- Email: [email protected]
Simultaneous Design and Planning of CO2 Transport Pipeline Network for Carbon Dioxide Capture and Sequestration Project
Krist V. Gernaey, Jakob K. Huusom and Rafiqul Gani (Eds.), 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering. 31 May – 4 June 2015, Copenhagen, Denmark © 2015 Elsevier B.V. All rights reserved.
Simultaneous Design and Planning of CO2 Transport Pipeline Network for Carbon Dioxide Capture and Sequestration Project Xiong Zou,a Hongguang Dong,a* Jian Li,a Jinqu Wanga a
School of Chemical Engineering, Dalian University of Technology, 2 Linggong Road, Dalian 116024, China [email protected]
Abstract Carbon dioxide Capture and Sequestration (CCS) is a major method to decrease the emissions from centralized large industrial plants. Multi-period planning and design of CCS is still a challenging problem. In this work, a superstructure-based mathematical model for the design and planning of multi-period CO2 transport pipeline network is presented. The mapping between incidence matrix and pipeline structure is employed and the model is formulated within a mixed integer nonlinear optimization framework where the objective function is to maximize the profit of CCS while satisfying mass, pressure drop and logic constraints. A real life example is studied to demonstrate the advantages of our proposed approach. Keywords: CCS, design, planning, supply chain, multiple-period.
1. Introduction Carbon dioxide (CO2) capture and sequestration (CCS) can significantly reduce emissions from large stationary sources of CO2, which include coal- and natural-gasfired power plants, as well as petro-chemical plants. CCS is a three-step process that includes: capture and compression, transportation (usually in pipelines), and injection and sequestration. The capital investment and operating cost of the pipeline network have a direct impact on the success or failure of a CCS project. Considering the complexity of the scheduling of network pipeline system, several techniques are used to enhance the model performance. A hierarchical approach was developed by Beschetto and Magatão et al (2012), where the problem is decomposed into planning and assignment levels and two MILP models were solved sequentially. Fimbres Weihs and Wiley (2012) used incidence matrix to express the structure of the CCS and they obtained the design of CCS network under the assumption of fixed state flow. Recently, Zhou et al (2014) introduced a new decomposition algorithm to overcome the computational difficulty. In their work, intermediate sites were included in the network superstructure and the optimal capture amount of CO2 was also considered. To the best knowledge of the authors, there is no current work that considers the influence of multiple-period planning in the procedure of network and pipeline design. In this work, a superstructure-based MINLP approach for simultaneous design and planning of CO2 transport pipeline network is presented in an attempt to maximize the
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profit in a CCS project under the framework of supply chain. The advantages of this approach are summarized below: 1. The diverse CO2 capture and sequestration capacities and costs in different sources and sinks are considered. The transporting amount of CO2 is optimization variable rather than predefined parameter. 2. Supplier-intermediate site-customer and supplier-supplier connections are introduced in the network superstructure to achieve the sharing mechanism of pipelines in the long distance transportation, which leads to cost reduction. 3. The fluctuations of plant capacity and cost in the time horizon are also considered in the model. The planning, network structure and design specification of each pipeline in multiple periods are optimized simultaneously.
2. Problem statement Consider a supply chain of CO2 with all alternative sources, sinks and intermediate sites. The following information should be provided: (1) The longitude and latitude values of place nodes (2) The CO2 capture and sequestration capacities of each source and sink in each time period (3) The seasons-dependent cost information of CCS (4) The physical property of CO2 stream in the compressed pressure and temperature.
3. Superstructure Our scenario of CO2 supply chain superstructure is schematically presented in Figure 1(a), which contains 9 sources, 2 intermediate sites and 3 sinks. The circle, the triangle, and the square represent the sources, the intermediate sites, and the sinks respectively. The sources and sinks are linked by pipelines, where CO2 is transported. Intermediate sites, where multiple streams could be mixed, also exist in the network. Each source is regarded as a supplier, which provides CO2 raw material at its own capture cost. Each pipeline and intermediate site is treated as a factory which transports CO2, and each sink is treated as a customer, who wants to buy CO2 product at the price of its own unit sequestration revenue. Supplier-supplier and supplier-intermediate sitecustomer connections are introduced in the network superstructure. The suppliersupplier and supplier-intermediate site connections are realized by reversal pipelines. Customers are assumed to be not link to each other. N1
N1
N10
N2
N10
N2
N3 N11
N3 N11
N4
N4
N12
N12
N6 N5
N6 N5
N13 N7
N13 N7
N14 N8
N14 N9
(a)
N8
N9 (b)
Figure 1. The superstructure of the example
Simultaneous Design and Planning of CO2 Transport Pipeline Network for Carbon Dioxide Capture and Sequestration Project
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To reduce the network complexity, the sources are divided into 3 parts based on cluster analysis method and only the sources in the same part are linked to each other with reversal pipeline. Each source is linked to 3 sinks respectively with directional pipeline. The first part includes N1, N2, and N3. The second part only has N4. The third part has N5-N9. The distance between sources in the different part is always overlong. So the superstructure can be simplified from Figure 1 (a) to (b) by eliminating these pipelines. The topology relationship between the pipelines and place nodes is expressed by a node-arc incident matrix. The columns of the incident matrix represent each of the pipeline links and the rows of the matrix represent each of the place nodes. The value of element wi,j in the matrix is determined by the following rules: wi,j=1 if pipeline j is the input of place node i; wi,j=-1 if pipeline j is the output of place node i; wi,j=0 if there isn’t a connection between pipeline j and place node i. Notice that all the pipelines, between sources and intermediate sites and between sources and sources, are bidirectional and that they are represented by two single directed pipelines which cannot be activated in the same time interval.
4. Mathematical formulation Some sets are defined for more logical and clear expression. Sinks, sources and intermediate sites are represented by set S(s1, s2, s3,..), O(o1, o2, o3,..), E(e1, e2, e3,..), respectively, and I={S,O,E}. Pipelines are represented by set J (j1ˈj2ˈj3...). Different seasons are represented by set T (t1, t2, t3, t4). 4.1. Mass balance constraints Carbon dioxide captured from sources should be compressed and then transported to sinks. The amount of CO2 captured is determined by the economic benefit and environmental regulation policy. Ps,t represents the capture capacity of source s in the time interval t and PPt represents the minimum capture quantity in the whole district based on regulation policy. Qj,t represents the flowrate of pipe j in time interval t. Cs,t represents the CO2 capture quantity of source s in time interval t. The mass balance constraints of sources are expressed as
¦ w
s, j
u Q j ,t
Cs , t , s S , t T
j
¦¦ w
s, j
s
u Q j ,t t PPt , t T
j
(1)
(2)
The amount of CO2 sequestrated should be smaller than the sequestration capacities of the sinks (Po,t). Similarly, the mass balance equation of each sink can be expressed as follow.
¦w
o, j
u Q j ,t
SEo ,t , o O, t T
j
(3)
There are no emission and storage of CO2 in the intermediate sites. The mass balance equation of each intermediate site can be expressed as follow.
¦w
e, j
j
u Q j ,t
0, e E , t T
(4)
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4.2. Pressure drop constraints The pressure drop (Pj,t) in the pipeline is relevant to diameter (dj), length (Lj), and physical properties. U and V are the density and viscosity of CO2 in 9 MPa, 283K.
Pj ,t
4.84 kdrop u L j u Q 2.84 u U 0.84 u V 0.16 , j J , t T j .t u d j
(5)
4.3. Logic relations For reversal pipelines, they are represented by a couple of pipelines, which are not activated at the same time, and their diameters should be the same. Binary variable yj,t is used to expressed whether the pipeline j is activated in time interval t. If a pipeline j is activated in time interval t, it is equal to 1. Otherwise, it is equal to 0.
y j ,t y j ' ,t d 1, if j and j' are couple pipelines
(6)
dj
(7)
d j ' , if j and j' are couple pipelines
When all the binary variables for the same pipeline j in different time intervals equal 0, the pipeline j does not exist. M1 is the upper bound of the pipeline diameter.
d j d M 1 u ¦ y j ,t , j J t
(8)
The diameter of a pipeline should not be too small if the pipeline exists. The lower bound of the pipeline diameter M2 is set as 0.15. M 2 u y j ,t d d j , j J , t T
(9)
Once the pipeline is activated in the time interval t, the flow in the pipeline should be suitable for real case, and it cannot be too small or too large. If the pipeline is not activated in the time interval t, the flow in the pipeline should be 0. The lower bound of flow M3 equals to 0.10 and the upper bound M4 equals to 30. M 3 u y j ,t d Q j ,t d M 4 u y j ,t , j J , t T
(10)
4.4. Objective function The profit is established with 5 items: government subsidy (GS), capture cost (Ccapture), transportation cost (Ctransportation), pipe cost (Cpipe) and sequestration cost (Csequestration). The unit capture cost Us,t, unit sequestration cost (Uo,t) and government subsidy of unit CO2 reduction(Ugs) are given. Transportation cost is proportional to pressure drop. Pipe cost is related to the length and diameter of the pipe. kdrop, kpipe and ktransport are the coefficients of pressure drop, pipe cost, transportation cost, respectively. The sequestration revenue of each sink equals to the government subsidy of CO2 reduction minus sequestration cost. Now the government subsidy is quite higher than the sequestration cost.
GS
¦¦ (U o
C pipe
gs
t
u ¦ ( wo , j u Q j ,t )) j
k pipe u ¦ ( L j u d 1.5 j ) j
(11)
(12)
Simultaneous Design and Planning of CO2 Transport Pipeline Network for Carbon Dioxide Capture and Sequestration Project
ktransport u ¦¦ Pj ,t
Ctransportation
j
Ccapture
¦¦ (U s
Csequestration
t
s ,t
o
Max Profit
t
(13)
t
u ¦ ( ws , j u Q j ,t ))
(14)
j
¦¦ (U
o ,t
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u ¦ ( wo , j u Q j ,t ))
(15)
j
GS C pipe Ctransportation Ccapture Csequestration
(16)
5. Example This example is abstracted from a real-life CCS project in north China. The emission, sequestration capacity (Ps,t Po,t) and capture, sequestration cost (Us,t , Uo,t) change with time periods. The computing platform is a PC with 6GB RAM memory, and Intel Core TM i7 CPU (2.67GHz). The solver DICOPT is used for solving the MINLP model to optimality in GAMS 22.5. Case 1. The base situation of fixed planning without intermediate sites in multipleperiod is solved, and the optimum results are given in Figure 2(a). Numbers around each place node represent the flowrate (kg/s) from t1 to t4 (up to down). The number in the last row represents the diameter (m) of pipelines. We have noticed that some sources are linked to the sinks directly. On the contrary, some sources prefer to link to the other sources. The total profit is 1.7427e9 $, which illustrates that the CCS project is profitable because of the government’s subsidy. Case 2. If there are intermediate sites embedded in superstructure, some new pipelines should be added into the former superstructure. The intermediate place N13 is serviced for N6, N7 and N8, and N14 is serviced for N7, N8, and N9. After optimizing the problem with intermediate sites, the results are presented in Figure 2(b) and we find that intermediate site N13 is not activated and pipeline connections between N7, N8 and N9 are different from Figure 2(a) due to the addition of intermediate site N14. The length of pipelines linking N7, N8 and N9 becomes shorter, but at the same time, a larger diameter pipeline which links N14 to N7 is used. As illustrated in Table 1, both pipe cost and transportation cost decrease. This result indicates that the added intermediate sites will provide a more completed superstructure and lead to a reduction in the total annual cost. Case 3. In the former two situations, all CO2 produced in the source should be captured and transported to sinks. In case 3, the minimum capture quantity in the whole district based on regulation policy is provided. Table 1. The total annual cost, pipe cost, transportation cost of different case studies
Example Case 1 Case 2 Case 3
Profit ($) 1.7427e9 1.7435 e9 2.1039 e9
Pipe cost ($) 7.3917e7 7.3292 e7 6.4475 e7
Transportation cost ($) 2.2952e7 2.2758 e7 2.0021 e7
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3.180, 5.500, 4.000, N10 3.500/ 0.610
4.200, 4.000, N1 4.000, 1.610, 3.000/ 1.000, 0.585 2.000, N11 N2 1.000/ N3 0.385 2.430, 3.470, 10.780, 1.500, 0.000, 1.500, N12 2.000, 2.000, 6.000, 3.500/ 0.000/ 3.680/ 0.487 9.630, 0.462 0.771 N6 1.000, 1.070, 2.000, N5 0.000, N7 6.180/ 3.000, 0.738 0.000/ 0.423 4.220, 2.000, 0.000, 0.000, N8 0.000, N9 0.000, 0.000/ 4.180/ 0.489 0.496 (a)
1.810, 0.000, 1.000, 0.000/ 0.344 N4
1.610, 3.180, 1.000, 5.500, 2.000, 4.200, 4.000, N10 1.000/ 4.000, 3.500/ N1 0.385 4.000, 0.610 3.000/ 0.585 N11 N2 N3 3.470, 2.430, 0.000, 10.780, 1.500, 2.000, 1.500, N12 2.000, 0.000/ 6.000, 3.500/ 0.462 3.680/ 0.487 0.771 9.630, N6 1.000, 6.220, N5 1.070, 2.000, 0.000, 0.000, N13 0.000, 6.180/ 3.000, N7 0.738 4.180/ 0.000/ 0.609 0.423 N14 2.000, 4.220, N8 N9 0.000, 0.000, 0.000, 0.000, 4.180/ 0.000/ 0.496 0.489 (b)
1.810, 0.000, 1.000, 0.000/ 0.344 N4
1.610, 4.060, 1.000, 5.500, 2.000, 1.610, 6.000, N10 1.000/ 4.000, N1 0.385 4.000, 3.500/ 0.655 3.000/ 0.553 N2
N3
N11
1.810, 0.000, 1.000, 0.000/ 0.344
1.550, N4 4.670, 1.500, 0.000, N12 0.000, 6.000, 3.500/ 3.680/ 0.462 6.220, 0.625 0.000, N6 0.000, 0.000, N5 6.180/ 6.220, 0.000, N13 0.649 0.000, 3.000, N7 0.000, 0.000/ 4.180/ 0.420 0.609 N14 2.000, 4.220, N8 0.000, N9 0.000, 0.000, 0.000, 4.180/ 0.000/ 0.496 (c) 0.489
Figure 2. The results of three cases in multiple periods.
The unit capture cost is higher in some sources and the capacity of sinks with lower sequestration cost is limited, so the trade-off between different sources and sinks should be considered. In Figure 2(c), we note that in some period there are no CO2 capture in some sources such as N2, N5, N7 and the diameters of some pipelines becomes smaller. As illustrated in Table 1, the pipe cost and transportation cost decrease substantially. If there is no restrict regulations from the government, disposing all the CO2 is not economical and the optimal flexible arrangement is more profitable.
6. Conclusions A superstructure-based mathematical model to simultaneously optimize the design and multiple-period planning of CO2 transport pipeline network from the perspective of supply chain is proposed. The structure of the pipeline network is mapped to the incidence matrix and cluster analysis is applied to reduce the complexity of the superstructure. The model is formulated within a mixed integer nonlinear optimization framework where the objective function is to maximize the profit of CCS with considering government subsidy and the cost of capture, transportation, pipeline, and sequestration, while satisfying mass, pressure drop and logic constraints. The results of multiple-period real life example indicate that appropriate intermediate places and flexible arrangement have economical advantages.
Acknowledgements This work is supported by the National Natural Science Foundation of China, under Grant No. 21276039.
References S. N. B. Magatão, L.Magatão, H. L. Polli, F. Neves Jr., L. V. R. Arruda, S. Relvas, A. P, F. D. Barbosa-Povóa, 2012, Planning and sequencing product distribution in a real-world pipeline network: an MILP decomposition approach. Ind. Eng. Chem. Res., 51(12), 4591-4609. G. A. Fimbres Weihs, D. E. Wiley, 2012, Steady-state design of CO2 pipeline networks for minimal cost per tonne of CO2 avoided. Int. J. Greenh. Gas Control. 8, 150-168. C. Zhou, P. Liu, Z. Li, 2014, A superstructure-based mixed-integer programming approach to optimal design of pipeline network for large-scale co2 transport. AIChE J. 60(7), 2442–2461.
Simultaneous Design and Planning of CO2 Transport Pipeline Network for Carbon Dioxide Capture and Sequestration Project Xiong Zou,a Hongguang Dong,a* Jian Li,a Jinqu Wanga a
School of Chemical Engineering, Dalian University of Technology, 2 Linggong Road, Dalian 116024, China [email protected]
Abstract Carbon dioxide Capture and Sequestration (CCS) is a major method to decrease the emissions from centralized large industrial plants. Multi-period planning and design of CCS is still a challenging problem. In this work, a superstructure-based mathematical model for the design and planning of multi-period CO2 transport pipeline network is presented. The mapping between incidence matrix and pipeline structure is employed and the model is formulated within a mixed integer nonlinear optimization framework where the objective function is to maximize the profit of CCS while satisfying mass, pressure drop and logic constraints. A real life example is studied to demonstrate the advantages of our proposed approach. Keywords: CCS, design, planning, supply chain, multiple-period.
1. Introduction Carbon dioxide (CO2) capture and sequestration (CCS) can significantly reduce emissions from large stationary sources of CO2, which include coal- and natural-gasfired power plants, as well as petro-chemical plants. CCS is a three-step process that includes: capture and compression, transportation (usually in pipelines), and injection and sequestration. The capital investment and operating cost of the pipeline network have a direct impact on the success or failure of a CCS project. Considering the complexity of the scheduling of network pipeline system, several techniques are used to enhance the model performance. A hierarchical approach was developed by Beschetto and Magatão et al (2012), where the problem is decomposed into planning and assignment levels and two MILP models were solved sequentially. Fimbres Weihs and Wiley (2012) used incidence matrix to express the structure of the CCS and they obtained the design of CCS network under the assumption of fixed state flow. Recently, Zhou et al (2014) introduced a new decomposition algorithm to overcome the computational difficulty. In their work, intermediate sites were included in the network superstructure and the optimal capture amount of CO2 was also considered. To the best knowledge of the authors, there is no current work that considers the influence of multiple-period planning in the procedure of network and pipeline design. In this work, a superstructure-based MINLP approach for simultaneous design and planning of CO2 transport pipeline network is presented in an attempt to maximize the
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profit in a CCS project under the framework of supply chain. The advantages of this approach are summarized below: 1. The diverse CO2 capture and sequestration capacities and costs in different sources and sinks are considered. The transporting amount of CO2 is optimization variable rather than predefined parameter. 2. Supplier-intermediate site-customer and supplier-supplier connections are introduced in the network superstructure to achieve the sharing mechanism of pipelines in the long distance transportation, which leads to cost reduction. 3. The fluctuations of plant capacity and cost in the time horizon are also considered in the model. The planning, network structure and design specification of each pipeline in multiple periods are optimized simultaneously.
2. Problem statement Consider a supply chain of CO2 with all alternative sources, sinks and intermediate sites. The following information should be provided: (1) The longitude and latitude values of place nodes (2) The CO2 capture and sequestration capacities of each source and sink in each time period (3) The seasons-dependent cost information of CCS (4) The physical property of CO2 stream in the compressed pressure and temperature.
3. Superstructure Our scenario of CO2 supply chain superstructure is schematically presented in Figure 1(a), which contains 9 sources, 2 intermediate sites and 3 sinks. The circle, the triangle, and the square represent the sources, the intermediate sites, and the sinks respectively. The sources and sinks are linked by pipelines, where CO2 is transported. Intermediate sites, where multiple streams could be mixed, also exist in the network. Each source is regarded as a supplier, which provides CO2 raw material at its own capture cost. Each pipeline and intermediate site is treated as a factory which transports CO2, and each sink is treated as a customer, who wants to buy CO2 product at the price of its own unit sequestration revenue. Supplier-supplier and supplier-intermediate sitecustomer connections are introduced in the network superstructure. The suppliersupplier and supplier-intermediate site connections are realized by reversal pipelines. Customers are assumed to be not link to each other. N1
N1
N10
N2
N10
N2
N3 N11
N3 N11
N4
N4
N12
N12
N6 N5
N6 N5
N13 N7
N13 N7
N14 N8
N14 N9
(a)
N8
N9 (b)
Figure 1. The superstructure of the example
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To reduce the network complexity, the sources are divided into 3 parts based on cluster analysis method and only the sources in the same part are linked to each other with reversal pipeline. Each source is linked to 3 sinks respectively with directional pipeline. The first part includes N1, N2, and N3. The second part only has N4. The third part has N5-N9. The distance between sources in the different part is always overlong. So the superstructure can be simplified from Figure 1 (a) to (b) by eliminating these pipelines. The topology relationship between the pipelines and place nodes is expressed by a node-arc incident matrix. The columns of the incident matrix represent each of the pipeline links and the rows of the matrix represent each of the place nodes. The value of element wi,j in the matrix is determined by the following rules: wi,j=1 if pipeline j is the input of place node i; wi,j=-1 if pipeline j is the output of place node i; wi,j=0 if there isn’t a connection between pipeline j and place node i. Notice that all the pipelines, between sources and intermediate sites and between sources and sources, are bidirectional and that they are represented by two single directed pipelines which cannot be activated in the same time interval.
4. Mathematical formulation Some sets are defined for more logical and clear expression. Sinks, sources and intermediate sites are represented by set S(s1, s2, s3,..), O(o1, o2, o3,..), E(e1, e2, e3,..), respectively, and I={S,O,E}. Pipelines are represented by set J (j1ˈj2ˈj3...). Different seasons are represented by set T (t1, t2, t3, t4). 4.1. Mass balance constraints Carbon dioxide captured from sources should be compressed and then transported to sinks. The amount of CO2 captured is determined by the economic benefit and environmental regulation policy. Ps,t represents the capture capacity of source s in the time interval t and PPt represents the minimum capture quantity in the whole district based on regulation policy. Qj,t represents the flowrate of pipe j in time interval t. Cs,t represents the CO2 capture quantity of source s in time interval t. The mass balance constraints of sources are expressed as
¦ w
s, j
u Q j ,t
Cs , t , s S , t T
j
¦¦ w
s, j
s
u Q j ,t t PPt , t T
j
(1)
(2)
The amount of CO2 sequestrated should be smaller than the sequestration capacities of the sinks (Po,t). Similarly, the mass balance equation of each sink can be expressed as follow.
¦w
o, j
u Q j ,t
SEo ,t , o O, t T
j
(3)
There are no emission and storage of CO2 in the intermediate sites. The mass balance equation of each intermediate site can be expressed as follow.
¦w
e, j
j
u Q j ,t
0, e E , t T
(4)
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4.2. Pressure drop constraints The pressure drop (Pj,t) in the pipeline is relevant to diameter (dj), length (Lj), and physical properties. U and V are the density and viscosity of CO2 in 9 MPa, 283K.
Pj ,t
4.84 kdrop u L j u Q 2.84 u U 0.84 u V 0.16 , j J , t T j .t u d j
(5)
4.3. Logic relations For reversal pipelines, they are represented by a couple of pipelines, which are not activated at the same time, and their diameters should be the same. Binary variable yj,t is used to expressed whether the pipeline j is activated in time interval t. If a pipeline j is activated in time interval t, it is equal to 1. Otherwise, it is equal to 0.
y j ,t y j ' ,t d 1, if j and j' are couple pipelines
(6)
dj
(7)
d j ' , if j and j' are couple pipelines
When all the binary variables for the same pipeline j in different time intervals equal 0, the pipeline j does not exist. M1 is the upper bound of the pipeline diameter.
d j d M 1 u ¦ y j ,t , j J t
(8)
The diameter of a pipeline should not be too small if the pipeline exists. The lower bound of the pipeline diameter M2 is set as 0.15. M 2 u y j ,t d d j , j J , t T
(9)
Once the pipeline is activated in the time interval t, the flow in the pipeline should be suitable for real case, and it cannot be too small or too large. If the pipeline is not activated in the time interval t, the flow in the pipeline should be 0. The lower bound of flow M3 equals to 0.10 and the upper bound M4 equals to 30. M 3 u y j ,t d Q j ,t d M 4 u y j ,t , j J , t T
(10)
4.4. Objective function The profit is established with 5 items: government subsidy (GS), capture cost (Ccapture), transportation cost (Ctransportation), pipe cost (Cpipe) and sequestration cost (Csequestration). The unit capture cost Us,t, unit sequestration cost (Uo,t) and government subsidy of unit CO2 reduction(Ugs) are given. Transportation cost is proportional to pressure drop. Pipe cost is related to the length and diameter of the pipe. kdrop, kpipe and ktransport are the coefficients of pressure drop, pipe cost, transportation cost, respectively. The sequestration revenue of each sink equals to the government subsidy of CO2 reduction minus sequestration cost. Now the government subsidy is quite higher than the sequestration cost.
GS
¦¦ (U o
C pipe
gs
t
u ¦ ( wo , j u Q j ,t )) j
k pipe u ¦ ( L j u d 1.5 j ) j
(11)
(12)
Simultaneous Design and Planning of CO2 Transport Pipeline Network for Carbon Dioxide Capture and Sequestration Project
ktransport u ¦¦ Pj ,t
Ctransportation
j
Ccapture
¦¦ (U s
Csequestration
t
s ,t
o
Max Profit
t
(13)
t
u ¦ ( ws , j u Q j ,t ))
(14)
j
¦¦ (U
o ,t
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u ¦ ( wo , j u Q j ,t ))
(15)
j
GS C pipe Ctransportation Ccapture Csequestration
(16)
5. Example This example is abstracted from a real-life CCS project in north China. The emission, sequestration capacity (Ps,t Po,t) and capture, sequestration cost (Us,t , Uo,t) change with time periods. The computing platform is a PC with 6GB RAM memory, and Intel Core TM i7 CPU (2.67GHz). The solver DICOPT is used for solving the MINLP model to optimality in GAMS 22.5. Case 1. The base situation of fixed planning without intermediate sites in multipleperiod is solved, and the optimum results are given in Figure 2(a). Numbers around each place node represent the flowrate (kg/s) from t1 to t4 (up to down). The number in the last row represents the diameter (m) of pipelines. We have noticed that some sources are linked to the sinks directly. On the contrary, some sources prefer to link to the other sources. The total profit is 1.7427e9 $, which illustrates that the CCS project is profitable because of the government’s subsidy. Case 2. If there are intermediate sites embedded in superstructure, some new pipelines should be added into the former superstructure. The intermediate place N13 is serviced for N6, N7 and N8, and N14 is serviced for N7, N8, and N9. After optimizing the problem with intermediate sites, the results are presented in Figure 2(b) and we find that intermediate site N13 is not activated and pipeline connections between N7, N8 and N9 are different from Figure 2(a) due to the addition of intermediate site N14. The length of pipelines linking N7, N8 and N9 becomes shorter, but at the same time, a larger diameter pipeline which links N14 to N7 is used. As illustrated in Table 1, both pipe cost and transportation cost decrease. This result indicates that the added intermediate sites will provide a more completed superstructure and lead to a reduction in the total annual cost. Case 3. In the former two situations, all CO2 produced in the source should be captured and transported to sinks. In case 3, the minimum capture quantity in the whole district based on regulation policy is provided. Table 1. The total annual cost, pipe cost, transportation cost of different case studies
Example Case 1 Case 2 Case 3
Profit ($) 1.7427e9 1.7435 e9 2.1039 e9
Pipe cost ($) 7.3917e7 7.3292 e7 6.4475 e7
Transportation cost ($) 2.2952e7 2.2758 e7 2.0021 e7
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3.180, 5.500, 4.000, N10 3.500/ 0.610
4.200, 4.000, N1 4.000, 1.610, 3.000/ 1.000, 0.585 2.000, N11 N2 1.000/ N3 0.385 2.430, 3.470, 10.780, 1.500, 0.000, 1.500, N12 2.000, 2.000, 6.000, 3.500/ 0.000/ 3.680/ 0.487 9.630, 0.462 0.771 N6 1.000, 1.070, 2.000, N5 0.000, N7 6.180/ 3.000, 0.738 0.000/ 0.423 4.220, 2.000, 0.000, 0.000, N8 0.000, N9 0.000, 0.000/ 4.180/ 0.489 0.496 (a)
1.810, 0.000, 1.000, 0.000/ 0.344 N4
1.610, 3.180, 1.000, 5.500, 2.000, 4.200, 4.000, N10 1.000/ 4.000, 3.500/ N1 0.385 4.000, 0.610 3.000/ 0.585 N11 N2 N3 3.470, 2.430, 0.000, 10.780, 1.500, 2.000, 1.500, N12 2.000, 0.000/ 6.000, 3.500/ 0.462 3.680/ 0.487 0.771 9.630, N6 1.000, 6.220, N5 1.070, 2.000, 0.000, 0.000, N13 0.000, 6.180/ 3.000, N7 0.738 4.180/ 0.000/ 0.609 0.423 N14 2.000, 4.220, N8 N9 0.000, 0.000, 0.000, 0.000, 4.180/ 0.000/ 0.496 0.489 (b)
1.810, 0.000, 1.000, 0.000/ 0.344 N4
1.610, 4.060, 1.000, 5.500, 2.000, 1.610, 6.000, N10 1.000/ 4.000, N1 0.385 4.000, 3.500/ 0.655 3.000/ 0.553 N2
N3
N11
1.810, 0.000, 1.000, 0.000/ 0.344
1.550, N4 4.670, 1.500, 0.000, N12 0.000, 6.000, 3.500/ 3.680/ 0.462 6.220, 0.625 0.000, N6 0.000, 0.000, N5 6.180/ 6.220, 0.000, N13 0.649 0.000, 3.000, N7 0.000, 0.000/ 4.180/ 0.420 0.609 N14 2.000, 4.220, N8 0.000, N9 0.000, 0.000, 0.000, 4.180/ 0.000/ 0.496 (c) 0.489
Figure 2. The results of three cases in multiple periods.
The unit capture cost is higher in some sources and the capacity of sinks with lower sequestration cost is limited, so the trade-off between different sources and sinks should be considered. In Figure 2(c), we note that in some period there are no CO2 capture in some sources such as N2, N5, N7 and the diameters of some pipelines becomes smaller. As illustrated in Table 1, the pipe cost and transportation cost decrease substantially. If there is no restrict regulations from the government, disposing all the CO2 is not economical and the optimal flexible arrangement is more profitable.
6. Conclusions A superstructure-based mathematical model to simultaneously optimize the design and multiple-period planning of CO2 transport pipeline network from the perspective of supply chain is proposed. The structure of the pipeline network is mapped to the incidence matrix and cluster analysis is applied to reduce the complexity of the superstructure. The model is formulated within a mixed integer nonlinear optimization framework where the objective function is to maximize the profit of CCS with considering government subsidy and the cost of capture, transportation, pipeline, and sequestration, while satisfying mass, pressure drop and logic constraints. The results of multiple-period real life example indicate that appropriate intermediate places and flexible arrangement have economical advantages.
Acknowledgements This work is supported by the National Natural Science Foundation of China, under Grant No. 21276039.
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