Cost coefficients

If the problem is dominated by equipment with a single specification (i.e., a single material of construction, equipment type, and pressure rating), then the capital cost target can be calculated from Eq. (7.21) with the appropriate cost coefficients. However, if there is a mix of specifications, such as different streams requiring different materials of construction, then the approach must be modified. 

Type Unit of size Cost coefficients a, SFr p (1975) Probability of occurrence Sij range, unit of size/kg tij range h/batch Standard size range... 

The batch plant shown in Fig. 7.4-6 is to be optimized. The required production capacity is 11070 m per year. The cost coefficients (see Eqn. 7.3-4) are given in Table 7.4-7. The fixed processing times in the batch units, /i. r, are given in Table 7.4-8 together with initial values of processing times in the semi-continuous units, 04-( and those found by optimization. The total batch times, volumes, and costs are also given in this table. 

A batch plant for 7 products and 10 batch stages (equipment units) is to be designed. Products must be manufactured within H = 6200 hours. Tables 7.4-13 to 7.4-15 show processing times tij, size factors Sij, and yearly production requirements g for all products and stages. Cost coefficients for all... 

In this separation, there are 4 distillation tasks (NT-4), producing 3 main product states MP= D1, D2, Bf) and 2 off-cut states OP= Rl, R2 from a feed mixture EF= FO. There are a total of 9 possible outer decision variables. Of these, the key component purities of the main-cuts and of the final bottom product are set to the values given by Nad and Spiegel (1987). Additional specification of the recovery of component 1 in Task 2 results in a total of 5 decision variables to be optimised in the outer level optimisation problem. The detailed dynamic model (Type IV-CMH) of Mujtaba and Macchietto (1993) was used here with non-ideal thermodynamics described by the Soave-Redlich-Kwong (SRK) equation of state. Two time intervals for the reflux ratio in Tasks 1 and 3 and 1 interval for Tasks 2 and 4 are used. This gives a total of 12 (6 reflux levels and 6 switching times) inner loop optimisation variables to be optimised. The input data, problem specifications and cost coefficients are given in Table 7.1. 

TOUT = outlet temperature of stream U = overall heat transfer coefficient CHU = unit cost of hot utility C = area cost coefficient NOK = total number of stages... 

Here, y is the binary variable associated with the separation of components m and n, such that if y = 0, then = 0 and if y = I, then < I. The second term models the intensity of separation, where the cost coefficient p for unit separation between two adjacent components m and n reflects the difficulty of separation between m and n. Q is the net flow through the separation network. The above formulation gives us an exact representation when we have sharp splits between adjacent components. As we mentioned earlier, nonsharp splits can be modeled by sharp splits followed by mixing, and an upper bound on the separation costs can be derived by enforcing A7 = 1 whenever = 1 (i.e., by assuming sharp splits) while a lower bound on the separation cost... 

The above problem will be referred to as Problem A in the following. The 7 inequality constraints in equations 1.4e to 1.4k are the bounds on the 7 variables (X4, xs, X2, Xe, Xio, Xg and X3) in the original problem, and they arise from the elimination of these variables from the 7 equality constraints in the model thus making them dependent variables. The cost coefficients in the profit are alkylate product value ( 0.063/octane-barrel), olefin feed cost ( 5.04 arrel), isobutane recycle cost ( 0.035/barrel), fresh acid cost ( 10.0/thousand pounds) and isobutane feed cost ( 3.36/barrel). The optimal solution for this SOO problem is also presented in Table 1.2. The reader can verify this using the Excel file Alkylation.xls in the folder Chapter 1 on the compact disk (CD) provided with the book. 

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