Remote Renewable Hubs For Carbon-Neutral Synthetic Fuel Production
Mathias Berger, David Radu, Ghislain Detienne, Thierry Deschuyteneer, Aurore Richel, Damien Ernst
RR EMOTE R ENEWABLE H UBS F OR C ARBON -N EUTRAL S YNTHETIC F UEL P RODUCTION P REPRINT VERSION
Mathias Berger ∗ Department of Electrical Engineering and Computer ScienceUniversity of LiègeLiège, Belgium [email protected]
David Radu
Department of Electrical Engineering and Computer ScienceUniversity of LiègeLiège, Belgium [email protected]
Ghislain Detienne
Fluxys SABrussels, Belgium [email protected]
Thierry Deschuyteneer
Fluxys SABrussels, Belgium [email protected]
Aurore Richel
Laboratory of Biomass and Green TechnologiesGembloux Agro-Bio Tech - University of LiègeGembloux, Belgium [email protected]
Damien Ernst
Department of Electrical Engineering and Computer ScienceUniversity of LiègeLiège, Belgium [email protected]
February 24, 2021 A BSTRACT
This paper studies the economics of carbon-neutral synthetic fuel production from renewable electric-ity in remote areas where high-quality renewable resources are abundant. To this end, a graph-basedoptimisation modelling framework directly applicable to the strategic planning of remote renewableenergy supply chains is proposed. More precisely, a graph abstraction of planning problems isintroduced, wherein nodes can be viewed as optimisation subproblems with their own parameters,variables, constraints and local objective, and typically represent a subsystem such as a technology,a plant or a process. Edges, on the other hand, express the connectivity between subsystems. Theframework is leveraged to study the economics of carbon-neutral synthetic methane productionfrom solar and wind energy in North Africa and its delivery to Northwestern European markets.The full supply chain is modelled in an integrated fashion, which makes it possible to accuratelycapture the interaction between various technologies on hourly time scales. Results suggest that thecost of synthetic methane production and delivery would be slightly under 200 e /MWh and 150 e /MWh by 2030 for a system supplying 100 TWh (higher heating value) annually that relies on solarphotovoltaic plants alone and a combination of solar photovoltaic and wind power plants, respectively,assuming a uniform weighted average cost of capital of 7%. The cost difference between these systemconfigurations mostly stems from higher investments in technologies providing flexibility required tobalance the system in the solar-driven configuration. Synthetic methane costs would drop to roughly124 e /MWh and 87 e /MWh, respectively, if financing costs were zero and only technology costswere taken into account. Prospects for cost reductions are also discussed, and options that wouldenable such reductions are reviewed. K eywords optimisation · renewable energy · carbon neutral · synthetic fuels · remote supply chain · linearprogramming · structured models · graph ∗ Corresponding author a r X i v : . [ ee ss . S Y ] F e b REPRINT VERSION - F
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Electricity generation from renewable resources combined with wide-ranging electrification has been a mainstayof European climate and energy policies, with the primary goal of decarbonising the power sector as well as othercarbon-intensive sectors.Major obstacles to such endeavours have nevertheless surfaced in recent years. Firstly, sectors like aviation, shipping,heating or industry have proved difficult to fully electrify. Indeed, feedstocks and energy carriers with specific propertiessuch as a high energy density are typically required [1]. Hence, the production of carbon-neutral synthetic fuels andfeedstocks from renewable electricity has been the focus of a growing body of literature. For example, the synthesisof carbon-neutral hydrogen [2], methane [3], methanol [4] and ammonia [5] have all been considered. A number ofdemonstration projects have been carried out as well [6]. Secondly, it has become clear that the technical renewablepotential of some European countries (i.e., the maximum amount of renewable electricity that may produced within acountry’s borders and exclusive economic zone, while accounting for a variety of land eligibility constraints [7]) isinsufficient to supply current energy demand levels (e.g., in densely-populated countries like Belgium [8, 9] or theUnited Kingdom [10]). It is still unclear whether pooling renewable resources at the European level would alleviate theproblem. On the hand other, it is well-documented that social acceptance issues tend to compound it [11].A simple solution consists in harvesting renewable resources in remote areas where they are abundant, synthesisingcarbon-neutral fuels or feedstocks using renewable electricity and transporting them back to demand centres [12, 13, 14].However, two conditions must be satisfied for such an approach to be worth pursuing. Firstly, transport should beenergy-efficient and cost-effective. This will often depend on the physics of the commodity considered and the maturityof technologies available to handle it. Secondly, very-high-quality renewable resources should be tapped. The qualityof such resources is typically estimated via the annual capacity factor of a given technology harnessing them, whichdirectly reflects the amount of electricity that may be produced per unit capacity. Since renewable power generationtechnologies usually have very low operating costs, the higher the capacity factor, the lower the electricity cost. Regionswith outstanding resources and vast technical potential include Patagonia (wind) [14], North Africa (sun and wind)[12] and Greenland (wind) [15]. Providing an accurate quantitative assessment of the economics and efficiency of suchremote renewable energy supply chains and pathways is critical to evaluate future sustainable energy supply optionsavailable to policy makers and society at large as well as to identify where to direct future research and innovationefforts.From a conceptual standpoint, a supply chain can be viewed as a networked system composed of dynamical subsystemsinteracting with each other. In order to tackle the problem formulated above, the collection of processes and technologiesforming a remote renewable energy supply chain must be analysed in an integrated fashion, which makes it possible toproperly capture the interactions between subsystems. In addition, a sufficient level of technical detail and temporalresolution should be used to properly model their operation [16]. This paper formalises these considerations andproposes a graph-based optimisation modelling framework directly applicable to the strategic planning and analysis ofremote renewable energy supply chains. More precisely, a graph abstraction of planning problems is introduced, whereinnodes can be viewed as optimisation subproblems with their own parameters, variables, constraints and local objective,and typically represent a subsystem such as a technology, a plant or a process. Edges, on the other hand, express theconnectivity between subsystems. The framework is then leveraged to study the economics of carbon-neutral syntheticmethane production from renewable electricity and atmospheric carbon dioxide in North Africa and its delivery toNorthwestern European markets. Synthetic methane is an appealing carbon-neutral energy carrier, as some downstreamtransport infrastructure is readily available in Northwestern European countries, and the liquefied methane chain ismature and cost-effective [17]. It would also avoid the replacement or upgrade of appliances and processes presentlyused for residential heating and in industry that a switch to other fuels would entail. In this paper, the carbon-neutralsynthetic methane supply chain is modelled end-to-end, from power generation in North Africa to methane regasificationin Northwestern Europe. A detailed description of each process and technology is provided, along with comprehensivedata resources. The modelling framework also served as a basis for the development of an open source optimisationmodelling language [18] and tool [19]. In the interest of transparency, the input files and full data enabling others toreproduce the analyses presented in this paper are also available in the associated repository [19].This paper is structured as follows. Section 2 reviews the relevant literature. Section 3 details the proposed modellingframework, while Sections 4 and 5 describe the case study and discuss results, respectively. Finally, Section 6 concludesthe paper and discusses future work directions.
To the best of the authors’ knowledge, [20] were the first to suggest the production of hydrogen from renewableelectricity in remote areas followed by the synthesis of hydrocarbons using captured carbon dioxide as a means of2
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24, 2021producing carbon-neutral fuels. The paper, however, did not provide a quantitative techno-economic analysis of theproposed supply chains. By contrast, [21] performed one of the first quantitative economic analyses of carbon-neutralsynthetic fuel production using carbon-neutral hydrogen and atmospheric carbon dioxide. Production cost estimates forthis route were found to be between 23.5 and 30.0 US$/GJ (which would roughly correspond to 74.1 and 94.6 e /MWh,using the 2020 average exchange rate of $1.142 for 1.0 e ). The production of carbon-neutral synthetic methane andliquid fuels in remote areas with abundant renewable resources has been considered in [12] and [22], respectively. In thefirst study, the authors estimate that the cost of producing synthetic methane from renewable electricity in the Maghreband North Africa (specifically in central and southern Algeria) and delivering it to Japan could be around 65-75 e /MWhby 2030 for a hybrid solar-wind system, assuming a uniform weighted average cost of capital (WACC) of 7%. It is notspecified whether the higher heating value (HHV) or the lower heating value (LHV) of methane was used to computethese costs. In the second study, the cost of producing synthetic methane in the same region and delivering it to Finlandis found to be between 100-110 e /MWh (HHV) by 2030 and between 90-100 e /MWh (HHV) by 2040, respectively,using a WACC of 7%. Finally, the economics of carbon-neutral fuel production is also analysed in [23]. Cost estimatesclose to 140-150 e /MWh (LHV) by 2030 and 110 e /MWh (LHV) by 2050 (using a WACC of 6% in both cases) arefound for synthetic methane production in North Africa (specifically in central and southern Algeria) and delivery toGermany based on both solar energy alone and hybrid systems combining solar and wind power plants.It is also informative to review the modelling approaches followed in these studies. Firstly, [21] do not specify thetechnologies used to implement the various conversion processes, and instead rely on a set of assumptions aboutconversion efficiencies and the cost of producing input commodities (in stoichiometric proportions) to come up with acost estimate for the final product. Then, [12] resort to a so-called annual-basis model estimating the annual number ofequivalent full load hours of renewable power production in order to calculate electricity and synthetic methane costsbased on a set of techno-economic assumptions. This method is equivalent to estimating annual power productionand costs using an average capacity factor value, and the model is therefore not temporally-resolved. A so-called hourly-basis model enabling the sizing of solar photovoltaic (PV) and wind power plants is mentioned in [12, 22], butno mathematical model is explicitly described and no computer code implementing it is made available, which makesthe approach difficult to interpret and scrutinise. Somewhat surprisingly, very minor differences in cost estimates areobserved between the annual-basis and hourly-basis models in [12]. In [23], an annual full load hour model similar tothat of [12] is used. For systems driven by variable renewable energy resources, it has been shown that using a hightemporal resolution (e.g., hourly) and adopting a proper level of technical detail (i.e., representing the flexibility oftechnologies, or lack thereof) is key for accurately sizing plants and estimating both investment and operating costsproperly [16]. It is worth noting that the aforementioned papers rely on models that have both a very low level oftechnical detail and a very low temporal resolution. Furthermore, none of these models makes it possible to designthe supply chain in an integrated fashion while properly accounting for interactions between subsystems. Similarshortcomings can be found in studies focussing on other energy carriers such as hydrogen [24, 14].The design and analysis of energy systems and supply chains has often been tackled using mathematical programmingtechniques in the literature [25, 26]. Different classes of models may be used, ranging from linear programs (LPs) tononlinear and mixed-integer (possibly nonconvex) nonlinear programs (NLPs and MINLPs) [27]. Parameter uncertaintymay also be taken into account [28]. The type of model used typically depends on the research scope, the availablecomputational resources and the data at hand. For example, the design of a single piece of equipment used in a processmay require NLP or MINLP models to accurately represent its physics and operating modes [29]. On the other hand,supply chains can be viewed as collections of interconnected plants or processes, which themselves rely on a variety ofcomplex pieces of equipment. Representing each of them in their full complexity would require vast amounts of dataand result in intractable models. Thus, for the purpose of strategic or high-level system design analyses, aggregate plantmodels are typically employed [30, 31]. In such models, mass and energy conservation laws are enforced at plant levelwhile accounting for basic operational constraints. Mass and energy balances are also enforced between interconnectedplants in order to guarantee consistency of flows at system level. Such approaches, which usually rely on LP or MILPmodels, have for instance been applied to the design of integrated biorefineries [32], the design of power-to-syngasprocesses [33] and power-to-chemicals networks [34, 35]. Such an approach is adopted in this paper, as discussed next. This section formally introduces the abstract graph-based optimisation modelling framework and describes how it canbe applied in the context of strategic energy supply chain planning.3
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In this paper, supply chain planning problems are formulated as a class of structured linear programs. These problemstypically involve the optimisation of discrete-time dynamical systems over a finite time horizon and exhibit a naturalblock structure that may be encoded by a sparse connected graph. A graph abstraction is therefore employed to representthem, wherein nodes model optimisation subproblems, while edges express the relationships between nodes and theirassociated variables. A global discretised time horizon and associated set of time periods common to all nodes are alsodefined. Each node is equipped with a set of internal, input and output variables. In addition, each one of these variablescan be viewed as a vector variable whose entries correspond to different time periods. A set of constraints is also definedfor each node, along with a local objective function representing its contribution to a system-wide objective. Finally, foreach edge, equality constraints involving the input and output variables of the nodes to which the edge is incident aredefined in order to express the relationships between nodes. In the following paragraphs, we formally define variables,constraints, objectives and formulate the abstract model that encapsulates the class of problems considered.Let T be the time horizon considered, let T = { , , . . . , T − } be the associated set of time periods, and let G = ( N , E ) be the undirected graph encoding the block structure of the problem considered, with node set N and edgeset E ⊆ N × N . Let I nx , I nu and I ny be the number of internal, input and output variables defined per time period at node n ∈ N , and let I nx = { , . . . , I nx } , I nu = { , . . . , I nu } and I ny = { , . . . , I ny } be the associated index sets. Now, let x ni ∈ R T , ∀ i ∈ I nx , u ni ∈ R T , ∀ i ∈ I nu , and y ni ∈ R T , ∀ i ∈ I ny , be the internal, input and output variables defined atnode n ∈ N , and let X n ∈ X n ⊆ R I nx × T , U n ∈ U n ⊆ R I nu × T and Y n ∈ Y n ⊆ R I ny × T be matrix variables obtainedby concatenating these internal, input and output variables. Let u nit and y njt denote the i th input variable and the j th output variable at time t ∈ T and node n ∈ N , respectively.Both equality and inequality constraints may be defined at each node n ∈ N . More precisely, an arbitrary numberof constraints that can each be expanded over a subset of time periods may be defined. Hence, we consider equalityconstraints of the form h nk ( X n , U n , Y n , t ) = 0 , ∀ t ∈ T nk , (1)with (scalar) affine functions h nk and index sets T nk ⊆ T , k = 1 , . . . , K n , as well as inequality constraints g nk ( X n , U n , Y n , t ) ≤ , ∀ t ∈ ¯ T nk , (2)with (scalar) affine functions g nk and index sets ¯ T nk ⊆ T , k = 1 , . . . , ¯ K n .Let F n : X n × U n × Y n → R denote the function defining the objective at node n ∈ N . In this paper, we considerlocal objectives of the form F n ( X n , U n , Y n ) = (cid:88) t ∈T f n ( X n , U n , Y n , t ) , (3)where, for each t ∈ T , f n is an affine function of X n , U n and Y n . In the following, for the sake of conciseness, F n will also be used to directly denote the value of the function.For each edge e = ( n, n (cid:48) ) ∈ E , a set of scalar equality constraints links either an input variable of node n ∈ N to anoutput variable of node n (cid:48) ∈ N or an output variable of node n ∈ N to an input variable of node n (cid:48) ∈ N for all timeperiods. Thus, for variables i and j , these constraints can be expressed as u nit = y n (cid:48) jt , ∀ t ∈ T , or y nit = u n (cid:48) jt , ∀ t ∈ T . (4)Furthermore, let H e : U n × Y n × U n (cid:48) × Y n (cid:48) → R T be an affine function such that the equality constraints associatedwith each edge e = ( n, n (cid:48) ) ∈ E can be compactly expressed as H e ( U n , Y n , U n (cid:48) , Y n (cid:48) ) = 0 . (5)Using this notation, the class of problems that can be represented in this framework reads min (cid:80) n ∈N F n ( X n , U n , Y n ) s.t. h nk ( X n , U n , Y n , t ) = 0 , ∀ t ∈ T nk , k = 1 , . . . K n , ∀ n ∈ N g nk ( X n , U n , Y n , t ) ≤ , ∀ t ∈ ¯ T nk , k = 1 , . . . ¯ K n , ∀ n ∈ N H e ( U n , Y n , U n (cid:48) , Y n (cid:48) ) = 0 , ∀ e = ( n, n (cid:48) ) ∈ E X n ∈ X n , U n ∈ U n , Y n ∈ Y n , ∀ n ∈ N . (6)4 REPRINT VERSION - F
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The framework presented in Section 3.1 can be readily leveraged to model energy systems and supply chains. In thiscase, nodes typically represent a technology, a plant or a process, and introducing a few generic (parametrised) nodesoften suffices to model a broad range of system configurations. In the following, some key modelling assumptions areintroduced, along with three generic nodes, namely conversion , storage and conservation nodes. Investment decisions are made by a single entity that also operates the system, andwhose goal is to minimise total system costs.
Perfect Foresight & Knowledge
The entity planning and operating the system has perfect foresight and knowledge,that is, future weather events and demand patterns, as well as all technical and economic parameters are assumed to beknown with certainty.
Investment & Operational Decisions
A static investment model is used, whereby investment decisions are made atthe beginning of the time horizon and assets are immediately available. Operational decisions are made at hourly timesteps. The investment and operational problems are solved simultaneously.
Technology & Process Models
The sizing and operation of technologies are modelled via a set of affine input-outputrelations that typically express mass and energy balances at plant or process level. Input or output dynamics areconsidered for some technologies, but only storage technologies have a simple state space representation.
In the following developments, Latin letters denote optimisation variables and indices, while Greekletters indicate parameters.
Conversion
Let n ∈ N be a node representing a so-called conversion technology that processes a set of commodities(e.g., an electrolysis plant splits water into hydrogen and oxygen using an electric current and therefore processesfour commodities). Commodity flows are modelled as input and output variables. An index i ∈ I n = I nu ∪ I ny isthus assigned to each commodity. The processing of commodities by technology n is modelled via a set of linearequations linking the flow of a reference commodity r ∈ I n (e.g., hydrogen may be taken as the reference commodityfor electrolysis plants) to the flow of all other commodities i ∈ I n \ { r } , which read q nrt − φ ni q ni ( t + τ ni ) = 0 , ∀ i ∈ I n \ { r } , ∀ t ∈ T n , (7)where q nit ∈ R + represents the flow of commodity i at time t , φ ni ∈ R + is the so-called conversion factor betweencommodity r and i (which may be derived, e.g., from stoichiometric coefficients or the enthalpy of the underlyingreaction), while τ ni ∈ N is the amount of time that may be required for the conversion process to take place and T n ⊆ T is a suitable subset of time periods. The capacity of a technology is typically modelled as an internal variable anddefined as the maximum flow of a reference commodity r (cid:48) ∈ I n according to which the technology is sized. Notethat r (cid:48) may be different from r (e.g., the size of electrolysis plants is typically expressed in terms of their electricalcapacity, although hydrogen may be the reference commodity used in Equation (7). Since a static investment model isconsidered, capacity deployments occur at the beginning of the time horizon and remain constant throughout, i.e., K n = K nt , ∀ t ∈ T \ { } , (8)where K nt ∈ R + denotes the new capacity of technology n . In the following, K n will be used as shorthand for K n .Thus, the total capacity of technology n is defined via q nr (cid:48) t − π nt ( κ n + K n ) ≤ , ∀ t ∈ T , (9)where π nt ∈ [0 , indicates the availability of technology n at time t and κ n ∈ R + represents the existing capacity.The so-called availability parameter π nt may for instance represent the instantaneous capacity factor of a renewablepower plant. The maximum capacity of a technology may be bounded, which leads to the introduction of an additionalconstraint, ( κ n + K n ) − ¯ κ n ≤ , (10)with ¯ κ n ∈ R + the maximum capacity of technology n that may be installed. A variety of operational constraints mayalso be considered. For instance, some conversion technologies may have a limited operating range, and may only work5 REPRINT VERSION - F
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24, 2021if a minimum flow of commodity i ∈ I n is maintained, which can be expressed as µ n ( κ n + K n ) − φ ni φ nr (cid:48) q nit ≤ , ∀ t ∈ T , (11)where µ n ∈ [0 , represents the minimum operating level (as a fraction of the installed capacity). Since the technologyis sized with respect to the flow of commodity r (cid:48) , the flow of a commodity i (cid:54) = r (cid:48) must be scaled by the ratio ofconversion factors in Eq. (11). The rate at which the flow of commodity i ∈ I n can vary may also be limited, leadingto the introduction of so-called ramping constraints, φ ni φ nr (cid:48) ( q nit − q ni ( t − ) − ∆ ni, + ( κ n + K n ) ≤ , ∀ t ∈ T \ { } , (12)and φ ni φ nr (cid:48) ( q ni ( t − − q nit ) − ∆ ni, − ( κ n + K n ) ≤ , ∀ t ∈ T \ { } , (13)with ∆ ni, + ∈ [0 , and ∆ ni, − ∈ [0 , the maximum rates at which flows can be ramped up and down (as a fraction ofthe installed capacity per unit time), respectively. Finally, the local objective function associated with this node reads F n = ν ( ζ n + θ nf ) K n + (cid:88) t ∈T θ nt,v q nr (cid:48) t , (14)where ν ∈ N is the number of years spanned by the optimisation horizon, ζ n ∈ R + represents the (annualised)investment cost (also known as capital expenditure, CAPEX), θ nf ∈ R + models fixed operation and maintenance (FOM)costs and θ nt,v ∈ R + represents variable operation and maintenance (VOM) costs, which may be time-dependent. Storage
Let n ∈ N be a node representing a storage technology . A storage technology is assumed to hold onecommodity, although its operation may involve other commodities (e.g., a compressed hydrogen storage system storeshydrogen but requires electricity to drive compressors). The inventory level of the storage system is defined as aninternal variable, while the charge and discharge flows are defined as input and output variables, respectively. Let i u ∈ I nu and i y ∈ I ny be the indices of the in/outflows of the commodity stored in technology n , respectively. Then, thebasic equation governing the operation of storage systems describes the inventory level dynamics, which reads e nt +1 − (1 − η nS ) e nt − η n + q ni u t + 1 η n − q ni y t = 0 , ∀ t ∈ T \ { T − } , (15)where e nt ∈ R + is the inventory level at time t , q ni u t ∈ R + and q ni y t ∈ R + represent commodity in- and outflows attime t , respectively, η nS ∈ [0 , is the self-discharge rate, η n + ∈ [0 , is the charge efficiency and η n − ∈ [0 , is thedischarge efficiency. The charge of a storage system may also require the consumption of another commodity i ∈ I nu (e.g., electricity consumed by compressors), which is typically modelled via an additional input variable q nit ∈ R + andequations q nit − φ ni u q ni u t = 0 , ∀ t ∈ T . (16)In order to avoid spurious transient effects in storage operation, inventory levels are typically required to be equal at thebeginning and at the end of the optimisation horizon, e n = e nT − . (17)The stock capacity of the storage technology is modelled as an internal variable and it is defined by the maximuminventory level. Since a static investment model is used, the stock capacity is constant throughout the entire timehorizon, i.e., E n = E nt , ∀ t ∈ T \ { } , (18)where E nt ∈ R + is the new capacity. In the following, E n will be used as shorthand for E n . The total storage capacityis therefore defined via e nt − ( (cid:15) n + E n ) ≤ , ∀ t ∈ T , (19)where (cid:15) n ∈ R + denotes the existing stock capacity. Note that the total stock capacity itself may be constrained, ( (cid:15) n + E n ) − ¯ (cid:15) n ≤ , (20)with ¯ (cid:15) n ∈ R + the maximum stock capacity that may be deployed. In addition, some storage technologies may require aminimum inventory level to be maintained, which can be expressed as σ n ( (cid:15) n + E n ) − e nt ≤ , t ∈ T , (21)6 REPRINT VERSION - F
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24, 2021where σ n ∈ [0 , represents the minimum inventory level (as a fraction of the stock capacity). The maximum inflowcapacity is sized independently of the stock capacity and is modelled using an internal variable that is also constantthroughout the time horizon considered, as in Eq. (8). It is defined as follows q ni u t − ( κ n + K n ) ≤ , ∀ t ∈ T , (22)where κ n ∈ R + denotes the existing flow capacity and K n ∈ R + is used as shorthand for the new capacity. Themaximum in- and outflows may be asymmetric, depending on the properties of the underlying technology, which ismodelled via q ni y t − ρ n ( κ n + K n ) ≤ , ∀ t ∈ T , (23)where ρ n ∈ R + represents the maximum discharge-to-charge ratio. Finally, the local objective function associated withthis node reads F n = (cid:104) ν ( ς n + ϑ nf ) E n + (cid:88) t ∈T ϑ nt,v e nt (cid:105) + (cid:104) ν ( ζ n + θ nf ) K n + (cid:88) t ∈T θ nt,v q ni u t (cid:105) . (24)where ς n ∈ R + and ζ n ∈ R + represent the stock and flow components of CAPEX, ϑ nf ∈ R + and θ nf ∈ R + model thestock and flow components of FOM costs, while ϑ nt,v ∈ R + and θ nt,v ∈ R + represent the stock and flow components ofVOM costs, which may be time-dependent. Conservation
Commodities typically obey local flow conservation laws, which can be modelled using conservationnodes . More precisely, one commodity is associated with a given conservation node. Using the usual notation,conservation laws can then be expressed as (cid:88) i ∈I nu q nit − (cid:88) i ∈I ny q nit − λ nt = 0 , ∀ t ∈ T , (25)where the first two terms on the left-hand side represent the total flow into and out of n , while λ nt ∈ R + representsthe demand at node n and time t . In some cases, a slack variable representing the unserved demand at node n may beadded on the left-hand side of Eq. (25) to promote feasibility and facilitate post-processing. Indeed, solutions with largenonzero slack values typically point to the structural inadequacy of system designs or result from modelling errors. Theunserved demand is modelled as an internal variable L nt ∈ R + and is penalised in the local objective function F n = (cid:88) t ∈T θ nt,L L nt , (26)where θ nt,L ∈ R + is the cost of unserved demand. The graph-based modelling framework discussed in Section 3.1 has been used as a basis for developing an optimisationmodelling language for structured linear programs called the graph-based optimisation modelling language (GBOML)[18]. The language blends elements from both algebraic [36] and object-oriented [37] modelling languages in order tofacilitate problem encoding and post-processing, promote model re-use and improve portability. A parser for GBOML,called the GBOML compiler, has also been implemented in Python 3.8 (using the PLY library), and is released asopen source software [19]. The GBOML compiler directly interfaces with both commercial and open source linearprogramming solvers (namely Gurobi, CPLEX and Clp), enabling users to model problems, interact with solverAPIs, query solutions and retrieve post-processed results in an integrated fashion. For the sake of transparency andreproducibility, the input file and full data allowing one to reproduce the case study and results discussed in Sections 4and 5 are also provided in the GBOML repository [19]. The full description of GBOML, which is beyond the scope ofthis paper, is detailed in a separate tutorial paper [18].
This case study aims to analyse the economics of producing carbon-neutral methane from renewable electricity inareas of North Africa where abundant and high-quality renewable resources are readily available, and exporting it toNorthwestern European markets. More specifically, the entire supply chain is modelled and optimised in an integratedfashion over a time horizon of one year with hourly resolution (i.e., T = 8760 ), from the remote generation of electricityto the synthesis and liquefaction of carbon-neutral methane in North Africa, to its eventual delivery and regasification ata Northwestern European gas terminal. Figure 1 displays a schematic of the supply chain considered.7 REPRINT VERSION - F
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24, 2021Figure 1: Remote carbon-neutral methane supply chain. Electricity is produced in a remote inland cluster in centralAlgeria and transported to a coastal cluster where carbon-neutral methane is synthesised and liquefied for export toNorthwestern European markets.
Cluster 1
INLAND
BatteryPV PanelsWind
COASTAL
Cluster 2
Direct air capture CO2 Storage
LCH LCH Storage H H Storage H O StorageElectrolysis H O H OBRINE FRESHSEA
DesalinationMethanation H CO CH H O CH LCH LiquefactionHVDC
DESTINATION
Cluster 3
LCH Storage
LCH LCH RegasificationShips
TO NETWORK
ElectricityHydrogenMethaneWaterCarbon Dioxide
Figure 2: Remote hub system configuration. Icons represent conversion and storage nodes, while bullets representconservation nodes.
A more detailed representation of the system configuration considered in this study is shown in Figure 2, where iconscorrespond to conversion and storage nodes, while bullets represent conservation nodes. For the sake of readability, theset of nodes is split into three clusters, which also correspond to the different geographical areas displayed in Figure 1.The nodes used to model this system are described in the following subsections.
Conversion nodes are discussed in this subsection. Tables 1 and 2 gather the techno-economic data used to modelconversion nodes along with the original data sources and complement the descriptions below.8
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24, 2021Table 1: Technical parameters used to model conversion nodes. In the model, power flows are measured in GW(GWh/h), energy is measured in GWh, mass flows are measured in kt/h, mass is measured in kt. φ φ φ µ ∆ + , − HVDC Interconnection [38, 39] - Electrolysis [40]
GWh el /kt H kt H O /kt H kt O /kt H - -/h Methanation [40, 41] kt H /kt CH kt CO /kt CH kt H O /kt CH - -/h Desalination
GWh el /kt H O - -/h Direct Air Capture [43]
GWh el /kt CO GWh heat /kt CO kt H O /kt CO - -/h CH Liquefaction
GWh el /kt LCH - -/h LCH Carriers [45] - LCH Regasification [44] - Solar PV
Solar photovoltaic panels are used for power generation. The plants are modelled with one output variablerepresenting the output power and one internal variable representing the plant capacity, respectively. Constraints (9) and(10) are used along with the local objective function (14). In order to construct the capacity factor time series π nt , threeyears (2015-2017) of irradiance data at hourly resolution are retrieved from the ERA5 database [55] for each grey pointin Figure 1 and converted into capacity factors using a generic transfer function [56] and TrinaSolar Tallmax M tiltedmodule data [57]. Sites with a three-year average capacity factor value exceeding 25% are retained (11 in total, shownby red crosses in Figure 1) and the associated time series are then aggregated (spatially averaged) into a single timeseries. The first 8760 hours of 2016 (which is a leap year) are used to define the time series π nt , which is illustrated inFigure 3 for a set of weekly periods. Wind Turbines
Wind turbines are used for generating power as well. Wind power plants are modelled in a similarfashion to solar PV plants, that is, with one output variable representing the power output and one internal variablerepresenting the plant capacity, respectively. Constraints (9) and (10) are used along with the typical local objectivefunction (14). In order to construct the capacity factor time series π nt , three years (2015-2017) of wind speed data athourly resolution are retrieved from the ERA5 database [55] for each grey point in Figure 1 and converted into capacityfactors using the transfer function of the Vestas V90 turbine available in the windpowerlib library [58]. Sites with athree-year average capacity factor value exceeding 50% are retained (5 in total, shown by blue crosses in Figure 1) andthe associated time series are then aggregated (spatially averaged) into a single time series. The first 8760 time periodsof 2016 are used to build π nt , which is also displayed in Figure 3.Figure 3: Capacity factor time series π nt used for solar PV and wind power plants. For all other nodes except liquefiedmethane carriers, π nt = 1 over the entire time horizon. 9 REPRINT VERSION - F
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24, 2021Table 2: Economic parameters used for conversion nodes. In the model, power flows are measured in GW (GWh/h),energy is measured in GWh, mass flows are measured in kt/h, mass is measured in kt, and money is measured in M e . CAPEX FOM ( θ f ) VOM ( θ v ) LifetimeSolar Photovoltaic Panels [23] M e /GW el M e /GW el -yr M e /GWh el yr Wind Turbines [46] M e /GW el M e /GW el -yr M e /GWh el yr HVDC Interconnection [47, 48] M e /GW el M e /GW el -yr M e /GWh el yr Electrolysis [49] M e /GW el M e /GW el -yr M e /GWh el yr Methanation [50] M e /GW CH (HHV) M e /GW CH -yr (HHV) M e /GWh CH (HHV) yr Desalination [51] M e /(kt H O /h) M e /(kt H O /h)-yr M e /kt H O yr Direct Air Capture [43] M e /(kt CO /h) M e /(kt CO /h)-yr M e /kt CO yr CH Liquefaction [52] M e /(kt LCH /h) M e /(kt LCH /h)-yr M e /kt LCH yr LCH Carriers [53] M e /kt LCH M e /kt LCH -yr M e /kt LCH yr LCH Regasification [54] M e /(kt CH /h) M e /(kt CH /h)-yr M e /kt CH yr HVDC Interconnection
Ultra high voltage direct current (HVDC) overhead lines (800 or 1100 kV) are assumedto be used for bulk power transmission from the first cluster (inland) to the second one (coastal hub) [47]. Note thatthe yellow area containing the solar and wind sites in Figure 1 is assumed to be a copper plate for the purpose of thisstudy, which implies that solar PV and wind power plants feed directly into the electricity interconnection and the costof the infrastructure connecting power plants to the HVDC interconnection is neglected. Voltage source converters(VSC) are well-suited for remote applications, as they are self-commutated and are much more controllable than typicalline-commutated (LC) alternatives, although they are more expensive and have higher conversion losses [38]. In thiscase, two VSC stations are placed on each side of an overhead HVDC cable whose length is assumed to be 1000 km.Losses in each converter station roughly amount to 1.8% of the power flowing through it, while approximately 1.5% ofthe power transiting through the HVDC cable is lost. Combining these figures yields the overall efficiency reported inTable 1. Economic data shown in Table 2 include the costs of both converter stations and the cable. The interconnectionis modelled using one input variable, one output variable and one internal variable. The input variable is the power flowfrom the conservation node of the first cluster, while the output variable represents the power flow to the conservationnode of the second cluster. The internal variable is the capacity of the converter-line pair. Investment costs in lines andconverter stations are accounted for in the local objective (14), along with operating costs.
Electrolysis Plants
Proton exchange membrane (also called polymer electrolyte membrane, PEM) electrolysis plants[59] are used for producing hydrogen. This technology makes it possible to split water into hydrogen and oxygen bythe passage of an electric current. Hence, the plants are modelled with two input, two output and one internal variables.The input variables represent the power and water inflows, the output variables represent the hydrogen and oxygenoutflows, while the internal variable is the plant capacity. The reference commodity r used in Equation (7) is hydrogen,while the commodity r (cid:48) according to which the technology is sized in Equation (9) is the power input. This technologyis flexible and can ramp up and down very quickly (usually within seconds). However, a minimum hydrogen productionlevel around − of the nominal capacity must be maintained when the plant is switched on. Electrolysis plants arealso assumed to operate at 20 bars and 40 ◦ C. Constraints (11) are therefore used to model plant operation. The usualobjective function is (14) also used.
Methanation Plants
Fixed-bed catalytic reactors are used to produce synthetic methane via the methanation ofcarbon dioxide (Sabatier) reaction [41]. This reaction enables the transformation of carbon dioxide and hydrogeninto methane and water (steam). Thus, plants are modelled with two input variables, two output variables and oneinternal variable. The input variables represent the hydrogen and carbon dioxide inflows, the output variables representthe methane and water (steam) outflows, while the internal variable is the plant capacity. Methane is taken as the10
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24, 2021reference commodity r used to describe the process in Equation (7) as well as the reference commodity r (cid:48) used forsizing the plant in Equation (9). Note that the input streams used in this system are very pure, which limits the riskof catalyst poisoning. Hence, alumina-supported nickel catalysts [60], which offer good selectivity and are relativelycheap, are assumed to be used. Plants are also assumed to operate at 300 ◦ C and 20 bar. Owing to the exothermicity ofthe reaction (the production of 1 kg of methane releases approximately 2.867 kWh of heat at or above 300 ◦ C [41]) andthe associated risk of thermal runaway [61], catalytic methanation reactors operate nearly continuously and a reactor isusually designed and sized for a (very) limited range of flow rates [62]. Hence, constraints (11), (12), (13) are used tomodel plant operation, while investment and operating costs are modelled via (14).
Water Desalination Plants
Reverse osmosis (RO) plants are employed to desalinate seawater and produce freshwater[63]. This technology essentially pumps seawater into a chamber featuring a porous membrane and produces a pressuredifferential across the membrane, enabling dead-end filtration and the recovery of freshwater on the other side of themembrane. The plants are modelled with one input variable, one output variable and one internal variable. The inputvariable is the power required to drive pumps, the output variable is the freshwater outflow and the internal variable isthe plant capacity. The reference commodity r (cid:48) according to which the plant is sized is the freshwater flowing out ofthe system. For mechanical reasons, membranes are usually designed to operate under constant pressure and plantstherefore operate more or less continuously. Hence, constraints (7),(9),(11), (12), (13) are used to model plant sizingand operation, while investment and operating costs are modelled via (14). Note that the seawater inflow and the brinedischarge are not modelled. The implicit assumptions are that seawater is freely available and the brine by-product canbe disposed of at no cost, without any restriction on pumped volumes. Direct Air Capture Units
Direct air capture units extract carbon dioxide from the atmosphere [64]. The process usedin this paper is the one proposed by [43]. Roughly speaking, this process relies on four main chemical reactions, whichare combined to form two chemical loops. In the first loop, aqueous sorbents are used in an air contactor to chemicallybind carbon dioxide and form dissolved compounds. These compounds then react with pellets in a fluidised-bed reactor,making it possible to recover the aforementioned sorbents and trap carbon in solid compounds. The second loopessentially recovers carbon dioxide by calcining the solid compounds and replenishes the pellet stock by hydrating(slaking) the solid product of the calcination reaction. The process requires electricity to power fans driving air throughthe contactors, pumps maintaining the flow of aqueous solutions as well as compressors compressing the output carbondioxide stream from atmospheric pressure to 20 bar (the associated energy expense is approximated via the polytropiccompression work, assuming a polytropic efficiency of 80%). The net power consumption is obtained as the differencebetween the total consumption of these subsystems and the power produced by a steam turbine recovering slaking heat.A sustained water supply is also necessary to form aqueous solutions, counter natural evaporation in the air contactorsand produce steam used in the slaker. Furthermore, a source of heat at around 900 ◦ C is required for the calcinationreaction. In the original design, natural gas is burnt via an oxy-fuel combustion process at the bottom of the calciner toprovide this heat, and the off-gases also fluidise the reactor. In this paper, it is assumed that the high temperature heat isprovided by burning hydrogen. Hence, the process is modelled using three input variables, one output variable and oneinternal variable. The input variables represent the power, water and hydrogen inflows, the output variable is the carbondioxide outflow and the internal variable is the plant capacity. The reference flow according to which the plant is sizedis the carbon dioxide outflow. None of the technologies implementing the various reactions really lend themselves tohighly variable operation. Constraints (7),(9),(11), (12), (13) are therefore used to model plant sizing and operation,while investment and operating costs are modelled via (14).
Methane Liquefaction Units
Liquefaction units turn gaseous methane into liquefied methane [44]. This technologytypically relies on compressors and pumps in order to progressively compress and cool the methane inflow, which iseventually throttled and liquefied via the Joule-Thomson effect. In this case, two input variables, one output variableand one internal variable are used. The input variables represent the methane inflow and the power consumptionof compressors and pumps, the output variable represents the liquefied methane outflow (which is the referencecommodity) and the internal variable represents the plant capacity. This technology is also relatively inflexible.Constraints (7),(9),(11), (12), (13) are used to model plant sizing and operation, while investment and operating costsare modelled via (14).
Liquefied Methane Carrier Vessels
Liquefied methane is transported to market with large ocean-going vesselspowered by dual fuel diesel electric (DFDE) engines [45]. These engines are particularly efficient and can run solely onnatural boil-off gas (i.e., gaseous methane resulting from the natural evaporation of liquefied methane stored on boardin insulated cargo tanks). This allows vessels to sail at a speed of 19 knots, with approximately 0.1% of their cargoevaporating due to natural boil-off per day spent at sea, which is used for propulsion (i.e., no other fuel is needed). Theliquefied methane heel that must usually be maintained for the return journey to guarantee that the onboard tanks remaincool (roughly 4-5% of the total cargo) is neglected in this paper. One input variable, one output variable and one internal11
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24, 2021Table 3: Technical parameters for storage nodes. In the model, power flows are measured in GW (GWh/h), energy ismeasured in GWh, mass flows are measured in kt/h, mass is measured in kt. η S η + η − σ ρ φ Battery Storage [65] - - - - -
Compressed H Storage [65]
GWh el /kt H Liquefied CO Storage [66]
GWh el /kt CO Liquefied CH Storage H O Storage [63]
GWh el /kt H O variable are used to describe a stylised carrier vessel. The input variable represents the flow of liquefied methane loadedat the coastal hub, the output variable represents the flow of liquefied methane unloaded at the destination, and theinternal variable is the vessel capacity. Eq. (7 is used to model the transport of liquefied methane, with τ = 116 hours,as the berthing and travel time between the coastal hub and the destination is assumed to take slightly less than 5 days.The conversion factor φ ≈ . represents the transport efficiency, computed from the boil-off consumption (0.125%of cargo per day) and trip duration (116 hours). In addition, loading and unloading may only be possible when thevessel is moored at the coastal hub and destination, respectively. This is enforced via Eq. (9) and time series π nt (withvalues equal to 0 or 1), which defines a berthing, mooring, loading and unloading schedule (loading or unloading takeplace when π nt = 1 ). For the sake of simplicity, π nt represents an aggregate schedule constructed from 7 different,non-overlapping schedules corresponding to individual carrier vessels. Some of these schedules are shown in Figure 4(loading and unloading is assumed to take 24 hours). The standard local objective (14) is used for the stylised carrier.Figure 4: Subset of non-overlapping schedules used to construct the aggregate schedule π nt of stylised liquefied methanecarriers. These time series are summed to obtain the aggregate schedule π nt . For all other nodes except wind and solarPV power plants, π nt = 1 over the entire time horizon. Liquefied Methane Regasification Units
Regasification units are used to transform liquefied methane into gaseousmethane at the destination [54]. The heat required to do so can come from a variety of sources. In this case, it isassumed to come from the combustion of a fraction of the methane (around 2%). Thus, one input variable, one outputvariable and one internal variable are used. The input variable represents the liquefied methane inflow, the outputvariable represents the gaseous methane outflow, and the internal variable is the plant capacity. Constraints (7),(9) areused to model plant sizing and operation, while investment and operating costs are modelled via (14).
Storage nodes are discussed in this subsection. Tables 3, 4 and 5 gather the techno-economic data used to model storagenodes along with the original data sources and complement the descriptions below.12
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24, 2021Table 4: Economic parameters for storage nodes (stock component). In the model, power flows are measured in GW(GWh/h), energy is measured in GWh, mass flows are measured in kt/h, mass is measured in kt, and money is measuredin M e . CAPEX FOM ( ϑ f ) VOM ( ϑ v ) LifetimeBattery Storage [65] M e /GWh M e /GWh-yr M e /GWh yr Compressed H Storage [65] M e /kt M e /kt-yr M e /kt yr Liquefied CO Storage [66] M e /kt M e /kt-yr M e /kt yr Liquefied CH Storage [67] M e /kt M e /kt-yr M e /kt yr H O Storage [63] M e /kt M e /kt-yr M e /kt yr Table 5: Economic parameters for storage nodes (flow component). In the model, power flows are measured in GW(GWh/h), energy is measured in GWh, mass flows are measured in kt/h, mass is measured in kt, and money is measuredin M e . CAPEX FOM ( θ f ) VOM ( θ v ) LifetimeBattery Storage [65] M e /GW M e /GW-yr M e /GW yr Liquefied CO Storage [66] M e /(kt/h) M e /(kt/h) M e /(kt/h) yr H O Storage [63] M e /(kt/h) M e /(kt/h) M e /(kt/h) yr Stationary Battery Storage
Nickel manganese cobalt (NMC) oxide lithium-ion batteries are used for short-termelectricity storage [65]. Power in- and outflows are modelled via one input and one output variables, respectively. Thestate of charge, power capacity and energy capacity, on the other hand, are modelled as internal variables. Constraints(15), (17), (19), (20), (22), (23) are used, while the local objective function is given in (24).
Hydrogen Storage Tanks
Compressed hydrogen storage tanks are considered in this paper. More precisely, over-ground, man-made steel storage vessels (type I) withstanding pressure levels around 200 bar and suitable for stationaryapplications are used [65]. Since hydrogen at 20 bar and 40 ◦ C is produced by electrolysis plants, the hydrogen inflowmust be compressed to 200 bar using electric compressors for storage purposes. The associated energy expense isapproximated via the polytropic compression work (assuming a polytropic efficiency of 80%) [68]. Thus, two inputvariables, one output variable, and three internal variables are used. The input variables represent the hydrogen inflowand the electricity consumption, the output variable is the hydrogen outflow, while the state of charge, the powercapacity and the energy capacity are modelled as internal variables. Constraints (15), (16), (17), (19), (20), (22), (23)are used, while the local objective function is (24.
Liquefied Carbon Dioxide Storage Tanks
Liquefied carbon storage tanks are used to store carbon dioxide. Liq-uefaction and regasification units are also required [66]. Liquefaction units consume electricity, while regasificationunits are assumed to use ambient heat to recover gaseous carbon dioxide. Hence, in this case, two input variables areused, one output variable and five internal variables are used. The input variables are the carbon dioxide inflow andthe power consumption of the liquefaction units, the output variable is the carbon dioxide outflow, while the internalvariables represent the state of charge, the tank capacity, capacities of liquefaction and regasification units, and the flows13
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24, 2021of liquefied carbon dioxide in and out of the tanks. Constraints (15), (16), (17), (19), (20), (22), (23) are used, while thelocal objective function is (24).
Liquefied Methane Storage Tanks
Liquefied methane is stored in full containment tanks, that is, tanks with bothinner and outer containment walls and such that the annular gap between both walls is sealed to prevent any gaseousleaks [67]. It is assumed that the boil-off gas keeping the content of the storage tanks cold is re-liquefied and pumpedback into the tanks but the electricity consumption required to do so is neglected. One input variable, one inputvariable and two internal variables are used. The input and output variables are the liquefied methane in- and outflow,respectively, while internal variables represent the state of charge and the storage capacity. Constraints (15), (17), (19),(20), (22), (23) are used, while the local objective function is (24).
Water Storage Tanks
Water is stored in tanks equipped with electric pumps [63]. Two input variables, one outputvariable and three internal variables are used. The input variables correspond to the water inflow and the powerconsumed by pumps, while the output variable is the water outflow. The internal variables represent the state of charge,the tank capacity and the flow capacity pipes feeding into the tank. Constraints (15), (17), (19), (20), (22), (23) are used,while the local objective function is (24).
Three input variables and two output variables are used. The input variables represent thepower inflows from the solar PV plant, the wind power plant and the battery, respectively, while output variablesrepresent the power outflow to the HVDC interconnection and the battery. Note that both in and outflows are used forthe battery, which correspond to discharge and charge flows, respectively.
Coastal Power Balance
One input variable and six output variables are used. The input variable is the power flowfrom the HVDC interconnection. The output variables represent the power flows to the direct air capture plant, theelectrolysis plant, the hydrogen storage system, the methane liquefaction units, the desalination plant and the liquefiedcarbon dioxide storage system.
Coastal Hydrogen Balance
Two input variables and three output variables are used. The input variables representthe flow from the electrolysis plants and the storage system. The output variables represent the flow to the direct aircapture plants, the methanation plants and the hydrogen storage system.
Coastal Water Balance
Three input variables and three output variables are used. The input variables represent flowsfrom the desalination plants, methanation plants and the storage system. The output variables represent flows to thestorage system, the electrolysis plants and the direct air capture units. It is assumed that any freshwater surplus maybe released into the environment without harm or used in other applications (e.g., cooling), and the typical equalityconstraint (25 is relaxed to an inequality guaranteeing that the sum of input variables is greater than the sum of outputvariables.
Coastal Carbon Dioxide Balance
Two input variables are used, along with two output variables. The input variablesare the flow from the direct air capture units and the storage system, while the output variables represent the flow to thestorage system and methanation plants.
Coastal Methane Balance
One input and one output variables are used, representing flows from the methanationplants and into the liquefaction units, respectively.
Coastal Liquefied Methane Balance
Two input variables and two output variables are used. The input variablesrepresent flows from the storage system and the liquefaction units, while the output variables represent flows to thestorage system and the liquefied methane carriers, respectively.
Destination Liquefied Methane Balance
Two input variables and two output variables are used. The input variablesrepresent flows from the liquefied methane carriers and the storage system. The output variables, on the other hand,model flows to the storage system and regasification units.
Destination Methane Balance
One input variable and one internal variable are used. The input variable is the flowfrom the regasification units and the internal variable represents the energy not served. The gas demand is set to
TWh (HHV) per annum with a flat profile. Hence, assuming that synthetic methane has a HHV of . kWh/kg,14 REPRINT VERSION - F
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24, 2021the demand profile is obtained as λ nt = (100 × / × (1 / . ≈ . kt/h, ∀ t ∈ T , while the cost ofunserved demand θ nt,L is set at M e /GWh. Note that using the LHV would have resulted in a higher mass flow rate. Four scenarios are considered. The first two scenarios study system configurations that rely on solar PV alone and acombination of solar PV plants and wind turbines for electricity generation, respectively. A uniform weighted averagecost of capital (WACC) of 7% is assumed for all technologies. This scenario represents the case where the fundsrequired to finance the system are borrowed on capital markets. Under these assumptions, for a technology conversionor storage technology n , the CAPEX values in Tables 2, 4 and 5 are used to compute ζ n = CAPEX n × w (1 − (1 + w ) − L n ) , (27)with L n the lifetime of technology n and w the WACC. Hence, ζ n represents the annualised cost of investing intechnology n .The last two scenarios study the same system configurations with updated financial assumptions. More specifically,these cases correspond to a hypothetical situation where the cost of financing the system is zero. Hence, the cost ofsynthetic methane production and delivery solely reflects the cost and efficiency of technologies in the supply chain. Inthis set-up, annualised investment costs are computed as follows ζ n = CAPEX n L n . (28) In the first scenario, a solar-only configuration with a uniform WACC of 7% is studied. In this set-up, synthetic methaneis delivered to market in gaseous form at 199.0 e /MWh, which is computed as the ratio of total (annualised) systemcost to methane volume delivered (100 TWh HHV per year). It is worth mentioning that using the LHV would haveincreased the cost per MWh, as this effectively reduces the amount of energy that can be retrieved per unit mass ofmethane delivered. ElectrolysisSolar PVHVDC InterconnectionBattery StorageHydrogen StorageDirect Air CaptureMethanationMethane LiquefactionLiquefied Methane RegasificationLiquefied Methane StorageDesalinationLiquefied Methane Carriers
Synthetic Methane Cost Breakdown (€/MWh)
Figure 5: Breakdown of synthetic methane cost at destination for Scenario 1. All contributions roughly sum to 199.0 e /MWh (HHV).The synthetic methane cost breakdown is provided in Figure 5, where each bar represents the contribution (in e /MWh)of the corresponding technology to synthetic methane cost. Each bar can also be interpreted as representing thecontribution of the corresponding technology to total system cost. Although electrolysis plants contribute the most tototal system cost (around 28%), solar PV plants are not far behind (roughly 26.5%), with the HVDC interconnection(13.7%) and batteries (8.9%) next. Overall, the technologies used to generate, transport and store electricity (shown ingold in Figure 5) represent the largest share of costs (slightly under 50%). Hydrogen storage plants, which are used15 REPRINT VERSION - F
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24, 2021as a buffer between flexible electrolysis and inflexible methanation plants, make up approximately 6.9% of total cost.Hence, the technologies producing and storing hydrogen (shown in cyan in Figure 5) account for roughly 35% of totalsystem cost. It is worth noting that the plants upstream of the inflexible plants (i.e., methanation, direct air capture anddesalination plants) make up almost 85% of total system cost. On the other hand, methanation plants make up a minorshare of total cost (5.8%), and the full methane chain (i.e., production, liquefaction, storage, transport and regasification,shown in dark orange in Figure 5) accounts for less than 10% of final product cost. Direct air capture plants alsorepresent a minor fraction of system cost (slightly less than 6%, shown in pink in Figure 5). Water desalination andstorage technologies are deployed in moderate quantities, resulting in a very small share of total costs (well under 1%),while carbon dioxide storage is not deployed.
Cluster 1
INLAND
Battery
PV Panels
Wind
COASTAL
Cluster 2
Direct air capture
CO2 Storage
LCH LCH Storage H H Storage H O Storage Electrolysis H O H OBRINE FRESHSEA
Desalination /d Methanation H CO CH H O CH LCH Liquefaction
HVDC
DESTINATION
Cluster 3
LCH Storage
LCH LCH Regasification
Ships
100 TWh
TO NETWORK
ElectricityHydrogenMethaneWaterCarbon DioxideCurtailment
Figure 6: Material and energy balance diagram for Scenario 1, along with technology capacities. All energy-equivalentflows of energy carriers other than electricity have been computed using their HHV, and all values have been roundedup to keep significant digits only.Analysing mass and energy balances provides some insight into system design and operation. Figure 6 displays massand energy balances (flow values are integrated over the full optimisation horizon of one year) along with technologycapacities. Firstly, as can be seen in Figure 6, the effective electricity production of solar PV power plants is slightlyover 230 TWh, which suggests that the full supply chain has a conversion efficiency of roughly 43.5%. However,the amount of curtailment is substantial and stands at 58.4 TWh, which represents approximately one quarter of theuseful power production. This decreases the capacity factor of the photovoltaic plants from the theoretical maximum of24.9% for the 2016 weather year (i.e., corresponding to the case where all electricity produced is used) to only 19.9%(taking only useful power production into account). The high rate of curtailment can be explained by the difficulty ofeffectively absorbing the highly variable power input from solar PV plants. This is a direct consequence of the fact thatthe operating regimes of several key conversion technologies are inflexible, which has two further implications. Firstly,battery and hydrogen storage systems are deployed at great cost in order to smooth the variability of the power supplyas much as possible. Secondly, solar PV plants, the HVDC interconnection and electrolysis plants are oversized, asthe level of smoothing required to guarantee steady power and hydrogen flows cannot be economically provided bystorage plants alone. This claim is supported by the fact that the HVDC interconnection and electrolysis plants havecapacity factors of 41.4% and 40.8%, respectively, while conversion technologies further down the supply chain havecapacity factors of 100%. In summary, storage technologies are deployed and plants upstream of inflexible technologiesare oversized in order to smooth the variable solar PV production, which leads to substantial over-investment and arelatively inefficient system design.
In the second scenario, a hybrid solar-wind configuration with a uniform WACC of 7% is considered. Synthetic methaneis delivered to market in gaseous form around 148.5 e /MWh.16 REPRINT VERSION - F
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Wind TurbinesElectrolysisSolar PVHVDC InterconnectionDirect Air CaptureMethanationHydrogen StorageMethane LiquefactionBattery StorageLiquefied Methane RegasificationLiquefied Methane StorageWater DesalinationLiquefied Methane Carriers
Synthetic Methane Cost Breakdown (€/MWh)
Figure 7: Breakdown of synthetic methane cost at destination for Scenario 2. All contributions roughly sum to 148.5 e /MWh (HHV).The cost breakdown is provided in Figure 7. The (absolute) contributions to total system cost only change for ahandful of technologies located upstream of the inflexible technologies. These technologies include solar PV and windpower plants, electrolysis plants, the HVDC interconnection and storage systems (both battery and hydrogen). Morespecifically, wind power plants now represent the largest fraction of total system cost (29.5%). The contribution ofelectrolysis plants (20.9%) is the second largest, while that of solar PV power plants (11.6%) is slightly larger than thatof the HVDC interconnection (10.2%), which are all much smaller than those seen in the first scenario (i.e., up to a 40%reduction). The shares of battery (2.3%) and hydrogen storage (4.4%) plants are also substantially smaller than thoseobserved in the previous scenario. However, technologies producing, storing and transporting electricity (shown in goldin Figure 7) make up around 53.6% of final product cost, which is slightly higher than Scenario 1. This is consistentwith the fact that the share of costs stemming from technologies producing and storing hydrogen (shown in cyan inFigure 7) decreases both in absolute and relative terms (i.e., it accounts for slightly more than 25% of final productcost). Furthermore, the share of costs associated with technologies processing methane and carbon dioxide remainconstant in absolute terms and therefore increase in relative terms (to 12.6% and 8% of total system cost, respectively,from less than 10% and 6% in the previous scenario).Inspecting energy and mass balances shown in Figure 8 reveals why the cost of synthetic methane is roughly 25% lowerin the hybrid solar-wind system. The total volume of electricity produced (227.7 TWh) is slightly smaller than that ofthe previous scenario (slightly over 230 TWh). In this case, however, roughly 60% of the electricity is provided by windpower plants and the remainder by solar PV plants. The total amount of electricity curtailed (54.0 TWh) is 7.5% lowerthan the previous scenario. Curtailment associated with wind power plants represents 95.9% of this total, resulting in acapacity factor around 24.3% for solar PV plants (which is very close to the theoretical maximum of 24.9% for 2016).The capacity factor of wind power plants (35.4%) is much lower than the theoretical maximum of 49.6% for 2016,which reflects the fact that some curtailment still takes place. These observations point to some oversizing of the windpower generation capacity, but the overall sizing of the renewable portfolio is more efficient than that of the previousscenario. Moreover, the flows transiting through the interconnection and the electrolysis plants are almost equal to theflows observed in the previous scenario, despite much smaller capacities for these technologies. This leads to capacityfactors of 74.0% and 73.5%, respectively, which are approximately 80% higher than those observed in the first scenario.Finally, the battery storage capacity decreased fourfold, while the hydrogen storage capacity decreased by roughly 50%.The annual electricity consumption of the latter also decreased threefold, which suggests that the hydrogen system isused less intensively in this configuration. In summary, the combined output of solar PV and wind power plants is muchsmoother than that of solar plants alone, which reduces the need for technologies providing flexibility to the system.The more efficient use of technologies in this scenario is therefore made possible by the apparent complementaritybetween solar PV and wind profiles in this region. In the third scenario, a solar-only configuration with zero financing costs is analysed. Hence, in this scenario, the cost ofsynthetic methane directly reflects the cost and efficiency of technologies in the supply chain. In this set-up, syntheticmethane is delivered to market in gaseous form around 124.4 e /MWh, which is roughly 38% cheaper than the first17 REPRINT VERSION - F
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Cluster 1
INLAND
Battery
PV Panels
Wind
COASTAL
Cluster 2
Direct air capture
CO2 Storage
LCH LCH Storage H H Storage H O Storage Electrolysis H O H OBRINE FRESHSEA
Desalination /d Methanation H CO CH H O CH LCH Liquefaction
HVDC
DESTINATION
Cluster 3
LCH Storage
LCH LCH Regasification
Ships
100 TWh
TO NETWORK
ElectricityHydrogenMethaneWaterCarbon DioxideCurtailment
Figure 8: Material and energy balance diagram for Scenario 2, along with technology capacities. All energy-equivalentflows of energy carriers other than electricity have been computed using their HHV, and all values have been roundedup to keep significant digits only.scenario. The cost breakdown is provided in Figure 9, and is qualitatively comparable to that observed in the firstscenario and Figure 5.
ElectrolysisSolar PVBattery StorageHVDC InterconnectionHydrogen StorageMethanationDirect Air CaptureMethane LiquefactionDesalinationLiquefied Methane RegasificationLiquefied Methane CarriersLiquefied Methane Storage
Synthetic Methane Cost Breakdown (€/MWh)
Figure 9: Breakdown of synthetic methane cost at destination for Scenario 3. All contributions roughly sum to 124.4EUR/MWh (HHV).Energy and material balances are shown in Figure 10, along with technology capacities. The capacity of solar PV plantsis slightly larger than that observed in Scenario 1, while the capacities of the HVDC interconnection and electrolysisplants are slightly smaller than those reported in the first scenario. The amount of curtailment is also higher (13.5%),which points to some further oversizing of solar PV capacity. The system configuration is otherwise comparable to thatshown in Figure 6.
In the fourth scenario, a hybrid solar-wind configuration with zero financing costs is studied. In this scenario, syntheticmethane is delivered to market in gaseous form around 87.4 e /MWh, which is approximately 40% cheaper than18 REPRINT VERSION - F
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LCH LCH Storage H H Storage H O Storage Electrolysis H O H OBRINE FRESHSEA
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Figure 10: Material and energy balance diagram for Scenario 3, along with technology capacities. All energy-equivalentflows of energy carriers other than electricity have been computed using their HHV, and all values have been roundedup to keep significant digits only.the second scenario. The cost breakdown is provided in Figure 11. The cost breakdown is qualitatively comparableto that displayed in Figure 7, except that the share of the HVDC interconnection is now smaller than those of themethanation and direct air capture plants. As a result of the updated financial assumptions, the renewable portfolio, theinterconnection and the electrolysis plants were sized slightly differently, as shown in Figure 12. Indeed, the capacity ofthe latter two technologies are smaller in this scenario than those observed in the second scenario, while the capacitiesof methanation and direct air capture plants remain the same. The system configuration in this scenario is otherwisecomparable to that displayed in Figure 8.
Wind TurbinesElectrolysisSolar PVMethanationDirect Air CaptureHVDC InterconnectionHydrogen StorageMethane LiquefactionBattery StorageWater DesalinationLiquefied Methane RegasificationLiquefied Methane CarriersLiquefied Methane Storage
Synthetic Methane Cost Breakdown (€/MWh)
Figure 11: Breakdown of synthetic methane cost at destination for Scenario 4. All contributions roughly sum to 87.4 e /MWh (HHV). Discrepancies exist between the results presented in Section 5 and synthetic methane production cost estimates publishedelsewhere in the literature. Indeed, recall that [21] provide cost estimates ranging between 74.1 and 94.6 e /MWh.19 REPRINT VERSION - F
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LCH LCH Storage H H Storage H O Storage Electrolysis H O H OBRINE FRESHSEA
Desalination /d Methanation H CO CH H O CH LCH Liquefaction
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DESTINATION
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LCH Storage
LCH LCH Regasification
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100 TWh
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Figure 12: Material and energy balance diagram for Scenario 4, along with technology capacities. All energy-equivalentflows of energy carriers other than electricity have been computed using their HHV, and all values have been roundedup to keep significant digits only.Furthermore, in [12], the cost of producing synthetic methane from renewable electricity in central and southern Algeriaand delivering it to Japan is estimated to be around 65-75 e /MWh in 2030 for a hybrid solar-wind system using a WACCof 7%. In [22], the cost of producing synthetic methane in the same region and delivering it to Finland is estimatedto be between 100-110 e /MWh (HHV) by 2030 and between 90-100 e /MWh (HHV) by 2040, respectively, using aWACC of 7%. Finally, in [23], a uniform WACC of 6% is used, yielding cost estimates around 140 e /MWh (LHV) fora solar PV configuration and around 150 e /MWh (LHV) for a hybrid solar-wind configuration. It is worth noting thatthe hybrid solar-wind configuration is slightly more expensive than the solar-powered system in their reference costscenario.The methods used in the aforementioned papers, which are discussed in Section 2, suffer from major shortcomings.More precisely, they completely smooth out the variability in power production signals. Furthermore, they do notmodel the supply chain in an integrated fashion. Hence, if the operation of some technologies further down the chain isinflexible (e.g. methanation plants), this typically removes the need for oversizing upstream technologies or deployingflexibility options such as storage systems to balance the variable power supply and satisfy operating constraints.Oversizing plants or deploying storage technologies is relatively expensive and both account for a substantial shareof the final methane cost, as discussed in Sections 5.1-5.4. For example, the fact that solar PV variability has beencompletely smoothed out by the full load hour model used in [23] explains the observation that solar-only and hybridsolar-wind configurations yield very close methane cost estimates, while the solar-only configuration is almost 35%more expensive than the hybrid wind-solar configuration considered in this paper assuming a WACC of 7%, and over40% more expensive assuming zero financing costs. Thus, the aforementioned papers underestimate final product costas a result of inadequate modelling choices. In addition, some of the techno-economic assumptions made in [12, 22]seem particularly optimistic. For example, the CAPEX of electrolysis and methanation plants is approximately two andthree times lower than the values used in this paper, respectively. These assumptions clearly lead to low methane costestimates but are poorly supported. Indeed, to the authors’ best knowledge, such assumptions do not appear elsewherein the literature or in publicly-accessible databases and are therefore difficult to cross-check.In Section 5, it was shown that methane cost estimates for scenarios assuming zero financing costs are substantiallylower than those found in the first two scenarios. The sensitivity of cost estimates to other techno-economic assumptionsis worth discussing as well. Firstly, although the cost assumptions made for key conversion technologies such aselectrolysis plants stand on the (moderately) optimistic side, actual costs remain highly uncertain to 2030 [69]. Inparticular, electrolysis plants make up a large share of total system cost and drastic cost reductions would have asubstantial impact on synthetic methane cost. In addition, several conversion technologies in the supply chain arevery inflexible. As discussed above, coupling these technologies with an intermittent power supply leads to the20 REPRINT VERSION - F
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24, 2021deployment of expensive storage technologies and some degree of oversizing of plants upstream of the inflexibleplants. Hence, improving the flexibility of key conversion technologies, especially methanation plants, would partlyalleviate the aforementioned issues and reduce methane costs. Moreover, the selection of different processes and betterintegration between technologies could improve overall system efficiency and possibly lead to further cost reductions.In particular, the direct air capture process used in this analysis requires high-temperature heat to calcine calciumcarbonate compounds and release the atmospheric carbon dioxide they trap. In this paper, it is assumed that this heat isprovided by burning hydrogen (slightly less than 20% of total production). A different capture process that only useslow to medium-temperature heat and electricity [70] could be used instead, as sufficient heat could be readily providedby nearby methanation plants (the production of 1 kg of methane releases approximately 2.87 kWh of high-temperatureheat [41]).
This paper studies the economics of carbon-neutral synthetic fuel production in remote areas where high-qualityrenewable resources are abundant. With this goal in mind, a graph-based optimisation modelling framework directlyapplicable to the strategic planning of remote renewable energy supply chains is proposed. The method is leveraged tostudy the economics of carbon-neutral synthetic methane production from solar and wind energy in North Africa. Morespecifically, the full supply chain is modelled and optimised in an integrated fashion over a full year with hourly timeresolution and basic operational constraints are taken into account, which is key for accurately capturing interactionsbetween subsystems. Results suggest that the cost of synthetic methane delivery to northwestern European consumerswould be around 199.0 e /MWh (HHV) and 148.5 e /MWh by 2030 for systems that rely on solar photovoltaic plantsalone and a combination of solar photovoltaic and wind power plants, respectively, assuming a uniform weighted averagecost of capital of 7%. These cost estimates are significantly higher than those previously published in the literature.This discrepancy can be partly explained by the fact that the methods used in previous studies failed to properly capturethe interactions between highly variable power generation plants (especially solar photovoltaic units) and very inflexibleconversion technologies such as methanation plants. Finally, results show that synthetic methane costs may drop toroughly 124.4 e /MWh and 87.4 e /MWh, respectively, if financing costs were zero and only technology costs weretaken into account.Several research directions can be pursued in future work. Firstly, quantitatively analysing some of the options suggestedfor cost reductions would provide more insight into the economic potential of an energy supply pathway based oncarbon-neutral methane synthesis in remote areas. Then, leveraging the framework to study different pathways involvingdifferent regions (and thus resource types and profiles) and energy carriers (e.g., hydrogen, methanol or ammonia),would allow one to draw a complete picture of energy supply options and to compare their respective merits. Finally,the graph-based modelling framework could be expanded in different ways. For instance, the class of problems that canbe represented could be broadened by introducing integer variables and nonlinear expressions. The graph representationcould also be exploited to facilitate preprocessing tasks and the analysis of model properties, eventually opening thedoor to the deployment of more efficient solution methods better exploiting problem structure.21 REPRINT VERSION - F
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Sets and Indices E , e set of edges and edge index G undirected graph with node set N and edge set E I nu set of input variables at node n I ny set of output variables at node n I n , i set of input and output variables at node n , and variable index N , n set of nodes and node index T , t set of time periods and time index Parameters ν ∈ N number of years spanned by optimisation horizon π nt ∈ [0 , (operational) availability of conversion node n at time t κ n ∈ R + existing capacity of technology n ¯ κ n ∈ R + maximum capacity of conversion node n µ n ∈ [0 , minimum operating level of conversion node n (fraction of capacity) ∆ ni, + ∈ [0 , maximum ramp-up rate for flow i and conversion node n (frac. of capacity per unit time) ∆ ni, − ∈ [0 , maximum ramp-down rate for flow i and conversion node n (frac. of capacity per unit time) φ ni ∈ R + conversion factor between reference flow r and flow i for conversion node n τ ni ∈ N conversion time delay for flow i of conversion node n η nS ∈ [0 , self-discharge rate of storage node n η n + ∈ [0 , charge efficiency of storage node n η n − ∈ [0 , discharge efficiency of storage node n σ n ∈ [0 , minimum inventory level of storage node n (fraction of capacity) ¯ (cid:15) n ∈ R + maximum inventory capacity of storage node n (cid:15) n ∈ R + existing inventory capacity of storage node n ρ n ∈ R + maximum discharge-to-charge ratio of storage node n λ nt ∈ R + demand at time t and conservation node n ζ n ∈ R + CAPEX of node n (flow component) θ nf ∈ R + FOM cost of of node n (flow component) θ nt,v ∈ R + VOM cost of node n (flow component) ς n ∈ R + CAPEX of storage node n (stock component) ϑ nf ∈ R + FOM cost of storage node n (stock component) ϑ nt,v ∈ R + VOM cost of storage node n (stock component) θ nt,L ∈ R + cost of unserved demand at conservation node n Variables q nit ∈ R + input/output flow variable i of node n at time t K n ∈ R + new flow capacity of node n e nt ∈ R + inventory level of storage node n at time t E n ∈ R + new stock capacity of storage node n L nt ∈ R + unserved demand at conservation node n and time t Author Contributions
Mathias Berger and Damien Ernst designed the research. Mathias Berger, David Radu and Ghislain Detienne collectedthe data. Mathias Berger performed the research and drafted the manuscript. David Radu, Ghislain Detienne, ThierryDeschuyteneer, Aurore Richel and Damien Ernst provided feedback on the research and manuscript.
Acknowledgments
The authors would like to thank Adrien Bolland, Hatim Djelassi and Virginie Pison for providing feedback on an earlierversion of this manuscript. The authors would also like to thank Julien Confetti for his precious help with the design offigures and schematics used in this paper. Finally, the authors would like to gratefully acknowledge the support of theFederal Government of Belgium through its Energy Transition Fund and the INTEGRATION project.22
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