Optimal Design of Piping Systems for District Heating
OPTIMIZATION IN DISTRICT HEATING SYSTEM DESIGN
OPTIMIZATION IN DISTRICT HEATING SYSTEM DESIGN-continue - CR95_170013
OPTIMIZATION IN DISTRICT HEATING SYSTEM DESIGN-continue - CR95_170014
CHAPTER 2: OPTIMAL PIPE DIAMETER FOR A SINGLE PIPE SEGMENT
COST OF PUMPING
COST OF PUMPING-continue - CR95_170017
COST OF PUMPING-continue - CR95_170018
COST OF PIPES AND PUMPS
TOTAL COST-continue - CR95_170020
TOTAL COST-continue - CR95_170021
A SIMPLE EXAMPLE
Technical assumptions
Figure 2. Load duration curve
Application
Table 1. Pressure drops and costs for discrete pipe sizes under maximum flow conditions
CHAPTER 3: THE CONSUMER'S HEAT LOAD
Figure 3. Schematic of a hydronic heating system radiator
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170029
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170030
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170031
Table 2. Errors from approximating the logarithmic mean temperature difference
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170033
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170034
Figure 5. Results for the return temperature models
Table 3. Return temperatures and flow rates calculated with the consumer models for n1 = n2 = 1.3
DESIGN OF A SINGLE PIPE SEGMENT WITH A CONSUMER MODEL
Figure 6. Mass flow rate function with and without consumer models, Tr = 60C
Figure 7. Mass flow rate function with and without consumer models, Tr = 55C
Table 4. Pressure drops and costs for discrete pipe sizes under maximum flow conditions with and without the consumer model
HEAT CONSUMER CONSTRAINTS
CHAPTER 4: CONSTRAINTS ON SYSTEMS WITH MULTIPLE CONSUMERS AND PIPES
DIFFERENTIAL PRESSURE CONSTRAINTS-continue
MAXIMUM ABSOLUTE PRESSURE CONSTRAINTS
MAXIMUM ABSOLUTE PRESSURE CONSTRAINTS-continue - CR95_170045
MAXIMUM ABSOLUTE PRESSURE CONSTRAINTS-continue - CR95_170046
MINIMUM ABSOLUTE PRESSURE CONSTRAINTS
MINIMUM ABSOLUTE PRESSURE CONSTRAINTS-continue - CR95_170048
MINIMUM ABSOLUTE PRESSURE CONSTRAINTS-continue - CR95_170049
CHAPTER 5: OPTIMAL DESIGN OF SYSTEMS WITH MULTIPLE PIPES AND CONSUMERS
SOME POSSIBLE APPROACHES-continue
PIPE AND PIPE JUNCTION LABELING SCHEME
SYSTEM OBJECTIVE FUNCTION-continue
SOLUTION STRATEGY
Constraint activity for consumer control valve pressure losses
Constraint activity for consumer control valve pressure losses-continue - CR95_170056
Constraint activity for consumer control valve pressure losses-continue - CR95_170057
Constraint activity for consumer control valve pressure losses-continue - CR95_170058
System constraint satisfaction
System constraint satisfaction-continue
Figure 8. Hypothetical pressure distribution under high and low flow conditions and absolute pressure constraints
A simplified objective function
A simplified objective function-continue
Constraint resolution by pipe size refinement
Figure 9. Method A
Figure 10. Method B
Figure 12. Slope of the pressure loss as a function of pipe diameter
Branch-and-bound method
Solution by the branch-and-bound method
Figure 13. Hypothetical branch-and-bound problem
Solution by the branch-and-bound method-continue
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE
Table 5. Assigned values for nodes of example in Figure 14
Table 7. Parameter values and optimal independent diameters for example of Figure 14
Table 8. Standard metric steel pipe sizes
Table 10. Pressure losses for the pipe segments in the example
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE-continue - CR95_170077
Table 12. Pipe size combinations for the example
Table 13. Constraint satisfaction and costs for the remaining combinations
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE-continue - CR95_170080
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE-continue - CR95_170081
Table 14. Pressure levels in the piping network
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE-continue - CR95_170083
CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS - CR95_170085
RECOMMENDATIONS-continue - CR95_170086
LITERATURE CITED - CR95_170087
LITERATURE CITED-continue - CR95_170088
APPENDIX A: APPROXIMATION OF THE FRICTION FACTOR
APPENDIX A: APPROXIMATION OF THE FRICTION FACTOR-continue - CR95_170090
Table A1. Constants for the friction factor equation
APPENDIX A: APPROXIMATION OF THE FRICTION FACTOR-continue - CR95_170092
APPENDIX B: COMPUTER PROGRAM LISTINGS
APPENDIX B: COMPUTER PROGRAM LISTINGS-continue
Subroutine WTRTBL(T,P,RHO,XH,DV)
Subroutine SATLN(T,P)
Function FUN(T,Z)
Program I2-C-GMT
Function FUN(T,C)
Program I1EQ3-26
Program I1
Report Documentation Page - CR95_170102
CR95_17
OPTIMIZATION IN DISTRICT HEATING SYSTEM DESIGN
OPTIMIZATION IN DISTRICT HEATING SYSTEM DESIGN-continue - CR95_170013
OPTIMIZATION IN DISTRICT HEATING SYSTEM DESIGN-continue - CR95_170014
CHAPTER 2: OPTIMAL PIPE DIAMETER FOR A SINGLE PIPE SEGMENT
COST OF PUMPING
COST OF PUMPING-continue - CR95_170017
COST OF PUMPING-continue - CR95_170018
COST OF PIPES AND PUMPS
TOTAL COST-continue - CR95_170020
TOTAL COST-continue - CR95_170021
A SIMPLE EXAMPLE
Technical assumptions
Figure 2. Load duration curve
Application
Table 1. Pressure drops and costs for discrete pipe sizes under maximum flow conditions
CHAPTER 3: THE CONSUMER'S HEAT LOAD
Figure 3. Schematic of a hydronic heating system radiator
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170029
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170030
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170031
Table 2. Errors from approximating the logarithmic mean temperature difference
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170033
SIMPLE MODEL FOR THE CONSUMER'S SPACE HEATING EQUIPMENT-continue - CR95_170034
Figure 5. Results for the return temperature models
Table 3. Return temperatures and flow rates calculated with the consumer models for n1 = n2 = 1.3
DESIGN OF A SINGLE PIPE SEGMENT WITH A CONSUMER MODEL
Figure 6. Mass flow rate function with and without consumer models, Tr = 60C
Figure 7. Mass flow rate function with and without consumer models, Tr = 55C
Table 4. Pressure drops and costs for discrete pipe sizes under maximum flow conditions with and without the consumer model
HEAT CONSUMER CONSTRAINTS
CHAPTER 4: CONSTRAINTS ON SYSTEMS WITH MULTIPLE CONSUMERS AND PIPES
DIFFERENTIAL PRESSURE CONSTRAINTS-continue
MAXIMUM ABSOLUTE PRESSURE CONSTRAINTS
MAXIMUM ABSOLUTE PRESSURE CONSTRAINTS-continue - CR95_170045
MAXIMUM ABSOLUTE PRESSURE CONSTRAINTS-continue - CR95_170046
MINIMUM ABSOLUTE PRESSURE CONSTRAINTS
MINIMUM ABSOLUTE PRESSURE CONSTRAINTS-continue - CR95_170048
MINIMUM ABSOLUTE PRESSURE CONSTRAINTS-continue - CR95_170049
CHAPTER 5: OPTIMAL DESIGN OF SYSTEMS WITH MULTIPLE PIPES AND CONSUMERS
SOME POSSIBLE APPROACHES-continue
PIPE AND PIPE JUNCTION LABELING SCHEME
SYSTEM OBJECTIVE FUNCTION-continue
SOLUTION STRATEGY
Constraint activity for consumer control valve pressure losses
Constraint activity for consumer control valve pressure losses-continue - CR95_170056
Constraint activity for consumer control valve pressure losses-continue - CR95_170057
Constraint activity for consumer control valve pressure losses-continue - CR95_170058
System constraint satisfaction
System constraint satisfaction-continue
Figure 8. Hypothetical pressure distribution under high and low flow conditions and absolute pressure constraints
A simplified objective function
A simplified objective function-continue
Constraint resolution by pipe size refinement
Figure 9. Method A
Figure 10. Method B
Figure 12. Slope of the pressure loss as a function of pipe diameter
Branch-and-bound method
Solution by the branch-and-bound method
Figure 13. Hypothetical branch-and-bound problem
Solution by the branch-and-bound method-continue
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE
Table 5. Assigned values for nodes of example in Figure 14
Table 7. Parameter values and optimal independent diameters for example of Figure 14
Table 8. Standard metric steel pipe sizes
Table 10. Pressure losses for the pipe segments in the example
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE-continue - CR95_170077
Table 12. Pipe size combinations for the example
Table 13. Constraint satisfaction and costs for the remaining combinations
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE-continue - CR95_170080
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE-continue - CR95_170081
Table 14. Pressure levels in the piping network
CHAPTER 6: A SIMPLE MULTIPLE-PIPEMULTIPLE-CONSUMER EXAMPLE-continue - CR95_170083
CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS - CR95_170085
RECOMMENDATIONS-continue - CR95_170086
LITERATURE CITED - CR95_170087
LITERATURE CITED-continue - CR95_170088
APPENDIX A: APPROXIMATION OF THE FRICTION FACTOR
APPENDIX A: APPROXIMATION OF THE FRICTION FACTOR-continue - CR95_170090
Table A1. Constants for the friction factor equation
APPENDIX A: APPROXIMATION OF THE FRICTION FACTOR-continue - CR95_170092
APPENDIX B: COMPUTER PROGRAM LISTINGS
APPENDIX B: COMPUTER PROGRAM LISTINGS-continue
Subroutine WTRTBL(T,P,RHO,XH,DV)
Subroutine SATLN(T,P)
Function FUN(T,Z)
Program I2-C-GMT
Function FUN(T,C)
Program I1EQ3-26
Program I1
Report Documentation Page - CR95_170102
CR95_17
