Minimum Total Area. Minimum Area => Counter-Current or Vertical Heat Transfer T ( C) Process, Energy and System. H (kw) Investment Cost

Transcription

1 Minimum Total Area T ( C) HP Minimum Area => Counter-Current or Vertical Heat Transfer CW H (kw) T. Gundersen TAC 0

2 Estimating Minimum Area Heat Transfer Equation for one Exchanger: Assume Counter-Current: A = Q / (U ΔT LM ) U is the total Heat Transfer Coefficient Departure from Counter-Current adjusted by f T Heat Transfer between Composite Curves: Assume Vertical Heat Transfer A min = Σ j (/ΔT LMj ) Σ i (q i )/(h i ) Bath Formula (j) for Enthalpy Intervals and (i) for Streams Requires large Number of Units and Splits Only used to estimate the T. Gundersen TAC 02

3 WS-8: Vertical Design and Area A min = j ΔT k LMj Stream T s T t mcp h C C kw/ C kw/m 2 C k q h k Specification: ΔT min = 0 C T. Gundersen TAC 03

4 T ( C) A A vertical criss cross = + = WS-8 cont. Vertical Design: 2 3 and 4 Criss-Cross Design: 2 4 and 3 H (kw) 66.4 m = + = = 250 m Q: Why?? Optimal Distribution of (U ΔT) - not only ΔT T. Gundersen TAC 04

5 Pre-Optimization of Total Annual Cost TAC ($/yr) TAC Energy TAC = f (E,U,A) E,U,A = f (ΔT min ) Pinch = f (ΔT min ) Design = f (Pinch) Near Optimal ΔT min Area ΔT min T. Gundersen TAC 05

6 TAC Pre-Optimization, ΔT min and Network Topology A B C ΔT ΔT 2 ΔT min T. Gundersen TAC 06

7 Area Considerations in Design Basic PDM has 2 important Limitations The Method uses a Sequential Strategy Targeting, MER Design, Network Optimization MER Design: One Exchanger (decision) at a time Optimization: One Loop / Path at a time Heat Transfer Area is not Considered Pinch Decomposition assures Minimum Energy The mcp Rules assure ΔT ΔT min, but not Optimal Use of Driving Forces w.r.t. total Area The Tick-off Rule (Maximum Duty for each Exchanger) assures fewest Number of Units Need Design Rules / Tools that include Area T. Gundersen TAC 07

8 Area Considerations in Design Extended PDM has 2 Additional Tools The Driving Force Plot (DFP) Graphical Diagram with ΔT versus T cold or T hot Tool that assures good Use of Driving Forces Only Qualitative Information (not Duty or Area) The Remaining Problem Analysis (RPA) Numerical Method where Data for accepted/proposed Exchangers and Targets for the Remaining Problem (Streams that are not yet Heat Integrated) RPA is therefore a Quantitative Tool that can handle Energy and Number of Units as well as total Area Design Tool that indicates whether each Decision brings us towards a Network close to the Targets T. Gundersen TAC 08

9 Driving Force Plot H H2 T α T β 2 2 α β 3 3 C C2 ΔT Q 3 2 T C Pinch Pinch T. Gundersen TAC 09

10 Trade-off between Units and Area Three-Way Trade-off E A U Minimum Energy requires U min,mer Minimum Units requires tick-off Minimum Area requires U max Minimum TAC requires a Balance between Energy Consumption, Number of Units and Total Area in the Network The Driving Force Plot must be used with Care! T. Gundersen TAC 0

11 Remaining Problem Analysis (RPA) H H kw C C Q: Will the Network still achieve its Target Values if Exchanger is accepted? T. Gundersen TAC

12 Remaining Problem Analysis (RPA) kw 50 Initial Targets based on all Stream Data: Q H,min, Q C,min U min,mer, A min Remaining Problem: Remove those Stream Segments that are involved in Exchanger Add Values for accepted Exchangers (will é ) and the Remaining Problem (will ê ) and compare with Targets T. Gundersen TAC 2

13 Remaining Problem Analysis (RPA) a b 60 a 50 A tot = A a + A min (RP) and the same for (b) and (c) U tot = + U min (RP) Q H,tot = 0 + Q H,min (RP) Q H,tot = Q b + Q H,min (RP) for (b) and the same for (b) and (c) for (a) and (c) c (A,U,Q) tot versus (A,U,Q) min? Same Logic for Q C,tot ; increases only for (c) T. Gundersen TAC 3

14 Extended PDM - Summary Tools like DFP and RPA are needed since: PDM is Sequential in Nature Many Alternatives for Industrial Problems Selection of Partners (Streams) in one Match Optimization of Stream Splits DFP is a Qualitative and Graphical Tool that should be used with great Care! RPA is a Quantitative, Numerical and Safe Tool, but how much additional Area is acceptable for each Exchanger? T. Gundersen TAC 4

15 Shell & Tube Exchangers Ref.: R.Smith, Chemical Process Design and Integration, Figures 5., T. Gundersen TAC 5

16 TEMA Diagrams A = Q / (U ΔT LM f T ) R = mcp C / mcp H = (T Hi T Ho )/(T Co T Ci ) P = efficiency = (T Co T Ci )/(T Hi T Ci ) T. Gundersen TAC 6

17 Driving Forces and the f T factor T. Gundersen TAC 7

18 Heat Exchangers: One Unit how many Shells 270 H 20 Pinch kw H2 4 Cb H kw kw 620 kw 880 kw kw 60 C2 Ca 440 kw C mcp (kw/ C) Q: How many Shells are required for Unit 4 as a -2 S&T Exchanger? T. Gundersen TAC 8

19 Fewest Number of Shells (Targeting) kw A T ( C) H (kw) U E U = but S = 3-4? T. Gundersen TAC 9

20 Shell & Tube - Summary Pure Counter-Current Exchangers are rare Thermal Stress Cleaning Options Space Requirements Shell & Tube is widely used in Industry Oil & Gas, Petrochemical and Chemical should be calculated on the basis of Number of Shells, not Units Targets for -2 Shell & Tube Exchangers Minimum Number of Shells S min Minimum Heat Transfer Area A min T. Gundersen TAC 20