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Simultaneous Optimization of Mass Exchanger Networks and Direct Reuse/Recycle Networks

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In the past two decades, various process integration methods have been proposed for the optimum synthesis of resource conservation networks, for the recovery of energy and material resources such as water, gas, and solvent. In this paper, a mathematical programming framework is proposed for simultaneous optimization of mass exchanger networks (MENs) and direct reuse/recycle networks (DRNs). Both MEN and DRN synthesis are now relatively established fields with numerous methods developed. Note however that there is a lack of work that considers both areas simultaneously. The newly proposed simultaneous optimization method in this work identifies opportunity for a DRN that allows the material waste to be recycled within the MEN, which is the main novelty of this work. The approach is demonstrated with a vinyl acetate monomer production problem. The latter consists of several mass exchange operations, in which an MEN is synthesized. Opportunity to develop an DRN is also identified, which allows its waste to be recycled without regeneration. Another novelty of the work is that, the supply and target compositions in the MEN problem are expressed in terms of mass ratios as the compositions are relatively large. Results show that the integrated network has a total annualized cost that is reduced by 24.9% as compared to the base case configuration, where both networks were solved independently. This shows the importance of considering entire process systems during process synthesis, as opposed to subsystems independently.

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Data Availability

Authors can confirm that all relevant data are included in the article.


AA :

Acetic acid

AT :

Acid tower

C 2 H 4 :


CO 2 :

Carbon dioxide


Direct reuse/recycle network


Heat exchanger network

H 2 O :


LP :

Linear programming


Mass exchanger network


Mixed-integer linear programming


Mixed-integer nonlinear programming


Mass separating agent


Nonlinear programming

O 2 :


PC :

Packing cost


Process flow diagram

SC :

Shell cost

SO 2 :

Sulfur dioxide


Total annualized cost


Total annualized cost of mass exchanger network


Total annualized cost of direct reuse/ recycle network


Vinyl acetate monomer

\({AA}_{bot}\)  :

Acetic acid component flowrate at bottom of absorber (kg/h)

\({AA}_{in}\) :

Total acetic acid component flowrate at inlet of absorber (kg/h)

\({AA}_{rtn}\) :

Percentage of acetic acid retained by vinyl acetate monomer (%)

\(AF\) :

Annualization factor (–)

\({b}_{i,j}\) :

Intercept of the equilibrium line (–)

\({bz}_{i,j,k}\) :

Binary coefficient of the existence of mass exchanger (–)

\({c}_{A}\) :

Fresh material cost coefficient (($ · h)/(kg · year))

\({c}_{D}\) :

Waste treatment cost coefficient (($ · h)/(kg · year))

\({c}_{j}\) :

Lean stream cost coefficient (($ · h)/(kg · year))

\({c}_{S}\) :

Shell cost coefficient ($/m1.57)

\({c}_{P}\) :

Packing cost coefficient ($/m3)

\({C}_{R}\) :

Concentration of fresh material (–)

\({C}_{SKj}\) :

Concentration of sink (–)

\({C}_{SRi}\) :

Concentration of source (–)

\({D}_{i,j,k}\) :

Diameter of column (m)

\({dy}_{i,j,k}\) :

Driving force of mass exchanger (–)

\({F}_{R}\) :

Total fresh material flowrate (kg/h)

\({F}_{R,SKj}\) :

Individual fresh material flowrate (kg/h)

\({F}_{SKj}\) :

Sink flowrate (kg/h)

\({F}_{SRi}\) :

Source flowrate (kg/h)

\({F}_{SRi, D}\) :

Waste treatment flowrate (kg/h)

\({F}_{SRi, SKj}\)  :

Flowrate at the connection between source and sink (kg/h)

\({G}_{i}\) :

Rich stream flowrate (kg/h)

\({H}_{i,j,k}\) :

Height of column (m)

\({K}_{W}\) :

Lump coefficient (kg/(m3 · h))

\({L}_{j}\) :

Lean stream/ MSA flowrate (kg/h)

\({lmcd}_{i,j,k}\) :

Logarithmic mean concentration difference (–)

\({m}_{i,j}\) :

Gradient of the equilibrium line (–)

\({me}_{i,j,k}\) :

Rate of mass exchanged (kg/h)

\({pz}_{i,j,k}\) :

Positive deviation (–)

\({sz}_{i,j,k}\) :

Negative deviation (–)

\(w\) :

Arbitrary constant (–)

\({x}_{j,k}\) :

Lean stream composition at location \(k\) (–)

\({x}_{j,supply}\) :

Lean stream supply composition (–)

\({x}_{j,target}\) :

Lean stream target composition (–)

\({y}_{i,k}\) :

Rich stream composition at location \(k\) (–)

\({y}_{i,supply}\) :

Rich stream supply composition (–)

\({y}_{i,target}\) :

Rich stream target composition (–)

\({\mathrm{z}}_{i,j,k}\) :

Relaxed binary coefficient of the existence of mass exchanger (–)

\({\Omega }_{i,j}^{UP}\) :

Upper bound of mass exchanged (kg/h)

\({\Omega }_{i,j}^{LOW}\) :

Lower bound of mass exchanged (kg/h)

\({\Gamma }_{i,j,k}\) :

Upper bound of driving force between rich and lean stream (–)


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Correspondence to Dominic C. Y. Foo.

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AI: Minimum Flowrate Calculation

Molar basis is used for minimum flowrate calculation

$$\begin{array}{c}\mathrm{Unreacted}\;\mathrm{AA}\;\mathrm{in}\;\mathrm{Stream}\;3=3000\;\mathrm{kg}/\mathrm h\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=49.957\;\mathrm{kmol}/\mathrm h\end{array}$$

= minimum MSA flowrate (kmol/h)

B = unreacted AA appear at the bottom of absorber (kmol/h)

Total AA in the inlet = (49.957 + A)  kmol/h

If 85% of AA is retained by VAM(De Lucas et al. 1992) then Eq. (33) becomes


The amount of unreacted acetic acid that is absorbed alongside with VAM and appear as bottom products. Equation (4) becomes


Note: The mass and molar fractions of \({L}_{1}\) are identical as they refer to the same component (kg AA/kg AA).

By solving Eqs. (A1) and (A2), a minimum AA-MSA of 84.43 kmol/h (5070.18 kg/h) is needed in Absorber I.

Table 7 shows the component flowrates of the rich and lean streams for the MEN.

Table 7 Component flowrates (kg/h) for rich \(({{\varvec{R}}}_{1})\) and lean \(({{\varvec{L}}}_{1}\; and\; {{\varvec{L}}}_{2})\) streams for the base case

Table 8 shows the component flowrates of the sinks and sources for the MEN.

Table 8 Component flowrates (kg/h) for sinks (\({SK}_{1} \& {SK}_{2}\)) and sources (\({SR}_{1} \& {SR}_{2}\)) for Scenario 2

Table 9 shows the calculation of mass ratios.

Table 9 Calculation for mass ratios based on Table 7 in the Appendix

Table 10 shows the changes of the effective concentration of water in the reactor.

Table 10 Effective concentration of water (reactor)

Table 11 shows the changes of the effective concentration of water in Absorber I.

Table 11 Effective concentration of water (Absorber I)

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Loh, H.T., Foo, D.C.Y., Short, M. et al. Simultaneous Optimization of Mass Exchanger Networks and Direct Reuse/Recycle Networks. Process Integr Optim Sustain 7, 989–1002 (2023).

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