Process unit mass balance oriented mathematical optimization for

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Process unit mass balance oriented mathematical optimization for hydrogen networks Qiao Zhang, Huachao Song, Guilian Liu, and Xiao Feng Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04318 • Publication Date (Web): 20 Feb 2018 Downloaded from http://pubs.acs.org on February 22, 2018

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Industrial & Engineering Chemistry Research

Process unit mass balance oriented mathematical optimization for hydrogen networks Qiao Zhang*, Huachao Song, Guilian Liu and Xiao Feng (School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, China, 710049)

Abstract: Hydrogen is becoming a more and more crucial resource for chemical industries. Hydrogen network integration is an effective tool in hydrogen resource conservation. Hydrogen sources inflow and outflow from different process units occurring consumption, generation, mixing and separation and consequently there is dependence for both hydrogen and contaminants species among those streams, especially when throughputs of process units fluctuate. Hydrogen network integration should account for such dependence so that real properties including flow rate and concentration can be obtained to perform reliable network integration. This paper proposes process unit mass balance to describe the dependence of hydrogen streams and establishes a corresponding

superstructure

as

problem

illustration.

A

mixed

integer

nonlinear

programing(MINLP) model is built to synthesize hydrogen networks for fresh hydrogen minimization. This method considers the tolerable disturbance of process unit and reliable fresh hydrogen target and internal sources profile. Two cases are employed to demonstrate its application. Key words: process unit mass balance; hydrogen network; mathematical model; integration; reliable

1. Introduction *

Corresponding author: Tel. 86-29-82664376. E-mail: [email protected]

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In order to produce clean fuels and environmental friendly chemicals, hydrogen has been widely used in chemical industries, especially petroleum enterprises. In recent years, as increasing hydroprocessing capacity and stricter environmental regulations, hydrogen consumption and its deficiency are both rising sharply. Hydrogen is mainly generated by steam methane reforming(SMR), an intensive energy consuming and CO2 emitting process and therefore efficient hydrogen resource usage makes great sense to energy saving and pollution reduction. Network integration is such an effective way has been a mature and widely applied methodology, which consists of pinch analysis and mathematical programming methodology. As pinch analysis methods, Alves and Towler1 plotted hydrogen concentration versus flow rate and hydrogen surplus diagram to determine the minimum fresh hydrogen demand. El-Halwagi et al.2 , Almutlaq3 and Zhao et al.4 proposed respective material recovery pinch diagram to minimize fresh hydrogen consumption by topologizing source and sink composite curves. Agrawal and Shenoy5 developed limiting composite curve as unified method for targeting and design of water and hydrogen networks. Based on those initial pinch diagrams, triangle rule coupled pinch diagrams6,7, PFFR for maximum purification feed flow rate8, optimum feed flow rate9, pinch sliding method10, optimal purification process identification11 and its integration with flow rate12 and concentration are successively developed to address hydrogen network integration problems with purification reuse, so as to further reduce fresh hydrogen consumption. In order to substitute algebraic operation for visual solution, Foo et al.13, Foo and Manan14 and Yang et al.15 set up respective algebraic targeting procedures on the basis of pinch analysis to minimize fresh hydrogen consumption of single contaminant hydrogen networks. However, those methods aforementioned can only be suitable to the case of single contaminant hydrogen networks. For


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multi-contaminant hydrogen networks, Zhao et al.16 extended hydrogen surplus diagram method1 from single to multiple case by selecting minimum target among all possible contaminant concentration sequences. Liu et al.17 proposed concentration potential for water networks to optimize allocations among sources and sinks to minimize the fresh water demand and it is also suitable to multi-contaminant hydrogen network case. Zhang et al.18 put forward a comprehensive ranking rule for sources and sinks to perform hydrogen allocation and targeting simultaneously. The pinch analysis based methods stated all above are based on absolute concentration property, indicating total flow rate of hydrogen and contaminants and absolute concentration of each component. In 2016, Zhang et al.19 first proposed relative concentration based pinch analysis for single contaminant hydrogen network synthesis. This method constructs source and sink composite curves in contaminant load versus hydrogen flow rate diagram and identifies the minimum fresh hydrogen demand by shifting them. As total flow rate and concentration normalization constraints relaxation, this method is superior to its counterparts5,6,8,9,11,12 in fresh hydrogen minimization when purification reuse is considered. Pinch analysis takes advantages of clear concepts and visual targeting process. However, such visual solution is not suitable to complex constraints network synthesis problems. Mathematical programming methodology is generally implemented by superstructure configuration, mathematical model and solution. Hallale and Liu20 maximized hydrogen direct reuse through considering pressure and equipment constraints optimized by a nonlinear programming (NLP) model. Liu and Zhang21 made trade-off of operation and capital cost among purifiers placement strategies. Ahmad et al.22 considered varying operation conditions and proposed multi-period hydrogen network optimization. Jiao et al.23 further addressed several



uncertainties for the design of flexible hydrogen network through a MINLP model. Liao et al.24,25 established MINLP models to maximize hydrogen reuse with compressors, purifiers, and threshold problems. Wu et al.26 set up a MINLP model employing hydrogen-to-oil ratio to minimize the total exergy consumption, and afterwards generalized it to minimize the total cost and the number of compressors27. Zhou et al.28 considered hydrogen sulfide removal and built a MINLP model to minimize total annual cost and soon Zhou et al.29 proposed sustainable hydrogen networks with both economic and environmental aspects and used a MINLP model to address optimization. Deng et al.30 employed intermediate hydrogen header and the number of connections to enhance expandability and flexibility of hydrogen network. Lou et al.31 carried out robust optimization for hydrogen network through linear correlation of hydrogen demand to throughput and linear programming (LP) model. Kuo and Chang32 proposed improved multi-period hydrogen network model considering variational case and adding seasonal variations and design options to minimize total operating cost. Liang et al.33 performed flexible and debottlenecking analysis of multi-period hydrogen networks by considering possible operational conditions fluctuation to minimize total annual cost. Jia and Zhang34 formulated a NLP model with light hydrocarbon production and integrated flash calculation to improve hydrogen network performance. Although the generation of C1-C3 and its influence on flash separation is considered, other contaminants, such as H2S and NH3 are not included. Jagannath et al.35 divided hydrogen networks into hydrogen sources, process unit, purifiers and fuel sinks to minimize total annualized cost. Although this method considers the balance of hydrogen inflow-outflow for each process unit, only one contaminant is taken into consideration. Unama et al.36 performed a flexible analysis that investigated the influence of crude oil composition, reaction temperature and pressure on H2S,


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light hydrocarbon and hydrogen profile in process streams, so as to obtain the minimum hydrogen cost. Those mathematical methods are performed by absolute concentration property, on the basis of relative concentration pinch diagram19, Zhang et al.37 further proposed mixed integer linear programming (MILP) model for fresh hydrogen minimization of multi-contaminant hydrogen network under three different circumstances. The results show that relative concentration property can reduce fresh hydrogen consumption for multi-contaminant hydrogen networks even more obvious than single contaminant case as the former relaxed concentration normalization for several contaminants while the latter is for only one. Mathematically, the more constraints relaxation is, the more improvement of objective will be. Mathematical programming methodology can deal with complex optimization problems and easily add or eliminate constraints, so it has been used even widely. However, they almost focus on certain throughout of each hydroprocessing unit and perform corresponding solution, namely static network. It is obvious that static case is not consistent with practical refinery hydrogen network of fluctuant case. In hydrogen networks, streams containing hydrogen are hydrogen sources while hydroprocessing units consuming hydrogen are process units. All hydrogen source streams excepting fresh hydrogen are internal sources as they are not fresh resource but distributed among all process units as input or output hydrogen streams, such as recycle hydrogen, purifier product hydrogen, purge gas, discharged fuel gas etc. For static hydrogen network, the inflow-outflow streams are steady state, so all streams can be treated as constants and solved by source-sink mapping superstructure. However, practical throughputs in refinery hydrogen networks have fluctuation which will cause fresh hydrogen demand and internal sources change as such circumstance is production condition change. Exactly, there is mass balance for both hydrogen and



contaminant components in each process unit under fluctuant hydrogen networks. Either pinch based conceptual or mathematical programming methods, their drawback is treating internal sources as fixed streams. Therefore, compared with the real minimum fresh hydrogen consumption target for static hydrogen network, the results determined by existing hydrogen network integration methods may not be reliable, and even worse results can happen on those for fluctuant cases. On such point of view, process unit mass balance is similar to water networks38, whose superstructure is water using unit oriented and mathematical model encompasses inlet-outlet water balance. Aiming to such goal, this paper proposes a rigorous process unit mass balance for hydroprocessing unit on the basis of relative concentration property to reflect the flow, conversion and profile of hydrogen and contaminants exactly, and then constructs a corresponding process unit mass balance oriented superstructure as problem illustration. Consequently, all necessary constraints are considered to establish a mixed integer nonlinear programming(MINLP) model for accurate process stream properties identification and fresh resource minimization. The rest section of this paper is organized as follows, section 2 describes the process unit mass balance oriented superstructure, and then section 3 is problem statement. Next, mathematical model is presented in detail. Case study is employed to demonstrate this method in section 4 and finally the conclusions are placed in the end.

2. Process unit mass balance oriented superstructure Traditional hydrogen networks integration problems, absolute and relative concentration basis, are performed by source-sink mapping superstructure, as show in Figures 1 and 2. On this occasion, sources except fresh resource are termed as fixed streams and sinks are certain demand with given flow rates and concentrations. Therefore, the synthesis is to minimize fresh hydrogen


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consumption with those known parameters. The difference of these two superstructures is the property benchmark.

Figure 1 Traditional absolute concentration based source-sink mapping superstructure for hydrogen networks

Figure 2 Relative concentration based source-sink mapping superstructure for hydrogen networks

20

37

Figure 1 uses total flow rate F and absolute concentration C to quantify sources and sinks and Figure 2 employs hydrogen flow rate H and relative concentration RC to improve the performance of previous one. Although relative concentration method can save more fresh hydrogen than its absolute counterpart, such source-sink mapping superstructures are not consistent with practical process because hydrogen sources are not independent but dependent. Figure 3 is a typical hydrorocessing process flowsheet, where fresh hydrogen and internal source are mixed and then sent to reactor. Separator is placed after reactor to remove the generated contaminants and the unreacted hydrogen is partly reused as recycle hydrogen and partly sent to other units or discharge. However, it is obvious that there is mass balance for hydrogen and contaminants of input and output streams after their consumption and generation, and furthermore the amounts of both consumption and generation are subject to the feed oil throughput. When fresh hydrogen flow rate or feed oil throughput fluctuates, the consumed hydrogen and generated contaminants also deviates current level, and so do the recycle hydrogen and the vent gas to other units or discharged. Furthermore, the larger throughput fluctuation margin is, the more deviation will be. Therefore, inflow, mixing, consumption, generation, accumulation and outflow of hydrogen and contaminants should be inspected together to form mass balance, so that the real flow rates, concentrations and their profile can be obtained to serve hydrogen network integration.



According to existing research and application, especially Jia and Zhang34 and Umana et al.36 mentioned in their papers, the contaminants involved in refinery hydroprocessing operations are H2S, NH3 and light hydrocarbons. Besides, practical refinery hydroprocessing operations also care about CO2, and CO, and they treat hydrocarbons and oxycarbide together as one component because they have similar influence on reactions and catalysts activity. Therefore, the contaminants considered in this paper are H2S, NH3 and carbon based hydrocarbons and oxycarbide.

Figure 3 A typical hydroprocessing process flowsheet

1

The red rectangle in Figure 3 highlights the process unit including reactors and possible separators. Its input and output are hydrogen streams with flow rate and species concentrations. An important premise should be primarily put forward: for static hydrogen network, the throughput for each process unit is certain, so the total pure hydrogen demand(hydrogen flow rate) is the sum of all units and it is also certain. Thus, whatever integration methods is employed, the hydrogen flow rate demand should be guaranteed while contaminant concentrations can be fluctuant as long as their concentrations are no larger than upper limits of corresponding process units. For fluctuant networks, total hydrogen flow rate depends on oil throughputs and input and output hydrogen streams and their compositions are also variational. The variation of hydrogen streams will disturb the process stability. Practically, the process unit shown in Figure 3 contains reaction and separation units, whose performances can be stable within certain disturbance of operation conditions. Once the disturbance exceeds certain level, the performance of process unit can not be guaranteed. However, hydrogen network integration will certainly involve retrofit, and


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therefore the retrofit should not exceed such level, otherwise the results are not reliable. Therefore, by taking into such disturbance tolerance into consideration, Figure 4 is the process unit mass balance oriented superstructure of hydrogen network after abstraction of Figure 3. Starting from one process unit j, for a hydrogen network with n process units and s contaminants, the process unit mass balance for all units forms a whole network superstructure shown in Figure 4. In each process unit j, hydrogen flows into the process unit through fresh hydrogen and other internal sources mixture where simultaneously contaminants are entrained. Hydrogen is consumed while contaminants are generated in chemical reaction. After reaction, the unreacted hydrogen and contaminants are sent to other units or discharge. Quantitatively, variable H represents hydrogen flow rate and variable RC denotes relative concentration. Variable V is feed oil throughput and parameter L is contaminant generation coefficient. Indices FH is short for fresh hydrogen, C is short for consumption, D is discharge and T is used to present internal source. Sets i, j and k represent internal source output of unit i, current process unit j and internal source input of unit k, respectively. Variable HjC is hydrogen consumption of chemical reaction in unit j, The product of parameter Lj,m times variable Vj, in oher words, Lj,m⋅Vj is generation of contaminant m and variable HjFH is fresh hydrogen consumption of unit j. Variables HTi,j and HTk,j are hydrogen supply from unit i to unit j and that from unit j to unit k, respectively. Variable HD is hydrogen discharge and generally to fuel gas system. Each variable RC with same set as that of H is the relative concentration of this stream.

Figure 4 Process unit mass balance based superstructure of hydrogen networks

Such superstructure indicates that on the basis of relative concentration property, the



hydrogen demand of each process unit is supplied by the mixture of fresh hydrogen and other internal sources. After reaction, the unreacted hydrogen, entrained and generated contaminants can supply hydrogen for each process unit. On contrast, each process unit can receive hydrogen from each unit. What should be emphasized is that differing to water networks, the internal source outputs a unit could be reused by itself, so i can equal to j and so does k and j. The reason is hydroprocessing unit has its recycle hydrogen stream for reaction while water using unit does not need. Specifically, when i, j and k are identical for a process unit, such hydrogen stream is recycle hydrogen. Meanwhile, contaminants mixture and transfer are accompanied during hydrogen supply and demand. Technically, each unit has content requirements of hydrogen and contaminants. Hydrogen to feed oil ratio on volume basis should not be lower than the floor level while relative concentration of each contaminant should not be higher than its upper limit. In addition, hydrogen to oil ratio involves throughput of each unit, and thus both fixed and fluctuant throughput cases, namely static and fluctuant networks37, can be performed in this superstructure. On account of relative concentration property and mass balance of hydrogen and contaminants in process units, such process unit mass balance oriented superstructure can entirely describe the inflow and outflow, consumption, generation, mixture and transfer of hydrogen and contaminants in each unit. When flow rate or concentration of any stream changes, its dependent streams can be accurately quantified by their mass balance relationship. As long as the retrofit is within tolerable disturbance, the target is reliable. Therefore, this superstructure is superior to traditional source-sink mapping superstructure on hydrogen network synthesis problem illustration.

3. Problem Statement


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For a hydrogen network with n process units, s contaminants. Detailed presentation of parameters, assumptions, variables and objective considered in this method are stated as follows. 3.1 Parameters 1 Current total flow rate and absolute concentration of both hydrogen and contaminants for each internal sources and fresh hydrogen; 2 For each process unit, minimum hydrogen to oil ratio on volume basis and upper limit of relative concentration for each contaminant; 3 For each process unit, current throughput, the correlation of feed throughput and hydrogen demand and the correlation of feed throughput and contaminants generation. 4 Upper and lower bounds of all hydrogen flow rate from fresh resource to process unit, as well as that from process unit to other units. 3.2 Model assumptions 1 Process unit mass balance accounts for chemical reactive hydrogen consumption and contaminants generation; 2 Only feed oil throughput is considered as the changing condition, and specifically the correlation of feed oil throughput and hydrogen demand for each process unit is linear. The same correlation is also applied to feed oil throughput and the amount of contaminant generation; 3 Pressure constraint is satisfied but not optimized in this model. 3.3 Variables and objective All hydrogen supply flow rate(H), relative concentration(RC) of all internal sources, fluctuation factor εj, throughput Vj and network structure xi,j are decision variables. The goal is to target real minimum fresh hydrogen consumption and profiles of internal sources as changing throughput of feed oil within tolerable disturbance, so as to investigate the influence of process unit mass balance on the whole network integration.



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4. Mathematical formulation The mathematical model encompasses constraints of property benchmark, process unit mass balance, hydrogen supply and demand, static and fluctuant networks and network structure. The target is to minimize fresh hydrogen consumption. 4.1 Relative concentration F =H +I

(1)

H = F ⋅ yH 2

(2)

I m = F ⋅ ym , (m = 1,2...s)

(3)

s

∑y

m

+ yH 2 = 1 (m = 1,2...s)

(4)

m =1

Those four Equations are absolute concentration definition and among them parameters F, H and I represent total flow rate, hydrogen and contaminant flow rates, ym and yH2 denote contaminant and hydrogen absolute concentrations, respectively. Eqs.(1)-(3) describe total flow rate, hydrogen flow rate and contaminants flow rate, respectively. Eq.(4) defines the absolute concentration normalization. After transformation, Zhang et al.19 proposed relative concentration: RCm =

Fym y = m ,(m = 1,2...s) FyH 2 yH 2

(5)

Eqs.(1)-(5) denotes relative concentration property benchmark and indicates the substitution of hydrogen flow rate and contaminants relative content for absolute basis. 4.2 Process unit mass balance n

n

H FH + ∑ HiT, j = H Cj + H Dj + ∑ H kT, j (i = 1,2...n, j = 1,2...n, k = 1,2...n) j i =1

(6)

k =1

Eq.(6) presents the hydrogen mass balance of process unit j. As illustrated in Figure 4, the left side consists of fresh hydrogen and internal sources is the inflow while the right outflow are consumption, discharge and internal supply. n

n

FH T T C Gen D D T T H FH j RCm + ∑ H i , j RCi , m + H j RC j , m = H j RC j , m + ∑ H k , j RCk , m ( j = 1,2...n, k = 1,2...n, m = 1,2...s) i =1

k =1

Where index Gen is contaminant generation. Similarly, Eq.(7) indicates the


(7)

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contaminants mass balance for each contaminant of process unit j, in which contaminants are embedded in fresh hydrogen, internal sources and simultaneously generated in reaction while accumulated and transported to other units and discharge. H Cj RCGen j , m = Lj , m ⋅ Vj ( j = 1,2...n, m = 1,2...s)

(8)

Eq.(8) assumes the linear correlation of contaminants flow rate and feed oil throughput for each contaminant in each process unit. 4.3 Hydrogen supply and demand constraints n

H FH + ∑ H iT, j ≥ H Cj ( j = 1, 2...n) j

(9)

i =1

Eq.(9) is hydrogen demand constraint, indicating that the inflow hydrogen flow rate should be no less than the reactive hydrogen consumption for each unit. n

n

FH T T FH H FH + ∑ H iT, j ) RC Cj , m,max ( j = 1,2...n, m = 1,2...s) j RCm + ∑ H i , j RCi , m ≤ ( H j i =1

(10)

i =1

Where index max is the relative concentration upper bound of contaminant m in unit j. Eq.(10) presents relative concentration should be no larger than its upper limit for each contaminant in each unit. 4.4 Static and fluctuant networks The same as the fluctuant network definition in relative concentration analysis of Zhang et al.37, this paper also employs linear correlation of hydrogen consumption and oil feed throughput, and simultaneous fluctuant factor to represent network fluctuation. They are given by Eq.(11) and Eq.(12), respectively. H Cj = K jV j + b j , j ∈ {1, 2,3...n}

(11)

Vj = (1 + ε j )VO, j , j ∈{1,2,3...n}

(12)

Where parameters Kj and bj are linear coefficients of oil throughput to hydrogen consumption in unit j and variable εj is the fluctuation margin of current oil throughput



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Vo,j(parameter) to target throughput Vj(variable). The margin εj will be specified upon practical refinery production and historical database. In addition, relative concentration is theoretically derived from hydrogen to oil ratio (HTO)26, and thus the minimum HTO should be guaranteed. H Cj Vj

≥ HTO min j , j ∈ {1,2,3...n}

(13)

Where index min denotes the lower bound. Eq.(13) restricts the lower bound of hydrogen to oil ratio on volume basis for each unit. 4.5 Network structure For hydrogen networks, pressure and available pipelines among process units are also constraints and their availability determines the network structure. Since pressure constraint is not optimized in this paper, the same as fluctuant network synthesis method37, binary variables xi,j, xi,k and xj are employed to describe the network structure among all streams and units. Meanwhile, the flow rate of hydrogen supplied to each unit should be neither too small nor too large, so both upper and lower bounds are needed to guarantee a meaningful allocation. HiT, ,jLO ⋅ xi , j ≤ HiT, j ≤ HiT, ,jUP ⋅ xi, j (i = 1,2...n, j = 1,2...n)

(14)

HkT,,jLO ⋅ xk , j ≤ HkT, j ≤ HkT,,UP j ⋅ xk , j ( j = 1,2...n, k = 1,2...n)

(15)

, LO ,UP H FH ⋅ x j ≤ H FH ≤ H FH ⋅ x j ( j = 1,2...n) j j j

(16)

Where indices LO and UP indicate lower and upper bounds of hydrogen. Eqs.(14)-(16) denote the upper and lower bounds of hydrogen flow rate from unit i to unit j, from unit j to unit k, as well as fresh hydrogen to process unit j, respectively. Furthermore, those upper and lower bounds are practical refinery data so that within those bounds any retrofit of hydrogen network will not exceed the tolerable disturbance. 4.6 Objective function Process unit mass balance is proposed in this method to reflect the real profile of internal


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sources and practical minimum fresh hydrogen demand under the same condition as existing methods, so the objective function is minimum fresh hydrogen consumption. n

Min

∑H

FH j

/ yH2

(17)

j =1

In summary, Eqs.(1)-(16) are constraints and Eq.(17) is the objective function. Since there are binary variables xi,j, xk,j and xj, and nonlinear terms, which are the products in Eqs.(7), (8) and (10), this is a mixed integer nonlinear programming(MINLP) model.

5. Case Studies In this section, two cases are employed to demonstrate the application and explain the superiority of the proposed method quantitatively. Case 1 is from literature1 and the second case is a practical refinery hydrogen network in China. Case 1 is employed as static network and Case 2 is used to perform fluctuant case. 5.1 Hydrogen network with single contaminant Case 1. This is a case from literature1, and it is a single contaminant hydrogen network. Tables 1 and 2 show the flow rate and absolute concentration of all sources and sinks and Figure 5 illustrates the current network. Specifically, the hydrogen demands of the 4 process units are the flow rate of hydrogen consumed in the 4 process units, and each one is the difference of input hydrogen flow rate and output hydrogen flow rate of the process units. Targeted by hydrogen surplus diagram integration method1, the minimum fresh hydrogen consumption is decreased from current 277.2 mol/s to 268.8 mol/s, and the corresponding waste discharge is also decreased 110.9 mol/s to 102.5 mol/s.

Table 1 Hydrogen network case with single contaminant



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Table 2. Source Data for the Hydrogen-Producing Processes in Example 1

Under the same hydrogen allocation network, the hydrogen supplied to units HCU and NHT are intact, and meanwhile the output hydrogen streams of these two units are also original values. We can retrofit hydrogen network from the original one shown in Fig.5 to Figure 6 which is determined by literature 1, and also Figure 7 given by this method. The comparison of blue numbers can clarify the reason why this method is reliable. In Figure 6, to save fresh hydrogen from 277.2 to 268.8 mol/s, and the discharged 102.5 mol/s, 70 % of CNHT purge as fuel gas, the total hydrogen stream sent to CNHT and DHT are decreased from 582.1 mol/s with hydrogen purity 82.1% to 573.7 mol/s with hydrogen purity 81.9%. As a result, the recycle hydrogen of unit DHT should be reduced from 277.2 to 271 mol/s and its purge gas 75.5mol/s should be sent to unit CNHT. Meanwhile, the recycle hydrogen of CNHT is reduced from 415.8 to 354.9 mol/s while its purge is increased from 41.6 to 102.5mol/s. In other words, the recycle hydrogen of unit DHT is reduced by 6.2mol/s and that of CNHT is reduced by 60.9 mol/s, equivalently 500 and 4911 Nm3/h. Therefore, it is probably that such retrofit is not reliable. On contrast, the retrofit network in Figure 7 is very close to current network Figure 5 and the recycle hydrogen for either process unit is intact and the input internal sources are from 277.2, 82.1% to 274, 82% and 304.9, 82.1% to 301.7, 82.1%, and the fresh hydrogen is from 277.2 to 270.8 mol/s, respectively. The reason for such result is that under process unit mass balance constraint, the contaminant amount input each process unit is rigorously restricted. In Figure 6, the contaminant flow rate of unit CNHT is 354.9×(1-70%)+75.5×(1-73%)+300.7×(1-81.9%)=181.3mol/s

while

in

Figure

5

it

is

415.8×(1-70%)+304.9×(1-82.1%)=179.3mol/s. The difference of the two is just 2 mol/s, which is


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also the difference of minimum fresh hydrogen flow rate of Figures 6 and 7: 270.8-268.8=2 mol/s. That is to say, 2 mol/s extra fresh hydrogen is used to avoid overload contaminant input of CNHT unit. Meanwhile, internal source distribution is from 581.2 mol/s, 82.1% to 575.7, 82%. Thus, although traditional methods can supply such a target, it is feasible but not necessarily reliable because they does not consider the tolerable disturbance and can not give hydrogen network with corresponding flow rate and concentration profiles of internal sources. Therefore, with process unit mass balance constraint, the fresh hydrogen target and the retrofit network can be guaranteed within the tolerable disturbance and thus the fresh hydrogen target is more reliable. Furthermore, the minimum fresh hydrogen targets obtained in this case is only static network, case 2 is employed below to discuss the case of fluctuant network.

Figure 5 The current hydrogen network of case 1

Figure 6 The optimized hydrogen network with traditional pinch analysis

Figure 7 The optimized hydrogen network with process unit mass balance

(unit for all flow rate numbers in Figures 5-7 is mol/s and all percentages are mol fraction)

5.2 Hydrogen network with multiple contaminants Case 2 is a practical multiple contaminants refinery hydrogen network in China. Table 3 shows the current data and maximum fresh hydrogen flow rate is 100000 Nm3/h with absolute hydrogen concentration of 99.5%. There are 5 internal sources and five hydroprocessing units with three contaminants H2S, NH3 and C representing carbon based components. All flow rates of internal sources and hydrogen demand are current data corresponding to throughputs in the



blankets. Table 4 gives the correlation coefficients of oil throughput to hydrogen consumption in each process unit, as well as the upper and lower bounds of each throughput. Table 5 lists all generation coefficients for the three contaminants in each process unit. All coefficients in Tables 4 and 5 are from refinery historical data base and engineers experience. These coefficients used in Eqs.(8) and (11) explain when throughput increases or decreases by 1 ton, how much hydrogen consumption and contaminants generation increase or decrease will be caused after reaction and separation in process unit shown in Figure 3. For case 2, absolute concentration20, relative concentration37 and process unit mass balance based mathematical programming methods are adopted to make comparison. Figures 8-10 are current static hydrogen networks obtained by absolute concentration, relative concentration and process unit mass balance, and their minimum fresh hydrogen targets are 71785.1, 67019.1 and 69304.8 Nm3/h, respectively. Such results indicate that absolute concentration property is too conservative because hydrogen consumption is restricted by total flow rate requirement which leading to too much hydrogen input when contaminants contents are satisfied, while relative concentration property is too optimistic as lack of hydrogen input-consumption-output balance. The fresh hydrogen target of static network determined by this method is between that obtained by the other two and it is more reliable because process unit mass balance overcomes their drawbacks and also has its own advantage of process unit mass balance. Meanwhile, all numbers in red are variational flow rates and hydrogen concentrations in these three figures. Similar to the internal sources difference in case 1, it can be seen that the flow rate and concentration of the output source from each process unit are also different because of input hydrogen change. Besides, in Figure 10, due to contaminant over generated and


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accumulation of process unit 2, its output source can not be fully reused and a part should be sent to other units or purifier for upgrade. Such phenomena is very common as the purge shown in Figure 3, however Figures 8 and 9 do not even purge any sources but fully reuse them and this is actually because neglecting upper and lower bounds HLO and HUP, as well as contaminants generation and the caused influence on contaminants concentration of output sources.

Table 3 A practical refinery multiple contaminants hydrogen network in China

Table 4 Current crude oil data and their correlation coefficients

Table 5 Contaminants generation coefficients for each process unit

Figure 8 Static hydrogen network of case 2 obtained by absolute concentration

Figure 9 Static hydrogen network of case 2 obtained by relative concentration

Figure 10 Static hydrogen network of case 2 obtained by process unit mass balance (unit for all flow rate numbers in Figures 8-10 is Nm3/h and all percentages are mol fraction)

The aforementioned case is static network, if any throughput in Table 3 fluctuates within its



upper and lower bounds, the network will be fluctuant. We choose process units 3 and 5 to perform fluctuant cases, respectively. The reason is that process unit 3 is key sink while unit 5 is non-key, and the two representatives have different influences on fresh hydrogen demand change37. For this refinery, historical database and practical production reveal that the margin is maximum plus 32% and minimum minus 32% with increment of 4%. Starting from static hydrogen network, fluctuation case can be performed and the results are illustrated by Figures 11 and 12. The fluctuation in each Figure spreads to both plus and minus regions with fresh hydrogen increase and decrease tendency accordingly. Figures 11 and 12 can reflects fresh hydrogen difference among absolute concentration, relative concentration and process unit mass balance methods. Red, blue and black curves represents minimum fresh hydrogen consumption versus fluctuation margin on absolute concentration, relative concentration and process unit mass balance based mathematical methods for process unit 3 and unit 5, respectively. By comparison, whatever the fluctuation margin is, the minimum fresh hydrogen consumption always has deviation to that of the other two methods.

Figure 11 Fresh hydrogen demand versus unit 3

Figure 12 Fresh hydrogen demand versus unit 5

fluctuation

fluctuation

Table 6 Fresh hydrogen consumption and CPU time comparison of three methods for Process unit 3

Table 7 Fresh hydrogen consumption and CPU time comparison of three methods for Process unit 5

Specifically, Tables 6 and 7 show the minimum fresh hydrogen consumption and CPU time


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for three methods under different throughput fluctuation margins. The CPU time for any throughput scenario selected is no more than 1.2 s with zero relative gap, so the solving time is never the bottleneck. As for the fresh hydrogen variational trend in Figure 11, when throughput of process unit 3 decreases from current 65 t/h to minimum capacity 44.2 t/h gradually, its output source will also deviates its current flow rate. Figure 13 quantified such change and the black curve denotes the specific flow rate as fluctuant range. Figure 13 only shows the flow rate deviation, even with regard to its hydrogen and contaminants concentrations. Extremely, when total flow rate of input hydrogen source decreased from current 46900.4(for 65t/h) to 33322.7 (for 44.2t/h)Nm3/h, the corresponding output source also changes from 28248.2 to 20604.3 Nm3/h; conversely, when input hydrogen increases from 46900.4 to 62129.4(for 85.8t/h) Nm3/h, the corresponding output source also changes from 28248.2 to 37486.8 Nm3/h. Figure 14 is the hydrogen network corresponding to minimum throughput of unit 3 in Figure 11 while Figure 15 configured the network with maximum throughput. It is very obvious that for fluctuant network, flow rates and concentrations, which are shown by red numbers, of all internal sources deviates even more from current level, so process unit mass balance method in this paper is definitely more accurate than existing approaches as latter ones neglect such deviation.

Figure 13 The internal source 3 variation as throughput fluctuation of process unit 3

Figure 14 The hydrogen network with minimum throughput of Process unit 3 in Figure 11



Figure 15 The hydrogen network with maximum throughput of Process unit 3 in Figure 11

Figures 16-18 are similar Figures 13-15, same conclusions can be deducted from their illustration. However, the difference of these three figures to previous three is the influence on fresh hydrogen consumption caused by process unit 3 is more severe than that of unit 5 because the curves in Figure 11 are steeper than that in Figure 12. The reason causing such result is process unit 3 is key unit but unit 5 is not. Figure 16 The internal source 5 variation as throughput fluctuation of process unit 5



What needs to be pointed out is that all results from Figures 5-18 are identified with existing network structure and compressor placement. Although pressure and compressors are not optimized, all results are obtained under current network structure and compressor placement. The retrofit involves only shut down of one compressor and reallocation of some pipelines and thus there is hardly capital cost increase. whatever single or multiple contaminants and static or fluctuant networks, process unit mass balance oriented method can always give more reliable targets than source-sink mapping based traditional approaches as measurement on flow rate and concentration of streams inflowing and outflowing process units. This method reveals the significant influence of process hydrogen mass balance on hydrogen network integration based on stream properties and tolerable disturbance. Therefore, it has contribution to not only theory but


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also application.

6. Conclusions This paper proposed a process unit mass balance oriented hydrogen network integration methodology. In order to reveal practical consumption, generation, accumulation and transport of hydrogen and contaminants, process unit mass balance is employed to quantify such dependence. Afterwards, a process unit mass balance oriented superstructure is built to substitute traditional source-sink mapping superstructure as problem illustration. As mathematical solution, a mixed integer nonlinear programming(MINLP) model is established to address the integration and optimization for both single contaminant hydrogen network and multiple case under static and fluctuant conditions within tolerable disturbance of all hydrogen allocations. The results of case studies demonstrate that the minimum fresh hydrogen and internal sources profile determined by this method are more reliable than existing ones, especially when throughput deviates current level. Therefore, the process unit mass balance based mathematical programming method is superior to previous studies. Aiming to analyze and optimize hydroprocessing units oriented hydrogen networks, the process unit mass balance in this paper is only performed on the process unit including hydrogenation reactions and separation together rather than individually. Many other related constraints, such as pressure level, separation, operating and investment costs etc., are not considered. When all these constraints aforementioned are incorporated into existing hydrogen networks, complex reaction-separation-transfer coupling network synthesis problems are formed. On the basis of this work, a model including all these constraints so that more practical network design can be identified is to be developed in near future.



Acknowledgements Financial support from the Postdoctoral Science Foundation of China under Grant 2016T90924 and the National Natural Science Foundation of China under Grant 21506169 is gratefully acknowledged.

Nomenclature Variables

F

total flow rate of a stream, mol/s or Nm3/h

ε

throughput flexibility factor

H

hydrogen flow rate, mol/s or Nm3/h

I

flow rate of impurities, mol/s or Nm3/h

RC

relative concentration of contaminant, mol%

V

oil feed flow rate, t/h

x

allocation variable

y

absolute hydrogen concentration, mol%

Sets

i

input of process unit from unit i

j

process unit j

k

output of process unit to unit k

m

contaminants

Indices

FH

fresh hydrogen

C

consumption


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D

discharge

T

internal

Gen

generation

LO

lower bound

UP

upper bound

min

minimum

O

current operating condition

Parameters

n

number of process unit

s

number of contaminants

b

correlation constant

K

correlation coefficient

HUP

Hydrogen allocation upper bound

HLO

Hydrogen allocation lower bound

HTO

hydrogen to oil ration, volume basis, V/V

L

contaminant generation coefficient

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List of Figures Figure 1 Traditional absolute concentration based source-sink mapping superstructure for hydrogen networks20 Figure 2 Relative concentration based source-sink mapping superstructure for hydrogen networks37



Figure 3

A typical hydroprocessing process flowsheet1

Figure 4 Process unit mass balance based superstructure of hydrogen networks Figure 5 The current hydrogen network of case 1 Figure 6 The optimized hydrogen network with traditional pinch analysis Figure 7 The optimized hydrogen network with process unit mass balance (unit for all flow rate numbers in Figures 6-7 is mol/s and all percentages are mol fraction) Figure 8 Static hydrogen network of case 2 obtained by absolute concentration Figure 9 Static hydrogen network of case 2 obtained by relative concentration Figure 10 Static hydrogen network of case 2 obtained by process unit mass balance (unit for all flow rate numbers in Figures 8-10 is Nm3/h and all percentages are mol fraction) Figure 11 Fresh hydrogen demand versus unit 3 fluctuation Figure 12 Fresh hydrogen demand versus unit 5 fluctuation Figure 13 The internal source 3 variation as throughput fluctuation of process unit 3 Figure 14 The hydrogen network with minimum throughput of Process unit 3 in Figure 10 Figure 15 The hydrogen network with maximum throughput of Process unit 3 in Figure 10 Figure 16 The internal source 5 variation as throughput fluctuation of process unit 5 Figure 17 The hydrogen network with minimum throughput of Process unit 5 in Figure 11 Figure 18 The hydrogen network with maximum throughput of Process unit 3 in Figure 11


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Figure 1 Traditional absolute concentration based source-sink mapping superstructure for hydrogen networks20



Figure 2 Relative concentration based source-sink mapping superstructure for hydrogen networks37


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Figure 3

A typical hydroprocessing process flowsheet1



Figure 4 Process unit mass balance oriented superstructure of hydrogen networks


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Figure 5 The current hydrogen network of case 1



Figure 6 The optimized hydrogen network with traditional pinch analysis


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Figure 7 The optimized hydrogen network with process unit mass balance (unit for all flow rate numbers in Figures 5-7 is mol/s and all percentages are mol fraction)



Figure 8 Static hydrogen network of case 2 obtained by absolute concentration


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Figure 9 Static hydrogen network of case 2 obtained by relative concentration



Figure 10 Static hydrogen network of case 2 obtained by process unit mass balance (unit for all flow rate numbers in Figures 8-10 is Nm3/h and all percentages are mol fraction)


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Figure 11 Fresh hydrogen demand versus unit 3 fluctuation



Figure 12 Fresh hydrogen demand versus unit 5 fluctuation


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List of Tables: Table 1 Hydrogen network case with single contaminant Table 2. Source Data for the Hydrogen-Producing Processes in Example 1 Table 3 A practical refinery multiple contaminants hydrogen network in China Table 4 Current crude oil data and their correlation coefficients Table 5 Contaminants generation coefficients for each process unit Table 6 Fresh hydrogen consumption and CPU time comparison of three methods for Process unit 3 Table 7 Fresh hydrogen consumption and CPU time comparison of three methods for Process unit 5



Table 1 Hydrogen network case with single contaminant Processes variable

units

HCU

NHT

CNHT

DHT

762.4

138.6

304.9

277.2

93.36

80.00

82.14

82.14

69.3

97.0

41.6

69.3

75.00

75.00

70.00

73.00

41.6

415.8

277.2

makeup Flow rate

mol/s

purity

mol%H2

purge Flow rate

mol/s

purity

mol%H2

recycle Flow rate

mol/s

1732.6

Flow rate

mol/s

2495.0

180.2

720.7

554.4

purity

mol%H2

80.61

78.85

75.14

77.57

Flow rate

mol/s

1801.9

138.6

457.4

346.5

purity

mol%H2

75.00

75.00

70.00

73.00

sink

source


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Table 2. Source Data for the Hydrogen-Producing Processes in Example 1 Flow rate

Sources

maximum

minimum

current

H2 purity

(mol/s)

(mol/s)

(mol/s)

mol% H2

SRU

623.8

0.0

623.8

93.00

CRU

415.8

415.8

415.8

80..00

Import

346.5

0.0

277.2

95.00



Page 50 of 55

Table 3 A practical refinery multiple contaminants hydrogen network in China Concentration of contaminants(%) Total flow

Absolute

rate(Nm3/h)

hydrogen(%)

FH

100000

Internal 1

streams

H2 S

NH3

C

99.5

0.09

0.3

0.11

50000

91.5

0.7

1.6

6.2

Internal 2

55000

89.9

2.16

6.34

1.6

Internal 3

28000

88

3.7

4.1

4.2

Internal 4

7500

90

0.6

8.3

1.1

Internal 5

7500

90

5.6

2.2

2.2

3.1

Hydrogen sources

Hydroprocessing units Unit 1

54062(76t/h)

92

3.2

1.7

Unit 2

94545(130t/h)

90.86

1.2

5.54

2.4

Unit 3

45821(65t/h)

89.8

2.1

2.3

5.8

Unit 4

7952(22t/h)

91.8

3.2

2.1

2.9

Unit 5

14361(18t/h)

90.5

2.2

6.5

3


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Table 4 Current crude oil data and their correlation coefficients Hydrogenation

Minimum hydrogen

The current

The fluctuant range

K

b

Unit 1

83.3

100

639

76

51.7~100.3

Unit 2

78

-140

623

130

88.4~171.6

Unit 3

152.2

5

473

65

44.2~85.8

Unit 4

73.6

81

335

22

15~29

Unit 5

135

-42

553

18

12.2~23.8

unit

to oil rate(V/V)

throughput(t/h)


of throughput(t/h)


Table 5 Contaminants generation coefficients for each process unit Process unit

L(Nm3/t) H2 S

NH3

C

Unit 1

2.5

5.25

5

Unit 2

2.86

8.36

6

Unit 3

5.1

3.3

4.7

Unit 4

2

2.2

1.8

Unit 5

3.9

2.1

4.5


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Table 6 Fresh hydrogen consumption and CPU time comparison of three methods for Process unit 3 Fresh hydrogen consumption(Nm3/h)

CPU time(s)

Fluctuation

Throughput

range

(t/h)

PUMS*

AC*

RC*

PUMS*

AC*

RC*

-0.32

44.2

62927.9

63254.4

59281.1

0.7

0.2

0.3

-0.28

46.8

63729.5

63314.9

59281.1

0.6

0.2

0.3

-0.24

49.4

64520.9

63414.7

59281.1

0.6

0.2

0.3

-0.20

52

65322.4

64184.87

60159.8

0.3

0.2

0.3

-0.16

54.6

66113.9

65704.9

61531.7

1

0.2

0.3

-0.12

57.2

66915.4

67225.0

62903.5

1.1

0.2

0.3

-0.08

59.8

67716.9

68745.0

64275.4

0.3

0.2

0.3

-0.04

62.4

68508.3

70265.1

65647.2

0.5

0.2

0.3

0

65

69304.0

71785.1

67019.1

0.3

0.2

0.3

0.04

67.6

70111.4

73305.2

68391.0

0.3

0.2

0.3

0.08

70.2

70902.8

74825.2

69762.8

0.6

0.2

0.4

0.12

72.8

71698.3

76345.2

71134.7

0.5

0.2

0.3

0.16

75.4

72495. 8

77865.3

72506.5

0.4

0.2

0.3

0.20

78

73297.3

79385.3

73878.4

0.6

0.2

0.3

0.24

80.6

74098.8

80905.4

75250.3

0.4

0.2

0.3

0.28

83.2

74900.3

82425.4

76622.1

0.4

0.2

0.3

0.32

85.8

75710.8

83945.5

77994.0

1.2

0.2

0.3

*PUMS: Process unit mass balance; AC: Absolute concentration; RC: relative concentration



Page 54 of 55

Table 7 Fresh hydrogen consumption and CPU time comparison of three methods for Process unit 5 Fresh hydrogen consumption(Nm3/h)

CPU time(s)

Fluctuation

Throughput

range

(t/h)

PUMS*

AC*

RC*

PUMS*

AC*

RC*

-0.32

12.24

67537.5

68276.9

63343.1

1

0.2

0.3

-0.28

12.96

67758.4

68308.4

63802.6

0.3

0.2

0.3

-0.24

13.68

67979.3

68753.9

64262.1

0.4

0.2

0.3

-0.20

14.4

68200.2

69259.1

64721.6

0.4

0.2

0.3

-0.16

15.12

68421.1

69764.3

65181.1

0.4

0.2

0.3

-0.12

15.84

68642.1

70269.5

65640.6

0.4

0.2

0.3

-0.08

16.56

68863.0

70774.7

66100.1

0.6

0.2

0.3

-0.04

17.28

69083.9

71279.9

66559.6

0.3

0.2

0.3

0

18

69304.0

71785.1

67019.7

0.3

0.2

0.3

0.04

18.72

69530.8

72290.3

67478.6

0.4

0.2

0.3

0.08

19.44

69751.7

72795.5

67938.1

0.4

0.2

0.4

0.12

20.16

69982.7

73300.7

68397.6

0.4

0.2

0.3

0.16

20.88

70203.6

73805.9

68857.1

0.4

0.2

0.3

0.20

21.6

70424.5

74311.1

69316.6

0.4

0.2

0.3

0.24

22.32

70645.4

74816.3

69776.1

0.4

0.2

0.3

0.28

23.04

70876.4

75321.5

70235.6

0.6

0.2

0.3

0.32

23.76

71097.3

75826.6

70695.1

0.5

0.2

0.3

*PUMS: Process unit mass balance; AC: Absolute concentration; RC: relative concentration


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Process unit mass balance oriented mathematical optimization for

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