Abstract
Recently, the synthesis of carbon–hydrogen–oxygen symbiosis networks (CHOSYNs) has been proposed for the multi-scale integration of process industries that deal mainly with hydrocarbons while enabling chemical reactions, separation, heating/cooling, pressurization/depressurization, and allocation of the participating streams and species. Because of the complexity of the design problem, there is a need for efficient optimization approaches to solve the problem. In this paper, two optimization approaches are presented based on disjunctive programming. Several objective functions are used to target resource conservation (e.g., minimum fresh usage and minimum waste discharge) and economics (e.g., minimum cost, maximum profit). The optimization formulations include the tracking of species and streams, the potential installation of industrial facilities to carry out chemical conversions and other tasks, and the allocation of streams from sources to sinks via newly added interceptors. The first approach is a two-stage mathematical programming method. In the first stage, an optimization model based on atomic balances is used to determine the targets for fresh resources and discharges of the system. In the second stage, a disjunctive optimization model with an economic objective is employed to determine the configuration and allocation of the network considering existing and new industrial plants involved in the eco-industrial plant. The second approach is a simultaneous method based on a disjunctive optimization model to determine the targets and network configuration. A case study is presented to show the applicability of the proposed approaches.
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Abbreviations
- i:
-
Internal source
- j:
-
Sink
- p, pp:
-
Plants p ∈ p1 ∪ p2
- p1 :
-
Existing plant
- p2 :
-
New plant
- r:
-
Fresh feed
- s:
-
Chemical specie
- α s :
-
Atomic coefficient for carbon in the chemical specie “s”
- α r :
-
Atomic coefficient for carbon in the fresh feed “r” (in the mixture)
- β r :
-
Atomic coefficient for hydrogen in the fresh feed “r” (in the mixture)
- β s :
-
Atomic coefficient for hydrogen in the chemical specie “s”
- γ s :
-
Atomic coefficient for oxygen in the chemical specie “s”
- γ r :
-
Atomic coefficient for oxygen in the fresh feed “r” (in the mixture)
- φ r, s :
-
Molar fraction of a chemical specie “s” in the fresh feed stream “r”
- φ i, s, p :
-
Molar fraction of a chemical specie “s” in an internal source for every plant
- τ j, s, pp :
-
Molar fraction of the chemical specie “s” in the stream required for the sink “j” for every plant
- \( {A}_{\mathrm{k},{\mathrm{p}}_1}^{\mathrm{Demand}\hbox{-} \mathrm{C}} \) :
-
Atomic flow needed of carbon in the sink “k” of the plant “p1”
- \( {A}_{\mathrm{k},{\mathrm{p}}_1}^{\mathrm{Demand}\hbox{-} \mathrm{H}} \) :
-
Atomic flow needed of hydrogen in the sink “k” of the plant “p1”
- \( {A}_{\mathrm{k},{\mathrm{p}}_1}^{\mathrm{Demand}\hbox{-} \mathrm{O}} \) :
-
Atomic flow needed of oxygen in the sink “k” of the plant “p1”
- \( {A}_{{\mathrm{p}}_1}^{\mathrm{Demand}\hbox{-} \mathrm{C}} \) :
-
Atomic flow of carbon needed in the plant “p1”
- \( {A}_{{\mathrm{p}}_1}^{\mathrm{Demand}\hbox{-} \mathrm{H}} \) :
-
Atomic flow of hydrogen needed in the plant “p1”
- \( {A}_{{\mathrm{p}}_1}^{\mathrm{Demand}\hbox{-} \mathrm{O}} \) :
-
Atomic flow of oxygen needed in the plant “p1”
- \( {A}_{\mathrm{i},{\mathrm{p}}_1}^{\mathrm{IntSource}\hbox{-} \mathrm{C}} \) :
-
Atomic flow of carbon in the internal source “i” from plant “p1”
- \( {A}_{\mathrm{i},{\mathrm{p}}_1}^{\mathrm{IntSource}\hbox{-} \mathrm{H}} \) :
-
Atomic flow of hydrogen in the internal source “i” from plant “p1”
- \( {A}_{\mathrm{i},{\mathrm{p}}_1}^{\mathrm{IntSource}\hbox{-} \mathrm{O}} \) :
-
Atomic flow of oxygen in the internal source “i” from plant “p1”
- \( {A}_{{\mathrm{p}}_1}^{\mathrm{IntSource}\hbox{-} \mathrm{Plant}\hbox{-} \mathrm{C}} \) :
-
Atomic flow of carbon of plant “p1”
- \( {A}_{{\mathrm{p}}_1}^{\mathrm{IntSource}\hbox{-} \mathrm{Plant}\hbox{-} \mathrm{H}} \) :
-
Atomic flow of hydrogen of plant “p1”
- \( {A}_{{\mathrm{p}}_1}^{\mathrm{IntSource}\hbox{-} \mathrm{Plant}\hbox{-} \mathrm{O}} \) :
-
Atomic flow of oxygen of plant “p1”
- Costr :
-
Unit cost of fresh feed “r”
- \( {\mathrm{CostPlant}}_{{\mathrm{p}}_2}^{\mathrm{given}} \) :
-
Installation cost for proposed new plants “p2”
- \( {D}_{\mathrm{s}}^{\mathrm{Max}} \) :
-
Maximum allowed discharge of chemical specie “s”
- \( {F}_{\mathrm{i},{\mathrm{p}}_1}^{\mathrm{source}} \) :
-
Mass flow of the internal source
- \( {F}_{\mathrm{k},{\mathrm{p}}_1}^{\mathrm{sink}} \) :
-
Mass flow needed in the sink “k”
- \( {F}_{\mathrm{i},{\mathrm{p}}_2}^{\mathrm{source}\hbox{-} \mathrm{given}} \) :
-
Molar flow of an internal source “s” for the new plant “p2”
- \( {G}_{\mathrm{s},\mathrm{k},{\mathrm{p}}_1} \) :
-
Molar flow needed in the sink “k”
- H y :
-
Hours of operation per year
- k f :
-
Annualization factor
- PMs :
-
Molecular weight of chemical specie “s”
- SellCosts :
-
Unit cost of chemical specie “s”
- \( {\mathrm{uc}}_{\mathrm{r}}^{\mathrm{fresh}} \) :
-
Unit cost for fresh feeds
- \( {W}_{\mathrm{s},\mathrm{i},{\mathrm{p}}_1} \) :
-
Molar flow of the internal source
- \( {y}_{\mathrm{s},\mathrm{i},{\mathrm{p}}_1}^{\mathrm{s}\mathrm{ource}} \) :
-
Composition of the internal source
- \( {y}_{\mathrm{s},\mathrm{k},{\mathrm{p}}_1}^{\mathrm{s}\mathrm{ink}} \) :
-
Composition of the stream needed in the sink “k”
- \( {z}_{{\mathrm{p}}_2}^{\mathrm{New}\hbox{-} \mathrm{plant}} \) :
-
Existence of new plants
- \( {\mathrm{CostPlant}}_{{\mathrm{p}}_2} \) :
-
Installation cost of selected new plans “p2”
- costFF:
-
Total cost by purchase of fresh feeds
- \( {D}_{{\mathrm{p}}_1}^{\mathrm{Discharge}\hbox{-} \mathrm{C}} \) :
-
Atomic flow of carbon in the discharges streams of the plant “p1”
- \( {D}_{{\mathrm{p}}_1}^{\mathrm{Discharge}\hbox{-} \mathrm{H}} \) :
-
Atomic flow of hydrogen in the discharges streams of the plant “p1”
- \( {D}_{{\mathrm{p}}_1}^{\mathrm{Discharge}\hbox{-} \mathrm{O}} \) :
-
Atomic flow of oxygen in the discharges streams of the plant “p1”
- \( {D}_{\mathrm{s},{\mathrm{p}}_1} \) :
-
Total molar flow of chemical specie “s” in the discharges streams of the plant “p1”
- \( {f}_{\mathrm{s},\mathrm{p}}^{\mathrm{fresh}\hbox{-} \mathrm{species}} \) :
-
Segregated streams of fresh feeds to plants
- \( {f}_{\mathrm{s},\mathrm{p},\mathrm{p}\mathrm{p}}^{\mathrm{s}\mathrm{ource}\hbox{-} \mathrm{species}} \) :
-
Segregated streams of internal sources to plants
- \( {f}_{\mathrm{s},\mathrm{p}}^{\mathrm{s}\mathrm{ource}\hbox{-} \mathrm{species}\hbox{-} \mathrm{waste}} \) :
-
Segregated streams of internal sources to network discharge
- \( {F}_{\mathrm{r}}^{\mathrm{fresh}} \) :
-
Molar flow of fresh feed “r”
- \( {F}_{\mathrm{s}}^{\mathrm{fresh}\hbox{-} \mathrm{species}} \) :
-
Molar flow of “s” in all fresh feeds streams
- \( {F}_{\mathrm{i},\mathrm{p}}^{\mathrm{source}} \) :
-
Molar flow of internal source “i” from a plant “p”
- \( {F}_{\mathrm{s},\mathrm{pp}}^{\mathrm{s}\mathrm{ink}\hbox{-} \mathrm{species}} \) :
-
Molar flow of chemical specie “s” required for the plant “PP”
- \( {F}_{\mathrm{j},\mathrm{s},\mathrm{pp}}^{\mathrm{sink}} \) :
-
Molar flow of chemical specie “s” required in the sink “j” in the plant “PP”
- \( {F}_{\mathrm{s},\mathrm{p}}^{\mathrm{s}\mathrm{ource}\hbox{-} \mathrm{species}} \) :
-
Molar flow of chemical specie “s” supplied by the plant “P” by all the internal sources
- \( {\mathrm{ProfitPlant}}_{{\mathrm{p}}_2} \) :
-
Profit of new plants “p2”
- TAC:
-
Total annual cost of the network
- \( {W}_{\mathrm{s}}^{\mathrm{s}\mathrm{pecies}} \) :
-
Molar flow of chemical specie “s” in the waste of the network
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Juárez-García, M., Ponce-Ortega, J.M. & El-Halwagi, M.M. A Disjunctive Programming Approach for Optimizing Carbon, Hydrogen, and Oxygen Symbiosis Networks. Process Integr Optim Sustain 3, 199–212 (2019). https://doi.org/10.1007/s41660-018-0065-y
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DOI: https://doi.org/10.1007/s41660-018-0065-y