Meysam Kamalinejad*,Majid Amidpour,S.M.Mousavi Naeynian

Department of Mechanical Engineering,K.N.Toosi University of Technology,Tehran 1999143344,Iran

Keywords:Cascade refrigeration cycle synthesis Cryogenic Lique fied natural gas MINLP

ABSTRACT Lique fied naturalgas(LNG)is the mosteconomicalway oftransporting naturalgas(NG)overlong distances.Liquefaction of NG using vapor compression refrigeration system requires high operating and capital cost.Due to lack of systematic design methods for multistage refrigeration cycles,conventional approaches to determine optimal cycle are largely trial-and-error.In this paper a novel mixed integer non-linear programming(MINLP)model is introduced to select optimal synthesis of refrigeration systems to reduce both operating and capital costs of an LNG plant.Better conceptual understanding of design improvement is illustrated on composite curve(CC)and exergetic grand composite curve(EGCC)of pinch analysis diagrams.In this method a superstructure representation of complex refrigeration system is developed to selectand optimize key decision variables in refrigeration cycles(i.e.partition temperature,compression configuration,refrigeration features,refrigerant flow rate and economic trade-off).Based on this method a program(LNG-Pro)is developed which integrates VBA,Refprop and Excel MINLP Solver to automate the methodology.Design procedure is applied on a sample LNG plant to illustrate advantages of using this method which shows a 3.3%reduction in total shaft work consumption.

1.Introduction

Natural gas(NG)is an attractive source of clean fossil fuel and the third primary energy source after crude oil and coal.It is also the fastest growing and second largest energy source for electricity generation.In 2012,NG consumption was 2987.1 million tons oil equivalent,or about 24%of the total primary energy consumed worldwide.World's primary energy consumption had an average growth rate of2.6%during the last 10 years,but LNG consumption growth rate was 7.85%[1].This growth means a promising future for LNG industry.Most NG reserves are offshore and away from demand centers.Liquefying NG and transporting it to distances further from 3000 km is the most economical way to export it to consuming market.LNG industry is very energy extensive and industrialsize LNG plants consume around 1181 kJof energy to liquefy 1 kg of NG[2].Heat integration inside a cycle or between differentcycles ofa cascade can greatly reduce shaftwork consumption.Therefore,energy is an immediate concern in LNG industry.Such refrigeration system involves some of the largest compressors in the world,usually driven by gas turbines or electric motors using NG as fuel.At most 90%of the entering feed gas to a modern LNG plant is shipped as exported LNG and 10%of the gas is consumed to produce the required shaft work to liquefy the remaining NG.High operating and capital cost of an LNG plant opens a challenging field for more investigation in refrigeration cycle and optimal configuration of compressors to reduce cost.

Obtaining the best refrigeration system configuration has caused many attentions due to its economic importance.Barnes and King[3]investigated the problems of synthesizing refrigeration cycles and provided a two-step approach to identify optimum cascade refrigeration systems.In the firststep,a limited numberofpromising choicesforconfigurations and design parameters were identified using graph decomposition principles.To minimize the cost of the configuration,the problem was represented as a network.Later,Cheng and Mah[4]proposed an interactive procedure for synthesizing refrigeration systems incorporating all the refrigeration features identified by Barnes and King.The refrigerants participating in a cycle were selected based on their allowable operating temperature range and the temperature of the process streams to be cooled.Townsend and Linnhoff[5]and Linnhoff and Dhole[6]used a set of qualitative guidelines based on pinch technology and exergy analysis for placing heat engines and heat pumps to minimize utility consumption.Aspelund[7]proposed a methodology based on pinch analysis to utilize pressure based exergy for sub-ambient processes,such as LNG.Shin et al.[8]proposed a mixed integer linear programming(MILP)formulation for optimizing boil-off gas(BOG)compressor operations in an LNG re-gasification terminal,and Del Nogal[9]presented an optimization framework for the design of mixed refrigerant cycles which was suitable for LNG.

These methods are generalin applicability and share some heuristics to find number of pressure levels,intermediate stages and partition temperature,besides focus has been placed on the process optimization ofonly a specific partofLNG plantand noton the cascade configuration.When applying these approaches to complex multistage refrigerant cycles the shortcoming ofthese methods arises.The cascade does notconverge as a result of both non-linearity in problem formulation and explosion of integer variables.To overcome this problem,a stepwise procedure has been introduced that the main parameters of a refrigeration cascade like partition temperature and pressure level are firstly determined and in the next step the refrigeration configurations and features are decided.CC and EGCC diagrams are added to analysis to give a better conceptual insight to the designer.

The complex nature of the heat and material balance equations in multi stream heat exchangers(MSHXs)and non-linearity of physical properties of natural gas and refrigerant mixtures makes computation of the model highly non-linear,which leads to use MINLP mathematics.In this paper a new method is introduced to find optimal synthesis of an LNGplantby mounting mixed integer non-linear programming on a superstructure and applying several industrial heuristics.MINLP method is a powerful tool for decision making problems and the new procedures applies it to determine the best compression configuration for the refrigeration cascade.

2.Theoretical Principles of Refrigeration and LNG Systems

In NG liquefaction process,acid gases and mercaptans are removed from sour NG.Cascade refrigeration is required to reach very low temperatures.A simplified cascade refrigeration cycle for mega scale LNG plant consists of three sub-cycles,each using a different pure refrigerant,(Fig.1).

Only one stage for each cycle is shown for simplicity but in real industrial cycles 2 or 3 pressure stages are available by using expansion valves and each stage shall have its own pre-saturator,economizer,de-superheater,etc.In the first cycle,propane leaves the compressor at high temperature and pressure and enters the condenser where the cooling water or air is the external heat sink.The condensed propane then enters the expansion valve where its pressure is decreased to the evaporator pressure and the temperature of hot streams decreases to-40°C.As the natural gas and methane are cooling down and ethane of lower cycle is condensing,the liquid refrigerant propane evaporates.Propane leaves the evaporator as superheated vapor and enters the compressor,thus completing the loop.The condensed ethane in the middle cycle expands in the expansion valve and evaporates as methane condenses and natural gas is further cooled and lique fied.In ethane cycle,temperature of hot streams decreases to-100°C.Finally,methane expands and then evaporates as natural gas is lique fied and subcooled to-160°C.As methane enters the compressor to complete the loop,the pressure of LNG is dropped in an expansion valve to the storage pressure[10].

Many refrigeration features are available which can be mounted over simple refrigeration cycles.These options reduce required compression shaftwork.A cascade refrigeration system and its P–h diagram are shown in Fig.2.The lower cycle absorbs heat at temperature levels 1–4 and rejects condensation heat to the upper cycle at temperature levels of 2–3.The upper cycle absorbs rejected heat from the lower cycle by operating at evaporation levels of 5–8,which is colder than levels 2–3.Finally,the heat in the upper cycle is rejected at levels 6–7 to external heat sinks like cooling water and air cooling systems.

Fig.2.A simple cascade refrigeration system diagram.

The reasons for using this kind of cascade refrigeration systems are two-folds.First,there are no single refrigerant in a single cycle to cover all temperature range of refrigeration.Second,in terms of energy consumption,using a single refrigerant for the whole refrigeration demand may consume more shaft work than using multiple refrigerants.Some basic features of refrigeration in a superstructure are described in Section 2.1.

Fig.1.Schematic of cascade refrigeration cycle.

2.1.Refrigeration features for shaft work saving

For a refrigeration system,it is possible to improve its performance by using following design options[11],as shown in Fig.3:

˙Economizer:as presented in Fig.3(a).In an economizer,the condensed refrigerant is flashed to an intermediate pressure,where the flash vapor is returned to the suction of the compressor and the remaining liquid is further expanded to a lowertemperature.As a result,the amount of vapor flowing through the lower pressure part is reduced,thus saving shaft work.

˙Aftercooler:as seen in Fig.3(a).With this option,the superheated refrigerant vapor is cooled down after compression by other available heat sinks before further compression.This causes reduction of required shaft work and the after-cooling duty.Also,after-coolers provide the opportunity of heat integration between refrigeration systems and processes.

˙Presaturator:as indicated in Fig.3(c).A presaturator has a similar structure as that of an economizer,but the partially compressed refrigerant vapor is presaturated in the flash vessel with the expense of evaporating some part of the refrigerant liquid from the corresponding economizer.This decreases the temperature of the refrigerantvaporentering the nextstage ofcompressor,and saves shaftwork.On the other hand,pre-saturation may have two drawbacks:(1)it requires a higher refrigerant flow rate which may cause more compression shaft work and(2)both economizer and presaturator,add an intermediate pressure level,which may cause an increase in capital cost for compressors.Several small compressors can be more expensive than a single large compressor,even though the total shaft work requirement is reduced.

˙Desuperheater:as displayed in Fig.3(c).Using a desuperheater in the final stage,the superheated refrigerant vapor is pre-cooled after compression by a warmer heat sink before entering the condenser.This adds the possibility of heat integration to processes.

Fig.3.Refrigeration system design options in a cycle.

2.2.Determining compression configuration scenarios for refrigeration

There are many refrigeration configurations and the optimalsynthesis of the cascade should be determined for the lowest capital and operating cost.Main decisions for a refrigeration cascade include compression configuration,number of stages in each compression section and refrigeration base temperature that are shown in Fig.4.

Fig.4.Compression configuration scenarios.

After deciding on these major components,a refrigeration superstructure could be established and then all other refrigeration features could be mounted on the obtained configuration and the superstructure will be optimized.

An important parameter to be determined in a cycle is the number of pressure levels and the associated pressure of it.Three possibilities are considered for pressure levels in a cycle.Any cycle may include one,two,or three pressure levels.Fig.4 represent different configurations of compressor which is a binary variable in our superstructure modeling.The maximum number of sections(volutes which can mechanically increase pressure from inlet to discharge)in a compressor set is 7 and they will be placed between pre-specified pressure levels as shown in Fig.4.

Seven scenarios for compression configuration are considered in Fig.4.The first scenario is a simple refrigeration cycle with no interstage.The second scenario has two compression stages which results in 2 pressure levels.Vapor refrigerant from the lower level is compressed to the highest pressure and the vapor from the medium pressure level is compressed to higher pressure and is mixed with the other stream.In the seventh scenario there are three stages with three pressure levels.Vapor refrigerant from the lower level is pressured to the second pressure leveland is mixed with the incoming refrigerantvapor.The mixture is pressured up to the third stage and is mixed with refrigerant vapor from the third level.All mixed refrigerant are compressed to the highest pressure and the heat load of the superheated vapor is rejected either to the higher cycle or to the ambient heat sink.All other scenarios could be defined similarly.

The above scenarios are mathematically modeled in Section 2.5 and an MINLP solver can find the best scenario which minimizes cascade shaft work and capital cost.The different refrigeration features like pre-saturator,economizer and desuperheater shall be mounted over the selected scenario and therefore energy consumption is further reduced.

2.3.Technical heuristics to find the bestrefrigeration cascade in LNG industry

Dealing with complicated problems like multistage refrigeration cascade,some industrial practices and constraints can help to achieve a realistic and applicable design.The below items are some practical guidelines which are used in the design of cascade systems:

˙Τhe size ofLNGplantdictates the complexity ofthe design.LNGplants with capacities less than 1 million ton perannual(MTPA)only use one cycle and the designer should avoid a cascade design.This single cycle can be a multistage cycle and all refrigeration features like economizer,presaturator,and re-boiler,could be applied.When the LNG plant size increases,it is logical to use two or three cycle in a cascade and same features used in single cycle could be used on it.[12].

˙Τhe lowest temperature of natural gas in a cascade is dictated by the required composition of produced LNG.LNG quality is determined by the main market which it shall be exported,for example the European market requires lower HHV(～970 MMBTU/SCF)and East Asia requires higher HHV(～1100 MMBTU/SCF).When the main market for plant is determined,the specification of product is known and the lowestrequired temperature willbe found.This temperature shall dictate suction pressure of the lowest cycle compressor.[12].

˙LNG plants are the largest vapor recompression cycle in the world.With regard to the pressure ratio and flow rate,best choice for compressors is the centrifugal ones.Compressor manufacturers build compressors which have at most seven stages as a normal practice and compression ratio of each stage is around 1.7.Pressure levels in the cycle are determined by multiplying base pressure to this ratio powered by number of sections between corresponding pressure levels[12].

˙Each cycle transfers heatload ofprocess stream and work ofcompressor to the uppercycle.The returning refrigerantfrom the highercycles should be fully condensed,as the main heat rejection usually occurs during condensation[13].

˙Partition temperatures are a very important characteristic of any LNG cascade.It divides compression load of refrigeration and temperature range where cooling occurs.There are two guidelines to place partition temperature between each cycle:

(1)Superheated refrigerant that is discharged from lower cycle to the upper cycle should be returned in liquid phase.[13]

(2)Discharge temperature of vapor stream of each compressor shall not exceed 135°C[14].

2.4.Design methodology to find optimal pressure level and intra-cycle partition temperature placement by using grand composite and exergetic grand composite curves

Refrigeration cascade design starts from the lowercycle to the upper cycle,as there is no externalheatload from any cycle to the lowestcycle.At first step as shown in Fig.5(a),the cooling demand curve is drawn in a grand composite curve(GCC),and then an initial partition temperature that divides cooling load between the lower and the upper cycles is assumed.Further,the refrigeration load of lower cycle is met,and the heatis rejected to the upper cycle and the GCC is updated as indicated in Fig.5(b).The effect of introducing a pressure level and refrigeration option in second cycle is shown in the grand composite curve(GCC)of Fig.5(c).At last the accumulated heat load is rejected to ambient heat sink.

If temperature axis of the GCC diagram is turned to Carnot factor,then exergetic grand composite curve(EGCC)is obtained[6].Introducing any new pressure level or refrigeration feature in a cycle results in lower exergy loss and compressor shaft work as displayed in Fig.6.

Fig.6 enables us to evaluate the effect of different design options in the refrigeration system quickly and visually.EGCC diagrams of a cascade help the designer to estimate required compression shaft work.EGCC guides design procedure to find the best compression configuration and partition temperature by minimizing the area encircled between utility line and EGCC diagram.

By using the developed theoretical principles and these heuristics,mixed integernon-linear mathematics can modelheat-materialbalance ofrefrigeration cascade which includes decision making parameters like existence or non-existence of pressure levels and compression configuration,selects between economizer and presaturator and minimizes capital and operating cost of plant.The MINLP method is used where logical selections or different sets of equations should be applied to different design scenarios.The MINLP method as a decision-making tool helps to determine the best configuration,which is discussed in Section 2.5.

2.5.Mixed integer non-linear programming model in refrigeration systems

MINLP is a form to model problems in which discrete variables are restricted to values of 0 and 1 and represent certain decisions which are necessary to deal with continuous variables[15].

In a refrigeration superstructure a framework is developed by allowing a bypass modelto take effectwhen a given option is eliminated from the superstructure.Such model has the following form:

Yikare Boolean variables thatdetermine whethera given term(heatmaterial balance)in a disjunction is true[hik(x,cik)≤0]or false[hik(x,cik)≥0].x and Cikare continuous variables,the latter being used to model annualized costs associated with each disjunction and Ω(Y)are logical relations assumed to be in the form of propositional logic involving only the Boolean variables.In g(x)≤0,0 represents thermodynamic and industrial constraints that are valid over the entire search space while the disjunction k∈SD states that atleast one subsetof constraints hik(x,cik)≤0,i∈Dikmustbe hold(i.e.,presaturator and an economizer cannot co-exist simultaneously in the same stage).Yikare auxiliary variables that control the part of the feasible space in which the continuous variable x lie,while the logicalcondition Ω(Y),expresses relations between the disjunctive sets.

Fig.5.Refrigeration cascade design procedure.

Fig.6.Effect of new refrigeration features and pressure level on shaft work reduction.

r(x)+Dy≤0 represents the generalmixed-integeralgebraic formulations in which the original disjunctions are transformed into algebraic equations.Ay≥a is a set of integer inequalities and dyTare linear cost terms.This form is moreflexible than rigorous modeling.Disjunctive programming can be used as a basis to formulate a mixed-integer program with 0–1 variables[15].

Figs.7 and 8 describe a superstructure model for a cycle between level k and the above level.

Fig.7.k th level of refrigeration cycle superstructure.V-vapour；L-liquid；C-condenser；H-heater；J-junction.

Consider a cycle operating between levels k and l,where k is below l.Key variables of interest are the refrigerant flow rates mklwithin cycles operating between levels k and l.Hklis the rejected heat to the cycle operating between levels k and l by level k,the work input Wklto the cycle,and the enthalpies,and.

The modeling equations are heat and material balances at various mixing and dividing points in the configuration.

Heat material balance at Points B and C is:

Heat material balance at junction A is:

Fig.8.Mixing and dividing streams in junction J of Fig.7 superstructure.

The linking relation between the absorbed heatby a cycle and the refrigerant flow rate is:

The relation between the flow rates of all cycles operating between levels below k and level k and the absorbed energy by them to level k is as follows:

Finally,the defining relation for the compression work is:

The fact that,when an option is omitted its related constraints or equations are sufficiently relaxed or unbounded which makes the minimization become robust and computationally efficient.Much less time is wasted to calculate and converge those virtually nonexisting equations.

In each intermediate pressure level of a cycle existence or nonexistence of refrigeration features that was discussed in Section 2.1 and other constraints is modeled by the following mathematical equations.

2.5.1.Vapor–liquid heat exchangers modeling

In a V–L heat exchanger,incoming saturated refrigerant liquid exchanges heat with refrigerant vapour after evaporation.Fig.9 shows the situation when a V–L heat exchanger is placed in the k th level of a refrigeration cycle.Discrete modeling is applied to describe the existence of a V–L heat exchanger in the k th level:

Fig.9.A V-L heat exchanger in the k th level.

Any liquid heat exchanger with saturated temperature higher than orequaltois possible,butonly one is needed.Thiscondition isdescribed by the first constraint of the left hand side.The third constraint guarantees validity ofheattransfer processes.On the other hand,ifa vapour heat exchanger is not placed,the condition of inlet stream of the compressor is simply set to equal to outlet conditions of the evaporator.This discrete model is transformed into a mathematical model by using“Big-M”transformation[15]:

2.5.2.Discrete modeling of after cooler

An aftercooler is considered when there is a suitable external heat sink,such as air,cooling water or cold utilities.The placement of an aftercooler in the k th level of a refrigeration cycle is shown in Fig.10.

Fig.10.Placement of an aftercooler in the k th level.

Discrete modeling formulation for placement of an aftercooler is:

2.5.3.Discrete modeling of pre-saturator and economizer

When an economizer is placed,the condensed refrigerant is flashed to an intermediate pressure,where the flash vapour is returned to the suction of the compressor.When a pre-saturator is installed,the compressed refrigerant vapour is presaturated in the flash vessel with the expense of evaporating part of the refrigerant liquid from the previous level.The dotted line in Fig.11 represents a pre-saturator option.

Fig.11.Presaturator option(dotted line).

The reason to discuss two options together is that they cannot coexist simultaneously in the same stage.For installing a pre-saturator,the model is:

And for installing an economizer,the model is:

Since a pre-saturator and an economizer are not possible to co-exist in the same level,the following constraint is required:

The complete mathematical formulations that describe selection of two options are expressed as:

The introduced procedure is incorporated in a program(LNG-Pro)which integrates VBA,Refprop and Excel MINLP Solver to automate the methodology.LNG-Pro starts optimization from the lowest cycle and after meeting the heat-material balance the MINLP solver determines which integration of above features minimizes compression shaft work.The developed programstarts optimization from the lowest cycle and after meeting the heat-material balance(HMB)and above constraints.Both rejected process heat load and load of compressor are shifted up to the highest and middle cycles.Intermediate pressure and flow rates are constrained not to allow temperature cross in MSHXs.The procedure is accomplished in two steps.In first step,a simple modelis established by omitting refrigeration features and scenarios and is only limited to have a sub-cooler as a refrigeration feature.The goal of this stage is to determine the main parameters of a cryogenic cascade like partition temperature and pressure level.This procedure is shown in Fig.12.The objective function is to minimize compression shaft work.The program tries to find partition temperature and a set of pressure levels(condensing and evaporating pressures)that can give the best match between hot and cold composite curves by adjusting refrigerant flow rate.If the search is successful,then pressure levels and/or the refrigerant flow rate are reduced progressively.The procedure is terminated when no set of valid refrigerant flow rate and pressure level can be found and temperature crosses occur in MSHXs.

The procedure in the second step determines refrigeration scenarios and features like sub-cooler,after cooler,Presaturator and economizer is shown in Fig.13.

The objective function for second step is to minimize OPEX and CAPEX of the plant.The program tries to find a set of refrigeration scenarios by adjusting refrigerant flow rate and/or refrigeration scenarios,the procedure terminates when either the refrigerant flow rate is too small or temperature crosses occur in MSHXs.

The procedure is applied on a mega scale LNG plant with the liquefaction capacity of 25 million·m3per day of natural gas that is equal to the upstream production rate of one standard phase of Iran's south pars gas field.The design procedure shows the method's ease of use,flexibility and applicability.

3.Sample LNG Plant Description

Suppose that there is a gas field with a capacity of around 90 BCM and lifecycle of LNG plant is 25 years.This amount of gas equals to an LNG plant with the capacity of 5.4 MTPA of LNG.Treated natural gas composition is propane 3%,ethane 5%,methane 90%,and nitrogen 2%on mole basis and its pressure is 9 MPa.A set of multi stream heat exchanger(MSHX)with an approach temperature of 5°C,compressors with isentropic efficiency of 82%and ambient temperature of 300 K is available.As the size of the plant is big enough,it could be partitioned into three different cycles[12].Evaporation rate after each expansion valve is assumed to be 5%,10%and 15%for the lowest,the middle and the highest cycle for the initial guess,and the base pressure is 0.225 and 0.115 and 0.115 MPa,respectively.

The design starts by establishing a simple refrigeration structure by using methods described in Section 2 to find compression configuration,number of stages in each compression section and refrigeration base temperature.

The nature of this phase of design is decision making and existence ornon-existence of a compression configuration orpressure levelintroduces 2 differentsets of integer variables.Natural gas and heat-material balance equations in the superstructure model are all non-linear.There are thousands ofrefrigeration configurations thatcan meetan LNGcycle thermodynamically,but these configurations must be constrained by many industrial limits and operational and economical parameters to tailor the best multistage cascade cycle for an LNG plant should be considered.

In the aforementioned superstructure all expenses have been annualized.The electricity cost for compressor driver is assumed to be 0.06$·(kW·h)-1and the cost of compressor as the main single component of a lique fier is estimated to be:740[shaft work(KW)]+612630,[16].The cost of compressor for such a plant is estimated to be around 12%of the total plant cost[16].

The LNG-Pro Program starts optimization by applying the aforementioned MINLP formulas in Section 2.5 and algorithm described in Fig.12.

Result summary of this step is represented in Table 1.

Composite curve(CC)and grand composite curve(GCC)of the selected LNG cascade are shown in Figs.14 and 15.These curves summarize heat load of hot and cold streams in the refrigeration system.Straight lines indicate evaporation temperature of refrigerants at different pressure levels.The area between hot and cold curves is an indicator of irreversibility and exergy loss in the system.These curves help in assuring that the heat material balance is met and no heat cross between hot and cold stream has happened.Fig.14 shows the pinch point that is the most critical place in our design.For a moreflexible and reliable design,the sharp edges in composite curve should be avoided and for saving energy consumption the area between these curves should be decreased.

Fig.12.First step of design procedure to find initial partition temperature and refrigerant flow.

Fig.16 shows driving force diagram of optimum refrigeration cycle between cold and hotstreams.Straightlines mean constantevaporation temperature of refrigerant.

If the above assumptions are changed,for instance,give more importance to operating cost(higher electricity price)or capital cost,different configuration will be obtained which are compatible to those conditions.Construction cost for such a plant is anticipated to be 2357.24 million$.

Table 1 summarizes base configuration that includes the main parameters of a refrigeration system like pressure levels and compression configuration.

In second step complimentary options such as economizer,aftercooler,pre-saturator and desuperheater are added to this structure.These options in superstructure model are disjuncted by Boolean variables and the problem is modeled by equations found in Sections 2.5.1 to 2.5.3.This model is solved by MINLP Solver Engine in LNG-Pro Program.LNG-Pro uses the algorithm of Fig.13 to find the best refrigeration configuration with pure refrigerant.

The final composite curve and grand composite curve and driving force diagrams of the cascade are shown in Figs.17–19.The calculated shaft work for the optimized multistage cascade is 206.87 MW which is well below the first step of 227.44 MW.This shaft work reduction is a direct result of mounting more refrigeration features that means more capital cost and a more complicated cycle.

The step by step progress in the design procedure is shown by comparing composite curve(CC)and grand composite curve(GCC)of Figs.14 and 15 with Figs.17 and 18.The introduction of complimentary refrigeration options has increased heat integration of cascade and has resulted in an inclined line of Fig.19.Driving force of the preliminary cascade(Fig.17)is reduced in driving force of the final model(Fig.19).This reduction results in a lower shaft work consumption of the final cascade.

Table 2 summarizes heat and power balance for the optimal cascade cycles.

Optimum cascade is modeled in Aspen-Plus and results are verified by it.Obtained results from LNG-Pro and Aspen-Plus are compared in Table 3.It shows required coincidence for conceptual modeling of the introduced procedure.

Fig.13.Second step of design procedure to find best compression configuration and refrigeration features by minimizing CAPEX and OPEX.

There is around 1%difference between LNG-Pro and Aspen-Plus in totalshaftwork consumption.This deviation arises from some simplifying assumption in LNG-Pro.The main goal of LNG-pro is to determine compression configuration and refrigeration features by minimizing annualized cost of an LNG plant by conceptual procedures.LNG-Pro does not intend to model refrigeration cycles rigorously which is a task of Aspen-Plus.In LNG-Pro,approach temperature of MSHX is limited to 5°C which is only applied at two ends of the exchanger,but in Aspen-Plus temperature approach is checked through full length of the exchanger.Simplifying assumptionsin LNG-Pro is required to speedup design during decision making stages which causes around 1%deviation from Aspen-Plus.

4.Conclusions

A stepwise design procedure for design ofcomplex refrigeration system is introduced in this paper.The introduced procedure solves the time consuming and exhausting mathematical procedures by applying a 2 phase approach to solve major decision making parameters.In first step important parameters like compression configuration,partition temperature and base pressure are determined.In this stage the heuristics are extensively used,which are elaborated to reduce calculation time.The MINLP solver tries to satisfy the major refrigeration requirements,like heat material balance equations,equal compressor load sharing for each cycle,rejecting all latent heat of superheated refrigerant of lower cycle to the upper cycle,and finding the best pressure level in each cycle.In the second step all refrigeration features like sub-cooler,economizer,and presaturator,are mounted on top of the optimum superstructure of the first step and then by minimizing the OPEX and CAPEX of the plant,the optimal synthesis of the LNG plant is found.The first step is a conceptual step to determine the major decisions in a refrigeration cycle and uses simplified assumptions to speedup calculation,butin the second step a more detailed simulation is used that includes complimentary refrigeration features.

This stepwise procedure is automated in a program(LNG-Pro)and is applied on a 5/4 MTPA LNG plant that uses 209.9 MW for compression shaft work.Energy consumption to liquefy 1 kg of natural gas in the 1st and the 2nd step is found to be 1255.47 and 1141.9 kJ·kg-1respectively.The finaldesign requires 3.3%less energy than normalLNGplants[2]and is modeled and verified in Aspen-Plus.

Table 1 Optimal compression configuration and refrigerant evaporation pressure level and minimized OPEX and CAPEX cost of plant

Fig.14.LNG cycle's composite curve after determining main refrigeration configuration.

Fig.15.LNG cycle's exergetic grand composite curve after determining main refrigeration configuration.

Fig.16.Driving force curve of LNG cycle after determining main refrigeration configuration.

Fig.17.LNG cycle's composite curve including all refrigeration features.

Fig.18.Exergetic grand composite curve of LNG cycle including all refrigeration features.

Fig.19.Driving force curve of LNG cycle including all refrigeration features.

Table 2 Heat and shaft work summary of the final refrigeration cascade

Table 3 Comparison between required shaft work of LNG-Pro and Aspen-Plus

Nomenclature

HVAPlatent heat of vaporization

hLliquid enthalpy

hVvapour enthalpy

M an arbitrary large number used in Big-M transformation