A Decision Support Model for Minimizing Sloshing Risk in LNG Discharge Operations

Transcription

1 A Decision Support Model for Minimizing Sloshing Risk in LNG Discharge Operations Egil Rokstad 1,3, Stein Ove Erikstad 1 and Kjetil Fagerholt 1,2 1 Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norway. 2 Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway. 3 FLEX LNG, Oslo, Norway Abstract In this paper we present an optimization model for the redistribution of cargo in order to reduce sloshing induced loads in LNG cargo tanks during regasification of LNG from an offshore floating regasification unit. The proposed model is a time discretized Integer Programming model, where a certain risk level is assigned to specific tank level states. The redistribution and discharge operation is modelled as a series of state transitions subject to a set of initialization and continuity constraints. The resulting scheme reduces the time each tank spends with filling levels within the barred zone, corresponding to filling levels of 15% - 45%, where high peak sloshing pressures are more likely to occur. Key words: LNG, sloshing, Natural gas shipping, Operations Research

2 2 1 Introduction Despite the recent global financial crisis, we have seen a considerable increase in the total transportation of Liquefied Natural Gas (LNG) worldwide. This growth is expected to continue, with several new and very large LNG carriers to be delivered, and with a continuous development of new gas fields located relatively far from the main markets. Most of the LNG carriers today are designed to discharge their cargo at special onshore terminals. The cargo is transferred in its liquid state using special cryogenic pumps and flow lines that can withstand the extreme low temperatures of the LNG (-163 C). The rate of development of new, remote gas fields, and the corresponding increase in seaborne LNG transportation, has made the availability of regas capacity at terminals in major gas markets a scarce resource. Extensions and development of additional capacity has been problematic due to public opinion, in particular in densely populated areas. This has lead to the development of alternative concepts for LNG discharge. One such concept is the Shuttle and Regas Vessel (SRV). A key feature of the SRV concept is the ability to regas the LNG cargo at an offshore site and send it to shore through a pipeline. The LNG is vaporized aboard the ship utilizing special LNG vaporization units, and then discharged through a buoy system to which the ship is moored. The buoy is connected to a riser, which then is connected to a sub-sea tie-in to an existing gas pipe system, or directly to the shore gas grid via sub-sea piping. By using this technology the SRV vessel in reality works like an offshore LNG importing terminal. Another concept is the Floating Storage and Regasification Unit (FSRU). The major difference between the SRV and FSRU concept is that the FSRU is able to receive cargoes from conventional LNG carriers via a ship-to-ship LNG transfer system, and store the received LNG aboard before regasification and discharge. Some of the main benefits by utilizing such offshore-based discharge technologies are shorter construction time, less investment in non-mobile constructions, less area needed onshore in the LNG importing region, and often easier location by avoiding conflicts often related to onshore based import terminals. The main drawbacks are prolonged discharge time and possible exposure to more harsh weather during unloading operations. In normal operation, the average discharge time of a re-gas vessel can typically be in the range of ½ - 2 weeks. This discharge time would depend on cargo capacity, send-out (re-gas) rate and the gas demand at the destination of the gas.

3 3 Sloshing is the motion of a fluid in a partially filled tank, which may sometimes be violent when affected by ship motion. The main factors that affect the motion of the behaviour of the fluid are the tank shape, the ship motion characteristics and its fill height. The exposure to offshore conditions may lead to certain ship motion characteristics that again can result in significant sloshing loads on the tank structure from the liquid motion of LNG inside the tanks. This may increase the probability of damage to the tanks and create leaks, a particular concern for some LNG containment systems. It should be noted that the sloshing phenomenon is a highly non-linear process that may call for model tests to produce a statistical base for measuring peak pressures regarding magnitude, location and duration. Several strategies have been proposed for reducing these loads, such as tank strengthening using super-reinforced boxes/panels in the tanks, operate in less severe weather, avoid unfavourable incoming wave angles, design the ship with smaller tank dimensions, changed tank design and/or introducing baffles in order to reduce liquid motions, and finally, improve operations planning to increase the time with near full or near empty tanks. In this paper, we will look further into the latter of these strategies, by proposing an optimization model that will suggest a scheme for the redistribution of cargo between tanks during the discharge operation. This scheme aims at minimizing the total time the vessel will spend in loading conditions where tank filling levels are in the region where sloshing-induced damages are more likely to occur, thus reducing the overall risk level of the discharge operation. To the authors knowledge, there exists no previous work on this problem. However, there are some references on studies dealing with problems that have some similarities. In the container shipping industry loading and discharge operations must be planned carefully, see for instance (Martin et al., 1988), (Avriel et al., 1998), (Wilson and Roach, 1999), (Kang and Kim, 2002) and (Li et al., 2008). However, while we in this paper are trying to determine the discharge operations that minimize the risk for sloshing-induced damage, the mentioned studies from the container shipping industry aim at minimizing the number of container moves. Fagerholt and Heimdal (1998) study a problem dealing with transfer of ballast between tanks in an offshore installation, which also has some similarities with ours. In Section 2, we explain in more detail the problem with cargo redistribution in order to reduce sloshing induced loads. Section 3 presents the optimization model that is developed to provide decision support on how to do the cargo redistribution during discharge operations. Section 4 provides a computational study, while summary and concluding remarks are given in Section 5.

4 4 2 Cargo redistribution and sloshing levels A commonly used term related to the sloshing phenomena is the so-called barred zone. This refers to those tank filling levels where sloshing with high peak pressures is likely to occur. Typically this range will be around filling levels of 15% - 45%. The principal idea behind cargo redistribution is to reduce the time each tank spends within the barred zone. In principle, this can be done by discharging all or several tanks to a level near the barred zone (for instance 45%). Then one tank at a time is taken quickly through the barred zone, utilizing excess cargo pump capacity to transfer liquid from the tank being emptied to the spare volume of the other tanks. In parallel some of the volume is re-gassed and sent out through the buoy. Since this process is relatively slow and require only a small share of the total pump capacity, the remaining pump capacity can redistribute cargo relatively fast. The re-distribution stops when all spare capacity in other tanks is filled up, or the tank that is being emptied is under the lower limit of the barred zone. In practice, the relation between filling level and sloshing criticality is not a 0-1 function as the barred zone concept would indicate. Each tank filling level can be related to a factor that quantifies the probability of corresponding sloshing loads. This may be a compound factor that comprises different pressure readings (average, peak) and different sea states and headings. In this paper, the risk of sloshing damage is assumed to be proportional to the max patch measured impact pressure in the tank, both for head and beam seas. This will be used as a basis for calculating the sloshing loads in the optimization model. This will more elaborated upon in Section 3.3. At any point of time during the discharge operation, the cargo engineer must make decisions on how to redistribute the cargo between the tanks in order to reduce the risk for sloshinginduced damages. The information available when making decisions may include: The cargo levels in each of the tanks The predicted send-out rate The weather forecast for the next days The wind, current and sea-state forecasts The seakeeping abilities of the ship The constrains for maximum allowed longitudinal bending-moment of the hull

5 5 On the basis of this information the cargo engineer must decide on how each tank should be discharged, how much shall be re-distributed between the tanks, and at what point of time this should be done. 3 Model development In order to provide the cargo engineer with decision support for the problem discussed in the previous section, we propose an optimization model. The main objectives for such an optimization model are: Give an initial advice at the beginning of the cargo discharge operation on how to plan the whole discharge process. Give a revised advice during the different stages of the discharge process as the conditions are changing and new information becomes available. We here propose an optimization model for providing decision support for the cargo engineer. The model consists of an objective function which sums a given measure for risk of sloshing for all tanks during the whole discharging period. The objective function will be minimized subject to constraints regarding physical restrictions of the tanks and the send-out rate. 3.1 Model formulation In the following we present the optimization model, which is a time discretized Integer Programming (IP) model. We start by defining the notation before the model is presented. Let C be the set of compartments or tanks onboard the LNG vessel, while N represents the set of possible states each tank can be in. Each state corresponds to a given filling level of the specific tank. Define T as the set of time periods (spanning the duration of the whole discharge operation). Let be the send-out rate, i.e. the amount of LNG that will be discharged during time period t, while the transition matrix states the amount of LNG that is added or subtracted to a tank c when going from state i to j. can both be a positive number (if LNG is added to the tank) or a negative number (if LNG is subtracted). The determination of the transition matrix is described more thoroughly in Section 3.2. Let be a penalty that estimates the risk for sloshing in tank c going from state i to j. How this is calculated will be elaborated upon in Section 3.3. Note that includes a time index, facilitating the possibility that the risk penalty can change over time (for instance if the weather is predicted to change).

6 6 Finally, let be a binary variable that is equal to 1 if tank c goes from state i to j in time period t, and 0 otherwise. Then we can present the IP model as follows: (1) (2) (3) (4) (5) The objective function (1) minimizes the total estimated penalty from sloshing load risk. Initializing constraints (2) ensure that each tank c starts in state 1 (usually representing 100 % filling level) in time period 1. Constraints (3) state that for each period t, each tank c must go from exactly one state to another, while constraints (4) are continuity constraints that make sure that if a tank enters a state in period t-1, it must leave (or remain in) the same state in period t. Constraints (5) ensure that the amount of LNG that is discharged in a given period must equal the change in volume summed over all tanks. Binary requirements for the variables are imposed by constraints (6). For the above model to work, the parameters (6) must be scaled in a way so that it is possible (and not too restrictive) to find combinations of states in constraints (5) such that the volume change summed over all tanks can be equal to the discharged amount in each period. Since the way the parameter is defined means that we have discretized the tank volumes into a limited number of allowable values, this may sometimes be too restrictive. This will especially be true in situations where the tanks onboard the vessel have different capacities and when the discharge rate varies over time. Therefore, we introduce some slack, represented by the parameter. Then, we can replace constraints (5) by the following two constraints:

7 7 (5a) Constraints (5a) and (5b) together ensure that that the change in volume summed over all tanks must be within the range. This means that we introduce some flexibility in order to provide better solutions. Constraints (5a) and (5b) can result in solutions that may, in principle, not be feasible as we allow the changes in tank volumes to not accurately correspond to what have been discharged in a given period. However, this is done under the assumption that feasibility can in practice easily be achieved by slight adjustments to the amount in each tank without changing the solution quality significantly. 3.2 Deciding the transition matrix The transition matrix is necessary for the model to maintain the send-out rate,, and to make sure that when liquid is removed from one tank it is added to another (or discharged). It is defined as, and represents the difference in volume in the tank between states j and i. Let us illustrate the calculation of following example: (5b) for a given tank by the Example 1: Calculation of for a given tank Let us consider a given tank, c, with a total volume of m 3. Let us assume, for simplicity, that the tank is discretized into six filling levels or states (in practice we will use a finer tank discretization). The six states have the following volumes: State Filling level [%] Tank volume [1 000 m 3 ] Table 1: Relation between state and tank volume (example)

8 8 Using the numbers in Table 1, we can define for tank c in the following way: S cij Determining the risk penalty The risk penalty,, is applied to estimate the risk for sloshing induced damages for any tank level or state. Since there is considerable uncertainty about the cargo tanks ability to withstand sloshing induced loads, it is assumed that the risk of structural damages in the tank is proportional to the level of sloshing induced forces. In (Tveitnes et al., 2005) and (Pastoor et al., 2004), the effect of sloshing was investigated for a typical sized LNG vessel with four membrane tanks. In those studies irregular sloshing experiments were conducted for both head and beam seas for different tank filling levels and sea severities. Normally, the head seas condition is most relevant, provided the vessel s ability to weather wane is kept intact. Further, the impact pressure was measured both at specific locations in the tank with patches, and uniformly across the tank cross section. Here, the patch load was the most severe. Thus, the patch load impact pressure for head seas has been used as a basis for the risk measure. The risk is captured in the optimization model by a penalty matrix that aggregates the average impact pressure magnitude of all states covered when going from state i to j, given by (7) where is the local state pressure impact level for the filling level corresponding to state k. By using the graph for head waves in Figure 1 and using a tank filling level discretization of 10% of the tank capacity, going from 80% to 70% filling level will for example impose a penalty of (15+20)/2 = Going from 70% to 40% gives a penalty of ( )/4 = The penalty matrix for head seas, extracted from the graph in Figure 1, is summarized in Table 2.

9 9 Figure 1: Patch load impact pressure for head seas, which forms the basis for the risk matrix (Image source: Tveitnes et al. 2005) Table 2: Penalty matrix for head seas The penalty matrix in Table 2 serves as a baseline, and may be adjusted to the actual operating context in which the unloading process takes place. Such adjustments may include: Tank location, size and geometry, taking into consideration the fact that tanks located amidship are less exposed than those towards the stern or bow, and that size and geometry differences may impose differences in impact pressure load. Actual sea state provided a reliable forecast is available.

10 10 Resonant periods in the tanks, that will significantly aggravate the sloshing forces when the period of the rolling and pitch motions of the vessel coincides with that of the tanks. These adjustments are not included in the model here. 4 Demonstration of model solutions In order to demonstrate the model behaviour and the solutions it provides, we present some tests for realistic problems. We have used Xpress MP to solve the model on an Intel Pentium Centrino 1.70 GHz processor with 1 Gb RAM. Section 4.1 presents the test cases, while the solutions for these cases are given in Section Test cases Table 3 shows the main information for three test cases for realistic LNG vessels, all having five LNG tanks. The vessel in case 1 has a total tank volume capacity of , while the vessels in cases 2 and 3 both have capacities of m 3. The discharge rate,, is 1 600, and m 3 /hour for the three vessels, respectively. This means that it takes 100 hours to discharge any of the three vessels. Case 1 Case 2 Case 3 Total cargo tank volume [1000 m 3 ] Tank 1 [1000 m 3 ] Tank 2 [1000 m 3 ] Tank 3 [1000 m 3 ] Tank 4 [1000 m 3 ] Tank 5 [1000 m 3 ] Discharge rate, [1000 m 3 /hour] Transfer capacity [1000 m 3 /hour] [1000 m 3 ] Number of time periods Table 3: Test instances The transfer capacity corresponds to the capacity for redistributing LNG between the tanks on the vessel. This is given as m 3 /hour for all vessels. This means for example that it takes 10 hours to redistribute the entire content of the largest tank on vessel 1. We have therefore chosen 10 hours as a natural duration of each time period. This means that it takes 10 time

11 11 periods to discharge the vessels (11 if we include the initial condition). In case 3 we have added one time period to this. We have for all cases used a discretization level of 10% of the tank capacities, giving 11 different states or tank fillings (like illustrated in the penalty matrix in Table 2). In case 2 a more complex penalty matrix has been used, where the risk penalty,, varies over time. As can be seen from Table 3, only case 3 includes the slack parameter. The effect from this is that in case 3 is that the amount of LNG discharged in each time period can vary between 13.5 and 17.5 m 3 (instead of being fixed at 15.5 m 3 ). In a real-life implementation of the model, a finer discretization of both states and time would possibly be needed. However, we believe the chosen discretization is sufficient to demonstrate the model s applicability. 4.2 Computational results Table 4 shows how the volume contained in the tanks vary over time in the solution for case 1. Time period Tank 1 Tank 2 Tank 3 Tank 4 Tank 5 Sum Table 4: Solution case 1, tank volumes [1 000 m 3 ] Figure 2 presents the same results graphically. We observe that the smallest tank (tank 5) is emptied through the barred zone first. Then follow the two medium sized tanks (tanks 3 and 4) before the two largest tanks (tanks 1 and 2) are emptied. All tanks are taken through the barred zone only once.

12 Tank filling [%] Tank 1 Tank 2 Tank 3 Tank 4 Tank Figure 2: Solution case 1, degree of tank filling [%] as a function time periods Similar results for cases 2 and 3 are presented in Figure 3. It can be noted that for both cases 2 and 3 the smallest tank (tank 5) is taken through the barred zone twice. a) Case 2 b) Case 3 Figure 3: Solutions cases 2 (a) and 3 (b), degree of tank filling [%] as a function time periods For all three cases we see that tank levels often have minor fluctuations from 80% to 100% and between 0 and 10% tank filling level. This is probably a pattern that a cargo engineer would not prefer, as it results in a larger number of transfer operations that is really required. The

13 13 reason that the model still provides these solutions can be explained from the penalty matrix in Table 2. The penalty of going from 80% to 100% is the same as staying at any of these two levels. We also see the same with the penalty of going between 0% and 10%. This means that the solution quality model-wise is indifferent between staying at any of these levels and having the minor fluctuations. By including cargo redistribution costs into the model, both related to cargo transfer energy consumption and to boil-off gas, these fluctuations are likely to be reduced. 5 Discussion and concluding remarks In this paper we have presented an optimization model that produces a scheme for the redistribution of cargo in order to reduce sloshing induced loads related to LNG discharge and regasification processes. By being able to empty the tanks quickly through the critical zone, the total time exposed to high sloshing loads, and hence the overall risk level, will be reduced. Even in the simple case of developing a fixed plan for a pre-defined operating scenario (wind, waves,...) the development of an optimal plan is not trivial. In the more complex situation involving the dynamic re-planning of the cargo redistribution as more information becomes available, and with corresponding time and resource constraints, the benefit of an optimization-based approach is even more profound. We have identified a number of possible areas for improving the model. This includes an extended penalty matrix taking additional risk-relevant aspects into account, such as those discussed in Chapter 3.3, and including the cargo redistribution costs into the model. Further, the current linear relationship between patch impact sloshing loads is likely to be too simplistic. Still, even with a more complex, non-linear load-risk relationship the basic approach will be the same, since the model is based on a discrete set of possible state transitions. 6 References Avriel, M., M. Penn, N. Shpirer and S. Witteboon (1998) Stowage planning for container ships to reduce the number of shifts. Annals of Operations Research 76, Fagerholt, K. and S. I. Heimdal (1998) Algorithms for effective transfer of ballast for an oil installation. Journal of the Operational Research Society 49, Kang, J-G. and Y-D. Kim (2002) Stowage planning in maritime container transportation. Journal of the Operational Research Society 53,

14 14 Li, F., C. Tian, R. Cao and W. Ding (2008) An integer linear programming for container stowage problem. Lecture Notes in Computer Science 5101, Martin, G. L., S. U. Randhawa and E. D. McDowell (1988) Computerized container-ship load planning: A methodology and evaluation. Computers and Industrial Engineering 14, Pastoor L. W., T. Tveitnes, S. Valsgård and H. O. Sele (2004) Sloshing in partially filled LNG tanks an experimental survey. Published by Det Norske Veritas (DNV), Høvik, Norway. Presented at Offshore Technology Conference, May 3-6, 2004, Houston, Texas, USA. Tveitnes, T., T. K. Østvold, L. W., Pastoor and H. O. Sele (2005) A sloshing design load procedure for membrane LNG carriers. Published by Det Norske Veritas (DNV), Høvik, Norway. Presented at GasTech, March 14-17, 2005, Bilbao, Spain. Wilson, I. D. and P. A. Roach (1999) Principles of combinatorial optimization applied to container-ship stowage planning. Journal of Heuristics 5,