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chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Research and Design

j ourna l ho me page: www.elsev ier .com/ locate /cherd

ptimization of refinery hydrogen network based on chanceonstrained programming

unqiang Jiaoa, Hongye Sua,, Weifeng Houb, Zuwei Liaoc

State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027,hejiang, ChinaZhejiang Supcon Software Co., Ltd., Hangzhou 310053, Zhejiang, ChinaState Key Laboratory of Chemical Engineering, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou10027, Zhejiang, China

a b s t r a c t

Deterministic optimization approaches have been developed and used in the optimization of hydrogen network in

refinery. However, uncertainties may have a large impact on the optimization of hydrogen network. Thus the con-

sideration of uncertainties in optimization approaches is necessary for the optimization of hydrogen network. A

novel chance constrained programming (CCP) approach for the optimization of hydrogen network in refinery under

uncertainties is proposed. The stochastic properties of the uncertainties are explicitly considered in the problem

formulation in which some input and state constraints are to be complied with predefined probability levels. The

problem is then transformed to an equivalent deterministic mixed-integer nonlinear programming (MINLP) prob-

lem so that it can be solved by a MINLP solver. The solution of the optimization problem provides comprehensive

information on the economic benefit under different confidence levels by satisfying process constraints. Based on

this approach, an optimal and reliable decision can be made, and a suitable compensation between the profit and

the probability of constraints violation can be achieved. The approach proposed in this paper makes better use of

resources and can provide significant environmental and economic benefits. Finally, a case study from a refinery inChina is presented to illustrate the applicability and efficiency of the developed approach.

2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Refinery; Hydrogen network; Uncertainty; Chance constraints; Optimization

and reduce the hydrogen usage cost in refinery, refiners shouldretrofit the hydrogen network as far as possible.. Introduction

uring the past decades, crude oil has been getting heaviernd contains more sulfur and nitrogen. The shrinking mar-et for heavy fuel oil and stricter legislation on sulfur contentn fuels throughout the world are forcing refiners to increaseheir use of hydrocracking and hydrotreating to upgrade heavyils to more valuable products and remove sulfur and nitro-en compounds from petroleum products (Towler et al., 1996;lves and Towler, 2002). As the demand for hydrogen grows,ydrogen is now getting scarce and becoming a critical issue tohe refiners worldwide. Hydrogen cost has become the secondost important cost after crude oil cost. Thus, it is becoming

ncreasingly more important to reduce hydrogen consumption Corresponding author. Tel.: +86 571 87951075; fax: +86 571 87952279.E-mail address: hysu@iipc.zju.edu.cn (H. Su).Received 20 May 2011; Received in revised form 3 February 2012; Acce

263-8762/$ see front matter 2012 The Institution of Chemical Engioi:10.1016/j.cherd.2012.02.016and improve the utilization ratio of hydrogen (Hallale and Liu,2001; Liu and Zhang, 2004).

Refineries generally take various measures to improvethis situation, such as increasing yield of hydrogen plant,expansion of hydrogen plant, building new hydrogen plants,constructing new hydrogen purifiers, purchasing hydrogenand retrofitting the hydrogen network. The comprehensivebenefits obtained by these measures are shown in Table 1 (Qu,2007). It is not difficult to find that retrofitting the hydrogennetwork is the best way to gain a better economic and environ-mental benefit by comparing with these costs listed in Table 1.Therefore, in order to lighten the load of hydrogen productionpted 29 February 2012neers. Published by Elsevier B.V. All rights reserved.

http://www.sciencedirect.com/science/journal/02638762www.elsevier.com/locate/cherdmailto:hysu@iipc.zju.edu.cndx.doi.org/10.1016/j.cherd.2012.02.016

1554 chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567

Nomenclature

Symbolsa capital cost coefficientAf annualizing factorb capital cost coefficientC costD pipe diameterE meanF flowrateL pipe lengthN normal distributionP pressurePI pricePower power consumptiont annual operating hoursTAC total annual costU a upper boundu a lower boundY binary variabley hydrogen purity in volume baseHc standard heat of combustion

Greek symbols probability level standard deviation

probability distribution function

Subscriptscomp compressors (comp = 1, . . ., COMP)f feed streams of purifiersfuel fuel systemH2 hydrogeni off-gas streams (i = 1, . . ., I)j hydrogen sources (j = 1, . . ., J)k hydrogen sinks (k = 1, . . ., K)max maximumMEM membrane separation unitmin minimump purifiers (p = 1, . . ., P)pipe pipline (pipe = 1, . . ., PIPE)power compressor powerPSA pressure-swing adsorption unit

SuperscriptsF flowrateP productR residual, uncertain variables

Table 1 Cost of several measures satisfying extra hydrogen de

Measures Investment cost ($ m3 d

Increasing yield of hydrogen plant 0 Expansion of hydrogen plant 7.0635.3 Building new hydrogen plants 35.3 Constructing new hydrogen purifiers 3.5314.12 Purchasing hydrogen 0 Retrofitting the hydrogen network 3.53 Refiners are interested in the lower-cost alternative of opti-mizing and revamping the hydrogen distribution network. Thecomplexity of the problem creates a need for systematic meth-ods and tools for hydrogen management. Recent researchshows that two main methods which are employed to designand optimize hydrogen network in refinery are graphical andmathematical programming approach.

Graphical methods were applied first for an efficient hydro-gen management system. Towler et al. (1996) first proposeda systematic approach to study the hydrogen network basedon the analysis of cost and value composite curves. Alvesand Towler (2002) proposed hydrogen pinch analysis for tar-geting the minimum hydrogen consumption of the wholehydrogen system by using an analogy to pinch analysis forheat exchanger networks. This analysis method is used toprovide quantitative insights and to identify the existence ofbottlenecks in the hydrogen distribution system. Liao et al.(2011a,b) obtained the optimal conditions for pinch problemsand proposed a rigorous targeting approach for hydrogen min-imization. This approach is more accurate and efficient thanother published targeting methods in providing an overalloptimal solution. Further, mathematical programming meth-ods were employed to solve these problems. Hallale and Liu(2001) first developed a superstructure-based optimizationapproach for hydrogen network accounting for the pressureconstraints as well as compressors for retrofit scenarios. Liuand Zhang (2004) proposed a systematic methodology forselection of appropriate purification processes and their inte-gration in design and optimization of hydrogen networks.Khajehpour et al. (2009) proposed reduced superstructurebased on experience and engineering judgment to optimizethe hydrogen network of an Iran refinery and employed agenetic algorithm for optimization. Liao et al. (2010) incor-porated the purification processes for refinery hydrogenmanagement and successfully demonstrated the applicationof superstructure based approach for retrofit design of anexisting refinery. Kumar et al. (2010) utilized mathematicalmodeling technique to optimize the hydrogen distributionnetwork in refinery. The linear programming (LP), nonlinearprogramming (NLP), mixed-integer linear programming (MILP)and MINLP models were developed and the characteristics ofthese models were analyzed. Ahmad et al. (2010) developedan improved approach for the design of flexible hydrogen net-works which can remain optimally operable under multipleperiods of operation. Jiao et al. (2011a) decomposed the opti-mization problem into two sub-problems, the optimization offeed routes of purification system and hydrogen supply net-work, and a sequential two-step method is employed to retrofitthe hydrogen network. Jiao et al. (2011b) presented a novelmulti-objective optimization approach to optimize the hydro-gen distribution network, and the relation between operatingcost and investment cost is explored based on the obtained

Pareto curve of optimization problem.

mand.1) Operating cost ($ m3) Total cost (million $)

0.0706 70.0741 8100.0671 90.01770.0353 240.03530.177 3170 0.3

chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567 1555

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However, all the reported results mentioned abovedopted deterministic mathematical programming methodso address the hydrogen network optimization problem. Theata used in those models are assumed to be known and con-tant. However, in real world, optimal decisions of designingnd optimization of hydrogen distribution network have to beade under various uncertain conditions. In practice, a refin-ry has uncertain supply of raw materials for hydrogen plantnd uncertain hydrogen demands from hydrogen consumers.o make a better design and optimization of hydrogen net-ork in refinery, the uncertainty of hydrogen supply has toe taken into account and at the same time the uncertainydrogen demands must be satisfied. In addition, due to thehanging market condition and changing operating conditionf refinery processes, the prices of the hydrogen product fromydrogen producers, electricity and hydrogen off-gas fromydrogen consumers are also uncertain factors. Therefore, it isecessary for refinery to access the potential impacts of thesemportant changes.

In most previous reported results on industrial pro-ess optimization, the stochastic properties of uncertaintiesave not been taken into account. In industrial practice,ncertainties are usually compensated by using conserva-ive decisions like an over-design of process equipment tovercome operability bottlenecks, or an overestimation ofperational parameters caused by worst case assumptionsf the uncertain parameters, which may leads to a signifi-ant deterioration of the objective function in an optimizationroblem. The main reason for these intuitive decisions ishe lack of systematic reliability analysis. In other cases, dueo profit expectations, an aggressive decision may be taken,hich will probably result in constraint violations and leado an accident, so frequent modifications of the operatingoint have to be made when the decision variables are imple-ented. A proper decision should be a tradeoff between valuesf profit and risk (Li et al., 2008). Consequently, the consid-ration of uncertainties and their stochastic properties inptimization approaches are necessary for the optimizationroblem of industrial process.During the past decades, several approaches have been

roposed for the quantitative treatment of uncertainty inhe design, planning, and scheduling of batch process plants.hese techniques have contributed to a better understandingf how uncertainty affects their performance (Sahinidis, 2004).ost of previous studies on optimization under uncertaintymployed the two-stage programming with the recourse for-ulation to deal with constraint violations. The two-stageodel divides the decision variables into two stages. Therst stage variables are those that have to be decided rightway, before any future realization of uncertain parameters.hen, the second-stage variables are those used as cor-ective measures or as recourse against any infeasibilitiesrising during the realization of the uncertainty. Moreover,n the recourse formulation, violation of the constraintss allowed, but penalized through penalty terms in thebjective function. It is suitable for this method to solveptimization problems under uncertainty when the objec-ive function and constraint violations can be described byhe same measurement such as process planning problemsnder demand uncertainties (Arellano-Garcia and Wozny,009). However, the exact values of the penalty terms areifficult to determine because they include intangible com-

onents. Thus, such a penalty term is not available in manyases.CCP approach pioneered by Charnes and Cooper (1959) andMiller and Wagner (1965) is a competitive tool for solvingoptimization problems under uncertainty. This method satis-fies the constraints at a predetermined confidence level usingthe known probability density or cumulative distributionof random variables. Rather than requiring that constraintscontaining the uncertain parameters always be satisfied orimposing penalties for infeasibilities, a probability of con-straint satisfaction, also known as the confidence level, can bespecified by the decision maker (Li et al., 2004b). Using crispequivalents or stochastic simulation methods, these problemscan be converted into deterministic ones. After that, deter-ministic optimization methods can be applied. Based on CCPapproach, the relationship between the profitability and reli-ability can be quantified. In other words, the solution of theproblem provides comprehensive information on the econom-ical achievement as a function of the desired confidence levelof satisfying process constraints. The CCP method has beenwidely used in different disciplines (Uryasev, 2000). Solutionapproaches based on CCP method have been developed andapplied in distillation processes (Schwarm and Nikolaou, 1999;Li et al., 2000, 2002a,b, 2008; Wendt et al., 2002; Arellano-Garciaand Wozny, 2009), production planning for chemical processesunder uncertain market conditions (Li et al., 2004a) and gasprocessing plant with uncertain feed conditions (Mesfin andShuhaimi, 2010). Furthermore, CCP approach is employed forthe synthesis and optimization of plant-wide waste man-agement policies under uncertainty, the variations in theexpected waste loads were considered, and plant-wide poli-cies with a desired degree of operational flexibility againstuncertainty are developed (Chakraborty and Linninger, 2003).Based on the work of Chakraborty and Linninger (2003), a novelmulti-period decision-making framework is proposed to findlong-term plant-wide operating policies together with opti-mal capital investment decisions under uncertainty with aplanning horizon of typically 5 years (Chakraborty et al., 2003).

In this paper, CCP approach is first adopted to addressthe hydrogen network optimization problem. Optimizationmodels are developed based on flowrate constraints, pressureconstraints, purity constraints, logistic constraints and pay-back period, etc. Furthermore, to make the proposed approachmore suitable for the real system and find a more practicalsolution for the optimization model, the inlet flowrates andpurities at the reactor inlet of hydrogen consumers are con-sidered as variables, the minimum pure hydrogen of hydrogenconsumer is considered and must be satisfied to achievedesired oil conversion rate and keep the catalysts activity.The objective function of optimization problem is the min-imum of total annual cost which includes operation costsand annualized capital costs. The stochastic constraints willhold with at least predetermined probability levels, and thechances are represented by the probabilities that the con-straints are satisfied. This problem is then transformed intoan equivalent deterministic problem, so that it can be solvedwith commercial software such as Lingo 8.0 (Snider, 2002).The solution of the problem provides a quantitative relationbetween the profit and the risk of constraint violation. Aproper decision can be made between values of profit and risk.The results can provide important management informationof hydrogen system under uncertainties for decision maker inrefinery.

The remainder of the paper is organized as follows. Wefirst introduce the basic attributes and characteristics for

chance constraint programming in Section 2. In Section 3, the

1556 chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567

Steady

atateLinear

Nonlinear Dynamic

SingleConstant

Time-

dependentJoint

process uncertainty constraint

Fig. 1 Classification of CCP problems.proposed stochastic mathematical formulation for optimiza-tion problem based on the deterministic model is brieflysummarized. Then, the CCP form of optimization model isintroduced, the deterministic equivalent representation of theobjective function and the constraints are addressed, and thestochastic optimization model is also simplified. Then aboveapproach is applied to a case study in Section 4. Section 5summarizes the work and provides some concluding remarks.

2. Chance constrained programming

As a kind of stochastic optimization approaches, CCP focuseson the reliability of the system, i.e., the systems ability to meetfeasibility under uncertainty. This reliability is expressed as aminimum requirement on the probability of satisfying con-straints. Thus, the objective function is expressed in termsof expected value, while constraints that are associated withrandom parameters are expressed in terms of a certain proba-bility of getting satisfied. It is suitable to solve the optimizationproblems with random variables included in constraints andsometimes in the objective function as well (Charnes andCooper, 1959; Miller and Wagner, 1965; Liu et al., 2003). Atypical CCP problem under uncertainty can be formulated asfollows:

minE[f (x, )]

subject to Pr{gj(x, ) 0, } j j = 1, 2, . . . , kothers;

where x Rn is a decision vector, is the stochastic vector witha probability density function (), and f(x, ) is the objectivefunction. The reliability or probability of complying with theinequality constraints is given by Pr{gj(x, ) 0,} j gj(x, ) arethe constraint functions, and j (0 j 1) represents the pre-determined confidence level of the constraint function to besatisfied. Since can be defined by the user, it is possible toselect different levels and make a compromise between thefunction value and risk of constraint violation. Pr {} denotesthe probability of the event {}. The word others denotesother deterministic constraints. As shown in Fig. 1, CCP prob-lems can be classified based on the properties of processes,uncertainties and constraint forms (Li et al., 2008).

Recent research shows that two methods mainly usedto address the CCP problem are integration and samplingapproach. Integration method adopts a direct way to trans-form the stochastic optimization problem into an equivalent

deterministic problem. Gaussian quadrature is first used toapproximate multivariate probability integrals. It is not largely

Make-up

hydrogen Recycle hydrogen

Liquid feedReactor

separation

tank

separa

tank

high pressurehydrogen

low preshydrog

Fig. 2 A typical process of hydrogaffected by the type of employed continuous probability dis-tribution and the location of discretization points is selectedthrough the optimization process. This method has been usedto address the design of different types of batch plants underuncertainty (Petkov and Maranas, 1997). Another numericalintegration approach to the multivariate integration is colloca-tion on finite elements. This computation depends decisivelyon the distribution of the uncertain variables concerned. Thisapproach has been used successfully in solving linear sys-tems, nonlinear systems, and process control problem underuncertainty (Li et al., 2002a, 2008; Wendt et al., 2002; Arellano-Garcia and Wozny, 2009). Sampling approach such as MonteCarlo sampling is also often employed to solve CCP problem.Sampling in a space is equivalent to multivariate integration.The basic idea of Monte Carlo methods is to generate a largeenough number of random variables and approximate themultivariate probability integral as the ratio of the number ofpoints within the integration region divided by the total num-ber of points (Tong, 1990). However, implementation of theMonte Carlo sampling method requires sampling from highdimensional probability distributions and this may be verydifficult and expensive in analysis and computing time.

3. Problem formulation

3.1. Problem statements

There are several processes for hydrogen production andconsumption in the refining industry. Among most com-mon production and consumption processes are catalyticreforming, steam methane reforming, partial oxidation,hydrotreating, hydrocracking, isomerization, etc. All theseprocesses compose a hydrogen network. In a hydrogen net-work, a source is defined as a stream supplying hydrogen tothe system. Hydrogen sources are the products of hydrogen-

producing processes, the offgases of hydrogen-consumingprocesses, or the imported hydrogen (or fresh hydrogen). A

Product

Gas

tion

stripper

fractionator

dry gas

sure

en

en consumption in a refinery.

chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567 1557

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Fig. 3 Superstructure for hydrogen network.ink is a stream that consumes hydrogen from the hydrogenetwork. Hydrogen sinks are the inlet streams of the variousydrogen-consuming units such as hydrotreaters and hydro-rackers (Hallale and Liu, 2001). In addition, hydrogen sourcesan be captured to make them more acceptable by using com-ressors and/or purifiers.Fig. 2 shows a diagram of a typical hydrogen consumer. A

iquid feed stream is mixed with a gas stream rich in hydro-en and fed into the hydrotreating or hydrocracking reactor.he reactor effluent is cooled and sent into a high pressureasliquid separator. The most of the gas from the separa-or is recycled into the reactor inlet after desulfurization. Aart of these gases need to discharge outward so as to keephe high purity of recycle hydrogen and avoid the accumu-ation of hydrogen sulfide in the system. The liquid productrom the bottom of high pressure gasliquid separator is sento a low-pressure separator. The product hydrogen from theow-pressure separator which has certain hydrogen purity isotential to be used as hydrogen source directly or sent to puri-ers after desulfurization. The liquid product from the bottomf the low pressure separator is sent to a stripper. The gas fromhe top of the stripper which is often called dry gas in refineryay be purified by purifiers after desulfurization or sent to the

uel gas system. Then, the liquid product from the bottom oftripper separator is sent to a fractionator. The gas from theop of the fractionator whose hydrogen purity is lower thanry gas is often sent to the fuel gas system.The variables that affect the hydrogen network optimiza-

ion process are the flowrates from hydrogen sources toydrogen sinks (Fj,k, Fi,p), the flowrates of compressor(Fcomp,k),he flowrates of product stream and residue stream of puri-ers (FPp, F

Rp ), the purities of hydrogen sinks (yk), the hydrogen

esidue purities of purifiers (yRp ), the purities of compressorsutlet (ycomp,k), and binary variables (Yj,k, Yi,p) which used tondicate the existence of hydrogen stream, pipelines, com-ressors and purifiers. According to the characteristics ofodel and the requirements of hydrogen management in

efinery, the flowrates from hydrogen sources to hydrogeninks (Fj,k, Fi,p) and binary variables (Yj,k, Yi,p) are selected ashe main decision variables for optimization in this study.

Due to the changing market condition, the changingxternal product demand for hydrogen consumers resultsn a change in the hydrogen consumption. Meanwhile, theperating conditions e.g. reactor temperature of hydrogenonsumers such as hydrotreating process, will change peri-dically in order to compensate for the catalyst deactivationue to coke formation. The changing operating conditions ofhe hydrotreating process also result in a change in the hydro-en consumption. Thus, the amount of hydrogen demandsf hydrogen consumers (Fk,min) is uncertain. The changingydrogen demands of hydrogen consumers also lead to ahange in the hydrogen off-gas supplies of hydrogen con-umers, so the amount of hydrogen off-gas supply fromydrogen consumers (Fi) is also uncertain. Besides, due to thehanging market condition and the supply and price of rawaterials, the amount of hydrogen supply of sources (Fj) and

he prices of hydrogen sources, electricity, and fuels (PIj,

PIe,

Ifuel) are also uncertain.The situations mentioned above happen frequently under

he current situations in refinery. Nowadays, almost all theesearchers employed deterministic modeling methods toptimize the hydrogen network. In this paper, the potential

ost of this type uncertainty are assessed, and CCP approach isemployed to optimize the hydrogen network through makingeffective use of existing purifiers and compressors, installingadditional equipments and process stream restructuring toaccomplish the minimum total annual cost that includes bothoperating costs and annualized capital costs.

To develop the optimization model, many factors shouldbe considered, including hydrogen supply devices, hydrogenconsumption devices, compressors, purifiers, pipe network,operating cost, capital cost, payback period, etc. Binary vari-ables are employed to indicate the existence of hydrogenstream, compressors, purification units and pipelines. Min-imizing the total annual cost (TAC) that includes operatingcost and investment cost is the objective functions of opti-mization problem. All the possible connections from sourcesto sinks should be also considered, and the final optimizationresults can be obtained by solving this superstructure model.The superstructure of hydrogen network optimization can bedescribed with Fig. 3.

3.2. Objective function

In this paper, the objective of the optimization problem is toachieve minimum TAC without having any major change com-pared to previous hydrogen network. The optimization task isto find the optimal hydrogen network so as to minimize TACby satisfying all possible constraints. The TAC that includesoperation costs and annualized capital costs is given by:

min TAC ={

CcompE(CH2 ) + E(Cpower) E(Cfuel)

+Af

COMP

comp=1Ccomp +

Pp=1

Cp +PIPE

pipe=1Cpipe

(1)

where CH2 , Cpower and Cfuel are the uncertain cost of hydrogen,power and fuel, Af is the annualizing factor, and Ccomp, Cp andCpipe are the capital costs of compressors, purifiers and pipe,respectively.

1558 chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567The cost of a hydrogen sources and the compressor powercost is expressed as Eqs. (2) and (3):

CH2 =J

j=1

(K

k=1Fj,k tj

PIj

)(2)

Cpower =PIe

Jj=1

Kk=1

(Powerj,k tcomp,k) (3)

where Fj,k is the flowrate from source j to sink k,PIj is the uncer-

tain price of source j, tj is the annual operating hours of source

j, Powerj,k is the power,PIe is the uncertain price of electricity,

and tcomp,k is the annual operating hours of compressor comp.The value created by fuel can be obtained through heat

value calculation (Hallale and Liu, 2001):

Cfuel = Ffuel (y Hc,H2 + (1 y) Hc,CH4 ) PIfuel (4)

where Ffuel is the flowrate of fuel, Hc is the standard heat of

combustion andPIfuel is the uncertain price of fuel.

The capital cost of new compressors and pipes can be cal-culated by Eqs. (5) and (6) (Peters and Timmerhaus, 1991):

Ccomp = acomp Yj,k + bcomp Powerj,k (5)

where acomp and bcomp are cost coefficients for compressors,and Yj,k is the binary variable which denotes the existence ofconnection between hydrogen source j and hydrogen sink k(Hallale and Liu, 2001).

Cpipe = (apipe Yj,k + bpipe D2) L (6)

where apipe and bpipe are the cost coefficients for pipe, and Dand L are the pipe diameter and pipe length, respectively.

The most common purifiers in refinery are pressure-swingadsorption (PSA) unit and membrane separation unit. Theinvestment costs of PSA unit and membrane separation unitcan be expressed via following formulations, respectively(Towler et al., 1996):

Cp,PSA = aPSA Yi,p + bPSA Fp,f (7)

Cp,MEM =(aMEM + bMEM

yMEM

) Fp,f (8)

where Cp,PSA and Cp,MEM are the capital costs of PSA unitand membrane separation unit, aPSA and bPSA are the costcoefficients for PSA unit, aMEM, bMEM, and yMEM are the costcoefficients for membranes separation unit, respectively, Yi,pis a binary variable which denotes the existence of connectionbetween hydrogen off-gas i and purifier p, and Fp,f is the inletflowrate of purifier p.

3.3. Constraints

3.3.1. Hydrogen source constraintsThe amount of gas available from each source must be greater

than or equal to the total amount sent to the sinks. Becausethe amounts of gas available from some sources are uncertainvariables, the availability of uncertain hydrogen supplies ofsources should be satisfied:

Fj K

k=1Fj,k (9)

Capacity restriction for each hydrogen source is stated as:

Kk=1

Fj,k Fj,max (10)

Logistic restriction: Binary variable Yj,k is used to indicate theexistence of hydrogen stream between source j and sink k:

Yj,k ={

1 if a source j is connected to the sink k

0 otherwise(11)

Considering general binary variable Yj,k, the relationshipsbetween Yj,k and Fj,k are stated as:

Yj,k = 1 Fj,k > 0 (12)

Yj,k = 0 Fj,k = 0 (13)

Therefore, based on the preceding binary variable Yj,k, theflowrates constraints are shown as:

Fj,k Yj,k UFj,k (14)

Fj,k Yj,k uFj,k (15)

where UFj,k

and uFj,k

are upper and lower bounds of Fj,k.Based on the binary variable Yj,k, the pressure constraints

between source and sink are expressed as:

Pk Pj Yj,k Uj,k (16)

Pk Pj + (1 Yj,k) Uj, k uj,k (17)

where Uj,k and uj,k are upper and lower bounds of pressuredifference between Pk and Pj.

3.3.2. Hydrogen sink constraintsIn order to maintain the normal operation of all the hydrogenconsumers, the sources must provide enough hydrogen foreach sink. To make the optimization model more suitable forthe real system, the flowrates and purities at the reactor inletof hydrogen consumer are considered as variables. The sinkconstraints are described as follows.

Flowrate balance:

Jj=1

Fj,k = Fk (18)

Hydrogen balance:

Jj=1

Fj,k yj = Fk yk (19)where Fk is the hydrogen demand of sink k, yj is the hydrogenpurity of source j and yk is the hydrogen purity of sink k.

chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567 1559

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3Bchflaf

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Tb

Ti

3HmpCphr

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s dr

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In refinery, each sink needs minimum pure hydrogen toaintain its current production, every sink needs to satisfy thencertain minimum pure hydrogen demands, and the purityf each sink has to be equal or greater than the minimumequirement purity to achieve desired oil conversion rate andeep the catalysts activity:

kyk Fk,min (20)

k,min yk < yk,max (21)

here Fk,min is the uncertain minimum pure hydrogen of sink and yk,min is the minimum purity requirement for sink k.

.3.3. Compressors constraintsecause of their operating characteristics, compressors areonsidered as both sinks and sources, different from otherydrogen consumers. Just like other hydrogen consumers, theowrate and the purity of compressors are considered as vari-bles. The constraints on the compressors can be described asollows.

The amount of gas fed to the compressor must be equal tohe amount which leaves it as well as its gas purity.

Flowrate balance:

J

j=1Fj,comp =

Kk=1

Fcomp,k (22)

he amount of pure hydrogen entering the compressor muste equal to the amount leaving.Hydrogen balance:

J

j=1Fj,comp yj =

Kk=1

Fcomp,k ycomp,k (23)

he amount of gas fed to one compressor must never exceedts maximum capacity.

Capacity limit:

J

j=1Fj,comp Fcomp,max (24)

.3.4. Purifiers constraintsydrogen is usually recovered from refinery off-gases. Theost common unit operations used for purifying hydrogen areressure-swing adsorption (PSA) and membrane separation.ompared to other process of hydrogen production, hydrogenurification technique has the lower recovery cost and higherydrogen purity, so it has been used more and more widely inefinery.

Purifiers such as PSA and membrane separation, can beonsidered as one sink (inlet stream) and two sources (theroduct stream and the residue stream) (Liu and Zhang, 2004).

Yi,p ={

1 if a off-ga

0 otherwishe flowrate balance and hydrogen balance for the purifiersre stated as the following.Flowrate balance:

Ii=1

Fi,p = Fp,f (25)

Fp,f = FPp + FRp (26)

Hydrogen balance:

Ii=1

Fi,p yi = Fp,f yp,f (27)

Fp,f yp,f = FPp yPp + FRp yRp (28)

where Fi,p is the flowrate of feed stream from off-gas i to puri-fier p, Fp,f is the inlet flowrate of purifier p, FRp is the residueflowrate of purifier p, yp,f is the feed stream purity of purifierp, yRp is the residue purity of purifier p and yi is the hydrogenpurity of off-gas i.

The amount of off-gas from each hydrogen consumershould be greater than or equal to the amount sent to thepurifiers. Because the amounts of off-gas available from somehydrogen consumers are uncertain variables, the availabilityof uncertain off-gas supplies of hydrogen consumers shouldbe satisfied:

Fi

Ii=1

Fi,p (29)

All the feed streams are purified by purifiers after mixture,so the feed purity of each purifier should be between that ofproduct and residue:

yRp yf yPp (30)

An existing purifier will have been designed for a specificflowrate and so there will be a maximum capacity constrainton each purifier.

Ii=1

Fi,p Fp,max (31)

In order to maintain the product hydrogen purity, every puri-fier has a purity requirement for feed streams.

yi yp,min (32)

where yp,min is the minimum hydrogen purity requirement forpurifier p.

Logistic restriction: Binary variable Yi,p is used to indicate theexistence of hydrogen stream between off-gas supplier andpurifier:

ainage equipment i is connected to the purifier p(33)

Considering the binary variable Yi,p, the relationships betweenYi,p and Fi,p are expressed as:

Yi,p = 1 Fi,p > 0 (34)Yi,p = 0 Fi,p = 0 (35)

1560 chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567Therefore, based on the preceding binary variable Yi,p, theflowrate constraints are represented as:

Fi,p Yi,p UFi,p (36)

Fi,p Yi,p uFi,p (37)

where UFi,p

and uFi,p

are upper and lower bounds of Fi,p.Based on the binary variable Yi,p, the pressure constraint

between off-gas supplier and purifier is expressed as:

Pp Pi Yi,p Ui,p (38)

Pp Pi + (1 Yi,p) Ui,p ui,p (39)

where Ui,p and ui,p are upper and lower bounds of pressuredifference between Pp and Pi.

3.4. Chance constrained optimization

In the above optimization problem, the objective function,equalities (2)(4) and the inequalities (9), (20) and (29) haverelation with uncertain variables. Thus the optimizationproblem can be defined as a CCP problem under chance con-straints. Chance constraints are applied for these equalitiesand inequalities. The basic formulation for chance con-strained optimization can be derived from the deterministicmodel developed in Sections 3.2 and 3.3. Accordingly, theobjective function can be redefined as (Liu et al., 2003):

minTAC = CH2 + Cpower Cfuel

+ Af

COMP

comp=1Ccomp +

Pp=1

Cp +PIPE

pipe=1Cpipe

(40)

The equalities (2)(4) together with the inequalities (9), (20) and(29) which involved in the chance constrained model can bedescribed from (41) to (46):

Pr

Jj=1

(K

k=1Fj,k tj

PIj

) CH2

H2 (41)

Pr

PIe

Jj=1

Kk=1

(Powerj,k tcomp,k) Cpower

power (42)

Pr{Ffuel(y Hc,H2 + (1 y) Hc,CH4 )

PIfuel Cfuel

} fuel

(43)

Pr

{Fj

Kk=1

Fj,k

} j (44)

Pr{Fk yk Fk,min

} k (45)

Pr

{Fi

Ii=1

Fi,p

} i (46)In these formulations, the value (0, 1) represents a user-predefined probability level, which is a parameter definedbased on the process requirement. Due to the existence ofuncertainty situation, the risk of violation of the constraintsshould be considered. A higher value ( 1) will be specified ifholding the constraints is more strongly desired. However, if ahigher probability level is specified, the optimization resultswill be more reliable, but the cost to be consumed will behigher. On the contrary, if a lower probability level is chosen,the cost to be consumed may be lower, but it is very possiblethat the constraints will be violated. Since can be defined bythe user, it is possible to select a suitable confidence level and make a compromise between the objective value and therisk of constraint violation (Li et al., 2004a).

To solve the optimization problem of hydrogen networkunder chance constraints, the inequalities in (41)(46) shouldbe transformed into an equivalent deterministic MINLP form,which can be solved with available MINLP solver. To do this, theprobability distribution function of the uncertain variables isrequired. According to the characteristics of the above chanceconstraints, the constraints can be divided into two types, oneis the constraints (42)(46), and the other is the constraint (41).At first, the first type of chance constraints, whose form iseasier than second type, can be directly transformed into thefollowing equivalent deterministic form:

CpowerJj=1

Kk=1(Powerj,k tj,k)

1power(power) (47)

CfuelFfuel(y Hc,H2 + (1 y) Hc,CH4 )

1fuel(1 fuel) (48)

Kk=1

Fj,k 1j (1 j) (49)

Fk yk 1k (k) (50)

Ii=1

Fi,p 1i (1 i) (51)

where 1 is the inverse function of the probability distribu-tion function. With the given value of probability level, theright-hand side of these inequalities can be easily calculated.

The transformation of the chance constraints (41) is noteasy, because there are summations of uncertain variables.In the following, we present how to transform the chanceconstraints (41) into an equivalent deterministic form (Liuet al., 2003). In this paper, we assume that these ran-dom variables conform to normal distribution. Let hk(F) =J

j=1

(Kk=1Fj,k tj

PIj

), hk(F) is normally distributed. For

chance constraint (41), by subtracting the mean and dividingby the standard deviation of hk(F), the chance constraint (41)can equivalently be written as:

Pr

{hk(F) E(hk(F))

(hk(F)) CH2 E(hk(F))

(hk(F))

} H2 (52)

where E(hk(F)) and (hk(F)) are respectively the mean and stan-dard deviation.

The left-hand side of the inequality within the probability

sign is a normally distributed random variable with a meanof zero and a variance of 1 (standardized form). This implies

chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567 1561

td

C

ws

3

Tveddtaltor

(

(

(

hat the chance constraint can be replaced by the followingeterministic equivalent expression:

H2

(CH2 E(hk(F))

(hk(F))

) H2 (53)

CH2 E(hk(F))(hk(F))

1H2 (H2 ) (54)

H2 J

j=1

(K

k=1Fj,k tj E

( PIj

))

1H2 (H2 )

J

j=1

(K

k=1Fj,k tj

PIj

) 0 (55)here represents the probability distribution function of atandard normal distribution.

.5. Model simplification

he above optimization model involved in lots of continuousariables and discrete variables, and there are many nonlinearqualities and inequalities in optimization model. However,irectly solving the hydrogen network optimization model isifficult and inefficient. It is necessary to examine the charac-eristic of variables before starting optimization procedure sos to eliminate excess or unrealistic variables from the formu-ation (Khajehpour et al., 2009). This simplification contributeso achieve feasible results faster. Number of variables of theptimization model would be eliminated with the followingules from experience and engineering judgment.

1) The hydrogen stream must flows from a higher pressuresource to a lower pressure sink. A higher pressure sourcecan directly supply hydrogen for a lower pressure sink.However, a lower pressure source cannot directly supplyhydrogen for a higher pressure sink. The lower pressuresource must be supercharged by compressors so as to sup-ply hydrogen for the higher pressure sink. Based on thisrule, higher pressure sources which can directly supplyhydrogen for sinks are promoted to use so as to save moreelectricity cost. However, for the sinks whose inlet pres-sure is higher than other sources and sinks and there areno matched compressors for the sinks, some lower pres-sure sources are not allowed to supply hydrogen for thesinks in order to reduce the investment costs of new com-pressors. Therefore, these unrealistic connections will beremoved from the system formulation before starting themathematical optimization procedure.

2) The total gas from one recycle compressor will only feedits reactor after desulfuration, so the recycle compres-sor and the consuming reactor are to be considered asa whole. Based on this rule, the recycle compressors arenot allowed to supply hydrogen for other sinks, and therecycle compressors are prohibited to consume hydrogenfrom other sources. Therefore, these connections betweenrecycle compressors and other sinks or sources will beeliminated to simplify the model.

3) A stream from the outlet of a hydrogen consumption

device to its makeup is not allowed. The stream shouldflows into fuels or be purified. According to this rule, theseconnections between hydrogen consumption device andits makeup will be eliminated, and these related variablesare removed from the model.

(4) The streams from some sources and sinks with higherpurity must be utilized in hydrogen consumption devicesor purified in purifiers. Therefore, sending these streamsdirectly to the fuel sink is forbidden. Based on this rule,hydrogen from some sources and sinks with higher purityshould be made effective use to save more hydrogen costfor refinery, and these unrealistic connections between thehydrogen streams and fuel will be removed from the opti-mization model.

(5) Some feed routes from some sources to some sinks arefixed due to special technological process and plant lay-out requirement, so those feed routes from these sourcesto other sinks are not considered so as to simplify theoptimization model.

(6) Some hydrogen consumption devices which need far lesshydrogen than other devices are not considered in theoptimization process, all the related variables of thesehydrogen consumption devices are removed from thesystem formulation before starting the mathematical opti-mization procedure.

(7) Not all the sources can supply hydrogen for sinks. All thehydrogen streams which can supply hydrogen for any sinkmust satisfy the constraints of purity and pressure. Hence,these feed routes which do not meet the constraints ofpurity and pressure should be eliminated directly beforestarting the mathematical optimization procedure.

(8) Not all the off-gases can be purified by purifiers. All thefeed streams purified by purifiers are under the constraintof purity and pressure. Therefore, the quantity of feedstreams into a purifier will greatly decrease.

In order to simplify the optimization model and decreasethe solving difficulty, some variables such as pressure, tem-perature and purity of some streams, sources and sinks mustbe determined, the unrealistic variables should be removedfrom the system formulation before starting the mathematicaloptimization procedure.

(1) The outlet purities of the sources are set to their operatingvalue.

(2) The inlet and outlet pressures of the compressors and inlettemperature are set to their operating value.

(3) The outlet purities of the purifiers are set to their operatingvalue.

According to the above simplification and assumption, theoriginal optimization problem under uncertainty is now trans-formed to the following deterministic MINLP problem:

Min f (x, y)

subject to

h(x, y) = 0g(x, y) 0

x 0y {0, 1}

Here x represents continuous variables (e.g., flowrates, pres-sures, purities), and y is integer variables (e.g., decisions forthe existence of hydrogen stream). h(x, y) = 0 denotes the

equality constraints (e.g., mass balances). g(x, y) 0 is theinequality constraints (e.g., specifications on capacity, logical

1562 chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567

SCR

FER

CCR

Hplant

PSA

PSAI

II

HT2

HT4

HT3

HT5

PX

HT1

HC

6190Nm3/h

8250Nm3/h

10310Nm3/h

23710Nm3/h

6185Nm3/h

16666Nm3/h

14583Nm3/h

18556Nm3/h

29896Nm3/h

fuel

C2

C1

C3

C4

C5

C6

Fuel7110Nm3/h

63.5%

Fuel6103Nm3/h

62%

Fig. 4 The original network in the case study.constraints). f(x, y) is the objective function (e.g., annualizedtotal cost). This problem can be solved with a MINLP comput-ing software Lingo 8.0 (Snider, 2002).

4. Case study

In this section, a case study is presented to demonstrate theapplication and effectiveness of the developed method. Theresults of the case study will illustrate the importance andimpact of uncertain factors on the retrofitting of hydrogennetworks. The objective of this case study is to optimize ahydrogen network with a tradeoff between profitability andreliability, compared to conventional deterministic optimiza-tion approaches.

The case study is taken from an existing refinery in China.The refinery mainly processes both high-sulfur crude so asto produce a full range of fuel products and other chemicalproducts. Hydrogen sources include two catalytic reformingunits (SCR and CCR), which supply the most of hydrogenfor hydrogen consumption devices. In addition, there aretwo hydrogen utilities: one hydrogen plants and a fertil-izer plant (FER). Two PSA plants are also used to purify thehydrogen product of SCR and CCR in the refinery so as toobtain higher purity hydrogen. The original hydrogen networkinvolves seven hydrogen consumers which are coking dieselhydrotreater (HT1), straight-run diesel hydrotreater (HT2),straight-run diesel hydrotreater (HT3), diesel hydrotreater(HT4), wax oil hydrotreater (HT5), p-xylene isomerization (PX)

and hydrocracking units (HC). A simplified block diagram ofthe original hydrogen network is illustrated in Fig. 4. The dataof hydrogen sources and sinks are listed in Table 2 and Table 3respectively. The purifiers data are shown in Table 4, includingthe hydrogen supply, product purity, residue purity, maximumcapacity, minimum feed purity, inlet pressure and outlet pres-sure. Table 5 shows the compressors data which includes theefficiencies of compressors and their operation ranges. Thecapital cost is annualized in 3 years, with 5% interest rate peryear. Considering the low purity of off-gases from hydrogenconsumers and PSA residual, a membrane separation unit isconsidered as the candidate purifier.

In order to make good use of hydrogen in refinery, hydro-gen supplies from CCR and SCR are the by-products, so thesehydrogen should be used up. The hydrogen supplies from CCRand SCR change with different feed throughput and operatingconditions, so the hydrogen supplies from CCR and SCR areuncertain variables. Hydrogen supplies from FER and Hplantare the optimization decision variables. Due to the changingmarket condition, the changing external product demand forhydrogen consumers results in a change in the hydrogen con-sumption. Hydrogen demands of all the hydrogen consumersare the uncertain variables. The changing hydrogen demandsof some hydrogen consumers also lead to a change in thehydrogen off-gas supplies of hydrogen consumers. Hydrogenoff-gas supplies from HT4, HT5, PX and HC are much morethan HT1, HT2 and HT3, so the former are considered as uncer-tain variables. Besides, due to the changing market conditionand the changing supply and price of raw materials, the pricesof hydrogen sources, electricity, and fuels are also regardedas uncertain variables. In this paper, we assume that these

random variables conform to normal distribution because itcan capture the essential features of these uncertain variables.

chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567 1563

Table 2 Hydrogen sources data in the case study.

Hydrogen sources Supply (N m3/h) Product purity (%) Outlet pressure (MPa)

SCR 4300049000 92.5 1.2CCR 3900045000 92 1.3FER 050000 98.5 6.8Hplant 032000 95 1.2HT1 off-gas1 430470 85 1.5HT1 off-gas2 200250 43 1.5HT2 off-gas1 9001200 62 125HT2 off-gas2 700800 45 1.25HT3 off-gas1 10001300 73 1.26HT3 off-gas2 9001140 45 1.26HT4 off-gas1 27003000 75 1.4HT4 off-gas2 15001800 47 1.4HT5 off-gas1 18002030 75 1.4HT5 off-gas2 13601500 50 1.4PX off-gas 52006000 75 2.6HC off-gas1 74008300 62 1.65I PSA off-gas 05000 5263.5 0.77II PSA off-gas 05800 5162 0.77

Table 3 Hydrogen sinks data in the case study.

Hydrogen sinks Flowrate (N m3/h) Minimum purity (%) Inlet pressure (MPa)

HT1 55906700 85 6HT2 77108400 85 4HT3 912010500 92 5HT4 2182024000 92 6HT5 2120023000 95 12PX 1330015000 95 3HC 4300047000 95 17

Table 4 Purifiers data in the case study.

Purifiers Supply(N m3/h)

Productpurity (%)

Residuepurity (%)

Maximumcapacity(N m3/h)

Minimumfeed purity

(%)

Inletpressure(MPa)

Outletpressure(MPa)

I PSA 050000 97.5 5263.5 60,000 63 1.3 1.2II PSA 045000 96.8 5162 55,000 55 1.3 1.2

Table 5 Compressors data in the case study.

C1 C2 C3 C4 C5 C6

Efficiency 0.92 0.91 0.92 0.9 0.9 0.9Minimum capacity (N m3/h) 0 0 0 0 0 0

3

TsH(4

Maximum capacity (N m /h) 8000 10,000

he mean and standard deviation of each uncertain hydrogenupply for SCR, CCR, HT4 off-gas1, HT4 off-gas2, HT5 off-gas1,T5 off-gas2, PX off-gas and HC off-gas1 is N (45000, 1350), N42000, 1260), N (2805, 84), N (1600, 48), N (1941, 58), N (1450,

4), N (5500, 165) and N (8000, 240), respectively. The mean and

Table 6 Comparison of CCP and deterministic optimization re

Million $/year CCP Mean method

TAC 154.646 139.324 Operating cost 154.24 138.918 Hydrogen 159.525 143.871 Electricity 15.334 15.051 Fuel 20.619 20.004 Capital cost 1.105 1.105 PSA Membrane 0.606 0.606 Compressor 0.472 0.472 Piping 0.027 0.027 15,000 30,000 20,000 50,000

standard deviation of each uncertain hydrogen demand forHT1, HT2, HT3, HT4, HT5, PX and HC is N (6000, 180), N (8000,240), N (10000, 300), N (23000, 690), N (22000, 660), N (14000,420), and N (45000, 1350), respectively. The mean and stan-

dard deviation of the price for catalytic reforming units (CR),

sults.

Margin method Original network

162.831 176.841162.475 176.841167.371 173.39415.066 12.498

19.962 9.0510.972 0.47 0.472 0.031

1564 chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567

0 1 2 3 4 5 6 7 8 9 10 11 1239000

40000

41000

42000

43000

44000

45000

46000

47000

48000

49000

Time period

Flo

wra

te (

Nm

3/h

)

SCR

CCR

Fig. 5 Distribution of the uncertain reformer hydrogensupply.

0 1 2 3 4 5 6 7 8 9 10 11 121000

2000

3000

4000

5000

6000

7000

8000

Time period

Flo

wra

te (

Nm

3/h

)

HT4 off- gas1 HT4 off- gas2 HT5 off- gas1 HT5 off- gas2 PX off- gas HC off- gas1

Fig. 6 Distribution of the uncertain hydrogen off-gassupply.

0 1 2 3 4 5 6 7 8 9 10 11 125000

10000

15000

20000

25000

30000

35000

40000

45000

HT1 HT2 HT3 HT4 HT5 PX HC

Flo

wra

te (

Nm

3/h

)

Time period

ble

7

The

per

centage

of

constra

int

violations

of

CCP

and

deter

min

istic

optim

ization

method

.

pro

ach

HT1

HT2

HT3

HT4

HT5

PX

HC1

SCR

CCR

HT4 off-ga

s1

HT4

off-ga

s2

HT5

off-ga

s1

HT5

off-ga

s2

PX

off-ga

s

HC

off-ga

s1

P

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

an

method

0.48

0.55

0.53

0.53

0.5

0.48

0.5

0.47

0.38

0.52

0.54

0.51

0.42

0.48

0.53

rgin

method

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Fig. 7 Distribution of the uncertain hydrogen demand.

PSA, FER, MEM, Electricity, and fuel is N (0.08, 0.0024), N (0.11,0.0033), N (0.15, 0.0045), N (0.09, 0.0027), N (0.09, 0.0027), and N(0.0046, 0.000138), respectively. These distribution character-istics of these variables in the future time period are shownfrom Figs. 5 to 8.

Tables 6 and 7 show the results of the CCP com-pared to those methods of the deterministic optimization

including mean method and margin method. In CCP, the con-fidence level is 0.95. In mean method, the expected value of

Ta Ap

CC

Me

Ma

chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567 1565

0 1 2 3 4 5 6 7 8 9 10 11 120.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Time period

Pri

ce

CR($/Nm3) PSA($/Nm

3) FER( $/Nm3)

MEM($/Nm3) Electr icity ($/Kwh) Fuel( $/107J)

Fig. 8 Distribution of the prices of hydrogen, electricitya

hpudiommbCtCioam

0.80 0.84 0.88 0.92 0.96 1.00

14.6

14.8

15.0

15.2

15.4

15.6

15.8

TA

C(1

07$

)

Con fid ence Level

Fig. 9 Optimal profit with different confidence levels.nd fuel.

ydrogen demands, hydrogen supplies and all the relatedrices are used to solve the optimization problem underncertainty. In margin method, the maximum of hydrogenemands, the minimum of hydrogen supplies and the max-mum of all the related prices are used to solve the uncertainptimization problem. Comparing the result of CCP with deter-inistic optimization, it can be found that TAC of meanethod, CCP approach and margin method increase in order,ut the percentage of constraint violations of mean method,CP approach and margin method decrease in order. Becausehe confidence level of CCP approach is fixed as 0.95, TAC ofCP approach is close to that of margin method. TAC of CCPs 8.186 million dollars less than that of margin method. TACf mean method is 15.322 million dollars less than that of CCP

pproach, but the percentage of constraint violations of meanethod is much higher than that of CCP approach. Compared

SCR

FER

CCR

MEM

I PSA

II PSA

18381N

30148N

546

93

2

18013 Nm3/h

7087 Nm3/h

Fuel16985 Nm3/h

0.7 MPa17%

36

C7

42779 Nm3/h

39927 Nm3/h

13015 Nm3/h1.2 MPa

93 %

Fig. 10 Optimized hydrogen newith mean method, CCP approach attaches more importanceto the probability of constraint satisfaction, and CCP approachtakes the cost into consideration on the basis of constraintsatisfaction. Therefore, it is suitable for CCP approach to solvethese optimization problems which has a higher request forconstraint satisfaction.

Fig. 9 shows the TAC profile versus the confidence levelof all chance constraints. It can be seen that the TAC willincrease if the required confidence level increases. A higherTAC (expected value) is needed, if the required confidence levelis higher. It can also be seen that the rate of increase of the TACis higher in the region of high confidence levels (e.g., 0.92).It can be noted that the TAC is more sensitive to the prede-fined confidence level when confidence level approaches themaximum reachable probability of satisfying the constraint.

The optimization procedure runs on a Personal Computer with4 GB RAM memory, and Celeron(R) 2.40 GHz processor. The

HT2

HT4

HT3

HT5

PX

HT1

HC

24502Nm3/h

m3/h

m3/h

6392Nm3/h

6 Nm3/h

1782 Nm3/h

96 Nm3/h

3605Nm3/h

14914 Nm3/h

20 Nm3/h C2

C3

C4

C6

5228 Nm3/h

450 Nm3/h

230 Nm3/h

1050 Nm3/h

750 Nm3/h

1150 Nm3/h

1020 Nm3/h

2667 Nm3/h

1521 Nm3/h

1845 Nm3/h

1378 Nm3/h

7605 Nm3/h

twork with CCP approach.

1566 chemical engineering research and design 9 0 ( 2 0 1 2 ) 15531567CPU time taken for the run to solve the problem for one givenconfidence level (i.e., a point in Fig. 9) is 1 min or so.

The proposed CCP takes into consideration the uncertaininformation including hydrogen supply, hydrogen demandsand prices of hydrogen sources, electricity, and fuels. Fig. 10shows a simplified block diagram of the optimization hydro-gen network using the proposed methodology when theconfidence level is 0.95. Compared to original hydrogen net-work, the optimized hydrogen network obtained using theproposed CCP method has made a great improvement, asshown in Fig. 10. Additional membrane separation unit, com-pressors and piping connections provide flexibility for betterutilization of hydrogen. Due to the higher pressure and purity,better use of hydrogen imported from the FER plant is made,consequently two compressors (C1 and C5) are shut down inthe improved network, which will greatly reduces the powercost. Meanwhile, a part of hydrogen from reforming units isutilized to supply the hydrogen consumers, which will reduceoperating costs of PSA units. Almost all the off-gases otherthan the residues from membrane separation unit are purifiedby the three purifiers, as a result more off-gases are utilized,and more high heat value fuel gas is produced. A comparisonof the cost breakdown for the CCP of hydrogen network withthe original hydrogen network is shown in Table 4.

The optimized hydrogen network obtained using the pro-posed CCP approach has a total annual cost of 154.646 milliondollars/year and results in a saving of 22.195 million dol-lars/year corresponding to a reduction of 12.55% in the totalannual cost compared to the original hydrogen network.

5. Conclusion

Under the current situations of unsteady supply of hydrogen,variations of hydrogen demand, etc., it is very important fordecision maker to assess the extra cost of these uncertaintiesin the optimization of hydrogen network in refinery. In thispaper, a CCP approach for the optimization of hydrogen net-work in refinery under uncertain conditions is addressed. Theuncertain hydrogen supply, uncertain hydrogen demand anduncertain prices of hydrogen, electricity, and fuels are consid-ered in the process of modeling. These uncertain variables areexplicitly introduced in the formulation of the optimizationmodel so that their impacts can be taken into account in thesolution. Furthermore, to make the proposed approach moresuitable for the real system and find a more practical solutionfor the optimization model, the inlet flowrates and puritiesat the reactor inlet of hydrogen consumers are consideredas variables, the minimum pure hydrogen of hydrogen con-sumers is considered and must be satisfied to achieve desiredoil conversion rate and keep the catalysts activity. Stochas-tic chance constrained mixed-integer nonlinear programmingmodels are presented to address the optimization problemunder uncertainties. The proposed method in this paper couldwell accommodate uncertain factors and handle constraintsin a suitable way. Based on the stochastic distributions ofthe uncertain variables, the problem can be transformed intoan equivalent deterministic MINLP problem. The branch andbound method in Lingo 8.0 is used to solve the proposedequivalent formulation in a case study. Then, the optimiza-tion problem is also solved with different confidence levels soas to obtain the relationship between profitability and reliabil-

ity. The computational results from CCP approaches can givea suitable compromise between profitability and reliabilitycompared to mean method and margin method. Optimizationresults show that the proposed CCP strategy can reduce theplant operation cost, save the investment cost, increase thewhole profit and provide important management informationof hydrogen system for decision maker in refinery.

Acknowledgements

Financial support from the National High TechnologyResearch and Development Program of China (2008AA042902),National High Technology Research and Development Pro-gram of China (2009AA04Z162), Program of IntroducingTalents of Discipline to University (B07031) and National Nat-ural science Foundation of China (21106129) is gratefullyacknowledged.

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Optimization of refinery hydrogen network based on chance constrained programming1 Introduction2 Chance constrained programming3 Problem formulation3.1 Problem statements3.2 Objective function3.3 Constraints3.3.1 Hydrogen source constraints3.3.2 Hydrogen sink constraints3.3.3 Compressors constraints3.3.4 Purifiers constraints

3.4 Chance constrained optimization3.5 Model simplification

4 Case study5 ConclusionAcknowledgementsReferences