OPTI_ENERGY - PowerPoint PPT Presentation

Loading...

PPT – OPTI_ENERGY PowerPoint presentation | free to download - id: 109b50-YzE0M



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

OPTI_ENERGY

Description:

9.1.1 Description of the system. A combined cycle cogeneration system that ... compressor isentropic efficiency. 44. 9.2.9 Sensitivity analysis. Fig. 9.2.3c. ... – PowerPoint PPT presentation

Number of Views:69
Avg rating:3.0/5.0
Slides: 57
Provided by: chri251
Learn more at: http://www.itc.polsl.pl
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: OPTI_ENERGY


1
OPTI_ENERGY
Summer School Optimization of Energy Systems and
Processes Gliwice, 24 27 June 2003
METHODS OF ENERGY SYSTEMS OPTIMIZATION
9. NUMERICAL EXAMPLES
9.1 Thermoeconomic Operation Optimization of a
System
2
9.1.1 Description of the system
A combined cycle cogeneration system that covers
the needs of a refinery in electricity and
steam. Two-way interconnection with the utility
grid.
  • Main components
  • Two gas-turbine electricity generators of 17 MWe
    each.
  • Two exhaust-gas boilers recovering heat from the
    gas turbine flue gases.
  • One steam-turbine electricity generator of 16
    MWe.
  • Two steam boilers of 60 ton/h each.
  • Two steam boilers of 30 ton/h each.

3
Fig. 9.1.1. Simplified diagram of
the combined-cycle cogeneration system.
4
9.1.1 Description of the system
Table 9.1.1. Steam grades used in the refinery.
5
9.1.2 Primary energy sources
  • Electricity supply from the utility grid.
  •  
  • Fuel gas (FG)
  • A by-product of the refinery process.
  • The largest primary energy source.
  • It consists of light hydrocarbons (methane to
    butane) and
  • a small percentage of hydrogen (about 5 by
    volume).
  • It is available at low pressure (LPFG) and high
    pressure (HPFG).
  • It cannot be stored. If not used, it is burned in
    the flares.

(continued)
6
9.1.2 Primary energy sources
(continued)
  • Fuel oil (FO).
  • Commercial industrial grade fuel oil (900 kg/m3,
    370 cSt at 50C max)
  • of low sulfur content (0.7 by weight,
    maximum).
  • The second largest primary energy source for the
    refinery.
  •  
  • Propane.
  • A sellable final product.
  • Its use as a fuel in the refinery depends on
    propane storage availability and its selling
    price.
  • There is actually a trade-off between FO and
    propane, and the use of one or the other depends
    on their selling price.

7
9.1.3 Energy conversion
  • The various fuels are converted to heat, steam
    and electricity.
  • Process heat needs are covered by fired heaters
    using FG and/or FO or by steam.
  • Steam is produced by steam boilers, and by waste
    heat boilers in the process units as well as in
    the cogeneration system.
  • Four grades of steam are produced. If the
    quantity of steam directly produced at a certain
    grade is not sufficient, then it is supplemented
    by desuperheating, which causes an exergy
    destruction and consequently must be avoided
    whenever possible.

8
9.1.4 The need for operation optimization
The energy needs of the refinery can be satisfied
by several primary energy sources through various
energy conversion systems.
  • Important considerations
  • Electricity can be produced (within certain
    limits) either by the gas turbines or by the
    steam-turbine generator. The optimum load
    distribution is requested.
  • Gas-turbine generators produce electricity and
    steam simultaneously. Thus, increased gas turbine
    level of electricity production results in an
    increase of steam availability, reducing the
    required production of steam by the steam
    boilers.
  • Increasing the level of electricity production by
    the steam-turbine generator results in reduced
    steam availability, thus increasing the required
    production of steam boilers.

(continued)
9
9.1.4 The need for operation optimization
  • Important considerations (continued)
  • Electricity can be exported to the utility grid.
    The quantity of the exported electricity affects
    the operation of the gas turbines, steam turbine
    and boilers.
  • Production and consumption of the various steam
    grades must be kept in balance to avoid degrading
    steam of higher levels to lower levels at a loss
    (i.e. without production of mechanical work).

A heuristic approach or past experience only is
not capable of determining the optimum mode of
operation. The application of an optimization
procedure is necessary.
10
9.1.5 The Optimization objective
Minimization of the capital and operating cost at
any instant of time
(9.1.1)
(9.1.2)
Inequality constraints on the independent
variables
(9.1.3)
11
9.1.5 The Optimization objective
(continued)
Net electric power produced by the cogeneration
system
(9.1.4)
Total electric power supplied by the cogeneration
system and the utility grid
(9.1.5)
An analysis and simulation of the system
including mathematical simulation of the main
components and important auxiliary equipment has
been performed.
12
9.1.6 Considerations on capital and operation
expenses
The introduction of capital depreciation,
maintenance and personnel costs in the objective
function has an impact on the optimum point only
if these costs can be expressed as functions of
independent variables. The available information
led to the following.
Four main subsystems are considered 1 fuel-oil
boilers, 2 steam-turbine generator,
3 gas-turbine generator No. 1 with exhaust
boiler, 4 gas-turbine generator No. 2 with
exhaust boiler.
(continued)
13
9.1.6 Considerations on capital and operation
expenses
(continued)
Capital cost
(9.1.6)
Maintenance and personnel costs
(9.1.7)
where
(9.1.8)
14
9.1.7 Description of the computer program
The direct application of a mathematical
programming algorithm has been used.
  • The computer program consists of the following
    parts
  • Main program
  • Optimization algorithm GRG2
  • Constraints subroutine GCOMP
  • Objective function FZ
  • Component simulation package
  • File DSTEAM

15
9.1.8 Numerical results
Results for typical load conditions
Usual practice (example)
Optimum mode of operation (for the same load
conditions)
16
Example of Sensitivity Analysis
Fig. 9.1.2. Effect of unit cost of electricity
purchased from the grid on the optimum operating
point.
17
Example of Sensitivity Analysis
Fig. 9.1.3. Effect of unit cost of fuel oil on
the optimum operating point.
18
9.1.9 Conclusions on the example
  • The application of an optimization procedure to a
    complex system is very beneficial if the common
    practice is replaced by the optimization
    procedure, a very significant reduction in
    operating expenses can be achieved with no need
    of additional investment.
  • The simplifying assumptions leave much room for
    further development and improvement of the
    procedure and the software.
  • In a further development, the limits of the
    system under optimization may be extended to
    include the refinery processes.
  • Off-line optimization has been applied, which is
    satisfactory when the plant operates at nearly
    constant conditions for relatively long periods
    of time. For frequent changes of conditions
    however, on-line optimization is necessary.
  • On-line optimization requires fast simulation and
    optimization software.

19
METHODS OF ENERGY SYSTEMS OPTIMIZATION
9. NUMERICAL EXAMPLES
9.2 Thermoeconomic Design Optimization of a
System
20
9.2.1 Description of the system and main
assumptions
The system consists of a gas-turbine unit with
regenerative air preheater, and a heat recovery
steam generator (HRSG).
Main Assumptions
a. The air and combustion gases behave as ideal
gases with constant specific heats. b. For
combustion calculations, the fuel is considered
as methane. c. All components, except the
combustion chamber, are adiabatic. d. Pressure
and temperature losses in the ducts connecting
the components are neglected. However, a pressure
drop due to friction is taken into consideration
in the air preheater (both streams), combustion
chamber and the HRSG. e. Mechanical losses in the
compressor and turbine are negligible.
21
Fig. 9.2.1. Flow diagram of the gas-turbine
cogeneration system.
22
Table 9.2.1. Thermodynamic parameters for the
system.
(continued)
23
Table 9.2.1. Thermodynamic parameters for the
system. (continued)
 
 
24
9.2.2 Preliminary Calculations
Steam temperature
T9 Tsat(20 bar) 212.37C
Preheated water temperature
Useful heat rate (product of the system)
Useful heat rate of the economizer
Useful heat rate of the evaporator
25
9.2.3 Thermodynamic Model of the System
It consists of 21 equations including 47
quantities (pressures, temperatures, mass flow
rates, heat transfer area, etc.). Examples
26
9.2.3 Thermodynamic Model of the System
(continued)
Quantities involved 47 Parameters given
or already calculated 21 Number of equations
available 21 Number of unknown quantities
(independent variables) 5
Selected independent variables
27
9.2.4 Economic model of the system
Installed capital cost functions of components
Compressor


Air preheater
Combustor
Turbine
HRSG
28
9.2.4 Economic model of the system
Annualized capital cost of a component including
depreciation and maintenance
(9.2.4)
Total annual cost of the system
(9.2.5)
where
Cr installed capital cost of component r,
FCR annual fixed charge rate,
maintenance factor,
cf cost of fuel per unit of energy,
t time period of operation during a year.
29
9.2.5 Thermoeconomic Functional Analysis of the
system

Fig. 9.2.2. Functional diagram of the system.
30
Functions (products) of the units
Compressor
Air preheater
Combustor
Turbine
HRSG
Junction
31
Additional functions
Function from the environment
Functions to the environment
Distribution of mechanical exergy (due to
pressure difference from the environment)
Shaft power from the turbine to the compressor
32
Additional functions
(continued)
Thermal exergy due to temperature increase in the
compressor
Thermal exergy from exhaust gases
Product of the air preheater given to the
junction
Combustion function given to the junction
Thermal exergy from the junction to the turbine
Thermal exergy from the junction to the HRSG
33
9.2.5 Thermoeconomic Functional Analysis of the
system
(continued)
Cost balance for each unit considering a
break-even operation (physical or monetary
costs)
(6.2.27)
The system of equations is solved for the unit
product costs, cn. The costs are distributed to
the units and to the final products by the
function distribution network.
34
9.2.6 Statement of the optimization problem
Optimization objective function (minimization of
the total cost rate of the system)
(9.2.28)
Equality constraints the thermodynamic and
economic model of the system.
Inequality constraints
(9.2.29)
35
Basic procedure for solution of the optimization
problem by the Functional Approach
1. Select an initial set of values for
x. 2. Determine the values of y by the system of
equality constraints. 3. Evaluate the Lagrange
multipliers. 4. Check the necessary conditions.
If they are satisfied to an acceptable degree of
approximation, then stop. Otherwise, select a new
set of values for x and repeat steps 2-4.
36
9.2.7 Application of the modular approach
Module 1 Compressor
Parameters and variables
Simulation model Eqs. (A.1), (A.2), Appendix A
in the text.
Module 2 Combustor and turbine
Parameters and variables
Simulation model
Eqs. (A.7) (A.9) and (A.11) (A.13).
37
9.2.7 Application of the modular approach
Module 3 Air preheater
Parameters and variables
Simulation model Eqs. (A.10), (A.18) (A.19).
Module 4 Heat recovery steam generator
Parameters and variables
Simulation model Eqs. (A.14), (A.15) (A.20),
(A.21).
38
9.2.8 Numerical results
Table 9.2.2. Optimization results for the
nominal set of parameter values.
39
9.2.8 Numerical results
Table 9.2.3. TFA values of functions at the
optimum point (in kW).
Table 9.2.4. TFA values of Lagrange multipliers
and unit product costs at the optimum point (in
/106 kJ).
40
9.2.9 Sensitivity analysis
Table 9.2.5. Sensitivity of the optimal solution
to the fuel price and capital cost.
41
9.2.9 Sensitivity analysis
Table 9.2.6. Sensitivity of the objective
function to the independent variables
, .
42
9.2.9 Sensitivity analysis
Fig. 9.2.3a. Effect of fuel price and capital
cost on the optimum value of compressor pressure
ratio.
43
9.2.9 Sensitivity analysis
Fig. 9.2.3b. Effect of fuel price and capital
cost on the optimum value of compressor
isentropic efficiency.
44
9.2.9 Sensitivity analysis
Fig. 9.2.3c. Effect of fuel price and capital
cost on the optimum value of preheated air
temperature.
45
9.2.9 Sensitivity analysis
Fig. 9.2.3c. Effect of fuel price and capital
cost on the optimum value of the objective
function.
46
9.2.10 General comments derived from the example
  • The application of three methods for the
    optimization of thermal systems has been
    demonstrated through this example. All three
    approaches have been successful in the particular
    application.
  • The direct use of an optimization algorithm is
    the simplest way, because it requires the least
    effort in system analysis, but it gives no
    information about the internal economy of the
    system (physical and economic relationships among
    the components).
  • Scaling of the variables and of the objective
    function is usually required in order to achieve
    convergence to the optimum point.
  • Since no method can guarantee convergence to the
    global optimum, there is need to start the search
    from different initial points. If the same final
    point is reached, then we are more or less
    confident that this is the true optimum.

47
METHODS OF ENERGY SYSTEMS OPTIMIZATION
9. NUMERICAL EXAMPLES
9.3 Environomic Analysis and Optimization of a
System
48
9.3.1 Description of the system and main
assumptions
Main Characteristics of the System
  • Fuel oil is considered in this example, because
    it is more polluting than the natural gas.
  • The system produces a specified amount of
    electric power.
  • The system is equipped with a flue gas
    desulfurization (FGD) unit for SO2 abatement. Its
    operation requires electricity, water and
    limestone.
  • The size and the capital cost of the FGD unit
    depend largely on the exhaust gas flow rate.
    Therefore, it is less expensive to desulfurize a
    partial flow at the maximum possible degree than
    the total flow at a lower degree.

49
Fig. 9.3.1. Gas-turbine system with flue gas
desulfurization unit.
50
9.3.1 Description of the system and main
assumptions
Mass and volume flow rates through the FGD unit
(9.3.1)
Degree of SO2 abatement
(9.3.2)
where
desirable degree of SO2 abatement,
mass, volume flow rate of exhaust gases through
the FGD unit,
total mass, volume flow rate of exhaust gases,
(9.3.3)
initial mass flow rate of SO2
final mass flow rate of SO2 (after abatement).
51
9.3.2 Statement of the optimization problems
Two thermodynamic objectives
Maximization of the cycle efficiency
(9.3.4)
Maximization of the net power density, defined
as
(9.3.5)
(9.3.6)
where
(9.3.7)
Independent variable
Comment
and w increase continuously with
and
52
9.3.2 Statement of the optimization problems
Thermoeconomic objective is the minimization of
the annual cost of owning and operating the
system
(9.3.8)
Independent variables
(9.3.9)
Environomic objective
(9.3.10)
(9.3.15)
Independent variables
53
9.3.2 Statement of the optimization problems
Capital cost of the FGD unit
(9.3.11)
Cost of resources for the first year
(9.3.12)
(9.3.13)
First year penalty for emitted SO2
(9.3.14)
54
9.3.3 Numerical results and comments
Table 9.3.1. Parameter values for optimization
of the system.
55
9.3.3 Numerical results and comments
Table 9.3.2. Optimization results.
56
9.3.3 Numerical results and comments
Comments on the results
  • The environomic optimum values of all the
    independent variables are higher than the
    thermoeconomic optimum values.
  • The thermoeconomic and environomic optima of rC
    are in between the values corresponding to the
    maximum efficiency and the maximum net power
    density.
  • The cycle efficiency obtains a higher value with
    the environomic optimization than with the
    thermoeconomic optimization.
About PowerShow.com