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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: [email protected] (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:[email protected]/10.1016/j.cherd.2012.02.016
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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
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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
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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.
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chemical engineering research and design 9 0 ( 2 0 1 2 )
15531567 1557
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lgTgtptlftlpfiotmfstd
thtfiroipmrst
eiocodtgohcshcm
t
P
troc
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.
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chemical engineering research and design 9 0 ( 2 0 1 2 )
15531567 1559
muork
F
y
wk
3Bchflaf
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Tb
Ti
3HmpCphr
cpTa
s dr
e
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
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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
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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
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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.
References
Alves, J.J., Towler, G.P., 2002. Analysis of refinery
hydrogendistribution systems. Ind. Eng. Chem. Res. 41
(23),57595769.
Ahmad, M.I., Zhang, N., Jobson, M., 2010. Modelling
andoptimization for design of hydrogen networks formulti-period
operation. J. Clean. Prod. 18 (9), 889899.
Arellano-Garcia, H., Wozny, G., 2009. Chance
constrainedoptimization of process systems under uncertainty: I.
Strictmonotonicity. Comput. Chem. Eng. 33 (10), 15681583.
Chakraborty, A., Linninger, A., 2003. Plant-wide
wastemanagement. 2. Decision making under uncertainty. Ind.
Eng.Chem. Res. 42 (2), 357369.
Chakraborty, A., Colberg, R.D., Linninger, A., 2003.
Plant-widewaste management. 3. Long-term operation and
investmentplanning under uncertainty. Ind. Eng. Chem. Res. 42
(20),47724788.
Charnes, A., Cooper, W.W., 1959. Chance-constrainedprogramming.
Manage. Sci. 6, 7379.
Miller, L.B., Wagner, H., 1965. Chance-constrained
programmingwith joint constraints. Oper. Res. 13 (6), 930945.
Hallale, N., Liu, F., 2001. Refinery hydrogen management for
cleanfuels production. Adv. Environ. Res. 6 (1), 8198.
Jiao, Y.Q., Su, H.Y., Hou, W.F., 2011a. An optimization method
forthe refinery hydrogen network and its application.
In:Proceedings of the 2011 4th International Symposium onAdvanced
Control of Industrial Processes, Hangzhou.
Jiao, Y.Q., Su, H.Y., Liao, Z.W., Hou, W.F., 2011b. Modeling
andmulti-objective optimization of refinery hydrogen network.Chin.
J. Chem. Eng. 19 (3), 990998.
Khajehpour, M., Farhadi, F., Pishvaie, M.R., 2009.
Reducedsuperstructure solution of MINLP problem in refineryhydrogen
management. Int. J. Hydrogen Energy 34 (22),92339238.
Kumar, A., Gautami, G., Khanam, S., 2010. Hydrogen
distributionin the refinery using mathematical modeling. Energy 35
(9),37633772.
Li, P., Arellano-Garcia, H., Wozny, G., 2008. Chance
constrainedprogramming approach to process optimization
underuncertainty. Comput. Chem. Eng. 32 (12), 2545.
Li, P., Wendt, M., Arellano-Garcia, H., Wozny, G., 2002a.
Optimaloperation of distillation processes under uncertain
inflowstreams accumulated in a feed tank. AIChE J. 48
(6),11981211.
Li, P., Wendt, M., Wozny, G., 2000. Robust model predictive
controlunder chance constraints. Comput. Chem. Eng. 24
(27),829834.
Li, P., Wendt, M., Wozny, G., 2002b. A probabilistically
constrainedmodel predictive controller. Automatica 38 (7),
11711176.
Li, P., Wendt, M., Wozny, G., 2004a. Optimal production
planning
for chemical processes under uncertain market conditions.Chem.
Eng. Technol. 27 (6), 641651.
-
chemical engineering research and design 9 0 ( 2 0 1 2 )
15531567 1567
L
L
L
L
L
L
M
P
i, W.K., Hui, C.W., Li, P., Li, A.X., 2004b. Refinery planning
underuncertainty. Ind. Eng. Chem. Res. 43 (21), 67426755.
iao, Z.W., Rong, G., Wang, J.D., Yang, Y.R., 2011a.
Rigorousalgorithmic targeting methods for hydrogen networks. Part
I:Systems with no hydrogen purification. Chem. Eng. Sci. 66
(5),813820.
iao, Z.W., Rong, G., Wang, J.D., Yang, Y.R., 2011b.
Rigorousalgorithmic targeting methods for hydrogen networks. Part
II:Systems with one hydrogen purification. Chem. Eng. Sci. 66(5),
821833.
iao, Z.W., Wang, J.D., Yang, Y.R., Rong, G., 2010.
Integratingpurifiers in refinery hydrogen networks: a retrofit case
study. J.Clean. Prod. 18 (3), 233241.
iu, B.D., Zhao, R.Q., Wang, G., 2003. Uncertain Programmingwith
Applications. Tsinghua University Press, Beijing (inChinese).
iu, F., Zhang, N., 2004. Strategy of purifier selection
andintegration in hydrogen networks. Chem. Eng. Res. Des. 82(A10),
13151330.
esfin, G., Shuhaimi, M., 2010. A chance constrained approachfor
a gas processing plant with uncertain feed conditions.Comput. Chem.
Eng. 34 (8), 12561267.
eters, M.S., Timmerhaus, K.D., 1991. Plant Design and
Economics for Chemical Engineers. McGraw-Hill,New York.Petkov,
S.B., Maranas, C.D., 1997. Multiperiod planning andscheduling of
multiproduct batch plants under demanduncertainty. Ind. Eng. Chem.
Res. 36 (11), 48644881.
Qu, G.H., 2007. Study on cost leadership strategy of
hydrogenutilization in petroleum refining plants.
Techno-Econ.Petrochem. 33 (2), 1922 (in Chinese).
Sahinidis, N.V., 2004. Optimization under
uncertainty:state-of-the-art and opportunities. Comput. Chem. Eng.
28(67), 971983.
Schwarm, A.T., Nikolaou, M., 1999. Chance-constrained
modelpredictive control. AlChE J. 45, 17431752.
Snider, S., 2002. Optimization Modeling with LINGO, fifth
edition.Lindo Systems Corporation, Chicago.
Tong, Y.L., 1990. The Multivariate Normal
Distribution.Springer-Verlag, New York.
Towler, G.P., Mann, R., Serriere, A.J-L., Gabaude, C.M.D.,
1996.Refinery hydrogen management: cost analysis
ofchemically-integrated facilities. Ind. Eng. Chem. Res. 35
(7),23782388.
Uryasev, S., 2000. Probabilistic Constrained
Optimization:Methodology and Applications. Dordrecht, Kluwer
AcademicPublishers.
Wendt, M., Li, P., Wozny, H., 2002. Nonlinear
chance-constrained
process optimization under uncertainty. Ind. Eng. Chem. Res.41
(15), 36213629.
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