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Synthesis of Material Interception Networks with P-Graph

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Abstract

A P-graph model was recently developed for direct reuse/recycle scheme for both in-plant resource conservation networks (RCNs) and inter-plant RCNs (IPRCNs). The proposed P-graph model allows visualization which expedites the assessment of optimal and near-optimal solutions. In this paper, the P-graph model will be extended to material interception schemes, i.e., material regeneration and pre-treatment. Material regeneration involves the use of purification unit for quality improvement of the process sources before they are reused/recycled to the sinks. Pre-treatment processes, on the other hand, involve the purification of fresh resources for use in processes with stringent quality requirement. Two literature case studies are solved to demonstrate the newly extended model.

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Authors and Affiliations

  1. Department of Chemical and Environmental Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500, Semenyih, Selangor Dahrul Ehsan, Malaysia

    C. H. Lim, P. S. Pereira, C. K. Shum, W. J. Ong, H. L. Lam & D. C. Y. Foo

  2. Chemical Engineering Department, De La Salle University, 2401 Taft Avenue, 0922, Manila, Philippines

    R. R. Tan

Authors
  1. C. H. Lim
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  2. P. S. Pereira
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  3. C. K. Shum
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  4. W. J. Ong
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  5. R. R. Tan
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  6. H. L. Lam
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  7. D. C. Y. Foo
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Corresponding author

Correspondence to D. C. Y. Foo.

Electronic supplementary material

ESM 1

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Appendix 1 Mathematical model

The optimization model for a material interception network is given in Eqs. A1–A5 (Foo 2012). Constraint in Eq. A1 describes the flowrate requirement of the sink, which is fulfilled by the flowrate allocated from process sources (F SRi, SKj), regenerated flowrates (F RP,SKj), as well as the fresh resource (F R, SKj). Equation A2 describes the flowrate sent from process and regenerated sources, as well as fresh resource feed must fulfill the minimum quality requirement of the process sinks (which may take the form of concentration or property). The flowrate balance in Eq. A3 indicates that flowrate of each process source may be allocated to sinks or interception unit, while the unutilized source will be sent for waste discharge (with flowrate F SRi, D). Equation A4 indicates that all variables of the superstructural model should take non-negative values. Since the flowrates and quality of the process sink and source, as well as the fresh resource feed are parameters, Eqs. A1–A4are linear. In other words, the superstructural model is a linear program (LP) for which any solution found is globally optimal.

$$ {\sum}_{\mathrm{i}}{F}_{\mathrm{SRi},\kern0.5em \mathrm{SK}j}+{F}_{\mathrm{R}\mathrm{P},\kern0.5em \mathrm{SK}\mathrm{j}}+{F}_{\mathrm{R},\kern0.5em \mathrm{SK}\mathrm{j}}={F}_{\mathrm{SKj}}\kern0.5em \forall j $$
(A1)
$$ {\sum}_{\mathrm{i}}{F}_{\mathrm{SRi},\kern0.5em \mathrm{SKj}}{q}_{\mathrm{SRi}}+{F}_{\mathrm{R}\mathrm{P},\kern0.5em \mathrm{SKj}}{q}_{\mathrm{R}\mathrm{out}}+{F}_{\mathrm{R},\kern0.5em \mathrm{SKj}}{q}_{\mathrm{R}}\ge {F}_{\mathrm{SKj}}{q}_{\mathrm{SKj}}\kern0.5em \forall j $$
(A2)
$$ {\sum}_{\mathrm{j}}{F}_{\mathrm{SRi},\kern0.5em \mathrm{SKj}}+{F}_{\mathrm{SRi},\kern0.5em \mathrm{RE}}+{F}_{\mathrm{SRi},\kern0.5em \mathrm{D}}={F}_{\mathrm{SRi}}\kern0.5em {\forall}_i $$
(A3)
$$ {F}_{\mathrm{SRi},\kern0.5em \mathrm{SKj}},{F}_{\mathrm{R},\kern0.5em \mathrm{SKj}},{F}_{SRi,\kern0.5em \mathrm{D}},{F}_{\mathrm{R}\mathrm{P},\kern0.5em \mathrm{SKj}},{F}_{\mathrm{SRi},\kern0.5em \mathrm{RE}}\ge 0\kern0.5em \forall i,j $$
(A4)

The objective of the optimization problem can be set to minimize the total operating costs (TOC) of the RCN (Eq. A5). Alternatively, we may also minimize the flowrates of both fresh resource (F R) and intercepted source (F RP) using the two-stage optimization approach (Foo 2012). Note that model is a linear program (LP) for which any solution found is globally optimal.

$$ \mathrm{minimize}\ \mathrm{TOC} $$
(A5a)
$$ \mathrm{TOC}=\left({\sum}_j{F}_{R,\mathrm{SK}j}{\mathrm{CT}}_{\mathrm{R}}+{F}_{\mathrm{R}\mathrm{P}}{\mathrm{CT}}_{\mathrm{R}\mathrm{W}}+{F}_{\mathrm{D}}{\mathrm{CT}}_{\mathrm{D}}\right)\mathrm{AOT} $$
(A5b)
where CTR, CTRW, and CT D are the unit costs of fresh resource, regenerated source, and waste discharge, AOT is the annual operating time.

Appendix 2 Degenerate solutions for case study 1

Table 5 Degenerate solution 1 for case study 1 with regeneration scheme (C Reg = 10 ppm)
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Table 6 Degenerate solution 2 for case study 1 with regeneration scheme (C Reg = 10 ppm)
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Lim, C.H., Pereira, P.S., Shum, C.K. et al. Synthesis of Material Interception Networks with P-Graph. Process Integr Optim Sustain 1, 225–235 (2017). https://doi.org/10.1007/s41660-017-0016-z

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