Hydrogen sulfide removal process embedded optimization of hydrogen network

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 8 1 6 3 e1 8 1 7 4

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Hydrogen sulfide removal process embedded optimization of hydrogen network Li Zhou, Zuwei Liao*, Jingdai Wang, Binbo Jiang, Yongrong Yang State Key Laboratory of Chemical Engineering, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, PR China

article info

abstract

Article history:

Due to the trend in tighter environmental regulations on heavier crude oil processing,

Received 11 April 2012

hydrogen has become an important strategic resource in modern refineries. Refiners have

Received in revised form

to improve the efficiency of hydrogen distribution networks to satisfy the increasing

27 July 2012

demand of hydrogen. Consequently, plenty of work has been focusing on optimizing

Accepted 31 August 2012

hydrogen reuse and purification schemes, which is known as hydrogen network integra-

Available online 2 October 2012

tion (HNI). In refineries, hydrogen purification techniques include hydrocarbon removal

Keywords:

membrane separation and pressure swing adsorption (PSA) are frequently employed in the

Hydrogen network

HNI study. However, the possibility of integrating H2S removal units into HNI study has

H2S removal network

been overlooked until recently. H2S removal units are usually modeled as mass exchangers

Desulfurization ratio

and independently studied as mass exchange networks (MEN). In the present work, an

Total annual cost

improved modeling and optimization approach has been developed to integrate H2S

units and hydrogen sulfide (H2S) removal units. Hydrocarbon removal units such as

removal units into HNI. By introducing a desulfurization ratio, Rdspl;i0 , simplified MEN is incorporated into hydrogen distribution network. Total annual cost (TAC) is employed as the optimizing object to investigate the tradeoffs between hydrogen distribution network cost and MEN cost. Pressure constraints and impurity concentrations are considered, and cost equations are established to determine the installation of new equipments in order to synthesis an economical network. A practical case study is used to illustrate the application and effectiveness of the proposed method. Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

Green house gas (GHG) emission has become a hot issue in modern society. A great number of GHG emissions are related to fuels. The largest fuel suppliers, oil refineries, are now facing challenges of producing cleaner fuels. The challenge

comes from the unbalance between hydrogen demand and supply. On the one hand, crude oil resources are getting heavier and the content of sulfur and nitrogen is increasing, while the product fuels with lower aromatic, sulfur and nitrogen content are required in order to meet environmental regulations. As a result, more and more hydro-treating

Abbreviations: DHT, Diesel hydro-treater; GCA, Gas cascade analysis; G/DHT, Gasoline and diesel hydro-treater; GHG, Green house gas; GHT, Gasoline hydro-treater; HNI, Hydrogen network integration; HP, High Pressure; HPlant, hydrogen plant; LP, Low Pressure; MEN, Mass exchange network; MINLP, Mixed integer non-linear problem; MSAs, Mass separating agents; PP, polypropylene unit; PSA, Pressure swing adsorption; RF, catalytic reformer; PE, polyethylene unit; TAC, Total annual cost. * Corresponding author. Fax: þ86 0571 87951227. E-mail address: [email protected] (Z. Liao). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2012.08.151

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processes are under construction to remove the undesired contents. Hydrogen demand will keep growing. On the other hand, reduction in the aromatics content of gasoline specification has cut down hydrogen production in the catalyst reforming unit, which used to be the traditional source of hydrogen in refineries. Consequently, hydrogen is becoming a critical issue for refineries. As it was considered as the best potential energy of the future [1], hydrogen resource is of great importance to our society. In a word, efficient usage of hydrogen is both critical to the refineries and our society. Though investments have been made in building up new hydrogen plants and work has been done on investigation of the efficient producing of hydrogen through steam methane reforming [2], the HNI technique is still of great importance for refinery hydrogen management. This is because hydrogen production is a GHG emission intensive industry. Implementing HNI requires full consideration of the performance of the whole hydrogen network. There are several practical considerations which must be tackled when optimizing hydrogen network as a whole: 1). Hydrogen concentration, which is the first essential stream property concerned when considering hydrogen reuse; 2). Impurity concentration, for example hydrogen sulfide, which can not only corrode the equipments but also cause damage to certain catalyst must be controlled at a certain level; 3). Pressure constraints, which is one of the essential considerations for a practical model. During the past decade, HNI has been extensively explored and the studies carried out can simply be classified into two major categories:  Pinch analysis approaches  Mathematical programming superstructures.

approaches

based

on

There are dozens of pinch analysis approaches as summarized by Foo [3], and they are graphical or algebraic based methods. These methods have two things in common: 1). They can provide minimum hydrogen utility consumption or off-gas discharge before system structure is obtained; 2). They usually manipulate three basic properties of hydrogen streams: flowrate, purity and impurity load. As early as 1996, Towler et al. [4] employed value composite curves to assess hydrogen resources. The first graphical hydrogen pinch analysis approach was developed by Alves [5], who proposed a hydrogen surplus diagram in the purity versus flowrate coordinate system. Subsequently, El-Halwagi et al. [6] developed an iterative-free graphical methodology in the impurity load versus flowrate coordinate system. This method was extended to systems with both pure and impure hydrogen resources [7,8]. Later, another coordinate system, the purity versus impurity load system, was employed by Agrawal and Shenoy [9] and Bandyopadhyay [10]. Foo [11] introduced an algebraic method, the gas cascade analysis (GCA), for targeting the minimum utility consumption. Liao et al. [12] presented a new algebraic method addressing the relationship between pinch simplification and the mathematical model. Pinch analysis techniques have also been extended to multiple impurity problems by Zhao et al. [13] and pressure constraint problems by Ding et al. [14]. Recently, pinch analysis for placing purifiers has been improved: optimal placements were

obtained for both remove ratio specified [15] and tail gas purity specified [16] purifier models. Pinch analysis methods are useful in giving design targets, while mathematical programming methods are powerful in detailed design. Hallale [17] proposed an MINLP optimization approach based on superstructure that fully accounts for pressure constraints and the existing equipments, which was then modified by Kumar [18] for considering variable inlet and outlet pressures of compressors. Liu and Zhang [19] developed an automated design approach for the selection of appropriate purification processes in hydrogen network, in which shortcut models for purification processes were developed. In order to lower the computation cost and obtain feasible solutions, Khajehpour [20] minimized the hydrogen waste through reduction of the superstructure by heuristic rules. Liao [21] incorporated compressors and purifiers into state-space superstructure, and developed a systematic approach for the integration of hydrogen network with purifiers. Considering the life cycle of hydrogenation catalysts, Ahmad [22] and Xuan et al. [23] extended the problem formula to cope with the multi-period operation problems. Jiao et al. [24] presented a multi-objective optimization approach to explore the tradeoffs between operating cost and investment cost. The aforementioned mathematical programming methods were only valid for single contaminant systems. Recently, Jia [25] considered the multi-component effect of hydrogen streams by integrating flash calculations, which made the obtained result more feasible. However, this approach requires iterative interactions between simulation and optimization procedures which may cause difficulty in convergence when integer variables are introduced. Nevertheless, multi-component consideration will direct the trend of HNI research, because the component constraint like hydrogen sulfide constraint cannot be ignored in real operation. Compared to single component optimization, multi-component HNI concerns not only methane contaminant, but also other impurities such as hydrogen sulfide. Consequently, not only the hydrocarbon removal units but also H2S removal units should be involved in the HNI study. However, the incorporation of H2S removal units into multi-component HNI remains unexplored. In refineries, H2S is a very important impurity which cannot be ignored because it will not only corrode the equipment but also harm certain catalysts. As a result, the content of H2S contaminant in the system is strictly controlled at a specific level in real production. There are several methods to remove H2S: 1) dry desulfurization; 2) wet desulfurization; 3) bio-desulfurization; 4) and desulfurization by membrane. Wet desulfurization process is widely used. This process utilizes an aqueous absorbent in a column to absorb H2S and yields a substantially H2S-free gas stream. In some refineries, H2S absorption unit has already been used to remove the overloaded hydrogen sulfide from the hydrogen flow so as to further excavate the potential of efficient hydrogen utilization. H2S removal units are usually modeled as mass exchangers and independently studied as mass exchange networks (MEN). MEN integration was initially introduced by El-Halwagi et al [26], aimed at synthesizing a network of mass exchange units which can preferentially transfer certain species from rich streams to the mass separating agents (MSAs) at

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 8 1 6 3 e1 8 1 7 4

minimum cost. El-Halwagi et al. [26] introduced a systematic two-staged procedure for the synthesis of cost-effective MEN. Thereafter, a linear transshipment model was established [27]. Then Hallale and Fraser developed a method for targeting the total annual cost of MEN in a series of works [28e31]. It should be emphasized that there is a tight connection between hydrogen network and H2S absorption processes. If we optimize the two systems separately, then it is likely to result in sub-optimal improvement or less practical solutions. To achieve the ultra-high efficient use of hydrogen resources as well as to improve the practicability of the technique proposed, it is reasonable and necessary to optimize the hydrogen network with desulfurization processes integrated as a whole. In the present work, we aim to develop a systematic optimizing approach that incorporates desulfurization processes with HNI. Desulfurization ratio, Rdspl;i0 , is introduced to connect hydrogen network and the hydrogen sulfide removal network. Desulfurization ratio, Rdspl;i0 , is a set of optimizable variables for each desulfurization column in the MEN. Total annual cost (TAC) is employed to learn the trade-offs between hydrogen distribution network cost and MEN cost and a real world case study is illustrated.

2.

Problem statement

Fig. 1 represents a typical hydro-treating unit. A liquid feed stream is mixed with a hydrogen stream, heated and fed to a hydro-treating reactor which is designated as hydrogen sink. The reactor operates at a high partial pressure of hydrogen to ensure a sufficient reaction rate and to protect the catalyst from coking. Therefore, part of the hydrogen is consumed in the reactor while a substantial fraction of hydrogen leaves the reactor with products. The reaction products include light fuels, light hydrocarbons, hydrogen sulfide and other gases. The reaction effluent is cooled and sent to a high-pressure

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(HP) separator. Part of the gas released from the HP separator is desulfurized (optional, shown as dashed line in Fig. 1), and re-compressed to mix with the hydrogen makeup, while the remaining gas is purged to avoid the build-up of contaminants in the loop. The liquid released from the HP separator is then sent to a low-pressure (LP) separator from which the purge gas is sent to the fuel system. The off-gases from both the HP separator and LP separator contain big amount of hydrogen, consequently they can be designated as internal hydrogen sources. It should be noted that the off-gas from HP separator may be reused directly to certain hydrogen sinks for the reserved hydrogen concentration and pressure level, while the off-gas from LP separator must be upgraded by purifier or compressor before reuse. Based on the above description of hydrogen consuming unit, the design problem of this work can be stated as: given a set of external hydrogen sources, H ¼ {hjh ¼ 1, 2, .., Nh}, a set of internal hydrogen sources, I ¼ {iji ¼ 1, 2, .., Ni}, a set of hydrogen sinks, J ¼ {jjj ¼ 1, 2, .., Nj}, a set of hydrocarbon remove units, PF ¼ {pfjpf ¼ 1, 2, .., Npf}, a set of desulfurization units, DS ¼ {dsjds ¼ 1, 2, .., Nds}; and a set of compressors, CP ¼ {cpjcp ¼ 1, 2, .., Ncp}, it is desired to synthesize a cost-optimal network that can fulfill the component requirements and pressure constraints of all hydrogen sinks. The detailed parameter specifications for each set of units are given as follows. For hydrogen source i, the flow rate, Fi, component concentration, yi,m, and pressure, Pi, are specified; for hydrogen sink j, the demand inlet flowrate, FDe j , demand inlet pressure, PDe j , the minimum allowable inlet hydrogen concentration, yMin j;H2 , and the maximum allowable inlet hydrogen sulfide concentration, yMax j;H2 S , are specified; for desulfurization unit, the initial concentration of lean streams, Xin, is specified. It is worth mentioning that in the present work, counter-current contact absorbers are selected as the desulfurization column, and ammonia is chosen as the chemical absorbent.

Fig. 1 e Schematic diagram of a typical hydrotreating unit.

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3.

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3.1.

Mathematical model

The state-space superstructure was first introduced by Bagajewicz and Manousiouthakis [32] and Bagajewicz et al. [33], which was then used as an alternative representation of the MEN and heat exchanger network. Thereafter, it was applied to a heat integrated water network to minimize the resource consumption [34], and later extended to the hydrogen network to capture rich network structures [21]. It has been modified in the present work to capture the feature of our desulfurization processes embedded hydrogen network. To be more specific, the hydrogen network in this work is demonstrated as a system of four interconnected blocks as shown in Fig. 2: 1) Hydrogen distribution section; 2) hydrocarbon removal section, where the hydrocarbons get removed and hydrogen concentration of relevant streams get upgraded, thus the waste streams whose hydrogen concentration is below the reuse level can be recovered and then reused. Usually, typical hydrocarbon removal processes include PSA, membrane separation and cryogenic separation. 3). Desulfurization section, i.e. H2S removal section, where the H2S contaminant gets partially removed from the process stream. 4). Compressor section, where the pressure level of streams get upgraded. As is known to us, compressors are among the most expensive equipments in refineries, we must take pressure constraints into consideration, in order to improve the practicability of the model. It’s worth noting that the inlets of the purifiers as well as the compressors can serve as hydrogen sinks, while the outlets are considered as hydrogen sources. Their detailed inner connections and corresponding mathematical models will be described in the following sections.

Simplified state-space superstructure

In order to improve the efficiency of calculation and obtain feasible results, it is necessary to reduce the superstructure before starting the optimization procedure, as Khajehpour did in their work [20]. The following rule is considered:  Assume that new compressors are preinstalled with their outlet pressures specified. As compressors are known to be one of the most expensive equipments in refineries, the possibility of new compressor installation is limited to some specific place. Thus the outlet pressures could be specified according to the downstream units.

3.2.

Hydrogen distribution network

This section consists of all hydrogen sources and hydrogen sinks, and it can also be expressed as the connection between several mixers and splitters [35]. All the hydrogen sources are splitters, while all the hydrogen sinks are mixers. The splitters split hydrogen stream inputs into several branches and send them to a mixer at the exit leading to the other blocks. These splitters and mixers are divided into different groups based on their original identities or their connections with the other blocks. To satisfy the stream mass balance, component mass balance as well as pressure constraint of each node, the following equations are given. Mass balance of each splitter and mixer: X j˛J

Fh;j þ

X

Fh;cp ¼ Fh

ch ˛H

cp˛CP

Fig. 2 e State-space representation of hydrogen network.

(1)

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X

X

Fpl;i;j þ

Fpl;i;cp þ

¼ F pl;i X

X X

Fh;j þ

i0 ˛I

X X

Fpl;i;dspl;i0 þ Fpl;i;fuel

Fpl;i;j þ Fre;j þ

F

pf ˛PF

X X

Fcp;j þ

pl˛PL i0 ˛I

cp˛CP

¼Fj

P pf ;j

X

pf ˛PF

Fdspl;i0

X

;j

(3)

cj ˛J

X

Fpl;i;fuel þ

Fcp;fuel þ

X pf ˛PF

cp˛CP

pl˛PL i˛I

F Rpf ;fuel þ

XX pl˛PL i0 ˛I

Fdspl;i0 ;fuel ¼ F fuel

Fpl;i;cp þ

X

pl˛PL i˛I

XX

Fh;cp þ

pl˛PL i0 ˛I

h˛H

Fdspl;i0 ;cp þ

X pf ˛PF

F Ppf ;cp ¼Fin cp ccp˛CP

X

Fcp;j þ

Fcp;pf þ Fcp;fuel ¼ Fout cp

ccp ˛CP

X i0 ˛I

X

Fpl;i;dspl;i0 ¼ Fin dspl;i0 X

Fdspl;i0 ;j þ

pf ˛PF

j˛J

Fpl;i;pf þ

Fdspl;i0 ;cp þ Fdspl;i0 ;fuel

X

(8)

Fcp;pf þ

X

F Ppf ;j þ

X X pl˛PL i0 ˛I

F Ppf ;cp ¼ F Ppf

Fdspl;i0 ;pf ¼ F pf

cpf ˛PF

cpf ˛PF

(9)

F Rpf ;fuel ¼ F Rpf

cpf ˛PF

Fh;j yh;m þ

h˛H

þ

XX

pl˛PL i0 ˛I

X X

XX

Fdspl;i0 ;j ydspl;i0 ;m þ

Fpl;i;fuel ypl;i;m þ

X X

pl˛PL i0 ˛I

X pf ˛PF

X

Fdspl;i0

;fuel ydspl;i0 ;m

Fcp;j ycp;m

cp˛CP

F Ppf ;j y Ppf ;m

Fcp;fuel ycp;m þ

X pf ˛PF

¼ F fuel yfuel;m

Fcp;pf ycp;m þ

X X pl˛PL i0 ˛I

cpf ˛PF; m˛M

Fdspl;i0

(15)

;pf ydspl;i0 ;m

(16)

yj;H2 S  yMax j;H2 S

(17)

cj ˛J

(18)

ch˛H

(19)

It should be emphasized that there are pressure constraints between the stream matches. For the units with inlet pressure demand, PDe j , a stream whose pressure cannot reach that demand is rejected. Consider general binary variable, Yp,q, the constraint can be expressed as:

where Up,q is the upper bound of pressure difference between Pq and PDe p ,for the existence of a stream, the following equations are given:

(12)

F Rpf ;fuel y Rpf ;m

cm˛M

cj ˛J

(11)

¼ F j yj;m cj ˛J; m˛M

cp˛CP

pl˛PL i˛I

þ

Fpl;i;j ypl;i;m þ Fre;j yre;m þ

pl˛PL i˛I

X

cpl ˛PL; i˛I; m˛M

  PDe p  1  Yp;q Up;q  Pq

Equations (1)e(4) represent the mass balance of external hydrogen sources, internal hydrogen utilities, hydrogen sinks and fuel system respectively, while the mass balance of inlet and outlet of compressors, desulfurization processes and hydrocarbon removal processes are expressed by Equations (5)e(11) respectively. As the hydrogen concentration of the residual gas from a hydrocarbon removal unit is quite low, it is directly sent to the fuel system, which is shown in Equation (11). The superscript P represents the product of a hydrocarbon removal unit and R stands for the residual. Equations (8), (10) and (11) illustrate that, the outlet of a desulfurization column can be sent to a hydrocarbon removal unit, but not vice versa. This is because hydrogen sulfide can also poison the adsorbent of the PSA process. It is also worth noting that the compressors and purifiers include both existing and new ones. The newly added ones require additional investment while the existing ones are constrained by the specified capacity. Components mass balance of each mixer: X

(14)

(10)

cp˛CP

j˛J

;cp ydspl;i0 ;m

Equations (12)e(16) demonstrate the components mass balance of hydrogen sinks, fuel system, compressors, desulfurization columns and hydrocarbon removal units respectively. While the concentration and capacity constraints cannot be violated, the following equations are given:

Fh  FCa h

cp˛CP

cp˛CP

pl˛PL i˛I

X

(7)

cpl ˛PL; i0 ˛I

¼ Fout dspl;i0 X X

X

X

Fdspl;i0

ccp ˛CP; m˛M

cp˛CP

yj;H2  yMin j;H2

cpl ˛PL; i˛I

Fdspl;i0 ;pf þ

pl˛PL i0 ˛I

in Fpl;i0 ;dspl;i ypl;i0 ¼ Fin dspl;i0 ydspl;i0 ;m

Fpl;i;pf ypl;i;m þ

X X

(6)

pf ˛PF

j˛J

Fh;cp yh;m þ

F Ppf ;cp y Ppf ;m ¼ Fin cp ycp;m

¼ F pf ypf ;m

(5) X

i0 ˛I

X h˛H

pl˛PL i˛I

(4) XX

X

þ

X X

XX

Fpl;i;cp ypl;i;m þ

pl˛PL i˛I

(2)

pl˛PL i˛I

X

X

cpl˛PL; i ˛I

h˛H

þ

Fpl;i;pf þ

pf ˛PF

cp˛CP

j˛J

X

(13)

cðp; qÞ˛O

(20)

Fp;q  UFp;q Yp;q  0 cðp; qÞ˛O

(21)

  Fp;q þ 1  Yp;q UFp;q  uFp;q

(22)

cðp; qÞ˛O

in which UFp;q and uFp;q are the upper and lower bounds of Fp,q. The existence of new equipment is decided by its inlet flowrate. Take desulfurization column as an example, the binary variable for the existence of a new desulfurization column is, Ydspl;i0 , the equation determines its existence can be expressed as: Ydspl;i ¼

X i0 ˛I

3.3.

Ypl;i;dspl;i0

cpl ˛PL; i0 ˛I

(23)

Hydrocarbon removal block

A hydrocarbon removal unit in a hydrogen network can be considered as one sink and two sources, corresponding to one inlet stream and two outlet streams [17], so three groups of stream variables will be considered. They are feed variables, Ppf, Fpf, ypf, product variables, PPpf ; FPpf ; yPpf , and residual variables, PRpf ; FRpf ; yRpf . Assuming that the inlet and outlet pressures of hydrocarbon removal units are settled before optimization, and by specifying the hydrogen recovery rate, Rpf, and the product purity, y Ppf ;H2 , of the unit, the relationships between the three streams can be stated as [17]:

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F Ppf y Ppf ;H2 ¼ Rpf F pf ypf ;H2 F Rpf þ F Ppf ¼ F pf

cpf ˛PF

(24)

cpf ˛PF

(25)

a stream with higher pressure is forbidden to mix with a stream with much lower pressure level, thus to avoid pressure loss.

For a compressor cp, the existing ones already have their capacity limited and inlet and outlet pressures specified, while for the newly added ones, these shall be determined according to the process requirement. The mass balance and capacity constraint can be described as:

The final operating pressure of a desulfurization column will be determined by its inlet stream base on the optimizing result. The outlet streams serve as new hydrogen sources and are sent back to the hydrogen distribution network. A detailed structure is shown in Fig. 3. As is shown, one desulfurization column is preinstalled for each stream and a stream can go to its own desulfurization column or to other desulfurization column which is operating under the same pressure level. These assumptions exclude the mix option between the high pressure stream and the low pressure stream, thus to avoid big pressure loss. Since all the hydrogen sources are required to satisfy the pressure demand of hydrogen sinks before they could be used, the streams with higher pressure may be used directly after desulfurization (or with less compression work), while the streams with lower pressure may need to be further compressed. Therefore these assumptions could reduce the number (or the work) of new compressor. The hydrogen sulfide removed by desulfurization column is definitely a very tiny part of the mass stream therefore the inlet and outlet flowrate of a desulfurization column are assumed to be identical, as shown in Equation (32).

out Fin cp ¼ Fcp

ccp ˛CP

(29)

out Fin dspl;i0 ¼ Fdspl;i0

Ca Fin cp  Fcp

ccp ˛CPexist

(30)

F Rpf y Rpf ;H2 þ F Ppf y Ppf ;H2 ¼ F pf ypf ;H2

cpf ˛PF

(26)

Equations (24)e(26) specify the hydrogen concentration variation of the streams during the hydrocarbon removal processes. As for the hydrogen sulfide concentration, we assume that it stays unchanged: ypf ;H2 S ¼ y Ppf ;H2 S

cpf ˛PF

(27)

ypf ;H2 S ¼ y Rpf ;H2 S

cpf ˛PF

(28)

Since the inlet hydrogen sulfide concentration of a hydrocarbon removal unit is already controlled at a relatively low level, this assumption can be rational.

3.4.

Compressors

In addition, the power consumption of a compressor, Powercp, is measured by the inlet and outlet pressures and the flowrate that goes through it [36]: Powercp ¼ acp

3.5.

 bcp  in Pout 1 Fin cp =Pcp cp

ccp ˛CP

(31)

Desulfurization section

cpl˛PL; i0 ˛I

The present work only concerns half of the MEN design, i.e. the distribution of the rich streams and simple design of the desulfurization column. In the range of compositions involved in the problem, the equilibrium solubility of hydrogen sulfide in ammonia is a linear relation, as stated by Hallale [28]. y ¼ mX þ c *

(33)

where y is the rich stream composition that would be in equilibrium with the corresponding MSA composition X. The value of m is 1.45 and b is 0. As the ideal equilibrium state

As stated in the second section, desulfurization units are optionally installed in refineries to remove the overloaded hydrogen sulfide from the HP separator purges in order to reuse the hydrogen. However, there is also reuse potential in the LP separator gases. Though the hydrogen concentrations of these gas streams from LP separator are relatively lower than that of the gas streams from HP separators, while the H2S concentrations are higher, those streams could be further reused after properly handled with purifiers. In order to optimize the capital cost of new equipments and in the mean while avoid a huge pressure loss caused by the mixing of streams with big pressure differences, different categories of desulfurization units operating under different pressure levels are recommended and the following assumptions are considered: 1) The operating pressure level of the desulfurization columns are roughly pre-fixed according to the pressure levels of the purge streams of the HP separator and the LP separator. 2) A stream can only connect to the desulfurization columns operating under the corresponding pressure level, and

(32)

Fig. 3 e Detailed representation for MEN.

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cannot be reached unless an infinitely large column is installed, the minimum allowable composition difference, ε, was introduced [26], and the following equation was given [37]:   Xin;Max ¼ yTar  c m  ε

(34)

In our case, the minimum allowable composition difference is considered when specifying the inlet concentration of the key component in the MSA. For the desulfurization column design, the theoretical number of trays NT is analytically calculated by making use of the Kremser equation [38].

CH2 ¼

X

eH2 Fh th

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(42)

h˛H

where eH2 is the unit price of hydrogen production, th is the annual operating time for hydrogen producer, s. The power consumption of compressors includes the power consumption of newly added compressors and the power consumption variation of the existing compressors caused by the inlet flow rate change. The power cost of a compressor is represented as: X epower Powercp tcp (43) Cpower ¼ cp˛CP

If As1 :     NT ¼ log yin  mxin  c yout  mxin  c ð1  1=AÞ þ 1=A log A (35) (36)

where A ¼ L/mG, which is the ratio of the operating line slope to the equilibrium line slope, and is called the absorption factor. In this work, the absorption factor is simply assumed to be 1. As stated before, tradeoffs exist between hydrogen distribution network cost and the MEN cost. The more hydrogen sulfide gets removed in the MEN, the more hydrogen can be reused in the hydrogen distribution network, while the cost of the MEN will increase and the cost of the hydrogen distribution network will decrease. Consequently, the desulfurization ratio, Rdspl;i0 , is selected as an optimizable variable to investigate the tradeoffs. cpl˛PL; i0 ˛I

pl;i0

(37)

0  Rdspl;i0  1 cpl˛PL; i0 ˛I

(38)

Then the following equation can be deduced: h  i  i.h  in in NT;dspl;i0 ¼ yin 1Rdspl;i0 yin dspl;i0  1Rdspl;i ydspl;i0 dspl;i0 mx c cpl˛PL; i0 ˛I

3.6.

ð39Þ

Objective function

TAC is employed as the design object: 0 TAC ¼ CH2 þ Cpower þ CMSA  Cfuel þ Af @

þ

X dspl;i

new

Cdspl;i0 þ

X

1 Cpipe A

X cpnew

Ccp þ

X

Cpf

pfnew

(40)

pipenew

in which the subscript “new” means additional units, Af is the annualizing factor, which is given as: ny

ny

Af ¼ fið1 þ fiÞ =ð1 þ fiÞ 1

(44)

pl˛PL i0 ˛I

If A ¼ 1 :   out y  mxin  c NT ¼ yin  yout

  ;in yout dspl;i0 ¼ 1  Rdspl;i0 yds

The cost for mass separating agent is calculated by: X X CMSA ¼ eMSA FMSA;dspl;i0 tdspl;i0

(41)

where fi is the fractional interest rate per year and ny is the number of years. The cost of hydrogen utility, i.e. the cost of producing hydrogen for a hydrogen network, or the cost of hydrogen imported to a hydrogen network is taken as proportional to its flowrate, and is given by:

The credit for the gas sent to the fuel system is calculated from the heating value of the combustible components of the gas, i.e. hydrogen and methane [17]:     (45) Cfuel ¼ yH2 DHc;H2 þ 1  yH2 DHc;CH4 eHeat where DHc is the standard heat of combustion and eHeat is the unit price of heat energy. The capital cost of a compressor is related to its power consumption, as given in Peters and Timmerhaus [39], the relationship is a linear one: Ccp ¼ acp þ bcp Power

(46)

where acp and bcp are constants. The capital cost of a PSA unit is correlated as a simple linear function of the feed flowrate according to Towler et al. [4]: CPSA ¼ aPSA þ bPSA FPSA

(47)

where aPSA and bPSA are cost coefficients for PSA. Membrane cost is far more complex to estimate due to high nonlinearity. This can be avoided by using the approximation regressed by Liao et al. [21]:   Cmemb ¼ amemb þ bmemb =ymemb;H2 Fmemb (48) where amemb and bmemb are cost coefficients for membrane. When considering the capital cost of a desulfurization column, the diameter and the height of the column should be calculated. Thus the problem might be hard to solve. Consequently, the capital cost of a desulfurization column is simply assumed to be $4552 per year per stage in the present work, according to Hallale [28] and Chen [40]. This simple correlation is convenient for illustrating the basic targeting method. Cdspl;i0 ¼ 4552NT;dspl;i0

cpl˛PL; i0 ˛I

(49)

According to Hallale [17], the investment of a pipe is expressed as a function of its length as well as the square of its diameter. The diameter squared, D2, is determined from the flowrate that goes through it: D2 ¼ 4Fr0 =pur

(50)

where u is the superficial gas velocity (usually 15e30 m/s), r is the density of the gas at the design conditions and r0 is the density at standard conditions.

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Fig. 4 e The existing hydrogen network in the base case. The length of a pipe, [, required connecting a source and a sink is not simply the straight-line distance between them, but the pipe bridges in real plants, which already took a convoluted route for reasons of layout or safety. The actual cost given by Hallale [17] is: Cpipe



 ¼ apipe þ bpipe D [ 2

Hplant

(51)

It should be stressed out that, as some of the cost estimating equations were obtained decade ago, corresponding NelsonFarrar cost indexes [41,42], NF, are introduced to account for the currency inflation. The conversion equation can be expressed as [43]: Ct2 ¼ Ct1 NFt2 =NFt1

Table 1 e Detailed stream data for base case.

RF

Make-up

(52) Recycle

4.

Case study

In this section a case study is presented to illustrate the application of the methodology developed. A real world refinery base case is chosen as the case study. The base case consists of two hydrogen producers and five hydrogen consumers. The hydrogen producers are hydrogen plant (HPlant) and catalytic reformer (RF). The hydrogen consumers are polyethylene unit (PE), gasoline hydro-treater (GHT), gasoline and diesel hydro-treater (G/DHT), polypropylene unit (PP) and diesel hydro-treater (DHT). The base case hydrogen network including the placement of the existing pipes and compressors is shown in Fig. 4. For the HP and LP purge streams of GHT unit which has already been recovered for reuse are not shown in the diagram. In addition, there is an idled PSA plant with feed and residual pressure specified at 2  106 Pa and 2  105 Pa which is not shown in the base case diagram. Since the hydrogen concentration of LP off-gases is not high enough for directly reuse and yet there’s recovery potential, the idled PSA plant is considered to be put into use. The recovery ratio and product hydrogen purity of the PSA unit are at 0.9 and 99% respectively. Table 1 gives detailed stream data and relevant operating conditions, while the physical pipe distances

HP-Purge

LP-Purge

F (mol/s) P (Pa) yH2 (%) yH2S (%) F (mol/s) P (Pa) yH2 (%) yH2S (%) F (mol/s) P (Pa) yH2 (%) yH2S (%) F (mol/s) P (Pa) yH2 (%) yH2S (%) F (mol/s) P (Pa) yH2 (%) yH2S (%) F (mol/s) P (Pa) yH2 (%) yH2S (%)

PE

GHT

G/DHT

6.20 2  106 99.00 0

3.72 2  106 99.00 0

27.28 2  106 99.00 0 33.48 2  106 90.00 0 60.76 2  106 94.04 0 724.07 6  106 95.00 0.00476 6.20 6  106 95.00 0.476 8.68 1  106 64.00 1.79

6.20 2  106 99.00 0

3.72 2  106 99.00 0

PP

DHT

3.72 2  106 90.00 0 3.72 2  106 90.00 0

62.00 2  106 90.00 0 62.00 2  106 90.00 0 1064.39 6  106 84.00 0.00476 12.40 6  106 84.00 0.476 3.72 1  106 60.00 2.21

Table 2 e Piping distances between the units for base case (m). Source

HPlant RF G/DHT DHT PSA

Sink PE

GHT

G/DHT

PP

DHT

400 1100 600 1300 1300

1900 1200 2100 1000 1000

200 900 0 1100 900

2400 1700 2600 1500 1500

900 200 1100 0 0

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Table 3 e Inlet stream concentration constraints of each hydrogen consumers.

yMin j;H2 ð%Þ yMax j;H2 S ð%Þ

PE

GHT

G/DHT

PP

DHT

86 0

86 0

86 0.44

86 0

84 0.45

Table 4 e The computation effort of the solver. Item

Time/s

Item

Time/s

Parsing Preprocessing Navigating Relaxation Total time elapsed

0.03 0.34 16.38 249.97 12000 s

Local Tightening Marginals Probing

488.67 172.98 0.25 11071.38

between the units are shown in Table 2. The inlet stream hydrogen constraints and impurity constraints are illustrated in Table 3. Furthermore, because the purge streams from G/ DHT unit and DHT unit contains H2S contaminant which will cause catalyst deactivation in the polyethylene unit and polypropylene unit, they are not allowed to be used in these units. The prices of hydrogen produced by hydrogen plant and catalyst reformer are 0.020 RMB/mol and 0.046 RMB/mol respectively. Electricity costs 0.75 RMB/kw h, and fuel costs 2.369  108 RMB/J. The capital cost is annualized in 5 years, with 5% interest rate per year.

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As shown in Fig. 4, four purge streams of hydrogen consumers with high hydrogen concentration are released as fuel gas, due to its high content of hydrogen sulfide. In order to take good use of the hydrogen in these streams, desulfurization columns are considered. Four desulfurization columns are preinstalled, which are denoted as ds1,3, ds1,5, ds2,3, ds2,5 corresponding to the HP purge streams and the LP purge streams of G/DHT unit and DHT unit respectively. According to the pressure data of the streams, the desulfurization columns are classified into two pressure levels: pressure level 1 (6  106 Pa) and pressure level 2 (1  106 Pa). For the zero pressure difference, the HP purges from G/DHT unit and DHT unit are allowed to be mixed and share the same desulfurization column (ds1,3 or ds1,5), and so are the LP purges. It should be emphasized that the physical location of the new desulfurization units are different, which make the columns different from each other. The MINLP problem is solved in GAMS software [44] using Baron [45] as solver (based on the PC specification: Intel D CPU 3.00 GHz, 4 GB RAM). A report of the solver calculation effort is listed in Table 4: In order to cut down the computational effort, the lower and upper bound for the variables are provided based on the industry experience. The initial values of the variables are given according to the refinery operating data. The optimal flowsheet from the MINLP optimization is shown in Fig. 5. The optimal result involves two new desulfurization columns, an additional compressor and several pipes, as represented by dashed lines. In the optimum result

Fig. 5 e Optimum retrofitted hydrogen network.

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Table 5 e Optimized design parameter for desulfurization towers.

Rdspl;i NT;dspl;i

ds1,3

ds2,5

0.814 5.247

0.828 5.020

Table 6 e Cost breakdown for the optimal solution of base case. Existing network Annual operating cost/RMB: HPlant: 2.250  107 RF: 1.380  108 Electricity: 1.047  107 Fuel: 5.252  106

Total annual cost: 1.657  108

Optimized network Annual operating cost/RMB: HPlant: 6.968  106 RF: 1.380  108 Electricity: 1.087  107 Fuel: 3.996  105 Desulfurization: 4.786  105 Annual capital cost/RMB: DS tower: 1.660  106 Compressor: 3.896  105 Piping: 0.636  105 Total annual cost: 1.580  108

removal units into hydrogen distribution networks. The optimization of the case study demonstrates an ultra-high efficient hydrogen usage compared to the original network. The technique can fully account for not only the trade-offs between HNI and MEN, but also the trade-offs between operating cost and investment cost. It should be noted that several simplifications in the MEN have been made in this study. A more rigorous method could cover the following aspects:  The optimization of the MSA in the MEN should be dedicatedly concerned.  The more general situation, when the absorption factor A s 1, will be included. This would make the problem more non-linear and result in a bigger superstructure. The current strategy for industrial application is to first use the proposed method to perform an initial analysis and roughly evaluate the hydrogen reuse potential through desulfurization and the corresponding investment cost. In order to build up a more accurate and general model, these points shall be covered in our future work.

Acknowledgements scheme, the HP purge stream of DHT unit is sent to mix with the HP purge stream of G/DHT unit, and desulfurized in ds1,3. 64.4% of the outlet stream from ds1,3 is sent to the recycle hydrogen compressor of G/DHT unit and reused. While the LP purge stream of G/DHT is sent to mix with the LP purge stream of DHT unit, and desulfurized in ds2,5, the outlet stream is recompressed to 2  106 Pa and then sent to PSA unit. The product from the PSA unit is sent to the make-up hydrogen compressor of DHT unit and reused, while the residual stream served as fuel gas. The optimized desulfurization ratio Rdspl;i0 and theoretical plate number NT of each desulfurization column are demonstrated in Table 5. With these new equipments, 82.8% of the purge streams are recovered and reused, contributing to the reduction of 25.68 mol/s on the hydrogen plant production, thus ￥ 7.67 million in TAC is saved. It should be noted that the capital cost of PSA is not included in this case. Detailed comparison is illustrated in Table 6. Comparing to the annual operating cost being saved (￥ 9.783 million), the additional annual capital cost (￥ 2.113 million) is acceptable.

5.

Conclusions

Hydrogen resource is a critical issue in refineries, as it is a valuable and environmental-friendly energy resource. Due to its corrosive nature on equipment and damage to certain catalysts, hydrogen sulfide is also an important aspect in petroleum refining processes. The economical use of hydrogen has been widely studied in HNI, while the efficient removal of hydrogen sulfide has been well developed by MEN integration. These two networks are tightly connected in refineries. A new modeling and optimization methodology has been developed to investigate the combination of these two systems. The desulfurization ratio, Rdspl;i0 , is employed to incorporate H2S

The financial support provided by the National Natural Science Foundation of China (21106129), the Specialized Research Fund for the Doctoral Program of Higher Education (20110101120019), the Fundamental Research Funds for the Central Universities (2011QNA4032) and the National Basic Research Program of China (2012CB720500) are gratefully acknowledged.

Notation Sets CP DS H I J M O PF PL

set of compressors set of desulfurization units set of hydrogen utilities set of hydrogen sources set of hydrogen sinks set of stream components set of all possible matches set of purifiers set of pressure levels

Symbols A Af a,b C D F fi G L N NF NT

absorb factor annualizing factor cost coefficients cost, RMB pipe diameter, stream flow rate, mol/s fractional interest rate per year gas flow rate of an absorber liquid flow rate of an absorber number Nelson-Farrar cost indexes theoretical number of trays

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 8 1 6 3 e1 8 1 7 4

ny P R TAC t U X Y DHc m c ex u [ r r0

number of years pressure, Pa removal ratio total annual cost operating time, s upper bounds of flow rate concentration of absorbents binary variable denoting the existence of a match standard heat of combustion coefficient in equilibrium relation constant in equilibrium relations unit price of x superficial gas velocity, m/s piping length, m density at the design conditions density at standard conditions

Subscripts cp compressor ds desulfurization tower exist existing equipment fuel fuel system h hydrogen utility hydrogen source/the corresponding pre-installed i,i0 hydrogen removal unit j hydrogen sink m component of a stream memb membrane MSA mass separating agent consumption new new equipment p splitter pf purifier pipe pipe power power consumption pl pressure level q mixer re recycle hydrogen Superscript * equilibrium composition Ca capacity of relative unit De demand of relative unit in inlet out outlet Max maximum Min minimum P product R residual Tar target composition

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