Minimizing Power Consumption Related to BOG Reliquefaction in an LNG Regasification Terminal

Transcription

1 This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. pubs.acs.org/iecr Minimizing Power Consumption Related to BOG Reliquefaction in an LNG Regasification Terminal Harsha N. Rao, Khai H. Wong, and Iftekhar A. Karimi* Department of Chemical & Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore Downloaded via on December 24, 2018 at 02:34:58 (UTC). See for options on how to legitimately share published articles. ABSTRACT: The generation of boil-off gas (BOG) is inevitable in liquefied-natural-gas (LNG) regasification terminals. It can be a safety concern and, in most cases, demands BOG reliquefaction before regasification. This study presents a fundamental thermodynamic analysis of the BOG reliquefaction LNG regasification process, which consumes significant power. We propose an evolving series of schemes that exploit the cryogenic energy of the send-out LNG to reduce the total power consumption. We synergistically integrate options such as BOG precooling, recompression, interstage cooling, and recondensation in our proposed schemes. We develop a nonlinear programming (NLP) formulation to minimize the power required for each scheme for a given amount of BOG. Under some idealistic assumptions, the optimal solutions to these NLPs give lower bounds on the total power consumption, which can be used to evaluate the cost-effectiveness of terminal operations. A novel scheme consisting of BOG precooling before compression and two-stage recondensation by direct mixing has the least power consumption. For a case-study terminal, it offers 11.9% lower power consumption than the best-reported design in the literature for 15% BOG. 1. INTRODUCTION Natural gas (NG), the cleanest fossil fuel, has been the fastestgrowing energy resource for more than two decades and will be so for the foreseeable future. It offers the highest efficiency in power generation with the lowest carbon emissions. Although pipelines are the best for transporting NG over short distances, today s diverse and long supply chains necessitate global NG transport over long distances. For this purpose, liquefied natural gas (LNG) is the most common and economical option that has overcome geopolitical constraints on the global gas supply. 1 NG from a gas reservoir is pretreated prior to its energyintensive liquefaction at an onshore plant or offshore vessel. The resulting LNG is stored in atmospheric storage tanks at a loading terminal before being shipped in specially insulated LNG tankers to a receiving terminal. The latter also stores the incoming LNG in atmospheric tanks and regasifies it continuously to supply NG to gas distribution grids or customers. From the time it is liquefied to the time it is regasified, LNG is continuously maintained at atmospheric pressure and cryogenic temperatures (about 160 C) through autorefrigeration. Despite extensive insulation, heat leakage into the LNG during this entire duration is unavoidable. This causes part of the LNG to vaporize throughout its supply chain to form what is known as boil-off gas (BOG). Managing BOG at various points (storage, loading, transport, unloading, and regasification) in the LNG supply chain 2,3 is critical, because transporting or storing it as a gas is uneconomical. Unless reliquefied and/or used in some form, BOG represents a loss of valuable product, and its flaring is becoming increasingly unacceptable. The loss of BOG also changes the LNG composition and quality over time. This affects the LNG trade, as LNG is priced based on its energy content. 3 Most regasification terminals deliver NG at high pressures (30 80 bar) to their gas grids or customers. Compressing atmospheric BOG to such high pressures is also uneconomical. Therefore, unless an opportunity for direct, gainful, complete, and inexpensive use of the BOG exists without much energy penalty, most regasification terminals employ a system to reliquefy the BOG. Efficient BOG management systems are thus very important. In fact, the power/energy required to manage BOG is a major cost for regasification terminals. Thus, minimizing the energy consumption at LNG regasification terminals is of great interest and a worthwhile undertaking that has received some attention in the literature. 4,5 BOG arises from several sources in a regasification terminal. The heat leaking continuously into the LNG storage tanks is an obvious source, but loading and unloading activities at the terminal are even larger sources. The tanks are typically far from the jetties, and the transfer lines connecting the two must be continuously kept cold to avoid substantial and periodic expansion/contraction of pipes and other infrastructure, which could cause damage. This line cooling is typically achieved by recirculating the LNG from the tanks continuously through the transfer lines. The recirculating LNG sweeps heat from the Received: April 7, 2016 Revised: June 8, 2016 Accepted: June 14, 2016 Published: June 14, American Chemical Society 7431

2 Figure 1. Schematic of a typical regasification terminal. surroundings, pumps, turbulence, and friction. In some terminals, this LNG is dumped back into the storage tanks, which generates a major portion of the total BOG. Most literature on LNG regasification has focused on exploiting the cryogenic energy of LNG to produce power by integrating various cycles such as Organic Rankine, Brayton, etc. 6,7 Most of these have focused on exergetic and/or energetic efficiency, and very few 8 10 have considered cost. In contrast, the literature on BOG management topics such as estimation, 2,11 13 minimization, 2,14,15 reliquefaction, 4,5,16 18 direct compression, 13 and utilization 19 is limited. Wordu and Peterside 12 estimated the BOG arising from the heat leak into an LNG storage tank. Hasan et al. 2 estimated BOG generation during loading, laden voyage, unloading, and ballast voyage of an LNG tanker and performed simulations to find the optimal heel for maritime transport. Adom et al. 11 studied the effect of pressure and heat leakage on BOG generation. Park et al. 14 simulated and optimized the line-cooling recirculation in an LNG receiving terminal. Lee et al. 15 suggested an unloading procedure for minimizing BOG generation in an operation with a combination of above-ground and in-ground LNG tanks. Jang et al. 17 presented an algorithm for an optimal operating schedule of BOG compression depending on the dynamic behavior of an LNG tank. Shin et al. 18 proposed a mixed integer linear problem (MILP) formulation to optimize BOG compressor operation based on the dynamics of tank pressure. Liu et al. 5 studied BOG reliquefaction by direct, multistage mixing with pressurized LNG. However, they did not use highpressure LNG (HP-LNG) for cooling, which can reduce the power usage significantly. Later, Park et al. 4 and Li et al. 16 studied the retrofit design of a BOG reliquefaction system. They used HP-LNG for some cooling, but did not maximize its use and did not consider all options for power reduction. Querol et al. 13 reviewed the various recondensation and direct compression options and proposed a combined heat and power system. Recently, Park et al. 19 integrated LNG regasification with a gas-to-liquid (GTL) plant that uses the BOG as a chemical feedstock. In this work, we study BOG reliquefaction at a typical regasification terminal (Figure 1). Using selected design/ operation guidelines, we evolve several novel reliquefaction schemes that maximize the use of LNG cold energy in different ways to substantially reduce power consumption. We begin with a precise problem statement, develop our reliquefaction schemes, and then evaluate them under some idealistic scenarios. For each scheme, we present a nonlinear programming (NLP) formulation to obtain its minimum power usage. Finally, we demonstrate significant power reductions from our schemes for the terminal considered by Park et al PROBLEM STATEMENT Consider the seawater-based LNG regasification terminal in Figure 1. On a long-term basis, it receives and gasifies F t/h (throughput) of LNG, on average, and supplies F t/h (tph) of NG (send-out rate) to a local gas distribution grid at specified conditions. Let βf tph (0 < β < 1) of BOG exit the tank tops at (P 1, T 1 ) and (1 β)f tph of LNG be available for send-out at (p 1, t 1 ). Normally, BOG is superheated (compared to tank conditions) as a result of the heat ingress into the tanks and/or downstream pipelines. We allow the user the flexibility to give BOG and LNG specifications independently based on real terminal data. With this setup, we address the following problem in this work. Given (1) the LNG throughput or gas send-out rate F t/h (tph) (with no loss of generality, we assume F = 1 tph); (2) the average composition and conditions (p 1, t 1 ) of the LNG available for send-out; (3) the average BOG composition, generation fraction β, and conditions (P 1, T 1 ); (4) the send-out temperature (T S ) and pressure (P S ); and (5) the ratio (p sw ) of the power required to pump seawater to the rate of heating required for regasification Obtain the minimum power consumption (kw) of the terminal per tonne of send-out NG for any given β, and the scheme of process steps to achieve the same Assuming that (1) the flows, compositions, temperatures, pressures, and pressure drops of streams are long-term averages (essentially, the dynamics of the terminal operation arising due to loading, unloading, delivery, recirculation cooling, vessel cooling, etc., are neglected by averaging over a long time); (2) the LNG and BOG compositions are in their normal ranges found in the industry (i.e., the nitrogen content is sufficiently low to make BOG reliquefaction possible); 7432

3 (3) the pumps and compressors are isentropic with 100% efficiency; (4) the heat exchangers are countercurrent with a minimum temperature approach of zero; (5) the pressure drops through the equipment and pipelines are zero; and (6) the net positive suction head (NPSH) for all pumps is zero. 3. BOG RECONDENSATION SCHEMES Let Figure 2 represent the pressure enthalpy (P H) diagram for the LNG feed. The thick solid line in green represents the Figure 2. P H diagrams for one-stage compression schemes. vapor liquid (V L) phase boundary, and the thin solid lines in yellow represent the isentropic curves. In this article, we use uppercase labels for the gaseous streams and lowercase labels for the liquid streams. Thus, let (P 1, H 1, T 1 ) on this P H diagram represent the BOG exiting the tanks, let (p 1, h 1, t 1 ) represent the LNG exiting the tanks, and let (P S, H S, T S ) represent the NG sent out to the gas grid or customers. Note that the LNG and BOG need not be in equilibrium, which is the reality in regasification terminals, contrary to the popular assumption of equilibrium. 5 We require a series of processing steps that transform the BOG at (P 1, H 1, T 1 ) and the LNG at (p 1, h 1, t 1 ) to the send-out NG at (P S, H S, T S ) using minimal power. We exploit the following basic thermodynamic facts: (1) Work for isentropic compression/pumping is given by the enthalpy change on a P H diagram. (2) Work for isentropic compression/pumping increases with the feed-fluid temperature. (3) Pumping needs much less energy than compression for a given pressure ratio. (4) The latent heat of vaporization decreases with pressure. Obviously, we must heat and pressurize β tph of the BOG and (1 β) tph of the LNG to obtain 1 tph of the send-out gas. As gas compression is much more energy-demanding than liquid pumping, we must maintain the LNG s liquid state and avoid compressing the BOG needlessly. Therefore, it is better to recondense the BOG first and then pump it to P S rather than compressing it all the way from P 1 to P S. Now, recondensing the BOG at P 1 is impossible in the absence of an external coolant. Hence, we must compress it to some P 2 > P 1 and then recondense it using any available LNG streams. To this end, we have two LNG streams. One is the LNG at (p 1, h 1, t 1 ). We can use it as such, if it can recondense all of the BOG while remaining liquid. If it cannot, then we must pump it to some p L > p 1 to make it a viable coolant (cooling potential increases with pressure). We call this pressurized LNG LP-LNG at (p L, h L, t L ) on the P H diagram. This is our primary coolant for recondensing the BOG at P 2. The second cold stream, called HP-LNG, is the cold ungasified version of the send-out NG. HP-LNG at (P S, h H, t H ) is a mixture of two LNG streams. One is the recondensed BOG (or RBOG), and the other is LP-LNG after it has recondensed the BOG. To lower the energy Figure 3. Process flow diagram for scheme

4 consumption in reliquefaction, we must reduce the BOG compression energy (thus P 2 ) as much as possible. To recondense the superheated BOG from (P 2, H 2, T 2 ), we must first cool it to its dew-point temperature (DPT 2 ) and then recondense it to its bubble-point temperature (BPT 2 ). Therefore, we heat a fraction y 1 of HP-LNG from (p S, h H, t H )to(p S, h H1, t H1 ) to cool the BOG from (P 2, H 2, T 2 )to(p 2, H 21, t H ). This heat exchange must respect the relations y ( h h ) = β( H H ) 1 H1 H 2 21 (1) DPT 2 t H t H1 T 2 (2) Equation 2 assumes DPT 2 t H, which holds for low P 2, because HP-LNG is a mixture of RBOG and heated LP-LNG. Throughout this work, we exclude the possibility that HP-LNG can recondense the BOG and limit its use for sensible cooling only. We can compress the BOG from (P 1, H 1, T 1 )to(p 2, H 2, T 2 ) in either one or more stages. For simplicity, we exclude three or more stages, but the methodology extends easily. 4. ONE-STAGE COMPRESSION Two possibilities exist for recondensing the BOG at P 2. We can mix it directly with LP-LNG (direct recondensation) as in existing terminals, or we can condense it indirectly using LP- LNG without mixing (indirect recondensation). Figure 2 shows the P H diagram for all of the one-stage compression schemes discussed below Indirect Recondensation. We first exhaust the cooling duty of HP-LNG (y 1 =1ineq 1) to cool the BOG from (P 2, T 2 )to(p 2, t H ). Then, we cool the BOG to DPT 2 and recondense it over the interval [DPT 2, BPT 2 ] in a series of countercurrent heat exchangers with LP-LNG (Figure 3). This requires the following cooling and condensation duty in total Q = β[ HP (, t ) HP (, BPT)] BOG 2 H 2 2 (3) where H(P,T) denotes the BOG enthalpy at (P, T). Since LP- LNG at (p L, t L ) is our primary coolant and must not be allowed to vaporize, its maximum cooling capacity is Q = (1 β)[ hp (, bpt ) h] LP L L L (4) where h(p,t) denotes the LNG enthalpy at (p, t) and bpt L is the bubble-point temperature of LP-LNG at p L. Clearly, the following relation must hold for complete recondensation of BOG Q Q LP BOG (5) To recondense the BOG over the interval [DPT 2, BPT 2 ], we use LP-LNG at (p L, t L ). Therefore (1 β)[ hp (, t ) h] L L1 L = β[ HP (,DPT) hp (,BPT)] t t DPT t (6) L L1 2 (7) bpt L1 L (8) BPT 2 t L (9) where t L1 is the exit temperature of LP-LNG from the recondenser. To cool the BOG to DPT 2 before recondensation, we use the LP-LNG at (p L, t L1 ) exiting the recondenser (1 β)[ hp (, t ) hp (, t )] L L2 L L1 = β[ HP (, t ) HP (, DPT)] t t t 2 H 2 2 (10) L1 L2 H (11) tl2 bptl (12) DPT 2 t L1 (13) where t L2 is the exit temperature of the LP-LNG. Equations 8 and 12 prevent the LP-LNG from vaporizing. Equations 7 and 13 provide the same upper bound for t L1. We now pump the LP-LNG at (p L, t L2 ) from the above cooler to (P S, t L3 ), pump the RBOG from (P 2, BPT 2 )to(p S, T 22 ), and then mix the two to get HP-LNG at (P S, h H, t H ). Hence h = (1 β) h( P, t ) + βh( P, T ) H S L3 S 22 (14) Next, pumping the seawater to regasify the HP-LNG from (P S, t H1 )to(p S, T S ) requires p sw [h S h(p S, t H1 )] kw. Adding the power required for compressing the BOG from P 1 to P 2 in one isentropic stage and also pumping the LNG streams isentropically, we obtain the total power consumption for the terminal as PC = p [ h h( P, t )] + β[ H H + h( P, T ) sw S S H1 2 1 S 22 HP ( 2, BPT)] 2 + (1 β)[ hl h1 + hp ( S, tl3) hp (, t )] L L2 (15) This completes our scheme 1.1 (first of the one-stage compression schemes) for recondensing the BOG indirectly with one-stage compression. To determine the minimum PC, we can solve the following nonlinear programming (NLP) problem (M1.1) with P 2 and P L as independent variables. M1.1: Minimize PC (eq 15) subject to eqs 1 12 and 14. We consider the Korean regasification terminal studied by Park et al. 4 for illustration. Although we study the terminal in full detail later for all values of β, for now, we use the specific case of β = 0.15 just to illustrate the effectiveness of our regasification schemes and the impact of process modifications. For β = 0.15 and p sw = , scheme 1.1 requires a power of kw per tonne of send-out gas Direct Recondensation. In scheme 1.1, LP-LNG and RBOG are eventually mixed to form HP-LNG. This is in contrast to the prevalent practice of recondensing BOG by directly mixing it with LP-LNG. 4 Since BOG is a result of vaporization, it must be slightly lighter in composition than the LP-LNG. From the BOG perspective, mixing it with the slightly heavier LP-LNG would increase its bubble-point temperature and decrease its latent heat of vaporization. As a result, its condensation load would reduce, which would essentially mean a lower P 2 and lower BOG compression energy. From a practical viewpoint, direct recondensation eliminates the resistances inherent in indirect heat transfer. However, it requires P2 = p L (16) (1 β) h + β[ H( P, t )] = h( P, t ) L 2 H 2 R (17) where t R is the recondenser temperature. Now, we can pressurize the recondensed liquid to P S to get HP-LNG and 7434

5 Figure 4. Process flow diagram for scheme 1.2. Figure 5. Process flow diagram for scheme 1.3. then follow the remaining operations in scheme 1.1. Then, the total power consumption is PC = p [ h h( P, t )] + β[ H H] sw S S H (1 β)[ hl h1] + [ h( PS, th) h( P2, tr )] (18) For this scheme (Figure 4), we can solve NLP problem M1.2 with P 2 as the only independent variable to obtain the minimum power consumption. M1.2: Minimize PC (eq 18) subject to eqs 1, 2, 16, and 17. For the case-study scenario defined in scheme 1.1, scheme 1.2 requires 2.11% lower power. This explains why all existing regasification terminals use direct instead of indirect recondensation Direct Recondensation with HP Precooling before Compression. In schemes 1.1 and 1.2, we compressed the BOG from the tanks directly. We can reduce the compression work, if we cool the BOG before compressing it (Figure 5). Hence, we now use a second portion (y 2 ) of the HP-LNG to precool the BOG to t H, in addition to that (y 1 ) already used to postcool the BOG after compression. For this precooling, we have β[ H H( P, t )] = y ( h h ) 1 1 H 2 H2 H (19) DPT 1 t H t H2 T 1 (20) y + y = 1 0 y, y (21)

6 Figure 6. Process flow diagram for scheme 1.4. The two HP-LNG portions exiting the precooler and the postcooler can now be recombined to form the feed to regasification. Therefore y h + y h = h( P, t ) 1 H1 2 H2 S H12 (22) Then, the total power requirement for this scheme (Figure 5)is PC = p [ h h( P, t )] + β[ H H( P, t )] sw S S H H + (1 β)[ h h ] + [ h( P, t ) h( P, t )] L 1 S H 2 R (23) In this case, we can solve NLP problem M1.3 to minimize the power usage. M1.3: Minimize PC (eq 23) subject to eqs 1, 2, 16, 17, and 19 22). M1.3 has P 2 and y 1 as independent variables. For β = 0.15, this scheme uses 3.98% lower power than scheme 1.2. To the best of our knowledge, no work in the literature has considered the option of using HP-LNG to precool the BOG Direct Recondensation with HP and MP Precooling before Compression. In scheme 1.3, HP-LNG could precool the BOG only to t H. Since t H DPT 1, we can reduce the compression work further by cooling the BOG to T 11 such that DPT 1 T 11 < t H. LP-LNG is the only viable option for this cooling, and we can use a fraction x (0 x 1) of the LP-LNG to achieve this. However, this fraction would reduce the muchneeded flow of LP-LNG to the recondenser, and hence increase P 2. Thus, we must minimize x to keep P 2 low. For the minimum value of x, the LP-LNG must exit the precooler at t H (zero-minimum approach). However, t H might exceed bpt L, and the LP-LNG might vaporize. Hence, to maintain the LP- LNG exiting the precooler as a liquid, we pump it from (p L, t L ) to some (p M > p L, t M ) so that bpt M t H. We call this new pressurized fraction of LP-LNG medium-pressure LNG (MP- LNG). We can now write x(1 β)[ h( p, t ) h( p, t )] = β[ H( P, t ) H( P, T )] M H M M 1 H 1 11 (24) T11 tm (25) tm th bptm (26) T11 DPT1 (27) where bpt M is the bubble-point temperature of MP-LNG at p M. Equation 27 is necessary to avoid liquid in the BOG entering the compression stage. Furthermore, we must rewrite eq 17 to use the decreased LP-LNG flow for recondensation (1 x)(1 β) hl + βh( P2, th) = [ β + (1 x)(1 β)] h( P2, tr) (28) The liquid at (P 2, t R ) from the recondenser should now be pressurized to (p M, t MR ) to mix with the MP-LNG at (p M, t H ). Thus hp (, t ) = [ β + (1 x)(1 β)] hp (, t ) M MC M MR + x(1 β) h( p, t ) M H (29) where t MC is the temperature of the resultant mixture. This mixture is now pumped to (P S, t H ) to form HP-LNG. With the other terminal operations as in the last scheme, we obtain the total power consumption as PC = p [ h h( P, t )] + β[ H H( P, T )] sw S S H (1 β)( h h ) + x(1 β)[ h( p, t ) h ] L 1 M M L + [ β + (1 x)(1 β)][ h( p, t ) h( P, t )] + [( hp, t ) hp (, t )] M MR 2 R S H M MC (30) This gives us NLP problem M1.4 with four independent variables (P 2, p M, T 11, and y 1 ) to obtain the minimum power consumption. M1.4: Minimize PC (eq 30) subject to eqs 1, 2, 16, 19 22, and Again, for the case-study scenario, scheme 1.4 (Figure 6) uses 6.13% lower power than scheme 1.3, which is the effect of MP precooling alone. The use of MP-LNG and MP precooling is absent in the regasification terminals known to us and is a novel option proposed in this study. Overall, precooling the BOG with both HP-LNG and MP-LNG reduced the power 7436

7 consumption by 9.86% compared to scheme 1.2, which has no precooling. All of the schemes considered so far assumed single-stage compression. If P 2 /P 1 exceeds 4 5, however, then two or more stages of compression become necessary. Therefore, we now consider two stages. 5. TWO-STAGE COMPRESSION With two compression stages, interstage cooling becomes possible. Therefore, we now modify scheme 1.4 by introducing a second stage of compression with intercooling. Figure 7 shows the P H diagram for the two-stage compression schemes discussed below. Figure 7. P H diagrams for two-stage compression schemes Direct Recondensation, HP and MP Precooling, and HP Intercooling. Let us compress the BOG from P 1 to P i in stage 1 and from P i to P 2 in the second stage. Also, we use HP-LNG to intercool the BOG from stage 1 to t H before it enters stage 2 (Figure 8). Then, we have β[ HP (, T) HP (, t )] = y[ hp (, t ) h] i i i H 3 S H3 H (31) DPT i t H t H3 T i (32) y + y + y = 1 0 y, y, y (33) y h + y h + yh = h 1 H1 2 H2 3 H3 H13 (34) where T i is the BOG temperature from stage 1, y 3 is the portion of the HP-LNG entering the intercooler, t H3 is its exit temperature, and h H13 is the enthalpy of the regasifier feed. The other terminal operations are the same as in scheme 1.4. The total power consumption for this scheme (Figure 8) is given by PC = p ( h h ) + β[ H( P, T) H( P, T )] sw S H13 i i i β[ H2 H( Pi, th)] + (1 β)( hl h1) + x(1 β)[ h( p, t ) h ] + [ β + (1 x)(1 β)] M M L [( hp, t ) hp (, t)] + [( hp, t ) hp (, t )] M MR 2 R S H M MC (35) In this case, NLP problem M2.1 with six independent variables (P 2, P i, p M, T 11, y 1, and y 2 ) gives the minimum power consumption. M2.1: Minimize PC (eq 35) subject to eqs 1, 2, 16, 19, 20, 24 29, and Two-stage compression reduced the power consumption by 1.47% compared to scheme 1.4 for the case-study scenario Direct Recondensation, HP and MP Precooling, and HP and MP Intercooling. A logical extension of the last scheme is to add MP-LNG intercooling. As discussed earlier, using the MP-LNG for this would decrease the amount of LP- LNG available for recondensation, and P 2 would increase accordingly. We thus use a fraction z (0 z 1) of MP-LNG for this additional intercooling and heat it to t H. Recall that the MP-LNG is a fraction x of the LP-LNG pressurized from p L to p M. For this case, we have Figure 8. Process flow diagram for scheme

8 Figure 9. Process flow diagram for scheme 2.2. Figure 10. Process flow diagram for scheme 2.3. zx(1 β)[ h( p, t ) h( p, t )] = β[ H( P, t ) H( P, T )] t T t bpt M H M M i H i i1 (36) M i1 H M (37) Ti 1 DPTi (38) (1 zx ) (1 β)[ hp (, t ) hp (, t )] M H M M = β[ HP ( 1, th) HP ( 1, T11 )] (39) where the BOG enters the second compression at T i1 and DPT i is its dew-point temperature at P i. The two MP-LNG fractions from MP precooling and MP intercooling are mixed with the recondensed liquid pumped to p M. The energy balance for this mixing is hp (, t ) = [ β + (1 x)(1 β)] hp (, t ) M MC M MR + zx(1 β) h( p, t ) + (1 z) x(1 β) h( p, t ) M H M H (40) The resultant mixture is then pressurized to (P S, t H ) and regasified as described in the previous cases. The total power requirement for this case is PC = p ( h h ) + β[ H( P, T) H( P, T )] sw S H13 i i β[ H2 H( Pi, Ti1)] + (1 β)( hl h1) + x(1 β)[ h( p, t ) h ] + [ β + (1 x)(1 β)] M M L [( hp, t ) hp (, t)] + [( hp, t ) hp (, t )] M MR 2 R S H M MC (41) For this scheme (Figure 9), we have NLP problem M2.2 with seven independent variables (P 2, P i, p M, T 11, T i1, y 1, and y 2 )to obtain the minimum power consumption. M2.2: Minimize PC (eq 41) subject to eqs 1, 2, 16, 19, 20, 25 28, 31 34, and For the case-study scenario, MP intercooling was not beneficial, as it increased power consumption compared to that of scheme 2.1. Thus, the increased process complexity from MP intercooling is not justified. 7438

9 5.3. Two-Stage Direct Recondensation, HP and MP Precooling. In schemes 2.1 and 2.2, we condensed the BOG after two stages of compression. Having two compression stages allows the freedom to recondense a part of the BOG after the first stage and then recondense the rest after the second stage using the liquid from the first recondenser. This gives a scheme (Figure 10) with two-stage recondensation. In this scheme, all of the BOG is compressed to a lower pressure than before, and only the uncondensed gas is compressed to a higher pressure. In addition, the saturated vapor feed to the second compression stage reduces the compression work. Figure 11 shows the P H diagram for this scheme. In this ( L+ Vhp )(, t ) + x(1 β)( hp, t ) = hp (, t ) i i M MR M H M MC (48) The remaining steps are as in scheme 2.1, and the total power use is PC = p ( h h ) + β[ H( P, T) H( P, T )] sw S H13 i i VHP i[ ( 2, TR3) HP ( i, tr1)] + (1 β)( hl h1) + x(1 β)[ h( p, t ) h ] + L[ h( P, t ) hp (, t )] + ( L+ V)[ hp (, t ) hp (, t)] + [( hp, t ) hp (, t )] M M L i 2 R2 i R1 i i M MR 2 R S H M MC (49) Finally, we solve NLP problem M2.3 with six independent variables (P 2, P i, p M, T 11, y 1, and y 2 ) to obtain the minimum power consumption. M2.3: Minimize PC (eq 49) subject to eqs 1, 2, 19, 20, 24 27, 31 34, and This scheme (Figure 10) uses 18.77% lower power than scheme 1.2 for the case-study scenario, and it is the best of all schemes. This novel and thermodynamically superior regasification scheme is the most important contribution of this work. More than two condensation stages would reduce power consumption even further, but at the expense of process complexity and capital cost. Figure 11. P H diagram for scheme 2.3. scheme, all constraints except the following for the first recondenser remain the same as in scheme 2.1 (1 x)(1 β) hl + βhp ( i, th) = LhP i ( i, tr1) + VHP i ( i, tr1) (42) Li + Vi = (1 x)(1 β) + β (43) P L = P i (44) The liquid from the first recondenser at (P i, t R1 ) is pumped to (P 2, t R2 ), whereas the uncondensed BOG is compressed from (P i, t R1 )to(p 2, T R3 ). A straightforward extension from the single-stage recondensation schemes is to use an HP cooler after the second compression stage and before the second recondensation stage to cool the compressed BOG from (P 2, T R3 )to(p 2, t H ). For this purpose, we use a fraction y 3 of HP- LNG, which is heated from (p S, h H, t H )to(p S, h H3, t H3 ). The corresponding energy balance and temperature approach constraints are β[ HP (, T ) HP (, t )] = y( h h) 2 R3 2 H 3 H3 H (45) DPT 2 t H t H3 T R3 (46) The liquid from the first recondenser pumped to (P 2, t R2 ) and the BOG from the HP cooler are mixed in the second recondenser to condense all of the BOG. In other words Lh( P, t ) + VH( P, t ) = ( L + V) h( P, t ) i 2 R2 i 2 H i i 2 R (47) Subsequently, the fully condensed liquid from the second recondenser is pressurized to (p M, t MR ) before being mixed with the MP-LNG from the MP cooler SOLUTION STRATEGY Solving NLP problems M1.1 M2.3 in an algebraic environment such as GAMS is inherently approximate, as obtaining accurate analytical expressions for the various thermophysical properties and transformation steps is a challenge. Therefore, we preferred to use an enumerative but ingenious approach based on rigorous process simulations using Aspen HYSYS with the Peng Robinson model from the HYSYS databank as the fluid package. We carefully prioritized the optimization variables for each scheme and used physical insights to fix all but one or two of these variables. We then enumerated the combinations of these variables using Case Study in Aspen HYSYS to find the optimal solution. We now describe our procedure separately for each scheme and present the numerical results for the illustrative case study with β = 0.15, as was used in sections 4 and Scheme 1.1. M1.1 has P 2 and p L as its two independent variables. Consider varying P 2 for a given p L while ensuring full BOG recondensation (the BOG leaves the recondenser at BPT 2 ). Because power consumption increases with P 2, we decrease P 2. The minimum acceptable P 2 is such that the minimum of the three end approaches in the LP-LNG cooler and recondenser becomes zero. We can compute this P 2 value easily using Adjust and Spreadsheet in Aspen HYSYS. Thus, we obtained the minimum P 2 for the given p L. Next, we used Case Study in Aspen HYSYS to simulate the above procedure for various p L values. For very low p L values, we observed that the LP-LNG exiting the LP cooler vaporized, which is not acceptable. Therefore, we considered only the acceptable p L values. Figure 12a shows plots for the minimum P 2 and corresponding total power as functions of p L for the illustrative case study. Values of p L 5.5 bar are clearly infeasible, and the total power increases slightly for p L 5.5 bar. Therefore, p L = 5.50 bar, P 2 = 5.90 bar, and power =12.33 kw represent the optimal solution for M1.1.

10 Industrial & Engineering Chemistry Research Figure 12. Plots for the case study. 7440

11 6.2. Scheme 1.2. P 2 is the only variable in M1.2. Therefore, we simply used Case Study to vary p L = P 2. Figure 12b shows plots of the vapor flow from the recondenser and the total power consumption versus P 2 for the illustrative case study. P bar is unacceptable because of incomplete recondensation, and total power increases with P 2. Therefore, p L = P 2 = 5.58 bar and power =12.07 kw is the optimal solution for M1.2. Alternatively, we could use Adjust to find the lowest feasible P 2 value directly Scheme 1.3. P 2 and y 1 are the two independent variables in M1.3.Wefixed y 1 by using just enough HP-LNG to ensure zero approach in the HP cooler. We did this automatically in Aspen HYSYS to reduce M1.3 to a singlevariable NLP problem. Then, using the procedure for M1.2, we obtained the plots of vapor flow from the recondenser and total power versus P 2 shown in Figure 12c. Therefore, P 2 = 5.58 bar, y 1 = 0.094, and power =11.59 kw is the optimal solution for M Scheme 1.4. M1.4 has two more variables in addition to P 2 and y 1, namely, p M and T 11.Wefixed a value of T 11 such that T 11 [DPT 1, t H ]. As in scheme 1.3, we fixed y 1 to force the minimum approach to zero in the HP cooler. Then, we fully utilized the cooling potential of the MP-LNG by fixing p M such that the MP-LNG exits the MP cooler at t H = bpt M. This is the optimal p M, because the MP-LNG in this case is similar to the LP-LNG in scheme 1.1. As p M increases beyond its minimum feasible value, the power increases slightly. Now, we can find the lowest P 2 that recondenses the BOG fully by using Adjust as in scheme 1.2. This fixes all variables for any T 11 value. By repeating this procedure for many values of T 11 (Figure 12d), we found that the power consumption decreases with T 11. Hence, T 11 = DPT 1 gives the minimum total power for M Scheme 2.1. M2.1 has P i, P 2, p M, T 11, y 1, and y 2 as the independent variables. We fixed a P i > P 1. As for scheme 1.4, we fixed y 1 and y 2 to make the minimum approaches zero in the HP coolers, p M to get the MP-LNG to exit the MP cooler at t H = bpt M, and T 11 = DPT 1. We then found the lowest value P 2 as in scheme 1.4. This fixes all variables for any P i. We repeated this procedure to obtain a plot of total power versus P i,as shown in Figure 12e. Table 2 (below) gives the optimal P i values and other variables Scheme 2.2. M2.2 has seven independent variables, namely, P i, P 2, p M, T i1, T 11, y 1, and y 2.Wefixed a P i > P 1 and a T i1 [DPT i, t H ]. As in scheme 2.1, we fixed y 1, y 2, p M, T 11, and P 2. Then, we used Case Study to enumerate all combinations of P i and T i1. Figure 12f shows that the total power and P 2 increase as T i1 decreases and that T i1 = t H gives the minimum power. This result holds for all P i. For T i1 = t H, scheme 2.2 reduces to scheme 2.1; hence, M2.2 has the same solution as M Scheme 2.3. M2.3 has P i, P 2, p M, T 11, y 1, and y 2 as independent variables. We fixed a P i > P 1. We also fixed y 1, y 2, p M, T 11, and P 2 as in scheme 2.2. This fixed all variables for any P i. We repeated this procedure for various P i to obtain Figure 12g and the optimal P i Scheme of Park et al. 4 This scheme has P i, P 2, and y 1 as independent variables. For a fixed P i,wefixed y 1 and P 2 as before. Then, we enumerated P i to get the minimum power. Figure 12h shows the resulting plot. 7. CASE STUDY To evaluate our schemes, we consider the Pyeongtaek LNG receiving terminal in South Korea studied by Park et al. 4 Table 1 lists the relevant composition data and process conditions for LNG, BOG, and send-out NG. We solved NLP problems Table 1. Stream Data for the Regasification Terminal from Park et al. 4 stream pressure (bar) temperature ( C) composition LNG % CH 4, 8.64% C 2 H 6, 1.44% C 3 H % n-c 4 H 10, 0.04% N 2, 0.27% i- C 4 H 10 BOG % CH 4, 0.04% C 2 H 6, 0.59% N 2 sendout NG % CH 4, 7.50% C 2 H 6, 1.25% C 3 H % n-c 4 H 10, 0.08% N 2, 0.23% i- C 4 H 10 M1.1 M2.3 for this terminal for 0.00 β We varied β just to illustrate its effects for a given BOG composition. The trend should hold for any other BOG, as our model is perfectly valid for any BOG composition. Table 2 reports the minimum power and optimal operating conditions for each scheme. As expected, the BOG compression pressure and total power increase with β for all schemes. Figure 13 compares the power as a function of β for all of our proposed schemes as well as that proposed by Park et al. (Figure 14). 4 To ensure a fair comparison, we simulated the scheme proposed by Park et al. 4 using our assumptions and optimized the results for each β value. Consider scheme 1.1 with indirect recondensation. The optimal solution occurs at P L and P 2 values that satisfy t L1 = DPT 2, t L2 = bpt L, and Q BOG = Q LP for any β. The first condition ensures a zero minimum temperature approach for both cooling and condensation, and the second forces the LP-LNG exiting the cooler to be a saturated liquid. Table 2 suggests p L < P 2 for all optimal solutions. For scheme 1.2 with direct recondensation, the minimum power corresponds to the lowest P 2 = p L at which the mixing of the LP-LNG and the BOG gives a saturated liquid. As β increases, eq 16 is satisfied at higher and higher P 2 values. Thus, the power increases with β. In comparison to the indirect recondensation, the direct mixing of the BOG with the heavier LP-LNG reduces the latent heat of the BOG. Therefore, P 2 and the power demand are slightly lower for direct versus indirect recondensation. As an illustration, consider β = 0.15 and P 2 = 5.58 bar. At this pressure, the BPTs of LP-LNG, BOG, and the BOG LNG mixture are , , and C, respectively. In other words, direct mixing increases the BPT of the BOG by roughly 2.72 C and decreases that of the LP-LNG by 0.47 C. However, the positive effect of the former (in reducing the BOG recondensation load) outweighs the negative effect of the latter (in reducing the cooling potential of the LP-LNG). The net effect is to reduce P 2 by 5.4% and, thus, the power by 2.1%. Given the other practical advantages of direct recondensation mentioned before, the prevalent practice of direct recondensation at LNG terminals is well justified. The addition of HP precooling to direct recondensation as in scheme 1.3 yields a significant reduction in power, as the lower BOG temperatures reduce the compression work without any change in the optimal recondensation pressure from scheme 1.2. This is particularly useful for higher β values. For example, for β = 0.15, the power is reduced by 3.98%. Therefore, it is clearly advisable to precool the BOG with the abundant HP- LNG before the compression stage. To our knowledge, this 7441

12 Table 2. Detailed Optimization Results for Various BOG Generation Scenarios in the Terminal Case Study pressure (bar) temperature ( C) power (kw) β P i P 2 p L p M T 11 T i1 pump compressor SW pump total reduction a (%) Scheme 1.1: Indirect Recondensation Scheme 1.2: Direct Recondensation Scheme 1.3: Direct Recondensation with HP Precooling Scheme 1.4: Direct Recondensation with HP and MP Precooling Scheme 2.1: Two-Stage Recondensation with HP and MP Precooling and HP Intercooling Scheme 2.2: Two-Stage Recondensation with HP and MP Precooling, and Intercooling Scheme 2.3: Two-Stage Recondensation with HP and MP Precooling Scheme from Park et al a Reduction (%) in power compared to scheme

13 Figure 13. Power consumption vs β for all schemes. very useful feature seems to be absent from existing LNG terminal designs. Scheme 1.4 further lowers the power use by achieving additional precooling from the MP-LNG prior to compression. Because of its much lower temperature, the MP-LNG is able to cool the BOG much further toward its DPT, which reduces the compression work significantly. For instance, for β = 0.15, the power consumption is decreased by 9.86% compared to that of scheme 1.2 and by 6.13% compared to that of scheme 1.3. However, as discussed before, the decreased flow of the LP- LNG available for recondensation increased P 2 by 15.53% for β = The reduction in compression work outweighed the power increase due to the higher P 2 value. Although this result is consistent across all β values, the effect of precooling is more profound for higher β values. The powerful effect of precooling is clearer as T 11 = DPT 1 gives the minimum power (Figure 12d). Note that the MP-LNG exits its cooler at bpt M. The reduction in power reaffirms the impact of BOG cooling prior to compression. Pumping a portion of the LP-LNG to MP- LNG made it possible to limit the increase in P 2. We now analyze the two-stage compression schemes (schemes ). As expected, having two stages with HP intercooling (scheme 2.1) reduces the power demand, particularly for higher β values. The effect of the second stage is negligible for low β values. For instance, for β = 0.15, two-stage compression reduces the power consumption by only about 1.47% compared to that of scheme 1.4. Again, P 2 remains unchanged irrespective of the compression stages, and the distribution of work between the two stages is crucial in reducing the power use (Figure 12e). Since the first compression is at a lower temperature as a result of the MP precooling, the optimal pressure ratio is higher for the first stage than for the second for all β (Table 2). Thus, two-stage compression with HP intercooling is beneficial for higher β values. The loss of LP-LNG to BOG precooling and intercooling in scheme 2.2 increases P 2 (Figure 12f) and the total power; hence, T i1 = t H gives the optimal solution. In other words, scheme 2.2 simplifies to scheme 2.1. However, MP intercooling might still benefit real designs with nonideal compression stages. The final scheme demonstrates the significant impact of twostep recondensation. Scheme 2.3 has the lowest power for any β value. For β = 0.15, the total power is 18.77% lower than for scheme 1.2 and 8.49% lower than for scheme 2.1 (Table 2). As explained before, this reduction occurs because only a portion of the BOG is compressed to P 2 and the feed BOG to the second compressor is the coldest possible. To judge the effectiveness of our proposed schemes, we simulated and optimized the best regasification scheme (Figure 14) reported by Park et al. 4 using the idealistic assumptions in our work. Their scheme consists of direct recondensation, twostage compression, HP intercooling, and HP cooling prior to recondensation. Table 2 and Figure 13 also include the optimized results for this scheme. Clearly, schemes 2.1 and 2.3 need much lower power than their scheme for any β value. As can be seen in Figure 13, the power reduction increases with β. Figure 14. BOG recondensation scheme proposed by Park et al

14 For β = 0.15, the power consumed by scheme 2.3 is 11.86% lower than that for Park et al. 4 and that consumed by scheme 2.1 is 3.68% lower. Although the reduction in scheme 2.1 is only due to BOG precooling before compression, that in scheme 2.3 is enhanced by two-stage recondensation. 8. CONCLUSIONS A thermodynamic analysis of BOG reliquefaction at a typical regasification terminal to minimize its power use is presented. Our analysis yielded a series of progressively evolving schemes, where the solution of an NLP problem gave the minimum power consumption. Using a case study from Park et al., 4 we established that direct recondensation is better than indirect recondensation, because the latent heat of vaporization of the BOG decreases as a result of direct mixing with the heavier LNG. Precooling the BOG before compression is extremely useful in reducing power consumption. However, introducing a second stage of recondensation has an even greater impact. Therefore, the scheme with the lowest power demand involved two stages of compression with BOG precooling by HP-LNG and MP-LNG and two stages of recondensation with HP cooling prior to each stage. This scheme reduced the power demand by as much as 18.77% compared to that of the simplest scheme (scheme 1.2) with single-stage compression, singlestage recondensation, and HP cooling before recondensation. It amounts to nearly 11.9% lower power than the best scheme reported by Park et al. 4 The idealistic scenarios assumed in this work provide lower bounds for the power used in regasification terminals. Clearly, all schemes need not be cost-effective, and some might be too complex. However, our work provides useful benchmarks for evaluating existing regasification terminals. AUTHOR INFORMATION Corresponding Author * cheiak@nus.edu.sg. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was funded in part under Energy Innovation Research Programme (EIRP) Award NRF2014EWTEIRP , administrated by the Energy Market Authority (EMA). The EIRP is a competitive grant call initiative driven by the Energy Innovation Programme Office and funded by the National Research Foundation (NRF) of Singapore. This work was also funded in part by the National University of Singapore through a seed grant (R /733) for CENGas (Center of Excellence for Natural Gas). We acknowledge AspenTech Inc. for allowing the use of HYSYS under an academic license provided to the National University of Singapore. NOMENCLATURE BPT = bubble-point temperature of BOG, C bpt = bubble-point temperature of LNG, C DPT = dew-point temperature of BOG, C F = mass flow rate of send-out natural gas, t/h H = gas-phase mass enthalpy, kj/t h = liquid-phase mass enthalpy, kj/t L = mass flow rate of liquid stream exiting recondenser 1 in scheme 2.3, t/h 7444 P = gas-phase pressure, bar p = liquid-phase pressure, bar p sw = ratio of seawater pump power to regasification heat duty T = gas-phase temperature, C t = liquid-phase temperature, C V = mass flow rate of vapor stream exiting recondenser 1 in scheme 2.3, t/h y = fraction of HP-LNG x = fraction of LP-LNG z = fraction of MP-LNG β = ratio of BOG to send-out natural gas Subscripts 1 = streams at inlet pressures P 1 or p 1 2 = streams at pressure P 2 L = streams at pressure p L i = streams at pressure P i M = streams at pressure p M H = streams at pressure p S (high pressure) S = streams at send-out pressure P S Abbreviations NG = natural gas BOG = boil-off gas LNG = liquefied natural gas LP-LNG = low-pressure liquefied natural gas MP-LNG = medium-pressure liquefied natural gas HP-LNG = high-pressure liquefied natural gas NLP = nonlinear programming NPSH = net positive suction head RBOG = recondensed boil-off gas REFERENCES (1) Mokhatab, S.; Mak, J. 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