluorescence sensor in Cedre’s circulating flume, it suggested that the calibration on Water Accommodated Fraction (WAF) of crude oil is more appropriate than on pure standards as the concentration based on the WAF calibration was close to gas chromatography–mass spectrometry (GC–MS) results. In several laboratories (e.g., Sintef and Cedre), the circulating flume tanks are regularly used to document oils in production about their behavior and dispersibility in view to define and optimize the most appropriate emergency plans.
The floating cells
The problem inherent with the previous mesoscale testing methods is the difficulty in characterizing the level of mixing energy in the testing facility in relation to a sea state. The floating cell therefore, is an alternative to overcome such difficulty. Floating cells are floating flexible enclosures moored in the real marine environment, in which experiments can be performed. These experiments benefit from real marine conditions, wind, temperature, but also natural waves. A floating cell is composed of a frame (3 m × 3 m) with floats hanging a vertical flexible plastic forming a curtain few meters height (0.8 m in the air and around 2 to 3 m in the water) (Fig. 2). As the curtain is flexible, it keeps “transparent” to the waves which can pass through with almost no perturbations: the agitation in the floating cells is the same as outside. To keep the curtain close to vertical, the curtain is weighted at its bottom. The bottom of the floating cells is open to the water column to let the natural dilution happens; the surface oil is contained by the curtain while the dispersed oil and soluble compounds can dilute almost naturally. In the meantime, the frame offers an easy path for the operator to move and work all around. Several floating cells can be operated simultaneously.
Floating cells benefit from true natural conditions. Therefore, there are adapted to weather the oil (true evaporation, emulsification, and photo-oxidation). They have been used to study the fate and behaviour of oil and chemical dispersant when spilled at sea, and to assess the combatting techniques, particularly the dispersion of oils weathered to various degrees. In order to link the observations to the very local conditions (wind, sun, temperature, etc.), a weather monitoring station has been set on a floating cell.
Cedre (France) used to run up to 6 floating cells, which opens the possibility to complete comparisons of several treatment products, to assess a treatment product according to different weathering stages, or to run comparative studies between different oils. The configuration and/or design of floating cells can be adapted to different objectives, such as OMA formation studies and sorbent testing, etc.
However, the floating cells have some limitations. As all the other mesoscale testing facilities, the spreading of the oil (or any floating pollutant) is limited by containment. Besides, as observed in the Ohmsett facility, the wind may prevent the oil from distributing evenly in the cells (the oil is often pushed to one side). Also, as to any outdoor facility, the operators must deal with the existing ambient conditions. The oil slicks attached to the curtains (especially for long-term experiments) could add a bias as well. Running the floating cells requires logistics support (e.g., a small boat), an authorized mooring location, the permit to run experimentation in an open environment, although the testing oil quantity (few litres) are very limited and the possible losses of oil are only non-persistent oil like dispersed oil or dissolved compounds (the persistent oil or emulsion is kept confined).
High pressure testing tanks
In 2015, the hyperbaric chamber of the SwRI (Southwest Research Institute, San Antonio TX) was used by Sintef to run a series of experiments on sub-sea dispersion using oil and natural gas. The purpose of these experiments was to check if pressure could change the subsea dispersants injection (SSDI) effectiveness as previously assessed in tests completed at ambient pressure (atmospheric) (Brandvik et al. 2016). The SwRI hyperbaric chamber is exceptionally large, with a diameter of 2.3 m and a height of 5.6 m (volume of 24 m3). Its rated pressure is 275 Bars (simulated pressure ≈2700 m). Oseberg crude oil was treated with 1 and 2% dispersant at different pressures (60, 120 and 170 Bars) and natural gas was added from time to time. The oil was either dead oil, or simulated lived oil obtained by spraying dead oil in a pressurized tank filled with natural gas in order to reach between 10 and 90% vol at testing pressure. The oil and gas effluent with or without dispersant were injected through a nozzle in the chamber filled with sea water and the rising oil plume was monitored using the Sintef’s SilCam (Fig. 3).
These studies indicated that SSDI effectiveness did not seem to depend on pressure (water depth) or the presence of gas provided one accounts for the effect of gas on the exit velocity. Also, gas bubble size could be significantly reduced due to dispersant injection. However, it must be noted that the investigated gas to oil ratio (GOR) range in this experiment does not cover all situations that can be encountered in oil fields. In addition, this experiment only investigated the formation of oil droplet, without further looking into the stability of the dispersion with time. At last, due to the risk of hydrate formation, conversely as planned, tests at low temperatures had to be canceled to keep over the domain of formation of hydrates. Certain water and oil samples taken from the chamber formed stable w/o emulsion during the progressive decompression before further analysis in the laboratory (the measurement of the inter facial tension). Due to the difficulties of carrying out tests under high pressure, most of the mesoscale experimental work was done at ambient pressure using vertical tanks (water column) or straight hydraulic canals.
Studies have been conducted under high pressure to explore its influence on oil droplet size and dispersion effectiveness. The droplet size formed by the live oil and gas under high pressure was investigated by Brandvik et al. (2019b) at SINTEF and SwRI. Their study indicated that the oil droplet size was independent of pressure, but negatively correlated with the gas void fraction. This result was also confirmed by Song et al. (2021), whose team reported insignificant difference on pre-dispersed oil droplet size distribution under high pressures (up to 150 bar). Brandvik et al. (2019c) further quantified the oil droplet size released from an orifice in seawater at low and high pressure (5 m and 1750 m depth), whose results also indicated the limited impact of on oil droplet sizes. Malone et al. (2018) investigated the influence of high hydrostatic pressure (150 Bars) and dissolved gases on the droplet size distribution, results showed that methane dissolved in the liquid oil increases the volume median droplet diameter significantly by up to 97%. Pesch et al. (2018) studied the rise velocity of live oil droplets under high pressure and validated the model using for the rise velocity calculation of oil droplets.
Large water column testing tanks
Vertical tanks have been used to study the oil behaviour in underwater for a long time. Cedre used a transparent mini column (0.3 m diameter for 3 m height) to observe and study the sedimentation behaviour of partially soluble chemicals in seawater. Based on this experience, Cedre further built a much larger column tank (hexagonal, 0.8 m width and 5 m height) equipped with large windows to study the behavior of contaminants, mostly with density lower than that of seawaters (Even 2003) and dispersed oil droplets. It has been possible to visualize the strange behavior of dispersed oil droplets, such as became elongated under the friction of the surrounding water during their ascent, form long tails, and seed tiny droplets behind then (Fig. 4) (National Academies of Sciences and Medicine 2020; Vanganse 2013). The equipment includes optical cameras for pictures that can be analysed afterward. In addition, the tank is equipped with outlets vertically dispatched every metre for sample collection. For safety reason, the tank has an outlet to extract any eventual harmful vapor.
Similarly, in 2005, Sintef built a much larger vertical tank, the “Tower Basin” (3 m diameter, 6 m height, 40 m3 sea water) (Fig. 5). This facility was used to study the underwater oil plume formation treated with and without dispersant. To simulate more realistically blowout conditions, the facility is designed to release oil and gas (air but possibly natural gas) and/or water at a desired pressure and temperature, with a known quantity. In addition, dispersant can be injected into the upstream and/or downstream of the oil release point (nozzle), in known quantity to achieve a specific DOR.
A lot of instruments are installed in the Tower Basin to monitor the dispersed plume up to three meters above the release point: the droplet size distribution of the dispersed oil is monitored using video cameras (3 to 6 cameras), particle size analyser (LISST 100X), particle visual microscope (PVM) and macro camera/laser; and an in-situ UV Fluorometer can be used to monitor the oil content/dissolved components in the water. There is possibility to take oil and water samples from the facility as well.
This facility was designed to study the behaviour of oil released into the water column under high pressure (i.e., with sufficient shear rate) and variable dispersant additions to promote oil dispersion. The main parameter used to assess the dispersant effectiveness is the changes in the size distribution of oil-droplets with and without dispersants. Usually, an efficiency test of a dispersant evaluates the evolution of the oil droplet sizes with the progressive increase of dispersants dosage (in steps every 0.5 to 2 min). The Tower Basin is a closed system and the oil concentration in the water can be gradually increases during the tests. Therefore, it is necessary to limit the number of consecutive tests and to settle, clean, and filter the water every night to reduce oil accumulation and avoid water changes with tank cleaning.
Several studies have been conducted at the Sintef Tower Basin and Cedre Experimental Column. Brandvik et al. (2017a) performed up-scaled experiments at the Sintef Tower Basin and generated new data set to test the modified Weber Equation’s ability to predict initial droplet sizes. Results showed that the experimental data could highly fit predicted values from the modified Weber algorithm. Brandvik et al. (2018) compared the effectiveness of different dispersant injection techniques for subsea dispersants injection, they found that smallest droplets could be observed when dispersant was injected immediately before or after the release opening. Brandvik et al. (2019a) proposed an expression for interfacial tension (oil–water) as a function of dispersant dosage based on the data regarding the relationship between dispersant dosage and interfacial tension obtained from experiments at Sintef Tower Basin. Aprin et al. (2016) simulated the chemical discharge experiments in the Cedre Experimental Column, they measured mass flow rate and draining time, then proposed a model based on Reynolds number power law to characterize the discharge coefficient. Table 1 compares the properties, advantages and disadvantages of different tanks.
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