Part 6 Synthesis of Heat Exchanger Networks 6

Part 6 Synthesis of Heat Exchanger Networks

6. 1 Sequential Synthesis Minimum Utility Cost

Example 1 Fcp (MW/C) Tin (C) Tout (C) H 1 1 400 120 H 2 2 340 120 C 1 1. 5 160 400 C 2 1. 3 100 250 Steam: 500 C Cooling water: 20 – 30 C Minimum recovery approach temperature (HRAT): 20 C

Heat Balances around Temperature Intervals

Transshipment Model

Remarks • LP for minimum utility consumption leads to the same results as the Problem Table in Pinch method. • The transshipment model can be generalized to consider multiple utilities to minimize total utility cost. • This model can be expanded so as to handle constraints on matches. • This model can also be expanded so as to predict the matches for minimizing the number of units. • We can embed the equations of the transshipment model within an optimization model for synthesizing a process system where the flows of the process streams are unknown.

Index Sets

Condensed Transshipment Model

Example 2 H 1 FCp (MW/K) 2. 5 Tin (K) 400 Tout (K) 320 H 2 3. 8 370 320 C 1 2. 0 300 420 C 2 2. 0 300 370 HP Steam: 500 K, $80/k. W-yr LP Steam: 380 K, $50/k. W-yr Cooling Water: 300 K, $20/k. W-yr HRAT: 10 K

Sequential Synthesis Minimum Utility Cost with Constrained Matches

Basic Ideas

Heat Exchange Options • Hot stream i and cold stream j are present in interval k (see figure in the previous page). • Cold stream j is present in interval k, but hot stream i is only present at higher temperature interval (see figure in the next page).

Index Sets

Expanded Transshipment Model

Match Constraints

Example 1 Fcp (MW/C) Tin (C) Tout (C) H 1 1 400 120 H 2 2 340 120 C 1 1. 5 160 400 C 2 1. 3 100 250 Steam: 500 C, $80/k. W-yr Cooling water: 20 – 30 C, $20/k. W-yr Minimum recovery approach temperature (HRAT): 20 C The match between H 1 and C 1 is forbidden.

Condensed Transshipment Model The annual utility cost: $9, 300, 000.

Expanded Transshipment Model Annual Utility Cost: $15, 300, 000 Heating Utility Load: 120 MW Cooling Utility Load: 285 MW

Sequential Synthesis Prediction of matches for minimizing the unit number

Objective Function

Heat Balances The constraints in the expanded transshipment model can be modified for the present model: 1. The heat contents of the utility streams are given. 2. The common index i can be used for hot process and utility streams; The common index j can be used for cold process and utility streams.

Heat Balances

Logical Constraints

Solution

Example 1 Fcp (MW/C) Tin (C) Tout (C) H 1 1 400 120 H 2 2 340 120 C 1 1. 5 160 400 C 2 1. 3 100 250 Steam: 500 C Cooling water: 20 – 30 C Minimum recovery approach temperature (HRAT): 20 C

Condensed Transshipment Model

MILP (i)

MILP (ii)

Solution

Alternative Solution

Solve MILP without Partition

Only 5 units! One less than the previous two!

Sequential Synthesis Automatic Generation of Network Structures

Basic Ideas • Each exchanger in the superstructure corresponds to a match predicted by the MILP model (with or without pinch partition). Each exchanger will also have as heat load the one predicted by MILP. • The superstructure will contain those stream interconnections among the units that can potentially define all configurations. The stream interconnections will be treated as unknowns that must be determined.

Superstructure for one hot stream and two cold streams

Embedded Alternative Configurations • • H 1 -C 1 and H 1 -C 2 in series H 1 -C 2 and H 1 -C 1 in series H 1 -C 1 and H 1 -C 2 in parallel with bypass to H 1 -C 2 • H 1 -C 1 and H 1 -C 2 in parallel with bypass to H 1 -C 1

Parameters and Unknowns

Objective Function

Equality Constraints

Inequality Constraints

Example 3 Stream Tin (K) Tout (K) Fcp (k. W/K) h (k. W/m^2 K ) Cost ($/k. W-yr) H 1 440 350 22 2. 0 - C 1 349 430 20 2. 0 - C 2 320 368 7. 5 0. 67 - S 1 500 - 1. 0 120 W 1 300 320 - 1. 0 20 Minimum temperature approach = 1 K Exchanger cost = 6600+670(Area)^0. 83

Solution