Optimization of multi-refinery hydrogen networks

I.A. Karimi and Rajagopalan Srinivasan (Editors), Proceedings of the 11th International Symposium on Process Systems Engineering, 15-19 July 2012, Singapore. © 2012 Elsevier B.V. All rights reserved.

Optimization of multi-refinery hydrogen networks Anoop Jagannatha, Ali Elkamelb and I.A.Karimia a

Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117576, Singapore b Chemical Engineering Department, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Abstract Hydrogen is an important feedstock and fuel in the refining and petrochemical industries. In this paper, we address the optimal synthesis of inter-plant hydrogen networks by modifying the superstructure-based one-plant model of Elkamel et al. (2011). The bilinear terms involved in the component balance equations of this model give rise to a nonconvex mixed integer nonlinear program (MINLP). A specialized outer-approximation algorithm is developed for solving this optimal synthesis problem to global optimality, where the lower bound on the global optimum is obtained by means of piecewise under-and-over estimators for the bilinear terms. We propose and compare several integration schemes to demonstrate significant cost savings. Keywords: Hydrogen networks, global optimization, superstructure

1. Introduction The escalating prices of crude oil and petroleum products have forced the refiners and petrochemical producers to operate under tight margins. In a bid to reduce costs, these industries continually seek innovative methods to conserve and manage their resources. Hydrogen is an important utility that is acquiring significant importance due to its cost and stringent environmental regulations. In a refinery, it is critical to design and operate the individual hydrocracker and hydrotreater units so as to minimize waste. However, it is equally or even more critical to optimize the usage of hydrogen throughout the whole refinery network. One common technique for optimal hydrogen management in a refinery is to perform a hydrogen pinch analysis to set targets for minimum hydrogen need. Recently, mathematical superstructure-based optimization methods have also been applied for optimizing the hydrogen consumption within a refinery. Most work so far has addressed hydrogen management within a single refinery. In refining / petrochemical complexes such as Jubail, Jurong Island, Houston, and Rotterdam, where multiple refineries and petrochemical plants exist in close proximity, it is better to expand the scope of integration and coordination from intra-plant to inter-plant. This may allow one to exploit inter-plant synergies and reduce costs. Resource/utility conservation and process integration have attracted much interest in the process industries to improve process sustainability. A properly designed inter-plant hydrogen network could play a significant role in reducing costs (economics), minimizing energy consumption (energy), and also conserving the environment by reducing the CO2 emissions associated with hydrogen production. Such integration efforts are in line with the flurry of research activities involving the integration of various utilities in a refinery such as fuel gas (Hasan et al., 2011) and water (Chew et al.

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(2008), Chen et al. (2010)). Chew et al. (2010a, 2010b) have also considered inter-plant resource conservation. The benefits of integration in refinery planning (Al-Qahtani and Elkamel 2008, 2009) has also prompted many researchers to work in the area of resource conservation owing to its potential benefits. In this work, we address retrofit-design and operation of optimal inter-refinery or multiplant hydrogen networks. However, the approach is also extendable to grass-root design as well. The objective is to minimize the total annualized cost of the entire system with the help of a mathematical superstructure-based optimization. We also propose and evaluate several schemes of this integration using a realistic case study.

2. Problem statement A petrochemical complex has several plants with processing units that produce, consume, or purify hydrogen. Let i denote a source that produces hydrogen, j denote a sink that uses hydrogen gas as fuel, u denote a hydroprocessing unit that needs hydrogen as feed, and k denote an existing compressor that can pressurize a hydrogen stream to supply to various consumers. The plants may also have some PSA (Pressure Swing Adsorption) units that can separate relatively pure hydrogen from a hydrogencontaining feed. Let m denote a PSA unit that could be installed in these plants. The goal is to determine (1) the PSA units to install and their sizes, (2) interconnections among various sources, sinks, and units, and (3) distribution of hydrogen flows among various units, so as to meet the hydrogen demands of all plants at minimal total annualized cost. The superstructure for this hydrogen network study can be obtained from Elkamel et al. (2011)

3. Model Formulation Let Fij , Fik , Fiu and Fim represent the gas flows (MMscfd) from source i to sink j, compressor k, hydroprocessing unit u, and PSA unit m respectively. Similarly, let Fkj , Fku and Fkm denote the gas flows from compressor k to fuel gas sink j, hydroprocessing unit u, and purification unit m respectively. If Fouti is the total gas flow from source i, then the mass balance around source i gives us, Fouti ¦ Fij  ¦ Fik  ¦ Fiu  ¦ Fim (1) j

k

u

m

Similarly, the mass and component balance around compressor k whose capacity FCk is given by Eq. (2)-(5). (2) ¦ Fik  ¦ Fuk  ¦ Fmk ¦ Fkj  ¦ Fku  ¦ Fkm i

u

¦F

ik

i

m

j

u

m

youti  ¦ Fuk youtuu  ¦ Fmk yPPSAm u

m

(¦ Fkj  ¦ Fku  ¦ Fkm ) ycompk

(3)

 ¦ Fmk )

(4)

j

u

m

J 1 J

Pwrk

CpT

¦F ¦F ik

i

uk

u

§ Po · ¸  1)(¦ F  ¦ F P © i¹  ¦ F d FC

K (¨

ik

i

mk

k

uk

u

m

(5)

m

Pwrk is the power of the compressor which is directly related to the flow and the parameters namely inlet Pi and outlet pressures Po , heat capacity Cp ,temperature T and

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efficiency K and J be the adiabatic index. Fkj , Fku , Fkm be the flow out from the compressor to fuel gas sink j, hydroprocessing unit u, and purification unit m respectively. Fuk , Fmk are the flows from the hydroprocessing unit u and purification unit m to the compressor k. The purity of hydrogen out from compressor, source and process unit are ycompk , youti , youtuu respectively. The hydroprocessing unit modeling equations is given in Eq. (6)-(8) where Fuj and Fum the flow from unit u to fuel gas sink j, and purification unit m. Fuu ' is the corresponding recycle stream to the processing unit. The flow and purity demand into the hydroprocessing unit is given by Finuu and

yinuu respectively and flow out is denoted by Foutuu .The equations for the purification unit are in Eq (9)-(12). Fmk and Fmu are the streams from the purification unit, whose yPPSAm , going to existing compressor and hydroprocessing unit. Fmj is the residue stream from the purification unit whose purity recovery is Rcvr and purity is

is yRPSAm . Eq.(13) and (14) is for fuel gas system.

¦F  ¦F  ¦F

Finuu

iu

ku

i

m

¦F

Finuu yinuu

iu

i

im

i

uk

¦F

im

i

k

m

m

mj

j

 ¦ Fmk  ¦ Fmu k

¦F

mj

k

j

yRPSAm  yPPSAm (¦ Fmk  ¦ Fmu ) (10)

Rcvr (¦ Fim youti  ¦ Fum youtuu  ¦ Fkm ycompk ) u

(9)

u

youti  ¦ Fum youtuu  ¦ Fkm ycompk u

(8)

u'

¦F

k

i

k

k

Finj j

u

k

¦F  ¦F  ¦F ij

kj

i

Finj j yinj j

m

ij

i

kj

k

¦F

mj

(11)

u

yRPSAm

(12)

j

(13)

u'

¦ F yout  ¦ F i

k

 ¦ Fuj

mj

k

u

yPPSAm (¦ Fmk  ¦ Fmu )

(1  Rcvr )(¦ Fim youti  ¦ Fum youtuu  ¦ Fkm ycompk ) i

(7)

u'

 ¦ Fum  ¦ Fuu '

 ¦ Fum  ¦ Fkm u

(6)

u'

k

uj

j

 ¦ Fuu '

youti  ¦ Fku ycompk  ¦ Fmu yPPSAm  ¦ Fuu ' youtuu

¦F ¦F

Foutuu

¦F

mu

k

ycompk  ¦ Fmj yRPSAm  ¦ Fuj youtuu m

(14)

u'

Since the hydrogen network problem is a gas network, the flow from any source p in general to any sink q, is possible only when the pressure of source Pp is greater than or equal to sink pressure Pq . In case of units whose pressure is known, the flows between them are fixed to zero when the pressure of source Pp is less than pressure of sink Pq . In case of equipments which need to be retrofitted, the pressure is unknown and hence a binary variable X pq is required to model the pressure difference between them. Elkamel et al.(2011) had not considered the piping cost in their model, so used only one type of binary variable to model the flow and pressure difference between the units. In our case, the piping cost becomes significant when considering refinery network integration. Hence we will require two levels of binary variables in our model one to show the existence of pressure difference X pq and other depicting the flow between them XFpq .Second, since we are interested in solving the model to global optimality, we

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introduce redundant cut into the model which aids to solve the model to global optimality given by Eq. (15). Moreover the constraint to depict the inter-plant/refinery connection is given by Eq. (16) where the connection between source and sink among refineries may or may not exist based on type of integration and r is index for refinery. By modeling the system using Eq.(1)-(14), we reduce the number of bilinear terms in comparison to the model of Elkamel et al. (2011) by [ŇKŇ+ŇUŇ+ŇMŇ] whereŇKŇ,ŇUŇandŇMŇare the number of compressors, hydroprocessing units and purification units respectively. Inclusion of piping cost, solving model to global optimality, introduction of redundant bound strengthening cuts, reduction in number of bilinear terms and multi-refinery network integration represent significant additions to the previous work (Elkamel et al. (2011)). (15) Fouti youti  Foutuu youtuu Finuu yinuu  Finj j yinj j

¦ ¦ XF

0

pq

r z r '

(16)

p pr qqr '

TAC

AF (¦ (aPSA X PSA  bPSA (¦ Fim  ¦ Fum  ¦ Fkm ))  m

i

u

k

¦

(a pipe X pipe  bpipe Fpq ))

pqOnew

OD(( Fouti OCH i )  OCE ¦ Pwrk )

(17)

k

Eq. (17) gives the total annualized cost as objective with aPSA , bPSA , a pipe , OCHi and

OCE as cost coefficients for PSA, pipeline, hydrogen cost and electricity cost. OD and AF are operating days in year and annualization factor respectively. Eq.(1)-(17) is globally optimized using the specialized outer approximation framework (Karuppiah et al. (2007)) where the lower bound on the global optimal is is obtained by the piecewise under-and-over estimators by the convexification of bilinear terms (Wicaksono and Karimi, 2008). A bivariate partitioning scheme is employed based on the Incremental Cost formulation for bilinear terms (Hasan and Karimi, 2009). When the gap between the lower bound and upper bound is below specific tolerance, then the algorithm is terminated.

4. Case Study Consider three existing different hydrogen networks. In this, we seek to retrofit these three hydrogen networks with purifier units namely the pressure swing adsorption unit. The objective used in all the comparison studies is the minimal total annualized cost (TAC). For the sake of convenience the results in Table 1 shows the costs as the total cost of three networks. Table 1. Optimization results for the case study

Cost(k$)

No Integration

Indirect Scheme 1

Indirect Scheme 2

Indirect Scheme 3

Direct Integration

H2 Elect Operational Piping PSA Capital TAC H2(MMscfd) Gas to fuel gas(MMscfd)

106036.150 4198.960 110235.110 861.508 23512.636 24374.144 112672.261 53018.075 6286.595

104415.185 4138.370 108553.920 4190.125 20457.954 24648.079 111018.670 52207.775 6016.295

104328.315 4124.500 108452.815 4390.770 20315.696 24706.465 110923.608 52164.340 5972.860

104269.550 4121.580 108391.130 4686.059 20046.700 24732.759 110864.576 52134.775 5943.295

104236.700 4200.780 108437.120 3418.491 19894.848 23313.339 110768.534 52118.350 5926.870

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In case of direct integration, the entire combined network is solved in which all possible interconnections exist among all the refineries. The decrease in the requirement of hydrogen in all the integration schemes shows a significant step towards the conservation of environment and energy. Secondly, there is also an effective usage of the hydrogen gas in the combined integrated network. Hence, an advantage could be seen in the operational cost and also in the hydrogen consumption when the refinery hydrogen networks are integrated. In the indirect integration scheme, there exists a centralized purification unit (pressure swing adsorption) through which the refinery interactions take place. In the first case of indirect integration (scheme 1), all the refineries are connected to only the centralized pressure swing adsorption unit and no connections exist among the refineries. In the indirect integration scheme (scheme 2), the hydrogen producers namely the hydrogen plant is allowed to connect with the other units of other refineries. In the final case of indirect integration (scheme 3), all the sources are allowed to connect with the sinks. From the different patterns of the integration, we observe that the both direct and integration offers better cost savings when compared to the case of no integration.

5. Conclusion A superstructure based mathematical optimization approach is developed for interplant/refinery hydrogen networks. Different integration schemes were studied and the results were analyzed. All the problems were solved to global optimality with specific tolerance. The results showed that significant savings could be achieved in case of integrated network in comparison to individual networks optimized separately.

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