BIPARTITE GRAPH FREE

Though there is extensive literature of thermodynamic methods to model heat source-to-sink (direct) integration, the conventional TSA methodology is the only option to model indirect integration for sites of fixed processes. ∑ t ∈ T p out F t, s e, p ∈ P, s e ∈ S E where Q p hot ¯ and Q p cold ¯ account for known heat contents M W k q / hr estimated per unit flowrate of output products of process p.Įnergy interactions in sites are developed according to two levels: (i) direct integration within each process, where heat is directly transferred from hot to cold streams and (ii) indirect integration, where hot-cold streams belonging to different processes exchange heat via steam production and reuse. Heat contents of select streams contribute to integration through expressions: Q p, s e hot / cold = Q p hot / cold ¯. The BBR is applied to select the annual operation schedule that repeats over the years thus, the following constraint applies: ∑ t ∈ T p r s F t, s e 1 − 1 = ∑ t ∈ T p r s F t, s e 4, p r ∈ P R. Operation capacities are bounded by constraints: ∑ t ∈ T p in F t, s e ≤ I C p and ∑ t ∈ T p in F t, s e ≥ I C p ⋅ 1 − D p ∀ p ∈ P, s e ∈ S E, where variables IC p is the maximum feasible (installation) capacity operated by process p and parameters D p accounts for allowed deviations. Seasonal deviations in operation capacities are limited by the use of logical constraints to avoid industrially impractical solutions fluctuations in operation are limited by sizing, materials and instrumental design used in each process. (2) F t, s e ⋅ Y p = F t ′, s e ′ p ∈ P, t ∈ T p in, t ′ ∈ T p out, s e ∈ S E Mass balances are recorded around product nodes and process units of BBR: Drying units ( p5- p9) are applied to dry biomass exiting storage units down to 15%.

BIPARTITE GRAPH FREE

Multiple storages ( p1- p4) are applied to reduce moisture content free of energy cost at each season moisture does not drop down less than 30% in storages. Storing is assigned to interconnections of subset T pr s – like t4 or t27 in Figure 2.a – that transfer chemical pr to next seasons. Also, let subsets: T pr in, T pr out, T p in and T p out, which refer to interconnections that load and exit product node pr and process unit p let f t be the flowrate (variable) of interconnection t the operation capacity of each process p is denoted by flowrates of interconnections, ∑ t ∈ T p in F t, s e, that load the process finally, let Y p be the known mass conversion rate output mass flowrate input mass flowrate of process p. Let the set of chemicals (product nodes) and paths (process units) of value chain: PR = be the seasons of biorefinery operation. The BBR ( Kokossis et al., 2015) is properly adjusted to the needs of this work and consists of three building blocks – product nodes, process units and interconnections (arcs) – to transform the unclear value chain into a representation, which is similar to a superstructure that translates arcs into chemicals flows. Kokossis, in Computer Aided Chemical Engineering, 2016 2.1 Value chain representation

Bipartite graph