Geological background of the study area
Based on regional structural analysis, the Huainan coalfield is located at the southern margin of North China Plate. In the west–east direction, the coal field boundary lies between the KouzijiNanzhaoji faults and the XinchengkouChangfeng faults. From north to south, the coalfield boundary lies between the ShangtangmingLongshan faults and YingshangDingyuan faults (Fig. 1)^{25,26}. The coalfield is a near east–west hedge tectonic basin with imbricate fan composed of nappe structures on both sides of the basin and simple synclinic structure in the interior (Fig. 1).
The coalbearing strata are Taiyuan formation of upper Carboniferous series, Shanxi formation and Xiashihezi formation of lower Permian series, and Shangshihezi formation of upper Permian series, with a total thickness of about 900 m and about 40 layers of coal seams^{27,28}. In the coalbearing strata, there are 9–18 coal layers with a single layer thickness greater than 0.7 m on average, the maximum thickness is 12 m, and the total thickness is 23–36 m, which are distributed in Shanxi formation, Xiashihezi formation and lower part of Shangshihezi formation. In this study, the CO_{2} emission sources were 10 coalfired power plants in the coalfield with numbered D1D10, respectively. Deep unworkable seams are CO_{2} storage sinks, which are bounded by faults and numbered B1B15, respectively (Fig. 1).
Evaluation method of CO_{2} geological storage potential
In deep unworkable seam, CO_{2} geological storage is mainly in adsorbed, dissolved and free states^{29}, and adsorption storage is the main storage form of coal seam^{30}. Considering the storage differences of different phase of CO_{2}, the following potential assessment model of CO_{2} storage can be adopted^{16,31}:
$$M_{{{\text{CO}}_{2} }} = 0.001\rho_{{{\text{CO}}_{2} }} M_{Coal} (m_{ab} + m_{d} + m_{f} )$$
(1)
where \(M_{{{\text{CO}}_{2} }}\) is CO_{2} storage capacity, t; ρ_{CO2} is the CO_{2} density, kg/m^{3}; M_{coal} is proved coal reserves, t; m_{ab}, m_{d} and m_{f} are the stored quantity of CO_{2} adsorbed, dissolved and free states in coal per unit mass, m^{3}/t.
In the unit mass coal, the storage potential of CO_{2} adsorbed state in deep unworkable seam can be characterized by the following formula^{16,31}:
$$m_{ab} = m_{ex} /(1 – pT_{c} /8Zp_{c} T)$$
(2)
where P is the reservoir pressure, which is also CO_{2} adsorption pressure, MPa; T_{c} is CO_{2} critical temperature, K; Z is the CO_{2} compression coefficient; p_{c} is CO_{2} critical pressure, MPa; T is the reservoir temperature, which also CO_{2} adsorption temperature, K; and m_{ex} is the CO_{2} excess adsorption amount per unit mass of coal, m^{3}/t, which can be calculated using the following DR adsorption model^{16,31}:
$$m_{ex} = m_{0} (1 – \rho_{f} /\rho_{a} )e^{{ – D\mathop {\left( {\ln (\rho_{a} /\rho_{f} )} \right)}\nolimits^{{^{2} }} }} + k\rho_{f}$$
(3)
where m_{0} is the maximum CO_{2} adsorption capacity of coal per unit mass tested by adsorption experiment, m^{3}/t; ρ_{f} and ρ_{a} are the densities of free and adsorbed CO_{2} under the real temperature and pressure conditions, kg/m^{3}; D is the adsorption constant, and k is the constant associated with Henry’s Law.
In coal reservoir, CO_{2} density is a function of pressure and temperature, which can be expressed as ρ_{f} = f(p, T), and can be further characterized as follows^{16,31,32}:
$$\rho_{g} = p/((1 + \delta \phi_{\delta }^{\tau } ) \cdot RT)$$
(4)
where δ = ρ_{c}/ρ_{f} is the CO_{2} reduced density; ρ_{c} is the CO_{2} critical density, kg/m^{3}; τ = T_{c}/T is the reduced temperature; and ϕ(δ,τ) is the Helmholtz free energy, which can be controlled by temperature and density^{16,31,32}:
$$\phi (\delta ,\tau ) = \phi^{0} (\delta ,\tau ) + \phi^{r} (\delta ,\tau )$$
(5)
where ϕ^{o}(δ, τ) is the Helmholtz free energy of ideal fluid, and ϕ^{r}(δ, τ) is the Helmholtz free energy of the residual fluid.
In deep unworkable seam, the storage potential of dissolved CO_{2} per unit mass of coal is a function of coal porosity, water saturation, coal density and CO_{2} solubility, which can be characterized as follows^{16,31}:
$$m_{d} = 1000 \cdot \varphi S_{w} S_{{CO_{2} }} /\rho_{Coal}$$
(6)
where φ is the coal porosity, %; S_{w} is the water saturation, %; \(S_{{{\text{CO}}_{2} }}\) is the CO_{2} solubility, and ρ_{coal} is the coal density, kg/m^{3}.
According to BoyleMariotte law, the free CO_{2} storage potential per unit mass of coal in deep unworkable seam can be characterized as follows^{16,31}:
$$m_{f} = 1000 \cdot \varphi S_{g} pT_{0} /(\rho_{visual} Zp_{0} T)$$
(7)
where S_{g} is the gas saturation, %; P_{0} is the standard atmospheric pressure, MPa; T_{0} is the temperature under the standard condition, K; and ρ_{visual} is the coal apparent density, kg/m^{3}.
Construction of matching model of CO_{2} sourcesink
CO_{2} source and sink matching
CO_{2} sourcesink matching is the basis of CCUS cluster deployment and its pipe network design and construction, with the goal of minimizing CO_{2} transportation cost and maximizing carbon removal. Its essence is the optimization planning of CCUS cluster system^{33,34}. Based on CO_{2} emission source, storage sink, storage geological process, transport network connecting source and sink and corresponding parameter data, the dynamic optimal matching between CO_{2} source and sink can be achieved in terms of target quantity, continuity and economic efficiency (Fig. 2).
The matching of CO_{2} source and sink is mainly based on the characteristics of large number, different types and scattered locations of CO_{2} emission sources (i.e., thermal power, steel, cement, chemical industry, etc.) and storage sinks (i.e., saltwater layer, CO_{2}ECBM, CO_{2}EOR, MCO_{2}ILU, CO_{2}SDR, etc.). Based on the discussion of constraint conditions and determination of objective function, the influence of regional geographical conditions, traffic, population density, transportation cost and transportation mode on CO_{2} transport between emission sources and storage sinks is fully considered in the CCUS system. The optimal matching of CO_{2} emission sources, storage sinks and transportation parameters was realized, so as to determine scientific and reasonable CO_{2} source and sink matching schemes (Fig. 2).
Objective functions
Based on the theory of network analysis in operations research, theoretical models of CO_{2} sourcesink matching within CCUS technology can be constructed in Huainan coalfield by using the minimum support tree method. The construction of theoretical models should meet the following basic assumptions: (1) Source and sink with the lowest cost should be firstly matched; (2) Allow the matching of one source with multi sinks or one sink with multi sources; (3) Sequestration sink must meet the requirement of CCUS planning period.
In this study, the lowest total cost of matching of CO_{2} sourcesink in CCS technology is taken as the objective function, namely:
$$COST_{\min } = \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{n} {(C_{C} + C{}_{T} + C_{S} } } )$$
(8)
where i refers to the ith CO_{2} source; j means the jth CO_{2} sink; m indicates the number of CO_{2} sources and the value is 10, and n indicates the number of CO_{2} sinks with the value of 15.

(1)
CO_{2} capture cost (i.e., C_{C})
Based on the analysis of the industrial sources report published by the National Energy Technology Laboratory of the United States, the average capture cost of CO_{2} source in coalfired power plants is $ 64.35 /t^{30,35}. Therefore, the capture cost of CO_{2} source in Huainan coalfield can be characterized as follows:
$$C_{C} = \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{n} {\omega_{ij} X_{ij} } }$$
(9)
where\(\omega_{ij}\) represents the CO_{2} capture cost in the i coalfired power plant, $/t; and X_{ij} represents CO_{2} transport amount from the i coalfired power plant to the j sequestration sink, t.

(2)
CO_{2} transportation cost (i.e., C_{T})
CO_{2} transport is most common by pipeline, ship and tanker, and pipeline transportation is suitable for directional transportation with large capacity, long distance and stable load, which mainly includes construction cost and operation and maintenance cost. The operation and maintenance cost accounts for about 1.5% of the construction cost^{35}, which can be calculated according to formula 10 and 11, respectively.
$$C_{T – j} = 9970 \times \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{n} {L^{1.13} X_{ij}^{0.35} } }$$
(10)
where L is the distance of pipeline transportation, km.
$$C_{T – y} = 0.015N \times 9970 \times \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{n} {L^{1.13} X_{ij}^{0.35} } }$$
(11)
where N represents the transportation cycle of the pipeline, year.
Therefore, CO_{2} transport cost can be characterized as follows:
$$C_{T} = (1 + 0.015N) \times 9970 \times \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{n} {L^{1.13} X_{ij}^{0.35} } }$$
(12)

(3)
CO_{2} sequestration cost (i.e., C_{S})
The cost of CO_{2} geological storage is closely related to the amount of CO_{2} storage and the type of storage site, and the average storage cost coefficient is $ 5.59 /t^{30,35}. Therefore, the cost of CO_{2} geological storage in coal reservoir can be characterized as follows:
$$C_{S} = \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{n} {\varepsilon_{ij} X_{ij} } }$$
(13)
where\(\varepsilon_{ij}\) is the sequestration cost factor of transporting CO_{2} from coalfired power plant i to sequestration sink j, $/t.
In summary, by substituting formulas (9), (12) and (13) into formula (8), the minimum objective function of total cost of CO_{2} sourcesink matching in CCS technology can be obtained:
$$MinZ = \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{n} {(\omega_{ij} X_{ij} + (1 + 0.015N) \times 9970 \times L^{1.13} X_{ij}^{0.35} + \varepsilon_{ij} X_{ij} } } )$$
(14)
Constraint conditions
Based on the basic assumptions of theoretical model, in the planning process of matching pipe network of CO_{2} sourcesink with CCS technology, the constraint conditions of the lowest total cost objective function are as follows:

(1)
The total amount of CO_{2} captured from all CO_{2} emission sources is equal to the total amount of pipeline transport, that is:
$$a_{i} = \sum\limits_{j = 1}^{n} {X_{ij} }$$
(15)
where a_{i} is the CO_{2} capture amount of the ^{i}th coalfired power plant.

(2)
The CO_{2} content transported by the pipeline to the storage site shall not exceed the storage capacity of the storage sink, that is:
$$b_{j} \ge \sum\limits_{i = 1}^{m} {X_{ij} }$$
(16)
where b_{j} is the storage capacity of the j^{th} storage sink.

(3)
The amount of CO_{2} captured in all coalfired power plants must not exceed the total capacity of all potential sequestration sinks, that is:
$$\sum\limits_{i = 1}^{m} {a_{i} } \le \sum\limits_{j = 1}^{n} {b_{j} }$$
(17)

(4)
Nonnegative constraint: the pipeline of CO_{2} transport content is nonnegative, that is:
Optimization of matching pipe network of CO_{2} sourcesink
The core idea of the mileage saving algorithm is to merge two transportation loops into one loop to reduce the transportation distance in the merging process, and keep cycling until the limit condition is reached, thus reducing the transportation cost. Specifically, three points, A, B and C, transport goods from A to B and C, where the distance from A to B is L_{AB} (unit: km), the distance from A to C is L_{AC} (unit: km), and the distance from B to C is L_{BC} (unit: km), if the transportation from A to B and A to C is separately completed, the transportation distance is 2 × (L_{AB} + L_{AC}) with including the round trip process (Fig. 3a). If from A to B, then from B to C, and finally from C back to A, then the transport distance is L_{AB} + L_{AC} + L_{BC} (Fig. 3a), then the distance saved is 2 × (L_{AB} + L_{AC}) − (L_{AB} + L_{AC} + L_{BC}) = L_{AB} + L_{AC} − L_{BC} > 0.
In CO_{2} sourcesink matching, each sink is taken as the distribution center and distributed with the connected source points. The basic principle is similar to the mileage saving method, except that there is only a transportation network from the source to the sink, and there is no return pipeline. Based on this, the idea of mileage saving method is introduced in this study, and it is improved to meet the needs of CO_{2} sourcesink matching and transportation network optimization. As shown in Fig. 3b, the CO_{2} emitted from points B and C is transported to the storage sink A for storage. The most direct way is from B to A, and then from C to A, with a transport distance of L_{AB} + L_{AC} (Fig. 3b). If it is transported from B to C and then from C to A or from C to B and then from B to A (Fig. 3b), the transport distance is L_{AC} + L_{BC} or L_{AB} + L_{BC}. L_{AB} and L_{AC} need to be compared to choose a route with a smaller distance for connection. If L_{BC} < L_{AB}/L_{AC}, then L_{AB} (L_{AC}) − L_{BC} is the savings; if L_{BC} > L_{AB}/L_{AC}, then L_{AB}/L_{AC} − L_{BC} is negative, which means no savings (Fig. 3b).