Modelling brash ice growth in ports

Transcription

1 22 nd IAHR International Symposium on Ice Singapore, August 11 to 15, 2014 Modelling brash ice growth in ports Kaj Riska 1, Rodolphe Blouquin 2, Edmond Coche 1, Sergey Shumovskiy 3, Dmitry Boreysha 3 1 Total E&P SA, DEV/ED/EC 2 place Jean Millier La Défense 6, Paris La Défense Cedex, FRANCE kaj.riska@total.com, edmond.coche@total.com 2 Bertin Technologies, BCM/SIMA 10bis, Avenue Ampère, Montigny-le-Bretonneux, FRANCE rodolphe.blouquin@bertin.fr 3 Yamal LNG 12A Nametkina Str., Moscow, RUSSIA d.boreysha@yamalspg.ru, shumovskiy@yamalspg.ru Abstract Repeated breaking of the ice cover by ships entering and leaving ports induces a thermomechanical process of ice accumulation which produces brash ice. Brash ice is a mixture of smaller ice floes (mean diameter 50 cm) and water among the floes. The water content is described by porosity which is one of the main variables controlling the growth. This water freezes after each passage of ships and is again broken with the next ship passage. This process stimulates ice growth and thus the thickness of brash ice can reach several meters, even in milder winter conditions like those in the Baltic. In Arctic ports, if the ship passages are frequent, the brash ice thickness may reach even 10 m, presenting a significant challenge to the ships and thus methods to control the growth are needed. This paper addresses numerical modelling of brash ice growth. A model to address the breaking freezing cycle has been developed taking into account the isolation, snow cover, porosity of brash ice, mechanical mixing of ice layers and other related factors. The model is tested and validated with the available full scale data and finally applied to designing a port in Russian Arctic; including a brash ice growth management system. The paper presents the elements of the numerical model as well as applications. Finally improvements to the model are presented based on some results observed in application.

2 1. Introduction During recent years, several projects of construction Arctic ports have emerged in connection with mining or oil and gas operations. One of the challenges faced in the port construction and operation is the brash ice growth due to repeated ship passages in the ice covered channels. As ships have to navigate in dredged channels, the same tracks are used during the whole ice season with repeated passages. This causes ice to be repeatedly broken followed by freezing. But contrary to what occurs in Baltic sea where under normal winter conditions (cumulative freezing degree days, CFDD, is around C days) brash ice thickness can reach several meters depending on the intensity of traffic (Sandkvist, 1981), the harsh weather conditions that can prevail in Arctic (CFDD up to C days between mid-october and mid May) can lead to more than 10 meters of brash ice, depending on traffic frequency. This value is noticeably greater than the maximum ice performance in brash ice of Arctic ships. In the context of the engineering and design work for the construction of an Arctic port, models for brash ice growth are necessary to evaluate and mitigate the potential problems that could emerge: In the channel leading to the port the dredged width of which must be sufficient to enable access to the port during the whole cold season; In the harbour basin the maximum brash ice thickness must be assessed with high confidence in order to design an ice control system that ensures navigability. Many models for brash ice growth have been set up before A detailed review of them is available in the report of Ettema & Huang (1990) that also contains an exhaustive review of literature/data available on measurements of icebreaking patterns and ice-fragment sizes for vessels moving through level ice, ice formation in frequently transited navigation channels or vessel tracks and the parameters that influence the track width and the amount of broken ice. Although this study is mainly dedicated to transits of river channels, the results and analyses are sufficiently generic to be applied to ice-covered navigation channels in general. Ettema & Huang (1990) reported that at least five formulations had been proposed for the brash ice formation in ship tracks. All of them are based on the classical solution of the Stefan degree day equation to give an expression of the accumulated brash ice thickness over the track after the i th vessel transit. The simplest but convenient formulation was made by Sandkvist (1981): h bi, eq M t M = h0 + α θi i= 1 where h bi,eq at time t M is the equivalent thickness of brash ice after M passages, defined as the resulting thickness of brash ice accumulated in a vessel track over a width equal to the vessel beam if all brash ice is contained in the track (see Figure 1 below). In [1], h 0 is the initial ice thickness before the first passage, Δθ i the value of freezing degree-days between passages i-1 and i and α is an empirical coefficient depending on the usual degree-day coefficient. By setting α = 12 mm/( C days) 0.5, Sandkvist was able to fit [1] with the field measurements of brash ice accumulated volume in two test channels at Luleå Harbour (Sweden) during winter 1978/79 (Sandkvist, 1981). This formulation was also used by Eranti et al. (1983) with α = 6.5 mm/( C days) 0.5 to estimate the ice formation in the Saimaa Channel (Finland). [1]

3 ACTUAL SIMULATED equivalent brash ice thickness h bi,eq Figure 1. Sandkvist s model of brash ice accumulation in a ship track (from Sandkvist, 1981). The drawback of all these formulations is that they rely on empirical coefficients. Moreover, once this coefficient is determined by fit with field measurements, it allows calculating the brash ice volume only for the studied channel. The other drawback is the dispersion of ice by the ship i.e. the horizontal motion of brash ice away from the broken channel. The Sandkvist model was developed further by Riska et al. (1997) for the purpose of assessing the thickness of brash ice in navigation channels for regulatory purposes. After measuring the channels to Finnish northern ports, the Sandkvist formulation was changed to h bi, eq M t M = h0 + α θi i= 1 1 p p where p is the porosity of brash ice (note that the constant α has slightly different definition in [1] and [2]). This formulation draws attention to the effect of the porosity, otherwise being the same as the earlier one. Authors measured channel thicknesses for several winters and noticed that the ratio between the equivalent (theoretical) and the actual average thickness is about 2. The basis of all previous brash ice growth models is empirical and, in the context of the engineering and design work for the construction of Arctic ports where no previous measurements are available, a Brash Ice Growth Model (BIGM) was developed dedicated to brash ice growth in an isolated ship track in fast ice conditions. After identification of relevant phenomena in sea ice / brash ice growth, a detailed computational model was developed: To model the solid ice regrowth in existing brash ice layer mainly driven by the longwave radiation heat flux and sensible heat flux for harsh weather Arctic conditions; To model the ice breaking resulting from vessel passage in an isolated channel; To model the operational scenarios with brash ice motions sideways. [2]

4 2. Brash Ice Model Description This model deals with repeated ice breaking events in a ship track. Various assumptions are made in developing the BIGM dedicated to the brash ice growth in isolated and frequently navigated ship tracks in Arctic regions. Since the objective of the brash ice model is to assess with reasonable confidence the maximum brash ice thickness for design, the ice decay that occurs with positive air temperature and high solar radiation is not included in this model. As a result, only the cold season (air temperature is lower than the freezing temperature of ice) is considered. The following phenomena were neglected when developing the BIGM: The impact of snowfall on brash ice growth; At the upper air/ice interface, the short-wave radiation (i.e. solar) heat flux Q SW and the turbulent latent heat flux Q L The oceanic heat flux Q W exchanged at the bottom surface of brash ice layer. a) Thermodynamic Model for Solid Ice Regrowth The BIGM is based on an equivalent Stefan model for brash ice growth. It basically considers that brash ice formation results from the downward displacement of an horizontal freezing front that forms an 1D solid layer over brash ice which is a two phase medium of apparent latent heat of freezing p L i (see Fig. 2). In order to take into account thermal inertia of ice, one dimensional unsteady heat conduction equation for temperature distribution T i (z,t) in conservational form is solved in the solid ice layer Ti ρici t z,t T z,t = λi z i z z Q with the boundary conditions (ρ i density, c i heat capacity and λ i thermal conductivity of ice): C [3] Figure 2. Schematic illustration of the thermodynamic brash ice growth model in a ship track. 4 T Ice-air interface QLW εlw σt0 QS λi = 0 [4] z where Q LW is the incoming long-wave radiation, ε LW σt 0 4 the outgoing long-wave radiation, Q S the sensible heat flux and the conductive flux in ice Q C that has been replaced by its expression 0

5 induced by Fourier s Law expressed at the upper surface. This upper boundary condition applies as long as T 0 < T f (freezing point of sea water). In thebigm, the heat fluxes Q LW and Q S are prescribed as external parameters and computed from a formula that depends on wind speed U za and temperature difference T 0 - T za (Parkinson & Washington, 1979). For the latter: Q S acacl 0 T Tza U za [5] where ρ a is the air density, c a the specific heat of air, C L the turbulent transfer coefficient. Subscripts 0 and za refer to the surface and the freeboard height of za in the air, respectively. Ice-brash ice interface Tb T f [6a] λ dt / dz = ρ pl dh / dt [6b] i i hi i i i hi This moving freezing boundary condition describes the solid ice layer developing through an existing brash ice layer of porosity p. It must be outlined that when the solid ice layer reaches the bottom of brash ice layer, the porosity is set to 1 in order to go back to the classical moving boundary condition of the Stefan problem. This equation is integrated over time and space to calculate the evolution of temperature profile and solid ice layer thickness. As solid ice layer thickness h i increases, the equivalent thickness of brash ice layer h bi diminishes in the same proportion, until a new ice breaking event occurs. b) Ice Breaking Model As the duration of ice breaking is short compared with the duration between two vessel passages, it is considered as instantaneous. Breaking is assumed to convert the existing solid ice layer into a brash ice of mean porosity p, resulting from mechanical ice breaking and considered constant. After each vessel passage, the solid ice layer thickness h i is set to 0 and the equivalent thickness of brash ice layer h bi is increased by h bi = h i /(1-p), as depicted in Fig. 3. Furthermore, the produced volume of ice also depends on how cold blocks resulting from ice breaking evolve as they are heated from the surrounding water that freezes to these blocks. We considered that the cold blocks resulting from ice breaking are mixed with existing brash ice layer instantaneously and return to thermal equilibrium at T f before regrowth of solid ice. This return at T f is accompanied by a homogeneous decrease of mean brash ice porosity p, deduced from the conservation of mass and energy in the brash ice layer. Moreover, the displacement of ice blocks out of the track after ice breaking as well as the presence of side ridges of brash ice accumulated at the channel edges (see Fig. 1) are not taken into account. Therefore the model calculates the equivalent thickness of brash ice, defined as the thickness of brash ice accumulated in a ship track over a width of ship beam if all brash ice is contained in the track. This definition is identical to the volume of brash ice per m 2 of ship track. The effective brash ice thickness that stays in the track can be deduced by the BIGM results via the knowledge of the brash ice volume pushed out from the ship track described by an empirical dispersion factor α pushed. It is noted that, once the brash ice layer is thicker than the regrowth solid ice layer (i.e. after few vessel transits), the assumption on the brash ice layer profile has no more impact on the solid ice regrowth and hence not on brash ice production either. This means that even if ice is pushed sideways, the changed channel profile does not influence the growth rate.

6 Finally, since the time needed by water and brash ice to calm before commencing to refreeze after an ice breaking event ( ¼ hour, Ettema et al., 1990) is small compared with the typical time duration between two vessel passages (roughly 24 hours), it is not taken into account. Figure 3. Illustration of the simulated brash ice growth between two ship passages 3. Results and Discussion The behavior of the BIGM solution is illustrated with several cases described below. a) Reference Case Table 1 contains data related to the Ob Bay that is used for input data. These data correspond to a cumulative freezing air temperature C days, calculated with T f =-0.2 C at salinity S=3 ppt that prevails in Ob Bay. Heat capacity, energy of melting L i and thermal conductivity, are assumed constant and equal to pure ice values. Mean wind speeds over Ob Bay are c. 8 m/s and do not significantly vary from one season to another. A short review (Ebert & Curry, 1993) estimates that <C L < which enables evaluation of the turbulent convective coefficient h c =ρ a c a C L U za is between W/m 2 /K. Annual mean value of 20 W/m 2 /K is used. Table 1. Monthly mean air temperature of severe winter at Ob Bay region and incoming longwave radiation Q LW in Arctic Ocean region (Maykut & Untersteiner, 1971). Mean monthly metocean data Month Air temperature T a Incoming long-wave ( C) of severe winter radiation Q LW (W/m²) October November December January February March April May It is assumed that the mean ice breaking frequency during cold season is once every 95h and the mean brash ice porosity after each ship passage is p = 0.2. It is also considered that the fast ice

7 period is effective between the beginning of November with initial value of solid ice thickness of 20 cm) till the end of April. In May, the solar radiation is sufficient and the air temperature low enough to stop the brash ice growth. Result is given in Fig. 4. Figure 4. Evolution of solid (blue) and brash (green) ice thickness. This case shows that the mean equivalent brash ice thickness is about 8.5 m at the end of the cold season, assuming this frequency. Considering that half of the brash ice is pushed outside of the ship track, see Riska et al. (1997), the actual brash ice thickness is about 4.3 m. b) Parametric Study A parametric study has been performed to evaluate the impact of input parameters variation on the brash ice thickness in the approach channel of an Arctic port. The 4 parameters whose value was modified are listed in Table 2 (values of reference case written in bold). The minimum, mean and maximum values are determined from data encountered in the literature of interest. Table 1. List of input parameters and associated 3 values used in the parametric study Parameter name Minimum value Mean value Maximum value Brash ice porosity p [-] Convective coefficient h_c [W/m 2 /K] Air temperature T_air Temperate (3750 C days) Severe (4283 C days) Hard (4650 C days) Ice breaking frequency f_b every 51.5 h every 27 h every 19 h The results obtained in terms of equivalent brash ice thickness at the end of the cold season. h_bi_end in this parametric study varies between 5.80 m and m. In order to compare the influence of these parameters, a sensitivity pattern of the brash ice thickness h_bi_end with respect to the input parameters is plotted in Fig. 5. These curves confirm that the more influential parameters are the brash ice porosity p and the ice breaking frequency f_b. The T_air curve also shows that brash ice growth is as sensitive to the

8 h_bi_end [m] air temperature history as to p and f_b. Nevertheless, as the variation of this parameter is smaller than for p and f_b, the resulting interval on h_bi_end is lower than one obtained for p and f_b. 12 Sensitivity pattern of brash ice thickness at the end of the cold season h_bi_end p h_c T_air f_b ,2 0,4 0,6 0,8 1 1,2 1,4 1,6 Normalized parameter Figure 5. Results of the parametric study - sensitivity of brash ice thickness to input parameters. 4. Conclusions The brash ice growth model includes all appropriate parameters that have been conceived to influence the ice thickness growth. The model illustrates the influence of the ice porosity. The model gives similar brash ice thicknesses that have been observed in other Arctic ports, mainly in Norilsk. A more thorough validation is still lacking but is under way based on extensive measurements in the Luleå port in winter The effect of ice dispersion by ship bow and propeller wake has been noticed this has a large effect on actual thicknesses. 5. Acknowledgements Yamal LNG and their shareholders: Novatek (60%), Total (20%) and CNPC (20%) are acknowledged for their support for this work. 6. References Ebert, E. & Curry J. A An Intermediate One-Dimensional Thermodynamic Sea Ice Model for Investigating Ice-Atmosphere Interactions, J. Geophys. Res., 98(C6): Eranti, E. Penttinen, M. & Rekonen, T Extending the Ice Navigation Season in the Saimaa Canal. Proc. 7th Int. POAC Conf. (POAC 83), Helsinki, Finland, Ettema, R. & Huang H.-P Ice Formation In Frequently Transited Navigations Channels. USA Cold Regions Research and Eng. Laboratory, CRREL Special Report Maykut, G.A. & Untersteiner, N Some Results from a Time Dependent Thermodynamic Model of Sea Ice, J. Geophys. Res. 76, Parkinson, C. L. & Washington W. M A Large-scale Numerical Model of Sea Ice, J. Geophys. Res., 84(C1): , Riska, K., Wilhelmson, M., Englund, K. & Leiviska, T Performance of Merchant Vessels in the Baltic. Winter Navigation Research Board, Res. Rpt 52, 72 p. Sandkvist, J Conditions in Brash Ice Covered Channels with repeated Passages. Proc. 6th Int. POAC Conf. (POAC 81), Quebec, Canada,

9 MODELLING BRASH ICE GROWTH IN PORTS Kaj Riska 1, Rodolphe Blouquin 2, Edmond Coche 1, Sergey Shumovskiy 3, Dmitry Boreysha 3,4 1 Total E&P SA, DEV/ED/EC 2 Bertin Technologies, BCM/SIMA 3 Yamal LNG 4 At present GazPromNeft AIM AND CONTENTS Describe the question tackled; Review methods to calculate brash ice growth; Present a procedure to estimate the brash ice growth in frequently visited ports; Present example calculations for an actual project; What next? Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

10 AIM AND CONTENTS Describe the question tackled; Review methods to calculate brash ice growth; Present a procedure to estimate the brash ice growth in frequently visited ports; Present example calculations for an actual project; What next? Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August BRASH ICE FORMATION AND GROWTH Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

11 WHAT IS REQUIRED TO GROW BRASH ICE? No ice drift protected waters or ports Frequent ice breaking events ship passages Freezing temperatures Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August BRASH ICE CHANNEL SHAPE Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

12 AIM AND CONTENTS Describe the question tackled; Review methods to calculate brash ice growth; Present a procedure to estimate the brash ice growth in frequently visited ports; Present example calculations for an actual project; What next? Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August THEORETICAL THICKNESS All methods account only for the theoretical thickness i.e. thickness without ice horizontal motion; Ice growth usually based on modified Stefan equation; Brash ice thickness increase at ship passage α thermal constant p porosity Sandkvist 1981, Ettema & al Riska & al Regression methods exist also but these are not generally applicable. Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

13 OBSERVED AND THEORETICAL BRASH ICE THICKNESS These are 2-3 times thicker than the observed thicknesses! Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August AIM AND CONTENTS Describe the question tackled; Review methods to calculate brash ice growth; Present a procedure to estimate the brash ice growth in frequently visited ports; Present example calculations for an actual project; What next? Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

14 THEORETICAL MODEL FOR BRASH ICE GROWTH Thermal boundary layer taken into account; Long wave radiation accounted for but not insolation; Snow cover (or brash ice above the water level) insulation effect accounted for; Constant porosity (general value used p = 0.2); Initial growth phase ignored. Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August THEORETICAL MODEL FOR BRASH ICE GROWTH Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

15 BREAKING AND FREEZING CYCLE Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August BREAKING AND FREEZING CYCLE Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

16 AIM AND CONTENTS Describe the question tackled; Review methods to calculate brash ice growth; Present a procedure to estimate the brash ice growth in frequently visited ports; Present example calculations for an actual project; What next? Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August APPLICATION TO SABETTA PORT Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

17 APPLICATION TO SABETTA PORT Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August APPLICATION TO SABETTA PORT Month Mean monthly metocean data Air temperature T a ( C) of severe winter Incoming long-wave radiation Q LW (W/m²) October November December January February March April May Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

18 h_bi_end [m] 22/07/2014 APPLICATION TO SABETTA PORT Ship every 95 h Porosity 0.2 Normal winter Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August APPLICATION TO SABETTA PORT Sensitivity pattern of brash ice thickness at the end of the cold season h_bi_end Parametric variation p h_c T_air f_b ,2 0,4 0,6 0,8 1 1,2 1,4 1,6 Normalized parameter Parameter name Minimum value Mean value Maximum value Brash ice porosity p [-] Convective coefficient h_c [W/m 2 /K] Air temperature T_air Temperate Severe Hard (3750 C days) (4283 C days) (4650 C days) Ice breaking frequency f_b every 51.5 h every 27 h every 19 h Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

19 AIM AND CONTENTS Describe the question tackled; Review methods to calculate brash ice growth; Present a procedure to estimate the brash ice growth in frequently visited ports; Present example calculations for an actual project; What next? Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August NEXT STEPS Development of the calculation routine to account for various layers; Thermal inertia in water (water heating); Validation of the calculation method with experiments at Lulea port. Theoretical model Spot tests (Sabetta) Field tests in Lulea port (Sweden) Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August

20 Thank you for attention any questions? Modelling Brash Ice Growth in Ports; Riska et al.- IAHR 2014 Singapore 12 August