Thermodynamic-Analysis-Based Design and Operation for Boil-Off

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Ind. Eng. Chem. Res. 2010, 49, 7412–7420

Thermodynamic-Analysis-Based Design and Operation for Boil-Off Gas Flare Minimization at LNG Receiving Terminals Chaowei Liu, Jian Zhang, Qiang Xu,* and John L. Gossage Dan F. Smith Department of Chemical Engineering, Lamar UniVersity, Beaumont, Texas 77710

The LNG (liquefied natural gas) receiving terminal is an important component of the entire LNG value chain. The handling of unloading BOG (boil-off gas) during LNG regasification at LNG receiving terminals significantly influences the BOG flare emission and energy consumption. In this work, thermodynamic-analysisbased design and operations are simultaneously considered to recover BOG with the minimum total energy consumption, a goal of which is to provide a cost-effective flare minimization strategy at LNG receiving terminals. A rigorous simulation-based optimization model and its solution algorithm are developed based on an LNG regasification superstructure. Case studies are used to demonstrate the efficacy of the developed methodology. The presented general optimization model and thermodynamic analysis also provide fundamental understandings of the LNG regasification process that are valuable for industrial applications. 1. Introduction LNG is a clear, noncorrosive, nontoxic, odorless cryogenic liquid at normal atmospheric pressure. It is natural gas (mostly methane) cooled to its liquefied state at atmospheric pressure. This requires cooling to a temperature of approximately -160 °C. The actual temperature required depends on the precise composition of the gas. Liquefying the natural gas reduces its volume by a factor of about 600 and thus permits LNG to be shipped economically: one LNG tanker usually can carry 130000 m3 of LNG, which, when vaporized, represents roughly 2.7 billion standard cubic feet of natural gas.1 The primary applications of natural gas are in home heating, in electric power generation, and as a feedstock for manufacturing various chemical products. The most common use of LNG in the United States is for energy “peakshaving”, a method by which local gas and electric power companies store gas for peak demand that cannot be met through their typical pipeline source in both winter and summer seasons.1 Because of both the rapid growth of the world’s energy demands and the increased depletion of the crude oil reserve, LNG is considered as one of the major alternative fuels in the coming decades. Generally, the LNG value chain includes natural gas production, liquefaction, transportation, receiving and regasification, distribution, and delivery. Among these sectors, the LNG receiving terminal is an important component of the LNG value chain connecting LNG sources to residential or industrial consumers. The terminal receives LNG from special ships, stores the liquid in special storage tanks, vaporizes the LNG, and then delivers the natural gas into the downstream gas pipeline network. It is designed to deliver a specified gas rate into a distribution pipeline and to maintain a reserve capacity of LNG. The amount of reserve capacity depends on expected shipping delays, seasonal variations of supply and consumption, and strategic reserve requirements.2 LNG receiving terminals are expected to operate nearly 365 days per year and have spare equipment on hand to achieve this availability. The United States has the largest number of LNG facilities in the world: 113 active LNG facilities spread across the country with a higher concentration of peakshaving and satellite facilities * To whom correspondence should be addressed. Tel.: 409-880-7818. Fax: 409-880-2197. E-mail: [email protected].

in the northeastern region.1 At present, the United States has four LNG receiving terminals. However, because of the anticipated increase in LNG demand, more than two dozen such facilities in nine coastal states are currently being studied, have filed applications, or have already been approved for construction (see Table 1). The impetus for these plans lies in the prediction that the dry natural gas production is predicted to grow from 18.8 trillion cubic feet (Tcf) in 2004 to 20.5 Tcf in 2030.3 During LNG loading, unloading, shipping, and storage, the product is kept at cryogenic temperatures. Because of heat leakage, natural gas continuously evaporates from the LNG: this vapor is called boil-off gas (BOG). If not handled properly, the boil-off gas has to be vented or flared, which causes economic losses and air emission problems. The major composition of BOG is methane. Its global warming potential is Table 1. Survey of LNG Terminal Development in North America19 index

location

capacity (bcfda)

Approved and Constructed or under Construction 1 2 3 4

Sabine, TX, U.S. Elba Island, GA, U.S. Pascagoula, MS, U.S. offshore Boston, MA, U.S.

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Corpus Christi, TX, U.S. Corpus Christi, TX, U.S. Corpus Christi, TX, U.S. Fall River, MA, U.S. Port Arthur, TX, U.S. Logan Township, NJ, U.S. Cameron, LA, U.S. Freeport, TX, U.S. Hackberry, LA, U.S. Pascagoula, MS, U.S. Port Lavaca, TX, U.S. Long Island Sound, NY, U.S. Bradwood, OR, U.S. Baltimore, MD, U.S. Port Pelican, U.S. MARADb Gulf of Mexico, U.S. MARADb Rivie`redu- Loup, QC, Canada Quebec City, QC, Canada Baja California, Mexico Manzanillo, Mexico

2 0.9 1.5 0.4

Approved but not under Construction

a

1 2.6 1.1 0.8 3 1.2 3.3 2.5 0.85 1.3 1 1 1 1.5 1.6 1 0.5 0.5 1.5 0.5

Billion cubic feet per day. b U.S. Maritime Administration.

10.1021/ie1008426  2010 American Chemical Society Published on Web 07/14/2010

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Figure 1. Schematic flowsheet of the basic design for LNG regasification.

approximately 21 times that of CO2 over a 100-year time period.4 Thus, the most common method of BOG disposal is destruction through flaring. However, to save raw materials and reduce unnecessary air emissions, BOG is expected to be recovered to the maximum extent, so as to minimize BOG venting and flaring and save the valuable energy. Whereas the BOG generation during LNG carrier transportation is rather small and constant, the BOG generation at LNG receiving terminals is usually significant, especially during unloading from LNG ships. Proper handling of BOG during both normal operations and ship unloading significantly affects both the operational efficiency and the safety of an entire LNG receiving terminal. Too much BOG inside a storage tank can cause safety issues and flaring problems, whereas overrunning BOG recovery systems generally means unnecessary energy consumption. Hence, the optimal design and operation for BOG processing is an urgent need. Certainly, such an effort will address multiple problems, including plant profitability, operational feasibility, and environmental impact, which will present tremendous challenges. Previous studies related to LNG receiving terminals/regasification plants mainly focused on modeling the temperature and pressure changes inside the LNG storage tank,5-7 as well as the control and optimization of pipeline and compressor station operations.8-11 The optimal management of BOG and the operating pressure in the LNG tank were studied experimentally by Doyer et al.5 Kirishnaswami et al. suggested a simulationbased optimization of a compressor station consisting of dissimilar centrifugal compressors.10 Wicaksono et al. proposed a superstructure and nonconvex mixed-integer nonlinear program to integrate jetty BOG optimally into the existing fuel gas network in an LNG plant.12 Shin et al. proposed a mixedinteger linear program model for BOG compressor operation to minimize power consumption and refine the operation policies based on a safety analysis of the dynamics of the tank pressure.2 Shin et al. also used an empirical model for the estimation of the boil-off rate in an LNG storage tank and proposed an optimal operation algorithm for safe and energy-saving BOG compressor operation.13 Hasan et al. performed extensive dynamic simulations of BOG during various steps of LNG transportation and studied the effects of various factors such as nitrogen content, tank pressure, ambient temperature, and voyage length to determine the optimal heels (where a heel is the minimum quantity of LNG retained in an LNG ship after unloading at an LNG terminal to maintain temperature, pressure, and/or production operations) for several scenarios of LNG transportation.14 Based on the current literature survey, fundamental studies on optimal design and operation for unloading BOG flare

Table 2. LNG Feed Composition component

mole composition (%)

methane (CH4) ethane (C2H6) propane (C3H8) butane (C4H10) pentane (C5H12) hexane (C6H14) nitrogen (N2)

97.98 1.40 0.40 0.10 0.01 0.01 0.10

minimization at LNG receiving terminals are still lacking. In this work, thermodynamic-analysis-based design and operation are simultaneously considered to recover BOG with the minimum total energy consumption. A rigorous simulationbased optimization model and its solution algorithm are presented. 2. Thermodynamic Analysis for BOG Flare Minimization 2.1. Regasification Process Description at LNG Receiving Terminal. Figure 1 shows the basic design of an LNG receiving terminal with its regasification facilities, where the LNG vessel operates at a temperature of -162 °C and a pressure of 1.08 bar. During the LNG unloading process, LNG is unloaded to an onshore LNG storage tank with 160000 m3 storage capacity by the ship pumps at a volume flow rate of 10000 m3/h. The BOG is generated mainly from two sources. One is from the heat leakage in the storage tank. Usually, about 0.1 vol % of the LNG in a tank is evaporated daily as BOG by heat transfer from the surroundings.13 The other source is heat leakage through the unloading arms and transfer lines, which causes excessive BOG generation during the LNG unloading process. Generally, about 0.6 vol % of LNG unloaded from the ship is vaporized hourly during transfer to the tank. A typical LNG feed composition, also used in this study, is listed in Table 2. The send-out LNG goes through an in-tank pump to increase its pressure to 11 bar, and then it is sent to one or more LNG send-out pumps to increase its pressure to about 73 bar. The high-pressure LNG is sent to the vaporizer, where the LNG is heated and vaporized to natural gas at 4 °C. Finally, it is sent to the downstream gas pipeline network at about 70 bar. A normal approach to BOG recovery employs compressors. As shown in Figure 1, the BOG generated in the LNG storage tank is partially diverted to the LNG ship through the vaporreturn blower to maintain the container pressure. To protect against an overpressure condition in the LNG container as the LNG vaporizes, the surplus BOG that cannot be sent back to the ship is routed to the BOG compressor/vent system. Because BOG contains about 98% methane, flaring it will waste a

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Figure 2. P-H chart of the basic design for LNG regasification.

potential energy source and cause negative environmental impacts. Thus, it is desirable to recover and reprocess the majority of surplus BOG. As shown in Figure 1, the send-out LNG before regasification should reach a discharge pressure of 73 bar, which is slightly higher than the pipeline pressure of 70 bar after a vaporizer; the final discharge pressure of the recovered BOG should be the same as pipeline pressure of 70 bar. 2.2. BOG Flare Minimization Opportunities. To quickly identify an appropriate design at the conceptual design stage, a thermodynamic-based analysis has been conducted. It employs the LNG pressure-enthalpy (P-H) chart for the analysis. As the composition of LNG is different from pure methane, the methane P-H chart cannot be directly used. Thus, to obtain the LNG P-H chart data, a rigorous simulation using Aspen Plus is employed.15 The simulator generally performs a series of calculations to obtain the LNG P-H data under different temperatures, based on the LNG feed composition. During the calculation, RKS-BM (Redlich-Kwong-Soave cubic equation of state with Boston-Mathias alpha function) is used as the thermodynamic property method, because it is the recommended property method for gas processing, refinery, and petrochemical applications.16 To determine the BOG flare minimization opportunities, the base design is used as an example. As shown in Figure 1, the basic design employs multistage BOG compression to compress BOG directly to the discharge pressure of 70 bar. Then, the compressed BOG is sent out with the evaporated LNG from the evaporator at the pipeline network pressure. No condenser is used to mix the BOG and LNG streams. Note that, here, the compression actually employs four compressors, increasing the pressure from 1.15 bar at B to 70 bar at P in Figure 1. The four compressors undertake compression ratios of 3.2, 3.2, 3.2, and 1.8, respectively. To characterize the operating status of each stream in Figure 1, an LNG P-H chart associated with the basic design was developed as shown in Figure 2. In Figure 2, the pressure axis is a logarithmic coordinate. The figure consists of multiple

isothermal lines. Every point on each line shows the equilibrium pressure and specific enthalpy (enthalpy per unit mass) at the fixed temperature. To characterize the phase-change information, the bubble-point line and dew-point line are also shown. The region to the left of the bubble-point line represents the region of pure liquid phase, the region to the right of the dew-point line represents the region of pure vapor phase, and the constrained zone between the bubble-point and dew-point lines suggests the region of mixed liquid-vapor phase. Note that the isothermal lines in Figure 2 are associated with the composition of LNG listed in Table 2. During the LNG regasification process, the compositions of the liquid and vapor streams will change slightly. Thus, the bubble-point and dew-point lines will have small offsets, which are neglected in this work for simplicity. This simplification does not influence our analysis, because the operating status of a stream can still be accurately identified in Figure 2 through its pressure and specific enthalpy values. Based on Figure 2, the initial and final operating statuses in Figure 1 can be identified; they are shown as points A (LNG just from the storage tank), B (BOG just from the storage tank), and R (the vaporized LNG sent out to the pipeline network). The operation of the basic design can be clearly illustrated in Figure 2. BOG is compressed from point B to point P through four-stage compression with an internal cooler after the third stage. The trajectory generally approaches an isentropic operating line. (Because the compressor adiabatic efficiency is considered, the trajectory should be below the associated isentropic line.) Note that the detailed path of the isotropic trajectory is not important. The real concern is the sum of the specific enthalpy changes of qc,1-qc,4 from B to P as shown in Figure 2. Quantitatively, the compressor work consumption (Wc,1) can be represented as Wc,1 ) (qc,1 + qc,2 + qc,3 + qc,4)Fc,1 /ηc,1

(1)

where Fc,1 is the BOG mass flow rate and ηc,1 is the compressors’ working efficiency (considering both mechanical and adiabatic efficiencies).

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Figure 3. Energy-saving opportunity for mass transfer from BOG to LNG.

In Figure 2, LNG is continuously compressed from point A to point O by a multistage send-out pump. The specific enthalpy change is characterized as qp,1. Similarly, the total work consumption of the send-out pump (Wp,1) can be formulated as Wp,1 ) qp,1Fp,1 /ηp,1

(2)

where Fp,1 is the pumped LNG mass flow rate and ηp,1 is the pump working efficiency. After the LNG is pressurized to point O, it is evaporated from point O to point Q in a vaporizer. Finally, the vaporized LNG is mixed with the BOG at point R and sent to the pipeline network. The theoretical energy consumption rate required for the evaporation is Qe ) qeFp,1 /ηe

(3)

where qe is the specific enthalpy change due to the evaporation operation and ηe is the evaporator thermal efficiency. Based on the above description, the total energy consumption rate for LNG regasification can be characterized as Etotal ) Wc,1 + Wp,1 + Qe ) (qc,1 + qc,2 + qc,3 + qc,4)/ηc,1 + Fp,1(qp,1 /ηp,1 + qe /ηe) (4) From Figure 2, qp,1 is obviously much smaller than the sum of qc,1-qc,4. Because the pump efficiency ηp,1, compressor efficiency ηc,1, and evaporator efficiency ηe are generally fixed, the opportunity for the reduction of the total energy consumption rate actually depends on the mass transfer from the BOG stream to the LNG stream. The BOG minimization opportunity can be explained by Figure 3. Generally, an ideal compression operation (through either a gas compressor or a liquid pump) will follow an isentropic line in the P-H diagram. As shown in Figure 3, the isentropic lines to the left of the two-phase region are steep, whereas those to the right of the two-phase region are flat. This means that the specific enthalpy change required to compress LNG is significantly smaller than that required to compress BOG

between the same starting and ending pressures, i.e., qp , qc in Figure 3. Thus, to compress one unit of mass to the same pressure level, it is better to go through a liquid pump instead of a gas compressor. Equally importantly, the compression of LNG to a higher pressure does provide much needed cooling capacity, which can be utilized to condense the compressed BOG with the same pressure. Additionally, the liquid pump usually has a higher working efficiency than the gas compressor. In the case study, for instance, the mechanical efficiency used for liquid pumps is 0.80, whereas the mechanical efficiency and the adiabatic efficiency used for gas compressors are 0.80 and 0.72, respectively, such that the compressor working efficiency is 0.576. Therefore, in terms of reducing the total energy consumption, it is desirable to conduct mass transfer from the BOG stream to the LNG stream, if the LNG stream has a sufficient cooling capacity. 2.3. Conceptual Design Superstructure. Based on the above analysis, it is natural to consider employing multiple reliquefaction stages to reduce the total energy consumption for BOG flare minimization. For instance, the BOG can be recovered through a series of compressors, pumps, and condensers. The number of BOG compressors is generally equal to the number of LNG send-out pumps. The output pressure of each BOG compressor is identical to the output pressure of the corresponding send-out pump (namely, the reliquefaction pressure). Then, part of the compressed BOG can be reliquefied in a condenser when mixed with the sent-out LNG stream. Thus, in the P-H chart of the basic design as shown in Figure 2, the envelope constructed by all operating points will shrink to the two-phase region (constrained by the bubble-point and dew-point lines). Because the energy consumption rate of the evaporator does not change too much, the design of multistage compression with reliquefaction supposedly will reduce the total energy consumption rate. For multistage compressors, interstage coolers can be used for safety, which would reduce the energy consumption as well. Generally, when a series of identical compressors is employed, if the flow rate does not change, the compression ratio at each stage should be roughly the same.17 In this work, however,

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Figure 4. Conceptual design superstructure of an LNG receiving terminal.

because the BOG flow rate might not be the same at each stage, the rigorous optimization of both design and operation is required to identify the optimal solution. 3. Optimal Design and Operation for BOG Flare Minimization A conceptual design superstructure is shown in Figure 4. Based on this superstructure, an optimization model can be generated. The objective is to minimize the total energy consumption rate for BOG flare minimization during the LNG unloading process. Three types of design and operating variables are used as the optimization control variables. The first two are (i) the total number of compression stages and (ii) the reliquefaction pressure ratios on each stage. As shown in Figure 3, if the reliquefaction pressure at each stage is set higher, the distance of the operating point from the bubble-point line will increase. This means that the LNG stream will obtain a greater cooling capacity, which can condense more BOG. However, a higher reliquefaction pressure will consume more energy at that stage. Thus, an optimal reliquefaction pressure should be identified. In this work, because the initial and final BOG pressures are known, as long as the compressor ratio at each stage is identified, the reliquefaction pressure will be fixed. Thus, the compressor ratio on each stage is actually used as an optimization variable. (iii) The third type of variable is the split ratio from the compressor outlet to the condenser on each stage. For multistage LNG reliquefaction process, each stage can condense part of the BOG. Thus, the split ratios also influence the total energy consumption rate. 3.1. Objective Function. The objective function is to find the optimal number of stages, the reliquefaction pressure ratio on each stage, and the split ratio of the compressor outlet BOG on each stage that can minimize the total energy consumption rate, as shown in the equation J ) min Etotal ri,xi,N

(5)

where N is the total number of stages; ri and xi (i ) 1 , · · · , N) are the compression ratio and the split ratio from the compressor outlet at the ith stage, respectively; and the total energy is calculated by eq 6, which is the sum of the work consumptions from all of the compressors and pumps, plus the energy consumption rate of the evaporator N

Etotal )

∑ (W

c,i

i)1

+ Wp,i) + Qe

(6)

3.2. Pressure Ratio Constraints. At the ith reliquefaction stage, the pressure ratios (ri) of the BOG compressor and the LNG pump should be the same. Generally, ri changes in the range from 1.5 to 3.5, as shown in eq 7. As the BOG pressure increases from 1.15 bar at the outlet of the LNG storage tank to 70 bar at the final pipeline network, the total compression ratio is around 60.9. Thus, the product of each stage compression ratio is constrained as shown in eq 8. 1.5 e ri e 3.5,

i ) 1, ..., N

(7)

N

∏r

i

) 60.9

(8)

i)1

3.3. Compressor Work. The compressor work on the ith stage is equal to the product of the BOG specific enthalpy change (qc, i ) and the mass flow rate (Fc,i) divided by the compressor working efficiency (ηc,i). qc, i and Fc,i are calculated based on the rigorous simulation. Actually, they are both functions of compression ratios and split ratios on the current stage and all previous stages. Wc,1 ) qc,1(r1) Fc,1(r1)/ηc,1

(9)

Wc,i ) qc,i(r1, ..., ri, x1, ..., xi-1) Fc,i(r1, ..., ri, x1, ..., xi-1)/ηc,i, i ) 2, ..., N (10) 3.4. Pump Work. Similarly to the compressor work calculation, the pump work on ith stage is the product of the LNG specific enthalpy change (qp, i ) and its mass flow rate (Fp,i), divided by the pump working efficiency (ηp,i). qp, i and Fp,i are calculated based on the rigorous simulation. Wp,1 ) qp,1(r1) Fp,1(r1)/ηp,1

(11)

Wp,i ) qp,i(r1, ..., ri, x1, ..., xi-1) Fp,i(r1, ..., ri, x1, ..., xi-1)/ηp,i, i ) 2, ..., N (12) 3.5. Evaporator Energy Consumption Rate. After the last stage, the LNG stream is evaporated to natural gas and sent to the pipeline network. The energy consumption rate in the evaporator is equal to the LNG specific enthalpy change (qe) in the evaporator multiplied by the mass flow rate (Fp,N) and divided by the evaporation efficiency (ηe). Qe ) qe(r1, ..., rN, x1, ..., xN-1) Fp,N(r1, ..., rN, x1, ..., xN-1)/ηe (13)

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Figure 5. Model representation of the ith reliquefaction stage.

3.6. Mass Balance Constraints. As in Figure 5, the compressor outlet flow rate, Fc,i, is split into two streams with different flow rates: one stream, with flow rate Fcond c,i , will be directed to the condenser with a split ratio of xi; the other, with flow rate Fout c,i , will be directly sent to the next-stage compressor. The mass balance equations are shown in eqs 14-16. Equation 17 shows that the pump outflow rate to the condenser is the same as the pump inflow rate. Equation 18 suggests that the condenser outlet streams (Fitop and Fibtm) and inlet streams cond (Fcond c,i and Fp,i ) should be in mass balance. Equation 19 shows the total mass balance of the ith stage. Fout c,i ) (1 - xi)Fc,i, Fcond c,i ) xiFc,i,

i ) 1, ..., N - 1 i ) 1, ..., N - 1

top Fc,i+1 ) Fout c,i + Fi ,

Fcond p,i ) Fp,i,

i ) 1, ..., N - 1

i ) 1, ..., N - 1

(14) (15) (16) (17)

cond top Fcond + Fbtm c,i + Fp,i ) Fi i ,

i ) 1, ..., N - 1

(18)

Fc,i + Fp,i ) Fc,i+1 + Fp,i+1,

i ) 1, ..., N - 1

(19)

3.7. Condenser Constraints. For each condenser, the top and bottom outflow rates and compositions are determined by the equilibrium equations, which are calculated by the rigorous simulation. They are all functions of the inflow rates, temperatures, compositions, and pressure ratios, which are shown in eqs 20-23. Equations 24 and 25 provide the BOG and LNG compositions at the next stage. Note that the values of Cc,1 and Cp,1 are given before the optimization.

Figure 6. Simulation-based optimization strategy.

current stage and all previous stages; it should not go beyond 100 °C because of the normal compressor specification. Otherwise, interstage coolers might be needed to satisfy the specification. Equations 26-28 give the constraints. Because there is no condenser on the last stage, the split ratio to the condenser should be zero, as shown in eq 29. out Tout c,1 ) Tc,1 (r1)

cond cond cond cond Ftop ) Ftop i i (Fc,i , Tc,i , Fp,i , Tp,i , r1, ..., ri, Cc,i, Cp,i), i ) 1, ..., N - 1 (20)

out Tout c,i ) Tc,i (r1, ..., ri, x1, ..., xi-1),

cond cond cond cond Fbtm ) Fbtm i i (Fc,i , Tc,i , Fp,i , Tp,i , r1, ..., ri, Cc,i, Cp,i), i ) 1, ..., N - 1 (21)

Tout c,i e 100,

cond out cond out Ctop ) Ctop i i (Fc,i , Tc,i , Fp,i , Tp,i , r1, ..., ri, Cc,i, Cp,i), i ) 1, ..., N - 1 (22) cond out cond out Cbtm ) Cbtm i i (Fc,i , Tc,i , Fp,i , Tp,i , r1, ..., ri, Cc,i, Cp,i), i ) 1, ..., N - 1 (23)

Cp,i+1 ) Cbtm i ,

i ) 1, ..., N - 1

top top Cc,i+1 ) (Fout c,i Cc,i + Fi Ci )/Fc,i+1,

(24)

i ) 1, ..., N - 1 (25)

3.8. Other Specifications. The compressor inflow temperature is a function of compression ratios and split ratios on the

(26) i ) 2, ..., N

i ) 1, ..., N

xN ) 0

(27) (28) (29)

4. Rigorous Simulation-Based Solution Strategy Figure 6 gives the solution algorithm for the optimal design and operation of the LNG regasification system. Because the normal compression ratio is usually in the range from 1.5 to 3.5 and the total pressure ratio change from the LNG storage tank to the pipeline network is about 60.9, the number of compression stages under a rough estimation can only change from four to six. Thus, there are only three alternative designs in terms of the total number of compression stages. For each candidate design, however, the optimization of the decision variables such as compression and split ratio at each stage needs

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Table 3. Optimization Result Comparisons under Different Designs variable

N)4

N)5

N)6

r1 r2 r3 r4 r5 r6 x1 x2 x3 x4 x5 Wc1 (kW) Wc2 (kW) Wc3 (kW) Wc4 (kW) Wc5 (kW) Wc6 (kW) Wp1 (kW) Wp2 (kW) Wp3 (kW) Wp4 (kW) Wp5 (kW) Wp6 (kW) N ∑i)1 Wc,i (kW) N ∑i)1 Wp,i (kW) Qe (kW) Etotal (kW)

2.6 2.8 3.2 2.7 s s 0.1 0.2 0.5 s s 824.8 1060.2 1356.5 783.1 s s 6.3 20.9 88.9 358.8 s s 4024.6 474.9 8541.1 13041

2.7 2.3 2.8 1.6 2.3 s 0.1 0.2 0.4 0.5 s 880.7 847.9 1216.7 356.1 463.4 s 6.9 16.3 64.8 70.0 356.7 s 3764.8 514.7 8243.4 12523

1.8 2.5 2.3 1.6 1.6 2.3 0.1 0.2 0.2 0.4 0.6 481.0 902.8 895.0 520.3 360.6 539.5 3.1 11.9 29.4 41.6 64.0 343.7 3699.2 493.7 8045.4 12238

rigorous and precise unit models. Therefore, this work employed a rigorous simulation-based solution strategy. As shown in Figure 6, the optimization starts by selecting one of the design scenarios and thus fixes the total number of stages. Then, a detailed simulation model can be generated based on the design superstructure. The decision variables left for the optimization model are the compression ratios and split ratios at each stage, which will be determined by rigorous simulationbased (or sequential-based) optimization with the sequential quadratic programming (SQP) method.18 To enhance the solution optimality, a multistart approach is employed by applying different initial values for these decision variables. The optimization results are recorded and validated. The calculation continues until all three alternative designs are enumerated. Finally, the best solution is identified by comparison. 5. Optimization Results and Discussion The optimization results obtained using the developed BOG minimization model and the solution algorithm are reported in Table 3. It shows that the four-, five-, and six-stage scenarios will have energy consumption rates of 13041, 12523, and 12238 kW, respectively. It shows that the energy consumption

Figure 7. Optimal flowsheet of a four-stage LNG regasification system.

decreases if more compression and reliquefaction stages are used, which follows the engineering sense. The energy consumption is reduced by 518 kW from the four-stage to the fivestage design and by 285 kW from the five-stage to the sixstage design. The compressor work costs about 30% of the total energy consumption during the LNG unloading process, whereas the pump work consumes only 4%. The majority of the total energy consumption is used for the LNG evaporation, which consists of around 66%. Table 3 also lists the optimization results in terms of the compression ratios and compressor outlet split ratios under different designs. Generally, the compressor outlet split ratio will increase stage by stage under a specific design, because the high-pressure LNG has more cooling capability to condense the BOG (see Figure 3), whereas the BOG flow rate decreases with increasing number of stages. The compression ratios change with respect to the BOG and LNG flow rates at each stage, which are all within the specified range from 1.5 to 3.5. The case studies have demonstrated that the design and operation optimizations should be considered simultaneously to improve the regasification operating performance at LNG receiving terminals, in terms of minimization of BOG flaring and reduction of energy consumption. A sensitivity analysis was also conducted for the optimal design with respect to the reliquefaction pressure ratio and the split ratio on each stage. For the reliquefaction pressure ratio, this analysis shows that the energy consumption is minimum at the obtained pressure ratios; increasing or decreasing 15% of the optimal pressure ratio on each stage separately increases the total energy consumption by about 0.2-0.3%. The split ratios are actually restricted by the active constraint of eq 28, and only a decrease of the optimal split ratios is in the feasible direction. The analysis shows that the third-stage split ratio among those of all stages has the most significant effect on the total energy consumption: a 15% decrease of its value will increase the total energy consumption by about 1.5%. Certainly, the operating cost (related to the total energy consumption rate) is not the only concern in the optimal design for the BOG recovery. The capital costs should also be taken into account. Although more compression and reliquefaction stages are beneficial for reducing operating costs, the associated capital costs also increase significantly. Thus, the operating and capital costs should be well balanced in reality. For these case studies, the four-stage LNG regasification system has the minimum capital costs (e.g., compressors, pumps, and condensers) and maintenance costs among the three designs. Meanwhile, the energy operating costs are 518 and 803 kW more than for

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Figure 8. P-H chart of a four-stage LNG regasification system.

the five- and six-stage regasification systems, respectively. Note that, although there is a large amount of BOG generation during the LNG unloading process in LNG receiving terminals, the total operating time under this situation is less than the normal operating time. Thus, the comparative operating cost savings of the four-stage LNG regasification system are not significant, and the capital costs should be the dominant factor. Therefore, the four-stage LNG regasification system is considered as the best design system in this case study. The rigorous simulation of the four-stage LNG regasification system was validated with the process simulator of Aspen Plus.15 The optimal design flowsheet is shown in Figure 7. Based on the rigorous simulation results, the P-H chart of the four-stage system is shown in Figure 8. The operation points (A-R) shown in Figure 7 are also indicated. As discussed, the BOG reliquefaction at the condenser of each stage actually pushes the real liquid and gas operation lines close to the equilibrium lines, such that the energy consumption can be reduced. From Figure 8, it is clear that the compressor work consumption is significant, which is actually also demonstrated in Table 3. Finally, it should be clarified that this study provides thermodynamic-analysis-based conceptual design and operation for BOG flare minimization during the LNG unloading and regasification process. The detailed process design and operability studies will comprise the next stage of work, which will also involve dynamic simulations. Certainly, dynamic simulations will present a very challenging task that requires much effort in the future. The development of this work is believed to have provided a solid foundation for this future thrust. 6. Concluding Remarks LNG receiving terminals are an important component of the entire LNG value chain, which becomes increasingly important nowadays in terms of world energy sustainability. In this work, thermodynamic-analysis-based design and operation are simul-

taneously considered to recover BOG with the minimum total energy consumption. This work develops a rigorous simulationbased optimization model and its solution algorithm based on the proposed LNG regasification superstructure. It shows that the four-stage LNG regasification system is the most desirable process for recovering BOG generation. The presented general optimization model and thermodynamic analysis provide fundamental understandings of the LNG regasification process at LNG receiving terminals that are valuable for industrial applications. Acknowledgment This work was supported in part by the Texas Commission on Environmental Quality (TCEQ), Texas Air Research Center, and Texas Hazardous Waste Research Center. Nomenclature Sets and Indices i ) 1, ..., N ) index of the reliquefaction stages Parameters ηc,i ) ith stage compressor working efficiency ηe ) evaporator thermal efficiency ηp,i ) ith stage pump working efficiency Variables Cc,i ) compressor inlet composition mass fraction vector of the ith stage Cibtm ) condenser bottom outlet composition mass fraction vector of the ith stage Ctop ) condenser overhead outlet composition mass fraction vector i of the ith stage Cp,i ) pump inlet composition mass fraction vector of the ith stage Etotal ) total energy consumption rate (kW) Fc,i ) compressed BOG mass flow rate at the ith stage (kg/s) cond Fc,i ) condenser inlet flow rate from the compressor at the ith stage (kg/s)

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Fout c,i ) BOG flow rate bypass of the condenser from the compressor at the ith stage (kg/s) Fibtm ) outlet flow rate from the bottom of the condenser at the ith stage (kg/s) Fitop ) outlet flow rate from the top of the condenser at the ith stage (kg/s) Fp,i ) pumped LNG mass flow rate at the ith stage (kg/s) cond Fp,i ) condenser inlet flow rate from the pump at the ith stage (kg/s) qc,i ) specific enthalpy change by the ith compressor (kJ/kg) qe ) specific enthalpy change by the evaporator (kJ/kg) Qe ) energy consumption rate for the evaporator (kW) qp,i ) specific enthalpy change by the ith pump (kJ/kg) ri ) stage compression ratio of the ith reliquefaction stage cond Tc,i ) condenser inlet temperature from the compressor at the ith stage (°C) out Tc,i ) compressor outlet temperature at the ith stage (°C) cond Tp,i ) condenser inlet temperature from the pump at the ith stage (°C) Wc,i ) compressor energy consumption rate (kW) Wp,i ) pump energy consumption rate (kW) xi ) compressor outlet split ratio to the condenser at the ith stage

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ReceiVed for reView November 5, 2009 ReVised manuscript receiVed June 14, 2010 Accepted June 22, 2010 IE1008426