Correspondence pubs.acs.org/IECR
Comments on “Continuous-Time Optimization Model for SourceSink Matching in Carbon Capture and Storage Systems” Jui-Yuan Lee and Cheng-Liang Chen* Department of Chemical Engineering, National Taiwan University, No 1, Sec 4, Roosevelt Rd, Taipei, 10617 Taiwan Sir: Tan et al.1 recently developed a continuous-time optimization model for carbon dioxide (CO2) source-sink matching in carbon capture and storage (CCS) systems. The model takes into account CO2 storage limitations and temporal issues of planning CCS. Our comment focuses on the formulation. In the model of Tan et al.,1 two decision variables are used, namely, Tstart and Bij. These two variables are correlated by the ij minimum duration constraint: (Tiend
−
Tijstart)
≥T
min
Bij
∀ i, j
when Bij = 0. Thus, there is no need to multiply these two terms by Bij and no bilinear product will occur. In this case, linearization is not needed. The modified objective function and CO2 storage constraint are as follows: max ∑ i
i
−
j
i
∑ (Tiend − Tijstart)Si ≤ Dj
(1)
i
−
Table 1. Comparison of the Linearized and Modified Models linearized
model statistics
(2)
j
objective value no. of equations no. of continuous variables no. of binary variables solution time (CPU s)
∀j (3)
i
The bilinear terms occurring in eqs 2 and 3 render the preliminary model of Tan et al.1 a mixed-integer nonlinear program (MINLP). To guarantee global optimality of the solution, the preliminary nonlinear model must be linearized. The linearization was achieved by replacing the bilinear product with a new continuous variable. An alternative to linearization is to modify the formulation. Since the nonlinearity of the preliminary model is due to the arbitrariness of Tstart ij , which takes on an arbitrary value when Bij = 0, the problem could be solved by defining Tstart more ij end thoroughly. It is suggested to let Tstart = T , which means that ij i sending CO2 from source i to sink j does not really start, when Bij = 0. The minimum duration constraint correlating Tstart and ij Bij is then reformulated as follows: Tiend(1 − Bij ) ≤ Tijstart ≤ Tiend − T minBij
∀ i, j
Tstart ij
min
© 2012 American Chemical Society
MILP model
case study 1
case study 2
case study 1
case study 2
570 68 21
596 118 37
570 48 11
596 82 19
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