The optimisation problem is formulated as a general framework for cross-border CCS network design and operation. The proposed framework accommodates CCS systems involving multiple CO₂ emission sources, domestic and foreign storage alternatives, transport routes, infrastructure options, jurisdictions, and policy scenarios. The case-specific source locations, storage sites, transport distances, costs, capacities, and policy parameters are introduced later in the case study section.

Given a set of CO₂ emission sources i ∈ I, candidate storage sinks j ∈ J, transport routes r ∈ R, transport modes m ∈ M, countries or jurisdictions k ∈ K, operating periods t ∈ T, infrastructure options d ∈ D, and policy scenarios s ∈ S, the model determines the least-cost configuration and operation of the CCS chain. The storage set J may be divided into domestic storage alternatives J^D and foreign or cross-border storage sinks J^F. A general CCS superstructure is depicted in Figure 1.

Therefore, captured CO₂ can be allocated either to domestic storage or to cross-border export routes. The cross-border pathway links source-country capture and export activities with host-country import, transport, injection, and geological storage activities. This structure allows the same optimisation framework to evaluate domestic-versus-export storage decisions, route and sink selection, infrastructure sizing, energy use, emissions accounting, and carbon-credit allocation.

The decision problem is to determine the amount of CO₂ captured, uncaptured, transported, lost, injected, and stored; the routes, modes, sinks, and infrastructure options selected; the energy consumed by capture, conditioning, transport, and injection; and the country-level physical emissions, allocated credits, and net emissions. The objective is to minimise total annual system cost, including capture, transport, storage, energy, infrastructure, risk or access premiums, carbon penalties, and carbon-credit benefits, while satisfying mass-balance, capacity, loss, storage, energy, accounting, and policy constraints. Table 1 summarises the general sets and system elements used in the optimisation framework.

The generalised superstructure provides the basis for the mixed-integer linear programming (MILP) formulation. The model includes continuous variables for CO₂ capture, export flow, domestic storage, hub flow, stored CO₂, energy use, physical emissions, allocated credits, and net emissions. Binary variables indicate route and sink activation, while integer variables represent infrastructure-sizing decisions such as the number of offshore pipelines selected for each sink. The objective function and constraints are presented in the following subsections.

The objective function minimises the total annual system cost. It includes CO₂ capture, shipping and port services, annualised offshore-pipeline construction, host-country injection, storage and service charges, domestic transport and storage, pipeline and injection electricity, carbon penalties, and country-specific credit benefits.

The capture-cost coefficient is treated as an all-inclusive monetary proxy. Therefore, capture electricity is used to calculate physical emissions but is not charged separately in the objective function. Liquefaction and reconditioning electricity are treated in the same way because their monetary costs are already included in the corresponding port-service coefficients. This treatment prevents the same energy requirement from being counted twice.

(1) $$ \min Z=C^{\text {cap }}+C^{\text {ship }+ \text { port }}+C^{\text {pipe,fix }}+C^{\text {store }+ \text { service }}+C^{\text {dom }}+C^{\text {elec }}+C^{\text {pen }}-B^{\text {credit }} $$

where Z is the total annual objective cost; C^cap is the capture cost; C^ship+port is the shipping and port-service cost; C^pipe,fix is the annualised offshore-pipeline construction cost; C^{store+service} is the host-country injection, storage and service cost; C^dom is the domestic transport and storage cost in the source country; C^elec is the separately charged offshore-pipeline and injection electricity cost; C^pen is the carbon-penalty cost; and B^credit is the monetary benefit obtained from the allocated storage credit.

The carbon-credit benefit is calculated using country- and scenario-specific credit values:

(2) $$ B_{s}^{\text {credit }}=H \sum_{k \in K} \sum_{t \in T} P_{k, s}^{\text {credit }} \mathrm{Cr}_{k, t, s} $$

where B_s^credit is the total annual credit benefit under scenario s; H is the horizon-to-year scaling factor; K is the set of participating countries; T is the set of representative operating periods; P_k,s^credit is the credit value applied by country k under scenario s; and Cr_k,t,s is the verified storage credit allocated to country k in period t under scenario s.

This formulation allows the same physical amount of stored CO₂ to have different monetary values depending on the credit value and the share assigned to the source and host countries. Credit allocation affects economic and accounting outcomes but does not change the physical storage location.

The expanded annual objective function is:

(3) $$ \begin{aligned} \min Z ={}& H \Bigg[ \sum_{i \in I} \sum_{t \in T} c_i^{\text{cap}} x_{i,t} + \sum_{r \in R} \sum_{t \in T} c_r^{\text{ship}+\text{port}} f_{r,t} + \sum_{j \in J^F} \sum_{t \in T} c_{j,s}^{\text{store}+\text{service}} z_{j,t} \\ &+ \sum_{i \in I} \sum_{t \in T} c_{i,s}^{\text{dom}} d_{i,t}^{\text{dom}} + \sum_{j \in J^F} \sum_{t \in T} c_{k^{\text{host}}}^{\text{elec}} \left( E_{j,t}^{\text{pipe}} + E_{j,t}^{\text{inj}} \right) \\ &+ \sum_{k \in K} \sum_{t \in T} P_{k,s}^{\text{pen}} \mathrm{PE}_{k,t} - \sum_{k \in K} \sum_{t \in T} P_{k,s}^{\text{credit}} \mathrm{Cr}_{k,t,s} \Bigg] \\ &+ \sum_{j \in J^F} \sum_{d \in D} C_{j,d}^{\text{pipe, fix}} n_{j,d} \end{aligned} $$

where c_i^cap is the capture-cost coefficient for source i; x_i,t is CO₂ captured from source i in period t; c_r^ship+port is the shipping and port-service cost for route r; f_r,t is the gross CO₂ flow on route r; c_j,s^{store+service} is the injection, storage, and service-cost coefficient for foreign sink j under scenario s; z_j,t is CO₂ stored at sink j; c_i,s^dom is the domestic transport-and-storage cost for source i; d_i,t^dom is CO₂ assigned to domestic storage; $$ c_{k^{\mathrm{host}}}^{\mathrm{elec}} $$ is the host-country electricity price; E_j,t^pipe and E_j,t^inj are offshore-pipeline and injection electricity use; P_k,s^pen is the carbon-penalty value for country k; PE_k,t is the physical-emission total assigned to country k; P_k,s^credit is the credit value for country k; Cr_k,t,s is the allocated storage credit; C_j,d^pipe,fix is the annualised construction cost of pipeline option d for sink j; n_j,d is the number of pipelines installed; I, R, J^F, D, K, and T are the sets of sources, routes, foreign sinks, pipeline options, countries, and operating periods, respectively; and H converts representative-period values into annual values.

Variable operating costs are multiplied by H, whereas annualised pipeline-construction costs are added once outside the scaling term. Capture, liquefaction, and reconditioning electricity contribute to physical emissions but are not charged separately because their monetary costs are included in the corresponding capture and port-service coefficients.

The physical constraints conserve CO₂ from its source to domestic or foreign storage. They also enforce capture limits, route capacities, transport losses, injection capacities, storage limits, import restrictions, and infrastructure-selection requirements.

The source balance divides gross emissions into captured and uncaptured CO₂:

(4) $$ x_{i, t}+u_{i, t}=E_{i, t} \quad \forall i \in I, t \in T $$

where x_i,t is CO₂ captured from source i in period t; u_i,t is uncaptured CO₂ released from source i; E_i,t is the gross CO₂ emission from source i; I is the set of emission sources; and T is the set of operating periods.

The technical capture fraction limits the share of source emissions that can be captured:

(5) $$ x_{i, t} \leq \eta_{i} E_{i, t} \quad \forall i \in I, t \in T $$

where η_i is the maximum technically achievable capture fraction for source i; E_i,t is the gross source emission; and x_i,t is the captured quantity.

The installed capture capacity provides a separate physical limit:

(6) $$ x_{i, t} \leq \bar{X}_{i, t} \quad \forall i \in I, t \in T $$

where $$ \bar{X} $$_i,t is the installed capture capacity available at source i in period t, and x_i,t is the amount captured. The capture fraction is not applied to $$ \bar{X} $$_i,t because technical capture efficiency and installed equipment capacity represent different constraints.

Captured CO₂ can be allocated to domestic storage or cross-border export:

(7) $$ x_{i, t}=\sum_{r \in R_{i}} f_{r, t}+d_{i, t}^{\text {dom }} \quad \forall i \in I, t \in T $$

where R_i is the set of export routes connected to source i; f_r,t is the CO₂ exported through route r; and d_i,t^dom is the CO₂ assigned to domestic storage in the source country.

Export flow is permitted only when the corresponding route is activated:

(8) $$ f_{r, t} \leq \bar{F}_{r, t} y_{r} \quad \forall r \in R, t \in T $$

where f_r,t is the export flow on route r; $$ \bar{F} $$_r,t is its maximum transport capacity; and y_r is a binary variable equal to 1 when route r is activated and 0 otherwise.

CO₂ arriving at the host-country import hub is calculated after shipping losses:

(9) $$ \mathrm{~h}_{j, t}=\sum_{r \in R_{j}}\left(1-\lambda_{r}^{\text {ship }}\right) f_{r, t} \quad \forall j \in J^{F}, t \in T $$

where h_j,t is the CO₂ arriving at the import hub serving foreign sink j; R_j is the set of routes supplying sink j; λ_r^ship is the shipping-loss fraction for route r; and f_r,t is the gross exported quantity.

The quantity stored at a foreign sink is calculated after offshore-pipeline losses:

(10) $$ z_{j, t}=\left(1-\lambda_{j}^{\text {pipe }}\right) \mathrm{h}_{j, t} \quad \forall j \in J^{F}, t \in T $$

where z_j,t is the CO₂ stored at foreign sink j; h_j,t is the CO₂ entering the offshore pipeline; and λ_j^pipe is the offshore-pipeline operating-loss fraction.

The case study uses λ_j^pipe = 0, meaning that all CO₂ entering the offshore pipeline is assumed to reach the sink. This does not mean pipeline leakage is physically impossible. It means that no unsupported routine-loss value is imposed when project-specific operating-loss data are unavailable. The equation permits a verified non-zero value in future applications.

Hub flow cannot exceed the foreign-available injection capacity of the selected sink:

(11) $$ \mathrm{~h}_{j, t} \leq \bar{Q}_{j, s}^{\text {avail }} w_{j} \quad \forall j \in J^{F}, t \in T $$

where $$ \bar{Q} $$_j,s^avail is the injection capacity available for imported CO₂ at sink j under scenario s; w_j is a binary variable equal to 1 when sink j is activated and 0 otherwise; and h_j,t is the hub flow supplied to that sink.

Annualised storage cannot exceed the available geological capacity:

(12) $$ H \sum_{t \in T} z_{j, t} \leq \bar{S}_{j} \quad \forall j \in J^{F} $$

where H is the horizon-to-year scaling factor; z_j,t is stored CO₂ in period t; and $$ \bar{S} $$_j is the storage capacity assigned to sink j over the modelled horizon.

The host-country import cap limits total cross-border delivery:

(13) $$ H \sum_{r \in R} \sum_{t \in T} f_{r, t} \leq \bar{M}_{s}^{\text {import }} $$

where $$ \bar{M} $$_s^import is the maximum annual import allowance under scenario s; f_r,t is the gross export flow; and H converts representative-period flow into an annual quantity.

A minimum-export constraint is applied only in scenarios designed to require cross-border participation:

(14) $$ H \sum_{r \in R} \sum_{t \in T} f_{r, t} \geq M_{s}^{\text {min }} $$

where M_s^min is the minimum annual export requirement under scenario s; f_r,t is the export flow; and H is the annual scaling factor. When M_s^min = 0, the model is not required to export CO₂.

Hub flow cannot exceed the installed offshore-pipeline capacity:

(15) $$ \mathrm{h}_{j, t} \leq \sum_{d \in D} \bar{P}_{d} n_{j, d} \quad \forall j \in J^{F}, t \in T $$

where $$ \bar{P} $$_d is the capacity of pipeline-diameter option d; n_j,d is the integer number of pipelines of option d installed for sink j; and D is the set of available pipeline options.

Pipeline construction is linked to sink activation:

(16) $$ n_{j, d} \leq \bar{N}_{d} w_{j} \quad \forall j \in J^{F}, d \in D $$

where n_j,d is the number of pipelines installed; $$ \bar{N} $$_d is the maximum allowable number of parallel pipelines of option d; and w_j is the sink-activation variable. This constraint prevents pipelines from being installed for an inactive sink.

Energy use is linked directly to CO₂ flow at each operating stage. Capture and export-terminal liquefaction take place in the source country. Import-terminal reconditioning, offshore-pipeline transport, and injection take place in the host country. Domestic storage requires capture electricity together with the electricity used for domestic pipeline transport and injection.

Electricity use is first calculated in physical units and is then converted into emissions using the appropriate country grid-emission factor. Capture, liquefaction and reconditioning electricity are used for emissions accounting but are not charged separately because their costs are included in the corresponding service coefficients. Offshore-pipeline and injection electricity for the foreign-storage pathway are priced separately.

Capture electricity is proportional to the amount of CO₂ captured:

(17) $$ E_{i, t}^{\mathrm{cap}}=a_{i}^{\mathrm{cap}} x_{i, t} \quad \forall i \in I, t \in T $$

where E_i,t^cap is capture electricity use at source i; a_i^cap is the capture-electricity coefficient; and x_i,t is captured CO₂.

Offshore-pipeline electricity depends on pipeline distance and transported CO₂:

(18) $$ E_{j, t}^{\mathrm{pipe}}=a_{j}^{\mathrm{pipe}} D_{j}^{\mathrm{pipe}} \mathrm{~h}_{j, t} \quad \forall j \in J^{F}, t \in T $$

where E_j,t^pipe is offshore-pipeline electricity use; a_j^pipe is the distance-based pipeline-energy coefficient; D_j^pipe is the offshore-pipeline distance to sink j; and h_j,t is the CO₂ entering the pipeline.

Injection electricity is proportional to the amount of CO₂ stored:

(19) $$ E_{j, t}^{\mathrm{inj}}=a_{j}^{\mathrm{inj}} z_{j, t} \quad \forall j \in J^{F}, t \in T $$

where E_j,t^inj is injection electricity use; a_j^inj is the injection-energy coefficient; and z_j,t is the quantity injected and stored.

Shipping emissions are proportional to the gross quantity exported:

(20) $$ \mathrm{SE}_{t}=\sum_{r \in R} a_{r}^{\mathrm{ship}} f_{r, t} \quad \forall t \in T $$

where SE_t is direct shipping-related CO₂ emissions in period t; a_r^ship is the shipping-emissions coefficient for route r; and f_r,t is the gross CO₂ flow transported through that route.

These energy requirements are included in the physical-emissions calculation but are not charged separately in the objective because their monetary contributions are included in the port-service coefficients.

The carbon-accounting framework separates physical operational emissions from allocated storage credits. This distinction is necessary because the country generating and capturing the CO₂ may differ from the country providing transport, injection, and geological storage services.

The model first calculates the physical emissions assigned to each participating country:

(21) $$ \mathrm{PE}_{k, t}=\mathrm{UE}_{k, t}+\mathrm{EE}_{k, t}+\mathrm{SE}_{k, t} \quad \forall k \in K, t \in T $$

where PE_k,t is the total physical emission assigned to country k; UE_k,t is uncaptured source emissions assigned to that country; EE_k,t is grid-related emissions from CCS energy use occurring in that country; and SE_k,t is direct shipping emissions assigned to that country under the modelled accounting boundary. Under the adopted boundary, $$ \mathrm{SE}_{k^{\mathrm{src}},t} $$ = SE_t and $$ \mathrm{SE}_{k^{\mathrm{host}},t} $$ = 0 because direct shipping emissions are assigned to the source country.

For the source country, physical emissions comprise uncaptured source emissions, grid emissions from capture and liquefaction, direct shipping emissions, and the energy-related emissions from domestic transport and injection when domestic storage is selected:

(22) $$ \mathrm{PE}_{k^{\mathrm{src}}, t}=\sum_{i \in I\left(k^{\mathrm{src}}\right)} u_{i, t}+\gamma_{k^{\mathrm{src}}}\left[\sum_{i \in I\left(k^{\mathrm{src}}\right)} E_{i, t}^{\mathrm{cap}}+a^{\mathrm{liq}} \sum_{r \in R} f_{r, t}+\left(a^{\mathrm{pipe}} D^{\mathrm{dom}}+a^{\mathrm{inj}}\right) \sum_{i \in I\left(k^{\mathrm{src}}\right)} d_{i, t}^{\mathrm{dom}}\right]+\mathrm{SE}_{k^{\mathrm{src}}, t} $$

where $$ \mathrm{PE}_{k^{\mathrm{src}},t} $$ is the physical-emission total for the source country; I(k^src) is the set of emission sources located in the source country; u_i,t is uncaptured CO₂; $$ \gamma_{k^{\mathrm{src}}} $$ is the source-country grid-emission factor; E_i,t^cap is capture electricity; a^liq is the liquefaction-energy coefficient; f_r,t is exported CO₂; a^pipe is the domestic pipeline-energy coefficient; D^dom is the assumed domestic pipeline distance; a^inj is the injection-energy coefficient; d_i,t^dom is CO₂ assigned to domestic storage; and $$ \mathrm{SE}_{k^{\mathrm{src}},t} $$ is direct shipping emissions assigned to the source country.

The domestic-storage emissions calculation includes the same quantified operating stages used for the export pathway: capture, pipeline transport, and injection. Monitoring is included in the monetary domestic-storage benchmark, but no separate monitoring-electricity value is added because the supporting source does not provide a defensible coefficient.

For the host country, physical emissions comprise electricity-related emissions from import-terminal reconditioning, offshore-pipeline transport and injection:

(23) $$ \mathrm{PE}_{k^{\mathrm{host}}, t}=\gamma_{k^{\mathrm{host}}}\left[a^{\mathrm{rec}} \sum_{j \in J^{F}} \mathrm{~h}_{j, t}+\sum_{j \in J^{F}}\left(E_{j, t}^{\mathrm{pipe}}+E_{j, t}^{\mathrm{inj}}\right)\right] $$

where $$ \mathrm{PE}_{k^{\mathrm{host}},t} $$ is the host-country physical-emission total; $$ \gamma_{k^{\mathrm{host}}} $$ is the host-country grid-emission factor; a^rec is the import-terminal reconditioning-energy coefficient; h_j,t is the CO₂ received at the import hub serving sink j; E_j,t^pipe is offshore-pipeline electricity; E_j,t^inj is injection electricity; and J^F is the set of foreign storage sinks.

The anonymised foreign sinks use the same host-country grid-emission factor because they are assumed to operate within the same host-country electricity system. This value is a country-level case-study input rather than a site-specific measurement.

Net accounting emissions are calculated after the allocated storage credit is deducted from physical emissions:

(24) $$ \mathrm{NE}_{k, t, s}=\mathrm{PE}_{k, t}-\mathrm{Cr}_{k, t, s} \quad \forall k \in K, t \in T, s \in S $$

where NE_k,t,s is the net accounting-emission balance for country k under scenario s; PE_k,t is the country’s physical operational emissions; and Cr_k,t,s is the verified storage credit allocated to that country.

A negative value of NE_k,t,s indicates that the allocated accounting credit exceeds the physical emissions generated by the modelled CCS operations. It represents an accounting outcome and should not be interpreted as physically negative emissions.

The credit-allocation formulation is defined using an explicit source–sink mapping to avoid ambiguity in the allocation of verified stored CO₂. Let A_i,j be a binary mapping parameter equal to 1 if captured CO₂ from source i can be allocated to storage sink j, and 0 otherwise. The variable z_i,j,t represents the amount of CO₂ from source i that is finally stored in sink j during period t, after transport and storage losses have been accounted for. This source–sink-specific storage variable ensures that the verified stored CO₂ is traced from its originating source to its final storage location.

The country-level credit allocated to country k in period t under scenario s is therefore expressed as:

(25) $$ Cr_{k, t, s} =\sum_{i \in I}\sum_{j\in J}A_{i,j}z_{i,j,t}[\alpha _s^{src}\delta _{i,k}^{src}+\alpha _s^{host}\delta _{j,k}^{host}]\quad \forall k,t,s $$

where Cr_k,t,s is the CO₂ storage credit allocated to country k in period t under scenario s, A_i,j is the source–sink mapping parameter, z_i,j,t is the verified CO₂ stored at sink j from source i, α_s^src is the share of the storage credit allocated to the source country, and α_s^host is the share allocated to the host storage country. The binary indicator δ_i,k^src equals 1 if source i is located in country k, and 0 otherwise. Similarly, δ_j,k^host equals 1 if storage sink j is located in country k, and 0 otherwise.

To prevent double counting, the source and host credit shares are constrained as:

(26) $$ \alpha _s^{src}+\alpha _s^{host}=1 \quad \forall s\in S $$

This formulation ensures that each unit of verified stored CO₂ is allocated only once across the participating countries, subject to α_source + α_host = 1. A value of α_source = 1 assigns the full storage benefit to the source country, whereas α_host = 1 assigns it entirely to the host country. Intermediate values represent shared-benefit arrangements. The α parameters affect the allocation and monetary value of the verified storage benefit but do not change the physical CO₂ flows or stored quantities. These cases are hypothetical policy scenarios used to test model behaviour and are not interpreted as established international carbon-accounting practices. In practice, the allocation rule would depend on bilateral agreements, domestic regulations, contractual terms, MRV requirements, infrastructure contributions, liability allocation, and agreed responsibilities for CO₂ transport and long-term storage.

The case study represents an anonymised Japan–Malaysia cross-border CCS system with two Japanese CO₂ source nodes, JP-Source 1 and JP-Source 2, and two Malaysian offshore storage sink nodes, MY-Sink 1 and MY-Sink 2. The pairing reflects a policy-relevant Asian source–host configuration: Japan represents a geographically compact industrial source country that may face a mismatch between future capture volumes and conveniently accessible domestic storage, whereas Malaysia represents a host country with emerging offshore storage ambitions. More broadly, the case illustrates how uneven distributions of industrial emissions and geological storage resources can motivate regional CO₂ transport and storage cooperation^[1,2]. JP-Source 1 represents a Japanese industrial CO₂ source with access to marine export infrastructure. JP-Source 2 has different source and route characteristics, which allows the model to test whether multiple sources converge on the same Malaysian sink or select different sinks as costs, capacities, and transport conditions change. Two Malaysian offshore sinks, MY-Sink 1 and MY-Sink 2, differ in their transport requirements, injection capacities, and commercial conditions. The export network contains four feasible routes: JP-Source 1–MY-Sink 1, JP-Source 1–MY-Sink 2, JP-Source 2–MY-Sink 1, and JP-Source 2–MY-Sink 2. A domestic Japanese storage alternative, JP-Domestic Sink, is also included to compare cross-border export with a non-export pathway. Figure 2 shows the network and Table 2 summarises the modelling role of each node and route.

Inputs are grouped as fixed engineering and country data, literature-derived benchmarks, anonymised system assumptions, derived route values, and scenario settings. Table 3 identifies each group’s provenance, MILP role, and scenario dependence, distinguishing model inputs from contextual information.

The scenario design is divided into four categories to represent the main decision dimensions in cross-border CCS, which include physical pathway selection, commercial and policy support, access constraints, and accounting allocation. This structure allows the analysis to examine how each dimension affects the economic competitiveness, CO₂ allocation, and distribution of verified-storage benefits between the source and host countries.

Reference pathways represent the two basic CCS options considered in the model, which are exporting CO₂ to Malaysia or storing it domestically in Japan. The commercial and policy-support scenarios then examine whether changes in economic conditions can improve the competitiveness of cross-border storage. The Low-Fee case reduces the Malaysian storage-service fee, while the Credit Support case introduces a storage-related credit benefit. Combined Competitiveness applies three favourable conditions together, which are a lower Malaysian storage-service fee, equal sharing of the storage credit between Japan and Malaysia, and higher domestic storage cost in Japan. Both domestic storage and export remain available, which allows the model to determine which pathway is preferred under these conditions.

The physical-access category examines whether an allocation requirement changes this decision. In the Forced Hybrid case, at least 1.0 MtCO₂/year must be exported to Malaysia, while the remaining CO₂ may still be stored in Japan. This represents a participation or access requirement.

The credit-allocation scenarios focus only on how the verified-storage benefit is shared between the two countries. The physical export system is kept unchanged, while the allocation parameters are varied. The Source Claim case assigns the full benefit to Japan (α_source = 1), Shared Credit divides it equally (0.5, 0.5), and Host Claim assigns the full benefit to Malaysia (α_host = 1). In all cases, α_source + α_host = 1 to ensure that the same storage benefit is counted only once. Credit Support and Combined Competitiveness use equal sharing between the two countries.

No storage credit is applied in the Reference, Low-Fee, or Forced Hybrid cases. When the credit mechanism is enabled, the benefit for each tonne stored is calculated from the shares assigned to Japan and Malaysia and their respective credit values. The credit changes the economic value of storage but does not change the physical location of the stored CO₂. MY-Sink 1 reservation and sink risk premiums are set to zero in all reported scenarios. Table 8 summarises the inputs changed in each scenario; all other model inputs remain unchanged.

This section examines how changes in economic support, physical-access conditions, and credit allocation affect the total system cost and selected CCS configuration. Table 9 presents the selected pathway, storage sink, CO₂ flow, operational emissions, and annual objective cost according to the four scenario categories defined in Section “Scenario design”.

Under the reference assumptions, Base Export has an annual objective cost of USD 0.484 billion, compared with USD 0.327 billion for the Domestic Japan benchmark. Both pathways capture 2.716 MtCO₂/year. However, the export pathway stores 2.674 MtCO₂/year in Malaysia after shipping losses, whereas the domestic pathway stores the full captured amount in Japan.

Commercial and policy support reduces the cost disadvantage of cross-border storage. The Low-Fee, Credit Support, and Combined Competitiveness cases reduce the annual objective cost to USD 0.468 billion, USD 0.443 billion, and USD 0.426 billion, respectively. In the Combined Competitiveness case, the model selects full export to MY-Sink 1 instead of the upper-end domestic alternative available within that scenario. Nevertheless, its cost remains approximately USD 99 million/year above the base domestic screening benchmark. Therefore, the result demonstrates that export can become competitive under a coordinated set of favourable conditions, but it does not establish that export is universally cheaper than domestic storage.

All unconstrained export cases select MY-Sink 1 because it has the lower delivered transport cost. The Forced Hybrid case produces a different physical configuration because the minimum-export requirement prevents the model from selecting a fully domestic pathway. It exports 1.000 MtCO₂/year, of which 0.985 MtCO₂/year is stored in Malaysia after shipping losses, while the remaining 1.716 MtCO₂/year is stored in Japan.

Credit allocation changes the distribution and monetary value of the verified storage benefit without changing the physical route or storage location. The Source Claim, Equal Sharing, and Host Claim cases provide annual credit benefits of USD49.79 million, USD41.36 million, and USD32.94 million, respectively. Their corresponding objective costs are USD0.434 billion, USD0.443 billion, and USD0.451 billion. All three cases retain full export to MY-Sink 1. The lower objective under Source Claim occurs because the modelled source-country credit value is higher than the host-country value, rather than because of a change in the physical CCS system.

Overall, the results show that pathway selection depends on the combined effect of commercial conditions, policy support, and physical constraints. Fee reductions and carbon credits improve export competitiveness, while access requirements can directly change the allocation between domestic and cross-border storage. Credit ownership mainly affects how the economic benefit is shared and does not, by itself, change the selected route. These comparisons should still be interpreted cautiously because domestic storage is represented by an aggregate screening benchmark, whereas the export network is modelled in greater physical detail. Therefore, the results support strategic comparison and identification of switching conditions, rather than a definitive project-level ranking of domestic and cross-border storage.

The emissions reported in Table 9 follow a matched operational boundary covering uncaptured CO₂, electricity-related emissions from capture, conditioning, pipeline transport and injection, and direct shipping emissions.

This section examines the cost difference between domestic and cross-border storage, identifies the main cost components, and compares the modelled values with published CCS cost ranges. Figure 3 shows an annual objective cost of USD 484.19 million for Base Export and USD 326.96 million for Domestic Screening, which gives a difference of USD 157.23 million/year. The Low-Fee and Credit Support cases reduce the export cost to USD467.72 million/year and USD442.83 million/year, respectively. Combined Competitiveness further reduces the objective to USD426.36 million/year and selects export over its upper-end domestic alternative of USD64.23/tCO₂. However, the base domestic pathway, at USD18.33/tCO₂, remains cheaper.

Figure 4 compares the objective-cost components per tonne of CO₂ captured. Capture contributes USD100/tCO₂ in all three pathways. The net objectives are USD178.27/tCO₂ for Base Export, USD120.38/tCO₂ for Base Domestic Storage, and USD156.98/tCO₂ for Combined Competitiveness. The lower service fee and shared carbon-credit benefit reduce the cost of the combined export case. Nevertheless, transport and host-country storage charges keep its objective above the base domestic benchmark.

Recent optimisation studies cover source–sink networks^[36], cluster and system abatement^[37], multi-period supply chains^[38-40], and industrial full-chain deployment^[41,42]. Figure 5 provides a scale check using studies with sufficiently comparable ranges, together with earlier transport and full-chain estimates^{[9,15,17,28,43]}. Cost scopes differ, so transport-only estimates cannot be ranked directly against objectives that include capture, conditioning, infrastructure, storage, penalties, and credits.

Overall, the results indicate that commercial and policy support can substantially reduce the cost of cross-border CCS, but it does not automatically make export cheaper than the lowest domestic benchmark. The Combined Competitiveness result is best interpreted as evidence of conditional competitiveness in which export becomes the preferred decision only when it is compared with the upper-end domestic alternative under the same scenario. The published ranges support the order of magnitude of the modelled costs, but these do not validate an exact project cost because the estimates depend on source type, transport distance, system capacity, financing assumptions, energy boundaries, and price year. Across the three pathways presented in Figure 4, capture remains the largest single positive cost component.

Transport and storage characteristics influence route and sink selection. These include shipping distance, line-haul cost, shipping loss, offshore-pipeline distance, and injection capacity. In the Base Export case, both sources deliver CO₂ to MY-Sink 1. Of the 2.716 MtCO₂/year exported, 2.674 MtCO₂/year is stored after a shipping loss of 1.53%. Compared with MY-Sink 2, the route to MY-Sink 1 is 638.3 km shorter and USD2.83/tCO₂ cheaper for JP-Source 1. For JP-Source 2, it is 561.2 km shorter and USD2.49/tCO₂ cheaper. The offshore pipeline serving MY-Sink 1 is also 15.2 km shorter. MY-Sink 1 receives 2.674 MtCO₂/year, which remains below its injection capacity of 3.7 MtCO₂/year. MY-Sink 2 provides a higher injection capacity of 5.0 MtCO₂/year but is not selected because its additional capacity is unnecessary at the modelled flow and does not offset its higher transport cost. Figure 6 compares the route and sink attributes.

Overall, the result shows that lower delivered transport cost determines sink selection when both sinks have sufficient capacity and share the same storage assumptions. However, MY-Sink 2 may become preferable at higher CO₂ flows, under tighter capacity conditions, or if its relative transport and storage costs decrease. Therefore, the selection of MY-Sink 1 should be interpreted as a result of the current case-study configuration.

This section explores how alternative credit-sharing arrangements affect the economic benefit and country-level accounting outcomes without changing the physical CCS system. All three α cases physically store 2.674 MtCO₂/year in Malaysia at MY-Sink 1. The Source Claim, Equal Sharing, and Host Claim cases provide annual credit benefits of USD49.79 million, USD41.36 million, and USD32.94 million, respectively. Their corresponding annual objective costs are USD0.434 billion, USD0.443 billion, and USD0.451 billion. The difference arises because Japan has a higher modelled carbon-credit value than Malaysia. Therefore, the allocation of a larger share to Japan produces a greater economic benefit and a lower system objective.

Figure 7 separates physical emissions, allocated storage credit, and the resulting net accounting balance. Under Source Claim, the net balances for Japan and Malaysia are -2.287 and +0.006 MtCO₂/year, respectively. Under Equal Sharing, the corresponding balances are -0.950 and -1.331 MtCO₂/year. Under Host Claim, the net balances become +0.387 and -2.669 MtCO₂/year. In every case, the CO₂ remains physically stored in Malaysia, and only the ownership and monetary value of the accounting benefit change.

Overall, the results show that credit allocation can materially affect the distribution of economic and accounting benefits even when the physical route, storage sink, and stored quantity remain unchanged. The lowest objective under Source Claim reflects Japan’s higher assumed credit value, not a more efficient physical configuration.

A matched operational boundary is applied to compare the emissions generated by domestic, export, and hybrid CCS pathways. The resulting operational emissions are 0.208 MtCO₂/year for Domestic Storage, 0.393 MtCO₂/year for Base Export, and 0.276 MtCO₂/year for Forced Hybrid. Base Export produces the highest operational emissions, mainly because it requires liquefaction electricity and long-distance shipping. Infrastructure-construction emissions and other full life-cycle effects are excluded from this comparison.

The Domestic Japan pathway stores the full captured quantity of 2.716 MtCO₂/year. Base Export sends 2.716 MtCO₂/year to Malaysia and stores 2.674 MtCO₂/year after shipping losses. Forced Hybrid exports 1.000 MtCO₂/year, of which 0.985 MtCO₂/year is stored in Malaysia, while the remaining 1.716 MtCO₂/year is stored in Japan. Figure 8 distinguishes the amount allocated to each pathway, the quantity reaching storage, and the associated operational emissions.

Overall, cross-border export achieves substantial CO₂ storage but produces higher operational emissions and slightly lower delivered storage because of additional conditioning, shipping, and transport losses. Forced Hybrid lies between the fully domestic and fully exported pathways because it uses both systems. These results show the operational trade-off between accessing foreign storage and the additional energy and emissions required for cross-border transport.

The sensitivity analysis evaluates both cost responsiveness and decision stability around the Combined Competitiveness case. Figure 9 illustrates one-at-a-time (OAT) objective-cost responses. The reference applies a USD 6.16/tCO₂ service fee, equal source–host credit shares, and a domestic downstream cost of USD 64.23/tCO₂, while the domestic reservation and sink-specific premiums are set to zero.

Five inputs are varied separately by ±10%: shipping cost, domestic pathway cost, country-specific credit values, service fee, and Malaysian storage-and-injection cost. In the credit test, the Japanese and Malaysian credit values change together by the same percentage. Each endpoint represents a separate MILP optimisation in which only one input changes, while all other inputs and scenario settings remain fixed.

The reference solution selects full export of 2.716 MtCO₂/year to MY-Sink 1, with an annual objective cost of USD 426.358 million. Malaysian storage-and-injection cost produces the largest endpoint range at USD 14.478 million/year. This is followed by shipping cost at USD 11.469 million/year, credit values at USD 8.273 million/year, and the service fee at USD 3.294 million/year. Higher credit values reduce the objective because the credit is treated as an economic benefit. Domestic pathway cost has no local effect because the model retains full export at both endpoints.

None of the ±10% changes alter the selected pathway or sink; every optimisation continues to select full export to MY-Sink 1. This indicates that the Combined Competitiveness decision is locally stable within the tested ranges. However, the result does not show that the decision would remain unchanged under larger variations or simultaneous changes in several inputs. The zero response to domestic cost also does not mean that domestic cost is generally unimportant, as it remains inactive within this limited range.

Overall, the OAT analysis identifies the inputs that have the strongest local effects on the optimised cost and tests whether moderate individual changes alter the infrastructure decision. As a local analysis within a deterministic MILP, it does not account for probability distributions, correlations between uncertain inputs, or combined uncertainty. Wider-range, multi-parameter, or probabilistic analyses would be required to identify switching thresholds and assess broader decision risk.